Penetration length and diameter development of vortex rings generated by impacting water drops

The formation of water drops underneath nozzles was studied numerically to provide the basis for repeatable experimental drop formation. The drops detached from the nozzle and impacted on a free water surface forming vortex rings. Experimental results obtained through kinematographic studies of the penetration and growth of these vortex rings are presented. Variations of the penetration depth were measured, depending on the nozzle height above the water surface where the drops were formed. The experiments revealed that it is the state of oscillation at impact that defines the penetration length. Interesting variations of the vortex ring diameter with time were recorded. A good overall understanding of the behavior of the diameter variation was obtained when it was plotted as a function of the penetration depth.     

Effect of solidification on drop fragmentation in liquid–liquid media

 This paper presents results of experimental and analytical investigation on molten alloy drop fragmentation in water pool. Emphasis is directed towards delineating the roles which melt to coolant heat transfer and melt solidification play in the fragmentation process. The strong impact of coolant temperature upon fragmentation process is addressed. A set of 23 drop fragmentation experiments were performed, in which 8 experiments employed a low melting point alloy, cerrobend-70 and 15 experiments using Pb–Bi eutectic alloy as drop fluid. The results show strong impact of coolant temperature on particle size distribution of the fragmented drops. A linear stability analysis of the interface between the two liquid fluids with thin crust growing between them, is performed. A modified dimensionless Aeroelastic number, for Kelvin–Helmholtz instability, is obtained and used as a criteria for fragmentation of molten drops penetrating into another liquid coolant media with lower temperature. The nondimensionalized mean diameter of the fragmented particles is correlated with the Aeroelastic number. Received on 26 March 2000     

相近韦伯数条件下激波波后液滴初期变形的影响机制

以实验结合数值模拟与理论分析的方法,研究韦伯数在2 100~2 700区间内,不同组合流动参数对液滴破碎初期变形的影响与作用机制。实验中通过高速摄影捕捉到一系列具有明显差异的液滴变形模态,表明在相近韦伯数下液滴的初期变形仍受到气流速度、密度等具体流动参数的显著影响。以刚性球体替代液滴进行外流数值模拟,利用球体表面气动力分布推算出的液滴表面变形趋势与实际变形形态吻合,表明液滴的初期变形特征与外流流动分离和涡特征具有一致性。对流场和理论变形数据的分析显示,流动分离发展阶段和稳定阶段对液滴作用力以及它们所诱导的液滴变形特征存在很大差异;分离发展与液滴变形过程的特征时间之比可由气液密度比的平方根表示,它决定了液滴早期变形的基本形态。分离发展阶段所占时间比例越高,即实验中气液密度比越高,则液滴更倾向于发展出单个显著的环形突起,反之则趋于形成多个相对均衡的突起。     

Drop impingement on a deep liquid surface: study of a crater's sinking dynamicsImpact d'une goutte sur une surface liquide profonde : étude de la dynamique d'enfoncement du cratère

When there is a drop impact on a liquid surface, two phenomena can appear depending on the impact Weber number: either vortex generation or jet formation; in this paper the second behavior is dealt with. Based on the comparison of experimental and theoretical results, the dynamic of splashing drops on deep liquid surfaces is analyzed; this work focuses on the crater's evolution and its maximum. The liquids used are water and ethyl-alcohol. Drop impacts are made with various impact velocities by creating drops from several heights above the liquid surface. A straightforward model to describe and predict the crater's sinking evolution is proposed and agrees well with the experimental results over a range of Weber numbers from 50 to 1500. To cite this article: D. Brutin, C. R. Mecanique 331 (2003).     

Flow of oil–water emulsions through a constricted capillary

The flow of oil-in-water emulsions through quartz micro-capillary tubes was analyzed experimentally. The capillaries were used as models of connecting pore-throats between adjacent pore body pairs in high-permeability media. Pressure drop between the inlet and outlet ends of the capillary was recorded as a function of time, for several values of the volumetric flow rate. Several distinct emulsions were prepared using synthetic oils in deionized water, stabilized by a surfactant (Triton X-100). Two oils of different viscosity values were used to prepare the emulsions, while two distinct drop size distributions were obtained by varying the mixing procedure. The average oil drop size varied from smaller to larger than the neck radius. The results are presented in terms of the extra-pressure drop due to the presence of the dispersed phase, i.e. the difference between the measured pressure drop and the one necessary to drive the continuous phase alone at the same flow rate. For emulsions with drops smaller than the capillary throat diameter, the extra-pressure drop does not vary with capillary number and it is a function of the viscosity ratio, dispersed phase concentration and drop size distribution. For emulsions with drops larger than the constriction, the large oil drops may partially block the capillary, leading to a high extra pressure difference at low capillary numbers. Changes in the local fluid mobility by means of pore-throat blockage may help to explain the additional oil recovery observed in laboratory experiments and the sparse data on field trials.     

