Aerodynamics Glossary

8/11/2019 Aerodynamics Glossary

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Aerodynamics Glossary

Wing Design TipA most difficult aspect of wing design can be choosing the correct airfoil cross sectional

shape. Although most airfoil shapes can support flight, only the right one will savethousands of dollars in operational costs over the life of the aircraft. MultiSurfaceAerodynamics is a digital wind tunnel that can compare the performance of many airfoilshapes to make the airfoil selection process easy.

Aerodynamic Center

The aerodynamic center is a point along the airfoil or wing about which the momentcoefficient does not vary with an angle of attack change.AirfoilAn airfoil is the cross section of a wing. The airfoil shape and variations in angle ofattack are primarily responsible for the lift and profile drag of the wing.

Angle of AttackThe angle of attack is defined as the angle between the plane of the wing (airfoil chord)and the direction of motion (free stream velocity). The angle of attack can be varied toincrease or decrease the lift acting on the wing. An increase in lift often results in anincrease in drag.Center of PressureA point along the airfoil about which the moment due to the lift is ero, i.e., it is the pointof action of the lift. The center of pressure will change its position when the angle ofattack changes.ChordThe chord is the dimension of the airfoil from its leading edge to trailing edge.

Circulation!irculation is a measure of the vorticity in the flow field. "or an inviscid flow field, thelift is e#ual to the product of the circulation about the airfoil, the density and the velocity.Computational Fluid Dynamics (CFD)!omputational fluid dynamics is the term given to a variety of numerical mathematicaltechni#ues applied to solving the e#uations that govern fluid flows and aerodynamics.Modern CFD results can rival the accuracy of wind tunnels in testing airfoils, wings andentire airplanes for certain test configurations.

Density

The mass of a substance contained in a given volume divided by the volume. "or a

incompressible fluid, the density is considered to be constant throughout the flow field.$owever, for a compressible fluid, the density can vary from one location to the ne%t inthe flow field. The speed of sound in a fluid depends on the ratio of pressure changes todensity changes in the fluid.Drag

&rag is an aerodynamic force opposing the direction of motion. &rag can be due tosurface viscosity (friction drag), pressure differences due to the shape of an ob'ect (formdrag), lift acting on an finite wing (induced drag) and other energy loss mechanisms in


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the flow such as wave drag due to shock waves and inefficiencies in engines.Drag CoefficientThe drag coefficient is defined as the drag(dynamic pressure reference area). Thereference area is usually the plan*form or flat pro'ection (the wing+s shadow at noon) areaof the wing.

Dynamic PressureThe dynamic pressure is defied as the product of the density and the s#uare of thevelocity divided by two. The dynamic pressure has units of pressure, i.e. "orceArea. Thedynamic pressure is used to non*dimensionalie forces and pressures in aerodynamics.Flap Deflection AngleThe flap deflection angle is the angle between the deflected flap and the chord line. Theangle is positive for a downwards deflection of the flap. &eflect the flap downwards toincrease the airfoil+s lift.LiftThe lift is a force acting perpendicular to the direction of flight. The lift is e#ual to thefluid density multiplied by the circulation about the airfoil and the free stream velocity. n

level flight, the lift developed by an airplane+s must be e#ual to the weight of the entireairplane.Lift CoefficientThe lift coefficient is defined as the lift(dynamic pressure reference area). Thereference area is usually the plan*form area of a wing or horiontal pro'ection of thewing.ean aerodynamic chordThis chord is located along the wing and has the aerodynamic property of the two*dimensional wing.!ACA Airfoils

-A!A airfoils are wing cross sectiondesigns invented by the !ACAorganiation.-A!A eventually became -ASA (-ational Aeronautics and Space Administration). $ereare a few popular airplanes that have -A!A airfoil wings

Airplane "oot Airfoil Tip Airfoil

/eech 01 Twin /onana -A!A 23145.4 -A!A 23142

/*46 "lying "ortress -A!A 1142 -A!A 1141

!essna 402 -A!A 2542 -A!A 1142

!essna 462 4763*later -A!A 2542 -A!A 2542 mod

!essna 001 !itation -A!A 23145 -A!A 23142

&ouglas &!*3 -A!A 2240 -A!A 2218

"airchild A#$%Thunderbolt -A!A 8648 -A!A 8643

Sikorsky S*84 S$*3 Sea 9ing -A!A 1142 -A!A 1142
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Panel ethodThis numerical method places singularities along the airfoil. n the case of :isual"oilor3DFoil, the singularities are vortices. The vorticity is distributed linearly along the panel.

Plain FlapA plain flap is a hinge attachment near the trailing edge of an airfoil. The length of theflap is measured as a percentage of the chord and the deflection is measured in degrees.Pressure CoefficientThe pressure coefficient is a non*dimensional form of the pressure. t is defined as thedifference of the free stream and local static pressures all divided by the dynamicpressure."eynolds !um&er

The ;eynolds number is a non*dimensional parameter that compares the inertia toviscous forces. f the ;eynolds number is low, then viscosity plays an importatant part in

the simulations.'tallAt low angles of attack, the lift developed by an airfoil or wing will increase with anincrease in angle of attack. $owever, there is a ma%imum angle of attack after which thelift will decrease instead of increase with increasing angle of attack. This is know as stall.9nowing the stall angle of attack is e%tremely important for predicting the minimumlanding and takeoff speeds of an airplane.'treamlines!ontours in the flow field that are tangent to the velocity vector.Wing LoadingThe total weight of the airplane divided by the plan form area of the wing.

Wing 'panThe span is the total length of the wing.
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Airfoilshave been represented in a number of differentways in the past. For example, coordinates have

been directly used to fit airfoil shapes using B-splines and Bzier curves2

via interpolation methods. Analytical

functions have also been derived to represent families of airfoils, for example, in the work reported by Hicks

and Henne.3

In a more recent work,4

Non-uniform rational B-splines (NURBS) were used first to approximate

existing airfoils, then adopted as a general parameterisation method to be used in optimisation. The concept

of using relatively few orthogonal functions to represent a large number of functions has also been exploited,

for example in a work reported by Robinson and Keane,5

where a set of orthogonal functions was developed

using numerical methods. These functions were then used to represent a family of airfoilsin a wing design

study. However, the basis functions derived by Robinson and Keane5

were believed to be dependent on the

particular familiar of airfoils. Although these numerically derived basis functions can be used in the design

of a particular set of airfoils, other airfoilsmay not be adequately represented using them.

The choice of parameterisation method, when coupled with optimisation techniques to find desirable

shapes in terms of user-defined objective functions and constraints, has a major effect on the final results,efficiency and effectiveness of particular search strategies. Giving the same CFDmodels, the parameterisation

Research Fellow, School of Engineering Sciences, University of Southampton, Highfield, SO17 1BJ, United Kingdom, and

AIAA Member.

Professor, School of Engineering Sciences, University of Southampton, Highfield, SO17 1BJ, United Kingdom.

1 of 8

American Institute of Aeronautics and Astronautics

Page 2effectively defines the optimisation problem formulation, the topology of the design space, and the landscape

of the objective functions. Although it is vitally important, it is also very difficult to come up with a set of

effective criteria that can be readily used to evaluate the pros and cons of differentparameterisation methods.

Wu6

compared three geometric representations in three case studies of cascade blade design using adjointmethods. After carrying out the optimisation, it has concluded that one of the methods using geometry

parameters is not suitable for two occasions.

There are a number of key issues that need to be addressed in the choise of parameterisation methods.

The first issue is the flexibility of any parameterisation method. Flexibility is interpreted here as the ability

to represent a wide range of differentshapes. Some parameterisation methods, for example, coordinate-

based methods, can accurately represent a variety of dramatically differentshapes and can also reflect subtle

changes in local areas, however it would be very difficult to use such an approach for optimisation problems

using high fidelity codes due to the large number of design variables and complexity of the design space. On

the other hand, methods using fewer variables may not be capable of generating shapes with high accuracy,

especially when used in inverse design problems where a target pressure distribution is sought. The second

issue when considering parameterisation methods is the accuracy or the optimum objective functions that

the final shape can achieve either in an inverse design study or direct optimisation work, respectively. The

accuracy should be measured in both geometric and aerodynamic senses. However, the optimal objective

function cannot be obtained without actually carrying out the optimisation, therefore, here an inverse designapproach is adopted to compare differentparameterisations.

