Morphing Wing Fighter Aircraft Synthesis/Design Optimization · Morphing Wing Fighter Aircraft...

Morphing Wing Fighter Aircraft Synthesis/Design

Optimization

Kenneth Wayne Smith Jr.

A thesis submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Science

In

Mechanical Engineering

Dr. Michael von Spakovsky, Chair

Dr. Walter O’Brien

Dr. Michael Philen

Dr. David Moorhouse

January 16, 2009

Blacksburg, Virginia

Keywords: exergy, morphing wing, optimization, aircraft, decomposition

Copyright © 2009 by Kenneth Wayne Smith Jr.

All other copyrighted items used by permission

ii

Morphing Wing Fighter Aircraft Design/Synthesis and Optimization

by Kenneth Wayne Smith Jr.

Abstract

This thesis presents results of the application of energy-based large-scale optimization of

a two-subsystem (propulsion subsystem (PS) and airframe subsystem-aerodynamics (AFS-A))

air-to-air fighter (AAF) with two types of AFS-A models: a fixed-wing AFS-A and a morphing-

wing AFS-A. The AAF flies 19 mission segments of a supersonic fighter aircraft mission and

the results of the study show that for very large structural weight penalties and fuel penalties

applied to account for the morphing technology, the morphing-wing aircraft can significantly

outperform a fixed-wing AAF counterpart in terms of fuel burned over the mission. The

optimization drives the fixed-wing AAF wing-geometry design to be at its best flying the

supersonic mission segment, while the morphing-wing AFS-A wing design is able to effectively

adapt to different flight conditions, cruising at subsonic speeds much more efficiently than the

fixed-wing AAF and, thus yielding significant fuel savings.

Also presented in this thesis are partially optimized results of the application of a

decomposition strategy for large-scale optimization applied to a nine-subsystem AAF consisting

of a morphing-wing AFS-A, turbofan propulsion subsystem (PS), environmental controls

subsystem (ECS), fuel loop subsystem (FLS), vapor compression/polyalphaolefin loop

subsystem (VC/PAOS), electrical subsystem (ES), central hydraulics subsystem (CHS), oil loop

subsystem (OLS), and flight controls subsystem (FCS). The decomposition strategy called

Iterative Local-Global Optimization (ILGO) is incorporated into a new engineering aircraft

simulation and optimization software called iSCRIPT™ which also incorporates the models

developed as part of this thesis work for the nine-subsystem AAF. The AAF flies 21 mission

segments of a supersonic fighter aircraft mission with a payload drop simulating a combat

situation. The partially optimized results are extrapolated to a synthesis/design which is believed

to be close to the system-level optimum using previously published results of the application of

ILGO to a five-subsystem AAF to which the partially optimized results of the nine-subsystem

AAF compare relatively well.

In addition to the optimization results, a parametric study of the morphing AFS-A

geometry is conducted. Three mission segments are studied: subsonic climb, subsonic cruise,

iii

and supersonic cruise. Four wing geometry parameters are studied: leading-edge wing sweep

angle, wing aspect ratio, wing thickness-to-chord ratio, and wing taper ratio. The partially

optimized AAF is used as the baseline, and the values for these geometric parameters are

increased or decreased up to 20% relative to an established baseline to see the effect, if any, on

AAF fuel consumption for these mission segments. The only significant effects seen in any of

the mission segments arise from changes in the leading-edge sweep angle and wing aspect ratio.

The wing thickness-to-chord ratio shows some effect during the subsonic climb segment, but

otherwise shows no effect along with the taper ratio in any of the three mission segments studied.

It should be emphasized, however, that these changes are made about a point (i.e.

synthesis/design), which is already optimal or nearly so. Thus, the conclusions drawn cannot be

generalized to syntheses/designs, which may be far from optimal. Also note that the results upon

which these conclusions are based may very likely highlight a weakness in the conceptual-level

drag-buildup method used in this thesis work. Further optimization studies using this drag-

buildup method may warrant setting the thickness-to-chord ratios and taper ratios rather than

having them participate in the optimization as degrees of freedom (DOF).

The final set of results is a parametric study conducted to highlight the correlation

between the fuel consumption and the total exergy destruction in the AFS-A. The results for the

subsonic cruise and supersonic cruise mission segments show that at least for the case when the

AFS-A is optimized by itself for a fixed specific fuel consumption that there is a direct

correlation between the fuel burned and total exergy destruction. However, as shown in earlier

work where a three-subsystem AAF with AFS-A, PS, and ECS is optimized, this may not always

be the case. Furthermore, based on the results presented in this thesis, there is a smoothing effect

observed in the exergy response curves compared to the fuel-burned response curves to changes

in AFS-A geometry. This indicates that the exergy destruction is slightly less sensitive to such

changes.

iv

Acknowledgements

This masters thesis is the product of a significant amount of work by myself and my

advisor, Dr. Michael von Spakovsky, as well as cooperation with an industry partner, TTC

Technologies Inc., and the Air Force Research Laboratories, specifically Dr. David Moorhouse

and Dr. Jose Camberos. The work was sponsored through a joint award of an SBIR Phase II

project to Virginia Tech and TTC Technologies.

I would firstly like to thank Dr. von Spakovsky for providing the opportunity to study this

topic, his sponsorship, his mentorship, his guidance, and his passion for his beliefs, all of which I

learned greatly from throughout my time as a graduate student at Virginia Tech.

Secondly, I would like to thank Dr. Ken Alabi of TTC Technologies Inc. for helping me

so much with learning their software and putting up with my seemingly numerous mistakes as

the code progressed through the stages of development and integration.

Thirdly, I would like to thank the members of the defense committee: Dr. Michael von

Spakovsky, Dr. Walter O’Brien, Dr. Michael Philen, and Dr. David Moorhouse for serving on

my committee and providing feedback on my thesis draft.

Fourthly, I would like to thank all my friends who helped me get through graduate school

and pulled me away from my work when necessary (or sometimes more than necessary), those in

Chi Alpha, you know who you are, and my new friends in Maryland who are seeing the

aftermath of finishing this project.

Fifthly, I would like to thank my family who has supported, encouraged, commiserated,

and advised me throughout this project. To my parents, Kenneth Sr. and Danlynne, for the work

ethic, endurance, and stubbornness to finish a project of this length that you imprinted in me, I

thank you as well.

But mostly, I would like to thank my Lord and Savior, Jesus Christ. For the strength,

endurance, ability, opportunity, family, friends, direction, love and direction, Father, I thank

You.

Proverbs 16:9

v

Table of Contents

Abstract ........................................................................................................................................... ii

Acknowledgements ........................................................................................................................ iv

Table of Contents .............................................................................................................................v

List of Figures ............................................................................................................................... IX

List of Tables ............................................................................................................................... XII

Nomenclature ............................................................................................................................... XV

Chapter 1 Introduction .....................................................................................................................1

1.1 Morphing-Wing Aircraft ....................................................................................................... 1

1.2 Aircraft System/Subsystem Synthesis/Design ...................................................................... 3

1.3 Modeling and Simulation ...................................................................................................... 5

1.4 Large-Scale Optimization and Mission Integration .............................................................. 7

1.5 Decomposition for Large-Scale Optimization ...................................................................... 9

1.6 The Use of Exergy Analysis................................................................................................ 10

1.7 Thesis Objectives ................................................................................................................ 11

Chapter 2 Literature Review ..........................................................................................................14

2.1 Benefits and Design Challenges for Morphing Aircraft ..................................................... 14

2.2 Study of Morphing-wing Effectiveness in Fighter Aircraft ................................................ 18

2.2.1 Airframe Subsystem – Aerodynamics (AFS-A) ........................................................... 19

2.2.2 Propulsion Subsystem (PS) .......................................................................................... 21

2.2.3 Most Important Results from Butt (2005) .................................................................... 21

2.3 Decomposition Strategies for Large-scale Aircraft Synthesis/Design Optimization .......... 22

2.4 Effects on Aircraft Synthesis / Design of Different Objective Functions ........................... 29

2.5 Exergy Methods for the Development of High Performance Vehicle Concepts ................ 35

2.6 Integrated Mission-Level Analysis and Optimization of High Performance Vehicle

Concepts ................................................................................................................................ 41

Chapter 3 Model Description and Synthesis/Design Problem Description ...................................47

3.1 Problem Definition .............................................................................................................. 47

3.2 Airframe Subsystem ............................................................................................................ 49

3.2.1 Lift and Drag ................................................................................................................ 50

3.2.2 Mission Analysis .......................................................................................................... 51

vi

3.2.3 Weight Fraction Model ................................................................................................. 54

3.2.4 Calculation of WTO ........................................................................................................ 55

3.2.5 Morphing-wing Considerations .................................................................................... 56

3.2.6 AFS-A Exergy Model ................................................................................................... 58

3.3 Propulsion Subsystem ......................................................................................................... 59

3.3.1 PS Layout and Station Definitions ............................................................................... 59

3.3.2 PS Thermodynamic Model ........................................................................................... 61

3.3.3 Thrust and Performance Calculations ........................................................................... 65

3.3.4 PS Exergy Model .......................................................................................................... 67

3.4 Environmental Controls Subsystem .................................................................................... 68

3.4.1 ECS Layout and Definitions ......................................................................................... 68

3.4.2 ECS Thermodynamic Model ........................................................................................ 69

3.4.3 ECS Exergy Model ....................................................................................................... 74

3.5 Vapor Compression / PAO Subsystem ............................................................................... 75

3.5.1 VC/PAOS Thermodynamic Model .............................................................................. 76

3.5.2 VC/PAOS Exergy Model ............................................................................................. 78

3.6 Fuel Loop Subsystem .......................................................................................................... 79

3.6.1 FLS Thermodynamic Model ........................................................................................ 80

3.7 Oil Loop Subsystem ............................................................................................................ 81

3.7.1 OLS Thermodynamic Model ........................................................................................ 82

3.7.2 OLS Exergy model ....................................................................................................... 84

3.8 Central Hydraulic Subsystem .............................................................................................. 85

3.8.1 CHS Thermodynamic Model........................................................................................ 85

3.8.2 CHS Exergy Model ...................................................................................................... 88

3.9 Electrical Subsystem ........................................................................................................... 89

3.9.1 ES Thermodynamic Model ........................................................................................... 91

3.9.2 ES Exergy Model ......................................................................................................... 92

3.10 Flight Controls Subsystem ................................................................................................ 93

3.10.1 FCS Thermodynamic Model ...................................................................................... 94

3.10.2 FCS Exergy Model ..................................................................................................... 94

vii

Chapter 4 Large-scale System Synthesis/Design Optimization Problem Definition and Solution

Approach ........................................................................................................................................96

4.1 AAF Aircraft System Synthesis/Design Optimization Problem ......................................... 96

4.1.1 System-Level Optimization Problem Definition .......................................................... 97

4.1.2 Need for Decomposition ............................................................................................... 99

4.2 Iterative Local-Global Optimization (ILGO) Approach ................................................... 100

4.2.1 Local-Global Optimization (LGO) ............................................................................. 100

4.2.2 ILGO Approach .......................................................................................................... 104

4.3 System-Level, Unit-Based Synthesis/Design Optimization Problem Definitions ............ 106

4.3.1 Subsystem Integration and Coupling Functions ......................................................... 106

4.3.2 AFS-A System-Level, Unit-Based Synthesis/Design Optimization Problem Definition

.......................................................................................................................................... 110

4.3.3 PS System-Level, Unit-Based Synthesis/Design Optimization Problem Definition . 114

4.3.4 ECS System-Level, Unit-Based Synthesis/Design Optimization Problem Definition116

4.3.5 VC/PAOS System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition .......................................................................................................................... 119

4.3.6 FLS System-Level, Unit-Based Synthesis/Design Optimization Problem Definition 123

4.3.7 OLS System-Level, Unit-Based Synthesis/Design Optimization Problem Definition

.......................................................................................................................................... 125

4.3.8 CHS System-Level, Unit-Based Synthesis/Design Optimization Problem Definition

.......................................................................................................................................... 128

4.3.9 ES System-Level, Unit-Based Synthesis/Design Optimization Problem Definition . 130

4.3.10 FCS System-Level, Unit-Based Synthesis/Design Optimization Problem Definition

.......................................................................................................................................... 132

4.4 Optimization Decision Variables and Variable Constraints ............................................. 134

4.5 Solution Approach............................................................................................................. 140

4.6 iScript™ Scripting Language and Optimization ............................................................... 141

Chapter 5 Results and Discussion ................................................................................................143

5.1 Two-Subsystem Optimization Results .............................................................................. 143

5.2 Nine-Subsystem Results .................................................................................................... 147

5.2.1 Preliminary Synthesis/Design Analysis ...................................................................... 147

viii

5.2.2 Projected Optimum and Comparison ......................................................................... 149

5.3 Parametric Study of the Morphing-Wing AFS-A ............................................................. 151

Chapter 6 Conclusions/Recommendations ..................................................................................159

References ....................................................................................................................................162

Appendix A Fan Performance Map Code ....................................................................................168

IX

List of Figures

Figure 1.1 Lockheed hunter-killer morphing aircraft concept (Bowman, Sanders, Weisshar,

2002). ........................................................................................................................................... 2

Figure 1.2 NASA Oblique-Wing Demonstrator, the NASA AD-1 (Dryden X-Press, 1979) ........ 3

Figure 2.1 Effect of morphing on the synthesis/design space of thrust to weight (T/W) vs wing

loading (W/S). ............................................................................................................................ 15

Figure 2.2 Mechanization of the mission adaptive wing (MAW) trailing edge. ......................... 16

Figure 2.3 Example of the benefit of mission adaptive wing (MAW) technology. ..................... 16

Figure 2.4 Mission Profile by segment or leg (Mattingly, Heiser, and Daley, 1987).................. 18

Figure 2.5 Subsystems and subsystem coupling functions (Rancruel, 2002). ............................. 27

Figure 2.6 Evolution of the gross take-off weight, fuel weight, AFS-A weight, and PS weight at

different points of the iterative local-global optimization (ILGO) approach (Rancruel,

2003)...…………………………………………………………………………………………28

Figure 2.7 Variation of vehicle specific thrust and exergy destruction rate with fan bypass ratio

and turbine inlet temperature for a fixed compressor pressure ratio of 8 for the supersonic

penetration mission segment (Periannan, 2005). ....................................................................... 31

Figure 2.8 Variation of vehicle specific thrust and exergy destruction rate with fan bypass ratio

and compressor pressure ratio for a fixed turbine inlet temperature of 1700° K for the

supersonic penetration mission segment (Periannan, 2005). ..................................................... 32

Figure 2.9 Variation of vehicle specific fuel consumption and exergy destruction rate with fan

bypass ratio and compressor pressure ratio for a fixed turbine inlet temperature of 1700 K for

the supersonic penetration mission segment (Periannan, 2005). ............................................... 33

Figure 2.10 Optimum gross takeoff weight with and without AFS-A DOF for objectives 1, 2,

and 3 (Periannan, von Spakovsky and Moorhouse, 2008)……………………………………..34

Figure 2.11 Optimum fuel weight with and without AFS-A DOF for objectives 1, 2, and 3

(Periannan, von Spakovsky, and Moorhouse, 2008)…………………………………………..34

Figure 2.12 Hypersonic vehicle configuration (Markell, 2005). ................................................ 35

Figure 2.13 A physical representation of the forebody and inlet component of the hypersonic

vehicle along with design and operational decision variables that govern the flow

characteristics throughout the inlet (Markell, 2005). ................................................................. 36

Figure 2.14 Propulsion subsystem components and airframe subsystem (Brewer, 2006). ........ 42

X

Figure 2.15 Total scramjet vehicle mission (Brewer, 2006). ....................................................... 42

Figure 3.1 Supersonic fighter aircraft mission from the RFP found in Mattingly, Heiser, and

Pratt (2002). ............................................................................................................................... 48

Figure 3.2 Free-body diagram of the aircraft (Rancruel, 2002). .................................................. 49

Figure 3.3 Engine system layout (Rancruel, 2002). ..................................................................... 60

Figure 3.4 Engine Station Definitions (Periannan, 2005). ........................................................... 60

Figure 3.5 ECS layout and components (Muñoz and von Spakovsky, 2001). ............................ 69

Figure 3.6 ECS station definitions (Rancruel, 2002). .................................................................. 70

Figure 3.7 Geometric parameters of the offset-strip fin (Muñoz and von Spakovsky, 1999). .... 72

Figure 3.8 VC/PAOS layout and station definitions (Rancruel, 2002). ....................................... 76

Figure 3.9 Schematic of the fuel loop subsystem (Rancruel, 2002). ........................................... 79

Figure 3.10 Oil loop subsystem schematic. ................................................................................. 82

Figure 3.11 Notional central hydraulics subsystem layout (simplified). ..................................... 86

Figure 3.12 Notional electrical subsystem schematic (simplified). ............................................. 90

Figure 4.1 Physical decomposition of a 2-unit system. ............................................................. 100

Figure 4.2 Multi-level optimization resulting in a set of nested optimizations. ........................ 103

Figure 4.3 An example of three subsystems and their associated coupling functions. .............. 104

Figure 4.4 Notional flow diagram of the application of the ILGO decomposition strategy to the

two-unit system of Figure 4.2. ................................................................................................. 106

Figure 4.5 Aircraft subsystem interactions and coupling functions. ......................................... 108

Figure 4.6 Diagram of optimization problem solution approach using ILGO. ......................... 140

Figure 5.1 Sensitivity analysis of morphing-wing effectiveness for different wing- and fuel-

weight penalties (Smith et al., 2007). ...................................................................................... 144

Figure 5.2 Total exergy destruction plus fuel exergy loss for each of the nine subsystems after

the first ILGO iteration. ........................................................................................................... 148

Figure 5.3 Variation of the mission segment fuel burned with variations in aspect ratio and the

sweep angle for mission segment 4 (subsonic climb at Mach 0.536 from a 20,000 ft to 41,700

ft altitude). ................................................................................................................................ 153


sweep angle for mission segment 5 (subsonic cruise at Mach 0.656 at a 41,700 ft altitude). . 154

XI


sweep angle for mission segment 17 (supersonic cruise at Mach 1.5 and 30,000 ft altitude). 155

Figure 5.6 Variation of the mission segment fuel burned with variations in thickness-to-chord

ratio for mission segment 4 (subsonic climb at Mach 0.536 from a 20,000 ft to 41,700 ft

altitude). ................................................................................................................................... 155

Figure 5.7 Variation of the mission segment exergy destruction with variations in aspect ratio

and the sweep angle for mission segment 5, subsonic cruise at Mach 0.656 at 41,700 ft altitude.

.................................................................................................................................................. 157

Figure 5.8 Variation of the mission segment exergy destruction with variations in aspect ratio

and the sweep angle for mission segment 17, supersonic cruise at Mach 1.5 and 30,000 ft

altitude...................................................................................................................................... 157

XII

List of Tables

Table 2.1 Mission Segment Definition and Description. .............................................................. 18

Table 2.2 AFS-A aerodynamics and model equations. ................................................................ 19

Table 2.3 Mission specifications (Rancruel, 2003). .................................................................... 26

Table 2.4 Comparison between the optimum ATA and the aircraft proposed by Mattingly,

Heiser, and Daley (1987), (Rancruel, 2003). ............................................................................. 28

Table 2.5 Comparison of the optimal combustor models (Markell, 2005). ................................ 38

Table 2.6 Optimal decision variable values for the energy and exergy based optimizations of a

scramjet engine with fixed thrust (Markell, 2005). .................................................................... 39

Table 2.7 Optimal design decision variable values for the single segment optimizations (Markell,

2005). ......................................................................................................................................... 40

Table 2.8 Optimal operational decision variable values for the partial mission (Markell, 2005).

.................................................................................................................................................... 40

Table 2.9 Optimal vehicle fuel mass flow rate comparison (Markell, 2005) .............................. 40

Table 2.10 Mission segment details (Brewer, 2006). .................................................................. 42

Table 2.11 Mission design and operational decision variables for the inlet, nozzle, combustor,

and airframe (Brewer, 2006). ..................................................................................................... 43

Table 2.12 Samples of results populations for sparse and dense optimal solution spaces. Note

that the very large numbers (i.e. E+15) represent infeasible solutions (Brewer, 2006). ........... 45

Table 2.13 Optimal objective function results (Brewer, 2006) ................................................... 46

Table 3.1 Air-to-air fighter (AAF) mission segments and details. .............................................. 48

Table 3.2 Master flight equation and governing flight equations. ............................................... 50

Table 3.3 Lift and drag equations for the AFS-A. ....................................................................... 50

Table 3.4 Mission segment model equations. .............................................................................. 52

Table 3.5 Weight fraction model equations. ................................................................................ 54

Table 3.6 Main subsystem weight calculations and 0TW . ............................................................. 55

Table 3.7 AFS-A exergy destruction rate equations. ................................................................... 59

Table 3.8 Low-bypass turbofan engine station definitions. ......................................................... 60

Table 3.9 Diffuser and nozzle equations...................................................................................... 61

Table 3.10 Fan and high pressure compressor equations. ........................................................... 62

Table 3.11 Burner and afterburner calculations. .......................................................................... 63

XIII

Table 3.12 High and low pressure turbine equations. .................................................................. 64

Table 3.13 Turbine cooling mixer and exhaust mixer equations. ................................................ 65

Table 3.14 Thrust and engine performance calculations. ............................................................ 65

Table 3.15 Inlet and nozzle drag and installed thrust equations. ................................................. 66

Table 3.16 PS exergy model equations. ....................................................................................... 67

Table 3.17 Thermodynamic model of the ECS (Periannan, 2005). ............................................. 70

Table 3.18 Geometric and heat transfer models of the compact heat exchangers. ...................... 72

Table 3.19 ECS exergy destruction rate equations. ..................................................................... 75

Table 3.20 VCPAOS model equations. ....................................................................................... 76

Table 3.21 Fuel loop subsystem thermodynamic model equations. ............................................ 80

Table 3.22 OLS pump work equations. ....................................................................................... 82

Table 3.23 OLS heating load equations. ...................................................................................... 83

Table 3.24 OLS exergy destruction equations. ............................................................................ 84

Table 3.25 Actuator flow estimation calculations. ...................................................................... 86

Table 3.26 Central hydraulic subsystem heating load equations (Majumar, 2003). .................... 88

Table 3.27 CHS subsystem exergy destruction equations (Bejan, 1996). ................................... 88

Table 3.28 Fighter aircraft power generation/empty weight estimate. ........................................ 91

Table 3.29 Electrical subsystem generator work. ........................................................................ 91

Table 3.30 ES heating load model equations. .............................................................................. 91

Table 3.31 ES exergy destruction model equations. .................................................................... 92

Table 3.32 Flight controls subsystem weight equations (Raymer, 1999). ................................... 94

Table 3.33 FCS actuator electrical power and fluid power requirements. ................................... 94

Table 3.34 FCS exergy destruction equations. ............................................................................ 95

Table 4.1 Number of coupling functions associated with each subsystem. ............................... 107

Table 4.2 AFS-A fixed-wing design and operational decision variables and inequality

constraints. ............................................................................................................................... 134

Table 4.3 AFS-A morphing-wing design and operational decision variables and inequality

constraints. ............................................................................................................................... 135

Table 4.4 AFS-A mission decision variables and inequality constraints................................... 135

Table 4.5 PS design and operational decision variables and inequality constraints. ................. 136

XIV

Table 4.6 ECS optimization synthesis / design and operational decision variables and inequality

constraints. ............................................................................................................................... 136

Table 4.6 FLS optimization decision variables and inequality constraints. .............................. 138

Table 4.8 VC/PAOS optimization synthesis / design and operational decision variables and

inequality constraints. .............................................................................................................. 139

Table 4.8 OLS optimization operational decision variables and inequality constraints. ........... 139

Table 5.1 Comparison of the optimum morphing-wing gross takeoff weights with a 6x wing-

weight penalty and the optimum fixed-wing gross takeoff weight (Smith et al. 2007). .......... 145

Table 5.2 Optimal fixed- versus morphing-wing AAF configuration and performance parameters

for the subsonic cruise and the supersonic penetration mission segments (Smith et al. 2007).

.................................................................................................................................................. 145

Table 5.3 AAF subsystem weights and the percentage of AAF empty weight after the first ILGO

iteration. ................................................................................................................................... 148

Table 5.4 AAF Subsystem percent weight reduction versus ILGO iteration (Rancruel, 2002). 149

Table 5.5 Projected AAF subsystem weights versus ILGO iteration based on the ILGO

progression from Rancruel (2002). .......................................................................................... 149

Table 5.6 Extrapolated nine-subsystem AAF gross takeoff weight and empty weight versus

ILGO iteration based on the ILGO progression from Rancruel (2002). .................................. 150

Table 5.7 Extrapolated AAF subsystem system-level optimum weights after seven ILGO

iterations along with the percentage of AAF empty weight. ................................................... 151

Table 5.8 Extrapolated subsystem optimum weights versus the optimum subsystem weights

from Rancruel (2002). .............................................................................................................. 151

Table 5.9 Baseline AAF configuration and performance for mission segment 4, 5, and 17. .... 152

XV

Nomenclature

A Area, aspect ratio FCS flight controls subsystem

AR inlet area FLS fuel loop subsystem

AAF air-to-air fighter g gravitational constant

AAFS airframe subsystem - aerodynamics

GA genetic algorithm

b wing span ILGO iterative local-global optimization

hB horizontal tail span cbK landing gear cross beam factor

BCA best cruise altitude dwK delta wing factor

BCM best cruise Mach mcK 1.45 for mission completion required, 1 otherwise

BCLM best climb Mach tpgK landing gear tripod factor

DC drag coefficient vsK sweep wing factor

0DC parasite drag coefficient vshK Constant = 1.425 if variable sweep wing, 1.00 otherwise

LC lift coefficient L lift, wing length

DwaveC wave drag coefficient aL Electrical routing distance (ft) from generators to avionics to cockpit

feC skin friction coefficient mL length of main gear

CHS central hydraulic subsystem nL length of nose gear

D drag mass flow rate

DOF degree of freedom M Mach number

ECS environmental controls subsystem cN number of crew

e Weissinger span efficiency enN number of engines

ES electrical subsystem genN number of generators

desEx exergy destroyed lN length of nose gear

wF fuselage width at horizontal interception sN number of flight control systems

XVI

uN Number of hydraulic utility functions (typ. 5-15)

V velocity

zN ultimate load factor stallV stall velocity

q dynamic pressure PAOSVC / vapor compression/PAO loop subsystem

Q flow rate, heating load W weight, work

OLS oil loop subsystem lW length of main gear

ORS optimum response surface dgW design gross weight

P pressure EmptyW aircraft empty weight

TOP power takeoff from PS TOW aircraft takeoff weight

PAO polyalphaolefin

PS propulsion subsystem

R specific gas constant, additional drag

Greek

S planform area of the wing angle of attack, fan bypass ratio

csS total area of flight control surfaces

design bleed air ratio

htS horizontal tail area taper ratio, shadow prices

refS reference area of wing LE leading edge sweep angle

wetS wetted area of wing pressure ratio, pi

sfc specific fuel consumption temperature ratio

t time

T thrust, temperature

instT installed thrust

tT total temperature

reqT thrust required

ct / thickness to chord ratio

v valve ratio

1

Chapter 1

Introduction

The energy-based economy is driving a new technology to the aircraft industry:

morphing-wing technology, or the ability of an aircraft to change the shape of its wings during

flight, is being researched heavily by both the military/government and the private aircraft

industry. The goal of the application of morphing technology is to develop an aircraft that can

adapt or change its aerodynamic performance to fly dissimilar missions or dissimilar mission

segments within a mission more efficiently than a fixed-wing aircraft.

A prime platform for investigating morphing technology is the fighter aircraft. Currently

designed fighter aircraft are being used for multiple roles, depending on the branch of the

military or even country in which the aircraft is being used. The designer of a fixed-wing aircraft

would find the dissimilar roles and requirements of the aircraft to be a design challenge, to say

the least. Even more of a challenge would be to design an aircraft that can perform all the roles

required in the most efficient manner, which has been proven to be impossible (e.g. a subsonic

high-endurance reconnaissance aircraft can not perform the role of a supersonic fighter aircraft

more efficiently than the fighter aircraft, nor vice versa). Morphing technology allows a system

designer to design an aircraft that can adapt to its flight conditions in order to meet the

performance requirements in the most efficient manner.

1.1 Morphing-Wing Aircraft

“Morphing wings” is the new catch phrase in the aerospace research industry today.

Morphing technology employed in aircraft wings has been proven, at least on a conceptual level,

to allow aircraft to outperform their fixed-wing counterparts over the entire mission in fuel

savings due to drag reduction and improved lift-to-drag ratios. “Morphing wings” can imply the

ability of an aircraft to change its aerodynamic performance from a very simple morphing, such

as flaps or slats, to a more extensive morphing such as variable wing length, sweep, and chord

lengths. An example of morphing wing aircraft is the Lockheed Martin Unmanned Air Vehicle

(UAV) concept which came out of the DARPA Morphing Aircraft Structures program is shown

in Figure 1.1. This concept has the ability fold its wings, effectively changing the flight

characteristics (by varying the wetted area and aspect ratio) of the aircraft extensively to allow a

2

mission that could include reconnaissance, loiter, and attack/low observeability configurations in

the same vehicle, encompassing the requirements of a hunter-killer mission. The hunter-killer

mission would involve first searching for and identifying the target, then destroying it with the

shortest delay in time between identification and destruction as possible. This type of mission

would normally be performed by a “package” or group of aircraft specializing in certain portions

of the hunter-killer mission. The Lockheed Martin UAV concept allows the package to be

eliminated, as the concept can perform all tasks in the hunter-killer mission due to the ability to

morph its wings.

Figure 1.1 Lockheed hunter-killer morphing aircraft concept (Bowman, Sanders, Weisshar, 2002).1

This variable geometry wing can rotate on a pivot, which significantly reduces the drag

of the wing in high-speed flight. The wing leading edge is near perpendicular to the flight

direction for takeoff and high endurance mission segments for maximum lift, but is rotated (or

swept back) to effectively reduce the induced drag and parasitic drag (due to wave drag) for

supersonic flight. Other examples of morphing wings have been investigated for the purpose of

building a single aircraft that can perform the duties of a group of aircraft. One such example is

1 Reprinted with permission from author.

3

the oblique-wing concept. This concept was investigated and tested under the DARPA Oblique

Flying-Wing Project with the NASA AD-1 (Ames Dryden AD-1).(Curry and Sim, 1982; Dryden

X-Press, 1979) which is shown in Figure 1.2.

Figure 1.2 NASA Oblique-Wing Demonstrator, the NASA AD-1 (Dryden X-Press, 1979)

1.2 Aircraft System/Subsystem Synthesis/Design

The synthesis/design process of the AAF is driven by the mission flown which defines

the customer requirements for the aircraft to be developed. The mission flown in this thesis

work is very similar to Rancruel (2003) and Butt (2005) but with some changes which are

discussed at length in Chapter 3. The flow chart of the synthesis/design process is shown in

Figure 1.3.

The first synthesis/design stage is the conceptual synthesis of the design. Viable

solutions to the requirements are developed and analyzed for cost, feasibility, manufacturability,

etc. in this stage. Synthesis, design, and operational variables are also investigated at this level

to verify the feasibility of the design. The conceptual synthesis stage has the most variation in

model design and performance as often the requirements are adjusted at this step as well,

depending on the level of technology required / available. The best solution for the requirements

is eventually chosen at this step based on multiple performance measures (e.g. cost, weight, ease

of manufacturing, performance, etc.)

The next stage is the preliminary synthesis/design. The configuration of the best solution

from the conceptual synthesis is frozen at this step, and more detailed testing and major

subsystem design commences on the solution. Databases of analytical data and performance

testing are compiled at the preliminary synthesis/design step as well. For example, the engine

4

sizing, weight, compressor and turbine stages, bypass ratios, etc. would be determined at this

stage of the synthesis/design process.

Figure 1.3 Aircraft synthesis/design stages (Raymer, 20062; Rancruel, 2002).

Following the preliminary synthesis/design stage is the detailed design stage. Actual

subsystems would be prototyped and set up for manufacturing, and subsystem performance in

the detailed design stage verified. The performance of the total system would be verified /

estimated again at this point as the subsystems are prototyped and tested. Tooling for

manufacturing would also be developed at the detailed design stage.

The final synthesis/design stage is manufacturing. Hopefully, after the first production

model is made, the design still meets all the requirements that were originally posed by the

customer. Often this is not the case and the synthesis/design needs to be revised slightly (or

perhaps drastically) to meet the original performance requirements. The prevalence of the total

system not meeting original performance requirements is evidence that a better synthesis/design

process/method may be needed.

2 Copyright 2006 by Daniel P. Raymer. Reprinted with permission from author.

5

Finally, each synthesis/design step often has a different design group

synthesizing/designing and optimizing a subsystem and its components somewhat independently

from all the other design groups. A more integrated synthesis/design/optimization process might

reduce the number of occurrences of the final synthesis/design not meeting the original

requirements.

1.3 Modeling and Simulation

An aircraft can be viewed as a system of subsystems. Each subsystem is a component or

group of components that can be logically separated from the rest of the components that make

up the system. Subsystem boundaries may be determined using a variety of criteria such as

logical physical boundaries, thermodynamic boundaries, time boundaries, etc.

After the subsystems are clearly defined, a model of each of the subsystems is developed.

A subsystem model can take on many different forms: a thermodynamic model, a geometric

model, an aerodynamic model, a kinetic model, etc. These models can be analytical, empirical,

or semi-empirical and can be zero-D or lumped-parameter models or 1-D, 2-D, or 3-D

computational fluid dynamics (CFD) model. Typical of the types of subsystem are geometric,

aerodynamic, and thermodynamic used in subsystem modeling, simulation, and large-scale

optimization are models with lumped parameter distributions. A lumped parameter distribution

indicates that properties that would normally have an infinite distribution of values are

represented by an averaged value. For example, the temperature of the air in a turbofan engine

would have an infinite distribution of temperatures throughout the engine; however, the

temperatures are “lumped” or averaged to one temperature at a given station in the engine and

calculated as such in the model equations.

Typically, each subsystem of an aircraft is defined as a group of components that perform

a given function. For example, the engine or propulsion subsystem (PS) provides the thrust to

the aircraft and power to other subsystems and is easily separable, thermodynamically from the

rest of the aircraft. Thus, it is considered a subsystem. The airframe subsystem (AFS) is

responsible for providing the aerodynamics required to fly the mission as well as house the other

subsystems. The fuel loop subsystem (FLS) consists of all the components associated with the

fuel tank and a set of associated heat exchangers which help condition the fuel and deliver it to

6

and from the engine. Other subsystems are defined in a similar fashion and each has a range of

operating conditions and parameters for the function it must perform.

Once the subsystem components and configurations have been defined, every subsystem

model (lumped parameter or otherwise) must be written in an engineering software language to

represent the model equations which simulate the subsystem behavior.

The coded model must then be validated to verify that it produces operating parameter

values close to previously published ones or which from engineering experience seem

reasonable. After validation, each subsystem is integrated with the other subsystems. Integrating

a subsystem involves defining each inter-subsystem interaction by assigning appropriate

variables between subsystems. For example, the thrust required by the airframe subsystem-

aerodynamics (AFS-A) to fly a specific part of the mission segment is assigned as a required

thrust from the engine. Thus, the thrust required by the AFS-A is an interaction between the

engine and AFS-A.

When all the subsystems are integrated, the modeling of aircraft is complete and the code

ready to use to simulate the aircraft’s behavior for a given design point. The simulation gives

feedback as whether or not the aircraft has been designed in a way that enables it to successfully

fly at that design point (usually the most difficult part of the mission to fly, i.e. supersonic flight),

and if so, how well the design flies at that design point compared to other syntheses

(configurations) / designs. When multiple simulations are ran and compared to each other to find

the best configuration / design, it can be said that the system is being optimized. Conventionally,

this is done by trial and error and not by using large-scale optimization. Furthermore,

conventionally, this process of synthesis / design of fixed-wing aircraft is performed only at the

design point and off-design operation is simply verified. However, large-scale optimization

would greatly enhance this process as would inclusion of the off-design mission segments

directly in the synthesis/design process along with the optimization. This requires a mission

integrated approach which is in fact a necessary approach when applying morphing-wing

technology to an aircraft. This is discussed along with large-scale optimization in the following

section.

7

1.4 Large-Scale Optimization and Mission Integration

When mathematical optimization is applied to the process of finding the “best” system

synthesis / design of a complex system, it is called large-scale optimization. To find this “best”

or optimum system requires a performance metric or optimization objective function by which

numerous syntheses / designs can be compared. For example, an optimization objective for a

power plant synthesis / design may be to maximize the power output or to minimize the

operating cost of the power plant. The optimization takes place by varying the system synthesis /

design and operating parameters and then evaluating system performance by running a system

simulation with the given synthesis / design and operating parameters. The independent system

synthesis / design variables are called the synthesis / design decision variables, while the

independent system operating variables are called operational decision variables. The variables

are called “decision” variables because they are being varied, or decided upon, during the

optimization to find the best system configuration and design.

A complete system optimization often requires that both the synthesis / design and

operational decision variables be varied to find the optimum system synthesis / design as

knowledge of system behavior during operation as well as the system’s physical characteristics

are needed to find the optimum system. The highly integrated and tightly coupled (i.e.

everything influences everything else) nature of synthesizing / designing an aircraft typically

requires that both synthesis / design variables and operational decision variables participate in

the optimization as is done in this thesis research. Unfortunately, a complete system

optimization for even a single design point can prove to have a very large computational burden

depending on the complexity and size of the system being optimized. This creates a need for

efficient and effective large-scale optimization algorithms and additional tools and methods to

manage the computational burden of optimizing such a large system.

Adding morphing-wing technology to an aircraft further increases the complexity of the

optimization problem. To fully investigate the benefits of morphing-wing technology, a single

design point optimization is not sufficient. Aircraft performance must be evaluated over the

entire mission since morphing wing technology is intended to improve the off-design

performance of the aircraft. If the aircraft is being synthesized / designed with only the design

flight conditions in mind, morphing-wing technology cannot show any benefit over a fixed-wing

aircraft. Of course, mission integrated optimization compounds the computational burden

8

significantly as additional operational decision variables are required for each operational

condition. In reality, this would require a dynamic, real-time optimization. Computationally,

this adds an additional computational burden to an already computationally challenged problem.

However, for purposes of synthesis / design, this dynamic behavior can be approximated by a

quasi-stationary approach. This is done by splitting the entire aircraft mission as defined, for

example, in Mattingly et al. (2002), into mission segments (see Figure 1.4). Separating the

mission into segments is a form of time decomposition which is common to aircraft synthesis /

design and makes the aircraft modeling quasi-stationary instead of dynamic. Operational

decision variables are then applied to each of the mission segments for each of the subsystems,

and the entire aircraft is optimized over the entire mission. In a sense, the aircraft no longer has

a “design point” per se but is instead optimized for its overall performance in the entire flight

envelope, from takeoff to landing.

