This paper presents large-eddy and direct numerical simulations of buoyancy-driven convection in sealed and open rapidly rotating cavities for Rayleigh numbers in the range 107–109, and axial throughflow Reynolds numbers 2000 and 5600. Viscous heating due to the Ekman layer scrubbing effect, which has previously been found responsible for the difference in sealed cavity shroud Nusselt number predictions between a compressible N-S solver and an incompressible counterpart using the Boussinesq approximation, is discussed and scaled up to engine conditions. For the open cavity with an axial throughflow, laminar Ekman layer behaviour of the mean flow statistics is confirmed up to the highest condition in this paper. The Buoyancy number Bo is found useful to indicate the influence of an axial throughflow. For the conditions studied the mean velocities are subject to Ra, while the velocity fluctuations are affected by Bo. A correlation, Nu′ = 0.169(Ra′)0.318, obtained with both the sealed and open cavity shroud heat transfer solutions, agrees with that for free gravitational convection between horizontal plates within 16% for the range of Ra′ considered.