hypersonic vehicle flight dynamics with coupled...

IntegratedHypersonic

Vehicle Model

Dalle et al.

IntroductionApproach

Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Hypersonic Vehicle FlightDynamics with Coupled

Aerodynamics andReduced-order Propulsive

ModelsAIAA Atmospheric Flight Mechanics

Conference

Derek J. Dalle, Scott G. V. Frendreis, James F. Driscoll, Carlos E. S.Cesnik

July 31, 2010

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Integrated Hypersonic Vehicle Model, AFM 2010 1/31


Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Overview

Motivation

Flight dynamics analysis forhypersonic vehicle

Use in control design andevaluation simulations

Six degrees of freedom

Goals

Technique independent of vehicle

Combine previous analysis codes

Trim vehicle for specifiedcondition

Future goals

Aerothermoelastic considerations

Distributable code

Two-dimensional vehicle geometry

Three-dimensional vehicle geometry

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Available models

HSV

Compiled at AFRL by Bolender,M. A. and Doman, D. B.

Simplified but fairly completemodel of completetwo-dimensional vehicle

Automatic vehicle trim

Aerodynamic models

Easily extensible to 3D vehicles

Compute quickly

Very compatible with type ofgeometry we intend to use

MASIV (Michigan-AFRL Scramjet In Vehicle)

Two-dimensional propulsion analysis code for wide class of vehicles

Produced by group at Michigan

Includes inlet and nozzle

Quasi-steady rigid body models

2.75

0.75

Origin (0,0)

2.12 1.005.368.15 1.78 3.60

2.75

5.40

1.830.11

Combustor/isolatorheight

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Integration method

Overview

Goal is to replace and improve HSV

Incorporate MASIV for propulsion analysis and local inclination methodsfor aerodynamics

Separate vehicle into regions to be handled by appropriate models

Multiple 2D propulsion simulations with spanwise numerical integration

Challenge

Three-dimensional vehicle andtwo-dimensional code

Inlet and nozzle integral parts ofpropulsion system

Region determination and 2Dgeometry determination

Approach

Limit to vehicles with flat inletsand nozzles

Isolate inlet, combustor, andnozzle from rest of vehicle

Locate edges of cowl and tracealong surface of vehicle

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Vehicle geometry

Source

Part of TSTO geometry

Provided by VSIVogel, J. M., Kelkar, A. G., Inger, G.,Whitmer, C., Sidlinger, A., andRodriguez, A., “Control-RelevantModeling of Hypersonic Vehicles,” 2009American Control Conference.

Model

Hypersonic vehiclewith triangularelements

4634 nodes

9046 faces

Vehicle length is 46 m

Isometric view of vehicle

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Vehicle components

Propulsion systems and remaining surfaces handled byseparate modelsThree two-dimensional cuts for propulsion modelAutomated utility to determine inlet and nozzle regions

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Propulsion geometry

15.54 m

3.41 m1.82 m 1.62 m

8.92 m

4.74 m2.78 m

21.24 m

Centerline propulsive geometry

3.34 m 4.74 m

7.47 m

1.76 m 1.62 m

8.92 m

2.78 m

21.24 m

Edge propulsive geometry

Two-dimensional model for entire propulsive system including inlet andnozzle

Considered at two locations to model three-dimensional vehicle

Geometries correspond to the dotted blue lines on the previous slide

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Vehicle Model

Dalle et al.


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Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Canonical vehicle for propulsive model

8 1a 1b1c

1d 2a 3a 4a 4b 5a 6a

Several inlet ramps for compression efficiencyArbitrarily shaped, variable-area ductFuel injection trough any number of portsJet mixing in combustorNozzle with recombination and external expansion

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

2D aerodynamic model (SAMURI)

Supersonic Aerodynamic ModelUsing Riemann Interactions

Uses oblique shock theory

Discrete expansion waves

Arbitrary number of waveinteractions

Accounts for calorically imperfectgas

Any geometry with no detachedwaves

Two diamond airfoils in M∞ = 2, α = 0 flow

Sample inlet geometry at M∞ = 8

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Modified shock-expansion theory

