AIAA 2000-5265 TCAT — A Tool For Automated Thermal ...

AIAA 2000-5265TCAT Ð A Tool For Automated ThermalProtection System Design

K. CowartJ. OldsSpace Systems Design LaboratoryGeorgia Institute of TechnologyAtlanta, GA

AIAA Space 2000 Conference and Exposition19-21 September 2000

Long Beach, California

For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.

AIAA-2000-5265

TCAT Ð A Tool For Automated Thermal Protection System Design

Karl K. Cowart , John R. Olds*

Space Systems Design LaboratorySchool of Aerospace Engineering

Georgia Institute of Technology, Atlanta, GA 30332-0150

ABSTRACT

This paper outlines the development of a newcomputational heat transfer tool for generating 1-Dtemperature profiles within thermal protection systemmaterials covering advanced reusable space launchvehicles. The Thermal Calculation Analysis Tool(TCAT) also contains an optimization capability todetermine the minimum thickness of thermalprotection materials required to prevent the vehiclesubstructure from exceeding its operatingtemperature limit. TCAT is designed to be used in theconceptual design environment with compatibleaeroheating analysis tools and an external materialsdatabase. The code is very fast (executes in minutes)and easy to use. Both single TPS material constructsand multi-layer TPS can be analyzed. TCAT iswritten in FORTRAN 77. A World Wide Webinterface has also been implemented to allow easyremote access to the code.

The heat transfer assumptions and numericaltechniques used to develop TCAT are discussed. Theresults of two test and validation cases are reported.The first test case involved TPS designs for a 10°half-angle cone, and the second analyzed TPSdesigns on a multiple angle wedge with angles of 5°and 10° . The designs involved sizing thermalprotection systems from each of the material groupsavailable from the WWW interface. The tilematerials that were chosen for the design test casesproduced unit weight values that ranged from 1.4~1.6lbm/ft2, and the blanket material TPS designs resultedin average unit weights between 0.4~0.6 lbm/ft2.

INTRODUCTION

Thermal protection system (TPS) sizing requiresthe selection of materials and a configuration thateffectively protects the launch vehicle and itscargo/passengers from the severe heatingenvironment encountered during reentry and ascent.The overall design process involves several levels:conceptual, preliminary, and detailed design. At theconceptual level, a large number of TPS concepts andideas are explored using engineering-level tools thatmust provide a reasonably accurate assessment of thematerials needed and the individual acreage weightsrequired.. In preliminary design, the design space isnarrowed as the concept becomes more defined.Higher fidelity tools enable the designer to increasethe level of analysis detail and explore key localheating phenomena. In detailed design, the externalvehicle shape and flight trajectory are set, and time isavailable to setup a high fidelity fluid-structuresanalysis to very accurately account for the temporaland spatial heating characteristics within the TPSsystem. The work in this paper is targeted at the levelof conceptual design. TCAT is meant to provide aquick-look analysis at several control points on thevehicleÕs surface and aid the TPS designer inselecting an appropriate acreage material andthickness with reasonable accuracy and speed.

In a previous paper first introducing TCAT,Cowart1 discussed the differences between Ôstatic,off-lineÕ and Ôdynamic, on-lineÕ TPS sizing. TheÔstatic, off-lineÕ sizing process is commonly used inconceptual design organizations. It typically requiresthe TPS designer to make Ôbest guessÕ engineeringassumptions in the early part of the design processthat do not change as the vehicle subsequentlychanges size or the trajectory changes. For example,TPS unit weights and distribution of key materialstypes might be selected based on historical databefore the vehicle design is even closed. Forexpedience, these estimates are often not revisited

- Graduate Research Assistant, School of Aerospace

Engineering, Student member AIAA.* - Assistant Professor, School of Aerospace Engineering,

Senior member AIAA.

Copyright © 2000 by Karl K. Cowart and John R. Olds.Published by the American Institute of Aeronautics andAstronautics, Inc. with permission.

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2American Institute of Aeronautics and Astronautics

during the remaining design closure process. Incontrast, Ôdynamic, on-lineÕ sizing calls forcontinuous updating of TPS unit weights, materialsdistributions, and thicknesses as the design processproceeds. This latter process is obviously morecomputationally intensive and requires a fastaeroheating analysis and TPS thickness optimizationmethod. In this previous paper, Cowart also reviewsthe computational tools selected by the authors todevelop a practical Ôdynamic, on-lineÕ TPS sizingstrategy; MINIVER2, TPSX3, ADS4, and TCAT.

This paper will cover the theory utilized in thedevelopment of TCAT, issues of numerical accuracyand execution time of TPS designs using TCAT,development of a World Wide Web interface for theTCAT tool, and dynamic TPS strategy validationresults and applications.

TCAT

Motivation

TCAT was developed for several reasons. First,it provides a means to calculate the transient in-depthconduction seen by the surface of the TPS materialthat protects a vehicle during ascent and reentry.Along with the in-depth conduction, radiation fromthe surface of the material is calculated along withthe temperature at the backface of the TPS material.TCAT adds speed and automation to the overalldesign process. Another feature of TCAT is thecapability for TPS thickness optimization.