Mission integrated synthesis/design is absolutely necessary for studying the effects of

morphing-wing technology in fighter aircraft; however, mission integration synthesis / design

and optimization creates a huge computational burden. The computational burden increase is

primarily due to an increase of degrees of freedom (DOF) or the number of variables the

optimization algorithm has “free” to decide upon for system simulation. An additional problem

is the non-linear response of aircraft performance with respect to the decision variables. This

and the large number of DOF as well as the fact that these may include a mix of discrete and

continuous variables limits the optimization algorithms that can be used, as many are unable to

find the overall aircraft optimum due to the variable search method used.

A solution to the dilemma of too many DOF which does not require a reduction in their

number is the use of decomposition strategies. A solution to the difficulties caused by the non-

linearities and the mix of discrete and continuous variables is the use of heuristic optimization

algorithms (.e.g., genetic algorithms, simulated annealing, etc.) or the use of hybrid heuristic-

nonheuristic optimization algorithms (e.g., surrogate, model-based optimization, etc.). A non-

heuristic algorithm is typically a gradient-based algorithm such as, for example, sequential

quadratic programming (SQP), generalized reduced-gradient (GRG), steepest descent, etc. A

discussion of the decomposition strategies and optimization algorithms used in this thesis

research appears in Chapter 4. However, a brief discussion of decomposition for large-scale

optimization is given in the following section.

9

1.5 Decomposition for Large-Scale Optimization

The size of a complete aircraft system optimization problem may require a decomposition

strategy to handle the huge (and perhaps prohibitively so) complexity of the optimization. There

are several different types of decomposition strategies (Frangopoulos, von Spakovsky, and

Sciubba, 2002) among which physical decomposition is a major player. Most of the physical

decomposition strategies in the literature can be characterized as Local-Global Optimizations

(LGOs). With LGO, the system is physically decomposed into a set of subsystems or units each

of which is characterized by its own set of decision variables. Each set of decision variables is

strictly local, i.e. affects in the main system only its corresponding unit. In a complex system,

however, there is always another set of decision variables which is not strictly local and which

acts at the so-called system level to affect some or all of the units. It is this division which leads

to a multi-level optimization problem in which at the system level an optimization occurs with

respect to its set of decision variables, while at the unit level individual optimizations of each

unit are carried out with respect to each individual set of unit-level decision variables. To

maintain the integrity of the overall system optimization, i.e. one which takes into account all of

the decision variables simultaneously, the unit-level optimizations must occur many times within

the system-level optimization, resulting in a set of so-called nested optimizations. Although such

a set can only approximate the so-called single-level optimization which occurs without

decomposition, it nonetheless may do so quite closely. However, the computational burden is

much greater than with the single-level optimization and may in fact be prohibitive.

To address this last problem as well as a number of others discussed in Chapter 4, a

physical decomposition strategy called Iterative Local-Global Optimization (ILGO) has been

developed and applied by Muñoz and von Spakovsky (2000a,b,c,d, 2001a,b) and Rancruel and

von Spakovsky (2006, 2004a,b, 2003a,b) to eliminate this problem of nested optimizations.

ILGO does this by eliminating the system-level optimization and, thus, the need for nested

optimizations and does so by bringing the system-level information down to the unit-level. This

is done by maintaining subsystem interactions via a set of coupling function and shadow price

pairs, which measure the effect that changes in the coupling functions have on the system

objective function. Elimination of the nested optimizations reduces much of the computational

burden of LGO and has the further advantage of permitting the subsystem optimizations to take

10

place simultaneously. ILGO, coupling functions, and shadow prices are discussed at more length

in Chapter 4.

1.6 The Use of Exergy Analysis

An emerging analysis tool for aircraft systems is exergy or available energy analysis.

The available energy of a system is defined as the largest amount of energy that can be

transferred from a system to a weight in a weight process while bringing the system to a mutual

stable equilibrium with a notional reservoir (Gyftopoulos and Beretta, 1991, 2004). The

usefulness of this analysis technique is realized in multi-component, highly-coupled energy

systems where identifying and correcting performance losses is made difficult using traditional

energy balance methods. Energy balances treat all forms of energy as equivalent, without

differentiating between the quality (ability to produce useful work) of energy crossing the system

boundary. Hence the energy from a high temperature source is treated in the same way as the

energy rejected to a low temperature sink. Energy balances do not provide information about

internal losses. For example, an energy balance for an isolated system in a not stable equilibrium

state shows that the process the system undergoes incurs no losses. This, however, is not true! In

fact, most of the causes of thermodynamic losses in thermal, chemical, and mechanical processes

such as heat transfer across finite temperature differences, mixing, combustion, and viscous flow

cannot be detected with energy balances since these losses are not associated with a loss of

energy (which can neither be created or destroyed) but instead with a decrease in the quality of

the energy.

An exergy or available energy approach overcomes these deficiencies since exergy

accounts for this loss in quality. The rate of loss of exergy internal to the system (i.e. the rate of

irreversibilities or entropy generated) provides information about the true inefficiencies of the

system. Hence an exergy analysis of a multi-component system such as the propulsion subsystem

(PS) of an aircraft indicates the extent to which its components contribute to the inefficiency of

the overall aircraft system. Unlike the energy method which is based on the First Law of

Thermodynamics alone, the concept of exergy and irreversibility is based on both the First and

Second Laws of thermodynamics. The irreversibility of a system, sub-system, or component can

be found by doing an exergy balance which combines unsteady or steady state balances of mass,

energy, and entropy into a single balance of exergy. The overall exergy destruction rate which is

11

directly proportional to the overall entropy generation rate and which appears in this single

balance can be determined directly from this balance. To determine the individual exergy

destruction rates which comprise this overall rate, a set of independent phenomenological

equations relating the exergy destruction rates to the various irreversible phenomena present in a

given process must be used.

Since the intention of this thesis research is to investigate morphing wing feasibility using

modeling, simulation, mission integration and optimization, exergy analysis is an additional tool

which can be employed for finding locations in the aircraft system needing the most

improvement and for categorizing the internal and external losses which occur in and out of the

aircraft. In other words, an exergy analysis can provide information about which components or

set of variables may be good candidates for further optimization or re-optimization and is useful

for setting up guidelines for process improvements since no matter what aerodynamic,

thermodynamic, kinetic or geometric phenomena are being modeled, a common quantity, i.e. the

exergy, can be used as the measure of process improvement or performance.

1.7 Thesis Objectives

The overall goal of this thesis work is to investigate the feasibility of applying morphing-

wing technology to an air-to-air fighter (AAF). The feasibility is investigated by modeling,

simulating, analyzing, and optimizing a morphing-wing fighter aircraft and comparing it to a

fixed-wing fighter aircraft. The aircraft model is an expansion by four subsystems on the five-

subsystem model developed and implemented by Rancruel (2003) and is intended to bring the

number of subsystems up to that of a complete aircraft system. It, thus, consists of nine

subsystems including the following: airframe subsystem-aerodynamics (AFS-A), propulsion

subsystem (PS), environmental controls subsystem (ECS), fuel loop subsystem (FLS), vapor

compression/polyalfaolephin subsystem (VC/PAOS), oil loop subsystem (OLS), central

hydraulic subsystem (CHS), electrical subsystem (ES), and flight controls subsystem (FCS). The

first five of these exist in the aircraft model of Rancruel (2003) while the latter four are

researched, developed, implemented, and validated here. Two additional subsystems exist in

both aircraft models, namely, the fixed and expendable payload subsystems. However, neither

involves synthesis/design or operational degrees of freedom (DOF) even though each plays a

role in the synthesis/design process. All the subsystems used are the same between the

12

morphing- and fixed-wing models with the exception of additional DOF for the morphing AFS-

A which are included to account for the wing geometry changing during flight.

To achieve the overall goal outlined above, the first objective of this thesis research

involves the research and development of four conceptual-level, lumped-parameter subsystem

models (thermodynamic and geometric) and extensive modification of the other five high-

fidelity, lumped-parameter subsystem models (aerodynamic, thermodynamic, and geometric)

which have already been fairly well documented in a previous Ph.D. dissertation (Muñoz, 2000)

and M.S. thesis (Rancruel, 2003) and in publications by Muñoz and von Spakovsky (2000a,b,c,d,

2001a,b) and Rancruel and von Spakovsky (2006, 2004a,b, 2003a,b). The subsystems are as

listed above. Note, however, that the AFS-A involves separate fixed-wing and geometry

morphing aerodynamics models. These along with the PS, ECS, FLS, and VC/PAOS are

modified from previous work and implemented in iSCRIPT™, which is a software language and

tool set being developed specifically for the purpose of aircraft mission integrated

synthesis/design modeling, analysis, and large-scale optimization by TTC Technologies, Inc.,

(TTC) as part of a U.S. Air Force AFRL Phase II SBIR in which Virginia Tech is a participant.

The remaining four subsystems, the OLS, ES, CHS, and FCS, are developed and implemented

specifically for this thesis work.

The second objective of this thesis research is to integrate all of the subsystems into an

overall aircraft system capable of flying an entire fighter aircraft mission. This requires defining

a complete mission able to thoroughly exercise the capabilities of both the fixed- and the

morphing-wing aircraft. It also requires assigning the proper wing- and fuel-weight penalties due

to morphing-wing technology (both explained in Chapter 3).

A third objective is to apply large-scale optimization using physical decomposition (i.e.

ILGO) to the mission integrated synthesis/design of both the fixed- and morphing-wing fighter

aircraft and then analyze and compare the results. The main comparison for the fixed- versus the

morphing-wing aircraft is a sensitivity study of the effects of the wing weight and fuel weight

penalties associated with the morphing technology as was done in Butt (2005) but with a much

more detailed and complete aircraft system.

The final or fourth objective is a study of the morphing-wing parameters that provide the

highest payoff in terms of fuel savings for three mission segments: subsonic climb, subsonic

cruise, and supersonic cruise. The effect of varying the wing parameters on the fuel burned is

13

compared to the exergy destruction plus exergy loss due to unburned fuel for the AFS-A to see a

correlation in trends. The results and conclusions drawn are then compared to those given in

Periannan, von Spakovsky, and Moorhouse (2008).

14

Chapter 2

Literature Review

Much research has been done in the areas of morphing-wing technology, exergy analysis,

and optimization, and how they relate to aircraft synthesis / design. This chapter reviews some

of the previous work done in this area in each of these areas.

2.1 Benefits and Design Challenges for Morphing Aircraft

Moorhouse, Sanders, von Spakovsky, and Butt (2005, 2006) illustrate the potential

benefits of applying morphing wings to an aircraft as well as the design challenges that are yet to

be overcome in applying morphing technology to aircraft. The aerospace industry has shown a

history of taking a current technology and expanding it to yield the next generation of aircraft.

Often the new designs end up looking like the old designs albeit with new materials or more

sophisticated electronics. The current aerospace customer needs a more affordable aircraft with

expanded mission capabilities. Technologies are already being applied to wings to allow wing

shape and, thus, aerodynamic performance to change depending on the requirements of the flight

conditions. An early example of wing morphing, i.e. wing twisting, was used by the Wright

brothers for roll control and is being ‘re-invented’ by the active aeroelastic wing (AAW)

program. Currently, variable wing sweep or “swing wings” are employed on many fighter

aircraft to allow better cruise endurance but without sacrificing high velocity flight performance.

Low order shape control is being used on aircraft in the form of Fowler flaps and

ailerons. These technologies have been hugely successful, enabling aircraft to reduce stall

speeds, increase lift, etc. to perform mission segments more successfully than otherwise may

have been possible. However, more extensive shape control or ‘morphing aircraft structure’ is

desired to allow drastic wing planform area and aerodynamic performance changes during flight.

The benefits of applying morphing wings to a fighter aircraft were investigated with a

model and a set of optimizations by Butt (2005; see Section 2.2 for details on the investigation).

The optimization results show that drastic morphing of an aircraft wing, including wing sweep,

wing length, and root and tip chord lengths could allow a fighter aircraft to use significantly less

fuel than a fixed-wing counterpart even for a much heavier morphing-wing aircraft. A point

perhaps not obvious to a designer is the fact that design constraints, which are determined by the

15

mission requirements, are relaxed due to the ability to morph the aircraft wings. Figure 2.1

shows an example of an aircraft synthesis/design space with the dark shaded region. However,

when morphing technology is used on the aircraft, the design space is expanded to include the

cross-hatched region.

Figure 2.1 Effect of morphing on the synthesis/design space of thrust to weight (T/W) vs wing loading (W/S)

(Periannan, von Spakovsky, and Moorhouse, 2008).

The increase in the design space indicates that morphing wings allow the aircraft to

perform the same mission as a fixed-wing counterpart, but with more flexibility in the design of

the wing loading and thrust to weight ratio.

Morphing-wing technology certainly shows very promising results for implementation on

paper; however, building a morphing-wing presents new challenges in design, implementation,

and control. The difficulty is how can the morphing technology be mechanized? The model in

Butt (2005) uses mission segment-by-segment morphing or a single configuration for the entire

mission segment. Would real-time shape control provide more benefit? One concept for real-

time shape control is the mission adaptive wing (MAW). An example of a trailing edge MAW is

shown in Figure 2.2.

The MAW allows the wing lift and drag to be dynamically adjusted (or morphed in ‘real

time’) during flight to outperform a fixed-wing counterpart. An example of such behavior could

be observed in a sustained turn. Figure 2.3 shows the benefit of employing MAW technology to

maximize the lift/drag ratio to allow a much smaller turning radius over that of a fixed-wing

aircraft. The MAW shows great promise as does the morphing-wing aircraft in Butt (2005).

Additional design risk is added when real-time morphing is implemented; furthermore, the level

16

Figure 2.2 Mechanization of the mission adaptive wing (MAW) trailing edge (Periannan, von Spakovsky,

and Moorhouse, 2008).

of aircraft integration required to successfully implement morphing technology is substantially

higher than what traditional design methods dictate today. The authors believe a new design

methodology must be used: the vehicle is considered a device in which all components are

Figure 2.3 Example of the benefit of mission adaptive wing (MAW) technology (Periannan, von Spakovsky,

and Moorhouse, 2008).

optimized to minimize exergy consumption at the system level. The authors assert three things

must be changed in traditional design methods. The first is in the philosophy of how structures

are designed. Wing structures must be designed for deformation characteristics from the start of

17

the design. The second change is that a better understanding of how to optimize the distribution

of sensors and actuators in addition to structural properties, such as mass and stiffness, needs to

be developed. The final change is to investigate the scalability of actuators and the degree of

deformation from a systems level perspective that is best suited to the design problem. The

exergy-based concept design method proposed by the authors shows good promise in solving

this third item as exergy is a metric common to all systems. The exergy-based objective function

for optimization requires an integration of the entire vehicle during the design process rather than

the traditional design assumption that minimum weight is the best design.

There are other challenges in employing morphing wings that must be overcome. The

example in Figure 2.3 should show that even for a simple model, non-linear design and analysis

is required in order to avoid the significant error which comes from assuming linearity. Flight

control issues of a wing capable of shape changing to modify roll characteristics, drag, and even

perhaps wing loading profiles would pose a significant design challenge. Previously, control

gains were set based on wind-tunnel testing with a re-design if flight testing showed

improvement was needed. The current design method is to use a neural network to actively

adjust gains based on actual in-flight aerodynamic performance. Perhaps this technology could

be employed to control morphing wings as well or would it be trying to catch up to the

constantly changing flight characteristics (forming too great of a computational burden)?

These authors as well as others have clearly shown that employing adaptive structures in

the next generation of aircraft will yield significant benefits in operating cost and performance

for aircraft that perform significantly dissimilar mission segments. They have also shown that

current design methodologies will be unable to accomplish the level of integration required to

successfully design (and eventually manufacture) a morphing-wing aircraft. Non-linear design

methods and an exergy-based optimization metric may be required to reach this level of

integration and some questions need answering as well. How fast do the wings need to change

shape? If they change slowly, will traditional flight control subsystems be sufficient for flight

control? If they change quickly, what will be the flight controls needed to compensate for

aerodynamic instability during shape change? These questions and design challenges must be

answered and overcome to continue to ‘re-invent and extend’ the adaptive structures that started

with the Wright brothers.

18

2.2 Study of Morphing-wing Effectiveness in Fighter Aircraft

Previous work has been done in the area of morphing-wing technology at Virginia Tech

(Butt, 2005). An afterburning turbojet propulsion subsystem (PS) and the aerodynamic aspects

of a morphing airframe subsystem (AFS-A) are used to perform a feasibility study of employing

morphing-wing technology in a supersonic fighter aircraft flying a mission as depicted in Figure

2.4 taken from Mattingly, Heiser, and Daley (1987). Butt separates the entire mission (originally

14 segments) into 22 segments to allow a more accurate estimation of aircraft behavior over the

entire mission (e.g., separates a subsonic-supersonic acceleration into 3 segments: subsonic,

transonic, and supersonic). The mission flown is a subset of the 22 mission segments in that

segments 3-21 are what are actually flown. The mission segments are detailed in Table 2.1.

Figure 2.4 Mission Profile by segment or leg (Mattingly, Heiser, and Daley, 1987).

Table 2.1 Mission Segment Definition and Description.

Mission Segments No. Name Description 1 Warm up 1 minute, military power 2 Take off 5 min at idle, take off + roll rotation 3 Subsonic Acceleration 1 Accelerate to climb speed 4 Subsonic Acceleration/Climb Climb at BCM/BCA 5 Subsonic Cruise 1 Cruise until cruise + climb range = 280 km 6 Combat Air Patrol/Loiter Patrol for 20 min and 9150 m and Mach for best endurance 7 Subsonic Acceleration 2 Accelerate to Mach 0.99 8 Transonic Acceleration 1 Accelerate to Mach 1.2 9 Supersonic Acceleration 1 Accelerate to Mach 1.5

10 Supersonic Penetration Mach 1.5 for 185 km 11 Combat Turn 1 Mach 1.6, one 260 degree 5g turn at max power

19

No. Name Description 12 Combat Turn 2 Mach 0.9, two 360 degree 5g turns at max power 13 Subsonic Acceleration 3 Accelerate from M = 0.9 to 0.99 14 Transonic Acceleration 2 Accelerate from M = 1 to M = 1.2 15 Supersonic Acceleration 2 Accelerate from M = 1.2 to M = 1.6 16 Deliver Expendables Deliver 2 AMRAAM, 2 AIM-9L, and ½ ammunition 17 Escape Dash M = 1.5 for 46 km 18 Supersonic Climb Climb to BCM/BCA from M = 1.5 to M = 1.2 19 Transonic Climb Climb to BCM/BCA from M = 1.2 to 1 20 Subsonic Cruise 2 Cruise at BCM/BCA for range of 278 km 21 Loiter Loiter at 9150m for 20 min at M for best endurance 22 Landing Land

2.2.1 Airframe Subsystem – Aerodynamics (AFS-A)

The aerodynamics model is developed from Raymer (1999), Mattingly, Heiser, and Pratt

(2002), Andersen (1998), and Nicolai (1975). Table 2.2 displays the airframe subsystem –

aerodynamics (AFS-A) calculations and model equations.

Table 2.2 AFS-A aerodynamics and model equations.

Component Variable Description Model Equation Master Flight Equation

T Thrust

g

Vh

dt

dWVDT

2

2

V Velocity

Drag

D Drag SqCD D

DC Drag coefficient

02

1 DLD CCKC

where 2min_

"0 min dragLDD CKCC

Induced Drag 1K

Induced drag factor (Nicolai, 1975)

Subsonic: eAR

K

11

Supersonic: LC

K1

1

Parasitic Drag 0DC

Parasitic Drag Coefficient

Subsonic: ref

wetfeDD S

SCCC min0

Supersonic: Dwaveref

wetfeD C

S

SCC

0

Wave Drag DwaveC

Coefficient of drag due to shock waves

S

qDC wave

Dwave/

20

Component Variable Description Model Equation

waveq

D

Wave drag efficiency factor

where for M = 1 to 1.2:

2max

2

9*2*2

l

A

q

D

q

D

HSwave

and for M > 1.2

HS

LEWD

waveq

DME

q

D

100

12.1386.0177.0

57.0

where HaackSearsHS

q

D

q

D

Exergy

PardesxE

Exergy destruction rate due to parasitic drag

T

VDTxE

Pardes00

where: SqCD D00

T

VDTxE i

desInd0

where: SqCD Dii InddesxE

Exergy Destruction Rate due to Induced Drag

The master flight equation is derived from a force balance on the aircraft. The drag on the

aircraft, D, must be overcome by the thrust, T. The drag coefficient equation for an uncambered

wing is also used in the model and the Wessinger span efficiency from Nicolai (1975) is used to

calculate the induced drag factor, K1. The lift curve slope, LC , is determined from supersonic

normal force curve slope charts presented in Raymer (1998), Nicolai (1975), and Anderson

(1999) where, for a high-performance uncambered aircraft dragLC min_ is approximately zero.

The parasitic drag coefficient, 0DC , takes on two different forms depending on whether

or not the aircraft is in the subsonic or supersonic flight regime. Cfe is the equivalent skin

friction coefficient and is chosen to be 0.0035 as recommended for an air force fighter (Raymer,

1998). Swet and Sref are the wetted areas of the aircraft and the exposed wing area, respectively;

and CDwave is the coefficient of drag due to the formation of shock waves during supersonic

flight. CDwave is calculated using a correlation for the Sears-Haack body wave drag where EWD is

an empirical wave drag efficiency factor which ranges from 1.8 to 2.2 for supersonic fighter

aircraft, M is the flight Mach number of the aircraft, and LE is the leading-edge sweep angle.

21

The exergy destruction rate in the AFS-A is due to the parasitic and induced drag losses,

and the equations are also shown in Table 2.2. The morphing AFS-A has a total of 4

synthesis/design and 72 operational decision variables because for each of the 18 mission

segments flown, 4 wing parameters are varied including wing sweep, wing length, root chord

length, and tip chord length. The fixed-wing AFS-A had a total of 4 synthesis/design decision

variables.

2.2.2 Propulsion Subsystem (PS)

The propulsion subsystem (PS) used in Butt (2005) is from Saravanamutto, Rogers, and

Cohen (2001). A schematic of an afterburning turbojet engine is shown in Figure 2.5. The

turbojet PS has 3 synthesis/design decision variables which are the compressor design pressure

ratio and the design corrected mass flow rates for the compressor and turbine. There are a total

of 44 operational decision variables for the PS: 18 compressor pressure ratios, 18 burner fuel/air

ratios, and an additional 8 afterburner fuel/air ratios.

Figure 2.5 Schematic of a single-spool turbojet engine with afterburner.

2.2.3 Most Important Results from Butt (2005)

The results of the large scale optimization show that the benefits of wing morphing are

very promising. The morphing aircraft take-off weight was established by multiplying the fixed-

wing weights and take-off fuel by penalty factors due to the morphing actuator weights and

power requirements. Figure 2.6 shows a sensitivity study of the morphing-wing fuel

consumption with respect to weight and fuel penalty factors. The optimum fixed-wing fuel

consumption is also displayed.

Fuel

Compressor Shaft

Burner

Burner

Turbine

Air

Diffuser

Afterburner

Products

Nozzle

22

Figure 2.6 Morphing-wing and fixed-wing fuel consumption comparison (Butt, 2005).

Figure 2.6 shows the wing weight penalty factors as well as the fuel consumption penalties. For

example, a morphing-wing aircraft that has wings 4 times the weight of the fixed-wing and

carries 25% more fuel at take off for actuator power uses approximately 2900 lb of fuel, which

shows an improvement of 10% over the fixed-wing aircraft at 3200 lb of fuel. Figure 2.6

indicates that even for very unreasonable morphing-wing weight and actuator power

consumption penalties (up to a factor of 7 for wing weight and a factor of 2 for the fuel weight) a

better-performing fighter aircraft can be attained by employing morphing technology.

2.3 Decomposition Strategies for Large-scale Aircraft Synthesis/Design

Optimization

The work of Muñoz (2000) illustrates multiple optimization algorithms as well as

different autonomous decomposition strategies for optimizing highly coupled, highly dynamic

energy systems. The optimization algorithms discussed and used include the following gradient-

based algorithms: the Method of Feasible Directions (MFD) and Sequential Quadratic

Programming (SQP) and the following nongradient-based optimization algorithms: simulated

annealing (SA) and Genetic Algorithms (GAs). The decomposition discussed and utilized

include time decomposition and physical decomposition. The latter in the literature can

generally be described as Local-Global Optimizations (LGO). An exception to this, is the

strategy developed by Muñoz (2000) and Muñoz and von Spakovsky (2000, a, b, c, d; 2001 a, b)

called Iterative Local-Global Optimization (ILGO) which is unique and addresses the major

23

drawback to LGO which is its large computational burden. Decomposition methods allow the

designer to create more complicated system models than would otherwise be possible for use

with large-scale optimization.

LGO works by physically decomposing a system into a set of units for which a set of

unit-level optimization sub-problems are established within the context of a reduced (i.e. smaller

than the original) system-level problem. This results in a set of a nested optimization problems

(i.e. the unit-level within the overall system-level) as well as a system-level optimum response

surface (ORS) which can be constructed implicitly or explicitly on the basis of the many unit-

level interactions (or coupling functions) between units. A search of this surface results in the

global optimum solution for the system.

Figure 2.7 illustrates the system-level ORS for a two-unit system as well as the unit-level

ORS generated by the sub-problem optimizations which in turn result in the system-level ORS

and the large computational burden with which LGO is strapped. In this figure, u12, and u21

represent the coupling functions between units 1 and 2; 2z is the set of local or unit-level decision

variables used in the sub-problem optimization of unit 2; and 2z , 2z

, and 2z are the objective

functions for the unit- and system-level optimization problems. The * superscript indicates

either a unit- or system-level optimum.

Now, in contrast to LGO, ILGO significantly reduces the computational burden by

eliminating the need for nested optimizations. It does so by embedding the system-level

optimization at the unit-level and in the process transforms the unit-level optimization sub-

problems into so-called system-level, unit-based optimizations. This eliminates the need to

implicitly or explicitly construct the system-level ORS which ILGO accomplishes by using ORS

slope information in the form of shadow prices as well as changes in the coupling functions to

move towards the system-level optimum. It is these shadow prices and coupling function

changes which embed the system-level information at the unit-level.

24

Figure 2.7 Unit- and system-level optimum response surfaces (ORSs; Rancruel, 2003).

Muñoz (2000) and Muñoz and von Spakovsky (2000 a, b, c, d, 2001 a, b) apply ILGO to

the optimization of a supersonic aircraft consisting of the following integrated subsystems: the

propulsion subsystem (PS), the environmental controls subsystem (ECS), the airframe

subsystem-aerodynamics (AFS-A), the expendable and permanent payload subsystems (EPAY

and PPAY), and the equipment group (EG). These authors show that ILGO can be used as an

effective physical decomposition strategy for large-scale optimization by comparing the results

from a mission-integrated synthesis/design optimization of the supersonic aircraft with and

without the use of ILGO. The results of this comparison show that the final system optimums

are within 0.5% of each other. Note, however, that in order to make this comparison, the actual

aircraft optimization problem with 153 degrees of freedom (109 for the ECS, 44 for the PS, and

0 for the AFS-A, EPAY, PPAY, and EG) had to be reduced down to one with only 52 degrees of

freedom (38 for the ECS, 14 for the PS, and 0 for the AFS-A, EPAY, PPAY, and EG) in order to

be able to solve the problem in a reasonable time frame without decomposition. Thus, for the

comparison, the optimizations with and without decomposition are based on this latter number.

A more involved application of ILGO and further validation of the effectiveness of this

approach is found in Rancruel (2003) and Rancruel and von Spakovsky (2006, 2004 a, b, 2003 a,

b). In their work, a more complete fighter-aircraft model with five subsystems with optimization

25

degrees of freedom (DOF) and three subsystems without DOF is optimized. A list of the

subsystems included is as follows:

PS – modeled with a modern performance code for on- and off- design performance

(FAST™ by Honeywell);

ECS – bootstrap type subsystem;

FLS – modeled as a transient subsystem;

Vapor Compression / Polyalphaolefin Loops Subsystem (VC/PAOS) – a vapor

compression refrigeration cycle with high and low temperature heat exchanger networks;

AFS-A - the only non-energy based subsystem; and,

EPAY, PPAY, and EG – involving no optimization DOF.

ILGO is used to physically decompose the system in order to be able to do the large-scale

synthesis / design of the tactical fighter aircraft, and optimization involving 493 DOF. ILGO

permits what had never been done before for highly dynamic, non-linear systems, namely a close

approach to the theoretical condition of “thermoeconomic isolation (TI)” (Frangopoulos and

Evans, 1984; von Spakovsky and Evans, 1993). TI is defined as the condition under which each

subsystem (or unit resulting from physical decomposition) of a system can be optimized

independently of the other subsystems and yet still result in a system optimum identical to what

would be attained without decomposition. For a more complete discussion, the reader is referred

to Rancruel (2003). Furthermore, as shown in Muñoz (2000), ILGO can be effectively used for

the large-scale optimization of energy systems consisting of several subsystems and many DOF,

while Rancruel (2003) shows that ILGO can also be extended to non-energy based subsystems

such as the AFS-A. By including the AFS-A with DOF in the aircraft synthesis / design

optimization process, overall aircraft performance can be improved.

The mission profile used in the synthesis / design optimization is the same as shown in

Figure 2.4 and used in Butt (2005). However, the mission is split up into segments slightly

differently than in Butt. The mission segment details are shown in Table 2.3.

The decomposition of the model is shown in Figure 2.5 along with the coupling functions

for the aircraft model used by Rancruel. The AFS-A uses the component buildup method for

parasitic drag estimation detailed in Raymer (2000). The supersonic parasitic drag is estimated

26

Table 2.3 Mission specifications (Rancruel, 2003).

Phase Description

1 Warm-up and take off, field is at 600 m pressure altitude with T=310 K. Fuel allowance is 5 min at idle power for taxi and 1 min at military power for warm-up. Take-off roll plus rotation must be ≤ 450 m on the surface with a friction coefficient = 0.05. STALLTO VV *2.1

2 Accelerate to climb speed and perform a minimum time climb in military power to best cruise mach number and best cruise altitude conditions (BCM/BCA)

3 Subsonic cruise climb at BCM/BCA until total range for climb and cruise climb is 280 km 4 Descend to 9150 m 5 Perform combat air patrol loiter for 20 min at 9150 m and a Mach number for best endurance 6 Supersonic penetration at 9150 m and M = 1.5. Range = 185 km

7

Combat is modeled by the following: Fire 2 AMRAAM missiles Perform one 360 deg., 5 g sustained turn at 9150 m, M=0.9 Accelerate from M = 0.8 to M = 1.6 at 9150 m at max. power Fire 2 AIM-9Ls and ½ ammo

Conditions at end of combat are M = 1.5 at 9150 m 8 Escape dash, at M = 1.5 and 9150 m for 46 km 9 Using military power, do a minimum time climb to BCM/BCA

10 Subsonic cruise climb to BCM/BCA 11 Subsonic cruise climb at BCA/BCM until total range from the end of combat equals 278 km 12 Descend to 3000 m 13 Loiter 20 min at 3000 m and a Mach number for best endurance

14 Descend and land, field is at 600 m pressure altitude with T = 310 K. A 2 s free roll plus braking distance must be ≤ 450 m. Runway has a friction coefficient = 0.18. STALLTD VV *15.1

using a correlation to the Sears-Haack body wave drag. The drag due to lift or induced drag is

estimated using the leading edge suction method also detailed in Raymer (2000). The thrust

requirements from the PS for each mission segment is determined using the master flight

equation (see Table 2.2) modified to account for individual subsystem drag due to the ECS air

requirements and the thermal management subsystem (TMS) which includes the VC/PAOS and

FLS. The empty weight of the aircraft is estimated using the component group weight method

from Raymer (1987) which was developed by studying previously built fighter aircraft and

applying regression analysis to the data.

The ECS is a bootstrap – type ECS similar to what is used in the F-16. The ECS provides

conditioned air to the pilot in the cockpit and the air-cooled avionics. This subsystem requires

bleed air from the PS and has two bleed ports: high and low pressure. Both bleed ports cannot be

active at the same time. The bootstrap-type ECS is defined as such because the compressor is

driven off its own process airflow rather than some other means of compressor power (such as

electrical power or shaft power from the PS).

27

Figure 2.5 Subsystems and subsystem coupling functions (Rancruel, 2003).

The aircraft also uses compact heat exchangers with off-set strip fins for the

thermodynamic model of all the heat exchangers; the F-16 uses the same type of heat

exchangers. Kays and London (1998), Shah and Webb (1982) and Shah (1981) provide the

thermodynamic models for the heat exchanger configurations considered here. The VC/PAOS

cools the portions of the avionics that require liquid cooling and uses the FLS as a heat sink as

well as a ram air heat exchanger as a cooling mechanism. The FLS is used as a heat sink for the

rest of the aircraft subsystems including the Central Hydraulic Subsystem (CHS) and the Oil

Loop Subsystem (OLS). Most of the fuel needed to cool the hydraulic subsystem and oil loop

subsystem is burned by the engine, but if any excess fuel is needed for cooling duties, it is cooled

in a ram air/fuel heat exchanger before being returned to the fuel tank.

The evolution of optimal weight with respect to the ILGO iterations for the takeoff

weight, AFS-A weight, fuel weight, and PS weight are shown in Figure 2.6. Notice that the

slope of the weight vs. ILGO iteration curve becomes nearly zero as the ILGO iterations increase

28

for all the subsystems displayed. This indicates an optimum has been reached, even possibly the

global optimum.

Figure 2.6 Evolution of the gross take-off weight, fuel weight, AFS-A weight, and PS weight at different

points of the iterative local-global optimization (ILGO) approach (Rancruel, 2003).

Finally, the optimum aircraft configuration is compared to the aircraft design proposed by

Mattingly, Heiser, and Daley (1987) to validate the results. The comparison is shown in Table

2.4. It is clear that the ILGO approach yields a superior aircraft to the one proposed by

Table 2.4 Comparison between the optimum ATA and the aircraft proposed by Mattingly, Heiser, and Daley (1987), (Rancruel, 2003).

Optimum Mattingly, Heiser, and Dailey (1987)

TOW , (lb) 22,396 23,800

FuelW , (lb) 7,194 7,707

refSTOW / , (lb/ft2) 61.49 64

TOSL WT / 1.13 1.27

refS , (ft2) 364.2 371.87

SLT , (lb) 25,306 30,226

AFSW , (kg) 3,100 4,200

29

Mattingly, Heiser, and Daley (1987). Furthermore, the results of Rancruel (2003) are reasonable

and the models behave as they should and are, thus, validated.

The objective functions used by Rancruel include minimize gross takeoff weight and

fuel consumption. Total cost was also defined as a system-level objective function; however, the

work of Muñoz (2000) shows that cost is linearly related to gross takeoff weight and is, thus, not

explicitly used as an objective function.

More work has been done with optimizing different objective functions in supersonic

fighter aircraft applications. The thesis work of Periannan (2005) investigates multiple objective

functions including exergy destruction minimization and the effects of the overall optimum

found with respect to allowing non-energy based subsystems to participate in the optimizations.

2.4 Effects on Aircraft Synthesis / Design of Different Objective Functions

The work of Periannan (2005) and Periannan, von Spakovsky, and Moorhouse (2008)

investigated five different objective functions, or figures of merit, for the analysis of a fighter

aircraft. The comparison is constructed to study the differences, if any, in the optimum vehicle

found for each objective function. The aircraft subsystem is assumed to consist of three

subsystems: a PS, an AFS-A, and an ECS. Initially, only the energy-based subsystems are

included with DOF in the optimization, namely, the PS and ECS. The AFS-A participates in the

optimization but without DOF. These optimizations are carried out for four of the five following

objectives (i.e. 1, 2, 4, and 5):

1. Minimize the gross take-off weight:

FUELECSPSETO WWWWW (2.1)

2. Minimize the exergy destruction in the PS and ECS plus exergy lost due to unburned fuel

loss:

FuelLossECSDEStotPSDEStotobj ExExExEx __2 (2.2)

3. Minimize the exergy destruction in the PS, ECS, and AFS-A plus exergy loss due to

unburned fuel loss:

FuelLossAAFSDEStotECSDEStotPSDEStotobj ExExExExEx ___2 (2.3)

4. Maximize thrust efficiency

fuelfuel

thrustthrust LHVm

W

(2.4)

30

5. Maximize thermodynamic efficiency

Max

FuelLossECSDEStotPSDEStotthrustthermo W

ExExEx

W

W __

max

1 (2.5)

where maxW is the maximum work rate the PS could provide if no other sources of losses existed

in the aircraft (an ideal system) or

FuelLossECSDESTotPSDESTotThrustMax ExExExWW __ (2.6)

Note that there is no AFS-A term included for the exergy destruction; however, it is included in a

second set of optimizations which include not only these AFS-A losses but AFS-A DOF as well.

These optimizations are discussed later in this section.

The PS used in all of these optimizations is a low-bypass afterburning turbofan. The

model equations are based on Mattingly, Heiser, and Daley (1987). Both the AFS-A and the ECS

are based on Rancruel (2003) and Muñoz (2000). All modeling for the AFS-A and PS is done

using the gPROMS™ dynamic modeling environment. The ECS is modeled using a C code

coupled to the gPROMS™ models for the other two subsystems. gPROMS™ is also used for all

optimizations. It uses a gradient-based approach, i.e. a sequential quadratic programming (SQP)

algorithm developed for mixed integer nonlinear programming (MINLP) problems.

The PS and ECS used by Periannan (2005) and Periannan, von Spakovsky, and

Moorhouse (2008) are described at length in Chapter 3 of the present thesis so their descriptions

will not be repeated here. The AFS-A model equations are similar to those described in Chapter

3. The only source of irreversibility modeled in the AFS-A is the parasitic drag or zero-lift drag

given by:

T

uDTEx Parasitic

DES AAFStot

0_

(2.7)

where 0T is the dead state temperature (set to the sea-level ambient temperature), ParasiticD is the

parasitic drag, u is the aircraft velocity, and T is the ambient temperature of the aircraft.

Prior to the optimizations, a parametric exergy analysis is performed on three

components in the PS to determine the effect of specific decision variables on the exergy-based

objective functions. The compressor pressure ratio, fan bypass ratio, and turbine inlet

temperatures are varied to see their effect on the exergy destruction rate, specific thrust, and

specific fuel consumption (SFC). Four different mission segments are examined including

31

warm-up/takeoff acceleration (mission segments 1 and 2), climb (mission segment 5), and

supersonic penetration (mission segment 8). Only the parametric study for the supersonic

penetration mission segment is presented here. Figure 2.7 shows the effects on the PS exergy

destruction rate and specific thrust with the variation in the three PS design decision variables.

Figure 2.7 Variation of vehicle specific thrust and exergy destruction rate with fan bypass ratio and turbine inlet temperature for a fixed compressor pressure ratio of 8 for the supersonic penetration mission segment (Periannan, 2005).

