Adaptive collision meshing and satellite droplet formation in spray simulations

Improved numerical methods and physical models have been applied to droplet collision modeling. Numerically, an adaptive collision mesh method is developed to calculate collision rate. This method produces a collision mesh that is independent of the gas phase mesh and adaptively refined according to local parcel number density. An existing model describing the satellite droplet formation during the collision process is improved to reflect the experimental findings that the satellite droplets are much smaller than the parent droplets. The adaptive collision mesh and the improved satellite model have been used to simulate three impinging spray experiments. The model was able to qualitatively predict the occurrence of small satellite drops and bi-modal post-collision drop size distributions. The effect of the collision mesh and the satellite droplet model on a high-speed non-evaporating diesel spray is also assessed.     

Modeling droplet collision and coalescence in an icing wind tunnel and the influence of these processes on droplet size distribution

A theoretical model of a two-phase air/dispersed water spray flow in an icing wind tunnel is presented here. The mutual interactions taking place within the dispersed phase known as binary droplet collisions, as well as gravitational sedimentation are considered. Where large droplets and low air stream velocities are concerned, the effect of gravity on droplet dynamics is considerable. Gravity causes the vertical deflection of droplet trajectories and an increase in liquid water content (LWC) in the bottom half of the wind tunnel. Droplet collision tends to influence the size, trajectory and velocity of droplets thus affecting the characteristics of the flow and, thereby, the formation of ice on the object placed in the wind tunnel. The present model simulates droplet motion and droplet collision in an icing wind tunnel, where it may be observed that bouncing, stable coalescence, or coalescence followed by separation are the possible outcomes of collision. In the theoretical examination, firstly, the effect of gravity on the vertical deflection of droplet trajectories and on the vertical distribution of the LWC near the icing object are taken into account, while droplet collision is disregarded. Then both factors are considered and collision outcome is determined together with the size and velocity of post-collision droplets. The initial droplet size distribution (DSD), as it occurs at the nozzle outlet, is estimated by a curve in accordance with previous experimental results. The DSD is determined theoretically near the icing object, which makes it possible to calculate the median volume diameter and the LWC of the aerosol cloud. The simulation results with regard to the LWC are compared to the experimental results obtained in this research and a satisfactory qualitative coincidence is to be found between them.     

A new predictive model for fragmenting and non-fragmenting binary droplet collisions

A new predictive model for collisional interactions between liquid droplets, which is valid for moderate to high Weber numbers (>40), has been developed and validated. Four possible collision outcomes, viz., bouncing, coalescence, reflexive separation and stretching separation, are considered. Fragmentations in stretching and reflexive separations are modeled by assuming that the interacting droplets form an elongating ligament that either breaks up by capillary wave instability, or retracts to form a single satellite droplet. The outcome of a collision, number of satellites formed from separation processes and the post-collision characteristics such as velocity and drop-size are compared with available experimental data. The comparisons include colliding mono- and poly-disperse streams of droplets of different fuels under atmospheric conditions, and the results agree reasonably well.     

Collision between high and low viscosity droplets: Direct Numerical Simulations and experiments

Binary droplet collisions are of importance in a variety of practical applications comprising dispersed two-phase flows. In the present work we focus on the collision of miscible droplets, where one droplet is composed of a high viscous liquid and the other one is of lower viscosity. This kind of collisions take place in, for instance, spray drying processes when droplets with different solid content collide in recirculation zones. The aim of this paper is to investigate the details of the flow inside the colliding droplets. For this purpose, two prototype cases are considered, namely the collision of equal sized droplets and the collision between a small and highly viscous droplet and a bigger low viscous droplet. A new experimental method has been developed in order to visualize the penetration and mixing process of two colliding droplets, where a fluorescence marker is added to one liquid and the droplets are excited by a laser. The results show a delay in the coalescence which takes place during the initial stage of a collision of droplets with different viscosities. Direct Numerical Simulations based on the Volume-of-Fluid method are used to study these collisions and to allow for a more detailed inspection of the mixing process. The method is extended to consider a second liquid with a different viscosity. In order to reproduce the delay of coalescence, an algorithm for the temporal suppression of the coalescence is applied. A predictive simulation of the delay is not possible, because the extremely thin air gap separating the droplets cannot be resolved by the numerics. This approach is validated by comparison with experimental data. The results provide local field data of the flow inside the collision complex, showing in particular a pressure jump at the liquid–liquid interface although no surface tension is present. The detailed analysis of the terms in the momentum balance show that the pressure jump results from the viscosity jump at the liquid–liquid interface.     

