Higher order accurate numerical simulation of shear flow past a circular cylinder with an attached arc-shaped control plate

Abstract

A numerical simulation of an incompressible, unsteady, laminar shear flow past a circular cylinder with an attached arc-shaped plate using higher order compact scheme is presented in this work. The timing accuracy of the scheme is second order, and its spatial accuracy is at least third order. The method calculates time-marching steady-state and unsteady flow very effectively for several different Reynolds values. Simulations are performed for Reynolds number $(Re) = 115$, using the shear parameter values $\kappa = 0.0, 0.05$. The radius of the circular cylinder is $R_0$ and the radius of the circular arc is ($1.5*R_0$). In cylindrical polar coordinates, the Navier–Stokes (N–S) equations are taken as the governing equations in their streamfunction—vorticity form. From the perspectives of stream function, vorticity contours, lift coefficient, and phase diagrams, we look at how the shear rate affects the process of vortex shedding. We have observed that the shear rate have a substantial impact on the evolution of the wake behind the cylinder and the phenomenon of vortex shedding. When comparing shear flow ($\kappa =0.05$) to uniform flow ($\kappa =0.0$), we noted significant differences in the vortex shedding behavior. In the case of uniform flow, the shedding is symmetric and occurs periodically, while shear flow leads to an asymmetric shedding pattern. In addition to demonstrating the impact of vortex shedding from the circular cylinder with an attached plate in shear flow, the numerical results also highlight numerous significant flow producing features with $\kappa$. To our knowledge, this is the first time a numerical investigation has been done to explore the vortex-shedding phenomena for a circular cylinder with an attached arc-shaped control plate.