Table 1. Percent of Dry Wt attributed to TPS forseveral space launch vehicles.

Vehicle % of Dry Wt. Dry Weight (lbs)

Hyperion5 6 123,250

Stargazer6 14 34,750

Shuttle7 16 154,739

In some vehicles, the TPS accounts for a highpercentage of the overall vehicle dry weight (Table1). Optimizing the weight of the TPS will lower thepercentage of the dry weight occupied by the TPS.This will lower the overall cost of the TPS materialand the presumably cost of the vehicle.

Thermal Analysis Methodology

TCAT uses a fully implicit method in order tosolve the parabolic, one-dimensional unsteady heatconduction equation (1) by marching in time.

¶¶

=¶

¶

T

t

T

xa

2

2(1)

The boundary conditions given in equations (2)and (3) are applied to the top and bottom surfaces ofthe TPS material, respectively.

q T kdT

dxxconv s- + = =es 4 0 0 at (2)

dT

dxx L= =0 at (3)

The top surface is defined as x = 0, and x = L isat the backface. Equation (2) is the energy balancerelationship for the top surface of the TPS material; itincludes convection from the flow field (calculatedexternally by MINIVER), radiation from the heatedsurface, and conduction absorbed by the TPSmaterial. All these quantities are summed to equalzero in order to preserve the conservation of energy.Equation (3) states that there is an adiabatic wall atthe backface of the material. This assumption isconservative because the temperature rise and decayof an adiabatic wall does not fully model the heatcapacitance of the actual complex structure thatphysically exists behind the TPS material. This levelof coupling between the underlying structure and theTPS layer would require methods of analysis that arenot within the target conceptual design capability.

Three different types of finite differencediscretization were used for obtaining the system ofequations needed to solve for the in-depthtemperature profile in the material as function oftime. A one-sided, forward implicit differencescheme was used at the top surface in order toincorporate the boundary condition given in equation(2). This discretization resulted in equation (4) and isaccurate on the order of O(Dt,Dx). Note that theexternal input qconv is a function of time also.

Tt

x

T q

k

t

xT T Tn

nconv n n n

11 1 1

1 4

1

12 2

11

11

12 2=

( ) -æ

è

çç

ö

ø

÷÷- -( ) +

++ + +a e s aD

DD

D(4)

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The heat equation was discretized at the interiornodes with a simple implicit central finite differencescheme resulting in equation (5) that is accurate onthe order of O(Dt,Dx2).

Tt

xT T T Ti

n iin

in

in

in= - - +( ) +-

+ +++ +a D

D 2 11 1

11 12 (5)

On the back surface of the material, a one-sidedimplicit backward finite difference scheme was usedto discretize the heat equation and couple theboundary condition from equation (3). This resultedin equation (6), which is accurate on the order ofO(Dt,Dx).

Tt

xT T TN

n NNn

Nn

Nn= - -( ) +-

+ + +22 1

1 1 1a D

D (6)

For a model of a tile in free space, a radiativeheat flux at the backface of the material can be usedas an alternative boundary condition instead of theadiabatic wall assumption in equation (3). This isgiven by equation (7), which states that the radiativeheat flux at the backface is equal to the conductiveheat flux through the material. As in equation (2), theconductive heat flux term is given by FourierÕs Lawand the radiative flux is a function of the backfacesurface emissivity, BoltzmannÕs constant, and thebackface surface temperature. The result of thediscretized heat equation at the backfaceincorporating this alternative boundary condition isgiven by equation (8) and accurate on the order ofO(Dt,Dx).

- =kdT

dxTN N Ne s 4 (7)

Tt

xT T

k xT TN

n NNn

Nn N

Nn

Nn= - - - ( )æ

èöø+-

+ + + +22 1

1 1 1 4 1a e sD

D D (8)

Numerical Solution Procedure

A system of nonlinear equations (9) resultedonce the heat equation was discretized at all nodes inthe material. This system of equations reflects the useof the top surface and backface boundary conditionsgiven by equations (2) and (3) respectively. The formof the equations has been modified in order to makethem easier and more efficient to solve with acomputational algorithm. The vector of temperatures

at the next time step is to be determined from thevalues as the current time step.

ft

x

t

k xT T

t

xT T

t

xkq

ft

xT

t

xT

n n n nconv

n n

11

21

11

1 3

11 1

2 21

11

1

22

2 11 2

2 21

12 2 2 2

12

= + + ( )æ

èç

ö

ø÷ - - -

æ

èç

ö

ø÷

= - + +æè

öø

-

+ + +

+ +

a aes

a a

a a a

D

D

DD

D

D

DD

D

D

D

D22

2 31

2

33

2 21 3

2 31 3

2 41

3

112 2

1 12

12

12

D

D

D

D

D

D

D

D

D

D

D

D

t

xT T

ft

xT

t

xT

t

xT T

ft

xT

t

x

n n

n n n n

NN

Nn N

+

+ + +

--

-+ -

-

= - + +æè

öø

- -

= - + +æ

a a a

a a

M M M

èèöø

- -

= - + +æè

öø

-

-+ - +

-

-+ +

Tt

xT T

ft

xT

t

xT T

Nn N

Nn

Nn

NN

Nn N

Nn

Nn

11 1

21

1

2 11

212

12

a

a a

D

D

D

D

D

D

(9)

This system is nonlinear due to the fourth orderradiation term in the top surface boundary condition,equation (2). Each equation in this system representsa nodal location in the material. Each is obtained bysubtracting the information at the current time level,n, from that required at the next time level, n+1, andsetting it equal to fi, where i = 1,..,N, with N being themaximum number of spatial nodes.

