Diffuse-interface modeling of liquid-vapor coexistence in equilibrium drops using smoothed particle hydrodynamics (original) (raw)
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High-fidelity simulation of drop collision and vapor–liquid equilibrium of van der Waals fluids
Proceedings of the Combustion Institute, 2017
The availability of a method to accurately predict the interaction of fuel drops and vapor-liquid equilibrium is crucial to the development of a predictive spray combustion model. The objective of this paper is to present such a method. A numerical method, based on the smoothed particle hydrodynamics (SPH), was coupled with a cubic equation of state for simulating the fuel drop dynamics and liquidvapor distributions at various temperatures in the present study. SPH is a Lagrangian particle-based method, which is useful to simulate the dynamics of fluids with large deformations without the need for a transport equation to track the interface. The present study, furthermore, coupled SPH with van der Waals equation of state to simulate the phenomena of liquid oscillation, drop collisions at high velocity and characteristics of vapor-liquid equilibrium. This approach was found to offer the convenience of using a single set of equations, without the need for submodels, to predict drop breakup or vaporization. A hyperbolic spline kernel function was employed to eliminate the tensile instability that often has been reported in the literature. The numerical method presented here was found to successfully model the merging, stretching separation, fragmentation, and generation of secondary droplets in high-velocity collisions. In predicting vapor-liquid equilibrium, a variable-smoothing-length function was implemented to better facilitate the evaluation of vapor density at low temperatures. Finally, the results of this study indicate that, as the critical temperature was approached, no clear distinction was observed between the liquid and gas phases.
Vapor condensation onto a non-volatile liquid drop
The Journal of Chemical Physics, 2013
Molecular dynamics simulations of miscible and partially miscible binary Lennard-Jones mixtures are used to study the dynamics and thermodynamics of vapor condensation onto a non-volatile liquid drop in the canonical ensemble. When the system volume is large, the driving force for condensation is low and only a submonolayer of the solvent is adsorbed onto the liquid drop. A small degree of mixing of the solvent phase into the core of the particles occurs for the miscible system. At smaller volumes complete film formation is observed and the dynamics of film growth are dominated by cluster-cluster coalescence. Mixing into the core of the droplet is also observed for partially miscible systems below an onset volume suggesting, the presence of a solubility transition. We also develop a non-volatile liquid drop model, based on the capillarity approximations, that exhibits a solubility transition between small and large drops for partially miscible mixtures and has a hysteresis loop similar to the one observed in the deliquescence of small soluble salt particles. The properties of the model are compared to our simulation results and the model is used to study the formulation of classical nucleation theory for systems with low free energy barriers.
Modeling the dynamics of liquid drops with SPH
2006
Recibido el 25 de noviembre de 2003; aceptado el 19 de junio de 2004 The method of Smoothed Particle Hydrodynamics (SPH) has been applied in the last 20 years to a wide range of problems involving solution of the continuum fluid-dynamic equations. A variationally consistent SPH formulation has recently been devised which works equally well for both compressible and incompressible fluids. An extension of this method which addresses the tensile instability for a viscous, heatconducting fluid has been applied to the condensation and binary coalescence collision of liquid drops using the van der Waals equation of state. Here we show and discuss the results obtained for some of these test cases. In particular, the benefits of correcting the tensile instability are described for both the formation of a stable liquid drop and the off-center coalescence of two liquid drops of equal size via a low-energy impact.
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A method has been proposed for determining interfacial free energy from the data of molecular dynamics simulation. The method is based on the thermodynamic integration procedure and is distinguished by applicability to both planar interfaces and those characterized by a high curvature. The workability of the method has been demonstrated by the example of determining the surface tension for critical nuclei of water droplets upon condensation of water vapor. The calculation has been performed at temperatures of 273-373 K and a pressure of 1 atm, thus making it possible to determine the temperature dependence of the surface tension for water droplets and compare the results obtained with experimental data and the simulation results for a "planar" vapor-liquid interface.
Diffuse-interface modeling of liquid-vapor phase separation in a van der Waals fluid
Physics of Fluids, 2009
We simulate liquid-vapor phase separation in a van der Waals fluid that is deeply quenched into the unstable range of its phase diagram. Our theoretical approach follows the diffuse-interface model, where convection induced by phase change is accounted for via a nonequilibrium ͑Korteweg͒ force expressing the tendency of the liquid-vapor system to minimize its free energy. Spinodal decomposition patterns for critical and off-critical van der Waals fluids are studied numerically, revealing the scaling laws of the characteristic length scale and composition of single-phase microdomains, together with their dependence on the Reynolds number. Unlike phase separation of viscous binary mixtures, here local equilibrium is reached almost immediately after single-phase domains start to form. In addition, as predicted by scaling laws, such domains grow in time like t 2/3. Comparison between 2D and 3D results reveals that 2D simulations capture, even quantitatively, the main features of the phenomenon.
