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.     

Numerical study on the dynamics of droplet passing through a cylinder obstruction in confined microchannel flow

The droplet dynamics passing through a cylinder obstruction was investigated with direct numerical simulations with FE-FTM (Finite Element-Front Tracking Method). The effect of droplet size and capillary number (Ca) was studied for both Newtonian and viscoelastic fluids. In the case of Newtonian droplet immersed in Newtonian medium, the droplet breakup induced by the geometric hindrance depends on the droplet size. As Ca increases, the short droplets (1.3 times longer than the channel width) break up while passing through the obstruction. However, the breakup does not occur for longer droplets (1.8 times longer than the channel width). When the viscoelastic fluid characterized by the Oldroyd-B model is considered, the Newtonian droplet immersed in viscoelastic medium breaks up into two smaller droplets while passing through the cylinder obstruction with increasing De_m (Deborah number of the medium). We also show that the normal stress difference plays a key role on the droplet breakup and the droplet extension. The normal stress difference is enhanced in the negative wake region due to the droplet flow, which also promotes droplet extension in that region. This numerical study provides information not only on underlying physics of the droplet flows passing through a cylinder obstruction but also on the useful guidelines for microfluidic applications.     

Droplet impact dynamics for two liquids impinging on anisotropic superhydrophobic surfaces

Droplet impingement experiments were performed on grooved hydrophobic surfaces with cavity fractions of 0, 80, and 93?% using droplets of water and a 50?%/50?% water/glycerol mixture. The influence of liquid viscosity, cavity fraction, and spreading direction, relative to the surface grooves, is explored qualitatively and quantitatively. The maximum droplet spread diameter, velocity of the rebounding jet, and the time delay between droplet impact and jet emission were characterized for Weber numbers, We, based on droplet impact speed and diameter, up to 500. The unequal shear stresses and contact angles influence the maximum spread diameters in the two primary spread directions. At We?>?100, the ratio of the spread diameter along the direction of the grooves to the spread diameter perpendicular to the grooves increases above unity with increasing We. The maximum droplet spread diameter is compared to recent predictive models, and the data reveal differing behavior for the two fluids considered. The results also reveal the existence of very high relative jet velocities in the range 5????We????15 for water droplets, while such jets were not observed for the more viscous mixture. Further, in the range 115????We????265, the water/glycerol jet formation dynamics are radically different from the water behavior. Most evident is the existence of two-pronged jets, which arise from the anisotropy of the surface and the unequal shear stresses and contact angles that prevail on the surfaces. It is these influences that give rise to differences in the maximum spread diameters in the two primary spread directions. Similar two-pronged jet emission was observed for water over the very narrow range of We from 91 to 96. The issuing jet velocities were also observed to increase with increasing cavity fraction for both fluids and over the entire range of We explored. Lastly, the elapsed time between droplet impact and jet emission decreased with increasing cavity fraction.     

Droplet formation in quickly stretched liquid filaments

Film splitting necessarily occurs in roll coating and unwanted droplets can occur at high machine speeds when the resulting filaments break up. To study this ‘misting’ problem, an apparatus was designed and built to simulate filament fluid mechanics. The device creates a filament by elongating a liquid bridge and stretches the filament at a high and constant rate of acceleration to mimic coating machine kinematics. Filament breakup was observed using a high-speed video camera and the images were analyzed to yield droplet size and number. With Newtonian fluids, a single droplet formed at Ohnesorge (Oh) numbers less than 0.1 and more and smaller droplets were produced at Oh numbers above 0.1. Associative polymer solutions, prepared as weakly elastic fluids to represent industrial coatings, produced even more and smaller droplets, but only for Ohnesorge numbers in the range of 0.01 to 0.1.     

