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 study on the properties of this pe-riodicity. For the spanwise periodicity within the gap, this study aims to ascertain its characteris-tics, its influences on the flow field, and its variation trend with increasing spacing ratio. By nu-merically 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 re-gimes: 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, de-pending 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 pa-rameters are provided for each flow regime, such as velocity, vorticity, force coefficient, separa-tion/reattachment angle, Strouhal number and Q-criterion.