Spray Droplet Size Distribution Research Articles

Effects of Nozzle Retraction Elimination on Spray Distribution in Middle-Posterior Turbinate Regions: A Comparative Study.

The standard multi-dose nasal spray pump features an integrated actuator and nozzle, which inevitably causes a retraction of the nozzle tip during application. The retraction stroke is around 5.5 mm and drastically reduces the nozzle's insertion depth, which further affects the initial nasal spray deposition and subsequent translocation, potentially increasing drug wastes and dosimetry variability. To address this issue, we designed a new spray pump that separated the nozzle from the actuator and connected them with a flexible tube, thereby eliminating nozzle retraction during application. The objective of this study is to test the new device's performance in comparison to the conventional nasal pump in terms of spray generation, plume development, and dosimetry distribution. For both devices, the spray droplet size distribution was measured using a laser diffraction particle analyzer. Plume development was recorded with a high-definition camera. Nasal dosimetry was characterized in two transparent nasal cavity casts (normal and decongested) under two breathing conditions (breath-holding and constant inhalation). The nasal formulation was a 0.25% w/v methyl cellulose aqueous solution with a fluorescent dye. For each test case, the temporospatial spray translocation in the nasal cavity was recorded, and the final delivered doses were quantified in five nasal regions. The results indicate minor differences in droplet size distribution between the two devices. The nasal plume from the new device presents a narrower plume angle. The head orientation, the depth at which the nozzle is inserted into the nostril, and the administration angle play crucial roles in determining the initial deposition of nasal sprays as well as the subsequent translocation of the liquid film/droplets. Quantitative measurements of deposition distributions in the nasal models were augmented with visualization recordings to evaluate the delivery enhancements introduced by the new device. With an extension tube, the modified device produced a lower spray output and delivered lower doses in the front, middle, and back turbinate than the conventional nasal pump. However, sprays from the new device were observed to penetrate deeper into the nasal passages, predominantly through the middle-upper meatus. This resulted in consistently enhanced dosing in the middle-upper turbinate regions while at the cost of higher drug loss to the pharynx.

The Effect of Internal Combustion Engine Nozzle Needle Profile on Fuel Atomization Quality

This article presents the results of research on the impact of changing the cross-section of an atomizer’s flow channel, which is caused by changing the flow geometry of the passive part of the needle on the drop diameter distribution of the fuel spray. A three-hole type H1LMK, 148/1 atomizer with hole diameters, dN, equal to 0.34 mm, is analyzed. A nozzle with a standard (i.e., unmodified) needle and three nozzles using needles with a modified profile in the flow part of the needle, marked by the code signatures 1L, 2L, and 3L, are tested. An increasing level of fuel turbulence characterizes the needles during the flow along their flow part due to the use of one (1L), two (2L), and three (3L) de Laval toroidal nozzles, respectively, obtained by mechanically shaping the outer surface of the flow part of the spray needle. The spray produced is tested using the Malvern Spraytec STP 500 device cooperating with the dedicated Malvern version 4.0. During the tests, measurements and an analysis of the spray droplet size distribution over the entire injection duration, equal to 7 ± 2 ms, are made for each nozzle. The experiment makes it possible to determine the effect of the nozzle needles’ profiles on the time distribution of the actual droplet diameters; the time distribution of the Sauter mean droplet diameters, D[3,2]; the percentile shares of the droplet diameters Dv (10), Dv (50), and Dv (90); the distribution span during the development of the spray stream; and the time distribution of the shares of the droplets with diameters belonging to selected diameter classes D[x1−x2] in the spray. The results of the measurements of the drop diameter distribution indicate that using atomizers with a modification to the flow channel allows for an increase in the share of droplets with smaller diameters compared to the standard atomizer.