Figure 2.7 proves to be very informative as to the behavior of the PS with respect to the

exergy-based objectives. Notice that the exergy destruction rate for a given specific thrust (and

compressor ration) generally decreases with decreasing turbine inlet temperature and bypass

ratio. The trade-off that this implies is that the lower bypass ratios result in better, more efficient

PS designs provided the turbine inlet temperature is lowered as well. Furthermore, mission

segment 8, the turbine inlet temperature has less of an effect on exergy destruction than the

bypass ratio. This, however, may not be the case for other mission segments as shown in

Periannan (2005).

Figure 2.8 shows the response of the exergy destruction rate and specific thrust to

changes in compressor pressure ratio and fan bypass ratio. The fixed parameter is the turbine

inlet temperature, which is set to 1700° K. It can clearly be seen that a higher pressure ratio is

beneficial for the overall performance of the PS since the highest pressure ratio results in the

highest specific thrust and lowest exergy destruction rate. Furthermore, the lower the losses (i.e.

the rate of exergy destruction), the smaller the vehicle with higher specific thrust, which has the

consequence of reducing the cost of the aircraft and the total fuel consumption.

32

Figure 2.8 Variation of vehicle specific thrust and exergy destruction rate with fan bypass ratio and compressor pressure ratio for a fixed turbine inlet temperature of 1700° K for the supersonic penetration mission segment (Periannan, 2005).

Finally, Figure 2.9 shows the effects on the PS exergy destruction rate and specific fuel

consumption variations with bypass ratio and compressor pressure ratio. The obvious conclusion

from this figure is that the highest pressure ratio and lowest bypass ratio produce the best

performing PS. However, the requirements for thrust may demand that more airflow be moved

by increasing the bypass ratio above the minimum constraint. In addition, note that at higher

compressor pressure ratios, the effects of bypass ratio on the exergy destruction rate and specific

fuel consumption is less than at lower pressure ratios.

Upon completion of the exergy analysis, Periannan (2005) and Periannan, von

Spakovsky, and Moorhouse (2008) return to the comparison of the optimization results for the

various objectives. As mentioned above, objectives 1, 2, 4, and 5 are compared to show which,

if any, of the objective functions yield a better overall vehicle. Recall that for this set of

optimizations only the PS and ECS have DOF. Figure 2.10 shows the optimum gross takeoff

weight yielded for each of the objective functions. All three runs for each objective function are

shown to give some confidence that a global optimum was found. The first optimum for each

objective function being higher than the subsequent two runs indicates that for the first

optimization of each objective that a local optima may have been found rather than the global

33

Figure 2.9 Variation of vehicle specific fuel consumption and exergy destruction rate with fan bypass ratio

and compressor pressure ratio for a fixed turbine inlet temperature of 1700 K for the supersonic penetration mission segment (Periannan, 2005).

optimum. However, the second two runs being nearly identical indicate that the global optimum

was likely found for all four objective functions. The result that none of the objective functions

yield a better aircraft is due to the fact that although the AFS-A participates in the optimization,

it has no DOF. In Butt (2005) and Brewer (2006), the thrust efficiency objective function

consistently yields the poorest design in terms of performance and fuel usage, the one for a

supersonic fighter and the other for a hypersonic vehicle. The difference in these optimizations

is that AFS-A DOF are included.

The next set of optimizations conducted in Periannan include AFS-A DOF. Only

objective functions 1 and 3 are used. Using objective function 5 instead of 2 allows the inclusion

of exergy losses (equation (2.7)) due to the AFS-A. Comparisons of the optimum results include

those with and without AFS-A DOF. Figures 2.10 and 2.11 summarize these results. For

example, the former shows that optimizing using objective 3 with AFS-A DOF reduces the gross

takeoff weight by about 4.5% over the optimum aircraft found without AFS-A DOF and with

objective 1. This difference is even more pronounced, as seen in Figure 2.11, where the fuel

weight is reduced by 9.8%. Even in a comparison with the optimum vehicle found using

objective 1 with AFS-A DOF, objective 3 with AFS-A DOF produces an optimum vehicle with a

5.8% reduction in fuel weight.

34

Figure 2.10 Optimum gross takeoff weight with and without AFS-A DOF for objectives 1, 2, and 3

(Periannan, von Spakovsky and Moorhouse, 2008).

Figure 2.11 Optimum fuel weight with and without AFS-A DOF for objectives 1, 2, and 3 (Periannan, von

Spakovsky, and Moorhouse, 2008).

Finally, although the work of Periannan (2005) and Periannan, von Spakovsky, and

Moorhouse (2008) also show the strengths of the gradient-based optimization in terms of speed,

a weakness of this type of algorithm is the need of generating several feasible but very different

initial points with which to start the optimizations. In a complex large-scale optimization

5000

6000

7000

8000

9000

10000

11000

objective 1 objective 3 objective 2

Gro

ss T

akeo

ff w

eig

ht

in k

g

With AFS-A DOF

Without AFS-A DOF

2000

2200

2400

2600

2800

3000

3200

3400

objective 1 objective 3 objective 2

Fu

el W

eig

ht

in k

g

With AFS-A DOF

Without AFS-A DOF

35

problem with many DOF, this can be a rather daunting task, to say the least. Even a single

starting point is problematic. The need for several very different ones is due to the susceptibility

of such algorithms to getting stuck at local optima. Genetic or hybrid genetic-gradient based

optimization algorithms are examples of how these difficulties can be overcome, and the

following sections provide illustrations of the application of the former to a hypersonic vehicle

using both exergy and non-exergy based objective functions.

2.5 Exergy Methods for the Development of High Performance Vehicle Concepts

The renewed interest in hypersonic vehicles has fueled new design technologies to be

employed in hypersonic vehicles. The work of Markell (2005) illustrates applying exergy

analysis and exergy destruction minimization to the hypersonic vehicle. Markell developed a 1-

D hypersonic vehicle model and a partial 3-segment hypersonic mission and a detailed exergy

model for his thesis work. Two objective functions are compared in the work: an exergy based

objective function and a more traditional objective function, namely, the thrust efficiency. The

hypersonic vehicle consists of two subsystems, a propulsion subsystem and an airframe

subsystem. The propulsion subsystem consists of a inlet, combustor, and nozzle component.

Markell performed multiple optimizations on just the propulsion subsystem for a single mission

segment and also optimized the entire vehicle for the partial three-segment mission. The 1-D

hypersonic vehicle is shown in Figure 2.13.

Figure 2.12 Hypersonic vehicle configuration (Markell, 2005).

The forebody serves as the means of compressing the incoming airflow with oblique

shock waves forming at the leading edge of the vehicle. The inlet further compresses the

incoming air with more oblique shocks forming off subsequent turning angles before entering the

combustor / cowl area of the propulsion subsystem. The forebody and inlet design is extremely

important in hypersonic vehicle flight due to no other means available for compressing the air

36

entering the combustor. The forebody design is also instrumental in maximizing the mass

capture into the combustor as well.

Figure 2.14 shows a diagram of the design variables associated with the forebody and

inlet of the hypersonic vehicle. The operational decision variable shown in the figure is the

angle of attack, or . Energy exchange is also included in the forebody and inlet model to

modify the flow to maintain shock-on-lip conditions which maximizes the mass capture area into

the combustor when the forebody and inlet must operate at off-design conditions.

Figure 2.13 A physical representation of the forebody and inlet component of the hypersonic vehicle along with design and operational decision variables that govern the flow characteristics throughout the inlet (Markell, 2005).

The exergy model for the hypersonic vehicle is somewhat involved, as losses are tracked

for friction, shock waves, combustion, and mixing throughout the vehicle. The inlet exergy

destruction has two contributors to total exergy destruction: friction and shocks. The entropy

rate due to friction in the inlet is given by:

1

2lnt

tirr

P

PR

m

Sfric

(2.8)

where m is the mass flow rate, R is the specific gas constant, and 12 tt PP is the total pressure

ratio in the inlet. The entropy generation rate due to the three oblique shocks in the inlet is

expressed by:

1

3

11 lnln31i

ti

ti

i

ipi

irr

P

PR

T

Tc

m

Sshocks

(2.9)

where the three oblique shock temperature and pressure properties are required to find each

oblique shock entropy rate. The total irreversibility rate for the inlet then becomes:

37

31

shocksfricinlet irrirrirr SSS (2.10)

The combustor is a constant area, hydrogen-fueled combustor in which the flow is

constrained to stay supersonic, defining a scramjet-type propulsion subsystem. The flow can

become subsonic if the combustor length is too long, inlet area is too small, or the initial

combustor flow Mach number is too low (designated 4M in Figure 2.14). The mixing equations

account for incomplete combustion but do not include species dissociation due to the

computational burden required to track dissociation. Heat loss from the combustor through the

combustor walls is also tracked using the Eckert Reference Enthalpy Method (Heiser and Pratt,

1994). The total irreversibility rate for the combustor is then

mixirrinccombirrhtirrfricirrCOMBirr SSSSS (2.11)

where the terms to the right of the equals are the entropy generation rates due to irreversible

losses resulting from friction, heat transfer, incomplete combustion, and mixing, respectively.

The nozzle heat losses are modeled using the Eckert Reference Enthalpy Method (Heiser

and Pratt, 1994), with an adjustment to the overall heat transfer rate, as it is known to over

predict the nozzle heat transfer rate. Half the heat transfer rate calculated by the Eckert method

is used to account for the nozzle plume separating from the vehicle in flight as suggested by

Riggins (2003). The frictional losses are calculated with a skin friction coefficient suggested by

Riggins (2004). Including the mixing and heat transfer in the nozzle, a control volume of the

nozzle an entropy generation of:

w

wallj

jj

j

jjmixnozzirr T

Q

P

PRsysymS

6

7

16

17

log (2.12)

where jy and js indicate the mole fraction and entropy of constituent j and the subscripts 6 and

7 indicate the nozzle entrance and exit conditions, respectively.

The airframe subsystem-aerodynamics (AFS-A) is modeled to account for pressure wave

forces, center of gravity, as well as frictional forces from skin friction. A simple diamond-airfoil

wing and elevons are also modeled with the AFS-A to provide additional lifting surface and to

balance vehicle moments during flight. Shock expansion theory is employed to calculate the

drag and lift of the diamond airfoils (Anderson, 2001). The total drag on the vehicle is converted

38

to a frictional force, fF , on the AFS-A which yields the total entropy generation rate due to

friction, i.e.

t

firr T

uFS

fric (2.13)

where u is the speed of the aircraft and tT the local skin temperature. The total AFS-A entropy

generation rate including shock losses is:

31shocksfricaero irrirrirr SSS (2.14)

The combustor is initially optimized for a single mission segment to compare to a

published hypersonic combustor model from Riggins (1997). The model in Riggins (1997) was

presented for a single mission segment optimization, so it was necessary to only optimize a

single mission segment for validation. The results show good agreement (see Table 2.5), so the

combustor model is considered validated. The model is then used to develop a number of

parametric studies which are not repeated here. The x(m) in Table 2.5 represents the station in

the vehicle. Zero meters is the inlet entrance, five meters is the combustor entrance, six meters is

the nozzle entrance, and eleven meter is the engine exit. M, T, P, and u are the Mach number,

temperature, pressure, and velocity of the flow in the vehicle, respectively.

Table 2.5 Comparison of the optimal combustor models (Markell, 2005).

Riggins Model (1996) Markell (2005)

x (m) M T (K) P (N/m2) u (m/s) M T (K) P (N/m2) u (m/s)

0 12.0 200 1000 3400 12 200 1000 3402.3

5.0 6.22 679 70900 3255.4 6.26 674.4 70417 3259.2

6.0 1.72 4350 647000 2283 1.73 1.73 645804 2288.3

11.0 5.12 1110 5500 3423 5.11 5.11 5541 3423.9

Next the optimum scramjet engine is determined for a fixed thrust based on two different

objectives. The first is an energy based figure of merit called overall the overall efficiency,

which is defined as

pthprf hm

Tu

0

0 (2.15)

where 0 , T, u0, fm , prh , th , and p are the overall efficiency, engine thrust, vehicle velocity,

fuel mass flow rate, fuel enthalpy, and thermodynamic and propulsive efficiencies, respectively.

39

The second objective function is the exergy based optimization objective function that uses

concepts from both the 1st and 2nd laws of thermodynamics. This objective function is defined as

trelease

irr

T

TQ

ST

0

0

1

1

(2.16)

where is the thermodynamic efficiency, 0T is the dead state temperature (see Gyftopolous and

Beretta, 1991), irrS is the (irreversible) entropy generation within the system, releaseQ is the

heat loss to the environment, and tT is the temperature of the system at the point of heat loss.

The results for these two optimizations are shown in Table 2.6. The two different objective

functions produce nearly the same optimum scramjet engine in that the fuel mass consumed fm ,

is nearly identical between the two optima. The variables in Table 2.6 are shown on the

hypersonic vehicle in Figure 2.4.

Table 2.6 Optimal decision variable values for the energy and exergy based optimizations of a scramjet engine with fixed thrust (Markell, 2005).

Obj. Function )(mX fb )(mX cowl )(mX ramp )(fb )(nozz

Obj. 1 8.6114 13.652 2.9049 4.6026 17.066 Obj. 2 8.4019 13.896 3.1784 4.5669 17.549

)(mLcomb cowl% )/( skgm f )( 2mveh

Obj. 1 1.1148 0.0016 2.6363 0.5 26.039 Obj. 2 1.1523 0.0113 2.6754 0.5 26.025

The partial mission flown consists of three segments: a Mach 8 cruise for 1000 nm, acceleration

and climb from Mach 8 to Mach 10 in less than 90 seconds, and finally a Mach 10 cruise for

1000 nm. Initially, each mission segment was optimized individually to find the best hypersonic

vehicle for a given mission segment based for each of three separate objectives: thrust efficiency,

exergy destruction rate, and the exergy destruction rate plus the rate of the exergy loss. The

results of these optimizations are shown in Table 2.7. Notice that the exergy destruction

objective function produces combustor lengths at or near the minimum of 0.5 m. This is due to a

deficiency in the second objective function which ignores the rate of fuel exergy lost out the back

end of the engine. Nonetheless, the results for all three objectives show that the combustor is the

largest source of exergy destruction.

40

Table 2.7 Optimal design decision variable values for the single segment optimizations (Markell, 2005).

Mach #

Obj. Funct.

)(mX fb )(mX cowl )(mX ramp )(fb )( )(nozz )(mLcomb cowl%

8 0 8.5303 12.619 2.4418 2.5501 1.7227 17.512 0.8933 0.0207

desxE 8.4284 14.313 3.1839 1.0000 0.9547 15.524 0.5000 0.0736

8-10

0 8.6716 13.616 3.2772 1.4914 1.2096 17.999 0.9451 0.0009

desxE 8.4101 13.441 2.7657 1.0365 2.2349 17.335 0.5007 0.0860

lossfueldes xExE 8.5617 12.603 2.6580 1.0000 1.1521 12.8238 0.8802 0.2432

10

0 8.4094 11.969 2.4620 1.7887 1.2350 15.842 0.7017 0.0136

desxE 8.5113 14.267 3.0703 1.2493 0.9818 16.057 0.5003 0.2272

lossfueldes xExE 8.4127 13.265 3.2994 1.0577 1.7537 15.537 0.7775 0.2019

The final comparison made in Markell (2005) is between optimizations to determine the

optimal hypersonic vehicle that can fly all three mission segments of the partial mission

optimally. The optimal operational decision variable values for the three mission segments are

shown in Table 2.8 and each vehicle optimal fuel mass flow rate is compared in Table 2.9. The

interesting result is that the third objective function produces a vehicle that flies at shallower

angles of attack, , and has a lower fuel mass flow rate, fm , than either of the other two

Table 2.8 Optimal operational decision variable values for the partial mission (Markell, 2005).

Objective Function

)( )( 2mS wing

1 2 3 1 2 3

0 1.7724 1.2 0.9 7.2033 5.76515 9.3670

desxE 1.4453 0.8 0.8 7.6983 9.2350 0.4869

lossfueldes xExE 1.1933 0.4 0.3 0.7908 3.2372 0.5065

Table 2.9 Optimal vehicle fuel mass flow rate comparison (Markell, 2005).

Objective Function 0

lossfueldes xExE

1 0.5434 0.5779

2 1.9856 2.3892

3 0.6944 0.7070

optimizations. In Table 2.8 the optimal vehicle for the third objective function requires much

less effective wing area, wingS , to fly the mission than that for the optimal vehicle based on the

41

first objective. In Table 2.9, the fuel mass flow rates required are compared and show that the

third objective (one of the exergy-based objectives) yields a better performing hypersonic vehicle

with an overall savings of 6.5% fuel over entire mission. The work of Markell lays the

framework for Brewer (2006), who uses the 1-D hypersonic vehicle to fly an entire hypersonic

mission.

2.6 Integrated Mission-Level Analysis and Optimization of High Performance

Vehicle Concepts

The work of Brewer (2006) involves the construction (in collaboration with Markell,

2005) of a 1-D hypersonic vehicle model and using a genetic algorithm (GA) to find the

hypersonic vehicle configuration that flies a Mach 6 to Mach 10 flight envelope in the most

efficient manner. All the hypersonic vehicle designs found to date in the literature are based on a

single mission segment or flight condition. The vehicle design in Brewer (2006) is based on a

mission which includes cruise, acceleration / climb, deceleration / descend, and turn mission

segments. This thesis work furthermore includes a comparison between three objectives: thrust

efficiency maximization (the traditional propulsion subsystem design optimization objective),

minimization of fuel mass consumption (the traditional weight-based design optimization

objective), and the minimization of exergy destruction plus fuel exergy loss (the non-traditional

design optimization objective).

As in Markell (2005), the 1-D hypersonic vehicle model consists of two subsystems: the

propulsion and airframe subsystems. Irreversible loss mechanisms modeled to account for

exergy destruction include losses due to shocks, friction, heat transfer, mixing, and incomplete

combustion. The airframe modeling includes trim and force accounting, while the inlet includes

the modeling of energy addition of subtraction to or from the flow in order to maintain shock-on-

lip operating conditions at all operating points. The hypersonic vehicle is shown in Figure 2.5.

The mission flown during the vehicle design optimizations is shown in Figure 2.16 and the

corresponding flight details are given in Table 2.10. The hypersonic vehicle has a total of seven

design decision variables including forebody position, fbX , cowl position, cowlX , ramp 1

position, 1rampX , forebody angle, fb , combustor length, combL , nozzle expansion angle, nozz ,

42

Figure 2.14 Propulsion subsystem components and airframe subsystem (Brewer, 2006).

Table 2.10 Mission segment details (Brewer, 2006).

Segment Description

1 Accelerate and climb from Mach 6 (at 23.2 km) to Mach 8 (at 26.9 km), t = 90 sec

2 Mach 8 cruise for 600 sec

3 Accelerate and climb from Mach 8 (at 26.9 km) to Mach 10 (at 30.0 km), t = 90 sec

4 Mach 10 cruise for 600 sec 5 Perform a 180°, 2g sustained turn at Mach 10 6 Descend and decelerate to Mach 6

Figure 2.15 Total scramjet vehicle mission (Brewer, 2006).

and percent nozzle length, nozz% . The single operational decision variable is the angle of attack

of the vehicle, 0 . The design and operational variables for the hypersonic vehicle are given in

Table 2.11.

43

The first optimization objective used is maximizing thrust efficiency. The overall

mission thrust efficiency is found from a weighted average of each mission segments thrust

efficiency, or

5

0

5

iif

iiif

tm

tm

i

i

(2.15)

Table 2.11 Mission design and operational decision variables for the inlet, nozzle, combustor, and airframe (Brewer, 2006).

where fim is the fuel mass flow rate, it is the segment time, and i is the mission segment thrust

efficiency. The second optimization objective function used is minimize fuel mass burned which

is defined as

5

oiififuel tmgW . (2.16)

where g is the gravitational constant. The final optimization objective function is that of

minimizing the exergy destruction plus exergy lost from unburned fuel in the combustor and is

defined as

5

0,,,,0

iiilossitotalirrilossDes txESTExEx (2.17)

where itotalirrS ,, is the total rate of entropy generated by the vehicle for the mission segment, i,

while ilossxE , is the rate of exergy loss due to unburned fuel in segment i. The irreversibilities

44

included in the total rate of entropy generated are those for the inlet, combustor, nozzle, and

airframe. The vehicle was optimized using a genetic algorithm (GA) Queuing Multi-Objective

Optimizer (QMOO) (Leyland, 2002). This type of algorithm is more suited to a hypersonic

vehicle optimization problem than a gradient-based optimizer due to the nature of the problem:

highly constrained, mixed-integer variables, and non-linear spaces in the solution space would

cause a gradient based method to often get stuck in local optima. There is also the difficulty of

finding one or more initial points in such a highly constrained problem with a gradient based

approach. QMOO was developed by Leyland and Molyneaux and Laboratoire d’Energetique

Industrielle (Laboratory of Industrial Energy Systems, LENI) at the Ecole Polytechnique

Federale de Lausanne (EPFL). Both the hypersonic vehicle and QMOO are developed in

MATLAB enabling a straightforward coupling of the GA and the model.

Due to the random nature of the GAs, multiple optimizations are needed to establish that

the algorithm has indeed found the global optimum instead of a local optimum. This problem,

however, is not exclusive to GA optimizations since many gradient-based methods require

multiple runs as well to verify that a true optimum (whether it be the global or “best” local

optimum) has been found.

The model validation is performed by comparing against previously published results

(Riggins, 1996; Bowcutt, 1992; and Starkey, 2004). The model results of Brewer (2006) are all

well within reasonable tolerances of those reported in these references. Note also, that at the

time of publication, there was no known documentation of mission-level optimization results for

a hypersonic aircraft in the literature and very little for single-segment hypersonic optimizations.

After validation, the optimizations for the three different objective functions are run. The

hypersonic mission proves to be a very difficult problem to solve, as the optimizations took up to

two months to complete, running constantly from start to finish on personal computers with

processors ranging in speeds from Pentium III equivalent clock speeds of 1.5 to 3.05 Ghz with

512 to 1024 MB of internal memory. The computational cost is due to the sparse optimal

solution space for the hypersonic mission. This is in contrast to an “easier mission to fly” or a

system that has a dense optimal solution space. A random sample of the solutions for a

hypersonic aircraft mission versus a morphing-wing supersonic aircraft mission (Butt, 2005) is

shown in Table 2.12. The sparse optimal solution space only shows two feasible solutions in the

45

random sample, while the dense solution set shows feasible solutions in every sample space

shown. The average number of feasible solutions in the 125-member population for the

hypersonic optimization is just 10%, while the average number of feasible solutions in the 70-

member population for the morphing-wing optimization is nearly 100%.

The sparse optimal solution space requires the constraints of the variables shown in Table

2.11 be restricted further to allow the optimum solution to be found in a more timely manner (1 –

2 weeks). The initial forebody angle is found by the GA (QMOO), while the rest of the angles

Table 2.12 Samples of results populations for sparse and dense optimal solution spaces. Note that the very large numbers (i.e. E+15) represent infeasible solutions (Brewer, 2006).

Sparse Optimal Solution Space Dense Optimal Solution Space Min. Exergy Destruction Plus Fuel Exergy Loss

Population Sample [GJ] (Brewer, 2006) Min Fuel Usage Population Sample [kg] (Butt, 2005)

5.0000E+15 5.0000E+15 5.0000E+15

5.0000E+15 5.0000E+15 5.0000E+15

5.0000E+15 5.0000E+15 5.0000E+15

5.0000E+15 5.0000E+15 5.0000E+15

5.0000E+15 1.4005E+02 5.0000E+15

1.4008E+02 5.0000E+15 5.0000E+15

5.0000E+15 5.0000E+15 5.0000E+15

5.9966E+02 5.9854E+02 6.1114E+02

5.4164E+02 5.3917E+02 5.6801E+02

5.9471E+02 5.5250E+02 5.7282E+02

5.7131E+02 5.8799E+02 5.7668E+02

5.7147E+02 5.5866E+02 5.5966E+02

5.9706E+02 5.7667E+02 5.4164E+02

5.8924E+02 5.6730E+02 6.0444E+02

on the hypersonic body are found by iteratively trying different ramp angles until a feasible

solution allows progression to the next angle on the forebody. This method, although very

computationally expensive, is still faster than simply allowing the GA to find a solution by

setting all the ramp angles to optimization decision variables as was attempted by Muñoz.

Brewer discovered that one of the weaknesses exhibited by QMOO was its inability to

suppress significant digits assigned to decision variables. A large amount of computational time

is wasted due to the fact that for each decision variable, QMOO would only vary the last 12 to 15

significant digits of the decision variable from one generation to the next (unless the decision

variable is flagged as an integer, of course). Any decision variable that is not defined as an

integer automatically has 15 significant digits and Brewer could not find a way to modify this

easily within the MATLAB QMOO code.

Despite the large amount of initial work and required tailoring of the design/operational

decision variable constraints, Brewer is able to attain results for all three objective functions.

These results are given in Table 2.13. As can be seen from the table, the second and third

46

Table 2.13 Optimal objective function results (Brewer, 2006).

Objective Function

Max. Thrust Efficiency Min. Fuel Mass Min. Exergy Destroyed

+ Fuel Exergy Lost Run 1 2 3 1 2 3 1 2 3

Thrust Efficiency [%]

34.52 34.48 32.97 29.38 26.40 26.41 28.76 29.89 26.57

Fuel Mass [kg]

1911 1911 2227 1717 1720 1744 1732 1797 1801

Exergy Destruction

[GJ] 153.7 151.1 166.2 145.2 139.3 140.2 140.0 142.3 143.1

objective functions, minimize fuel mass and minimize exergy destroyed plus fuel exergy lost,

respectively, yielded very similar optima. The explanation for the similarities can be found in

one simple fact: the main source of exergy, or available energy, on the vehicle is found in the

fuel. If the fuel mass required to fly the mission is minimized this is, in reality, minimizing the

largest source of exergy destruction: fuel combustion. The thrust efficiency objective function,

which is purely a “first law of thermodynamics” performance metric, yields a significantly worse

performing vehicle in terms of fuel mass burned and exergy destruction than the other “second

law of thermodynamics” based objective functions, despite having a higher thrust efficiency than

the other two optimal vehicles.

47

Chapter 3

Model Description and Synthesis/Design Problem Description

This chapter discusses the synthesis/design problem as well as the subsystem models

used in this thesis work.

3.1 Problem Definition

Solving the air-to-air fighter (AAF) synthesis/design optimization problem starts with

developing appropriate subsystem models for the aircraft. Next, the mission is examined in

detail to enable mission segments (or logical pieces of the mission) to be defined. Each

subsystem is then prepared to “fly the mission” by defining the interactions with the other

subsystems. Individual subsystem model convergence is checked by running optimizations on

the decoupled or non-interacting subsystems before they are integrated. Finally, the subsystems

are integrated and the coupling functions and optimization synthesis / design and operational

decision variables are defined. Multiple optimizations for each different objective function and

AFS-A configuration (i.e. morphing / fixed-wing) are then run to verify that a global optimum

has been reached. The subsystems modeled in this thesis include the following:

Airframe subsystem – Aerodynamics (AFS-A);

Propulsion Subsystem (PS);

Environmental Controls Subsystem (ECS);

Fuel Loop Subsystem (FLS);

Vapor Compression / Polyalphaolefin Subsystem (VC/PAOS);

Oil Loop Subsystem (OLS);

Electrical Subsystem (ES);

Central Hydraulic Subsystem (CHS);

Flight Controls Subsystem (FCS).

The fighter aircraft mission flown is shown conceptually in Figure 3.1. The details of the

mission are derived from a request for proposal (RFP) found in Mattingly, Heiser, and Pratt

(2002) and the mission segments are given in Table 3.1.

48

Figure 3.1 Supersonic fighter aircraft mission from the RFP found in Mattingly, Heiser, and Pratt (2002).3

Table 3.1 Air-to-air fighter (AAF) mission segments and details.

Mission Segment

Description

1 Warm-up and take off, 2000 ft altitude, 1 min for military power warm up, takeoff ground roll + 3 s rotation distance < 1500 ft, STALLTO VV *2.1

2 Accelerate to best subsonic climb Mach (BCLM) 3 Minimum time to climb to 20,000 ft at military power 4 Continue minimum time to climb to best cruise Mach (BCM1) and best cruise altitude (BCA1) 5 Subsonic cruise until total distance for climb/cruise is 150 nmi 6 Perform combat air patrol loiter for 20 min at 30,000 ft and best mach for endurance (BCM2) 7 Accelerate to Mach 0.8 8 Accelerate to Mach 1.2 9 Accelerate to Mach 1.5, total time for acceleration t < 50 s

10 Supersonic Penetration at Mach 1.5 until total distance for accel + supersonic penetration is 100 nmi, supercruise if possible (no afterburning)

11 Combat segment: perform 360 degree, 5 g sustained turn at 30,000 ft, M = 1.6 12 Combat segment: perform two 360 degree, 5 g sustained turns at 30,000 ft, M = 0.9 13 Combat Segment: Accelerate from Mach 0.8 to Mach 1.0 in max power 14 Combat Segment: Accelerate from Mach 1.0 to Mach 1.2 in max power 15 Combat Segment: Accelerate from Mach 1.2 to Mach 1.6 in max power 16 Combat segment: drop payload of 2 AIM-9L’s and 250 rds of 25mm ammunition (1309 lb) 17 Escape dash at M = 1.5 and 30,000 ft for 25 nmi, supercruise if possible 18 Climb/decelerate to BCM and BCA at military power, no distance credit

19 Subsonic cruise at best cruise mach (BCM3) and best cruise altitude (BCA2) until total distance is 150 nmi from escape dash

20 Loiter for 20 minutes at 10,000 ft and best mach for endurance (BCM4) 21 Descend and land

3 ©AIAA, reprinted with permission.

49

Note that each best cruise Mach or best cruise altitude for a given mission segment is unique to

the other best cruise Mach or best cruise altitudes for the aircraft in different mission segments

(e.g. 21 BCMBCM and 21 BCABCA ). The subsequent sections in Chapter 3 detail the

previously bulleted subsystems that comprise the AAF, starting with the AFS-A.

3.2 Airframe Subsystem

The airframe subsystem-aerodynamics (AFS-A) is the largest subsystem in the AAF and

serves not only as the structure required to house the other subsystems but also as the subsystem

that produces lift and the aerodynamics required to fly the mission. The airframe houses all the

subsystems mentioned in Chapter 3 as well as the rest of the items not detailed in the following

sections. The items not detailed are accounted for simply by a fixed weight value.

The AFS-A is developed from Raymer (2000) as well as Rancruel (2003) and is based on

drag-polar relationships. The free-body diagram of the aircraft is shown in Figure 3.2. Analysis

of Figure 3.2 and an energy balance will yield the master flight equation which is given in Table

Figure 3.2 Free-body diagram of the aircraft (Rancruel, 2003).

3.2. The “clean” drag term of the master flight equation, D , is the drag due to AFS-A

aerodynamics. Additional drag from other subsystems (such as the FLS ram/air heat exchanger)

is accounted for in the term, R . The thrust, T , is the installed thrust of the propulsion subsystem

(PS) which is detailed in Section 3.3.

The lift, L , and drag, D , terms are determined using the lift-drag polar relationship from

Mattingly, Heiser and Daly (1987) and Raymer (2000) which is detailed in section 3.2.1. The

analysis of the mission follows the lift-drag discussion. The AFS-A weight equations are

50

presented in Section 3.2.3 and, finally, the calculation of the takeoff weight completes the

discussion of the AFS-A.

Table 3.2 Master flight equation and governing flight equations.

Component Variable Description Model Equations

Master Flight Equation

T Thrust

g

V

dt

dW

dt

dhWVRDT

2

2

D Clean Drag R Additional Drag V Aircraft Velocity W Aircraft instantaneous weight

Governing Flight Equation

T Installed Thrust

g

Vh

dt

d

VW

RD

W

T ii

i 2

1 2

iV Velocity of aircraft at segment, i

ih Altitude of aircraft at segment, i g Gravitational acceleration

3.2.1 Lift and Drag

The total drag on the aircraft is a combination of parasitic drag or “zero-lift drag” as well

as drag due to lift or “lift-induced drag”. This section details the lift and drag relationships and

equations that were used to develop the aerodynamics model of the AFS-A. In short, the drag

model used is the component buildup method called the “Parasite-Drag Buildup Method”

detailed in Raymer (2000). The supersonic wave drag is calculated using the Sears-Haack

supersonic wave drag correlation. A summary of the general equations for the lift and drag

relationships is given in Table 3.3.

Notice that the total drag on the aircraft is a combination of the drag due directly to the

performance characteristics of the aircraft as well as the additional drag from other subsystems

shown in the master flight equation in Table 3.2. The wave drag is calculated using the Sears-

Table 3.3 Lift and drag equations for the AFS-A.


Clean Drag

D Clean Drag

DqSCD

where

2LDoD KCCC

q Dynamic Pressure

S Wing Reference Area

DC Total Drag coefficient

K Lift factor

Parasitic Drag DoC

Coefficient of parasitic drag

tailDofuselageDowingDoDo CCCC ___

canopyDowaveDomiscDo CCC ___

51


Wave Drag waveDoC _ Coefficient of shock wave drag

HaackSears

LEwd

waveq

DME

q

D

100

12.1386.0177.0

57.0

S

q

D

C waveDowave

Lift-induced Drag

LC Coefficient of lift

qS

WC TO

L

Weight fraction of aircraft

Haack wave drag correlation shown in Table 3.3. The wave drag constant, wdE , is set to 2 in

this thesis work in order to correspond to currently built fighter aircraft. The clean drag is the

only drag accounted to the AFS-A in the exergy destruction calculations (see Section 3.2.5);

however, other subsystem drag must be included in the master flight equation to accurately

predict AFS-A performance.

3.2.2 Mission Analysis

The mission consists of many dissimilar mission segments as well as a payload drop.

Some important equations for the mission segments are given in Table 3.4 with a subsequent

discussion of the individual mission segments.

The first mission segment includes a 60 second warm-up at military power (full throttle

in the main burner, no afterburning), then takeoff/acceleration, and finally, a ground roll for

takeoff. The total distance for acceleration and ground roll is constrained to not exceed 1500 ft.

The final aircraft speed at the end of the ground roll is set to 1.2 times the estimated stall speed,

stallV , which is initially estimated in order to calculate the drag and lift characteristics. The actual

stall speed is recalculated, and the actual drag and lift parameters are iterated until convergence

to increase accuracy. The aircraft velocity at the end of segment 1 is 1.2* stallV .

The second mission segment is a horizontal acceleration segment with a specified time of

30 seconds. The aircraft accelerates from 1.2* stallV to the best climb Mach (BCLM). The best

52

climb Mach is a degree of freedom (DOF) for the second mission segment in the AFS-A

optimization problem.

Table 3.4 Mission segment model equations.


Takeoff model

A Warm-up weight fraction 60*1 SFC

W

W

W

W

TO

A

i

fA

max2 LTO

Astall CS

WgV

stallB VV 1.1

2

/exp BB V

TRDg

SFC

stallc VV 2.1

g

VV

TRD

SFC BCC 2

50/

exp22

CBATOW

W 1

1

stallV Stall speed

maxLC Takeoff lift coefficient

BV Velocity at end of acceleration

B Takeoff acceleration weight fraction

CV Velocity at end of ground roll

1 Final weight fraction for takeoff

1W Weight of aircraft after mission segment 1

Climb model

G Glide ratio (vertical velocity/horizontal velocity) Ae

CG

W

T Do

2

where for 30LE

64.0*045.0178.1 68.0 ARe

for 30LE

1.3cos*045.0161.4 15.068.0 LEARe

SbAR

2

AR Aspect Ratio

e Weissinger span efficiency

DoC Coefficient of parasitic drag

b Wing span

S Wing reference area

Sustained turn model

d Time to turn 1

2

2

ng

Vxd

Aeq

SWn

SWn

Cq

D

L

Do

1

DLn

W

T

x Number of turns

n Load factor for turn

53

The third and fourth mission segments are sequential, constant Mach, minimum time-to-

climb segments in military power from 2000 ft to the best cruise altitude (BCA1). The climb

angle is determined by the excess thrust available from the PS. The horizontal distance traveled

for the third and fourth mission segments is tracked because the total distance for segments three,

four, and five is 150 nmi.

Mission segment five is a cruise segment at best cruise Mach (BCM1) and altitude

(BCA1). The BCM1 and BCA1 are AFS-A DOF. Mission segment six is a 20 minute loiter

segment at 30,000 ft at best Mach for endurance (BCM2), which is also an AFS-A DOF.

Mission segments seven, eight, and nine split up the acceleration from BCM2 to Mach

1.5: BCM2 to Mach 1.0, Mach 1.0 to Mach 1.2, and, finally, Mach 1.2 to Mach 1.5. Each of the

three segments is time constrained to 15 seconds for a total acceleration time of 45 seconds.

Mission segment ten is a supersonic penetration mission segment at Mach 1.5 that

continues until the total distance traveled for segments seven, eight, nine, and ten is 100 nautical

miles. Segment ten specifies to supercruise (supersonic cruise without afterburning) if possible.

The combat simulation consists of a single 5-g sustained turn at Mach 1.6 and two 5-g

sustained turns at Mach 0.9, acceleration from Mach 0.8 to Mach 1.6 at maximum power (full

throttle for the main burner and afterburner), and a payload drop of 1309 lbs which is calculated

from firing two AIM-9L’s and 250 rounds of 25 mm ammunition. The combat simulation ends

with the aircraft at Mach 1.6, and a supercruise (if possible) escape dash at 30,000 ft from 25

nautical miles follows the combat simulation.

Mission segment eighteen is a deceleration / climb at military power to best cruise Mach,

BCM3, and best cruise altitude, BCA2. This mission segment usually does not include a weight

drop as the energy equation for this segment involves a trade of kinetic energy for potential

energy. Mission segment nineteen is simply a 150 nautical mile cruise at BCM3 and BCA2.

The final mission segment before landing is a 20 minute loiter / observation mission

segment at best cruise mach and best cruise altitude until the total distance since the escape dash

is 150 nautical miles.

The descent and landing mission segment has a 6 minute time allowance with no weight

drop for the descent. The final weight fraction to account for the landing, ground roll, braking

and taxi is set to 997.0if WW . The weight fraction calculations are presented in the

following section.

54

3.2.3 Weight Fraction Model

The gross weight of the AAF decreases after each mission segment due to the burning of

fuel in the PS. The gross weight decreases are tracked in each mission segment using weight

fractions, or initial to final mission segment weight ratios that are calculated based on the aircraft

energy change over the mission segment, specific fuel consumption (SFC), and flight

conditions/aerodynamics.

The mission segments are first categorized into mission segment type: for example, loiter,

cruise, horizontal acceleration, constant speed climb, climb / acceleration, etc. The master energy

equation for the weight fraction calculation is shown in Table 3.5 as well as the main derivatives

of the master equation with a discussion following.

