Droplet Momentum Research Articles

Two-Phase Eulerian/Lagrangian Model for Nucleating Steam Flow

This paper describes an Eulerian/Lagrangian two-phase model for nucleating steam based on classical nucleation theory. The model provides an approach for including spontaneous homogeneous nucleation within a full Navier-Stokes solution scheme where the interaction between the liquid and gas phases for a pure fluid is through appropriately modeled source terms. The method allows for the straightforward inclusion of droplet heat, mass, and momentum transfer models along with nucleation within complex flow systems as found, for example, in low pressure steam turbines. The present paper describes the solution method, emphasizing that the important features of nucleating steam flow are retained through comparison with well-established 1-D solutions for Laval nozzle flows. Results for a two-dimensional cascade blade and three-dimensional low pressure turbine stage are also described.

Effect of Surface Tension and Evaporation on Phase Change of Fuel Droplets

A model is developed which describes the phase-change process (evaporation) of fuel droplets in a gas turbine engine combustor. To develop this model we have employed the conservation laws (droplet momentum, heat and mass transfer). Specifically, we used Newton's second law of motion in conjunction with the thermal expansion of the droplet. In this study the droplet density is considered to be a function of temperature, ρ p = ρ p (T p ). As a consequence, the thermal expansivity α = -ρ p -1 (dρ p /dT p ) is introduced, which has a significant effect on the evaporation process. Furthermore, the conditions on the droplet's surface are determined by taking into account the effect of surface tension on the fuel vapor pressure. The droplet characteristics such as position, velocity, temperature, and diameter are described by a system of six ordinary differential equations, which are solved numerically using a variable step Runge-Kutta algorithm of order 5(4). Due to the above conditions, our results differ from those reported in the literature [1-5J.

On the dynamic behavior of a liquid droplet impacting upon an inclined heated surface

The dynamic behavior of a water droplet impinging upon a heated surface was shown to be significantly different, depending on the normal momentum of the impinging droplet before impact. This experimental study focused mainly on the effects of the impinging angle of the droplet on impact dynamics and its dependence on surface temperature. At the surface temperature of the nucleate boiling regime, disintegration of the droplet did not occur, whereas the deforming droplet adhered to the surface. The liquid film was spread and contracted several times on the horizontal surface, but the expanded droplet merely slipped without noticeable contraction on the inclined surfaces. In the film boiling regime, the impinging droplet spread over the surface as a liquid film separated from the surface by the vapor produced. Depending on the magnitude of the normal momentum of droplet, disintegration into several irregular shapes of liquid elements occurred in the case of the horizontal and 30°-inclined surfaces. The impinging droplet in the case of the 60°-inclined surface did not break up and tended to recover its original spherical shape.

Experimental Investigation of the Evaporation of Droplets in Axial Acoustic Fields

The effect of axialacoustic Ž elds on the evaporationof individualdroplets is investigatedboth experimentallyand theoretically. A setup was developed in which images of droplets moving through an acoustic Ž eld were acquired using a state-of-the-art, high-speed, intensiŽ ed video system. The evaporation rates of droplets were determined from the droplet diameters measured from these images. Experimental investigations using methanol droplets showed that the presence of an acoustic Ž eld signiŽ cantly enhances the evaporation of droplets. The evaporation rate is a strong function of the acoustic amplitude, but increases only slightlywith frequency. The effect of acoustic oscillations on water and methanol droplet evaporation was theoretically modeled by numerically integrating the differential equations for droplet mass, momentum,and heat transfer. The model uses quasisteady correlations for momentumheat and mass transfer. The model predicted the measured trends correctly. However, the quantitative agreement of these predictions with the experimental data depends strongly on the correlations for Nussult and Sherwood numbers used to model the energy and mass transfer, respectively.

