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In this study, an electrostatic sprayer which had been previously designed and constructed was evaluated in order to quantify the charging of droplets. Liquid atomization was achieved by using an ultrasonic nozzle. The nozzle maximum flow rate was 25 milliliters per minute and vibration frequency was about 30 kHz. The induction method was used for charging the output droplets. All experiments were carried out within a closed environment with a fixed ambient humidity and temperature to reduce the effect of environmental factors. The independent parameters in this study included: voltage at four levels of 1.5, 3, 5 and 7 kV; air flow speed at six levels of 14, 14.9, 17, 20.2, 21.6 and 23 m s-1; charging electrode radius in two levels of 10 and 15 millimeters, horizontal distance between the electrode and nozzle tip at four levels of 1.5, 6, 10 and 15 millimeters; and liquid flow rate at three levels of 5, 12 and 25 milliliters per minutes. For evaluation of the system, the charging quantities of droplets were measured in different states. The maximum charging occurred at 5 ml min-1 flow rate, voltage of 7 kV, air flow speed of 23 m s-1 and the resulting current was 0.24 μA. On dividing the electrical current by the liquid flow rate and changing the scale, the mean charge to mass ratio was 1.032 μC g-1. Increasing voltage increased the charging quantity slightly but higher voltages and lower air speeds decreased it. The effect of the faster air speed on droplet charging phenomena is positive and the smaller electrode radius causes less charge induction on the droplets. The quantity of droplets charging first increased with increased distance between ring electrode and nozzle tip, and then it was either reduced and/or fixed.

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In this article, for the first time the numerical solution of Godunov method with HLLC Riemann solver is extended for a hyperbolic five equations two-fluid model. The flow field is considered for two-space dimensional case. So far, two main difficulties include non-monotonic behavior of mixture sound relation and inability of shock transition from interface was mentioned during working with this model. In this research these difficulties were overcome by selecting an appropriate mixture sound relation and appropriate discretization of non-conservative term. The mutual effect of shock wave impact with a droplet and two droplets with different diameters were simulated and studied. During the shock wave impact with 1.47 and 6 Mach with the droplet, a complicated shape of interface was formed with high pressure zone and low pressure zone of cavitations. The results obtained from the present attempt were compared with the experimental and related similar results of that obtained by the other numerical methods and models. The comparison of the results was good. It was also concluded that the numerical method used in the present work has enough accuracy with high capability in capturing two-phase flow interfacial instability and shock wave impact transmission from the droplet.

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In this study, the collision of two drops using Lattice Boltzmann numerical method in two-phase flow has been investigated. The simulation for incompressible fluid is based on the model represented by Lee. The prominent feature of this model is to simulate fluids with high density ratios. Thus, the model has easily been compared with experimental results and its validity has been investigated. Using this simulation, the variation of non-dimensional parameters such as Weber number, Reynolds number, Impact parameter, density ratio, kinematic viscosity ratio, diameter ratio and velocity ratio of two drops were studied. Considering the results, it was shown that the Reynolds number, density ratio and relative velocity ratio have no effect on separation or coalescence of drops collision; while the variation of Weber number, Impact Parameter and kinematic viscosity ratio results in separation or coalescence. Moreover, by increase in Weber number, Reynolds number or density ratio or decrease in kinematic viscosity, the number of oscillations and the time needed to reach equilibrium increases. Likewise, the amplitude of oscillation and the deformation of the drops increase when the Weber number, Reynolds number or density ratio rise or the kinematic viscosity lowers.