Temporal analysis of breakup for a power law liquid jet in a swirling gas

The breakup mechanism and instability of a power law liquid jet are investigated in this study. The power law model is used to account for the non-Newtonian behavior of the liquid fluid. A new theoretical model is established to explain the breakup of a power law liquid jet with axisymmetric and asymmetric disturbances, which moves in a swirling gas. The corresponding dispersion relation is derived by a linear approximation, and it is applicable for both shear-thinning and shear-thickening liquid jets. Analysis results are calculated based on the temporal mode. The analysis includes the effects of the generalized Reynolds number, the Weber number, the power law exponent, and the air swirl strength on the breakup of the jet. Results show that the shear-thickening liquid jet is more unstable than its Newtonian and shear-thinning counterparts when the effect of the air swirl is taken into account. The axisymmetric mode can be the dominant mode on the power law jet breakup when the air swirl strength is strong enough, while the non-axisymmetric mode is the domination on the instability of the power liquid jet with a high We and a low Re _n . It is also found that the air swirl is a stabilizing factor on the breakup of the power law liquid jet. Furthermore, the instability characteristics are different for different power law exponents. The amplitude of the power law liquid jet surface on the temporal mode is also discussed under different air swirl strengths.     

Spreading of inkjet droplet of non-Newtonian fluid on solid surface with controlled contact angle at low Weber and Reynolds numbers

The dynamics of inkjet droplet of non-Newtonian fluid on glass substrates was investigated experimentally and compared with that of Newtonian fluid. The non-Newtonian fluids used here were 100 ppm solutions of polyethylene oxide (300k, 600k and 900k) dissolved in the 1:1 mixture of water and glycerin. Weber number (We) was 2–35 and Ohnesorge number was fixed at 0.057 ± 0.003. The wettability of solid substrate was also varied. The diameter of inkjet droplets in the present study was about 50 μm and was much smaller than the size of the previous studies on drop impact. Due to the development of a thin and long thread at the rear of the main drop the jetting window of polymer solution was much narrower than that of Newtonian fluid, and hence the experimental range of Weber number was restricted. The impact scenarios of non-Newtonian inkjet droplets were found to be qualitatively different from those of Newtonian droplets during the receding phase while they were almost the same as the Newtonian fluid case during the kinematic phase. The spreading diameter at the equilibrium was well correlated with the modified Weber number (We′ = We/(1 − cos θ_eq)) as in the case of Newtonian fluid, where θ_eq is the equilibrium contact angle. The similarity or disparity between the Newtonian and non-Newtonian cases was discussed considering the conformation of polymer chains during each stage of drop deformation.     

液体环轴对称抛洒首次破碎的理论分析

对于水和无水乙醇环形轴对称抛洒实验的首次破碎结果的分析表明，在给定实验条件下，液体密度大约是气体的1000倍，液体首次破碎的过程分2个阶段:首先，界面不稳定性非线性发展，液体尖钉在惯性力和空气阻力的作用下，拉伸变细变长；然后在射流不稳定性的作用下，断裂成液体珠串。这个理论分析给出的首次破碎的平均液体直径与实验结果基本一致。理论分析表明，无水乙醇破碎液滴的平均直径比水液滴小，是无水乙醇表面张力值仅为水的1/3的一个必然结果。     

An experimental study of a water droplet impinging on a liquid surface

An experimental study is presented for water droplet impingement on a liquid surface. The impaction process was recorded using a high-speed digital camera at 1,000 frames/s. The initial droplet diameter was fixed at 3.1 mm ± 0.1 mm, and all experiments were performed in atmospheric air. The impact velocity was varied from 0.36 m/s to 2.2 m/s thus varying the impact Weber number from 5.5 to 206. The impacted liquid surface consisted of two fluids, namely water and methoxy-nonafluorobutane, C₄F₉OCH₃ (HFE7100). The depth of the water and HFE7100 pool was varied from 2 mm to 25 mm. The collision dynamics of water in the HFE7100 pool was observed to be drastically different from that observed for the water droplet impingement on a water pool. The critical impact Weber number for jet breakup was found to be independent of liquid depth. Water–HFE7100 impact resulted in no jet breakup over the range of velocities studied. Therefore, no critical impact Weber number can be defined for water–HFE7100 impact. Received: 27 June 2001/Accepted: 29 November 2001     

Bag breakup of nonturbulent liquid jets in crossflow

An experimental investigation of the bag breakup of round nonturbulent liquid jets in gaseous crossflow at room temperature and pressure is described. Pulsed photography, pulsed shadowgraphy, and high-speed imaging were used to observe the column and surface waves along the liquid jet and the formation and breakup of bags. Measurements included: wavelengths of column and surface waves, jet velocities, the number of bags along the liquid jet, the number of nodes per bag, droplets sizes and velocities, and trajectories of droplets. Present results show that the column waves of a nonturbulent liquid jet in crossflow within bag breakup regime can be explained based on Rayleigh–Taylor instability. The number of nodes per bag affected the breakup mechanism of the bags. Three distinctive sizes of droplets were produced due the breakup of the bag membrane, the ring strings and the ring nodes. The size of the droplets resulting from the breakup of the bag membrane was constant independent of the crossflow Weber number. Finally different trajectories were observed for the three groups of droplets.     

