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NASA NTRS1989

Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. Part 1: Velocity selection

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. In the first part, the bubble velocity U relative to the fluid velocity at infinity is determined for small surface tension T by determining transcendentally small correction to the asymptotic series solution. It is found that for any relative bubble velocity U in the interval (U(c),2), solutions exist at a countably infinite set of values of T (which has zero as its limit point) corresponding to the different branches of bubble solutions. U(c) decreases monotonically from 2 to 1 as the bubble area increases from 0 to infinity. However, for a bubble of arbitrarily given size, as T approaches 0, solution exists on any given branch with relative bubble velocity U satisfying the relation 2-U = cT to the 2/3 power, where c depends on the branch but is independent of the bubble area. The analytical evidence further suggests that there are no solutions for U greater than 2. These results are in agreement with earlier analytical results for a finger. In Part 2, an analytic theory is presented for the determination of the linear stability of the bubble in the limit of zero surface tension. Only the solution branch corresponding to the largest possible U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.

Tanveer, Saleh↗

DOE OSTI2012

Static and dynamic response of a fluid-fluid interface to electric point and line charge

We consider the behavior of a dielectric fluid-fluid interface in the presence of a strong electric field from a point charge and line charge, respectively, both statically and, in the latter case, dynamically. The fluid surface is elevated above its undisturbed level until balance is reached between the electromagnetic lifting force, gravity and surface tension. We derive ordinary differential equations for the shape of the fluid-fluid interface which are solved numerically with standard means, demonstrating how the elevation depends on field strength and surface tension coefficient. In the dynamic case of a moving line charge, the surface of an inviscid liquid-liquid interface is left to oscillate behind the moving charge after it has been lifted against the force of gravity. We show how the wavelength of the oscillations depends on the relative strength of the forces of gravity and inertia, whereas the amplitude of the oscillations is a nontrivial function of the velocity at which the line charge moves. - Highlights: Black-Right-Pointing-Pointer Fluid surface elevation analyzed near a static point and line charge. Black-Right-Pointing-Pointer Elevation determined by interaction of gravity, dielectric force and surface tension. Black-Right-Pointing-Pointer Dynamic equation of motion for the moving line charge is derived. Black-Right-Pointing-Pointer Surface waves behind moving charge calculated and analysed for different velocities.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1973

Design of propellant acquisition systems for advanced cryogenic space propulsion systems

This paper presents results of work conducted to expand the technology base and evolve practical propellant surface tension acquisition system designs for future cryogenic space vehicles. Surface tension screen device channel flow analysis and supporting tests showed that reasonable mesh sizes could provide the required retention performance. Integrated subsystem studies and development showed that practical and effective screen surface tension acquisition devices could be designed for typical applications, but that other interfacing feed subsystems are often constrained by the design of the particular acquisition device. These constraints may dominate the total feed system performance.

Burge, G. W.↗

NASA NTRS1995

Microgravity: Teacher's guide with activities for physical science

This guide is an educational tool for teachers of grades 5 through 12. It is an introduction to microgravity and its application to spaceborne laboratory experiments. Specific payloads and missions are mentioned with limited detail, including Spacelab, the International Microgravity Laboratory, and the United States Microgravity Laboratory. Activities for students demonstrate chemistry, mathematics, and physics applications of microgravity. Activity objectives include: modeling how satellites orbit Earth; demonstrating that free fall eliminates the local effects of gravity; measuring the acceleration environments created by different motions; using a plasma sheet to observe acceleration forces that are experienced on board a space vehicle; demonstrating how mass can be measured in microgravity; feeling how inertia affects acceleration; observing the gravity-driven fluid flow that is caused by differences in solution density; studying surface tension and the fluid flows caused by differences in surface tension; illustrating the effects of gravity on the burning rate of candles; observing candle flame properties in free fall; measuring the contact angle of a fluid; illustrating the effects of gravity and surface tension on fiber pulling; observing crystal growth phenomena in a 1-g environment; investigating temperature effects on crystal growth; and observing crystal nucleation and growth rate during directional solidification. Each activity includes a background section, procedure, and follow-up questions.