DROPLET SIZE DISTRIBUTION VARIATION OF PENDENT FIRE SPRINKLER SPRAY DEPENDING ON THE MEASUREMENT LOCATION

Droplet size of sprinkler sprays is related to the rate of evaporation and penetration of a fire plume. However, sprinkler sprays have various droplet sizes even at one location. Therefore, it is essential to examine the droplet size distribution depending on the location to predict the fire suppression performance of the sprinkler spray. To examine the droplet size distribution of spray from a pendent sprinkler head, acrylic plates were installed around the sprinkler head and a gap was made on one side of the wall. A charge-coupled device camera was installed to capture the droplet images both on a plane parallel to the sprinkler frame arm and on a plane perpendicular to the frame arm. Droplet information was obtained by deriving the image from the brightness and gradient images extracted from the original image. Large droplets, exceeding 1.5 mm in diameter, were observed in the mainstream of the spray. The probability of observing small droplets decreased as the droplets moved downstream. Spherical droplets were observed in the mainstream of the frame arm direction, while nonspherical droplets were observed in the perpendicular direction to the frame arm because of high velocity. The number-based cumulative distribution function (CDFs) fitted using the Rosin-Rammler distribution function provided the best fitting results. The volume CDFs fitted using the Rosin-Rammler distribution function yielded acceptable adjusted R<sup>2</sup> values. In this case, the coefficient m related to D<sub>v50</sub> and the coefficient n related to the width of the distribution increased with increasing radial and vertical locations.

Prediction of sodium leakage droplet size distribution in sodium-cooled fast reactor loop

Sodium spray fire is a significant containment-related safety concern in sodium-cooled fast reactors (SFRs). The droplet size distribution of sodium spray is an important factor affecting the combustion intensity of sodium spray fire. Due to the unstable chemical properties of sodium, water is usually used to simulate sodium to carry out spray experiments, and the droplet size relationship between them needs to be obtained. Based on the unstable wave theory, the droplet size similarity model characterized by liquid physical property parameters and atomization pressure difference is developed and verified from the two aspects of pressure and physical property parameters, and compared with existing models. Furthermore, an experimental facility of water atomization using a nozzle to simulate a break is built and the droplet size of water atomization under the differential pressure range of 1.0 bar–6.0 bar is obtained. The droplet size similarity model is used to predict the sodium atomization droplet size at 300–600 °C under different pressures based on these experimental data.

Study on reactivity characteristic of TDA droplet group with gaseous phosgene for preparing TDI

Toluene diisocyanate stands as a pivotal chemical, predominantly synthesized through the phosgenation reaction between toluene diamine and phosgene. To address the inherent limitations of existing phosgenation methods, we pioneered a novel phosgenation reaction based on flash atomization and confirmed its feasibility with preliminary theoretical calculations. This manuscript delves deeper into the superiority of this method and refines its reaction parameters. By integrating the discrete phase model with the Eulerian model, we studied the reaction dynamics of droplet sprays, exploring the effects of spray velocity, droplet size, phosgene temperature, and particle size distribution on the reaction. Our results highlight that, with a mean droplet diameter of 70 μm and a spray velocity of 40 m/s, an impressive reaction yield of 97.4 % can be achieved. This research enriches our understanding of the gas–liquid two-phase phosgenation method, setting the stage for its future exploration and potential applications in Toluene diisocyanate and other isocyanate industry.

Near-field plume-to-plume interaction of multi-hole GDI injector under elevated ambient density conditions

Spray collapse can occur in the multi-hole injector under elevated ambient density conditions due to the plume-to-plume interaction. Numerous studies have investigated spray collapse in high ambient density conditions, but limited literature is available regarding the near-field plume-to-plume interaction triggering the spray collapse due to the optical density of the spray in the near field. In this study, an X-ray phase-contrast imaging (XPCI) technique that can visualize the spray structure and dynamics in the near field is applied to resolve the optical difficulties. With this method, the plume-to-plume interaction of a multi-hole gasoline direct injection injector is analyzed by measuring the transverse spray droplet size and axial velocity distributions under various ambient densities and injection pressures. The results showed that in the high ambient density condition with the low injection pressure, the spray droplet size started to increase, and the axial velocity remained stagnant from around 3 mm axial location as a result of plume-to-plume interaction and following spray collapse. The region of large droplets appeared asymmetric based on the hole arrangement. As the injection pressure increased in the high ambient density condition, the plume-to-plume interaction was suppressed in the near field and the spray collapse appeared farther downstream. Through the results, the spray collapse phenomenon and associated mechanism in the near field were discussed considering the droplet collision/coalescence and pressure structure in the spray.

