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

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 substrate porosity. Our findings reveal that cubic-lattice porous substrates exhibit a performance enhancement factor comparable to typical rough surfaces used in heat-transfer enhancement applications, indicating that porous substrates may offer a promising alternative. By employing analytical velocity and temperature shifts, we construct synthetic mean profiles, from which we derive analytical formulas for the friction coefficient and Stanton number. Validation against DNS data demonstrates agreement within 5% in the fully rough regime. The framework establishes a direct link between surface-induced shifts in mean profiles and key engineering quantities like friction and heat transfer coefficients, ensuring its applicability to both wall-modelled simulations and various conditions, including permeable or impermeable rough-wall scenarios.