改进的浸入边界-晶格Boltzmann法的蠕动流分析
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摘要
基于改进的浸入边界-晶格Boltzmann方法研究蠕动流问题,采用晶格Boltzmann法描述流场,用改进的浸入边界法实现管壁运动-流体流动之间的相互作用,将变形管壁的运动速度作为速度源引入晶格Boltzmann方程,代替了传统浸入边界-晶格Boltzmann法中固态变形力与流体速度之间的转换。分析了管道内蠕动流场的分布情况,研究了各相关参数如振幅比、频率、液体黏度以及波数对流量的影响,数值结果与已有的结果进行了对比,证实了本研究方法的合理性与有效性。
引文
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[2]Blake J R,Vann P G,Winet H.A model of ovum transport[J].Journal of Theoretical Biology,1983,102(102):145-166.
[3]Eytan O,Elad D.Analysis of intra-uterine fluid motion induced by uterine contractions[J].Bulletin of Mathematical Biology,1999,61(2):221-238.
[4]Taber L A,Zhang J,Perucchio R.Computational model for the transition from peristaltic to pulsatile flow in the embryonic heart tube[J].Journal of Biomechanical Engineering,2007,129(3):441-449.
[5]Fung Y C,Yih C S.Peristaltic transport[J].Journal of Applied Mechanics,1967,35(4):669-675.
[6]Jaffrin M Y,Shapiro A H.Peristaltic pumping[J].Fluid Mechanics,1971,3(3):13-37.
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[9]Haroun M H.Effect of wall compliance on peristaltic transport of a Newtonian fluid in an asymmetric channel[J].Mathematical Problems in Engineering,2006,2006(3):39-62.
[10]Srinivas S,Pushparaj V.Non-linear peristaltic transport in an inclined asymmetric channel[J].Communications in Nonlinear Science&Numerical Simulation,2008,13(9):1782-1795.
[11]Tong P,Vawter D.An analysis of peristaltic pumping[J].Journal of Applied Mechanics,1972,39(4):857-862.
[12]Brown T D,Hung T K.Computational and experimental investigations of two-dimensional nonlinear peristaltic flows[J].Journal of Fluid Mechanics,1977,83(2):249-272.
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[14]Peskin C S.Flow patterns around heart valves:a numerical method[J].Journal of Computational Physics,1972,10(2):252-271.
[15]Navidbakhsh M,Rezazadeh M.An immersed boundary-lattice Boltzmann model for simulation of malaria-infected red blood cell in micro-channel[J].Scientia Iranica,2012,19(5):1329-1336.
[16]Wang N T,Fogelson A L.Computational methods for continuum models of platelet aggregation[J].Journal of Computational Physics,1999,151(2):649-675.
[17]Fauci L J,Mcdonald A.Sperm motility in the presence of boundaries[J].Bulletin of Mathematical Biology,1995,57(5):679-699.
[18]Vahidkhah K,Abdollahi V.Numerical simulation of a flexible fiber deformation in a viscous flow by the immersed boundary-lattice Boltzmann method[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(3):1475-1484.
[19]Miller L A,Peskin C S.When vortices stick:an aerodynamic transition in tiny insect flight[J].Journal of Experimental Biology,2004,207(17):3073-3088.
[20]Chen Shiyi,Doolen G D.Lattice Boltzmann method for fluid flows[J].Annual Review of Fluid Mechanics,1998,30(1):329-364.
[21]Grunau D,Chen Shiyi,Eggert K.A lattice Boltzmann model for multiphase fluid flows[J].Physics of Fluids A,1993,5(10):2557-2562.
[22]Fallah K,Khayat M,Borghei M H,et al.Multiplerelaxation-time lattice Boltzmann simulation of nonNewtonian flows past a rotating circular cylinder[J].Journal of Non-Newtonian Fluid Mechanics,2012(177-178):1-14.
[23]Lim C Y,Shu Chang,Niu Xiaodong,et al.Application of lattice Boltzmann method to simulate microchannel flows[J].Physics of Fluids,2002,14(7):2299-2308.
[24]Pan Chongxun,Luo Lishi,Miller C T.An evaluation of lattice Boltzmann schemes for porous medium flow simulation[J].Computers&Fluids,2006,35(8):898-909.
