A model for droplet entrainment in heated annular flow

The ability to accurately predict droplet entrainment in annular two-phase flow is required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. Most annular flow entrainment models in the open literature are formulated in terms of dimensionless groups, which do not directly account for interfacial instabilities. However, many researchers agree that there is a clear presence of interfacial instability phenomena having a direct impact on droplet entrainment. The present study proposes a model for droplet entrainment, based on the underlying physics of droplet entrainment from upward co-current annular film flow that is characteristic to light water reactor safety analysis. The model is developed based on a force balance and stability analysis that can be implemented into a transient three-field (continuous liquid, droplet, and vapor) two-phase heat transfer and fluid flow systems analysis computer code.     

Flow and atomization characteristics of a twin-fluid nozzle with internal swirling and self-priming effects

A twin-fluid nozzle was proposed for low-pressure atomization. The nozzle is featured by swirling air flows in the mixing chamber. Liquid medium is thereby inhaled due to the pressure difference. An experimental work was performed to investigate the atomization performance of the nozzle and the hydrogen peroxide solution served as the liquid medium. Droplet size and droplet velocity were measured. Effects of the diameter of the air-injection orifice and the air-injection pressure were investigated. The results show that small droplet size is achieved with the proposed nozzle. As the spray develops, Sauter mean diameter (SMD) of the droplets decreases first and then increases, irrespective of the variation of the air-injection orifice diameter and the air-injection pressure. Overall SMD varies inversely with the air-injection orifice diameter and air-injection pressure. Near the nozzle, cross-sectional velocity distribution exhibits a peak-valley pattern, which is replaced with uniformized velocity distributions away from the nozzle. Similarity of cross-sectional radial velocity distribution at different air pressures is evidenced. Furthermore, the correlation between droplet size and droplet velocity is established.     

Modeling of droplet entrainment phenomena at a quench front

The phenomena of droplet entrainment at a quench front is of practical importance as a clear understanding of the underlying mechanisms required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. The present study proposes a model for droplet entrainment at a quench front that is based on the best-understood physics related to the Lagrangian quenching phenomenon characteristic to light water reactor (LWR) safety analysis. The model is based on a film boundary layer and stability analysis that attempts to match the characteristic time and length scales of the entrainment phenomenon. This model has been developed such that direct implementation can be made into any two-phase flow simulation code with a three-field (continuous liquid, droplet, and vapor) flow model. Comparisons with integrated transient test data independent of those used for model development have been performed to verify the applicability of the proposed model for the prediction of the entrainment rate of liquid droplets at a quench front under typical reflood conditions envisioned in LWRs.     

Experimental analysis of the flow characteristics of a pressure-atomised spray

An experimental setup has been created to allow measurements of the properties of the gas phase, the liquid phase and the mixture in a pressure-atomised spray of water, in terms of both mean quantities and Reynolds stresses. This setup involves laser Doppler velocimetry for determining the velocity of either the gas or liquid phase, according to the parameters used, such as seeding or no-seeding of the ambient air, laser source power, or photo-multiplier gains, droplet tracking velocimetry for determining the velocity and characteristic size of the droplets, and a single optical probe for determining the mean volume fraction of the liquid, from which the liquid mean mass fraction and the mean density of the mixture are inferred. The experimental conditions, in particular in terms of liquid and gas Weber numbers, were chosen in a range for which the liquid phase turbulent kinetic energy should be mainly responsible for the liquid-jet primary break-up, these flow conditions lying within the second wind-induced atomization regime. Results reported herein are more specifically focused on the region ranging from 400 nozzle diameters to 800 nozzle diameters, where the liquid core is disrupted. They provide new information about the formation and properties of such pressure-atomised sprays, in particular in terms of the role played by the Reynolds stresses resulting from the slip velocity between the liquid and the gas. The mean slip velocity is directly related to the turbulent flux of liquid. Such information will be used in the future to develop new turbulence models since very limited experimental information is so far available for these terms.     

