Distribution of the velocity profiles of the liquid phase in a gas-liquid flow with small gas contents

Artilce [1] gives the results of measurement of the friction at the wall of a channel under bubble conditions, in a wide range of Reynolds numbers. It is shown that the concept of laminar flow conditions has no meaning when it is applied to the flow of a two-phase mixture, since, even with very small Reynolds numbers, the level of the pulsations of the friction is high, and the spectrum of the pulsations of the friction is continuous. In this case, the mean friction is much greater than the calculated; here the value of the resistance coefficient is not a single-valued function of the Reynolds number. The present article gives the results of measurement of the velocity profiles of the liquid phase, carried out using an electro diffusion method. It is shown that, with Reynolds numbers corresponding to turbulent flow conditions, the profile of the velocity in a two-phase mixture is close to turbulent and does not depend on the gas content.     

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.     

Magnetic resonance imaging of velocity fields, the void fraction and gas dynamics in a cavitating liquid

In acoustic cavitation, the relationship between the bubble dynamics on the microscale and the flow properties on the macroscale is critical in determining sonochemical reaction kinetics. A new technique was developed to measure the void fraction and estimate water mobility in the vicinity of cavitating bubbles using phase-encoded magnetic resonance imaging with short characteristic measurement timescales (0.1–1 ms). The exponential behavior of the NMR signal decay indicated the fast diffusion regime, with the relationship between local mechanical dispersion D _mix and the average bubble radius R, D_mix >> \frac2R²10^-4s, D_{\rm mix}\gg \frac{2R^2}{10^{-4}\hbox{s}}, resulting in dispersion of orders of magnitude greater than diffusion in quiescent water. For two different samples (water and a surfactant solution), the independent measurements of three-dimensional void fraction and velocity fields permitted the calculation of compressibility, divergence and vorticity of the cavitating medium. The measured dynamics of the dissolved gas, compared with that of the surrounding liquid, reflected the difference in the bubble coalescence and lifetimes and correlated with the macroscopic flow parameters.     

气液混输悬链线立管系统两相流特性实验

严重段塞流是海洋工程气液混输管线--立管系统中常见的一种特殊有害流动现象, 采用水平--下倾--悬链线立管气液混输组合管道系统, 通过系列实验在悬链线立管中获得了严重段塞流、间歇流和震荡流等流型, 阐述了这些流动现象的形成机理, 提出了能够产生严重段塞流的判定准则. 结果表明, 悬链线立管严重段塞流具有明显周期性, 在一个周期内的流动特征可分为液塞形成、液体出流、液气喷发及液体回流等4个阶段, 进而给出了各阶段中相关流动参数的变化规律. 在实验中同时还对悬链线与垂直立管中严重段塞流形成机理进行了比较分析, 发现两者在液塞形成阶段有显著差别. 其中, 在悬链线立管中液塞形成之前首先需要经历一个气液混合液塞形成过程, 而垂直立管则没有这个过程.      

Experimental study of vortex emission behind bluff obstacles in a gas liquid vertical two-phase flow

Vortex emission behind cylinders with trapezoidal cross section was experimentally studied in air-water vertical two-phase flows (liquid velocities vary from 45 cm/s to 2 m/s inside a 15 cm ID pipe); the void fraction ranged from 0 to 25%. The measurements were performed at room pressure and temperature. Two flow regimes were observed. For void fraction smaller than 10% vortex emission remained stable and its frequency sharply defined. However, the rms amplitude of the associated pressure fluctuations strongly decreased. These results were explained by bubble trapping inside the vortex cores. This effect was verified experimentally and analyzed using optical fiber probe measurements. Above a 10% void fraction, vortex emission became erratic. Its spectrum became broader but could be identified up to 25% void fraction.     

