Large-eddy simulation of turbulent flow over an array of wall-mounted cubes submerged in an emulated atmospheric boundary-layer

Document Type : Research Article

Author

Aerospace Engineering Department, Amirkabir University of Technology, Tehran, Iran

Abstract

Turbulent flow over an array of wall-mounted cubic obstacles has been numerically investigated using large-eddy simulation. The simulations have been performed using high- performance computations with local cluster systems. The array of cubes is fully submerged in a simulated deep rough-wall atmospheric boundary-layer with high turbulence intensity characteristics of environmental turbulent flows. Four different approaches have been tested to reproduce the approaching highly turbulent inflow condition. Significant influence of the inlet boundary condition on the predictive streamwise root mean squared velocity (and second-order turbulence statistics if generalized) have been observed. A pro- posed method based on inserting a solid grid at the inlet of the domain with superimposed correlated random fluctuations has been selected as the inlet boundary condition to conduct the simulations. Three different subgrid-scale (SGS) models have been also used to compare their predictive performance in turbulence statistics and temporal energy spectra. It was observed that the choice SGS model does not have considerable effect on the second-order turbulence statistics, however, it was influential on the predicted energy level in the energy spectra. It was also observed that the flow reaches a self-similar states after the second row of obstacles which was different from the reported value in some of the previous studies.