In this work, three datum airfoils, two from the NACA supercritical airfoilsfamily (NACA0406 and

NACA0610) and the third being the RAE2822, are used as reference shapes to compare differentparam-

eterisation methods for airfoil design. The paper is organised as follows. Section two describes different

parameterisation methods for airfoil design. The geometry modelling and flow analysis of the airfoil prob-

lems are described in section three. Results and discussions are presented in section four, with conclusions

given in section five.

II. Parameterisation of Airfoil Geometry


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Figure 1. The first three numerically derived or-

thogonal basis functions.

Geometry parameterisation methods have attracted

renewed interests in recent years, especially in the con-

text of multidisciplinary design optimisation (MDO).

Samareh7

identified three categories of parameterisation

methods in the context of MDO. These include the dis-

crete approach, CAD-based approaches, and free-form de-

formation methods. Indeed, all these differentapproaches

could be implemented in most modern CAD systems.

Several parameterisation methods have been proposed

in previous papers for airfoil geometry, for example, the

NACA supercritical airfoilsare defined as a series of y-

coordinates at prescribed chord wise locations.8

The sec-

ond approach models the geometry as the linear combina-

tion of a basis airfoil and a set of perturbation functions,

defined either analytically4

or numerically,5as shown in

Eq. (1). The coefficients of the perturbation functions in-

volved are then considered as the design variables. A set

of such orthogonal basis functions derived from a group

of base airfoilswas developed by Robinson and Keane5

to

provide an efficient means to define the airfoil for optimi-

sation study in preliminary design, for example.

y(x) =0

y0

(x) +

wi

fi

(x)

(1)

A third, and more geometrically intuitive method, is to use geometric parameters such as leading edge

radius, thickness-to-chord ratio or maximum thickness to define the airfoil shape. An airfoil parameterisation

using 11 geometry parameters was presented by Sobieczky9

and used by Oyama etc.10

A fourth method uses

the control points of Non-uniform Rational B-splines (NURBS) curves to define the airfoils.4

This method is2 of 8


Page 3also used by Li11, 12

in which a B-pline interpolation through 35 points is used to define the airfoil geometry.

The advantage of this approach is that free-form geometrical shapes can be accommodated with fewer design

variables compared to the direct use of coordinates. However, due to difficulties in controlling the relative


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positions of the control points, free-form parameterisations are usually used in the inverse design approach,

where only a subset of control points are allowed to change in a relatively small range to meet a target

pressure distribution.

One of the key issues in deciding the parameterisation method is the balance the requirements of ro-

bustness and flexibility, and these decisions are also strongly dependent on the goal of the design activity.

Although free-form parameterisations may well be able to generate radical new shapes, this is not suitable

for designs where the aim is to meet a specific pressure distribution, due to the poor efficiency caused by the

large search space that arises in the optimisation process. Another disadvantage of free form parameterisa-tion is the inherent difficulties encountered when trying to generate airfoil-like shapes: Usually additional

geometrical constraints need to be imposed. Two differentparameterisation methods are implemented in

the current work to compare their effectiveness. The first approach is to use a set of numerically derived

basis function to define the airfoil,5

in this case, only a small number of design variables are involved. The

basis functions used are illustrated in Figure 1. The second approach uses a B-spline interpolation based on

34 points as shown in Figure 2. The y coordinates of the points are used as design variables while the chord

wise coordinates of the points are fixed. Both methods are implemented in the CAD system ProEngineer.13

Airfoil shapes from the family of supercritical airfoils8

and RAE2822 are chosen in the current work as ref-

erence airfoilsin the comparison. The number of parameters involved in the two parameterisation methods

are summarized in Table 1.Table 1. Summary of different parameter methods for airfoils

Method

Number of parameters Description of the parameters

Numerical Basis Functions

5

Weights for the basis airfoil functions

B-spline interpolation

34

Point coordinates

III. Geometry Modelling and Flow AnalysisX/C

Y

/

C0

0.25

0.5

0.75

1

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

Figure 2. Airfoil Modelling using B-spline inter-

polation.

To compare the flexibilities of differentparameterisa-

tion methods in representing differentairfoil shapes, three

existing airfoilsNACA0406, NACA0610, and RAE4822

are chosen as the modelling targets for these parameter-isations. The difference between the target airfoil and

approximated airfoil is defined as

diff =

abs(ftarget

(xi

) f(xi

))


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(2)

where xi

(i = 1, ..., n) are the chordwise coordinates used

in the definition of the target airfoils. This quantity is

minimised using a global optimisation algorithm for dif-

ferent parameterisation methods and then used as an in-

dication of the flexibility of the methods. To remove theeffect of the optimisation techniques that may not pro-

duce the optimum results, a large number of iterations

has been carried out for the minimisation problem.

The airfoil models are all implemented using ProEngi-

neer and exported in the form of a STEP file, which is

then imported into Gambit. A boundary layer is attached

to the lower and upper surface of the airfoils, and size

functions are also used to give better control of the mesh and to reduce the computational time for the

problem. An unstructured mesh generated using Gambit14

for solving the N-S equations is shown in Figure

3. The mesh contains 11356 cells (compared with 87305 cells without using the size function). In both cases,3 of 8


Page 4the node spacing on the airfoil surfaces and farfield circle are the same, with size functions giving better

control of the transition of size of the cells in between. The computation time is reduced from around 40

minutes to less than 20 minutes for most geometries on a Xeon 2.4Ghz compute node with 1Gb memory.

The flow model used in the current work is based on the Navier-Stoke model from Fluent.14

The

pressure distribution of the upper and lower surfaces are used in the comparison. Here, the cruise condition

(M

= 0.73) is used when calculating the lift and drag values. The Spalart-Allmaras viscosity model is

used.

IV. Results and AnalysisFigure 3. Unstructured mesh used for solving the N-S

equations by Fluent

It is not straightforward to compare alternative

parameterisation methods. There are two impor-

tant considerations when a parameterisation model

is built around an existing geometry: the first is

the flexibility of the model, i.e., how many different

shapes can this model represent. The second is be

the robustness of the model, i.e., can the model gen-

erates the desired shape for large number of different

designs. In general models with more design vari-

ables will be able to represent more complex shapes,

and will be more likely to produce novel designs us-

ing optimisation. However, that will be more expen-

sive in the search as the design space will have higherdimensions, and chances of failure or not generating

desired shapes will be higher.

The best results for approximations of the tar-

get airfoilsare shown in Table 2. The results are

produced by minimising the objective function computed using (2). A genetic algorithm (GA) from OP-

TIONS15

is used in the current work, however, the first population is not generated randomly, rather, it

is generated using a Design of Experiment (DoE) method plus one point describing a user specified base


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design to obtain more uniform coverage of the design space as well as to provide the best possible guess.

The DoE method used here is a Latin Hyper Cube method. The base design specified by the user can play

an important role in accelerating the search process as the GA used in this work always maintains the best

solution in the population. A single base design is used in the orthogonal basis function approach for all

three target airfoilsand in the B-spline approach for RAE2822 approximation. The two base designs used

in B-spline interpolation for NACA0406 and NACA0610 are NACA0403 and NACA0606, respectively.

