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.     

Evaluation of FFT-based cross-correlation algorithms for PIV in a periodic grooved channel

The design of a pneumatic droplet generator to produce small (~0.2 mm diameter) water droplets on demand is described. It consists of a cylindrical, liquid-filled chamber with a small nozzle set into its bottom surface, connected to a gas cylinder through a solenoid valve. Rapidly opening and closing the valve sends a pressure pulse to the liquid, ejecting a single droplet through the nozzle. Gas in the chamber escapes through a vent hole so that the pressure drops rapidly and more droplets do not emerge. We photographed droplets as they emerged from the nozzle, and recorded pressure fluctuations in the chamber. We determined the duration of the pressure pulse required to generate a single drop; longer pulses produced satellite drops. The length of the water jet when its tip detached and the diameter of the droplet that formed could be predicted using results from linear stability analysis. The peak pressure in the cavity could be increased by raising the supply pressure, increasing the width of the pressure pulse, or by reducing the size of the pressure relief vent.     

Effect of secondary flow on droplet distribution and deposition in horizontal annular pipe flow

In horizontal annular dispersed pipe flow the liquid film at the bottom is thicker and rougher than at the top of the pipe. A turbulent pipe flow experiencing a variation of roughness along the pipe wall will show a secondary flow. Such secondary flow, consisting of two counter-rotating cells in the cross-section of the tube, can change the distribution of the droplets inside the pipe and their deposition at the wall. Here, we compare the behaviour of the droplets (dispersed phase) with and without secondary flow, using large-eddy simulations. It is shown that the presence of secondary flow increases the droplet concentration in the core of the pipe and the droplet deposition-rate at the top of the pipe.     

After fogging process in water injected gas turbine systems

In gas turbine system with after fogging, water droplets are injected after compressor. After fogging could have more significant potential for enhancement of specific power production compared to inlet fogging alone, since a larger water injection rate is possible. Transient analysis of after fogging process is carried out by using a heat and mass transfer modeling on water droplet evaporation. Transient variables such as droplet diameter and air temperature are evaluated as the droplet evaporation proceeds for different values of initial droplet diameter, pressure ratio of compressor, and water injection ratio. The evaporation time for injected droplets are also estimated. Present results show that the evaporation time decreases sensitively with increasing pressure ratio or initial droplet diameter. However, the effect of water injection ratio on evaporation time is relatively insignificant unless water injection ratio is near the critical ratio.     

Comparison of multicomponent fuel droplet vaporization experiments in forced convection with the Sirignano model

The vaporization of multicomponent fuel droplets was studied experimentally in a heated flow and the results were compared to the model proposed by Abramzon and Sirignano. The droplet was suspended on a permanent holder which was set up in a thermal wind-tunnel. This wind-tunnel was fitted with a video recording system and an infra-red camera. The period during which the droplet was suspended on the holder before the opening of the hot air flow damper was recorded. This first sequence corresponds to the droplet vaporization in natural convection, whose initial experiment conditions, especially diameter, temperature, composition of the droplet, are well known. Then the damper was turn on, and the sequence of forced convection begun. The initial diameter of the droplet was recorded by the video system. The other initial conditions of this second sequence cannot be determined experimentally. The distribution of temperature in the droplet and the surface temperature, the mass fraction distribution in the droplet and the surface mass fraction were unknown. These unknown parameters were determined by coupling our experiment with a model using “the film concept” in natural convection. Experimental results were compared with the calculations and found satisfactory, in natural convection as well as in forced convection initiated by this method. The method was tested in the case of a fuel mixture droplets (heptane–decane) for different initial concentrations and variable durations of the sequence in natural convection.     

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.     

A pneumatic droplet-on-demand generator

The design of a pneumatic droplet generator to produce small (~0.2 mm diameter) water droplets on demand is described. It consists of a cylindrical, liquid-filled chamber with a small nozzle set into its bottom surface, connected to a gas cylinder through a solenoid valve. Rapidly opening and closing the valve sends a pressure pulse to the liquid, ejecting a single droplet through the nozzle. Gas in the chamber escapes through a vent hole so that the pressure drops rapidly and more droplets do not emerge. We photographed droplets as they emerged from the nozzle, and recorded pressure fluctuations in the chamber. We determined the duration of the pressure pulse required to generate a single drop; longer pulses produced satellite drops. The length of the water jet when its tip detached and the diameter of the droplet that formed could be predicted using results from linear stability analysis. The peak pressure in the cavity could be increased by raising the supply pressure, increasing the width of the pressure pulse, or by reducing the size of the pressure relief vent.     

Observation of water condensate on hydrophobic micro textured surfaces

We visually observed that a dropwise condensation occurred initially and later changed into a filmwise condensation on hydrophobic textured surface at atmosphere pressure condition. It was observed that the condensate nucleated on the pillar side walls of the micro structure and the bottom wall adhered to the walls and would not be lifted to form a spherical water droplet using environmental scanning electron microscope.     