Effects of gas and droplet characteristics on drop-drop collision outcome regimes

Droplet-droplet collisions occur in many spray systems. The collision of two spherical droplets in a gas is considered in terms of the five primary phenomenological outcomes: slow coalescence (SC), bounce (B), fast coalescence (FC), reflexive separation (RS), and stretching separation (SS). The boundaries that separate these outcomes were investigated herein in terms of droplet viscosity and surface tension as well as gas pressure and density. Gas effects are not accounted for previous models, but can be important for hydrocarbon drops in pressurized sprays associated with many fuel systems. Based on a comprehensive review of available drop-drop collision data, phenomenological models were proposed herein for a wide variety of test conditions. For slow coalescence/bouncing (SC/B), increasing droplet viscosity and gas pressure were found to increase the probability of a bouncing outcome of the collision. For the B/FC boundary, increasing droplet viscosity and gas density were also found to increase bouncing probability. In both cases, the variations can be explained in terms of the stability of the gas layer that develops between the droplets. Additionally, the Brazier-Smith model for the FC/SS boundary was modified to increase robustness for a wide range of droplet viscosities. In general, the present models reasonably predicted collision outcomes for a large variety of gas pressures and densities as well as droplet viscosities and surface tensions. These are also the first models to include gas effects and the first models of the SC/B boundary. However, the droplet diameters of the data set were limited in range from 200 to 400 microns. Significantly larger droplet collisions may include effects on initial non-sphericity while significantly smaller drop collisions may include effects on non-continuum flow and gas viscosity.     

A STUDY ON DROPLET VELOCITY OF ETHANOL DURING ELECTROSPRAYING PROCESS AT CONE-JET MODE

研究液滴在静电喷雾下的速度特性是理解喷雾形态的形成及演化的关键.结合锥射流模式下乙醇静电喷雾实验数据,建立了静电喷雾二维轴对称模型.基于离散相液滴运动方程、连续相空气运动方程、电场方程以及用户自定义函数,进行了数值求解,获得了锥射流模式下的乙醇静电喷雾形态、空间电场分布以及液滴速度场分布.考虑了不同空气入口流速的影响,得到了乙醇/空气同轴射流静电喷雾形态的变化规律.结果表明,喷雾外围液滴与空气流场有较强的相互作用,导致喷雾中轴线附近的液滴速度分布变化较小,而在喷雾外围处的液滴速度分布沿径向剧烈变化;随着空气入口速度的增大,乙醇/空气同轴射流静电喷雾形态先趋于发散,当空气入口速度大于喷雾外围液滴轴向速度时,喷雾形态则趋于聚拢.因此,除改变施加电压、液体流量和电极结构外,通过控制空气入口速度来影响喷雾液滴速度场,也可获得不同的静电喷雾效果.     

A unified spray model for engine spray simulation using dynamic mesh refinement

This study is based on dynamic mesh refinement and uses spray breakup models to simulate engine spray dynamics. It is known that the Lagrangian discrete particle technique for spray modeling is sensitive to gird resolution. An adequate spatial resolution in the spray region is necessary to account for the momentum and energy coupling between the gas and liquid phases. This study uses a dynamic mesh refinement algorithm that is adaptive to spray particles to increase the accuracy of spray modeling. On the other hand, the accurate prediction of the spray structure and drop vaporization requires accurate physical models to simulate fuel injection and spray breakup. The present primary jet breakup model predicts the initial breakup of the liquid jet due to the surface instability to generate droplets. A secondary breakup model is then responsible for further breakup of these droplets. The secondary breakup model considers the growth of the unstable waves that are formed on the droplet surface due to the aerodynamic force. The simulation results are compared with experimental data in gasoline spray structure and liquid penetration length. Validations are also performed by comparing the liquid length of a vaporizing diesel spray and its variations with different parameters including the orifice diameter, injection pressure, and ambient gas temperature and density. The model is also applied to simulate a direct-injection gasoline engine with a realistic geometry. The present spray model with dynamic mesh refinement algorithm is shown to predict the spray structure and liquid penetration accurately with reasonable computational cost.     

