Agradecimentos: Engineering and Physical Sciences Research CouncilEngineering & Physical Sciences Research Council (EPSRC) [EP/P004091]

This paper presents buoyancy-induced flow for a sealed rotating cavity with rotational Rayleigh number Ra in the range 10(7) - 10(9). DNS for an incompressible model with the Boussinesq approximation is compared with LES for a compressible gas flow model. The compressible solver's solutions show the...

This paper presents buoyancy-induced flow for a sealed rotating cavity with rotational Rayleigh number Ra in the range 10(7) - 10(9). DNS for an incompressible model with the Boussinesq approximation is compared with LES for a compressible gas flow model. The compressible solver's solutions show the shroud Nusselt number Nu scales with Ra-0.286, in close agreement with the corrected experimental correlation and the Ra-2/7 scaling for gravitational heat convection between horizontal plates, but differs from the Nu alpha Ra-1/3 scaling given by the incompressible solver. The shroud thermal boundary layer thickness, based on the root mean square of the temperature fluctuation, can be estimated with lambda(*) = 0.5Nu(-1). Velocities scale approximately with Omega a root beta Delta T . Disc laminar Ekman layer behaviour is confirmed up to Ra = 10(9). An Ekman layer scrubbing effect, associated with the viscous energy dissipation, is considered to be mainly responsible for the difference in Nu between the two solvers at Ra = 10(9), in spite of rather small Eckert number. The analysis of the turbulent kinetic energy budget shows a dominant constant buoyancy production in the core. The use of the incompressible formulation for the considered problem is restricted by the applicable range of the Boussinesq approximation characterised by the buoyancy parameter beta Delta T and neglect of viscous heating and compressibility effects characterised by the Eckert number Ec = Omega(2) r(m)(2)/(C-p Delta T)

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