Direct droplet production from a liquid film: a new gas-assisted atomization mechanism

X-ray lithography and micro-machining have been used to study gas-assisted liquid atomization in which a liquid film was impinged by a large number of sonic micro-gas jets. Three distinct breakup regimes were demonstrated. Two of these regimes share characteristics with previously observed atomization processes: a bubble bursting at a free surface (Newitt et al. 1954; Boulton-Stone & Blake 1993) and liquid sheet disintegration in a high gas/liquid relative velocity environment (Dombrowski & Johns 1963). The present work shows that suitable control of the gas/liquid interface creates a third regime, a new primary atomization mechanism, in which single liquid droplets are ejected directly from the liquid film without experiencing an intermediate ligament formation stage. The interaction produces a stretched liquid sheet directly above each gas orifice. This effectively pre-films the liquid prior to its breakup. Following this, surface tension contracts the stretched film of liquid into a sphere which subsequently detaches from the liquid sheet and is entrained by the gas jet that momentarily pierces the film. After droplet ejection, the stretched liquid film collapses, covering the gas orifice, and the process repeats. This new mechanism is capable of the efficient creation of finely atomized sprays at low droplet ejection velocities (e.g. 20 μm Sauter mean diameter methanol sprays using air at 239 kPa, with air-to-liquid mass ratios below 1.0, and droplet velocities lower than 2.0 m s−1). Independent control of the gas and the liquid flows allows the droplet creation process to be effectively de-coupled from the initial droplet momentum, a characteristic not observed with standard gas-assisted atomization mechanisms.

Joint probability density function of droplet sizes and velocities in a transient diesel spray

Comparisons of joint probability density distribution obtained from the raw data of measured droplet sizes and velocities in a transient diesel fuel spray with computed joint probability density function were made. Simultaneous droplet sizes and velocities were obtained using PDPA. Mathematical probability density functions which can fit the experimental distributions were extracted using the principle of maximum likelihood. Through the statistical process of functions, mean droplet diameters, non-dimensional mass, momentum and kinetic energy were estimated and compared with the experimental ones. A joint log-hyperbolic density function presents quite well the experimental joint density distribution which were extracted from experimental data.

Modeling of solidification of molten metal droplet during atomization

A mathematical model to describe the solidification behavior of an atomized droplet during flight, in terms of nucleation temperature, recalescence temperature, nucleation position, solid fraction at nucleation temperature, and droplet temperature and velocity, is formulated. The concept of transient nucleation is applied to model the short nucleation event. A maximum droplet velocity exists, beyond which the droplet velocity shows an inflection phenomenon during the flight. The velocity of smaller droplets is higher at a shorter flight distance and lower at a longer flight distance. Variations of the gas flow patterns have more effects on smaller droplets, and the effects are more significant at a longer flight distance. A minimum surface heat-transfer coefficient exists as the droplet flies. Prior to nucleation or recalescence, smaller droplets have lower temperature at a given flight distance. Smaller droplets have lower nucleation temperature. Medium-size (around 80-µm) droplets fly over the shortest flight distance before the nucleation starts. Smaller droplets have a larger solid fraction at the end of recalescence. Atomization gas has more effects on the droplet momentum than on the heat content of the droplet.

Mathematical modeling of three-dimensional heat and fluid flow in a moving gas metal arc weld pool

Mathematical models capable of accurate prediction of the weld bead and weld pool geometry in gas metal arc (GMA) welding processes would be valuable for rapid development of welding procedures and empirical equations for control algorithms in automated welding applications. This article introduces a three-dimensional (3-D) model for heat and fluid flow in a moving GMA weld pool. The model takes the mass, momentum, and heat transfer of filler metal droplets into consideration and quantitatively analyzes their effects on the weld bead shape and weld pool geometry. The algorithm for calculating the weld reinforcement and weld pool surface deformation has been proved to be effective. Difficulties associated with the irregular shape of the weld bead and weld pool surface have been successfully overcome by adopting a boundary-fitted nonorthogonal coordinate system. It is found that the size and profile of the weld pool are strongly influenced by the volume of molten wire, impact of droplets, and heat content of droplets. Good agreement is demonstrated between predicted weld dimensions and experimently measured ones for bead-on-plate GMA welds on mild steel plate.

A Numerical Study of Droplet Evaporation and Combustion in the Presence of an Oscillating Flow

The two-dimensional, unsteady, laminar conservation equations for mass, momentum, energy, and species transport in the gas phase are solved numerically in spherical coordinates in order to study heat and mass transfer, and combustion around a single spherical droplet. The droplet mass, momentum, and energy equations are also solved simultaneously with the gas phase equations in order to investigate the effects of droplet entrainment and heating in the oscillating flow with and without a steady velocity. The numerical solution for the case of single droplet combustion gives the droplet diameter and temperature variation as well as the gas phase velocity, temperature, and species concentrations as a function of time. The effects of frequency, amplitude of oscillating flow, and velocity ratio of oscillating flow amplitude to the steady velocity on droplet combustion are also investigated. The droplet burning history is not governed by the d2-law in the presence of oscillating flow, unlike the case of quiescent ambient conditions.

