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An explicit algebraic model for the subgrid-scale passive scalar flux

  • Amin Rasam (a1), Geert Brethouwer (a1) and Arne V. Johansson (a1)

Abstract

In Marstorp et al. (J. Fluid Mech., vol. 639, 2009, pp. 403–432), an explicit algebraic subgrid stress model (EASSM) for large-eddy simulation (LES) was proposed, which was shown to considerably improve LES predictions of rotating and non-rotating turbulent channel flow. In this paper, we extend that work and present a new explicit algebraic subgrid scalar flux model (EASSFM) for LES, based on the modelled transport equation of the subgrid-scale (SGS) scalar flux. The new model is derived using the same kind of methodology that leads to the explicit algebraic scalar flux model of Wikström et al. (Phys. Fluids, vol. 12, 2000, pp. 688–702). The algebraic form is based on a weak equilibrium assumption and leads to a model that depends on the resolved strain-rate and rotation-rate tensors, the resolved scalar-gradient vector and, importantly, the SGS stress tensor. An accurate prediction of the SGS scalar flux is consequently strongly dependent on an accurate description of the SGS stresses. The new EASSFM is therefore primarily used in connection with the EASSM, since this model can accurately predict SGS stresses. The resulting SGS scalar flux is not necessarily aligned with the resolved scalar gradient, and the inherent dependence on the resolved rotation-rate tensor makes the model suitable for LES of rotating flow applications. The new EASSFM (together with the EASSM) is validated for the case of passive scalar transport in a fully developed turbulent channel flow with and without system rotation. LES results with the new model show good agreement with direct numerical simulation data for both cases. The new model predictions are also compared to those of the dynamic eddy diffusivity model (DEDM) and improvements are observed in the prediction of the resolved and SGS scalar quantities. In the non-rotating case, the model performance is studied at all relevant resolutions, showing that its predictions of the Nusselt number are much less dependent on the grid resolution and are more accurate. In channel flow with wall-normal rotation, where all the SGS stresses and fluxes are non-zero, the new model shows significant improvements over the DEDM predictions of the resolved and SGS quantities.

