Direct numerical simulation for backward-facing step flow with turbulence anisotropy analysis in a fully staggered curvilinear grid

A coordinate transformation for a finite difference method using a fully staggered curvilinear grid is applied to solve the incompressible Navier–Stokes equation with a direct numerical method. Without turbulence models, backward facing step simulations are performed with Reynolds numbers ranging from 1.5 × 104 to 3.7 × 104. From a time-averaged result, it is shown that the mainstream velocity rapidly decreases, and downward momentum increases near the end of the recirculating vortex region because of a drastic change of the effective cross-sectional area from the time-averaged flow. The turbulent fluctuation and Reynolds stress are intensified near the end of the recirculating vortex, in which the results show reasonable agreements with the experiment. The Reynolds-averaged Navier–Stokes (RANS) turbulence model and large eddy simulation (LES) are also performed using OpenFOAM. Although the RANS model could not produce the turbulent fluctuations, the time-averaged velocity profile shows a reasonable agreement with the experiment. For the LES, the viscosity near the boundary layer is overestimated due to the sub-grid scale eddy viscosity, thus it could not resolve the boundary layer correctly which leads different trend of velocity profile compared to the experiment. Turbulent anisotropic behaviors are also studied with the turbulent anisotropic invariant map. From the result, it is confirmed that turbulent anisotropic behaviors show different characteristics depending on the location of the backward-facing step, and the anisotropic behavior which is close to the isotropic is only observed in the two-separated narrow regions after the step where the gradient of the root mean square magnitude of velocity fluctuation is starting to increase.