Hostname: page-component-7c8c6479df-24hb2 Total loading time: 0 Render date: 2024-03-19T04:42:56.378Z Has data issue: false hasContentIssue false

Subgrid effects on the filtered velocity gradient dynamics in compressible turbulence

Published online by Cambridge University Press:  06 April 2020

Jia-Long Yu
Affiliation:
Department of Modern Mechanics, CAS Center for Excellence in Complex System Mechanics, University of Science and Technology of China, Hefei, Anhui230026, PR China
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, CAS Center for Excellence in Complex System Mechanics, University of Science and Technology of China, Hefei, Anhui230026, PR China State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
Email address for correspondence: xlu@ustc.edu.cn

Abstract

The subgrid effects on the dynamics of the filtered velocity gradient tensor (VGT) in compressible turbulence are studied by means of statistical analysis of the invariants of the filtered VGT in compressible mixing layers. The evolution of the filtered VGT is determined by the interaction among the invariants, the pressure effects, the viscous effects and the subgrid effects. Based on the probability fluxes in the plane of the second ($Q$) and the third ($R$) invariants of the filtered VGT, it is found that the flux for the subgrid effect term changes most with the dilatation compared to the other terms. Further, a Schur decomposition of the filtered VGT into its normal part and non-normal part, which represent the local effect and the non-local effect of the flow dynamics, respectively, is used to deal with their effects of the velocity gradient. It is revealed that the compressibility is mainly related to the normal effect while the behaviour of the subgrid-scale (SGS) energy dissipation is mainly associated with the non-normal effect. A backscattering region of the SGS energy dissipation in the $Q$$R$ plane is identified in the locally expanded regions, which is determined by the non-normal effect. Further, an SGS model with the non-local effect is proposed to give a better prediction of the SGS energy dissipation.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by 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