[25]郭亚丽,徐鹤函,沈胜强,等.利用格子Boltzmann方法模拟矩形腔内纳米流体Raleigh-Benard对流[J].物理学报,2013,62(14):1691-1702.Guo Yali,Xu Hehan,Shen Shengqiang,et al.Nanofluid Raleigh-Benard convection in rectangular cavity:simulation with lattice Boltzmann method[J].Acta Physica Sinica,2013,62(14):1691-1702.(in Chinese)
[26]Fauci L J.Peristaltic pumping of solid particles[J].Computers&Fluids,1992,21(4):583-598.
[27]Chrispell J,Fauci L.Peristaltic pumping of solid particles immersed in a viscoelastic fluid[J].Mathematical Modelling of Natural Phenomena,2010,20(5):67-83.
[28]Connington K,Kang Qinjun,Viswanathan H,et al.Peristaltic particle transport using the lattice Boltzmann method[J].Physics of Fluids,2009,21(5):711-715.
[29]Waldrop L,Miller L.Large-amplitude,short-wave peristalsis and its implications for transport[J].Biomechanics and Modeling in Mechanobiology,2016,15(3):629-642.
[30]Liu Feifei,Ren Xiaofei,Wei Shoushui,et al.Bio-inspired micro pump model based on the movement pattern of sperm[J].International Journal of Hybrid Information Technology,2016,9(11):323-336.
[31]Guo Zhaoli,Shi Baochang,Wang Nengchao.Lattice BGK model for incompressible navier–stokes equation[J].Journal of Computational Physics,2000,165(1):288-306.
[32]Zhang Junfeng,Johnson P C,Popel A S.Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows[J].Microvascular Research,2009,77(3):265-272.
[33]Zinner G,Geister B.An extrapolation method for boundary conditions in lattice Boltzmann method[J].Physics of Fluids,2007,14(14):2007-2010.
[34]Chen Shiyi,Martínez D,Mei R.On boundary conditions in lattice Boltzmann methods[J].Physics of Fluids,1998,8(9):2527-2536.
[35]Yong K S,Kang J,Kang S.Assessment of algorithms for the no-slip boundary condition in the lattice Boltzmann equation of BGK model[J].International Journal for Numerical Methods in Fluids,2008,58(12):1353-1378.
[2]Blake J R,Vann P G,Winet H.A model of ovum transport[J].Journal of Theoretical Biology,1983,102(102):145-166.
[3]Eytan O,Elad D.Analysis of intra-uterine fluid motion induced by uterine contractions[J].Bulletin of Mathematical Biology,1999,61(2):221-238.
[4]Taber L A,Zhang J,Perucchio R.Computational model for the transition from peristaltic to pulsatile flow in the embryonic heart tube[J].Journal of Biomechanical Engineering,2007,129(3):441-449.
[5]Fung Y C,Yih C S.Peristaltic transport[J].Journal of Applied Mechanics,1967,35(4):669-675.
[6]Jaffrin M Y,Shapiro A H.Peristaltic pumping[J].Fluid Mechanics,1971,3(3):13-37.
[7]Hanin M.The flow through a channel due to transversally oscillating walls(mean flow rate calculated for flow in two dimensional channel generated by transverse deflection oscillations along walls)[J].Israel Journal of Technology,1968,6:67-71.
[8]Weinberg S L,Eckstein E C,Shapiro A H.An experimental study of peristaltic pumping[J].Journal of Fluid Mechanics,1971,49(3):461-479.
[9]Haroun M H.Effect of wall compliance on peristaltic transport of a Newtonian fluid in an asymmetric channel[J].Mathematical Problems in Engineering,2006,2006(3):39-62.
[10]Srinivas S,Pushparaj V.Non-linear peristaltic transport in an inclined asymmetric channel[J].Communications in Nonlinear Science&Numerical Simulation,2008,13(9):1782-1795.
[11]Tong P,Vawter D.An analysis of peristaltic pumping[J].Journal of Applied Mechanics,1972,39(4):857-862.
[12]Brown T D,Hung T K.Computational and experimental investigations of two-dimensional nonlinear peristaltic flows[J].Journal of Fluid Mechanics,1977,83(2):249-272.
[13]Takabatake S,Ayukawa K,Okura M.Numerical analysis of two-dimensional peristaltic flows(3rd report,pumping characteristics of peristaltic transport)[J].Nihon Kikai Gakkai Ronbunshu B Hen/transactions of the Japan Society of Mechanical Engineers Part B,1985,51(467):2365-2372.
[14]Peskin C S.Flow patterns around heart valves:a numerical method[J].Journal of Computational Physics,1972,10(2):252-271.