Calculate the pressure on each panel

Include angular velocity of each panel

~v =~v∞ +~ω×~r

Find deflection angle

sinδ =− n̂ ·~v‖~v‖

Use Prandtl-Meyer theory if δ < 0 and shock if δ > 0

p = p∞

(2γ

γ + 1M2 sin2

β− γ−1γ + 1

)If δ≤ δmax, i.e. there can be an attached shock, use oblique shock relation

tanδ = 2cotβM2 sin2

β−1M2(γ + cos2β) + 2

If shock is detached, interpolate the shock angle

β = βmax +δ−δmax

π/2−δmax(π/2−βmax)

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Modified shock-expansion theory

Higher surface pressures shown in red

Pressures on inlet and nozzle surfaces not used

Pressures shown at trim angle of attack

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Performance of propulsive components

01

2

3

0

2

40

500

1000

1500

2000

Φα [◦]

Fx[kN]

Installed thrust

01

2

3

0

2

41000

1500

2000

2500

3000

Φα [◦]

Fz[kN]

Lift from inlet and nozzle

Includes inlet, combustor, and nozzle

High equivalence ratios due to poor mixing

Jagged performance caused by wave interactions

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Trim methodology

Cost function

Minimization approach to trim

Eliminate net forces and moments

J =[~FB ~NB

]W

[~FB~NB

]Continuous optimization technique

Control variables

Fuel-air equivalence ratio

Elevator angle

Surrogate model

Propulsive model has some discontinuities

Used a curve-fit model for propulsive model

Maintained full model for aerodynamic model

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Trim states

State Name Surrogate Full model‖~vB‖ Velocity magnitude 2.40 km/s 2.40 km/s−zE Altitude 26 km 26 km

α Angle of attack 2.89 deg 2.86 degβ Sideslip angle 0 deg 0 degθ Pitch Euler angle 2.89 deg 2.86 degφ Roll Euler angle 0 deg 0 deg

v̇B,x x-component of~̇vB −1.87×10−5 m/s2 4.28×10−1 m/s2

v̇B,z z-component of~̇vB 1.45×10−5 m/s2 8.89×10−5 m/s2

ω̇B,y y-component of ~̇ωB −1.52×10−8 rad/s2 −1.59×10−6 rad/s2

δe Elevator deflection angle 26.9 deg 27.4 degΦ Equivalence ratio 1.73 1.95

Extra thrust in full model

Similar results for control variables

Using state obtained from surrogate model did not give trimmed flightusing the full model

Very large elevator angles

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Inlet flow near trim state

Darker shades of blue representhigher temperatures

Maximum temperature of 780 K

Compression ratio of p2/p∞ = 6.77(edge) and p2/p∞ = 4.50 (center)

Shock completely goes intoengine Inlet temperature at left or right edge

Inlet temperature contours along centerline

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Nozzle profile near trim state

Temperatureprofiles

Maximumtemperature of1600 K

Divergent plume

Notice shockcoming off of plume

Fairly symmetric

None of the wavesin the nozzle willcause huge jumpsin performancewith small changesin flightparameters

Edge nozzle profile

Centerline nozzle profile

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Robust inlet optimization

Single-condition designApparently excellent performanceat one conditionDifficult/impossible to control(high sensitivities)Performance curve is jaggedNarrow operating range

Range of conditionsOperating range specified as partof designPerformance curves smoothwithin that range

improved design

single-condition design

6 7 8 9 100.3

0.4

0.5

0.6

0.7

0.8

M¥

p 0,2

�p 0

,¥

single-condition design

improved design

6 7 8 9 10

40

50

60

70

M¥

p 2�p ¥

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Additional applications

Design tools

Numerous suggestedimprovements for vehicle

Extensive design tools for 2Dpropulsion code exist

Would like to be able to use codeto design a vehicle for a specificrange of flight conditions

