Reynolds number effect on the wake of two staggered cylinders

Abstract

This work aims to investigate, based on the measured/reported Strouhal number (St) and the flow structure, the Reynolds number (Re) effect on the wake of two identical cylinders with a diameter of d over P[sup ∗] = P/d = 1.2–4.0 and α = 0°–90°, where P is the center-to-center spacing between the two cylinders and α is the angle of incident flow with respect to the line through the two cylinder centers. The Re range examined is from 1.5×10³ to 2.0×10⁴. Two hotwires were used to measure St simultaneously behind each of the two cylinders. The St-Re relationship is classified into four distinct types, i.e., types 1–4. Each is linked to distinct initial conditions, viz., interactions between the four shear layers around the cylinders. Type 1 occurs at small P[sup ∗], not exceeding 1.25. The two cylinders act like a single body, producing a single St across the wake throughout the range of Re examined. On the other hand, type 2 occurs at small α (<10°). Although single valued, the St in type 2 displays a sudden jump with increasing Re due to a switch in the shear layer, separated from the upstream cylinder, from overshooting to reattachment on the downstream cylinder (type 2A) or from reattachment to coshedding vortices (type 2B), depending on P[sup ∗]. Type 3 is in the region of intermediate P[sup ∗] [(1.2–1.5)–2.2] and α (10°–75°). Two distinct St occur at low Re. The lower and the higher ranges of St are associated with the downstream and upstream cylinders, respectively. With increasing Re, the higher St collapses to the lower, which is attributed to a change in the inner shear layer, separated from the upstream cylinder, from squeezing through the gap between cylinders to reattachment on the downstream cylinder. Type 4 occurs at large P[sup ∗] (>1.2–2.2) and again exhibits at low Re two St, above and below the Strouhal number St[sub 0] in the wake of an isolated cylinder, both changing suddenly or progressively to St[sub 0] with increasing Re, which results from a change in the inner shear layer, separated from the upstream cylinder, from reattachment on the downstream cylinder to forming vortices between the cylinders. These types of Re-St relationships are also connected to the flow structure modes reported in literature. The dependence of the St and St-Re relationships on P[sup ∗] and α is provided, which may be used for the prediction of St in related problems.