Experimental study of successive collision of two water droplets with a solid

The collision of two successive droplets with a solid is investigated experimentally by means of a flash photographic method. The pre-impact diameters of two droplets are 0.56 mm and 0.45 mm. The impact velocity of droplets is approximately 2.7 m/s. The spacing between the two droplets is varied as a parameter. The physics of interaction phenomena between two droplets on the solid is studied from an experimental viewpoint.     

Investigation of droplet collisions for solutions with different solids content

The collision behaviour of droplets and the collision outcome are investigated for high viscous polymer solutions. For that purpose, two droplet chains produced by piezoelectric droplet generators are directed towards each other at a certain angle so that individual droplet pairs collide. For recording the collision event, one double-image and one high-speed CCD camera were used. One camera is positioned perpendicular to the collision plane recording the outcome of the collision, and the second camera is aligned parallel to the collision plane to assure that the droplet chains are exactly in one plane. A new approach for tracking droplets in combination with an extended particle tracking velocimetry algorithm has been developed. Time-resolved series of pictures were used to analyse the dynamics of droplet collisions. The three different water soluble substances were saccharose and 1-Ethenyl-2-pyrrolidone (PVP) with different molecular weights (K17, K30). The solvent was demineralised water. The solids contents ranged from 20 to 60 %, 5 to 25 % and 5 to 35 %, yielding dynamic viscosities in the range of 2–60 mPa s. Results were collected for different pairs of impact angles and Weber numbers in order to establish common collision maps for characterising the outcomes. Here, relative velocities between 0.5 and 4 m/s and impact parameters in the interval from 0 to 1 for equal-sized droplets (Δ = 1) have been investigated. Additionally, satellite formation will be discussed exemplarily for K30. A comparison with common models of different authors (Ashgriz and Poo in J Fluid Mech 221:183–204, 1990; Estrade et al. in Int J Heat Fluid Flow 20:486–491, 1999) mainly derived for low viscous droplets revealed that the upper limit of their validity is given by an Ohnesorge number of Oh = 0.115 and a capillary number of Ca = 0.577. For higher values of these non-dimensional parameters and hence higher dynamic viscosities, these models are unable to predict correctly the boundaries between collision scenarios. The model proposed by Jiang et al. (J Fluid Mech 234:171–190, 1992), which includes viscous dissipation, is able to predict the boundary between coalescence and stretching separation for higher viscosities (i.e. Oh > 0.115 and Ca > 0.577). However, the model constants are not identical for different solution properties. As a conclusion, an alteration of the collision appearance takes place because of the relative importance between surface tension and viscosity.     

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.     

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.     

气相中双液滴正碰过程数值模拟研究

液滴碰撞现象普遍存在于动力装置燃烧室喷嘴的下游区域,影响燃料的雾化性能。为了揭示相同直径的双液滴中心碰撞机理,求解了轴对称坐标系下的N-S方程,采用VOF(Volume of Fluid)方法捕捉液滴碰撞过程中气液自由表面的演化规律。利用Qian等提供的实验结果对计算模型进行数值校验,验证了模型的准确性。在此基础上,研究了环境压强对液滴碰撞反弹后不同结果(分离和融合)的影响,分析了环境压强和Weber数对液滴碰撞分离的影响。结果表明,液滴在碰撞反弹后的状态(分离或融合)是由液滴间气膜压强与环境气动阻力共同作用的结果,环境压强对液滴碰撞分离过程基本没有影响;Weber数越大,碰撞过程中变形的幅度越大。     

Hydrodynamics and boiling phenomena of water droplets impinging on hot solid

The collision of single water droplets with a hot Inconel 625 alloy surface was investigated by a two-directional flash photography technique using two digital still cameras and three flash units. The experiments were conducted under the following conditions: the pre-impact diameters of the droplets ranged from 0.53 to 0.60 mm, the impact velocities ranged from 1.7 m/s to 4.1 m/s, and the solid surface temperatures ranged from 170 °C to 500 °C. When a droplet impacted onto the solid at a temperature of 170 °C, weak boiling was observed at the liquid/solid interface. At temperatures of 200 or 300 °C, numerous vapor bubbles were formed. Numerous secondary droplets then jetted upward from the deforming droplet due to the blowout of the vapor bubbles into the atmosphere. No secondary droplets were observed for a surface temperature of 500 °C at the low-impact Weber numbers (∼30) associated with the impact inertia of the droplets. Experiments using 2.5-mm-diameter droplets were also conducted. The dimensionless collision behaviors of large and small droplets were compared under the same Weber number conditions. At temperatures of less than or equal to 300 °C, the blowout of vapor bubbles occurred at early stages for a large droplet. At a surface temperature of 500 °C, the two dimensionless deformation behaviors of the droplets were very similar to each other.     

