Hypersonic flight involves a variety of complex flow phenomena that directly impact the aerothermodynamic loading of high-speed vehicles. The turbulence encountered during a typical flight trajectory influences and interacts with the shock waves on and around the surface of a vehicle and its propulsion system, affecting both aerodynamic and power plant performance. These interactions can be studied by isolating a turbulent flow convected through a normal shock, commonly referred to as the canonical shock-turbulence interaction (STI) problem. Scale-resolving computational fluid dynamics (CFD) and linear interaction analysis (LIA) have been crucial in studying this problem and formulating scaling laws that explain the observed behavior. In this work, an extensive review of the theoretical (LIA) and numerical (CFD) work on the canonical STI is presented. The majority of the work conducted to date has focused on calorically perfect gases with constant heat capacities. However, in hypersonic flows, chemical and thermal non-equilibrium effects may alter the nature of the interaction. As a result, relevant LIA and CFD studies addressing high-enthalpy phenomena are also succinctly discussed.
REFERENCES
1.
J.
Longo
, K.
Hannemann
, and V.
Hannemann
, “The challenge of modeling high speed flows,” DLR Report
2
, 1
(2007
).2.
G.
Settles
and L.
Dodson
, “Supersonic and hypersonic shock/boundary-layer interaction database
,” AIAA J.
32
, 1377
(1994
).3.
V.
Theofilis
, S.
Pirozzoli
, and P.
Martin
, “Special issue on the fluid mechanics of hypersonic flight
,” Theor. Comput. Fluid Dyn.
36
, 1
(2022
).4.
H.
Olivier
and S.
Gu
, “Flow characterization and modeling of hypersonic wind tunnels
,” VKI Lecture Series, von Karman Institute for Fluid Dynamics STO-EN AVT-325-01, Sint-Genesius-Rode, Belgium (2018
).5.
S.
Gu
and H.
Olivier
, “Capabilities and limitations of existing hypersonic facilities
,” Prog. Aerosp. Sci.
113
, 100607
(2020
).6.
E.
Johnsen
, J.
Larsson
, A.
Bhagatwala
, W.
Cabot
, P.
Moin
, B.
Olson
, P. S.
Rawat
, S.
Shankar
, B.
Sjögreen
, H.
Yee
et al, “Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves
,” J. Comput. Phys.
229
, 1213
(2010
).7.
J.
Larsson
, S.
Lele
, and P.
Moin
, “Effect of numerical dissipation on the predicted spectra for compressible turbulence,” Annu. Res. Briefs
47
—57
(2007
).8.
M.
Di Renzo
, L.
Fu
, and J.
Urzay
, “HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics
,” Comput. Phys. Commun.
255
, 107262
(2020
).9.
M.
Di Renzo
and S.
Pirozzoli
, “HTR-1.2 solver: Hypersonic task-based research solver version 1.2
,” Comput. Phys. Commun.
261
, 107733
(2021
).10.
P.
Volpiani
, “Numerical strategy to perform direct numerical simulations of hypersonic shock/boundary-layer interaction in chemical nonequilibrium
,” Shock Waves
31
, 361
(2021
).11.
M.
Bernardini
, D.
Modesti
, F.
Salvadore
, S.
Sathyanarayana
, G.
Della Posta
, and S.
Pirozzoli
, “STREAmS-2.0: Supersonic turbulent accelerated Navier-Stokes solver version 2.0
,” Comput. Phys. Commun.
285
, 108644
(2023
).12.
S.
Sathyanarayana
, M.
Bernardini
, D.
Modesti
, S.
Pirozzoli
, and F.
Salvadore
, “High-speed turbulent flows towards the exascale: STREAmS-2 porting and performance
,” arXiv:2304.05494 (2023
).13.
F.
De Vanna
, F.
Avanzi
, M.
Cogo
, S.
Sandrin
, M.
Bettencourt
, F.
Picano
, and E.
Benini
, “URANOS: A GPU accelerated Navier-Stokes solver for compressible wall-bounded flows
,” Comput. Phys. Commun.
287
, 108717
(2023
).14.
F.