Vogt, Gregory L.↗

DOE OSTI2025

An Overview of the Molten Salt Thermal Properties Database–Thermophysical, Version 4.0 (MSTDB-TP V.4.0)

A central repository of thermophysical and thermochemical properties of molten salt compositions of relevance to molten salt reactors (MSRs) is vital in supporting the broad community of MSR developers, who are at various stages of developing and deploying their reactor designs. In general, these MSR designs differ significantly from developer to developer (e.g., with respect to the hardness of the neutron spectra, level of fissile loading, target multicomponent temperatures and power levels, and moderating capabilities). Therefore, the fuel and coolant salts being considered vary greatly: they may be chlorides or fluorides, they utilize different actinides at different ratios, and the cations in the melt are selected based on perceived advantages and disadvantages. Considering the general need for thermal properties, and the vastness of the array of potential candidate salt mixtures, the Molten Salt Thermal Properties Database (MSTDB) was initiated in 2018 with the goal of providing thermophysical and thermochemical characterization of key molten salt compounds and mixtures across their temperature and compositional domains. The MSTDB is thus divided into the thermophysical arm (MSTDB-TP) and the thermochemical arm (MSTDB-TC). The MSTDB is an effort funded by the Department of Energy, Office of Nuclear Energy (DOE-NE) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, and the MSR Campaign. This report provides an overview of the MSTDB-TP v4.0 in terms of the data contained within, the state of the tools used to access the data, the availability of predictive models that leverage the raw data in the database, the preliminary status of developmental efforts that are currently underway, and an account of future goals for MSTDB-TP. The primary goal for the update from MSTDB-TP v.3.1 to v4.0 was the incorporation of surface tension data into the database; this property is important for thermal hydraulics modeling and species transport in other tools that have been developed under the NEAMS program. A breakdown of the surface tension data that have been added into MSTDB-TP v4.0 is provided herein, and the manner in which the quality of the data has been assessed is also documented. For MSTDB-TP v4.0, newly published thermophysical property data—primarily from collaborative experimental efforts under the MSR Campaign—have been incorporated into the database, and the resulting expansion is documented here. Because of the size to which MSTDB-TP has grown, the raw data format has now been recast into JavaScript Object Notation (JSON) format for easier connection with the MSTDB-TP application programming interface (API). Saline; the pre-existing comma-separated value (CSV) format has been deprecated but is still maintained, accessible, and up to date. As a final effort in packaging the MSTDB-TP v4.0 update, the graphical user interface (GUI) for MSTDB has been updated to allow full accessibility to the density and viscosity predictive models, which are based on Redlich-Kister expansions of MSTDB-TP raw data. Some other major aspects of this report, in terms of preliminary and future work, include: (1) documentation of the formalism and preliminary testing of a kinetic theory model that may act as a predictive model for thermal conductivity; (2) documentation of the candidate predictive models that may be considered in the future for surface tension, making use of the surface tension data now in MSTDB-TP v4.0; (3) a preliminary account of a data collection process that will enable the filling of additional gaps within MSTDB-TP, namely with data which have been collected computationally (e.g., through ab initio molecular dynamics).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2001

Float Zone Growth of Alloy Semiconductor Crystals: Influence of Solutocapillary Convection

Growth techniques with large free melt surfaces are affected by convective flows induced by gradients of the surface tension. In the case of dilute semiconductor alloys (in our case: germanium-silicon), the impact of solutocapillary convection (due to the concentration dependence of the surface tension) has to be taken into account in addition to the "normal" thermocapillary convection (due to the temperature dependence of the surface tension). Theoretical considerations, based on experimental temperature profiles, growth geometry, segregation coefficient, and measured values for the temperature and concentration coefficients of the surface tension, lead to the conclusion that for the germanium rich side of the Ge(1-x)Si(x) system, the contribution of solutocapillary convection is, at least in front of the solid-liquid interface, the dominant factor. It results in an additional flow roll with a flow direction opposite to the thermocapillary flow, similar to the ones reported for metal alloys or high Prandtl-number fluids.

