基于格子Boltzmann两相模型的粘弹流体挤出胀大分析

挤出胀大的数值模拟是非牛顿流体研究中具有挑战性的问题．本文运用格子Boltzmann方法(LBM)分析Oldroyd-B和多阶松弛谱PTT粘弹流体的挤出胀大现象，采用颜色模型模拟出口处粘弹流体和空气的两相流动，通过重新标色获得两种流体的界面，并最终获得胀大的形状．Navier-Stokes方程和本构方程的求解采用双分布函数模型．将胀大的结果与解析解、实验解和单相自由面LBM结果进行了比较，发现格子Boltzmann两相模型结果与解析解和实验结果相吻合，相比于单相模型，收敛速度更快，解的稳定性更高．研究了流道尺寸对胀大率的影响，并对挤出胀大的内在机理进行了分析．

Analysis of Viscoelastic Fluid Extrusion Swell Based on Lattice Boltzmann Two-Phase Model

The numerical simulation of extrusion swell is a challenging task in non-Newtonian research. In this paper the lattice Boltzmann method is applied to the extrusion swell simulation of viscoelastic fluid described by the Oldroyd-B and multi-mode PTT constitutive equations. Two-phase flow outside channel is simulated using the color model and the free surface of flow obtained by recoloring. The Navier-Stokes equations and the constitutive equations are solved using double distribution functions. A set of numerical tests is conducted to show that the numerical results are in agreement with some available analytical solutions and experimental data. The convergence speed of the two-phase model is faster than that of the single-phase model. The effect of channel size on the swelling rate is studied, and the intrinsic mechanism of extrusion swelling is analyzed.