Session J35: Atomization and Sprays I

High-fidelity simulation and modeling of aerodynamic breakup of vaporizing droplets

The aerodynamic breakup and vaporization of a droplet are investigated through high-fidelity interface-resolved simulations. The droplet is initially stationary and at saturation temperature, and is suddenly subjected to a uniform superheated vapor stream. The sharp liquid-gas interface is tracked using the geometric Volume-of-Fluid (VOF) method. The incompressible Navier-Stokes equations are solved in conjunction with a two-fluid model for thermal energy advection and conduction, with an embedded Dirichlet boundary condition for temperature at the interface. The phase-change model is implemented in the adaptive multiphase flow solver, Basilisk, in which an adaptive quadtree/octree mesh is used for spatial discretization. Different drop liquids, including water, acetone, and armonoia, are considered. Parametric simulations were performed for different Weber (We) and Stefan (St) numbers, which characterize the droplet deformation and vaporization. The range of We covers the vibrational, bag, and multi-mode breakup modes. Particular attention is focused on characterizing the interaction between droplet deformation and vaporization. The results indicate an increase in the droplet vaporization rate with We, and a novel droplet vaporization model for the Nusselt number is developed. We have also observed a significant variation of critical Weber number with St.   

Fragmentation of liquid sheets of emulsion: competition between interfacial and viscous effects

Sprays of emulsion are used widely from cosmetics to agriculture. Understanding the governing principles of emulsion fragmentation allows for the design of sprays with desired characteristics, such as droplet size. Sprays are formed when liquid sheets and ligaments break up into droplets. The composition of a liquid sheet is known to affect its destabilization. Indeed, the addition of a dispersed phase, liquid or solid, reduces the expansion and lifetime of the liquid sheet. In this study, we investigate the destabilization of liquid sheets of emulsion. We vary the viscosity of the dispersed phase and alter surfactant concentrations to vary the spreading parameter. Using high-speed imaging, we capture the expansion and fragmentation of single-drop impacts of emulsions on a small surface. We show that both viscosity and interfacial properties influence the destabilization. We use a modified Capillary number to compare the effect of viscous and interfacial stresses on the fragmentation of liquid sheets of emulsion.   

Toward fully-resolved simulations of the bag breakup of a single drop

When an isolated drop is suddenly subjected to a uniform gas stream, the drop will experience deformation and even breakup. When the Weber number based on the drop diameter and free-stream velocity is just above the critical threshold, the drop first deforms into a bag before topology change finally occurs due to the rupture of the bag sheet. The present study aims to demonstrate that 3D simulations are necessary to resolve the turbulent wake, so that the drop acceleration and deformation can be accurately captured, assuming the droplet Reynolds number is high, as in most droplet aerobreakup problems. Since a high mesh resolution is required to resolve the thin bag sheet, it is surprisingly expensive to simulate the bag breakup of a single drop, even with sophisticated numerical techniques, including the Volume-of-Fluid (VOF) method and adaptive mesh refinement. Though disjoining pressure is not included in the Navier-Stokes equation, a numerical cutoff length, larger than the cell size, is introduced in the VOF-based manifold death method to pinch the two interfaces when the thickness is smaller than the cutoff length. The effect of the numerical cutoff length on the bag inflation and breakup dynamics is investigated in detail. Only for tiny droplets with a diameter lower than a hundred microns, the numerical cutoff length can be similar to the physical cutoff length scale that is dictated by disjoining pressure and one can claim that the simulations are close to fully resolving the bag breakup of a single drop. For larger drops, it remains infeasible to fully resolve the bag breakup and subgrid models for thin liquid sheet evolution and breakup are needed.   

The study of droplet internal circulation and its interaction with droplet deformation

The study of liquid droplet is important for applications like spray-painting, fire suppression, and spray combustion. Droplet morphology has a great impact in these applications, for example, in spray conditions, droplets of various sizes are generated from jet atomization, and the large droplets have strong deformation. The highly deformed droplets have very different characteristics compared to spherical droplets, but many studies on droplet dynamics are based on the spherical droplet assumption. To develop a more accurate modeling of liquid droplet in jet simulations, we use numerical approaches to investigate the mechanism of droplet deformation. Weber number, which measures the balance of surface tension and inertia, is a key non-dimensional group that quantifies droplet deformation. However, droplets with same Weber number do not always have an identical shape. For example, our previous work[Lin and Palmore, 2022] demonstrated that internal circulation also influences droplet shape. Therefore, a deeper understanding in droplet internal circulation is needed. In this work, we will explore a wider range of droplet parameters relevant to a wide array of applications for droplets to study the interaction between droplet internal circulation and deformation.   

