Structural Bifurcation Analysis of Unsteady Flow Separations from the Surface of Solid Cylinders in Laminar Shear Flows

Abstract:  Fluid flow past bluff bodies has been an area of intensive investigation for the past several decades due to its large number of practical applications and complex flow aspects like boundary layer, flow separation, and shear layer etc. Separation occurs on the wide area of a bluff body, which produces a high pressure drag force and a larger wake region. Hence, over the last century, several experimental, analytical and numerical researches have been carried out successfully in which most of the published literatures are concentrated on uniform flow. However, when the incoming flow is not uniform, but sheared, the wake has complex flow behavior due to presence of velocity gradient. It causes a complicated interaction between the boundary layers and the flow separation from the solid surface of the bluff body. In reality, shear flow occurs more commonly than uniform flows. The Couette flow is the simplest case of shear flow. The fluid flow is called planar shear flow if there exists a velocity gradient in the cross flow direction. An example of such flow is horizontal subsea pipelines in the seashore (boundary layer flow).  Due to the complex flow properties, this type of problems has attracted large number of researchers.

The purpose of the present work is to understand the unsteady flow separation from cylinders surface in shear flows using theoretical structural bifurcation analysis, which is found to be a very useful tool to understand the flow separation around solid objects and vortex shedding phenomenon. Through this study exact location and the time of occurrence of structural bifurcations (flow separations) can be obtained. We first aim to study the unsteady flow separation for the case of shear flow past single straight and inclined square cylinder in Cartesian coordinates and vortex shedding phenomenon for different Reynolds numbers and shear parameter values. We then aim to explore the flow phenomena for the case of shear flow past multiple square cylinders and wake interference among them in various arrangements. At the end, we solve the problem of shear flow past circular cylinder in polar coordinates and analyzed the unsteady flow separation using structural bifurcation analysis.