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.     

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。     

Experimental study of non-uniform inlet conditions and three-dimensional effects of vertical air–water two-phase flow in a narrow rectangular duct

To study the three-dimensional interfacial structure development in vertical two-phase flow, air–water upflow experiments were performed in a rectangular duct. Various non-uniform two-phase profiles were created by injecting air from individually controlled spargers at the duct inlet into uniformly injected water flow. A four-sensor conductivity probe was used to measure local void fraction, interfacial area concentration, bubble velocity and Sauter mean diameter at three axial locations to record the development of two-phase parameters. Experimental results showed that the lateral development across the wider dimension of the duct was significant with a non-uniform inlet profile when compared to a uniform inlet profile. It is postulated that lift, wall and turbulent forces are the major contributors to the lateral distribution of the two-phase interfacial structures making this an useful experiment for benchmarking three-dimensional two-fluid models. In examining the interfacial area, the shearing-off of group 1 bubbles (defined as the smaller spherical and distorted bubbles) from the skirt region of group 2 bubbles (defined as the bigger cap and churn bubbles), the coalescence of group 2 bubbles due to wake entrainment, and random collision are the major source and sink mechanisms of interfacial area concentration.     

DROPLET COLLISION AND COALESCENCE MODEL

A new droplet collision and coalescence model was presented,a quick-sort method for locating collision partners was also devised and based on theoretical and experimental results,further advancement was made to the droplet collision outcome. The advantages of the two implementations of smoothed particle hydrodynamics (SPH) method were used to limit the collision of droplets to a given number of nearest droplets and define the probability of coalescence,numerical simulations were carried out for model validation.Results show that the model presented is mesh-independent and less time consuming,it can not only maintains the system momentum conservation perfectly,but not susceptible to initial droplet size distribution as well.     

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.     

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.     

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.      

Transition between coalescence and bouncing of droplets on a deep liquid pool

This study focused on the bouncing of sub-millimetric droplets (below 0.7 mm) of three different fluids, distilled water, technical ethanol and 1-propanol on a deep liquid pool of the same fluids. Four different flow regimes including low-energy-collision coalescence, bouncing, high-energy-collision coalescence, and partial coalescence were observed in the experiments. These regimes were plotted in velocity-diameter diagrams, which showed that there was a diameter limit, D ≈ 0.2 mm, above which the low-energy-collision coalescence was inhibited. The contact time, in which the impinging droplets and the liquid surface interacted in the bouncing process, was studied, and the results showed the same characteristic time scale of the contact time as those of Richard et al. (in Nature 417, 2002, 811) and Thoroddsen and Takehara (in Phys. Fluids 12 (6), 2000, 1265–1267). The restitution coefficients for all fluids were investigated, and the water data agreed well with the values reported in the literature (Bach et al., J. Fluid. Mech. 518, 2004, 157–185; Jayaratne and Mason, Proc. R. Soc. Lond. A 280 (1383), 1964, 545–565). Based on stable restitution coefficients, which varied with fluids, the effects from both viscosity and surface tension were discussed. Further, a correlation (K = We · Oh^−0.58) was generalized to characterize the two transitions between coalescence (both high-energy- and low-energy-collision types) and bouncing, and a comparison with the model and data of Huang and Zhang (in Petrol Sci. 5, 2008, 62–66) showed that the generalized model characterized the coalescence-bouncing threshold well for the experimental fluids in the present study and oil with much higher viscosity.     

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...     