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Corresponding author

Email address for correspondence: rasam@mech.kth.se

References

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Abe, H. & Antonia, R. A. 2009 Near-wall similarity between velocity and scalar fluctuations in a turbulent channel flow. Phys. Fluids 21, 025109.
Baggett, J. S., Jiménez, J. & Kravchenko, A. G. 1997 Resolution requirements in large-eddy simulations of shear flows. In Annual Research Briefs (ed. P. Moin), pp. 51–66. Center for Turbulence Research, Stanford University.
Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1989 Improved subgrid-scale models for large-eddy simulation. AIAA Paper 80-1357.
Batchelor, G. K. 1949 Diffusion in a field of homogeneous turbulence. Austral. J. Sci. Res. 2 (4), 437450.
Bradshaw, P. & Huang, G. P. 1995 The law of the wall in turbulent flow. Proc. R. Soc. Lond. A 451, 165188.
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.
Chevalier, M., Schlatter, P., Lundbladh, A. & Henningson, D. S. 2007 SIMSON a pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. 2007:07. KTH Mechanics, Stockholm.
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman’s estimate revisited. Phys. Fluids 24, 011702.
Chumakov, S. 2008 A priori study of subgrid-scale flux of a passive scalar in isotropic homogeneous turbulence. Phys. Rev. E 78, 036313.
Clark, R. A., Ferziger, J. H. & Reynolds, W. C. 1979 Evaluation of subgrid-scale models using an accurately simulated turbulent flow (part 1). J. Fluid Mech. 91, 116.
Davidson, L. 2009 Large eddy simulations: how to evaluate resolution. Intl J. Heat Fluid Flow 30, 10161025.
Debusschere, B. & Rutland, C. J. 2004 Turbulent scalar transport mechanisms in plane channel and Couette flows. Intl J. Heat Mass Transfer 47, 17711781.
Gatski, T. B. & Wallin, S. 2004 Extending the weak-equilibrium condition for algebraic Reynolds stress models to rotating and curved flows. J. Fluid Mech. 518, 147155.
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325336.
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 17601765.
Geurts, B. J. & Fröhlich, J. 2002 A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14, L41L44.
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, 229255.
Grundestam, O., Wallin, S. & Johansson, A. V. 2005 An explicit algebraic Reynolds stress model based on a nonlinear pressure strain rate model. Intl J. Heat Fluid Flow 26, 732745.
Higgins, C. W., Parlange, M. B. & Meneveau, C. 2004 The heat flux and the temperature gradient in the lower atmosphere. Geophys. Res. Lett. 31, L22105.
Jiménez, C., Ducros, F., Cuenot, B. & Bédat, B. 2001a Subgrid scale variance and dissipation of a scalar field in large eddy simulations. Phys. Fluids 13, 17481754.
Jiménez, C., Valiño, L. & Dopazo, C. 2001b A priori and a posteriori tests of subgrid scale models for scalar transport. Phys. Fluids 13, 24332436.
Johansson, A. V. & Wikström, P. M. 1999 DNS and modelling of passive scalar transport in turbulent channel flow with a focus on scalar dissipation rate modelling. Flow Turbul. Combust. 63, 223245.
Kader, B. A. & Yaglom, A. M. 1972 Heat and mass transfer laws for fully turbulent wall flows. Intl J. Heat Mass Transfer 15, 23292351.
Kang, H. S. & Meneveau, C. 2001 Passive scalar anisotropy in a heated turbulent wake: new observations and implications for large-eddy simulations. J. Fluid Mech. 442, 161170.
Kang, H. S. & Meneveau, C. 2002 Universality of large eddy simulation model parameters across a turbulent wake behind a heated cylinder. J. Turbul. 3, N32.
Kawamura, H., Ohsaka, K., Abe, H. & Yamamoto, K. 1998 DNS of turbulent heat transfer in channel flow with low to medium-high Prandtl number fluid. Intl J. Heat Fluid Flow 19, 482491.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Lesieur, M. & Métais, O. 1996 New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech. 28, 4582.
Li, B.-Y., Liu, N.-S. & Lu, X.-Y. 2006 Direct numerical simulation of wall-normal rotating turbulent channel flow with heat transfer. Intl. J. Heat Mass Transfer 49, 11621175.
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4 (3), 633635.
Lundbladh, A., Henningson, D. S. & Johansson, A. V. 2004 An efficient spectral integration method for the solution of the Navier–Stokes equations. Tech. Rep. Aeronautical Research Institute of Sweden, Bromma.
Marstorp, L., Brethouwer, G., Grundestam, O. & Johansson, A. V. 2009 Explicit algebraic subgrid stress models with application to rotating channel flow. J. Fluid Mech. 639, 403432.
Marstorp, L., Brethouwer, G. & Johansson, A. V. 2007 A stochastic subgrid model with application to turbulent flow and scalar mixing. Phys. Fluids 19, 035107.
