Performance investigation of 2D lattice Boltzmann simulation of forces on a circular cylinder

Abstract

The lattice Boltzmann method (LBM) is employed to simulate the uniform flow past a circular cylinder. The performance of the two-dimensional LBM model on the prediction of force coefficients and vortex shedding frequency is investigated. The local grid refinement technique and second-order boundary condition for curved walls are applied in the calculations. It is found that the calculated vortex shedding frequency, drag coefficient and lift coefficient are consistent with experimental results at Reynolds numbers lower than 300. For the high Reynolds number flow, although the simulation by the combined model of LBM and large eddy simulation method is numerically stable, the simulated results deviate from those of experiments, similar to the reported results by conventional numerical methods. It is suggested that this is mainly due to the three-dimensionality of the flow.

Keywords

lattice Boltzmann method / flow past a circular cylinder / large eddy simulation / grid refinement / secondorder curved boundary treatment / drag and lift coefficients

References

[1] Mcnamara G. R., Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata[J]. Physical Review Letters, 1988, 61(20): 2332-2335.

[2] Chen H., Chen S., Matthaeus W. H. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method[J]. Physical Review A, 1992, 45(8): R5339-5342.

[3] Qian Y., D’humieres D., Lallemand P. Lattice BGK models for Navier-Stokes equation[J]. Europhysics Letters, 1992, 17 479-484.

[4] Chen S., Doolen G. D. Lattice Boltzmann method for fluid flows[J]. Annual Review of Fluid Mechanics, 1998, 30 329-364.

[5] He X., Luo L. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation[J]. Physical Review E, 1997, 56(6): 6811-6817.

[6] Li Y., Shock R., Zhang R., et al. Numerical study of flow past an impulsively started cylinder by the lattice-Boltzmann method[J]. Journal of Fluid Mechanics, 2004, 519 273-300.

[7] Al-Jahmany Y. Y., Brenner G., Brunn P. O. Comparative study of lattice-Boltzmann and finite volume methods for the simulation of laminar flow through a 4:1 planar contraction[J]. International Journal for Numerical Methods in Fluids, 2004, 46 903-920.

[8] Yoshino M., Matsuda Y., Shao C. Comparison of accuracy and efficiency between the lattice Boltzmann method and the finite difference method in viscous/thermal fluid flows[J]. International Journal of Computational Fluid Dynamics, 2004, 18(4): 333-345.

[9] Aidun C. K., Clausen J. R. Lattice-Boltzmann method for complex flows[J]. Annual Review of Fluid Mechanics, 2010, 42 439-472.

[10] Wagner L., Hayot F. Lattice Boltzmann simulations of flow past a cylindrical obstacle[J]. Journal of Statistical Physics, 1995, 81(1/2): 63-70.

[11] He X., Doolen G. D. Lattice Boltzmann method on a curvilinear coordinates system: Vortex shedding behind a circular cylinder[J]. Physical Review E, 1997, 56(1): 434-440.

[12] Cheng Yongguang. Nonuniform mesh grid algorithm for lattice Boltzmann method based on interpolation[J]. Journal of Wuhan University of Hydraulic Electrical Engineering, 2000, 33(5): 26-31.

[13] Wang Long. Simulation of flow around cylinder with lattice Boltzmann method[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2002, 38(5): 647-652.

[14] Hou S., Sterling J., Chen S., et al. A lattice subgrid model for high Reynolds number flows[J]. Fields Institute Communications, 1996, 6 151 166

[15] Guo Z., Zheng C., Liu Zhaohui. Large eddy simulation of flow past a circular cylinder based on lattice Boltzmann method[J]. Journal of Engineering Thermophysics, 2002, 23(4): 479-481.

[16] Wolf-Gladrow D. A. Lattice-gas Cellular Automata and Lattice Boltzmann Models: An Introduction[M]. 2000, Hong Kong: Springer.

[17] Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond[M]. 2001, Oxford: Oxford University Press.

[18] Filippova O., Hänel D. Grid refinement for lattice-BGK models[J]. Journal of Computational Physics, 1998, 147 219-228.

[19] Lin C. L., Lai Y. G. Lattice Boltzmann method on composite grids[J]. Physical Review E, 2000, 62(2): 2219-2225.

[20] Dupuis A., Chopard B. Theory and applications of an alternative lattice Boltzmann grid refinement algorithm[J]. Physical Review E, 2003, 67 066707.

