Secondary atomization of water and isooctane drops impinging on tilted heated surfaces

The present paper reports an experimental study aimed at characterizing the effects of heat transfer on the secondary atomization, which occurs during droplet impact on hot surfaces at conditions reproducing those occurring at fuel injection in internal combustion engines. The experiments consider single isooctane and water droplets impacting at different angles on a stainless steel surface with known roughness and encompass a range of Weber numbers from 240 to 600 and heat transfer regimes from the film-vaporization up to the Leidenfrost regime. The mechanisms of secondary breakup are inferred from the temporal evolution of the morphology of the impact imaged with a CCD camera, together with instantaneous measurements of droplet size and velocity. The combination of a technique for image processing with a phase Doppler instrument allows evaluating extended size distributions from 5.5 μm up to a few millimetres and to cover the full range of secondary droplet sizes observed at all heat transfer regimes and impaction angles. Temporal evolution of the size and velocity distributions are then determined. The experiments are reported at impact conditions at which disintegration does not occur at ambient temperature. So, any alteration observed in droplet impact behavior is thermally induced. The analysis is relevant for port fuel injection systems, where droplets injected to impact on the back surface of the valves, behave differently depending on fuel properties, particularly when the use of alcohols is considered, even as an additive to gasoline.     

Improved droplet breakup models for spray applications

The current study examines the performance of two zero-dimensional (0D) aerodynamically-induced breakup models, utilized for the prediction of droplet deformation during the breakup process in the bag, multi-mode and sheet-thinning regimes. The first model investigated is an improved version of the widely used Taylor analogy breakup (TAB) model, which compared to other models has the advantage of having an analytic solution. Following, a model based on the modified Navier–Stokes (M-NS) is examined. The parameters of both models are estimated based upon published experimental data for the bag breakup regime and CFD simulations with Diesel droplets performed as part of this work for the multi-mode and sheet-thinning regimes, for which there is a scarcity of experimental data. Both models show good accuracy in the prediction of the temporal evolution of droplet deformation in the three breakup regimes, compared to the experimental data and the CFD simulations. It is found that the best performance of the two is achieved with the M-NS model. Finally, a unified secondary breakup model is presented, which incorporates various models found in the literature, i.e. TAB, non-linear TAB (NLTAB), droplet deformation and breakup (DDB) and M-NS, into one equation using adjustable coefficients, allowing to switch among the different models.     

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.     

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.     

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.     

Breakup of Newtonian and non-Newtonian fluids in air jets

The breakup of droplets of non-Newtonian fluids has been investigated by high speed photography and impaction following preliminary results of Newtonian fluids, which confirmed the suitability of the measurement techniques. Single droplets with diameters from 2.4 to 3.3 mm, were arranged to fall under gravity into a jet of air with velocities up to 36o m/s. The droplets of Newtonian fluids, water and Diesel oil, were atomised in the expected manner within three main regimes characterised by the Weber number of the droplet and air jet conditions, while similar droplets of non-Newtonian fluids were found not to atomise but to develop under shear and stretching into ligaments of fluid separated from a local region of their surface; these ligaments were elongated until breakup occurred, though not into small droplets as with the Newtonian fluids. Some of the non-Newtonian fluids (TEP with 7.5% and lo% K125, with and without water) were found not to break up at the maximum speed of the tests and they will be re-examined at higher jet velocities. Increase in the concentration of K125 in TEP resulted in higher critical speed for a given droplet diameter.The authors would like to thank Prof. J. H. Whitelaw of Imperial College for many discussions and useful suggestions during the course of this work, and Dr. G. Cambray of CBDE for his valuable administrative support     

An experiment on the breakup of impinging droplets on a hot surface

Breakup characteristics of liquid droplets impinging on a hot surface are investigated experimentally with the wall temperatures in the Leidenfrost temperature range of 220–330°C for n-decane fuel. Factors influencing droplet breakup are wall temperature, impinging velocity, droplet diameter and impinging angle. The 50% breakup probability shows that the impinging velocity decreases linearly with the droplet diameter increase and there exists an optimum impinging angle near 80° having the minimum value in the impinging velocity for given wall temperature and droplet size. Near the wall temperature of 250°C corresponding to the Leidenfrost temperature, a peculiar nonlinear behavior in the breakup probability is observed.This work was supported by the Turbo and Power Machinery Research Center, Seoul National University.     

