Single-component Droplets Research Articles

Evaluation of equilibrium and non-equilibrium evaporation models for many-droplet gas-liquid flow simulations

A variety of liquid droplet evaporation models, including both classical equilibrium and non-equilibrium Langmuir–Knudsen formulations, are evaluated through comparisons with experiments with particular emphasis on computationally efficient procedures for gas–liquid flow simulations. The models considered are those used in droplet laden flow calculations such as direct numerical simulations for which large numbers of individual (isolated) droplet solutions are obtained. Diameter and temperature evolution predictions are made for single-component droplets of benzene, decane, heptane, hexane and water with relatively large initial sizes ∼1 mm vaporizing in convective air flows. All of the models perform nearly identically for low evaporation rates at gas temperatures significantly lower than the boiling temperature. For gas temperatures at and above the boiling point, large deviations are found between the various model predictions. The simulated results reveal that non-equilibrium effects become significant when the initial droplet diameter is <50 μm and that these effects are enhanced with increasing slip velocity. It is additionally observed that constant properties can be used throughout each simulation if both the gas and vapor values are calculated at either the wet-bulb or boiling temperature. The models based on the Langmuir–Knudsen law and a corrected (for evaporation effects) analytical heat transfer expression derived from the quasi-steady gas phase assumption are shown to agree most favorably with a wide variety of experimental results. Since the experimental droplet sizes are all much larger than the limit for non-equilibrium effects to be important, for these conditions the most crucial aspect of the current Langmuir–Knudsen models is the corrected analytical form for the heat transfer expression as compared to empirical relations used in the remaining models.

Condensation of uranium hexafluoride in supersonic Laval nozzle flow

carried in a mixture of argon and methane was studied experimentally in a continuously operating supersonic Laval nozzle. The onset of condensation was detected by Rayleigh light scattering. Measurements of static pressure in the nozzle, together with the equations of isentropic flow, permitted the determination of the relation between the pressure of UF6, Pk, and the temperature, Tc, at the observed onset of condensation. The experiments addressed conditions of condensation onset in the range 80<Tc<160 K and 0.1<Pk<3.0 Torr. We found that there was no influence of the pressure of the carrier gas argon, which ranged from 3.5 to 68 Torr at onset points, on the onset of condensation. The dependence of the supersaturation ratio on temperature at the onset could be expressed by a straight line as deduced by P.P. Wegener and B.J.C. Wu from the classical theory of homogeneous nucleation [Adv. Colloid Interface Sci. 7, 325 (1977)]. These results indicate that supersonic expansion in the nozzle formed single-component droplets of UF6 in a mixture of UF6, CH4, and Ar under the experimental conditions studied herein.

Elastic and Inelastic Light Scattering from Distilling Microdroplets for Thermodynamic Studies

The evaporation rates of single-component droplets and the related thermodynamics of binary component droplets consisting of 1-iodododecane and 1-bromotetradecane have been explored using elastic and inelastic (Raman) light-scattering to determine the droplet size and chemical composition as diffusion-controlled evaporation proceeded. Single droplets were levitated electrodynamically in a chamber and exposed to a vapor-free nitrogen gas stream. Elastic scattering data for the single components, obtained at the same temperature, were used to determine the optical parameters and transport process parameters needed to interpret binary droplet Raman data for mixtures of the halogenated hydrocarbons. Evaporation rate theory coupled with a UNIFAC thermodynamic model for activity coefficients was shown to agree very well with experimental data collected from binary droplets. Results indicate that Raman intensity ratios associated with the C-I and C-Br bonds can be used to follow changes in composition quantitatively, but for greater accuracy more detailed analysis of the effects of morphology-dependent resonances on the Raman effect is needed.

Effects of Marangoni Convection on Transient Droplet Evaporation

Abstract Results from a computational model of transient droplet vaporization are presented. In this model, axisymmetric flows around translating single component droplets are assumed. The governing equations are expressed in finite volume form and solved numerically for transient velocity, species and temperature profiles. Fully variable properties in the gas and liquid phases are allowed (except for liquid densities, which are held constant), and pressures of 1 and 10 atm are considered. A unique feature of the calculations is the inclusion of surface-tension gradients resulting from droplet surface temperature variations. Results show that surface-tension gradients significantly affect droplet internal temperature and velocity fields even when initial droplet Reynolds numbers, based on droplet diameters and free-stream conditions, are as large as 50. When surface-tension gradients are allowed at high initial Reynolds numbers (SO), droplet internal circulation rates are found to be initially increased f...

Numerical calculation of the transition from subcritical droplet evaporation to supercritical diffusion

The unsteady spherically symmetrical evaporation of a cold single-component droplet in atmospheres at pressures above the critical pressure of the liquid and at temperatures above the critical temperature of the liquid is modelled. High pressure phase equilibrium is assumed at the droplet surface, and solubility of the ambient gas in the droplet, temperature and composition inhomogeneities within the droplet, real gas effects and variable property effects are considered. Depending on the ambient conditions, the droplet surface reaches the critical state and vanishes. Thereafter, a pure diffusion problem is treated.