[21] Chen H., Filippova O., Hoch J., et al. Grid refinement in lattice Boltzmann methods based on volumetric formulation[ J] Physica A, 2006, 362 158-167.

[22] He X., Zou Q., Luo L., et al. Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model[J]. Journal of Statistical Physics, 1997, 87(1/2): 115-136.

[23] Mei R., Luo L., Shyy W. An accurate curved boundary treatment in the lattice Boltzmann method[J]. Journal of Computational Physics, 1999, 155 307-330.

[24] Bouzidi M., Firdaouss M., Lallemand P. Momentum transfer of a Boltzmann-lattice fluid with boundaries[J]. Physics of Fluids, 2001, 13(11): 3452-3459.

[25] Guo Z., Zheng C., Shi B. An extrapolation method for boundary conditions in lattice Boltzmann method[J]. Physics of Fluids, 2002, 14(6): 2007-2010.

[26] Ladd A. J. C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation Part 1. Theoretical foundation[J]. Journal of Fluid Mechanics, 1994, 271 285-309.

[27] Jordan S. K., Fromm J. E. Oscillatory drag, lift and torque on a circular cylinder in a uniform flow[J]. The Physics of Fluids, 1972, 15(3): 371-376.

[28] Braza M., Chassaing P., Haminh H. Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder[J]. Journal of Fluid Mechanics, 1986, 165 79-130.

[29] Henderson R. D. Details of the drag curve near the onset of vortex shedding[J]. Physics of Fluids, 1995, 7(9): 2102-2104.

[30] Kravchenko A. G., Moin P., Shariff K. B-Spline method and zonal grids for simulations of complex turbulent flows[J]. Journal of Computational Physics, 1999, 151 757-789.

[31] Meneghini J. R., Saltara F., Siqueira C. L. R., et al. Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements[J]. Journal of Fluids and Structures, 2001, 15 327-350.

[32] Wieselberger C. Neuere feststellungen über die Gesetze des Flüssigkeits- und Luftwiderstandes[J]. Physikalische Zeitschrift, 1921, 22 321-328.

[33] Tritton D. J. Experiments on the flow past a circular cylinder at low Reynolds numbers[J]. Journal of Fluid Mechanics, 1959, 6 547-567.

[34] Williamson C. H. K. Defining a universal and continuous Strouhal-Reynolds number relationship for the laminar vortex shedding of a circular cylinder[J]. The Physics of Fluids, 1988, 31(10): 2742-2744.

[35] Hammache M., Gharib M. A novel method to promote parallel vortex shedding in the wake of circular cylinders[J]. Physics of Fluids A, 1989, 1(10): 1611-1614.

[36] Sheard G. J., Hourigan K., Thompson M. C. Computations of the drag coefficients for low-Reynolds-number flow past rings[J]. Journal of Fluid Mechanics, 2005, 526 257-275.

[37] Rajani B. N., Kandasamy A., Majumdar S. Numerical simulation of laminar flow past a circular cylinder[J]. Applied Mathematical Modeling, 2009, 33 1228-1247.

[38] Roshko A. On the Development of Turbulent Wakes from Vortex Streets, Report 1191 [R]. National Advisory Committee for Aeronautics (NACA), 1954.

[39] Lei C., Cheng L., Kavanagh K. A finite difference solution of the shear flow over a circular cylinder[J]. Ocean Engineering, 2000, 27(3): 271-290.

[40] Zhao M., Cheng L., Teng B., et al. Numerical simulation of viscous flow past two circular cylinders of different diameters[J]. Applied Ocean Research, 2005, 27 39-55.

[41] Breuer M. Numerical and modeling influences on large eddy simulations for the flow past a circular cylinder[J]. International Journal of Heat and Fluid Flow, 1998, 19 512-521.

[42] Beaudan P, Moin P. Numerical Experiments on the Flow Past a Circular Cylinder at Sub-critical Reynolds Number, Report No. TF-62[R]. Department of Mechanical Engineering, Stanford University, 1994.

[43] Kravchenko A. G., Moin P. Numerical studies of flow over a circular cylinder at Re_D=3 900[J]. Physics of Fluids, 2000, 12(2): 403-417.

[44] Ong L., Wallace J. The velocity field of the turbulent very near wake of a circular cylinder[J]. Experiments in Fluids, 1996, 20(6): 441-453.