It can be seen that the approximations using orthogonal basis function can produce better results for

the NACA supercritical airfoilsNACA0406 and NACA0610 than for the RAE2822, this is not surprising,as the set of basis functions used were derived from a family of airfoilscontaining these two. The errors are

believed to be caused by the smoothing process in the derivation of these basis functions.5

For NACA0406

and NACA0610, the orthogonal basis functions also produce better results than the B-spline interpolation

approach, this is because more variables are used in the B-spline interpolation and so it would be much more

expensive to obtain the optimum if a comparable number of iterations were used for both cases. However, a

differentstory arises for RAE2822. Since it was not included in the process of deriving the basis functions,

this leads to greater error when compared with the B-spline interpolation approach. This indicates the wider

applicability of the B-spline approach, at the higher cost of reaching the optimum.Table 2. Best Approximation of target airfoils for different parameterisations

Method

RAE2822 NACA0406 NACA0610

Numerical Basis Functions0.2217

0.0582

0.1595


0.1552

0.0758

0.1993

However, similarity in geometry does not always guarantee similar pressure distribution, especially for4 of 8


Page 5transonic flows where small perturbations in shape will lead to large variations in pressure. Therefore, the

pressure distributions of the approximated shape are also compared to that of the original airfoils, as shownin Figure 4. It can be seen from Figure 4 that the orthogonal basis function approach always produces

smooth pressure distributions; also errors are generally bigger in the leading and trailing edge areas than in

the middle section of the airfoils.

Figure 5 shows the results of approximation using the B-spline interpolation approach. It can be seen that

close agreement can be achieved using B-spline interpolation through 34 points apart from the leading edge

area, which indicates that more points need to be placed within this area to achieve better results. Moreover

the chordwise coordinates can also be varied, but this would involve higher computational cost while not

necessarily increasing the accuracy of the approximation. Another advantage of the B-spline approach is its

ability to carry out local shape tunning by varying a subset of the coordinates, while it would be difficult

to perform this with the basis function approach, in which, any changes in the coefficients will change the

shape globally.

The approach adopted in the current work is essentially an inverse design method. However, it is not

used to seek a prescribed pressure distribution, as the definition of the pressure distribution itself is a design

problem and accurately re-generating the prescribed pressure distribution often leads to degradation ofperformancein other conditions. This method can be used to evaluate differentparameterisations before

carrying out optimisations using the high fidelity codes.

V. ConclusionsTwo airfoil parameterisation approaches are studied in this paper to analyse their flexibility and robust-

ness in producing optimal shapes when used in optimisation studies. Global optimisation methods are used

to analysis the accuracy these two parameterisations can achieve when used to model three target airfoils.

The B-spline approach produces better results in terms of accuracy at a higher computational cost while

the basis function approach is more efficient while producing less accurate results. Further work will in-


16/43

volve the combination of the basis function approach in the initial stages of design combined with B-spline

interpolation for the final tuning of the shapes.

AcknowledgementThe work described here is supported by the UK e-Science Pilot project: Grid-Enabled Optimisation and

Design Search for Engineering (Geodise) (UK EPSRC GR/R67705/01). Financial support from EPSRC is

greatly acknowledged.

References1Raymer, D.P., Aircraft Design: A Conceptual Approach, AIAA Educational Series 1999.2

Cosentino, G. B. and Holst, T. L., Numerical Optimisa tion Design of Advanced Transonic Wing Configurations, May,

1984.3

Hicks, R. M. and Henne, P. A., Wing Design by Numerical Optimisation, Journal of Aircraft, Vol. 15, No. 7, 1978, pp.

407-413.4

Lepine, J., Guibault, F., Trepanier, J.-Y., and Pepin, F., Optimized Nonuniform Rational B-spline Geometrical Repre-

sentation for Aerodynamic Design of Wings, AIAA Journal, Vol. 39, No. 11, 2001.5

Robinson, G. M. and Keane, A. J., Concise Orthogonal Representation of Supercritical Airfoils, Journal of Aircraft, Vol.

38, No. 3, 2001, pp. 580-583.6

Wu, H.Y., Yang, S.C., Liu, F. and Tsai, H.M., Comparison of Three Geometric Representations of Airfoilsfor Aero-

dynamic Optimization, AIAA 2003-4095, 16th AIAA Computational Fluid Dynamics Conference, June 23-26, Orlando, FL,

20037

Samareh, J. A., Survey of shape parameterization techniques for high-fidelity multidisciplinary shape optimisation, AIAA

Journal, Vol. 39, No. 5, 2001, pp. 877-884.8

Charles D.H., NASA Supercritical Airfoils , A Matrix of Family-Related Airfoils, NASA Technical Paper 2969, Mar. 1990.9

Sobieczky, H., Parametric Airfoilsand Wings, Notes on Numerical Fluid Mechanics, edited by K. Fujii and G. S. Du-

likravich, Vol. 68, Vieweg Verlag, 1998, pp. 71-88.10

Oyama, A., Obayashi, S., and Nakamura, T., Real-coded Adaptive Range Genetic Algorithm Applied to Transonic Wing

Optimisation, Springer, Paris, France, 2000, pp. 712-721.11

Li, W., Huyse, L., and Padula, S., Robust airfoil optimisation to achieve drag reduction over a range of Mach numbers,

Structural and Multidisciplinary Optimisaiton, Vol. 24, 2002, pp. 38-50.

5 of 8


Page 6X/C

Y

/

C0

0.25

0.5

0.75

1

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06RAE2822Orthfoil-Approximation

(a) Approximation of geometry to RAE2822 by basis functions

approachX/C

P

r

e

s

s

ur

e

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o

e

f

f

i

c

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-0.5

0

0.5

1RAE2822

Orthfoil-approximation

(b) Comparison of pressure distributions for RAE2822 using

basis functionsX/C

Y

/

C

0

0.25

0.50.75

1

-0.03

-0.02

-0.01

0

0.01

0.02

0.03NACA0406

Orthfoil-Approximation

(c) Approximation of geometry to NACA0406 by basis func-

tions approachX/C

P

r

e

s

s

u

r

e

C

o

e

f

f

i

ci

e

n

t

s0

0.25

0.5

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-1

-0.5

0

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1NAC0406Orthfoil-approximation

(d) Comparison of pressure distributions for NACA0406 using

basis functionsX/C

Y

/

C0

0.25

0.5

0.75

1

-0.05-0.04

-0.03

-0.02

-0.01

0

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0.02

0.03

0.04

0.05NACA0610Orthfoil-Approximation

(e) Approximation of geometry to NACA0610 by basis func-

tions approachX/C

P

r

e

s

s

u

r

e

C

o

e

f

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ic

i

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1NACA0610

Orthfoil-approximation

(f) Comparison of pressure distributions for NACA0610 using

basis functions


18/43


19/43

0

0.5

1NAC0406

B-Spline Interpolation

(d) Comparison of pressure distributions for NACA0406 using

B-spline interpolationX/C

Y

/

C0

0.25

0.5

0.75

1

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05NACA0610B-Spline Interpolation

(e) Approximation of geometry to NACA0610 by B-spline in-

terpolationX/C

P

r

e

s

s

u

r

e

C

o

e

f

f

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c

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t

s0

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-1

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1NACA0610

B-Spline Interpolation

(f) Comparison of pressure distributions for NACA0610 using


Figure 5. Comparisons of geometry and pressure distributions for approximations using B-spline interpolations

7 of 8


Page 812

Li, W., Profile Optimisation Method for Robust Airfoil Optimisation in Viscous Flow, NASA /TM-2003-212408, 2003.13

ProEngineer, http://www.ptc.com, 2004.14

Fluent, http://www.fluent.com, 2004.15

Keane, A.J., OPTIONS Design Exploration System, http://www.soton.ac.uk/ajk, 2004

8 of 8


This is the html version of the file http://aero#comla.stanford.edu/Papers/!yoto$4.pdf.Googleautomatically generates html versions of documents as we crawl the we.To lin! to or oo!mar! this page" use the following url: http://www.google.com/search?q=cache:w!-comla.sta!ford.ed(/Papers/,yoto0$.pdf&'o(r!als&)performa!ce&of&differe!t&airfoi

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20/43

These search terms have een highlighted: performance different airfoils cfdThese terms only appear in lin!s pointing to this page:journals

Page 1

A Two-Dimensional Multigrid-Driven Navier-Stokes

Solver for Multiprocessor ArchitecturesJuan J. Alonso, Todd J. Mitty, Luigi Martinelli, and Antony Jameson

Department of Mechanical and Aerospace Engineering

Princeton University

Princeton, New Jersey 08544 U.S.A.Abstract

A two-dimensional unsteady Navier-Stokes solver has been parallelized using a domain decomposition

approach and the PVM message passing library. Several options for the treatment of multigrid and

implicit residual smoothing are examined. Results for the unsteady flow over a pitching NACA 64A010

airfoil are presented.

