Dynamic mode decomposition analysis and fluid-mechanical aspects of viscoelastic fluid flows past a cylinder in laminar vortex shedding regime

Abstract

This study presents an extensive numerical investigation to understand the effect of fluid viscoelasticity on the flow dynamics past a stationary cylinder in the laminar vortex shedding regime. The governing equations, namely, mass, momentum, and Oldroyd-B viscoelastic constitutive equations, have been solved at a fixed value of the Reynolds number of 100 and over a range of values of the Weissenberg number as 0≤Wi≤2 and polymer viscosity ratio as 0.5≤β≤0.85. In particular, for the first time, this study presents a detailed analysis of how the fluid viscoelasticity influences the coherent flow structures in this benchmark problem using the dynamic mode decomposition (DMD) technique, which is considered to be one of the widely used reduced order modeling techniques in the domain of fluid mechanics. We show that this technique can successfully identify the low-rank fluid structures in terms of the spatiotemporal modes from the time-resolved vorticity field snapshots and capture the essential flow features by very few modes. Furthermore, we observe a significant difference in the amplitude and frequency associated with these modes for Newtonian and viscoelastic fluids otherwise under the same conditions. This, in turn, explains the differences seen in the flow dynamics between the two types of fluids in an unambiguous way, such as why the fluid viscoelasticity suppresses the vortex shedding phenomenon and decreases the energy associated with the velocity fluctuations in viscoelastic fluids than that in Newtonian fluids. However, before performing the DMD analysis, we also present a detailed discussion on the various fluid-mechanical aspects of this flow system, such as streamline patterns, vorticity fields, drag and lift forces acting on the cylinder, etc. This will ultimately set a reference platform for delineating the importance of the DMD analysis to get further insight into flow physics.