幂律流体圆柱绕流的格子波尔兹曼模拟

董波; 李维仲; 冯玉静; 孙涛

doi:10.6052/0459-1879-13-299

幂律流体圆柱绕流的格子波尔兹曼模拟

doi: 10.6052/0459-1879-13-299

大连理工大学海洋能源利用与节能教育部重点实验室, 大连116024

基金项目: 国家自然科学基金青年科学基金（51206017）和国家自然科学基金（51276030）资助项目.

详细信息

作者简介:
董波，讲师，博士后，主要研究方向：两相流、计算流体力学.

中图分类号: O373
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出版历程
- 收稿日期: 2013-09-13
- 修回日期: 2013-10-11
- 刊出日期: 2014-01-18

LATTICE BOLTZMANN SIMULATION OF A POWER-LAW FLUID PAST A CIRCULAR CYLINDER

Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116024, China

Funds: The project was supported by the National Natural Science Foundation of China (51206017) and National Natural Science Foundation of China (51276030).

摘要

摘要: 基于插值补充格子波尔兹曼方法和幂律流体的本构方程，建立了贴体坐标系下适用于幂律流体的格子波尔兹曼模型，模拟了幂律流体的圆柱绕流问题，采用非平衡外推格式处理圆柱表面的速度无滑移边界，利用应力积分法确定曳力系数和升力系数，并与基于标准的格子波尔兹曼方法和有限容积法获得的数值数据进行对比，吻合良好. 进行了网格无关性验证之后，分析了稳态流动时，不同雷诺数下幂律指数对于尾迹长度、分离角、圆柱表面黏度分布、表面压力系数及曳力系数的影响，以及非定常流动中，幂律指数对于流场、曳力系数、升力系数和斯特劳哈尔数的影响. 获得的变化规律与基于其他数值模拟方法得到的结果相一致，充分验证了模型的有效性和正确性. 结果表明：插值补充格子波尔兹曼方法可以用来模拟幂律流体在具有复杂边界流场内的流动问题，通过引入不同的非牛顿流体本构方程，该方法还可以进一步应用于其他类型的非牛顿流体研究中.
- 插值补充格子波尔兹曼方法 /
- 幂律流体 /
- 曳力系数 /
- 升力系数 /
- 圆柱绕流
Abstract: Based on the interpolation-supplemented lattice Boltzmann method and constitutive equation for power-law fluid, a lattice Boltzmann model for power-law fluid in body-fitted coordinates is proposed and applied to simulate steady and unsteady flows of a power-law fluid past a circular cylinder, respectively. The non-equilibrium extrapolation boundary scheme is adopted for the non-slip velocity at the circular cylinder surface. The drag coefficient and lift coefficient are calculated by integrating the total stresses on the boundary of the circular cylinder, respectively, and the results are in good agreement with those obtained by using the conventional lattice Boltzmann method and finite volume method. After performing the grid sensitivity tests, in terms of steady flow, the effects of power-law index on the wake length, separation angle, viscosity distribution over cylinder surface, pressure coefficient and drag coefficient are further analyzed. Moreover, as for unsteady flow, the influences of power-law index on the flow field, drag coefficient, lift coefficient and Strouhal number are investigated. The validation and capability of the model are demonstrated by the good agreement between the simulation results and the ones obtained by other numerical simulation methods. The simulations show that the interpolation-supplemented lattice Boltzmann method can be used to study power-law fluid flow in flow field with complex boundaries, and it can be further applied to study other types of non-Newtonian fluid flow problems by using different constitutive equations.
- interpolation-supplemented lattice Boltzmann method /
- power-law fluid /
- drag coefficient /
- lift coefficient /
- flow past a circular cylinder

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参考文献(22)

Williamson CHK. Vortex dynamics in the cylinder wake. Annual Review of Fluid Mechanics, 1996, 28(1): 477-539

Fornberg B. A numerical study of steady viscous flow past a circular cylinder. Journal of Fluid Mechanics, 1980, 98(4): 819-855

Dennis SCR, Chang GZ. Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100. Journal of Fluid Mechanics, 1970, 42(3): 471-489

