Laminar vortex shedding past a flat plate at 90°

Abstract

Fluid flows such as rowing and animal flight involve both acceleration and vortex shedding. Some of such flows also involve complex fluids, as in blood flow from the left atrium into the left ventricle in a human heart. Among the complexities of such fluids, we are interested in the viscoelastic nature. The effect of acceleration in vortex dynamics and forces has been studied for a long time. However, there have been discrepancies in the origin of the unsteady forces and modelling them. It is still not very well understood how unsteady forces scale in laminar, highly separated flows? On the other hand, the presence of viscoelasticity alters the vortex dynamics and hence the forces. It has been well studied how the viscoelasticity may affect steady state forces. However, the change in vortex dynamics and forces due to presence of viscoelasticity during acceleration is not well understood. This experimental study aims to add to the literature on unsteady force modelling, effect of viscoelasticity in unsteady forces and vortex dynamics.

To begin with, shear and extensional rheological experiments were performed to identify a weakly elastic fluid. An experimental setup was built with a linear traverse, PIV system and force sensor. The experiments were performed with an accelerating flat plate (aspect ratio of two), in the identified viscoelastic fluid and also in a viscosity matched Newtonian fluid for one-one comparison. To understand the vortex dynamics, we use FTLE fields, Lamb-Oseen model, and Q-criteria. We quantify the vortex formation time and other properties of a vortex ring.

Overall, we observe that both the vortex growth rate and the decay rate are enhanced by the presence of viscoelasticity. We extend the idea of optimal vortex formation to two time-scales instead of one. One, when the plate no longer provides energy and the other, when the vortex is filament free without any more addition of coherent fluid parcels. Furthermore, a limit for optimal vortex formation is proposed to indicate a completely different type of vortex dynamics at lower accelerations. The drag reduction and enhancement due to the presence of viscoelasticity qualitatively agrees well with the trend in literature. In terms of unsteady forces, we try to interpret an equivalent mass for potential flow's added mass in separated Newtonian flows. We propose a model using wake's mass, and it reasonably agrees with our experimental results in Newtonian cases. We use FTLE ridges and vortex-frame streamlines to estimate wake mass, along with a literature driven model for third dimension. Furthermore, we also propose that the added mass in separated flows is time varying and eventually reaches a constant value. Moreover, the effect of viscoelasticity is primarily observed in unsteady forces for acceleration less than optimal vortex formation limit.