Table 3.5 Weight fraction model equations.


Master weight fraction equation

if WW Final/initial weight ratio

g

Vh

uV

sfc

W

W

W

W

i

i

i

fi 2)1(

exp2

1

where

TRDu /

sfc Specific fuel consumption V Aircraft velocity g Gravitational acceleration

i Weight ratio for segment i

Climb h Altitude

huV

sfc

W

W

i

f

)1(exp D Clean drag

R Additional drag

Acceleration T Installed thrust

g

V

uV

sfc

W

W

i

f

2)1(exp

2

Cruise S Range for cruise

SCC

V

sfc

W

W

LD

i

fexp

Loiter t Time for loiter

tKCV

sfc

W

WD

i

f14exp

The weight fraction of the aircraft starts out at 1 and decreases throughout the mission

until the aircraft lands. The aircraft weight is the product of each mission segment weight

fraction, i , multiplied by the gross aircraft takeoff weight, TOW . Wing loading, SW , is a

strong function of weight fraction, and the average weight of the aircraft is used to calculate the

wing loading for each mission segment. The average weight fraction is iterated to increase

accuracy when a large weight drop occurs in a mission segment. The takeoff weight calculations

are detailed in the following section.

55

3.2.4 Calculation of WTO

The gross takeoff weight, TOW , of this model is primarily developed from component

weight estimates in Raymer (2000). The method of estimating fuel weight and empty weight

from Mattingly, Heiser, and Pratt (2002) was initially used. However, this method proved to be

somewhat slow and sometimes non-convergent for this application. The method used for this

thesis is to allow gross takeoff weight to be a design decision variable and participate in the

optimization. Using this method requires an initial fuel weight to be estimated to conceptually

size some of the components. For this work, the initial fuel weight was estimated to be 40% of

0TW . Each subsystem and component weight is then estimated to find the empty weight of the

aircraft, EMPTYW . The actual fuel weight is found by subtracting 0TW from EMPTYW . If the

aircraft runs out of fuel during the mission, the chosen TOW is simply thrown out and a new TOW

is chosen along with a new set of decision variable values.

The conceptual sizing method in Raymer (2000) details an iterative process to decrease

the amount of fuel at take-off to the amount required to fly the mission to avoid taking off with

excess fuel. This iteration is not used with the following justification: a lower TOW can be found

by simply picking a better AFS-A design. This avoids spending computational time trying to

make a likely “worse” solution improve by finding the actual amount of fuel the aircraft needs to

fly the mission. Allowing the 0TW to be a DOF forces the optimizer to find the takeoff weight

and corresponding aircraft design and operational decision variable values that minimize the

difference between fuel used for the mission and fuel at takeoff. Table 3.6 outlines the main

subsystem weight calculations and the final 0TW equation. Note that the Nomenclature section

defines the variables that are used but not defined in Table 3.6.

Table 3.6 Main subsystem weight calculations and 0TW .


AAFSW

wingW Wing Weight (lb)

806.0260.00.2

_

4.0785.0622.05.0

10001316.3

)/()(0103.0

htzdg

h

wtailh

rootwzdgvsdwwing

SNW

B

FW

ctASNWKKW

tailhW _ Horizontal Tail

Weight (lb)

gearmainW _ Main Landing Gear Weight (lb)

gearnoseW _ Nose Landing Gear Weight (lb)

56


fuselageW Fuselage weight (lb)

525.05.0290.0_

973.025.0_

)(

)(

nwnllgearnoze

mlltpgcbgearmain

NLNWW

LNWKKW

685.0849.05.025.035.0499.0 WDLNWKW zdgdwffuselage

eds

enddvginductionair

DLL

NKLKW

373.0

498.1182.0643.0_

/*

29.13

zSLenmountsengine NTNW 579.0795.0_ 013.0

inductionairW _ Inlet duct weight (lb)

mountsengineW _ Engine mount weight (lb)

PSW PSW Engine weight (lb)

81.0exp)(063.0 25.01.1 MTW SLPS

FLSW FLSW Fuel Loop subsystem weight (lb)

DuctingMechanicalTankFuelHXFLS WWWWW _

ECSW ECSW

Environmental controls subsystem weight (lb)

DuctingMechanicalHXECS WWWW

PAOVCW / PAOVCW /

Vapor compresson/PAO loop subsystem weight

MechanicalHXVCPAOS WWW

CHSW CHSW Central hydraulic subsystem weight

664.0887.16 uvshCHS NKW (kg)

OLSW OLSW Oil loop subsystem weight

023.182.37 enOLS NW

FCSW FCSW Flight controls subsystem weight

127.0484.0489.0003.0*28.36 cscsFCS NNSMW

ESW Rated

System generating capability (kW, or kVA)

091.010.010.0152.02.172 genacmcES NLNRatedKW

TOW Gross takeoff weight fuelFCS

ESCHSECSFLSVCPAOSECSPSAAFSTO

WW

WWWWWWWWW

3.2.5 Morphing-wing Considerations

The AFS-A must account for morphing-wing technology, not only with respect to

aerodynamic performance but also with respect to takeoff weight and in-flight weight fractions.

In order to account for aerodynamics performance, five wing geometry parameters are allowed to

vary over the mission:

Aspect ratio, A ;

57

Wing length, L ;

Wing sweep angle, LE ;

Thickness to chord ratio, ct ; and

Taper ratio, .

The AFS-A morphing is treated in a quasi-stationary sense in that the wing geometry may

change for each of the 21 mission segments, but the change is considered an instantaneous

change (no time allowance for wing geometry change is considered). In other words, each of the

mission segments has a unique wing configuration for the morphing AFS-A. Note that the

payload drop (mission segment sixteen) has no time allowance, thus, the wing configuration for

that segment has no effect on the aircraft aerodynamics or performance. The morphing-wing

AFS-A has a total of 20 unique wing configurations for the 21 mission segments flown. The

fixed-wing AFS-A has a single configuration for the entire mission and does not change wing

geometry during the mission.

The actuation cost and additional weight of adding morphing wings to the aircraft must

also be taken into account in the morphing-wing aircraft. This is done by using wing weight and

fuel penalties to account for the additional actuators required for morphing wings and the energy

required to morph the wings, respectively.

The wing weight penalties are factors that are multiplied by the equivalent fixed-wing

weight and are added to the aircraft takeoff weight. For example, if an aircraft wing with a

specified geometry weighs 2,000 lb and the morphing wing weight penalty is 2, the actual wing

weight will be 4,000 lb. A difficulty in calculating the wing weight of a morphing-wing is

picking the geometry at which to calculate the equivalent wing weight before multiplying by the

wing weight penalty. Analysis of the wing weight equation in Table 3.6 indicates that the largest

wing weight is yielded by using the following values of the morphing-wing geometry:

Lowest aspect ratio, A ;

Largest wing length, L ;

Largest sweep angle, LE ;

Smallest thickness to chord ratio, ct ; and

58

Largest taper ratio, .

Using this method to establish the wing weight puts the morphing-wing aircraft at the largest

disadvantage with respect to gross takeoff weight. Note that the work of Butt (2005) used a

sweep angle of zero to establish the equivalent fixed-wing weight. Thus, the sensitivity study

presented at the end of Butt (2005) should have larger wing penalties showing a greater

advantage over the fixed-wing weight than in this thesis work. Consequently, the performance

metric to compare the fixed-wing performance to the morphing-wing performance in this work

will be the gross takeoff weight, TOW .

The fuel weight penalties are used to account for the power required to morph the wings.

After the aircraft takeoff weight and total fuel weight is established, the fuel weight penalties are

multiplied by the total fuel weight to find the morphing fuel weight. The morphing fuel is

reserved for morphing the wings and is not available to the PS to fly the mission. For example,

if the aircraft has 10,000 lb of total fuel, and the fuel penalty is 25%, then there will be 2,500 lb

of “morphing fuel”, leaving 7,500 lb of fuel available to fly the mission. The morphing fuel is

expended over the mission at the same rate as the fuel penalty. For example, if the fuel penalty

is 25% and the aircraft burns 1000 lb of fuel on a mission segment, 250 lb of morphing fuel is

used as well (in addition to the 1000 lb used to fly the aircraft) to account for the energy required

to morph the wings. Note that if excess fuel is sized at takeoff, then excess morphing fuel will

also be sized at takeoff which implies that excess fuel will be carried throughout the mission.

The aircraft weight fractions are updated at the end of each mission segment to reflect the

morphing fuel utilized. The usage of the morphing fuel is not taken into account in the exergy

destruction calculations since how exactly it is being used, i.e. the details of the actuators, is

unknown at this design stage. The AFS-A exergy model is presented in the following

subsection.

3.2.6 AFS-A Exergy Model

The exergy destruction in the AFS-A is composed of two unique parts: the exergy

destruction due to parasitic drag and that due to lift-induced drag (or simply induced drag). The

parasitic drag and induced drag equations are shown in Section 3.2.1 and the exergy destruction

rate equations are given in Table 3.7.

59

The exergy destruction in the AFS-A was tracked for every mission segment. The only

mission segment that has zero exergy destruction is the instantaneous payload drop mission

segment 16 (see Table 3.1).

Table 3.7 AFS-A exergy destruction rate equations.


Exergy destruction rate due to parasitic drag

PardesxE Exergy destruction rate due to parasitic drag

ambdes T

VDTxE

Par00

where Doparasite qSCD

0D Zero lift or parasitic drag q Dynamic pressure S Wing reference area

DoC Coefficient of parasitic drag

Exergy destruction rate due to lift-induced drag

InddesxE Exergy destruction rate due to lift induced drag

amb

ides T

VDTxE

Ind0

where iDi qSCD

2LD KCC

i

iD Drag due to lift or lift induced drag

LC Coefficient of lift

Lift factor

Tightly coupled with the AFS-A is the propulsion subsystem which is detailed in the

following section.

3.3 Propulsion Subsystem

The propulsion subsystem (PS) used in this thesis work is a low bypass afterburning

turbofan engine with the on- and off-design models based primarily on Mattingly, Heiser, and

Pratt (2002). The following subsections detail the PS model used in this thesis work.

3.3.1 PS Layout and Station Definitions

PS is made up of the following components: fan, high pressure compressor, burner /

combustor, high pressure turbine, low pressure turbine, exhaust mixer, afterburner, and nozzle.

The PS system layout and station definitions are shown in Figure 3.3. The station definitions

must be clear to track properties and operating conditions through the PS. Thus, Figure 3.4 and

Table 3.8 give further explanation and formally define the PS nomenclature. Notice in Figure

3.4 that the bleed air consumption is not shown.

60

Figure 3.3 Engine system layout (Rancruel, 2002).

Figure 3.4 Engine Station Definitions (Periannan, 2005).

The bleed air is used by the environmental control subsystem (ECS), which is detailed in Section

3.4 and Section 4.5.

Table 3.8 Low-bypass turbofan engine station definitions.

Station Description 0-1 Free stream to diffuser inlet 1-2 Diffuser 2-3 Fan entry to high pressure compressor entry 3 High pressure compressor exit 3’ Fan exit to bypass duct 3a Burner entry 4 Burner exit 4a Coolant mixer 1 exit, high pressure turbine entry 4b High pressure turbine exit 4c Coolant mixer 2 exit 5 Low pressure turbine exit, mixer entry 5’ Fan bypass duct exit to mixer entry 6 Exhaust mixer entry, afterburner entry 7 Afterburner exit, nozzle entry

7 8 9 1

Bleed air Cooling air #2

Cooling air #1

High pressure spool

Low pressure spool

Fan High

pressure Compressor

5 4c 4a

4 3a

3 3’ 2

Low pressure turbine

Coolant mixer 2

Last rotor

First rotor

Coolant mixer 1

Mixer After

Burner

5’

6

Burner Inlet Nozzle

61

Station Description 8 Exhaust nozzle throat 9 Exhaust nozzle exit

The turbofan engine is a much more complicated engine than the turbojet used in Butt

(2005) and requires flow and energy balancing through the engine and somewhat involved

iterations to find the off-design performance. In short, the PS is modeled with a reference or

“design” engine and each mission segment is considered as being “off design” at conditions at

which the engine was not specifically designed to operate most efficiently. The thermodynamic

model of the PS follows.

3.3.2 PS Thermodynamic Model

The thermodynamic models and design equations of the PS components are detailed in

this section. The off-design operation of the PS is used for every mission segment, while the

design calculations are used to “build” a reference engine. The off-design simulation requires

either an equation solver or iterative process. The latter is used for this thesis model. A

comprehensive list and order of calculation of the off-design equations are not repeated here, but

may be found in Mattingly, Heiser, and Pratt (2002).4

3.3.2.1 Free Stream and Diffuser

The engine analysis must start at the free stream conditions. First, the known properties

of the air are converted to total or stagnation properties. Temperature and pressure are first

converted from standard atmospheric conditions to the actual conditions of the aircraft, which are

corrected using tables and interpolation from Heiser and Pratt (1994). The equations and

constants for freestream and diffuser entry and exit properties are shown in Table 3.9.

Table 3.9 Diffuser and nozzle equations.


Freestream

r Isentropic freestream temperature recovery ratio

1

202

11

rr

r M

rt TT 00

rt PP 00

r Isentropic freestream temperature recovery ratio

0tT Total/stagnation temperature

0tP Total/stagnation pressure

4 ©AIAA. The low-bypass turbofan equations are reprinted with permission. See the Mattingly, Heiser, and Pratt

(2002) for the comprehensive list of turbofan equations.

62


Diffuser

d Total pressure ratio

0

2

t

td P

P = Rspecd max

97.0max d

0

2

t

td T

T =1

Rspec =1 for M0 ≤ 1

35.10 1075.01 MRspec for M0 > 1

maxd Total pressure due to wall friction

d Total temperature ratio

Rspec Ram recovery coefficient

Nozzle

n Total pressure ratio

7

9

t

tn P

P

17

9 t

tn T

T n Total temperature ratio

3.3.2.2 Fan and High Pressure Compressor

The fan and high pressure compressor components are driven by the low and high

pressure turbines, respectively, via the low pressure and high pressure spools, respectively. The

fan and high pressure compressor are used to compress the incoming air before combustion. The

fan runs at a lower pressure ratio than the high pressure compressor, and typically spins slower

than the high pressure spool as well. The fan and high pressure compressor calculations are

given in Table 3.10.

Table 3.10 Fan and high pressure compressor equations.


Fan

'c Total pressure ratio 2

3'

'

t

tc P

P ,

2

3'

'

t

tc T

T

1'

1/1

'

''

c

c

cc

=

1

1

2

3

23

2

t

t

tt

t

P

P

TT

T

TcmW pccc ''' . =

1

1

2

3

'

2''

' c

c

t

t

c

tpcc P

PTcm

fandr

fandrfanfanC mm

'c Total temperature ratio

'c Efficiency

'cW Power

Ccm ' Corrected mass flow rate

Compressor

cH Total pressure ratio

1

1/1

cH

cHcH

cHcH

=

1

1

3

'3

3'3

'3

t

t

tt

t

P

P

TT

T

'3

3'

t

tcH P

P ,

'3

3

t

tcH T

T

cH Total temperature ratio

cH Efficiency

63


cHW Power

1.

1

3

33

'

' cH

cH

t

t

cH

tpcHcHpcHcHcH P

PTcmTcmW

cHcdr

cHcdrcHcHC mm

'

' cHCm Corrected mass flow rate

c Total pressure ratio for the compressor section cHcc '

3.3.2.3 Main Burner and Afterburner

The fuel is added to the airstream in the main burner and afterburner (if being used) and

ignited. Note that the main burner only adds fuel to the core air flow, while the afterburner adds

fuel to both the core and bypass air as both streams are combined in the mixer before entering the

afterburner section. Fixed efficiencies and pressure ratios are used for both the main burner and

afterburner. The equations are given in Table 3.11.

Table 3.11 Burner and afterburner calculations.


Burner

burn Efficiency 98.03344

PRfAB

apcatptburn hm

TCmTCm

97.03

4 at

tburn P

P ,

at

tburn T

T

3

4

0TC/hf

pcbPR

cHcr '

0

4

TC

TC

pc

tpt

burn Total pressure ratio

burn Total temperature ratio

f Fuel/air ratio

Enthalpy ratio

Afterburner

AB Efficiency 97.06677

PRfAB

tpmtpABAB hm

TCmTCm

97.06

7 t

tAB P

P ,

6

7

t

tAB T

T

ABpcABPR

ptpMMtLmtHmABAB TCh

CCff

0

2121

/

/

1

11

0

7

TC

TC

pc

tpABAB

AB Total pressure ratio

AB Total temperature ratio

ABf Fuel/air ratio

AB Enthalpy ratio

64

3.3.2.4 High and Low Pressure Turbines

The high and low pressure turbines allow expansion and work extraction in the core of

the engine. The high pressure turbine vanes are cooled by coolant mixers with bleed air extracted

from the fan. The equations describing the high and low pressure turbine behavior are given in

Table 3.12.

Table 3.12 High and low pressure turbine equations.


High Pressure Turbine

tH Total pressure ratio

t

t

tH

tHtH

1

1

1

,

4

4

t

bttH P

P

/11

11

'

'

121 cHcrmH

cHcrtH f

tHmbcHcdr

tHmbcHcdrtHtHC mm

1'

1'

tH Total temperature ratio

tH Efficiency

tHCm Corrected mass flow rate

Low pressure Turbine

tL Total pressure ratio t

t

tL

tLtL

1

1

1

,

ct

ttL P

P

4

5

//11

/111

'

'

2121 cHcrtHtHmL

mPTOcrtL f

Ca

( Where, 00 TCm/PC pcTOTO )

tLmtHmbcHcdr

tLmtHmbcHcdrtLtLC mm

21'

21'

tL Total temperature ratio

tL Efficiency

tLCm Corrected mass flow rate

3.3.2.5 Coolant Mixers and Exhaust Mixer

Turbine cooling is required to avoid exceeding material design temperature limits in the

turbines in the PS (the limit imposed is 3200 R). The turbine cooling is performed in the coolant

mixers with air bled off of the high pressure compressor. The amount of turbine cooling

required depends on the temperature of the burner.

After the turbine section, the bypass and core airstreams are combined in the mixer

section of the turbofan engine. The mixed streams then enter the afterburner section. The

equations for the coolant mixers and exhaust mixer are given in Table 3.13.

65

Table 3.13 Turbine cooling mixer and exhaust mixer equations.


Coolant Mixer 1

21, Coolant mixer ratios 000,16/2400421 tT

where RTt 24004

otherwise 021

1cmix Total temperature ratio 121

'1211 11

/11

f

f cHcrcmix

11 cmix 1cmix Total pressure ratio

Coolant Mixer 2

2cmix Total temperature ratio 2121

11'2121

2 11

}{11

f

f tHcmixcHcrcmix

12 cmix 2cmix Total pressure ratio

Exhaust Mixer

M Total temperature ratio

),,(

),,()'1(

1

/1

11'

666

555

6

5

5

6

'

5555'

6

5

5

6

21215

5

''

'

RMMFP

RMMFP

A

A

P

P

TCTC

C

C

T

T

fm

m

Mt

tM

tptp

p

p

t

tM

M Total pressure ratio

' Mixer bypass ratio

3.3.3 Thrust and Performance Calculations

The overall performance equations of the PS are detailed in Table 3.14. The uninstalled

thrust is the engine thrust produced without any losses attributed to the engine cowl or nozzle

drag.

Table 3.14 Thrust and engine performance calculations.


Overall Engine Performance

0f Total fuel consumption

1/11 210 ABfff

nABMtLtHbcHcdrt

P

P

P

P '9

0

9

9

2

11

9

99 1

1

2

AB

AB

P

PM t

AB

88 /)1(990

9

PP

C

C

T

T

t

ABpAB

pc

2

11

9

9

0

9 8

8

11

P

P

V

V t

r

AB

000 TgRMV ccc where 174.32cg lbm*ft/(lbf*s2)

9

9

P

Pt Total/static pressure ratio in nozzle

9M Nozzle exit Mach

0

9

T

T Overall

temperature ratio

0

9

V

V Overall velocity

ratio

0V Aircraft velocity (ft/s)

66


Thrust

0m

F Uninstalled specific thrust (lbf/lbm/s)

0

0

20

90

0

9

9

00

0

90

0

0

3600

/1

11

11

1

mF

fS

M

PP

T

T

V

V

R

Rf

V

Vf

g

V

m

F

cc

ABc

S Uninstalled specific fuel consumption (1/h)

F Uninstalled thrust (lbf)

Subsonic inlet drag is estimated by assuming a worst case scenario of massive flow

separation at the lip of the inlet and no recovery of additive drag. Additive drag is defined as the

positive drag acting on the streamtube which encloses the air that enters the engine inlet

(Mattingly, Heiser, and Daley, 1987).

Supersonic inlet drag is estimated somewhat conservatively using the idea of the inlet

“swallowing” its projected image. This, in effect, means that the inlet area, 1A , is larger or equal

to the flow capture area, 0A , and that the inlet must have the ability to vary its geometry. Also,

the excess air captured by the inlet must be vented via boundary layer bleed ports. The excess

air vented is at a lower velocity than the aircraft, thus, creating drag from the momentum loss.

The supersonic inlet loss coefficient reflects this momentum loss drag. The inlet and nozzle drag

and installed thrust equations are given in Table 3.15.

Table 3.15 Inlet and nozzle drag and installed thrust equations.


Inlet Drag

inlet Inlet loss coefficient

For M0 < 1.0:

000

20

0

120

0

1

1

0 1

aMmFg

MA

AM

T

T

M

M

cinlet

For M0 > 1.0:

00

2

1

200

0

1

1

1

1

21

amFg

MMA

A

cinlet

0M Freestream Mach

1M Inlet Mach

0A Area of engine capture streamtube

1A Inlet area

0M Freestream Mach

1M Inlet Mach

0T Freestream temperature

1T Inlet temperature

67


Nozzle Drag

nozzle Nozzle loss coefficient

For M0 < 0.8:

00

0

9100 2

am

Fg

A

AACM

c

D

nozzle

For 0.8 < M0 < 1.2:

00

0

9100 2

am

Fg

A

AACM

c

DP

nozzle

For M0 > 1.2:

1

exp4.11

2.1 20

200

M

M

C

MC

D

D

10A Nozzle inlet area

9A Nozzle throat

0a Freestream speed of sound

DC Convergent nozzle pressure drag coefficient

DPC Experimental pressure drag coefficient

Installed Thrust T Installed thrust (lbf)

inletnozzleFT 1*

The DC term and DPC terms in Table 3.15 are nozzle pressure drag coefficients derived

using the “integral mean slope” (IMS) method discussed in Mattingly, Heiser, and Pratt (2002).

3.3.4 PS Exergy Model

The exergy model for the PS was developed on a component by component basis. This

accounting structure provides a much more detailed picture of losses and inefficiencies which

allows a designer to very quickly see areas needing improvement within the PS. The exergy

destruction calculations are shown in Table 3.16. Notice also that the unburned fuel is taken into

account in the exergy destruction equations.

Table 3.16 PS exergy model equations.


Fan fandesxE _

Exergy destruction rate in the fan

2

3

2

320_

''lnln

P

PR

T

TCmTxE cpcfandes

High Pressure Compressor

cHdesxE _

Exergy destruction rate in the high pressure compressor

'3

3

3

330_ lnln

' P

PR

T

TCmTxE cpccHdes

68


Burner burnerdesxE _

Exergy destruction rate in the burner

fuelcorefuelburnerdes hmxE **35.0 __

High Pressure Turbine

tHdesxE _

Exergy destruction rate in the high pressure turbine

4

4

4

440_ lnln

P

PR

T

TCmTxE b

ta

bptatHdes

Low Pressure Turbine

tLdesxE _

Exergy destruction rate in the low pressure turbine

c

ttL

c

tptctLdes P

PR

T

TCmTxE

4

5

4

540_ lnln

Mixer mixerdesxE _

Exergy destruction rate in the mixer

r

iiMpMimixerdes yR

p

pR

T

TCmxE

1

''

_ lnlnln

Afterburner ABdesxE _

Exergy destruction rate in the afterburner

fuelABfuelABdes hmxE **35.0 __

Unburned unburnlossxE _

Exergy loss rate due to the fuel lost out the back of the PS

ABdes

ABburnerdesbunburnloss

xE

xExE

_

__

*

1*1

The PS is not only closely coupled to the AFS-A but also to other aircraft subsystems.

One of these is the environmental controls subsystem (ECS), which uses bleed air from the PS as

the working fluid to perform its cabin and avionics cooling duties (see Figure 3.5). The ECS is

detailed in the following section.

3.4 Environmental Controls Subsystem

The environmental controls subsystem (ECS) is responsible for cooling the low-heat

generation avionics boxes and keeping the cabin temperature and humidity at comfortable levels

for the pilot. The system is a bootstrap system similar to that used in the F-16. The ECS consists

of four compact heat exchangers, a water separator, and an air-cycle machine.

3.4.1 ECS Layout and Definitions

The ECS flow rate and input air conditions are determined by two bleed ports located in

the PS. The low pressure bleed port is located midway on the high pressure compressor in the

PS, while the high pressure bleed port is located immediately after the high pressure compressor.

Figure 3.5 shows the bootstrap type ECS along with the PS. The bleed air input pressure to the

ECS is controlled via a pressure regulating valve (PRV).

69

Figure 3.5 ECS layout and components (Muñoz and von Spakovsky, 2001).

Following the path of the bleed air flow from the PS shows that the bleed air is first

cooled in the primary heat exchanger via ram air. A portion of the bleed air is then compressed

and cooled first through the secondary heat exchanger, then through the bleed air/PAO heat

exchanger, and finally through the regenerative heat exchanger. The air is then expanded over

the turbine that drives the compressor. The water separator removes the water from the air

which finally makes it to the cabin and low-heat generating avionics (i.e. air-cooled avionics).

The following subsections detail the ECS thermodynamic model, heat exchangers, and ECS

exergy model.

3.4.2 ECS Thermodynamic Model

The thermodynamic model of the ECS consists of multiple components. The ECS model

is based primarily on the work of Muñoz and von Spakovsky (2001a,b), Periannan (2005), and

Rancruel (2003). The station definitions may be seen in Figure 3.6, and the model equations for

the ECS components are given in Table 3.17.

70

Figure 3.6 ECS station definitions (Rancruel, 2002).

Table 3.17 Thermodynamic model of the ECS (Periannan, 2005).

Variable Description Model Equation

9T Load thermodynamic temperature loadTT 9

9P Load thermodynamic pressure loadPP 9

8T Water separator inlet temperature 98 TT

8P Water separator inlet pressure wsPPP 98

6

7

T

T Turbine temperature ratio

1

6

7

6

7 11P

P

T

Ttb

t Turbine efficiency

Fv Turbine velocity factor

14028

Y

YT

NFv

in

1

1

PRY

6T Regenerative hot-side exit temperature. Cmin is the smallest of the heat capacities C5 and C8’. Also, rhx is the heat exchanger effectiveness.

5

8556 C

C'TTTT min

rhx

6P

Regenerative heat exchanger hot-side exit

pressure. A correlation is used for the pressure

drop. 5

56 1 P

P

PP

Preconditioning

Sub-system

Bootstrap

Sub-system

Preconditioning

Sub-system

Bootstrap

Sub-system

3‘

3‘

4‘

8‘

71


5T

Bleed air / hot PAOS heat exchanger hot-side

exit temperature. Cmin is the smallest of the heat

capacities C4’ and C14.

'

min'rhx_pao/bleed' C

CTTTT

414445

5P Bleed air / hot PAOS heat exchanger hot-side

exit pressure. A correlation is used for the

pressure drop.

''

PP

PP 4

45 1

'T4 Secondary regenerative heat exchanger hot-side

exit temperature. Cmin is the smallest of the heat

capacities C4 and C10.

4

444 C

CTTTT min

ohx_ondsec'

'P4 Secondary regenerative heat exchanger hot-side

exit pressure. A correlation is used for the

pressure drop.

44

4 1 PP

PP '

3

4

T

T Compressor temperature ratio

11

1

1

3

4

3

4

P

P

T

T

cp

c Compressor efficiency

shaftw Shaft work of the compressor and turbine 7634 hhhhwshaft

3T Primary heat exchanger hot-side exit

temperature. Cmin is the smallest of the heat

capacities C2 and C12.

2

223 C

CTTTT min

ohx_pri

3P Primary heat exchanger hot-side exit pressure. A

correlation is used for the pressure drop. 2

23 1 P

P

PP

k Ram inlet scoop mass flow ratio. ukuii

fr Ram inlet scoop pressure recovery factor

ofo PrPi

iT

Ram scoop inlet temperature (“i” equals 10 or

12 and Ti* is the temperature at sonic

conditions; see Anderson, 1984). 212

1

i*

i

i

MT

T

iP

Ram scoop inlet pressure (“i” equals 10 or 12

and Pi* is the pressure at sonic conditions; see

Bejan (1996).

2

1

212

11

ii*

i

i

M)(MP

P

oiP

Ram scoop inlet stagnation pressure (“i” equals

10 or 12 and Poi* is the stagnation pressure at

sonic conditions; see Davenport (1983).

)(i

i*o

oi M)(

MP

P

i

12

12

1

121

72


iD

fL

4

Ram scoop inlet augmented friction factor; f

assumed equal to 0.01 and L and D are the

length and the diameter of the ram air duct,

respectively, see Davenport (1983).

2

2

2

2

12

1

2

114

i

i

i

i

i M)(

M)(ln

M

M

D

fL

dragD Drag due to the presence of the ram air inlet and

outlet (e). Pressure drag has been ignored. edrag uumD

1311orP Ram air pressure just ahead of the ram scoop

exit (states 11 or 13). 12101210

1311 1 oror

or PP

PP

3.4.2.1 Heat Exchangers

The heat exchanger thermodynamic models used in this thesis work are primarily from

Shah (1981) and Kays and London (1984). The models are compact, offset-strip fin type heat

exchangers and focus on the liquid/air heat exchange, although the thermodynamic model may

be applied to any general heat exchanger with the proper derivation from the general case. The

geometric parameters of the offset-strip fin are shown in Figure 3.7.

Figure 3.7 Geometric parameters of the offset-strip fin (Muñoz and von Spakovsky, 1999).

The weights of the heat exchangers are found using the fin geometry and density. Table

3.18 shows the compact heat exchanger model equations.

Table 3.18 Geometric and heat transfer models of the compact heat exchangers.


Lh Hot-side length Assigned value

Lc Cold-side length Assigned value

t s h=b

a

73


hD Hydraulic diameter thhlsl

shlDh

2

frA Frontal area nfr LLA

Ratio of minimum free flow area to frontal area fr

O

A

A

Heat transfer area / volume between plates hD

4

t

f

A

A Fin area / total area

hs

hs

A

A

t

f

2

pN Number of plates ahh

ahLnN

rb

bnpp 2

2

bpV

rpV Volume between plates, bleed and ram air side

bprbp hNLLVb

)1(

bprbp hNLLVr

A Heat transfer area VpA

OA Minimum free flow area L

ADA h

O 4

G Mass velocities OA

mG

eR Reynolds number

he

DGR

f

j

Friction and Colburn coefficients (Muñoz and von Spakovsky, 1999)

For *ee RR (laminar flow)

2659030530185607422062439 ....eR.f

0678014990154105403065220 ....eR.j

f

j

Friction and Colburn coefficients (Muñoz and von Spakovsky, 1999)

For 1000 *ee RR (turbulent flow):

2423068200093602993086991 ....eR.f

1733019550103704063024350 ....eR.j

wA Wall conduction area )N(LLA prbw 12

wR Wall thermal resistance ww

w Ak

aR

l Fin length tb

l 2

H Height abbnabH chplatesh 22

74


fA Finned area

2

12

kt

hm , HLAfr

ml

mlf

)tanh( ,

A

AffO 11

frA Frontal area

f Fin efficiency

o

Outside overall surface efficiency

n Mixture molar flow rate

OA

mG

,

k

cP p

r

32

r

p

P

jGch

j Colburn factor

G Maximum mass velocity

Pr Prandtl number

h Heat transfer coefficient

U Overall heat transfer coefficient h

phcpcmin cncnC ,min

hph

cpcmax cncnC ,max

rOw

bO hAR

hAUA 111

, maxminr C/CC

minC

UANTU

minC Minimum heat capacity

maxC Maximum heat capacity

rC Heat capacity ratio

NTU Number of transfer units

Effectiveness

1

11 780220 .

r.

r

NTUCexpNTUC

exp

P The core pressure drop

e

ie

m

i

o

e

ic

iK

A

Af

K

P

G

P

P

2

22

1

1211

2

The ECS exergy model is discussed in the following subsection.

3.4.3 ECS Exergy Model

The ECS exergy model losses are primarily due to the heat exchangers and air cycle

machine (consisting of a turbine/compressor) losses. No exergy destruction is attributed to the

“conditioned” air exiting the cockpit and avionics after it is used. Any excess bleed air from the

PS is considered to be negligible. The exergy destruction rate equations for the ECS heat

exchangers are shown in Table 3.19.

75

Table 3.19 ECS exergy destruction rate equations.


Cold Side coldP

DESxE

Exergy destruction rate on the cold side of the heat exchanger due to the pressure drop

outcoldincoldcoldcoldcoldP

DES PPTRmxE /ln0

Hot Side hotP

DESxE

Exergy destruction rate on the hot side of the heat exchanger due to the pressure drop

outhotinhothothothotP

DES PPTRmxE /ln0

Temperature gradient

TDESxE

Exergy destruction rate due to a temperature drop

outhot

inhot

outcold

incold

T

T

T

TPcoldcoldPhothot

TDES T

dTcm

T

dTcmTxE

1

0

Total Exergy Destruction Rate

HXDESxE Total exergy destruction rate in the heat exchangers

hotP

DEScoldP

DEST

DESDES xExExExEHX

The exergy destruction calculations for the compressor and turbine ECS components are

found in Table 3.16 as one turbine or compressor is treated the same as another in terms of the

exergy destruction. The ECS interacts with the PS via bleed air and the vapor compression /

polyalphaolefin subsystem (VC/PAOS), which is detailed in the following section.

3.5 Vapor Compression / PAO Subsystem

The vapor compression / PAO subsystem (VC/PAOS) consists of three loops: the cold

PAO loop, the hot PAO loop, and the vapor cycle. The VC/PAOS serves as a heat sink for the

ECS via a PAO / bleed air heat exchanger and for the high-heat generation avionics via the cold

PAO loop. The hot PAO loop rejects heat to the fuel loop subsystem (FLS) and to a ram air /

PAO heat exchanger. The motor driving the compressor on the vapor cycle and the pumps on

the hot and cold PAO loops are all driven via electrical power from the electrical subsystem

(ES). The VC/PAOS layout and station definitions are shown in Figure 3.8.

76

Figure 3.8 VC/PAOS layout and station definitions (Rancruel, 2002).

3.5.1 VC/PAOS Thermodynamic Model

The thermodynamic models of the vapor cycle compressor and the PAO / ram air heat

exchanger in the VC/PAOS are based on a perfect gas model. The load temperature (or the

temperature of the ‘Avionics Box’ in Figure 3.8) is given by Figliola, Tipton, and Ochterbeck

(1997), and the physical model is from Greene (1992). The model equations for the VC/PAOS

thermodynamic model are presented in Table 3.20.

Table 3.20 VCPAOS model equations.


Initial Condition loadT

Load temperature of the high-heat generation avionics

loadTT 10

77


Cold PAO Loop Pump

AvioQ

Heat transfer rate required by the liquid cooled avionics

pPAOPAO

Avio

Cm

QTT

1011

PAOm Mass flow rate in the cold PAO loop 01109

01109

01109

01109

TT

TT

hh

hh ssp

pW Pump work rate 110901109 PPvTTcWP

0110901109

01109

PPvTTc

PPvp

pipeboxAvioEvapp PPPPPP _01109

pPAOC Heat capacity of the PAO

p Pump efficiency

pP Pressure rise across the pump

Evaporator

loadQ

Heating load due to the avionics box and the pump temperature rise

)( 910 hhmQ vapload

)()( 91078 hhmhhmQ paovapEvap

Vap

EvapEvap

VapEvap m

Qh

m

CTThh

7

min7978

9

min109910 C

CTTTT evap

99

10910 1 P

P

PP

77

878 1 P

P

PP

EvapQ Heating load on the evaporator

Evap Evaporator effectiveness

vapm Vapor mass flow rate in the evaporator

Compressor

cW Compressor work rate

11

1

1

8

5

8

5

P

P

T

T

cp

85 hhmW vapc

net

load

W

QCOP

COP Vapor compression cycle coefficient of performance

Condenser

EvapQ Heat transfer rate in the evaporator

CompEvapCond QQQ

)()( 42165 hhmhhmQ paovapCond

Vap

CondCond

VapEvap m

Qh

m

CTThh

5

min4556

4

min45412 C

CTTTT evap

55

566 1 P

P

PP

44

41212 1 P

P

PP

CompQ Heat transfer rate in the compressor

Cond Condenser effectiveness

CondQ Heat transfer rate in the condenser

Expansion Valve valPr Pressure ratio of the

expansion valve

0706 hh assumes isenthalpic 0)()( 6767 PPvTTcv

CondEvapcomval PP PrPr

78


Hot PAO Loop Pump

p Pump efficiency

01201

01201

01201

01201

TT

TT

hh

hh ssp

0120101201 PPvTTcW p

0120101201

01201

PPvTTc

PPvp

pW Pump work rate

pPAOC Heat capacity of the PAO

Bleed Air / Hot PAO Heat Exchanger

hxpaobleed _/

Bleed air / PAO heat exchanger effectiveness

1

min_1_/12 C

CTTTT inbleedhxpaobleed

11

2 1 PP

PP

Fuel / Hot PAO Heat Exchanger

hxpaofuel _/ Fuel / PAO heat exchanger effectiveness

2

min_2_/23 C

CTTTT infuelhxpaofuel

22

3 1 PP

PP

Ram Air / PAO Heat Exchanger

hxpaoram _/ Ram air / PAO heat exchanger effectiveness

3

min_3_/34 C

CTTTT inramrhxpaoram

33

4 1 PP

PP

Note that the VC/PAOS ram air inlet has the same thermodynamic model as the inlet

ducts in the ECS. The heat transfer model for the condenser and evaporator is from Liu and

Kakac (2000). The compact heat exchanger model for effectiveness is from Incropera and

DeWitt (1990) and applies to single-pass, cross-flow heat exchangers with unmixed fluids. The

thermodynamic properties of the PAO are based on data from the CRC Handbook (1976);

Zabransky et al. (1996); and the JANAF Thermochemical Tables (1998).

3.5.2 VC/PAOS Exergy Model

The exergy component models of the VC/PAOS are effectively the same as those of the

ECS. No additional unique components are introduced in the VC/PAOS; and, thus, the exergy

destruction equations are not repeated here.

