Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T17:15:34.820Z Has data issue: false hasContentIssue false
  • English
  • Français

Large eddy simulation investigation of the canonical shock–turbulence interaction

Published online by Cambridge University Press:  06 November 2018

N. O. Braun Open the ORCID record for N. O. Braun [Opens in a new window] ,
D. I. Pullin  and
D. I. Meiron
N. O. Braun*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, MC 105-50 Caltech, Pasadena, CA 91125, USA
D. I. Pullin
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, MC 105-50 Caltech, Pasadena, CA 91125, USA
D. I. Meiron
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, MC 105-50 Caltech, Pasadena, CA 91125, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

High resolution large eddy simulations (LES) are performed to study the interaction of a stationary shock with fully developed turbulent flow. Turbulent statistics downstream of the interaction are provided for a range of weakly compressible upstream turbulent Mach numbers $M_{t}=0.03{-}0.18$, shock Mach numbers $M_{s}=1.2{-}3.0$ and Taylor-based Reynolds numbers $Re_{\unicode[STIX]{x1D706}}=20{-}2500$. The LES displays minimal Reynolds number effects once an inertial range has developed for $Re_{\unicode[STIX]{x1D706}}>100$. The inertial range scales of the turbulence are shown to quickly return to isotropy, and downstream of sufficiently strong shocks this process generates a net transfer of energy from transverse into streamwise velocity fluctuations. The streamwise shock displacements are shown to approximately follow a $k^{-11/3}$ decay with wavenumber as predicted by linear analysis. In conjunction with other statistics this suggests that the instantaneous interaction of the shock with the upstream turbulence proceeds in an approximately linear manner, but nonlinear effects immediately downstream of the shock significantly modify the flow even at the lowest considered turbulent Mach numbers.

