Low-Reynolds-number droplet motion in a square microfluidic channel

In this study, we investigate computationally the low-Reynolds-number droplet motion in a square micro-channel, a problem frequently encountered in microfluidic devices, enhanced oil recovery and coating processes. The droplet deformation and motion are determined via a three-dimensional spectral boundary element method for wall-bounded flows. The effects of the flow rate, viscosity ratio and droplet size on the interfacial dynamics are identified for droplets smaller and larger than the channel size and for a wide range of viscosity ratio. Owing to the stronger hydrodynamic forces in the thin lubrication film between the droplet interface and the solid walls, large droplets exhibit larger deformation and smaller velocity. Under the same average velocity, a droplet in a channel shows a significantly smaller deformation and higher velocity than in a cylindrical tube with the same size, owing to the existence of the corners’ area in the channel which permits flow of the surrounding fluid. A suitable periodic boundary implementation for our spectral element method is developed to study the dynamics of an array of identical droplets moving in the channel. In this case, the droplet deformation and velocity are reduced as their separation decreases; the reduction is influenced by the flow rate, viscosity ratio and more significantly the droplet size.     

Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques

A new approach for simultaneous planar measurement of droplet velocity and size with gas phase velocities is reported, which combines the out-of-focus imaging technique ‘Interferometric Laser Imaging Droplet Sizing’ (ILIDS) for planar simultaneous droplet size and velocity measurements with the in-focus technique ‘Particle Image Velocimetry’ (PIV) for gas velocity measurements in the vicinity of individual droplets. Discrimination between the gas phase seeding and the droplets is achieved in the PIV images by removing the glare points of focused droplet images, using the droplet position obtained through ILIDS processing. Combination of the two optical arrangements can result in a discrepancy in the location of the centre of a droplet, when imaging through ILIDS and PIV techniques, of up to about 1 mm, which may lead to erroneous identification of the glare points from droplets on the PIV images. The magnitude of the discrepancy is a function of position of the droplet’s image on the CCD array and the degree of defocus, but almost independent of droplet size. Specifically, it varies approximately linearly across the image along the direction corresponding to the direction of propagation of the laser sheet for a given defocus setting in ILIDS. The experimental finding is supported by a theoretical analysis, which was based on geometrical optics for a simple optical configuration that replicates the essential features of the optical system. The discrepancy in the location was measured using a monodisperse droplet generator, and this was subtracted from the droplet centres identified in the ILIDS images of a polydisperse spray without ‘seeding’ particles. This reduced the discrepancy between PIV and ILIDS droplet centres from about 1 mm to about 0.1 mm and hence increased the probability of finding the corresponding fringe patterns on the ILIDS image and glare points on the PIV image. In conclusion, it is shown that the proposed combined method can discriminate between droplets and ‘seeding’ particles and is capable of two-phase measurements in polydisperse sprays.     

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.     

Gas temperature in the trace of water droplets streamlined by hot air flow

In order to obtain the knowledge necessary for developing new effective fire extinguishing technologies, we determined experimentally the gas temperature in the trace of water droplets streamlined by hot air flow. It was important to establish how much the temperature in the droplet trace decreases and how fast it recovery to the initial temperature field after the droplet evaporation. The following parameters were varied: droplet size from 1.3 mm to 1.7 mm, velocity from 1 m/s to 5 m/s, initial airflow temperature from 473 K to 773 K, number of droplets (one or two), and the arrangement of droplets relative to the hot inflow (serial or parallel). The study proves the theoretical hypothesis about a significant influence of evaporation on the temperature in the water droplet trace. When a temperature trace of water droplets is formed, irrespective of their arrangement, the role of the evaporation process strengthens with the gas flow temperature rising. Furthermore, the study specifies typical longitudinal dimensions of the aerodynamic and temperature traces of water droplets. It has been established that when droplets are located in series and in parallel, their combined impact on the temperature and velocity of the gas flow in the medium differs rather considerably.     