Liquid velocity distribution in two-phase bubble flow

An improved analytical treatment is developed which makes possible the satisfactory prediction of the liquid velocity distribution in two-phase bubble flow.In the analysis, the shear stress in the liquid phase is regarded as important. When the fluctuation of turbulent velocity can be subdivided into two components: one due to the inherent liquid turbulence independent of the existence of the bubble, (u′, υ′), and the other due to the additional liquid turbulence by the bubble agitation, (u″, υ″), it is possible to split the shear stress into two components, - ?$\text{u′υ′}$ and - ?$\text{u″υ″}$ corresponding to (u′, υ′) and (u″, υ″), respectively.A basic equation for the liquid velocity distribution is derived from further development of this treatment. The agreement between the measured velocity profiles and those calculated is quite close especially in the core region of a duct.     

Slug velocity and liquid layer thickness before an abrupt contraction in horizontal gas–liquid flow

This work presents the results of an experimental investigation into the effects of an abrupt area contraction on the upstream gas-liquid intermittent flow; in particular, the slug velocity (the velocity of slugs as seen from a fixed observer) and the thickness of the liquid layer in the stratified region between two slugs were measured by means of optical probes just before the contraction, and compared with the values obtained in a straight pipe with the same inner diameter and under the same flow conditions. The superficial velocities of the liquid were from 0.6 and 0.9 m/s, while that of the gas ranged from 0.3 to 5 m/s. The results indicate that the abrupt contraction results in a substantial reduction of slug velocity, and in a growth of the liquid layer thickness.     

Hydrodynamic and thermal fields analysis in gas-solid two-phase flow

The present work aims to investigate numerically the flowfield and heat transfer process in gas-solid suspension in a vertical pneumatic conveying pipe. The Eulerian-Lagrangian model is used to simulate the flow of the two-phases. The gas phase is simulated based on Reynolds Average Navier-Stokes equations (RANS) with low Reynolds number k-ε model, while particle tracking procedure is used for the solid phase. An anisotropic model is used to calculate the Reynolds stresses and the turbulent Prandtl number is calculated as a function of the turbulent viscosity. The model takes into account the lift and drag forces and the effect of particle rotation as well as the particles dispersion by turbulence effect. The effects of inter-particles collisions and turbulence modulation by the solid particles, i.e. four-way coupling, are also included in the model. Comparisons between different models for turbulence modulation with experimental data are carried out to select the best model. The model is validated against published experimental data for velocities of the two phases, turbulence intensity, solids concentration, pressure drop, heat transfer rates and Nusselt number distribution. The comparisons indicate that the present model is able to predict the complex interaction between the two phases in non-isothermal gas-solid flow in the tested range. The results indicate that the particle-particle collision, turbulence dispersion and lift force play a key role in the concentration distribution. In addition, the heat transfer rate increases as the mass loading ratio increases and Nusselt number increases as the pipe diameter increases.     

Phase and velocity distributions in vertically upward high-viscosity two-phase flow

The two-phase pressure drop in vertical industrial pipes is mainly determined by gravitation and acceleration of the fluid, which means that the void fraction is key an important parameter in any model to predict pressure drops. Typically, these models are applied in industry to size pumps and, e.g., emergency relief systems. There is a shortage of void fraction data in the literature for liquids with a dynamic viscosity above 1000 mPa s. Adiabatic experiments have been performed of mixtures of nitrogen and solutions of polyvinylpyrrolidone (Luviskol^®) in water with dynamic viscosities in the range 900–7000 mPa s. Inner tube diameter was 54.5 mm. Mass flux and quality were varied in a wide range: 8–3500 kg/m²/s and 0–82%, respectively. The corresponding superficial velocities were 0.005–3.4 m/s for the liquid and 0–30 m/s for the nitrogen. For comparison, reference measurements were taken of mixtures of nitrogen with water (1 mPa s). Care has been taken to measure only well-developed flows.     