De Vanna
, M.
Bernardini
, F.
Picano
, and E.
Benini
, “Wall-modeled LES of shock-wave/boundary layer interaction
,” Int. J. Heat Fluid Flow
98
, 109071
(2022
).15.
D.
Passiatore
, L.
Sciacovelli
, P.
Cinnella
, and G.
Pascazio
, “Shock impingement on a transitional hypersonic high-enthalpy boundary layer,” Phys. Rev. Fluids
8
, 044601
(2023
).16.
G. D.
Posta
, M.
Blandino
, D.
Modesti
, F.
Salvadore
, and M.
Bernardini
, “Direct numerical simulation of supersonic boundary layers over a microramp: Effect of the Reynolds number,” J. Fluid Mech.
974
, A44
(2023
).17.
M.
Di Renzo
, C. T.
Williams
, and S.
Pirozzoli
, “Stagnation enthalpy effects on hypersonic turbulent compression corner flow at moderate Reynolds numbers,” Phys. Rev. Fluids
9
, 033401
(2024
).18.
M. D.
Renzo
and J.
Urzay
, “Direct numerical simulation of a hypersonic transitional boundary layer at suborbital enthalpies,” J. Fluid Mech.
912
, A29
(2021
).19.
J.
Larsson
, V.
Kumar
, N.
Oberoi
, M.
Di Renzo
, and S.
Pirozzoli
, “Large-eddy simulations of idealized shock/boundary-layer interactions with crossflow
,” AIAA J.
60
, 2767
(2022
).20.
S.
Zhang
, X.
Li
, J.
Zuo
, J.
Qin
, K.
Cheng
, Y.
Feng
, and W.
Bao
, “Research progress on active thermal protection for hypersonic vehicles
,” Prog. Aerosp. Sci.
119
, 100646
(2020
).21.
S.
Lee
, P.
Moin
, and S.
Lele
, “Interaction of isotropic turbulence with a shock wave
,” Technical Report
, Stanford University CA Department of Mechanical Engineering
, 1992
.22.
S.
Lee
, S.
Lele
, and P.
Moin
, “Direct numerical simulation of isotropic turbulence interacting with a weak shock wave
,” J. Fluid Mech.
251
, 533
(1993
).23.
S.
Lee
, “Large Eddy simulation of shock turbulence interaction,” Annual Research Briefs (Stanford University, 1993
).24.
V. K.
Veera
and K.
Sinha
, “Modeling the effect of upstream temperature fluctuations on shock/homogeneous turbulence interaction
,” Phys. Fluids
21
, 025101
(2009
).25.
K.
Sinha
, “Evolution of enstrophy in shock/homogeneous turbulence interaction
,” J. Fluid Mech.
707
, 74
(2012
).26.
R.
Quadros
and K.
Sinha
, “Modelling of turbulent energy flux in canonical shock-turbulence interaction
,” Int. J. Heat Fluid Flow
61
, 626
(2016
).27.
R.
Quadros
, K.
Sinha
, and J.
Larsson
, “Turbulent energy flux generated by shock/homogeneous-turbulence interaction,” J. Fluid Mech.
796
, 113
(2016
).28.
S.
Karl
, J.
Hickey
, and F.
Lacombe
, “Reynolds stress models for shock-turbulence interaction,” in Proceedings of the International Symposium on Shock Waves
(Springer
, 2017
), pp. 511
–517
.29.
J.
Vemula
and K.
Sinha
, “Reynolds stress models applied to canonical shock-turbulence interaction
,” J. Turbul.
18
, 653
(2017
).30.
S.
Roy
, U.
Pathak
, and K.
Sinha
, “Variable turbulent Prandtl number model for shock/boundary-layer interaction
,” AIAA J.
56
, 342
(2018
).31.
N.
Braun
, “An LES and RANS study of the canonical shock-turbulence interaction
,” Ph.D. thesis (California Institute of Technology
, 2018
).32.
S.
Roy
and K.
Sinha
, “Turbulent heat flux model for hypersonic shock–boundary layer interaction
,” AIAA J.
57
, 3624
(2019
).33.
J.