Downstream pressure and elastic wall reflection of droplet flow in a T-junction microchannel

This paper discusses pressure variation on a wall during the process of liquid flow and droplet formation in a T-junction microchannel. Relevant pressure in the chan-nel, deformation of the elastic wall, and responses of the droplet generation are analyzed using a numerical method. The pressure difference between the continuous and dis-persed phases can indicate the droplet-generation period. The pressure along the channel of the droplet flow is affected by the position of droplets, droplet-generation period, and droplet escape from the outlet. The varying pressures along the channel cause a nonuniform deformation of the wall when they are elastic. The deformation is a vibration and has the same period as the droplet generation arising from the process of droplet formation.     

Maximum spreading of electrically charged droplets impacting on dielectric substrates

In this work, the electric charging effect on the spreading of droplet impacting on dielectric substrates has been investigated. The charged water droplets were directed on the paraffin wax and the Teflon-coated plates. The impinging behavior was visualized and recorded using a CCD camera to identify the maximum extent of the flattened droplets. Droplet diameter and velocity approaching the wall were measured as well. The diameter of the electrically charged droplet at the maximum spread turned out to be larger compared to that of neutral droplet (at the maximum spread), and the difference becomes larger with increasing of the electric charge ratio (defined as the ratio of the actual electric charge to the Rayleigh limit). This phenomenon is considered to be due to reduction of effective interfacial tensions between the liquid and the gas and between the liquid and the solid by electric charging. Finally, an improved model was proposed to predict the maximum spreading ratio for electrically charged droplets by introducing correlations on the liquid–gas and the liquid–solid interfacial tensions.     

Droplet evaporation on porous and non-porous ceramic solids heated from top

 This paper presents the results of an experimental investigation, of the effect of radiation heat, on the evaporation of five droplet sizes of pure water, softly deposited on porous and non-porous ceramic solids, at temperature ranging from 75 to 250 °C. Both solids were instrumented with several surface and in-depth thermocouples, and had the same thermal properties. Results show that, the droplet evaporation time, and the surface recovery time for the porous solid were shorter than that of non-porous solid for the same droplet size under identical conditions. Also, smaller droplets were more efficient for cooling both solids. The results were compared with data for the evaporation of water droplets on similar ceramic solids heated from bottom (Abu-Zaid M; Atreya A (1994) J Heat Transfer 116: 694–701). The comparison shows that, the heat radiation has a significant effect of reducing evaporation time, recovery time, and droplet volume of influence for both solids, at the same initial surface temperature. Received on 6 December 1999 / Published online: 29 November 2001     

Experimental study of water droplet boiling on hot, non-porous surfaces

In this paper, the results of a series of experimental tests on single- and multi-droplet boiling systems are presented and discussed. The main objectives of the present study are: a) to investigate experimentally the effect of the boiling onset on the evaporation rate of water droplets; b) to measure the evolution of the solid surface temperature during evaporation; c) to examine the possibility of improving spray cooling efficiencies. The behavior of small water droplets (from 10 to 50 μl) gently deposited on hot, non-porous surfaces is observed. The evaporation of multi-droplet arrays (50 and 100 μl) under the same conditions of the single-droplet tests is analyzed. In particular, the conditions which determine the onset of nucleate and film boiling are stressed out. In the experimental tests, the interaction of different materials with several multi-droplet systems is monitored by infrared thermography. The spray cooling efficiency is related to the solid temperature decrease as a function of the water mass flux. In the present study, the effect of varying the droplet volume and the mass flux is also analyzed and discussed. The results on the droplets evaporation time and on the solid surface transient temperature distribution are also compared with the data obtained by the same authors during the analysis of droplet evaporation in total absence of nucleate and film boiling. In order to analyze the different behavior of the evaporating droplet as a function of the solid surface thermal conductivity, evaporative transients on aluminum, stainless steel and macor (a glass-like, low-conductivity material) are considered. Received on 20 February 1998     

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.     

Study of droplet flow in a T-shape microchannel with bottom wall fluctuation

Droplet generation in a T-shape microchannel, with a main channel width of 50 μm, side channel width of 25 μm, and height of 50 μm, is simulated to study the effects of the forced fluctuation of the bottom wall. The periodic fluctuations of the bottom wall are applied on the near junction part of the main channel in the T-shape microchannel. Effects of bottom wall's shape,fluctuation periods, and amplitudes on the droplet generation are covered in the research of this protocol. In the simulation,the average size is affected a little by the fluctuations, but significantly by the fixed shape of the deformed bottom wall, while the droplet size range is expanded by the fluctuations under most of the conditions. Droplet sizes are distributed in a periodic pattern with small amplitude along the relative time when the fluctuation is forced on the bottom wall near the T-junction,while the droplet emerging frequency is not varied by the fluctuation. The droplet velocity is varied by the bottom wall motion,especially under the shorter period and the larger amplitude. When the fluctuation period is similar to the droplet emerging period, the droplet size is as stable as the non-fluctuation case after a development stage at the beginning of flow, while the droplet velocity is varied by the moving wall with the scope up to 80% of the average velocity under the conditions of this investigation.     