On the impact of viscous drops onto dry smooth surfaces

An experimental study of the impact of glycerol/water drops onto a dry glass surface at Reynolds and Weber numbers around the splashing/deposition threshold is presented. Some new observed phenomena that may shed further light on the mechanisms underlying air bubble entrainment and splashing for high-viscosity liquids are presented and discussed. The experiments were recorded with a high-speed camera using two complementary lighting setups that enhance the visualization of different features of the air entrainment phenomena: backlighting with a light diffuser and oblique lighting without diffuser. Besides the ring of micro-bubbles surrounding the central entrapped bubble and the cloud of bubbles entrained as a result of the interaction between a levitated thin film and the solid surface, which have been studied by other authors in previous works, a second ring of micro-bubbles that delimits the outer cloud of bubbles has been detected in our investigation. Attention is mainly focused on analyzing the dependency of the behavior of the two rings of micro-bubbles on the drop impact velocity, the ranges of the relevant dimensionless numbers in which the rings are formed and the existence, in certain impact conditions, of an abrupt increase in the size of the second ring, which substantially modifies the impact outcome.     

On the nonlinear stability of a swirling liquid jet

The nonlinear deformation and atomization of a rotating column is considered using an axisymmetric boundary element formulation. Swirl has been considered by superposing a potential vortex to the bulk flow of the jet. The resulting model has been shown to reproduce the classical linear result due to Ponstein and parametric studies are conducted in the nonlinear regime to determine wave shapes and droplet sizes. As with prior nonlinear column breakup studies, results indicate that satellite drops are formed from the main wave under virtually all conditions. The ratio of the main drop to satellite drop diameter is shown to be remarkably constant over a variety of wave numbers/column lengths thereby providing a potential approach to produce tightly controlled bimodal sprays.     

A rationally-based correlation of mean fragment size for drop secondary breakup

A correlation was derived for the Sauter mean diameter of fragments produced in the bag and multimode drop breakup regimes for drops having Ohnesorge numbers less than 0.1. Development of the correlation focused on the growth of capillary instabilities on the toroidal rim seen during the final stages of bag breakup. The model linked the time scale for drop breakup and the time scale associated with growth of the unstable waves. The instability scale was approximated from the results of linear stability theory for capillary waves on liquid cylinders. The drop breakup scale was based on correlations available in the literature for drops subjected to a rapid (relative to drop deformation time scales) rise in relative velocity. Though development focused on bag breakup, the resultant expression was also shown to correlate the multimode regime data reasonably well.     

Drop impact on a hot surface: effect of a polymer additive

The impact of a drop on a hot surface is studied for Weber numbers between 20 and 220, and wall temperatures between 120 and 180°C. Drops of pure water are compared with drops of a dilute polyethylene oxide water solution (0.02% M). The additive is shown to inhibit drop splashing, the ejection of secondary droplets and mist formation. As previously observed, the polymer can also prevent drops from bouncing off a cold wall. This is no longer true if the wall is above the dynamic Leidenfrost temperature, which is lower for the polymer solution.     

Collision of water drop on water

A series of experiments are performed to study the collision of a water drop with various impact velocities, ranged from 0 to 600 cm/s, onto a water surface. Three kinds of phenomena have been recorded. Two of them named “penetration” and “cleavage”, were observed for low impact velocity (up to 100 cm/s). Their common characteristics are that no obvious disturbances on the surface were observed during the colliding process. Namely no splashing jets nor obvious crater were observed. By penetration we mean that a drop fallen into water becomes a ring, which penetrates the water smoothly with a velocity of several centimeters per second. During the penetrating process no obvious change of its configuration was observed. The falling height corresponding to penetration is proportional to volume of the original drop. Some periodicity of the falling heights (corresponding to penetration) was revealed. The phenomenon named “cleavage” occurs when the impact velocity is other than that corresponding to penetration, then the drop cleaves into an “inverted cauliflower” after falling below the surface of water. It almost does not decend. By diffusing and slowly expanding it vanishes in the vessel water several minutes after. These two kinds of phenomena, as we know, have not been reported before. As the impact velocity approaches or exceeds 100 cm/s, the third kind of phenomena, the splash, appears. The diameter and depth of the crater occuring in the case of splash, together with the time for the crater to reach its maximum size, and the time for the rebounding column to begin to rise are given as functions of the falling height of the drop.     