The VC/PAOS interfaces with a number of subsystems, including the ECS (cooling loads

for the bleed air and liquid-cooled avionics), the ES (to power the pumps and compressor), and

the FLS which serves as a heat sink for the hot PAO loop. This latter subsystem is discussed

next in the following section.

79

3.6 Fuel Loop Subsystem

The fuel loop subsystem (FLS) consists of a fuel tank, pumps, fuel lines, and controls

required to supply fuel to the PS as well as the hardware necessary to use the fuel as a heat sink

by the other subsystems. The FLS thermodynamic model is based on the work of Rancruel

(2003) and Periannan (2005). The FLS system schematic is shown in Figure 3.9.

Figure 3.9 Schematic of the fuel loop subsystem (Rancruel, 2002).

The fuel from the fuel tank is first pressurized by the pump and then is heated by the hot

PAO loop via a compact heat exchanger. The fuel is then passed through the fuel / oil heat

exchanger where it is further heated by the engine cooling/lubricating oil in the oil loop

subsystem (OLS). The fuel is interfaced with the central hydraulic subsystem (CHS) as a heat

sink again before finally being burned in the PS. Notice that the fuel loop does not end at the PS

but allows for excess fuel to be pumped through the loop if additional cooling capacity is needed

80

to meet the heating load requirements of the other subsystems. The additional fuel is cooled in

the fuel / ram-air heat exchanger before it is returned to the fuel tank to avoid heating the fuel

beyond acceptable limits.

3.6.1 FLS Thermodynamic Model

The thermodynamic model of the FLS is similar to the ECS and VC/PAOS in that

compact heat exchangers are also used. The model equations for the heat exchangers can be

found in section 3.4.2.1. The fuel tank temperature is not monitored as was done in Rancruel

(2003), but rather a constraint is imposed on the allowable temperature of the excess fuel

returning to the fuel tank. The FLS thermodynamic model equations are presented in Table 3.21.

Table 3.21 Fuel loop subsystem thermodynamic model equations.


Fuel tank

outfuelm _ Mass flow rate of fuel leaving the tank

T

TTTC

TΤCmm

addpao

paofuel

outpaoaddpaooutfuelfuelp

outpaoinpaopaopoutfuel

_

/

___

___

)(*

)(*)*(

SFCmm outfueladdfuel __

)(** ___/ TTCmQ addfueloutfuelpfuelHXPAOfuel

addfuelfuelp

inramPStofuelminpramfuelPStofueladdfuel mC

TTCmTT

_

___/___ *

)(*)*(*

addfuelm _

Fuel added to the fuel required by the PS

addfuelT _

Temperature of the fuel returning to the tank

SFC Specific fuel consumption (by the PS)

PStofuelT __

Temperature of the fuel to the PS

Fuel / PAO heat exchanger

paofuel / Fuel / PAO heat exchanger effectiveness

)T(T*Cp)*m(

)T(T*Cp)*m(

Q

Q

fuel_inpao_inmin

pao_outpao_inpao

max

actual

fuel/pao

Fuel / Oil heat exchanger

oilfuel / Fuel / oil heat exchanger effectiveness )T(T*Cp)*m(

)T(T*Cp)*m(

fuel_inoil_inmin

oil_outoil_inoil

fuel/oil

Fuel / Hydraulic Oil heat exchanger

hydfuel /

Fuel / hydraulic oil heat exchanger effectiveness

)T(T*Cp)*m(

)T(T*Cp)*m(

fuel_inhyd_inmin

hyd_outhyd_inhyd

fuel/hyd

Fuel / Ram-Air heat exchanger

ramfuel / Fuel / ram air heat exchanger effectiveness )T(T*Cp)*m(

)T(T*Cp)*m(

Q

Q

ram_infuel_inmin

ram_inram_outram

max

actual

fuel/ram

81

The FLS serves as the main thermal management subsystem (TMS) in the aircraft. The

FLS exergy model is described by the same equations as for both the VCPAOS and ECS, and

thus, the equations are not presented again in this section. The FLS interfaces with a number of

subsystems as a heat sink, one of which is the OLS which, as previously mentioned, is the

subsystem responsible for cooling and lubricating the engine bearing surfaces. The OLS is

discussed in the following section.

3.7 Oil Loop Subsystem

The oil loop subsystem (OLS) lubricates and cools the PS bearing surfaces. The OLS

may perform secondary functions as well such as cooling the auxiliary power unit (APU) or

operating thrust reversers; however, secondary OLS functions are not modeled in this thesis.

The oil loop subsystem used in this thesis is similar to the type used in the Pratt and

Whitney F100-PW-100 (early F-15 engine) with a few exceptions: a fuel/oil cooler is used here

instead of the air / oil cooler as was used in the F100-PW-100. A simplified diagram of the OLS

is shown in Figure 3.10.

Aircraft generally have two different configurations for OLSs: either a “hot tank” or a

“cold tank” configuration. The former configuration (see Figure 3.10) pumps the oil directly

from the scavenger pumps to the oil tank. The supply (or pressure) pump moves the hot oil first

through the oil cooler and finally to the oil nozzles at the various bearings. The “cold tank”

configuration has the scavenger pumps moving the oil through the oil cooler before heading to

the tank, thus, the name “cold tank.” It is advantageous to have a “hot tank” design in fighter

aircraft because the oil and air separation is more efficient.

Multiple scavenger pumps are located throughout the bearing sumps in a jet engine for

redundancy as well as for location (a sump is usually needed at each main bearing location). The

scavenger pumps have much greater total capacity than the supply pump so the scavenger pumps

will inherently pump a quantity of air as well as oil. This requires oil and air separation and an

OLS typically has an internal deaerator on the tank. All the pumps on the OLS are driven by a

gearbox on the low pressure spool of the PS.

82

Figure 3.10 Oil loop subsystem schematic.

The supply pump in an OLS is usually an internal/external gear, rotary, positive-

displacement type pump which can effectively pressurize any system over its design limits if

enough shaft power is available, and the pump does not encounter mechanical failure. This

necessitates placing relief valves throughout the system to avoid over-pressurization.

3.7.1 OLS Thermodynamic Model

The OLS interacts with the PS, FLS, and AFS-A in the aircraft. The interaction with the

PS is not only via the heating load, as previously mentioned, but also via the shaft power

required to power the supply, booster, and scavenger pumps. The work required by the OLS

pumps is calculated using the equations in Table 3.22.

Table 3.22 OLS pump work equations.


Pump Work

pumpW Shaft power required

mpump

PQW

*

where

fluid

mQ

m Pump efficiency

Q Volumetric flow rate

83

The OLS heating load on the FLS must be established to have a fully integrated model.

The development of the OLS model proved to be difficult because of the lack of information on

this subsystem. Two statements found in Hudson (1986) were used along with some PS

performance/setting correlations to develop the heating load model for the OLS. Hudson (1986)

states that the OLS cooling load is 31% of the total aircraft heating load and that the ECS is 21%

of the total aircraft heating load during cruise conditions. These two statements are used as the

basis of heating load model for the OLS. The ECS heating load is well-defined; thus, a

relationship for the OLS was developed relative to the uninstalled cruise thrust and ECS heating

load during cruise conditions. Cruise was defined as the flight conditions for mission segment

19.

Once the ECS heating load is established for segment 19, the OLS heating load can be

estimated using the aforementioned correlation provided by Hudson (1986). This requires the

maximum and minimum thrust at the given cruise conditions which are found using the thrust

correction for altitude (versus sea level take-off thrust) and a maximum/minimum estimated

engine operating speed (which is found using 11,500 RPM for maximum rpm, and 4,200 RPM

for minimum-sustainable RPM). Next, a percentage of the total available thrust can be

developed for the engine/aircraft pair for cruise conditions from the maximum and minimum

thrust for the engine and the required thrust to fly at cruise conditions. For example, the thrust

required for cruise is 25% of the maximum thrust of the engine at those operating conditions.

This percentage is carried over to the heating load as a correlation between uninstalled thrust and

heating load on the OLS. Thus, for any uninstalled thrust setting in the PS, a corresponding

heating load on the OLS can be found. The heating load equations and correlations used in the

OLS model are given in Table 3.23.

Table 3.23 OLS heating load equations.


OLS Heat Exchanger Load

HXccOLSfuelQ _/

Cooling load on the fuel from the OLS at cruise conditions

HXccECSfuelHXccOLSfuel QQ _/_/21

31

HXccECSfuelQ _/

Cooling load on the fuel from the ECS at cruise conditions

HXOLSfuelQ _/

Cooling load on the fuel from the OLS at a given sea level, equivalent thrust SLTT max

maxT Maximum thrust at altitude

cruiseT Uninstalled cruise thrust from

84


the PS

std

ambient

P

P

maxmax

* RPMT

TRPM cruise

cc

cruise

cruiseHXccOLSfuel T

TTQQ

TRPM

RPMT

min_/min

maxmax

minmin

1

min_/

min

min_/

* QTslopeQ

TT

QQslope

QTHXOLSfuel

cruise

HXccOLSfuelQT

minT

Estimated minimum thrust at altitude from the RPM relationship

ccRPM Estimated engine RPM at cruise

QTslope

Slope of the heating load versus the installed the thrust curve (assumes a linear relationship)

T Uninstalled thrust

The heat exchanger in the OLS is the same as the compact heat exchangers detailed in

section 3.4.2.1. Note that the weight of the heat exchanger is accounted to the FLS since the heat

exchanger is owned by the FLS and not the OLS in this thesis work.

A schedule of stainless steel tubing and predicted mass flow rates of the OLS were

initially used to model the OLS. The results showed that the pressure drops due to frictional

losses were negligible in terms of the exergy destruction and pumping losses. Thus, the final

OLS model used in this thesis work does not estimate tube sizing or calculate friction losses.

3.7.2 OLS Exergy model

Exergy destruction is caused in the OLS by pressure losses due to fluid friction or

restriction, temperature losses due to heat transfer across finite temperature differences,

unrestrained expansions, or mechanical inefficiencies. The exergy equations for the OLS are

given in Table 3.25.

Table 3.24 OLS exergy destruction equations.


Exergy Destroyed

0T Ambient temperature

1

1

midealactualPump PQWWxE

outhot

inhot

outcold

incold

T

T

T

TPcoldcoldPhothot

TDES T

dTcm

T

dTcmTxE

1

0


m Mechanical efficiency of the pump

PumpxE Exergy destruction rate due to pumping irreversibilities

TDESxE

Exergy destroyed due to the heat exchanger temperature gradient

85

It is important to note that for this subsystem, there are actually a total of 6 pumps that

generate entropy: the main pump, booster pump, and the four scavenger pumps. The total exergy

destruction in the OLS is approximated by finding the pumping losses and exergy destruction in

the fuel/oil heat exchanger. We now turn to the central hydraulic subsystem (CHS) which is the

next subsystem that interfaces with the FLS by means of a heat interaction. The CHS is detailed

in the following section.

3.8 Central Hydraulic Subsystem

Hydraulics are used to actuate flight control surfaces as well as various other systems in

the aircraft (e.g. the landing gear, nose-wheel steering, etc.). Hydraulics are attractive to use in

aircraft because they are able to transfer large amounts of power from a central location to where

it is needed by means of small diameter hoses. However, despite the advantages of hydraulics,

traditional central hydraulic subsystems (CHS) may have a limited future in fighter aircraft. The

More Electric Aircraft (MEA) initiative started the fighter aircraft industry moving in the

direction of eliminating the CHS by using electric actuation rather than hydraulics. State-of-the-

art (SOTA) aircraft have replaced the hydraulics on primary flight control surfaces with electric

actuators and motors. Ultimately, the CHS will likely be eliminated from future fighter aircraft

for environmental reasons, reliability, maintainability, and operations and support (O & S) costs.

A traditional CHS is modeled in this thesis work, although MEA considerations are taken into

account in the electrical subsystem.

The CHS has the following characteristics: accessory gearbox driven pumps, triple

redundant hydraulic lines for flight critical loads, and a fuel/hydraulic oil heat exchanger. The

two hydraulic pumps are typically interconnected by power take-offs from the accessory drive

gearbox. The following hydraulic power consumers on the fighter aircraft have been modeled in

the CHS model: ailerons, tail (assume fully moveable), rudder, and landing gear. An example of

a CHS layout is shown in Figure 3.11.

3.8.1 CHS Thermodynamic Model

The CHS thermodynamic model includes sizing the actuators, pumps, and estimating the

flow required by the non-flight critical subsystems that are hydraulically actuated. Sizing the

86

hydraulic actuators requires an estimate of the flight control surface and rudder areas as well as

the landing gear weight and drag. A high-resolution sizing of the flight control surfaces would

require a dynamic analysis of the aircraft as well as roll characteristics and even possibly wind

tunnel testing. Obviously, that level of detail is not feasible for a conceptual design study such

as the present one. Thus, currently built aircraft were studied for aileron and rudder sizing

estimations and corresponding control surface sizing. Main and nose landing gear specifications

were also estimated to determine actuator sizing.

The flight control actuator sizing must be sized by the most constrained mission segment

to ensure that the flight control surfaces can operate properly throughout the mission. In this

case, the maximum opposing force to the flight control surfaces is when the aircraft is flying at

the highest dynamic pressure. The actuator flow estimation and sizing equations are shown in

Table 3.25.

Table 3.25 Actuator flow estimation calculations.


Actuator Flow Estimation

maxF Theoretical maximum available force from an actuator (losses included)

PDF 2max 7854.0

PDFavail27.0

D Piston diameter (m)

P Pressure at the piston (N/m2)

availF Force available (approximate)

Flight Controls

High Lift Devices

Landing Gear

Braking

Cargo Bay

Hydraulic Reservoirs

Gearbox Driven Pumps

Electric Pump

Valve

Figure 3.11 Notional central hydraulics subsystem layout (simplified).

87


Q Flow rate into the piston (m3/s)

act

actcyl

VD

Q

VAQ

*4

*

2

where

reqFF max

actV Velocity of the actuator (m/s)

cylA Area of the cylinder (m2)

Actuator Design

reqF Max force on the actuator

CSLareq AqCF ** max

2max 2

1VMAXq

aLaC *2

maxq Maximum dynamic pressure encountered by the aircraft

CSA Surface area of the control surface

LaC Coefficient of lift for a flat plate (simple)

a Angle of the control surface to the freestream (radians)

Although, as stated above, the actuators must be sized for the highest load they

encounter, the pump sizing method is somewhat different. The CHS pumps are sized to the

highest flow required at the lowest RPM. This design point usually occurs during landing, when

the engine is at a relatively low operating speed and many hydraulic functions are taking place

such as extending the landing gear, extending the flaps, deploying the slats, etc. Thus, the main

gear and nose gear are sized for the aircraft, and the total flow rates required estimated.

The actuator sizing for the flight control surfaces determine the flow rates and little

deviation from the design flow rate is observed even at a lower opposing force (lower dynamic

pressure). When the flow rate is known for the highest flow rate mission segment, the pump can

be sized to that flow rate and pressure requirement. A side effect of traditional hydraulic pump

sizing is that the pump is generally oversized in high engine RPM situations which sacrifices

pump operating efficiency. However, if an electrically powered pump were used instead of the

shaft-driven pump, this disadvantage would be removed.

Now, as to the working fluid, the hydraulic oil must be cooled due to heat generated by

friction in the actuators and hydraulic lines. The hydraulic oil is cooled via a fuel/hydraulic oil

heat exchanger. Similarly to the OLS, the heat exchanger weight is accounted to the FLS and is

not included in the CHS. The CHS heating load equations are given in Table 3.26. Note that the

equation units are listed in Table 3.26 because the constant in the heating load equation is not for

a general case.

88

Table 3.26 Central hydraulic subsystem heating load equations (Majumar, 2003).


Heating Load Estimation

CHSE Heating load on CHS heat exchanger (kW)

CHSCHS PQE 1*10*966.38 5 Q Flow rate of oil (gpm)

P System pressure (psi)

CHS System efficiency

in

outCHS W

W

where

actactout VFW

PQWin

outW Actuator work required

actF Force required in the actuator

actV Velocity required from actuator

inW Work supplied to actuator

For the CHS model, the system pressure is set to 4000 psi, while the system efficiency,

, varies from 20% to nearly 90% depending on the required actuator power and the power

supplied to the actuator. The actuator equations are presented in more detail in Section 3.10.

The exergy model for the CHS is detailed in the following section.

3.8.2 CHS Exergy Model

The CHS destroys exergy due to irreversibilities in the heat exchanger, actuator

inefficiencies, frictional losses in the hydraulic lines, and inefficiencies in the hydraulic pumps

and motors. The exergy destruction equations are given in Table 3.27. Note that the frictional

Table 3.27 CHS subsystem exergy destruction equations (Bejan, 1996).


Exergy Destroyed

genS Entropy generation rate

inpgen T*

Pm

T

Tln*cmS

1

2 for:

inp T*c*P

0TSxE genCHS

1

1

midealactualPump PQWWxE

CHSxE Exergy destruction rate

Fluid density

0T Dead state temperature


m Mechanical efficiency of the pump

PumpxE Exergy destruction rate due to pump irreversibilities

losses in the hydraulic lines are the cause of exergy destruction as well. Thus, the hydraulic lines

are sized to permit no more than a 25% pressure drop from the pump to the actuator in full-flow

conditions.

89

Finally, CHS power takeoff requirement is a small contributor to the total engine power

takeoff term, (see Table 3.12). More important in this sense is the electrical subsystem (ES),

which is responsible for the majority of the shaft power required from the PS. The ES is, thus,

detailed next.

3.9 Electrical Subsystem

Aircraft ESs have been a subject of much research recently. The main reason is the More

Electric Aircraft (MEA) program started by the Air Force in 1991 (Pearson, 1998; Weimer,

2003; Cloyd, 1997; Moir, 1999). The goal of the program was to transition currently built and

future aircraft away from traditional shaft-powered subsystems and towards electrically powered

ones. The MEA program required a more reliable, higher output, and more survivable electrical

power generation and distribution subsystem.

The ES model is based on MEA considerations as well as on a second program focused

on the power distribution subsystem called the Power Management and Distribution System for a

More Electric Aircraft (MADMEL). Northrup Grumman built a demonstrator of the

technologies developed under this program, and the ES components sized in this thesis are based

on the MADMEL demonstrator.

The model that is used here is patterned after the F-35 in that it employs two integrated

270 VDC starter/generators (IS/Gs) and an integrated power unit (IPU). The main generators are

switched reluctance machines (SRMs) with multiple channels, each of which are supported by a

channel (non-electrically isolated) SRM (Elbuluk and Kankam, 1996). Switched reluctance

machines are chosen due to high power densities and advantages in reliability and fault

tolerances compared to synchronous and induction machines. The power requirements are set up

to model an aircraft that has electro-hydrostatic or electro-mechanical actuators (EHA or EMA,

respectively) since industry seems to be moving in that direction. The 270 VDC generation is

claimed to have better efficiency than previously built aircraft generators as well as being

required for high powered/high voltage flight control actuators. 5 The power distribution

subsystem includes 28 VDC and 115 AC converters. The battery weight and chargers is also

included in the ES weight. A simplified schematic of the ES is shown in Figure 3.12.

5 Raymer (1999) states that an F-16 sized plane with electrically powered flight control actuators requires about 80

kW of additional power generation capacity.

90

minimum of three phases. The IPU is also an SRM; however, it is a three-phase, two-

This thesis work involved performing a small survey of currently built aircraft and their

power generation capabilities to establish an MEA-based power generation capacity for the

aircraft. Notably the F/A-18, F-22, F-16, F-35 and Eurofighter Typhoon were studied to

establish generating capacity guidelines. The power generation capacity was correlated to the

gross takeoff weight of the aircraft. The fighter aircraft previously built have lower electrical

loads than the newer models because traditional aircraft have more mechanically actuated

subsystems. For example, the Eurofighter Typhoon has an empty weight of approximately

11,000 kg and has two 30 kVA generators supplying 115/200 VAC, 400 HZ, three-phase power.

The weight-to-power-generation ratio for the Typhoon is 5.5 VA/kg6, which is significantly

lower than the MEA based F-22 and F-35 which are approximately 9.7 W/kg and 8.3 W/kg,

respectively. The guidelines developed for ES generating capacity and component weights are

shown in Table 3.28. The weight equation for the electrical subsystem may be found in Section

3.2.4.

6 VA (volt-amperes) is a measure of alternating current (AC) power, while W is a measure of direct current (DC)

power. For the purposes of this work, the AC power is considered to have a power factor of near unity which makes the units of VA nearly equivalent to W. This allows a direct comparison between the weight-to-power-generation ratios with a VA or W rating.

270 VDC BUS #1 270 VDC BUS #2

270 VDC Integrated

Starter/Generators

DC/AC Converter

DC/DC Converter

115 VAC BUS 270 VDC BUS 28 VDC BUS

DC/DC Converter

DC/AC Converter

115 VAC BUS270 VDC BUS 28 VDC BUS

Power Distribution Centers (PDCs)

IS/G #1

IS/G#2

IPU

Batteries

Figure 3.12 Notional electrical subsystem schematic (simplified).

91

Table 3.28 Fighter aircraft power generation/empty weight estimate.


Non-MEA Aircraft Power Generation

tradkWR _ Estimated system electrical power generation capacity for a non-MEA aircraft (kW) EtradkW WR *2.6_

EW Empty aircraft weight (kg)

MEA Aircraft Power Generation mea_kWR

Estimated system electrical power generation capacity for an MEA aircraft (kW)

Emea_kW W*.R 38

3.9.1 ES Thermodynamic Model

The ES requires shaft power from the PS and cooling from the VC/PAOS. The power

takeoff (or power extraction) from the low pressure spool of the PS is simply the amount of shaft

power required by the generators for a given mission segment. The generating efficiency is set

to 85%, and the power takeoff equations are shown in Table 3.29.

Table 3.29 Electrical subsystem generator work.


Electrical Subsystem Work

ES_TOP Power takeoff required for electrical subsystem

g

genoutESTO

WP

_

_

genoutW _

Electrical work rate required for a given mission segment

g Generator efficiency

Some of the ES components must be cooled to avoid overheating. The main generators

and components are designed to be cooled by the VC/PAO subsystem. Note that the subsystem

would be designed to route PAO through various heatsinks and hot areas in the electrical

components rather than through a heat exchanger. Table 3.30 gives the heating load equations

from the generators and the ES components. The transmission lines generally do not require

active cooling because they are oversized to handle current spikes.

Table 3.30 ES heating load model equations.


Generator Heating Load

genESPAOQ _/

Cooling load on the PAO loop from the ES generators

sThm

STWT

TQ

dt

STUdirrs

kk

o

0

001

For steady state, no heat interactions and no mass interactions:

irrESTOgenout STPW 0__0

thus

genoutW _ Electrical work rate required for

a given mission segment

ES_TOP Power Take-off required for the ES


0T Ambient Temperature

92


genirrS _

Entropy generated in the generators

genoutESTOirr WPST __0

From an entropy balance, the entropy that must be removed from the component is as follows:

genirrgenESPAO

ST

Q_

0

_/

Component Heating Load

cinW _

Electrical work rate entering a component coutcincirr WWST ___0

Similarly to the generators, the entropy that must be removed in a heat interaction from the component is as follows:

cirrcESPAO

ST

Q_

0

_/

coutW _ Electrical work rate leaving a

component

cirrS _

Entropy generated in a component

cESPAOQ _/ Cooling load on the PAO loop

from the ES components

Note that the heating load in both the generators and components is the exergy

destruction rate, which is the ambient temperature multiplied by the entropy generation rate in

that component. This makes sense because the components are converting some form of

electrical energy into another with no planned heat interactions. If the components were 100%

efficient, the energy balance would indicate no active component cooling is required; however,

real components are obviously less than 100% efficient.

3.9.2 ES Exergy Model

The exergy destroyed in the ES is primarily due to power generation and component

losses. The three main components are as follows:

Generators;

Other electrical components (inverters, converters, ELMCs, etc.); and

Transmission lines (ohmic heat loss).

The equations for the ES exergy destruction are shown in Table 3.31. We now conclude with the

final subsystem, i.e. that for flight control.

Table 3.31 ES exergy destruction model equations.


Exergy Destroyed in the ES Components

irrS Entropy generation rate

irre_in

e_outkk

ST)W

W(QT

T

dt

)STU(d

0

00 1

For steady state and no heat interaction:

irreoutein STWW 0__0

thus

0T Ambient temperature

cESxE _ Exergy destruction rate for a

component

e_inW Electrical work rate into the component

93

e_outW Electrical work rate out of the component

eouteinirrcES WWSTxE __0_

e_inclostc_ES W)(WxE 1

c Component efficiency

Exergy Destroyed in the ES Generators

genESxE _ Exergy destroyed in the generators

ES_TOggen_out PW

gen_outES_TOgengen_ES WPSTxE 0

ES_TOP Power takeoff required for the ES

gen_outW Work rate leaving the generators


Exergy Destroyed in the Lines

transESxE _

Exergy destruction rate due to transmission losses (Elgerd, 1998)

RixE transES2

_

A

lR

i Current in the line

R Total resistance of the line Resistivity of the transmission line

A Cross sectional area of the line

l Length of the conductor

Total Exergy Destruction in the ES

ESxE Rate of exergy destruction in the ES transESgenEScESES xExExExE ___

3.10 Flight Controls Subsystem

The flight controls subsystem (FCS) consists of the actuators required to operate the

flight control surfaces as well as the control hardware associated with the actuators. The two

main types of flight control actuators that are discussed here are the traditional hydraulic

actuators and electro-mechanical/hydraulic actuators. Having one type of actuator or the other

changes many items on an aircraft. For example, traditional hydraulic actuators require a central

hydraulic subsystem (CHS) including accessory gearbox driven hydraulic pumps, triple

redundant hydraulic lines, emergency hydraulic power subsystems, a hydraulic oil reservoir, etc.

Electro-mechanical/hydraulic style actuators are localized, meaning they are installed as a single,

easily-replaceable unit that locally houses its own oil (if electro-hydraulic) or gear system

(electro-mechanical) and has no other dependence on the rest of the aircraft except for a power

connection and control connections. Electrically powered actuation devices (EPAD) have been

tested in currently built fighter aircraft and are being used on production aircraft as well.

94

3.10.1 FCS Thermodynamic Model

The FCS weight must be estimated for this model. The equation in Table 3.32 is based

on previously built fighter aircraft and requires the number of hydraulic functions, the number of

mechanical functions, the total area of the control surfaces, and the yawing moment of inertia of

the aircraft. After the weight of the FCS has been estimated, it must be included in the empty

weight of the aircraft.

Table 3.32 Flight controls subsystem weight equations (Raymer, 2006).


Flight Controls Subsystem Weight

FCSW Weight of flight controls subsystem (kg)

127.0484.0489.0003.028.36 cscsFCS NNSMW

M Mach number

csS Total area of control surfaces (ft2)

sN Number of flight control surfaces

cN Number of crew

The actuator sizing was detailed in the CHS model so it will not be repeated here.

However, the power required by the actuators must be estimated to determine the CHS system

efficiency (see Table 3.26). The actuator power model equations are shown in Table 3.33. Note

that Majumdar (2003) states that a well designed actuator should have a range of losses from 2%

to no more than 8%. Also note that the larger diameter piston cylinders generally have lower

loss percentages because the break-away force and frictional forces are small compared to the

force being applied to the piston.

Table 3.33 FCS actuator electrical power and fluid power requirements.


Actuator Electrical and Fluid Power

elecP Electrical power Required

t

dFP

PP

actact

act

actelec

*

actP Actual power required to

move the load (no losses)

act Actuator Efficiency act 92-98%

fluidP Fluid power supplied to the actuator15 QPPfluid *

Q Flow rate of hydraulic fluid

3.10.2 FCS Exergy Model

The FCS destroys exergy due to inefficiencies in the actuators alone, since the other

losses will be attributed to the AFS-A (drag), ES (if electrically powered actuators), or CHS (if

95

fluid powered actuators). The exergy destroyed is, thus, simply the power supplied to the

actuator, minus the actual power translated to the flight control surface by the actuator. The

exergy destruction equations are given in Table 3.34.

Table 3.34 FCS exergy destruction equations.


Exergy Destruction rate in the FCS

FCSxE Exergy Destroyed

1

1

actreqFCS WxE

reqW Work rate required by actuator

The subsystem models included in the AAF have now been discussed. The following

chapter details the system synthesis/design, problem definition, and solution approach taken for

this thesis work.

96

Chapter 4

Large-scale System Synthesis/Design Optimization Problem

Definition and Solution Approach

This chapter discusses the optimization problem definition, optimization decision

variables and limits, subsystem integration, a decomposition approach called iterative local

global optimization (ILGO), the solution approach, and the iSCRIPT™ engineering

modeling/optimization software as applied to the fighter aircraft system.

4.1 AAF Aircraft System Synthesis/Design Optimization Problem

The fighter aircraft system consists of subsystems that are very tightly coupled in that one

subsystem can affect the other subsystem operation and/or design significantly by changing a

single design or operational decision variable. The nine subsystems modeled all play a role in

the optimization. However, some such as the ES, FCS, and CHS do so via a set of system-level

degrees of freedom (DOF) called coupling functions, while the remaining subsystems do so visa

vie both a set of coupling functions and a set of local (subsystem specific) decision variables.

The former subsystems, thus, in effect participate only passively in the optimization since they

have no local decision variables but nonetheless still alter their configurations, sizes, and energy

consumption since these are dependent on the aircraft geometry (e.g., the CHS and FCS) and

aircraft size (e.g., the ES). The interdependence of the subsystems is further illustrated by

considering the PS and ECS. The ECS is dependent on the PS bleed port air properties in that

any operational or design change in the PS requires a subsequent change in the ECS operational

decision variables. Also, any change in the requirement of bleed air in the ECS changes the

specific thrust of the PS and, thus, the overall aircraft performance.

The optimization problem presented by the fighter aircraft requires large-scale

optimization methods to handle the size of the problem. The objectives listed in Chapter 1 are

accomplished by performing the following optimizations:

Perform an optimization of the entire aircraft consisting of 9 subsystems with a

morphing-wing AFS-A and with exergy destruction and exergy fuel loss

minimization as the objective;

97

Perform an optimization of the PS and fixed-wing AFS-A with fuel burned

minimization as the objective;

Perform an optimization of the PS and morphing-wing AFS-A with fuel burned

minimization as the objective, make a comparison to the fixed-wing results and

distinguish this work from that of Butt (2005);

Perform a parametric analysis on the morphing AFS-A based on minimum fuel

burned; and

Perform a parametric analysis on the morphing AFS-A based on minimum exergy

destruction and perform analysis between minimum fuel burned results and minimum

exergy destruction results.

For the purposes of the large-scale optimizations affected in this research, a decomposition

strategy is used. It is described in the following sections. However, before giving this

description, the system-level optimization problem is defined in the next section.

4.1.1 System-Level Optimization Problem Definition

Three different objective functions are utilized in the definition of the system-level

optimization problem in this thesis: i) total exergy destruction plus fuel exergy lost, ii) gross

takeoff weight, and iii) fuel burned. Each is minimized with respect to a set of decision variables

and equality and inequality constraints.

Nine-Subsystem AAF Aircraft System-Level Optimization Problem

The first of the objective minimizations is expressed as a minimization of the total exergy

destruction, totaldesEx _ , plus the fuel exergy loss, lossfuelEx _ , due to unburned fuel lost out the

back end of the PS, i.e.,

Minimize

lossfuelFCSdesESdes

CHSdesOLSdesVCPAOSdes

FLSdesECSdesPSdesAFSdeslossfueltotaldes

ExExEx

ExExEx

ExExExExExEx

___

___

______

(4.1)

w.r.t YX

,

98

subject to 0/

FCS

ES

CHS

OLS

PAOSVC

FLS

ECS

PS

AAFS

h

h

h

h

h

h

h

h

h

H , 0/

FCS

ES

CHS

OLS

PAOSVC

FLS

ECS

PS

AAFS

g

g

g

g

g

g

g

g

g

G (4.2)

where the vectors X

and Y

represent the synthesis / design and operational decision variables,

respectively. The vectors of equality constraints, H

, represent the geometric and

thermodynamic models for each subsystem. The vectors of inequality constraints, G

, represent

the physical limits on the independent and dependent variables of the system.

Two-Subsystem AAF Aircraft System-Level Optimization Problem

The second objective function minimization is that of minimizing the gross takeoff

weight and is expressed as follows

Minimize PSAFSTO WWW (4.3)

w.r.t. PSPSAAFSAAFS YXYX

,,,

subject to

,0

AAFSh 0

AAFSg (4.4)

,0

PSh 0

PSg (4.5)

Where the vectors of equality constraints, AAFSh

and PSh

, represent the geometric and

thermodynamic models, and the vectors of inequality constraints, AAFSg

and PSg

, represent the

physical limits imposed on the independent and dependent variables. The third objective

function is minimized in a similar fashion and is given by

99

Minimize

n

iFueliburnedFuelburnedFuel iloss

WWW1

__ (4.6)

where n is the total number of mission segments, and i is the mission segment. Equation (4.6)

is minimized with respect to the same set of decision variables and subject to the same set of

constraints as for the previous objective. Furthermore, it can be shown that this last objective is,

in fact, equivalent to the previous one since the amount of fuel burned is directly proportional to

the gross takeoff weight of the aircraft. For this reason, only objectives one and three are used to

generate the results presented in Chapter 5.

Now having defined the system-level objective of the optimization, a discussion of the

need for decomposition in large-scale optimization is presented next.

4.1.2 Need for Decomposition

Large-scale engineering optimization problems may require decomposition techniques or

strategies in order to make the manageable or even solvable. Such techniques reduce the

problem into sub-problems. The aircraft optimization problem in this thesis work is much too

large to handle as a single problem; and thus, both physical and time decomposition strategies

are used. Physical decomposition results in a set of aircraft subsystems and boundaries, which

for the aircraft of this thesis are detailed in Chapter 3. The particular physical decomposition

technique used here is called iterative local-global optimization (ILGO) developed by Muñoz

and von Spakovsky (2001a,b, 2003) and applied to a 5-subsystem fighter by Rancruel and von

Spakovsky (2003, 2004).

Time decomposition is used to split the mission, represented by a timeframe from

mission start to mission completion, into the stationary mission segments of a quasi-stationary

description. The mission segments are defined based on the aircraft flight characteristics (e.g.

climb, cruise, loiter, accelerate, etc.) or requirements (e.g. drop a payload, fly a distance, loiter an

amount of time). Individual mission segments are modeled as steady state and transient behavior

is approximated via the quasi-stationary description. The resulting mission segments are given

in Table 3.1 of Chapter 3. Initially, every mission segment was split into 5-7 smaller segments to

increase fuel burn/gross weight calculation accuracy. However, it was found that in mission

segments with little-changing flight characteristics (e.g., loiter, cruise), a single time step gave

sufficient accuracy. Note that decreasing the number of time steps in each segment significantly

100

decreases the computational burden as well, since the aerodynamics, weight fractions, etc. are

updated for each time step within the mission segment. Now, before applying these

decomposition strategies to the system-level optimization problems, a description of ILGO is

given in the following sections.

4.2 Iterative Local-Global Optimization (ILGO) Approach

The purpose of this section is not to give a detailed discussion of ILGO since it was not

developed in this thesis work, but rather to give a top-level overview of the ILGO decomposition

strategy for large-scale optimization. The reader is referred to Muñoz and von Spakovsky

(2000a,b,c,d; 2001a,b) for details on this strategy. A basic discussion of local-global

optimization (LGO), however, must precede the discussion of ILGO since the former is the basis

for most if not all of the physical decomposition strategies found in the literature. In the process,

the differences between LGO and ILGO are highlighted and the uniqueness of the ILGO

approach revealed.

4.2.1 Local-Global Optimization (LGO)

Section 2.3 of Chapter 2 discusses the existence / requirement of the ORS (see Figure 2.7)

in the LGO approach and also the computational burden required to explicitly or implicitly

generate the ORS for a problem of any magnitude. For further explanation, consider the

following system problem that has been decomposed into two subsystems or units as shown in

Figure 4.1. The vectors 1Z

and 2Z

are the so-called local-level decision (i.e., independent)

variables for each unit and the arrows between the two units are represented by vectors of the

functions, 12u

and 21u

, that couple the two units.

Figure 4.1 Physical decomposition of a 2-unit system.

1Z 2Z

21

12

u

u

2R 1R

101

The system-level objective function, C , is expressed as a sum of the unit-contributions,

i.e., 21 CC . Each of the unit contributions to the system-level objective function has a set of

terms that define the unit contribution. For example, for the first unit, one might have that

1111 capitalCRkC (4.7)

In equation (4.7), 1R is an external resource used by unit 1 (e.g., fuel or power) and 1capitalC is a

function related to the size of the unit (e.g., weight/volume or cost) while 1k is a conversion

factor.

For each of the units, the coupling functions bring resources from the other unit

depending on the needs of the receiving unit. The amount of these resources and the external

ones depend on the values of the decision variables of the coupled units. So, looking only at the

contribution of the first unit to the system-level objective function, C , the following expression

is written:

1212121121111 1,,,,,, ZCZZZuZZZuZRkC capitalsyssys

(4.8)

where 1capitalC is, for example, the capital cost in a thermoeconomic problem and sysZ

the set of

system-level decision (i.e., independent) variables which cannot be assigned strictly locally, i.e.,

to one unit only. In thermodynamic problems, this term is either ignored as is done in a

stationary system problem or is converted into a physical term such as weight for a non-

stationary system problem. The reader is referred to the Evans-El-Sayed formalism for more

information about thermoeconomics in the context of decomposition (Evans and El-Sayed,

1970).

Considering both units with the system-level optimization problem is as follows:

Minimize

221212112222

121212112111

2

1

,,,,,,

,,,,,,

ZCZZZuZZZuZRk

ZCZZZuZZZuZRkC

capitalsyssys

capitalsyssys

(4.9)

w.r.t. sysZZZ

,, 21

subject to the primary constraints

02

1

h

hH (4.10)

102

02

1

g

gG (4.11)

and to the secondary constraints

0,, 2112

sysZZZu (4.12)

0,, 2121

sysZZZu (4.13)

where the vectors of equality constraints, H

, represent the physical and thermodynamic models

for each subsystem. The vectors of inequality constraints, G

, represent the physical limits on

the independent and dependent variables associated with each unit in the system. Equations 4.12

and 4.13 indicate that the coupling functions take on the values

and

constrained by the

following two expressions:

maxmin 1212 uu

(4.14)

maxmin 2121 uu

(4.15)

Problem (4.9) can be physically and mathematically decomposed into a set of two subproblems

which must be repeatedly solved for different values of

and

constrained within the limits

set by expressions (4.14) and (4.15). The two subproblems are, thus, expressed as

Subproblem 1:

Minimize 11111 1,, ZCZRkC capital

(4.16)

w.r.t. 1Z

subject to 01

h (4.17)

01

g (4.18)

Subproblem 2:

Minimize 22222 2,, ZCZRkC capital

(4.19)

w.r.t. 2Z

subject to 02

h (4.20)

02

g (4.21)

Note that for a subproblem, either

is fixed for a given optimization and

is calculated (i.e., a

result of the subproblem optimization) or vise versa. For example, in the case of subproblem 2,

if

is fixed for subproblem 1, then it must be calculated in subproblem 2; conversely, if

is

103

fixed for subproblem 1, then it must be calculated in subproblem 2. Also, note that the repeated

optimizations required of subproblems 1 and 2 in effect result in a set of nested optimizations for

which the inner part of the nest is comprised of the set of subproblem optimizations and the outer

part of the nest of a single system-level optimization with the

and

as decision variables.

