Investigation of Strouhal frequencies of two staggered bluff bodies and detection of multistable flow by wavelets

The results of a wind tunnel investigation of the Strouhal frequencies of two identical, stationary, parallel circular cylinders arranged in staggered configurations, carried out in a uniform cross-flow at a Reynolds number of 5.5×104, are presented in this paper. Results of measurements of the Strouhal frequencies of a square cylinder (prism) and a circular cylinder arranged in tandem and in some selected staggered configurations are also presented. In the case of two circular cylinders, the investigation was performed at staggered angles of α=10°, 25°, 45°, 60° and 75° in the range of T/D=0.1-5.0, where α is the angle between the free-stream flow and the line connecting the centers of the cylinders, T is the gap width between the cylinders, and D is the diameter of a cylinder. The new findings in this study for two circular cylinders are: (i) three stable flow patterns with regard to Strouhal numbers were identified for α=25° in the range of T/D=1.1-1.8 and (ii) two stable flow patterns with regard to Strouhal numbers were identified for α=45° in the range of T/D=0.8-2.1. Intermittent mutual lock-in of the two frequencies of two cylinders caused such multistable flow patterns. These multistable flow patterns and the intermittent lock-in phenomenon were elucidated from wavelet analysis results of fluctuating pressures simultaneously stored from the surfaces of the cylinders. Strouhal number distributions for α=60° and 75° were almost the same in nature as those of α=45°. When a square cylinder and a circular cylinder were arranged at α=25° with the square cylinder being used as the upstream cylinder, the downstream cylinder was found to shed vortices always in synchronization with the upstream cylinder. For α=60°, when the square cylinder was used as the upstream cylinder, both cylinders were found to be locked-in to shed vortices with an intermediate Strouhal number for a certain range of values of T/D.