# Recent Advances in Hypersonic Aerothermodynamics for RLV ...

### Transcript of Recent Advances in Hypersonic Aerothermodynamics for RLV ...

1

Recent Advances in Hypersonic Aerothermodynamics

for RLV/TPS Design and Analysis+

P.C. Chen, D.D. Liu, L. Tang, K.T. Chang, and X.W. Gao

ZONA Technology*, Scottsdale, AZ, www.zonatech.com Introduction For hypersonics and space access, the National Aerospace Initiative (NAI) goals are: (i) Hypersonics- flight demonstrate increasing Mach number capability each year, reaching Mach 12 by 2012; (ii) Space Access � demonstrate technologies that will drastically increase space access and reliability while decreasing cost. In response to these initiatives, needed technologies were identified by NASA/DoD, to support safe but cost effective launch and recoverable systems. To this end, integrated software development in aerothermodynamics, aerothermoelasticity, thermal protection systems (TPS) and multidisciplinary design optimization (MDO) for RLV in extreme environment are among the urgent enabling technologies. With ongoing supports of several government agencies, together with our in-house R&D resources, we have been gradually building up a Hypersonic Aerodynamics/Aerothermodynamics for TPS (HYAAT) software system whose capability now ranges from RLV/TPS to space-access vehicle for their design/analysis. The HYAAT system was initiated by a continuing AFRL contractual support [1], its progress and development has been reported in [2, 3, 4]. The purpose of this paper is to report our recent advances made of the HYAAT system. The HYAAT system consists of 4 major modules (see Fig. 1). These include: the Aerodynamics/Aerothermodynamics module, the TPS sizing module, the ASTROS module, and the Trajectory module. Here we will confine our reporting only to the progress of the first two modules, since they are the central pieces in the present R&D efforts. The aerodynamics/aerothermodynamics module has been generalized from a lower-hierarchy Panel method approach, ZONAIR [5] to include several higher hierarchy CFD approaches consisting of DSMC, Boltzmann/BGK, Navier-Stokes, Euler and Proper Orthogonal Decomposition (POD) flow solvers. The HYAAT road maps due to the latter are shown in Fig 2. The TPS sizing module using the NASA supported MINIVER has been improved to add-in an automated optimization scheme for TPS weight minimization while satisfying all aerothermal and structural constraints. In what follows we will go into the specifics of these two improved modules. Whenever appropriate, applications to basic configurations and several hypersonic flight vehicles will be presented to demonstrate the validity of the HYAAT methodology. Aerodynamics/Aerothermodynamics Module The earlier module presented in Fig 1 involves ZONAIR as aerodynamics module and it is coupled with the Aerothermodynamic module using a modified SHABP. Here the improved module presented in Fig 2 replaced this module with high-level CFD methods using the POD technique. Current R&D in this is a part of a grand plan to integrate ZONAIR and the high-level CFD methods into a Computational Fluid/Aero-thermodynamics Software Toolbox (CFAST). The integrated toolbox is presented as a Pyramid as shown in Fig 3.

2

CFAST Pyramid This pyramid structure (Fig 3) consists of two fluid dynamics approaches (layers): the Gas-kinetic and the Continuum. The gas-kinetic approach (layer) consists of the microscopic solvers of DSMC (Direct Simulation Monte Carlo), the Boltzmann equation and the so-called BGK approximation [6]. The continuum approach (layer) contains all the macroscopic solvers from RANS (Reynolds averaged Navier-Stokes) to potential flow (e.g., CFL3D [7] to ZONAIR [5]). The left-hand face of the pyramid lists the aerodynamic methods whereas the right-hand face the aerothermodynamic methods. The two arrows along the slopes indicate the user�s preference for computational efficiency or flow physics. For example, for conceptual design of a RLV, one needs to apply ZONAIR at the bottom layer. For accuracy in detailed analysis in heat rate prediction, one needs to examine the solutions due to RANS/LAURA [8] and BGK [9] in the upper layer (Fig 3). Further the CFAST pyramid is supported by four kinds of mesh/grid generations: surface panels, structured grids, unstructured grids and a grid free scheme (according to Hui�s unified Lagrangian-Euler coordinate, ULEC, formulation [10]). Next, we will describe methods in each layer of the CFAST pyramid from top down. Boltzmann/BGK approach Shown in Table 1 are the Continuum (macroscopic) and Gas-kinetic (microscopic) approaches of CFD methods contained in the CFAST pyramid. The conventional Euler/Navier-Stokes based CFD methods in accord with macroscopic description are only valid in the continuum regime. The gas-kinetic DSMC and direct Boltzmann integration approaches follow the microscopic description and are theoretically valid for the whole flow regime, thereby suitable as a unified methodology.

Continuum Transitional Free Molecule

Flow regimes Kn→0 Kn<0.01 0.01<Kn<1 Kn>1 Continuum CFD (macroscopic) Euler Navier-Stokes Burnett

DSMC Gas-kinetic CFD (microscopic) Boltzmann/BGK

Table 1 − Valid ranges of CFD flow models vs Flow regimes

However, the use of DSMC and direct Boltzmann solver in the continuum and near-continuum regimes is computationally very costly. For this reason, we turned to the BGK approximation of Boltzmann equation [6] as a first measure. Substantial progress has been made in implementing the gas-kinetic BGK scheme in the mainstream finite-volume CFD framework and generalizing it to account for nonequilibrium flows [9] (e.g., Fig 4-Fig 11). Continuum CFD Methods

• CFL3D [7]: Euler/thin-layer NS, 2D/3D, steady/unsteady, turbulence models Original code is supported by NASA Langley. With support of NSF, we have created highly accurate MVP (Monotonicity/Vorticity-Preserving) reconstruction module to enhance the resolution of fine flow structures such as the vortices, turbulence eddy, and acoustic waves, etc. As one of the leading groups in CFL3D methodology, ZONA is officially a CFL3D commercialization company per ZONA/NASA software release agreement 2002.

