Geometrical optimization of a triangular arrangement of cylinders submitted to a laminar forced convective flow

Abstract

The present numerical work studies a triangular arrangement of cylinders submitted to transient, two-dimensional, transient, laminar, incompressible flows with forced convective heat transfer by means of Constructal Design. The simulations were performed for flows with Reynolds and Prandtl numbers of ReD = 100 and Pr = 0.71. The conservation equations of mass, momentum and energy are solved with the Finite Volume Method (FVM). The occupied area of three cylinders are a problem restriction, while the ratios ST/D (distance from the center-to-center posterior cylinders and the diameter) and SL/D (distance from the frontal cylinder to the posterior cylinders) are the degrees of freedom. It is worthy to mention that all cylinders have the same diameter. The main purpose here is to evaluate the ratio ST/D which minimizes the drag coefficient and maximizes the heat transfer rate (Nusselt number) between the cylinders and the surrounding flow, i.e., a multi-objective problem. For all cases it was considered a fixed ratio of SL/D = 3.5. Results showed that the fluid dynamic and thermal behavior of the flow was highly influenced by the ratio ST/D. The minimal drag coefficient (CD) and the maximal Nusselt number (NuD) are obtained for ST/D = 1.5 and 5.5, respectively. However, the best arrangements considering the multi-objective problem (drag and heat transfer) were achieved for the region ST/D ~ 2.0, near of the optimal shape obtained for the fluid dynamic problem, contrarily to noticed for a flow over a pair of cylinder studied in the