The Reynolds number effect from subcritical to high transcritical on the steady and unsteady loading on a rough circular cylinder

Abstract

Force and surface pressure measurements on a 2D rough circular cylinder were carried out over a wide range of Reynolds numbers in the high-pressure wind tunnel in Göttingen. The Reynolds number spanned values from subcritical up to high transcritical 15×103 ≤ Re ≤ 12×10^6. The cylinder had a mean relative surface roughness of ks/D = 1.2×10^-3. By means of piezoelectric balances the unsteady lift and drag forces were measured. The mean surface pressure distribution was obtained with the use of 59 static surface pressure tabs at various span-wise and circumferential locations on the cylinder. Statistical analysis of the time-dependent forces, in combination with the mean surface pressures, provided information on the spatial organization of the flow field properties around the cylinder as function of the Reynolds number. In the critical Reynolds regime two discontinuities at two separate Reynolds numbers were observed. They were accompanied by critical fluctuations in the lift force and the formation of a separation bubble at each side of the cylinder. The discontinuous jumps were initialized by a downstream movement of the separation point and an upstream movement of the transition point. The asymmetric flow field in-between both critical Reynolds numbers led to a steady lift force that was cancelled again after passing the second critical Reynolds number. At the latter Reynolds number the width of the wake and CD were minimum. In the super- and transcritical flow states the boundary layer separations took place at about the apex of the cylinder. In comparison to the subcritical and critical regimes all measured flow field properties reached intermediate steady plateaus in the transcritical state. For the Strouhal number this plateaus was at St = 0.23, for the base pressure at Cp,base = -0.9 and for the drag coefficient at CD ≈ -0.84.