Automation

Eliminate reliance on surrogatemodels

Smoother performance ofpropulsion system

More robust numerical methodfor trim

Flight envelope

Find flight conditions where thevehicle can be trimmed

Ranges of flight Mach numberand altitude

Requires method to determinethat trim is not possible

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Conclusions

Reduced-order model

2D propulsive model

3D aerodynamic model

Automatic integration of models

All performed in MATLAB

Trim analysis

Excess thrust using full model

Constructed surrogate forpropulsive model

Able to trim with about 3 hrs ofcomputation

Large elevator deflection angle

Large equivalence ratio

Vehicle design

Reduce nose-down moment

Higher compression in inlet

Larger control surfaces

Narrower combustor

Necessary improvements

Smoother propulsion model

Aeroelastic analysis

Thermal analysis

Automated design tools

More robust trim method

Turn into a distributable code

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Acknowledgments

MACCCS group, Sean M. Torrez, Matt L. Fotia, TorstensSkujins, Nate FalkiewiczAFRL/AFOSR, Michael W. Oppenheimer, MichaelA. Bolender, David B. DomanVSI AerospaceThis research was supported by U.S. Air Force ResearchLaboratory grant FA 8650-07-2-3744 for the Michigan AirForce Research Laboratory Collaborative Center forControl Science.This research was also supported by NASA grantNNX08AB32A, administered by Donald Soloway andJorge Bardina, technical monitors.

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Vehicle inertia properties

Symbol Name Valuem Mass 2.22×105 kgIxx Moment of inertia about x-axis 3.42×106 kg ·m2

Iyy Moment of inertia about y-axis 3.95×107 kg ·m2

Izz Moment of inertia about z-axis 3.95×107 kg ·m2

Ixy Product of inertia 0 kg ·m2

Ixz Product of inertia 0 kg ·m2

Iyz Product of inertia 0 kg ·m2

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Shock/expansion theory

Oblique shocksPerfect-gas obliqueshock analyticsolutiona

Cubic polynomial forsinβ where β is thewave angleThree solutions

Weak oblique shockStrong oblique shockEntropy-destroyingshock

aThompson, M. J. “A Note on theCalculation of Oblique Shock WaveCharacteristics.” Journal ofAerospace Sciences. 1950 vol. 27,pp. 741-744

control volume A

control volume B

Illustration of two control volumes around a diamond airfoil

Net fluxes into A must be the sameas net fluxes into BDrag is not a function of the controlvolume used to compute it

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

The case for expansion shocks

Discrete expansions

Finite-strength waves aredifferent from continuousexpansionsOne degree of freedom (waveangle) and three constraints(mass and momentumconservation)

Solution

Use downstream state forextra degrees of freedomLeads exactly to the obliqueshock conditionsStill accurate if expansionsare split into several shocks

Control volume

Control volume around an expansion withnexp = 1

Net mass/momentum fluxinto control volume must bezeroSame for any other controlvolume that does not crossthe surface

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Discretized expansion waves

DiscretizationMakes conditions a piecewiseconstant function of angleUsing angles based on Guassianquadrature minimizes∫

σA

σB

(M(σ)− M̃(σ))2 dσ

Puts waves near edges of expansionGoal is to keep accuracy high andnexp low

ConservationUse expansion shocksEstimate of state B will be slightlyinaccurate

σ

A

B

Smooth expansion with δ = 18.4◦and M∞ = 1.5

Sample expansion with nexp = 4

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Vehicle Model

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Components

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ResultsPerformance

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Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Riemann problem

Discontinuous regionscome in contact whenshocks intersectRegions B and C musthave the same pressureDensity and temperaturemay differFlow matches directionWaves separate regions Afrom B and D from CMain limiter of codeperformance

Zoom in on a generic flow

A

B

C

D

ΘB

ΘA

ΘD

ΣA

ΒA

ΣD

ΣC

ΜD

ΜC

Sketch of two interacting waves.

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Comparison of SAMURI and CFD

Results from CFD++.

Results from reduced-order model.