Nonlinear modeling of drop size distributions produced by pressure-swirl atomizers

An axisymmetric boundary element method (BEM) has been developed to simulate atomization processes in a pressure-swirl atomizer. Annular ligaments are pinched from the parent sheet and presumed to breakup via the linear stability model due to Ponstein. Corrections to Ponstein’s result are used to predict satellite droplet sizes formed during this process. The implementation provides a first-principles capability to simulate drop size distributions for low viscosity fluids. Results show reasonable agreement with measured droplet size distributions and the predicted SMD is 30–40% smaller than experiment. The model predicts a large number of very small droplets that cannot typically be resolved in an experimental observation of the spray. A quasi-3-D spray visualization is presented by tracking droplets in a Lagrangian fashion from their formation point within the ring-shaped ligaments. A complete simulation is provided for a case generating over 80,000 drops.     

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.     

Dynamics and Breakup of Pulse Microjets of Polymeric Liquids

The possibilities of controlling the dynamics and breakup of pulsed low-viscosity liquid microjets by means of small amounts of polymeric additives are considered. Significant differences between the breakup of pulse jets of Newtonian and viscoelastic polymeric liquids are recorded by means of high-speed photography. In flight a standard Newtonian fluid jet fragments into many secondary droplets. Depending on the molecular parameters, for a polymeric liquid three variants of the behavior of the jet in flight are possible: (1) the jet tail fragments into several secondary droplets; (2) the entire tail flows into the leading drop without loss and a single drop is formed; (3) the drop ejected from the nozzle returns to the nozzle under the action of elastic internal stresses in the tail. Criteria for the transition from one regime of jet motion to another are proposed.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 45–63.Original Russian Text Copyright © 2005 by Bazilevskii, Meyer, and Rozhkov.     

剪切变稀流体液滴撞击疏水表面回弹现象及最大铺展的研究

非牛顿流体液滴撞击固体表面的行为广泛存在于多种工农业生产中, 然而目前相关研究主要关注牛顿流体, 非牛顿流变特性对液滴撞击动力学的影响机制还有待探索. 本文研究了纯剪切变稀流体(质量分数≤ 0.03%的黄原胶水溶液)液滴撞击疏水表面后的最大铺展及回弹行为. 通过高速摄像技术捕获液滴撞击疏水表面的运动过程及形态变化, 研究了液滴的铺展回缩过程. 实验结果表明, 在相同We下, 剪切变稀特性对液滴撞击疏水表面后的铺展阶段影响很小, 但对回缩阶段影响很大. 黄原胶浓度增加使得液滴依次表现出部分回弹、完全回弹和表面沉积三种不同的回弹行为. 利用能量守恒定律推导出了液滴能在疏水表面上回弹的临界无量纲高度ξ_c理论值. 发现牛顿流体与非牛顿流体液滴最大无量纲高度ξ_max均符合标度律ξ_max ~ αWe斜率随黄原胶浓度增大而减小. 基于有效雷诺数Re_eff, 提出了一种有效黏度μ_eff表达式, 并据此建立了剪切变稀流体的最大无量纲直径β_max预测模型. 该模型在较广We区间与实验测量值取得了良好一致.      

Nonlinear analysis of the surface tension driven breakup of viscoelastic filaments

The surface tension driven breakup of viscoelastic filaments into droplets is qualitatively different from that of Newtonian liquid filaments. Disturbances on filaments of dilute polymer solutions often grow to a configuration consisting of nascent droplets connected by a thin ligament; the breakup time for this configuration is much longer than that predicted by extensions of Rayleigh's linear stability theory. We present here a nonlinear analysis of surface tension driven breakup of viscoelastic filaments using two complementary approaches that given equivalent results: a transient finite element solution and a one-dimensional thin filament approximation. We show that significant nonlinear effects lead to the experimentally-observed nascent droplet-ligament configuration, and we predict the entire evolution of the filament profile. Agreement with available experimental data for profile evolution and breakup of jets of Newtonian fluids and dilute polymer solutions is excellent.     