Flash-boiling effect on the droplet size distribution in low-pressure sprays formed at various ambient pressures and liquid temperatures — Experimental study and modelling

Flash-boiling injection occurs when a liquid is injected into an environment below its saturation pressure. It can be achieved either by reducing the ambient pressure or preheating the injected liquid. The goal of this work was to understand the influence of flash boiling on the droplet size distribution, depending on how it was achieved, and to model this influence in the function of the superheat parameters. For this purpose, systematic experimental tests were conducted, which covered a broad spectrum of fluid temperature and ambient pressure conditions. The tests showed that both liquid temperature and ambient pressure affect the droplet size distributions. Moreover, depending on the way of achieving flash boiling, the results were substantially different, even though the same superheating, expressed as the saturation to ambient pressure ratio, was maintained. Nevertheless, a similar and consistent pattern of droplet size reduction could be observed between the data series grouped by liquid temperature. Based on the experimental results, a model for simulating droplet size distribution at given superheat conditions was proposed. It takes into account the global trend of droplet size reduction observed for each fluid temperature. The model was found to simulate the droplet size probability density functions with satisfactory agreement under all performed experimental conditions.

Effects of [formula omitted]-pentanol blending on soot formation in swirl-stabilized turbulent spray flames of Jet A-1 in a laboratory gas turbine combustor

Although the influence of alcohol supplement on soot in hydrocarbons fuel combustion in laminar flames and transportation engines is widely investigated, the information from well-controlled spray flames with clean boundary conditions are scarce, especially with kerosene type fuels doped with n-pentanol. Favorable physical properties of n-pentanol makes it an attractive oxygenated fuel extender for transportation fuels. We investigated the effects of adding 10% and 20% n-pentanol, by energy content, to a JetA-1 fuel on sooting characteristics of spray combustion in a swirl-stabilized model combustor. At an identical fuel feed rate, two different air flow rates were considered yielding global equivalence ratios of 0.64 and 0.69. Flow field generated by the combustion of swirling air and the injected fuel was measured using stereoscopic particle image velocimetry, and a diffraction based instrument was utilized to quantify the spray droplet size distribution. Laser-induced incandescence was used to measure the soot concentration distribution within the combustor and to estimate the primary soot particle sizes. Very small but measurable changes were observed in the spray droplet characteristics caused by the addition of n-pentanol to JetA-1. 10% replacement of JetA-1 by n-pentanol reduced the soot volume fractions and the total soot loading in the combustor significantly when the global equivalence ratio was 0.69, whereas with global equivalence ratio of 0.64, soot loading was almost zero. When the n-pentanol replacement increased to 20%, no soot was detected for both air flow rates, probably due to soot volume fractions well below the lower limits of laser-induced incandescence. The primary soot particle diameters covered a range from 25 to 50 nm mostly unaffected by the presence of n-pentanol in JetA-1.