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.      

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.     

Collision and merging of two equal droplets of propanol

Equally spaced and uniform droplets are produced by a vibrating orifice and move away in a straight line. They intersect with an exactly equal string of droplets and collide one by one. With stroboscopic lighting and multiple exposures, they are photographed. Thus successive stages of the collision process are shown on a single photo. The droplets can be made to collide with or without angular momentum by adjusting the aim of the emitting orifices. The impacting speeds can be varied from 2.8 to 11.7 m/s. Droplet sizes from 70 to 200 m are employed. Motions of the coalesced drop after the merging are bizarre and well-displayed. The results are important for spray modeling. When the streams of droplets merge at higher speeds, they may distort to the extent that the two streams of droplets merge to a single continuous sinuous stream.List of symbols b collision parameter - d diameter - p pressure difference - f frequency - u impact velocity - v droplet velocity - V liquid feed rate - x, y, z rectangular coordinates - angle between droplet stream and symmetry line - G generator - i initial, before the collision - P particle - T droplet - 1, 2 first and second droplet generator     

A Quasimolecular Approach for Discrete Study of Droplet Collision

A discrete numerical method based on a molecular approach has been used as an alternative technique for the study of liquid drop dynamics. The Weber number and the Impact number are found to be the key parameters that determine the outcome of collision of two liquid droplets. This study confirms the experimental fact that the number of daughter droplets resulting from the collision of two droplets increases with the Impact number for a large Weber number. The shapes of the droplets at different phases during collision are in accord with the experimental observation.     

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.     

Oldroyd-B黏弹性液滴碰撞过程的数值模拟

复杂的流变特性使凝胶推进剂的雾化过程存在一定困难,这制约了它的发展.聚合物胶凝剂的加入使凝胶推进剂具有黏弹性,从而在雾化时会产生黏弹性液滴,因此为了进一步认识凝胶推进剂的雾化机理、提高凝胶推进剂的雾化性能,对黏弹性液滴的碰撞行为进行数值模拟研究.针对凝胶推进剂雾化过程中出现的液滴撞击现象,考虑流体具有的黏弹性效应,采用...     

Modeling of binary droplet collisions for application to inter-impingement sprays

In this paper, we focused on modeling the collision phenomenon between two liquid droplets for application in spray simulations. It has been known that the existing O’Rourke collision model widely used in CFD codes is inaccurate in determining collision outcomes and droplet behavior. In addition, since the collision probability of the model follows a statistical approach involving computational cell geometry, the prediction results should be strongly dependent on the cell size. As a result, to more accurately calculate droplet collisions, the technique for predicting the droplet velocity and its direction after collision must be extended for use in spray modeling. Further, it is also necessary to consider all the possible collision outcomes, such as bouncing, stretching separation, reflexive separation and coalescence. Therefore, this paper describes the appropriateness of a composite concept for modeling collision outcomes and the implementation of deterministic collision algorithms into a multidimensional CFD code for the calculation of post-collisional droplet movements. Furthermore, the existing model does not consider the formation of satellite droplets. For this reason, our present modeling concept includes a fragmenting droplet collision model. Using the present model, we have validated the collision interactions between liquid droplets under high Weber number conditions by comparing our calculations with experimental results from a binary droplet collision. This paper also deals with the application of the model to inter-impingement sprays by analyzing the atomization characteristics, such as mean droplet size and velocity, spray tip penetrations and spray-shapes of the impinging spray using the suggested collision algorithms and then comparing the results with available experimental data.     

