Abstract
A control approach is proposed in this study that controls the growth of a spatially growing mixing layer in an open loop. Due to the similarity of the mixing layer dynamics in the temporal and spatial domains, the control is exercised in the temporal domain that leads to optimization of the layer in the spatial domain. The proportional-integral-derivative (PID) control in the temporal domain uses Navier–Stokes equations as the plant model. Apart from being prohibitively expensive, control in the spatial domain presents convective time delay problems. These barriers are circumvented by solving the control problem in the temporal domain very rapidly, based on a given set point in the linear regime. Once the set point in the temporal domain is reached, the corresponding initial conditions in the temporal domain are mapped to inflow boundary conditions in the spatial domain. With these mapped inflow boundary conditions in the spatial domain, the spatial development of the mixing layer is followed, which confirms the efficacy of control in the spatial domain. The present control methodology offers a new paradigm for control of the spatially growing mixing layer.
Issue Section:
Special Papers
References
1.
Kaul
,
U. K.
, 1988
, “
Do Large Structures Control Their Own Growth in a Mixing Layer? An Assessment
,” J. Fluid Mech.
,
190
, pp. 427
–450
.10.1017/S00221120880013992.
Kaul
,
U. K.
, 1989
, “
On Some Aspects of Wave Interactions in Plane Mixing Layers
,” Wave Phenomena: Theoretical, Computational and Practical Aspects
,
H. C. M.
Lui Lam
, ed.,
Springer-Verlag
, New York.3.
Kaul
,
U. K.
, 1991
, “
Growth of Instabilities in Two Types of Mixing Layer
,” NASA Tech Briefs, Report No. ARC-12567.4.
Kaul
,
U. K.
, 2012
, “
Efficient CFD-Based Flow Control in Free Shear Layers Using Simple PID Control
,” NASA Ames Research Center, Moffett Field, CA, NASA Invention Disclosure, Report No. NASA-ARC-16984-1.5.
Kaul
,
U. K.
, 2013
, “
Efficient CFD-Based PID Control of Free Shear Layer Flow
,” AIAA
Paper No. 2013-2986.10.2514/6.2013-29866.
Kaul
,
U. K.
, 2014
, “
First Principles Based PID Control of Mixing Layer: Role of Inflow Perturbation Spectrum
,” AIAA
Paper No. 2014-2222.10.1115/2014-22227.
Brown
,
G. L.
, and
Roshko
,
A.
, 1974
, “
On Density Effects and Large Structure in Turbulent Mixing Layers
,” J. Fluid Mech.
,
64
(4
), pp. 775
–816
.10.1017/S002211207400190X8.
Winant
,
C. D.
, and
Browand
,
F. K.
, 1974
, “
Vortex Pairing: The Mechanism of Turbulent Mixing Layer Growth at Moderate Reynolds Number
,” J. Fluid Mech.
,
63
(02
), pp. 237
–255
.10.1017/S00221120740011219.
Ho
,
C.
, and
Huang
,
L.-S.
, 1982
, “
Subharmonics and Vortex Merging in Mixing Layers
,” J. Fluid Mech.
,
119
, pp. 443
–473
.10.1017/S002211208200143810.
Oster
,
D.
, and
Wygnanski
,
I.
, 1982
, “
The Forced Mixing Layer Between Parallel Streams
,” J. Fluid Mech.
,
123
, pp. 91
–130
.10.1017/S002211208200297311.
Mungal
,
M. G.
, and
Dimotakis
,
P. E.
, 1984
, “
Mixing and Combustion With Low Heat Release in a Turbulent Shear Layer
,” J. Fluid Mech.
,
148
, pp. 349
–382
.10.1017/S002211208400238X12.
Bell
,
J. H.
, and
Mehta
,
R. D.
, 1990
, “
Development of a Two-Stream Mixing Layer From Tripped and Untripped Boundary Layers
,” AIAA J.
,
28
(12
), pp. 2034
–2042
.10.2514/3.1051913.
Delville
,
J.
,
Bellin
,
S.
,
Garem
,
J. H.
, and
Bonnet
,
J. P.
, 1988
, “
Analysis of Structures in a Turbulent, Plane Mixing Layer by Use of a Pseudo Flow Visualization Method Based on Hot-Wire Anemometry
,” Proceedings of the Second European Turbulence Conference
, Advances in Turbulence 2,
H.-H.