Vemula
and K.
Sinha
, “Explicit algebraic Reynolds stress model for shock-dominated flows
,” Int. J. Heat Fluid Flow
85
, 108680
(2020
).34.
F.
Lacombe
, S.
Roy
, K.
Sinha
, S.
Karl
, and J.
Hickey
, “Characteristic scales in shock–turbulence interaction
,” AIAA J.
59
, 526
(2021
).35.
S.
Jamme
, J.-B.
Cazalbou
, F.
Torres
, and P.
Chassaing
, “Direct numerical simulation of the interaction between a shock wave and various types of isotropic turbulence,” Flow Turbul. Combust.
68
, 227
(2002
).36.
N.
Grube
, E.
Taylor
, and P.
Martin
, “Numerical investigation of shock-wave/isotropic turbulence interaction,” in Proceedings of the 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
(AIAA, 2011
), p. 480
.37.
J.
Larsson
, I.
Bermejo-Moreno
, and S.
Lele
, “Reynolds- and Mach-number effects in canonical shock–turbulence interaction
,” J. Fluid Mech.
717
, 293
(2013
).38.
L.
Kovasznay
, “Turbulence in supersonic flow
,” J. Aeronaut. Sci.
20
, 657
(1953
).39.
H.
Ribner
, NACA Report No. 1164, 1954
.40.
H.
Ribner
, “Shock-turbulence interaction and the generation of noise
,” Technical Report, National Aeronautics and Space Administration, Cleveland OH Lewis Research Center
, 1955
.41.
F.
Moore
, Unsteady Oblique Interaction of a Shock Wave with a Plane Disturbance
(National Advisory Committee for Aeronautics
, 1953
), Vol. 1165
.42.
C.-T.
Chang
, “Interaction of a plane shock and oblique plane disturbances with special reference to entropy waves
,” J. Aeronaut. Sci.
24
, 675
(1957
).43.
S.
Lele
, “Shock-jump relations in a turbulent flow
,” Phys. Fluids A: Fluid Dyn.
4
, 2900
(1992a
).44.
C.
Cambon
, G.
Coleman
, and N.
Mansour
, “Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number
,” J. Fluid Mech.
257
, 641
(1993
).45.
L.
Jacquin
, C.
Cambon
, and E.
Blin
, “Turbulence amplification by a shock wave and rapid distortion theory
,” Phys. Fluids A: Fluid Dyn.
5
, 2539
(1993
).46.
J.
Larsson
and S.
Lele
, “Direct numerical simulation of canonical shock/turbulence interaction,” Phys. Fluids
21
, 126101
(2009
).47.
C.
Huete
, A.
Cuadra
, M.
Vera
, and J.
Urzay
, “Thermochemical effects on hypersonic shock waves interacting with weak turbulence,” Phys. Fluids
33
, 086111
(2021
).48.
T.
Jackson
, M.
Hussaini
, and H.
Ribner
, “Interaction of turbulence with a detonation wave
,” Phys. Fluids A: Fluid Dyn.
5
, 745
(1993
).49.
C.
Huete
, A. L.
Sánchez
, and F. A.
Williams
, “Theory of interactions of thin strong detonations with turbulent gases,” Phys. Fluids
25
, 076105
(2013
).50.
A.
Cuadra
, C.
Huete
, and M.
Vera
, “Effect of equivalence ratio fluctuations on planar detonation discontinuities
,” J. Fluid Mech.
903
, A30
(2020
).51.
T.
Jin
, K.
Luo
, Q.
Dai
, and J.
Fan
, “Simulations of cellular detonation interaction with turbulent flows
,” AIAA J.
54
, 419
(2016
).52.
C.
Huete
, T.
Jin
, D.
Martínez-Ruiz
, and K.
Luo
, “Interaction of a planar reacting shock wave with an isotropic turbulent vorticity field,” Phys. Rev. E
96
, 053104
(2017
).53.
K.
Iwata
, S.
Suzuki
, R.
Kai
, and R.
Kurose
, “Direct numerical simulation of detonation–turbulence interaction in hydrogen/oxygen/argon mixtures with a detailed chemistry
,” Phys. Fluids
35
, 046107
(2023
).54.