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[1] I. P. Castro and A. G. Robins. The flow around a surface-mounted cube in uniform and turbulent streams. J. Fluid Mech., 79:307–335, 1977.
[2] A. Okajima. Strouhal numbers of rectangular cylinders. J. Fluid Mech., 123:379–398, 1982.
[3] H. J. Hussein and R. J. Martinuzzi. Energy balance for turbulent flow around a surface mounted cube placed in a channel. Phys. Fluids, 8:764–780, 1996.
[4] M. J. Brown, R. E. Lawson, D. S. DeCroix, and R. L. Lee. Comparison of centerline velocity measurements obtained around 2D and 3D building arrays in a wind tunnel. Technical Report LA-UR-01-4138, Los Alamos National Laboratory, 2001.
[5] D. Sumner, J. L. Heseltine, and O. J. P. Dansereau. Wake structure of a finite circular cylinder of small aspect ratio. Exper. Fluids, 37:720–730, 2004.
[6] M. S. Adaramola, O. G. Akinlade, D. Sumner, D. J. Bergstrom, and A. J. Schenstead. Turbulent wake of a finite circular cylinder of small aspect ratio. J. Fluids Struct., 22:919–928, 2006 .
[7] D. Sumner and J. L. Heseltine. Tip vortex structure for a circular cylinder with a free end. J. Wind Eng. Ind. Aero., 96:1185–1196, 2008.
[8] R. J. Martinuzzi and B. Havel. Vortex shedding from two surfacemounted cubes in tandem. Int. J. Heat Fluid Flow, 25:364–372, 2004.
[9] D. Sumner, M. D. Richards, and O. O. Akosile. Strouhal number data for two staggered circular cylinders. J. Wind Eng. Ind. Aero., 96:859–871, 2008.
[10] H. C. Lim, I. P. Castro, and R. P. Hoxey. Bluff bodies in deep turbulent boundary layers: Reynolds-number issues. J. Fluid Mech., 571:97–118, 2007.
[11] H. Wang, Y. Zhou, C. Chan, and T. Zhou. Momentum and heat transport in a finite- length cylinder wake. Exper. Fluids, 46:1173–1185, 2009.
[12] H. F. Wang and Y. Zhou. The finite-length square cylinder near wake. J. Fluid Mech., 638:453–490, 2009.
[13] P. Sattari, J. A. Bourgeois, and R. J. Martinuzzi. On the vortex dynamics in the wake of a finite surface-mounted square cylinder. Exper. Fluids, 52:1149–1167, 2012.
[14] J. A. Bourgeois, P. Sattari, and R. J. Martinuzzi. Alternating half-loop shedding in the turbulent wake of a finite surface-mounted square cylinder with a thin boundary layer. Phys. Fluids, 23:095101, 1–15, 2011.
[15] F. S. Lien, E. Yee, and Y. Cheng. Simulation of mean flow and turbulence over a 2D building array using high-resolution CFD and a distributed drag force approach. J. Wind Eng. Ind. Aero., 92:117–158, 2004.
[16] F.-S. Lien and E. Yee. Numerical modelling of the turbulent flow developing within and over a 3-D building array, part I: A high resolution Reynolds-averaged Navier-Stokes approach. Boundary-Layer Meteorol., 112:427–466, 2004.
[17] J. L. Santiago, A. Martilli, and F. Mart´ın. CFD simulation of airflow over a regular array of cubes. Part I: Three-dimensional simulation of the flow and validation with wind-tunnel measurements. BoundaryLayer Meteorol., 122:609–634, 2007.
[18] K. B. Shah and J. H. Ferziger. A fluid mechanicians view of wind engineering: Large eddy simulation of flow past a cubic obstacle. J. Wind Eng. Ind. Aero., 67:211–224, 1997.
[19] R. Martinuzzi and C. Tropea. The flow around surface-mounted, prismatic obstacles placed in a fully developed channel flow. J. Fluids Eng., 115:85–92, 1993.
[20] S. Schmidt and F. Thiele. Comparison of numerical methods applied to the flow over wall-mounted cubes. Int. J. Heat Fluid Flow, 23:330– 339, 2002.
[21] S. R. Hanna, S. Tehranian, B. Carissimo, R. W. MacDonald, and R. Lohner. Compar- isons of model simulations with observations of mean flow and turbulence within simple obstacle arrays. J. Atmos. Env., 36:5067–5079, 2002.
[22] B. Niˇceno, A. D. T. Dronkers, and K. Hanjali´c. Turbulent heat transfer from a multi- layered wall-mounted cube matrix: A large eddy simulation. Int. J. Heat Fluid Flow, 23:173–185, 2002.
[23] Y. Cheng, F. S. Lien, E. Yee, and R. Sinclair. A comparison of large eddy simulations with a standard k−ǫ Reynolds-averaged Navier-Stokes model for the prediction of a fully developed turbulent flow over a matrix of cubes. J. Wind Eng. Ind. Aero., 91:1301–1328, 2003.
[24] I. Afgan, C. Moulinec, R. Prosser, and D. Laurence. Large eddy simulation of turbulent flow for wall mounted cantilever cylinders of aspect ratio 6 and 10. Int. J. Heat Fluid Flow, 28:561–574, 2007.
[25] R. F. Shi, G. X. Cui, Z. S. Wang, C. X. Xu, and Z. S. Zhang. Large eddy simulation of wind field and plume dispersion in building array. J. Atmos. Env., 42:1083–1097, 2008.
[26] J. H. Lee, H. J. Sung, and P.-A˚. Krogstad. Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall. J. Fluid Mech., 669:397–431, 2011.
[27] M. Saeedi and B.-C. Wang. Large-eddy simulation of turbulent flow over an array of wall-mounted cubic obstacles. In Direct and LargeEddy Simulation 9 (DLES9), 2013. Dresden, Germany.
[28] R. K. Madabhushi and S. P. Vanka. Large eddy simulation of turbulence-driven secondary flow in a square duct. Phys. Fluids A, 3:2734–2745, 1991.
[29] P. Sagaut. Large Eddy Simulation for Incompressible Flows: An Introduction. Springer, Berlin, 2nd edition, 2002.
[30] F. E. Ham, F. S. Lien, and A. B. Strong. A fully conservative second-order finite difference scheme for incompressible flow on nonuniform grids. J. Comp. Phys., 177:117– 133, 2002.
[31] M. Germano, U. Piomelli, P. Moin, and W. H. Cabot. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A, 3:1760–1765, 1991.
[32] D. K. Lilly. A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A, 4:633–635, 1992.
[33] Y. Morinishi and O. V. Vasilyev. A recommended modification to the dynamic two- parameter mixed subgrid scale model for large eddy simulation of wall bounded turbu- lent flow. Phys. Fluids, 13:3400– 3410, 2001.
[34] B.-C. Wang and D. Bergstrom. A dynamic nonlinear subgrid-scale stress model. Phys. Fluids, 17:035109, 1–15, 2005.