Thus, the LGO decomposition results in a multi-level optimization which reduces an

overall system-level problem into a set of smaller subsystem problems which in theory should be

easier to solve. In fact, for large-scale system optimization problems involving many degrees of

freedom and non-linearities, such a multi-level approach may be the only way to arrive at a

solution. However, it introduces an additional computational burden due to the nesting. This

may become so large that it renders the problem unsolvable at least from a practical standpoint.

The multi-level optimization resulting from the application of LGO to the two-unit system of

Figure 4.1 is illustrated in Figure 4.2.

Figure 4.2 Multi-level optimization resulting in a set of nested optimizations.

Note that in this figure, there are a total of three optimization loops shown: one each for units 1

and 2 as well as a third at the system-level. Multi-level optimization requires a new unit-level

optimization for each iteration (i.e., completion) of the system-level optimization loop. As

already mentioned, such nesting can become very computationally burdensome. ILGO was

Unit- system

interactions

System-level optimization

Unit-level optimizations

System - optimizer

Simulations

Unit 1 Unit 2

104

specifically developed to address this difficulty. The following section gives an overview of this

approach.

4.2.2 ILGO Approach

Iterative local-global optimization (ILGO) is a decomposition strategy for large-scale

optimization developed by Muñoz and von Spakovsky (2000a,b,c,d; 2001a,b) which eliminates

the need for nested optimizations found with LGO. It not only reduces the computational burden

of multi-level optimization but also allows the optimal decentralized development of aircraft

subsystems in the context of an overall system-level optimization.

ILGO eliminates the nesting of LGO by embedding at the unit-level the system-level

information found in the outer loop of the LGO optimization. In doing so, the outer optimization

loop is no longer needed since it is implicitly present at the unit-level. The embeddiong is

accomplished via a set of coupling functions and a set of associated “shadow prices”. The

coupling functions are simply the unit-level or subsystem-level interactions required as inputs or

outputs by each physical unit. These functions, thus, “couple” or integrate the unit-level

problems with each other. Figure 4.3 shows an example of a simple three unit system with

2112 ,uu

unit 2 and unit 1 interactions

3113,uu


3223,uu


Figure 4.3 An example of three subsystems and their associated coupling functions.

coupling functions. The functions’ associated shadow prices measure changes in the optimal

values of the local (unit-level) functions with respect to changes in the coupling functions. The

shadow prices allow the decomposed optimizations to progress along the system-level ORS in

the direction of the system-level optimal solution. Furthermore, the unit-level objective

functions used by LGO are morphed into system-level unit-base objective functions in ILGO.

For example, the unit-level objective functions (equations (4.16) and (4.19)) of the two-unit

3113,uu

3223,uu

2112 ,uu

Unit 2

Unit 1

Unit 3

105

system depicted in Figure 4.1 are transformed into system-level unit-base objective functions as

follows:

)1(210

221

)1(120

2120

*211' uuCCC (4.22)

)2(210

121

)2(120

1120

*122 ' uuCCC (4.23)

where the last here terms in each of these equations are 1st order Taylor Series expansions about

some reference point “o” on the ORS relative to changes of the coupling functions 12u and 21u

with respect to unit 1 (equation (4.22)) or unit 2 (equation (4.24)), respectively. The s' in these

equations are the partial derivatives associated with these expansions. They are, in fact, the

shadow prices. Note that for purposes of simplification, the vectors 12u

and 21u

in equations

(4.16) and (4.19) have been assumed to contain only a single coupling function each (i.e. 12u or

21u ). As should be evident, optimizing equations (4.22) or (4.23) in effect optimizes not only

the local objective (equation (4.16) or (4.19)) of each unit but each unit’s system-level effects via

the additional terms appearing in equations (4.22) and (4.23). Thus, each local optimization not

only optimizes the unit but also optimizes the system as a whole. For more details of the ILGO

formalism, the reader is referred to Muñoz and von Spakovsky (2000a,b,c,d; 2001a,b), Rancruel

(2002, 2005), and Rancruel and von Spakovsky (2005, 2006).

To understand how the process of optimization with ILGO proceeds, a notional flow

diagram is given in Figure 4.5. As with Figure 4.2, there are two units participating in the

optimization. The key differences with ILGO are no system-level simulations required and the

outer loop optimization has been eliminated. Each system-level, unit-based optimization results

in a new set of shadow price and coupling function values which are then used in a new ILGO

iteration unless convergence has been reached. Based on past experience, the number of

iterations required for convergence for even complex systems is less than six or seven.

In the following sections, the ILGO decomposition is applied to the AAF aircraft

optimization problem which is the subject of this thesis.

106

4.3 System-Level, Unit-Based Synthesis/Design Optimization Problem Definitions

Section 4.1 defines the system-level optimization problem. The following sections define

the system-level, unit-based synthesis/design optimization problems for each subsystem starting

with the AFS-A. However, the subsystem integration and coupling functions for the AAF fighter

are defined first in the next section.

4.3.1 Subsystem Integration and Coupling Functions

Subsystem integration is necessary for the overall system optimum synthesis/design to be

found. Subsystem integration, in a programming sense, requires subsystem interactions to be

defined explicitly between the subsystem models. In the context of the fighter aircraft system,

subsystem integration is a very involved process due to the number of subsystem interactions

present. An additional difficulty is added to the integration process when a subsystem has a two

– way interaction (e.g., a heating interaction between two subsystems) since this may involve a

pinch temperature difference constraint that affects both subsystems.

Unit-level optimizations

New ILGO Iteration

- optimizer Decomposition

(define subsystem boundaries, coupling)

System-level information is sent to the system-level unit-base subproblems

(shadow prices, coupling function changes)

System-level, unit-based optimization results

ILGO Start

Unit 1 Unit 2

Convergence

Figure 4.4 Notional flow diagram of the application of the ILGO decomposition strategy to the two-unit system of Figure 4.2.

107

While a subsystem interaction is simply an operating parameter (e.g., bleed air

temperature) or a design parameter (e.g., subsystem weight) required by one subsystem from

another, applying the ILGO decomposition to a system requires that the subsystem interaction

not be treated as a real-time interaction as it would in an overall system simulation, but rather as

an independent variable or fixed parameter during a local or unit-level optimization. The

interactions are updated after each ILGO iteration to effectively maintain the subsystem

interactions despite the de-coupled local optimizations. The subsystem interactions are, thus,

called “coupling functions” within the context of ILGO as they are not to be confused with the

subsystem interactions as found in the LGO decomposition which are maintained in real time

and result in the multi-level optimizations of the LGO approach. The reader is referred to the

work of Muñoz and von Spakovsky (2000a,b,c,d; 2001a,b), Rancruel (2002, 2005), and Rancruel

and von Spakovsky (2005, 2006) for details on coupling functions and the updating methods.

The AAF aircraft system of this thesis has numerous subsystem interactions and each

subsystem is highly dependent on the other subsystems for both design and operational

considerations. The fighter aircraft subsystem interactions are shown in Figure 4.5 with an

explanation of the main interactions following the figure. Figure 4.5 does not give a

comprehensive list of all of the subsystem interactions; however, Figure 4.5 does clearly

illustrate the interdependence and tight coupling of the aircraft subsystems. A comprehensive

list of all coupling functions is not given here because of the very large number involved, i.e.

488. However, the number associated with each subsystem is given in Table 4.1 where for the

Table 4.1 Number of coupling functions associated with each subsystem.

Subsystem Input (fixed within

subsystem) coupling functions

Output (variable within subsystem) coupling

functions

AFS-A 88 88

PS 115 162

ECS 93 72

VC/PAOS 50 41

FLS 94 41

ES 6 21

FCS 6 1

CHS 6 41

OLS 30 21

Totals 488 488

108

application of ILGO used here the input coupling function and associated shadow price values

are assumed fixed in any given ILGO iteration while the output coupling function and shadow

price values are determined by each subsystem optimization in a given ILGO iteration.

Interaction

2112 ,uu

Uninstalled thrust, OLS power takeoff

3223,uu

Bleed air properties, bleed air mass flow required

4224 ,uu

Fuel flow rate required, FLS power takeoff

62u

ES power takeoff

5115 ,uu

OLS weight, mission segment time

5445,uu

FLS weight, drag, ram air properties, mission segment time

5225,uu

PS weight, drag, AFS-A thrust required, specific fuel consumption, mission segment time

6556 ,uu

ES weight, TOW , mission segment time

5335,uu

ECS weight, drag, ram air properties, mission segment time

9339 ,uu

Bleed air/PAO heat exchanger properties

7557 ,uu

CHS weight, mission segment time

8778,uu

Control surface sizing, hydraulic oil flow rate required

8558 ,uu

FCS weight, aircraft wing and tail geometry, mission segment time, flight conditions

9559 ,uu

VC/PAOS weight, drag, ram air properties, mission segment time

Figure 4.5 Aircraft subsystem interactions and coupling functions.

Note that each of the subsystem connections in Figure 4.1 has a two way arrow which

indicates that there is a coupling function vector for each direction of the interaction. The one

exception is the interaction between the ES and PS, 62u

, which represents the shaft power

takeoff (i.e. power extraction from the low pressure turbine), ,TOP required from the PS to

generate power for the aircraft. There is no interaction required by the PS from the ES.

2. PS

PSPS

PSPS

GH

YX

,

,

5. AFS

AFSAFS

AFSAFS

GH

YX

,

,

3. ECS

ECSECS

ECSECS

GH

YX

,

, 4. FLS

FLSFLS

FLSFLS

GH

YX

,

,

9. VC/PAOS

VCPAOSVCPAOS

VCPAOSVCPAOS

GH

YX

,

,

6. ES

ESES GH

,

1. OLS

OLSOLS

OLSOLS

GH

YX

,

,

8. FCS

FCSFCS GH

,

7. CHS

CHSCHS GH

,

5115 ,uu

8778,uu

8558 ,uu

12u

2112 ,uu

3223,uu

9339 ,uu

5225,uu

5335 ,uu

9559 ,uu

62u

5445,uu

4224,uu

6556 ,uu

7557 ,uu

109

The subsystem interactions are now briefly discussed starting with the AFS-A. Every

aircraft subsystem has a weight associated with it, and each subsystem weight must be defined as

a coupling function to the AFS-A. In addition, the AFS-A requires a certain amount of thrust to

fly the aircraft as well as specific fuel consumption, ,sfc rates for the corresponding thrust.

Thus, both the thrust required and the corresponding sfc are interactions with the PS. Also, the

subsystems that are associated with inlet ducts (i.e., the ECS, FLS, and VC/PAOS) have

momentum drag associated with the inlet / exit ducts and these drag values are an interaction

with the AFS-A as well. An additional AFS-A subsystem interaction results from the wing

geometry of the AFS-A and the FCS. The wing geometry is used as a basis for estimating

control surface sizing in the FCS. Note that the morphing-wing AFS-A wing geometry that is

used to size the FCS is the same geometry as used for establishing the wing weight (see

subsection 3.2.5).

The PS is the next most highly integrated and interdependent subsystem. The PS requires

power takeoff (or power extraction from the low-pressure spool), ,TOP values from the OLS, ES,

FLS, CHS, and VCPAOS (the CHS and VCPAOS power takeoff interactions with the PS are not

shown in Figure 4.1). The ECS requires bleed air temperature and pressure from both the high

and low pressure bleed ports of the PS. In addition, the ECS specifies the bleed air mass flow

rate required from the PS, which affects the total performance of the PS depending on the mass

flow rate required and which bleed port is selected by the ECS. The OLS requires uninstalled

thrust values from the PS to estimate the heating load on the FLS/OLS heat exchanger. The PS

also outputs the sfc for each mission segment to the FLS (and to the previously mentioned AFS-

A).

The VC/PAOS interfaces with the ECS via the bleed air / polyalphaolefin (PAO) heat

exchanger. The PAO temperature and heat exchanger physical geometry are all coupling

functions between the ECS and VC/PAOS. The model and ILGO decomposition was initially

set up to only have a heat interaction as a coupling function, but the optimization then created a

thermodynamically impossible heat exchanger (i.e., the exit temperature of the bleed air side or

“hot side” of the heat exchanger was significantly lower than the PAO side or “cold side” exit

temperature). The thermodynamic characteristics of the heat exchanger, thus, had to be “owned”

by one of the unit-level optimizations to avoid this scenario. Consequently, the bleed air/PAO

110

heat exchanger geometry is sized in the ECS code, while the heat exchanger weight and exergy

destruction is accounted to the VC/PAOS.

The interdependence of the subsystems can be seen very easily when one observes the

effects on the rest of the aircraft of changing one subsystem parameter. For example, if the

weight of a subsystem increases 100 kg, the aircraft requires more lift during cruise, more thrust

during acceleration, and subsequently more fuel. Also, if the increased weight is due to a

subsystem requiring additional cooling (e.g., additional power generating capacity in the ES

increases the subsystem weight and cooling requirements), then the VC/PAOS is affected and

perhaps even the ECS ram air inlet duct sizing, etc. Needless to say, if one item on an aircraft is

changed significantly, it generally requires a synthesis / design or operational change in many

other subsystems on the aircraft due to the high level of integration in such systems. This effect

is even more pronounced if the aircraft is being optimized to find the best synthesis/design and if

“over designing” a subsystem is not an acceptable solution.

Having outlined and discussed the coupling functions for the AAF aircraft system and its

subsystems, the optimization decision variables and their associated variable constraints are

discussed next.

4.3.2 AFS-A System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition

The AFS-A synthesis/design and operational decision variables are presented in Section

4.4 as are the variable inequality constraints, which are based on typical fighter aircraft

configurations (Raymer, 2002) and previous work done in fighter aircraft optimization

(Periannan, 2004; Rancruel, 2005; Butt, 2005; Smith et al. 2007). The system-level objectives

that used for the AFS-A in this thesis work are minimizing the exergy destruction plus exergy

loss due to unburned fuel exiting the rear of the PS and minimizing the fuel burned. Both are

determined with respect to the entire mission.

Now, it is only for the former system level objective, which is used for the nine-

subsystem AAF aircraft system optimization, that the ILGO decomposition strategy is used.

Thus, a set of system-level unit-base optimization problems for the nine-subsystems must be

determined as described in Section 4.2. That for the AFS-A is as follows:

111

AFS-A System-Level, Unit-Based Exergy Destruction Optimization Problem

Minimize

n

iireqireqTiisfciousij

iousiju

j iAltM

j iiit

j

n

iijij

Dj

jjWFCSdes

CHSdesESdesOLSdesPAOSVCdes

FLSdesECSdesPSdesAAFSdesAAFSdes

Tsfcu

AltMt

DWEx

ExExExEx

ExExExExEx

1varvar

3

1

5

1,

6

1

5

1

4

1 1

8

1

*

****/

***

,

'

(4.24)

w.r.t. AAFSAAFS YX

,

subject to

0

AAFSh (4.25)

0

AAFSg (4.26)

where the vector of equality constraints, AAFSh

, represents the aerodynamic and geometric

model of the AFS-A and the vector of inequality constraints, AAFSg

, the physical limits

imposed on the subsystem. The superscript “*” indicates the optimum value from the previous

ILGO iteration of a given subsystem objective function.

Problem (4.24) represents the system-level minimization resulting from varying the AFS-

A (or local) decision variables only. The local or unit-based objective function is denoted by

AAFSdesEx

and the expression for the system-level, unit-based objective function, AAFSdesEx

' ,

includes products of paired shadow prices and associated coupling functions. As to the shadow

prices given in problem (4.24), the first summation represents the subsystem weights, the first

double summation term represents the drag of the inlet ducts (one term for each mission segment

for the ECS, FLS, and VC/PAOS), the double summation term represents the time for the

mission segments that are functions of the mission decision variables (i.e., the mission segment

112

time is determined by ,1BCM ,2BCM ,BCLM etc.), the next double summation is for the three

subsystems that require the mission decision variable values from the AFS-A (i.e., the PS, ECS,

and FLS), the next coupling function represents the miscellaneous AFS-A coupling functions not

listed here, and the last summation couples the AFS-A and the PS with the thrust required and

fuel consumption rate. All told, the AFS-A has 88 input and 88 output shadow prices (see

Section 4.3.1). The shadow prices for the coupling functions given in Problem (4.24) are defined

as

8

1

*

j j

jdes

jW W

Ex (4.27)

3

1 1

*

j

n

i ij

jdes

ijD D

Ex (4.28)

8

1

5

1

*

j i i

jdes

it t

Ex (4.29)

3

1

5

1

*

, ,j i i

jdes

iAltM AltM

Ex (4.30)

iousij

jdes

iousiju u

Ex

var

*

var

(4.31)

and the final two shadow prices represent a total of 40 unique shadow prices, one for each of the

mission segment legs excluding the payload drop mission segment

i

dessfc sfc

ExAAFSPS

i

*

(4.31)

i

AAFSPS

ireqreq

desT T

Ex

*

(4.32)

Note that there are both input and output shadow prices for every subsystem. For example, an

input shadow price for the AFS-A is equation (4.24) since the specific fuel consumption, ,sfc is

an interaction with the PS and is defined in the PS. Thus, the value of the shadow price is

constant within the AFS-A system-level, unit-based optimization. In contrast, an output shadow

113

price example is equation (4.32) as the thrust required to fly the aircraft is determined in the

AFS-A and is output to the PS. Were all the shadow prices for the AFS-A explicitly stated here,

88 input and 88 output shadow prices would be defined for the AFS-A for a total of 176 shadow

prices.

Equations (4.27) through (4.32) represent the effect of the marginal changes in the

optimum value of the system-level, unit-based objective function for the AFS-A due to changes

in the coupling functions. Problem (4.24) has sixteen additional terms, ,jW ,ij

D ,it

,, AltM ,variousiju

,

isfc

and

ireqT that represent the variations in the coupling functions

and are defined as

8

1

*

jjjj WWW

(4.33)

3

1 1

*

j

n

iijijij

DDD

(4.34)

6

1

5

1

*

j iijijij

ttt

(4.35)

6

1

5

1

*,,,j i

ijijijAltMAltMAltM

(4.36)

*varvarvar iousijiousijiousij uuu (4.37)

n

iiii

sfcsfcsfc1

* (4.38)

n

iireqireqireq TTT

1

* (4.39)

where the superscript "" indicates the optimum coupling function value from the previous ILGO

iteration. Similarly to the shadow prices above, equations (4.33) to (4.39) are not

comprehensive; the AFS-A has 176 total equations, one for each shadow price, but the examples

provided here are adequate for generating the other equations. The PS system-level, unit-based

synthesis/design optimization problem definition is next.

114

4.3.3 PS System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition

The PS system-level, unit-based optimization problem is defined as follows:

PS System-Level, Unit-Based Exergy Destruction Optimization Problem

Minimize

n

i

iinstiinstT

ihlbleedihlbleedPihlbleedihlbleedT

ibleedibleedmiTOiTOPiisfc

iousiiousiui

iitPSPSWCHSdes

ESdesOLSdesESdesPAOSVCdes

ECSdesAAFSdeslossfueldesPSdeslossfueldesPSdes

T

PT

mPsfc

utWEx

ExExExEx

ExExExExExEx

1,_,_,_,_

varvar

5

1

*

****/

**__

''

(4.40)

w.r.t. PSPS YX

,

subject to

0

PSh (4.41)

0

PSg (4.42)

where the vector of equality constraints, PSh

, represents the thermodynamic and geometric

model of the PS and the vector of inequality constraints, PSg

, the physical limits imposed on the

subsystem. The superscript “*” indicates the optimum value from the previous ILGO iteration of

a given subsystem objective function.

Problem (4.40) represents the system-level minimization resulting from varying the PS

decision variables only. The local or unit-based minimization objective function is denoted by

PSdesEx plus an additional term, ,_ lossfueldesEx to account for the unburned fuel lost out the back

of the PS expressed. The expression for the unit-based, system-level objective function,

lossfuelPS desdes ExEx_

'' , includes products for paired shadow prices and associated coupling

functions. The first represents the weight of the PS, the second represents the time coupling with

115

the AFS-A, the third represents the various other coupling functions, and the six within the

summation are the PS interactions. The shadow prices are defined as

PS

AAFSdes

PSW W

Ex

*

(4.43)

5

1

*

i i

PSdes

it t

Ex

(4.44)

iousij

jdes

iousiju u

Ex

var

*

var

(4.45)

And the next six shadow prices which represent a total of 240 independent shadow prices are

defined as

i

PAOSVCFLSAAFSdes

isfc sfc

Ex

*/,, (4.46)

iTO

CHSPAOSVCESFLSdes

iTOP P

Ex

*,/,, (4.47)

ibleed

ECSdes

ibleedm m

Ex

*

(4.48)

ihlbleed

ECSdes

ihlbleedT T

Ex

,_

*

,_

(4.49)

ihlbleed

ECSdes

ihlbleedP P

Ex

,_

*

,_

(4.50)

iinst

OLSAAFSdes

iinstT T

Ex

*, (4.51)

where equations (4.44), (4.45), (4.46), (4.47), (4.48), (4.49), (4.50), and (4.51) represent a total

of 5, 11, 60, 80, 20, 40, 40, and 20 unique shadow prices, respectively. All told, the PS has 115

input, or fixed, shadow prices and 162 output (or variable i.e. internally calculated) shadow

prices for a total of 277 shadow prices for the PS.

Equations (4.43) through (4.51) represent the effect of marginal changes in the optimum

value of the system-level, unit-based objective function for the PS due to changes in the coupling

116

functions. Problem (4.40) has nine additional terms, ,PSW ,it ,variousiu

,i

sfc ,iTOP

,ibleedm ,,_ ihlbleedT ,,_ ihlbleedP and

iinstT that represent variations in the coupling functions

listed above and are defined as

*PSPSPS WWW (4.52)

5

1

0*

iiii ttt (4.53)


*

ii sfcsfcsfci

(4.55)

iTOTOTO PPPii

* (4.56)

ibleedbleedbleed mmmii

* (4.57)

ihlbleedhlbleedhlbleed TTT

ii*

,_,_,_ (4.58)

ihlbleedhlbleedhlbleed PPP

ii*

,_,_,_ (4.59)

iinstinstinst TTTii

* (4.60)


iteration. Similarly to the AFS-A, equations (4.52) to (4.60) are not comprehensive; the PS has

277 total equations, one for each shadow price, but the examples provided here are adequate for

generating the other equations. The ECS system-level, unit-based synthesis/design optimization

problem definition is next.

4.3.4 ECS System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition

The ECS system-level, unit-based optimization problem is defined as follows:

ECS System-Level, Unit-Based Exergy Destruction Optimization Problem

117

Minimize

n

i ihlbleedihlbleedPihlbleedihlbleedT

ibleedibleedmiECSiECSD

iousiiousiui

iit

inletinletAHXPAObleedHXPAObleedW

ECSECSWPAOSVCdes

PSdesAAFSdesECSdesECSdes

PT

mD

ut

AW

WEx

ExExExEx

1 ,_,_,_,_

varvar

5

1

_/_/

*/

**'

(4.61)

w.r.t. ECSECS YX

,

subject to

0

ECSh (4.62)

0

ECSg (4.63)

where the vector of equality constraints, ECSh


model of the ECS and the vector of inequality constraints, ECSg

, the physical limits imposed on

the subsystem. The superscript “*” indicates the optimum value from the previous ILGO

iteration of a given subsystem objective function.

Problem (4.61) represents the system-level minimization resulting from varying the ECS


.ECSdesEx The expression for the unit-based, system-level objective function,

ECSdesEx' , includes

products for paired shadow prices and associated coupling functions. The first shadow price

represents the weight of the ECS, the second represents the weight of the bleed air / PAO heat

exchanger, the third represents the area of the inlet for the ram air / PAO heat exchanger, the

fourth represents the time coupling with the AFS-A, the fifth represents the various other

coupling functions, and the four within the summation are the ECS interactions. The shadow

prices are defined as

118

ECS

desW W

ExECSAAFS

ECS

*

(4.64)

HXPAObleed

PAOSVCdes

HXPAObleedW W

Ex

_/

*/

_/

(4.65)

inlet

desA A

ExECSPAOSVC

inlet

*/ (4.66)

5

1

*

i i

ECSdes

it t

Ex

(4.67)

iousij

jdes

iousiju u

Ex

var

*

var

(4.68)

and the next four shadow prices which represent 144 independent shadow prices are defined as

iECS

AAFSdes

iECSD D

Ex

*

(4.69)

ibleed

PAOSVCPSdes

ibleedm m

Ex

*/, (4.70)

ihlbleed

PAOSVCPSdes

ihlbleedT T

Ex

,_

*/,

,_

(4.71)

ihlbleed

PAOSVCPSdes

ihlbleedP P

Ex

,_

*/,

,_

(4.72)

where equations (4.67), (4.68), (4.69), (4.70), (4.71), and (4.72) represent a total of 5, 13, 28, 28,

48, and 48 unique shadow prices, respectively. The ECS has a total of 93 input and 72 output

shadow prices for a total of 165 shadow prices.

Equations (4.64) through (4.72) represent the effect of marginal changes in the optimum

value of the system-level, unit-based objective function for the ECS due to changes in the

coupling functions. Problem (4.61) has nine additional terms, ,ECSW ,_/ HXPAObleedW ,inletA

,it ,variousiu

,iECSD ,

ibleedm ,,_ ihlbleedT andihlbleedP ,_ that represent variations in the

coupling functions listed above and are defined as

*ECSECSECS WWW (4.73)

119

*_/_/_/ HXPAObleedHXPAObleedHXPAObleed WWW (4.74)

*inletinletinlet AAA (4.75)

5

1

0*

iiii ttt (4.76)


*iii ECSECSECS DDD (4.78)

ibleedbleedbleed mmm

ii*

(4.79)

ihlbleedhlbleedhlbleed TTTii

*,_,_,_

(4.80)

ihlbleedhlbleedhlbleed PPPii

*,_,_,_

(4.81)


iteration. Equations (4.73) to (4.81) are not comprehensive but rather represent 165 total

equations for the ECS, one for each shadow price, but the examples provided here are adequate

for generating the other equations. The VC/PAOS system-level, unit-based synthesis/design

optimization problem definition is next.

4.3.5 VC/PAOS System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition

The VC/PAOS system-level, unit-based optimization problem is defined as follows:

VC/PAOS System-Level, Unit-Based Exergy Destruction Optimization Problem

Minimize

120

4

1 ,_,_

,_,_

1

_/_/'//

varvar

5

1

_/_/

//*

/

*

/

*

/

*

///'

i ihlbleedihlbleedP

ihlbleedihlbleedTibleedibleedm

n

i FLSfuelFLSfuelm

iHXPAOfueliHXPAOfuelQiPAOSVCiPAOSVCD

iousiiousiui

iit

inletinletAHXPAObleedHXPAObleedW

PAOSVCPAOSVCWPAOSVCFLSdesPAOSVCECSdes

PAOSVCPSdesPAOSVCAAFSdesPAOSVCdesPAOSVCdes

P

Tm

m

QD

ut

AW

WExEx

ExExExEx

(4.82)

w.r.t. PAOSVCPAOSVC YX // ,

subject to

0/

PAOSVCh (4.83)

0/

PAOSVCg (4.84)

where the vector of equality constraints, PAOSVCh /


model of the VC/PAOS and the vector of inequality constraints, PAOSVCg /

, the physical limits

imposed on the subsystem. The superscript “*” indicates the optimum value from the previous

ILGO iteration of a given subsystem objective function.

Problem (4.82) represents the system-level minimization resulting from varying the

VC/PAOS decision variables only. The local or unit-based minimization objective function is

denoted by PAOSVCdesEx

/while the expression for the system-level, unit-based objective function,

PAOSVCdesEx/

' , includes products for paired shadow prices and associated coupling functions.

The first pair accounts for the effects of changes in the weight of the VC/PAOS, while the

second pair represents the weight of the bleed air / PAO heat exchanger, the third represents the

area of the inlet for the ram air / PAO heat exchanger which is sized in the ECS. The fourth pair

represents the time coupling with the AFS-A, the fifth represents the various other coupling

functions. The pairs within the summation from i to n account for the effects of changes in the

121

VC/PAOS inlet drag, the heat interaction with the FLS via the fuel / PAO heat exchanger, and

the mass flow rate of the fuel in the FLS while the three shadow price / coupling function pairs

within the final summation account for the effects of changes in the bleed air / PAO heat

exchanger working fluid properties.

The formulation of the bleed air / PAO heat exchanger pair is unique to the VC/PAOS

and ECS. The heat exchanger is “owned” by the ECS and the influence of this heat exchanger

on both the ECS and VC/PAOS is represented by more than just a heat interaction coupling

function. The properties of both working fluids (bleed air and PAO) are defined as coupling

functions so the optimization does not find a thermodynamically impossible heat exchanger such

as one having the hot-side exit temperature lower than the cold-side inlet temperature. Thus,

additional coupling functions are defined for the PAO working fluid properties at the bleed

air/PAO heat exchanger so that the optimization can size the heat exchanger properly.

Furthermore, the heat exchanger weight is passed from the ECS to the VC/PAOS as a coupling

function as the bleed air / PAO heat exchanger weight is accounted in the VC/PAOS. The

shadow prices for the VC/PAOS are defined as

PAOSVC

AAFSdes

PAOSVCW W

Ex

/

*

/

(4.85)

HXPAObleed

AAFSdes

HXPAObleedW W

Ex

_/

*

_/

(4.86)

inlet

ECSdes

inletA A

Ex

*

(4.87)

5

1

*/

i i

PAOSVCdes

it t

Ex

(4.88)

iousij

jdes

iousiju u

Ex

var

*

var

(4.89)

and the next six shadow prices, which represent 84 independent shadow prices, are defined as

iPAOSVC

AAFSdes

iPAOSVCD D

Ex

/

*

/

(4.90)

122

iHXPAOfuel

FLSdes

iHXPAOfuelQ Q

Ex

_/

*

_/

(4.91)

iFLSfuel

FLSdes

iFLSfuelm m

Ex

*

(4.92)

ibleed

ECSdes

ibleedm m

Ex

*

(4.93)

ihlbleed

ECSdes

ihlbleedT T

Ex

,_

*

,_

(4.94)

ihlbleed

ECSdes

ihlbleedP P

Ex

,_

*

,_

(4.95)

where equations (4.88), (4.89), (4.90), (4.91), (4.92), (4.93), (4.94), and (4.95) represent a total

of 5, 4, 20, 20, 20, 8, 8, and 8 unique shadow prices, respectively. The VC/PAOS has a total of

50 input shadow prices and 48 output shadow prices for a total of 96 shadow prices.

Equations (4.85) through (4.95) represent the effect of the marginal change in the

optimum value of the coupling function on the system-level, unit-based objective function for the

VC/PAOS due to changes in the coupling functions. Problem (4.82) has seven additional terms,

,/ PAOSVCW ,_/ HXPAObleedW ,inletA ,it ,variousiu

,/ iPAOSVCD ,_/ iHXPAOfuelQ ,FLSfuelm

,ibleedm ,,_ ihlbleedT and ihlbleedP ,_ that represent the effect that the variation in the

VC/PAOS decision variables has on the coupling functions listed above, equations (4.85)

through (4.95), and are defined as

*/// PAOSVCPAOSVCPAOSVC WWW (4.96)

*_/_/_/ HXPAObleedHXPAObleedHXPAObleed WWW

(4.97)

*inletinletinlet AAA (4.98)

5

1

0*

iiii ttt (4.99)


123

*/// iii PAOSVCPAOSVCPAOSVC DDD (4.101)

*

_/_/_/ iHXPAOfueliHXPAOfueliHXPAOfuel QQQ (4.102)

ibleedbleedbleed mmm

ii*

(4.103)

ihlbleedhlbleedhlbleed TTTii

*,_,_,_

(4.104)

ihlbleedhlbleedhlbleed PPPii

*,_,_,_

(4.105)


iteration. Similarly to the ECS, equations (4.96) to (4.105) are not comprehensive but rather

represent 96 total equations for the VC/PAOS, one for each unique shadow price. The FLS

system-level, unit-based synthesis/design optimization problem definition is next.

4.3.6 FLS System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition

The FLS system-level, unit-based optimization problem is defined as follows:

FLS System-Level, Unit-Based Exergy Destruction Optimization Problem

Minimize

n

i iPAOSVCOLSCHSFLSiPAOSVCOLSCHSFLSQiisfc

iFLSTOiFLSTOPiFLSiFLSD

iousiiousiui

iitFLSFLSWOLSdes

CHSdesPAOSVCdesECSdes

PSdesAAFSdesFLSdesFLSdes

Qsfc

PD

utWEx

ExExEx

ExExExEx

1 /,,/,,

varvar

5

1

*

**/

*

**'

(4.106)

w.r.t. FLSFLS YX

,

subject to

0

FLSh (4.107)

124

0

FLSg (4.108)

where the vector of equality constraints, FLSh


model of the FLS and the vector of inequality constraints, FLSg




Problem (4.106) represents the system-level minimization resulting from varying the FLS


.FLSdesEx The expression for the unit-based, system-level objective function,

FLSdesEx' , includes

products for paired shadow prices and associated coupling functions. The first pair accounts for

the effects of variations in the FLS weight, the second pair for the mission segments with

variable time, the third pair for various other interactions, while the pairs in the summation

reflect the effect of variations in the FLS coupling functions. The FLS shadow prices are defined

as

FLS

AAFSdes

FLSW W

Ex

*

(4.109)

5

1

*

i i

FLSdes

it t

Ex

(4.110)

iousij

jdes

iousiju u

Ex

var

*

var

(4.111)

And the next four shadow prices, which represent 120 independent shadow prices, are defined as

iFLS

AAFSdes

iFLSD D

Ex

*

(4.112)

iFLSTO

PSdes

iFLSTOP P

Ex

*

(4.113)

i

PSdes

isfc sfc

Ex

*

(4.114)

125

iPAOSVCOLSCHSFLS

PAOSVCOLSCHSdes

iPAOSVCOLSCHSFLSQ Q

Ex

/,,

*/,,

/,,

(4.115)

where equations (4.110), (4.111), (4.112), (4.113), (4.114), and (4.115) represent a total of 5, 9,

20, 20, 20, and 60 unique shadow prices, respectively. The FLS has a total of 94 input shadow

prices and 41 output shadow prices for a total of 135 shadow prices.



FLS due to changes in the coupling functions. Problem (4.106) has seven additional terms,

,FLSW ,it ,variousiu

,

iFLSD ,iFLSTOP ,isfc and iPAOSVCOLSCHSFLSQ /,, that represent

variations in the coupling functions listed above and are defined as

*FLSFLSFLS WWW (4.116)

5

1

0*

iiii ttt (4.117)


*

FLSFLSFLS DDDii (4.119)

*

iFLSiFLSiFLS TOTOTO PPP (4.120)

*iii sfcsfcsfc (4.121)

iPAOSVCOLSCHSFLSiPAOSVCOLSCHSFLSiPAOSVCOLSCHSFLS QQQ *

/,,/,,/,, (4.122)


iteration. Similarly to the ECS, equations (4.116) to (4.122) are not comprehensive but rather

represent 135 total equations for the FLS. The OLS system-level, unit-based synthesis/design


4.3.7 OLS System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition

The OLS system-level, unit-based optimization problem is defined as follows:

OLS System-Level, Unit-Based Exergy Destruction Optimization Problem

126

Minimize

n

iiOLSFLS

iOLSFLSQiuninstiuninstT

iiousiiousiuiitOLSOLSWFLSdes

PSdesAAFSdesOLSdesOLSdes

QT

utWEx

ExExExEx

1

5

1varvar

*

**'

(4.123)

w.r.t. OLSOLS YX

,

subject to

0

OLSh (4.124)

0

OLSg (4.125)

where the vector of equality constraints, OLSh


model of the OLS and the vector of inequality constraints, OLSg





OLS decision variables only. The local or unit-based minimization objective function is denoted

by OLSdesEx while the expression for the system-level, unit-based objective function,

OLSdesEx' ,

includes products for paired shadow prices and associated coupling functions. The first pair

accounts for the effects of changes in the weight of the OLS, the second pair represents the time

coupling with the AFS-A. The pairs within the summation from i to n account for the effects of

changes in the uninstalled thrust from the PS and the heat interaction with the FLS via the fuel /

oil heat exchanger. The OLS shadow prices are defined as

OLS

AAFSdes

OLSW W

Ex

*

(4.126)

5

1

*/

i i

PAOSVCdes

it t

Ex

(4.127)

127

iousij

jdes

iousiju u

Ex

var

*

var

(4.128)

and the next two shadow prices, which represent 40 independent shadow prices, are defined as

iuninst

AAFSdes

iuninstT T

Ex

*

(4.129)

iOLSFLS

FLSdes

iOLSFLSQ Q

Ex

*

(4.130)

where equations (4.128), (4.129) and (4.130) represent 5, 20, and 20 unique shadow prices,

respectively. The OLS has a total of 30 input shadow prices and 21 output shadow prices for a

total of 51 shadow prices.



FLS due to changes in the coupling functions. Problem (4.123) has five additional terms,

,OLSW ,it ,variousiu

,iuninstT and iOLSFLSQ that represent the effect that the variation in

the OLS decision variables has on the coupling functions listed above and are defined as

*OLSOLSOLS WWW (4.131)

5

1

0*

iiii ttt (4.132)


*

uninstuninstuninst TTTii (4.134)

iOLSFLSOLSFLSOLSFLS QQQ

ii*

(4.135)


iteration. Again, equations (4.131) to (4.135) are not comprehensive but rather represent 51 total

equations for the OLS. The CHS system-level, unit-based synthesis/design optimization

problem definition is next.

128

4.3.8 CHS System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition

The CHS system-level, unit-based optimization problem is defined as follows:

CHS System-Level, Unit-Based Exergy Destruction Optimization Problem

Minimize

n

iiCHSFLS

iCHSFLSQiCHSTOiCHSTOP

iousiiousiuCHSCHSW

FLSdesPSdesAAFSdesCHSdesCHSdes

QP

uW

ExExExExEx

1

varvar

***'

(4.136)

subject to

0

CHSh (4.137)

0

CHSg (4.138)

where the vector of equality constraints, CHSh


model of the CHS and the vector of inequality constraints, CHSg



iteration of a given subsystem objective function. Note that the CHS has no design decision

variables and/or operational decision variables, thus there are no vectors of design decision or

operational decision variables associated with problem (4.136) and only the shadow prices and

coupling function pairs vary during the local optimization of the CHS.


