From Sheared Annular Centrifugal Rayleigh-B\'enard Convection to Radially Heated Taylor-Couette Flow: Exploring the Impact of Buoyancy and Shear on Heat Transfer and Flow Structure

Abstract

We investigate the coupling effect of buoyancy and shear based on an annular centrifugal Rayleigh-B\'enard convection (ACRBC) system in which two cylinders rotate with an angular velocity difference. Direct numerical simulations are performed in a Rayleigh number range 10^6 \le Ra \le 10^8, at fixed Prandtl number Pr=4.3, inversed Rossby number Ro^{-1}=20 and radius ratio \eta=0.5. The shear, represented by the non-dimensional rotational speed difference \Omega, varies from 0 to 10, corresponding to an ACRBC without shear and a radially heated Taylor-Couette flow with only the inner cylinder rotating, respectively. A stable regime is found in the middle part of the interval of \Omega, and divides the whole parameter space into three regimes: buoyancy-dominated regime, stable regime, and shear-dominated regime. Clear boundaries between the regimes are given by linear stability analysis. In the buoyancy-dominated regime, the flow is a quasi-two-dimensional flow on the r\varphi plane; as shear increases, both the growth rate of instability and the heat transfer is depressed. In the shear-dominated regime, the flow is mainly on the rz plane, and the heat transfer in this regime is greatly enhanced. The study shows shear can stabilize buoyancy-driven convection and reveals the complex coupling mechanism of shear and buoyancy, which may have implications for fundamental studies and industrial designs.