Lattice Boltzmann Method For The Simulation Of Sudden Expansion Flows

The sudden expansion problem of Non-newtonian fluid has been widely used in production practice. There are many methods to simulate this kind of physical problem,such as:finite-volume method, finite-element method. Lattice Boltzmann Method is an effective method to simulate this kind of physical method which allows straightforward calculations of the local shear rate to the second-order accuracy. The intension of the article is to simulate the power-law fluids and the viscoelastic fluids and the two-phase fluids in the sudden expansion flow whiche is based on LBM, separately. The work is mainly on:Firstly, in order to test our model for the power-law fluids, we apply it to the simulation of the steady 2D poiseuille. The simulation result agrees well with the analytical result. Then, we apply it to the sudden expansion flow. It is found that:when the Re and u0 is constant, the umaxis increasing with the increasing of n, the x coordination of the center vortex increase and the y coordination decreses, Lr increases. When the n is constant, the χ coordination and Lr is increasing and y coordination is decreasing with the increasing of Re. In addition to that, the streamlines becomes asymmetry.Secondly, in order to test our model for the viscoelastic fluids, we apply it to the simulation of the steady 2D poiseuille. The simulation result agrees well with the analytical result. Then, we apply it to the sudden expansion flow. It is found that:when Re and vs is constant, the Axx、Axy、Ayy is more active with the increasing of Wi, the x coordination and y coordination of the center vortex increases, Lr decreases, when the Wi, vs is constant, the x coordination and Lr is increasing and y coordination is decreasing with the increasing of Re, but the Axx、Axy、Ayy is constant. In addition to that, the change of the Rv and vs don’t have an effect on the streamlines.It is also proposed a two-phase model, which is based on the Shan-Doolen model. Then we apply it to simulate the seperation process of the two phases; the sudden expansion fluid flow (the right boundary is closed); the sudden expansion fluid flow (the right boundary is opened).