Andreopoulos, Y. & Honkan, A. 2001 An experimental study of the dissipative and vortical motion in turbulent boundary layers. J. Fluid Mech. 439, 131163.CrossRefGoogle Scholar
Atkinson, C., Chumakov, S., Bermejo-Moreno, I. & Soria, J. 2012 Lagrangian evolution of the invariants of the velocity gradient tensor in a turbulent boundary layer. Phys. Fluids 24, 105104.CrossRefGoogle Scholar
Bechlars, P. & Sandberg, R. D. 2017a Evolution of the velocity gradient tensor invariant dynamics in a turbulent boundary layer. J. Fluid Mech. 815, 223242.CrossRefGoogle Scholar
Bechlars, P. & Sandberg, R. D. 2017b Variation of enstrophy production and strain rotation relation in a turbulent boundary layer. J. Fluid Mech. 812, 321348.CrossRefGoogle Scholar
Blackburn, H. M., Mansour, N. N. & Cantwell, B. J. 1996 Topology of fine-scale motions in turbulent channel flow. J. Fluid Mech. 310, 269292.CrossRefGoogle Scholar
Borue, V. & Orszag, S. A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 131.CrossRefGoogle Scholar
van der Bos, F., Tao, B., Meneveau, C. & Katz, J. 2002 Effects of small-scale turbulent motions on the filtered velocity gradient tensor as deduced from holographic particle image velocimetry measurements. Phys. Fluids 14, 24562474.CrossRefGoogle Scholar
Buxton, O. R. H. & Ganapathisubramani, B. 2010 Amplification of enstrophy in the far field of an axisymmetric turbulent jet. J. Fluid Mech. 651, 483502.CrossRefGoogle Scholar
Cantwell, B. J. 1992 Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids A 4, 782793.CrossRefGoogle Scholar
Chacin, J. M. & Cantwell, B. J. 2000 Dynamics of a low Reynolds number turbulent boundary layer. J. Fluid Mech. 404, 87115.CrossRefGoogle Scholar
Chertkov, M., Pumir, A. & Shraiman, B. I. 1999 Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11, 23942410.CrossRefGoogle Scholar
Chevillard, L., Meneveau, C., Biferale, L. & Toschi, F. 2008 Modeling the pressure Hessian and viscous Laplacian in turbulence: comparisons with direct numerical simulation and implications on velocity gradient dynamics. Phys. Fluids 20, 101504.CrossRefGoogle Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765777.CrossRefGoogle Scholar
Chong, M. S., Soria, J., Perry, A. E., Chacin, J., Cantwell, B. J. & Na, Y. 1998 Turbulence structures of wall-bounded shear flows found using DNS data. J. Fluid Mech. 357, 225247.CrossRefGoogle Scholar
Chu, Y. B. & Lu, X. Y. 2013 Topological evolution in compressible turbulent boundary layers. J. Fluid Mech. 733, 414438.CrossRefGoogle Scholar
Danish, M. & Meneveau, C. 2018 Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence. Phys. Rev. Fluids 3, 044604.CrossRefGoogle Scholar
Dhamankar, N. S., Blaisdell, G. A. & Lyrintzis, A. S. 2017 Overview of turbulent inflow boundary conditions for large-eddy simulations. AIAA J. 56, 13171334.CrossRefGoogle Scholar
Elsinga, G. E. & Marusic, I. 2010 Evolution and lifetimes of flow topology in a turbulent boundary layer. Phys. Fluids 22, 015102.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 17601765.CrossRefGoogle Scholar
Gomes-Fernandes, R., Ganapathisubramani, B. & Vassilicos, J. C. 2014 Evolution of the velocity-gradient tensor in a spatially developing turbulent flow. J. Fluid Mech. 756, 252292.CrossRefGoogle Scholar
Hadjadj, A. & Kudryavtsev, A. 2005 Computation and flow visualization in high-speed aerodynamics. J. Turbul. 6, N16.CrossRefGoogle Scholar
Hamlington, P. E., Schumacher, J. & Dahm, W. J. A. 2008 Local and nonlocal strain rate fields and vorticity alignment in turbulent flows. Phys. Rev. E 77, 026303.Google ScholarPubMed
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202228.CrossRefGoogle Scholar
Jimenez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in homogeneous isotropic turbulence. J. Fluid Mech. 255, 6590.CrossRefGoogle Scholar
Keylock, C. J. 2018 The Schur decomposition of the velocity gradient tensor for turbulent flows. J. Fluid Mech. 848, 876905.CrossRefGoogle Scholar
Klein, M., Sadiki, A. & Janicka, J. 2003 A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186, 652665.CrossRefGoogle Scholar
Lawson, J. M. & Dawson, J. R. 2015 On velocity gradient dynamics and turbulent structure. J. Fluid Mech. 780, 6098.CrossRefGoogle Scholar
Lee, K., Girimaji, S. S. & Kerimo, J. 2009 Effect of compressibility on turbulent velocity gradients and small-scale structure. J. Turbul. 10, 118.Google Scholar
