On the Spanwise Periodicity within the Gap between Two Different-Sized Tandem Circular Cylinders at Re = 3900

Abstract

Although the spanwise periodicity within the gap between two tandem circular cylinders has been observed by some researchers, there is a lack of systematic research on the properties of this periodicity. For the spanwise periodicity within the gap, this study aims to ascertain its characteristics, its influences on the flow field, and its variation trend with increasing spacing ratio. By numerically simulating the flow around two tandem circular cylinders with a diameter ratio of d/D = 0.6 and seventeen spacing ratios (L/D = 1.00~6.00) at Re = 3900, this study shows four flow regimes: Reattachment Flow (L/D = 1.00~3.15), Bi-stable Flow (L/D = 3.24), Intermittent Lock-in Co-shedding (L/D = 3.30~3.50), and Subharmonic Lock-in Co-shedding (L/D = 4.00~6.00). Further, depending on the spanwise periodicity length of the time-averaged flow structures (i.e., Pz) within the gap, Reattachment Flow is, for the first time, subdivided into three new sub-flow regimes: Small-scale Periodic Reattachment (L/D = 1.00~1.50, Pz/D = (0, 4]), Large-scale Periodic Reattachment (L/D = 2.00~2.25, Pz/D > 4) and Non-periodic Reattachment (L/D = 2.50~3.15, no spanwise periodicity). The formation mechanisms are elaborated by analyzing the combined effect of both the L/D value and the spanwise-averaged time-averaged reattachment angle of the downstream cylinder. Moreover, this study proves that the newly defined Small-scale Periodic Reattachment and Large-scale Periodic Reattachment are responsible for the pronounced asymmetry of the flow along the transverse direction within the gap. In addition, detailed flow properties and statistical parameters are provided for each flow regime, such as velocity, vorticity, force coefficient, separation/reattachment angle, Strouhal number, and Q-criterion.