Numerical modeling and experimental measurements of a high speed solid-cone water spray for use in fire suppression applications

Experimental measurements and numerical simulations of a high-speed water spray are presented. The numerical model is based on a stochastic separated flow technique that includes submodels for droplet dynamics, heat and mass transfer, and droplet–droplet collisions. Because the spray characteristics near the nozzle are difficult to ascertain, a new method for initialization of particle diameter size is developed that assumes a Rosin–Rammler distribution for droplet size, which correctly reproduces experimentally measured Sauter and arithmetic mean diameters. By relating the particle initialization to lower moments of the droplet statistics, it is possible to take advantage of measurements without substantial penalties associated with the greater experimental uncertainty of individual droplet measurements. Overall, very good agreement is observed in the comparisons of experimental measurements to computational predictions for the streamwise development of mean drop size and velocity. In addition, the importance of modeling droplet–droplet collisions is highlighted with comparison of selected droplet–droplet collision models.     

Droplet formation from a pulsed vibrating micro-nozzle

Micro-droplet formation from a passive vibrating micro-nozzle driven by a pulsed pressure wave is numerically simulated. The micro-nozzle is formed from an orifice in a thin walled plate that is allowed to freely vibrate due to the pressure loading on the plate. The analysis couples the fluid flow from the nozzle and the resultant droplet formation with the nozzle vibration calculated using large deflection theory. The problem is made nondimensional based on the capillary parameters of time, velocity and pressure. The applied pressure and nozzle material properties are varied to alter the vibration characteristics of the orifice plate used to form the nozzle. The initiation of drop formation is found to coincide with a threshold impulse input, defined as the product of the pressure magnitude and the pulse duration. Increasing the impulse can result in multiple satellite droplet formation, but the effect on the primary droplet size is minor. The vibration of the nozzle only weakly influences the droplet break-off time, but is shown to significantly affect the droplet volume, shape, and satellite droplet formation.     

微型管中液滴流动的三维数值模拟

对于微型设备中的低雷诺数流动,毛细力和黏性力起主导作用. 应用相场方法,引入自由能泛函,研究了二相流体在微型管中流动问题及表面浸润现象,并给出了微型管中二相流体的无量纲输运方程. 针对方形微管道,利用差分法给出了输运方程的数值求解方法.最后,模拟了方形直管中的液滴流动和变形的过程,并给出了液滴前后压力差与其它主要物理参数之间的变化关系. 结果表明,压力差随液滴半径增大而增加,而随毛细管系数的增大而减小.     

Dipole Electromagnetic Radiation by a Charged Drop Oscillating in a Uniform Electrostatic Field

The intensity of electromagnetic radiation generated by a charged drop oscillating in a uniform electrostatic field is studied within the framework of analytical calculations retaining the terms of the second order of smallness with respect to the ratio of the droplet oscillation amplitude to the droplet radius. It is found that the charge induced in the drop surface oscillations generates a dipole radiation detected in the first-order calculations and a self-charge detected with allowance for the second-order terms only. It is shown that the order of the magnitude of the total intensity of radiation generated by a cloud can be determined from small-droplet radiation. Among two radiation sources, namely, the radiation generated by small droplets oscillating at low modes and the radiation generated by hydrometeors oscillating at high modes, the first plays a dominant role.     

Numerical study of a single drop impact onto a liquid film up to the consequent formation of a crown

In this paper, the whole dynamic process of a single drop impact onto a thin liquid surface up to the consequent formation of a thin crown is numerically studied using the smoothed particle hydrodynamics (SPH) method. Especially, the gravity, artificial viscosity, and surface tension are introduced into the model. The obtained SPH numerical results are compared with experimental results. The numerical model of the SPH method is valid for simulating the dynamic process of a single drop impact onto a liquid surface. Meanwhile, it is found that the whole dynamic process mainly depends on the depth of the liquid pool and the initial velocity of the droplet.     

