Pressure waves in a separated gas-liquid layer in a horizontal duct with a step

Pressure wave propagation into a separated gas-liquid layer in a horizontal duct with a step is investigated analytically. The linear solution is derived assuming a large density ratio of liquid to gas. The solution can be found first for the gas layer and then for the liquid layer. The linear wave in a liquid layer is valid even for fairly large initial pressure ratios, and clearly exhibits the dispersive characteristics of the pressure wave in a liquid layer. As the initial pressure ratio is increased, the pressure wave in the gas layer becomes a shock wave. Thus, its effect on the wave in a liquid layer can be found analytically by modifying the boundary condition in part. The wave in a liquid layer consists of a main wave, which propagates with the shock speed in gas, and a precursor wave, whose front propagates with the speed of sound in liquid. The precursor wave has an oscillatory structure; its amplitude increases with increasing shock strength and also with liquid layer thickness.     

Numerical Study of the Near-Wall Gas-Droplet Jet in a Tube with a Heat Flux on the Surface

A model for calculating the flow of a turbulent mixture of air and suspended liquid particles injected into the near-wall region is developed within a unified approach of mechanics of heterogeneous media in the two-velocity and two-temperature approximation of the Eulerian approach. The influence of droplet evaporation in the near-wall jet on heat transfer between the two-phase gas-droplet flow and the wall is studied in the case of heat addition to the latter. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 5–17, January–February, 2006.     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

Interaction of an external supersonic flow with the subsonic layer near a wavy wall

A solution of the problem of supersonic flow past a wavy wall with an adjacent subsonic layer is obtained. The solution is a generalization of the well-known solutions [1] of the linear problem of purely subsonic and purely supersonic flow past a wavy wall and goes over into these solutions in the limiting cases of infinite and zero wall-layer thickness, respectively. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 97–103, January–February, 1997.     

Propagation of pressure waves in a gas-liquid medium with a cluster structure

Propagation of a stepwise shock wave in a liquid containing spherical gas-liquid clusters is experimentally studied. Measured results are compared with available theoretical models. It is shown that resonant interaction of gas-liquid clusters in the wave can increase the amplitude of oscillations in the shock wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 50–60, May–June, 2005.     

MOVEMENT AND SPLASHING OF A DROPLET IMPACTING ON A WET WALL

壁面液体层的存在对液滴撞击壁面的运动具有重要的影响。采用气液两相流动相界面追踪的水平集和流体体积复合方法和壁面润湿模型，实现了液滴撞击湿润壁面运动的数值求解；在此基础上，开展了液滴撞击湿润壁面运动的研究。研究结果表明：液滴以不同速度撞击湿润壁面时，会呈现出黏附铺展、波动运动、皇冠几何体运动以及飞溅运动等几种不同的运动形态，液滴撞击湿润壁面后的压力分布是不同运动形态形成的主要原因；飞溅运动是一定条件下皇冠几何体运动的一种特殊形态，液滴从皇冠几何体侧壁顶端的飞溅分离满足毛细破碎理论；撞击速度对分离液滴的运动方向影响较小，而对壁面液体层厚度的影响则较大；撞击速度和壁面液体层厚度对分离液滴形态、飞溅分离位置、飞溅速度以及飞溅发生时刻等都具有一定的影响。     

Motion of a sphere in a vibrating liquid in the presence of a wall

A solution is obtained for the problem of the motion of a sphere in an ideal liquid bounded from outside by a wall which performs specified vibrations far from the sphere. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences. Novosibirsk 630090, Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 125–132, July–August. 1999.     

Forced oscillations of a gas bubble in a spherical volume of a compressible liquid

A spherically symmetric problem of oscillations of a single gas bubble at the center of a spherical flask filled with a compressible liquid under the action of pressure oscillations on the flask wall is considered. A system of differential-difference equations is obtained that extends the Rayleigh-Plesset equation to the case of a compressible liquid and takes into account the pressure-wave reflection from the bubble and the flask wall. A linear analysis of solutions of this system of equations is performed for the case of harmonic oscillations of the bubble. Nonlinear resonance oscillations and nearly resonance nonharmonic oscillations of the bubble caused by harmonic pressure oscillations on the flask wall are analyzed. Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 111–118, March–April, 1999.     

Interaction of steady shear flows of a barotropic liquid

A mathematical model describing plane-parallel vortex flows of a barotropic liquid with a free boundary in a long-wave approximation is considered. For a particular class of solutions, the solvability of the problem of decay of an initial discontinuity of small amplitude is demonstrated and an algorithm of solution is proposed. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 79–90, September–October, 1999.     

