Instabilities and Transition on a Rotating Cone–Old Problems and New Challenges

Abstract

An experimental investigation of instabilities and transition in the boundary layer on a rotating broad ($120^{\circ }$ apex angle) cone through hot-wire measurements combined with local linear stability analysis (LLSA) has been undertaken. The rotating-cone flow is susceptible to both cross-flow and centrifugal instabilities. For broad cones, the cross-flow instability dominates over the centrifugal instability, and vice versa for slender cones. Although stationary vortical disturbances from the cross-flow instability are dominant on the broad cone (in this case 24–26 vortices develop), we have identified an initially slowly growing nonstationary mode with a much smaller wavenumber, which close to transition increases its growth rate dramatically. We report on a detailed process to identify the wavenumber of the measured nonstationary disturbance, as well as quantitative comparisons between experimental results and LLSA.