Material removal associated with condensation on a droplet in motion

This paper treats a three-phase, multicomponent fluid mechanics-heat and mass transfer problem. Solutions to the nonlinear, coupled boundary layer equations that govern laminar condensation heat and mass transfer in the vicinity of the forward stagnation point of a spherical cold water drop translating in a saturated mixture of five components are presented. The environment surrounding the drop is composed of a condensable (steam), a noncondensable and nonabsorbable (air), a noncondensable but absorbable (e.g. elemental iodine), a chemically reactive component (e.g. methyl iodide), and a particulate substance. The dispersed and the continuous phases have been treated simultaneously. The effect of chemical reaction between a reactive component in the continuous phase and an additive (e.g. hydrazine) in the droplet liquid has also been considered. The droplet sizes, the thermodynamic range, and the nature of chemical constituents chosen for the illustrative calculations are closely related to the operating conditions that are likely to prevail in the containment spray atmosphere of a nuclear reactor following a loss of coolant accident. The choice of elemental iodine and methyl iodide has an added feature. The mass transfer resistance for elemental iodine is almost entirely in the gaseous phase while the absorption of methyl iodide could be regarded as a liquid-phase resistance-controlled process. Mass transport, in the presence of condensation, is seen to depend in a rather complicated manner on droplet radius.     

Instability of a Charged Droplet in an Inhomogeneous Electrostatic Field of a Rod of Finite Thickness

The instability of a charged droplet of an ideal liquid in an inhomogeneous electrostatic field of a rod of finite thickness maintained at a constant electrostatic potential is investigated within the framework of analytic asymptotic calculations. It is shown that the mode amplitudes and the drop oscillation frequencies increase with the rod thickness. The critical conditions of instability of the droplet reduce by several times as compared with the critical conditions of implementation of its instability in the electrostatic field of an infinitely thin filament maintained at a constant electrostatic potential. An analytic dependence between the charge and field parameters, critical for implementation of the instability of a charged droplet in an inhomogeneous electrostatic field and dependent on the rod thickness, is found.     

Viscosity of a Newtonian fluid calculated from the deformation of droplets covered with a surfactant under a linear shear flow

The viscosity of small fluid droplets covered with a surfactant is determined using drop deformation techniques. This method, proposed by Hu and Lips, is here extended to the case of the presence of a surface-active adsorpted at the liquid–liquid interface, to consider more general scenarios. In these experiments, a droplet is sheared by another immiscible fluid of known viscosity, both Newtonian liquids. From the steady-state deformation and retraction mechanisms, the droplet viscosity is calculated using an equation derived from the theories of Taylor and Rallison. Although these theories were expressed for surfactant-free interfaces, they can be applied when a surfactant is present in the system if the sheared droplet reaches reliable steady-state deformations and the surfactant attains its equilibrium adsorption concentration. These determinations are compared to bulk viscosities measured in a rheometer for systems with different viscosity ratios and surfactant concentrations. Very good agreement between both determinations is found for drops more viscous than the continuous phase.     

The fate of soluble and insoluble surfactant monolayers subjected to drop impacts

Surfactant monolayers were formed on a water surface and subjected to water drops falling from a nozzle. Surface tension was measured during these experiments to determine the effect of the drop impacts on the surfactant monolayer. The purpose of this work was to determine whether monolayers can be altered by drop impacts without the formation of a splash. Accordingly, a small fall height was used to avoid drop splashes and concomitant surfactant loss by droplet ejection. The relevance of this work pertains to the fate of surfactant monolayers during rain events. Results are presented for a soluble and insoluble surfactant. The results show that the insoluble monolayer is virtually unaffected by the drops, indicating that the monolayer immediately reforms after the drop impact. The soluble monolayer shows significant changes in measured surface tension during droplet impact when the surfactant concentration is high.     

On the nonlinear stability of a swirling liquid jet

The nonlinear deformation and atomization of a rotating column is considered using an axisymmetric boundary element formulation. Swirl has been considered by superposing a potential vortex to the bulk flow of the jet. The resulting model has been shown to reproduce the classical linear result due to Ponstein and parametric studies are conducted in the nonlinear regime to determine wave shapes and droplet sizes. As with prior nonlinear column breakup studies, results indicate that satellite drops are formed from the main wave under virtually all conditions. The ratio of the main drop to satellite drop diameter is shown to be remarkably constant over a variety of wave numbers/column lengths thereby providing a potential approach to produce tightly controlled bimodal sprays.     

Measurement of the surface concentration (liquid) of an evaporating multicomponent droplet using pendant droplet method

The surface concentration on the liquid side of the interface of an evaporating multicomponent droplet could be different from the bulk concentration. In this work, surface tension is used as a means to measure surface concentration of an evaporating multicomponent droplet. Surface tension is measured using pendant droplet method that relies on the best fit between theoretical and experimental drop profiles. Surface tension is a surface property, and it exhibits a dependence on concentration. Hence, it is an ideal candidate to track the variation of surface concentration during the evaporation of a multicomponent droplet. This method is used to study the evaporation of ethanol–water and methanol–water droplets. The correctness and applicability of this technique are critically assessed, and important observations are made for single droplet evaporation for these binary mixtures.     