Large eddy simulation and experiment of shear breakup in liquid-liquid jet: Formation of ligaments and droplets

Understanding the shear breakup in jet flows and the formation of droplets from ligaments is important to determine the final droplet size distribution (DSD). The initial droplet size, which affects the final DSD, is considered to be generated by the shear breakup. Large eddy simulation (LES) was performed to investigate the shear breakup in liquid-liquid jet flows. The explicit Volume of Fluid (VOF) model with the geometric reconstruction scheme was used to capture the oil-water interface. The estimated oil distribution including wave peaks, ligaments, droplets and water streaks were compared to the experiments with a good agreement. The estimated DSD matched with the measurements favorably well. In the simulation, the formation of droplets with a smooth and curved surface from ligaments or sheet-like structures was obtained. Different mechanisms were observed along with the shear layer including the formation of droplets from ligament through the capillary forces, breakage of a droplet into smaller ones and attachment of a droplet to a ligament. The destructive shear forces and resisting surface tension forces were quantified on stretching and retracting ligaments. The influence of internal viscous force was found to be negligible due to low oil viscosity. The critical capillary number was found to be larger than 5.0 for ligaments breaking with the shear breakup. The capillary number was below unity for retracting ligaments. The coalescence of two equal-sized droplets was obtained in the shear breakup region. The shear stress magnitude at the contact region increased more than two folds. The total surface area decreased nearly 20% after the coalescence.     

Experiments on the dynamics of droplet collisions in a vacuum

Highly controlled experiments of binary droplet collisions in a vacuum environment are performed in order to study the collision dynamics devoid of aerodynamic effects that could otherwise obstruct the experimental observations by causing distortion or even disintegration of the coalesced mass. Pre-collision droplets are generated from capillary stream break-up at wavelengths much larger than those generated with the typical Rayleigh droplet formation in order to reduce the interactions among the collision products. Experimental results show that the range of droplet Weber number necessary to describe the boundaries between permanent coalescence and coalescence followed by separation is several orders of magnitude higher than has been reported in experiments conducted at standard atmospheric pressures with lower viscosity liquids (i.e. hydrocarbon fuels and water). Additionally, the time periods of both the oblate and prolate portions of the coalesced droplet oscillation have been measured and it is reported for the first time that the time period for the prolate portion of the oscillation grows exponentially with the Weber number. Finally, new pictorial results are presented for droplet collisions between non-spherical droplets. Received: 30 June 1998/Accepted: 15 October 1999     

Understanding droplet coalescence and its use to estimate interfacial tension

The study of coalescence of polymer droplets is presented in the viscosity ratio range (p) going from 0.1 to 10. It is shown that the determination of the characteristic time of coalescence is a good way to estimate the interfacial tension. Polydimethylsiloxane (PDMS) is mixed with polyisobutylene (PIB) and the temperature change provides a way to modify the interfacial tension of the PDMS/PIB system significantly, as measured using a pendant drop apparatus. We obtain a dependence of the reduced coalescence time as a function of p^-1/2 which gives access to the interfacial tension. This technique can be an interesting choice for estimating interfacial tension without requiring sophisticated techniques. In a further attempt to correlate these observations with a theoretical model (Verdier C (2001) Polymer 42), the flow field inside and outside the droplets is investigated. PIV measurements are carried out where the evidence of elongational regimes is demonstrated. Such experiments are also interesting for future comparisons with numerical results.     

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.     

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.     

水击谐波流场中乳化油液滴粒径的PIV测量

为了掌握乳化油液滴在水击谐波流场中的碰撞、破裂、聚集和变形等微观形态的变化规律,采用粒子图像测速(PIV)技术对水平方管中乳化油液滴的水击谐波流场进行了测量,分析了在水击谐波流场中,不同激振力作用下乳化油液滴的粒径变化。测量结果表明,在水击谐波流场作用下,乳化油液滴平均粒径的增长率随着激振力的减小而减小,随着作用时间的增大呈增加趋势,直至粒径处于一种动态平衡;乳化液滴随着激振力增大到达波节聚集位置的时间减少,可见增大水击谐波激振力有利于乳化液滴的聚集并合并为大尺度的液滴,从而有效地提高了水击谐波流场作用下的油水分离效果。     

Experimental study on local characteristics of oil–water dispersed flow in a vertical pipe

The local flow characteristics of oil–water dispersed flow in a vertical upward pipe were studied experimentally. The inner diameter and length of the test section are 40 mm and 3800 mm, respectively. A double-sensor conductivity probe was used to measure the local interfacial parameters, including interfacial area concentration, oil phase fraction, interfacial velocity, and oil drops Sauter mean diameter. The water flow rates varied from 0.12 m/s to 0.89 m/s, while the oil flow rates ranged from 0.024 m/s to 0.198 m/s. Typical radial profiles of interfacial area concentration, oil phase fraction, interfacial velocity, and oil drops Sauter mean diameter are presented. An interesting phenomenon is that the local and cross-section-averaged interfacial area concentrations display concave change with water flow rate under constant oil flow rate. The physical mechanism of such a variation is discussed in details.     

