Influence of mixed convection laminar flows on the geometrical evaluation of a triangular arrangement of circular cylinders

摘要

The present numerical study performs a geometrical evaluation of a triangular arrangement of circular cylinders subjected to transient, two-dimensional, incompressible, laminar, and aiding mixed convective flows by means of Constructal Design. It is investigated a multiobjective problem: maximize Nusselt number (Nu_D) and minimize drag coefficient (C_D). In order to investigate the influence of buoyancy forces over design of the arrangement of cylinders five different Grashof numbers (Gr_D) are studied leading to different Richardson numbers: Ri = Gr_D/Re_D ~2 = 0.1, 0.5, 1.0, 5.0 and 10.0. For all simulations, constant Reynolds and Prandtl numbers (Re_D = 100 and Pr = 0.71) are considered. For geometric evaluation, the problem is subjected to two constraints (cross-sectional area of three cylinders and an occupation area for the arrangement) and two degrees of freedom (the ratio between the longitudinal pitch and cylinder diameter (S_L/D) and ratio between the transversal pitch and cylinder diameter (S_T/D)). In numerical simulations, the conservation equations of mass, momentum and energy are solved using Finite Volume Method (FVM). Results showed that buoyancy forces in mixed convective flows have strong influence over design of the studied cylinders arrangement. For instance, the effects of S_T/D and S_L/D over C_D and Nu_D changed significantly for different Ri evaluated. Concerning the multiobjective evaluation, for Ri = 0.1 (forced convective flows) intermediate ratios of S_T/D and S_L/D, different from that achieved for the isolated purposes, conducted to the best multiobjetive performance, while for Ri = 10.0 (natural convective flows) the best shape is the same reached for the thermal objective, i.e., the multiobjective analysis for natural convective flow was guided by thermal purpose.