Nucleation of Droplets in a Binary Mixture

We revisit the theory of condensation of a droplet in a vapour with the aim of finding the effect that the surface tension has on the phase diagram of a binary mixture. For that purpose we consider condensation under volume control and rederive the Gibbs phase rule. The Gibbs phase rule is equivalent to the common tangent construction for two free enthalpies corresponding to different pressures: in this case, the pressure in the vapour and the pressure in the droplet. Explicit results are calculated for a droplet mixed from incompressible liquids and for a vapour that is an ideal gas mixture. It turns out that in a certain range of volumes the equilibrium state of droplet and vapour has a higher free energy than the vapour alone. At the lower bound of that range of volumes a stable droplet of finite size will nucleate and consequently the vapour pressure will drop. The usual condensation line in a (p, X ₁)-phase diagram without surface tension is thus replaced by two lines: One for the incipient condensation and one for its completion; both lie above the condensation line without surface tension.     

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.     

Towards the problem of droplet injection in a vapor with the aim of reducing the pressure

As applied to the analysis of sprinkler systems which inject droplets into a vapor in the case of emergency pressure increases, the process of vapor condensation on a single droplet is considered. For the specification of the intensity of interphase heat and mass transfer, the solution of an unsteady heat conduction problem is used. Approximate formulas describing the laws of the pressure drop in a vapor-droplet system due to the condensation of the vapor phase are obtained.     

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.     

Spreading and fingering in a yield-stress fluid during spin coating

We study the deformation, spreading, and fingering of small droplets of a yield-stress fluid subjected to a centrifugal force on a rotating substrate. At low rotation rates and for small enough droplets, the droplets deform elastically but retain their essentially circular contact line. For large enough droplet volumes and rotation speeds, however, one or more fingers eventually form and grow at the edge of the drop. This fingering is qualitatively different from the contact line instability observed in other fluids, and appears to be a localized phenomenon that occurs when the stress at some point on the perimeter of the drop exceeds the yield stress.     

STATIC SPREADING OF DROPLET IMPACT ON SOLID SURFACE：INFLUENCE FACTOR

通过建立液滴撞击固体平壁的静态铺展力学平衡的数学模型,从理论上得到了静态铺展半径与液滴物性参数、以及液滴与固体壁面接触角之间关系的数学表达式,将理论结果与数值模拟的结果进行了比较,两者吻合较好.比较了不同条件下液滴的静态铺展半径的变化规律,分别得到了液滴密度、体积、表面张力和接触角等因素对液滴静态铺展半径的影响规律.     

平壁液滴静态铺展影响因素的研究

通过建立液滴撞击固体平壁的静态铺展力学平衡的数学模型,从理论上得到了静态铺展半径与液滴物性参数、以及液滴与固体壁面接触角之间关系的数学表达式,将理论结果与数值模拟的结果进行了比较,两者吻合较好.比较了不同条件下液滴的静态铺展半径的变化规律,分别得到了液滴密度、体积、表面张力和接触角等因素对液滴静态铺展半径的影响规律.      

A numerical study of droplet motion/departure on condensation of mixture vapor using lattice Boltzmann method

Droplet motion/departure, which is governed by external force acceleration coefficient, droplet radius and surface wettability on solid surfaces under external forces such as gravitational force, play a significant role in characterizing condensation heat transfer, especially when high fractional non-condensable gases (NCG) present. However, due to the challenge in visualizing the vapor/steam velocity field imposed by droplet motion/departure, the detailed mechanism of droplet motion/departure on condensing surfaces has not been completely investigated experimentally. In this study, droplet motion/departures on solid surfaces under external forces and their interactions with steam flow are simulated using two dimensional (2D) multiphase lattice Boltzmann method (LBM). Large external force acceleration coefficient, droplet radius and contact angle, lead to large droplet deformation and high motion/departure velocity, which significantly shortens the droplet residual time on the solid surface. Our simulation shows that steam vortices (lateral velocity) induced by droplet motion/departure can greatly disturb the vapor flow and would be intensified by increasing external force acceleration coefficient, droplet radius, and contact angle. In addition, the location of vortex center shifts in the ascending direction with increase of these factors. The average lateral velocities induced by droplet motion/departure at various conditions are obtained. The mass transfer resistance is substantially reduced owing to the droplet motion/departure, leading to an enhanced heat flux. The experimental results are compared to validate the influence of droplet motion/departure on condensation heat transfer performance, especially for steam–air mixture with the presence of high fractional NCG.