Numerical investigation of turbulent-jet primary breakup using one-dimensional turbulence

Primary breakup to form droplets at liquid surfaces is an important fundamental process to study as it determines the initial properties of the dispersed phase, which affect mixing rates, secondary breakup, droplet collisions, and flow separation within the dispersed flow region. Primary breakup can be regarded as one of the least developed model components for simulating and predicting liquid jet breakup. However, it is of paramount importance in many technical applications, e.g. fuel injection in engines and spray painting. This paper presents a numerical investigation of primary breakup of a turbulent liquid jet in still air at standard conditions using the one-dimensional turbulence (ODT) modeling framework. ODT is a stochastic model that simulates turbulent flow evolution along a notional 1D line of sight by applying instantaneous maps to represent the effect of individual turbulent eddies on property profiles. An important feature of ODT is the resolution of all relevant scales, both temporal and spatial. The restriction to one spatial dimension in ODT permits affordable high resolution of interfacial and single-phase property gradients, which is key to capturing the local behavior of the breakup process and allows simulations at high Reynolds and Weber numbers that are currently not accessible to direct numerical simulations (DNS).This paper summarizes our extensions of the ODT model to simulate geometrically simple jet breakup problems, including representations of Rayleigh wave breakup, turbulent breakup, and shear-driven breakup. Each jet breakup simulation consists of a short temporal channel section to initialize a turbulent velocity profile at the nozzle exit followed by an adjacent jet section. The simulations are carried out for jet exit Reynolds number of 11,500, 23,000, 46,000 and 92,000 while the Weber number is varied within the range 10²–10⁷. We present results on breakup statistics including spatial locations of droplet release, droplet sizes and liquid core length. The results on primary breakup are compared to experimental results and models.     

Experimental study of atomization patterns produced by the oblique collision of two viscoelastic liquid jets

Experimental observations and analysis are presented for the formation and atomization of the fluid sheet created by obliquely colliding jets of viscoelastic fluids. Solutions of mono-disperse polystyrene (PS) in diethylphthalate and of poly-disperse polyethylene oxide (PEO) in glycerol/water mixtures were used to investigate the effects of fluid elasticity on the break-up patterns generated by the impact of two jets ejected from nozzles with an internal diameter of 0.85 mm. Various regimes of behaviour were identified which depend on the jet speed. The structures observed for these elastic fluids differ somewhat from those previously reported for Newtonian viscous fluids, and also show different behaviours depending on the degree of viscoelasticity. This study focuses on the periodic atomization, the so-called fishbone pattern, which occurs when the impinging jets form a liquid sheet which breaks up into a regular succession of ligaments and droplets. High-speed flash photography reveals that low concentrations of polymers significantly affect the evolution of the sheet and its fragmentation, the shapes of the ligaments, and the final drop sizes. The maximum fishbone angle is defined and shown to be a useful tool to describe the variation of the atomization pattern with polymer concentration. For the PS solutions the variation of maximum fishbone angle with reduced polymer concentration (c/c^*) follows a single master curve, but although the same is true for PEO with high molecular weights, the curves remain separate for low molecular weights. Observation of the fishbone patterns formed by the oblique impact of jets may provide a useful tool to observe and characterize inter-chain interaction in high speed extensional flow of polymer solutions.     

An Eulerian–Lagrangian hybrid model for the coarse-grid simulation of turbulent liquid jet breakup

In this paper we present a numerical model for the coarse-grid simulation of turbulent liquid jet breakup using an Eulerian–Lagrangian coupling. To picture the unresolved droplet formation near the liquid jet interface in the case of coarse grids we considered a theoretical model to describe the unresolved flow instabilities leading to turbulent breakup. These entrained droplets are then represented by an Eulerian–Lagrangian hybrid concept. On the one hand, we used a volume of fluid method (VOF) to characterize the global spreading and the initiation of droplet formation; one the other hand, Lagrangian droplets are released at the liquid–gas interface according to the theoretical model balancing consolidating and disruptive energies. Here, a numerical coupling was required between Eulerian liquid core and Lagrangian droplets using mass and momentum source terms. The presented methodology was tested for different liquid jets in Rayleigh, wind-induced and atomization regimes and validated against literature data. This comparison reveals fairly good qualitative agreement in the cases of jet spreading, jet instability and jet breakup as well as relatively accurate size distribution and Sauter mean diameter (SMD) of the droplets. Furthermore, the model was able to capture the regime transitions from Rayleigh instability to atomization appropriately. Finally, the presented sub-grid model predicts the effect of the gas-phase pressure on the droplet sizes very well.     