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

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

Drag coefficients of spherical liquid droplets Part 2: Turbulent gaseous fields

The drag of non-evaporating, spherical, liquid droplets was measured in turbulent flow fields at parametric ranges relevant to spray combustion, characterized by the droplet Reynolds number, and the intensity and spatial scales of turbulence. The experimental apparatus comprised a wind-tunnel and a piezo-electric droplet generator. The procedure was to inject water droplets of uniform size co-currently and continuously with vertical turbulent air flows while droplet velocity was measured at different elevations using laser-Doppler velocimetry. Turbulence was characterized using hot-wire anemometry prior to droplet injection. Drag coefficients were calculated using these main measurements and the law of conservation of mechanical energy. Reynolds numbers were investigated in the range 10–100, in terms of the equivalent spherical diameter of a droplet, and the mean relative speed between the ambient gaseous field and the droplets. Weber numbers were much less than unity so droplets were effectively spherical. Relative intensities of turbulence were investigated in the range 20–65 percent, in terms of the mean relative speed. Spatial scales of turbulence were large in comparison to the droplets; the ratio between the spatial integral scale and the droplet diameter was in the range 11–38, and the Kolmogorov scale was comparable in size or smaller than the droplet diameter. Experimental data showed that the drag in turbulent fields under these conditions is not significantly different than that of solid spheres in a quiescent field at the same Reynolds number.The financial support of the Natural Sciences and Engineering Research Council of Canada and the Manufacturing Research Corporation of Ontario is gratefully acknowledged.     

Grouping and trapping of evaporating droplets in an oscillating gas flow

A new approach to the analysis of droplet grouping in an oscillating gas flow is suggested. This is based on the investigation of droplet trajectories in the frame of reference moving with the phase velocity of the wave. Although the equations involved are relatively simple, the analysis shows distinctive characteristics of grouping and non-grouping cases. In the case of grouping, droplet trajectories converge to the points for which the ratio of flow velocity in this frame of reference and the amplitude of flow oscillations is less than 1, and the cosine of the arc sine of this ratio is positive. In the case of non-grouping, droplet trajectories in this frame of reference oscillate around the translational velocity close to the velocity of flow in the same frame of reference. The effect of droplet size on the grouping pattern is investigated. It has been pointed out that for the smaller droplets much more stable grouping is observed. The effect of droplet evaporation is studied in the limiting case when the contribution of the heat-up period can be ignored. It is shown that evaporation can lead to droplet grouping even in the case when the non-evaporating droplets are not grouped. This is related to the reduction in droplet diameter during the evaporation process. Coupling between gas and droplets is shown to decrease the grouping tendency. A qualitative agreement between predictions of the model and in-house experimental observations referring to Diesel engine sprays has been demonstrated.     

Large-Eddy Simulation of Interactions Between a Reacting Jet and Evaporating Droplets

Large-eddy simulation of a turbulent reactive jet with and without evaporating droplets is performed to investigate the interactions among turbulence, combustion, heat transfer and evaporation. A hybrid Eulerian–Lagrangian approach is used for the gas–liquid flow system. Arrhenius-type finite-rate chemistry is employed for the chemical reaction. To capture the highly local interactions, dynamic procedures are used for all the subgrid-scale models, except that the filtered reaction rate is modelled by a scale similarity model. Various representative cases with different initial droplet sizes (St ₀) and mass loading ratios (MLR) have been simulated, along with a case without droplets. It is found that compared with the bigger, slow responding droplets (St ₀ = 16), smaller droplets (St ₀ = 1) are more efficient in suppressing combustion due to their preferential concentration in the reaction zones. The peak temperature and intensity of temperature fluctuations are found to be reduced in all the droplet cases, to a varying extent depending on the droplet properties. Detailed analysis on the contributions of respective terms in a transport equation for grid-scale kinetic energy (GSKE) shows that the droplet evaporation effect on GSKE is small, while the droplet momentum effect depends on St ₀. When the MLR is sufficiently high, the bigger (St ₀ = 16) droplets can have profound influence on GSKE, and consequently on the formation and evolution of large-scale flow structures. On the other hand, the turbulence level is found to be lower in the droplet cases than in the pure flame case, due to the dissipative droplet dynamic effect.     