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To determine the droplet characteristics of agricultural spray nozzles through Water Sensitive Paper (WSP), the non-circular and overlapped spots appearing on the water sensitive paper surfaces are eliminated. In the conventional approach, the procedure is done according to the subjective self determined estimation of the operator. The objective of this study was to develop a practical alternative to the conventional approach to Spot Elimination (SE) from WSP surfaces. Droplet samples were taken through application of seven different spray nozzles. Papers were placed within and outside the domain of spraying area and scanned at 600 pixels per inch resolution following their collection. The diameter and roundness values of each spot on multiple WSP samples were determined through image processing software. The overlapped spots and the non-circular ones were manually eliminated by the operator. Spot Roundness (SR) ranged from 0.051 to 6.283 and from 0.130 to 6.283 prior to, and following SE, respectively. Results indicated a linear relationship between minimum SR value and volume median diameter of the droplets. Regression analysis revealed the optimal SR variation interval to be between 0.765 and 2.356 for SE. Characteristics of the spots remaining out of this range were compatible with the characteristics of the droplets conventional SE (when the spots subjectively eliminated). When the volumetric diameters (DV) in the conventional SE approach were compared with the optimum SR variation interval (for 10, 50 and 90 percent ratios) their absolute relative error ratios and confidence intervals at 95% level of significance level found as 2.8%±1.4, 1.8%±0.9, and 3.8%±1.5, respectively.

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In present work, models that predict contact angle of a droplet with a solid surface, are considered and compared with each other. Two phases were assumed to be Newtonian, incompressible and immiscible fluids. OpenFOAM software is applied to simulate the two phases interface by using Color function VOF (CF-VOF) method. Different models for contact angle of a droplet as Tanner and Yokoi models are implemented in the OpenFOAM. In addition, the dynamics and statics contact angle models were used to compare with recent models in order to choose the best one. The outcome of study shows, even though the static contact angle model is simple to understand, however, it could be the best model to predict the droplet behavior in a wide range of different conditions. The fluid viscosity effect was also considered in different models of the present study. It concluded that the fluid viscosity affects the type of pattern of droplet impact and as viscosity of fluid increases; more energy is needed to uplift the droplet again from the surface. Kelvin-Helmholtz instability (K-H) was also simulated and explained in details which initiates on the interface of two fluids due to velocity differences of droplet and the surrounded air.

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A theoretical nonlinear droplet deformation model with an accurate estimation of aerodynamic force, which is appropriate for Lagrangian droplet tracking schemes, is presented and validated. The modeling is based on keeping track only of the fundamental oscillation mode. This conventional approach has been used in many deformation-based breakup models including Taylor Analogy Breakup, Droplet Deformation and Breakup, and Nonlinear Taylor Analogy Breakup. However, these models have some shortcomings such as the use of several calibration coefficient, two-dimensional analysis, and rough approximation of aerodynamic forces in large deformations. This paper is intended to amend these defects. The formulation is based on mechanical energy equation. The pressure distribution profile around the deformed droplet is approximated using a piecewise sinusoidal function which depends on Reynolds number and droplet deformation. The final kinetic equation is numerically solved using a fourth-order Runge-Kutta method and the results are compared with those of other models, experiments, and a Volume of Fluid simulation. Numerical results show that the present model predicts slightly greater deformations in comparison with other models for the unsteady case, which is more consistent with the experimental data. Considering the steady case, the results of present model stand between that of Taylor Analogy Breakup and Nonlinear Taylor Analogy Breakup model, and provide satisfactory predictions. The stream lines obtained from simulation match those of calculated analytically suggesting the appropriateness of the assumptions used in the modeling. Overall, the present model is found to be appropriate for the estimation of droplet deformation.

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The aim of this study is numerical investigation of a evaporating and non-reacting diesel spray operating in a high pressure and high temperature constant volume combustion chamber, as an essential step in simulation of liquid fuels combustion. To this end, the impact of droplets diameter distribution on estimating two critical characteristic parameter i.e. liquid and vapor penetration lengths is studied using the open-source OpenFOAM code. In order to determine droplets diameter distribution effect, three different distribution ranging from 0.25-100 micron is chosen and the liquid and vapor penetration lengths are individually calculated for each distribution. The results are validated against the experimental data published by Sandia National Laboratory. The results show while the droplets diameter distribution has a remarkable effect on the predicted value of the liquid length, so that leads to overestimate liquid penetration lengths up to more than two times; its effect on the vapor length prediction is negligible. Also assuming a nozzle diameter distribution leads to non-physically increase in the value of liquid length. This non-physically prediction may lead to misleading prediction of spray impingement to piston and the cylinder walls resulting an error in unburnt hydrocarbons concentration as well as the engine efficiency estimation.

