粘弹流体轴对称流动的格子Boltzmann方法

基于BGK碰撞模型,通过在迁移方程中引入作用力项,建立了粘弹流体的轴对称格子Boltzmann模型.通过Chapman-Enskog展开,获得了准确的柱坐标下轴对称宏观流动方程.采用双分布函数对运动方程和本构方程进行迭代求解,模拟分析了粘弹流体管道流动,获得了流场中的速度和构型张量的分布,通过与解析解进行比较,验证了模型的准确性.研究了作为粘弹流体流动基准问题的收敛流动,对涡旋位置进行了定量分析,将回转长度的计算结果与有限体积法进行了比较,两种数值结果十分吻合.研究结果表明,模型能够准确表征粘弹流体的轴对称流动,具有较广阔的应用前景.

Lattice Boltzmann Method for Axisymmetric Flows of Viscoelastic Fluid

Based on BGK collision model, a new axisymmetric lattice Boltzmann model was proposed for viscoelastic fluid flows by introducing a force term in the transport equation. The precise form of the macroscopic flow equations in the cylindrical polar coordinate system was derived through Chapman-Enskog analysis. The equations of motion and constitutive relation were solved iteratively using double distribution function. The model was used to simulate the flows of viscoelastic fluids in the straight pipe. The model accuracy was verified by comparing the results of velocity and conformation tensor with the analytical solution. The contraction flow as a benchmark for viscoelastic fluid flow was also studied. The position of the vortex was analyzed quantitatively. The obtained re-attachment length agrees very well with the result of the finite volume method. The research results show that the model can accurately characterize the axisymmetric flows of viscoelastic fluids and has broad application prospects.