Fernholz
and
H. E.
Fiedler
, eds., Aug. 30–Sept. 2,
Springer Verlag
, Berlin, pp. 251
–256
.14.
Delville
,
J.
, 1997
, Plane Turbulent Mixing Layer From C.E.A.T. Poitiers
,
CEAT/LEA UMR CNRS 6609
,
Poitiers Cedex, France
.15.
Ely
,
R.
, and
Little
,
J.
, 2013
, “
Mixing Layer Excitation by Dielectric Barrier Discharge Plasma Actuators
,” AIAA
Paper No. 2013-1012.10.1115/2013-101216.
Ely
,
R.
, and
Little
,
J.
, 2013
, “
The Mixing Layer Perturbed by Dielectric Barrier Discharge
,” AIAA
Paper No. 2013-2753.10.1115/2013-275317.
Huerre
,
P.
, and
Monkewitz
,
P. A.
, 1985
, “
Absolute and Convective Instabilities in Free Shear Layers
,” J. Fluid Mech.
,
159
(1
), pp. 151
–168
.10.1017/S002211208500314718.
Nagarajan
,
K. K.
,
Cordier
,
L.
,
Airiau
,
C.
, and
Kourta
,
A.
, 2009
, “
POD Based Reduced Order Modelling of a Compressible Forced Cavity Flow
,” 19 e‘Me Congre’s Francais de Mecanique, Marseille.
19.
Cordier
,
L.
,
Noack
,
B. R.
,
Tissot
,
G.
,
Lehnasch
,
G.
,
Delville
,
J.
,
Balajewicz
,
M.
,
Daviller
,
G.
, and
Niven
,
R. K.
, 2013
, “
Identification Strategies for Model-Based Control
,” Exp Fluids
,
54
(8
), p. 1580
.10.1007/s00348-013-1580-920.
Parezanovic
,
V.
,
Laurentie
,
J.-C.
,
Carine
,
F.
,
Delville
,
J.
,
Bonnet
,
J.-P.
,
Spohn
,
A.
,
Duriez
,
T.
,
Cordier
,
L.
,
Noack
,
B. R.
,
Abel
,
M.
,
Segond
,
M.
,
Shaqarin
,
T.
, and
Brunton
,
S. L.
, 2015
, “
Mixing Layer Manipulation Experiment From Open-Loop Forcing to Closed-Loop Machine Learning Control
,” Flow Turbul. Combust.
,
94
(1
), pp. 155
–173.
10.1007/s10494-014-9581-121.
Duriez
,
T.
,
Brunton
,
S. L.
, and
Noack
,
B. R.
, 2016
, “
Machine Learning Control - Taming Nonlinear Dynamics and Turbulence
,” Fluid Mechanics and Its Applications
,
Springer International Publishing
,
Switzerland
.22.
Martin
,
R. A.
, and
Kaul
,
U. K.
, 2014
, “
Optimization of Perturbation Parameters for Simulated Free Shear Layer Flow
,” AIAA
Paper No. 2014-2223.10.1115/2014-222323.
Li
,
H.
,
Tan
,
J.
,
Gao
,
Z.
, and
Noack
,
B. R.
, 2020
, “
Machine Learning Open-Loop Control of a Mixing Layer
,” Phys. Fluids
,
32
, p. 111701.10.1063/5.003007124.
Shaqarin
,
T.
,
Noack
,
B. R.
, and
Morzyński
,
M.
, 2018
, “
The Need for Prediction in Feedback Control of a Mixing Layer
,” Fluid Dyn. Res.
,
50
(6
), p. 065514
.10.1088/1873-7005/aae45325.
Roos
,
F. W.
, and
Kegelman
,
J. T.
, 1986
, “
Control of Coherent Structures in Reattaching Laminar and Turbulent Shear Layers
,” AIAA J.
,
24
(12
), pp. 1956
–1963
.10.2514/3.955326.
Ho
,
C.-M.
,
Zohar
,
Y.
,
Foss
,
J. K.
, and
Buell
,
J. C.
, 1991
, “
Phase Decorrelation of Coherent Structures in a Free Shear Layer
,” J. Fluid Mech.
,
230
, pp. 319
–337
.10.1017/S002211209100080027.
Fujisawa
,
N.
