Numerical simulation of the viscous incompressible fluid flow and heat transfer in a plane channel with backward-facing step

The paper deals with the results of solving the problem of steady-state flow of a viscous incompressible fluid in a plane channel with a backward-facing step and a heated bottom wall for the Reynolds number in the range $100\leqslant \mathrm{Re}\leqslant1000$ and the expansion ratio of a plane channel in the range $1.11 \leqslant ER \leqslant 10$. The study was carried out by numerical integration of the 2-D Navier–Stokes equations in velocity-pressure formulation on uniform grids with a step which equals to 1/300. Correction of the results is confirmed by comparing them with the literature data. Detailed flow patterns and fields of stream overheating depending on two basic parameters of the problem $\mathrm{Re}$ and $ER$ are demonstrated. It is shown that with the increase of parameters $\mathrm{Re}$ and $ER$ the structure of flow becomes much more complicated, that is, there is an increase of the number of vortices and their sizes up to the formation of a vortex behind the backward-facing step with two centers of rotation. It is also stated that the typical height of the heating zone of the flow depends weakly on $\mathrm{Re}$ and $ER$ and eventually, near the exit of the channel, equals approximately half of the channel height. For all centers of vortices their main characteristics are defined: location, extremums of stream function, vorticity. Complex nonmonotonic behaviors of the coefficients of friction, hydrodynamic resistance and heat transfer (Nusselt number) along the channel are analyzed. It is shown that these coefficients strongly depend both on Reynolds number and on expansion ratio, reaching the maximum values at the maximum values of $\mathrm{Re}$ and $ER$.