This system of equations is iteratively solvedusing the Newton-Raphson method, which is theapplication of NewtonÕs root solving method appliedto a system of non-linear equations. The first step inthe Newton-Raphson method requires the formationof the Jacobian matrix, J , which is defined byequation (10).

Jf

Ti ji

jn

i j N

,

, ,..,

=¶

¶ +=

11

(10)

Once the Jacobian is formed, the problem takeson the form Ax = b given by equation (11), where Ais the Jacobian and is a tridiagonal matrix, x is thechange in temperature at time level n+1, and b = Ð fat time level n.

¶¶

¶¶

¶¶

¶¶

¶¶

¶¶

¶¶

¶¶

¶¶

¶¶

¶

+ +

+ + +

+ + +

-

-+

-

-+

f

T

f

Tf

T

f

T

f

Tf

T

f

T

f

T

f

T

f

T

f

n n

n n n

n n n

N

Nn

N

Nn

N

1

11

1

21

2

11

2

21

2

31

3

21

3

31

3

41

1

21

1

11

0 0 0 0

0 0 0

0 0 0

0 0 0

O O O

--+

-+ +

-

+

-

¶¶¶

¶¶

æ

è

çççççççççççç

ö

ø

÷÷÷÷÷÷÷÷÷÷÷÷

æ

è

ççççççç

ö

ø

÷÷÷÷÷÷÷

=

-

-

-

-

-11

11 1

1

2

3

1

11

2

3

1

0 0 0 0

Tf

T

f

T

T

T

T

T

T

f

f

f

f

Nn

N

Nn

N

Nn

N

N

n

N

D

D

D

D

D

M M

ffN

næ

è

ççççççç

ö

ø

÷÷÷÷÷÷÷

(11)

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This is solved by making an initial guess for thetemperature at time level n+1, and iteratively solvingfor DTn+1 at each spatial node using the ThomasAlgorithm8. Prior to the next iteration step thetemperature at time level n+1 is updated by Tn+1 =Tn+1 + DTn+1.

Convergence is reached when the magnitude ofthe two-norm for both the DTn+1 vector and the f n

vector on the right hand side of equation (11) fallbelow 1x10-6. The definition of the vector two-normis given by equation (12). Also, the maximumnumber of iterations at each time level is limited to1000.

g gii

N

22

1

1 2

= åæèç

öø÷

=

/(12)

The initial guess for the temperature profile within the material for the first n+1 time step is assumedto be 1000 K. For each additional n+1 time step, theinitial guess for the temperature profile is assumed tothe final converged temperature profile from theprevious time step.

TCAT can analyze up to 100 spatial nodes in asingle material or 100 nodes total when severaldisparate TPS materials are layered together. Whendifferent materials are layered together, it is assumedthat perfect contact exists and equation (13) gives theinterface condition for the heat transfer between thematerials.

kdT

dxk

dT

dxii

ii

--

æè

öø

= æè

öø1

1

(13)

Also, it is assumed that no kinetic reactionsoccur in the boundary layer; therefore, chemicalequilibrium exists, while thermal equilibrium doesnot. Additionally, all material properties are heldconstant throughout the analysis. At this time,temperature dependent material properties are notincorporated in TCAT, but can be added as linearinterpolations or cubic spline functions.

TCAT ACCURACY vs. EXECUTION TIME

In order to determine trade off betweennumerical accuracy and execution time of TCAT, astudy of various temporal and spatial discretization

step sizes was performed. The time step is theamount of time incremented between time leveliterations in the solution of the heat equation, and thespatial step is the distance between nodes in thenumerical discretization of the TPS material stack.As the number of nodes in the material is increased,the spatial step is decreased. This sweep analysis wasperformed on the windward and leeward sides of the10° half-angle cone, Figure 1, at a point two feetfrom its tip. A reference trajectory10 from STS-1 wasused to calculate convective heating at both points.

Figure 1. Schematic of 10° Half-Angle Cone.

The leeward side time step and spatial stepsweeps were conducted using AFRSI blanketmaterial3. The time sweep range was from 1 to 200seconds with calculations being conducted attemporal increments of 1, 2, 5, 10, 25, 50, 100, and200 seconds. The spatial step was controlled by thenumber of nodes that were placed in the AFRSIblanket material and ranged from 10 to 80 nodes.

As validation, an external thermal analysis code,SINDA was used to provide reference results for thistest case. SINDA is a commercial software analysistool capable of complex, high fidelity analysis.analysis. The TCAT solution whose temperatureresults agreed best with the SINDA results wasselected as the reference condition for which tocompare other TCAT results. The SINDA solutionthat was used for the comparison utilized the sametrajectory as the TCAT combination solutions.