Effect of atomizer and cross-flows on liquid and gelled Jet A-1 fuel injection

The current study aims to experimentally investigate the effect of atomizer and cross-flow velocities on liquid and gelled Jet A-1 fuels. For gelled Jet A-1, Jet A-1 liquid, Thixatrol® ST and rectified xylene are the base fuel, gellant and solvent, respectively. Gelled Jet A-1 is prepared by adding 85% by weight of base fuel along with 7.5% by weight of gellant and solvent, each at optimum processing conditions. Atomization using a simple-plain-orifice atomizer is investigated to understand its effect on Jet A-1 gel fuel break-up without air cross-flow. Based on the investigation from qualitative flow visualization and quantitative analysis of Jet A-1 gel fuel break-up, a modified simple-plain-orifice atomizer called an internally impinging air-blast atomizer is made. Primary atomization using this new atomizer is studied to understand the break-up of liquid and gelled Jet A-1 gel fuels without any air cross-flow. Secondary atomization of liquid and gel fuel is investigated by transversely injecting fuel into different low-speed subsonic air cross-flow environments. Laser sheet Imaging (LSI) technique is used to capture spray images of both fuels. Break-up mechanisms of both liquid and gel fuels were observed, and the results were compared. Information on the cross-flow air mass flow rate effect on the liquid and gel spray is extracted by developing an algorithm in MATLAB using an image processing tool. Relative droplet size distribution of liquid and gel spray revealed their dependence on cross-flow air mass flow rate. Total droplet count of both liquid and gel fuel decreases significantly as the cross-flow Reynolds’ number increases. At higher cross-flow Reynolds’ number, gel droplets in the flow are observed to be more as compared to liquid fuel.

A Novel Experiment Approach for Measurement Breakup Length, Cone Angle, Sheet Velocity, and Film Thickness in Swirl Air-Blast Atomizers

<div>Measuring the dynamic parameters of liquid fragments generated in the near-field of atomizing sprays poses a significant challenge due to the random nature of the fragments, the instability of the spray, and the limitations of current measuring technology. Precise determination of these parameters can aid in improving the control of the atomization process, which is necessary for providing suitable spray structures with appropriate flow rates and droplet size distributions for various applications such as those used in heat engines. In piston and gas turbine engines, controlling spray characteristics such as penetration, cone angle, particle size, and droplet size distribution is crucial to improve combustion efficiency and decrease exhaust emissions. This can be accomplished by adjusting the structural and/or operating parameters of the fuel supply system. This article aims to measure the breakup length, spray cone angle, axial velocity, breakup time, and liquid sheet film thickness for a swirl air-blast atomizer used in a gas-steam engine. The measurement was conducted using a shadowgraph imaging system developed specifically for this study, consisting of a high-speed camera, a lens, and a light source. While lasers are commonly used as light sources in the literature, this study utilized a special LED high-speed pulse light generator, which is cheaper, easier to handle, and provides a more uniform background. Images were processed using a MATLAB code developed for this study. Although the breakup zone is naturally random and the breakup location significantly varies with time, the novel method developed in this study helps quantify critical parameters under different operating conditions.</div>

Probabilistic derivation of droplet velocity using quadrature method of moments

Abstract Accurately prediction of dispersion and polydispersity of droplet flow is not a trivial task due to the complex behavior of the droplet size distribution (DSD) and the strong state of the instantaneous velocity of a droplet on the shape and size of the droplet. Describing the distribution of sizes and velocities of droplets initially formed in sprays is an essential piece of information needed in spray modeling, which is used to define the initial state of the spray droplets in the downstream two-phase flow fields’ predictive computations. The predictive model for the droplet size and velocity distributions in sprays is formulated as the droplet’s velocity magnitude has a power–law relationship with the droplet in this study. The present model incorporates the deterministic and stochastic aspects of the spray formation process. The quadrature method of moments (QMOM) is applied to solve numerically the transport equations of the probability density function coupled with conserved source terms incompressible Navier-Stokes equations for the liquid phase. The sub-models are connected by different source terms signifying the liquid-gas interaction. Equations of transport for spray moments are derived from DSD, and closure is attained using a gamma distribution. The integer spray moments concerning the volume are used to construct the continuous distribution of QMOM. In contrast, the velocity moments are used to determine the droplet velocity as a constant function of the droplet diameter. The model is first applied to simulate a diesel spray tip penetration under nonreactive conditions with different droplet velocity profiles to validate the approach with experimental data. An additional case of a liquid nitrogen spray is applied to show the gamma distribution’s ability to describe spray drop size distribution. The model generally predicts reasonable agreement with the experimental for both cases.

