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.     

椭球液滴撞击超疏水表面反弹过程数值分析

液滴在自由落体或受外力作用时常发生椭球形变,对其撞击超疏水壁面的运动形态及形成二次液滴有较大影响.本文假定具有不同轴向半径比值(AR)的椭球形液滴,采用耦合水平集-体积分数(CLSVOF)方法对椭球形液滴撞击超疏水平壁面进行数值模拟研究,对椭球形液滴撞击超疏水平壁面反弹过程运动形态和AR对二次液滴形成的影响进行分析.研...     

Self-similar solution to the problem of the expansion of a cylindrical column of conducting gas in a longitudinal magnetic field

The nonstationary radial motion of a long cylindrical column of conducting gas in a time-varying longitudinal magnetic field is considered. Exact solutions are found by the method of separating the variables for the system of equations of magnetohydrodynamics on the assumption that the statistical pressure of the plasma at the boundary of the column is proportional to the external magnetic pressure. Some numerical computations are performed and the energetic characteristics of the interaction process are calculated. The ratio of the useful work done by the gas over an infinite time interval to the initial energy of the column is given as a function of the magnetic Reynolds number. We note that a similar method was applied in [1], where not only was the average temperature taken over the cross section, but the inertia of the medium was also neglected. When the inertia is taken into account, we have the additional requirement that the statistical pressure be proportional to the magnetic pressure at the boundary of the column.A physically similar model may be interpreted, for example, as the expansion of a compressible conducting gas column in a nonconducting incompressible fluid situated in a permeable cylinder of some radius R infinite along the axis of symmetry. The requirement that the statistical pressure be proportional to the magnetic pressure reduces to the condition that the external pressure on the boundary of the permeable cylinder of radius R should vary according to a specific law, which may easily be determined.     

Rewetting of a solid cylinder with precursory cooling

A model for the rewetting of a solid cylinder is solved by the Wiener-Hopf technique. A constant heat transfer coefficient is assumed in the wetted part of the cylindrical rod, whereas an exponentially decaying heat flux is assumed in that part of the solid which is cooled by a mixture of vapor and liquid droplets (the precursory cooling). Accurate predictions of the rewetting velocity are obtained for a wide range of model parameters. The results of the present solution are found to compare favorably with a separation of variables solution obtained by Olek (1987). Values of the rewetting velocity where precursory cooling is neglected are recovered as a particular case. The decomposition in the form of infinite products presented here is shown to yield results which agree well with those derived from a decomposition by Evans (1984), employing the Cauchy theorem.Work done at Paul-Scherrer Institute PSI (formerly EIR), CH-5303 Würenlingen, Switzerland.     

Deformation and regimes of liquid column during water exit of a partially submerged sphere using the front-tracking lattice Boltzmann method

When a solid sphere exits water at a given velocity, the liquid column is pulled out of a liquid reservoir. The present study focuses on the dynamic deformation of the liquid column and on the identification of the liquid column regime on the Weber number and dimensionless time (We-t*) map. The three-dimensional model of water exit has been established on the basis of the lattice Boltzmann method. A mass tracking algorithm was incorporated to capture the free surface, where the liquid–gas​ two-phase flow is simplified to a single-phase free surface flow. The surface tension is included by adding a perturbation term and the gravity as a body force is introduced in form of calculating the equilibrium distribution with an altered velocity. The contact angle condition in numerical simulation is not considered. The accuracy of the numerical results is demonstrated through the comparisons with the prior numerical and the experimental results in the literature. A parametric study has been conducted numerically on the radius and volume and of liquid column. Besides, the relationship between the pinch-off time of a liquid column and the Froude number has been obtained. Moreover, the evolution of the liquid column shape with a wide range of the Weber number and time scales are discussed based on the number of ligaments and droplets. The liquid column exhibits different characteristics and has been divided into three regimes. The transition between different regimes has been analyzed and the critical Weber number is given.     

Vortex on the surface of a viscous fluid

The system of Navier-Stokes equations is solved for boundary conditions corresponding to the case when an axisymmetric tangential transversal load acts at the surface of a gravity viscous incompressible fluid of infinite depth. An integral representation is obtained for the shape of the free surface under the prolonged effect of a stationary vortex load. The example of a tangential load, similar to a concentrated vortex, is examined. In this case a column is squeezed out of the fluid, the height of the column being directly proportional to the square of the moment of the transverse tangential forces and inversely proportional to the square of the product of the dynamic fluid viscosity and the area of the tangential stress distribution. The depth of the annular funnel being formed in front of the column is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–132, July–August, 1978.     

Flow field around collapsing bubble trains: Theoretical analysis

A method of successive approximations is utilized to analyze the potential flow field around freely rising collapsing bubble trains. For simplicity, the analysis is confined to a two bubble column. An infinite series solution is obtained and the truncation errors are quantitatively analyzed.     