Tables 2Ð5 list the maximum relative percenterror calculated for each of the combinations of timestep and number of nodes considered. Time steps areshow in the table rows in values of seconds. Thepercent errors in the tables represent the maximumerror of the surface and backface temperatures ofeach test combination compared to the sametemperatures of the reference combination.

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The definitions of the maximum relative errorsused to calculate the values in Tables 2Ð5 are givenby equations (14) and (15), respectively.

surface rel error(ref surf temp - test case surf temp)

avg ref surface temperature

*100 =

max

( )(14)

backface relative error(ref backface temp - test case backface temp)

avg ref backface temperature

*100 =

max

( )

(15)

The reference combination for the leeward sidenumerical analysis was a time step of 1 sec with 40nodes within the AFRSI material. In addition toAFRSI, this stack also consisted of RTV adhesiveand a simple Graphite/Epoxy (GrEx) sublayer. RTVand GrEx were discretized with 10 nodal points forall of the possible combinations considered in theleeward numerical sweep analysis.

The average reference temperatures used forcalculating the maximum relative error in Tables 2and 3 were 1103¡ R and 691¡ R, respectively. Theseare the average temperatures that occurred on the topsurface and backface of the AFRSI material stack forthe time duration of the heating analysis.

It can be seen that the lowest relative error forthe surface temperature comparison in Table 2occurred for a time step of 2 seconds and 40 nodes.This indicates that for a 1 second increase in the timestep the maximum deviation of the surfacetemperature profile from reference solution is 1.06 %.It is desired to find a combination that will yieldaccurate results within 5Ð10% of the referencesolution and still require low CPU times. Shortexecution times are desired so that rapid and accuratecalculation results are returned for TCAT analysesconducted over the World Wide Web. It was foundthat circled values in the table have an execution timeof approximately 30 seconds per body pointcompared to three minutes for the reference solutionson an SGI Octane workstation with a 250 Mhz R12k.

The asterisks in the tables indicate that a solutionwas not obtained for the considered combination. It issuspected that for each of the combinations with anasterisk, and in fact, for all of the combinations with50 or more nodes, round-off errors (due to small Dx)were significant and negatively affected the results.This is evident by the nearly constant or increasingvalues of the relative error that occurred as the time

Table 2. Maximum Relative Percent Error forLeeward Point Surface Temperatures.

Number of Nodes

10 20 30 40 50 60 70 80

1 9.5 5.5 4.1 Ref 38.3 36.4 34.8 33.7

2 10.3 6.0 4.6 1.06 37.6 35.6 * *

5 12.6 7.3 6.0 16.5 * * * *

10 16.5 11.7 10.5 9.2 * * * *

25 25.8 22.9 22.0 24.3 * * * *

50 42.7 40.0 39.1 39.4 * * * *

100 81.7 82.7 84.0 87.8 66.9 66.1 * *

200 97.2 97.1 96.6 96.4 92.9 92.4 91.9 91.9

Table 3. Maximum Relative Percent Error forLeeward Point Backface Temperatures.

Number of Nodes

10 20 30 40 50 60 70 80

1 10.2 8.5 5.0 Ref 6.4 9.7 12.6 14.9

2 10.2 8.5 5.0 0.04 6.4 9.7 * *

5 10.1 8.4 4.9 9.9 * * * *

10 9.9 8.3 4.8 0.14 * * * *

25 9.6 7.9 4.6 0.40 * * * *

50 9.0 7.4 4.3 0.66 * * * *

100 7.0 5.5 3.2 3.3 5.8 9.6 * *

200 3.7 2.6 1.0 1.5 3.5 5.7 11.7 11.7

Table 4. Maximum Relative Percent Error forWindward Point Surface Temperatures.

Number of Nodes

10 20 30 40 50 60

1 12.40 6.77 3.55 1.93 0.79 Ref

2 14.51 10.30 7.54 5.93 4.98 4.40

5 15.86 10.55 9.74 9.45 9.29 9.14

10 22.13 19.58 19.02 18.82 18.72 18.60

25 43.26 41.55 41.19 41.07 40.99 40.89

50 67.09 67.04 67.03 67.03 * *

Table 5. Maximum Relative Percent Error forWindward Point Backface Temperatures.

10 20 30 40 50 60

1 8.71 8.15 6.83 5.16 2.95 Ref

2 8.70 8.14 6.82 5.17 2.96 0.01

5 8.62 8.06 6.76 5.13 2.97 0.06

10 8.58 8.02 6.74 5.13 3.01 0.12

25 8.48 7.93 6.68 5.12 3.14 0.36

50 8.31 7.76 6.58 6.58 * *

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step and the number of nodes were increased. Thisproblem might be alleviated by non-dimensionalizingthe spatial terms in the governing equations prior tonumerical solution.

The maximum values for the relative error of thetime step and nodal number sweep analysisconducted on the windward side of the cone are givenin Tables 4 and 5. The reference solution for thewindward side analysis was selected like the leewardside analysis, but the windward side LI-900 tile TPSstack had four other material layers below the top tilematerial. These included two layers of RTV adhesive,a strain isolator pad, and a simple layer of GrExbackface material. Each of these had 10 nodes thatwere held constant for each of the combinations thatwere analyzed in Tables 4 and 5. Considering CPUtime and accuracy tradeoffs, the best combinations oftime step and number of nodes are indicated by thecircled elements.