3

• Unified Langrangian/Eulerian Coordinates CFD Method [10]: ULEC is a �gridless� scheme for high-level CFD methods, in that one can start off an initial grid to proceed with the computation. Since time or artificial time is one of the coordinates, which also representing the flow streamlines, the advantages of ULEC amount to: (i) Sharply resolved slip lines and shocks and (ii) Flow generated grid. ULEC method generates a space marching (steady) solver and a time-marching (unsteady) solver. Its Space-Marching solver is (i) specific for steady supersonic/hypersonic flows and (ii) Computationally very efficient (typically 1/1000 of the computing time of the time-marching schemes), see Figs 12-13. Its Time-Marching solver is (i) General for any flow regimes, subsonic/supersonic or mix flow (Fig.14); (ii) Computationally less efficient than the Space-Marching scheme, and (iii) Readily extendable to aeroelastic applications.

POD-Based CFD However, the low computational efficiency of the above high-level CFD methods would prevent sufficient iterations in the design cycles. On the other hand, the lower-level aerodynamic methods such as ZONAIR are inadequate to accurately predict blunted-nose aerodynamics and lee-side aerodynamics under high angles of attack, among other stringent hypersonic problems. This prompts us to apply the Proper Orthogonal Decomposition (POD) technique to the CFD results and construct an efficient yet accurate Reduced Order Model (ROM) via Response Surface Method (RSM), to compliment the lower-level aerodynamic methods such as ZONAIR, for rapid aerothermodynamic analysis. For a complex geometry such as X-34 at a stringent flow condition, say at high angle of attack, the POD/RSM method could provide accurate CFD solution on the lee-side of the X34 which only requires a few seconds on a PC. Figs. 15-16 show POD/RSM solutions versus direct CFD solutions for X-34. Hypersonic Panel Method-ZONAIR ZONAIR is an expedient high-fidelity 3D panel code for rapid design/analysis of very complex wings/bodies. It is an ideal method for rapid conceptual design, for it is a compromise between the computational expediency with solution accuracy among all the methods concerned (see Fig 17). More importantly, it covers the unified subsonic, sonic, supersonic and hypersonic flight regimes. Given flight conditions, it provides aerodynamic pressures/forces/magnitudes generator to efficiently create aerodynamic and loads databases for rigid/elastic bodies, their 6DOF simulation and critical loads identification. ZONAIR is formulated based on the unstructured surface panel scheme that is compatible to the finite element methods. This enables the direct adoption of off-the-shelf finite element pre- and post-processors such as PATRAN, I-DEAS, FEMAP, etc. for ZONAIR panel model generation (see Fig 18). The specific capabilities of ZONAIR are also clearly stated in Fig 18. ZONAIR consists of many submodules for various disciplines that include (1) AIC matrix generation module, (2) 3-D spline module, (3) Trim module, (4) Aeroheating module, (5) Vortex roll-up module, and (6) Aerodynamic stability derivative module. The interrelationship of ZONAIR with other engineering software systems such as the pre-processor, structural finite element method (FEM), Computational Fluid Dynamics (CFD) method, six degree-of-freedom (6 d.o.f.) and critical loads identification is depicted in Fig 18. ZONAIR has been under continuous development by ZONA throughout the last decade. Its current version has proven capability accounting for multi-body interference, ground interference, wave reflection and store-separation, aerodynamics in hypersonic/supersonic as well as subsonic

4

flow domains (Table 1). By comparison, ZONAIR is clearly the best choice as an expedient and versatile aerodynamic methodology. In what follows, we present the results of several hypersonic aerodynamics/aerothermodynamics applications based on ZONAIR and CFL3D [7]. These include:

− CKEM (Compact Kinetic Energy Missile) at M = 6.0, α = 2° (Figs 19(a)&(b)) − 15° Blunt Cone at M = 10.6 and α = 5° (Figs 20(a)&(b)) − X-34 at M = 6.0, α = 9° and altitude = 183 Kft (Figs 21(a)&(b))

TPS Sizing/Optimization The TPS sizing objective is to minimize the TPS weight while satisfying the thermal protection requirement and the load-carrying requirement of the combined RLV/TPS structure. The developed TPS sizing procedure can be demonstrated by a constructed prototypical TPS/AFRSI (Advanced Flexible Reusable Surface Insulation) model [11] (Figs 22 and 23). Here we adopt the complex variable differentiation technique to derive the sensitivity of the NASA aerothermal code MINIVER for TPS sizing/optimization procedure (Fig 24). Minimum thicknesses for all six layers of the selected TPS are posed as a part of the constraints. The initial temperature is 100°F and the maximum temperature constraint at the 6th layer (bottom) is 300°F (Fig 24) (Note that each layer has its own maximum temperature constraint posed as well). The complex variable differentiation sensitivity is shown to be superior to that obtained by conventional finite difference method for temperature changes of layer 6 due to a thickness change in layer 3 (Fig 25). With the computed MINIVER sensitivity, TPS optimization can then be carried out by ASTROS, an automated structural optimization tool; the procedure is shown in Fig 26. The final outputs in terms of final (optimized) thickness, temperature and weight for each layer are listed in Fig 27. In summary, an optimization procedure for TPS weight sizing has been developed using ASTROS optimizer operated on MINIVER by means of an innovative Complex Variable Differentiation-derived sensitivity. The result is a TPS/OPT module. For demonstration, TPS/OPT is applied to a prototypical TPS subsystem with a given heat-flux input at point A of X-43. The optimized total TPS weight is found to be reduced by 30% terminated after the 3rd design cycle, while satisfying all TPS temperature constraints. References [1] Liu, D.D., Chen, P.C., Tang, L., Chang, K.T., Chemaly, A., and Kamhawi, H., �Integrated

Hypersonic Aerothermoelastic Methodology for Transatmospheric Vehicle (TAV)/Thermal Protection System (TPS) Structural Design and Optimization,� AFRL-VA-WP-TR-2002-3047, 2002.

