On the transition behavior of laminar flow through and around a multi-cylinder array

Abstract

We numerically investigated the transitional behavior of two-dimensional laminar flows through and around a square array of 100 circular cylinders. The solid fraction of the array ϕ ranged from 0.007 85 to 0.661 and the Reynolds number Re (based on the free-stream velocity and the side length of the array) varied from 40 to 200. Globally, the first transition appears at the onset of vortex shedding, where the critical Reynolds number Recr is estimated from the Stuart-Landau equation. The results show that Recr ranges from 40 to ∼45 for the investigated range of ϕ. It is found that Recr increases quadratically with ϕ and the critical Reynolds number for an individual cylinder (Rdcr) increases linearly with ϕ. The subsequent transitions largely depend on ϕ, as revealed from the total drag and lift coefficients, Strouhal number, and the instantaneous vorticity field. For sufficiently small ϕ at high Re, the global vortex shedding is suppressed due to the weakened interaction between cylinders in the array. Several more cases with ϕ of 0.007 85 for Re between 400 and 4000 are also calculated to visualize the suppression behavior. The global transition behaviors are closely related to the secondary frequency (SF) observed from the power spectra of the local velocity. It is highly possible that the SF results from the cylinder interaction in the array. The local instabilities induced by cylinder interactions would promote the onset of global vortex shedding at small Re. Also, the local instabilities still exist even though the global vortex shedding is suppressed at large Re.