Aspect-ratio dependence of heat and angular momentum transport in turbulent Taylor-Couette flows with axial thermal forcing

Abstract

• Scaling law of transports determined in finite systems can be extrapolated to large-scale flows. • Coherent turbulent structures in form of Taylor vortices promote heat and angular transports. • Magnitudes of both heat and angular momentum transport depend on domain aspect-ratio. We report numerical studies of the effects of geometry factors, i.e. the aspect ratio Γ and radius ratio η , on the axial heat transport N u and the radial angular momentum transport N ω by turbulent Taylor-Couette flows that are subjected to a vertically destabilizing temperature gradient. For a given Reynolds number R e the magnitudes of both N u and N ω exhibit a pronounced aspect-ratio dependence. The angular momentum transport is reduced in long cylinders, since endwall effects are weakened as Γ increases. For the heat transfer in large- Γ cylinders, a significant N u -reduction appears for low- R e regime, whereas N u can be greatly enhanced in the regime of turbulent Taylor vortex (TV). The former N u -reduction is associated with the process that the thermal plumes are swept away by the Ekman vortices near the boundaries, and the fluid exchange is severely restricted between adjacent vortices in the bulk region. The latter N u -enhancement is attributed to the strengthened shears arising in large- Γ cylinders, resulting in a more turbulent boundary layer. Moreover, the pronounced inter-mixing of turbulent TVs continuously pumps the hot (cold) fluids into the bulk, intensifying the transport processes. It is found that although the constraints from the endwalls impact the global heat and angular momentum transport in the low- R e regime, they hardly affect their scaling properties in the high- R e regime with large Γ . We thus expect that the scaling relationship of N u ( R e ) and N ω ( R e ) determined with finite Γ can be extrapolated to large-scale, and even vertically unbounded industrial and geophysical flows.