The combination of 40 nodes with a time step of10 seconds was selected for subsequent leeward sideWWW applications, and a combination of 40 nodesand a 5 second time step was selected for windwardside applications.

WORLD WIDE WEB INTERFACE

Software Coupling

The motivation for the dynamic TPS sizingsolution strategy is to have TCAT, ADS, and TPSXcoupled in order to conduct the heating analysis anddynamic TPS sizing strategy via a WWW interface.This was accomplished using hyper-text-markup-language (HTML) and common-gateway-interface(CGI) Perl9 scripting. The HTML and CGIprogramming was done on a UNIX platform.

http://www.ssdl.gatech.edu/~ralexander/tcat_intro.html

Note that MINIVER is a restricted access codeand cannot be executed via a public web site.Therefore, a text file formatted to resembleMINIVERÕs summary output file format (filename.s)must be provided by the user. This file must containconvective heating values for each surface point as afunction of time through the trajectory. Users with an

authorized version of MINIVER may upload anactual MINIVER summary file to the TCAT web sitefor TPS sizing analysis.

At the initiation of the interface, the user isgreeted by an animated GIF for the TCAT program,shown in Figure 2. After going through the greeting,the user views the main working environment of theweb interface. The interface window as seen inFigure 3 is subdivided into three different frames: aheader at the top of the window with input and outputwindows on the lower left and right hand sides,respectively. The input window provides the userwith six different TPS design options. The first threeinvolve design options of TPS systems that includeseveral materials for the fuselage, cowl, and wing ofa vehicle. The three remaining options allow the userto chose a particular TPS material and size it for thefuselage, cowl, and wing of a vehicle.

Figure 2. Screen Capture of TCAT Greeting.

Figure 3. Screen Capture of TCAT WorkingEnvironment.

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The next two subsections given an overview theprocesses carried out by the scripts written for theautomated TPS sizing analysis being discussed. Bothscripts collect inputs for t user via the web, and passthe data to TCAT. In this form, TCAT not onlyanalyzes the temperature profile through the material,but increases or decreases the tile thickness tomaintain a maximum backface temperature limit. Thefunctionality for this constrained optimization of TPSthickness is provided by integrating TCAT withADS4, a relatively ease to obtain numericaloptimization package.

Multiple Material Design Script

The first part of this script obtains theinformation from the website input frame and parsesthe information into the mesh type variableÒ$FORM{$name}Ó. Next, the script goes through theMINIVER (or MINIVER-like) output file and createsindividual files for each of the body points thatcontain time, convective heat rate, and radiationequilibrium temperature. This is accomplished byusing an until-end-of-file-loop that searches line-by-line of the short version of the MINIVER output file.The MINIVER output file contains blocks of data foreach of the points defined in the MINIVER inputdeck. Each block of data begins with a line of textfollowed by columns of data that include informationsuch as time, heat rate, heat load, etc., and ends witha Ò-1Ó flag. The until-end-of-file-loop starts at thetext line, and parses through the columns of data untilthe Ò-1Ó flag is reached. This process is done for allof the body point blocks until the end of theMINIVER output file is reached.

Once this is completed, the script determines theTPS material to be used at a particular body pointbased on the radiation equilibrium temperature. Thisis accomplished by a ÒforÓ loop with nested if/thenconditional statements. The ÒforÓ loop marchesthrough the body points, and the conditionalstatements determine the material to be used based ontemperature limits. In order to prevent a patchwork ofmaterials from being chosen, an intelligent systemhad to be created. This was accomplished by lookingat three different body points at a time anddetermining that the materials used were the same forthose three points. If the materials on the two ends

were different from the one in the middle and themiddle material had a higher temperature limit, thenthe CGI script would switch the outer materials tothat of the middle one. If the materials on the endshave higher temperature limits, then the middlematerial is changed to match those on the ends. Afterthe materials are determined, the heating analysis isconducted. This is completed by a ÒforÓ loop usingsystem-level calls that execute the FORTRAN codewritten for the heating analysis. After the heatinganalysis is completed, values for materialthicknesses, unit weights, and acreage percentagesare determined. These are in turn printed to theoutput window of the user web-interface.

Single Material Design Script

The process for a single TPS material is the sameas that for several materials except that the CGI scriptdoes not determine the TPS material used. Instead,the user determines the material to be used as aninput on the web-interface.

TPS Materials Selection

The TPS materials for the multiple TPS materialdesign option are selected by the CGI script based onthe maximum multi-use temperature obtained fromTPSX . These materials are segregated into threedifferent groups: Shuttle technology materials, nextgeneration RLV materials, and a combination of thetwo groups. Tables 6 Ð 8 list the materials in each ofthe groups. The user supplies the TPS material in thesingle material design options. Also, the user has theoption of selecting the type of backface material thatis used in the TPS sizing analysis. There are twomaterial options the user can choose for the backface:graphite epoxy and titanium aluminide.