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In this research, the use of the exact difference method forcing scheme in the pseudo-potential multiphase model is suggested for the simulation of a droplet impact on a thin liquid film at a density ratio of 1000, and the effect of inertia, surface tension, and gravity forces are considered by means of their corresponding non-dimensional numbers (i.e. the Reynolds, Weber, and Bond numbers). For this reason, the Palabos open source software is modified by implementing the exact difference method in it. The results of our simulations in different Reynolds and Weber numbers show that the Weber number has a slight influence on the crown layer radius, meanwhile, the Reynolds number has a direct effect on the crown radius. The crown height is increased with an increase in the Reynolds and Weber numbers. Furthermore, the comparison between the pseudopotential model simulations and the free-energy model shows that crown shape is related on the surface tension in addition to the non- dimensional numbers and with a noticeable increase in surface tension the crown tip becomes bigger. The influence of the gravity force is investigated through the Bond number. According to the results, the crown height is noticeably affected by the Bond number. When the Bond number decreases, the crown radius and height increase. Therefore, the proposed model with the capability of being used for multiphase problems with large density ratios while producing a low spurious current could be utilized for a vast variety of other multiphase problems as well.

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In this study evaporation of biodiesel droplet under different operating conditions is investigated. The model is a common droplet vaporization model for multicomponent fuels. In this model, gas phase quasi-steady equations are solved analytically and energy and species transport equation in liquid phase are solved numerically. The sub-models are modified to consider high pressure effects. Peng-Robinson equation of state is used for gas phase and phase equilibrium is determined using fugacity. Effects of pressure on the thermophysical and transport properties of gas phase are considered. Five biodiesel with different composition are studied. These biodiesel have different composition of methyl esters. Biodiesel composition has little effects on droplet lifetime and maximum difference is about 20%. It is observed that increasing ambient temperature leads to decrease in droplet lifetime and increases temperature gradient inside droplet. Ambient pressure has different effects on droplet vaporization behavior at different ambient temperature. At lower temperature environment, increasing of pressure increases the droplet lifetime while at higher temperatures droplet lifetime first increases and then decreases with pressure. Increasing initial velocity of droplet reduces the droplet lifetime. Results show that at high pressures, droplet temperature reach to values near to critical temperature and accuracy of quasi-steady approximation decreases. Radius of vapor influenced sphere increases with temperature and decreases with pressure.

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In this paper, simultaneous impact of two parallel drops on a thin liquid film is investigated using the lattice Boltzmann method. The purpose of this study is to investigate the effects of surface tension (characterized by Weber number), distance between two drops, and gas kinematic viscosity on the impact. The developed numerical model in this paper which is based on the Shan and Chen pseudo-potential two-phase model makes it possible to access large density ratios, low viscosities, and tunable values of surface tension independent of the density ratio. The model is validated by comparing the coexistence densities with those of Maxwell analytical solution, evaluating the Laplace law for a droplet, and simulating single droplet impact on a thin liquid film. Simulation results of two drops simultaneous impact show that after impact, two jets raised between the drops join each other and form a central jet. Height of this jet increases with time leading to separation of secondary droplets from its tip. When the surface tension value is decreased, the central jet height is increased, but size of the separated droplets is reduced. The crown shape observed in single drop impact is also seen in simultaneous impact of two drops. Increasing distance between two drops leads to a smaller central jet height and an increase in the crown radius. The crown height, however, was found to be independent of the distance. Finally, increasing gas kinematic viscosity reduces the central jet rising speed and delays separation of secondary droplets from the jet.