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.     

A multiphysics model for charged liquid droplet breakup in electric fields

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

Experimental investigation of the impaction of water droplets on cylindrical objects

The impaction of water droplets on isothermal cylindrical wires has been investigated experimentally in the present study. Mono-size droplets of 110, 350 and 680 μm in diameter were generated using piezoelectric droplet generators. The effects of droplet velocity and wire size were varied parametrically to reveal the impacting phenomena. Typical modes of the impaction outcome are disintegration and dripping. For droplets impacting on small wires, finer drops are disintegrated if the impacting droplet velocity is high, and larger dripping drops are observed if the velocity is low. For droplets impacting on large wires, bigger pendent drops are gradually formed which would eventually detach from the wires under the influence of gravity. In addition, droplets impacting on wires with waxy surface generate smaller dripping drops than that of the non-waxed wires. A non-dimensional regime map and new formulations in terms of the droplet Weber number, the wire Bond number and the size ratio of the wire diameter to incoming droplet diameter have been established to identify the regime for each mode of outcome and to predict the size of the dripping drops within the experimental limits.     

The Motion Behavior of a Group of Charged Droplets in Liquid-Liquid Electrostatic Spray

The droplet sizes and electrical charges under different applied electrical voltages are experimentally measured for a liquid-liquid electrostatic spray system. Considering droplet size and charge distributions, the two-dimensional motion for a group of charged droplets in a liquid-liquid electrostatic atomization system is simulated. From measured droplet size and charge distributions, the simulation can obtain the velocities and positions in a two-dimensional domain for all simulated droplets at different times. The various forces acting on droplet as well as their effects on droplet velocity and trajectory are analyzed and the liquid-liquid electrostatic atomization characteristics are revealed. In addition, for one-dimensional motion trajectory of larger droplet, the comparison between simulation and experiment is also conducted and a general agreement can be obtained.     

Study of the shock-induced acceleration of hexane droplets

An experimental study of the interaction of a shock wave with a hexane droplet is presented. The main goal of the experiments was to record images of the process and measure basic parameters describing movement, dispersion and evaporation of the droplets engulfed by a shock wave propagating in air. A shock tube with a visualization section was used for this research. Photography of the process allowed one to measure the positions, velocities and sizes of mist clouds created by the interaction processes. Analysis of the pictures shows that there is no qualitative difference between cases for different size droplets, but shock Mach number had a significant effect on the process. Quantitative analysis shows that under certain conditions, a catastrophic breakup mechanism of dispersion occurred. The droplets are shattered into a mist cloud before they achieve mechanical equilibrium with the surrounding gas. The approximate time for the complete dispersion and acceleration of the fuel droplet varies from 300 to 500 μs, and depends both on the droplet diameter and shock velocity. The dispersion time is controlled principally by the droplet diameter, and to a lesser extent, the shock Mach number. This paper is based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.     

Experimental investigation of viscous effects upon a breakup of droplets in high-speed air flow

The deformation and disintegration of water and silicone oil droplets were investigated experimentally in a shock tube. Optical visualization was performed by means of the shadowgraph method. Droplets with diameters in the range of 200 to 500 m were generated by an oscillating capillary. The smallest Weber number in the present experiments is close to the critical value of the breakup. The droplets disintegrated in the stamen or bag mode for moderate values of the Weber number. The effect of the viscosity of the liquid on the breakup mode and the breakup time is discussed.     

