Session Q17: Drops: Instability and Break-up

Break-up in a gas-liquid atomizer in conjunction with an electro-spray

Multiphysics control of sprays can modify the atomization and dispersion of droplets and has many applications in fields like combustion, propulsion, agriculture, and chemical processing. We study the effect on atomization of electric charge and an external electric field in conjunction with high momentum coaxial gas. We quantify the acceleration and size distribution of the droplets with an electric field of 30kV and gas Reynolds numbers ~5x10^3-5*10^4. The electric field impacts both the atomization of the spray in the near field and the resulting droplets' velocity/acceleration in the mid-field. High-speed imaging of scattered light is analyzed to track individual droplets. Image processing was used to identify droplet tracks and derive velocity and acceleration. Statistical analysis applied to tracks shows dependency with momentum ratio and electrostatic stresses of the droplet size and number density distributions, with increasing M or E resulting in a greater number of smaller droplets, and much higher radial acceleration, with higher droplet spray dispersion.   

Liquid sheet breakup and droplet evolution in agricultural sprays

Spraying is a common process in everyday life with applications in agriculture, drug administration, printing, and painting. For agriculture purposes, small droplets are needed to enhance coverage of agricultural sprays, but not so small that they cause drift of the sprayed pesticides. Spray drift can cause the deposition of chemicals to undesired areas with a negative impact on livestock, ecosystems, and human health. In this work, different factors influencing spray breakup and droplet size distributions are discussed. Herein we experimentally measure the droplet size distribution of sprays from agricultural spray nozzles. The sprays were either homogeneous or contained an emulsion, and the dynamic surface and interfacial tensions were varied. We identified the influence on spray volume fraction below 150 μm and on the volume median diameter, which are correlated with the spray drift risk and deposition, respectively. The results of this work will help to understand the factors affecting a droplet size during a spraying process, towards increased efficacy of spraying pesticides.   

A numerical study of surface tension effects on the break-up behavior of transcritical fuel droplets

The role of surface tension is typically neglected in transcritical flow simulations. However, recent experiments and theoretical studies have shown that surface tension persists at high pressures. It is still, however, unproven if the presence of the surface tension force significantly changes the flow and mixing behavior in transcritical flow problems. A fully compressible diffuse-interface method is developed to simulate the breakup of a single transcritical droplet impacted by a shockwave to replicate the high-speed convective flows at engine-relevant conditions. Using this model, we investigate the significance of surface tension on droplet break-up by implementing the surface tension coefficients between the fuel (n-dodecane) and the surrounding fluid (nitrogen) obtained from molecular dynamics simulations. The breakup mode of the transcritical droplets is identified for a wide range of velocity, temperature, and pressure conditions.   

Aerodynamic breakup of submillimeter drops in high-speed flows

Aerobreakup of liquid drops are important to many droplet applications, such as fuel injection. When a liquid drop is subjected to a gas stream of high velocity, the drop can deform and break into small droplets. The drop aerobreakup is controlled by multiple dimensionless parameters. The Weber number (We) has been commonly used to characterize the different breakup regimes. While the effects of Weber and Ohnesorge numbers on the aerobreakup of a drop in unbounded domain have been extensively studied, the effect of the Reynolds number (Re) based on gas properties are less understood and will be investigated through detailed numerical simulations in the present paper. Attention will be focused on the moderate We regime, where the drop mostly breaks in the bag mode. In previous studies for millimeter drops, Re is too large to be relevant. However, for applications where drops are small and the relative velocity is high, Re can be quite small when the drop breaks. Parametric simulations of Re and We are performed to systematically investigate the effect of Re on the drop aerobreakup dynamics. The simulations are performed using the Basilisk solver, where the mass-momentum consistent VOF method is used to capture the interfacial dynamics on an adaptive mesh. The reduced Re is found to induce significant changes in the drop acceleration, deformation, bag morphology, and the bag breakup dynamics, which in turn lead to significant variation in the size and spatial distributions of the children droplets formed.    

The Landscape of Newtonian Droplet Breakup under Impulsive Acceleration

We examine the complete landscape of parameters which affect secondary breakup of a Newtonian droplet under impulsive acceleration. A Buckingham-Pi analysis reveals that the critical Weber number We_cr for a non-vibrational breakup depends on the density ratio (ρ), the drop (Oh_d) and the ambient (Oh_o) Ohnesorge numbers. Volume of fluid (VOF) based numerical simulations are performed using Basilisk to conduct a reasonably complete parametric sweep of the non-dimensional parameters involved. It is found that, contrary to current consensus, even for Oh_d ≤ 0.1, a decrease in Oh_d has a substantial impact on the breakup morphology, motivating plume formation, and in turn affecting We_cr. It is observed that in addition to ρ (which previous studies had observed), Oh_o affects whether local inertia or aerodynamic drag is the dominant force acting on the droplet. This behavior manifests in simulations through the observed pancake shapes and ultimately the breakup morphology (forward or backward bag). We summarize these results and present physical explanations of the observed behavior.   

