Hydrodynamic Stability of Swirling Flows of Newtonian and Non-Newtonian Fluids

Abstract

A rigorous linear convective instability analysis has been carried out for swirling flows of Newtonian and non Newtonian fluids near rotating disk. The BEK family of flows are instrumental in turbomachinery and in rotor-stator systems. There are widely applicable turbomachinery applications that involve Newtonian fluids (e.g. water, steam, oil) in various industrial processes. In petroleum industries, non-Newtonian fluids such as Carreau fluid and Bingham fluid are widely used. As a result, study on Newtonian and non Newtonian fluids is highly beneficial in engineering and science, and they have piqued the interest of several academics and experts. The primary goal of this dissertation is to look into the impacts of radial surface stretching, and surface roughness on the hydrodynamic stability of spinning disk boundary layer flows of Newtonian and non-Newtonian fluids. Because the stretching mechanism aids in cooling industrial machine walls, this research is vital from an industrial standpoint. The impacts of the stretching mechanism and surface roughness on the convective instability of the aforementioned swirling flows in the presence of the Coriolis force have been investigated numerically for the very first time in the literature . The Kármán similarity transformations are used to convert the system of PDEs representing the governing equations into a system of highly non-linear, fully coupled ODEs. These system of self-similar equations are then solved numerically to produce the mean flow solutions. Subsequently, a linear convective instability analysis is performed using the Chebyshev collocation method to obtain the neutral stability curves. Based on the stability curves, a radial stretch of the disk has a globally stabilizing impact on both the inviscid Type-I and viscous Type-II instability modes of Bödewadt flow and Ekman flow. However, it has a globally destabilizing influence on the instability modes of Kármán swirling flow in presence of the Coriolis force. The roughness of the disk has a globally destabilizing influence on the Type-I and Type-II modes for the stagnation point flow over a rotating disk. Furthermore, the stability curves reveal that when the disk is expanded radially, shear thinning fluids of the Carreau model show a globally stabilizing effect. In contrast, shear-thickening fluids show a globally destabilizing impact. An energy analysis of the flows has been undertaken simultaneously to verify the above physical occurrences. The acquired results strongly confirm the previously published findings and will be used as a standard for our future research.