Numerical simulation of flow around an orbiting cylinder at different ellipticity values

This paper deals with the numerical simulation of low Reynolds number flow (Re=120–180) past a circular cylinder in orbital motion. The Navier–Stokes equations, pressure Poisson equations and continuity are written in primitive variables in a noninertial system fixed to the orbiting cylinder and solved by the finite difference method. Ellipticity values between 0 and 1.2 (from pure in-line oscillation through a full circle and beyond) were investigated. Sudden changes in state (jumps) are found when time-mean or root-mean-square values of force coefficients or energy transfer are plotted against ellipticity. Pre- and post-jump analysis was carried out by investigating limit cycles, time-histories, phase angles and flow patterns. These investigations revealed that ellipticity can have a large effect on the energy transfer between the incompressible fluid and a circular cylinder forced to follow an orbital path, and that small changes in the amplitude of transverse motion can have a dramatic effect. The phase angle was altered by about 180° at the jumps. Also investigated were the direction of orbit, which affects the state curves belonging to the time-mean values of lift only, and the effect of initial conditions, which alters the location of jumps without changing the state curves.