JFM classification

Turbulent Flows: Compressible turbulence Compressible Flows: Shock waves Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 500 - 535
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Agui, J. H., Briassulis, G. & Andreopoulos, Y. 2005 Studies of interactions of a propagating shock wave with decaying grid turbulence: velocity and vorticity fields. J. Fluid Mech. 524, 143–195.Google Scholar
Barre, S., Alem, D. & Bonnet, J. P. 1996 Experimental study of a normal shock/homogeneous turbulence interaction. AIAA J. 34 (5), 968–974.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bermejo-Moreno, I., Larsson, J. & Lele, S. K. 2010 LES of canonical shock-turbulence interaction. In Annual Research Briefs, pp. 209–222. Stanford University.Google Scholar
Blaisdell, G. A.1991 Numerical simulation of compressible homogeneous turbulence. PhD thesis, Stanford University.Google Scholar
Braun, N. O., Pullin, D. I. & Meiron, D. I. 2018 Regularization method for large eddy simulations of shock-turbulence interactions. J. Comput. Phys. 361, 231–246.Google Scholar
Chang, C.-T. 1957 Interaction of a plane shock and oblique plane disturbances with special reference to entropy waves. J. Aero. Sci. 24 (9), 675–682.Google Scholar
Chung, D. & Pullin, D. I. 2010 Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence. J. Fluid Mech. 643, 279–308.Google Scholar
Chung, D. & Pullin, D. I. 2009 Large-eddy simulation and wall modelling of turbulent channel flow. J. Fluid Mech. 631, 281–309.Google Scholar
Deiterding, R., Radovitzky, R., Mauch, S. P., Noels, L., Cummings, J. C. & Meiron, D. I. 2006 A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading. Engng Comput. 22 (3–4), 325–347.Google Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.Google Scholar
Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C. & Poinsot, T. 1999 Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys. 152 (2), 517–549.Google Scholar
Freund, J. B. 1997 Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound. AIAA J. 35 (4), 740–742.Google Scholar
Garnier, E., Sagaut, P. & Deville, M. 2002 Large eddy simulation of shock/homogeneous turbulence interaction. Comput. Fluids 31 (2), 245–268.Google Scholar
Ghosal, S., Lund, T. S., Moin, P. & Akselvoll, K. 1995 A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluid Mech. 286, 229–255.Google Scholar
Hickel, S., Egerer, C. P. & Larsson, J. 2014 Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction. Phys. Fluids 26 (10), 106101.Google Scholar
Hill, D. J., Pantano, C. & Pullin, D. I. 2006 Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock. J. Fluid Mech. 557, 29–61.Google Scholar
Hill, D. J. & Pullin, D. I. 2004 Hybrid tuned center-difference-WENO method for large eddy simulations in the presence of strong shocks. J. Comput. Phys. 194 (2), 435–450.Google Scholar
Honein, A. E. & Moin, P. 2004 Higher entropy conservation and numerical stability of compressible turbulence simulations. J. Comput. Phys. 201 (2), 531–545.Google Scholar
Jacquin, L., Cambon, C. & Blin, E. 1993 Turbulence amplification by a shock wave and rapid distortion theory. Phys. Fluids A 5 (10), 2539–2550.Google Scholar
Jamme, S., Cazalbou, J.-B., Torres, F. & Chassaing, P. 2002 Direct numerical simulation of the interaction between a shock wave and various types of isotropic turbulence. Flow Turbul. Combust. 68 (3), 227–268.Google Scholar
Kitamura, T., Nagata, K., Sakai, Y., Sasoh, A. & Ito, Y. 2017 Changes in divergence-free grid turbulence interacting with a weak spherical shock wave. Phys. Fluids 29 (6), 065114.Google Scholar
Kosović, B., Pullin, D. I. & Samtaney, R. 2002 Subgrid-scale modeling for large-eddy simulations of compressible turbulence. Phys. Fluids 14 (4), 1511–1522.Google Scholar
Kovasznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aero. Sci. 20 (10), 657–674.Google Scholar
Larsson, J., Bermejo-Moreno, I. & Lele, S. K. 2013 Reynolds-and Mach-number effects in canonical shock–turbulence interaction. J. Fluid Mech. 717, 293–321.Google Scholar
Larsson, J. & Lele, S. K. 2009 Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids 21 (12).Google Scholar
Lee, S. 1992 Large eddy simulation of shock turbulence interaction. In Annual Research Briefs, pp. 73–84. Stanford University.Google Scholar
Lee, S., Lele, S. K. & Moin, P. 1993 Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 251, 533–562.Google Scholar
Lee, S., Lele, S. K. & Moin, P. 1997 Interaction of isotropic turbulence with shock waves: effect of shock strength. J. Fluid Mech. 340, 225–247.Google Scholar
Lele, S. K. 1992 Shock-jump relations in a turbulent flow. Phys. Fluids A 4 (12), 2900–2905.Google Scholar
Liu, X.-D., Osher, S. & Chan, T. 1994 Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115 (1), 200–212.Google Scholar
Livescu, D. L. & Li, Z. 2017 Subgrid-scale backscatter after the shock-turbulence interaction. AIP Conference Proceedings, vol. 1793, p. 150009. AIP Publishing.Google Scholar
Livescu, D. & Ristorcelli, J. R. 2008 Variable-density mixing in buoyancy-driven turbulence. J. Fluid Mech. 605, 145–180.Google Scholar
Livescu, D., Ristorcelli, J. R., Gore, R. A., Dean, S. H., Cabot, W. H. & Cook, A. W. 2009 High-Reynolds number Rayleigh–Taylor turbulence. J. Turbul. 10, N13.Google Scholar
Livescu, D. & Ryu, J. 2016 Vorticity dynamics after the shock–turbulence interaction. Shock Waves 26 (3), 241–251.Google Scholar
Lombardini, M.2008 Richtmyer-meshkov instability in converging geometries. PhD thesis, California Institute of Technology.Google Scholar
Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25 (12), 2193–2203.Google Scholar
Mahesh, K.1996 The interaction of a shock wave with a turbulent shear flow. PhD thesis, Stanford University.Google Scholar
Mahesh, K., Lele, S. K. & Moin, P. 1997 The influence of entropy fluctuations on the interaction of turbulence with a shock wave. J. Fluid Mech. 334, 353–379.Google Scholar
Misra, A. & Pullin, D. I. 1997 A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9 (8), 2443–2454.Google Scholar
Moore, F. K.1954 Unsteady oblique interaction of a shock wave with a plane disturbance. NACA Tech. Note TN-2879.Google Scholar
Petersen, M. R. & Livescu, D. 2010 Forcing for statistically stationary compressible isotropic turbulence. Phys. Fluids 22 (11).Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Pullin, D. I. & Saffman, P. G. 1994 Reynolds stresses and one-dimensional spectra for a vortex model of homogeneous anisotropic turbulence. Phys. Fluids 6 (5), 1787–1796.Google Scholar
Ribner, H. S.1953 Convection of a pattern of vorticity through a shock wave. NACA Tech. Note TN-2864.Google Scholar
Ribner, H. S.1954 Shock-turbulence interaction and the generation of noise. NACA Tech. Note TN-3255.Google Scholar
Ribner, H. S. 1986a Spectra of noise and amplified turbulence emanating from shock-turbulence interaction. AIAA J. 25 (3), 436–442.Google Scholar
Ribner, H. S.1986b Spectra of noise and amplified turbulence emanating from shock-turbulence interaction: Two scenarios. Tech. Rep. University of Toronto.Google Scholar
Ryu, J. & Livescu, D. 2014 Turbulence structure behind the shock in canonical shock–vortical turbulence interaction. J. Fluid Mech. 756, R1.Google Scholar
Samtaney, R., Pullin, D. I. & Kosovic, B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13 (5), 1415–1430.Google Scholar
Schwarzkopf, J. D., Livescu, D., Baltzer, J. R., Gore, R. A. & Ristorcelli, J. R. 2016 A two-length scale turbulence model for single-phase multi-fluid mixing. Flow Turbul. Combust. 96 (1), 1–43.Google Scholar
Schwarzkopf, J. D., Livescu, D., Gore, R. A., Rauenzahn, R. M. & Ristorcelli, J. R. 2011 Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids. J. Turbul. (12), N49.Google Scholar
Sinha, K., Mahesh, K. & Candler, G. V. 2003 Modeling shock unsteadiness in shock/turbulence interaction. Phys. Fluids 15 (8), 2290–2297.Google Scholar
Tian, Y., Jaberi, F. A., Li, Z. & Livescu, D. 2017 Numerical study of variable density turbulence interaction with a normal shock wave. J. Fluid Mech. 829, 551–588.Google Scholar
Towns, J., Cockerill, T., Dahan, M. L., Foster, I., Gaither, K., Grimshaw, A., Hazlewood, V., Lathrop, S., Lifka, D., Peterson, G. D., Roskies, R., Scott, J. R. & Wilkins-Diehr, N. 2014 XSEDE: accelerating scientific discovery. Comput. Sci. Engng 16 (5), 62–74.Google Scholar
Voelkl, T., Pullin, D. I. & Chan, D. C. 2000 A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation. Phys. Fluids 12 (7).Google Scholar
Wouchuk, J. G., Huete Ruiz de Lira, C. & Velikovich, A. L. 2009 Analytical linear theory for the interaction of a planar shock wave with an isotropic turbulent vorticity field. Phys. Rev. E 79, 066315.Google Scholar
Zank, G. P., Zhou, Y., Matthaeus, W. H. & Rice, W. K. M. 2002 The interaction of turbulence with shock waves: a basic model. Phys. Fluids 14 (11), 3766–3774.Google Scholar