Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-06-12T19:25:22.466Z Has data issue: false hasContentIssue false
  • English
  • Français

Quasi-dynamic subgrid-scale kinetic energy equation model for large-eddy simulation of compressible flows

Published online by Cambridge University Press:  23 August 2022

Han Qi ,
Xinliang Li ,
Running Hu  and
Changping Yu Open the ORCID record for Changping Yu [Opens in a new window]
Han Qi
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Xinliang Li
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Running Hu
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Changping Yu*
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
*
†Email address for correspondence: cpyu@imech.ac.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

A quasi-dynamic subgrid-scale (SGS) kinetic energy one-equation eddy-viscosity model is introduced in this paper for large-eddy simulation (LES) of compressible flows. With the additional SGS kinetic energy equation, the SGS kinetic energy can be predicted properly. Then, using the dual constraints of SGS kinetic energy and the SGS kinetic energy flux, the eddy-viscosity model can be determined exactly. Taking a similar scheme as the expansion of the SGS stress, other unclosed quantities in the equations to be solved could be well modelled separately. Therefore, with the advance of the equations, all the model coefficients can be determined dynamically. Differing from the classic dynamic procedure, the new methodology needs no test filtering, and thus it could also be called a quasi-dynamic procedure. Using direct numerical simulation of compressible turbulent channel flow, the $a$ $priori$ test shows that the key modelled quantities of the suggested model display high correlations with the real values. In LES of compressible turbulent channel flows of the Mach number being $1.5$ and 3.0, the proposed model can precisely predict some important quantities, including the mean velocity, Reynolds stress and turbulent flux, and it can also supply more abundant turbulent structures. For the compressible flat-plate boundary layer, the new model can correctly predict the transition process, mean velocity and turbulence intensities in the turbulent region. The results show that the proposed model has the advantage of scale adaptivity. Finally, the new model is applied to LES of turbulent mixing in spherical converging Richtmyer–Meshkov instability, and the accurate results show that the new model has a good ability for LES of complex fluids.

JFM classification

Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A22
Check for updates
Copyright
© The Author(s), 2022. 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

