Turbulent heat transfer past a sudden expansion with a porous insert using a nonlinear model

This work presents numerical investigations for turbulent flow and heat transfer in a backward-facing step with and without porous inserts. Two classes of the model were employed, namely linear and nonlinear turbulence closures. The entire set of transport equations was discretized by means of the control volume method and the system of algebraic equations obtained was relaxed using the SIMPLE (Semi Implicit Pressure-Linked Equations) method. Results were first validated against the experimental data and the simulations follow experimental values and trends. Computations further indicated that when using the porous insert, the size, shape, and length of the recirculating region were drastically reduced in addition to being pushed toward the channel exit, leading eventually to a complete bubble suppression for thicker inserts. A more permeable medium gave better results in quickly suppressing the circulatory motions. By including porous inserts in the channel, turbulence generated due to the shear inside the recirculating region was damped, whereas high levels of k were concentrated within the permeable structure. Large variations for the skin friction factor along the bottom wall were also smoothed out by placing inserts, spanning from a typical distribution for an unobstructed back-step flow to a standard parallel channel flow distribution as the inserts got ticker. On the other hand, at the upper wall, flow pushed toward the top surface gave rise to a sudden increase of the skin friction factor, which was later stabilized downstream the flow. Heat transfer analysis followed showing damping for Nu at the bottom wall as the thickness of the porous substrate was increased. Overall, the thickness of the insert played a dominant role in changing the final flow and heat transfer characteristics rather than the porosity or permeability of the porous material. Finally, this work indicated that the sudden increase of Nu around the reattachment point, known to be undesirable in many practical situations for causing additional thermomechanical loads on the surface, may by avoided by the use of a porous obstacle past the back-step.