1 INTRODUCTIONIn recent years, computational fluid dynamics (CFD) has been gaining acceptance as a design tool in industry.

Advancements in algorithm development and computational hardware have led to more complex modeling

of fluid flows. Although current inviscid models can accurately predict the coefficient of lift for an airfoil

in transonic flow, viscous effects such as shock wave/boundary layer interaction can significantly modify

important aspects ofa flow. Furthermore, unsteady phenomena ofpatent viscous character, such as buffeting,

can not be predicted with the help ofinviscid models. Such viscous phenomena directly impact the design

ofengineering configurations, and therefore, it is necessary to enhance the viscous prediction capability of

CFDtools.

Increasingly complex fluid flow models require high performancecomputing facilities. A cost effective

solution for problems of this type requiring fast CPUs and large internal memory is the use of a parallel

computing paradigm. For computational efficiency, one typically incorporates convergence acceleration tech-

niques such as multigrid and implicit residual smoothing. Message passing becomes necessary in this new

environment, and severely limits the performanceof processes that are inherently communication intensive.

In this paper we present a parallelized version ofa well established Navier-Stokes solver, FLO103 [1].

This computer program has recently been enhanced to include Jamesons implicit multigrid approach [2] for

the efficient calculation ofunsteady viscous flows. Calculations are performed on an IBM SP1 multiproces-

sor computer with a domain decomposition approach, and message passing is handled by PVM (Parallel

Virtual Machine) software [3]. Several methods for implementing convergence acceleration techniques such

as multigrid and implicit residual smoothing are studied.

2 NAVIER-STOKES EQUATIONS DISCRETIZATIONThe two-dimensional, unsteady, compressible Navier-Stokes equations may be written in divergence form for

a Cartesian coordinate system (x, y) as

w

t

+

f

x

+

g

y

=


21/43

R

x

+

S

y

,

(1)where w is the vector offlow variables, f and g are the convective fluxes, and R and S are the viscous fluxes

in each ofthe coordinate directions. With Reynolds averaging, turbulence effects can be taken into account

with a turbulence model. In this work, a Baldwin-Lomax model was used. In integral form, Equation 1 can

1

Page 2be applied to each finite volume ofa computational domain to yield a set ofcoupled first-order differential

equations ofthe form

d

dt

(wij

Vij

) + E(wij

) + NS(wij

) + D(wij

) = 0

,

(2)

where E(wij

) are the convective Euler fluxes, NS(wij

) are the Navier-Stokes viscous fluxes, and D(w

ij) are

the artificial dissipation fluxes added for numerical stability. For unsteady problems, Equation 2 is modified

by introducing a pseudo-time formulation to improve computational performance[2].

3 PARALLELIZATION STRATEGYFLO103P is parallelized using a domain decomposition model, a SIMD (Single Input Multiple Data) strategy,

and the PVM Library for message passing. Flows were computed on a C-mesh of size ni

nj

= 102464. This

domain was decomposed into subdomains containingni

Np

nj

points, whereNp

is the number ofsubdomains

used. Communication between subdomains was performed through halo cells surrounding each subdomain

boundary. A two-level halo was sufficient to calculate the convective, viscous, and dissipative fluxes for all

cells contained in each processor. In the coarser levels ofthe multigrid sequence, a single level halo suffices

since a simplified model ofthe artificial dissipation terms is used.

For problems with a low task granularity (ratio ofthe number ofbytes received by a processor to the

number of floating point operations it performs), large parallel efficiencies can be obtained. Unfortunately,


22/43

convergence acceleration techniques developed in the 1980s base their success on global communication in

the computational domain. Thus, current multigrid and implicit residual smoothing techniques [4] are bound

to hinder parallel performancein traditional mesh sizes. In order to effectively deal with the parallelization

ofthese two techniques, we propose several ideas.

In this paper, static load balancing is performed at the beginning of the calculation. Since the number

ofcells remains constant throughout the calculations, the domain can be partitioned into subdomains with

an equal number ofcells. Except for some domains where an additional message across the wake is required,

this provides for perfect load balancing.

4 PARALLEL MULTIGRIDThe full approximation multigrid technique enhances the convergence rate of a scheme by performing com-

putations on a series ofincreasingly coarser meshes. The calculations performed in each ofthese meshes are

driven by the residuals at the previous finer level, and the results obtained are interpolated to the corre-

sponding finer mesh. The explicit time-stepping acts as a smoothing operator for the high frequency errors

in each level, thus damping the dominant error mode at the finest level and accelerating convergence. A

more detailed discussion of this procedure can be found in [4]. If domain decomposition is used for parallel

calculations, the size ofthe meshes contained in each processor at the coarser levels ofthe multigrid cycle

is quite small (typically 8 or 16 cells). Most ofthe CPU time is then wasted sending information back and

forth between processors. This situation worsens for multigrid W-cycles, where equilibrium in the coarser

meshes is established repeatedly before traversing the series back to the finest level. Previous authors [5]

have attempted to deal with this problem in the Euler equations by limiting message passing to only some

stages in the Runge-Kutta time-stepping scheme, or passing the boundary data exclusively at the finest levelin the series. This usually led to a decrease in the convergence rate ofthe numerical algorithm, presenting a

clear tradeoff between the improved parallel performanceand the increasing number of cycles required for a

similar level ofconvergence. In this work, we examine three differentapproaches to the implementation ofthe

multigrid algorithm. First, the full multigrid algorithm is implemented with message passing at all required

points such that the parallel program exactly recovers the results ofthe serial code. Second, multigrid is

applied independently within each subdomain to completely avoid inter-processor communication. Third,

and last, at coarse multigrid levels where communication overhead dominates CPU time, a single processor

will be used to gather, compute, and scatter information. Parallel speed-up curves for these three cases are

also presented.

2

Page 3

"DUMB" PROCESSOR W-CYCLEParallelT

T

T

T

T

T

T

Fine

Coarse

Single Proc.

"LAZY" PROCESSOR W-CYCLEParallel

T

T

T

T

T

T

T

Fine

Coarse

No work

Figure 1: Lazy-Dumb Multigrid Approach.

4.1 Full multigrid approximationThis first approach was an attempt to implement a parallel program that exactly reproduced the output of

the single processor code in which message passing is not necessary. In order to achieve this goal, boundaryinformation was passed among processors on all multigrid levels at the beginning of all five stages of the

Runge-Kutta time-stepping. Additional messages were required in order to process convergence information,

calculate force coefficients, and compute the eddy viscosity in the turbulence model. This procedure recovers

the serial version convergence rate, at the expense ofpoor parallel performance.

4.2 Implicit multigrid within subdomainsThe second approach used to deal with the multigrid algorithm was to completely decouple the subdomains

on the coarser levels ofthe series in order to minimize the number ofmessages passed when very little

computation is being performed. As expected, this approach restores parallel efficiency to higher levels, but

it suffers from a decreased convergence rate. Clearly, the success of the multigrid technique is due to the


23/43

increased communication between differentparts ofthe computational mesh at all levels, and the transfer of

this information is limited by the isolation of the coarser levels in each subdomain. The degradation of the

convergence rate is especially bad when interdomain boundaries lie close to regions ofhigh gradients (such

as shock waves and stagnation points). In some ofthese cases, a converged solution cannot be obtained.

