Numerical Investigation of Fluid Flow past Four Cylinders at Low Reynolds Numbers

Abstract

A numerical investigation on the effects of separation ratios and Reynolds numbers on the flow around four square cylinders in diamond arrangement has been carried out using the lattice Boltzmann method. The separation ratios between the cylinders vary from $g^{\ast }=1$ to 15. The Reynolds numbers based on the diameter of the square cylinder and the inlet uniform inflow velocity are selected from Re = 80 to 160. The computations show that a total of five different flow regimes are observed over the selected ranges: single bluff-body, quasi-unsteady, chaotic flow, in-phase synchronized vortex shedding, and antiphase synchronized vortex shedding flow regimes. It is found that the flow features significantly depend on both the separation ratio and Reynolds number, with the former’s influence being more than the latter’s. We found that the critical spacing for four square cylinders in diamond arrangement for selected Reynolds numbers (80 ≤ Re ≤ 160) is in the range of 2 ≤  $g^{\ast }$  ≤ 5. The results reveal that the presence of secondary cylinder interaction frequencies indicates that, for chaotic flow regime, the wake pattern is not stable and there is a strong interaction of gap flows and continuous change in the direction of shed vortices behind the cylinders. The effects of the $g^{\ast }$ and Re on fluid forces, vortex shedding frequency, and flow separation have been examined in detail.