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The interactions between vortical structures and spherical particles or droplets is of practical issues in two-phase flows. The interactions bring major changes in the flow field particularly when coupled with particle rotation. It is observed that the heat transfer rate is significantly influenced during the time that the vortices’ cores are in the vicinity of the particle. In this paper, transient heat transfer of a rotating spherical particle interacting with a pair of vortices in incompressible and viscous flow is studied using numerical solution of the Navier-Stokes and energy equations in the range of 20≥Re≤100 and non-dimensional rotational velocities 0≤Ω≤1, by computational code which has been developed by the authors. In order to ensure the accuracy of the calculation, the results are compared with numerical data reported in the literature and good agreement between results was observed. Then the effect of circulation direction of two vortices interacting with a particle by spin on its heat transfer rate was investigated. Also distribution of heat transfer coefficient at the particle surface with separate rotation around three different axes in two cases of interacting and non-interacting with vortices is given and the results of heat transfer coefficient are presented. The results show that particle rotation for Ω≤0.5, in both presence and absence of vortices in flow field has negligible effects on the particle heat transfer rate; however, with increasing of particle spin significant effects on heat transfer coefficient has been observed that due to the circulation direction of vortices, different amounts are obtained.

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The aim of present article is investigation of evaporation of single- and multi-component fuels droplet and study the effect of unsteadiness term on it. Two approaches are used; a fully transient and quasi-steady approaches. The species, momentum, and energy equations for gas phase and species and energy equations for liquid phase are solve numerically by assuming variable properties with respect to temperature. The results obtained from the fully transient approach show an acceptable compliance with experimental data at atmospheric pressure in a wide range of fuel volatility and ambient temperature for the single- and multi-component fuels. Heptane, decane, and hexadecane are used in order to investigate the effects of fuel volatility on evaporation.The steadiness of processes in the gas phase has been checked by using two measures of unsteadiness related to the mass and heat diffusion of fuel vapor on the droplet surface. The deviations of the results of the quasi-steady approach from the fully transient have been justified by the unsteadiness measures. The results show that fuel and ambient temperature have significant effects on the unsteadiness. For heavier fuels and higher ambient temperature, the diviation of quasi- steady approach from fully transient increases. Also the diviation becomes higher when the differences between volatility of component increase. Therefore, it is concluded that the quasi-steady approach presents reasonable results for lighter fuels in the case of single component and whenever the volatilities of components are very close.

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Spray combustion is utilized in a number of engineering applications such as energy conversion, military industrial, furance and propulsion devices. Current work focused on the effect of liquid fuel droplet diameter on the efficiency of the combustion chamber and formed emission such as NOx and CO in a two-dimensional axisymmetric combustion chamber. The discrete phase model approach employed for simulating Combustion. The gas phase is simulated using an Eulerian approach; while the droplets are treated with a Lagrangian method. The coupling between the two phases and effect of radiation is considered. The mixture-fraction/probability density function (PDF) equilibrium chemistry model is used to predict the combustion of the vaporized fuel. Also, the conservative equations of mass, momentum and energy in the turbulent flow field were solved in conjunction with the k–ε two equation turbulence model. A numerical simulation was carried out to study the influence of droplet size on the formation and emission of NOx and other contaminants. This effect was investigated under different droplet diameter and type of injection. The following conclusions be drawn: Smaller droplets produce higher NOx emission than the larger ones. Larger droplets produce higher CO than Smaller ones.