, and
Takizawa
,
Y.
, 2003
, “
Study of Feedback Control of Edge Tone by Simultaneous Flow Visualization
,” Meas. Sci. Technol.
,
14
, p. 14121419
.28.
Pastoor
,
M.
,
King
,
R.
,
Noack
,
B. R.
, and
Tadmor
,
G.
, 2005
, “
Observers and Feedback Control for Shear Layer Vortices
,” Proceedings of the 44th IEEE Conference on Decision and Control and the European Control Conference, Seville, Spain, Dec. 12–15, Paper No. MoA15.3
.10.1109/CDC.2005.158220629.
Pastoor
,
M.
,
Henning
,
L.
,
Noack
,
B. R.
,
King
,
R.
, and
Tadmor
,
G.
, 2008
, “
Feedback Shear Layer Control for Bluff Body Drag Reduction
,” J. Fluid Mech.
,
608
, pp. 161
–196
.10.1017/S002211200800207330.
Zaman
,
K. B. M. Q.
, and
Hussain
,
A. K. M. F.
, 1981
, “
Turbulence Suppression in Free Shear Flows by Controlled Excitation
,” J. Fluid Mech.
,
103
(-1
), pp. 133
–159
.10.1017/S002211208100127431.
Wei
,
M.
, and
Freund
,
J. B.
, 2005
, “
A Noise-Controlled Free Shear Flow
,” J. Fluid Mech.
,
546
(-1
), pp. 123
–152
.10.1017/S002211200500709332.
Rumsey
,
C. L.
, 2009
, “
Successes and Challenges for Flow Control Simulations (Invited)
,” AIAA
Paper No. 2008-4311.10.1115/2008-431133.
Collis
,
S. S.
,
Joslin
,
R. D.
,
Seifert
,
A.
, and
Theofilis
,
V.
, 2004
, “
Issues in Active Flow Control: Theory, Control, Simulation, and Experiment
,” Prog. Aerosp. Sci.
,
40
(4–5
), pp. 237
–289
.10.1016/j.paerosci.2004.06.00134.
Brehm
,
C.
,
Gross
,
A.
, and
Fasel
,
H. F.
, 2006 “
Closed-Loop Control of Low-Pressure Turbine Laminar Separation
,” AIAA
Paper No. 2006-3021.10.1115/2006-302135.
Brunton
,
S. L.
, and
Noack
,
B. R.
, 2015
, “
Closed-Loop Turbulence Control: Progress and Challenges
,” ASME App. Mech. Rev.
,
67
(5
), p. 050801
.10.1115/1.403117536.
Rowley
,
C. W.
,
Williams
,
D. R.
,
Colonius
,
T.
,
Murray
,
R. M.
, and
MacMynowski
,
D. G.
, 2006
, “
Linear Models for Control of Cavity Flow Oscillations
,” J. Fluid Mech.
,
547
(-1
), pp. 317
–330
.10.1017/S002211200500729937.
Roshko
,
A.
, 1990
, “
Phenomenological Modeling: Present and Future
,” Whither Turbulence? Turbulence at the Crossroads, Lecture Notes in Physics
, Vol.
357
,
Springer
, Berlin, pp. 486
–489
.38.
Roshko
,
A.
, 1992
, “
Instability and Turbulence in Shear Flows
,” Theoretical and Applied Mechanics
,
S. R.
Bodner
,
J.
Singer
,
A.
Solan
and
Z.
Hashin
, eds.,
Elsevier Science Publishers B.V
., Amsterdam, The Netherlands.39.
Qunzhen Wang
,
Q.
, and
Squires
,
K. D.
, 1998
, “
Transport of Heavy Particles in a Three-Dimensional Mixing Layer
,” ASME J. Fluids Eng.
,
120
(3
), pp. 613
–620
.10.1115/1.282070840.
Snider
,
D. M.
, and
Andrews
,
M. J.
, 1996
, “
The Simulation of Mixing Layers Driven by Compound Buoyancy and Shear
,” ASME J. Fluids Eng.
,
118
(2
), pp. 370
–376
.10.1115/1.281738841.
Ladeinde
,
F.
,
Liu
,
W.
, and
O'Brien
,
E. E.
, 1998
, “
Turbulence in Compressible Mixing Layers
,” ASME J. Fluids Eng.