Pressure contours; darkest is p/p∞ = 90

Maximum error is about 6%

CFD model included viscosity

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

The Michigan/AFRL Scramjet In Vehicle code

InletWave interactions solved using exact solutionExpansions discretizedArbitrary number of distinct regions tracked

CombustorRealistic fuel-air mixing from jet lawsFinite-rate chemistry pre-tabulated from flamelet solutionsVariable fuel injection and duct area changeWill incorporate isolator to cover ram/scram transition

NozzleUses same aerodynamic model as inletUses conditions from combustor (can be non-uniform)Incorporates finite-rate chemistry

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Propulsion model code description

MASIV Data flow

Inlet Combustor Nozzle

SAMURI SAMURI

Force/Moment

Design

Conditions

SolutionOptions

Station 2

Options SolutionStation 5

MASIV

User only interacts with green blocksDefault vehicle design provided

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Vehicle Model

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Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

2D Aerodynamic Model

SAMURI data flow

Geometry

Preprocess

Set x = xmin

Geometryand states

Set y = ymin

Update wavepositions

x = xmax

no

Find next x y = ymaxyes

Find next y

no

Find type ofinteraction

Solve

Wait forexit signalExit

yes

Output

Conditions

Basically a sweep through the flow domainOnly works for supersonic flowAll of the flow physics in the “Solve” block

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Bibliography

Korte, J. J., “Parametric Model of an Aerospike Rocket Engine,” 38thAerospace Sciences Meeting, AIAA Paper 2000-1044, 2000.

McBride, B. J., Zehe, M. J., and Gordon, S., “NASA Glenn Coefficients forCalculating Thermodynamic Properties of Individual Species,” NASATechnical Paper 2002-211556, 2001.

Bolender, M. A. and Doman, D. B., “Nonlinear Longitudinal DynamicalModel of an Air-Breathing Hypersonic Vehicle,” Journal of Spacecraftand Rockets, Vol. 44, No. 2, 2007, pp. 374-387.

Chavez, F. R. and Schmidt, D. K., “Analytical Aeropropulsive/AeroelasticHypersonic-Vehicle Model with Dynamic Analysis,” Journal of Guidance,Control, and Dynamics, Vol. 17, No. 6, 1994, pp. 1308-1319.

O’Brien, T. F., Starkey, R. P., and Lewis, M. J., “Quasi-One-DimensionalHigh-Speed Engine Model with Finite-Rate Chemistry,” Journal ofPropulsion and Power, Vol. 17, No. 6, 2001, pp. 1366-1374.

Higgins, K. and Schmidt, S., “Simulation of a Sonic Jet Injected into aSupersonic Cross-Flow,” 16th Australasian Fluid Mechanics Conference,2007.

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Vehicle Model

Dalle et al.


Vehicle

Components

ModelPropulsive

Aerodynamic

ResultsPerformance

Trim

Interactions

Conclusions

AppendixVehicle

Gas model

Code descriptions

References

Papers by our group

Dalle, D. J., Fotia, M. L., and Driscoll, J. F., “Reduced-Order Modeling ofTwo-Dimensional Supersonic Flows with Applications to ScramjetInlets,” Journal of Propulsion and Power, Vol. 26, No. 3, 2010, pp.545-555.

Frendreis, S. G. V., Skujins, T., and Cesnik, C. E. S.,“Six-Degree-of-Freedom Simulation of Hypersonic Vehicles,” AIAAAtmospheric Flight Mechanics Conference & Exhibit, 2009, AIAA Paper2009-5601.

Torrez, S. M., Driscoll, J. F., Dalle, D. J., and Fotia, M. L., “PreliminaryDesign Methodology for Hypersonic Engine Flowpaths,” 16thAIAA/DLR/DGLR/ International Space Planes and Hypersonic Systemsand Technologies Conference, 2009, AIAA Paper 2009-7289.

Dalle, D. J., Torrez, S. M., and Driscoll, J. F., “Reduced-Order Modeling ofReacting Supersonic Flows in Scramjet Nozzles,” 46thAIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,2010.

Frendreis, S. G. V., and Cesnik, C. E. S., “3D Simulation of a FlexibleHypersonic Vehicle,” AIAA Atmospheric Flight Mechanics Conference &Exhibit, 2010.

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hypersonic vehicle flight dynamics with coupled...

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