Direct Numerical Simulation of Radial Convection in a Cylindrical Annulus With and Without Rotation

Abstract

Abstract In rotating systems with temperature gradients, convection may occur due to gravitational or centrifugal effects. In cases where rotation is strong enough so that the centrifugal acceleration is higher than gravity, the flow is induced by centrifugal buoyancy and gravitational effects can be neglected. The problem of flow induced by centrifugal buoyancy in a cylindrical annulus has been used as a canonical setup to investigate industrial configurations, such as buoyancy-driven flows occurring in gas turbine secondary air systems, as well as geophysical flows, such as convection in the core of planets and the global circulation of the atmosphere. Due to the constraints imposed by the Taylor-Proudman theorem, such flows are quasi-homogeneous along the axial direction, and heat transfer as well as turbulent fluctuations tend to be suppressed by the action of the Coriolis force. Previous work has demonstrated that when the annulus is bounded by parallel disks, boundary layers scaling consistently with laminar Ekman layers are formed near each of the disks, even though the flow is purely buoyancy-induced. Also, the Nusselt number measured on the outer cylindrical surface has been shown to scale with the Rayleigh number as in natural convection between horizontal plates. In the present work we use direct numerical simulation (DNS) to investigate buoyancy-induced flow in an air-filled cylindrical annulus bounded by two adiabatic parallel disks, with and without rotation around the axis. In both cases the outer cylindrical surface is at a higher temperature than the inner one, so that a radial acceleration directed outwards induces an unstable stratification. In the case with rotation, the flow is induced by the centrifugal acceleration in the radial direction, and Coriolis forces are considered. For the case without rotation, the Coriolis terms are suppressed in the calculations, whereas the radial acceleration is the same as in the rotating case. Statistics are obtained and compared in the two cases, including the time-averaged Nusselt number, mean temperature profiles, velocity and temperature fluctuations, as well as terms of the turbulent kinetic energy equation. By analysing such statistics, the extent to which rotation suppresses heat transfer and turbulent fluctuations, as well as the contribution of each term to the turbulent kinetic energy budget, can be assessed.