Influence of the boundary of a column of incompressible liquid in investigating axisymmetric oscillations of a solid sphere in a cavity

Axisymmetric oscillations of a rigid spherical body in a column of ideal incompressible liquid with a plane boundary in the form of a free liquid surface or a rigid wall within a round cylindrical cavity are considered. The potential and pressure fields are plotted; expressions are obtained for the kinetic energy of the system and the hydrodynamic forces acting on the body. The resistance of the liquid to accelerated movement of the body is determined as a function of the distance to the boundary, for various parameter values. For specified oscillations of the body, the results obtained for axisymmetric conditions in a halfspace are compared with those obtained in an infinite cylindrical cavity. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 11–18, December, 1999.     

Reduction of electron density in a plasma by injection of liquids

In this paper, the authors have investigated the physics of various processes relevant to the reduction of electron density in a plasma by addition of water droplets; two processes have in particular been analyzed in some detail, viz, the electron attachment to charged dielectric droplets and the emission of negative ions by vaporization from these droplets. The results of these analyses have been applied to a study of the kinetics of reduction of electron density and charging of droplets in an initially overionized plasma, after addition of water droplets. A number of simplifying assumptions including uniform size and charge on droplets and negligible change in the radius of the droplet due to evaporation have been made. Heat transfer between the droplets and the plasma has been neglected. It has also been assumed that the Debye radius is much greater than the radius of the droplets, which limits the treatment to droplets having radii, less than one micron (for electron densities of the order of 10¹⁸m^–3.).The authors have also studied the reduction of electron density by the suspension of water droplets in an equilibrium plasma. The investigation is purely theoretical in nature; considerable experimental work is necessary to validate the theoretical considerations.     

Experimental study of successive collision of two water droplets with a solid

The collision of two successive droplets with a solid is investigated experimentally by means of a flash photographic method. The pre-impact diameters of two droplets are 0.56 mm and 0.45 mm. The impact velocity of droplets is approximately 2.7 m/s. The spacing between the two droplets is varied as a parameter. The physics of interaction phenomena between two droplets on the solid is studied from an experimental viewpoint.     

Hysteresis and Horizontal Redistribution in Porous Media

It is well known that multiphase flow in porous media exhibits hysteretic behaviour. This is caused by different fluid–fluid behaviour if the flux reverses. For example, for flow of water in unsaturated soils the process of imbibition and drainage behaves differently. In this paper we study a new model for hysteresis that extends the current playtype hysteresis model in which the scanning curves between drainage and imbibition are vertical. In our approach the scanning curves are non-vertical and can be constructed to approximate experimentally observed scanning curves. Furthermore our approach does not require any book-keeping when the flux reverses at some point in space. Specifically, we consider the problem of horizontal redistribution to illustrate the strength of the new model. We show that all cases of redistribution can be handled, including the unconventional flow cases. For an infinite column, our analysis involves a self-similar transformation of the equations. We also present a numerical approach (L-scheme) for the partial differential equations in a finite domain to recover all redistribution cases of the infinite column provided time is not too large.     

The rapid cooling of a hot gas discharge by liquid sprays

The cooling effect of liquid droplets introduced into a hot gas stream flowing in an adiabatic duct is analysed. The coupled interaction between the changes in the droplets and in the surrounding gas conditions is examined as a result of droplets vaporization. It was found that the use of liquid sprays as a rapid cooling process for a hot gas discharge is quite effective.     

Entrainment and condensation effects in the upward acceleration of a liquid column

The instability-governed entrainment rate of the lower surface of a subcooled water column accelerated upwards by an expanding steam mass is measured. It is found that the entrainment rate is approximately proportional to the fourth root of the acceleration. This would be the case if the characteristic length scale in the late stages of Taylor instability were governed by linear instability theory. In addition to the linear displacement measurements, the steam pressure in the lower driver section was monitored as a function of time. Estimates of the concentration, radius and age distribution of the entrained droplet population were made by modeling the bubble-and-spike breakup into discrete droplets. This allows the steam condensation rate, and hence the steam pressure, at each instant of time to be computed. This is compared with the observed steam pressure history. Reasonable agreement is found. One can thus estimate the reduction in work potential in the case of a steam explosion in the lower plenum of a pressurized-water nuclear reactor.     