It is important to note that the next generationRLV materials are currently under development;therefore, specific information (i.e. materialproperties and unit weights) is restricted in TPSX andcannot be published at this time. It can only bementioned that such materials are included in designoptions for a restricted version of TCAT. On theother hand, information about the Shuttle technologymaterials group is not restricted, and is available foruse on the unrestricted WWW version of TCAT.

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Table 6. Shuttle Technology Materials.

Windward Materials Leeward Materials

RCC tiles FRCI tiles

LI-2200 tiles AFRSI blankets

FRCI tiles FRSI blankets

Table 7. Next Generation RLV Materials.


RCC tiles CFBI blankets

SiC tiles AFRSI-2500 blankets

TUFI tiles AFRSI-2200 blankets

DURAFRSI blankets

Table 8. Group Combination of Materials.


RCC tiles CFBI blankets

SiC tiles AFRSI-2500 blankets

AETB-12 tiles AFRSI-2200 blankets

AETB-8 tiles DURAFRSI blankets

LI-900 tiles PBI blankets

Materials used are either blankets or tiles. Eachmaterial is modeled as a TPS material stackup wherethe material chosen is the one that is sized. Theblanket materials consist of a three layer stackup thatincludes the blanket insulation, an adhesive, and thebackface material. Five materials make up tileconfiguration: a tile, an adhesive, a strain isolatorpad, an adhesive, and the backface material. Figures4 and 5 show schematics.

TUFI tiles are not modeled like those shown inFigure 5. Instead, they are approximated aslaminates. The actual TUFI surface layer is modeledas a constant thickness layer on the surface of the tilewhile AETB-8 tile material, placed underneath, issized by ADS. Figure 6 shows this arrangement.

Figure 4. Schematic for Three Material Stack.

Figure 5. Schematic for Five Material Stack.

Figure 6. Schematic for Laminate Materials.

DYNAMIC TPS DESIGN STRATEGYRESULTS AND APPLICATIONS

Single Material Design

A 10° half-angle cone (Fig. 1) was chosen inorder to demonstrate and test the user interfacecreated for the one material TPS design option. Thechosen trajectory was the STS-1 reentry trajectory10.Body points were placed two feet apart on the surfaceof the cone resulting in 30 body points for both theleeward and windward sides. The TPS materials ofchoice were LI-900, 9 lb/ft3 ceramic tiles, for thewindward side and AFRSI, Advanced FlexibleReusable Surface Insulation, blankets for the leewardsurface (Figures 7 and 8).

The heating analysis was conducted using TCATin order to size the TPS materials at body pointsdefined along the centerline of the leeward andwindward sides of the cone. The calculated thicknessvalues were then used to determine an average unitweight, equation (16), for each material of the TPS.

average TPS unit weight average TPS thickness TPS density = ( )( ) (16)

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Figure 7. LI-900 Tile Sample.3

Figure 8. AFRSI Blanket Sample.3

The heating analysis was not conducted at the tipof the cone because TCAT is not capable of capturing2-D heating effects. It was determined that SHARPmaterials were needed at the tip of the cone becauseaccording to MINIVER calculations the radiationequilibrium temperature exceeded 3500° F. SHARPmaterials are ultra high temperature ceramics, such ashafnium diboride, that can withstand extremetemperatures resulting from high heating rates. Thesematerials are under development by NASA AmesResearch Center, and their design application is as asmall radii leading edge, passive TPS for slenderhypersonic vehicles.

Results of the TPS sizing for each side of thecone are given in Table 9. The unit weight obtainedfor the LI-900 tiles was approximately 1.42 lbm/ft2

with thicknesses ranging from 1.78 to 2.25 inches. Atypical unit weight for windward side tiles is between1.4 and 1.6 lbm/ft2. The unit weight for the LI-900tiles is therefore a good approximation of the averageunit weight for the tiles on the windward side of thecone. The 0.5 lbm/ft2 unit weight for the AFRSIblankets, includes a 0.3 lbm/ft2 added areal weight.

The desired range for the unit weight of leeward sideblankets is from 0.4 to 0.6 lbm/ft2. The thicknesses ofthe AFRSI blankets on the leeward side of the coneranged from 0.25 to 1.68 inches.

Table 9. Output for 10° Half-angle Cone HeatingAnalysis.

Output Value

LI-900 Unit Weight 1.42 lbm/ft2

LI-900 Area to Body Area Ratio 0.33

LI-900 Average Thickness 1.9 in

AFRSI Unit Weight 0.50 lbm/ft2

AFRSI Area to Body Area 0.67

AFRSI Average Thickness 0.40 in

1.750

2.000

2.250

2.500

2.750

3.000

0 1 2 3 4 5

SLP Iterations

Thi

ckne

ss, i

n

point w1 point w5 point w10

Figure 9. LI-900 Thickness Iteration History.

Figure 9 shows examples of the iteration historyof the LI-900 tile thickness for several body points onthe windward side of the 10° half-angle cone. The

locations of the body points are 2, 10, and 30 feetfrom the tip of the cone, respectively. The thicknessof the each tile was controlled by the optimizerprogram ADS. ADS changed the thickness of thetiles at each of the body points in order to satisfy thetemperature constraints that were set. As introducedin Reference 1, ADS is segmented into three levels:strategy, optimizer and one-dimensional search. Thesettings for each level used in this application aregiven in Table 10. As can be seen from Figure 9 thethickness of the tile material at each of the bodypoints converged to the minimum required thickness

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within 4 to 5 iterations, and the thickness decreasedfor points further back on the cone.

