Reduced-order Modeling of Reacting Supersonic Flows in...

Scramjet NozzleModel

Dalle, Torrez,Driscoll

Vehicle ModelMotivation

MASIV Code

AerodynamicModelFlow Model

Gas Model

Scramjet Nozzle1D Comparison

2D Comparison

Conclusions

AppendixPrograms

Performance

References

Reduced-order Modeling ofReacting Supersonic Flows in

Scramjet Nozzles46th AIAA/ASME/SAE/ASEE Joint Propulsion

Conference & Exhibit

Derek J. Dalle, Sean M. Torrez, James F. Driscoll

October 17, 2010

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Scramjet Nozzle Model, JPC 2010 1/29




MASIV Code


Gas Model


2D Comparison

Conclusions

AppendixPrograms

Performance

References

Canonical propulsion flowpath

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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Integration with hypersonic vehicle

Three-dimensional vehicle with triangular panels

Propulsion flowpath modeled as two-dimensional

Vogel, J. M., Kelkar, A. G., Inger, G., Whitmer, C., Sidlinger, A., andRodriguez, A., “Control-Relevant Modeling of Hypersonic Vehicles,” 2009American Control Conference.

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2D Comparison

Conclusions

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Control design and evaluation

Control of air-breathinghypersonic vehicles notwell studiedCFD not yet appropriatefor this problemImportant for our view ofoptimizationRequires very fast modelGoal is a vehicle modelthat can be used bycontrol designers on asingle computerInlet and combustormodels also developed

6 6.5 7 7.5 8 8.5 9 9.5 10 10.5−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

M[1]F

/(ρin

u2 in

Ain

)[1]

Installed Thrust

Plot of thrust for various flight Mach numbers ofone scramjet design.

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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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Information flow in 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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Aerodynamic model (SAMURI)

Supersonic AerodynamicModel Using RiemannInteractions

Uses oblique shock theory

Discrete expansion waves

Arbitrary number of waveinteractions

Accounts for caloricallyimperfect gas

Any geometry with nodetached waves

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

Sample inlet geometry at M∞ = 8

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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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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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Conclusions

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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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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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Finte-rate chemistry

A

B

C

D D′

A′

C′

B′

D′′

A′′

Compatible with most reduced mechanismsMass fractions update periodically along streamlinesGenerates new regions with each chemistry updateConditions still considered constant in each polygonNo chemistry across width of wave

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Reduced chemical mechanism

Hydrogen-Air combustion mechanisma

33 one-way reactions and 14 species (including Argon)Program contains interpreter to use any mechanism

aJachimowski, C. J. “An analytic study of the Hydrogen-Air reaction mechanism with application to SCRAMJETcombustion.” NASA Technical Paper 2791, 1988

1 H2 +O2 → 2OH

2 H+O2 → OH+O

3 O+H2 → OH+H

4 OH+H2 → H2O+H

5 2OH→ H2O+O

6 H+OH+M→ H2O+M

7 2H+M→ H2 +M

8 H+O+M→ OH+M

9 H+O2 +M→ HO2 +M

10 HO2 +H→ H2 +O211 HO2 +H→ 2OH

12 HO2 +H→ H2O+O

13 HO2 +O→ O2 +OH

14 HO2 +OH→ H2O+O215 2HO2 → H2O2 +O216 H+H2O2 → H2 +HO217 O+H2O2 → OH+HO218 OH+H2O2 → H2O+HO219 H2O2 +M→ 2OH+M

20 2O+M→ O2 +M

21 2N+M→ N2 +M

22 N+O2 → NO+O

23 N+NO→ N2 +O

24 N+OH→ NO+H

25 N+NO+M→ HNO+M

26 H+HNO→ NO+H227 O+HNO→ NO+OH

28 OH+HNO→ NO+H2O

29 HO2 +HNO→ NO+H2O230 HO2 +NO→ NO2 +OH

31 H+NO2 → NO+OH

32 O+NO2 → NO+O233 NO2 +M→ NO+O+M

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Nozzle geometry

Nozzle may have smooth surfacebut modeled as a series of flatramps hereSignificant expansion ratio andflow dominated by expansion fansLower exhaust plume boundaryaffected by freestream pressureand wave interactionsPotentially affected byrecombination of radical speciesfrom the combustorDifficult to define optimum buteasy to obtain good performance

H4

H5

H6

L5y

x

Sample scramjet nozzle geometry

Corresponding solution (temperature)

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Geometry and boundary conditions

GeometryGeometry from last slideMostly external expansionExpansion ratio of 5Emphasizestwo-dimensional flow

ConditionsFlight Mach number of 1810% dissociationVery high exit velocitySelected to emphasizerecombination

Property Freestream Post-combustorρ 0.001966 kg/m3 0.002240 kg/m3

p 149.1 Pa 1094 PaT 264.2 K 1400 Ku 5865 m/s 5131 m/s

YN2 0.755590 0.734173YO2 0.231522 0YAr 0.012888 0.012523

YH2O 0 0.227974YH 0 0.001417

YOH 0 0.023913

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References

Validation models

SAMURI with chemistryTwo-dimensional waveinteraction modelJachimawski chemicalmechanismInviscid solutionMost accuratereduced-order model

SAMURI without chemistryTwo-dimensional waveinteraction modelFrozen chemistryInviscid solutionFastest model

Two-dimensional CFDCommercial CFD++packageJachimawski chemicalmechanismViscous solutionApproximately 300,000cells

Quasi-1D modelFind plume usingSAMURIOne-dimensional solutionJachimawski mechanismInviscid solution

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Exhaust plume

0 1 2 3 4 5

0.0

0.5

1.0

1.5

2.0

2.5

x [m]

y[m

]