Droplet deposition and momentum transfer in annular flow

Droplet deposition and momentum transfer in annular flow

Two dimensional modeling of momentum and thermal behavior during spray atomization of γ-TiAl

A two dimensional model was formulated for the study of the momentum and thermal behavior of atomized droplets of γ-TiAl. The velocity, temperature, flight time, cooling rate and solidification behavior of droplets were numerically investigated as a function of the axial distances from the atomization zone and the radial distances from the central line of the spray cone. The velocity, temperature, cooling rate, flight time and solidification behavior of a droplet strongly depend on the initial position ( r 0) and the diameter of the droplet ( D). The two dimensional droplet size distribution in the spray cone changes from being heterogeneous to being almost homogeneous as axial flight distance increases. The two dimensional distribution of the fraction solidified in the spray cone is heterogeneous. The fraction solidified in the spray at any given axial distance increases with increasing radial distance from the spray axis.

Droplet deposition and momentum transfer in annular flow

AbstractEntrainment and deposition in gas‐liquid annular upflow are known to account for as much as 20% of the pressure gradient, through droplet acclelerations in the core refion. Momentum is transerred from the core when droplets decelerate upon impactwith the liquid film. It is usually assumed that all of this momentum is transferred to the film, essentially driving the film upwardin conjunction with interfacial friction. New data, abtained for annular gas‐liquid upflow in a 5.08‐cm‐ID tube, are used in a momentum balance analysis to determine the mechanismof momentum transfer from depositing droplets. Measurements include the liquid film thickness, wall shear stress, pressure gradient, entrained liquid fraction, droplet deposition rate, droplet centerline axial velocity, and mass‐average drop size for two gas‐liquid systems. This analysis supports the idea that large droplets displace the film locally and decelerate primarily at the wall, effectively transferring negligible momentum to the liquid film.

Combustion of a single droplet in the presence of an oscillating flow

The two-dimensional, unsteady, laminar conservation equations for mass, momentum, energy and species transport in the gas phase are solved numerically in spherical coordinates. This is to study the heat and the mass transfer, and the combustion around a single spherical droplet. The droplet mass and momentum equations are also solved simultaneously with the gas phase equations in order to investigate the effects of droplet entrainment in the oscillating flow with and without a steady velocity. The numerical solution for a single droplet combustion gives the droplet diameter variation as well as the gas phase velocity, temperature and species concentrations as a function of time. The effects of frequency, amplitude of oscillating flow, velocity ratio of oscillating flow amplitude to the steady velocity, ambient temperature and initial droplet diameter on the droplet combustion are also investigated. The droplet burning history is not governed by thed2-law in the presence of oscillating flow, unlike to the case under quiescent ambient conditions.

Tracking of raindrops in flow over an airfoil

The splashback that occurs when raindrops impact an airfoil results in an 'ejecta fog' of small droplets around the leading edge. Acceleration of these droplets by the air flow field is a momentum sink for the air flow and has been hypothesized to contribute to the degradation of airfoil performance in heavy rain. Presented here is a one-way coupled Eulerian-Lagrangian particle tracking scheme to evaluate droplet number densities and momentum sink terms around a NACA 64-210 airfoil section for three rainfall rates. A laminar air flow field is determined with a standard CFD code and input to the particle tracking algorithm. Raindrops are assumed to be non-interacting, non-deforming, non-evaporating, and non-spinning spheres and are tracked through the curvilinear grid used by the air flow code. A simple model is used to simulate impacts and the resulting splashback on the airfoil surface.