4.3 Lazy-Dumb multigrid approachIn order to preserve the convergence rate ofthe original multigrid algorithm, and somehow improve the

parallel efficiency ofthe first approach we propose the following procedure: calculations on the finer levels are

performed as in 4.1; when the algorithm shifts the solution to a user-specified coarse mesh, all the processors

in the calculation pass their flow variables and grid locations to a single processor which computes the coarser

levels of multigrid without the need for message passing. This processor is termed dumb since it performs

everyone elses work. The rest ofthe processors in the computation wait until the calculation needs to be

performed on the finer levels, at which point they receive the information from the dumb processor and

proceed once more in parallel. These processors are called lazy since they avoid carrying out part ofthe

work that was, in theory, assigned to them. In our program, the level at which the transfer is done can be

specified as an input, allowing for investigations of the optimal location of this transition point. Figure 1

presents this procedure graphically. Note that this construction can be extended to a hierarchy ofdumb

processors for larger calculations involving more processors.

3

Page 4

5 IMPLICIT RESIDUAL SMOOTHINGImplicit residual smoothing (or averaging) is a technique that couples the residuals at any given point with

those ofall the other cells in the domain, increasing the support ofthe scheme, and allowing a larger time step

than that permitted by the Courant-Friedrichs-Lewy (CFL) restriction. Once more, this is a communication

intensive procedure that negatively impacts parallel performancein a multiprocessor environment.

5.1 Fully implicit residual smoothingSerial implementations ofthis technique usually split the problem into the implicit coupling along each of

the two coordinate directions. The direction which is normal to the airfoil surface presents no difficulties

since all the required data resides in the appropriate processors (in this decomposition), allowing calculations

to proceed in parallel. In the coordinate direction that is parallel to the airfoil surface, the residuals that

are to be coupled reside in differentprocessors. Moreover, the solution procedure (Thomas algorithm for a

tridiagonal system) is inherently serial. A brute force method allows only one processor to be active at a

time in the forward elimination and back substitution phases, while the remaining processors are idle. Since

the residual smoothing procedure consumes about 30% ofthe time ofthe total calculation, this idle time

causes parallel performanceto drop-off considerably.

5.2 Implicit residual smoothing within subdomainsIn a very similar fashion to the multigrid performed implicitly within blocks, and in an attempt to reduce

the amount ofmessages passed, residual smoothing was performed implicitly within blocks, with no global

coupling ofthe residuals. Once more, as expected, although parallel performanceimproves, the convergence

rate degrades to unacceptable levels. As in the corresponding multigrid procedure, this lack ofcoupling

between domains often led to instability in the calculations.

5.3 Iterative implicit residual smoothingAn alternative to the previous approach is to perform an iterative solution of the smoothing problem.

Messages containing the boundary residuals are passed at the beginning ofeach iteration, and the relaxation

process proceeds in parallel. It has been observed in practice that in order to obtain the increase in CFL

number provided by the fully implicit version (from 3 to about 6), at least two iterations are required.

In these calculations, three iterations were performed and a CFL number of 6 was used without stabilityproblems. The matrix problem is setup in each subdomain and a Jacobi relaxation procedure is performed

on all subdomains concurrently.

6 RESULTSA summary of the results for the differentmultigrid approaches is presented in Figure 2. The full multigrid

approach produces results with an optimum convergence rate, but with a parallel performancethat degrades

for a large number of processors. One must take into account, that for these meshes ( ni

nj


24/43

= 1024 64)

granularity becomes too large as the number ofprocessors increases. This makes efficient parallel calculations

not viable for a number of processors larger than 8. The multigrid performed implicitly within blocks (see

Section 4.2) exhibits better parallel performance, but at a very high cost. When the total cost to achieve

a solution converged to the same level through these two procedures is computed, the second technique

requires about twice the number ofcycles making this approach less than desirable. Finally, the lazy-

dumb version ofthe algorithm performs slightly better when the dumb processor computes the two

coarsest levels ofthe sequence. When the three coarsest levels are assigned to the dumb processor, parallelperformancedegrades since the amount of time required by the dumb processor exceeds that needed for

all processors (with poor parallel performance). Notice that wall time was used to compute the parallel

efficiencies in all cases. Ifthe unused CPU time ofthe lazy processors were to be factored in, the gain

would be larger. It must also be mentioned that the implementation ofthis approach introduces a higher

level ofcomplexity to the multigrid algorithm, since the memory management on both types ofnodes differs

4

Page 5considerably from the traditional one. As a payoff for the additional work, this approach exhibits the exact

same rate ofconvergence as the full multigrid algorithm.

Evaluating the performanceof multigrid in meshes that are relatively small places a strong restriction

on the parallel efficiencies that can be achieved. Calculations using very large meshes (three-dimensional

calculations, two-dimensional LES calculations, etc) will benefit from the full multigrid algorithm and willachieve parallel performances on the order of 90% since most of the time will be spent on the finer levels of

the sequence. Nevertheless, for engineering calculations, reasonable speed-ups can be obtained through this

method.

The performanceresults of the differentmethods used to implement residual smoothing are presented in

Figure 3. The fully implicit approach is clearly unacceptable even for a small number of processors. While

the approach that uses implicit residual smoothing within blocks exhibits a parallel performanceof 96% for

8 processors, the degradation ofthe convergence rate disqualifies it as a possible candidate. Finally, the

iterated residual smoothing preserves both the convergence rate and a reasonable parallel speed-up, and is

chosen as the candidate for engineering calculations.

Figure 4 presents a detail of the domain decomposition for a calculation involving four processors for a

typical airfoil section. Figure 5 shows the pressure contours at differentpoints on the oscillation period of

a NACA 64A010 airfoil at a Reynolds number of 106

,M

= 0.796, and a reduced frequency, kc

= 0.202.

These results were obtained with the O-mesh version ofthe program. One can clearly see how the shock

waves strengthen and weaken as the airfoil pitches up and down.

The lines that intersect the pressure contour lines are the interprocessor boundaries ofthe O-mesh.

Perfect continuity ofthese contour lines validates the accuracy ofthe code even for the cases where strong

shocks are close to the interprocessor boundaries. For more details, please refer to [6].

7 CONCLUSIONSA parallelized, two-dimensional, unsteady Navier-Stokes flow solver has been developed. Parallelization

was realized using a domain decomposition approach to achieve proper load balancing and computational

efficiency. PVM communication software was used for message passing between processors. Strategies for

dealing with two convergence acceleration techniques, namely implicit residual smoothing and multigrid, andthe performanceofeach ofthese techniques have been evaluated.

It is observed that for meshes of sizes typically used in engineering calculations, acceptable parallel

performances can be achieved with up to 8 processors. A larger number of processors is not suitable for this

type ofcalculation. For larger meshes, the multigrid technique is still quite favorable even in multiprocessor

architectures. Implicit residual smoothing can be performed in an iterative fashion without an observable

impact in the convergence rate while retaining good parallel performance. All calculations used the public

distribution ofthe PVM software developed at Oak Ridge National Labs. Preliminary results with the IBM

optimized version ofthis message passing standard (PVMe), on both the SP1 and SP2 platforms, confirm

the expected trends in which parallel performances improve considerably. Finally, results for the unsteady


25/43

pressure field around a pitching NACA 64A010 atM

= 0.796 were computed on the IBM SP1 system.

References[1] Martinelli, L., Jameson, A., Validation ofa Multigrid Method for the Reynolds Averaged Equations,

AIAA Paper 88-0414, AIAA 26th Aerospace Sciences Meeting, Reno, January 1988.

[2] Jameson, A., Time Dependent Calculations Using Multigrid, with Applications to Unsteady Flows

Past Airfoilsand Wings, AIAA Paper 91-1546, AIAA 10th Computational Fluid Dynamics Conference,

Honolulu, June 1991.

[3] Geist, A., Beguelin A., Dongarra J., Jiang W., Manchek, R., Sunderam V., PVM 3 Users Guide and

Reference Manual, Oak Ridge National Laboratory, May 1993.

