Control of vortex breakdown by temperature gradients

Abstract

An axial gradient of temperature can either suppress or enhance vortex breakdown (VB). The underlying mechanism of such VB control is centrifugal or/and gravitational convection. An additional thermal-convection flow directed oppositely to the base flow suppresses VB while a co-flow enhances VB. Our numerical simulations of a compressible flow in a sealed cylinder induced by a rotating bottom disk clearly reveal these effects. We vary the temperature gradient (ε), Mach (Ma), Froude (Fr), and Reynolds (Re) numbers, and the aspect ratio (h). As ε increases (ε>0 corresponding to a temperature gradient parallel to the downward near-axis flow), the VB “bubble,” which occurs at ε=0, diminishes and then totally disappears. The opposite temperature gradient (ε<0) enlarges the VB bubble and makes the flow unsteady. These effects of centrifugal convection become more prominent with increasing Ma and Re. Density variations induced by the temperature gradients are more important for VB control than those induced by the increase in Ma. A new efficient time-evolution code for axisymmetric flows of an ideal gas has facilitated these simulations.