Effect of Pulsation in Relative Vortex Strength on the Evolution of A Material Line In A Pair Of Viscous Vortices

Abstract

Vortices are part of many real flow situations. Vortices help in enhancing mixing which in turn is helpful in improving heat transfer and chemical reaction rates. Mixing is natural in turbulent flow regime. Inducing good mixing in laminar flows is a challenge. To improve mixing in laminar flows, principles of chaotic mixing can be utilized. Chaotic mixing can be induced in the presence of interacting vortices. In this present work, pair of similar viscous vortices is considered. The influence of the oscillation in the relative strength of vortices on a material line is studied. Cases of these vortices rotating in the same sense and opposite sense are studied separately. Pairs of Rankine as well as Lamb-Oseen vortices are investigated. Evolution of a material line is one of the simple yet effective ways to visualize mixing. In this work, evolution of a line of 10000 particles placed along the line joining the center of the vortices is investigated. The evolution of the material line with time is tracked by tracking position of individual particles using Runge-Kutta marching scheme of the 4th order. Mixing is quantified using a simple measure called Total Average Deviation (TAD). Investigations on varying amplitudes and frequencies of oscillations have been carried out. In all the cases considered, TAD values give considerable insights into mixing of particles in the material line. TAD curve is plotted with TAD values along the vertical axis and initial x-coordinate position along the horizontal axis. Oscillation in TAD curve indicates mixing among nearby particles. Large TAD values with no oscillation in the TAD curve indicate that there is a bulk transport of the material line without mixing among them. Low TAD values with no oscillation in the TAD curve indicate less deviation from the steady case.