Not Participating

Atmospheric scientists have shown that falling water droplets can take on several mode shapes and that the frequency is dependent on the droplet size. However, droplets larger than the capillary length (average dia. < 3 mm) are often neglected because they eventually break-up into smaller droplets. Some have attempted to figure out what the break-up looks like numerically but experimentalists attempting to validate the numerical results have failed, as   these break-ups seem to happen in random ways. Here we show through careful experimentation that the release mechanism, geometry and surface conditions play significant roles in the mode and frequency of the droplet after release. The mode and frequency are measured by high-speed camera and radial decomposition. These mode shapes greatly affect when and how the droplet breaks up, indicating that droplet break up is predictable but very sensitive to initial conditions. The largest recorded raindrop is 8.6 mm diameter and here we offer advice on how to make droplets that are nearly spherical when released up to 20 mm in diameter!   

Interaction of Liquid Droplets with Supersonic Flows around Projectiles with Sharp and Blunted Leading Edges

Precipitation and suspended droplets in the atmosphere present a significant erosion risk to vehicles traveling and high-supersonic and hypersonic speeds. We will present the results of simulations considering the interactions of droplets with both sharp and blunt projectiles in a high-supersonic (Mach 3) flow environment. We use an empirical drag model and the KHRT aerodynamic breakup model to provide physically-reasonable droplet behavior, and describe the interaction of the droplets with the flow field in the post-shock region of the flow as well as the boundary layer along the projectile surface.  We investigate the influence of body geometry and the interplay with droplet clouds of varying densities and particle sizes.    

Contraction dynamics of viscoelastic filaments

Liquid filaments/ligaments---elongated drops---arise in diverse applications including ink-jet printing, 3D printing, crop spraying, and atomization coating. In these and other applications, whether such elongated drops retract back into a single drop or break up into multiple smaller droplets during contraction is a critical issue from a performance standpoint. Historically, there has existed a disconnect between computational and experimental studies of filament contraction. In computations, the fluid within filaments is taken to be quiescent at the initial instant t = 0.  While doing so is expedient in simulations, it is nearly impossible to create a filament that is quiescent at t = 0 in experiments. Moreover, the working fluids in applications often contain performance-enhancing additives which render the fluids non-Newtonian. Here, we investigate the effect of adding polymer to a filament of an otherwise Newtonian fluid (solvent). Simulation results are reported that clarify the role of elastic stresses during contraction of viscoelastic filaments in situations in which the filament fluid at the initial instant is either quiescent or already in motion.    

Satellite Droplet Formation and Elimination in Binary Droplet Collision

In drop-drop collisions with large Weber number (We), separations frequently occur, featuring the fragmentation after a tentative coalescence. Our experiments showed that, in both head-on and off-center collisions of two identical drops, at least one satellite droplet can be formed after pinching of the coalesced drop. The simulations of head-on collision demonstrate the asymmetrical pinching necks of the temporarily coalesced drop, in agreement with the universal features of pinching free-surface flow and the scaling laws. This allows two pinched free-surfaces with mirrored asymmetrical profiles, permitting the satellite droplet formation upon breakup (Huang, Pan & Josserand, Phys. Rev. Lett., 2019). For the simulations of off-center collisions, when the neck of the tentatively coalesced drop forms at the drop center, the maximum pressure in the neck makes the maximum velocities to locate at two sides of the center. This makes the local radius along the drop to decrease fastest at two sides close to the primary drops, leading to two pinched points and thus the satellite droplet formation. Via slight breaking of the symmetry, no satellite droplet could be observed in head-on collision, thus providing a possible implication for controlling undesirable drop formation.   

Understanding the evolution of dilute emulsions with single-drop breakup experiments in isotropic turbulence

In this work we investigate the breakup of drops much larger than the Kolmogorov scale in homogeneous isotropic turbulence. We use a novel GPU code to perform thousands of independent direct numerical simulations of single drops at different Weber numbers, and gather statistics of the breakup process, in particular, the breakup time and the daughter drops-size distribution. This extensive database reveals that for small Weber numbers the survival time of single drops resemble a memoryless process characterised by a single parameter, the breakup rate. This quantity depends exponentially on the inverse of the Weber number, matching the celebrated model of Coulaloglou and Tavlarides (Chem. Eng. Sci, 1977), but not on the Reynolds number of the drop. These results show that breakup is possible for drops smaller than the maximum stable diameter, but that it becomes exponentially less likely as the drop diameter decreases. In the absence of coalescence and for sufficiently high Reynolds number, this non-vanishing breakup probability leads to and endless fragmentation process in the inertial range of isotropic turbulence, suggesting that, in real flows, drop-size distributions reach a statistically steady state in time scales much larger than previously thought. We provide an estimate of these time-scales, and show how the asymptotic evolution of dilute emulsions can be modelled with a stochastic approach based on the data gathered in our simulations.