Experimental investigation of crossflow air effect on spray characteristics of gelled Jet-A1 fuel using an internally impinging air-blast atomizer

The present study aims to experimentally analyse the influence of crossflow aerodynamic parameters on the spray characteristics of gelled Jet-A1 fuel. A Jet-A1 gel fuel is prepared by combining 85 percentage by weight (wt. %) of Jet-A1 liquid as base fuel with an organo-gel solution having Thixatrol ST (7.5 wt. %) as gelling agent and Rectified xylene (7.5 wt. %) as solvent. Shear flow test is performed on the gel fuel using a rotational rheometer, to understand its non-Newtonian rheological properties. An internally impinging air blast atomizer is used to study the gel spray characteristics by injecting the gel fuel transversely into the subsonic cross flowing airstream environment. Gel spray images are captured by generating a laser sheet along the midplane of the test section across the crossflow air stream direction using the Laser Sheet Photography (LSP) technique. The captured gel spray images are used to visualize the gel spray structure in both spray axis as well as the crossflow air stream direction. These images are then investigated by developing an algorithm in MATLAB using an image processing tool. By incorporating the canny edge detection method into the MATLAB code, gel spray characteristics such as droplet size distribution, Sauter-mean-diameter, Arithmetic-mean-diameter, windward trajectories, and maximum penetration height are determined. Further, the effect of aerodynamic parameters such as crossflow Reynolds’ number and aerodynamic Weber number on the gel spray characteristics are investigated. Droplet size distribution and maximum penetration height of gelled Jet-A1 spray revealed its dependence on crossflow Reynolds’ number. Sauter-Mean-Diameter of gel droplets and windward trajectories of the gel spray decreases significantly as the aerodynamic Weber number increases. Thus, it can be concluded that the fineness of the spray is also a function of the crossflow aerodynamic parameters other than the atomizer.

Establishing quantitative relationships between changes in nasal spray in vitro metrics and drug delivery to the posterior nasal region

Nasal sprays are typically characterized using in vitro spray metrics such as spray cone angle and droplet size distribution. It is currently not clear how these in vitro metrics correlate with regional nasal deposition, and these relationships could help explain the impact of product differences. In this study, the effects of changes in spray cone angle, spray velocity, spray ovality and droplet size distribution on regional nasal deposition were analyzed using a validated computational fluid dynamics model in recently developed adult characteristic nasal airway anatomies. The impact of the spray on the surrounding air phase was included. Results indicated that changes in spray cone angle largely influenced the nasal posterior deposition (PD) of the drug. Changes in the plume ovality and characteristic droplet size moderately influenced PD, but the results were dependent on the insertion conditions and nasal geometry. Changes in spray velocity and uniformity constant of the droplet size distribution had only minimal influence on PD. The rank order of metrics having the greatest to least impact on PD was cone angle ≫ plume ovality ≫ characteristic droplet size ≫ velocity ≫ size distribution uniformity constant. Overall, results from this study established quantitative relationships for predicting expected changes in PD.

In Vitro Comparison of Local Nasal Vaccine Delivery and Correlation with Device Spray Performance.

This study is the first vaccine candidate in vitro investigation with a focus on finding a correlation between the spray characteristics and the delivery efficiency of the local deposition in the nasal airways of infants under 24months using various intranasal devices. In vitro tests were developed to measure the spray characteristics of four intranasal delivery devices and how they regionally deliver a candidate vaccine formulation matrix in five nasal airway replicas (3 to 24months). The correlation between the spray performance, geometric parameters, and delivery efficiency were assessed. All four devices performed consistently in terms of spray characteristics and were capable of delivering a high percentage of the candidate vaccine to the target areas, with a minimum delivery efficiency of 80%. Moreover, the delivery efficiency was affected by either the spray droplet size distribution or the distance between the nozzle tip and the internal nasal valve. Correlations between the spray performance and the in vitro local dose deposition were established. The infant nasal model tests can be complementary to device spray performance evaluation. In the absence of in vivo correlations, they can also facilitate the process of new product development by estimating delivery a priori.