The density and structure of ice accretion predicted by a random‐walk model

AbstractA random‐walk, ballistic‐type model is used to simulate the ice accretion process due to impinging supercooled droplets. the model is applicable over a wide range of growth conditions including, in the limit, growth where the droplets freeze virtually as spheres (dry growth), and growth where the droplets spread into and across the ice surface losing their identity (wet growth). The structure and density of the ice are determined by the probabilities governing droplet motion and freezing during their random walk along the ice deposit. A relationship between the Macklin parameter, commonly used to relate atmospheric conditions to ice density, and the probabilities of droplet motion has been established. The ice density and accretion structure perdicted by the random‐walk model agree qualitatively with experimental observations at the stagnation line on a fixed circular cylinder. The model also predicts finger‐like ice structures for small values of droplet momentum, also in keeping with observations.

Thermal-Hydraulics of OC-OTEC Spout Flash Evaporators

A mechanistic model was developed for the thermal-hydraulic processes in the spout flash evaporator of an OC-OTEC plant. Nonequilibrium, two-fluid, conservation equations were solved for the two-phase flow in the spout, accounting for evaporation at the gas-liquid interface, and using a two-phase flow regime map consisting of bubbly, churn-turbulent and dispersed droplet flow patterns. Solution of the two-phase conservation equations provided the flow conditions at the spout exit, which were used in modeling the fluid mechanics and heat transfer in the evaporator, where the liquid was assumed to shatter into a spray with a log-normal size distribution. Droplet size distribution was approximated by using 30 discrete droplet size groups. Droplet momentum conservation equations were numerically solved to obtain the residence time of various droplet size groups in the evaporator. Evaporative cooling of droplets was modeled by solving the 1-D heat conduction equation in spheres, and accounting for droplet internal circulation by an empirical thermal diffusivity multiplier. The model was shown to favorably predict the available single-spout experimental data.

Profiles of Droplets Density, Momentum Flux and Velocity in a Diesel Spray

The Profile of the velocity of a diesel spray, which is a liquid-gas two phase flow with high velocity, is a significant phenomenon to analyze the mixing and combustion processes in a diesel engine. It is impossible to measure the velocity because a large number of droplets and entrained air exist in the spray. In the experiments presented here, the composed velocity of droplets and entrained air was calculated by using a model built under certain assumptions, using the droplet area density measured with the laser light extinction method and the momentum flux measured with a newly developed probe. The validity of the model was examined by comparing the velocity profile with the measured data and that predicted by the numerical calculations based on the well-known KIVA code for diesel spray. As a result, the profiles of droplet density, momentum flux and velocity in a diesel spray are very similar to those in unsteady gas and water jets.

Particle size and velocity measurement in flames by laser anemometer

The size and velocity of droplets are measured simultaneously by a particle counting Laser Doppler Anemometer (LDA) in kerosene fuel sprays under both burning and non-burning conditions. This measurement technique enables rapid measurement of size and velocity of particles in spray flames for particle diameters larger than the fringe spacing up to, at least, 300 μm. The time dependent variations in local spray structure can be measured at particle counting rates of 2 kHz with spray densities of, at least, 10 10 particles/m 3 . Particle sizes are derived from pulse height analysis of the mean LDA signals and velocities are determined simultaneously, by measuring Doppler shift frequencies. The performance and accuracy of the system is determined by analysis, using geometrical optics theory, coupled with calibrations using a monosized particle generator. The measurements demonstrate that droplet velocity is a function of droplet diameter for both burning and non-burning conditions. The technique enables temporally averaged local size distributions to be measured. Spatially averaged size distributions are derived from the simultaneously acquired velocity data. Comparison of results obtained under burning and non-burning conditions show changes in size distribution due to preferential vaporization of small droplets, acceleration due to thermal expansion of gases and corresponding changes in droplet momentum.

Interpretation of Pitot Pressure in Compressible Two-Phase Flow

An analysis is presented of the dynamics of small droplets near the mouth of a purged or unpurged pitot tube in two-phase flow. Under certain conditions, that part of the total pressure which is attributable to loss of droplet momentum is shown to be only weakly dependent upon droplet size and density, vapour viscosity, tube size and purging rate. A new method is formulated for calculating the velocity from measured static and total pressures in compressible flow, which does not include the assumption that the fluid behaves as a homogeneous equilibrium mixture. When compared with results based upon the mixture assumption, for condensing flows of steam at low pressures, the new method yields velocities which are greater by one or two per cent and which approach the dry vapour values as the wetness fraction tends to zero. The absolute accuracy of the method has yet to be determined through experiment.