CHS interactions only as the CHS has no decision variables. The local or unit-based

minimization objective function is denoted by CHSdesEx while the expression for the system-

level, unit-based objective function, CHSdesEx' , includes products for paired shadow prices and

associated coupling functions. The first pair accounts for the effects of changes in the weight of

the CHS, the second pair accounts for the effects of changes in various coupling functions in the

CHS, and the pairs within the summation from i to n account for the effects of changes in the

129

uninstalled thrust from the PS and the heat interaction with the FLS via the fuel / hydraulic oil

heat exchanger. Notice that problem (4.136) has no shadow price and coupling function pair

representing the AFS-A mission segment times since the CHS is calculated within the OLS unit-

level optimization and the time variables are directly assigned. The CHS shadow prices are

defined as

CHS

AAFSdes

CHSW W

Ex

*

(4.139)

iousij

jdes

iousiju u

Ex

var

*

var

(4.140)

iCHSTO

PSdes

iCHSTOP P

Ex

*

(4.141)

iCHSFLS

FLSdes

iCHSFLSQ Q

Ex

*

(4.142)

where equations (4.140), (4.141), and (4.142) each represent 6, 20, and 20 unique shadow prices,

respectively. The CHS has a total of 6 input shadow prices and 41 output shadow prices for a

total of 47 shadow prices.



CHS due to changes in the coupling functions. Problem (4.136) has four additional terms,

,CHSW ,var iousiu

,iCHSTOP and iCHSFLSQ that represent the effect that the variation in the

CHS degrees of freedom has on the coupling functions listed above and are defined as

*CHSCHSCHS WWW (4.143)


*

iCHSiCHSiCHS TOTOTO PPP (4.145)

iCHSFLSCHSFLSCHSFLS QQQ

ii*

(4.146)

130


iteration. Again, equations (4.143) to (4.146) are not comprehensive but rather represent 47 total

equations for the CHS. The ES system-level, unit-based synthesis/design optimization problem

definition is next.

4.3.9 ES System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition

The ES system-level, unit-based optimization problem is defined as follows:

ES System-Level, Unit-Based Exergy Destruction Optimization Problem

Minimize

n

iiESTO

iESTOP

EmptyEmptyWi

iitESESW

PSdesAAFSdesESdesESdes

P

WtW

ExExExEx

1

5

1

**'

(4.147)

subject to

0

ESh (4.148)

0

ESg (4.149)

where the vector of equality constraints, ESh


model of the ES and the vector of inequality constraints, ESg

, the physical limits imposed on the

subsystem. The superscript “*” indicates the optimum value from the previous ILGO iteration of

a given subsystem objective function.

Problem (4.147) represents the system-level minimization resulting from varying the ES


ESdesEx while the expression for the system-level, unit-based objective function, ESdesEx' ,


accounts for the effects of changes in the weight of the ES, the second pair is the AFS-A mission

131

segment time, the third pair represents the AAF empty weight, and the pair within the summation

accounts for the effects of changes in the shaft power extracted from the PS. Note that the ES

has no design decision variables and/or operational decision variables, thus there are no vectors

of design decision or operational decision variables associated with problem (4.147) and only the

shadow prices and coupling function pairs vary during the local optimization of the ES. The ES

shadow prices are defined as

ES

AAFSdes

ESW W

Ex

*

(4.150)

5

1

*

i i

ESdes

it t

Ex

(4.151)

Empty

AAFSdes

EmptyW W

Ex

*

(4.152)

iESTO

PSdes

iESTOP P

Ex

*

(4.153)

where equations (4.153) represents 20 unique shadow prices. The ES has a total of 6 input

shadow prices and 21 output shadow prices for a total of 27 shadow prices.

Equations (4.150) to (4.153) represent the effect of the marginal change in the optimum

value of the coupling function on the unit-based, system-level objective function for the ES.

Problem (4.147) has four additional terms, ,ESW ,it ,EmptyW and iESTOP that represent the

effect that the variation in the ES degrees of freedom has on the coupling functions listed above

and are defined as

*ESESES WWW (4.154)

5

1

0*

iiii ttt (4.155)

*EmptyEmptyEmpty WWW (4.156)

n

iiESTOiESTOiESTO PPP

1

*

(4.157)

132


iteration. Equations (4.154) through (4.157) are comprehensive for the ES in this thesis work

and represent 27 total equations for the ES. The FCS system-level, unit-based synthesis/design


4.3.10 FCS System-Level, Unit-Based Synthesis/Design Optimization Problem

Definition

The FCS system-level, unit-based optimization problem is defined as follows:

FCS System-Level, Unit-Based Exergy Destruction Optimization Problem

Minimize

sssWsA

WALbrrCttC

FCSFCSWAAFSdesFCSdesFCSdes

WA

WALbCC

WExExEx

_

_

'

_

_

*

(4.158)

subject to

0

ESh (4.159)

0

ESg (4.160)

where the vector of equality constraints, FCSh


model of the ES and the vector of inequality constraints, FCSg



iteration of a given subsystem objective function. Note that the FCS has no design decision

variables and/or operational decision variables, thus there are no vectors of design decision or

operational decision variables associated with problem (4.155) and only the shadow prices,

representing the subsystem interactions, vary during the local optimization of the FCS.

Thus, problem (4.158) represents the system-level minimization resulting from variation

in the FCS interactions only. The local or unit-based minimization objective function is denoted

by FCSdesEx while the expression for the system-level, unit-based objective function,

FCSdesEx' ,

133


accounts for the effects of changes in the weight of the FCS. The subsequent paired shadow

prices and coupling functions account for the effects of changes in the wing tip and root chord

lengths, wing span, wing length, aileron chord / wing chord, and aileron span / wing span. The

FCS shadow prices are defined as

FCS

AAFSdes

FCSW W

Ex

*

(4.161)

t

AAFSdes

tC C

Ex

*

(4.162)

r

AAFSdes

rC C

Ex

*

(4.163)

b

ExAAFSdes

b

*

(4.164)

L

ExAAFSdes

L

*

(4.165)

WA

ExAAFSdes

WA _

*

_

(4.166)

ss

AAFSdes

sWsA WA

Ex

_

*

_

(4.167)

The ES has a total of 6 input shadow prices and 1 output shadow prices for a total of 7 shadow

prices. The ES is calculated within the OLS, thus no coupling functions related to mission

decision variables are required.

Equations (4.161) to (4.167) represent the effect of the marginal change in the optimum

value of the coupling function on the system-level, unit-based objective function for the FCS.

Problem (4.158) has seven additional terms, ,FCSW ,tC ,rC ,b ,L ,_WA and ss WA _

that represent the effect that the variation in the FCS degrees of freedom has on the coupling

functions listed above and are defined as

*FCSFCSFCS WWW (4.168)

134

*ttt CCC (4.169)

*rrr CCC (4.170)

*bbb (4.171)

*LLL (4.172)

*___ WAWAWA (4.173)

*___ ssssss WAWAWA (4.174)


iteration. Again, the FCS has no design decision or operational decision variables that

participate in the optimization. This concludes the discussion of the system-level, unit-based

synthesis/design optimization problem definitions for the AAF model developed in this thesis

work.

4.4 Optimization Decision Variables and Variable Constraints

This section details the optimization synthesis / design, operational, and mission decision

variables and constraints for each of the subsystems included in this thesis work. The first

subsystem to be detailed is the AFS-A. The fixed-wing AFS-A decision variables and variable

constraints are given in Table 4.2

Table 4.2 AFS-A fixed-wing design and operational decision variables and inequality constraints.

Component Design Decision Variables Constraints

Fixed-wing AFS-A

TOW Gross takeoff weight (lb) 000,60000,10 TOW

wingL Wing length (ft) 6530 wingL

LE Leading edge sweep angle 6015 LE

AR Aspect ratio 102 AR Taper ratio 10

ct

Thickness-to-chord ratio 15.006.0 ct

tailAR Tail aspect ratio 5.65.3 tailAR

tailct

Tail thickness-to-chord ratio 25.006.0 tailc

t

135

The fixed-wing AFS-A has only a single configuration for the mission and, therefore, has

a total of 8 design decision variables. Note that the gross takeoff weight, TOW , participates in the

optimization as a means to establish the aircraft takeoff weight and fuel weight.

The morphing-wing AFS-A design and operational decision variables and variable

constraints are given in Table 4.3. Note that the design decision variables are listed first and

only take one value for the entire mission. The operational decision variables each have 20 (one

for each mission segment) unique values, thus, the morphing-wing AFS-A has 20 unique wing

configurations which brings the total number of optimization decision variables for the AFS-A to

103.

Table 4.3 AFS-A morphing-wing design and operational decision variables and inequality constraints.


Morphing-wing AFS-A

TOW Gross takeoff weight (lb) 000,60000,10 TOW

tailAR Tail aspect ratio 5.65.3 tailAR

tailct Tail thickness-to-chord ratio 25.006.0

tailct

Operational Decision Variables Constraints

L Wing length (ft) 6530 L

LE Leading edge sweep angle 6015

AR Aspect ratio 102 AR Taper ratio 10

ct

Thickness-to-chord ratio 15.006.0 ct

The AFS-A also has 6 mission decision variables that participate in the optimization. This set of

variables is given in Table 4.4. The variable names correspond to the mission segments detailed

Table 4.4 AFS-A mission decision variables and inequality constraints.

Component Mission Decision Variables Constraints

AFS-A Mission

1BCM Best cruise Mach #1 0.116.0 BCM 2BCM Best cruise Mach #2 0.126.0 BCM 3BCM Best cruise Mach #3 0.136.0 BCM 1BCA Best cruise altitude 1 (ft) 000,551000,30 BCA

2BCA Best cruise altitude 2 (ft) 000,552000,30 BCA

BCLM Best climb Mach 0.15.0 BCLM

in Table 3.1. The mission variables could have been included in any of the other subsystems;

but since the mission decision variables affect the AFS-A performance and weight fractions

significantly, it makes sense to have them participate in the AFS-A optimization. Note that each

136

of these mission decision variables affects the time required to fly the mission which is an

integration concern for all the subsystems. Also note that the takeoff weight, TOW , is a decision

variable for both the fixed-wing and morphing-wing AFS-A optimizations.

The next set of subsystem decision variables and inequality constraints to be discussed

are those for the PS. The model of the PS has a reference or design engine so there are decision

variables associated with the reference conditions of the engine as well. The decision variables

and corresponding variable constraints for the PS are given in Table 4.5. Note that the mission

defined in Table 3.1 requires military or maximum power for some of the mission segments

which removes the decision variables for the corresponding mission segment. Thus, the PS has a

total of 11 design decision variables and 27 operational decision variables.

Table 4.5 PS design and operational decision variables and inequality constraints.


Propulsion Subsystem

0M Design Mach number 7.18.0 0 M

Alt Design altitude 000,50000,30 Alt

0m Design total mass flow rate (lb/s) 4006.0 0 m

c Design total compressor pressure ratio 0.300.6 c

'c Design fan pressure ratio 0.60.2 ' c

Design bypass ratio 85.025.0

4tT Design burner temperature (R) 32001000 4 tT

7tT Design afterburner temperature (R) 36001000 7 tT

5M Design mixer Mach number for core 6.04.0 5 M

TOP Design power takeoff (kW) 0.4000.0 TOP

Design bleed air ratio 03.000.0 Operational Decision Variables Constraints

4tT Burner temperature (R) 32001000 4 tT

7tT Afterburner temperature (R) 36001000 7 tT

Next comes the ECS. The decision variables and the corresponding constraints are

shown in Table 4.6. The ECS has a total of 23 synthesis / design decision variables. Note,

however, that there are two possible configurations for the regenerative heat exchanger. This

requires that another independent set of regenerative heat exchanger variables must be used as

well bringing the total to 28 synthesis / design decision variables.

Table 4.6 ECS optimization synthesis / design and operational decision variables and inequality constraints.


137

Primary Heat Exchanger

bFin Bleed-air fin type 2011 bFin

rFin Ram-air fin type 2011 rFin

bL Bleed-air side length, m 9.05.0 bL

rL Ram-air side length, m 9.006.0 rL

nL Non-flow length, m 9.05.0 nL

Secondary Heat Exchanger



bL Bleed-air side length, m 9.05.0 bL



Regenerative Heat Exchanger

hFin Hot-side (bleed air) fin type 2011 hFin

cFin Cold-side (from the water separator) fin type

2011 cFin

hL Hot-side length, m 5.03.0 bL

cL Cold-side length, m 3.015.0 cL


Bleed Air / PAO Heat Exchanger


rFin PAO fin type 2011 rFin

bL Bleed-air-side length, m 9.05.0 bL

rL PAO-side length, m 9.006.0 rL


Compressor desPR Design compressor pressure ratio

0.38.1 desPR

Inlet Duct 1 1A Inlet duct 1 area, cm2 2208 1 A

Inlet Duct 2 2A Inlet duct 2 area, m2 2208 2 A

Component Operational Decision Variables Constraints

Pressure Regulating Valve vvPR Pressure setting 0.60.1 vvPR

Bleed Port Bleed Bleed port selection (high or low pressure bleed port)

)1,0(Bleed

Air Cycle Machine hotv Hot-air bypass 0.10.0 hotv

Splitter bypassv Compressor bypass 0.10.0 bypassv

Regenerative Heat Exchanger regm Regenerative heat exchanger mass flow rate, kg/s

2.00.0 regm

138

Because of certain difficulties encountered during the optimization process in this thesis

work, the ECS flies only 4 of the 21 mission segments to establish the ECS subsystem synthesis /

design and subsystem interactions. The mission segments flown are warmup and takeoff

(segment 1), subsonic climb (segment 4), supersonic turn (segment 11), and subsonic cruise

(segment 19). This brings the total number of operational variables to 20, though if the entire

mission were used, 100 operational decision variables would be required for the ECS. (In the

work of Rancruel (2003), the subsonic cruise mission segment was used as the design segment.)

The next subsystem to be discussed is the FLS. The synthesis / design decision variables

and constraint limits for the FLS are given in Table 4.7. The FLS optimization only has 8

Table 4.7 FLS optimization decision variables and inequality constraints.


Ram Air / Fuel Heat Exchanger

rFin Ram air fin type 2011 rFin

fFin Fuel side fin type 2011 fFin

rL Ram air side length, m 9.005.0 rL

fL Fuel side length, m 9.005.0 fL


Fuel/Oil Heat Exchanger

cL Cold-side length (m) 90050 .L. c

hL Hot-side length (m) 9010 .L. n

nL Non-flow length (m) 9010 .L. n

synthesis / design decision variables since the heat exchangers are sized in other subsystems.

Note that the fuel added to the PS-required fuel mass flow rate, addfuelm _ , is an operational

variable. However, the fuel added to the flow is iterated within simulation and does not

participate as a decision variable in the optimization (see section 3.6.1). Thus, the FLS has no

operational decision variables.

The synthesis / design and operational decision variables and inequality constraints for

the VC/PAOS are shown in Table 4.8. The VC/PAOS flies only a single mission segment to

establish its synthesis / design conditions and performance. The mission segment chosen is the

most constrained mission segment of the four flown by the ECS which is the segment with the

highest cooling load required from the cold PAO loop. If the entire mission were being

optimized, a total of 60 operational decision variables would participate in the optimization;

139

however, for this thesis work, the VC/PAOS has 20 synthesis / design decision variables and

only 3 operational decision variables.

Table 4.8 VC/PAOS optimization synthesis / design and operational decision variables and inequality constraints.

Component Synthesis / Design Decision Variables Constraints

Condenser

vFin Vapor-side fin type 2011 vFin

pFin Liquid-side fin type 2011 pFin

vL Vapor-side length, m 9.05.0 vL

pL Liquid-side length, m 9.006.0 pL


Evaporator

vFin Vapor-side fin type 2011 vFin

pFin Liquid-side fin type 2011 pFin

vL Vapor-side length, m 9.05.0 vL

pL Liquid-side length, m 9.006.0 pL


Ram Air / PAO Heat Exchanger

hFin Hot-side (bleed air) fin type 2011 hFin


hL Hot-side length, m 5.03.0 hL



Fuel / PAO Heat Exchanger

pFin Bleed-air fin type 2011 pFin

fFin Fuel-side fin type 2011 fFin

pL Bleed-air side length, m 9.05.0 pL

fL Fuel-side length, m 9.005.0 fL



Mass Flow Rates

vaporm Vapor mass flow rate, kg/s 2.22.0 vaporm

hotpaom _ Hot PAO loop mass flow rate, kg/s 5.32.0 _ hotpaom

coldpaom _ Cold PAO loop mass flow rate, kg/s 5.32.0 _ coldpaom

The next subsystem is the OLS. Its operational decision variables and variable

constraints are given in Table 4.9. The OLS heat exchangers are sized in the FLS. The OLS has

a total of 20 operational decision variables.

Table 4.9 OLS optimization operational decision variables and inequality constraints.


OLS operational variables oilm Mass flow rate of oil, kg/s 0.40 oilm

140

Finally, the remaining subsystems, the ES, CHS, and FCS are passive subsystems in

terms of the optimization as they have no local design or operational decision variables

associated with them in this thesis work. They do, however, participate via system-level degrees

of freedom, i.e. via coupling functions. Thus, they must be considered in the subsystem

integration as their operation has a direct effect on the overall system-level objective function

and on system performance.

4.5 Solution Approach

Both physical and time decomposition are applied in this thesis work to the AAF aircraft

which is modeled and optimized based on 9 subsystems separated by physical or thermodynamic

boundaries and flown over a mission separated into 21 time segments. Even though the AFS-A,

PS, ECS, FLS, VC/PAOS, CHS, OLS, ES, and FCS are modeled and optimized separately,

coupling functions update the subsystem interactions between ILGO iterations. Each of the

subsystem optimizations, thus, represent a unit (or local) component of the overall system

optimization problem.

Figure 4.6 shows the notional flow of the ILGO approach for the AAF aircraft system.

Starting from the individual subsystem optimizations in Figure 4.6, the ILGO process is as

follows:

Figure 4.6 Diagram of optimization problem solution approach using ILGO.

Simulate Dependent Subsystems

Assign shadow prices to the subsystems and pass these and their updated coupling functions to the subsystems

Individual Subsystem Optimizations

AFS-A

PS

ECS

FLS

VCPAOS

OLS

ILGO Iteration

Calculate the system-

level objective function

Calculate the new shadow

prices

CHS ES FCS

Update the coupling functions

141

1. The initial subsystem optimizations start with arbitrary values for the coupling functions

and shadow prices, but within specified limits.

2. After the AFS-A, PS, ECS, FLS, OLS, and VC/PAOS are optimized, the CHS, ES, and

FCS are simulated based on outputs from the optimized subsystems.

3. The overall system-level objective value is calculated.

4. New shadow prices are calculated based on the initial result.

5. The ILGO iteration count is incremented.

6. The coupling function values are updated based on the individual subsystem optimization

results.

7. Finally, new shadow prices are assigned to the appropriate unit-level subproblems and

these and their associated updated coupling function values are passed to the subsystems

so that the next set of individual subsystem optimizations can proceed.

The explanation of ILGO provided here is merely a top-level overview. The reader is once again

directed to Muñoz and von Spakovsky (2000a,b,c,d; 2001a,b), Rancruel (2002, 2005), and

Rancruel and von Spakovsky (2005, 2006) for a detailed explanation of ILGO and the other

facets of the ILGO approach mentioned here. The software package used in this thesis work is

briefly described in the following subsection.

4.6 iScript™ Scripting Language and Optimization

The software used for the optimization of this thesis work is called iSCRIPT™ which is

in development by TTC Technologies, Inc. iSCRIPT™ was developed under an Air Force Small

Business Innovative Research (SBIR) Phase II project. The reasons for using iSCRIPT™

include the following attributes that make it attractive for this thesis work:

Quick learning curve for the programming syntax;

Built-in optimization tools;

Component-based programming structure;

Automated ILGO; and

Automated parallelization for the optimization.

142

Another large contributing factor to the decision to use iSCRIPT™ is the fact that the

subsystems were already mostly written (or being written) in iSCRIPT™ as a demonstration to

the Air Force and industry. The optimization in iSCRIPT™ is performed on two levels. The

unit or subsystem level is optimized using a genetic algorithm (GA) developed by researchers at

the Laboratoir d’energetique industrielle at the Ecole Polytechnique Federale de Lansanne in

Lausanne, Switzerland (Leyland, 2002). The parameter set in the original implementation was

condensed to five parameters by TTC including the population size, initial evaluations,

convergence criteria, mutation frequency, and maximum number of generations to simplify the

user interaction with the method. To arrive at a system-level optimum, the ILGO decomposition

strategy is implemented in iSCRIPT™.

GAs are based on Darwin’s theory of natural selection or “survival of the fittest.” The

initial population or set of optimization decision variable values is generated by stepping through

the range of values possible for each optimization variable. After the initial population is

generated, the algorithm reorders the optimization variables based on the values of the objective

functions they yield, i.e., the solutions are ordered from the best to the worst solution based on

the value of the objective. The GA then selects the better sets of optimization decision variable

values, called “parents”, mutates them slightly, then repopulates the bottom half of the

population with the mutated optimization decision variable values or “offspring” of the parents.

The new population members or sets of decision variable values are then evaluated in the model

and the entire population is again reordered from the best to the worst solution and the selection-

mutation-repopulation process continues until the convergence criteria is met or until the

maximum number of generations specified is reached.

The implementation of ILGO in iSCRIPT™ uses a gradient-based method to converget

the decomposed system to a system-level optimum. In this approach, gradients are computed

using the shadow prices of the coupling functions between the subsystems. The gradients are

used along with the coupling functions to search the system-level ORS for the overall system

optimum. The shadow prices represent the effect of the unit-level coupling functions on the

system-level objective function. Such an approach allows multiple subsystem optimizations to

take place at the same time since each subsystem is effectively isolated from the others while at

the same time assuring a system-level optimum by periodically updating the subsystem

interactions between ILGO steps via coupling functions.

143

Chapter 5

Results and Discussion

This chapter discusses the results obtained during this thesis work. The first section starts

with a set of results from the first phase of this thesis work that is an extension of the work of

Butt (2005) from a paper presented at the 2007 AIAA Thermophysics Conference held in Miami,

FL (Smith, et. al, 2007). The next section presents results and analysis of a partial optimization

of the 9 subsystem AAF that is written in iSCRIPT™ along with predicted optimal results and

analysis. The final section is a parametric study of the morphing AFS-A behavior.

5.1 Two-Subsystem Optimization Results

The work of Smith, et al. (2007) studies the benefits of using morphing wing technology

in an AAF. Two subsystems are modeled: the AFS-A, both morphing- and fixed-wing models,

and a turbofan PS as described in Chapter 3. The AFS-A models were developed and used by

Butt (2005). The morphing-wing AFS-A is physically similar to that described in Chapter 3 with

a few differences which are as follows:

root- and tip-chord lengths are operational decision variables while the AFS-A

described in Chapter 3 uses the taper ratio as the operational decision variable to

establish the root- and tip-chord lengths;

morphing AFS-A wing-weights are established based on setting the wing sweep to

zero. This makes the wing-weight estimate lower than if the wing had some amount

of sweep, thus, the metric to compare fixed-wing and morphing-wing results in

Smith et al. (2007) is gross takeoff weight; and

wing-weight penalties and fuel-weight penalties are established in the manner

described in Section 3.2.5.; however, the excess fuel that is carried to power the

actuators that morph the wings is not expelled in Smith et al. (2007) in order to

match what was done in Butt (2005).

The mission flown in Smith et al. (2007) is similar to that described in Chapter 3 but with

some differences. The AAF model does not fly the entire mission but rather flies a subset of the

144

mission and no DOF are associated with the mission (i.e. the mission segments are fixed and do

not participate in the optimization) as was done in the work of Butt (2005).

The optimization is handled in MATLAB™ using a genetic algorithm developed by

Leyland (2002). The fixed-wing AFS-A has 4 synthesis/design decision variables (wing length,

wing sweep, and root- and tip- chord lengths) while the morphing-wing AFS-A has the same

number of synthesis / design decision variables and a total of 72 operational decision variables

(18 sets of wing length, wing sweep, and root- and tip- chord lengths). The turbofan PS has 9

synthesis/design decision variables (Mach number, mass flow rate, altitude, compressor pressure

ratio, fan pressure ratio, bypass ratio, main burner temperature, afterburner temperature, and

mixer Mach number) and 28 operational decision variables (nineteen main burner temperatures

and nine afterburner temperature settings). The optimization objective function used is that of

minimizing the fuel burned over the mission.

Figure 5.1 shows the sensitivity of the total fuel consumed over the mission with respect

to the wing- weight and fuel- weight penalties for the morphing-wing AAF. Note that the fixed-

wing result is shown in Figure 5.1 with the red horizontal line. The shaded area below the red

line indicates the fuel savings region (i.e. any combination of wing-weight and fuel-weight

Figure 5.1 Sensitivity analysis of morphing-wing effectiveness for different wing- and fuel-weight penalties (Smith et al., 2007).

145

penalties within the shaded area outperform the fixed-wing result in terms of fuel burned over

the mission). As mentioned previously, the metric to compare the fixed-wing and the morphing-

wing result is the gross takeoff weights. A sample of the optimum gross takeoff weights for the

6x wing-weight penalty and the fixed-wing gross takeoff weight optimum for the AAF is given

in Table 5.1.

Table 5.1 Comparison of the optimum morphing-wing gross takeoff weights with a 6x wing-weight penalty and the optimum fixed-wing gross takeoff weight (Smith et al. 2007).

Morphing-Wing Fuel Penalty and Gross Takeoff Weights Fixed- Wing

Fuel Penalty 3% 10% 25% 50% 75% 100% N/A

(lbm) 19,473 19,917 20,844 22,330 23,757 25,138 14,959

The morphing-wing gross takeoff weights shown in Table 5.1 are only for the 6x wing-

weight penalty while the final column in Table 5.1 gives the optimum gross takeoff weight for

the fixed-wing AAF. The reader should notice that the two highest fuel penalties, 75% and

100%, for the 6x wing-weight penalty burn more fuel than the fixed-wing result shown in Figure

5.1. However, these two aircraft have gross takeoff weights 59% and 68% heavier, respectively,

than the fixed-wing gross takeoff weight of 14,959 lbm. The interesting result is that a morphing-

wing aircraft that has a gross takeoff weight 49.3% higher (for the 6x wing-weight penalty and

50% fuel-weight penalty) than the fixed-wing aircraft burns approximately 100 lb less fuel than

the fixed-wing AAF over the entire mission.

Table 5.2 shows the comparison between the fixed-wing AAF and the morphing-wing

AAF configurations for two mission segments, namely, the subsonic cruise segment and the

supersonic penetration segment. The flight conditions of these two mission segments are at

Mach 0.9 and a 42,000 ft altitude and at Mach 1.5 and a 30,000 ft altitude, respectively. The first

four rows in Table 5.2 are AFS-A design/operational parameters while the final four rows in

Table 5.2 are engine operating conditions and design parameters.

Table 5.2 Optimal fixed- versus morphing-wing AAF configuration and performance parameters for the subsonic cruise and the supersonic penetration mission segments (Smith et al. 2007).

Morphing-Wing Fixed-Wing

Mission Cruise Supersonic Penetration

Cruise Supersonic Penetration

Wing length (ft) 35.50 29.09 41.4301

146

Morphing-Wing Fixed-Wing

Mission Cruise Supersonic Penetration

Cruise Supersonic Penetration

Leading edge wing sweep (deg) 13.16 43.63 41.7168

Root-chord length (ft) 4.04 4.00 5.0138

Tip-chord length (ft) 1.53 1.68 2.6809

Burner temperature (°R) 2365.7 3198.7 2956.5 2938.8

Fuel consumption (lbm) 76.8 712.2 210.1 662.2

Design air mass flow rate (lbm/s) 154.3 158.9

Design Mach 1.35 1.55

Note that the fixed-wing leading edge sweep angle is nearly the same as the morphing-

wing for the supersonic penetration mission segment. This indicates that the fixed-wing design

tended toward the more stressing aerodynamic flight condition: supersonic flight. The

morphing-wing AAF, however, with the ability to change its wing geometry, increased the

leading edge sweep angle and decreased the wing length for the supersonic mission segment.

Also notice that the morphing-wing AAF moved to a smaller sweep angle to create a high aspect

ratio wing during the cruise segment with the end result of burning only about 1/3 of the fuel of

the fixed-wing AAF in cruise.

The explanation for the morphing-wing AAF burning slightly more fuel than the fixed-

wing AAF for the supersonic mission segment is simple: the two AAFs have nearly the same

aerodynamic properties during supersonic flight from their wing geometry; however, the

morphing-wing AAF is heavier and, thus, requires more thrust for sustained supersonic flight.

The increase in thrust requirements for the morphing-wing AAF can be seen by the higher burner

temperature (i.e., higher throttle setting).

Note also that the design air mass flow rates are nearly the same for the morphing- and

fixed-wing AAF with the morphing-wing design air mass flow rate being slightly lower than that

for the fixed-wing engine. The telling result here is the design Mach number. Notice in Table

5.2 that the morphing-wing AAF has a much lower design Mach number than the fixed-wing

AAF (1.35 versus 1.55). This indicates that the optimum engine for the morphing vehicle tends

towards subsonic flight as that is where the morphing-wing aircraft shows the greatest benefit

over the fixed-wing aircraft. The physical characteristics and operating conditions shown in

147

Table 5.2 clearly highlight the potential benefits of morphing-wing technology in fighter aircraft

for the AAF consisting of a PS and AFS-A.

Results for the nine-subsystem AAF described in Chapter 3 are presented next.

5.2 Nine-Subsystem Results

The second phase of this thesis work started out by developing the models for the nine

subsystems (i.e. AFS-A, PS, ECS, VC/PAOS, FLS, OLS, ES, CHS, and FCS) described in

Chapter 3, coding and testing the models for a single flight condition, and then updating the code

so that each of the subsystems could fly the 21 segments of the mission described in Chapter 3.

The next step was to integrate the subsystems so that they could “talk” to each other via the

coupling functions within ILGO. The third step was to validate each individual subsystem

within the total AAF system, and the final step was to optimize the AAF using the ILGO

decomposition strategy. All but the final step were carried to completion within this thesis work

due to time and resource limitations. Thus, the following sections present a partial ILGO of the

nine-subsystem AAF system starting with a preliminary synthesis/design exergy analysis.

5.2.1 Preliminary Synthesis/Design Analysis

The nine-subsystem AAF that is partially optimized has the morphing-wing AFS-A as

described in Chapter 3. The set of results presented here represents the subsystem configurations

after the first ILGO iteration. The total exergy destruction plus fuel exergy loss is shown in

Figure 5.2 and the subsystem weights are given in Table 5.3.

Note that the AFS-A and PS dominate the exergy destruction (plus exergy fuel loss) of

the other subsystems in the AAF. This is primarily due to the fact that they consume the largest

amounts of exergy in the AAF: the AFS-A consumes exergy in terms of drag, the PS consumes

exergy during fuel combustion. The other subsystems are not insignificant in terms of aircraft

operation; but in terms of the overall exergy destruction plus fuel exergy loss objective function,

they could be considered negligible. The fact that the AFS-A and PS destroy and lose the most

exergy over the mission would indicate that they are also the subsystems with the most potential

for improvement.

An initial examination of the exergy destruction results shown in Figure 5.2 for the OLS

may lead one to think the result is in error; however, the OLS exergy destruction is only being

tracked for the pump losses. Also, the exergy destruction in the fuel / oil heat exchanger is

148

Figure 5.2 Total exergy destruction plus fuel exergy loss for each of the nine subsystems after the first ILGO

iteration.

accounted to the FLS, and no other energy processes are included in the OLS model. Finally,

taking into account that the weight of the OLS is 0.1% of the gross takeoff weight, the total

exergy destruction for the OLS appears to be reasonable.

When considering the subsystem weights given in Table 5.3, the PS and AFS-A again

have the largest contribution to the gross takeoff weight of the AAF but in a lesser sense. The PS

and AFS-A are easily the heaviest of the subsystems. The resulting weights of the partially

optimized subsystems are given in Table 5.3.

Table 5.3 AAF subsystem weights and the percentage of AAF empty weight after the first ILGO iteration.

AFS-A PS ECS VC/PAOS FLS ES CHS OLS FCS Weight (lbm) 14980.8 5418.3 1297.1 1608.1 491.5 929.5 325.3 37.8 429.3

% empty weight 58.7% 21.2% 5.1% 6.3% 1.9% 3.6% 1.3% 0.1% 1.7%

Note that the subsystem total exergy destruction plus fuel exergy loss (in Figure 5.2) and

weight results (in Table 5.3) are for a partially optimized solution as only the first ILGO iteration

had completed after a few months of execution. The perceived cause of the lengthy execution is

discussed at the end of this chapter. Previous results of the ILGO decomposition applied to a

completed five-subsystem AAF synthesis / design optimization (Rancruel, 2002) are used to

extrapolate the AAF objective function values and subsystem weights found in the present thesis

work towards a system-level optimum. These results are discussed next.

2.6E+07

2.5E+08

6.1E+041.7E+05

4.7E+052.5E+05 3.5E+05

2.2E+01

2.6E+04

1

10

100

1,000

10,000

100,000

1,000,000

10,000,000

100,000,000

1,000,000,000

AFS‐A PS ECS VCPAOS FLS ES CHS OLS FCS

Total Exergy Destruction Plus Fuel Exergy Loss (kJ)

Subsystem Total Exergy Destruction Plus Fuel Exergy Loss

149

5.2.2 Projected Optimum and Comparison

Although only a partial optimization was completed for the nine-subsystem AAF in this

thesis work, previous results of an ILGO decomposition applied to a fixed-wing AAF are used to

predict the optimum for the nine-subsystem AAF system. For example, the work of Rancruel

(2002), previously discussed in Chapter 2, applies ILGO to a fixed-wing AAF system flying a

very similar mission. The weight of each of the subsystems modeled in Rancruel (2002) is

tracked versus each ILGO iteration and the percentage improvement of the subsystem weights is

shown in Table 5.4. If the weight reduction percentages are applied to the result of the first

Table 5.4 AAF Subsystem percent weight reduction versus ILGO iteration (Rancruel, 2002).

ILGO Iteration WTO WPS WECS WVC/PAOS WFLS

Average Reduction

1 -- -- -- -- -- --

2 13.0% 17.1% 20.0% 22.0% 17.9% 18.0%

3 5.3% 9.5% 15.3% 15.6% 15.2% 12.2%

4 3.2% 2.6% 8.2% 7.4% 12.8% 6.9%

5 1.0% 4.5% 3.6% 3.2% 2.9% 3.0%

6 1.4% 1.9% 1.9% 2.1% 2.4% 1.9%

7 0.2% 0.8% 1.9% 2.1% 0.8% 1.1%

ILGO iteration given in the previous section, the resulting optimum AAF system weights are

extrapolated to those given in Table 5.5. Note that no percentage improvement is assumed for

the OLS due to the fact that the OLS weight equation (see Table 3.6) is only a function of the

number of engines. The ES weight is calculated based on AAF empty weight, which is a

Table 5.5 Projected AAF subsystem weights versus ILGO iteration based on the ILGO progression from Rancruel (2002).

ILGO #

AFS-A (lb)

PS (lb)

ECS (lb)

VCPAOS (lb)

FLS (lb)

ES (lb)

CHS (lb)

OLS (lb)

FCS (lb)

1 14980.8 5418.3 1297.1 1608.1 491.5 929.5 325.3 37.8 429.3

2 11611.4 4491.5 1037.7 1255.1 403.7 926.2 325.3 37.8 419.9

3 10705.5 4063.7 879.2 1059.0 342.3 913.6 325.3 37.8 414.4

4 9988.4 3956.8 807.1 980.5 298.4 905.8 325.3 37.8 409.3

5 9944.7 3778.6 778.3 949.2 289.6 903.5 325.3 37.8 408.0

6 9622.1 3707.3 763.9 929.6 282.6 899.9 325.3 37.8 404.4

7 9628.4 3678.8 749.5 909.9 280.4 899.5 325.3 37.8 404.4

150

function of the other subsystem weights. Thus, an iteration for the ES weight (which is a

function of the AFS-A empty weight) is required. The FCS weight is scaled based on the AAF

empty weight, EmptyW , (which consists of the sum of the subsystem weights) but only decreases

weight at a reduced rate compared to EmptyW due to the nature of the FCS equation (see Table

3.6). The FCS weight prediction equation derived is as follows for the ith ILGO iteration:

489.0)1(

1 1

i

FCSiAAFS

iiAAFSi

FCS WW

WW (5.1)

Finally, the CHS weight is not a function of aircraft weight but rather of the number of

hydraulic functions and the level of redundancy on the AAF aircraft. Thus, no improvement was

assumed when projecting the optimum CHS result.

The AAF gross takeoff weight and fuel weight are also extrapolated from the first ILGO

iteration result to completion based on the results from Rancruel (2002) and these extrapolated

results are given in Table 5.6. Note that the empty weight percent improvement is result of the

Table 5.6 Extrapolated nine-subsystem AAF gross takeoff weight and empty weight versus ILGO iteration based on the ILGO progression from Rancruel (2002).

ILGO # TOW (lbm)

% Improvement EmptyW (lbm) %

Improvement

0 60000.0 -- 39665.5 --

1 38599.5 -35.7% 25517.8 -35.7%

Extrapolated Results:

2 33590.4 -13.0% 20508.7 -19.6%

3 31822.5 -5.3% 18740.8 -8.6%

4 30791.2 -3.2% 17709.5 -5.5%

5 30496.5 -1.0% 17414.9 -1.7%

6 30054.6 -1.4% 16972.9 -2.5%

7 29995.6 -0.2% 16913.9 -0.3%

gross takeoff weight and subsystem weight improvement predictions. The predicted system-

level optimum subsystem weights after seven ILGO iterations for the nine-subsystem AAF are

shown in Table 5.7. The optimum results from Rancruel (2002) after seven ILGO iterations are

for a fixed-wing AAF system and greater improvements are expected from an AAF with

morphing-wing technology so the extrapolated optimums shown here may indeed be

conservative.

151

Table 5.7 Extrapolated AAF subsystem system-level optimum weights after seven ILGO iterations along with the percentage of AAF empty weight.

AFS-A PS ECS VC/PAOS FLS ES CHS OLS FCS Weight (lbm) 9628.4 3678.8 749.5 909.9 280.4 899.5 325.3 37.8 404.4 % empty weight 56.9% 21.7% 4.4% 5.4% 1.7% 5.3% 1.9% 0.2% 2.4%

The AAF aircraft system sized in Rancruel (2002) was a much smaller aircraft overall

than the one optimized here. However, some conclusions can be made about the integrity of this

model from a comparison between the two. The extrapolated subsystem weights from this thesis

work are compared to the subsystem weight results from Rancruel in Table 5.8. The

Table 5.8 Extrapolated subsystem optimum weights versus the optimum subsystem weights from Rancruel (2002).