含气泡油滴撞击油膜壁面时气泡的变形与破裂

油--气润滑过程中润滑油液滴受高速气流扰动易形成含气泡油滴,微气泡将对油滴撞击壁面时的运动过程以及壁面油膜 层的形成质量产生重要影响. 基于耦合的水平集--体积分数 方法,对含气泡油滴撞击油膜壁面行为进行数值模拟研究, 考察含气泡油滴撞击油膜壁面时气泡的变形运动过程,探讨气泡破裂的动力学机制,分析气泡大小、碰撞速度和液体黏度等因素对含气 泡油滴撞壁过程中气泡变形特征参数的影响规律. 研究表明:含气泡油滴撞击油膜壁面后气泡会发生变形,并破裂形成膜液滴;气泡随同 液滴运动过程中,气泡内外压力和速度梯度变化是使气泡发生破裂的主要诱因. 气泡大小对气泡破裂方式影响较大,气泡较小时发生单 点破裂,而气泡较大时更容易发生多处破裂. 不同大小气泡受力差异较大,气泡大小与破裂发生时刻没有明显相关性. 碰撞速度和液体 黏度对气泡的变形、破裂和破裂发生时刻都具有一定的影响. 碰撞速度越大,油滴动能越大,更容易产生气泡变形和破裂现象. 液体黏 度增大,在油滴撞壁运动前期促进气泡变形,而在运动后期可以阻延气泡破裂行为发生.      

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.     

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 modeling and experimental measurements of water spray impact and transport over a cylinder

This study compares experimental measurements and numerical simulations of liquid droplets over heated (to a near surface temperature of 423 K) and unheated cylinders. The numerical model is based on an unsteady Reynolds-averaged Navier–Stokes (RANS) formulation using a stochastic separated flow (SSF) approach for the droplets that includes submodels for droplet dispersion, heat and mass transfer, and impact on a solid surface. The details of the droplet impact model are presented and the model is used to simulate water spray impingement on a cylinder. Computational results are compared with experimental measurements using phase Doppler interferometry (PDI). Overall, good agreement is observed between predictions and experimental measurements of droplet mean size and velocity downstream of the cylinder.     

Flow characteristics of spray impingement in PFI injection systems

The present paper addresses an experimental study of the dynamic exchanges between the impact of an intermittent spray and the liquid film formed over the target, based on detailed phase Doppler anemometry (PDA) measurements of droplet size, velocity and volume flux in the vicinity of the impact. The flow configuration is that of a pulsed injector spraying gasoline onto a flat disc to simulate the port fuel injection (PFI) of an internal combustion engine operating at cold-start conditions. The measurements evidence that the outcome of impact cannot be accurately predicted based on the characteristics of the free spray, but requires precise knowledge of the flow structure, induced by the target. The implications for spray–wall interaction modelling are then discussed based on the application of conservation equations to the mass, momentum and energy exchanged between the impinging droplets and the liquid film. The results show that the liquid film starts to form in the vicinity of the stagnation region at early stages of injection and a non-negligible proportion of droplets impinging at outer regions splash after interaction with the film. Film disruption is mainly driven by the intermittent axial momentum of impinging droplets, which enhances the vertical oscillations. The radial momentum imparted to the liquid film at the stagnation region is fed back onto secondary droplets emerging later during the injection cycle at outwards locations, where momentum of impacting droplets is much smaller. As a consequence, although the number of splashed droplets is enhanced by normal momentum, their size and ejection velocity depends more on the radial spread induced onto the liquid film and, hence, on the radial momentum at impact. The analysis further shows that existing spray–wall interaction models can be improved if the dynamic exchanges between the impacting spray and the liquid film are accounted.     

A multiphysics model for charged liquid droplet breakup in electric fields

A computational multiphysics model for simulating the formation and breakup of droplets from axisymmetric charged liquid jets in electric fields is developed. A fully-coupled approach is used to combine two-phase flow, electrostatics, and transport of charged species via diffusion, convection, and migration. A conservative level-set method is shown to be robust and efficient for interface tracking. Parametric simulations are performed across a range of fluid properties corresponding to commonly used liquids in inkjet printing and spray applications to examine their role in jet evolution and droplet formation. Specifically, the effects of electric potential drop, surface tension, viscosity, and mobility are investigated. Droplet velocity and size distributions are calculated, and the corresponding mean values are found to increase and decrease respectively with increasing electric field strength. The variations in droplet velocity and size are quantified, and droplet size and charge levels agree well with experimental values. Increasing mobility of charged species is found to enhance jet velocity and accelerate droplet formation by shifting charge from the liquid interior to the interface.     

