The highly accurate simulation of turbulent rotating flows within cavity is of interest for both engineering applications, such as designing rotational machinery, and fundamental research, as one of the simplest cases where the turbulent boundary layers are three-dimensional. Attempting to compute these flows using statistical approaches has had only partial success. Indeed, the turbulence model must be able to solve the low-Reynolds number regions near the disks and in the core and to predict precisely the location of the transition from the laminar to the turbulent regime, even though it is bounded by instabilities. Thus, Large Eddy Simulation (LES) constitutes a valuable way to compute such complex flows.
In a first part, we provide a numerical benchmark of three high-order LES in the case of an enclosed rotor-stator cavity of radius ratio 0.29 and aspect ratio 5 under isothermal conditions. At a Reynolds number Re= 4.105, the LES codes catch the main features of such flows with positive spiral arms along the rotating disk and thin vertical structures along the stator. Predictions of the mean velocities and rms fluctuations globally agree with the experimental data measured at IRPHE. A detailed analysis of the results provides an insight on the role of the approximation methods and of the sub grid modelling on the solution.
In a second part, buoyancy effects are investigated under the Boussinesq approximation for various Rayleigh and Reynolds numbers. Some instantaneous views reveal that the temperature field is strongly affected by the hydrodynamic structures even at large Rayleigh numbers, which is confirmed by the averaged results. The evolution of the averaged Bolgiano length scale with the Rayleigh number indicates that temperature fluctuations may have a large influence on the dynamics only at the largest scales of the system for Rayleigh numbers larger than 10 millions.
Finally, some work prospects to reach operating conditions in real rotating machineries are presented. It includes the numerical treatment of the cylindrical coordinate singularity along the rotation axis and a multi-domain decomposition technique, used to increase the spatial resolution.