GEOMETRIC EVALUATION OF FOUR STAGGERED CYLINDERS ARRAY SUBJECTED TO FORCED CONVECTIVE FLOWS BY MEANS OF CONSTRUCTAL DESIGN

Abstract

This work presents a numerical study on the geometric evaluation of forced convective flows over four staggered arrangement of four cylinders. The forced convective flow is considered incompressible, two-dimensional, laminar and unsteady. Geometry varies according to Constructal Design method. The objectives are the maximization of Nusselt number (Nu_D) and minimization of drag coefficient (C_D) between the cylinders and the surrounding flow. Simulations were performed considering Reynolds numbers of Re_D = 10, 40 and 150 and air as working fluid, i.e., Prandtl number is assumed Pr = 0.71. The problem presents three degrees of freedom: S_T/D (ratio between transversal pitch of the intermediate cylinders and the cylinders diameter), S_L1/D (ratio between the frontal and intermediate cylinders longitudinal pitch and the cylinders diameter) and S_L2/D (ratio between the intermediate and posterior cylinders longitudinal pitch and the cylinders diameter). However, S_L1/D and S_L2/D measures were kept fixed at 1.5 and S_T/D varies in the range 1.5 ≤ S_T/D ≤ 5.0. The conservation equations of mass, momentum and energy conservation are solved with the Finite Volume Method (FVM). Optimal results for fluid-dynamic study in all Re_D cases occurred for the lowest values of S_T/D, i.e., (S_T/D)_o,f = 1.5. For thermal analysis, Nu_D behavior was assessed, where optimal results for Re_D = 10 and 40 occurred for the highest values of S_T/D, whilst, for Re_D = 150, the optimal value was achieved for the intermediate ratio of S_T/D = 4.0.