The fate of soluble and insoluble surfactant monolayers subjected to drop impacts

Surfactant monolayers were formed on a water surface and subjected to water drops falling from a nozzle. Surface tension was measured during these experiments to determine the effect of the drop impacts on the surfactant monolayer. The purpose of this work was to determine whether monolayers can be altered by drop impacts without the formation of a splash. Accordingly, a small fall height was used to avoid drop splashes and concomitant surfactant loss by droplet ejection. The relevance of this work pertains to the fate of surfactant monolayers during rain events. Results are presented for a soluble and insoluble surfactant. The results show that the insoluble monolayer is virtually unaffected by the drops, indicating that the monolayer immediately reforms after the drop impact. The soluble monolayer shows significant changes in measured surface tension during droplet impact when the surfactant concentration is high.     

Investigation of binary drop rebound and coalescence in liquids using dual-field PIV technique

Experiments on binary drop collisions within an index-matched liquid were conducted for Weber numbers (We) in the range of 1–50. Drop pairs of water/glycerin mixture were injected horizontally into silicone oil and, due to gravitational effects, travelled on downward trajectories before colliding. A dual-field high-speed PIV measurement system was employed to quantify drop trajectories and overall collision conditions while simultaneously examining detailed velocity fields at the collision interface. Sequences of velocity and vorticity fields were computed for both larger and smaller fields of view. In the We range examined, both rebounding and coalescing behavior occurred. Coalescence was found to result from a combination of vortical flow within drops and strong drop deformation characteristic of higher We. Flow through the centers of opposing ring vortices, strengthened by drop deformation, enhanced drainage of the thin film in the impact region, leading to film rupture and coalescence. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

穿透现象和液滴形状的关系

拍摄了下落水滴周期性形变的照片，穿透现象（指水滴和水面碰撞后变成环状，穿入水中，直到池底）是在水滴为扁椭球形状或接近扁椭球形状时和水面碰撞发生的．表面张力是改变水滴形状的手段     

Vortex rings in radially confined domains

The dynamics of vortex rings generated within confined domains are relevant to important hydrodynamic processes such as flow past heart valves or severe arterial constrictions. However, despite their importance, these flows have not received much attention to date. This study examines the development and evolution of radially confined vortex rings. Time-resolved digital particle image velocimetry was used to investigate two levels of radial confinement and a range of vortex ring strengths. We found that for severely confined vortex rings, the formation time and peak circulation values were unaffected for L/D ₀?<?4 cases and slightly affected for larger L/D ₀ cases. After pinch-off, circulation decay was observed with an approximately constant normalized circulation decay rate. We found that with increasing circulation strength, the nondimensional time delay between the pinch-off and the onset of circulation decay reduced due to an increased vortex ring diameter within the confinement domain and a reduction in the necessary time for the surface induced and core vorticity regions to interact. This study uncovers the dynamics of radially confined vortex rings and show that the nondimensional rate of circulation decay is dependent on the vortex ring confinement ratio (ratio of the vortex ring orifice diameter to the diameter of the outer cylinder), and the time delay between the vortex pinch-off and the onset of circulation is dependent on the vortex ring circulation strength.     

带扰流小槽道内单相流动阻力特性实验

采用水作为工质, 实验研究入口或出口端加入圆柱扰流的不同高宽比多槽道散热器的压降特性; 结果表明: 单位长度压降随雷诺数成线性关系. 提出了雷诺数、水力学直径和槽道高宽比的拟合准则; 拟合公式在实验数据误差范围内很好反应类似系统的流阻特性. 对于线切割小槽道, 其摩阻系数和雷诺数成反比, 且较圆管理论值偏大; 对线切割槽道阻力特性分析发现, 表面粗糙度是其最主要的影响因素, 而扰流对其影响较小; 在槽道前部设置扰流柱可以增强换热.      