LES-CMC of high-altitude relight in an RQL aeronautical combustor

Large-Eddy Simulations with the Conditional Moment Closure sub-grid combustion model and detailed chemistry for kerosene were performed for the ignition process in an Rich-Quench-Lean aviation gas turbine combustor at high-altitude conditions. The simulations used realistic boundary conditions for the flow inlet and spray droplet size distributions and velocity. Due to the large droplets, the Central Recirculation Zone (CRZ) is filled with fuel, mostly in liquid form. The first phase of the ignition process is critical and the results show that the spark kernel must provide enough energy to evaporate the spray and pyrolyse the fuel for the flame to grow and establish in the corner of the combustor. The second phase is characterised by the flame burning the mixture in the scorner and propagating around the Inner Shear Layer. This phase is also critical, as the flame needs the prevaporised fuel and smaller droplets in the corner to sufficiently increase the temperature and be able to propagate inside the CRZ, filled with liquid fuel and cold air. If this propagation inside the CRZ is achieved, phase three is accomplished and the burner is fully ignited. The simulations demonstrate the particular importance of detailed chemistry and proper boundary conditions for flame ignition simulations in high-altitude relight conditions.

Topological transitions of Jet A-1 lean azimuthal flames (LEAF)

Prior studies about liquid fuel combustion in a vitiated air environment have shown increased combustion efficiency with reduced NOx, CO, and soot emissions. The concept of lean azimuthal flame (LEAF), which can be associated to the latter combustion mode, is based on opposed injections of air and liquid fuel sprays in an axisymmetric chamber with a central outlet, which can result in a highly turbulent toroidal reaction zone. The mixture of fresh air and hot combustion products of each spray provides a vitiated cross-flow configuration to the next spray distributed along the chamber circumference, leading to ignition and sequential combustion of the sprays by the others. The present paper deals with a LEAF combustor with air-assisted spray atomization, which has not been investigated so far. The combustor is fueled with Jet A-1 and operated from 15 to 25 kW with variations in the atomization-air to liquid mass flow ratio (ALR). This study focuses on the flame topology transitions as a function of atomizer ALR. Experimental results based on flame chemiluminescence and OH planar laser-induced fluorescence show two flame topologies: tubular and LEAF topology for ratio of 2 and 4, respectively (denoted ALR2 and ALR4). The spray Mie scattering indicates a significant presence of unburnt droplets for ALR2, whereas quick evaporation is observed for ALR4 cases. In this paper, we propose and validate a basic model based on the spray droplet size distribution, and the evaporation and convection timescales, which are the prominent factors governing the flame topology. Indeed, for ALR2, the evaporation timescale is longer than the convective timescale, which causes incomplete spray evaporation and insufficient vitiated environment, leading to a tubular flame topology and preventing a LEAF to develop. In contrast, for ALR4, the spray evaporation timescales are smaller than the convective timescales, which aids the LEAF topology.

Estimation of spray flow characteristics using ensemble Kalman filter

Spray flows are widely used in several industrial applications, such as combustion engines. Accurate measurement of spray flow characteristics requires sophisticated equipment and techniques. In recent years, the discrete droplet method (DDM), which analyses droplet scattering, has become a mature technique and has been applied to various analyses. We propose an estimation system based on particle image velocimetry (PIV) measurements and an ensemble Kalman filter, together with DDM, to efficiently investigate spray flow characteristics. The proposed method performs data assimilation on the velocity distribution in a two-dimensional cross-section obtained by PIV to estimate the characteristics of the spray flow in three dimensions. In this study, the system was constructed so that droplet particle is ensembled during data assimilation to estimate the droplet diameter distribution indirectly. The proposed method can be used to estimate the spray velocity and droplet size distribution. The numerical solution obtained using DDM was used as a criterion for assimilation and validated by conducting twin experiments. The results showed that, in terms of spray velocity, the estimation error for the velocity component parallel to the main flow was 2% and that for the velocity component perpendicular to the main flow was around 10%. Finally, the velocity and particle size distributions of the spray stream and the three-dimensional droplet distribution were estimated by assimilating the velocity distributions measured by PIV. This technique predicts the spray angle and droplet size distribution from the two-dimensional velocity field of the PIV only and is expected to contribute to the development of injectors and atomizers.