,
120
(1
), pp. 48
–53
.10.1115/1.281965942.
Pham
,
H. T.
, and
Sarkar
,
S.
, 2014
, “
Large Eddy Simulations of a Stratified Shear Layer
,” ASME J. Fluids Eng.
,
136
(6
), p. 060913
.10.1115/1.402641643.
Snider
,
D. M.
, and
Andrews
,
A. J.
, 1996
, “
The Structure of Shear Driven Mixing With an Unstable Thermal Stratification
,” ASME J. Fluids Eng.
,
118
(1
), pp. 55
–60
.10.1115/1.281751144.
Paschereit
,
C. O.
,
Gutmark
,
E.
, and
Weisenstein
,
W.
, 1998
, “
Suppression of Combustion Instabilities by Acoustic Control of Shear Layer Properties
,” Advances in Turbulence VII, Fluid Mechanics and Its Applications
, Vol.
46
, pp. 293
–296
. 10.1007/978-94-011-5118-445.
Pandey
,
K. M.
, and
Sivasakthivel
,
T.
, 2011
, “
CFD Analysis of Mixing and Combustion of a Scramjet Combustor With a Planer Strut Injector
,” Int. J. Environ. Sci. Dev.
,
2
(2
), pp. 102
–108
.10.7763/IJESD.2011.V2.10546.
Fiedler
,
H. E.
, and
Fernholz
,
H.-H.
, 1990
, “
On Management and Control of Turbulent Shear Flows
,” Prog. Aerosp. Sci
,
27
(4
), pp. 305
–387
.10.1016/0376-0421(90)90002-247.
Yuan
,
C. C. L.
,
Krstic
,
M.
, and
Bewley
,
T. R.
, 2004
, “
Active Control of Jet Mixing
,” IEE Proc. Control Theory Appl.
,
151
(6
), pp. 763
–772
.10.1049/ip-cta:2004105348.
Cattafesta
,
L.
,
Garg
,
S.
,
Choudhari
,
M.
, and
Li
,
F.
, 1997
, “
Active Control of Flow-Induced Cavity Resonance
,” AIAA
Paper No. 07-1804.10.1115/07-180449.
Cattafesta
,
L.
,
Williams
,
D.
,
Rowley
,
C.
, and
Farrukh
,
A.
, 2003
, “
Review of Active Control of Flow-Induced Cavity Resonance
,” AIAA
Paper No. 2003-3567.10.2514/6.2003-356750.
Williams
,
D. R.
, and
Rowley
,
C. W.
, 2006
, “
Recent Progress in Closed-Loop Control of Cavity Tones
,” AIAA
Paper No. 2006-0712.10.1115/2006-071251.
Cattafesta
, III
,
L. N.
, Song
,
Q.
, Williams
,
D. R.
, Rowley
,
C. W.
, and
Alvi
,
F. S.
, 2008
, “
Active Control of Flow-Induced Cavity Oscillations
,” Prog. Aerosp. Sci.
,
44
(7–8
), pp. 479
–502
.10.1016/j.paerosci.2008.07.00252.
Rowley
,
C. W.
, and
Williams
,
D. R.
, 2006
, “
Dynamics and Control of High-Reynolds-Number Flow Over Open Cavities
,” Annu. Rev. Fluid Mech.
,
38
(1
), pp. 251
–276
.10.1146/annurev.fluid.38.050304.09205753.
Bernardini
,
C.
,
Benton
,
S. I.
,
Chen
,
J.-P.
, and
Bons
,
J. P.
, 2013
, “
Exploitation of Subharmonics for Separated Shear Layer Control on a High-Lift Low-Pressure Turbine Using Acoustic Forcing
,” ASME J. Turbomach.
,
136
(5
), p. 051018
.10.1115/1.402558654.
Betchov
,
R.
, and
Criminale
,
W. O.
, Jr.
, 1967
, Stability of Parallel Flows
,
Academic Press
,
New York, London
.55.
Corcos
,
G. M.
, and
Sherman
,
F. S.
, 1984
, “
The Mixing Layer: Deterministic Models of a Turbulent Flow—Part 1: Introduction and the Two-Dimensional Flow
,” J. Fluid Mech.
,
139
, pp. 29
–65
.10.1017/S002211208400025256.
Kim
,
J.
