The Numerical Simulation Of Viscoelastic Fluid Flow Based On The Lattice Boltzmann Method

The numerical simulation of viscoelastic fluid is of important value in engineering application, but its complex constitutive equation results in many practical engineering problems losing theoretical solution. The numerical simulation research has always been the hot spot, especially for the extrusion swell problem, although researchers have made a lot of effort, there still exist various problems in this aspect. The lattice Boltzmann method is a new numerical simulation method developed nearly 20 years, different from The traditional numerical method, it is a kind of mesoscopic method based on the theory of molecular motion, whose physical picture is clear, boundary conditions are easy to handle and parallel performance is quiet good, because of these advantages, LBM has been deeply loved by masses of mathematics and mechanics workers since it was born. In this paper, the research content derived from the national natural science fund project named "the numerical simulation research of viscoelastic fluid extrusion swelling and multiphase flow based on the lattice Boltzmann method " is raising a lattice Boltzmann model to simulate the viscoelastic fluid flow as well as the transient extrusion swell.Double distribution functions are adopted to solve the Navier-Stokes equations and Oldroyd-B constitutive equation in this article. The constitutive equation is solved by the convection diffusion LBM, obtaining the elastic stress tensor reflected the elastic effect, and then the stress tensor is introduced into the control equations, helping solve Navier-Stokes equations. Based on this method, the 2D Poiseuille flow of viscoelastic fluid is firstly simulated by FORTRAN assembly language, getting the flow distribution in the runner, the results show that the error between the theoretical solution and LBM numerical solution is quite small, and the speed and configurational tensor curves agree with the theoretical solution curve well. Then the typical 2D convergence flow of viscoelastic fluid is analyzed, getting the distributions of inlet and outlet velocities as well as configuration tensor, Besides, the influence of maximum inlet speed, viscosity, and Wi on the vortex is studied, finding that the vortex area produced in flow passage is decreased with the increase of these parameters. Finally the single-phase LBM with free surface is innovatively introduced to the numerical simulation of the transient extrusion swelling of viscoelastic fluid, proposing a lattice Boltzmann method for the viscoelastic free surface flow, the calculating domain is divided into the gas phase, liquid phase and free surface in this method which brings in the lattice volume fraction and quality and tracks the free surface through computing the quality changes between lattice points. This method is used to find the position of melt interface at different time, successfully simulating the transient extrusion swell phenomenon, in addition, the influence of solvent viscosity ratio Rv and inlet velocity on the extrusion swell are analyzed. In a word, the successful simulation of extrusion swell not only solves the problem of moving interface in the process of extrusion swell, but also expands the lattice Boltzmann method to the free surface flow of viscoelastic fluid field.