Bharti RP, Chhabra RP, Eswaran V. Steady flow of power law fluids across a circular cylinder. The Canadian Journal of Chemical Engineering, 2006, 84(4): 406-421

D'Alessio SJD, Pascal JP. Steady flow of a power-law fluid past a cylinder. Acta Mechanica, 1996, 117(1-4): 87-100

Chhabra RP, Soares AA, Ferreira JM. Steady non-Newtonian flow past a circular cylinder: A numerical study. Acta Mechanica, 2004, 172(1-2): 1-16

Bharti RP, Chhabra RP, Eswaran V. Two-dimensional steady poiseuille flow of power-law fluids across a circular cylinder in a plane confined channel: Wall effects and drag coefficients. Industrial & Engineering Chemistry Research, 2007, 46(11): 3820-3840

Sivakumar P, Prakash Bharti R, Chhabra RP. Effect of power-law index on critical parameters for power-law flow across an unconfined circular cylinder. Chemical Engineering Science, 2006, 61(18): 6035-6046

Patnana VK, Bharti RP, Chhabra RP. Two-dimensional unsteady flow of power-law fluids over a cylinder. Chemical Engineering Science, 2009, 64(12): 2978-2999

邬小军. 静止和转动圆柱绕流的格子波尔兹曼模拟. [硕士论文]. 武汉: 华中科技大学, 2009 (Wu Xiaojun. The lattice Boltzmann method simulation of the flow past static and rotating circular cylinder. [Master Thesis]. Wuhan: Huazhong University of Science and Technology, 2009(in Chinese))

龚帅, 郭照立. 流向振荡圆柱绕流的格子波尔兹曼方法模拟. 力学学报, 2011, 43(1): 11-17 (Gong Shuai, Guo Zhaoli. Lattice Boltzmann simulation of the flow around a circular cylinder oscillating streamwisely.it Chinese Journal of Theoretical and Applied Mechanics, 2011,43(1):11-17 (in Chinese))

龚帅, 郭照立. 横向振荡圆柱绕流的格子波尔兹曼方法模拟. 力学学报, 2011, 43(5): 809-818 (Gong Shuai, Guo Zhaoli. Lattice Boltzmann simulation of flow over a transversely oscillating circular cylinder. Chinese Journal of Theoretical and Applied Mechanics, 2011,43(5):809-818 (in Chinese))

Ku X, Lin J. Numerical simulation of the flows over two tandem cylinders by lattice Boltzmann method. Modern Physics Letters B, 2005. 19(28-29): 1551-1554

Nejat A, Abdollahi V, Vahidkhah K. Lattice Boltzmann simulation of non-Newtonian flows past confined cylinders. Journal of Non-Newtonian Fluid Mechanics, 2011, 166: 689-697

He X, Doolen G. Lattice Boltzmann method on curvilinear coordinates system: Flow around a circular cylinder. Journal of Computational Physics, 1997, 134(2): 306-315

He X, Doolen GD. Lattice Boltzmann method on a curvilinear coordinate system: Vortex shedding behind a circular cylinder. Physical Review E, 1997, 56(1): 434-440

Chai Z, Shi B, Guo Z, et al. Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows. Journal of Non-Newtonian Fluid Mechanics, 2011, 166: 332-342

何雅玲,王勇,李庆. 格子波尔兹曼方法的理论及应用. 北京: 科学出版社, 2008 (He Yaling, Wang Yong, Li Qing. Lattice Boltzmann Method: Theory and Applications. Beijing: Science Press, 2008 (in Chinese))

Lee T, Lin CL. An eulerian description of the streaming process in the lattice Boltzmann equation. Journal of Computational Physics, 2003, 185(2): 445-471

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

Mei R, Yu D, Shyy W, et al. Force evaluation in the lattice Boltzmann method involving curved geometry. Physical Review E, 2002, 65(4): 041203

Soares AA, Ferreira JM, Chhabra RP. Flow and forced convection heat transfer in crossflow of non-Newtonian fluids over a circular cylinder. Industrial & Engineering Chemistry Research, 2005, 44(15): 5815-5827

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