动力机器地基随机振动研究

在土层中取一变截面土柱,从一维波动方程出发,采用复弹性模量,计及土的弹性模量沿深度的变化和阻尼影响,推导出动力机器简谐扰力作用下地基土垂直振动的位移,并在此基础上,计算出位于机器下方地基土对机器随机扰力的动力响应．     

Motion,deformation, and coalescence of ferrofluid droplets subjected to a uniform magnetic field

In this article, we present the motion, deformation, and coalescence of ferrofluid droplets suspended in a nonmagnetic fluid, subjected to a uniform magnetic field in both vertical and horizontal directions. A coupling between the simplified multiphase lattice Boltzmann method and the self-correcting scheme is constructed to numerically solve the two-dimensional flow field and the magnetostatics equations, respectively. The Cahn-Hilliard equation is employed to seize the diffuse interface between magnetic and nonmagnetic fluids. In order to validate the model, deformation of a ferrofluid droplet suspended in nonmagnetic fluid is simulated as a test case and the results are compared with numerical and experimental results. Furthermore, a detailed analysis on the behavior of falling ferrofluid droplets and the coalescence between a pair of ferrofluid droplets under the effect of different magnetic fields and different droplets configurations are also presented in this article. The results provide significant insight and a better understanding of these phenomena. It is found that for higher values of magnetic bond number and susceptibility, the droplet deformation is significant and the falling process is faster while a reverse behavior is observed for higher values of Eötvös number. Moreover, the magnetic energy density exhibits an interesting behavior in the vicinity of the droplets. It is concentrated between the droplets with a nonuniform distribution when the droplets are close to each other.     

Thermocapillary migration of liquid droplets in a temperature gradient in a density matched system

An experimental investigation of thermocapillary flow in droplets of a vegetable oil (partially hydrogenated soybean oil) immersed in silicone oil was conducted in a test cell with a heated top wall and a cooled bottom wall. The liquids are nearly immiscible and have equal densities at a temperature below the room temperature, thus providing a simulation of low-gravity conditions by reducing the buoyancy forces. The interfacial tension between the two oils was measured in the temperature range 20–50°C using a capillary tube and d/dT was determined to be negative. Droplets ranging in sizes from 3 mm to 1 cm diameter were injected into the silicone oil. The vertical temperature profile in the bulk liquid (silicone oil) produces temperature variations along the interface which induce variations in the interfacial tension. The flow inside the droplet driven by the resulting interfacial shear stresses was observed using a laser light-sheet flow visualization technique. The flow direction is consistent with the sign of d/dT. The observed maximum surface velocities are compared to the theoretical predictions of Young et al. (1959).For short times after injection, the droplets were driven by this flow towards the hot wall above the matched-density temperature until the droplets reached a point where the forces due to the flow and buoyancy were equal. After longer times, the droplets moved to the cold side due to suspected density changes caused by mass transfer from the droplets to the silicone oil. This was confirmed by tests under isothermal conditions, where it was observed that droplets of all sizes fell to the cold bottom eventually.Thus, even though the thermocapillary flow inside the droplets persisted for long times in spite of the mass transfer, the migration of droplets towards the hot side was eventually affected by uncontrolled buoyancy forces resulting from density changes due to mass transfer. While additional liquids are being tried, it is suggested from the present experience that reduced gravity experiments will probably be necessary to provide unambiguous data for the migration of droplets.     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

Grazing impact of continuous droplet streams with a superhydrophobic surface

When high-velocity droplets make grazing impact with a superhydrophobic surface, the droplets undergo significant deformation before recoiling and rebounding from the surface. Two distinct operating regimes describe the response of the reflected droplet stream after impact. In the first regime, the droplets remain discrete and uniform after the impact, but exhibit rotation and significant oscillations. This regime dominates if each droplet can clear the impact region before the next droplet arrives. In the second regime, droplets cannot avoid coalescing into a puddle at the surface. A secondary jet is ejected from the puddle which breaks up into a random droplet stream after traveling a short distance due to the lack of a forced unstable perturbation. The droplet-to-droplet spacing in the incoming stream determines which regime rules, with the critical value correlated by a Weber number. In the first regime, a detailed accounting of the kinetic and potential energies reveals that neither droplet oscillation nor rotation can fully account for the loss of translational kinetic energy, indicating significant internal circulation must occur in the droplets at impact. An application of droplet rebound from a superhydrophobic surface is proposed.     

气云爆轰的一维模型

激波作用下，悬浮液谪在高温、高压和高速气流中变形、蒸发、剥离甚至破碎。雾化燃料经过一段延迟时间后点火燃烧释放出大量的能量。这些能量由局部爆炸波所携带，通过碰撞传递给引导微波，从而使气云爆轰波自持。文中提出的气云爆轰的一维模型考虑了上述基本过程，并从理论上推导了点火面和ＣＪ面的判据。通过计算，文中讨论了气云爆轰的松弛结构和影响ＣＪ爆速的因素，爆速的计算值与实验值基本相符。     

Evaporation of a droplet larger than the Kolmogorov length scale immersed in a relative mean flow

An experimental effort to understand the contribution of turbulence to the evaporation rate of fuel droplets has been performed with particular attention to conditions when the turbulence scale is smaller than the droplet diameter. N-heptane has been chosen as working fluid to give measurable evaporation rates from droplet images over relatively short experiment times. An active turbulence grid wind tunnel is built for the requirements of this experiment. A camera triggered by a pulse generator takes images of the droplets pinned on wires across the tunnel. The results show a small increase in evaporation rate with increasing turbulence intensity, and that mean flow around the droplets has more impact on evaporation than does the turbulence state.