[2] Liu, D.D., Chen, P.C., Tang, L., Chang, K.T., �Expedient Hypersonic Aerothermodynamics Methodology for RLV/TPS Design,� AIAA paper 2002-5129, 11th AIAA/AAAF International Conference: Space Planes and Hypersonic Systems and Technologies, Sep, 2002, Orleans, France.

[3] Chen, P.C., Liu, D.D., Tang, L., Chang, K.T., �Hypersonic Aerothermodynamics/Aerothermoelastics Methodology for RLV/TPS Design and Analysis,� AIAA paper 2003-0897, 41th AIAA Aerospace Sciences Meeting, Jan, 2003, Reno, Nevada.

[4] Chen, P.C., Liu, D.D., Tang, L., Chang, K.T., Gao, X.W., �Hypersonic Aerothermodynamics using ZONAIR for RLV/TPS Design and Analysis,� Thermal and Fluids Analysis Workshop (TFAWS) 2003, Aug, 2003, ODU center, Hampton, Virginia.

5

[5] Chen, P.C. and Liu, D.D. �Unified Hypersonic/Supersonic Panel Method for Aeroelastic Applications to Arbitrary Bodies,� Journal of Aircraft, Vol. 39, No. 3, May-June 2002.

[6] Bhatnagar, P.L., Gross, E.P., and Krook, M., �A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems,� Physical Review, Vol. 94 (1954), pp.511.

[7] Krist, S.L., Biedron, R.T. and Rumsey, C.L., �CFL3D User�s Manual Version 5.0,� NASA Langley Research Center, Hampton, VA, 1997.

[8] Cheatwood, F.M., Gnoffo, P.A., �User�s Manual for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA),� NASA-TM-4674, April 1996.

[9] Tang, L., and Xu, K., �Unified Gas-Kinetic Computational Algorithm for Continuum and Rarefied Flows,� AIAA-2004-1179, 2004.

[10]Hui, W.H., and Tang, L., �A Unified Coordinates Approach to Computational Fluid Dynamics,� AIAA-2003-4239, 2003.

[11] Myers, D.E., Martin, C.J., and Blosser, M.L., �Parametric Weight Comparison of Advanced Metallic, Ceramic Tile, and Ceramic Blanket Thermal Protection Systems,� NASA-TM-2000-210289.

6

Parametric Geometry

Trajectory Analysis

FEM Model Mesh Generator

ASTROS* Structural Optimization

• Trim Analysis for Flight Loads• Ply thickness as design variables• Closed-Loop System Using ASE

Module• Strength, Flutter and Divergent

Constraints

TPS Sizing

• Optimization/Sensitivity• Heat Transfer Analysis• TPS Design Concept• Stress Analysis

• Aerodynamic Force & Moment Database

ZONAIR Unified Hypersonic Aerodynamics

• Mach Number List• Angle of Attack List• Control Surface Deflection List

• Aerodynamic Pressure Distribution Database

• Mach Number, Altitude and Angle of Attack Time History

• AIC

• Trim Solutions of Trajectory

• Shear Loads

• Shock Loads

• TPS Mass & Stiffness

• Material Property Degradations

• Temperature on Load-Carry Structures

• Total Mass

Back to Trajectory• Propulsion

• Mass

• Temperature Ch and q Time History on OML

• Temperature Distribution Database

6 78

31

Aerothermodynamic Analysis

• Compressible Boundary Layer• Aero-Heating• Provide q, Cf , Ch

(S/HABP)(S/HABP)

2

4

(MINIVER, SINDA, ASTROS*)(MINIVER, SINDA, ASTROS*)

• Minimum Fuel• Re-entry• Exo-atmosphere• Orbital Transfer

5

(POST)(POST)

• Mission Requirement

Cf

Aerothermoelastic Optimization

WeightModel

Aerodynamic ModelMesh Generator

Parametric Geometry

Trajectory Analysis

FEM Model Mesh Generator

ASTROS* Structural Optimization

• Trim Analysis for Flight Loads• Ply thickness as design variables• Closed-Loop System Using ASE

Module• Strength, Flutter and Divergent

Constraints

TPS Sizing

• Optimization/Sensitivity• Heat Transfer Analysis• TPS Design Concept• Stress Analysis

• Aerodynamic Force & Moment Database

ZONAIR Unified Hypersonic Aerodynamics

• Mach Number List• Angle of Attack List• Control Surface Deflection List

• Aerodynamic Pressure Distribution Database

• Mach Number, Altitude and Angle of Attack Time History

• AIC

• Trim Solutions of Trajectory

• Shear Loads

• Shock Loads

• TPS Mass & Stiffness

• Material Property Degradations

• Temperature on Load-Carry Structures

• Total Mass

Back to Trajectory• Propulsion• Propulsion

• Mass• Mass

• Temperature Ch and q Time History on OML

• Temperature Distribution Database

6 78

31

Aerothermodynamic Analysis

• Compressible Boundary Layer• Aero-Heating• Provide q, Cf , Ch

(S/HABP)(S/HABP)

2

4

(MINIVER, SINDA, ASTROS*)(MINIVER, SINDA, ASTROS*)

• Minimum Fuel• Re-entry• Exo-atmosphere• Orbital Transfer

5

(POST)(POST)

• Mission Requirement

• Mission Requirement

Cf

Aerothermoelastic Optimization

WeightModel

Aerodynamic ModelMesh Generator

ZONAIR in HYAAT

Work

ZONA: Blocks 1-5TSI: Blocks 6-7

Challenges

• MDO tool• Data transferal

(Temperature to Structure)• Aero/AeroTE Hyp/Sup• TPS load-carrying as well

HYpersonic Aerodynamic Aerothermoelastics for TPS program

Fig. 1 HYAAT software system

•Parametric Geometry

Trajectory Analysis

FEM Model Mesh

Generator

ASTROS* Structural Optimization

• Trim Analysis for Flight Loads• Flutter, Divergent and Gust

Load Analysis• Closed-Loop System Using

ASE Module• Strength, Flutter and Divergent

Constraints

TPS Sizing

• Heat Transfer Analysis• TPS Design Concept• Stress Analysis

•Aerodynamic Force & Moment Database

CFD/POD Hypersonic Aerodynamic and Aerothermal

Analysis

• Mach Number List• Angle of Attack List• Control Surface Deflection List• Aero-Heating• Provide CL, CD, q, Cf , Ch

