Axisymmetric numerical simulations of turbulent flow in rotor stator enclosures

Abstract

We present axisymmetric numerical simulations of transitional and chaotic flow regimes in rotor–stator cavities of radial aspect ratio approximately 8. These simulations are carried out using a second order time and space accurate algorithm which integrates the axisymmetric unsteady Navier–Stokes equations in stream function-azimuthal vorticity-azimuthal velocity form. Detailed flow analysis has been carried out for selected values of the rotational Reynolds number ( Re θ ) up to 10 6. At the largest value considered, computations have been performed using 4096 mesh points in the radial direction, which has required using a multi-domain decomposition algorithm implemented on a parallel machine. The limitations and consequences of the axisymmetry assumption are first discussed and checked against available experimental results. The evolutions of the instantaneous flow structure and of its first and second order statistic moments as the Reynolds number increases are discussed. It is shown that the dynamics of the flow mainly consists of travelling waves propagating in the stator and rotor boundary layers and of inertial waves in the core region, and that for moderate Reynolds numbers ( Re θ ≃3×10 5), the rotor boundary layer is almost completely steady while large amplitude fluctuations are found in the stator boundary layer. The evolution of second order moments confirms the fundamentally asymmetrical role of the boundary layers along the rotor and along the stator. A turbulent kinetic energy budget is shown which exhibits some specific features attributed to the rotation effects and to a lesser extent to the axisymmetry assumption.