Mehdizadeh, A. & Oberlack, M. 2010 Analytical and numerical investigations of laminar and turbulent Poiseuille–Ekman flow at different rotation rates. Phys. Fluids 22, 105104.
Meneveau, C. 1994 Statistics of turbulence subgrid-scale stresses: necessary conditions and experimental tests. Phys. Fluids 6, 815833.
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 132.
Meneveau, C., Lund, T. S. & Cabot, W. H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353385.
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341377.
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.
Monin, P. S. 1965 On the symmetry of turbulence in the surface layer of air. Izv. Akad. Nauk SSSR Atmos. Ocean. Phys. 1, 4554.
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau } = 590$ . Phys. Fluids 11 (4), 943945.
Oberlack, M., Cabot, W., Petterson Reif, B. A. & Weller, T. 2006 Group analysis, direct numerical simulation and modelling of a turbulent channel flow with streamwise rotation. J. Fluid Mech. 562, 383403.
Peng, S.-H. & Davidson, L. 2002 On a subgrid-scale heat flux model for large eddy simulation of turbulent thermal flow. Intl J. Heat Mass Transfer 45, 13931405.
Piomelli, U. & Liu, J. 1995 Large eddy simulation of rotating channel flows using a localized dynamic model. Phys. Fluids 7 (4), 839848.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Porté-agel, F., Pahlow, M., Meneveau, C. & Parlange, M. B. 2001a Atmospheric stability effect on subgrid-scale physics for large-eddy simulation. Adv. Water Resour. 24, 10851102.
Porté-agel, F., Parlange, M. B., Meneveau, C. & Eichinger, W. E. 2001b A priori field study of the subgrid-scale heat fluxes and dissipation in the atmospheric surface layer. J. Atmos. Sci. 58, 26732698.
Rasam, A., Brethouwer, G., Schlatter, P., Li, Q. & Johansson, A. V. 2011a Effects of modelling, resolution and anisotropy of subgrid-scales on large eddy simulations of channel flow. J. Turbul. 12, N10.
Rasam, A., Brethouwer, G., Wallin, S. & Johansson, A. V. 2011b Stochastic and non-stochastic explicit algebraic models for LES. In Proc. 7th Intl Symp. on Turbulence and Shear Flow Phenomena, Ottawa, Canada.  http://www.tsfp7.org/papers/7A2P.pdf.
Rodi, W. 1972 The prediction of free turbulent boundary layers by use of a two equation model of turbulence. PhD thesis, University of London.
Rodi, W. 1976 A new algebraic relation for calculating the Reynolds stresses. Z. Angew. Math. Mech. 56, T219.
Sagaut, P. 2010 Large Eddy Simulation for Incompressible Flows: An Introduction, 3rd edn. Springer.
Salvetti, M. V. & Banerjee, S. 1995 A priori tests of a new dynamic subgrid-scale model for finite-difference large-eddy simulations. Phys. Fluids 7, 28312847.
Shih, T. H. & Lumley, J. L. 1986 Second-order modelling of near-wall turbulence. Phys. Fluids 29 (4), 971975.
Sjögren, T. & Johansson, A. V. 2000 Development and calibration of algebraic nonlinear models for terms in the Reynolds stress transport equations. Phys. Fluids 12, 15541572.
Tafti, D. K. & Vanka, S. P. 1991 A numerical study of the effects of spanwise rotation on turbulent channel flow. Phys. Fluids A 3, 642656.
Tsubokura, M., Kobayashi, T., Taniguchi, N. & Kogaki, T. 1999 Subgrid scale modelling for turbulence in rotating reference frames. J. Wind Engng Ind. Aerodyn. 81, 361375.
Voke, P. R. 1996 Subgrid-scale modelling at low mesh Reynolds number. Theoret. Comput. Fluid Dyn. 8, 131143.
Wallin, S. & Johansson, A. V. 2000 An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J. Fluid Mech. 403, 89132.
Wallin, S. & Johansson, A. V. 2002 Modelling streamline curvature effects in explicit algebraic Reynolds stress turbulence models. Intl J. Heat Fluid Flow 23, 721730.
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, 125163.
Wikström, P. M., Wallin, S. & Johansson, A. V. 2000 Derivation and investigation of a new algebraic model for the passive scalar flux. Phys. Fluids 12, 688702.
Winckelmans, G. S., Jeanmart, H. & Carati, D. 2002 On the comparison of turbulence intensities from large-eddy simulation with those from experiment or direct numerical simulation. Phys. Fluids A 14, 18091811.
Wu, H. & Kasagi, N. 2004 Turbulent heat transfer in a channel flow with arbitrary directional system rotation. Intl J. Heat Mass Transfer 47, 45794591.
Yoshizawa, A. 1988 Statistical modelling of passive-scalar diffusion in turbulent shear flow. J. Fluid Mech. 195, 541555.
Yoshizawa, A., Tsubokura, M., Kobayashi, T. & Taniguchi, N. 1996 Modelling of the dynamic subgrid-scale viscosity in large eddy simulation. Phys. Fluids 8, 22542256.
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An explicit algebraic model for the subgrid-scale passive scalar flux

  • Amin Rasam (a1), Geert Brethouwer (a1) and Arne V. Johansson (a1)

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