•Mach Number, Altitude and Angle of Attack Time History

•AIC

•Trim Solutions of Trajectory

•Shear Loads

•Shock Loads

•TPS Mass & Stiffness

•Material Property Degradations

•Temperature on Load-Carry Structures

•Total Mass

Back to Trajectory

• Propulsion

• Mass

•Temperature Ch and q Time History on OML

•Temperature Distribution Database

7Weight Model

8

31

4

(MINIVER, SINDA, ASTROS*)(MINIVER, SINDA, ASTROS*)

•Minimum Fuel•Re-entry•Exo-atmosphere

•Orbital Transfer

5

(POST)(POST)

• Mission Requirement

Aerothermoelastic Optimization

•Parametric Geometry

Trajectory Analysis

FEM Model Mesh

Generator

FEM Model Mesh

Generator

ASTROS* Structural Optimization

• Trim Analysis for Flight Loads• Flutter, Divergent and Gust

Load Analysis• Closed-Loop System Using

ASE Module• Strength, Flutter and Divergent

Constraints

TPS Sizing

• Heat Transfer Analysis• TPS Design Concept• Stress Analysis

•Aerodynamic Force & Moment Database

CFD/POD Hypersonic Aerodynamic and Aerothermal

Analysis

• Mach Number List• Angle of Attack List• Control Surface Deflection List• Aero-Heating• Provide CL, CD, q, Cf , Ch

•Mach Number, Altitude and Angle of Attack Time History

•AIC

•Trim Solutions of Trajectory

•Shear Loads

•Shock Loads

•TPS Mass & Stiffness

•Material Property Degradations

•Temperature on Load-Carry Structures

•Total Mass

Back to Trajectory

• Propulsion• Propulsion

• Mass• Mass

•Temperature Ch and q Time History on OML

•Temperature Distribution Database

7Weight Model

8Weight ModelWeight Model

8

31

4

(MINIVER, SINDA, ASTROS*)(MINIVER, SINDA, ASTROS*)

•Minimum Fuel•Re-entry•Exo-atmosphere

•Orbital Transfer

5

(POST)(POST)

• Mission Requirement

• Mission Requirement

Aerothermoelastic Optimization

ZONA CFD/POD Module in HYAAT

Fig. 2 ZONA CFD/POD module in HYAAT system

7

AML

High-Order Panels Structured

Grid

Euler + LATCHBGK-Euler

Navier-

Stokes/

Laura

Grigen/Tecplot/Fluidview

Unstructured

Grid

ULEC

Gridless

BGK -Navier-Stokes

BGK BGK

Mor

e Fl

ow P

hysic

s

Long

er C

ompu

ting

Tim

e

More Complex Geometry

Faster Computing Time

ZONAIR +SHABPZONAIR/Potential

. .

. .

. .

DSMC/BoltzmannInterface

AML

High-Order Panels Structured

Grid

Euler + LATCHBGK-Euler

Navier-

Stokes/

Laura

Grigen/Tecplot/Fluidview

Unstructured

Grid

ULEC

Gridless

BGK -Navier-Stokes

BGK BGK

Mor

e Fl

ow P

hysic

s

Long

er C

ompu

ting

Tim

e

More Complex Geometry

Faster Computing Time

ZONAIR +SHABPZONAIR/Potential

. .

. .

. .

DSMC/BoltzmannInterface

ZONA Fluid/Aerothermo-dynamics Software Toolbox (FAST)

Fig.3 CFAST software system

Mesh and density Temperature

Case 1. Hypersonic flow passing a cylinder(NASA TM-100484)- Demonstrate superior accuracy of BGK scheme- M∞=8.03, Re=1.835x105, T∞=124.94°k, TW=294.44°k- 63x35 points- Rec=50 based on the first mesh size away from wall

ZONA BGK Computational Tool (4)

Fig.4

8

Surface pressure and heat transfer distribution- Both BGK-NS and CFL3D predict reasonable surface

pressure distribution � inviscid phenomenon- BGK-NS predicts reasonable heat transfer on surface

whereas CFL3D overpredicts more than 3 times- Poor grid resolution in boundary layer is forgiving for

BGK-NS but not CFL3D

0

0.2

0.4

0.6

0.8

1

-90 -60 -30 0 30 60 90θ

Pres

sure

presentCFL3Dexperiment

0

0.003

0.006

0.009

0.012

-90 -60 -30 0 30 60 90θ

heat

-tran

sfer

presentCFL3Dexperiment

ZONA BGK Computational Tool (5)

Fig.5

Case 2. Type IV shock interaction (NASA TM-100484)- Demonstrate superior accuracy of BGK scheme- M∞=8.03, Re=1.94x105, T∞=122.11°k, TW=294.44°k- Incident shock position: y=0.3271x+0.4147 - 181x101 points- CFL3D fails to produce a converged solution

ZONA BGK Computational Tool (6)

Fig.6

9

Case 3. Double cone case (Run 28 in AIAA-2003-3641)- Demonstrate superior accuracy of BGK scheme- M∞=9.59, Re=13090, T∞=185.56°k, TW=293.33°k- 500x200 points- CFL3D fails to produce a converged solution

ZONA BGK Computational Tool (7)

Fig.7

Case 4. Alsmeyer nitrogen shock structure (JFM 1976)- Demonstrate the feasibility of using BGK scheme for thermal

non-equilibrium flowsimulation

- See strong non-equilibriumeffect

- See little rarefaction effect- Equilibrium BGK-NS:

Non-equilibrium BGK-NS:

Non-equilibrium BGK-Xu:- ZR=4

]wv)Uu[(e)(g22

21

22225

ξξλπλρ ++++−−=

T),,,(Sd)fg( 0000=∫ =− Ξψ

)(]wv)Uu[(RT RTe)()(g22

21

22223

ξξλλ

πλ

πλρ +−++−−= T

cR

R*R )Z

,,,(Sd)fg(τεερΞψ −=∫ =− 000

*ττ →

ZONA BGK Computational Tool (8)

Fig.8

10

- M∞=11 case (ZR=5)

ZONA BGK Computational Tool (9)

Fig.9

0

2

4

6

8

10

-0.05 0 0.05 0.1 0.15 0.2 0.25x (cm)

ρ/ρ1

experimentnonequilibrium BGK-NS

ZONA BGK Computational Tool (10)Case 5. Kewley & Hornung nitrogen shock dissociation

(Chemical Physics Letters, 1974)- Demonstrate the feasibility of using BGK scheme for chemical

non-equilibrium flowsimulation

- ρ1=0.0467 kg/m3,u1=4800 m/s,p1=4133 N/m2

- Non-equilibriumBGK-NS:

22222222 22

5ηλξλ

πλ

πλ

ρ V)N()N(

TV

])Uu[(K

V)N(

T)N()N( e)()(g −+−−=

])Uu[()N(

T)N()N( )N()N(Te)(g

2223

ζλπ

λρ +−−=

ττ

/)fg(uff

/)fg(uff)N()N()N(

x)N(

t

)N()N()N(x

)N(t

−=+

−=+ 2222

T)N(V

)N()N(

)N(V

*)N(V)N()N()N()N()N()s()s()s()s(

s)W,hW,,W,W(Sd)fg( 22

2

2222

05

10 ε

τ

εερψ &&&& +

><

−−==Ξ−∑ ∫

=

Fig.10

11

Case 6. Cylinder case (AIAA-01-2962)- Demonstrate the validity Kn range of BGK scheme- With slip b.c. only, BGK-NS already matches the test

data up to Kn=0.8

Simple modeling of wing leading edge and nose of space vehicles

ZONA BGK Computational Tool (11)

Fig. 11

Flow past a thin concave body of y=(tan3°°°°)x+0.0476x2 (M∞∞∞∞=15)

Grid Cp contours

X

Y

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X

Y

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.080.0750.0710.0670.0630.0580.0540.0500.0460.0420.0370.0330.0290.0250.0210.0160.0120.0080.0040

t=0

Grid Cp contours

X

Y

0 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

X

Y

0 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.90.080.070.060.050.040.030.020.020.010.00

t=1.32

X

Y

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

X

Y

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.90.080.070.060.050.040.030.020.020.010.00

t=0.44

X

Y

0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

X

Y

0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.90.080.070.060.050.040.030.020.020.010.00

t=1.71

X

Y

0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

X

Y

0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.90.080.070.060.050.040.030.020.020.010.00

t=0.9

X

Y

0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X

Y

0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.080.070.060.050.040.030.020.020.010.00

t=2

Fig.12

12

Channel flows (M∞∞∞∞=1.8)

Grid Mach contours

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5 t=0

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5Mach

21.894741.789471.684211.578951.473681.368421.263161.157891.052630.9473680.8421050.7368420.6315790.5263160.4210530.3157890.2105260.1052630

t=0

t=0

Grid Mach contours

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5 t=2

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5Mach

21.894741.789471.684211.578951.473681.368421.263161.157891.052630.9473680.8421050.7368420.6315790.5263160.4210530.3157890.2105260.1052630

t=2

t=2

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5 t=0.4

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5Mach

21.894741.789471.684211.578951.473681.368421.263161.157891.052630.9473680.8421050.7368420.6315790.5263160.4210530.3157890.2105260.1052630

t=0.4

t=0.4

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5 t=6

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5Mach

t=6

t=6

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5 t=1

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5Mach

t=1

t=1

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5 t=12

X

Y

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5Mach

t=12

t=12

Fig.13

Cp contours of a thick concave body of y=(tan35°°°°)x+0.3x2 (M∞∞∞∞=15)

X

Y

0 0 .2 5 0.5 0 .7 5 10

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 .7

0 .8

0 .9

1

2 .07051 .9221 .77351 .6251 .47651 .3281 .17951 .0310 .88250 .7340 .58550 .4370 .28850 .14

Fig. 14

13

X Y

Z0.20.150.10.050

-0.05-0.1-0.15-0.2

X Y

Z0.050.00625

-0.0375-0.08125-0.125-0.16875-0.2125-0.25625-0.3

X Y

Z-0.04-0.07875-0.1175-0.15625-0.195-0.23375-0.2725-0.31125-0.35

X Y

Z

0.20.150.10.050

-0.05-0.1-0.15-0.2

X Y

Z

0.050.00625

-0.0375-0.08125-0.125-0.16875-0.2125-0.25625-0.3

X Y

Z

-0.04-0.07875-0.1175-0.15625-0.195-0.23375-0.2725-0.31125-0.35

CFD

PODAoA 2 AoA 15 AoA 30

� CFD solutions vs. POD reconstruction with 3 modes (M∞=2)

Proper Orthogonal Decomposition (1)

Fig. 15

X Y

Z0.140.121250.10250.083750.0650.046250.02750.00875

-0.01

X Y

Z0.030.02450.0190.01350.0080.0025

-0.003-0.0085-0.014

X Y

Z0.0190.0148750.010750.0066250.0025

-0.001625-0.00575-0.009875-0.014

X Y

Z

0.140.121250.10250.083750.0650.046250.02750.00875

-0.01

X Y

Z

0.030.02450.0190.01350.0080.0025

-0.003-0.0085-0.014

X Y

Z

0.0190.0148750.010750.0066250.0025

-0.001625-0.00575-0.009875-0.014

CFD

PODAoA 2 AoA 15 AoA 30

� CFD solutions vs. POD reconstruction with 3 modes (M∞=10)