Modeling of droplet collision-induced breakup process

The present article proposes a new droplet collision model considering droplet collision-induced breakup process with the formation of satellite droplets. The new model consists of several equations to investigate the post-collision characteristics of colliding droplets and satellite droplets. These equations are derived from the conservations of droplet mass, momentum, and energy between before and after collision, and make it possible to predict the number of satellite droplets, and the droplet size and velocity in the analytical way. To validate the new collision model, numerical calculations are performed and their results are compared with experimental data published earlier for binary collision of water droplets. It is found from the results that the new model shows good agreement with experimental data for the number of satellite droplets. It can be also shown that the predicted mean diameter by the new model decrease with increasing the Weber number because of the collision-induced breakup, whereas the O’Rourke model fails to predict the size reduction via the binary droplet collision.     

Experimental study of the flow regimes resulting from the impact of an intermittent gasoline spray

The present paper reports a complete set of measurements made with a two-component phase Doppler anemometer of the two-phase flow generated at the impact of a transient gasoline spray onto a flat surface. The spray is generated by a pintle injector and the fuel used was gasoline. The measurements of droplet size–velocity were processed to provide time fluxes of number, mass, normal momentum, and energy of the poly-dispersion of droplets ejected at impact, and analyzed based on predictive tools available in the literature. The results show that splash is the dominant mechanism by which secondary droplets are ejected from the surface, either in the stagnation region or in the core region of the spray. In the stagnation region, a large fraction of each incident droplet adheres to the surface and the axial incident momentum contributes with a larger parcel than tangential momentum. As a result, the normal velocity of ejected droplets is much smaller than that of the original incident droplets, while tangential velocity is enhanced. The region near the stagnation point is immediately flooded upon impact of the leading front of the spray, forming a liquid film that is forced to move radially outwards as droplets continue to impinge during the steady period. Spray/wall interaction in the core region thus occurs in the presence of a moving thin liquid film, which enhances transfer of tangential momentum. As a result, film spreading and dynamics as a result of impingement forces are crucial to accurate model spray/wall interaction. The outer region of the spray is dominated by the vortical structure induced by shear forces, which entrains small responsive secondary droplets to re-impinge. Furthermore, prediction of the outcome of spray impact requires a precise knowledge of the two-phase flow in the presence of the target.     

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.     

A moment method for splashing and evaporation processes of polydisperse sprays

A new moment method for the modelling of polydisperse sprays is proposed that simultaneously takes into account the dispersion in droplet size and droplet velocity. For the derivation of this Eulerian method the kinetic spray equation is used which constitutes a partial differential equation for the probability density function of droplets. To reduce the complex kinetic spray equation to a form that can be managed with the available numerical procedures, moment transforms with respect to the droplet velocity and the droplet size are conducted. The resulting moment equations are closed by choosing an approximate probability density function which applies to polydisperse sprays. The method is successfully tested for configurations in which a polydisperse spray is either splashed, evaporated or effected by a Stokes drag force. The tests are organised in such a way that crossing of two spray distributions is always included. The new method is able to capture the polydisperse nature of sprays as well as the bi-(or multi-) modal character of the droplet velocity distribution function, for example, when droplets cross each other.     

Linear and nonlinear inversion schemes to retrieve collision kernel values from droplet size distribution change

This study presents an attempt to retrieve collision kernel values from changes in the droplet size distribution due to collision growth. Original linear and nonlinear inversion schemes are presented, which use the simple a priori assumption that the total collision rate is given by the sum of the gravitational and turbulent contributions. Our schemes directly handle binned (discretized) size distributions and, therefore, do not require any assumptions on distribution functional forms, such as the self-similarity assumption. To validate the schemes, three-dimensional direct numerical simulation (DNS) of colliding droplets in steady isotropic turbulence is performed. In the DNS, air turbulence is calculated using a pseudo-spectral method, while droplet motions are tracked by the Lagrangian method. Comparison between the retrieved collision kernels and the collision kernels obtained directly from the DNS show that for low Reynolds number flows both the linear and nonlinear inversion schemes give good accuracy. However, for higher Reynolds number flows the linear inversion scheme gives significantly larger retrieval errors, while the errors for the nonlinear scheme remain small.