LES of the non-isothermal transitional flow in rotating cavity

Abstract

The paper presents the 3D LES study of the non-isothermal transitional and turbulent flow in rotor/stator sealed cavity with a rotating inner and a stationary outer cylinder. The stator and the outer cylinder are warmer than the rotor and the inner cylinder. Computations have been performed for the cavity of aspect ratio L = ( R 1 − R 0)/2 h = 5, curvature parameter Rm = ( R 1 + R 0)/( R 1 − R 0) = 3, Reynolds numbers Re = Ω R 1 2 / ν = 75 , 000 – 300 , 000 , thermal Rossby numbers B = β( T 2 − T 1) = 0.01–0.4, and for the cavity ( L = 9, Rm = 1.5, Re = 100,000–150,000, B = 0.01–0.4). Computations we based on the efficient pseudo-spectral Chebyshev–Fourier method (Serre, E., Pulicani, J.P., 2001. A three-dimensional pseudospectral method for rotating flows in a cylinder. Computers and Fluids, 30, 491). In Large Eddy Simulations we used a version of the dynamic Smagorinsky eddy viscosity model proposed by Meneveau (Meneveau, C., Lund, T.S., Cabot, W.H., 1996, A Lagrangian dynamic subgrid-scale model of turbulence. Journal of Fluid Mechanics, 319, 353–385), in which the averaging is performed over the particle pathline. This approach allowed us to perform computations for higher Reynolds numbers for confined rotating flows, which are strongly inhomogeneous and anisotropic. Results showed that the turbulence is concentrated mostly in the stator boundary layer with a maximum at the junction between the stator and the outer cylinder. For the cavity of aspect ratio L = 5 the stator boundary layer was fully turbulent for Re ⩾ 100,000, whereas the rotor boundary layer was still laminar. The influence of the thermal Rossby number on the flow structure and the basic state was not significant. The correlation formulas, for predicting the distribution of local Nusselt numbers along disks as well as the correlation formulas for the averaged Nusselt numbers depending on the Reynolds numbers are given on the basis of our results.