High Speed Image Analysis of Liquid Sheet Atomization created by a Doublet Impinging Jet Injector

In this study we experimentally determined a variety of spray and atomization characteristics of a doublet impinging jet injector using high speed imaging. Impinging jet injectors are of interest as they are commonly used in rocket engines to atomize the propellants before ignition and have complex flow interactions that are difficult to study both experimentally and numerically. The injector, in this study, used water as a propellant simulant and was tested under a variety of Reynolds and Weber numbers. The spray was illuminated by a backlight which created a shadowgraph of the atomization process and was captured at a rate of 20,000 fps by using a high-speed camera. The mechanism of the atomization process is known to be the wave instabilities, generated by the impact of the streams, that then cause the breakup of the spray into ligaments and ultimately droplets. Post-processing of the shadowgraph images was used to capture and characterize the major elements of the atomization process from the liquid sheet wave instabilities to the ligaments to the droplets. Additionally, techniques were developed for the tracking of both the ligaments and droplets which allowed for greater insight into the dynamic process of atomization.   

Fragmentation of Colliding Liquid Rims

Wave splashing is an important pathway through which sea sprays are generated, which are crucial for enhancing the transfer of mass, momentum and energy at the air-sea interface. We investigate the transverse collision of two liquid rims as a possible model for understanding the wave splashing phenomena. Interfacial perturbations with fixed maximum wavenumbers and amplitudes are introduced to the rims before their collision, whose subsequent morphological development is simulated by solving the two-phase incompressible Navier-Stokes equation with the adaptive mesh refinement (AMR) technique. We first show the self-similar evolution of the interfacial and velocity profiles of the expanding lamellae forming between the two rims, and develop scaling laws for the evolution of liquid rims at their border. We then analyse the formation and growth of transverse ligaments on top of the rims, which we find to originate from the initial corrugated geometry of the perturbed rim surface rather than hydrodynamic instabilities acting on the decelerating lamella rims. Novel scaling models are proposed for predicting the decay of the ligament number density due to the ongoing ligament merging cascade. Lastly, we present the size and velocity statistics of the rim collision fragments and discuss their possible connections with the drop statistics of breaking waves.   

Manifold Death and the breakup of bags in atomizing flows

The breakup of liquid masses by high speed air flow, or atomization, involves the formation of thin sheets or bags, that perforate at so-called weak spots, followed by a rapid expansion of holes as the Taylor-Culick rim advances. Similar hole formation is observed in floating bubbles, where it leads to bubble death and droplet impact. In some situations, large numbers of holes are observed to coexist, while in other situations a single hole rapidly expands before other holes can form. The numerical procedure we propose to handle hole formation is Manifold Death. We describe this procedure and also give simple statistical estimates for the number of holes that can be observed during the breakup of a single bag, that is the number of coexisting holes. Two models are discussed, one in which breakup is triggered by external random events such as the impact of a microdroplet on the sheet, and one in which breakup is triggered by a distribution of impurities, such as bubbles or oil droplets, immersed inside the sheet. A dimensionless number involving the typical sheet or bag thickness at breakup h_c and the local strain rate γ  predicts the number of coexisting holes. This prediction is compared to experiments.   

Fuel Droplet Breakup in High-Pressure Propulsion Systems Using an Integrated Molecular-Dynamics and Direct Numerical Simulation Approach

The secondary breakup of fuel droplets into child droplets significantly impacts the mixing and combustion processes in liquid-fueled propulsion systems. In the pursuit of enhanced engine performance and reduced emissions, the design of propulsion systems is shifting towards pressures higher than the nominal critical pressure of the fuel and air. This leads to transcritical conditions, wherein the subcritical fuel is injected into the supercritical air, causing fuel to transition from a liquid-like to a gas-like behavior. Experimental analyses at low convective flow speeds have characterized the transcritical behavior as a transition from classical evaporation dominated by surface tension effects into a gas-like diffusion behavior at higher pressure and temperature. However, the transcritical droplet breakup mechanisms under high-speed conditions involving shockwaves have remained unresolved. In this study, the breakup behavior of a single subcritical n-dodecane droplet in a supercritical environment interacting with a shockwave is developed by a fully compressible multiphase Direct Numerical Simulation (DNS) approach with real-gas and surface effects. Molecular Dynamics simulations (MD) are utilized to study the interfacial behavior of an n-dodecane droplet to predict the surface tension coefficient under varying ambient conditions. This study integrates MD and continuum-based modeling by developing a data-driven model for breakup and evaporation at transcritical conditions.