5

Page 61

2

3

4

5

6

7

8

1

2

3

4

5

6

7

8

Number of Processors

Parallel Speedup

Comparison of Parallel Speedups of Multigrid Methods

solid Full multigrid

Implicit within blocks

..LazyDumb 2 levels in dumb processor

..... LazyDumb 3 levels in dumb processor

Figure 2: Summary ofParallel Speed-ups for Differ-

ent Approaches to the Multigrid Technique.1

2

3

4

5

6

7

8

1

2

3

4

5

6

7

8

Number of Processors

Parallel Speedup

Comparison of Parallel Speedups of Residual Smoothing Methods

solid fully implicit

..implicit within blocks

explicit iteration

Figure 3: Summary ofParallel Speed-ups for Differ-

ent Implicit Residual Smoothing Approaches.129x6 5129x6 5

129x6 5129x6 5

Figure 4: Domain Decomposition for a NACA 0012 Airfoil at a 10 degree Angle of Attack.

[4] Jameson, A., Transonic Flow Calculations, Princeton University Report 1651, March 1984, in Numerical

Methods in Fluid Dynamics, edited by F. Brezzi, Lecture Notes in Mathematics, Vol. 1127, Springer-

Verlag, 1985, pp. 156-242.

[5] Yadlin, Y. and Caughey, D. A., Block Multigrid Implicit Solution ofthe Euler Equations ofCompressible

Fluid Flow, AIAA Journal, 29(5):712-719.

[6] Alonso, J. J., Martinelli, L., and Jameson A., Multigrid Unsteady Navier-Stokes Calculations with

Aeroelastic Applications, 33rd AIAA Aerospace Sciences Meeting, AIAA Paper 95-0048, Reno, NV,

January, 1995.

6

Page 7

1

2

3

4


26/43

5

6Figure 5: Mach Number Contours. Pitching Airfoil Case.Re = 1.0 106

,M

= 0.796, Kc

= 0.202. Read

figures by lines.

7

This is the html version of the file http://www.aoe.vt.edu/%mason/Mason&f/'onfig(ero)i*ift.pdf.Googleautomatically generates html versions of documents as we crawl the we.To lin! to or oo!mar! this page" use the following url: http://www.google.com/search?q=cache:h1)performa!ce&of&differe!t&airfoils&i!&cfd*+hl=e!+gl=i!+ct=cl!,+cd=$7

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Page 1

W.H. Mason

4/5/06

8. High-Lift Aerodynamics8.1 Introduction: Why high lift?

For transonic transports, the high-lift system design is a critical part of the configuration

design.

To achieve reasonable field performancewhile also obtaining efficient transonic

cruise the

design will require a fairly sophisticated high lift system. From a paper by Boeing

aerodynamicists1

: (presumably referring to the B-777)

A 0.10 increase in lift coefficient at constant angle of attack is equivalent to reducing

the

approach attitude by one degree. For a given aft body-to-ground clearance angle, the

landing gear may be shortened for a savings of airplane empty weight of 1400 lb.

A 1.5% increase in maximum lift coefficient is equivalent to a 6600 lb increase in

payload

at a fixed approach speed

A 1% increase in take-offL/D is equivalent to a 2800 lb increase in payload or a 150

nm

increase in range.

For fighters, devices are also scheduled allow efficient maneuver.
http://www.aoe.vt.edu/~mason/Mason_f/ConfigAeroHiLift.pdfhttp://www.aoe.vt.edu/~mason/Mason_f/ConfigAeroHiLift.pdf


27/43

High-lift systems are also critical for STOVL and V/STOL aircraft. They also use the

propulsion

system to help generate the lift. It always seemed to me peculiar to design fighter aircraft,

or

virtually any military aircraft, to operate from traditional runways. The one thing the

adversary isgoing to know is the exact location of your runways. So a STOVL capability seems to be

critical

in a serious confrontation.

Current status: Typical values of CLmax

are shown in Table 1. They come from papers by Brune

and McMasters,2

Roskam and Lan,3

and Sanders.4

Table 1. Values of CLmax

for some airplanes.*

* Note that there is a significant variation of values from differentsources.

Clearly the 727 emphasized short fields, and thus required a higher CLmax

Anyone who ever

looked out the window while landing in a 727 noticed the elaborate high lift system

employed.

Model

C

Lmax

B-47/B-52

1.8

367-80/KC-135

1.78

707-320/E-3A

2.2

727

2.79

DC-9

3.0

737-2003.2

747/E-4A

2.45

767

2.45

777

2.5


28/43

Page 2

8-2 W. H. Mason, Configuration Aerodynamics

Some Key Aspects:

Compressibility can be important early.

Reynolds number scaling from WT to flight may be problematic. Today simple high lift systems are critical, the high manufacturing cost for high lift

systems

is important.

Classes of problems

High lift for a single element airfoil

Multi-element airfoils

Use of blowing in some form: Powered Lift

Computing:

Requires consideration of viscous immediately. (unlike typical cruise airfoil analysis

and

design, where some insight can usually be gained ignoring viscous effects).

Predicting high-lift is done almost entirely with Navier-Stokes (RANS) codes

(exception,

Prof. Mark Drelas MSES5

code). A recent summary of the computational capability is by

Rumsey and Ying.6

Single elementairfoils

The key example of how to obtain high lift on a single element airfoil is the story of

Liebecks high lift airfoil7

and the Stratford pressure recovery shape of the pressure

distribution. This introduces the classic paper by A.M.O. Smith.8

See section 8.5 below.

Multi-elementairfoils:

Understanding the physics: Section 6.3 of A.M.O. Smiths paper8

is critical to understanding

the physics. Know what is meant by: 1. The slat effect, 2. The circulation effect, 3., The

dumping effect, 4. Off-the-surface pressure recovery, and 5. The fresh boundary layer

effect.

Note: some people combine the circulation and dumping effects and call it the vaneeffect.

See section 8.5 below for details.

Design: See the recent survey by C.P. van Dam,9

Existing systems on commercial transports: Rudolph has surveyed the high-lift systems

on

current subsonic transport aircraft.10


29/43

8.2 Types of Trailing Edge Devices

To begin we include a number of examples of high-lift devices as drawn by Dick Kita of

Grumman.11

These are fairly realistic drawings, as opposed to many of the drawings in

textbooks, which are cartoonish. Kita worked in high lift for many years. Im aware of his

work

on the Gulfstream II and F-14, but he worked on many other Grumman aircraft high-lift

systems

as well.

Of the large number of papers addressing high lift, several deserve mention. Pepper, et al12

provides a more current look at high lift, while the Boeing 777 high lift system

development, as

well as the overall design process, is available in the paper by Nield.13

A valuable description of

high lift on transports in contained in Gratzer.14

The use of powered lift is covered in the survey

by Korbacher.15

Somewhat dated but valuable resources are the book by Hoerner and Borst,16

and the book by McCormick17

(recently reissued unchanged from the 1967 edition as a Dover

paperback). Perhaps the best chapter on high lift in a basic text is the chapter in Shevell.18

Page 3High-Lift Aerodynamics 8-3

a) basic devices

Figure 8-1. Examples of typical trailing edge devices. Note that the Fowler flap also adds

area,

so that part of the CLmax

increase is simply due to the use of the original reference area

in computing the CL

. (from Dick Kitas Grumman talk, Feb. 1985)

Page 4


b) other trailing edge devices

Figure 8-1. Examples of typical trailing edge devices.

(from Dick Kitas Grumman talk, Feb. 1985)

Page 5


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may even decrease.19

Considering the adverse effect of Mach number on CLmax

, notice the low Mach numbers at which

the effects take place. Its rather surprising to the uninitiated.

Page 10


Figure 8-7. Effect of leading edge slats.


Leading edge slats work to protect the leading edge from separation. Therefore, they

dont really

do anything until you reach the angle of attack where the leading edge flow would let

go

without the slats for protection. Thus the slats allow the lift to continue to rise to higher

angles of

attack.

Page 11

High-Lift Aerodynamics 8-11

Figure 8-8. Effects of various types of leading edge devices on CLmax

.


Differentleading edge devices differ in their effectiveness. This is Kitas estimate of

how each

type of device affects the performanceof the wing.