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The aim of the present study was to investigate the influence of nozzle configurations on spray drift and explain the influences using several atomization characteristics (length of spray sheet, spray angle, velocity distribution of flow field, fluctuation of velocity, and droplet size). Nozzles manufactured by one company (Lechler GmbH, Germany) were tested by spraying local tap water in a wind tunnel at an operating pressure of 0.3 MPa and under room temperature. The nozzles tested were compact air-induction flat fan nozzles (IDK120-02, IDK120-03), standard flat fan nozzles (ST110-02, ST110-03), and hollow-cone swirl nozzles (TR80-02, TR80-03). The atomization process was recorded using a Particle Image Velocimetry (PIV) system, droplet size was measured by a Sympatec Helos laser-diffraction particle-size analyzer, and spray drift was evaluated in a wind tunnel with deposition measured using a calibrated fluorometer (Turner-Sequoia model 450). Results showed that spray drift was significantly different among nozzle types (P<0.0005) and that nozzle configurations influenced breakup length, spray angle, droplet size, and velocity. Nozzles producing larger droplet sizes had lower velocity. Smaller droplets were produced when longer and wider spray sheets were produced. Compared to ST and TR nozzles, IDK nozzles started to breakup in the center of the liquid sheet, producing droplets with larger diameter, lower velocity, and less velocity fluctuation. The IDK nozzle is a good choice for low spray drift at higher wind speeds.

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Prediction of spray droplet diameter distribution depends on the various parameters such as physical properties, fluid velocity, and discharge environment and injector geometry. The stage of forming droplets has a great variety in size and therefore will be predictable with a statistical approach. The maximum entropy principle is one of the most popular and best ways to predict the spray droplet size distribution along with the conservation equations. Due to some drawbacks in this model, the predicted results do not match well with the experimental data. It is suggested to improve the available energy source in the MEP model equation by numerical solution of flow inside the injector based on the CFD technique. This will enhance the calculation accuracy of the turbulent kinetic energy of the output spray. In fact, by using this sub-model in the maximum entropy model, the prediction accuracy of the spray characteristics is improved. Also, the requirement of the maximum entropy model to the experimental data as inputs has been reduced. By the present coupled model, the effect of spray upstream on the droplet size distribution can be considered with a good accuracy. The results show a close agreement with the available experimental data.

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The supercooled steam in low pressure turbines creates the nucleation phenomenon. In most modeling approaches, to reduce the computation time a monodispersed model is used. However, experimental evidence even on one dimensional condensing flow demonstrates the existence of droplets with several sizes. In this paper to develop the modeling of the droplets more realistic, a polydispersed model is used along with the one dimensional HHL Riemann solver. In this study, a simple method is proposed for polydispersed model in Eulerian-Eulerian method. In this scheme, first, a number of elements are considered in the nucleation region and the droplets formed in each of the elements are put into a group. Then the new droplets formed in consecutive elements are distributed based on the ratio between the number of droplets in each group available for merging constrained by having the same number of groups. These groups grow individually until the end of the nozzle and each group has their own wetness, temperature, number of droplets and radius. Based on the results of the proposed polydispersed, the nucleation rate and the number of droplets are found to be more than the results of the monodispersed model, but the average droplet radius is less, with 10% differences is closer to the empirical radius of the Moore nozzle. The pressure distributions for both models have good agreement with experimental data, but in overall, the results of the proposed polydispersed method is significantly closer to experimental results especially with regards to the droplet radius.

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In this research, the impact of a completely molten hollow droplet and a semi-molten hollow droplet on a surface is simulated numerically. At first, the production process of hollow particles from the agglomerated particles is addressed analytically. By this model, one can predict the particle diameter, solid core diameter and shell thicknesses of produced particle. The results of this section show that hollow particle may hardly develop at small initial porosity values (p=0.2). Then, the collected data from analytical model is used as input data for numerical simulation. In the numerical model, the central solid core was assumed to be a fluid with high viscosity. Due to high impact velocity, volume and density changes of the trapped gas inside droplet are important. Therefore the compressible form of governing equations is used. The results show that the hydrodynamic and solidification behavior of a completely molten droplet and a semi-molten droplet during impact process are different. In the semi-molten state, the central solid core prevents the formation of a counter jet. For this reason, a hollow semi-molten droplet is solidified faster than a completely molten hollow droplet. The overall time of solidification in the completely molten state is 35 μs and the corresponding time for semi-molten state, is 12 μs. Moreover the splat of a semi-molten hollow droplet is more continues compared with a completely molten droplet

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