Very similar plumeRecombination makes plume slightly biggerViscosity seems to not have a noticeable effect

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2D Comparison

Conclusions

AppendixPrograms

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References

Importance of two-dimensional model

0 1 2 3 4 5

200

400

600

800

1000

x [m]

p[P

a]

Quasi-1D

CFD

2D, no chemistry

2D, with chemistry

Pressure

0 1 2 3 4 5

800

900

1000

1100

1200

1300

1400

x [m]

T[K

]

Quasi-1D

CFD

2D, no chemistry

2D, with chemistry

Temperature

Very similar pressure results for all 2D models

Slight temperature increase in initial part of nozzle due tochemistry

Pressure is approximately constant across boundary layer

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Importance of boundary layer

Boundary layer has ahuge effect

Velocity isapproximately thesame as thrust

Chemistry has smalleffect

Very large kineticenergies compared torecombination heatrelease

0 1 2 3 4 5

5150

5200

5250

5300

5350

5400

5450

x [m]

u[m

/s]

Quasi-1D

CFD

2D, no chemistry

2D, with chemistry

Velocity plot

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Mass fraction results

0 1 2 3 4 50.228

0.230

0.232

0.234

0.236

0.238

x [m]

Y H2O

Quasi-1D

CFD

2D, no chemistry

2D, with chemistry

YH2O plot

0 1 2 3 4 5

0.005

0.010

0.015

0.020

x [m]

Y OH

Quasi-1D

CFD

2D, no chemistry

2D, with chemistry

YOH plot

Approximately similar results

Something causes H2O to dissociate in CFD

Error in 2D model seems to be due to missing boundary layers

Accuracy of 1D model is likely a coincidence

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2D temperature plots

CFD

1400

1000

400

400

18001400

1200

SAMURI

Maximum temperature 2700 K

Similar results in inviscid regions

Large boundary layer

Note shock wave starting at cowl trailing edge

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2D x-velocity plots

CFD

5500

5000

5700

5600

SAMURI

Maximum velocity 5865 m/s

Similar results in inviscid regions

Large boundary layer

Can calculate viscous drag using control volume

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2D plots of OH mass fraction

CFD

0.002

0.022

0.022

0.0020.004

0.008

0.016

SAMURI

Accurate in the 1D region near inflow

Reaction rate higher in high-temperature boundary layers

More time to recombine in lower velocity regions

Plots for other species very similar

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Conclusions

MASIV

SAMURI wave model able to analyze nozzles

Capable of analyzing finite-rate chemistry

Computational time less than one second

Nozzle flow physics

Viscosity very important

Has usual effects on temperature, velocity, and thrustAlso plays a role in recombination

Two-dimensional nature of flow more important than justdetermining the exhaust plume

Energy due to recombination small compared to kinetic energy

Recombination happens very quickly in most nozzles

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Acknowledgments

MACCCS group, Scott G. V. Frendreis, Matt L. Fotia,Torstens Skujins, Nate Falkiewicz, Carlos E. S. CesnikAFRL/AFOSR, Michael W. Oppenheimer, MichaelA. Bolender, David B. DomanThis 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, technicalmonitor.

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MASIV Code


Gas Model


2D Comparison

Conclusions

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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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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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MASIV Code


Gas Model


2D Comparison

Conclusions

AppendixPrograms

Performance

References

Bibliography

Vogel, J. M., Kelkar, A. G., Inger, G., Whitmer, C., Sidlinger, A., andRodriquez, A., “Control-Relevant Modeling of Hypersonic Vehicles,” 2009American Control Confernce, 2009.

Oppenheimer, M. W., Skujins, T., Bolender, M. A., and Doman, D. B., “AFlexible Hypersonic Vehicle Model Developed with Piston Theory,” 2007Atmospheric Flight Mechanics Conference and Exhibit, AIAA Paper No.2007-6396, August 2007.

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.

Jachimowski, C. J., “An analytic study of the Hyrdogen-Air reactionmechanism with application to SCRAMJET combustion,” NASATehcnical Paper 2791, 1988

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MASIV Code


Gas Model


2D Comparison

Conclusions

AppendixPrograms

Performance

References

Papers by our group

Torrez, S. M., Dalle, D. J., and Driscoll, J. F., “Dual Mode Scramjet Design toAchieve Improved Operational Stability,” 46th AIAA/ASME/SAE/ASEE JointPropulsion Conference and Exhibit, 2010.Dalle, D. J., Fotia, M. L., and Driscoll, J. F., “Reduced-Order Modeling ofTwo-Dimensional Supersonic Flows with Applications to Scramjet Inlets,” Journalof 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-FreedomSimulation of Hypersonic Vehicles,” AIAA Atmospheric Flight Mechanics Conference& Exhibit, 2009, AIAA Paper 2009-5601.Torrez, S. M., Driscoll, J. F., Dalle, D. J., and Fotia, M. L., “Preliminary DesignMethodology for Hypersonic Engine Flowpaths,” 16th AIAA/DLR/DGLR/International Space Planes and Hypersonic Systems and Technologies Conference,2009, AIAA Paper 2009-7289.Dalle, D. J., Frendreis, S. G. V., Driscoll, J. F., and Cesnik, C. E. S., “HypersonicVehicle Flight Dynamics with Coupled Aerodynamics and Reduced-order PropulsiveModels,” AIAA Atmospheric Flight Mechanics Conference and Exhibit, 2010.Frendreis, S. G. V., and Cesnik, C. E. S., “3D Simulation of a Flexible HypersonicVehicle,” AIAA Atmospheric Flight Mechanics Conference & Exhibit, 2010.

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