Multicomponent droplet evaporation at intermediate Reynolds numbers

The convective evaporation of a binary hydrocarbon droplet (decane-hexadecane) in air at 1000 K and at a pressure of 10 atmospheres has been studied using numerical methods. All transient effects including droplet size and velocity variations, heat and mass transfer within the liquid phase, and thermophysical property variations with temperature and concentration in both phases are included in the analysis. As the rate controlling process, liquid phase mass transfer is examined in detail. It is demonstrated that the existing drag coefficient, Sherwood number, and Nusselt number correlations originally developed for single-component droplets can be used for multicomponent droplets as well.

Vaporization behavior of fuel droplets in a hot air stream

Tm GASIFICATION behavior of a liquid droplet provides a fundamental input for the modeling of many spray systems, and has been studied extensively [l-4]. Theoretical analysis for the multicomponent fuel droplet presents several complexities absent in a similar analysis for the single component droplet. First, the phase-change process at the droplet surface and the transport of a fuel vapor mixture in the gas phase need to be properly described. Second, the evaporation process is inherently time varying due to the continuous change in the composition and temperature of the droplet as vaporization proceeds. Another difference between the two cases is due to the phenomenon of microexplosion [2]. The earlier viewpoint [2] of multicomponent droplet vaporization assumes that the composition and temperature within the droplet are spatially uniform but time varying. Such theories predict that the gasification process is similar to batch distillation in that the sequence of gasification is controlled by the volatility differentials among the different components. However, Sirignano [4] showed that even in the limit of high vortex strength, the internal liquid circulation can only reduce the characteristic length scale for diffusion by a factor of three. Landis and Mills [S] investigated the vaporization of a bi-component fuel droplet in a stagnant atmosphere. A quasi-steady gas-phase model was used and the equations governing the unsteady mass and heat diffusion within the droplet were solved numerically. Results when compared with rapid mixing behavior showed significant differences. A unique feature of the diffusion-dominated droplet gasification mechanism is the possible attainment of approximately steady-state temperature and concentration profiles within the droplet, which then leads to a steady-state gasification rate. Based on this concept, Law and Law [6] formulated a d2-law model for multicomponent droplet vaporization and combustion. As indicated above, the literature on the gasification behavior of an isolated droplet is extensive. However, most of these studies deal with droplet combustion or evaporation under high-temperature conditions. Not much information is available on the behavior of evaporating droplets in relatively low-temperature air streams. Under such conditions, the possibility of an envelope flame is precluded and the droplet gasification rate is low. The droplet heat-up time may not be negligibly small compared to its lifetime, although the latter is relatively large and the liquid-phase transient processes may still be important. In this paper, the vaporization behavior of pure and multicomponent fuel droplets flowing in a well-characterized laminar flow is studied. The predictions of three vaporization models are compared with the experimental data.

Precision of light scattering techniques for measuring optical parameters of microspheres

This experimental and theoretical study of light scattering techniques addresses the questions of deconvolution of light scattering data (phase functions and optical resonance spectra) from droplets and the uniqueness of that deconvolution for the measurement of size and refractive index of microspheres. Theory and experiment are compared for single component and multicomponent microdroplets and for layered microspheres levitated in electrodynamic balances. Size changes of the order of 1 A have been measured by tracking resonance shifts of slowly evaporating single component droplets. For multicomponent droplet evaporation, which involves simultaneous size and refractive index changes, and for rapid evaporation, precision is reduced to approximately 1 part in 10(4) for each parameter.

Determination of vapor pressure from droplet evaporation kinetics

Evaporation kinetics of suspended single droplets are investigated in the temperature range 20 to 55°C, using Mie resonance spectroscopy. Experiments are carried out with a single-component organic droplet electrodynamically suspended either in a flowing N 2 gas or in a vacuum, depending upon the volatility of the organic compound. A data analysis method is developed, which produces a best-fit empirical correlation in the form 1 n p= A+ B T +C 1 n T+DT k, that is valid over a temperature range spanning up to 9 decades on the vapor pressure scale. No estimate of the actual value of either the diffusivity or the evaporation coefficient is needed. This is accomplished by combining the high-temperature vapor pressure data available in the literature with the droplet evaporation rates measured in this work at lower temperatures. Results presented here for methanesulfonic acid, glycerol, oleic acid, and dioctyl phthalate clearly demonstrate the usefulness of the technique for ultra-low vapor pressure determinations.

Quasi-steady diffusion-controlled droplet evaporation and condensation

This theoretical investigation deals with the vaporization or condensation rate of a motionless liquid droplet using the quasi-steady diffusion-controlled model. A single-component liquid droplet is considered to be undergoing a phase change within a binary mixture of ideal gases (vapor plus noncondensable gas). Droplet vaporization rates corresponding to specified ambient conditions have been calculated by numerical solution of the variable-property governing equations. Results are presented for water and a series of pure hydrocarbon liquids for a range of ambient conditions of interest. A dimensionless correlation is given for the hydrocarbon vaporization and condensation rates. The pressure variation in the region surrounding a droplet undergoing vaporization or condensation has been investigated by numerical integration of the momentum equation. The resulting calculations indicate that the pressure decreases with increasing distance from the droplet for condensation as well as vaporization. Finally, criteria are given for estimating when the pressure gradient and viscous dissipation may be of significance in the energy equation.