Dold, P.↗

NASA NTRS2002

Length Scale and Gravity Effects on Microgravity Boiling Heat Transfer

Boiling is a complex phenomenon where hydrodynamics, heat transfer, mass transfer, and interfacial phenomena are tightly interwoven. An understanding of boiling and critical heat flux in microgravity environments is of importance to space based hardware and processes such as heat exchange, cryogenic fuel storage and transportation, electronic cooling, and material processing due to the large amounts of heat that can be removed with relatively little increase in temperature. Although research in this area has been performed in the past four decades, the mechanisms by which heat is removed from surfaces in microgravity are still unclear. In earth gravity, buoyancy is an important parameter that affects boiling heat transfer through the rate at which bubbles are removed from the surface. A simple model describing the bubble departure size based on a quasistatic force balance between buoyancy and surface tension is given by the Fritz [I] relation: Bo(exp 1/2) = 0.0208 theta where Bo is the ratio between buoyancy and surface tension forces. For small, rapidly growing bubbles, inertia associated with the induced liquid motion can also cause bubble departure. In microgravity, the magnitude of effects related to natural convection and buoyancy are small and physical mechanisms normally masked by natural convection in earth gravity such as Marangoni convection can substantially influence the boiling and vapor bubble dynamics. CHF (critical heat transfer) is also substantially affected by microgravity. In 1 g environments, Bo has been used as a correlating parameter for CHF. Zuber's CHF model for an infinite horizontal surface assumes that vapor columns formed by the merger of bubbles become unstable due to a Helmholtz instability blocking the supply of liquid to the surface. The jets are spaced lambda(sub D) apart, where lambda(sub D) = 2pi square root of 3[(sigma)/(g(rho(sub l) - rho(sub v)](exp 1/2) = 2pi square root of 3 L Bo(exp -1/2) = square root of 3 lambda(sub c) and is the wavelength that amplifies most rapidly. The critical wavelength, lambda(sub c), is the wavelength below which a vapor layer underneath a liquid layer is stable. For heaters with Bo smaller than about 3 (heaters smaller than lambda(sub D)), the above model is not applicable, and surface tension effects dominate. Bubble coalescence is thought to be the mechanism for CHF under these conditions. Small Bo can result by decreasing the size of a heater in earth gravity, or by operating a large heater in a lower gravity environment. In the microgravity of space, even large heaters can have low Bo, and models based on Helmholtz instability should not be applicable. The macrolayer model of Haramura and Katto is dimensionally equivalent to Zuber's model and has the same dependence on gravity, so it should not be applicable as well. The goal of this work is to determine how boiling heat transfer mechanisms in a low-g environment are altered from those at higher gravity levels. Boiling data using a microheater array was obtained under gravity environments ranging from 1.8 g to 0.02 g with heater sizes ranging from 2.7 mm to 1 mm. The boiling behavior for 2.7 mm at 0.02 g looked quite similar to boiling on the 1 mm heater at 1 g-the formation of a large primary bubble surrounded by smaller satellite bubbles was observed under both conditions. The similarity suggests that for heaters smaller than some fraction of I(sub c), coalescence and surface tension dominate boiling heat transfer. It also suggests that microgravity boiling can be studied by studying boiling on very small heaters.

Kim, Jungho↗

DOE OSTI2014

Calculation of contact angles at triple phase boundary in solid oxide fuel cell anode using the level set method

A level set method is applied to characterize the three dimensional structures of nickel, yttria stabilized zirconia and pore phases in solid oxide fuel cell anode reconstructed by focused ion beam-scanning electron microscope. A numerical algorithm is developed to evaluate the contact angles at the triple phase boundary based on interfacial normal vectors which can be calculated from the signed distance functions defined for each of the three phases. Furthermore, surface tension force is estimated from the contact angles by assuming the interfacial force balance at the triple phase boundary. The average contact angle values of nickel, yttria stabilized zirconia and pore are found to be 143°–156°, 83°–138° and 82°–123°, respectively. The mean contact angles remained nearly unchanged after 100 hour operation. However, the contact angles just after reduction are different for the cells with different sintering temperatures. In addition, standard deviations of the contact angles are very large especially for yttria stabilized zirconia and pore phases. The calculated surface tension forces from mean contact angles were close to the experimental values found in the literature. Slight increase of surface tensions of nickel/pore and nickel/yttria stabilized zirconia were observed after operation. Present data are expected to be used not only for the understanding of the degradation mechanism, but also for the quantitative prediction of the microstructural temporal evolution of solid oxide fuel cell anode. - Highlights: • A level set method is applied to characterize the 3D structures of SOFC anode. • A numerical algorithm is developed to evaluate the contact angles at the TPB. • Surface tension force is estimated from the contact angles. • The average contact angle values are found to be 143o-156o, 83o-138o and 82o-123o. • Present data are expected to understand degradation and predict evolution of SOFC.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Closed-form theoretical model of the secondary drop size in partial coalescence—Capturing pertinent timescales and viscous forces

