Direct numerical simulation of low-Prandtl fluid flow over a confined backward facing step

Abstract

The paper presents the direct numerical simulation (DNS) of a confined backward facing (BFS) step geometry with a flow of two fluids with Prandtl numbers 0.005 and 0.1. The expansion ratio of the BFS geometry is equal to 2.25 and the outflow of the geometry has a shape of a rectangle. The geometry is surrounded by no-slip walls and has no periodic boundaries. Additionally, a step wall and a heater are simulated, which are thermally coupled with each other and to the fluid domain. A recycling boundary condition is used to achieve a fully turbulent inflow boundary condition with a constant mass flow rate. The friction Reynolds number of the flow in the channel before the step is around 207 and the Reynolds number based on the bulk velocity at the inflow and the hydraulic diameter of the inflow is approximately 7100. The reattachment zone was found at about 7.9 step heights downstream of the step. Because the step is confined in the span-wise direction, the average flow exhibits strong 3D features. These features significantly increase the averaging times to achieve sufficiently low statistical uncertainties of flow properties. The DNS is performed with moderate spatial resolution on 30 million grid points, however, it took very long averaging time and 8 million time steps to obtain acceptable statistical uncertainties. In the paper we explore the 3D features and give first and second order statistics for flow and thermal fields, which are relevant for the validation of RANS modelling approach. To this regard, an advanced and well calibrated turbulent heat flux model, called AHFM-NRG+, is selected for validation in this paper.