Multiple Material Designs

As discussed earlier, TPS materials for thisdesign option are chosen from three different TPSmaterial groups. These are Shuttle technologymaterials, next generation RLV materials, and acombination of the Shuttle technology and nextgeneration RLV material groups. The 10° half-anglecone in Figure 1 and a five-foot wide wedgeconfiguration were flown along the STS-1 reentrytrajectory and used to size TPS for the three materialgroups. Only results from the Shuttle technologymaterials group will be presented due to the sensitivenature of the next generation RLV and groupcombination TPS materials.

10° Half Angle Cone - Shuttle Technology Materials

The inputs for this analysis are the same as thosefor the single TPS material analysis except for thefact that the TPS materials were not input by the user.Instead, TCAT determined the TPS at each pointbased on the maximum radiation equilibriumtemperature predicted by MINIVER. Results of theanalysis showed that a combination of FRCI tiles,Fibrous Reinforced Composite Insulation, and LI-2200 tiles, a 22 lbm/ft3 rigid ceramic tile, were usedon the windward surface, and AFRSI blankets wereused on the leeward surface of the cone.

Table 11 gives a detailed description of theoutput for the analysis of the 10° cone with theShuttle technology materials. The thicknesses for theAFRSI blankets ranged from 0.25 to 1.65 inches. TheLI-2200 tile thicknesses ranged from 1.45 to 1.89inches, and the FRCI tiles were between 1.21 and1.70 inches thick. Again, the AFRSI unit weightincludes a 0.3 lbm/ft2 additive areal weight. The unitweight of the AFRSI blankets is a reasonableestimate, but the values for the LI-2200 and FRCI tile

unit weights are rather high in comparison to thetarget range discussed previously. The high unitweight value for the LI-2200 tiles most likely occurssince they roughly only account for 1% of the wettedTPS body area. This means that where the LI-2200tiles are placed they are rather thick. Since their unitweight is based on the average thickness times thedensity of the material the unit weight will be high. Inorder to lower the unit weight value for LI-2200 morepoints on the cone need to be covered with thinnerLI-2200 tiles. The unit weight obtained for the FRCItiles is more desirable, but is still quite high. TheFRCI unit weight is high for the same reason givenfor the LI-2200 unit weight. It is important tomention that these materials are Shuttle technology.Once again, it is expected that more recentadvancements in material technology will lead tolower unit weights for TPS materials. Figure 10 givesan illustration of the TPS layout for the Shuttletechnology materials on the 10° half-angle cone.

Table 11. Shuttle Era TPS Materials on 10°Half-Angle Cone.

Output Value


AFRSI TPS Area to Body Area 0.67



LI-2200 TPS Area to Body Area 0.0990


FRCI Unit Weight 1.43 lbm/ft2

FRCI TPS Area to Body Area 0.2310

FRCI Average Thickness 1.44 in

Figure 10. Shuttle Technology TPS MaterialMapping on 10° Half-Angle Cone.

Multiple Angle Wedge - Shuttle TechnologyMaterials

The multiple angle wedge configuration, shownin Figure 11, is a different analysis than that of the10° half-angle cone. In this analysis, tangent wedgeapproximations were used instead of tangent cone

Table 10. ADS Settings.

ADS Operation Level Setting

Strategy Sequential Linear Programming

Optimizer Modified Method of FeasibleDirections

One DimensionalSearch

Golden-Section Method

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approximations for the flow analysis conducted byMINIVER. Also, the body area percentages coveredby blankets and tiles were different. The amount ofsurface area covered by tiles is 50%, with the samepercentage for blankets. Further, there will becompressibility effects from the surface of the wedgedue to the change in the flow angle over the surfaceof the wedge. The surface area used for thecalculations was 909 ft2 with SHARP materials usedon the leading edge of the nose due to the highradiation equilibrium temperatures at the tip of thewedge.

Figure 11. Schematic of Multiple Wedge TestArticle.

Table 12 shows that AFRSI was selected as thematerial of choice for the leeward side of the wedgewith a unit weight of 0.49 lbm/ft2 including the 0.30lbm/ft2 added areal weight; the thickness for theAFRSI blankets ranged from 0.25 to 1.60 inches. Thematerials selected for the windward side of the wedgewere LI-2200 tiles and FRCI tiles. There was a smallarea at the tip of the wedge that required LI-2200,and the recorded thickness was 1.89 in. The FRCI tilethicknesses ranged from 1.31 to 1.69 inches. The unitweight for the LI-900 material was relatively high at3.46 lbm/ft2. This is due to the fact that the areacovered by LI-900 is only 0.17% of the total surfacearea. The FRCI unit weight was 1.40 lbm/ft2, whichshows that if more surface area is available for theTPS material to occupy, then the unit weight willdecrease. Figure 12 gives an illustration of the TPSlayout for the Shuttle technology materials on themultiple angle wedge.