S.
Suzuki
, K.
Iwata
, R.
Kai
, and R.
Kurose
, “A DNS study of detonation in H2/O2 mixture with variable-intensity turbulences,” Proc. Combust. Inst.
40
, 105337
(2024
).55.
A.
Cuadra
, M.
Vera
, M.
Di Renzo
, and C.
Huete
, “Linear theory of hypersonic shocks interacting with turbulence in air,” in AIAA SciTech 2023 Forum, AIAA, paper 2023-0075 (2023
).56.
A.
Cuadra
, C. T.
Williams
, M.
Di Renzo
, and C.
Huete
, “Compressibility and vibrational-excitation effects in hypersonic shock-turbulence interaction
,” Technical Report, Summer Program Proceedings, Center for Turbulence Research, Stanford University
, 2024
.57.
A.
Cuadra
, C.
Huete
, and M.
Vera
, “Combustion Toolbox: An open-source thermochemical code for gas- and condensed-phase problems involving chemical equilibrium
,” arXiv:2409.15086 (2024b
).58.
G. V.
Candler
, “Rate effects in hypersonic flows
,” Annu. Rev. Fluid Mech.
51
, 379
(2019
).59.
60.
S.
Ghosh
and P. P.
Kerkar
, “Non-equilibrium effects on DNS of hypersonic shock/turbulence interaction,” in AIAA SCITECH 2022 Forum (2022
), p. 2015
.61.
C.
Williams
, M.
Di Renzo
, and P.
Moin
, “Computational framework for direct numerical simulation of shock-turbulence interaction in thermochemical nonequilibrium
,” Technical Report, Annual Research Briefs, Center for Turbulence Research
, 2022
.62.
C.
Williams
, M.
Di Renzo
, J.
Urzay
, and P.
Moin
, “Navier-Stokes characteristic boundary conditions for high-enthalpy compressible flows in thermochemical non-equilibrium
,” J. Comput. Phys.
509
, 113040
(2024
).63.
D.
Donzis
, “Amplification factors in shock-turbulence interactions: Effect of shock thickness,” Phys. Fluids
24
, 011705
(2012a
).64.
D.
Donzis
, “Shock structure in shock-turbulence interactions,” Phys. Fluids
24
, 126101
(2012b
).65.
B. J.
McBride
, NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species
(National Aeronautics and Space Administration, John H. Glenn Research Center
, 2002
).66.
A.
Cuadra
, C.
Huete
, and M.
Vera
, “Combustion Toolbox: A MATLAB-GUI based open-source tool for solving gaseous combustion problems
,” version 1.1.0. (2024c
).67.
A.
Cuadra
, Development of a wide-spectrum thermochemical code with application to planar reacting and non-reacting shocks
, Ph.D. thesis (Universidad Carlos III de Madrid
, 2023
).68.
69.
M. R.
Petersen
and D.
Livescu
, “Forcing for statistically stationary compressible isotropic turbulence,” Phys. Fluids
22
, 116101
(2010
).70.
B.
Bottin
, “Thermodynamic properties of arbitrary perfect gas mixtures at low pressures and high temperatures
,” Prog. Aerosp. Sci.
36
, 547
(2000
).71.
O.
Askari
, “Thermodynamic properties of pure and mixed thermal plasmas over a wide range of temperature and pressure,” J. Energy Res. Technol.
140
, 032202
(2018
).72.
K.
Mahesh
, S.
Lele
, and P.
Moin
, “The influence of entropy fluctuations on the interaction of turbulence with a shock wave
,” J. Fluid Mech.
334
, 353
(1997
).73.
C.
Huete
, J.
Wouchuk
, and A.
Velikovich
, “Analytical linear theory for the interaction of a planar shock wave with a two-or three-dimensional random isotropic acoustic wave field,” Phys. Rev. E
85
, 026312
(2012
).74.
M.
Smart
, “Scramjets
,” Aeronaut. J.
111
, 605
(2007
).75.
M.