Page 12


Figure 8-9. Estimated performanceof various types of high lift systems.


This is Kitas estimate of the typical best performanceyou can get from various types

of high-

lift systems. You can see that sweeping the trailing reduces the effectiveness of all the

systems.

The curve labeled advanced is typical of projections made in advanced departments,

where the

assumption is that an advanced technology development effort can improve the

performanceof

any system. This may or may not be true.

Page 13



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Figure 8-10. Effects of flap deflection on drag.


In addition to lift, flaps make a large change in drag. Clearly, you dont want the flaps

deployed

at low lift, and thus flaps arent deflected in cruise. As lift increases, there may be an

optimumflap deflection schedule, and this is done, for example, on the F-18, where the flaps are

scheduled with angle of attack and Mach number. This was also done on the Grumman

X-29.

Page 14


Figure 8-11. Flap effects on pitching moment.


Flap deflection also produces a large change in pitching moment. This is an important

consideration, since you need to be able to trim this pitching moment. In the case of the

Beech

Starship, the canards actually changed sweep to be able to generate the required force. So

this

effect cannot be ignored in developing the high lift system.

Page 15


Figure 8-12. Definition of gap and overlap.


In developing the high lift system, the selection of the gap between the slot and main

element,and the overlap have been found to be two of the key parameters. A lot of wind tunnel

time,

and more recently computer resources, are spent trying to identify the values of these

parameters

that produce the highest lift. Figure 8-12 provides Kitas definition of these parameters.

8.5 Physics of high lift: A.M.O. Smiths analysis of the high lift aerodynamics

Now that weve surveyed the characteristics of high lift systems, we need to examine the

physical basis for the operation and limits of high lift systems. A.M.O. Smith wrote the

book

on the physics of high-lift systems8

and is required reading. His message: you need to carry as

much lift (load) as you can on the airfoils upper surface without separating the boundary

layer.

His classic paper describes the physics associated with the high-lift characteristics we

described


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above, and how to achieve the available high lift performance. We summarize his

description

here.

To obtain insight into the characteristics of pressure distributions as they affect boundary

layer separation, Smith introduced the use of a canonical pressure distribution. He felt

stronglythat this was necessary to understand and compare possible separation on different

airfoils. It is

Page 16


essentially another type of dimensionless or scaled pressure distribution. For boundary

layer

investigations it is found that the best scaling factor is the velocity just before the

deceleration

begins. In Smiths canonical system, Cp= 0 represents the start of the pressure rise and Cp

= +1

the maximum possible value, that is, ue

= 0.The velocity at the start of the pressure rise is u0

.

Thus, the canonical pressure distribution is defined as

Cp

= 1ue

u0

2

The next step is to examine the best way to specify the pressure distribution to allow thepressure to recover to as close as possible to Cp

= +1. Smith made a parametric study of various

possibilities to gain insight into the best way to prescribe a pressure distribution to

delay

separation. However, here we look at his limiting case. It makes use of an analysis by

Stratford


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that was done to estimate separation before the days when boundary layer computer

programs

were available and their use routine (1959). Using Stratfords analysis, it is possible to

define a

pressure distribution where the boundary layer is everywhere just on the verge of

separation. Todo this, we manipulate the Stratford criteria:

Cp

x

dCp

dx

106

R

(

)1

10

1

2

= S

Note that originally, Stratford used this relation to say that separation occurred when the

quantity

on the LHS of the equation reached the value of S (typically 0.35). However, we can

define a Cp

distribution using this relation that is everywhere equal to S, just on the verge ofseparation, and

this pressure distribution is the best way to achieve a very large pressure recovery without

separation. Figure 8-13 shows the resulting pressure distribution. Examining this pressure

distribution, several key observations can be made. The initial slope is infinite, and then

decreases. Thus, when the boundary layer is thin, it can withstand a very large pressure

gradient.


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As the boundary layer thickens (either when it starts to recover, or as it recovers) it

cannot

sustain the large pressure gradient, and the pressure gradient to maintain attached flow

decreases.

This illustrates the idea that thick boundary layers are more likely to separate than thin

boundarylayers. Note also that the Reynolds number effect is relatively weak. Finally, the

boundary layer

could recover all the way to Cp

= +1, but to attain this,x would need to go to infinity. These

shapes are the best possible pressure distributions to use to recover the pressure without

separating the boundary layer. as Smith notes, the only way to do better is to use some

sort of

active boundary layer control (suction or blowing).

Page 17High-Lift Aerodynamics 8-17-0.20

0.0

0.20

0.40

0.60

0.80

1.0

0.0

0.50

1.0

1.5

2.0

Canonical

Cp

x - feetsolid line U0

/v = 10^6

dashed line U0

/v = 10^7

Figure 8-13. Stratford Limiting flows for two differentReynolds numbers.

Single elementairfoils: The key is how to obtain high lift on a single element airfoil, and

isessentially the story of Liebecks high lift airfoil7

and the Stratford pressure recovery shape of

the pressure distribution described above, as told by Smith.8

The question of how much lift you


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can obtain on a single element airfoil involves how low the pressure can be on the upper

surface,

and how the pressure can recover to a positive pressure coefficient at the trailing edge

and keep

the boundary layer attached. Smith describes two aspects of the problem. In the first case,

heexplains the limit of the pressure coefficient in terms of the vacuum Cp

when a zero pressure is

specified on the airfoil upper surface. Thus, using the definition of Cp

,

Cp

=

p p

1

2

U

2

we can obtain an alternate form using q = 1

2

U

2

=

2

P

M

2

, that is

Cp

=

p p

2

p

M

2


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Page 18


and vacuum Cp

occurs when the pressure is zero:

Cp

vac

=

2

M

2

Then, he points out that only a value of 70% of the vacuum Cp

has been achieved in practice.

This results in a Cp

limit ofM

2

Cp

= 1 for of 1.4.

Next, Liebeck and Smith used the analytical analysis by Stratford illustrated above to

specify

a pressure distribution that allows the most lift to be obtained. Given this pressure

distribution,

an inverse method is used to obtain the associated airfoil shape. The result is the Liebeck

family

of high lift airfoils.

Multi-elementairfoils: Understanding the physics: read section 6.3 of A.M.O. Smithspaper.

The five ideas are:

1. The slat effect. The slat protects the leading edge of the main element. Thats why its

effect

is only observed near CLmax

of the single element. Thought of as a point vortex, the slat velocity

acts to reduce the velocity around the leading edge of the main element.

2. The circulation effect. The downstream element causes the upstream element to be in a

high

velocity region, inclined to its mean line. To meet the Kutta condition, the circulation hasto be

increased. Instead of the airfoil deflecting as a plain flap, the trailing edge is placed in an

inclined

flow, something else (the downstream element) turns the flow.

3. The dumping effect. The trailing edge of the forward element is in a region of velocity

appreciably higher than the freestream velocity. Thus, the boundary layer can come off

the


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forward element at a higher velocity. You dont have to recover back to Cp = +0.2 for

attached

flow, relieving the pressure rise on the boundary layer, alleviating separation problems

and

permitting increased lift. The suction lift can be increased in proportion to UTE

2

for the same

margin against separation.

4. Off-the-surface pressure recovery. The boundary layer leaves the trailing edge faster

than the

freestream, and now becomes a wake (a viscous phenomena). The recovery back to

freestream

velocity can be more efficient way from contact with the wall. Wakes withstand more

than

boundary layers. Note that the wake can actually separate out in the flowfield. Note: for

a well

designed high lift system the local boundary layers and wakes remain separate. If they

merge,

everything is more complicated.

5. The fresh boundary layer effect. Thin boundary layers can sustain a greater pressure

gradient

than a boundary layer. Thus, three thin boundary layers (on three airfoil elements) are

more

effective than one thick boundary layer (single element).

Note: some people combine the circulation and dumping effects and call it the vane

effect.

