重力场内流体-纤维流固耦合分析
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摘要
为了研究计及重力场的流体与柔性体耦合的动力行为,探究其动力学内在规律,基于格子玻尔兹曼方法(lattice Boltzmann method,LBM)、浸入边界法(immersed boundary method,IBM)和动量交换原理(momentum exchange,ME)结合的ME-IBMLBM理论,采用有限差分法(finite difference method,FDM)对二维空间里受重力场影响的单根柔性纤维在均匀流场中的运动特性进行了数值模拟,探究了不同流体速度(U_0)、纤维长度(L_x)和线密度(M)下单根柔性纤维在多场耦合作用下的动态响应。研究结果表明,在一定的U_0、L_x、M条件下,一端固定柔性纤维运动在多场耦合作用下有稳态与非稳态两种基本运动形式,与实际情况相符。根据模拟数据分析,发现纤维可在以下三种多场耦合模型中呈现稳态运动:(1)若U_0=0. 02、L_x=30,M应小于0. 2;(2)若M=0. 25、U_0=0. 02,L_x应小于26;(3)若M=0. 3、L_x=36,U_0应大于0. 06。
In order to study the dynamic behaviors of the fluid coupled with the flexible body within gravity field,numerical simulation of the motion characteristics of single flexible fiber in a two-dimensional space affected by the gravity field and uniform flow field based on the finite difference method( FDM) combined with the lattice Boltzmann method( LBM),immersed boundary method( IBM) and momentum exchange( ME) has been implemented. Especially,the dynamic response of single flexible fiber with one end fixed and different lengths under different fluid inlet speeds and fiber densities under multiple fields has been investigated. Results show that the flexible fiber with one end fixed can reach the two basic motion,i e,steady state motion and unsteady state motion,which is in the condition of multi-field coupling and certain U_0,L_x,M,this is consistent with the actual situation.According to the simulation results,it is found that fiber reaches steady state motion in the following three multifield coupling models:(1) U_0= 0. 02、L_x= 30,M is less than 0. 2;(2) M = 0. 25、U_0= 0. 02,L_xis less than 26;(3) M = 0. 3、L_x= 36,U_0 is greater than 0. 06
In order to study the dynamic behaviors of the fluid coupled with the flexible body within gravity field,numerical simulation of the motion characteristics of single flexible fiber in a two-dimensional space affected by the gravity field and uniform flow field based on the finite difference method( FDM) combined with the lattice Boltzmann method( LBM),immersed boundary method( IBM) and momentum exchange( ME) has been implemented. Especially,the dynamic response of single flexible fiber with one end fixed and different lengths under different fluid inlet speeds and fiber densities under multiple fields has been investigated. Results show that the flexible fiber with one end fixed can reach the two basic motion,i e,steady state motion and unsteady state motion,which is in the condition of multi-field coupling and certain U_0,L_x,M,this is consistent with the actual situation.According to the simulation results,it is found that fiber reaches steady state motion in the following three multifield coupling models:(1) U_0= 0. 02、L_x= 30,M is less than 0. 2;(2) M = 0. 25、U_0= 0. 02,L_xis less than 26;(3) M = 0. 3、L_x= 36,U_0 is greater than 0. 06
引文
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6曾泳春.纤维在喷嘴高速气流场中运动的研究和应用[D].上海:东华大学,2003Zeng Yongchun.Research and application of fiber movement in nozzle high velocity airflow field[D].Shanghai:Donghua University,2003
7 Tian F B,Luo H,Zhu L,et al.An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments[J].Journal of Computational Physics,2011,230(19):7266-7283
8袁海专.基于LBM的两类流固问题与带表面活性剂流体问题的数值方法研究[D].湘潭:湘潭大学,2014Yuan Haizhuan.Two kinds of fluid-solid problems based on LBM and numerical methods with surfactant fluid problems[D].Xiangtan:Xiangtan University,2014
9郭照立,郑楚光.格子Boltzmann方法的原理和应用[M].北京:科学出版社,2008:15-68Guo Zhaoli,Zheng Chuguang.Principle and application of lattice Boltzmann method[M].Beijing:Science Press,2008:15-68
10 Peskin C S.The immersed boundary method[J].Acta Numerica,2003,11:479-517
11 Kim Y,Peskin C S.Penalty immersed boundary method for an elastic boundary with mass[J].Physics of Fluids,2007,19(5):220-337
12 Guo Z,Zheng C,Shi B.Discrete lattice effects on the forcing term in the lattice Boltzmann method[J].Physical Review E,2002,65:046308
13 Zhu L.Peskin C S.Simulation of a flexible flapping filament in a flowing soap film by the immersed boundary method[J].Journal of Computational Physics,2002,179(2):452-468
14 Connell B S H,Yue D K P.Flapping dynamics of an flag in a uniform stream[J].Journal of Fluid Mechanics,2007,581(1):33-67
2 Kong L X,Platfoot R A.Computational two-phase air/fiber flow within transfer-channels of rotor spinning machines[J].Textile Research Journal,1997,67(4):269-278
3 Zou Z,Cheng L,Xi B,et al.Investigation of fiber trajectory affected by some parameter variables in vortex spun yarn[J].Textile Research Journal,2015,85(2):180-187
4 Zhu L,Peskin C S.Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method[J].Journal of Computational Physics,2002,179(2):452-468
5 Huang W,Shin S J,Sung H J.Simulation of flexible filaments in a uniform flow by the immersed boundary method[J].Journal of Computational Physics,2007,226(2):2206-2228
6曾泳春.纤维在喷嘴高速气流场中运动的研究和应用[D].上海:东华大学,2003Zeng Yongchun.Research and application of fiber movement in nozzle high velocity airflow field[D].Shanghai:Donghua University,2003
7 Tian F B,Luo H,Zhu L,et al.An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments[J].Journal of Computational Physics,2011,230(19):7266-7283
8袁海专.基于LBM的两类流固问题与带表面活性剂流体问题的数值方法研究[D].湘潭:湘潭大学,2014Yuan Haizhuan.Two kinds of fluid-solid problems based on LBM and numerical methods with surfactant fluid problems[D].Xiangtan:Xiangtan University,2014
9郭照立,郑楚光.格子Boltzmann方法的原理和应用[M].北京:科学出版社,2008:15-68Guo Zhaoli,Zheng Chuguang.Principle and application of lattice Boltzmann method[M].Beijing:Science Press,2008:15-68
10 Peskin C S.The immersed boundary method[J].Acta Numerica,2003,11:479-517
11 Kim Y,Peskin C S.Penalty immersed boundary method for an elastic boundary with mass[J].Physics of Fluids,2007,19(5):220-337
12 Guo Z,Zheng C,Shi B.Discrete lattice effects on the forcing term in the lattice Boltzmann method[J].Physical Review E,2002,65:046308
13 Zhu L.Peskin C S.Simulation of a flexible flapping filament in a flowing soap film by the immersed boundary method[J].Journal of Computational Physics,2002,179(2):452-468
14 Connell B S H,Yue D K P.Flapping dynamics of an flag in a uniform stream[J].Journal of Fluid Mechanics,2007,581(1):33-67