The Economical Computation of Unsteady Turbulent Flow Structures in Rotating Cavities (original) (raw)

Proceeding of Sixth International Symposium on Turbulence and Shear Flow Phenomena

This paper reports computations of three-dimensional, unsteady turbulent flows in enclosed rotating cavities of axisymmetric geometries, through the numerical solution of the unsteady Reynolds-averaged Navier-Stokes (URANS) equations. Three cases are computed: a co-rotating cavity with a stationary outer shroud of aspect ratio s/R=0.5; and two counter-rotating cavities of s/R=0.12, with disc speed ratios Ƚ of-1 (anti-symmetric) and-0.5 (asymmetric). A general-geometry flow solver is employed, with a thirdorder bounded discretisation scheme for convective transport and the second-order Crank-Nicolson scheme for temporal discretisation. Turbulence is modelled through the use of the high-Reynolds-number k-İ with a threedimensional extension of an advanced, analytical wall function, used to model the effects of near-wall turbulence. In the co-rotating cavity, four pairs of stable structures are predicted around the outer part of the cavity, which rotate at half the angular speed of the discs, with the inner third in solid-body rotation. In the anti-symmetric counter-rotating cavity, fewer and more chaotic structures are predicted, with low rotational speed, but which reach the cavity centre. In the asymmetric case, the three-dimensional structures are generated from the surface of the slower disc and travel inwards, forming spirals. The resolved unsteady motion makes a substantial contribution to the overall turbulent kinetic energy. Time-averaged velocity profiles are in close agreement with corresponding experimental traverses.