Simultaneous entrainment of oil and water droplets in high Reynolds number gas turbulence in horizontal pipe flow

We develop a 1D cross sectional concentration profile model for oil and water droplets that coexist in the turbulent gas phase (of Re ∼ 10⁶) in near horizontal stratified pipe flows. Entrainment of the oil and water mixture from a liquid film near the bottom of the pipe into the gas is modeled based on earlier single-fluid entrainment correlations. A Gamma distribution for the droplet sizes based on the breakup of liquid filaments, is adopted. An explicit algebraic–exponential formula for the total concentration profile for either phase can then be derived.     

On the calculation of wall temperatures in the post dryout heat transfer region

A non-equilibrium post dryout heat transfer model for calculating the wall temperature distribution in vertical upflows is presented in this study. The model is based upon the three path heat transfer formulation developed by MIT researchers (Laverty & Rohsenow 1964, Forslund & Rohsenow 1968, Hynek et al. 1969 and Plummer et al. 1974) that involves heat transfer from wall to vapor, from wall to droplets in contact with the wall and from vapor to liquid droplets in the vapor core. Downstream gradients for the bulk vapor temperature, vapor quality, droplet size and vapor velocities are identical to those used by Hynek et al. (1969) and Plummer et al. (1974). Conditions at the dryout location are calculated using a modified version of a technique developed by Hynek et al. (1969).A procedure for determining an average droplet diameter based on a size distribution is introduced. Migration of droplets through the boundary layer and droplet deposition flux are predicted with the model of Gani? & Rohsenow (1979). Heat transfer from the wall to the impinging liquid droplets is calculated with a correlation by Holman & McGinnis (1969). Mechanisms contributing to wall to droplet heat transfer are identified as (a) droplet-wall contact, (b) intensive droplet evaporation inside the boundary layer, and (c) destruction of the boundary layer due to droplet migration to, and rebound from, the hot surface. The significance of the average droplet size and size distribution is demonstrated through its control over the free stream evaporation and droplet deposition rates.Predicted uniform heat flux wall temperature profiles for water, nitrogen and freon 12 are in good agreement with the data of Era et al. (1966), Bennett et al. (1967), Forslund & Rohsenow (1968), Ling et al. (1971), Groeneveld (1972) and Janssen & Kervinen (1975).     

Droplet production from disintegrating bubbles at water surfaces. Single vs. multiple bubbles

We experimentally determine the droplet production rate at a water surface where either single or multiple bubbles (bubbly flow) with similar mean diameters disintegrate and produce film and jet droplets. A detailed assessment of film drop production from bubbly flow is important, since most presently used correlations are based on single-bubble measurements. Moreover, jet drops––even though they contain a much larger fluid volume––are de-entrained into the water surface in most technical and geophysical applications. Detailed phase Doppler anemometry (PDA) measurements are performed in the vicinity of the water surface with long sampling times. For a considered mean diameter of approximately 3 mm, the size distribution of the non spherical bubbles is determined from photographic images. From single-bubble measurements we find, consistent with literature data, a narrow size distribution of the jet drops with a mean diameter of 477 μm. For bubbly flow, the maximum is shifted to somewhat smaller jet drop diameters (425 μm) and the production of film droplets increases significantly. We relate this increase to the coalescence of bubbles prior to their disintegration at the surface. Our results therefore show that for a fixed bubble size and gas flow rate the number of film drops entrained from a bubbly flow is underestimated, if the estimate is based on single-bubble data.     

航空发动机轴承腔中油滴运动与沉积的特性分析

本文在获得轴承腔中气相介质流场的基础上,采用Lagrangian方法建立油滴在气相介质流场中运动的分析模型,通过瞬时步进法数值模拟油滴的运动过程,获得了油滴直径和旋转轴转速对油滴运动过程中的速度和轨迹影响的规律.基于获得的油滴与腔壁碰撞前的运动状态,以及结合油滴与腔壁的碰撞模型,实现了油滴直径和旋转轴转速对碰撞后油滴沉积率和动量转移率影响规律的分析.结果表明:油滴直径和旋转轴转速对油滴速度及轨迹,以及油滴沉积率及动量转移率都有很大影响,而且前者的影响更为明显.与国外同等条件下的试验结果对比表明,本文提出的油滴运动与沉积特性分析方法具有较好的可靠性和精度.碰撞前后油滴运动状态和沉积率及动量转移率的计算,为下一步油膜厚度和速度的计算,继而为轴承腔润滑设计和换热分析提供了初始条件.