A molecular dynamics simulation of droplet evaporation
International Journal of Heat and Mass Transfer, 2003
A molecular dynamics (MD) simulation method is developed to study the evaporation of submicron droplets in a gaseous surrounding. A new methodology is proposed to specify initial conditions for the droplet and the ambient fluid, and to identify droplet shape during the vaporization process. The vaporization of xenon droplets in nitrogen ambient under subcritical and supercritical conditions is examined. Both spherical and non-spherical droplets are considered. The MD simulations are shown to be independent of the droplet and system sizes considered, although the observed vaporization behavior exhibits some scatter, as expected. The MD results are used to examine the effects of ambient and droplet properties on the vaporization characteristics of submicron droplets. For subcritical conditions, it is shown that a spherical droplet maintains its sphericity, while an initially non-spherical droplet attains the spherical shape very early in its lifetime, i.e., within 10% of the lifetime. For both spherical and non-spherical droplets, the subcritical vaporization, which is characterized by the migration of xenon particles that constitute the droplet to the ambient, exhibits characteristics that are analogous to those reported for ''continuum-size'' droplets. The vaporization process consists of an initial liquid-heating stage during which the vaporization rate is relatively low, followed by nearly constant liquidtemperature evaporation at a ''pseudo wet-bulb temperature''. The rate of vaporization increases as the ambient temperature and/or the initial droplet temperature are increased. For the supercritical case, the droplet does not return to the spherical configuration, i.e., its sphericity deteriorates sharply, and its temperature increases continuously during the ''vaporization'' process.
Evaporation and fluid dynamics of a sessile drop of capillary size
Physical Review E, 2009
Theoretical description and numerical simulation of an evaporating sessile drop are developed. We jointly take into account the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the drop and the diffusion of vapor in air. A shape of the rotationally symmetric drop is determined within the quasistationary approximation. Nonstationary effects in the diffusion of the vapor are also taken into account. Simulation results agree well with the data of evaporation rate measurements for the toluene drop. Marangoni forces associated with the temperature dependence of the surface tension, generate fluid convection in the sessile drop. Our results demonstrate several dynamical stages of the convection characterized by different number of vortices in the drop. During the early stage the street of vortices arises near a surface of the drop and induces a non-monotonic spatial distribution of the temperature over the drop surface. The initial number of near-surface vortices in the drop is controlled by the Marangoni cell size which is similar to that given by Pearson for flat fluid layers. This number quickly decreases with time, resulting in three bulk vortices in the intermediate stage. The vortices finally transform into the single convection vortex in the drop, existing during about 1/2 of the evaporation time.
Physical Review E, 2015
The rapid evaporation and explosive boiling of a van der Waals (vdW) liquid drop in microgravity is simulated numerically in two-space dimensions using the method of smoothed particle hydrodynamics. The numerical approach is fully adaptive and incorporates the effects of surface tension, latent heat, mass transfer across the interface, and liquid-vapor interface dynamics. Thermocapillary forces are modeled by coupling the hydrodynamics to a diffuse-interface description of the liquid-vapor interface. The models start from a nonequilibrium square-shaped liquid of varying density and temperature. For a fixed density, the drop temperature is increased gradually to predict the point separating normal boiling at subcritical heating from explosive boiling at the superheat limit for this vdW fluid. At subcritical heating, spontaneous evaporation produces stable drops floating in a vapor atmosphere, while at near-critical heating, a bubble is nucleated inside the drop, which then collapses upon itself, leaving a smaller equilibrated drop embedded in its own vapor. At the superheat limit, unstable bubble growth leads to either fragmentation or violent disruption of the liquid layer into small secondary drops, depending on the liquid density. At higher superheats, explosive boiling occurs for all densities. The experimentally observed wrinkling of the bubble surface driven by rapid evaporation followed by a Rayleigh-Taylor instability of the thin liquid layer and the linear growth of the bubble radius with time are reproduced by the simulations. The predicted superheat limit (T s ≈ 0.96) is close to the theoretically derived value of T s = 1 at zero ambient pressure for this vdW fluid.
International Journal of Heat and Fluid Flow, 2014
Simulations of single droplets rising in a quiescent liquid were performed for various initial droplet diameters. The continuous phase was water and the dispersed phase was either n-butanol, n-butyl acetate or toluene, thus resulting in three standard test systems for liquid-liquid extraction. For the simulations, a level set based code was developed and implemented in the open-source computational fluid dynamics (CFD) package OpenFOAM ® . To prevent volume (or mass) loss during the reinitialisation of the level set function, two methods published recently were used in the code. The contiuum surface force (CSF) model and the ghost fluid method (GFM) were applied to model interfacial forces, and their influence on grid convergence, droplet shapes and rise velocities was investigated. Grid convergence studies show a reasonable behaviour of the GFM, whereas the CSF model is less reliable, especially for systems with high interfacial tension. The results for droplet shape and terminal rise velocity are in excellent agreement with experimental and numerical investigations from literature. correctly predicted, and the influence of the smoothing of interfacial forces on velocity oscillations is studied. Simulations of oscillating droplets remain stable, but the frequencies of the velocity oscillations differ from experimental results.