Proper Orthogonal Decomposition (2)

Fig.16

14

ZONAIR Capability vsOther Aerodynamic Codes

ZONAIR is a versatile tool for rapid aerodynamic database generation� Aerodynamic AIC matrix readily coupled with FEM� Force/moment coefficients� Multi-body interference aerodynamics� Accurate aerodynamics for aeroheating prediction

YesYesYesNoAllYes 30 hrs/ X-34Euler/N-SCFD3D

NoYesNoNoAllNo<< 10 minAnalytical/EmpiricalAP98

NoYesNoNoAllNo<< 10 minAnalytical/EmpiricalDATCOM

NoNoNoNoNo subsonicsNo<<10 minAnalytical/EmpiricalMINIVER

YesNoLow-Order PanelNoEmpirical for

hypersonicsNewtonian

S.L.<10 minPotential + EmpiricalAPAS

YesNoConstant Order PanelYesAllYes10 min/

X-34Potential +

PEFZAERO

YesYesLinear-Order PanelYesAllYes20 min/

X-34Potential +

PEFZONAIR

YesNoYesNoSupersonic/ SubsonicNo 20 min/

X-34PotentialPANAIR

2 Body Aero Interference

High AOA

Geometry High

Fidelity

AIC for Structural

FEM

Hypersonic/Supersonic/

Subsonic Mach No.

Streamline Solution for Aeroheating

Computational EfficiencyMethodCode

YesYesYesNoAllYes 30 hrs/ X-34Euler/N-SCFD3D

NoYesNoNoAllNo<< 10 minAnalytical/EmpiricalAP98

NoYesNoNoAllNo<< 10 minAnalytical/EmpiricalDATCOM

NoNoNoNoNo subsonicsNo<<10 minAnalytical/EmpiricalMINIVER

YesNoLow-Order PanelNoEmpirical for

hypersonicsNewtonian

S.L.<10 minPotential + EmpiricalAPAS

YesNoConstant Order PanelYesAllYes10 min/

X-34Potential +

PEFZAERO

YesYesLinear-Order PanelYesAllYes20 min/

X-34Potential +

PEFZONAIR

YesNoYesNoSupersonic/ SubsonicNo 20 min/

X-34PotentialPANAIR

2 Body Aero Interference

High AOA

Geometry High

Fidelity

AIC for Structural

FEM

Hypersonic/Supersonic/

Subsonic Mach No.

Streamline Solution for Aeroheating

Computational EfficiencyMethodCode

Fig.17

ZONAIR and Interfacing Capability w/ other Softwares

� Unified high-order subsonic/supersonic/hypersonic panel methodology � Aerodynamic influence coefficient (AIC) matrix for rapid data retrieval� Unstructured surface panel scheme compatible to the finite element method� Rapid panel model generation using COTS/FEM pre- and post-processors � Accurate streamline solution with axisymmetric analogy for aerothermodynamics� Trim module for flexible loads and aeroheating module for TPS design/analysis� Multibody interference/separation aerodynamics� Pressure interpolation scheme for transonic flexible loads generation� Aerodynamic database for 6 DOF simulation and critical loads identification

CAD

Off-the-shelf pre-processor

�PATRAN

�I-DEAS

�FEMAP

��

ZONAIR Panel Model

3-D Spline

AIC generation

Aeroheating

Trim analysis

Aerodynamic force/ moment

generation

Pressure interpolation

FEM solution

CFD/Wind-tunnel pressures

ZONAIR

and loads database

6 d.o.f. simulation

Critical loads identification

CAD

Off-the-shelf pre-processor

�PATRAN

�I-DEAS

�FEMAP

��

Off-the-shelf pre-processor

�PATRAN

�I-DEAS

�FEMAP

��

AML

Automated mesh generation

Aerodynamics

CAD

Off-the-shelf pre-processor

�PATRAN

�I-DEAS

�FEMAP

��

Off-the-shelf pre-processor

�PATRAN

�I-DEAS

�FEMAP

��

ZONAIR Panel ModelZONAIR Panel Model

3-D Spline

AIC generation

Aeroheating

Trim analysis

Aerodynamic force/ moment

generation

Pressure interpolation

FEM solution

CFD/Wind-tunnel pressures

ZONAIR

and loads database

6 d.o.f. simulation

Critical loads identification

3-D Spline

AIC generation

Aeroheating

Trim analysis

Aerodynamic force/ moment

generation

Pressure interpolation

FEM solution

CFD/Wind-tunnel pressures

ZONAIR

and loads database

6 d.o.f. simulation

Critical loads identification

CAD

Off-the-shelf pre-processor

�PATRAN

�I-DEAS

�FEMAP

��

Off-the-shelf pre-processor

�PATRAN

�I-DEAS

�FEMAP

��

AML

Automated mesh generation

Aerodynamics

Fig. 18

15

Pointed-Nose CKEM Body: AerodynamicsM∞∞∞∞ = 6.0, αααα = 2°°°°

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 5 10 15 20 25 30 35 40

x (in.)

Cp

CFL3DZONA7U

Wind-Side Inviscid Surface Pressure Distribution (φφφφ= 180)

Streamlines Computed by ZONA7U/ZSTREAM, M = 6.0

ZONA7U CFL3D/Euler

Inviscid Surface Pressure Distribution

0.150.140.130.120.110.10.090.080.070.060.050.040.030.020.010

0.150.140.130.120.110.10.090.080.070.060.050.040.030.020.010

Fig.19(a)

0

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0 10 20 30 40

x (in.)

qdot

(Btu

/ft2 -s

)

CFL3D+LATCHZONA7U+SHABP

Pointed-Nose CKEM Body: AerodynamicsM∞∞∞∞ = 6.0, αααα = 2°°°°, P∞∞∞∞ = 2.66 psf, T∞∞∞∞ = 89.9°°°°R, TW = 540°°°°R

ZONA7U CFL3D/Euler

Laminar Heat Transfer Rate (Btu/ft2s)

0.450.430.410.390.370.350.330.310.290.270.250.230.210.190.170.150.130.110.090.070.05

0.450.430.410.390.370.350.330.310.290.270.250.230.210.190.170.150.130.110.090.070.05

Wind-Side Laminar Heat Transfer Rates (φφφφ= 180°°°°)

“Cut-out” due to singularity at stagnation point

Fig. 19(b)

16

15º Blunt Cone: AerodynamicsM = 10.6, αααα = 5º

Inviscid Surface Pressure Distribution

1.81.641.481.321.1610.840.680.520.360.20.04

1.81.641.481.321.1610.840.680.520.360.20.04

ZONAIR CFL3D/Euler

Wind Side

Lee Side

0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 16 18x (in.)

