Hydrodynamic instability with convective heat transfer through a curved channel with strong rotational speed

Abstract

In this paper, a comprehensive numerical study on viscous incompressible fluid flow and heat transfer through a loosely coiled square duct has been presented. Spectral method is used as a basic tool to solve the system of non-linear partial differential equations. Numerical calculations are carried out for the Dean number Dn = 1000 with a temperature difference across the vertical sidewalls for the Grashof number Gr = 100, where the outer wall is heated and the inner wall cooled. A rotation of the duct about the center of curvature is imposed in the positive direction for the Taylor number 0≤Tr≤2000 and combined effects of the centrifugal, Coriolis and buoyancy forces are investigated. First, steady solutions are obtained by the Newton-Raphson iteration method. As a result, three branches of asymmetric steady solutions with two- to four-vortex solutions are obtained. Then, time evolution calculations as well as power spectrum density of the unsteady solutions are obtained and it is found that the unsteady flow undergoes through various flow instabilities, if Tr is increased in the positive direction. Nusselt numbers are calculated as an index of convective heat transfer, and it is found that convective heat transfer is significantly enhanced by the secondary flow. Finally, a comparison between the numerical and experimental investigations has been provided. It is found that there is a good agreement between the numerical and experimental investigations.