Di Renzo
, “HTR-1.3 solver: Predicting electrified combustion using the hypersonic task-based research solver
,” Comput. Phys. Commun.
272
, 108247
(2022
).76.
C.
Williams
, M.
Di Renzo
, and J.
Urzay
, “Two-temperature extension of the HTR solver for hypersonic turbulent flows in thermochemical nonequilibrium
,” Technical Report, Center for Turbulence Research Annual Research Briefs
, 2021
.77.
T. J.
Poinsot
and S. K.
Lele
, “Boundary conditions for direct simulations of compressible viscous flows
,” J. Comput. Phys.
101
, 104
(1992
).78.
M.
Cavcar
, “The international standard atmosphere (ISA),” Anadolu Univ., Turkey
30
, 1
(2000
).79.
S.
Pirozzoli
, “Numerical methods for high-speed flows
,” Annu. Rev. Fluid Mech.
43
, 163
(2011a
).80.
P.
Moin
and K.
Mahesh
, “Direct numerical simulation: A tool in turbulence research
,” Annu. Rev. Fluid Mech.
30
, 539
(1998
).81.
A.
Harten
, B.
Engquist
, S.
Osher
, and S. R.
Chakravarthy
, “Uniformly high order accurate essentially non-oscillatory schemes, III
,” J. Comput. Phys.
131
, 3
(1997
).82.
G.-S.
Jiang
and C.-W.
Shu
, “Efficient implementation of weighted ENO Schemes
,” J. Comput. Phys.
126
, 202
(1996
).83.
L.
Fu
, X. Y.
Hu
, and N. A.
Adams
, “A family of high-order targeted ENO schemes for compressible-fluid simulations
,” J. Comput. Phys.
305
, 333
(2016
).84.
S.
Lee
, S.
Lele
, and P.
Moin
, “Interaction of isotropic turbulence with shock waves: Effect of shock strength
,” J. Fluid Mech.
340
, 225
(1997
).85.
G.-Y.
Zhao
, M.-B.
Sun
, and S.
Pirozzoli
, “On shock sensors for hybrid compact/WENO schemes
,” Computers Fluids
199
, 104439
(2020
).86.
J.
von Neumann
and R. D.
Richtmyer
, “A method for the numerical calculation of hydrodynamic shocks
,” J. Appl. Phys.
21
, 232
(1950
).87.
A.
Jameson
, W.
Schmidt
, and E.
Turkel
, “Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes,” in Proceedings of the 14th Fluid and Plasma Dynamics Conference
(1981
), p. 1259
.88.
A. W.
Cook
, “Artificial fluid properties for large-eddy simulation of compressible turbulent mixing,” Phys. Fluids
19
, 055103
(2007
).89.
A.
Mani
, J.
Larsson
, and P.
Moin
, “Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks
,” J. Comput. Phys.
228
, 7368
(2009
).90.
M.
Onofri
and R.
Paciorri
, Shock Fitting: Classical Techniques, Recent Developments, and Memoirs of Gino Moretti
(Springer
, 2017
).91.
J.
Sesterhenn
, J.
Dohogne
, and R.
Friedrich
, “Direct numerical simulation of the interaction of isotropic turbulence with a shock wave using shock-fitting,” C. R. Méc.
333
, 87
(2005
).92.
P.
Rawat
and X.
Zhong
, “Numerical simulation of shock-turbulence interactions using high-order shock-fitting algorithms,” in Proceedings of the 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
(AIAA, 2010
), p. 114
.93.
P.
Rawat
and X.
Zhong
, “Direct numerical simulations of turbulent flow interactions with strong shocks using shock-fitting method,” in Proceedings of the 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
(AIAA, 2011
), p. 649
.94.
X.
Wang
and X.
Zhwang
, “Effect of compressibility on strong shock and turbulence interactions,”in Proceedings of the AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
(AIAA, 2012
), p. 1243
.95.
S.
Pirozzoli
, “Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates
,” J. Comput. Phys.
230
, 2997
(2011b
).96.
C. A.
Kennedy
and A.
Gruber
, “Reduced aliasing formulations of the convective terms within the Navier–Stokes equations for a compressible fluid
,” J. Comput. Phys.