[15]Navidbakhsh M,Rezazadeh M.An immersed boundary-lattice Boltzmann model for simulation of malaria-infected red blood cell in micro-channel[J].Scientia Iranica,2012,19(5):1329-1336.
[16]Wang N T,Fogelson A L.Computational methods for continuum models of platelet aggregation[J].Journal of Computational Physics,1999,151(2):649-675.
[17]Fauci L J,Mcdonald A.Sperm motility in the presence of boundaries[J].Bulletin of Mathematical Biology,1995,57(5):679-699.
[18]Vahidkhah K,Abdollahi V.Numerical simulation of a flexible fiber deformation in a viscous flow by the immersed boundary-lattice Boltzmann method[J].Communications in Nonlinear Science and Numerical Simulation,2012,17(3):1475-1484.
[19]Miller L A,Peskin C S.When vortices stick:an aerodynamic transition in tiny insect flight[J].Journal of Experimental Biology,2004,207(17):3073-3088.
[20]Chen Shiyi,Doolen G D.Lattice Boltzmann method for fluid flows[J].Annual Review of Fluid Mechanics,1998,30(1):329-364.
[21]Grunau D,Chen Shiyi,Eggert K.A lattice Boltzmann model for multiphase fluid flows[J].Physics of Fluids A,1993,5(10):2557-2562.
[22]Fallah K,Khayat M,Borghei M H,et al.Multiplerelaxation-time lattice Boltzmann simulation of nonNewtonian flows past a rotating circular cylinder[J].Journal of Non-Newtonian Fluid Mechanics,2012(177-178):1-14.
[23]Lim C Y,Shu Chang,Niu Xiaodong,et al.Application of lattice Boltzmann method to simulate microchannel flows[J].Physics of Fluids,2002,14(7):2299-2308.
[24]Pan Chongxun,Luo Lishi,Miller C T.An evaluation of lattice Boltzmann schemes for porous medium flow simulation[J].Computers&Fluids,2006,35(8):898-909.
[25]郭亚丽,徐鹤函,沈胜强,等.利用格子Boltzmann方法模拟矩形腔内纳米流体Raleigh-Benard对流[J].物理学报,2013,62(14):1691-1702.Guo Yali,Xu Hehan,Shen Shengqiang,et al.Nanofluid Raleigh-Benard convection in rectangular cavity:simulation with lattice Boltzmann method[J].Acta Physica Sinica,2013,62(14):1691-1702.(in Chinese)
[26]Fauci L J.Peristaltic pumping of solid particles[J].Computers&Fluids,1992,21(4):583-598.
[27]Chrispell J,Fauci L.Peristaltic pumping of solid particles immersed in a viscoelastic fluid[J].Mathematical Modelling of Natural Phenomena,2010,20(5):67-83.
[28]Connington K,Kang Qinjun,Viswanathan H,et al.Peristaltic particle transport using the lattice Boltzmann method[J].Physics of Fluids,2009,21(5):711-715.
[29]Waldrop L,Miller L.Large-amplitude,short-wave peristalsis and its implications for transport[J].Biomechanics and Modeling in Mechanobiology,2016,15(3):629-642.
[30]Liu Feifei,Ren Xiaofei,Wei Shoushui,et al.Bio-inspired micro pump model based on the movement pattern of sperm[J].International Journal of Hybrid Information Technology,2016,9(11):323-336.
[31]Guo Zhaoli,Shi Baochang,Wang Nengchao.Lattice BGK model for incompressible navier–stokes equation[J].Journal of Computational Physics,2000,165(1):288-306.
[32]Zhang Junfeng,Johnson P C,Popel A S.Effects of erythrocyte deformability and aggregation on the cell free layer and apparent viscosity of microscopic blood flows[J].Microvascular Research,2009,77(3):265-272.
[33]Zinner G,Geister B.An extrapolation method for boundary conditions in lattice Boltzmann method[J].Physics of Fluids,2007,14(14):2007-2010.
[34]Chen Shiyi,Martínez D,Mei R.On boundary conditions in lattice Boltzmann methods[J].Physics of Fluids,1998,8(9):2527-2536.
[35]Yong K S,Kang J,Kang S.Assessment of algorithms for the no-slip boundary condition in the lattice Boltzmann equation of BGK model[J].International Journal for Numerical Methods in Fluids,2008,58(12):1353-1378.