From sheared annular centrifugal Rayleigh–Bénard 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–Bénard convection (ACRBC) system in which two cylinders rotate with an angular velocity difference. Direct numerical simulations are performed in a Rayleigh number range $10^6\leq Ra\leq 10^8$ , at fixed Prandtl number $Pr=4.3$ , inverse Rossby number $Ro^{-1}=20$ , and radius ratio $\eta =0.5$ . The shear, represented by the non-dimensional rotational speed difference $\varOmega$ , 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 for $\varOmega$ , and divides the whole parameter space into three regimes: buoyancy-dominated, stable and shear-dominated. Clear boundaries between the regimes are given by linear stability analysis, meaning the marginal state of the flow. 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 are depressed. In the shear-dominated regime, the flow is mainly on the $rz$ plane. The shear is so strong that the temperature acts as a passive scalar, and the heat transfer is greatly enhanced. The study shows that shear can stabilize buoyancy-driven convection, makes a detailed analysis of the flow characteristics in different regimes, and reveals the complex coupling mechanism of shear and buoyancy, which may have implications for fundamental studies and industrial designs.