Hydrodynamic Behavior of Different No-Slip Condition on the Curved Boundaries in the Lattice Boltzmann Method

Document Type : Research Article

Authors

1 زنجان-مهندسی- گروه مهندسی مکانیک

2 Department of Mechanical Engineering, University of Zanjan

Abstract

This paper examines the various methods of applying no-slip boundary condition on a fixed and rotary cylinder in the lattice Boltzmann framework. For this purpose, five methods of bounce[1]back, linear and quadratic method of Yu and the linear and quadratic method of Bouzidi are chosen. The main challenge in all of these methods is how to calculate and interpolate the unknown distribution functions at the points around the boundary points. Results show that in the stable conditions (Re=20 and Re=40), the maximum error of calculation of the separation angle is 6.7 % and it is related to the bounce-back method, while in the stable conditions, a significant difference cannot be seen between the bounce-back and other methods. Also, the linear method of Bouzidi has the most error in calculating the separation length (6% for Re=20 and 8.82 % for Re=40). By increasing the Reynolds number and increasing the rotational velocity, a difference in the lift coefficient in the early times, t*> 7.78 grows for the conditions of k=0.2 and Re=200, between the bounce-back and other methods, however with increasing time, this difference reduces, whereas the three methods of linear Yu, linear Bouzidi and quadratic Bouzidi, continue to produce similar results.

Keywords

Main Subjects


[1] A.A. Mohamad, Lattice Boltzmann method: fundamentals and engineering applications with computer codes, Springer Science & Business Media, 2011.
[2] M. Sukop, DT Thorne, Jr. Lattice Boltzmann Modeling Lattice Boltzmann Modeling,  (2006).
[3] K. Timm, H. Kusumaatmaja, A. Kuzmin, The lattice Boltzmann method: principles and practice, in, Springer: Berlin, Germany, 2016.
[4] T. Lee, G.K. Leaf, Eulerian description of high-order bounce-back scheme for lattice Boltzmann equation with curved boundary, The European Physical Journal Special Topics, 171(1) (2009) 3-8.
[5]  S. Chen, S. Bao, Z. Liu, J. Li, C. Yi, C. Zheng, A heuristic curved-boundary treatment in lattice Boltzmann method, EPL (Europhysics Letters), 92(5) (2010) 54003.
[6]  S. Tao, Z. Guo, Boundary condition for lattice Boltzmann modeling of microscale gas flows with curved walls in the slip regime, Physical Review E, 91(4) (2015) 043305.
[7]  P.-H. Kao, R.-J. Yang, An investigation into curved and moving boundary treatments in the lattice Boltzmann method, Journal of Computational Physics, 227(11) (2008) 5671-5690.
[8]  J.C. Verschaeve, B. Müller, A curved no-slip boundary condition for the lattice Boltzmann method, Journal of Computational Physics, 229(19) (2010) 6781-6803.
[9] J. Latt, B. Chopard, O. Malaspinas, M. Deville, A. Michler, Straight velocity boundaries in the lattice Boltzmann method, Physical Review E, 77(5) (2008) 056703.
[10]  L. Budinski, MRT lattice Boltzmann method for 2D flows in curvilinear coordinates, Computers & Fluids, 96 (2014) 288-301.
[11]  Y. Kuwata, K. Suga, Anomaly of the lattice Boltzmann methods in three-dimensional cylindrical flows, Journal of Computational Physics, 280 (2015) 563-569.
[12]  Z.-m. Zhao, P. Huang, S.-t. Li, Lattice Boltzmann model for shallow water in curvilinear coordinate grid, Journal of Hydrodynamics, 29(2) (2017) 251-260.
[13]  A. Velasco, J. Muñoz, M. Mendoza, Lattice Boltzmann model for the simulation of the wave equation in curvilinear coordinates, Journal of Computational Physics, 376 (2019) 76-97.
[14]  O. Filippova, D. Hänel, Boundary-fitting and local grid refinement for lattice-BGK models, International Journal of Modern Physics C, 9(08) (1998) 1271.9721
[15]  R. Mei, L.-S. Luo, W. Shyy, An accurate curved boundary treatment in the lattice Boltzmann method, Journal of computational physics, 155(2) (1999) 307.033
[16]  R. Mei, W. Shyy, D. Yu, L.-S. Luo, Lattice Boltzmann method for 3-D flows with curved boundary, Journal of Computational Physics, 161(2) (2000) 680-699.
[17]  D. Yu, R. Mei, L.-S. Luo, W. Shyy, Viscous flow computations with the method of lattice Boltzmann equation, Progress in Aerospace Sciences, 39(5) (2003) 329-367.
[18]  D. Yu, R. Mei, W. Shyy, A unified boundary treatment in lattice boltzmann method, in:  41st Aerospace Sciences Meeting and Exhibit, 2003, pp. 953.
[19]  O.R. Mohammadipoor, H. Niazmand, S. Mirbozorgi, Alternative curved-boundary treatment for the lattice Boltzmann method and its application in simulation of flow and potential fields, Physical Review E, 89(1) (2014) 013309.
[20]  O.R. Mohammadipour, S. Succi, H. Niazmand, General curved boundary treatment for two-and threedimensional stationary and moving walls in flow and nonflow lattice Boltzmann simulations, Physical Review E, 98(2) (2018) 023304.
[21]  A.J. Ladd, Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation, Journal of fluid mechanics, 271 (1994) 285-309.
[22]  A.J. Ladd, Short-time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation, Physical Review Letters, 70(9) (1993) 1339.
[23]  M.h. Bouzidi, M. Firdaouss, P. Lallemand, Momentum transfer of a Boltzmann-lattice fluid with boundaries, Physics of fluids, 13(11) (2001) 3452-3459.
[24]  S. Dennis, G.-Z. Chang, Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100, Journal of Fluid Mechanics, 42(3) (1970) 471-489.
[25]  M. Coutanceau, C. Menard, Influence of rotation on the near-wake development behind an impulsively started circular cylinder, Journal of Fluid Mechanics,158(1985)399-446 .