TOW PSW ECSW AFSW FLSW PAOSVCW /

Rancruel (2002) (lbm) 22443.1 2275.2 573.2 6834.3 704.4 511.5 Predicted Optimum (lbm) 29995.6 3678.8 749.5 9628.4 280.4 909.9 % Difference 34% 62% 31% 41% -60% 78%

extrapolated optimums compare relatively well to the results from Rancruel (2002) with one

exception: the weight of the FLS. The explanation for this difference may be because only one

ILGO iteration had completed for the nine-subsystem AAF aircraft system. The initial coupling

function values are arbitrarily set (within limits) for this first ILGO iteration and the subsystem is

optimized without any knowledge of the actual coupling function values from the other

subsystems until this first iteration has completed. Obviously, after this first iteration, the

coupling function values are no longer arbitrary and are updated with actual values for the

subsystem interactions. In other words, the weight of the FLS could have actually increased in

the second ILGO iteration due to having real interactions with the other subsystems. However,

further investigation of the FLS behavior must be left to future work as must verification of the

extrapolated system-level optimum found here.

The following section briefly addresses the highest-payoff operational decision variables

and their effect on the morphing AFS-A model.

5.3 Parametric Study of the Morphing-Wing AFS-A

The benefits of adding morphing-wing technology to an aircraft that flies dissimilar

mission segments has been addressed in the literature review (Butt, 2005) and in the first set of

152

results presented in this thesis (Smith et al. 2007). The morphing-wing AFS-A used in both

studies has been allowed to morph significantly. The benefits of a limited amount of morphing

such as that due to variable wing sweep, high-lift devices, etc. is known. However, the ability to

significantly morph the wing in ways that are not widely used in production (e.g., via wing

length and taper ratio) are addressed in this section via multiple parametric studies.

The first parametric study shows the variation of mission segment fuel burned for three

flight conditions: subsonic climb (Mach 0.536 from a 20,000 ft to 41,700 ft altitude), subsonic

cruise (Mach 0.656 at a 41,700 ft altitude) and supersonic cruise (Mach 1.5 at a 30,000 ft

altitude) which correspond to mission segments 4, 5, and 17, respectively, as found in the

partially optimized subsystem of the nine-subsystem AAF aircraft. A second parametric study of

the subsonic cruise and supersonic cruise mission segments is conducted to compare the exergy

destruction versus the fuel consumption results from the first parametric study to see the trends

of the former with respect to the fuel burned performance metric for the mission segment.

The baseline AFS-A configuration and performance for the 4th, 5th, and 17th mission

segments is given in Table 5.9. Note that the sweep angles, LE , wing lengths, L , and

thickness-to-chord ratios, ct / , are not significantly different between the subsonic and

supersonic mission segments. Furthermore, the performance metric for the mission segment is

the fuel burned. Note also that the PS is not re-optimized for these parametric studies and any

Table 5.9 Baseline AAF configuration and performance for mission segment 4, 5, and 17.

Subsonic Climb

Segment 4

Subsonic Cruise

Segment 5

Supersonic Cruise

Segment 17

LE (deg) 30.3 27.4 27.9

L (ft) 53.4 53.8 52.5

AR 6.09 3.12 3.11

0.30 0.23 0.23

ct / 0.072 0.071 0.073

refS (ft2) 691 731 349

AAF Performance

DL CC / 11.1 11.3 3.4

Fuel Burned (lbm) 437.7 1179.8 225.3

Mission Fuel Burned (lbm)

11299.5

153

decrease in AFS-A fuel burned is due to the energy equation for the specific flight condition (see

Table 3.5) with fixed inputs for sfc from the PS.

The first parametric study looks at the effect of varying the aspect ratio and sweep angle

with respect to the fuel burned for the mission segment. The parametric study performed on the

subsonic climb segment, mission segment 4, is shown in Figure 5.3. The resulting effect of

Figure 5.3 Variation of the mission segment fuel burned with variations in aspect ratio and the sweep angle

for mission segment 4 (subsonic climb at Mach 0.536 from a 20,000 ft to 41,700 ft altitude).

changing the aspect ratio and sweep angle is very small since changing the aspect ratio by 10%

and the sweep angle by 20% from the baseline only yields a change in fuel consumption of 5.7

lbm. The sweep-angle variation shows very little effect on performance as the three different

curves representing the different sweep angles are very close to each other, while the aspect ratio

must be increased beyond the “knee” in the curve to see any appreciable change in the mission

segment. In this case, it appears the partially optimized solution for this mission segment is near

the unit-level optimum solution as little improvement is shown over the baseline fuel

consumption of 437.7 lbm and little sensitivity is observed to fuel burned for changes in sweep

angle or aspect ratio for the subsonic climb mission segment.

The second flight condition (subsonic cruise at Mach 0.656) results show some different

trends and appear in Figure 5.4. Notice that similar to the subsonic climb segment, there is a

436

437

438

439

440

441

442

443

2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5

Fuel Burned in M

ission Segm

ent (lbm)

Aspect Ratio

‐20% Sweep

+20% Sweep

Baseline Sweep

154

definitive “knee” in the curve for the mission segment fuel burned; however, a continued

increase in aspect ratio has a negative effect on the fuel burned. Also, the sweep angle has a

greater effect in this case as compared to the subsonic climb mission segment. Note also that

increasing both wing sweep angle and aspect ratio causes fuel consumption to spike, indicative

of the loss of wing surface area (because the wing length is held constant). Finally, note that

the fuel burned for mission segment 5 for the partially optimized AAF is 1179.8 lbm and little


for mission segment 5 (subsonic cruise at Mach 0.656 at a 41,700 ft altitude).

improvement potential is shown in Figure 5.4 (only a 0.8% improvement in fuel consumption for

a 20% sweep angle decrease and a 10% increase in aspect ratio) so that the design of the AFS-A

may have already been near the unit-level optimum solution for the subsonic cruise mission

segment as well.

However, subsonic and supersonic flight may yield different results. The results for the

supersonic parametric study are shown in Figure 5.5. The baseline configuration burns 225 lbm

of fuel, but a 20% increase in sweep angle to 36.4 deg for the supersonic mission segment burns

only 190 lbm of fuel for a 15.8% decrease in fuel consumption. A 10% increase in aspect ratio

yields an 11.7% decrease in fuel burned or 198 lbm. The most improved point in Figure 5.5 is for

a 20% increase in sweep angle and 20% increase in aspect ratio for a 31% decrease in fuel

consumption over the baseline configuration. This parametric study indicates that the partially

1160

1170

1180

1190

1200

1210

1220

1230

1240

1250

1260

1270

2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

Fuel Burned oin M

ission Segm

ent (lbm)

Aspect Ratio

‐20% Sweep

BaselineAR

+10% AR

‐10%

AR

+20% AR

155

optimized solution, the baseline, is not fully optimized as the parametric study yields a

significant decrease in fuel consumption.


for mission segment 17 (supersonic cruise at Mach 1.5 and 30,000 ft altitude).

A second study is conducted to see the variation of fuel consumption with variations in

the thickness-to-chord ratio, ct / , and taper ratio, , for both the subsonic and supersonic

mission segments. The subsonic climb mission segment results are shown in Figure 5.6.

Figure 5.6 Variation of the mission segment fuel burned with variations in thickness-to-chord ratio for

mission segment 4 (subsonic climb at Mach 0.536 from a 20,000 ft to 41,700 ft altitude).

156

Changing the taper ratio showed no measureable effect on the subsonic climb mission, but the

thickness to chord ratio did have some effect and the result also indicates the baseline aircraft

configuration was at a near-optimum value.

The supersonic cruise mission segment study showed less than a 1% change for fuel

consumption for an increase or decrease of the thickness-to-chord ratio by 10% and/or a 20%

increase or decrease in the taper ratio. This highlights the fact that in supersonic flight, the wing

thickness and taper ratio make a smaller contribution to the total drag via the skin friction drag

and that the total drag is dominated by the wave drag in supersonic flight. The subsonic cruise

segment was similarly insensitive to changes in the thickness-to-chord and taper ratio with

respect to fuel consumption.

The conclusion from the taper ratio and thickness to chord ratio study is that either the

taper ratio and thickness to chord ratio have a negligible effect on the aircraft performance in

cruise flight, or more likely that the drag buildup method and lift calculations do not have the

resolution required to effectively measure their effect on aircraft performance. The only

measurable effect found on fuel consumption was the thickness-to-chord ratio during the

subsonic climb segment. Furthermore, it should be emphasized that these changes are made

about a point (i.e., synthesis/design), which is already optimal or nearly so. Thus, the conclusions

drawn cannot be generalized to syntheses/designs, which may be far from optimal. Because the

change in fuel consumption for significant change in thickness-to-chord ratios and taper ratios

was negligible for the subsonic and supersonic cruise segments, the results will not be given

here.

The results of the first two parametric studies for varying aspect ratio, sweep angle, taper

ratio, and thickness-to-chord ratio are based on using fuel burned as the performance metric. To

show what the results would be if the performance metric were changed to exergy destruction, a

final parametric study is conducted. This study examines the variation in mission segment

exergy destruction with variations in aspect ratio and sweep angle for the subsonic cruise and

supersonic cruise mission segments (segments 5 and 17, respectively). The baseline sweep and

aspect ratio are shown in Table 5.9; and the taper ratio is varied up to 20% from the baseline,

while the sweep angle is increased and decreased 20% from the baseline. The subsonic cruise

results are shown in Figure 5.7, and the supersonic cruise results are shown in Figure 5.8.

157

Figure 5.7 Variation of the mission segment exergy destruction with variations in aspect ratio and the sweep

angle for mission segment 5, subsonic cruise at Mach 0.656 at 41,700 ft altitude.

Figure 5.8 Variation of the mission segment exergy destruction with variations in aspect ratio and the sweep

angle for mission segment 17, supersonic cruise at Mach 1.5 and 30,000 ft altitude.

The subsonic cruise results in Figure 5.7 follow the fuel burned results in Figure 5.4

relatively closely. Note that the “bump” for the ‘+20% Sweep’ curve in Figure 5.4 barely

appears in Figure 5.7 (i.e., is significantly smoothed out). There may be multiple reasons for the

158

fuel consumption result being more volatile than the exergy destruction result, such as the fact

that the fuel burned is technically dependent on the PS, which in this case is considered to be

constant. The bump may disappear with additional PS optimizations. That being said, the trends

of the exergy destruction results follow the fuel burned results quite well for the subsonic cruise

segment.

The supersonic cruise segment total exergy destruction trends shown in Figure 5.8 follow

the mission segment fuel burned trends shown in Figure 5.5 also rather well. The conclusion at

least for the case when the AFS-A is optimized by itself for a fixed sfc is that the exergy

destruction is directly proportional to the fuel consumption of the AAF in supersonic cruise and

subsonic cruise. However, as shown in Periannan, von Spakovsky, and Moorhouse (2008)

where a three-subsystem AAF aircraft with AFS-A, PS, and ECS is optimized, this may not

always be the case. Furthermore, the exergy destruction result presented here appears to have a

smoother response than the fuel burned result for changes in the AFS-A wing geometry.

159

Chapter 6

Conclusions/Recommendations

This thesis work produced a number of conclusions and recommendations related to the

morphing-wing AAF synthesis/design optimization problem. The first set of results from Smith

et al. (2007) was meant to be an extension of the work of Butt (2005) and a stepping stone for the

new PS model being used in the nine-subsystem AAF. The work and research required to have

all 9 subsystems fly the mission and integrating the subsystems for the nine-subsystem AAF

proved to be the bulk of the work for this thesis. However, a few conclusions and

recommendations are drawn, which include the following:

1. The morphing-wing AFS-A and turbofan PS results compare well with Butt (2005). The

high wing-weight and fuel-weight penalties for morphing-wing technology still show an

improvement over a fixed-wing AAF flying the same mission. However, the morphing-

wing-fuel and wing-weight penalties are arbitrarily set due to a lack of information about

the methods used to morph the wings. Further study is recommended to establish the

actual structural weight penalties and power requirements for the morphing-wing

technology.

2. The results given in Smith et al. (2007) allude to the possibility of a new paradigm or way

of thinking to be adopted for supersonic fighter aircraft design. A fixed-wing supersonic

AAF design can typically be viewed as “design a supersonic AAF that can fly at subsonic

speeds” while the morphing-wing supersonic AAF design could be viewed as “design a

subsonic AAF that can fly at supersonic speeds.” In other words, morphing-wing

technology is an enabling technology that allows aircraft designers to move away from

designing aircraft for supersonic flight, enabling them instead to concentrate on an

efficient aircraft design that has the capability of flying at supersonic speeds.

3. The partially optimized nine-subsystem results show a single one inconsistency with

previous results from Rancruel (2002), namely, in the FLS weight. However, this is

somewhat to be expected due to the fact that the set of results produced here is not for a

fully optimized solution and does not have the interactions with the other subsystems

established at actual values since only the first ILGO iteration completed. That being

160

said, the FLS weight equations and subsystem interactions may need to be studied in

more detail to verify model accuracy.

4. The extrapolated optimum solutions for the nine-subsystem AAF are likely conservative

compared to the results shown in Rancruel (2002) because of the additional benefit of

morphing-wing technology. The PS in particular should have a smaller design mass flow

rate and design Mach number, which would likely, along with the benefits of morphing-

wing technology, drive the empty weight lower than what is found here.

5. The difficulty of optimizing the nine-subsystem AAF proved to be in calculation time

and resources available. It is believed that the calculation time of the iSCRIPT™

software package is significantly slower than what was expected, in particular, when

calculation-heavy code is running. Initial partial optimizations of the nine-subsystem

AAF showed the estimated time-to-optimize at nearly 7 months using parallel processing

on an Intel Q6600-based (quadruple core, 2.4 GHz) PC.

6. Further validation of every subsystem model and additional integration within the AAF

was not feasible during this thesis work considering the calculation / optimization time

and human resources available to do the work. Thus, additional work on improving

calculation times and on subsystem validation and integration not only at the unit-level

but also at the system-level is recommended. Full validation and verification of the nine-

subsystem AAF requires a significant amount of computing power using the iSCRIPT™

software platform.

7. A recommendation for further study would be to use advanced fixed-wing fighter aircraft

designs such as a blended-wing-body (BWB) to represent the most advanced fixed-wing

technology available. The aerodynamics model of a BWB would likely require a higher-

fidelity drag model to model the BWB’s flight performance compared to that of the

morphing-wing AFS-A on a conceptual level.

8. The negligible effect of varying the thickness-to-chord ratio and taper ratio in the

morphing-wing parametric studies for subsonic and supersonic cruise flight highlights the

possibility that the component drag buildup method used does not have the resolution

required to show a measurable effect of varying these wing geometry parameters. If

further study is to be done with the drag model from Raymer (2003), it is recommended

161

that the thickness-to-chord ratio be set to a constant parameter for cruise segments and

not participate as a DOF in the optimization except perhaps during climb segments.

9. The high-payoff wing parameters to morph should be investigated further. The benefits

of the application of variable wing sweep is well known via the F-14 Tomcat. However,

drastic wing morphing may not be possible in the near future and the best-value-

geometry morphing with the highest payoff and least risk should be identified via cost /

benefit studies and pursued.

10. The structural weight and power required for discrete types of morphing need to be

established (e.g., the penalties for wing length morphing, the penalties for variable wing

sweep, etc.), and conceptual-level optimizations should be used to find the best set of

morphing parameters to study.

11. The exergy destruction and fuel consumption were compared to find trends in their

predictions of the AAF for both supersonic and subsonic cruise mission segments. The

exergy destruction objective trend directly correlates with the fuel burned objective trend

(at least for the AFS-A optimized in isolation) but has a smoother response than the fuel

burned objective for changes in the AAF wing configuration. The supersonic cruise

flight condition matches better than the subsonic cruise flight condition. Recommended

further study in this area would be to perform a parametric study of the AFS-A, but

allowing the PS and possibly another subsystem such as the ECS to optimize (or at least

vary the throttle setting) for each set of AFS-A wing geometries to see if the direct

correlation between fuel consumption and exergy destruction is maintained, or instead

follows the trends shown in Periannan, von Spakovsky, and Moorhouse (2008).

162

References

1. Anderson Jr., J. D., 2001, Fundamentals of Aerodynamics, 3rd Edition, New York: McGraw-Hill.

2. Anderson, J.D. , 1984, Fundamentals of Aerodynamics, New York: McGraw-Hill. 3. Anderson, J.D. Jr., 1999, Aircraft Performance and Design, WCB/McGraw-Hill 4. Bejan, 1996, Entropy Generation Minimization, pg 37 5. Bejan, A. 1996. Entropy Generation Minimization: The Method of Thermodynamic

Optimization of Finite-Sized Systems and Finite-Time Processes. Boca Raton, FL: CRC Press, Inc.

6. Beretta, G. P., Gyftopoulos, E. P., Park, J. L., and Hatsopoulos, G. N., 1984, Quantum Thermodynamics: A New Equation of Motion for a Single Constituent of Matter, Il Nuovo Cimento, 82 B, 2, pp. 169-191.

7. Beretta, G. P., 2006, Steepest-Entropy-Ascent Irreversible Relaxation Towards Thermodynamic Equilibrium: The Dynamical Ansatz that Completes the Gyftopoulos-Hatsopoulos Unified Theory with a General Quantal Law of Causal Evolution, International Journal of Thermodynamics, ICAT, Istanbul, Turkey, Sept., vol. 9, no. 3.

8. Bolz, R. E., & Tuve, G. L. (1973). CRC handbook of tables for applied engineering science. 2d ed. Editors: Ray E. Bolz [and] George L. Tuve. CRC handbook series. Cleveland, Ohio: Chemical Rubber.

9. Bowcutt, K., Hypersonic Aircraft Optimization Including Aerodynamic, Propulsion, and Trim Effects, AIAA Paper No. 19925055, 1992.

10. Bowman, J., Sanders, B., Weisshaar, T., 2002, Evaluating the Impact of Morphing Technologies on Aircraft Performance, AIAA Paper 2002-1631.

11. Brewer, K.M., 2006. Exergy Methods for Mission-Level Analysis and Optimization of Generic Hypersonic Vehicle Concepts. Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, M.S. Thesis.

12. Butt, J.R., 2005. A Study of Morphing Wing Effectiveness in Fighter Aircraft using Exergy Analysis and Global Optimization Techniques. Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, M.S. Thesis.

13. Chase, M. W. 1998. NIST-JANAF thermochemical tables. Journal of physical and chemical reference data, no. 9. [Washington, D.C.]: American Chemical Society

14. Cloyd, J.S.; A status of the United States Air Force’s More Electric Aircraft Initiative. Energy Conversion Engineering Conference, 1997. IECEC-97.

15. CRC, 1976. Handbook of Tables for Applied Engineering Science. CRC Press. 16. Crowe, 2001. Engineering Fluid Dynamics. pg 16, 418-419. 17. Curry, R.E. and Sim, A.G. 1982, “The Unique Aerodynamic Characteristics of the AD-1

Oblique-Wing Research Airplane,” AIAA paper 82-1329, AIAA 9th Atmospheric Flight Mechanics Conference, Aug 9-11 1982, San Diego, CA.

18. Davenport, C.J., 1983, “Correlations for Heat Transfer and Flow Friction Characteristics of Louvered Fin,” AIChE Symposium Series, No.225, 79, 19-27.

19. Dryden X-Press, 1979, AD-1 Construction Completed, Feb 23, p. 2. 20. El-Sayed, Y.M. and Evans, R.B., 1970, Thermoeconomics and the Design of Heat Systems,

Journal of Engineering for Power, ASME Transactions, vol. 118, October, N.Y. 21. Elgerd, O.I., van der Puije, P.D. 1998. Electric Power Engineering. pg 74, 75

163

22. Figliola R. S., Tipton, R., Ochterbeck, J.M.,1997. “Thermal Optimization of the ECS on an Aircraft with an Emphasis on System Efficiency and Design Methodology,” Society of Automotive Engineers, Inc. 971241 pp 137-143.

23. Frangopoulos, C.A., Evans R.B., 1984, Thermoeconomic Isolation and Optimization of Thermal System Components, Second Law Aspects of Thermal Design, HTD Vol. 33, ASME, N.Y., N.Y., August.

24. Frangopoulos, C.A., von Spakovsky, M. R., Sciubba, E., 2002, A Brief Review of Methods for the Design and Synthesis Optimization of Energy Systems, International Journal of Applied Thermodynamics, ICAT, Istanbul, Turkey, December, vol. 5, no. 4.

25. Greene R., 1992, Compressors, Selection, Usage, and Maintenance, McGraw Hill Inc, USA. 26. Gyftopoulos, E. P., and Beretta, G. P., 1991, Thermodynamics: Foundations and

Applications, Macmillan Publishing Co., New York. 27. Gyftopoulos, E. P. and Beretta, G. P., 2005, Thermodynamics – Foundations and

Applications, Dover Pub., N. Y. 28. Hatsopoulos, G. N. and Gyftopoulos, E. P., 1976a,b,c,d, A Unified Quantum Theory of

Mechanics and Thermodynamics – Part I: Postulates, Part IIa: Available Energy, Part IIb: Stable Equilibrium States, Part III: Irreducible Quantal Dispersions, Foundations of Physics, 6, 1, pp. 15-31, 2, pp. 127-141, 4, pp .439-455, 5, pp. 561-570.

29. Heiser, W. H., and Pratt, D. T., 1994, Hypersonic Airbreathing Propulsion, AIAA, Inc., Washington, D.C.

30. Hudson W. A. and Levin M. L., 1986. Integrate Aircraft Fuel Thermal Management. Rockwell International Corp. El Segundo, CA. Intersociety Conference on Environmental Systems (16th: 1986: San Diego, Calif.). Aerospace environmental systems: proceedings of the Sixteenth ICES conference. Pg 11-25.

31. Incropera F. and DeWitt D., 1990, Fundamental of Heat and Mass Transfer. John Wiley and Sons, Inc.

32. Kakac S. and Liu H., 2002, Heat Exchangers Selection, Rating, and Thermal Design. CRS press.

33. Kays, W. M. and London, A. L., 1984, Compact Heat Exchangers, McGraw-Hill, Inc. pp 14, 16, 17, 18, 166, 287.

34. Kotas, T.J., 1985, The Exergy Method of Thermal Plant Analysis. 35. Leyland, G.B., 2002, Multi-Objective Optimization Applied to Industrial Energy Problems,

Department of Mechanical Engineering, University of Auckland, M.S. Thesis. 36. Majumdar, 2003, Oil Hydraulic Systems: Principles and Maintenance, McGraw-Hill, Inc.

pp 100-101, 133, 256, 320-323. 37. Maldonado, M.A.; Shah, N.M.; Cleek, K.J.; Walia, P.S.; Korba, G.J.; 1997; Power

Management and Distribution System for a More-Electric Aircraft (MADMEL) – program status, Energy Conversion Engineering Conference. Proceedings of the 32nd Intersociety, Volume 1, 27-July—August. Page(s): 274-279

38. Markell, K. C., 2005, Exergy Methods for the Generic Analysis and Optimization of Hypersonic Vehicle Concepts, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, M.S. Thesis.

39. Mattingly, J.D., Heiser, W.H. and Daley, D.H., 1987, Aircraft Engine Design, AIAA Education Series, New York, New York.

40. Mattingly, J. D., Heiser, W.H., and Pratt, D.T., 2002, Aircraft Engine Design, AIAA Education Series, Washington, DC.

164

41. Moir, I.; “More-electric aircraft-system considerations, Electrical Machines and Systems for the More Electric Aircraft (Ref. No. 1999/180)”, IEE Colloquium on 9 Nov. 1999, Page(s):10/1 - 10/9

42. Moir, I., Seabridge, A., 2001, Aircraft Systems: mechanical, electrical, and avionics subsystems integration, pg 164

43. Moorhouse D. J., Sanders B., von Spakovsky, M.R., and Butt, J., 2005, Benefits and Design Challenges of Adaptive Structures for Morphing Aircraft, International Forum on Aeroelasticity and Structural Dynamics 2005 (IFASD’05), AIAA, DLR, Bogenhausen, Germany, June 28th to July 1st.

44. Moorhouse D. J., Sanders B., von Spakovsky, M.R., and Butt, J., 2006, Benefits and Design Challenges of Adaptive Structures for Morphing Aircraft, The Aeronautical Journal, Royal Aeronautical Society, London, England, vol. 110, no. 1105, March, 2006, p 157-162.

45. Moran, M. J., 1989, Availability Analysis: a Guide to Efficient Energy Use, ASME Press, New York, New York.

46. Muñoz J. R., von Spakovsky M.R., 1999, A Second Law Based Integrated Thermoeconomic Modeling and Optimization Strategy for Aircraft / Aerospace Energy System Synthesis and Design (Phase I - Final Report), final report, Air Force Office of Scientific Research, New Vista Program, December.

47. Muñoz, J.R., von Spakovsky, M.R., 2000, The Use of Decomposition for the Large-Scale Synthesis / Design Optimization of Highly Coupled, Highly Dynamic Energy Systems - Theory, International Mechanical Engineering Congress and Exposition – IMECE’2000, ASME, Orlando, Nov. 5-10, AES-Vol. 40.

48. Muñoz, J.R., von Spakovsky, M.R., 2000, The Use of Decomposition for the Large-Scale Synthesis / Design Optimization of Highly Coupled, Highly Dynamic Energy Systems - Application, International Mechanical Engineering Congress and Exposition –IMECE’2000, ASME, Orlando, Nov. 5-10, AES-Vol. 40.

49. Muñoz, J.R., von Spakovsky, M.R., 2000, Decomposition in Energy System Synthesis / Design Optimization for Stationary and Aerospace Applications, 8th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA, September 6-8.

50. Muñoz, J.R., von Spakovsky, M.R., 2000, An Integrated Thermoeconomic Modeling and Optimization Strategy for Aircraft / Aerospace Energy System Design, Efficiency, Costs, Optimization, Simulation and Environmental Aspects of Energy Systems (ECOS’00), Twente University, ASME, Netherlands, July 5-7.

51. Muñoz, J.R., von Spakovsky, M.R., 2001, A Decomposition Approach for the Large Scale Synthesis/Design Optimization of Highly Coupled, Highly Dynamic Energy Systems, International Journal of Applied Thermodynamics, March, vol. 4, no. 1.

52. Muñoz, J.R., von Spakovsky, M.R., 2001, The Application of Decomposition to the Large Scale Synthesis/Design Optimization of Aircraft Energy Systems, International Journal of Applied Thermodynamics, June, vol. 4, no.2.

53. Muñoz, J.R., von Spakovsky, M.R., 2003, Decomposition in Energy System Synthesis / Design Optimization for Stationary and Aerospace Applications, AIAA Journal of Aircraft, special issue, Vol. 39, No. 6, Jan-Feb.

54. Nicolai, L., 1975, Fundamentals of Aircraft Design, published by the author. 55. Nist-janaf thermochemical tables, fourth edition. 1998. [S.l.]: American Institute Of Phy.

165

56. Pearson, W.; The More Electric/All Electric Aircraft – A Military Fast Jet Perspective; All Electric Aircraft (Digest No. 1998/260) June 1998; Page(s) 5/1 – 5/7

57. Periannan, V., 2005, Investigation of the Effects of Different Objective Functions/Figures of Merit on the Analysis and Optimization of High Performance Aircraft System Synthesis/Design, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, M.S. Thesis.

58. Periannan, V., von Spakovsky, M. R., and Moorhouse, D. J., 2008, “A study of various energy- and exergy-based optimisation metrics for the design of high performance aircraft systems”, The Aeronautical Journal, vol. 112, no. 34

59. Periannan, V., von Spakovsky, M.R., Moorhouse, D., 2008, Energy versus Exergy-Based Figures of Merit for the Optimal Synthesis/Design of High Performance Aircraft Systems, The Aeronautical Journal, Royal Aeronautical Society, London, England, vol. 112, no. 1134, pp 449-458.

60. Rancruel, D. F., 2003, A Decomposition Strategy Based on Thermoeconomic Isolation Applied to the Optimal Synthesis/Design and Operation of an Advanced Fighter Aircraft System, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, M.S. Thesis.

61. Rancruel, D. F., von Spakovsky, M. R., 2003a, “Decomposition with Thermoeconomic Isolation Applied to the Optimal Synthesis/Design of an Advanced Fighter Aircraft System”, International Journal of Thermodynamics, ICAT, Istanbul, Turkey, September, vol. 6, no. 3.

62. Rancruel, D. F., von Spakovsky, M. R., 2003b, “A Decomposition Strategy Applied to the Optimal Synthesis/Design and Operation of an Advanced Fighter Aircraft System: A Comparison with and without Airframe Degrees of Freedom”, International Mechanical Engineering Congress and Exposition – IMECE’2003, ASME Paper No. 44402, N.Y., N.Y., November.

63. Rancruel, D. F., von Spakovsky, M. R., 2004a, “Advanced fighter aircraft sub-systems optimal synthesis/design and operation: Airframe integration using a thermoeconomic approach”, 10th AIAA/ISSMO Multi-disciplinary Analysis and Optimization Conference, Aug. 30 - Sept. 1, Albany, New York, vol. 6, p 3403-3415.

64. Rancruel, D. F., von Spakovsky, M. R., 2004b, “A Decomposition Strategy based on Thermoeconomic Isolation Applied to the Optimal Synthesis/Design and Operation of an Advanced Tactical Aircraft System, Efficiency, Costs, Optimization, Simulation and Environmental Aspects of Energy Systems” (ECOS’04), Guanajuato, Mexico, ASME, July.

65. Rancruel, D. F., von Spakovsky, M. R., 2004, “Use of a Unique Decomposition Strategy for the Optimal Synthesis/Design and Operation of an Advanced Fighter Aircraft System”, 10th AIAA/ISSMO Multi- disciplinary Analysis and Optimization Conference, Aug. 30 - Sept. 1, Albany, New York.

66. Rancruel, D., 2005, Dynamic Synthesis/Design and Operation/Control Optimization Approach Applied to a Solid Oxide Fuel Cell based Auxiliary Power Unit under Transient Conditions, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Ph.D. Dissertation.

67. Rancruel, D. F., von Spakovsky, M. R., 2006, “A Decomposition Strategy based on Thermoeconomic Isolation Applied to the Optimal Synthesis/Design and Operation of an Advanced Tactical Aircraft System”, Energy: The International Journal, Elsevier, available

166

on-line at http://dx.doi.org/10.1016/j.energy.2006.03.004, vol. 31, no. 15, December, p 3327-3341.

68. Raymer, Daniel P., 1999, Aircraft Design: A Conceptual Approach, AIAA Education Series, Reston, VA.

69. Raymer, Daniel P., 2006, Aircraft Design: A Conceptual Approach, Fourth Edition, AIAA Education Series, Reston, VA.

70. Riggins, D.W., “Evaluation of Performance Loss Methods for High-Speed Engine and Engine Components”, Journal of Propulsion and Power, Vol. 13, No. 2, March-April 1997.

71. Riggins, D. W., “High-Speed Engine/Component Performance Assessment Using Exergy and Thrust Based Methods,” NASA Contractor Report 198271, 1996.

72. Riggins, D. W., Private Communication, July 2003 - July 2004 73. Roskam, J., Airplane Design Part: II, 1985, pp 110, 185-186. 74. Saravanamuttoo, H.I.H., Rogers, G.F.C, Cohen, H., 2001, Gas Turbine Theory, Pearson

Education Limited, Harlow, England. 75. Shah, R. K., 1981, Compact Heat Exchanger Design Procedure in Heat Exchangers:

Thermal Hydraulic Fundamentals and Design, S. Kakac, AE Bergles, and F. Matinger editors, Hemisphere Publishing Corporation, pg 495-536

76. Shah, R.K. and Webb, R.L., 1982, Compact and Enhanced Heat Exchangers, in Heat Exchangers: Theory and Practice, J. Taborek, G.F. Hewitt, and N. Agfan editors, Hemisphere Publishing Corporation, pp 435-468

77. Smith, C. E., von Spakovsky, M.R., 2007, Time Evolution of Entropy in a System Comprised of a Boltzmann Type Gas: An Application of the Beretta Equation of Motion, International Mechanical Engineering Congress and Exposition – IMECE’2007, ASME Paper No. IMECE2007-42933, N.Y., N.Y., November.

78. Smith, K., Butt, J., von Spakovsky, Moorhouse, D., 2007, A Study of the Benefits of Using Morphing Wing Technology in Fighter Aircraft Systems, 39th AIAA Thermophysics Conference, Miami, FL, June 25-28.

79. Starkey, R. P., “Scramjet Optimization for Maximum Off Design Performance,” AIAA Paper No. 20043343, 2004.

80. Szargut J., Morris D.R., Steward F.R. (1988). Exergy Analysis of Thermal, Chemical and Metallurgical Processes. 332 pp. Hemisphere Publ. Corp., New York.

81. von Spakovsky, M.R., and Evans, R.B., 1993, Engineering Functional Analysis (Part I), Journal of Energy Resources Technology, ASME Transactions, Vol. 115, No. 2, N.Y., June.

82. von Spakovsky, M.R., 2008, The Second Law: A Unified Approach to Thermodynamics Applicable to All Systems and All States, Keenan Symposium: Meeting the Entropy Challenge, MIT, American Institute of Physics (AIP), AIP Proceedings, Cambridge, MA, October 2007.

83. von Spakovsky, M.R., Smith, C. E., Verda, V., 2008, Quantum Thermodynamics for the Modeling of Hydrogen Storage on a Carbon Nanotube, International Mechanical Engineering Congress and Exposition – IMECE’2008, ASME Paper No. IMECE2008-67424, N.Y., N.Y., Oct.-Nov.

84. Weimer, J.A.; “The Role of Electric Machines and Drives in the More Electric Aircraft”, Electric Machines and Drives Conference, 2003. IEMDC’03. IEEE International, Volume 1, 1-4 June 2003. Page(s): 11-15

167

85. Zábranský, M., Ruzicka, V., Majer, V., and Domalski, E.S., (1996). Heat capacity of liquids: Critical review and recommended values. Journal of physical and chemical reference data, no. 6. [Washington, D.C.]: American Chemical Society.

168

Appendix A

Fan Performance Map Code

function [eff] = fan(xfan, Pi_cprim, Pi_cprimR) Pi_cprimR_map = 1.821; PRf = Pi_cprim/Pi_cprimR*Pi_cprimR_map; %Curve fitted equations for fan map, mattingly page 159, the elseif loops %progress from left to right across the fan map and checks for above stall %conditions or too low of flow rates. Low flow rates will set the %efficiency of the fan to 70%. Design fan efficiency is 0.89 (mattingly %pg 125. xact = xfan; ystall = 0.00013089775410*xact^2 -0.00518069645313*xact + 1.26052318037349; ycal2 = 0.00000005785153*xact^4 -0.00001162747108*xact^3 + 0.00092003348112*xact^2 -0.02526078062955*xact + 1.35610991970601; %left 80% ycal3 = 0.00000000685532*xact^5 -0.00000278371525*xact^4 + 0.00044925428731*xact^3 - 0.03590113760590*xact^2 + 1.42444807870004*xact + -21.31564085462291; %right 80% ycal4 = 0.00000265672539*xact^3 -0.00041471513906*xact^2 + 0.02982941208547*xact + 0.48191930572447; %left 82% ycal5 = 0.00000740839366*xact^3 -0.00168038353132*xact^2 + 0.13433234460665*xact -2.40691063865553; %right 82% ycal6 = -0.00000154556212*xact^3 + 0.00021313171573*xact^2 + 0.01364862191487*xact -0.13343794806055; %left 84% ycal7 = 0.00000187730332*xact^4 -0.00063352000447*xact^3 + 0.08021250388788*xact^2 -4.50398173025479*xact + 95.86165686002784; %right 84% yop = 0.00017181510217*xact^2 -0.01465955277341*xact + 1.56921934760171; %operating line if ((xact > 110 | xact < 30)) %if actual percentage of design flow rate is out of operating range set eff to 75% eff = 0.78; else if ystall >= PRf & PRf > ycal2 & PRf > yop & xact <= 90 %if PRf is greater than 78% eff, and less than stall, calc eff - assumes next line is 78% eff eff = 0.8-0.02*(PRf-ycal2)/(ystall-ycal2); else if ycal4 < PRf & PRf <= ycal2 & ystall >=PRf & PRf > yop & xact<=90 %PRf is less than 82% eff, greater than 80% eff, less than 90%, calc eff eff = 0.82-0.02*(PRf-ycal4)/(ycal2-ycal4); else if ycal4 < PRf & ystall >=PRf & PRf > yop & xact>90 %PRf is less than 82% eff, greater than 80% eff, over 90%, calc eff eff = 0.82-0.02*(PRf-ycal4)/(ystall-ycal4); else if ycal4 > PRf & PRf >= ycal6 & ystall >=PRf & PRf > yop & ((xact <= 100 & xact >=75)) %greater than 82% eff, above the 84% curve only eff = 0.84-0.02*(PRf-ycal6)/(ycal4-ycal6);

169

else if ycal4 > PRf & PRf >= yop & xact >100 %greater than 82% eff, over 100% eff = 0.89-0.07*(PRf-yop)/(ycal4-yop); else if ycal4 >= PRf & PRf >=yop & xact < 75 %greater than 82% eff, left of the 84% curve, over operating line eff = 0.89-0.05*(PRf-yop)/(ycal4-yop); else if yop < PRf & PRf <= ycal6 & ((xact<100 & xact >75)) %greater than 84% eff, over operating line eff = 0.89-0.05*(PRf-yop)/(ycal6-yop); else if PRf >= ycal3 & PRf<= ycal5 & ((xact>=65 & xact<=110)) %between 80 and 82% efficient, under operating line eff = 0.82-0.02*(ycal5-PRf)/(ycal5-ycal3); else if PRf>=ycal5 & PRf<=ycal7 & ((xact>=73 & xact<=100)) %between 82 and 84% efficient, only under 84% curve, under operating line eff = 0.84-0.02*(ycal7-PRf)/(ycal7-ycal5); else if PRf>=ycal7 & PRf<=yop & ((xact>=73 & xact<=100)) %between 84 and 89% efficient, under operating line eff = 0.89-0.05*(yop-PRf)/(yop-ycal7); else if PRf>=ycal5 & PRf<=yop & xact<73 %between 82 and 89% efficient, left of 84% curve, under op line eff = 0.89-0.07*(yop-PRf)/(yop-ycal5); else if PRf>=ycal5 & PRf<=yop & xact>=100 %between 82 and 89% efficient, right of 84% curve, under op line eff = 0.89-0.07*(yop-PRf)/(yop-ycal5); else eff = 0.78; %if points are off the fan map, give 78% default efficiency end end end end end end end end end end end end end

Morphing Wing Fighter Aircraft Synthesis/Design Optimization · Morphing Wing Fighter Aircraft...

Documents

Transcript of Morphing Wing Fighter Aircraft Synthesis/Design Optimization · Morphing Wing Fighter Aircraft...