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     

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.     

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.     

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.     

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.     

Modeling surface tension of a two‐dimensional droplet using smoothed particle hydrodynamics

Surface tension plays a significant role at the dynamic interface of free‐surface flows especially at the microscale in capillary‐dominated flows. A model for accurately predicting the formation of two‐dimensional viscous droplets in vacuum or gas of negligible density and viscosity resulting from axisymmetric oscillation due to surface tension is solved using smoothed particle hydrodynamics composed of the Navier‐Stokes system and appropriate interfacial conditions for the free‐surface boundaries. The evolution of the droplet and its free‐surface interface is tracked over time to investigate the effects of surface tension forces implemented using a modified continuous surface force method and is compared with those performed using interparticle interaction force. The dynamic viscous fluid and surface tension interactions are investigated via a controlled curvature model and test cases of nonsteady oscillating droplets; attention is focused here on droplet oscillation that is released from an initial static deformation. Accuracy of the results is attested by demonstrating that (i) the curvature of the droplet that is controlled; (ii) uniform distribution of fluid particles; (iii) clean asymmetric forces acting on the free surface; and (iv) nonsteady oscillating droplets compare well with analytical and published experiment findings. The advantage of the proposed continuous surface force method only requires the use of physical properties of the fluid, whereas the interparticle interaction force method is restricted by the requirement of tuning parameters.     

The effect of surfactants on the instability of a rotating liquid jet

It has long been known that the presence of surfactants on the free surface of a liquid jet can create surface tension gradients along the interface. The resulting formation of tangential stresses along the surface lead to Marangoni type flows and greatly affect the resulting dynamics of rupture. In this way surfactants can be used to manipulate the breakup of a liquid jet and control the size of droplets produced. In this paper we investigate the effects of insoluble surfactants on the breakup of rotating liquid jets with applications to industrial prilling. Using a long wavelength approximation we reduce the governing equations into a set of one-dimensional equations. We use an asymptotic theory to find steady solutions and then carry out a linear instability analysis on these solutions. We show that steady state centreline solutions are independent of viscosity to leading order and that the most unstable wavenumber and growth rate of disturbances decrease as the effectiveness of surfactants is increased. We also numerically solve these equations using a finite difference scheme to investigate the effects of changing the initial surfactant concentration and other fluid parameters. Our results show that differences in breakup lengths between rotating surfactant-laden jets and surfactant-free jets increase with the rate of rotation. Moreover, we find that satellite droplet sizes decrease as the rate of rotation is decreased with the effect of surfactants amplifying the reduction in sizes. Furthermore, the presence of surfactants at fixed rotation rates is shown to produce larger main droplets at low disturbance wavenumbers whilst satellite droplets are smaller for moderate disturbance wavenumbers κ≈0.7.     

Surface breakup of a non-turbulent liquid jet injected into a high pressure gaseous crossflow

We employ detailed numerical simulations to understand the physical mechanism underlying the surface breakup of a non-turbulent liquid jet injected transversely into a high pressure gaseous crossflow under isothermal conditions. The numerical observations reveal the existence of shear instability on the jet periphery as the primary destabilization mechanism. The temporal growth of such azimuthal instabilities leads to the formation of interface corrugations, which are eventually sheared off of the jet surface as sheet-like structures. The sheets next undergo disintegration into ligaments and drops during the surface breakup process. The proposed instability mechanism is inherently an inviscid mechanism, contrary to the previously suggested mechanism of surface breakup (known as “boundary layer stripping”), which is relied on a viscous interpretation. The numerically obtained length and time scales of the shear instabilities on the jet laterals are compared with the results of Behzad et al. (2015) on temporal linear stability analyses of a jet in crossflow at near the nozzle. The stability characteristics of the most amplified modes (i.e., the wavenumber and the corresponding growth rate) obtained from the numerical simulations and the stability analyses are in good agreement.     

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.     

Modeling the evolution of droplet size distribution in two-phase flows

A theoretical model is developed in the present study to simulate droplet motion and the evolution of droplet size distribution (DSD) in two-phase air/dispersed water spray flows. The model takes into account several processes which influence DSD and droplet trajectory: droplet collision and coalescence, evaporation and cooling, gravitational settling, and turbulent dispersion of dispersed phase. The DSDs determined by the model at different locations in a two-phase flow are evaluated by comparing them to experimental observations obtained in an icing wind tunnel. The satisfactory coincidence between simulation and experimental results proves that the model is reliable when modeling two-phase flows under icing conditions. The model is applied for two particular examples in which the modification of DSD is calculated in two-phase flows under conditions describing in-cloud icing and freezing drizzle.     

