Simulating flows in backward-facing step for various expansion ratios by finite element-lattice Boltzmann

Abstract

The development of fluid flow in a channel with constant width and a backward-facing step was investigated through numerical simulation. For the first time, by employing the finite element lattice Boltzmann method, a series of numerical calculations were performed to explore the flow behavior across various Reynolds numbers and expansion ratios (the ratio of the outlet section width to the inlet section width). Analysis was conducted on the macroscopic flow parameters, including velocity fields, streamlines, and reattachment points, for different Reynolds numbers and expansion ratios. It was found that the reattachment length in flows over a backward-facing step is dependent on both the Reynolds number and the expansion ratio, rather than being a function of a singular variable. It was concluded, as the Reynolds number increases, the reattachment length also increases. For a Reynolds number range of 10≤ReD≤100, this increase can be described by an exponential relationship, with an expansion ratio of 1.94. The impact of the expansion ratio is less pronounced at lower Reynolds numbers when compared to that at higher ones. The minimum skin friction factor within the return zone is significantly influenced by the Reynolds number, emphasizing the dominant effects of viscosity in near-wall flows. The lattice Boltzmann method is a computationally efficient algorithm for simulating fluid flows through complex geometries, potentially offering significant processing time savings.