Figure 12. Shuttle Technology TPS MaterialMapping on Multiple Angle Wedge.

Table 12. Shuttle Technology TPS Materials OnMultiple Angle Wedge.

Output Value


AFRSI TPS Area to Body Area 0.5000



LI-2200 TPS Area to Body Area 0.0167


FRCI Unit Weight 1.40 lbm/ft2

FRCI TPS Area to Body Area 0.4833

FRCI Average Thickness 1.40 in

CONCLUSIONS AND RECOMMENDATIONS

The integration of 1-D TPS analysis involved thecoupling of four design tools: TCAT, ADS,MINIVER, and TPSX . TCAT, the ThermalCalculation Analysis Tool, is an original code writtenfor this research that uses finite difference methodscoupled with optimization techniques in order to aconduct a transient, trajectory-based heating analysisto design and size the TPS of an RLV. TheAutomated Design Synthesis tool (ADS) is asoftware package that uses algorithms for the solutionof constrained and unconstrained optimizationproblems. MINIVER is a restricted access analysiscode that models the flowfield heating effects ofimportant regions of an RLV. The ThermalProtection System Expert (TPSX ) is a materialproperties database that is used for the selection ofmaterials that will provide the thermal barrierinsulation to the surface of an RLV.

A user interface was created in order to conductthe heating analysis and dynamic TPS sizing strategyvia the World Wide Web. This was accomplishedusing hyper-text-markup-language (HTML) andcommon-gateway-interface (CGI) scripting. TheHTML and CGI programming was done on a UNIXplatform which provided the freedom of using theCGI scripts.

A numerical analysis of the accuracy andexecution time for the TCAT heating code wasconducted by performing a sweeping analysis of thetime step and spatial resolution. Results showed thatthe time required to perform the heating analysis at a

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single body point on a given geometry could belowered from three minutes for an accurate solutionto approximately 30 seconds with only a ten percentloss in accuracy.

Also, several applications demonstrating theperformance of the automated dynamic TPS sizingstrategy over the WWW were performed. Resultsshowed that the TCAT tool can perform well as anacerage TPS design tool, and they proved thefunctionality of the TCAT tool in conceptual levelRLV design.

There are some recommendations if future workrelated to this research is pursued:

1. The simple implicit method used to conduct theheating analysis in TCAT should be replacedwith the Crank-Nicolson method. This is thesame method used in the heating code SINDA. Itis proven that the Crank-Nicolson methodrequires fewer nodes and less execution time.Along with this, it is numerically more accuratethan the simple implicit scheme.

2. It is also recommended that a Òproblem specificoptimizerÓ be written for the TPS sizing portionof the design strategy. ADS is a Ògeneralproblem optimizerÓ in the sense that it wascreated to handle many different types ofengineering design problems. It was found thatADS has many controlling parameters that haveto be fine-tuned in order to achieve an optimalanswer. A Òproblem specific optimizerÓ canalleviate this fine-tuning issue.

ACKNOWLEDGMENTS

This research has been funded under CooperativeAgreement NCC2-5332, with NASA Ames ResearchCenter and by the United States Air Force Institute ofTechnology.

The authors would like to thank the members ofthe Georgia Institute of Technology Space SystemDesign Laboratory (SSDL) for their support.

REFERENCES

1 . Cowart, K., and Olds, J., ÒIntegratingAeroheating and TPS Into Conceptual RLVDesign,Ó AIAA 99-4806, November 1999.

2 . Engel, C.D. and Konishi, S., ÒMINIVERUpgrade for the AVID SystemÓ, NASA CR172213, August 1993.

3. TPS-X database web site, NASA Ames ResearchCenter, http://asm.arc.nasa.gov

4 . Vanderplaats, G.N., ÒA Fortran Program forAutomated Design Synthesis, Version 1.00.ÓNASA CR 172460, October 1984.

5. Olds, J., Bradford, J., Charania, A., Ledsinger,L., McCormick, D., Sorensen, K., "Hyperion: AnSSTO Vision Vehicle Concept Utilizing Rocket-Based Combined Cycle," AIAA 99-4944,November 1999.

6. Olds, J., Ledsinger, L., Bradford, J., Charania,A., McCormick, D., Komar, D. R.., ÓStargazer:A TSTO Bantam-X Vehicle Concept UtilizingRocket Based Combined-Cycle Propulsion,ÓAIAA 99-4888, November 1999.

7. Macconochie, I.O., and Klich, P.J., ÒTechniquesFor The Determination of Mass Properties ofEarth-To-Orbit Transportation Systems,Ó NASATM 78661, June 1978.

8 . Press, W.H., Teukolsky, S.A., Vetterling,W.T.,Flannery, B.P., Numerical Recipes in Fortran 77,2nd Edition, Cambridge University Press, 1992.

9 . Holzner, S., Perl Core Language: Little BlackBook, Coriolis Technology Press, 1999.

10. Engel, C.D., and Schmitz, C.P., ÒUpgrade Forthe AVID System, Volume II: LANMIN InputGuide,Ó NAS1-17896, Remtech, Inc., Alabama,May 1987.

AIAA 2000-5265 TCAT — A Tool For Automated Thermal ...

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