8.6 Computational methods for high liftSignificant effort has been devoted to improving prediction capabilities for high lift

systems. As

stated in the introduction, the best recent survey is by Runsey and Ying.6

In the meantime, for

low speed predictions of the maximum lift for a single element airfoil, XFOIL can be

used.

experience shows that its predictions are slightly higher than experimental results.

Nevertheless,

this is rea remarkable capability of a code than be run on a laptop PC.

Page 19


8.7 Passive and active boundary layer control

Passive Boundary Layer Control: The boundary layer can be prevented from separating

by the

use of vortex generators, snags and fences.20


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Active boundary layer control: If suction or blowing is used to suppress boundary layer

separation, the blowing (which is generally preferred to suction) is known as boundary

layer

control (BLC), if the amount of blowing exceeds the value required for BLC, then the

blowing is

know as powered lift. The key parameter used to describe the amount of blowing is theblowing coefficient, defined as:

C

=

mj

Vj

qc

where the subscriptj refers to the jet, and q is the dynamic pressure. Blowing for BLC

was usedoften in early fighters, but is not used nearly as much today. The F-4 Phantom originally

had

blowing on both the leading edges and over the trailing edge flap. However, to improve

transonic

maneuver characteristics and to improve resistance to departure, the leading edge

blowing was

replaced by leading edge slats.21

8.8 Powered Lift

A huge class of concepts have been tried to increase maximum lift using high pressure air

fromthe engine. Some examples of powered lift concepts are:

propeller slipstream deflection (Brequet 941/McDonnell Model 188)

externally blown flaps (McDonnell DouglasYC-15/C-17)

internally blown flaps

upper surface blowing (Boeing YC-14, NASA QSRA, Ball-Bartoe JetWing)

vectored thrust (AV-8 Harrier)

jet flaps (Hunting H.126)

jet augmentor wings (NASA-deHavilland Augmentor Wing Aircraft)

circulation control (advocated by Hokie Bob Englar22

, A-6 CCW)8-9 Configuration Integration issues

The best airplane CLmax

you can achieve with a mechanical high lift system is about 3 3.5

The military and civil air regulations require a margin between CLmax

and the operating CL


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of the airplane. This must be accounted for during design. For example, the approach

speed must be 1.3 times the stall speed. This would suggest that the maximum approach

CL

is only 59% of the CLmax

. However, some relief is available because the measured stallspeed, Vsmin

is usually about 0.94 times the stall speed in 1g steady flight (the wind tunnel

case). This means that you can use a CL

of about 67% of the CLmax

.9,23

Increased span can be used to reduce the induced drag, so a bigger flap angle can be

used

before a climb limit is encountered, but this is a heavy solution.

Sweep decreases max lift

Page 20


2D to 3D: lots of losses dont be mislead by 2D CLmax

values, the real 3D value will be

much less.

The maximum CL

available for takeoff and landing for many swept-wing airplanes is

actually the limit on angle of attack to avoid tailscrape. The best high-lift configuration integration description also involves powered lift. The

YC-14 AIAA Case Study24

is highly recommended.

Finally, issues not covered but worth mentioning: the concept of the Gurney flap7

and the need

for accuracy around the leading edge.

8-10 Exercises

1. Examine the predictive capability of XFOIL for CLmax

. Use the data from Abbott and von

Doenhoff supplied previously for the NACA 0012 and 4412 airfoilsat a Reynolds

number of

6 million and free transition. Comment on your results.

2. Read the high lift paper by A.M.O. Smith. Summarize what you learned in one page.

Pay


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special attention to the details of single and multielement airfoilsdescribed in Sections 3-

6.

8-11 References1

Garner, P.L., Meredith, P.T., and Stoner, R.C., Areas for Future CFDDevelopment as

Illustrated by Transport Aircraft Applications, AIAA Paper 91-1527, 1991.2G.W. Brune and J.H. McMasters, Computational Aerodynamics Applied to High Lift

Systems, Chapter 10 ofApplied Computational Aerodynamics, P. Henne, Ed. Progress

in

Astronautics and Aeronautics, Vol. 125, AIAA, Washington, 1990.3

Jan Roskam and C-T Edward Lan,Airplane Aerodynamics andPerformance,

DARcorporation,

Kansas, 1997, pp. 343.4

Karl L. Sanders, High-Lift Devices, A Weight and PerformanceTrade-Off

Methodology,Society of Allied Weight Engineers (SAWE) Technical Paper 761, May 1969.5

Mark Drela, Design and Optimization Method for Multi-Element Airfoils, AIAA Paper

93-

0969, Feb. 1993.6

Christopher L. Rumsey and Susan X. Ying, Prediction of high lift: review of present

CFD

capability, Progress in Aerospace Sciences, Vol. 38, pp. 145-180, 2002. (note that

articles in

Progress in Aerospace Sciences are available for download through the Virginia Tech

University

Library if you search Addison and have a vt.edu address)7

Robert H. Liebeck, Design of Subsonic Airfoilsfor High Lift, Journal of Aircraft, Vol.

15,

No. 9, Sept. 1978, pp. 547-561.8

A.M.O. Smith, High-Lift Aerodynamics, 37th

Wright Bothers Lecture,Journal of Aircraft,

Vol. 12, No. 6, June 19759

C.P. van Dam, The aerodynamic design of multi-element high-lift systems for transportairplanes, Progress in Aerospace Sciences, Vol. 38, pp. 101-144, 2002. (note that

articles in

Progress in Aerospace Sciences are available for download through the Virginia Tech

University

Library if you search Addison and have a vt.edu address)10

Peter K.C. Rudolph, High-Lift Systems on Commercial Subsonic Airliners, NASA CR


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4746, Sept. 1996.

Maintaining an accurate leading edge contour is critical at high lift conditions. Once after a navy depot had

repainted an F-14 wing, a small ridge was left on the leading edge where the upper and lower surface paint

overlapped. This was enough to cause early stall. Ed Heinemann reported a similar experience on a

Douglas airplane

during World War II in his autobiography.

Page 21


Dick Kita, Mechanical High Lift Systems, Grumman Aerodynamics Lecture Series,

Grumman Aerospace Corporation, Feb. 1985.12

C.P. van Dam, J.C. Vander Kam, and J.K. Paris, Design-Oriented High-Lift

Methodology for

General Aviation and Civil Transport Aircraft,Journal of Aircraft, Vol. 38, No. 6,

November-

December 2001, pp. 12076-1084.13

B. N. Nield, An overview of the Boeing 777 high lift aerodynamic design,

Aeronautical

Journal, Nov. 1995. pp. 361-371.14

L.B. Gratzer, Analysis of Transport Applications for High Lift Schemes, AGARD LS

43,

1971.15

G.K. Korbacher, Aerodynamics of Powered High-Lift Systems,Ann. Rev. of Fluid

Mech.,

1974.16

S.F. Hoerner and H.V. Borst, Fluid Dynamic Lift, 1975.17

B.W. McCormick, Jr.,Aerodynamics of V/STOL Flight, Dover, 1999.18

Shevelle, Fundamentals of Flight, 2nd

ed., Prentice-Hall, 1989.19

John H. McMasters and M.D. Mack, High Reynolds Number Testing in Support of

Transonic

Airplane Development (Invited Paper), AIAA Paper 92-3982, July 1992.20

D.G. Mabry, Design features which influence flow separations on aircraft,

Aeronautical

Journal, Dec. 1988, pp. 409-415.21

D.H. Bennett and W.A. Rousseau, Seven Wings the F-4 Has Flown, Evolution of

Aircraft

Wing Design Symposium, Dayton, OH, AIAA Paper 80-3042, March 1980.22


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Englar, Robert J., Smith, Marilyn J., Kelley, Sean M., Rover, Richard C., III,

Development of

circulation control technology for application to advanced subsonic transport aircraft,

AIAA

Paper 93-0644.23

A. Flaig and B. Hilbig, High-Lift design for large civil aircraft, in AGARD High-Lift

System Aerodynamics, R 415, 1993.24

John K. Wimpress and Conrad F. Newberry, The YC-14 STOL Prototype: Its Design,

Development, and Flight Tes

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