Studying the Oscillating Flow around Unconfined Obstacle of Elliptical Cross-Section

Abstract

The present paper focuses on the effect of geometric shape of a cylindrical body submerged in an oscillating flow by means of numerical investigations. The cylindrical body has an elliptic cross-section with a variation of its elliptic ratio (ratio between major and minor axes of the elliptic section). The flow direction is oriented along the major axis. Three regimes from (Tatstuno and Bearman) maps are studied namely, a symmetric regime A and two other asymmetric regimes D and F. The flow field structures, the Morison coefficients of longitudinal forces and the root mean square (r.m.s.) of transverse forces are computed with respect to the elliptic ratio variation. For the case of cylinders with slightly elliptic cross-section, vortices and pressure fields are very similar to those of a circular cylinder. For the case of regime A, the vortex shedding is always symmetric despite the unbreakable variation of the elliptic ratio. On the other hand, the reduction of the elliptic ratio weakens the asymmetry of the flow for regimes D and F. Moreover, the flow in each regime becomes completely symmetric at a given value of the elliptic ratio. In fact, the predicted longitudinal component of the force acting on the cylinder decreases with the reduction of this ratio. This results in the same manner on the behavior of Morison coefficients. With regard to the symmetric regime A, the transverse force does not manifest itself for all considered ratios. On the other hand, the transverse force in the case of asymmetric regimes decreases rapidly with increasing the ellipticity of the cylinder. The present study showed us that the inertia coefficient is sensitive to the vortex path; however, the drag coefficient is independent of the vortex path. Both coefficients depend simultaneously on Reynolds number and the geometric shape of the body.