Li, Y., Chevillard, L., Eyink, G. & Meneveau, C. 2009 Matrix exponential-based closures for the turbulent subgrid-scale stress tensor. Phys. Rev. E 79, 016305.Google ScholarPubMed
Li, Y. & Meneveau, C. 2006 Intermittency trends and Lagrangian evolution of non-Gaussian statistics in turbulent flow and scalar transport. J. Fluid Mech. 558, 133142.CrossRefGoogle Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633635.CrossRefGoogle Scholar
Lozano-Durán, A., Holzner, M. & Jiménez, J. 2015 Numerically accurate computation of the conditional trajectories of the topological invariants in turbulent flows. J. Comput. Phys. 295, 805814.CrossRefGoogle Scholar
Lozano-Durán, A., Holzner, M. & Jiménez, J. 2016 Multiscale analysis of the topological invariants in the logarithmic region of turbulent channels at a friction Reynolds number of 932. J. Fluid Mech. 803, 356394.CrossRefGoogle Scholar
Lüthi, B., Holzner, M. & Tsinober, A. 2009 Expanding the QR space to three dimensions. J. Fluid Mech. 641, 497507.CrossRefGoogle Scholar
Lüthi, B., Ott, S., Berg, J. & Mann, J. 2007 Lagrangian multi-particle statistics. J. Turbul. 8, N45.CrossRefGoogle Scholar
Martin, J., Ooi, A., Chong, M. S. & Soria, J. 1998 Dynamics of the velocity gradient tensor invariants in isotropic turbulence. Phys. Fluids 10, 23362346.CrossRefGoogle Scholar
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219245.CrossRefGoogle Scholar
Moin, P., Squires, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 27462757.CrossRefGoogle Scholar
Ooi, A., Martin, J., Soria, J. & Chong, M. S. 1999 A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141174.CrossRefGoogle Scholar
Pantano, C. & Sarkar, S. 2002 A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329371.CrossRefGoogle Scholar
Perry, A. E. & Chong, M. S. 1994 Topology of flow patterns in vortex motions and turbulence. Appl. Sci. Res. 53, 357374.CrossRefGoogle Scholar
Piomelli, U., Cabot, W. H., Moin, P. & Lee, S. 1991 Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3, 17661771.CrossRefGoogle Scholar
Pirozzoli, S. & Grasso, F. 2004 Direct numerical simulations of isotropic compressible turbulence: influence of compressibility on dynamics and structures. Phys. Fluids 16, 43864407.CrossRefGoogle Scholar
da Silva, C. B. & Pereira, J. C. F. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20, 055101.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99164.2.3.CO;2>CrossRefGoogle Scholar
Soria, J., Sondergaard, R., Cantwell, B. J., Chong, M. S. & Perry, A. E. 1994 A study of the fine-scale motions of incompressible time-developing mixing layers. Phys. Fluids 6, 871884.CrossRefGoogle Scholar
Suman, S. & Girimaji, S. S. 2010 Velocity gradient invariants and local flow-field topology in compressible turbulence. J. Turbul. 11, 124.Google Scholar
Taguelmimt, N., Danaila, L. & Hadjadj, A. 2016 Effects of viscosity variations in temporal mixing layer. Flow Turbul. Combust. 96, 163181.CrossRefGoogle Scholar
Taveira, R. R. & da Silva, C. B. 2013 Kinetic energy budgets near the turbulent/nonturbulent interface in jets. Phys. Fluids 25, 015114.CrossRefGoogle Scholar
Thompson, K. W. 1987 Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 68, 124.CrossRefGoogle Scholar
Vaghefi, N. S. & Madnia, C. K. 2015 Local flow topology and velocity gradient invariants in compressible turbulent mixing layer. J. Fluid Mech. 774, 6794.CrossRefGoogle Scholar
Vaghefi, N. S., Nik, M. B., Pisciuneri, P. H. & Madnia, C. K. 2013 A priori assessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence. J. Turbul. 14, 4361.CrossRefGoogle Scholar
Verstappen, R. 2011 When does eddy viscosity damp subfilter scales sufficiently? J. Sci. Comput. 49, 94110.CrossRefGoogle Scholar
Wang, L. & Lu, X. Y. 2012 Flow topology in compressible turbulent boundary layer. J. Fluid Mech. 703, 255278.CrossRefGoogle Scholar
Xu, C. Y., Chen, L. W. & Lu, X. Y. 2010 Large-eddy simulation of the compressible flow past a wavy cylinder. J. Fluid Mech. 665, 238273.CrossRefGoogle Scholar
Yoshizawa, A. 1986 Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29, 21522164.CrossRefGoogle Scholar
Yu, J. L. & Lu, X. Y. 2019 Topological evolution near the turbulent/non-turbulent interface in turbulent mixing layer. J. Turbul. 20, 300321.CrossRefGoogle Scholar