Numerical modeling and experimental measurements of water spray impact and transport over a cylinder

This study compares experimental measurements and numerical simulations of liquid droplets over heated (to a near surface temperature of 423 K) and unheated cylinders. The numerical model is based on an unsteady Reynolds-averaged Navier–Stokes (RANS) formulation using a stochastic separated flow (SSF) approach for the droplets that includes submodels for droplet dispersion, heat and mass transfer, and impact on a solid surface. The details of the droplet impact model are presented and the model is used to simulate water spray impingement on a cylinder. Computational results are compared with experimental measurements using phase Doppler interferometry (PDI). Overall, good agreement is observed between predictions and experimental measurements of droplet mean size and velocity downstream of the cylinder.     

Instantaneous and simultaneous planar velocity field measurements of two phases for turbulent mixing of high pressure sprays

This paper describes the tests of accuracy and the first application of a combined planar visualization technique. Its goal is two-phase flow discrimination, i.e. simultaneous measurements of velocity of droplets and ambient gas in the case of two-phase flow mixing, at the same location and with possible conditioning by “apparent diameter” (AD) of the droplets. It combines the mature techniques of particle image velocimetry (PIV), planar Mie scattering diffusion (PMSD), planar laser-induced fluorescence (PLIF), and it necessitates two synchronized cross-correlation systems, digital image treatment and analysis. This technique was developed with the objective of better describing the mixing between liquid and gaseous phases as in the case of high-pressure spray atomization in quiescent ambient gas. The basic principle of separation is to seed the ambient gas with micrometer particles and to tag the liquid with fluorescent dye. We use digital image treatment and analysis to discriminate between the phases. We use two cross-correlation PIV systems in order to obtain the velocity field of the droplets and gas simultaneously and separately at the same location. The digital image processing for separating the phases involves geometric measurement of droplet shapes. This leads to measurement of droplet parameters close to their real diameter, which could be used for analysis of actual mixing. A synchronized system composed of two CCD cameras is used for image recording, and two Nd:YAG lasers are used for generating pulsed light sheets at times t and t + δt. Tests were performed to check for different sources of errors. The combined technique was applied to measurements in high-pressure spray flow atomizing in a quiescent ambient gas, and first results are presented.     

An experimental and numerical study into turbulent condensing steam jets in air

 Temperatures, velocities, and droplet sizes are measured in turbulent condensing steam jets produced by a facial sauna, for varying nozzle diameters and varying initial velocities (Re=3,600–9,200). The release of latent heat due to droplet condensation causes the temperature in the two-phase jet to be significantly higher than in a single-phase jet. At some distance from the nozzle, droplets reach a maximum size and start to evaporate again, which results in a change in sign of latent heat release. The distance of maximum size is determined from droplet size measurements. The experimental results are compared with semi-analytical expressions and with a fully coupled numerical model of the turbulent condensing steam jet. The increase in centreline temperature due to droplet condensation is successfully predicted. Received: 5 April 2000 / Accepted: 15 November 2000     

Numerical modelling of film cooling with and without mist injection

Two-phase CFD calculations, using a Lagrangian model and commercial code Fluent 6.2.16, were employed to calculate the gas and droplet flows and film cooling effectiveness with and without mist on a flat plate. Two different three dimensional geometries are generated and the effects of the geometrical shape, size of droplets, mist concentration in the coolant flow and temperature of mainstream flow for different blowing ratios are studied. A cylindrical and laterally diffused hole with a streamwise angle of 30° and spanwise angle of 0° are used. The diameter of film cooling (d) hole, and the hole length to diameter ratio (L/d) for both of geometries are 10 mm and 4, respectively. Also the blowing ratio ranges from 1.0 to 2.0, and the mainstream Reynolds number based on the mainstream velocity and hole diameter (Re _d) is 6,219. The results are shown for different droplets diameters (1–10 μm), concentrations (1–5%) and mainstream temperatures (350–500 K). The centreline effectiveness and distribution of effectiveness on the surface of cooling wall are presented.     

