Large eddy simulation and measurements of turbulent enclosed rotor-stator flows

Abstract

Turbulent flows are studied in an actual enclosed rotor-stator configuration with a rotating hub and a stationary shroud. Besides its fundamental importance—the disk boundary layer is one of the simplest platforms for investigating the underlying structure of three-dimensional boundary layers—this cavity models more complex configurations relevant to rotating machinery. Large eddy simulation is performed using a spectral vanishing viscosity technique that is shown leading to stable discretizations without sacrificing the formal accuracy of the spectral approximation. Numerical results and velocity measurements have been favorably compared for a large range of rotational Reynolds numbers (105⩽Re=Ωb2∕ν⩽106) in an annular cavity of curvature parameter Rm=(b+a)∕(b−a)=1.8 and of aspect ratio G=(b−a)∕h=5, where a and b are, respectively, the inner and outer radii of the rotating disk and h is the interdisk spacing. In the detailed picture of the flow structure that emerges, the turbulence is confined mainly in the boundary layers including in the Stewartson layer along the external cylinder. For Reynolds numbers Re⩾105, the stator boundary layer is turbulent over most of the cavity. On the other hand, the rotor layer becomes progressively turbulent from the outer radial locations, although the rotating hub is shown to destabilize the inner part of the boundary layers. The isosurface maps of the Q-criterion reveal that the three-dimensional spiral arms observed in the unstable laminar regime evolve to more axisymmetric structures when turbulence occurs. At Re=106, the flow is fully turbulent and the anisotropy invariant map highlights turbulence structuring, which can be either a “cigar-shaped” structuring aligned on the tangential direction or a “pancake-shaped” structuring depending on the axial location. The reduction of the structural parameter a1 (the ratio of the magnitude of the shear stress vector to twice the turbulence kinetic energy) under the typical limit 0.15, as well as the misalignment between the shear stress vector and the mean velocity gradient vector, highlight the three-dimensional nature of both rotor and stator boundary layers with a degree of three-dimensionality much higher than in the idealized system studied by Lygren and Andersson [J. Fluid Mech. 426, 297 (2001); ZAMP 55, 268 (2004); and Int. J. Heat Fluid Flow 27, 551 (2006)].