Session G27: Flow Instability: Multiphase Flow

Direct numerical simulation of ventilated vortex breakdown

This research explores the breakdown behavior of two-phase vortices, as found in hydrofoil and propeller wakes using high-fidelity Direct Numerical Simulation. The flow field is initialized with a q-vortex, incorporating a multiphase adjustment proposed by Bosschers [Int. J. Multiph. Flow, 105, 122-133 (2018)], and an isotropic turbulence perturbation. Initially, the study examines the breakdown of a single-phase vortex tube, characterizing the secondary vortex rings and their role in the eventual large amplitude vortex breakdown. Next, this is extended to two-phase vortex behavior and a regime map covering a range of Reynolds and Weber number combinations is produced. The influence of the secondary vortical structures on the interface breakdown is also investigated, and contrasted with the single-phase vortex behavior. The turbulence characteristic is investigated through the turbulent kinetic energy spectrum. Additionally, the evolution of the bubble size population is analyzed to shed light on the ventilated vortex breakdown process.   

Unraveling the Complexity of Dusty Channel Flow: A Comprehensive Stability Analysis

We investigate the stability of dusty channel flow, driven by an imposed pressure gradient, where particles are in a dilute suspension. Saffman¹, and later, Klinkenberg et al² studied the stability under homogeneous particle loading. Klinkenberg et al² found that the addition of particles results a small suppression of exponentially growing modes. 

In contrast, our work incorporates a more realistic base mass fraction profile, inspired by experiments on dusty channel flows. We include Stokes drag as well as the viscosity variation caused by particles, based on Einstein's viscosity formula.

Combining numerical and analytical methods, we conduct a comprehensive investigation. Intriguingly, our results are  remarkable and unexpected: the presence of even small quantities of particles leads to significant destabilization.

1. Saffman, P. G. (1962). On the stability of laminar flow of a dusty gas. J. Fluid Mech. 13(1):120-128.

2. Klinkenberg, J., De Lange, H., and Brandt, L. (2011). Modal and non-modal stability of particle-laden channel flow. Phys. Fluids, 23, 0064110.   

Using vibration to generate bespoke emulsions

We investigate emulsion formation due to fragmentation of the interface between two stably stratified layers of immiscible liquids in a horizontally vibrated container. The horizontal oscillation, which drives an oscillatory shear flow between the fluid layers, is redirected into vertical forcing near the vibrating end-walls by harmonic sloshing. We find that the sloshing front is destabilized into subharmonic surface waves (SWs) through a Faraday instability.  The critical forcing accelerations for the onset of these waves match predictions of the Mathieu equation with a modified shear rate evaluated over the Stokes layer thickness. A further increase in forcing acceleration leads to droplets breaking off the tips of the SWs. For a small viscosity ratio between the upper and lower layer (N=9), the droplet formation is irregular. However, for N=45 we can tune the forcing parameters to generate trains of monodisperse droplets moving away from the end wall, where the droplet size increases with acceleration. Our system offers the potential for large volumes of bespoke surfactant-free emulsions, e.g., for solvent extraction, which can rapidly phase-separate upon interruption of the forcing.