Formation and Dissipation of Karman Vortex Street in an Accelerating Flow Past a Circular Cylinder

Abstract

Prediction of Karman vortex street in a flow past circular cylinder has become a benchmark problem and many new numerical methods are validated by reproducing the phenomena. The formation and dissipation of Karman vortex street occurs in a range of Reynolds number. But, the conventional Navier-Stokes equations derived in inertial frame of reference based on constant relative velocity are limited to fluid flow problem at a given freestream velocity or Reynolds number. Therefore, in order to capture the formation and dissipation of karman vortex street, several simulations are to be carried out at different freestream velocites. Even then, such simulations will not reveal the continous phenomena of formation and dissipation of vortices. In this work, Navier-Stokes equations are obtained from first principles for fluid flow problems with linear external acceleration in relative acceleration frame of reference, in a form most suited for numerical study. Using these equations, numerical simulation of accelerating flow over circular cylinder is carried out for Reynolds number range, 68 to 1360. The formation and dissipation of Karman vortex street is captured in a single simulation and the results are compared with conventional simulations at various Reynolds numbers. The issues in physical modeling and numerics of using constant freestream acceleration are also discussed in brief. From these simulations, it is demonstrated that the physical phenomena obtained by solving conventional Navier-Stokes equations at various freestream velocities can obtained in a single simulation by using the Navier-Stokes equations written in relative acceleration frame of reference. These equation can be used to explore the physics of accelerating flows in a continuous scenario, without undertaking numerous conventional simulations at various constant freestream velocities.