Oscillating cylinder in viscous fluid: Calculation of flow patterns and forces

Abstract

Laminar and large-eddy-simulation (LES) calculations with the dynamic Smagorinsky model evaluate the flow and force on an oscillating cylinder of diameter D = 2R in otherwise calm fluid, for β = D2/νT in the range 197-61400 and Keulegan-Carpenter number K = UmT/D in the range 0.5-8 (ν kinematic viscosity, T oscillation period, Um maximal velocity). Calculations resolving the streakline patterns of the Honji instability exemplify the local flow structures in the cylinder boundary layer (β ~ 197-300, K ~ 2) but show that the drag and inertia force are not affected by the instability. The present force calculations conform with the classical Stokes-Wang solution for all cases below flow separation corresponding to K <2 (with β < 61400). The LES calculations of flow separation and vortical flow resolve the flow physics containing a large range of motion scales; it is shown that the energy in the temporal turbulent fluctuations (in fixed points) are resolved. Accurate calculation of the flow separation occurring for K > 2 has strong implication for the force on the cylinder. Present calculations of the force coefficients for K up to 4 and β = 11240 are in agreement with experiments by Otter (Appl Ocean Res 12:153-155, 1990). Drag coeffients when flow separation occurs are smaller than found in U-tube experiments. Inertia coefficients show strong decline for large K (up to 8) and moderate β = 1035 but is close to unity for K = 4 and β = 11240. The finest grid has 2.2 × 106 cells, finest radial Δr/R = 0.0002, number of points along the cylinder circumference of 180, Δz/R = 0.044 and a time step of 0.0005T. © 2010 The Author(s).