Accelerated micropolar fluid--flow past an uniformly rotating circular cylinder

TL;DR

This study investigates the unsteady flow around a rotating circular cylinder in a micropolar fluid, using advanced numerical methods to analyze effects on lift, drag, vortex formation, and boundary layer behavior.

Contribution

It introduces a numerical scheme combining Adams-Bashforth, Fourier Series, Runge-Kutta, and SOR methods for solving micropolar fluid flow around a rotating cylinder.

Findings

Increased micropolarity enhances lift and reduces drag.

Cylinder rotation delays vortex shedding and dissolves boundary layers.

Rotation reduces micropolar spin boundary layer and affects vortex dynamics.

Abstract

In this paper, we formulated the non-steady flow due to the uniformly accelerated and rotating circular cylinder from rest in a stationary, viscous, incompressible and micropolar fluid. This flow problem is examined numerically by adopting a special scheme comprising the Adams-Bashforth Temporal Fourier Series method and the Runge-Kutta Temporal Special Finite-Difference method. This numerical scheme transforms the governing equation for micropolar fluids for this problem into system of finite-difference equations. This system was further solved numerically by point SOR-method. These results were also further extrapolated by the Richardson extrapolation method. This scheme is valid for all values of the flow and fluid-parameters and for all time. Moreover the boundary conditions of the vorticity and the spin at points far from the cylinder are being imposed and encountered too. The results are compared with existing results (for non-rotating circular cylinder in Newtonian fluids). The comparison is good. The enhancement of lift and reduction in drag was observed if the micropolarity effects are intensified. Same is happened if the rotation of a cylinder increases. Furthermore, the vortex-pair in the wake is delayed to successively higher times as rotation parameter increases. In addition, the rotation helps not only in dissolving vortices adjacent to the cylinder and adverse pressure region but also in dissolving the boundary layer separation. Furthermore, the rotation reduces the micropolar spin boundary layer also.