Cp

TestCFL3DZONA7U

� Test- CFL3D+ ZONAIR

0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 16 18x (in.)

Cp

TestCFL3DZONA7U

� Test- CFL3D+ ZONAIR

0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 16 18x (in.)

Cp

TestCFL3DZONA7U

� Test- CFL3D+ ZONAIR

0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 16 18x (in.)

Cp

TestCFL3DZONA7U

� Test- CFL3D+ ZONAIR

Inviscid Surface Pressure Distribution Fig.20(a)

Laminar Heat Rate: 15º Blunt ConeM∞∞∞∞ = 10.6, αααα = 5°°°°, P∞∞∞∞ = 2.66 lb/ft2, T∞∞∞∞ = 89.971°°°°R, TW = 540°°°°R

1211109876543210

1211109876543210

ZONAIR + SHABP CFL3D/Euler + LATCH

Wind Side

“Cut-out” due to singularity at stagnation point

0

2

4

6

8

10

0 2 4 6 8 10 12 14 16 18( )

qdot

(Btu

/ft2 -s

)

TestCFL3D+LATCHZONA7U+SHABP

� Test- CFL3D + LATCH+ ZONAIR + SHABP

0

2

4

6

8

10

0 2 4 6 8 10 12 14 16 18( )

qdot

(Btu

/ft2 -s

)

TestCFL3D+LATCHZONA7U+SHABP

� Test- CFL3D + LATCH+ ZONAIR + SHABP

Fig. 20(b)

17

X-34 Wing-Body: AerodynamicsM∞∞∞∞ = 6.0, αααα = 15.22°°°°

-0.04 0.12 0.28 0.44 0.6 0.76 0.92 1.08 1.24 1.4 1.56 -0.04 0.12 0.28 0.44 0.6 0.76 0.92 1.08 1.24 1.4 1.56

-0.04 0.12 0.28 0.44 0.6 0.76 0.92 1.08 1.24 1.4 1.56 -0.04 0.12 0.28 0.44 0.6 0.76 0.92 1.08 1.24 1.4 1.56

-0.04 0.12 0.28 0.44 0.6 0.76 0.92 1.08 1.24 1.4 1.56 -0.04 0.12 0.28 0.44 0.6 0.76 0.92 1.08 1.24 1.4 1.56

ZONAIR

ZONAIR

ZONAIR

CFL3D

CFL3D

CFL3D

Front View

Wind-Side

Lee-Side

Fig.21(a)

Aeroheating of X-34M∞∞∞∞ = 6.0, αααα = 15.22º, h = 112 Kft., Hot Wall, Emissivity = 0.8, Turbulent

300 500 700 900 1100 1300 1500 1700300 500 700 900 1100 1300 1500 1700

18001700160015001400130012001100

18001700160015001400130012001100

15001200900600300

15001200900600300

ZONAIR+SHABP

ZONAIR+SHABP

ZONAIR+SHABP

CFL3D+LATCH

CFL3D+LATCH

CFL3D+LATCH

Front View

Wind-Side

Lee-Side

“Cut-out” due to singularity at stagnation point

Streamlines

Fig.21(b)

18

0

200

400

600

800

0 200 400 600 800 1000time (s)

Tem

pera

ture

(F)

M ax TouterM ax TinteriorM ax Tskin

Elementary TPS Sizing of AFRSI

0

1

2

0 200 400 600 800time (s)

heat

rate

(Btu

/ft^2

-s)

� TPS element selected on windward centerline of X-34 (point A @ L = 50��)� Heat Rate Input provided by ZONAIR+SHABP from trajectory/aeroheating� Minimum TPS weight obtained by MINVER/EXITS

AFRSI Definition

� Touter and Tinterior are the temperatures at the outer edge and (1) to (5) interior layers of the TPS. Tskin is the temperature at the nodes within the skin layer 6.

Point A

L

Point A

L

Heat Flux History

Input

TPS Sizing

Output

Layer 3material

Thickness Normalizedweight, TPS

Normalizedweight, layer 3

MaxTouter

MaxTinterior

MaxTskin

Q-Felt insulation 0.456 in 1.000 1.000 708.7° F 696.4° F 300.3° FQ-Felt 3.5PCF 0.638 in 0.694 0.408 713.6° F 702.0° F 300.2° F

6LB Dynaflex 0.560 in 1.118 1.228 696.9° F 681.6° F 300.2° F

Layer 3material

Thickness Normalizedweight, TPS

Normalizedweight, layer 3

MaxTouter

MaxTinterior

MaxTskin

Q-Felt insulation 0.456 in 1.000 1.000 708.7° F 696.4° F 300.3° FQ-Felt 3.5PCF 0.638 in 0.694 0.408 713.6° F 702.0° F 300.2° F

6LB Dynaflex 0.560 in 1.118 1.228 696.9° F 681.6° F 300.2° F

Layer 1 - Coating (0.01 in. HRSI Coating)

Layer 2 - Outer Fabric (0.015 in. Outer Fabric AB312)

Layer (3) Insulation a. Q-Felt Insulation (standard) b. Q-Felt 3.5PCF x (inches) c. 6LB Dynaflex(Insulation layer size is to be determined)

Layer 4 - Inner Fabric (0.009 in. Inner Fabric AB312)Layer 5 � Adhesive (0.008 in. RTV Adhesive)

Layer 6 - Structure (0.011 in. Aluminum)

Thickness and Weight Solution of Layer (3)/AFRSI

Max Touter

Max Tinterior

Max Tskin

Max Touter

Max Tinterior

Max Tskin

Fig.22

Development of an Optimization Procedure for TPS Sizing (I)

� A six layer TPS system is selected as the test case

� Heat flux time history is obtained from windward side of X-34centerline.