三维非连续变形分析方法碰撞分析及其应用

将具有完备动力学理论的非连续变形分析(DDA)方法应用于块体碰撞研究。基于三维DDA(3D DDA)方法,按时步输出块体碰撞过程速度变化和接触嵌入量,进而得到块体碰撞恢复系数、冲量、冲击力。以此为参考指标,采用斜抛、面-面对心等碰撞模型,验证3D DDA方法模拟块体碰撞的有效性,并将3D DDA方法应用于多米诺骨牌倾倒、滚石边坡成灾及防护等算例分析,探讨了多米诺骨牌倾倒机制、滚石启动及运动行为、滚石灾害防护方案。结果表明:多米诺骨牌间距越大,同一块体被碰撞时间越迟,其最终稳定时间也越迟,与下一块体碰撞的动能越大;滚石运动呈侧向平动及转动三维运动特征,每一次碰撞,均引起动能、轨迹或状态的显著变化;滚石拦挡设施弹簧刚度越大,越先达到最大冲击力,最大冲击力随弹簧刚度的增加而减小;可结合树木阻挡效应,耗散滚石动能,降低滚石飞跃高度,使滚石灾害减轻或控制在防护范围以内。     

The liquid deposition fraction of sprays impinging vertical walls and flowing films

The impingement of coarse sprays with a mean diameter in the order of millimeters on vertical walls with and without an additionally supplied wall film was studied at conditions well below the Leidenfrost limit. The fraction of the sprayed liquid deposited on the wall was determined experimentally and theoretically for various impingement angles with the help of a flat fan spray directed against the wall. The deposition fraction shows a distinct minimum in the range of intermediate impingement angles. This fact cannot be described by single-droplet-based deposition-splash criteria when considering the droplet’s impact momentum alone. The investigation demonstrates that the measurement results can be explained by including the collision of splashed droplets with incoming ones. In principle, the entrainment of the primary spray’s fine fraction in the gas flow field may also be of relevance. For the coarse and relatively sparse sprays investigated, the importance of the collisions in determining the overall balance of deposited and splashed liquid was estimated by event statistics derived from Monte Carlo simulations. The main outcome of wall interaction for the coarse spray is splashing. The splashed droplets form a secondary spray. When the impingement angle is steep, the splashed liquid is redirected towards the wall as a result of the collision between the incoming primary spray and splashed droplets.     

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.     

Unsteady flow around impacting bluff bodies

The flow resulting from the collision without rebound of generic bluff bodies with a wall in a still viscous fluid is investigated both computationally and experimentally. Emphasis is on the case of a circular cylinder impact (two-dimensional geometry), but comparisons with the flow generated by the impact of a sphere (axisymmetric geometry) are included. For normal cylinder impacts, the two counter-rotating vortices forming behind the body during its motion continue their trajectory towards the wall after the collision, leading to the generation of opposite-signed secondary vorticity at the cylinder and wall surfaces. Secondary vortices forming from this vorticity at higher Reynolds numbers exhibit a short-wavelength three-dimensional instability. Comparison with the sphere impact reveals significant differences in the scales of the vortices after the collision, due to the additional vortex stretching acting in the axisymmetric geometry. This leads to a delay in the onset of three-dimensionality and to a different instability mechanism. Oblique cylinder impacts are also considered. For increasing impact angles, the wall effect is gradually reduced on one side of the cylinder, which favours the roll-up of the secondary vorticity and increases the rebound height of the vortex system.     

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.     

Contribution to 3D impact problems: collisions between two slender steel barsUne contribution aux problèmes d'impact en trois dimensions : collisions entre deux barres élancées

This Note deals with the three-dimensional phenomenon of collision between two slender steel bars. The problem posed is whether the restitution concept developed in rigid-body theory is relevant in the case of such slender contactors. Some elements of an answer are provided through the use of two complementary approaches of collision, a theoretical one based on coefficients of restitution and series of experiments. Our main conclusion is that the alleged Newton coefficient of restitution varies according to the impact location on the rods. To cite this article: C. Le Saux et al., C. R. Mecanique 332 (2004).     

Breakup of a droplet at high velocity impacting a solid surface

We have studied the collision between a droplet of different liquids with high impact energy and a solid plate with varied surface roughness, which is characterized by a dimensionless Weber number (We, defined as the impact inertia of the droplet normalized by its surface force) extending up to 12,000 for water. To make such collision, a technique was developed to generate a single droplet with speed up to 42 m/s, which was initially driven by upstream air flow through a nozzle and accelerated to nearly the same velocity of the high-speed flow downstream. Via a high-speed photographing system, the various splashing mechanisms were investigated and a specific prompt splash on a smooth plate was found at sufficiently high We, which was different somehow from the conventionally defined one that was generally believed to occur only on a rough surface. The radius when multiple secondary droplets were shed out of the rim of the expanding lamella was found to scale almost invariantly with We at large values, whereas the coupled effect of liquid viscosity might affect the ultimate value.