REFERENCES

Bardina, J., Ferziger, J.H. & Reynolds, W.C. 1984 Improved turbulence models based on large-eddy simulation of homogeneous incompressible turbulent flows. Rep. No. TF-19, Department of Mechanical Engineering, Stanford.Google Scholar
Bedford, K.W. & Yeo, W.K. 1993 Conjunctive filtering procedures in surface water flow and transport. In Large Eddy Simulation of Complex Engineering and Geophysical Flows (ed. B. Galperin & S.A. Orszag), pp. 513–539. Cambridge University Press.Google Scholar
Bin, Y., Xiao, M., Shi, Y., Zhang, Y. & Chen, S. 2021 A new idea to predict reshocked Richtmyer-Meshkov mixing: constrained large-eddy simulation. J. Fluid Mech. 918, R1.CrossRefGoogle Scholar
Borue, V. & Orszag, S. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31.CrossRefGoogle Scholar
Chai, X. & Mahesh, K. 2012 Dynamic $k$-equation model for large-eddy simulation of compressible flows. J. Fluid Mech. 699, 385–413.CrossRefGoogle Scholar
Clark, R.A., Ferziger, J.H. & Reynolds, W.C. 1979 Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1–16.CrossRefGoogle Scholar
Coleman, G.N., Kim, J. & Moser, R.D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.CrossRefGoogle Scholar
De Stefano, G., Brown-Dymkoski, E. & Vasilyev, O.V. 2020 Wavelet-based adaptive large-eddy simulation of supersonic channel flow. J. Fluid Mech. 901, A13.CrossRefGoogle Scholar
Eyink, G.L. 2006 Multi-scale gradient expansion of the turbulent stress tensor. J. Fluid Mech. 549, 159–190.CrossRefGoogle Scholar
Garnier, E., Adams, N. & Sagaut, P. 2013 Large Eddy Simulation for Compressible Flows. Springer.Google Scholar
Genin, F. & Menon, S. 2010 Dynamics of sonic jet injection into supersonic crossflow. J. Turbul. 11 (4), 30.CrossRefGoogle Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W.H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Horiuti, K. 1985 Large-eddy simulation of turbulent channel flow by one-equation modeling. J. Phys. Soc. 54 (8), 2855–2865.CrossRefGoogle Scholar
Horiuti, K. 1997 A new dynamic two-parameter mixed model for large-eddy simulation. Phys. Fluids 9 (11), 3443–3464.CrossRefGoogle Scholar
Horiuti, K. & Tamaki, T. 2013 Nonequilibrium energy spectrum in the subgrid-scale one-equation model in large-eddy simulation. Phys. Fluids 25, 125104.CrossRefGoogle Scholar
Kim, W.W. & Menon, S. 1999 An unsteady incompressible Navier–Stokes solver for large eddy simulation of turbulent flows. Intl J. Numer. Meth. Fluids 31 (6), 983–1017.3.0.CO;2-Q>CrossRefGoogle Scholar
Leoni, P.C.D., Zaki, T.A., Karniadakis, G. & Meneveau, C. 2021 Two-point stress-strain-rate correlation structure and non-local eddy viscosity in turbulent flows. J. Fluid Mech. 914, A6.Google Scholar
Li, X., Yan, L. & He, Z. 2013 Optimized sixth-order monotonicity-preserving scheme by nonlinear spectral analysis. Intl J. Numer. Meth. Fluids 73, 560–577.CrossRefGoogle Scholar
Lilly, D.K. 1967 On the application of the eddy viscosity concept in the inertial sub-range of turbulence. NCAR Manuscript, p. 123.Google Scholar
Lilly, D.K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4 (3), 633–635.CrossRefGoogle Scholar
Liu, S., Meneveau, C. & Katz, J. 1994 On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83–119.CrossRefGoogle Scholar
Lombardini, M., Hill, D.J., Pullin, D.I. & Meiron, D.I. 2011 Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations. J. Fluid Mech. 670, 439–480.CrossRefGoogle Scholar
Lombardini, M., Pullin, D.I. & Meiron, D.I. 2014 Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth. J. Fluid Mech. 748, 85–112.CrossRefGoogle Scholar
Martín, M.P., Piomelli, U. & Candler, G.V. 2000 Subgrid-scale models for compressible large-eddy simulation. Theor. Comput. Fluid Dyn. 13 (5), 361–376.Google Scholar
Meneveau, C. 2012 Germano identity-based subgrid-scale modeling: a brief survey of variations on a fertile theme. Phys. Fluids 24 (12), 121301.CrossRefGoogle Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32 (1), 1–32.CrossRefGoogle Scholar
Meneveau, C., Lund, T.S. & Cabot, W.H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385.CrossRefGoogle Scholar
Metais, O. & Lesieur, M. 1992 Spectral large-eddy simulation of isotropic and stably stratified turbulence. Annu. Rev. Fluid Mech. 239, 157–94.CrossRefGoogle Scholar
Moeng, C.H. 1984 A large-eddy simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41 (13), 2052–2062.2.0.CO;2>CrossRefGoogle Scholar
Moin, P., Squire, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 2746–2757.CrossRefGoogle Scholar
