Laminar natural convection in a square cavity with 3D random roughness elements considering the compressibility of the fluid

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Natural convection in a three-dimensional square cavity with random artificial roughness on both vertical walls is studied numerically for a Rayleigh number of 106. Based on consideration of realistic conditions, the roughness is generated using a given power spectrum density, and a compressible solver with preconditioning that uses a dual time-stepping method is established to handle the low velocity of the natural convection flow. The compressible solver demonstrates satisfactory accuracy in terms of the average Nusselt number when compared with incompressible benchmark solutions. However, the results for the local Nusselt number from the compressible and incompressible solvers differ. As the temperature difference between the two vertical sidewalls increases, the maximum value of the local Nusselt number increases, but in the downstream region, the local Nusselt number actually decreases. The cavity with rough sidewalls has a similar Nusselt number to the average Nusselt number of a hot sidewall in the case of a smooth cavity. Because of the effects of the roughness on the thermal and velocity boundary layers, the rough cavity case shows a better heat transfer performance than the smooth cavity case in the upstream region, but in the downstream region, the heat transfer in the rough case becomes worse than that in the smooth case.