Large eddy simulation of high-Reynolds-number atmospheric boundary layer flow with improved near-wall correction

doi:10.1007/s10483-020-2559-7

Abstract

Abstract: It is highly attractive to develop an efficient and flexible large eddy simulation (LES) technique for high-Reynolds-number atmospheric boundary layer (ABL) simulation using the low-order numerical scheme on a relatively coarse grid, that could reproduce the logarithmic profile of the mean velocity and some key features of large-scale coherent structures in the outer layer. In this study, an improved near-wall correction scheme for the vertical gradient of the resolved streamwise velocity in the strain-rate tensor is proposed to calculate the eddy viscosity coefficient in the subgrid-scale (SGS) model. The LES code is realized with a second-order finite-difference scheme, the scale-dependent dynamic SGS stress model, the equilibrium wall stress model, and the proposed correction scheme. Very-high-Reynolds-number ABL flow simulation under the neutral stratification condition is conducted to assess the performance of the method in predicting the mean and fluctuating characteristics of the rough-wall turbulence. It is found that the logarithmic profile of the mean streamwise velocity and some key features of large-scale coherent structures can be reasonably predicted by adopting the proposed correction method and the low-order numerical scheme.

Key words: atmospheric boundary layer, near-wall correction, large-eddy simulation (LES), very-large-scale motion

2010 MSC Number:

35Q30

Shengjun FENG, Xiaojing ZHENG, Ruifeng HU, Ping WANG. Large eddy simulation of high-Reynolds-number atmospheric boundary layer flow with improved near-wall correction. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 33-50.