227
, 1676
(2008
).97.
S. K.
Lele
, “Compact finite difference schemes with spectral-like resolution
,” J. Comput. Phys.
103
, 16
(1992b
).98.
F.
Ducros
, V.
Ferrand
, F.
Nicoud
, C.
Weber
, D.
Darracq
, C.
Gacherieu
, and T.
Poinsot
, “Large-eddy simulation of the shock/turbulence interaction
,” J. Comput. Phys.
152
, 517
(1999
).99.
S.
Hickel
, C.
Egerer
, and J.
Larsson
, “Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction,” Phys. Fluids
26
, 106101
(2014
).100.
J.
Hoste
, “Assessment of scale resolving turbulence models in the TAU code for canonical shock-turbulence interaction
,” Technical Report DLR-FB-2020-28.169S
(DLR, 2023
).101.
C.
Wang
and C.-W.
Shu
, “An interface treating technique for compressible multi-medium flow with Runge–Kutta discontinuous Galerkin method
,” J. Comput. Phys.
229
, 8823
(2010
).102.
D. S.
Hoskin
, R. L.
Van Heyningen
, N. C.
Nguyen
, J.
Vila-Pérez
, W. L.
Harris
, and J.
Peraire
, “Discontinuous Galerkin methods for hypersonic flows
,” Prog. Aerosp. Sci.
146
, 100999
(2024
).103.
F. M.
D'Afiero
, M.
Mihaescu
, and A.
Hanifi
, “Very-low-dissipation, physics-based, and parameter-free shock capturing for discontinuous Galerkin methods,” Phys. Fluids
36
, 126115
(2024
).104.
N.
Grube
and M.
Martín
, “Compressibility effects on Reynolds stress amplification and shock structure in shock--isotropic turbulence interactions,” J. Fluid Mech.
958
, A1
(2023
).105.
X.
Gao
, I.
Bermejo-Moreno
, and J.
Larsson
, “Parametric numerical study of passive scalar mixing in shock turbulence interaction
,” J. Fluid Mech.
895
, A21
(2020
).106.
A.
Kusuhata
, K.
Tanaka
, T.
Watanabe
, K.
Nagata
, and A.
Sasoh
, “Local geometry of a weak normal shock wave interacting with turbulence,” Phys. Fluids
35
, 086110
(2023
).107.
K.
Tanaka
, T.
Watanabe
, K.
Nagata
, A.
Sasoh
, Y.
Sakai
, and T.
Hayase
, “Amplification and attenuation of shock wave strength caused by homogeneous isotropic turbulence
,” Phys. Fluids
30
, 035105
(2018
).108.
K.
Tanaka
, T.
Watanabe
, and K.
Nagata
, “Statistical analysis of deformation of a shock wave propagating in a local turbulent region
,” Phys. Fluids
32
, 096107
(2020
).109.
C.
Chen
and D.
Donzis
, “Shock–turbulence interactions at high turbulence intensities
,” J. Fluid Mech.
870
, 813
(2019
).110.
C.
Chen
and D.
Donzis
, “Amplification of transverse Reynolds stresses in shock–turbulence interactions
,” AIAA J.
60
, 6235
(2022
).111.
J.
Ryu
and D.
Livescu
, “Turbulence structure behind the shock in canonical shock–vortical turbulence interaction,” J. Fluid Mech.
756
, R1
(2014
).112.
D.
Livescu
and J.
Ryu
, “Vorticity dynamics after the shock–turbulence interaction
,” Shock Waves
26
, 241
(2016
).113.
D.
Livescu
and Z.
Li
, “Subgrid-scale backscatter after the shock-turbulence interaction,” AIP Conf. Proc.
1793
, 150009
(2017
). 114.
I.
Bermejo-Moreno
, “Subgrid-scale modeling of shock-turbulence interaction for large-eddy simulations,” Center Turbul. Res. Annu. Res. Briefs
247
(2009
).115.
M.
Pino Martín
, U.
Piomelli
, and G. V.
Candler
, “Subgrid-scale models for compressible large-eddy simulations
,” Theor. Comput. Fluid Dyn.