Droplet imaging velocimeter and sizer: a two-dimensional technique to measure droplet size

This paper discusses the droplet imaging velocimeter and sizer (DIVAS), a two-dimensional technique to measure droplet size from very small droplets (a few microns) to very large drops (millimeters), as well as droplet velocity and concentration. DIVAS uses a particle imaging velocimetry (PIV) configuration; that is, pulsed lasers illuminate the droplets in the measurement plane and CCD cameras collect the off-axis scattered light, thus yielding a small measurement volume and correspondingly a high number density measurement capability. DIVAS is based on glare point imaging as described by van de Hulst and Wang (Appl Opt 30(33):4755–4763, 1991). By measuring the separation of cross-polarized glare points, DIVAS is capable of measuring droplet size down to a few microns with sub-pixel resolution. The measurement of large drops from the separation of glare points is straightforward. However, the paper discusses that large drops are often non-spherical and more advanced signal processing is required to retrieve their size. Both analytical studies and experiments are presented to demonstrate the feasibility of the technique.     

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.     

Droplet interactions in thermocapillary motion

The dynamics of two spherical droplets, whose movement is driven by variations in interfacial tension caused by a temperature gradient, are analyzed using a method of reflections. Both droplets have the same internal fluid properties but may differ in size, and the configuration of the droplets is arbitrary relative to the direction of the undisturbed temperature gradient. The method of reflections is based on an analysis of the thermal and hydrodynamic disturbances produced by a single droplet placed in an arbitrarily varying temperature field. The results for two-droplet interactions are correct to 0(r⁻⁶) where r is the center-to-center distance between the droplets. For the specific case of bubbles oriented parallel with the undisturbed temperature gradient, my results agree very well with numerical calculations found in the literature. The results for two, identical droplets are used to find the 0(ø) effect on mean droplet velocity of a bounded suspension, where ø is the volume fraction of the droplets. In general, the interactions between droplets moving by thermocapillary effects are much weaker than in the case of sedimentation.     

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.     

PTV investigation of phase interaction in dispersed liquid–liquid two-phase turbulent swirling flow

An investigation of dispersed liquid–liquid two-phase turbulent swirling flow in a horizontal pipe is conducted using a particle tracking velocimetry (PTV) technique and a shadow image technique (SIT). Silicone oil with a low specific gravity is used as immiscible droplets. A swirling motion is given to the main flow by an impeller installed in the pipe. Fluorescent tracer particles are applied to flow visualization. Red/green/blue components extracted from color images taken with a digital color CCD camera are used to simultaneously estimate the liquid and droplet velocity vectors. Under a relatively low swirl motion, a large number of droplets with low specific gravity tend to accumulate in the central region of the pipe. With increasing droplet volume fraction, the liquid turbulence intensity in the axial direction increases while that in the wall-normal direction decreases in the central region of the pipe. In addition, the turbulence modification in the present flow is strongly dependent on the droplet Reynolds number; however, the interaction of droplet-induced turbulences is significant due to vortex shedding, particularly at high droplet Reynolds numbers and higher droplet volume fraction.     

Droplet-based flows in serpentine microchannels: Chemical reactions and secondary flows

Mixing is an essential operation in many microfluidic devices. Droplet-based micromixers utilize droplets for mixing enhancement. In the present study, a novel three-dimensional simulation is conducted which has the ability to capture not only the mixing process, but also the chemical reactions inside liquid droplets. This two-phase model is used for simulating the reacting flow inside a serpentine microchannel and explores the effects of droplet size and reaction rate on the production and consumption of species in droplets. It is observed that the chemical reaction in each droplet, begins from its front area. Furthermore, it is shown that the production of species does not depend on water fraction (ratio of water flow rate to total flow rate) and for all droplet sizes, only depends on the reaction rate. Moreover, different transient generated vortices and secondary flows are studied in the presence and absence of droplets and explained in details based on the position of droplets. It is found that during the passage of droplets through a microchannel bend, the number of cross-sectional vortices changes and the velocity magnitude in these secondary flows increases dramatically.     

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.