Temporal features of thermal flows over a rotating cylinder in a channel: Multigrid based simulations

Abstract

The purpose of this study is to simulate thermal flows via quasi-Newtonian modeling by employing Finite Element Methods (FEM), as well as Newton Multigrid Solvers (NMS). A heated rotating cylinder is exposed to an inflowing fluid stream in a channel to facilitate the thermal energy transfer in the fluid. The NMS may be more easily parallelized as a result of an excessive number of degrees of freedom. The discretization of a dimensionless system of partial differential equations that are to be solved over an extensive computational domain is accomplished by using the higher-order stable finite element pair. Temporal discretization is performed using a 2nd order Crank-Nicolson scheme. By applying the Newton method, the discretized nonlinear system of algebraic equations is transformed into a linear form. To compute the linearized subproblems that arise from each nonlinear sweep, a geometric multigrid approach has been put in place. The whole framework has been implemented in an open-source finite element software Featflow. It has been deduced that in a clockwise rotation of the cylinder, more fluid will move from above the cylinder, and when it is rotated in an anticlockwise direction, more fluid will move from bottom side of the cylinder. In addition to this, there is a correlation between an increase in the rotational parameter ω and a reduction in both the lift coefficient CL and drag coefficient CD. The benchmark values of CD and CL fits very well with the available data for certain special cases of this study.