One of the most important outcomes of partial drop coalescence is the ratio of the secondary drop radius to the primary drop radius, known as the drop ratio, ri. This ratio is thought to be approximately constant and independent of physical parameters of the fluids involved. However, here we reveal that ambient fluid viscosity can alter the size of the secondary drop and the drop ratio consequently. Using scaling analysis, we derive a model that predicts the behavior of the drop ratio as a function of the Ohnesorge number, a dimensionless ratio of viscous to inertial forces. In addition, we present our experimental results of coalescing drops on a planar interface under the influence of surface tension gradients. A high-speed digital camera is used to observe the evolution of drops as they coalesce with a bulk liquid. We show that this process is influenced by the surface tension gradient between the drop and the bulk liquid. The ratio of the secondary drop to the primary drop in partial coalescence is smaller than the reported values for coalescence without a surface tension gradient. The analytical model derived through this study is based on a new modified Ohnesorge number that includes surface tension gradients. Our analytical model is compared against other models and the results illustrate good agreement with our experimental findings and experimental data in the literature.

42 ENGINEERING↗

DOE OSTI2014

An efficient algorithm for incompressible N-phase flows

We present an efficient algorithm within the phase field framework for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids, with possibly very different physical properties such as densities, viscosities, and pairwise surface tensions. The algorithm employs a physical formulation for the N-phase system that honors the conservations of mass and momentum and the second law of thermodynamics. We present a method for uniquely determining the mixing energy density coefficients involved in the N-phase model based on the pairwise surface tensions among the N fluids. Our numerical algorithm has several attractive properties that make it computationally very efficient: (i) it has completely de-coupled the computations for different flow variables, and has also completely de-coupled the computations for the (N−1) phase field functions; (ii) the algorithm only requires the solution of linear algebraic systems after discretization, and no nonlinear algebraic solve is needed; (iii) for each flow variable the linear algebraic system involves only constant and time-independent coefficient matrices, which can be pre-computed during pre-processing, despite the variable density and variable viscosity of the N-phase mixture; (iv) within a time step the semi-discretized system involves only individual de-coupled Helmholtz-type (including Poisson) equations, despite the strongly-coupled phase–field system of fourth spatial order at the continuum level; (v) the algorithm is suitable for large density contrasts and large viscosity contrasts among the N fluids. Extensive numerical experiments have been presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts. In particular, we compare our simulations with the de Gennes theory, and demonstrate that our method produces physically accurate results for multiple fluid phases. We also demonstrate the significant and sometimes dramatic effects of the gravity, density ratios, pairwise surface tensions, and drop sizes on the N-phase configurations and dynamics. The numerical results show that the method developed herein is capable of dealing with N-phase systems with large density ratios, large viscosity ratios, and pairwise surface tensions, and that it can be a powerful tool for studying the interactions among multiple types of fluid interfaces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1985

Water ball collision

What happens if a stainless steel ball hits a water ball in the weightless space of the Universe? In other words, it was the objective of our experiments in the Space to observe the surface tension of liquid by means of making a solid collide with a liquid. Place a small volume of water between 2 glass sheets to make a thin water membrane: the 2 ass sheets cannot be separated unless an enormous force is applied. Also, fill a cup with water to the brim, place a sheet of paper on top of it, and turn the cup upside down gently: the water inside the cup does not spill out. It is obvious from these phenomena that the surface tension of water is far greater than presumed. On the earth, however, it is impossible in most cases to observe only the surface tension of liquid, because gravity always acts on the surface tension