Acetone Droplet Behavior in Reacting and Non Reacting Turbulent Flow

Acetone droplet characteristics in reacting and non-reacting turbulent flow are predicted and compared to experimental data. Investigations are conducted to study the effects of surrounding environment properties on the velocities, dispersion, and evaporation of a relatively volatile spray fuel that featured a wide range of Stokes numbers. The simulations are performed in the framework of Reynolds Averaged Navier Stokes equations along with the Eulerian-Lagrangian approach in which 12 different classes of the dispersed phase. The phase transition is modeled by the Langmuir-Knudsen law that accounts for non equilibrium effects based on a consistent determination of the molar mass fraction on the droplet surfaces. For the droplet dispersion, the Markov sequence model is improved by adding a correction drift term to the fluid fluctuation velocity at the parcel position along the droplet trajectory. This correction term aimed at accounting for the non-homogeneity effects in the turbulent flow. The combustion is captured using the Bray-Moss-Libby model that is extended to account for the partially premixed spray combustion. The chemistry is described with the flamelet model using a recent detailed reaction mechanism that involves 84 species and 409 reactions for which the Lewis number is not set to the unity. Mean droplet velocities for reacting and non-reacting test cases are compared with experimental data. Good agreement is observed. The spray is interacting with the nozzle edge developing new classes and relatively dense region. Hence the RMS-velocities close to the nozzle exit plan demonstrate discrepancies. The droplets group combustion effect is found to be important in the modeling of the burning velocity which influences the flame propagation. Reasonable agreements between the numerical and the experimental results are also observed in the spray flux and temperature profiles.     

The spray characteristics of a pressure-swirl injector with various exit plane tilts

The gasoline spray characteristics of a pressure-swirl injector were investigated with various exit plane tilts. The analysis focused on the correlation between tilt angle and flow angle. Mie-scattering technique and phase Doppler anemometry were employed to analyze the macroscopic spray development and droplet size distribution of the spray. An analytical method for mass flux estimation was applied to understand the velocity distribution at the nozzle exit. The results showed that the spray shape and velocity distribution of the spray were more asymmetrical at high tilt angles. In particular, an opened hollow cone spray was formed when the tilt angle is greater than the complementary flow angle. The pressure drop inside the spray, one of the crucial factors for the swirl spray collapse at various surrounding conditions, was attenuated in this opened hollow cone spray since the pressure inside the spray was assimilated to the surrounding air pressure. The spray collapse at high fuel temperature and back pressure conditions did not appear when the tilt angle is larger than the complementary flow angle due to the reduced pressure drop inside the spray. However, tilt angle should be optimized to fulfill the requirements of spray robustness and avoid the locally rich area. The droplet size of 70° tilted nozzle spray shows a value similar to that of the original swirl spray in the plane that includes nozzle axis and the major axis of exit surface ellipse (Major axis plane) while it shows an increased value in the plane that includes nozzle axis and the minor axis of exit surface ellipse (Minor axis plane).     

PDA measurements of droplet size and mass flux in the three-dimensional atomisation region of water jet in air cross-flow

The main objective of this paper is to develop a technique to measure the global droplet properties in the atomisation region of a water jet issuing in a high-speed air cross-flow. Knowledge of these global properties allows comparison of the break-up outcome of geometrically different water nozzles. This is achieved by extending a PDA system to enable measurements in three-dimensional droplet flows. First, the droplet size and the spatial droplet distribution are measured by the PDA method. The global droplet properties are then obtained by using the measured local mass flux as a weighting factor in integrating the local droplet size. To facilitate the measurement of mass flux in three-dimensional flows, the PDA method is extended so that the reference area for the mass flux is derived as a function of both the geometry of the measurement volume and the flow direction. In the present application of three-dimensional droplet flow (a water jet in air cross-flow), a simple method is developed to measure the three velocity components of droplets by means of a two-component PDA system. The paper outlines the measurement technique and the procedure of estimating the global droplet size and the global droplet size spectra from local droplet properties and local mass flux. Received: 26 July 1998/Accepted: 23 February 1999     

Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible.Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.     

Numerical modeling and experimental measurements of a high speed solid-cone water spray for use in fire suppression applications

Experimental measurements and numerical simulations of a high-speed water spray are presented. The numerical model is based on a stochastic separated flow technique that includes submodels for droplet dynamics, heat and mass transfer, and droplet–droplet collisions. Because the spray characteristics near the nozzle are difficult to ascertain, a new method for initialization of particle diameter size is developed that assumes a Rosin–Rammler distribution for droplet size, which correctly reproduces experimentally measured Sauter and arithmetic mean diameters. By relating the particle initialization to lower moments of the droplet statistics, it is possible to take advantage of measurements without substantial penalties associated with the greater experimental uncertainty of individual droplet measurements. Overall, very good agreement is observed in the comparisons of experimental measurements to computational predictions for the streamwise development of mean drop size and velocity. In addition, the importance of modeling droplet–droplet collisions is highlighted with comparison of selected droplet–droplet collision models.     