Study of the effects of the injector length/diameter ratio on the surface properties of turbulent liquid jets in still air using X-ray imaging

The disintegration of turbulent liquid jets in gases, a process termed turbulent primary breakup, has many industrial applications, especially in liquid injection systems whose injector internal flow results in enhanced turbulence generation. An investigation was carried out by using X-ray diagnostics at the Advanced Photon Source (APS) facility of Argonne National Laboratory on two injectors with a smooth entry followed by round passage with different length-to-diameter ratios of 10 and 40, operating at the same injection speed. The test matrix was designed to eliminate cavitation and to isolate the effect of length/diameter ratio of the injector passage and to determine the importance of jet turbulence compared to aerodynamic forces. The X-ray diagnostics used allowed the surface and internal topography of liquid jets to be visualized and the spatial distribution of the surface ligaments to be revealed in the near-injector region. The present results show that the separation distance between a ligament and its neighbors depends on the ligament sizes, and the injector length/diameter ratio affects the rates of breakup.     

Deformation and orientation of single droplets during shear flow: combined effects of confinement and compatibilization

Combined effects of geometrical confinement and compatibilization on the deformation and orientation of single droplets during steady-state shear flow are investigated in a counter-rotating cell by means of microscopic observations. The model system consists of polydimethylsiloxane droplets of varying sizes and viscosities in a polyisobutylene matrix. To this system, a premade polyisobutylene–polydimethylsiloxane block copolymer is added as compatibilizer in different concentrations. For each droplet, the equilibrium interfacial tension is determined by comparing droplet axes with the predictions of the confined Minale model for uncompatibilized droplets at the appropriate degree of confinement. Although large reductions in interfacial tension are seen for all compatibilized droplets, it is shown that the effect of compatibilization on droplet deformation and orientation can efficiently be taken into account in the equilibrium capillary number. This way, for all viscosity ratios and confinement ratios, steady-state data for compatibilized and uncompatibilized droplets coincide, and agree well with the predictions of the confined Minale model at sub-critical conditions. For near-critical capillary numbers, compatibilization slightly reduces droplet deformation and postpones breakup, irrespective of the degree of confinement.     

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.     

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.     

Droplet coalescence in the shear flow of model emulsions

During the flow of an emulsion, droplets of the dispersed phase can deform, break up, coalesce or migrate to other regions within the flow field. Understanding these different processes is relevant to morphology development in immiscible polymer blends. Here, emulsions of castor oil in silicone oil were employed to study shear-induced coalescence alone; the conditions chosen were such that drop breakup and drop migration did not occur. A cone-and-plate device and tubes of varying length were used to examine the influence of the average shear rate, the time of shearing, concentration of the dispersed phase, and temperature on the average droplet size. It was found that the extent of “demixing” was not influenced by the spatially non-homogeneous nature of flow in a tube; results correlated very well with the average shear rate. On the other hand, coalescence was significant even when the concentration of the dispersed phase was as low as 0.5%, and it became more important as the concentration was increased. Other results were that the extent of coalescence could be promoted by lowering the shear rate. In quantitative terms, it was found that available coalescence theory gave the correct order of magnitude for the average steady-state droplet size as a function of the imposed shear rate, but the actual variation of drop size with shear rate was gentler than that predicted by theory. An unusual observation was that, under some circumstances, the droplets did not coalesce but simply stuck to each other and maintained their separate identity. Received: 25 March 1999/Accepted: 22 July 1999     

Shock–Free Breakup of Droplets. Temporal Characteristics

In the present paper, we consider the shock–free breakup of droplets in their encounter with a layer (sheet) of a moving gas in the absence of pressure perturbations when the droplets are affected by a short U–shaped pulse of aerodynamic forces. Under a high pressure of the ambient gas medium p₀ = 20—80 bar, the droplets (ethanol or liquid oxygen) have a chance to break up after stay in a thing (2—5 mm thick) gas layer (jet) moving with a velocity of 1—10 m/sec. A distinctive feature of the process is that the characteristic time of droplet deformation and the period of natural oscillations coincide with the residence time for the droplets in the region of their interaction with the gas stream. Empirical formulas are proposed for determination of the total breakup time and the duration of the droplet disintegration stage in shock–free breakup.     

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 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.     

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.     

Three dimensional phase-field investigation of droplet formation in microfluidic flow focusing devices with experimental validation

In this paper, the droplet formation process at a low capillary number in a flow focusing micro-channel is studied by performing a three-dimensional phase field benchmark based on the Cahn–Hilliard Navier–Stokes equations and the finite element method. Dynamic moving contact line and wetting condition are considered, and generalized Navier boundary condition (GNBC) is utilized to demonstrate the dynamic motion of the interface on wall surface. It is found that the mobility parameter plays a very critical role in the squeezing and breakup process to control the shape and size of droplets. We define the characteristic mobility M_c to represent the correct relaxation time of the interface. We also demonstrate that the characteristic mobility is associated with the physical process and should be kept as a constant as the product of the mobility tuning parameter χ and the square of interfacial thickness ε². This criterion is applied for different interfacial thicknesses to correctly capture the physical process of droplet formation. Moreover, the size of the droplet, the velocity of the droplet along the downstream, and the period of droplet formation are compared between the numerical and experimental results which agree with each other both qualitatively and quantitatively. The presented model and criterion can be used to predict the dynamic behavior and movement of multiphase flows.