Layer 1 - HRSI Coating (h1 = 0.01 in.) Layer 2 - Outer Fabric AB312 (h2 = 0.015 in.) Layer 3 - Q-Felt 3.5PCF Insulation (h3 = 1.2in) Layer 4 - Inner Fabric AB312 (h4 = 0.009 in.) Layer 5 � RTV Adhesive (h5 = 0.008 in.)

Layer 6 - Aluminum Structure (h6 = 0.011 in.)

)(.

tq

0

1

2

0 200 400 600 800time (s)

heat

rate

(Btu

/ft^2

-s)

Description of the selected test case

Fig. 23

19

� For a given heat flux applied on the outer boundary, the objective is to minimize the total weight of the TPS system while keeping the temperature at each layer (Ti) below their respective maximum operational temperature, Toi.

� Minimize:

TPS Sizing Optimization Using Complex-Variable Differentiation Sensitivity

� TPS sizing will be automated by developing an optimization driver of the MINIVER/EXITS code.

Typical TPS Sizing Problem

∑=

=n

iihiW

1ρ where ρi is the

density of the ith layer.Subjected to: Ti < Toi i = 1,2…nDesign variables: hi > 0 i = 1,2…n

� The complex-variable differentiation can provide �numerically exact� derivatives of a complicated function. -The variable h of a real function T(h) is replaced by h + i∆h.

-For small ∆h: ( ) ( ) K+∂∂+=+

hThihThihT ∆∆ Yields:

( )( )

+

+=

∂∂ 20 h

hhihTIm

hT ∆

∆∆

� To incorporate the complex variable technique into the MINIVER/EXITS module for sensitivity analysis is straightforward simply by declaring all variables in the MINIVER/EXITS module as complex variables.

-The imaginary part of the thickness input of MINIVER/EXITS represents a small incremental thickness.-The sensitivity is the imaginary part of the temperature output divided by the incremental thickness.

x

Layer 1

Layer 2

Layer n h n

h 2

h 1

T o

x

Layer 1

Layer 2

Layer n h n

h 2

h 1

T o

q&q&

Fig.24

Development of an Optimization Procedure for TPS Sizing (II)

Validation of complex variable differentiation for sensitivity� Temperature change at Layer 6 due to the change of thickness of layer 3 ( T6/ h3) is

computed using both the Complex Variable Differentiation (CV) and the Finite Difference(FD) techniques.

� In order to demonstrate the robustness of the CV, ∆h3=10-30 (near machine zero) is assignedfor the CV technique whereas ∆h3 for the FD technique varies from 10-2 to 10-6.

� Results show that the accuracy of the FD technique depends on ∆h3 but the CV techniquedoes not.

relative error of sensitivity at layer 6 (FD - CV)/CV

0.0001

0.001

0.01

0.1

1

10

100

0 200 400 600 800 1000 (sec)

Erro

r %

∆h = e-2

∆h = e-3

∆h = e-4

∆h = e-6

complex variable differentiation, ∆∆∆∆h3 = e-30

-80

-60

-40

-20

0

0 200 400 600 800 1000

time (sec)

3

6hT

∂∂

∂ ∂

Fig.25

20

TPS Optimization using MINIVER/OPT

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4

wei

ght (

lbm

/ft^2

)

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8

wei

ght (

lbm

/ft^2

)

Temperature History at Structure Layer

0

100

200

300

400

500

0 200 400 600 800 1000Time (sec)

Tstr (F)

initial (W = 0.777lbm/ft^2)

5th cycle (W = 0.590lbm/ft^2)

final (W = 0.668lbm/ft^2)

Temperature History at the Structure Layer During Optimization (Case B)

Weight Variation During Optimization

(b) Case B with 1.5x (in 396 Sec)q&

(a) Case A with a given (in 263 Sec) q&Optimization Cycle

Optimization Cycle

Fig.26

Development of an Optimization Procedure for the TPS Sizing (III) Optimization Results with upper bound = 1.0�

� All design variables reduce to the minimum thickness (0.0072�) except layer 3(h3 = 0.68496�).

� The total weight is reduced from the initial weight =0.777 lbs/ ft2 to the finalweight = 0.54256 lbs/ft2

Note: For structure layer (6), thickness is not a design variable.upper bound thickness = 1.0 in, lower bound = 0.0072 in with original heat flux of X1004601 trajectory

0.011300.00.0110.22173300Aluminum6

0.0072300.00.0080.28588550RTV-5605

0.0075300.00.0090.16661.52024AB312 Fabric4

0.68496701.61.20.18753.51800Q-Felt3

0.0072704.90.0150.16661.52040AB312 Fabric2

0.0072705.20.010.201042300HRSI Coating1

Optimized Design (in)

Max Temp in the Layer (°F)

Initial Thickness (in)

Specific Heat (But/lbm °F)

Density (lbm/ft^3)

Temp Limit (°F)MaterialLayer

0.011300.00.0110.22173300Aluminum6

0.0072300.00.0080.28588550RTV-5605

0.0075300.00.0090.16661.52024AB312 Fabric4

0.68496701.61.20.18753.51800Q-Felt3

0.0072704.90.0150.16661.52040AB312 Fabric2

0.0072705.20.010.201042300HRSI Coating1

Optimized Design (in)

Max Temp in the Layer (°F)

Initial Thickness (in)

Specific Heat (But/lbm °F)

Density (lbm/ft^3)

Temp Limit (°F)MaterialLayer

Fig.27