Modelling friction and heat transfer in turbulent forced convection over porous lattices

Abstract

We perform direct numerical simulations (DNS) to investigate how cubic-lattice porous substrates influence momentum and heat transfer in turbulent channel flows. The simulations span friction Reynolds numbers from 260 to 1500, Prandtl numbers of 0.5, 1, and 2, and substrate porosities of 50%, 71%, and 87%. We show that theories developed for rough- wall turbulence can be extended to porous surfaces by replacing the roughness height with the inverse of the streamwise Forchheimer coefficient. The shifts in the mean velocity and temperature profiles follow existing fully rough momentum and thermal theories, enabling their prediction with rough-wall models. Combining these models with synthetic temperature and velocity profiles, we derive analytical formulas for the friction coefficient and Stanton number that agree with our DNS data to within 5%. The performance enhancement factor, which measures heat-transfer augmentation relative to the pressure-drop penalty at constant pumping power, is comparable to that obtained for rough surfaces. This suggests that porous substrates provide an alternative method for enhancing heat transfer in turbulent flows.