P.C. ChenD.D. LiuLei Tang

7430 E. Stetson Drive, Suite 205, Scottsdale, AZ 85251-3540, Tel (480) 945-9988, Fax (480) 945-6588, E-mail: pc@zonatech.com

ZONAIR for RLV/TPS Design and AnalysisFrom SHABP to ZONAIR

Presented at the 14th Annual Thermal & Fluids Analysis Workshop, August 18-22 2003, Hampton, VA

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

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

ZONAIR vs S/HABP

√√Blunt Nose

√√AML Mesh

-Multi-Body/Ground Effect AerodynamicsInterference

Supersonic/HypersonicUnified Subsonic/Supersonic/

HypersonicMach Range

Zoby’s convective heating equations

Zoby’s convective heating equations

Viscous & Thermal

- Quanstream- Mach no Dependent

- ZSTREAM- Finite Element Based - Mach no Dependent

Streamline

Analytical/ Empirical Potential + Perturbed EhlerInviscid

S/HABP ∈ SHVDZONAIR ∈ HYAATMethod

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

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

θ

n

surface element

1

′x3

n

η

ξ′x 2 ′x

(x0,y0)

(x,y)

u0

v0

ZSTREAM for Stream Line Solution

• Aeroheating analysis requires inviscid flow streamlines• QUADSTREAM in SHABP is not robust for

quadrilateral panels and is Mach number independent• ZSTREAM is finite-element-based derived from

ZONAIR surface velocities

FEM-based

Marching from position (xo, yo) to (x, y)

15º Blunt Cone: AerodynamicsM = 10.6, α = 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

Inviscid Surface Pressure Distribution

Laminar Heat Rate: 15º Blunt ConeM∞ = 10.6, α = 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(i )

qdot

(Btu

/ft2 -s

)

TestCFL3D+LATCHZONA7U+SHABP

� Test- CFL3D + LATCH+ ZONAIR + SHABP

X-34 Wing-Body: AerodynamicsM∞ = 6.0, α = 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

Aeroheating of X-34M∞ = 6.0, α = 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

0

200

400

600

800

0 200 400 600 800 1000time (s)

Tem

pera

ture

(F)

Max To uterMax Tinterio rMax 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

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 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

• 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 nh n

h 2

h 1

To

x

Layer 1

Layer 2

Layer nh n

h 2

h 1

To

q&q&

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∂

∂

∂ ∂

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

TPS Optimization using MINIVER/OPT

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4

optimizaton cycle

wei

ght (

lbm

/ft^2

)

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8

optimization cycle

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

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