, 2003
, “
Control of Turbulent Boundary Layers
,” Phys. Fluids
,
15
(5
), p. 1093
.10.1063/1.156409557.
Joshi
,
S. S.
,
Speyer
,
J. L.
, and
Kim
,
J.
, 1997
, “
A Systems Theory Approach to the Feedback Stabilization of Infinitesimal and Finite-Amplitude Disturbances in Plane Poiseuille Flow
,” J. Fluid Mech.
,
332
, pp. 157
–184
.10.1017/S002211209600374658.
Kim
,
J.
, and
Bewley
,
T. R.
, 2007
, “
A Linear Systems Approach to Flow Control
,” Annu. Rev. Fluid Mech.
,
39
(1
), pp. 383
–417
.10.1146/annurev.fluid.39.050905.11015359.
Patnaik
,
P.
,
Sherman
,
F. S.
, and
Corcos
,
G. M.
, 1976
, “
A Numerical Simulation of Kelvin-Helmholtz Waves of Finite Amplitude
,” J. Fluid Mech.
,
73
(2
), pp. 215
–240
.10.1017/S002211207600135360.
Corcos
,
G. M.
, and
Sherman
,
F. S.
, 1976
, “
Vorticity Concentration and the Dynamics of Unstable Free Shear Layers
,” J. Fluid Mech.
,
73
(2
), pp. 241
–264
.10.1017/S002211207600136561.
Michalke
,
A.
, 1964
, “
On the Inviscid Instability of the Hyperbolic Tangent Velocity Profile
,” J. Fluid Mech.
,
19
(4
), pp. 543
–556
.10.1017/S002211206400090862.
Michalke
,
A.
, 1965
, “
On Spatially Growing Disturbances in an Inviscid Shear Layer
,” J. Fluid Mech.
,
23
(3
), pp. 521
–544
.10.1017/S002211206500152063.
Noack
,
B. R.
, 2022
,
private communication
.64.
Noack
,
B. R.
, 2016
, “
From Snapshots to Modal Expansions Ridging Low Residuals and Pure Frequencies
,” J. Fluid Mech.
,
802
, pp. 1
–4
.10.1017/jfm.2016.41665.
Li
,
H.
,
Fernex
,
D.
,
Semaan
,
R.
,
Tan
,
J.
,
Morzyński
,
M.
, and
Noack
,
B. R.
, 2021
, “
Cluster-Based Network Model
,” J. Fluid Mech.
,
906
, p. A21
.10.1017/jfm.2020.78566.
Blanchard
,
A. B.
,
Maceda
,
G. Y. C.
,
Fan
,
D.
,
Li
,
Y.
,
Zhou
,
Y.
,
Noack
,
B. R.
, and
Sapsis
,
T. P.
, 2021
, “
Bayesian Optimization for Active Flow Control
,” Acta Mech. Sin.
,
37
(12
), epub.10.1007/s10409-021-01149-067.
Riley
,
J. J.
, and
Metcalfe
,
R. W.
, 1980
, “
Direct Numerical Simulation of a Perturbed Turbulent Mixing Layer
,” AIAA
Paper No. 80-0274.10.1115/80-027468.
Riley
,
J. J.
,
Metcalfe
,
R. W.
, and
Orszag
,
S. A.
, 1986
, “
Direct Simulations of Chemically Reacting Turbulent Mixing Layers
,” Phys. Fluids
,
29
(2
), p. 406
.10.1063/1.86572469.
Ho
,
C.-M.
, and
Huerre
,
P.
, 1984
, “
Perturbed Free Shear Layers
,” Annu. Rev. Fluid Mech.
,
16
(1
), pp. 365
–424
.10.1146/annurev.fl.16.010184.00205370.
Metcalfe
,
R. W.
,
Orszag
,
S. A.
,
Brachet
,
M. E.
,
Menon
,
S.
, and
Riley
,
J. J.
, 1987
, “
Secondary Instability of a Temporally Growing Mixing Layer
,” J. Fluid Mech.
,
184
, pp. 207
–243
.10.1017/S002211208700286671.
Monkewitz
,
P. A.
, 1988
, “
Subharmonic Resonance, Pairing and Shredding in the Mixing Layer
,” J. Fluid Mech.
,
188
, pp. 223
–252
.10.1017/S002211208800071072.