Investigation of double-diffusive convection during the solidification of a binary mixture (NH4Cl–H2O) in a trapezoidal cavity

The solidification of binary mixture (NH₄Cl–H₂O) inside a trapezoidal cavity is investigated experimentally in this study. The effect of the initial concentration of ammonium chloride (0–19.8%) and boundary temperatures (−30 to 0°C) on the solidification process was investigated. Particle image velocimetry (PIV) technique was used for the visualization of the dynamic field in the melt. Thirty-two thermocouples were used to monitor the temperature distribution inside the cavity and on the cooling walls. The convective flow field, the temperature distribution, the frozen layer thickness and the moving solid/liquid interface were obtained for different initial concentrations of ammonium chloride and various boundary temperatures. The results obtained in the course of this study reveal that: (1) the process of solidification is slower with an increase in initial concentration levels of the binary solution: as the concentration increases, the time needed to get the same thickness of frozen layer increases; (2) an increase in the initial concentration of ammonium chloride solution reduce significantly the temperature in the melt; and (3) the initial concentration play a significant role in the evolution of convection flow patterns.     

Study of a Mixing Layer Formed by a Supersonic Main Stream of Air and a Co-Flowing Supersonic Helium Jet

The development of large-scale organised motions in a compressible mixing layer is studied experimentally using holographic interferometry, pressure and turbulence measurements. The mixing layer was formed behind the base of a parallel strut with a Mach 2 air main stream and a co-flowing two-dimensional slot jet (aspect ratio = 45) of helium at a Mach number of 1.2. The mixing layer exhibited highly organised vortical structures which were elongated and inclined approximately 45–50° to the flow direction. The mixing layer showed a linear growth and the mean velocity data indicated self-similar behaviour at sufficiently downstream distances. The results have shown that the thickness of the primary boundary layer has a strong influence on the growth and structure of the mixing layer. This revised version was published online in July 2006 with corrections to the Cover Date.     

Impact on the boundary of a compressible two-layer fluid

Within the framework of the acoustic approximation a solution of the plane nonstationary problem of impact on a fluid boundary is found. The fluid occupies the lower half-plane and consists of two layers with given speeds of sound and densities. The upper layer has a constant depth and is bounded above by a plate with a given normal velocity. The solution is constructed using the Fourier and Laplace integral transforms. Numerical calculations are performed for piston impact across a rigid screen and the impact of a jet with an aerated head on a rigid wall. It is shown that the presence of an interlayer with reduced speed of sound and/or density considerably changes the evolution of the hydrodynamic pressure distribution over the impacting surface: the absolute pressure maximum decreases but pressures of significant amplitude are maintained for a longer time than for a homogeneous fluid.     

Optimization of shock-wave action on a spherical bubble in an ideal incompressible liquid

The possibility of controlling the oscillations of a spherical gas bubble in an ideal incompressible liquid is subjected to theoretical analysis. Liquid surface tension forces are not taken into account. The optimization process realizing a maximum of the radius amplitude and a maximum of the gas pressure in the bubble for a given impulsive change of pressure at infinity is considered. A shock-resonance bubble oscillation procedure giving stepwise pressure changes at the extrema of the radius is constructed. This problem is of interest in connection with the investigation of cavitation erosion [1] and processes in biological tissues [2–4]. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1988.     

Linear Stability Analysis of a Viscous Liquid Sheet in a High-Speed Viscous Gas

Air-assisted atomizers in which a thin liquid sheet is deformed under the action of a high-speed air flow are extensively used in industrial applications, e.g., in aircraft turbojet injectors. Primary atomization in these devices is a consequence of the onset and growth of instabilities on the air/liquid interfaces. To better understand this process, a temporal linear instability analysis is applied to a thin planar liquid sheet flowing between two semi-infinite streams of a high-speed viscous gas. This study includes the full viscous effects both in the liquid and gas basic states and perturbations. The relevant dimensionless groups entering the non-dimensional Orr–Sommerfeld equations and boundary conditions are the liquid and gas stream Reynolds numbers, the gas to liquid momentum flux ratio, the gas/liquid velocity ratio, the Weber number and the equivalent gas boundary layer to liquid sheet thickness ratio. Growth rates and temporal frequencies as a function of the wave number, varying the different dimensionless parameters are presented, together with neutral stability curves. From the results of this parametric study it is concluded that when the physical properties of gas and liquid are fixed, the momentum flux ratio is especially relevant to determine the instability conditions. It is also observed that the gas boundary layer thickness strongly influences the wave propagation, and acts by damping sheet oscillation frequency and growth. This is especially important because viscosity in the basic gas velocity profile has always been ignored in instability analysis applied to the geometry under study. This revised version was published online in July 2006 with corrections to the Cover Date.     