Shock wave interactions with particles and liquid fuel droplets

Shock waves traveling through a multiphase flow environment are studied numerically using the Flux Corrected Transport (FCT) algorithm. Both solid particles and liquid droplets are used as the dispersed phase with their trajectories being computed using a Lagrangian tracking scheme. The phases are coupled by including source terms which account for mass transfer, momentum, and energy exchange from the dispersed phase in the governing equations of motion for the gas phase. For solid particles, droplet size effects are examined at constant mass loading. Deceleration of the shock wave is observed with effects increasing with decreasing particle size. The equilibrium velocity attained is found to agree with analytical results for an equivalent dense gas with a modified specific heat ratio. For liquid droplets, a droplet breakup model is introduced and the results show a faster attenuation rate than with the solid particle model. The inclusion of vaporization to the breakup model is seen to increase the attenuation rate but does not alter the final equilibrium velocity. When an energy release model is used in the simulations, behavior resembling a detonation is observed under certain conditions, with energy release coupling with and accelerating the shock front. Received 17 July 2000 / Accepted 20 August 2002 / Published online 4 December 2002 Correspondence to: Dr. K. Kailasanath (e-mail: kailas@lcp.nrl.navy.mil)     

Multiscale simulations and experiments on water jet atomization

Numerical simulation of primary atomization at high Reynolds number is still a challenging problem. In this work a multiscale approach for the numerical simulation of liquid jet primary atomization is applied, using an Eulerian-Lagrangian coupling. In this approach, an Eulerian volume of fluid (VOF) method, where the Reynolds stresses are closed by a Reynolds stress model is applied to model the global spreading of the liquid jet. The formation of the micro-scale droplets, which are usually smaller than the grid spacing in the computational domain, is modelled by an energy-based sub-grid model. Where the disruptive forces (turbulence and surface pressure) of turbulent eddies near the surface of the jet overcome the capillary forces, droplets are released with the local properties of the corresponding eddies. The dynamics of the generated droplets are modelled using Lagrangian particle tracking (LPT). A numerical coupling between the Eulerian and Lagrangian frames is then established via source terms in conservation equations. As a follow-up study to our investigation in Saeedipour et al. (2016a), the present paper aims at modelling drop formation from liquid jets at high Reynolds numbers in the atomization regime and validating the simulation results against in-house experiments. For this purpose, phase-Doppler anemometry (PDA) was used to measure the droplet size and velocity distributions in sprays produced by water jet breakup at different Reynolds numbers in the atomization regime. The spray properties, such as droplet size spectra, local and global Sauter-mean drop sizes and velocity distributions obtained from the simulations are compared with experiment at various locations with very good agreement.     

圆环旋转黏性液体射流破碎液滴粒径与速度数量密度分布相关性研究

压力旋流喷嘴被广泛应用于航空发动机、船用发动机、车用汽油缸内直喷发动机、燃气轮机等动力机械的燃油喷射系统中.以压力旋流喷嘴射流为研究对象,开展了圆环旋转黏性液体射流破碎液滴粒径与速度数量密度分布相关性问题研究.对于液体射流,以往的研究往往对破碎液滴粒径数量密度分布或速度数量密度分布进行单独研究,对于这两种数量密度分布之间关系的研究较少;从相关性的角度对圆环旋转黏性液体射流破碎液滴粒径与速度数量密度分布之间的关系进行研究.采用最大熵原理方法建立了圆环旋转黏性液体射流破碎液滴粒径与速度联合概率密度函数.对圆环旋转黏性液体射流破碎液滴粒径与速度联合概率密度函数进行了讨论,对圆环旋转黏性液体射流破碎液滴粒径数量密度分布与速度数量密度分布的相关性问题进行了研究.研究结果表明,为了给出正确的圆环旋转黏性液体射流破碎液滴粒径与速度联合概率密度函数,射流守恒约束条件中必须同时包括质量守恒定律、动量守恒定律以及能量守恒定律;破碎液滴粒径的数量密度分布与速度数量密度分布密切相关;射流旋转强度对破碎液滴粒径数量密度与速度数量密度分布结构影响不大,对破碎液滴粒径数量密度和速度数量密度的分布区域影响较大.      