Morinishi, Y., Tamano, S. & Nakabayashi, K. 2004 Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls. J. Fluid Mech. 502, 273–308.CrossRefGoogle Scholar
Moser, R.D., Haering, S.W. & Yalla, G.R. 2021 Statistical properties of subgrid-scale turbulence models. Annu. Rev. Fluid Mech. 53 (1), 255–286.CrossRefGoogle Scholar
Nicoud, F. & Ducros, F. 1999 Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 63, 183–200.CrossRefGoogle Scholar
Nicoud, F., Toda, H.B., Cabrit, O., Bose, S. & Lee, J. 2011 Using singular values to build a subgrid-scale model for large-eddy simulations. Phys. Fluids 23, 085106.CrossRefGoogle Scholar
Patel, N., Stone, C. & Menon, S. 2003 Large-eddy simulation of turbulent flow over an axisymmetric hill. AIAA Paper 2003-976.CrossRefGoogle Scholar
Piomelli, U. & Zang, T.A. 1991 Large-eddy simulation of transitional channel flow. Comput. Phys. Commun. 65, 224–230.CrossRefGoogle Scholar
Pirozzoli, S., Grasso, F. & Gatski, T.B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at $m=2.25$. Phys. Fluids 16 (3), 530–545.CrossRefGoogle Scholar
Pomraning, E. & Rutland, C.J. 2002 Dynamic one-equation nonviscosity large-eddy simulation model. AIAA J. 40 (4), 689–701.CrossRefGoogle Scholar
Porte-Agel, F., Meneveau, C. & Parlange, M.B. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261–284.CrossRefGoogle Scholar
Ronchi, C., Ypma, M. & Canuto, V.M. 1992 On the application of the Germano identity to subgrid-scale modeling. Phys. Fluids A 4 (12), 2927–2929.CrossRefGoogle Scholar
Rozema, W., Bae, H.J., Moin, P. & Verstappen, R. 2015 Minimum-dissipation models for large-eddy simulation. Phys. Fluids 27, 085107.CrossRefGoogle Scholar
Sayadi, T. & Moin, P. 2012 Large eddy simulation of controlled transition to turbulence. Phys. Fluids 24, 114103.CrossRefGoogle Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18 (4), 376–404.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weath. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Stevens, B., Moeng, C.H. & Sullivan, P.P. 1999 Large-eddy simulation of radiatively driven convection: sensitivities to the representation of small scales. J. Atmos. Sci. 56, 3963–3984.2.0.CO;2>CrossRefGoogle Scholar
Tejada-Martínez, A.E. & Jansen, K.E. 2004 A dynamic smagorinsky model with dynamic determination of the filter width ratio. Phys. Fluids 16 (7), 2514–2528.CrossRefGoogle Scholar
Vreman, A.W. 2004 An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16, 3670–3681.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1994 On the formulation of the dynamic mixed subgrid-scale model. Phys. Fluids 6, 4057–4059.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1996 Large-eddy simulation of the temporal mixing layer using the Clark model. Theor. Comput. Fluid Dyn. 8 (4), 309–324.CrossRefGoogle Scholar
Wang, B.-C., Yee, E., Bergstrom, D.J. & Iida, O. 2008 New dynamic subgrid-scale heat flux models for large-eddy simulation of thermal convection based on the general gradient diffusion hypothesis. J. Fluid Mech. 604, 125–163.CrossRefGoogle Scholar
Wong, V.C. 1992 A proposed statistical-dynamic closure method for the linear or nonlinear subgrid-scale stress. Phys. Fluids A 4 (5), 1080–1082.CrossRefGoogle Scholar
Yoshizawa, A. 1986 Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29, 2255–2271.CrossRefGoogle Scholar
Yoshizawa, A. 1991 A statistically-derived subgrid model for the large-eddy simulation of turbulence. Phys. Fluids A 3 (8), 2007–2009.CrossRefGoogle Scholar
Yoshizawa, H.K. 1985 A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows. J. Phys. Soc. Japan 54 (8), 2834–2839.CrossRefGoogle Scholar
Yu, C., Hong, R., Xiao, Z. & Chen, S. 2013 Subgrid-scale eddy viscosity model for helical turbulence. Phys. Fluids 25, 095101.CrossRefGoogle Scholar
Yu, C., Xiao, Z. & Li, X. 2017 Scale-adaptive subgrid-scale modelling for large-eddy simulation of turbulent flows. Phys. Fluids 29 (3), 035101.CrossRefGoogle Scholar
Yu, C., Zuoli, X. & Xinliang, L. 2016 Dynamic optimization methodology based on subgrid-scale dissipation for large eddy simulation. Phys. Fluids 28, 015113.CrossRefGoogle Scholar
Yuan, Z., Xie, C. & Wang, J. 2020 Deconvolutional artificial neural network models for large eddy simulation of turbulence. Phys. Fluids 32 (11), 115106.CrossRefGoogle Scholar
Zang, Y., Street, R.L. & Koseff, J.R. 1993 A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows. Phys. Fluids A 5, 3186–3196.CrossRefGoogle Scholar
Zhou, H., Li, X., Qi, H. & Yu, C. 2019 Subgrid-scale model for large-eddy simulation of transition and turbulence in compressible flows. Phys. Fluids 31, 125118.Google Scholar