Computational Modelling of Turbulent Flows Using an Adaptive Mesh Finite Element Method: A Benchmarking Study

Abstract

Modelling turbulence is essential in the chemical and bioprocess industry due to the mixing it creates. In the past, engineers have used two-equation Reynolds Averaged Navier–Stokes (RANS) k –$\epsilon$ model due to its economical nature; however, it lacks accuracy; whereas direct numerical simulation (DNS) is computationally expensive. Large eddy simulation (LES) turbulence model provides a bridge between the above two models as it resolves the larger scales and models the smaller universal scales of motion. The finite element method (FEM) has become popular in computational mechanics due to the ease with which it can handle unstructured meshes (as opposed to the finite difference method) and the ease in obtaining higher order accurate schemes (through the use of higher order shape functions) as compared to finite volume method. Although there is some work on the solution of LES turbulence model using FEM in the literature, there is a lack of clarity when it comes to the use of different discretisation schemes and solvers. The current work presents a detailed numerical analysis of turbulent flow over a two-dimensional backward-facing step (BFS) using a continuous Galerkin finite element method in an open-source finite element framework—Fluidity, which allows fully unstructured aniostropic adaptive mesh refinement along with the use of distributed parallelism. Fixed and adaptive mesh parallelised simulations are presented for a Reynolds number of 2000 for incompressible flow. The use of different LES models (second-order Smagorinsky and dynamic tensorial), non-linear relaxation parameters and velocity–pressure shape function pairs are thoroughly investigated. The primary reattachment length was calculated and compared against experimental data, finding a good match. Thus, it was concluded that the anisotropy of turbulence, which was captured using this method, can be modelled effectively using an adaptive mesh finite element method.