Strouhal numbers in the wake of two inline cylinders

Abstract

The dominant vortex frequencies f s in the wake of two tandem circular cylinders of identical diameter d have been measured simultaneously using two hot wires placed behind each cylinder. Measurements were conducted over the Reynolds number Re (≡U ∞ d/ν, where U ∞ and ν are the free-stream velocity and the kinematic viscosity of fluid, respectively) =800–4.2×104 and the cylinder centre-to-centre spacing L/d=1–15. The Strouhal number St (≡f s d/U ∞) exhibits a strong dependence on L/d and Re. For L/d (L/d)c, co-shedding occurs, that is, vortices are shed from the upstream as well as the downstream cylinder, and their frequencies are found to be identical. St climbs with increasing L/d, approaching a constant between 0.18 and 0.22 for L/d>10. The St–Re relationship is classified into four categories, based on their behaviours, which are associated with distinct flow physics—category 1: for 1≤L/d 5 is characterized by co-shedding only. The present measurements reconfirm the previous observation of a bi-stable flow at the transition from the reattachment to co-shedding regime. It is found for the first time that another bi-stable flow occurs at the transition from category 1 to 2, that is, the stable reattachment co-exists with the stable rollup (behind the downstream cylinder) of shear layers separating from the upstream cylinder, resulting in two distinct vortex-shedding frequencies even at the same Re and L/d. The St behaviour is further discussed along with flow visualization using the laser-induced fluorescence technique.