Flow structure analysis around an oscillating circular cylinder at low KC number: A numerical study

Abstract

Flow fields around an oscillating circular cylinder are studied by solving the incompressible Navier-Stokes equations in primitive variable formulation. A finite volume method with a pressure predictor-corrector scheme is used and the solution procedure is accelerated by a local time stepping technique. Numerical tests are carried out at the Keulegan-Carpenter number KC < 20 and Reynolds number Re < 4000. For the symmetrical flow (at either very low KC or low Re), the vorticity decaying effect is dominant in the flow field. At higher Re, the vorticity convection becomes stronger, eventually leading to the inception of the asymmetrical flow pattern. It was found that within this critical regime the artificial disturbances imposed to the flow field play an important role in determining the flow patterns: if the flow falls into the symmetrical category, it remains symmetrical even with the artificial disturbances; while if the flow falls into the unsymmetrical category, the artificial disturbances are necessary for the correct predictions. An inception boundary of the asymmetrical flow in the KC — Re plane can thus be defined through a systematic study of the response of the flow field to the small disturbances. For the asymmetrical flow (at higher KC and/or Re), several distinguished flow patterns are identified in the numerical simulations, including quasi-symmetrical flow, diagonal vortex pair shedding, transverse street and double vortex pairs shedding. Agreement between the present results and the flow visualization (particle tracing) is generally good. The forces acting on the cylinder are also predicted for both the symmetrical and the asymmetrical flows. The conventional drag and inertia coefficients are deduced and compared with other numerical and experimental results, also showing good agreement.