Numerical simulation of the deformation and breakup of a two-core compound droplet in an axisymmetric T-junction channel

The rheological behaviors of a compound droplet in a confined geometry are of importance in many industrial and natural processes. However, a detailed numerical simulation of the finite deformation and its transition to the breakup of the multi-core compound droplet in an axisymmetric T-junction channel is still lacking. The present study is to fill this gap through the numerical simulations of a two-core compound droplet that deforms and breaks up in this channel configuration. The numerical results are obtained by the axisymmetric front-tracking method. Our new finding is that the compound droplet in the channel can experience the finite deformation or the breakup depending on the flow condition or the configuration of the channel. In the finite deformation mode (i.e. non-breakup mode), the droplet rapidly reaches the maximum deformation before approaching the perpendicular rigid wall. The most deformation occurs with the outer droplet, and the inner droplet closer to the wall is less deformed than the other inner core droplet. In the breakup mode, three breakup patterns are recognized: (i) breakup type I occurring when breaking up only the outer droplet; (ii) breakup type 2 occurring when breaking up only the inner droplets; (iii) breakup type 3 occurring when breaking up both inner and outer droplets. The transition from the non-breakup mode to the breakup mode is available when increasing the Reynolds number Re (from 0.16 to 40.0), the capillary number Ca (from 0.04 to 4.0), the size R_o of the outer droplet and the middle-to-outer fluid viscosity ratio μ₂₁, or decreasing the size R_i of the inner droplets, the radial size C₂ of the channel (normalized by the channel axial size C₁) and the interfacial tension ratio of the inner to the outer droplets. The transition diagrams based on some of these parameters are also proposed to provide a more complete picture of the two-core compound droplet behaving in the axisymmetric T-junction channel..     

Numerical study of a compound droplet moving toward a rigid wall in an axisymmetric channel

Dynamical behaviors of compound droplets including those interacting with rigid walls in an axisymmetric channel appear in various industrial and natural processes. However, so far, no detailed investigation has been carried out for such interactions of compound droplets. Motivating from this missing gap, we here numerically study the finite deformation and breakup of an initially concentric compound droplet when it moves toward a rigid wall at the bottom of an axisymmetric vertical channel. The method used is a finite difference-based front-tracking method. The numerical results reveal that when the compound droplet is delivered toward the wall, it is deformed and can break up into smaller droplets. For the cases of finite deformation (i.e. non-breakup), while the outer droplet is radially stretched, the inner droplet first moves downward in the direction of the outer flow but then gets back. Thereby, a thin film is created between the outer and inner interfaces at the droplet top and thus prevents the outer droplet further deforming and breaking up. In contrast, if breakup happens, the outer droplet is further stretched, and most of the middle fluid moves outward toward the outer droplet edge to form a blob. Breakup can be available in one of three patterns: off-axis breakup, on-axis breakup, and inner breakup. The off-axis breakup mode only happens with the outer droplet while the inner breakup mode is only for the inner droplet. Various parameters are investigated to show the transition between a non-breakup mode to a mode of breakup. Such parameters contributing the transition include the Capillary number Ca (varied in the range of 0.01–2.5), the channel aspect ratio (varied in the range of 0.4–2.0), the ratio of the inner to outer droplet radii (varied in the range of 0.3–0.8), the droplet size relative to the channel size (varied in the range of 0.2–0.9), the interfacial tension ratio of the inner to outer interfaces (varied in the range of 0.1–4.0), and the viscosity ratio of the middle to outer fluids (varied in the range of 0.16–6.3). In contrast, some others, e.g. the Reynolds number, the viscosity ratio of the inner to the outer, do not induce any transition. From the numerical results, regime diagrams of breakup and non-breakup based on these parameters are proposed.     

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.