An efficient approach to simulate natural convection in arbitrarily eccentric annuli by vorticity-stream function formulation

Abstract

The global method of polynomial-based differential quadrature (PDQ) and Fourier expansion-based differential quadrature (FDQ) is applied in this work to simulate the natural convection in an annulus between two arbitrarily eccentric cylinders. The vorticity-stream function formulation in the curvilinear coordinate system is taken as the governing equation, and the pressure single value condition is converted to an explicit formulation to update the stream function value on the inner cylinder wall. The present approach is very efficient, which combines the high efficiency and accuracy of the differential quadrature (DQ) method with simple implementation of pressure single value condition. When the present approach is applied to the concentric case, it was found that the computed stream function on the inner cylinder is almost zero and the flow field is symmetric. The computed average equivalent conductivity for the concentric case also agrees very well with available data in the literature. For the eccentric case, it was found that the computed stream function on the inner cylinder is not zero and there is a global circulation. The present result confirms the findings by Guj and Stella.