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References

[1] MENEVEAU, C. and KATZ, J. Scale-invariance and turbulence models for large-eddy simulation. Annual Review of Fluid Mechanics, 32, 1-32(2000)
[2] YANG, Z., LU, X. H., GUO, X., LIU, Y., and SHEN, L. Numerical simulation of sediment suspension and transport under plunging breaking waves. Computers and Fluids, 158, 57-71(2017)
[3] BOSE, S. T. and PARK, G. I. Wall-modeled large-eddy simulation for complex turbulent flows. Annual Review of Fluid Mechanics, 50, 535-561(2018)
[4] LI, W., HE, Y., ZHANG, Y., SU, J., CHEN, C., YU, C. W., and GU, Z. LES simulation of flow field and pollutant dispersion in a street canyon under time-varying inflows with time varying-simple approach. Building and Environment, 157, 185-196(2019)
[5] SHI, B., YANG, X., JIN, G., HE, G., and WANG, S. Wall-modeling for large-eddy simulation of flows around an axisymmetric body using the diffuse-interface immersed boundary method. Applied Mathematics and Mechanics (English Edition), 40(3), 305-320(2019) https://doi.org/10.1007/s10483-019-2425-6
[6] JIMÉNEZ, J. Coherent structures in wall-bounded turbulence. Journal of Fluid Mechanics, 842, P1(2018)
[7] MARUSIC, I. and MONTY, J. P. Attached eddy model of wall turbulence. Annual Review of Fluid Mechanics, 51, 49-74(2019)
[8] CHOI, H. and MOIN, P. Grid-point requirement for large eddy simulation:Chapman's estimation revisited. Physics of Fluids, 24(1), 011702(2012)
[9] PIOMELLI, U. Wall-layer models for large-eddy simulations. Annual Review of Fluid Mechanics, 34, 349-374(2002)
[10] PIOMELLI, U. Wall-layer models for large-eddy simulations. Progress in Aerospace Sciences, 44(6), 437-446(2008)
[11] DEARDORFF, J. W. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. Journal of Fluid Mechanics, 41, 453-480(1970)
[12] SCHUMANN, U. Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. Journal of Computational Physics, 18(4), 376-404(1975)
[13] MOENG, C. H. A large-eddy-simulation model for the study of planetary boundary-layer turbulence. Journal of the Atmospheric Sciences, 41(13), 2052-2062(1984)
[14] PIOMELLI, U., FERZIGER, J., MOIN, P., and KIM, J. New approximate boundary conditions for large eddy simulations of wall-bounded flows. Physics of Fluids A:Fluid Dynamics, 1(6), 1061-1068(1989)
[15] BALARAS, E., BENOCCI, C., and PIOMELLI, U. Two-layer approximate boundary conditions for large-eddy simulations. AIAA Journal, 34(6), 1111-1119(1996)
[16] CUI, G. X., XU, C. X., FANG, L., SHAO, L., and ZHANG, Z. A new subgrid eddy-viscosity model for large-eddy simulation of anisotropic turbulence. Journal of Fluid Mechanics, 582, 377-397(2007)
[17] YANG, X. I. A., SADIQUE, J., MITTAL, R., and MENEVEAU, C. Integral wall model for large eddy simulations of wall-bounded turbulent flows. Physics of Fluids, 27(2), 025112(2015)
[18] LARSSON, J., KAWAI, S., BODART, J., and BERMEJO-MORENO, I. Large eddy simulation with modeled wall-stress:recent progress and future directions. Mechanical Engineering Reviews, 3(1), 15-00418(2016)
[19] BRASSEUR, J. G. and WEI, T. Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling. Physics of Fluids, 22(2), 021303(2010)
[20] WU, P. and MEYERS, J. A constraint for the subgrid-scale stresses in the logarithmic region of high Reynolds number turbulent boundary layers:a solution to the log-layer mismatch problem. Physics of Fluids, 25(1), 015104(2013)
[21] YANG, X. I. A., PARK, G. I., and MOIN, P. Log-layer mismatch and modeling of the fluctuating wall stress in wall-modeled large-eddy simulations. Physical Review Fluids, 2(10), 104601(2017)
[22] CHATTERJEE, T. and PEET, Y. T. Effect of artificial length scales in large eddy simulation of a neutral atmospheric boundary layer flow:a simple solution to log-layer mismatch. Physics of Fluids, 29(7), 075105(2017)
[23] MASON, P. J. and THOMSON, D. J. Stochastic backscatter in large-eddy simulations of boundary layers. Journal of Fluid Mechanics, 242, 51-78(1992)
[24] CABOT, W. and MOIN, P. Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow. Flow, Turbulence and Combustion, 63(1-4), 269-291(2000)
[25] NICOUD, F., BAGGETT, J. S., MOIN, P., and CABOT, W. Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation. Physics of Fluids, 13(10), 2968-2984(2001)
[26] TEMPLETON, J. A.,WANG, M., and MOIN, P. An efficient wall model for large-eddy simulation based on optimal control theory. Physics of Fluids, 18(2), 025101(2006)
[27] TEMPLETON, J. A., MEDIC, G., and KALITZIN, G. An eddy-viscosity based near-wall treatment for coarse grid large-eddy simulation. Physics of Fluids, 17(10), 105101(2005)
[28] KAWAI, S. and LARSSON, J. Wall-modeling in large eddy simulation:length scales, grid resolution, and accuracy. Physics of Fluids, 24(10), 015105(2012)
[29] CHEN, S., XIA, Z., PEI, S., WANG, J., YANG, Y., XIAO, Z., and SHI, Y. Reynolds-stressconstrained large-eddy simulation of wall-bounded turbulent flows. Journal of Fluid Mechanics, 703, 1-28(2012)
[30] LEE, J., CHO, M., and CHOI, H. Large eddy simulations of turbulent channel and boundary layer flows at high Reynolds number with mean wall shear stress boundary condition. Physics of Fluids, 25(11), 110808(2013)
[31] PORTÉ-AGEL, F., MENEVEAU, C., and PARLANGE, M. B. A scale-dependent dynamic model for large-eddy simulation:application to a neutral atmospheric boundary layer. Journal of Fluid Mechanics, 415, 261-284(2000)