Numerical simulations of droplet train and free surface jet impingement

The cooling behavior of the impingement of a droplet train, and free surface jets over a heated and pre-wetted surface is explored employing an Algebraic Volume-of-Fluid methodology. The code is based on a modified version of the two-phase numerical solver interFoam (OpenFOAM) (Trujillo and Lewis, 2012). Two versions of the free surface jet are studied. The first consists of a fully-developed profile exiting the nozzle, and the second is characterized by a uniform velocity distribution. Results show that both jet configurations have higher cooling performance than the droplet train locally and globally, with the fully-developed case being the most effective of the two jet arrangements. Locally, the performance is measured by radial profiles of the boundary-layer-displacement thickness and heat transfer coefficient. Globally, the cooling effectiveness is directly proportional to the surface area that resides within the high-convection region, i.e. before the boundary layer separation point. On a temporal basis, the liquid film within the impingement region of the droplet train exhibits pronounced variations in velocity magnitude and film thickness. This is directly attributed to the nature of continuous droplet impacts affecting the impingement region, and gives rise to an unsteady cooling and heating of the fluid near the wall. In contrast for the jets, the film and the corresponding free surface are nearly steady with only minor perturbations.     

Atomized non-equilibrium two-phase flow in mesochannels: Momentum analysis

Two-phase pressure drop measurements are very difficult to make while the fluid is in non-equilibrium condition, i.e. while phase change is taking place. This is further complicated when an atomized liquid is introduced in the system at much higher velocity than other components such as liquid layer, vapor core, and entrained droplets. The purpose of this paper is to develop a model to predict the two-phase pressure characteristics in a mesochannel under various heat flux and liquid atomization conditions. This model includes the momentum effects of liquid droplets from entrainment and atomization. To verify the model, an in-house experimental setup consisting of a series of converging mesochannels, an atomization facility and a heat source was developed. The two-phase pressure of boiling PF5050 was measured along the wall of a mesochannel. The one-dimensional model shows good agreement with the experimental data. The effects of channel wall angle, droplet velocity and spray mass fraction on two-phase pressure characteristics are predicted. Numerical results show that an optimal spray cooling unit can be designed by optimizing channel wall angle and droplet velocity.     

The influence of thermal expansion flow on droplet evaporation

It has been demonstrated recently that it follows from conservation of mass that unsteady temperature fields create flow in an incompressible fluid with a temperature-dependent density even in the absence of gravity. The paper studies the influence of thermal expansion flow on spherically symmetric evaporation of an isolated droplet. A model problem of a droplet evaporating at a constant rate is first considered. In this idealized situation one can use the assumption of a thin thermal boundary layer to solve analytically the unsteady moving-boundary heat conduction problem to find the temperature field inside the droplet both with and without the thermal expansion flow. Next evaporation of a fuel droplet in a diesel engine is studied numerically. The heat diffusion equation is solved in the liquid phase while the standard quasi-steady model is used for the gas phase. The results of the calculation show that for high ambient temperatures the influence of the thermal expansion flow on the droplet lifetime can be considerable.     

Modeling the evolution of droplet size distribution in two-phase flows

A theoretical model is developed in the present study to simulate droplet motion and the evolution of droplet size distribution (DSD) in two-phase air/dispersed water spray flows. The model takes into account several processes which influence DSD and droplet trajectory: droplet collision and coalescence, evaporation and cooling, gravitational settling, and turbulent dispersion of dispersed phase. The DSDs determined by the model at different locations in a two-phase flow are evaluated by comparing them to experimental observations obtained in an icing wind tunnel. The satisfactory coincidence between simulation and experimental results proves that the model is reliable when modeling two-phase flows under icing conditions. The model is applied for two particular examples in which the modification of DSD is calculated in two-phase flows under conditions describing in-cloud icing and freezing drizzle.     

垂直上升气液环状流流动参数的数值计算

提出了一个新的气核-液膜耦合模型来求解垂直上升气液环状流在充分发展段的流动参数.本模型考虑了液膜、气核以及它们之间的相互影响和作用.模型中基本的气核区域和液膜区域的质量和动量方程由Fluent6.3.26进行求解,而液滴方程以及相界面上的夹带和沉积作用通过用户自定义接口函数UDF(User Defined Functi...     

Effects of the gas phase molecular weight and bubble size on effervescent atomization