A modified SPH method to model the coalescence of colliding non-Newtonian liquid droplets

This paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non-Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas-to-liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head-on binary collision of vdW liquid droplets. Both Newtonian and non-Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off-center binary collision of non-Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non-Newtonian liquid droplets without tensile instability.     

Benchmarking of the one-dimensional one-group interfacial area transport equation for reduced-gravity bubbly flows

In order to properly design and safely operate two-phase flow systems, especially those deployed on future space missions, it is necessary to have accurate predictive capabilities. The application of a novel predictive method, the interfacial area transport equation (IATE), to dynamically predict the change of interfacial area concentration for reduced-gravity two-phase flows is described in this paper. Fluid particle interaction mechanisms such as coalescence and breakup that are present in reduced-gravity two-phase flows have been studied experimentally as reported in a previous paper by the current authors [Vasavada et al., 2007]. These mechanisms represent the source and sink terms in the IATE and their mechanistic models are benchmarked using experimental data obtained in a 25 mm inner diameter ground-based test section wherein reduced-gravity conditions were simulated. The comparison of the predictions from the model against experimental data shows good agreement. It has been found that, in contrast to the hypothesis extended in the literature, the wake entrainment based coalescence mechanism is present in reduced-gravity two-phase flows and in some cases is more important than coalescence due to random collision. Physics based arguments are extended to support this conclusion.     

The use of single-point measurements to characterize dynamic behavior in sprays

In an effort to derive dynamic information from a single-particle counting device such as the phase-Doppler interferometer (PDI), a one-dimensional motion model and a sequential sorting algorithm have been developed to calculate the distance and velocity difference between consecutive droplets in sprays, as well as the number of droplets in close proximity (grouplets) and the frequency of grouplet formation. By focusing on sprays that are primarily uni-directional, this model can be used to highlight dynamic behavior and provide information that may indicate tendencies for clustering, collision, coalescence or evaporation among the droplets – information that is not available when considering the histograms of droplet size and velocity normally produced by PDIs. The motion model and sorting algorithm are validated for a mono-sized droplet stream generated by piezo-electric excitation, and are then applied to two other sprays to determine dynamic behavior. For a pressurized-liquid nozzle emitting water, the expected trends of droplet deceleration and spatial dispersion are found moving away from the exit of the nozzle, and significant in velocity differences between closely-spaced droplet pairs are observed. No dominant frequencies are present in the grouping of the droplets. For a droplet-laden air jet excited at a known frequency, similar results are calculated for droplet spacing, grouping and velocity differences, and the driving frequency is also obtained from analysis of the sequentially-sorted PDI data. Although the models developed assume an idealized PDI system, real operating characteristics of PDI systems place limits on the accuracy of these analyses. Received: 10 October 1998/Accepted: 5 October 1999     

Deposition of micron liquid droplets on wall in impinging turbulent air jet

The fluid mechanics of the deposition of micron liquid (olive oil) droplets on a glass wall in an impinging turbulent air jet is studied experimentally. The spatial patterns of droplets deposited on a wall are measured by using luminescent oil visualization technique, and the statistical data of deposited droplets are obtained through microscopic imagery. Two distinct rings of droplets deposited on a wall are found, and the mechanisms of the formation of the inner and outer rings are investigated based on global diagnostics of velocity and skin friction fields. In particular, the intriguing effects of turbulence, including large-scale coherent vortices and small-scale random turbulence, on micron droplet deposition on a wall and coalescence in the air are explored.