Intranasal delivery of a synthetic Entamoeba histolytica vaccine containing adjuvant (LecA + GLA-3 M−052 liposomes): In vitro characterization

Amebiasis, a disease caused by the parasite Entamoeba histolytica, is estimated to cause millions of infections and at least 55,000 deaths globally each year. With no vaccine currently available, there is an urgent need for an accessible means of stimulating protective mucosal immunity. The objective of this study was to characterize the nasal spray of a novel amebiasis vaccine candidate from a syringe-based liquid atomization device, the Teleflex MAD Nasal™, in both adult and infant nasal airways.Human ergonomic testing was completed to determine realistic actuation parameters. Spray pattern, plume geometry, and droplet size distribution were measured to evaluate reproducibility of free plume characteristics. The Alberta Idealized Nasal Inlet (AINI) and three realistic infant nasal airways were used to determine the in vitro deposition profile in adult and infant airways, respectively.Collectively, in vitro results demonstrated the feasibility of delivering the vaccine candidate to target sites within the nasal airways. Penetration through the nasal airways that could lead to deposition in the lungs was below the limit of quantification for both adult and infant geometries, indicating a low likelihood of adverse events due to lung exposure. These results support continued investigation of intranasal delivery of the synthetic Entamoeba histolytica vaccine.

Computational fluid dynamics characterization of the hollow-cone atomization: Newtonian and non-Newtonian spray comparison

Disintegration of liquid masses in a free-surface flow is still an open question in the field of small-scale spray applications such as dispensing of detergents or sanitizing products. In this context, the pressure-swirl atomizer is widely investigated. It allows to improve several spray characteristics through the formation and breakup of a conical liquid sheet that results in the well-known hollow-cone atomization. From this perspective, the characterization of a small-scale pressure-swirl spray under laminar flow conditions is the focus of this work. The configuration of the device and the physical properties of the discharged liquid are the key parameters that modify the attributes of such multiscale flow. In this regard, the entire picture of the fragmentation process is structured into multiple stages: internal nozzle flow, outer displacement of the liquid–gas interface, droplet spread into the atmosphere, and droplet-wall interactions on a collection surface. Through the computational fluid dynamics, we analyze the influence of the main fluid/packaging parameters on the hollow-cone spray properties, and on the whole atomization process. Reynolds and Ohnesorge numbers are coupled with the Sauter mean diameter to distinguish different breakup mechanisms and spray performances. The solution of the entire spray system is performed by implementing the volume-of-fluid-to-discrete-phase-model, which allows to capture the liquid–gas interface displacement and track the droplets produced downstream the primary atomization, simultaneously. With this Eulerian–Lagrangian hybrid model, we link key features of the hollow-cone spray process to spray pattern and droplet size distribution for both Newtonian and non-Newtonian fluid properties.

Semi-Empirical Model of Droplet Size Distribution From the Maximum Entropy Principle in Sodium Spray

When a sodium leakage accident occurs in the sodium-cooled fast reactor, the leaked sodium reacts violently with the air in the form of droplets, resulting in the phenomenon of sodium spray fire. The droplet size distribution formed by liquid sodium injection is the key factor affecting the accident analysis of sodium spray fire. Based on the theory of the maximum entropy principle, a semi-empirical model of sodium spray droplet size distribution is constructed, which is constrained by the mass equation or the momentum equation with viscous resistance, respectively. Based on the existing liquid fuel droplet size distribution experiment results and the sodium spray fire experiment results, the semi-empirical model is verified, which shows that the prediction result with the semi-empirical model constrained by the momentum equation is in good agreement with the experimental result with the error of about 20%. Furthermore, the proposed sodium spray droplet model is compared with other models of the empirical model, the semi-empirical model, and the model based on the maximum entropy principle constrained by the simplified mass equation. The simulation result with the proposed model matches the experimental data better with minor error.