Session L17: Vortex Evolution and Interaction

Interactions of periodically generated vortex rings

Periodically generated vortex rings are observed in nature such as cardiovascular flows. We set up a series of simulations to study the dynamics of vortex rings in both transient and quasi-steady state. Our set-up consists of a circular cylinder through which a periodic pulsed jet is pushed into a tank. Our visualizations showed that for test cases with high non-dimensional period (T^*, i.e., equivalent to formation time) or low Re, the stopping vortices surrounding the leading ones remain circular and intact; however, by decreasing T^* and increasing Re the stopping vortices become unstable and form hairpin vortices. Our observations in quasi-steady state showed that two distinct interaction patterns exist. For cases with short T^*, vortex pairing occurs after about one period downstream, which makes reaching the quasi-steady take longer. The stability of pairing process is affected by the Re. For cases with higher T^*, a train of vortex rings is generated in the quasi-steady state.   

The influence of collision angle on vortex reconnection during the symmetrical collision of vortex rings

Limitations on the common vortex tube arrangements, namely the anti-parallel and the orthogonal configurations, constrain the parameter space of vortex reconnection studies to Reynolds number only in the literature. In a recent article by Hernandez and Reyes [Phys. Fluids 29, 103604 (2017)], the symmetrical collisions of three and six vortex rings in the incompressible laminar regime were numerically investigated. This particular configuration of vortex collision exhibits a similar vortex reconnection process to the common setups, but offers the ability to adjust the collision angle, which enables the investigation of the geometrical influence on the vortex reconnection phenomenon. We employ pseudo-spectral simulations to perform a parametric study by varying both the collision angle and Reynolds number for the symmetrical collision of vortex rings. We find that the collision angle does play a role in the reconnection process, where the reduction in the impact angle leads to increases in both the circulation transfer rate and the final circulation transferred to the collision plane. Furthermore, the circulation transfer mechanism is reported, which provides additional insights into the vortex reconnection phenomenon.
  

Helicity Decay in Vortex Rings

The helicity of vortex loops is captured in the loops' linking, writhe, and twist. In viscous fluids, helicity loses its conserved status and is dissipated through only one of these modes -- twist. By generating helical vortices using hydrofoils, we are able to measure their helicity and its decay over a range of viscosities. We report the dissipation and exchange dynamics and interpret them in terms of the evolution of the vortex core geometry and size, which we resolve using a novel method.   

Effect of temperature gradients on axial vortex breakdown

In this study, we do a direct numerical simulation to understand the effect of temperture gradient on an axial vortex breakdown. 
This is achieved by rotating the top lid of a cylinder which is heated at the bottom and cooled at the top. 
We study the dynamics of the confined fluid inside the cylinder, at different rotational rates of the lid and heating of the end walls. 
The problem finds application in natural flows where fluid rotates over heated surface as in hurricanes, as well as in engineering problems involving breakdown bubbles which used for aerodynamic stabilization of flames in a premixed swirl combustor.
A three dimensional Navier Stokes simulation of such a problem is less explored, that we undertake here. 
The initially swirl flow establishes a breakdown bubble as rotational rate is increased, and gets modified to generate non-axisymmetry in flow, when temperature gradients are applied.
Also, we propose a simple analytical model, which relies on inviscid nature of breakdown bubble phennomena, to capture the stagnation points at the axis. 
This confirms that, at increased rotational rates, spatial localization of azimuthal vorticity induces negative velocity causing vortex breakdown bubble.   

DNS of the interaction between counter rotating vortices

Understanding the nature of interaction between a pair of vortex filaments is essential to predict cavitation inception in the filaments. DNS is used to study the effect of core radius on the dynamics of the interaction between a pair of unequal strength counter-rotating vortices. The simulations examine conditions that lead to lowest pressure in either of the vortices. The extent of stretching and deformation of the filament cores is analysed and the variation in collapse time, minimum pressure and maximum vorticity with radii ratio are discussed.