Turbulence structure and heat transfer in a sudden expansion with a porous insert using linear and non-linear turbulence models

Flow past a sudden expansion is found in a number of engineering equipment of practical relevance. This article presents numerical results for turbulence structure and heat transfer in flow past a two-dimensional backward-facing-step channel with a porous insert using linear and non-linear eddy viscosity macroscopic models. The expansion ratio is 1:3. The non-linear turbulence models are known to perform better than classical eddy-diffusivity models due to their ability to simulate important characteristics of the flow. Parameters such as porosity, permeability and thickness of the porous insert are varied in order to analyze their effects on the flow pattern, particularly on the damping of the recirculating bubble after the porous insertion. The numerical technique employed for discretizing the governing equations is the control-volume method. The SIMPLE algorithm is used to correct the pressure field. Wall functions for velocity and temperature are used in order to bypass fine computational close to the wall. Results showed that the recirculating bubbles simulated with the linear model were shorter than those calculated with non-linear theories. Thickness of the insert had a more pronounced effect in suppressing the recirculating bubble than permeability or porosity. Results for the statistical field indicate that using porous inserts dampens generation of turbulence along the channel and concentrate conversion of mean mechanical energy into turbulence inside the porous material. Inserting a porous substrate past the expansion seems to be a practical way to decrease the sudden variations on C-f and St.