A Closer Investigation of the Mean Aerodynamic Forces for Two Staggered Circular Cylinders in Cross-Flow

Two circular cylinders of equal diameter in a staggered configuration, with centre-to-centre pitch ratios of P/D = 1.125 – 4.0, were tested in the subcritical Reynolds number regime, at Re = 3.0×10⁴ – 8.0×10⁴. The incidence angle of the cylinder configuration was varied in small increments from α = 0° – 90° and the mean aerodynamic forces were measured on both the upstream and downstream cylinders. Based on the force measurements, the behaviour of the cylinders was broadly grouped into three categories, depending on P/D. For closely spaced staggered configurations, P/D = 1.125 – 1.25, the aerodynamic forces on both the upstream and downstream cylinders varied significantly with α. Several critical incidence angles were identified for each cylinder that corresponded to local maximum, minimum, or discontinuous behaviour in the forces, which were related to shear layer reattachment and the influence of the gap flow. For moderately spaced staggered configurations, P/D = 1.5 – 2.5, shear layer reattachment and the subsequent transition to gap flow at small α were responsible for the inner lift peak, a corresponding minimum drag, and a loss of lift with increasing α, which becomes more abrupt as P/D is increased. For widely spaced staggered configurations, P/D = 3.0 – 4.0, the two cylinders undergo Ka´rma´n vortex shedding for the entire range of α. At small α, the forces on the downstream cylinder are affected by vortex impingement, and the outer lift peak replaces the inner lift peak. This outer lift peak exhibits some sensitivity to the Reynolds number.