Combined Forced and Free Convective Flow in a Vertical Porous Channel: The Effects of Viscous Dissipation and Pressure Work

Buoyant flow is analysed for a vertical fluid saturated porous layer bounded by an isothermal plane and an isoflux plane in the case of a fully developed flow with a parallel velocity field. The effects of viscous dissipation and pressure work are taken into account in the framework of the Oberbeck–Boussinesq approximation scheme and of the Darcy flow model. Momentum and energy balances are combined in a dimensionless nonlinear ordinary differential equation solved numerically by a Runge–Kutta method. Both cases of upward pressure force (upward driven flows) and of downward pressure force (downward driven flows) are examined. The thermal behaviour for upward driven flows and downward driven flows is quite different. For upward driven flows, the combined effects of viscous dissipation and pressure work may produce a net cooling of the fluid even in the case of a positive heat input from the isoflux wall. For downward driven flows, viscous dissipation and pressure work yield a net heating of the fluid. A general reflection on the roles played by the effects of viscous dissipation and pressure work with respect to the Oberbeck–Boussinesq approximation is proposed.     

Analytical Solution to Subsurface Air Pressure in a Three-Layer Unsaturated Zone with Atmospheric Pressure Changes

In this study, a solution to one-dimensional vertical airflow induced by the time-dependent atmospheric pressure fluctuations is developed in a three-layer unsaturated zone. The discrete atmospheric pressure data are transformed into a continuous boundary condition using the Fourier series analysis. The solution is applied to interpret the field air pressure data in a three-layer unsaturated zone reported in previous studies. The new solution improves the previous solution by reducing the required data measurement and input. The new solution is found to be accurate enough for the purpose of this study by comparing with a numerical solution developed in COMSOL Multiphysics. Given the necessary hydrogeological parameters, the new solution is capable of calculating the air permeability of each layer above a specified depth where the air pressures are known. Sensitivity analysis of the new solution shows that location, thickness, and air permeability of the less permeable layer impose large influence on the propagation of the atmospheric pressure fluctuations. Variations of air-filled porosity in soil layers in/below the less permeable layer may lead to greater amplitude attenuation and phase lag of air pressure than those in soil layers above the less permeable layer.     

Investigation of the effect of the pressure oscillation intensity on the quality of dispersion of a gas in a liquid

The results of an experimental investigation of the effect of the intensity of the pressure oscillations in a wave disperser on the quality of dispersion of a gas in a liquid are given. The results were obtained by designing an apparatus that ensures the variation of the oscillation amplitude at a constant frequency. It is shown that the pressure oscillation amplitude significantly affects the degree of dispersion of the gas in the liquid, a higher quality of dispersion being achieved at the maximum oscillation amplitude. The high quality of dispersion is confirmed both by photos of the flow patterns of the gas-liquid mixture flowing from the disperser and by the kinetic characteristics of dissolution of atmospheric oxygen in water.     

Structure of a turbulent bore in a homogeneous liquid

A mathematical model for the propagation of nonlinear long waves is constructed with allowance for nonhydrostatic pressure distribution and the development of a surface boundary layer due to wave breaking. The problem of the structure of a bore in a homogeneous liquid is solved. In particular, the transition of a wave bore to a turbulent bore as its amplitude increases is described within a single model. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 56–68, March–April, 1999.     

Convective and diffusive surfactant transfer in multiphase liquid systems

Laser interferometry was used to investigate diffusive and convective mass transfer in a multicomponent fluid mixture with a liquid–liquid or liquid–gas interface. For this purpose, an immobile gas bubble or insoluble fluid droplet, having the shape of a short cylinder with a free lateral surface, was inserted into a thin liquid layer. In the case of non-uniform distribution of the dissolved surfactant component, the Marangoni convection near the drop/bubble was initiated by the surface tension inhomogeneities, depending on the surfactant concentration. The applied experimental techniques allowed us to study the structure and evolution of the convective flows and concentration fields in a liquid layer, which due to its small thickness were nearly two-dimensional. Making use of both the vertical and horizontal orientation of the liquid layer, we investigated the mass transfer process at different levels of the interaction between gravity and capillary forces. During the experiments, we detected new solutocapillary phenomena, which were found to be caused by oscillatory regimes of solutal convection occurring around air bubbles and chlorobenzene drops in heterogeneous aqueous solutions of alcohol with a vertical surfactant concentration gradient. The role of the oscillatory instability in the processes of drop saturation by the surfactant from its water solution and an inverse process of surfactant extraction from the drop into the surrounding homogeneous fluid (water) was determined. A reasonable explanation for the driving mechanisms of the discovered effects has been proposed.     

Asymptotic solution of the problem of the action of a stamp on an elastic layer lying on the surface of a compressible fluid of infinite depth

This paper considers a two-dimensional linear unsteady problem of rigid-stamp indentation on an elastic layer of finite thickness lying on the surface of a compressible fluid of infinite depth. The Lamé equations holds for the elastic layer, and the wave equation for the fluid velocity potential. Using the Laplace and Fourier transforms, the problem is reduced to determining the contact stresses under the stamp from the solution of an integral equation of the first kind, whose kernel has a logarithmic singularity. An asymptotic solution of the problem is constructed for large times of interaction. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 131–142, March–April, 2008.