The effervescent atomization from an industrial Coker feed nozzle is compared for two different gas densities (air and mixed gas of 81.4 vol.% helium/18.6 vol.% nitrogen) at equivalent operating temperatures. The application is to observe the similarity of lab tests using air at 20 °C to the industrial process using steam at 300-400 °C. The effects of operating conditions, such as gas to liquid mass ratio, mixing pressure and void fraction on the flow regime, bubble size, and droplet size distribution were also examined in this study. The experiments were performed using mixtures of water with air or mixed gas, which resulted in gas to liquid mass ratios ranging from 1% to 4%.Stroboscopic back scattered imagery (SBSI) indicates that the average bubble size inside the nozzle conduit is similar when air and water are used as the process fluids, when compared to the case when mixed gas and water are used as the process fluids. Under similar conditions, the Phase Doppler Particle Anemometer (PDPA) data indicate that the droplet size in the spray is similar when using either mixed gas or air as the atomization gas.Experimental results obtained by high-speed video shadowgraphy (HSVS) indicate that the flow pattern inside the nozzle feeding conduit was slug flow with a tendency to attain annular flow with increased air to liquid mass ratios. Thus, from the experimental results it is evident that the smaller molecular weight of the mixed gas versus air (8.4 versus 29) does not significantly reduce the bubble (<±10% difference) and droplet size (<±1.5% difference), indicating a weak dependence of the gas phase density on two-phase atomization. This confirms that laboratory experiments on effervescent nozzles using air have reliable similarity to systems that use high temperature steam for the gas phase.     

Theoretical analysis of heat and mass transfer in swirl atomizers

In this study, theoretical analyses have been performed to investigate the effects of atomizer construction and controlled pressure difference of swirl atomizers. The analysis of fluid field in the swirl chamber is governed by mass/energy conservation rules; in the region outside the nozzle, the analysis of oscillation of liquid sheet is based on Squire’s expression for the amplitude growth rate. With some physical assumptions of control volume, initial values and model correlation, analytical results make it possible to predict film thickness, velocity distribution, spray cone angle and droplet size directly. The distribution of velocity profile and boundary layer thickness in the swirl chamber have been established with the aid of MATLAB. Based on the results we obtained, we here propose the change of individual design parameter and its corresponding flow number to optimize the performance of swirl atomizers.     

Modelling and simulation of sprays in laminar flames

In the present paper we model and numerically simulate steady, laminar, premixed spray flames. The gasphase is described in Eulerian form by the equations governing the conservation of overall mass, momentum, energy and species mass. The liquid phase is described in Lagrangian form by the overall continuity equation, which reduces to an equation for the droplet size, the equations of motion, the energy equation and a droplet density function transport equation. The latter is the so-called spray equation, which, at any position in the chemically reacting flowfield, describes the joint distribution of droplet size, droplet velocity and droplet temperature. Herein the spray equation is solved using a Monte Carlo method. Detailed models of the exchange of mass, momentum and energy between the gaseous and the liquid phase are taken into account. The results presented in this paper are for an octane-air flame, where small amounts of liquid octane in form of a liquid spray are added to a fresh, unburnt gaseous octane-air mixture.Presented at Euromech Colloquium 324: The Combustion of Drops, Sprays and Aerosols, 25th–27th July 1994, Marseilles, France.     

Comparison of multicomponent fuel droplet vaporization experiments in forced convection with the Sirignano model

The vaporization of multicomponent fuel droplets was studied experimentally in a heated flow and the results were compared to the model proposed by Abramzon and Sirignano. The droplet was suspended on a permanent holder which was set up in a thermal wind-tunnel. This wind-tunnel was fitted with a video recording system and an infra-red camera. The period during which the droplet was suspended on the holder before the opening of the hot air flow damper was recorded. This first sequence corresponds to the droplet vaporization in natural convection, whose initial experiment conditions, especially diameter, temperature, composition of the droplet, are well known. Then the damper was turn on, and the sequence of forced convection begun. The initial diameter of the droplet was recorded by the video system. The other initial conditions of this second sequence cannot be determined experimentally. The distribution of temperature in the droplet and the surface temperature, the mass fraction distribution in the droplet and the surface mass fraction were unknown. These unknown parameters were determined by coupling our experiment with a model using “the film concept” in natural convection. Experimental results were compared with the calculations and found satisfactory, in natural convection as well as in forced convection initiated by this method. The method was tested in the case of a fuel mixture droplets (heptane–decane) for different initial concentrations and variable durations of the sequence in natural convection.     

A detailed experimental investigation of well-defined,turbulent evaporating spray jets of acetone

This paper aims at investigating the detailed structure of turbulent non-reacting dilute spray flows using advanced laser diagnostics. A simple spray jet nozzle is designed to produce a two-phase slender shear flow in a co-flowing air stream with well-defined boundary conditions. The carrier flow is made intentionally simple and easy to model so that the focus can be placed on the important aspects of droplet dispersion and evaporation, as well as turbulence–droplet interactions. Phase Doppler interferometry is employed to record droplet quantities, while planar laser-induced fluorescence imaging is applied separately to obtain acetone vapour data. Measurements are conducted for four acetone spray jets in air at several axial stations starting from the nozzle exit. The combined liquid and vapour mass fluxes of acetone integrated across the jet at downstream locations agree satisfactorily with the total mass flow rate of acetone injected.