A NUMERICAL STUDY OF OSCILLATORY FLOW ABOUT A CIRCULAR CYLINDER FOR LOW VALUES OF BETA PARAMETER

Abstract

A Hybrid Lagrangian/Eulerian Discrete Vortex Method has been used to simulate the flow around a circular cylinder in planar oscillatory flow at a value of the viscous scale parameter, β, of 76. A number of techniques are examined for estimating the forces acting on the cylinder. Surface pressure is calculated using the normal gradient of vorticity at the surface, by integrating the equation of motion along a radial line from the outer boundary of the mesh to the cylinder surface and by using Poisson’s equation. Predictions are compared with existing analytical results for low Keulegan Carpenter numbers and with recent measurements up to Keulegan Carpenter numbers of 30, made at a β of 70. These comparisons show that Wu's method, based on the generalized Blasius equation, gives accurate predictions and that surface pressure is predicted most accurately by using integration along a radial line. There is found to be good agreement between the computed and measured in-line forces across a range of KC values. Numerical flow field data is presented in the form of visualizations and, in order to be able to compare directly with visualization from experiments, passive markers are introduced into the computations. All the major vortex-shedding regimes observed in experiments at KC values up to around 30 are reproduced in the simulations.