Numerical Study of an triangular arrangement of cylinders submitted to forced convective laminar flow

Abstract

The present work studies the convection heat transfer by forced convection through a triangular arrangement for three cylinders considering a laminar, two dimensional, incompressible and unsteady flow. Regarding to the numerical solution for the main equations, the solution is ran by using a computational code based on the FVM (Finite Volume Method). The Constructal Design method is applied to optimize the geometry arranged for the three cylinders. Simulations were run for flows with Reynolds and Prandtl numbers of 100 and 0.71, respectively. The optimization considers which ratio S_T/D (transversal step over diameter) and S_L/D (longitudinal step over diameter) minimize the drag coefficient and maximize the heat transfer rate (from Nusselt number) between the cylinders and the surrounding cross flow. Results showed that the fluid dynamics and thermal behavior were heavily influenced by the ratios S_T/D and S_L/D. The minimum drag coefficient (Cd) was found for the configuration S_L/D = 5.0 and S_T/D = 1.5, while the maximum Nusselt number (NuD) lies over the S_L/D = 1.5 and S_T/D = 5.5 ratios. However, the best arrangements considering the multi-objective function (drag and heat transfer) were achieved into an optimal region and not for a specific configuration. Among the analyzed cases, can be highlighted the S_L/D = 5.0 - S_T/D = 2.0; and S_L/D = 5.0 - S_T/D = 2.5 configurations. The first two values presented benefits for the fluid dynamic problem and the last ones showed a slight advantage for the thermal process.