13
, 361
(2000
).116.
B.
Vreman
, B.
Geurts
, and H.
Kuerten
, “Subgrid-modelling in LES of compressible flow
,” Appl. Sci. Res.
54
, 191
(1995
).117.
A.
Saghafian
, High-Fidelity Simulations and Modeling of Compressible Reacting Flows
(Stanford University
, 2014
).118.
E.
Garnier
, P.
Sagaut
, and M.
Deville
, “Large eddy simulation of shock/homogeneous turbulence interaction
,” Comput. Fluids
31
, 245
(2002
).119.
M.
Germano
, U.
Piomelli
, P.
Moin
, and W.
Cabot
, “A dynamic subgrid-scale eddy viscosity model
,” Phys. Fluids A: Fluid Dyn.
3
, 1760
(1991
).120.
P.
Moin
, K.
Squires
, W.
Cabot
, and S.
Lee
, “A dynamic subgrid-scale model for compressible turbulence and scalar transport
,” Phys. Fluids A: Fluid Dyn.
3
, 2746
(1991
).121.
I.
Bermejo-Moreno
, J.
Larsson
, and S.
Lele
, “LES of canonical shock-turbulence interaction,” Annu. Res. Briefs
209
(2010
).122.
N.
Braun
, D.
Pullin
, and D.
Meiron
, “Large eddy simulation investigation of the canonical shock–turbulence interaction
,” J. Fluid Mech.
858
, 500
(2019
).123.
N.
Braun
, D.
Pullin
, and D. I.
Meiron
, “Regularization method for large eddy simulations of shock-turbulence interactions
,” J. Comput. Phys.
361
, 231
(2018
).124.
G.
Erlebacher
, M. Y.
Hussaini
, C. G.
Speziale
, and T.
Zang
, “Toward the large-eddy simulation of compressible turbulent flows,” ICASE Report No. 90-76 (NASA Langley Research Center, 1990
).125.
C. G.
Speziale
, G.
Erlebacher
, T.
Zang
, and M.
Hussaini
, “On the subgrid-scale modeling of compressible turbulence
,” Tech. Rep. (1987
).126.
M. P.
Martın
and G. V.
Candler
, “Subgrid-scale model for the temperature fluctuations in reacting hypersonic turbulent flows
,” Phys. Fluids
11
, 2765
(1999
).127.
C.
Williams
, “Subgrid-scale modeling of turbulence-chemistry interaction for hypersonic boundary layers in chemical nonequilibrium
,” Technical Report, Annual Research Briefs, Center for Turbulence Research, Stanford University
, 2023
.128.
Y.
Tian
, F.
Jaberi
, Z.
Li
, and D.
Livescu
, “Numerical study of variable density turbulence interaction with a normal shock wave
,” J. Fluid Mech.
829
, 551
(2017
).129.
R.
Boukharfane
, Z.
Bouali
, and A.
Mura
, “Evolution of scalar and velocity dynamics in planar shock-turbulence interaction
,” Shock Waves
28
, 1117
(2018
).130.
X.
Gao
, “Direct numerical simulation of mixing and combustion under canonical shock turbulence interaction
,” Ph.D. thesis (University of Southern California
, 2020
).131.
P.
Dimotakis
, “The mixing transition in turbulent flows
,” J. Fluid Mech.
409
, 69
(2000
).132.
B.
McManamen
, D.
Donzis
, S.
North
, and R.
Bowersox
, “Velocity and temperature fluctuations in a high-speed shock–turbulence interaction,” J. Fluid Mech.
913
, A10
(2021
).133.
Y.
Sethuraman
and K.
Sinha
, “Modeling of thermodynamic fluctuations in canonical shock–turbulence interaction
,” AIAA J.
58
, 3076
(2020
).134.
C.
Huete
, A. L.
Sánchez
, and F. A.
Williams
, “Linear theory for the interaction of small-scale turbulence with overdriven detonations,” Phys. Fluids
26
, 116101
(2014
).© 2025 Author(s). Published under an exclusive license by AIP Publishing.
2025
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