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 (NuD) and minimization of drag coefficient (CD) between the cylinders and the surrounding flow. Simulations were performed considering Reynolds numbers of ReD = 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: ST/D (ratio between transversal pitch of the intermediate cylinders and the cylinders diameter), SL1/D (ratio between the frontal and intermediate cylinders longitudinal pitch and the cylinders diameter) and SL2/D (ratio between the intermediate and posterior cylinders longitudinal pitch and the cylinders diameter). However, SL1/D and SL2/D measures were kept fixed at 1.5 and ST/D varies in the range 1.5 ≤ ST/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 ReD cases occurred for the lowest values of ST/D, i.e., (ST/D)o,f = 1.5. For thermal analysis, NuD behavior was assessed, where optimal results for ReD = 10 and 40 occurred for the highest values of ST/D, whilst, for ReD = 150, the optimal value was achieved for the intermediate ratio of ST/D = 4.0.