Strouhal numbers in the wake of two inline cylinders

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(infinity)d/nu, where U-infinity and nu are the free-stream velocity and the kinematic viscosity of fluid, respectively) =800-4.2x10(4) and the cylinder centre-to-centre spacing L/d=1-15. The Strouhal number St (=f(s)d/U-infinity) exhibits a strong dependence on L/d and Re. For L/d<(L/d)(c), which is a critical value and ranges between 3.5 and 5, there is no vortex street formed in the gap between the cylinders, and St measured behind the downstream cylinder drops rapidly for increasing L/d. 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 1less than or equal toL/d<2, the shear layers separated from the upstream cylinder roll up behind the downstream cylinder; category 2: for 2less than or equal toL/dless than or equal to3, there is a transition from the shear layer rollup behind to reattachment on the downstream cylinder; category 3: for 3<L/dless than or equal to5, transition from the reattachment to co-shedding regime occurs at a critical Reynolds number; and category 4: the flow for 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.