Geometrical investigation of forced convective flows over staggered arrangement of cylinders employing constructal design

The current numerical work conducted a geometrical investigation of forced convective flows over a staggered arrangement of four cylinders applying constructal design. The main objectives are to determine designs maximizing the Nusselt number (NuD) and minimizing the drag coefficient (CD) of the cylinders at three distinct Reynolds numbers (ReD = 10, 40, and 150) considering Pr = 0.71. The problem involves two constraints: cross-sectional area of the cylinders and the occupation area of the arrangement, and three degrees of freedom: ST/D, SL1/D and SL2/D. These represent the ratios between the transversal pitch, the longitudinal pitch between the frontal and intermediate cylinders, and the longitudinal pitch between the intermediate and posterior cylinders over the diameter. The introduction of two longitudinal pitches enabled an exploration of the generation of asymmetrical patterns in the flow direction. Results indicated a strong dependency of the arrangement design on the Reynolds number. Moreover, asymmetrical configurations generally benefited both performance indicators for the present conditions. The most favorable arrangements for the fluid dynamics were achieved with the lowest ST/D, more concentrated longitudinal pitches for ReD = 10, and asymmetrical pitches for ReD = 40 and 150. Concerning the thermal purpose, the highest magnitude of ST/D and asymmetrical longitudinal pitches led to the highest NuD. For ReD = 10, the intermediate cylinders are near the upstream one; for ReD = 40 the length of the arrangement increases with the intermediate cylinders near the downstream one, and for ReD = 150, the arrangement occupied all the length of occupation area with slight asymmetry.