Little
,
J. C.
, and
Kaul
,
U. K.
, 2015
, “
Mixing Layer: Numerical and Experimental Control Strategies
,” AIAA
Paper No. 2015-3343.10.1115/2015-334373.
Benard
,
N.
,
Pons-Prats
,
J.
,
Periaux
,
J.
,
Bugeda
,
G.
,
Bonnet
,
J. P.
, and
Moreau
,
E.
, 2015
, “
Multi-Input Genetic Algorithm for Experimental Optimization of the Reattachment Downstream of a Backward-Facing Step With Surface Plasma Actuator
,” AIAA
Paper No. 2015-2957.10.1115/2015-295774.
Benard
,
N.
,
Pons-Prats
,
J.
,
Periaux
,
J.
,
Bugeda
,
G.
,
Braud
,
P.
,
Bonnet
,
J. P.
, and
Moreau
,
E.
, 2016
, “
Turbulent Separated Shear Flow Control by Surface Plasma Actuator: Experimental Optimization by Genetic Algorithm Approach
,” Exp Fluids
,
57
(2
), p. 22
.10.1007/s00348-015-2107-375.
Kaul
,
U. K.
, 2009
, “
EDLFLOW: A Next-Generation High-Order High-Fidelity All-Speed Time-Accurate Flow Solver for Simulating Fluid Flows
,” NASA Ames Research Center, Moffett Field, CA, NASA Invention Disclosure, Report No. NASA-ARC-16349-1.76.
Kaul
,
U. K.
, June 2013
, “
Stability Enhanced High-Order Hyperviscosity-Based Shock Capturing Algorithm
,” AIAA J.
,
51
(6
), pp. 1516
–1521
.10.2514/1.J05170477.
Kaul
,
U. K.
, 2013
, “
A Stability-Enhanced High-Order Hyperviscosity-Based Shock-Capturing Algorithm
,” NASA Ames Research Center, Moffett Field, CA, Report No. NASA/SP-2013-216498.78.
Lele
,
S.
, 1992
, “
Compact Finite Difference Schemes With Spectral-Like Resolution
,” J. Comput. Phys
,
103
(1
), pp. 16
–42
.10.1016/0021-9991(92)90324-R79.
Gaitonde
,
D. V.
,
Shang
,
J. S.
, and
Young
,
J. L.
, 1999
, “
Practical Aspects of High-Order Accurate Finite Volume Schemes for Electrodynamics
,” AIAA
Paper No. 97-0363.10.1115/97-036380.
Bernard
,
P. S.
, July 2008
, “
Grid-Free Simulation of the Spatially Growing Turbulent Mixing Layer
,” AIAA J
,,
46
(7
), pp. 1725
–1737
.10.2514/1.3420581.
Yu
,
S. T.
,
Tsai
,
Y.-L. P.
, and
Hsieh
,
K. C.
, 1992
, “
Runge-Kutta Methods Combined With Compact Difference Schemes for the Unsteady Euler Equations
,” AIAA
Paper No. 92-3210.10.1115/92-321082.
Yu
,
S. T.
,
Hsieh
,
K. C.
, and
Tsai
,
Y.-L. P.
, 1995
, “
Simulating Waves in Flows by Runge-Kutta and Compact Difference Schemes
,” AIAA J.
,
33
(3
), epub.10.2514/3.1247083.
Yu
,
S. T.
,
Hultgren
,
L. S.
, and
Liu
,
N.-S.
, 1994
, “
Direct Calculations of Waves in Fluid Flows Using High-Order Compact Difference Scheme
,” AIAA J
,
32
(9
), epub.10.2514/6.1993-14884.
Jameson
,
A.
,
Schmidt
,
W.
, and
Turkel
,
E.
, 1981
, “
Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes
,” AIAA
Paper No. 81-1259.10.1115/81-125985.
Zohar
,
Y.
, and
Ho
,
C.-M.
, 1996
, “
Dissipation Scale and Control of Fine-Scale Turbulence in a Plane Mixing Layer
,” J. Fluid Mech.
,
320
, pp. 139
–161
.10.1017/S002211209600748386.
Fujiwara
,
T.
,
Taki
,
S.
, and
Arashi
,
K.
, 1986
, “
Numerical Analysis of a Reacting Flow in H2/O2 Rocket Combustor, Part 1: Analysis of Turbulent Shear Flow
,” AIAA
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