[32] KOVASZNAY, L. S. G., KIBENS, V., and BLACKWELDER, R. F. Large-scale motion in the intermittent region of a turbulent boundary layer. Journal of Fluid Mechanics, 41, 283-325(1970)
[33] RAO, K. N., NARASIMHA, R., and NARAYANAN, M. A. B. The bursting phenomenon in a turbulent boundary layer. Journal of Fluid Mechanics, 48, 339-352(1971)
[34] KIM, K. C. and ADRIAN, R. J. Very large-scale motion in the outer layer. Physics of Fluids, 11(2), 417-422(1999)
[35] ADRIAN, R. J., MEINHART, C. D., and TOMKINS, C. D. Vortex organization in the outer region of the turbulent boundary layer. Journal of Fluid Mechanics, 422, 1-54(2000)
[36] DELLAMO, J. C. and JIMNEZ, J. Spectra of the very large anisotropic scales in turbulent channels. Physics of Fluids, 15(6), L41-L44(2003)
[37] HUTCHINS, N. and MARUSIC, I. Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. Journal of Fluid Mechanics, 579, 1-28(2007)
[38] HU, R. and ZHENG, X. Energy contributions by inner and outer motions in turbulent channel flows. Physical Review Fluids, 3(8), 084607(2018)
[39] ADRIAN, R. J. Hairpin vortex organization in wall turbulence. Physics of Fluids, 19(4), 041301(2007)
[40] MARUSIC, I., MCKEON, B. J., MONKEWITZ, P. A., NAGIB, H. M., SMITS, A. J., and SREENIVASAN, K. R. Wall-bounded turbulent flows at high Reynolds numbers:recent advances and key issues. Physics of Fluids, 22(6), 065103(2010)
[41] SMITS, A. J., MCKEON, B. J., and MARUSIC, I. High-Reynolds number wall turbulence. Annual Review of Fluid Mechanics, 43, 353-375(2011)
[42] CHUNG, D. and MCKEON, B. J. Large-eddy simulation of large-scale structures in long channel flow. Journal of Fluid Mechanics, 661, 341-364(2010)
[43] FANG, J. and PORTÉ-AGEL, F. Large-eddy simulation of very-large-scale motions in the neutrally stratified atmospheric boundary layer. Boundary-Layer Meteorology, 155(3), 397-416(2015)
[44] BOU-ZEID, E., MENEVEAU, C., and PARLANGE, M. A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Physics of Fluids, 17(2), 025105(2005)
[45] JACOB, C. and ANDERSON, W. Conditionally averaged large-scale motions in the neutral atmospheric boundary layer:insights for aeolian processes. Boundary-Layer Meteorology, 162(1), 21-41(2017)
[46] ZHANG, Y., HU, R., and ZHENG, X. Large-scale coherent structures of suspended dust concentration in the neutral atmospheric surface layer:a large-eddy simulation study. Physics of Fluids, 30(4), 046601(2018)
[47] GERMANO, M., PIOMELLI, U., MOIN, P., and CABOT, W. H. A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A:Fluid Dynamics, 3(7), 1760-1765(1991)
[48] LILLY, D. K. A proposed modification of the Germano subgrid-scale closure method. Physics of Fluids A:Fluid Dynamics, 4(3), 633-635(1992)
[49] KIM, K., BAEK, S. J., and SUNG, H. J. An implicit velocity decoupling procedure for the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids, 38(2), 125-138(2002)
[50] GROTZBACH, G. Direct numerical and large eddy simulations of turbulent channel flows. Encyclopedia of Fluid Mechanics, 6, 1337-1391(1987)
[51] TOWNSEND, A. The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge (1976)
[52] MARUSIC, I., MONTY, J. P., HULTMARK, M., and SMITS, A. J. On the logarithmic region in wall turbulence. Journal of Fluid Mechanics, 716, R3(2013)
[53] STEVENS, R. J. A. M., WILCZEK, M., and MENEVEAU, C. Large-eddy simulation study of the logarithmic law for second-and higher-order moments in turbulent wall-bounded flow. Journal of Fluid Mechanics, 757, 888-907(2014)
[54] PERRY, A. E. and ABELL, C. J. Asymptotic similarity of turbulence structures in smooth-and rough-walled pipes. Journal of Fluid Mechanics, 79, 785-799(1977)
[55] PERRY, A. E., HENBEST, S., and CHONG, M. S. A theoretical and experimental study of wall turbulence. Journal of Fluid Mechanics, 165, 163-199(1986)
[56] HUTCHINS, N., CHAUHAN, K., MARUSIC, I., MONTY, J., and KLEWICKI, J. Towards reconciling the large-scale structure of turbulent boundary layers in the atmosphere and laboratory. Boundary-Layer Meteorology, 145(2), 273-306(2012)
[57] LEE, J. H. and SUNG, H. J. Very-large-scale motions in a turbulent boundary layer. Journal of Fluid Mechanics, 673, 80-120(2011)
[58] MARUSIC, I. and HEUER, W. D. C. Reynolds number invariance of the structure inclination angle in wall turbulence. Physical Review Letters, 99(11), 114504(2007)
[59] CHAUHAN, K., HUTCHINS, N., MONTY, J., and MARUSIC, I. Structure inclination angles in the convective atmospheric surface layer. Boundary-Layer Meteorology, 147(1), 41-50(2013)
[60] LIU, H., BO, T., and LIANG, Y. The variation of large-scale structure inclination angles in high Reynolds number atmospheric surface layers. Physics of Fluids, 29(3), 035104(2017)
[61] TUTKUN, M., GEORGE, W. K., DELVILLE, J., STANISLAS, M., JOHANSSON, P. B. V., FOUCAUT, J. M., and COUDERT, S. Two-point correlations in high Reynolds number flat plate turbulent boundary layers. Journal of Turbulence, 10, N21(2009)
[62] LIU, H., WANG, G., and ZHENG, X. J. Spatial length scales of large-scale structures in atmospheric surface layers. Physical Review Fluids, 2(6), 064606(2017)
[63] BROWN, G. L. and THOMAS, A. S. W. Large structure in a turbulent boundary layer. The Physics of Fluids, 20(10), S243-S252(1977)
[64] CARPER, M. A. and PORT-AGEL, F. The role of coherent structures in subfilter-scale dissipation of turbulence measured in the atmospheric surface layer. Journal of Turbulence, 5, 040(2004)
[65] HOMMEMA, S. E. and ADRIAN, R. J. Packet structure of surface eddies in the atmospheric boundary layer. Boundary-Layer Meteorology, 106(1), 147-170(2003)