Numerical investigation of different modes of internal circulation in spherical drops: Fluid dynamics and mass/heat transfer

The results of detailed, three-dimensional numerical simulations of fixed spherical drops in a uniform flow are presented. The fluid dynamics outside and inside of the drops as well as the internal problem of mass (or heat) transfer are studied. Liquid drops in both a liquid and a gaseous ambient phase are considered. Special emphasis is put on the investigation of different modes of internal circulation.At low Reynolds numbers of the inner fluid, the flow field inside the drop resembles the well known Hill’s vortex solution. However, at higher internal Reynolds numbers, stable steady or quasi-steady alternative modes of internal circulation are found. As these modes are not cylindrical symmetric around the streamwise axis, the often applied assumption of a two-dimensional, axisymmetric flow field is not justified in these cases. Thus, major discrepancies to previous numerical studies are obtained. However, it is shown that experimental results support our findings.For liquid drops surrounded by a liquid, a major influence of the state of internal circulation on the drag is discovered, whereas the drag is nearly unaltered in the case of a liquid drop in gas.Concerning the internal problem of mass/heat transfer, the various internal flow modes show different characteristics. At low internal Peclet numbers, higher Sherwood numbers are reached for the Hill’s vortex-like cases, whereas at higher Peclet numbers, the transfer is faster for the alternative modes. For cases with a Hill’s vortex-like solution, asymptotic Sherwood numbers for very high Peclet numbers of around 20 are found, whereas no upper limit for cases with alternative modes can be determined. In the present study a maximum internal Sherwood number of 130 is reached, more than six times the maximum value for a case with a Hill’s vortex-like internal solution.     

Production of secondary drops during the single water drop impact onto a plane water surface

The normal impact of single water drops onto a plane water surface was studied experimentally to reveal the amount of secondary drops produced from the rim of crown-like interfacial structure. Within the experimental ranges tested, the ratio of the total mass of secondary drops to the mass of primary drop was approximately within 0–1 and correlated well as the function of dimensionless parameter K that consisted of the impact Weber number We and the Ohnesorge number Oh (K = We Oh ^−0.4). The dependences of the number and the mean diameter of secondary drops on K and dimensionless film thickness were also investigated.     

Experimental investigation on splashing and nonlinear fingerlike instability of large water drops

The fluid physics of the splashing and spreading of a large-scale water drop is experimentally observed and investigated. New phenomena of drop impact that differ from the conventional Rayleigh–Taylor instability theory are reported. Our experimental data shows good agreement with previous work at low Weber number but the number of fingers or instabilities begins to deviate from the R–T equation of Allen at high Weber numbers. Also observed were multiple waves (or rings) on the spreading liquid surface induced from pressure bouncing (or pulsation) within the impacting liquid. The first ring is transformed into a radially ejecting spray whose initial speed is accelerated to a velocity of 4–5 times that of the impacting drop. This first ring is said to be “splashing,” and its structure is somewhat chaotic and turbulent, similar to a columnar liquid jet surrounded by neighboring gas jets at relatively high impact speed. At lower impact speeds, splashing occurs as a crown-shaped cylindrical sheet. A second spreading ring is observed that transforms into fingers in the circumferential direction during spreading. At higher Weber number, the spreading of a third ring follows that of the second. This third ring, induced by the pressure pulsation, overruns and has fewer fingers than the second, which is still in a transitional spreading stage. Several important relationships between the drop impact speed, the spray ejection speed of the first ring, and the number of fingers of the second and third rings are presented, based on data acquired during a set of drop impact experiments. Issues related to the traditional use of the R–T instability are also addressed.     

Impact of buoyancy on vortex ring development in the near field

The development of a buoyant vortex ring in the near field was examined experimentally, and the findings were compared with those of a non-buoyant ring with a similar Reynolds number. The experiments were performed in a water tank, and the vortices were produced by a cylindrical tube of aspect ratio 2. Laser sheet flow visualization and PIV measurements were carried out. In the near field, the initial column of the buoyant fluid breaks down due to the presence of Rayleigh–Taylor instability at the buoyant fluid interface. Subsequently, a large diameter vortex ring with a large spreading rate, compared with the non-buoyant ring, emerges. The celerity of buoyant vortex continued to decrease throughout the range examined, in contrast to the constant celerity of the non-buoyant ring. The vorticity in the core of buoyant and non-buoyant vortex rings is symmetric and has a Gaussian distribution. However, the buoyant vortex ring evolves into a thin core ring, whereas the non-buoyant ring becomes a thick core ring shortly after the ring formation. This difference is brought on by the rapid entrainment and the significant growth of the buoyant ring following the breakup of the initial formation.