Lattice Boltzmann method for direct numerical simulation of viscoplastic turbulent flow

Abstract

Turbulent flows of viscoplastic fluids are present in a number of industrial applications. However, the development of simulation methods and models for non-Newtonian turbulence are still in its early days. In this thesis, a numerical scheme based on lattice Boltzmann method (LBM) was developed for viscoplastic fluid flows. Then, this scheme was used in direct numerical simulations of viscoplastic turbulent channel flow. A complete numerical methodology for Bingham fluid flow was formulated, as well as the Chapman-Enskog expansion for the demonstration of its macroscopic equivalence. The use of regularization of ghost moments has resulted in remarkably stable simulations, at very low or high relaxation frequencies. A great characteristic of LBM is the possibility of representing infinite viscosity by setting the relaxation frequency to zero. This enables the representation of the Bingham constitutive equation without artifacts. Steady-state and transient benchmark cases were solved in order to validate the present LB scheme. For the turbulent channel flow with Bingham fluid, the friction Reynolds number was fixed at 180, while the Bingham number varied from 0 (Newtonian) to 0.15. It is shown that unyielded portions of material travel along with the flow around the centerline. Unlike some studies suggested, these unyielded spots do not disappear quickly, but rather have a significant life-time. Another interesting outcome is that the yield stress has the effect on increasing the turbulence anisotropy, by making the spanwise and normal velocity fluctuations lower, while the streamwise component increases. In general, the direct numerical results achieved by LBM were very similar to those obtained by other numerical methods.