Simulation of liquid jet primary breakup: Dynamics of ligament and droplet formation

Primary atomization of liquid injected at high speed into still air is investigated to elucidate physical processes by direct numerical simulation. With sufficient grid resolution, ligament and droplet formation can be captured in a physically sound way. Ligament formation is triggered by the liquid jet tip roll-up, and later ligaments are also produced from the disturbed liquid core surface in the upstream. Ligament production direction is affected by gas vortices. Disturbances are fed from the liquid jet tip toward upstream through vortices and droplet re-collision. When the local gas Weber number is O(1), ligaments are created, thus the ligament or droplet scale becomes smaller as the bulk Weber number increases. Observation of droplet formation from a ligament provides insights into the relevance between the actual droplet formation and pinch-off from a slow liquid jet in laboratory experiments. In the spray, the dominant mode is the short-wave mode driven by propagative capillary wave from the ligament tip. An injection nozzle that is necessary for a slow jet is absent for a ligament, thus the long-wave (Rayleigh) mode is basically not seen without the effect of stretch. By the present simulation, a series of physical processes have been revealed. The present result will be extended to LES modeling in the future.     

Application of maximum entropy method for droplet size distribution prediction using instability analysis of liquid sheet

This paper describes the implementation of the instability analysis of wave growth on liquid jet surface, and maximum entropy principle (MEP) for prediction of droplet diameter distribution in primary breakup region. The early stage of the primary breakup, which contains the growth of wave on liquid–gas interface, is deterministic; whereas the droplet formation stage at the end of primary breakup is random and stochastic. The stage of droplet formation after the liquid bulk breakup can be modeled by statistical means based on the maximum entropy principle. The MEP provides a formulation that predicts the atomization process while satisfying constraint equations based on conservations of mass, momentum and energy. The deterministic aspect considers the instability of wave motion on jet surface before the liquid bulk breakup using the linear instability analysis, which provides information of the maximum growth rate and corresponding wavelength of instabilities in breakup zone. The two sub-models are coupled together using momentum source term and mean diameter of droplets. This model is also capable of considering drag force on droplets through gas–liquid interaction. The predicted results compared favorably with the experimentally measured droplet size distributions for hollow-cone sprays.     

Spray features in the near field of a flow-blurring injector investigated by high-speed visualization and time-resolved PIV

In a flow-blurring (FB) injector, atomizing air stagnates and bifurcates at the gap upstream of the injector orifice. A small portion of the air penetrates into the liquid supply line to create a turbulent two-phase flow. Pressure drop across the injector orifice causes air bubbles to expand and burst thereby disintegrating the surrounding liquid into a fine spray. In previous studies, we have demonstrated clean and stable combustion of alternative liquid fuels, such as biodiesel, straight vegetable oil and glycerol by using the FB injector without requiring fuel pre-processing or combustor hardware modification. In this study, high-speed visualization and time-resolved particle image velocimetry (PIV) techniques are employed to investigate the FB spray in the near field of the injector to delineate the underlying mechanisms of atomization. Experiments are performed using water as the liquid and air as the atomizing gas for air to liquid mass ratio of 2.0. Flow visualization at the injector exit focused on a field of view with physical dimensions of 2.3 mm × 1.4 mm at spatial resolution of 7.16 µm per pixel, exposure time of 1 µs, and image acquisition rate of 100 k frames per second. Image sequences illustrate mostly fine droplets indicating that the primary breakup by FB atomization likely occurs within the injector itself. A few larger droplets appearing mainly at the injector periphery undergo secondary breakup by Rayleigh–Taylor instabilities. Time-resolved PIV is applied to quantify the droplet dynamics in the injector near field. Plots of instantaneous, mean, and root-mean-square droplet velocities are presented to reveal the secondary breakup process. Results show that the secondary atomization to produce fine and stable spray is complete within a few diameters from the injector exit. These superior characteristics of the FB injector are attractive to achieve clean combustion of different fuels in practical systems.