粘弹性流体流固耦合的数值模拟研究

发布时间：2018-03-23 18:30

本文选题：数值方法　切入点：流固耦合　出处：《中国科学技术大学》2017年硕士论文

【摘要】：本文主要发展了一种可以用于处理粘弹性流体流固耦合的数值方法,并用该方法模拟了单根柔性丝线和铰接在固定圆柱后端的柔性丝线在粘弹性流体中的流固耦合问题。主要工作及研究成果如下:(1)发展了一套模拟粘弹性流体流固耦合的有效数值方法,其中:采用格子波尔兹曼方法(LBM)求解不可压Navier-Stokes(N-S)方程;非线性有限元方法(nFEM)求解柔性固体的运动方程;有限差分方法(FDM)求解粘弹性流体的本构方程,其中对流项离散采用无震荡的高阶迎风格式(VONOS格式);最后,采用罚方法的浸没边界方法实现流固耦合。(2)验证了该方法的可靠性。通过模拟粘弹性流体的二维伯肖叶流动,将计算结果与该问题解析解进行对比;计算经典的圆柱绕流问题,与前人的工作进行对比,验证了该方法中粘弹性流体运动方程求解器的可靠性。另外,通过模拟牛顿流体中丝线的拍动问题,并与前人结果进行对比,验证了流固耦合求解器的可靠性。(3)研究流体弹性效应对单根丝线拍动特性的影响。计算结果发现,对于流体弹性效应较弱的情况(We20),柔性丝线从稳定(静止)模态过渡为周期性拍动模态的临界质量比随着We数的增加显著增大;而对于弹性效应较强的情况(We20),临界质量比随着We数的增加渐近地趋于一常值。另外还发现,当质量比给定时,拍动丝线的阻力系数、拍动幅值和拍动频率均随We数的增加而减小。以上发现表明,流体弹性效应的增强对丝线拍动和尾迹流动失稳脱涡具有明显的抑制作用。(4)研究了流体弹性效应对铰接在固定圆柱后的丝线拍动特性的影响。计算结果发现,在粘弹性流体中,圆柱后的丝线的运动模态除了简单的对称模态(模态S)和非对称模态(模态A),还存在着一种过渡模态(模态I),丝线从模态A转变到模态S的临界长度LAS以及从模态A转变到模态I的临界长度LAI均随着流体弹性的增强而增加。同时,计算结果还发现,不同长度、不同抗弯刚度的丝线所受的阻力随着We数的增加而呈现不同的变化趋势。
[Abstract]:In this paper, a numerical method for fluid-solid coupling of viscoelastic fluids is developed. This method is used to simulate the fluid-solid coupling problem between a single flexible wire and a flexible wire hinged at the end of a fixed cylinder in viscoelastic fluid. The main work and research results are as follows: 1) A set of simulated viscoelastic fluid fluid-solid has been developed. Coupled effective numerical method, The lattice Boltzmann method is used to solve the incompressible Navier-Stokes N-S equation; the nonlinear finite element method is used to solve the motion equation of flexible solid; and the finite difference method is used to solve the constitutive equation of viscoelastic fluid. The convection term is discretized by the high-order upwind scheme without oscillations, and the Vonos scheme is used. Finally, the method is proved to be reliable by using the immersion boundary method of penalty method to realize fluid-solid coupling. The computational results are compared with the analytical solution of the problem, the classical cylinder flow problem is calculated and compared with the previous work, which verifies the reliability of the viscoelastic fluid motion equation solver in this method. By simulating the flapping of filaments in Newtonian fluid and comparing with the previous results, the reliability of fluid-solid coupling solver is verified. In the case of weak elastic effect of fluid, the critical mass ratio of flexible wire from stable (static) mode to periodic flapping mode increases significantly with the increase of We number. For the case of strong elastic effect, the critical mass ratio gradually tends to a constant with the increase of We number. It is also found that when the mass ratio is given, the drag coefficient of the flapping thread is obtained. The amplitude and frequency of flapping decrease with the increase of We number. The enhancement of fluid elastic effect has obvious inhibitory effect on filaments flapping and wake flow instability and devortex. The influence of fluid elastic effect on filaments flapping behind fixed cylinder is studied. The calculated results show that in viscoelastic fluids, In addition to the simple symmetric mode (mode S) and asymmetric mode (mode A), there exists a transition mode (mode I _ (1)), the critical length of the silk line from mode A to mode S (LAS) and the mode (mode). The critical length LAI of the transition from state A to mode I increases with the enhancement of fluid elasticity. It is also found that the resistance of the silk lines with different lengths and different bending stiffness varies with the increase of the number of We.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O353.4

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