Numerical investigation of vortex onset in supersonic Taylor-Couette flow

The compressible flow between concentric cylinders, in the case where the inner cylinder rotates and the outer one is at rest, has been computed using a pseudospectral/finite difference method. The onset of turbulence in rarefied supersonic gap flows for flywheel applications, and particularly the impact of surface roughness on the development of Taylor vortices, has been explored. An immersed boundary method using an external force field was employed to model the surface roughness. The Navier-Stokes code was validated against results from the literature for a supersonic wide-gap flow. To validate the immersed boundary method, the rotor wall was replaced by a smooth offset wall modeled with an external force field. Very good agreement with the analytical solution for steady Couette flow was achieved. The growth of Taylor vortices in a narrow gap with smooth walls was studied first. Then, the external force field was used to create a riblet on the rotor to investigate the influence of the roughness of the rotor on the flow and, more particularly, on the onset of the instability. The most interesting feature is the early appearance of vortices for Taylor numbers where the flow with smooth walls is in the subcritical regime.