Kazuo Fujimoto↗

DOE OSTI2020

Hydrodynamics of countercurrent flows in a structured packed column: effects of initial wetting and dynamic contact angle

The structured packed column has gained considerable attention as a prospective technology to mitigate carbon dioxide emissions from thermal power plants. The computational flow investigation of such systems is a multiscale problem, and local hydrodynamics plays a key role in overall column efficiency. Accordingly, multiphase flow studies in the representative elementary unit (REU) of a packed column can offer insights into the local flow behavior such as flow pattern, interfacial area, etc. The interfacial area plays a key role in the overall interphase mass transfer and thereby in separation efficiency. The predicted effective area matches well with corresponding ones in experiments for Mellapak 250.Y packings. The contact angle (i.e., solid substrate behavior) is one of the critical factors that dictates wettings, and thereby the interfacial area. The dynamic contact angle (DCA) was considered in order to explore the effects of contact angle hysteresis on the interfacial area. DCA has more pronounced impact on the interfacial area for a solvent possessing a higher value of surface tension and equilibrium contact angle. The interfacial area shows temporal undulation and does not achieve a pseudo steady state due to the capillary force. In contrary, the interfacial area gets a net value for a solvent having low surface tension value. Further, specification of the static contact angle at the solid substrate shows the least value of the interfacial area. We also extensively studied the effect of the initial sheet condition (dry vs wet) on the interfacial area. The initially wetted sheets show slightly higher value of the interfacial area as compared to the initially dry sheets at a fixed flow rate for a solvent having high surface tension value. Wetting hysteresis decreases with increasing liquid loads. On the other hand, wetting hysteresis does not occur for a solvent having value of low surface tension and equilibrium contact angle.

structured packings, dynamic contact angle, interf↗

NASA NTRS1990

Investigation of surface water behavior during glaze ice accretion

A series of experimental investigations that focused on isolating the primary factors that control the behavior of unfrozen surface water during glaze ice accretion were conducted. Detailed microvideo observations were made of glaze ice accretions on 2.54 cm diam cylinders in a closed-loop refrigerated wind tunnel. Distinct zones of surface water behavior were observed; a smooth wet zone in the stagnation region with a uniform water film, a rough zone where surface tension effects caused coalescence of surface water into stationary beads, and a zone where surface water ran back as rivulets. The location of the transition from the smooth to the rough zone was found to migrate towards the stagnation point with time. Comparative tests were conducted to study the effect of the substrate thermal and roughness properties on ice accretion. The importance of surface water behavior was evaluated by the addition of a surface tension reducing agent to the icing tunnel water supply, which significantly altered the accreted glaze ice shape. Measurements were made to determine the contact angle behavior of water droplets on ice. A simple multizone modification to current glaze ice accretion models was proposed to include the observed surface roughness behavior.

Hansman, R. John, Jr.↗

DOE OSTI2025

A Geometric Volume of Fluid-Based Multiphase Flow Solver Extension to the Reacting Flow Solver, PeleLM

A new algorithm is presented to simulate multiphase flows with surface tension in a pathway for spray combustion simulation. The algorithm combines capabilities from two open-source packages, including the interface reconstruction library (IRL), a library of computational geometry routines to enable the volume of fluid (VOF) method, and PeleLM, a solver for the reacting Navier-Stokes equations. Additionally, surface tension is implemented using the continuum surface force (CSF) model with an improved height function technique in the volume fraction field. Spurious errors in volume fraction arising from our combined strategy are corrected through a topology-based method that improves both numerical stability and accuracy. Multiple validation simulations are conducted, including (i) translations and rotations of Zalesak's disk, (ii) a stationary circular droplet with surface tension, (iii) an oscillating elliptical droplet, and (iv) three-dimensional deformation of a spherical droplet. Results indicate that the combined scheme retains the favorable properties of each of the component algorithms.

42 ENGINEERING↗

DOE OSTI2016

Development of DPD coarse-grained models: From bulk to interfacial properties

A new Bayesian method was recently introduced for developing coarse-grain (CG) force fields for molecular dynamics. The CG models designed for dissipative particle dynamics (DPD) are optimized based on trajectory matching. Here we extend this method to improve transferability across thermodynamic conditions. We demonstrate the capability of the method by developing a CG model of n-pentane from constant-NPT atomistic simulations of bulk liquid phases and we apply the CG-DPD model to the calculation of the surface tension of the liquid-vapor interface over a large range of temperatures. The coexisting densities, vapor pressures, and surface tensions calculated with different CG and atomistic models are compared to experiments. Depending on the database used for the development of the potentials, it is possible to build a CG model which performs very well in the reproduction of the surface tension on the orthobaric curve.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Contact angles from Young’s equation in molecular dynamics simulations

In this work, we propose a method to calculate the equilibrium contact angle of heterogeneous 3-phase solid/fluid/fluid systems using molecular dynamics simulations. The proposed method, which combines the phantom-wall method [F. Leroy and F. Müller-Plathe, J. Chem. Phys. 133, 044110 (2010)] and Bennett’s acceptance ratio approach [C. H. Bennett, J. Comput. Phys. 22, 245 (1976)], is able to calculate the solid/fluid surface tension relative to the solid surface energy. The calculated relative surface tensions can then be used in Young’s equation to estimate the equilibrium contact angle. A fluid droplet is not needed for the proposed method, in contrast to the situation for direct simulations of contact angles. In addition, while prior free-energy based methods for contact angles mainly focused on the wetting of fluids in coexistence with their vapor on solid surfaces, the proposed approach was designed to study the contact angles of fluid mixtures on solid surfaces above the fluid saturation pressures. Using the proposed approach, the contact angles of binary Lennard-Jones fluid mixtures on a non-polar solid substrate were calculated at various interaction parameters and the contact angle of water in equilibrium with CO 2 on a hydrophilic polar silica surface was obtained. For both non-polar and polar systems, the calculated contact angles from the proposed method were in agreement with those obtained from the geometry of a cylindrical droplet. The computational cost of the proposed method was found to be comparable to that of simulations that use fluid droplets, but the new method provides a way to calculate the contact angle directly from Young’s equation without ambiguity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1995

Hydrodynamic Stability of Multicomponent Droplet Gasification in Reduced Gravity

This investigation addresses the problem of hydrodynamic stability of a two-component droplet undergoing spherically-symmetrical gasification. The droplet components are assumed to have characteristic liquid species diffusion times that are large relative to characteristic droplet surface regression times. The problem is formulated as a linear stability analysis, with a goal of predicting when spherically-symmetric droplet gasification can be expected to be hydrodynamically unstable from surface-tension gradients acting along the surface of a droplet which result from perturbations. It is found that for the conditions assumed in this paper (quasisteady gas phase, no initial droplet temperature gradients, diffusion-dominated gasification), surface tension gradients do not play a role in the stability characteristics. In addition, all perturbations are predicted to decay such that droplets were hydrodynamically stable. Conditions are identified, however, that deserve more analysis as they may lead to hydrodynamic instabilities driven by capillary effects.

Aharon, I.↗

DOE OSTI2017

An interface capturing scheme for modeling atomization in compressible flows

The study of atomization in supersonic flow is critical to ensuring reliable ignition of scramjet combustors under startup conditions. Numerical methods incorporating surface tension effects have largely focused on the incompressible regime as most atomization applications occur at low Mach numbers. Simulating surface tension effects in compressible flow requires robust numerical methods that can handle discontinuities caused by both shocks and material interfaces with high density ratios. In this work, a shock and interface capturing scheme is developed that uses the Harten–Lax–van Leer–Contact (HLLC) Riemann solver while a Tangent of Hyperbola for INterface Capturing (THINC) interface reconstruction scheme retains the fluid immiscibility condition in the volume fraction and phasic densities in the context of the five equation model. The approach includes the effects of compressibility, surface tension, and molecular viscosity. One and two-dimensional benchmark problems demonstrate the desirable interface sharpening and conservation properties of the approach. Simulations of secondary atomization of a cylindrical water column after its interaction with a shockwave show good qualitative agreement with experimentally observed behavior. Three-dimensional examples of primary atomization of a liquid jet in a Mach 2 crossflow demonstrate the robustness of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