Phase split of liquid–liquid two-phase flow at a horizontal T-junction

This paper provides data on the split of liquid/liquid two-phase flow at a horizontal T-junction. Phase maldistribution was measured for kerosene–water flow at the T-junction with equal pipe diameters of 67.4 mm. Data were taken with both stratified flow with a mixture at interface and dispersed flows approaching the junction. The degree of phase maldistribution was not very great but preferential emergence of either phase from the side-arm was observed depending on the flow rates of the two-phases. There are similarities with the limited split data from liquid/solid flows and the degree of separation is seen to depend on the dispersed/continuous phase density ratio. The data were compared to predictions from the correlation by Seeger et al. The Seeger equation gives but reasonable agreement.     

A multiphase,micro-scale PIV measurement technique for liquid film velocity measurements in annular two-phase flow

Prediction methods for two-phase annular flow require accurate knowledge of the velocity profile within the liquid film flowing at its perimeter as the gradients within this film influence to a large extent the overall transport processes within the entire channel. This film, however, is quite thin and variable and traditional velocimetry methods have met with only very limited success in providing velocity data. The present work describes the application of Particle Image Velocimetry (PIV) to the measurement of velocity fields in the annular liquid flow. Because the liquid is constrained to distances on the order of a millimeter or less, the technique employed here borrows strategies from micro-PIV, but micro-PIV studies do not typically encounter the challenges presented by annular flow, including very large velocity gradients, a free surface that varies in position from moment to moment, the presence of droplet impacts and the passage of waves that can be 10 times the average thickness of the base film. This technique combines the seeding and imaging typical to micro-PIV with a unique lighting and image processing approach to deal with the challenges of a continuously varying liquid film thickness and interface. Mean velocity data are presented for air–water in two-phase co-current upward flow in a rectangular duct, which are the first detailed velocity profiles obtained within the liquid film of upward vertical annular flow to the authors’ knowledge. The velocity data presented here do not distinguish between data from waves and data from the base film. The resulting velocity profiles are compared with the classical Law of the Wall turbulent boundary layer model and found to require a decreased turbulent diffusivity for the model to predict well. These results agree with hypotheses previously presented in the literature.     

Rheological behaviour of two-phase flow of solid particles in a gas

The present investigation was concerned with the rheological behaviour of dilute suspensions of solid particles in a gas in a vertical cocurrent flow moving upwards. Starting from the experimentally determined dependence of the pressure drop on the concentration of solid particles and the Reynolds number of the carrier medium in the steady flow region, the rheological parameters were estimated using pseudo-shear diagrams. Air was the carrier medium and the dispersed phase was one of six fractions of polypropylene powder and five fractions of glass ballotini. The results show that the investigated two-phase systems have pseudoplastic character which becomes more pronounced with increases in concentration, equivalent diameter and density of solid particles in the flowing suspension. C _d coefficient of particle resistance - d _e equivalent diameter of particles - D column diameter - Fr Froude number - g gravitational acceleration - K rheological parameter - L length - n rheological parameter - p _t pressure drop due to friction - p _m total pressure drop - p _ag pressure drop due to acceleration of the gas phase - p _as pressure drop due to acceleration of the solid phase - p _g hydrostatic pressure of the gas phase - p _s specific effective weight of the dispersed phase - r radius - Re Reynolds number - Re _p Reynolds number of a particle - Re _G generalized Reynolds number - Re _G1 generalized Reynolds number relating to the end of the laminar flow region - Re _G2 generalized Reynolds number relating to the beginning of the turbulent flow region - w _z axial component of velocity - u _t steady free-fall velocity of a single particle - w average velocity - w _g average velocity of the gas phase - w _s average velocity of the dispersed phase of solid particles - relative mass fraction of solid particles - x _s volume fraction of solid particles - _g coefficient of pressure drop due to friction - µ dynamic viscosity - _g density of the gas phase - _m density of the suspension - _s density of solid particles - _ds density of the dispersed phase - _w shear stress at the wall     

Solution of the direct problem of the flow of a two-phase mixture of a gas and foreign solid or liquid particles in a laval nozzle

Within the framework of a two-liquid (two-velocity and two-temperature) model of a continuous medium, the article considers the flow of a mixture of a gas and foreign particles in the subsonic, transonic, and supersonic parts of a Laval nozzle. In the case of a thin layer of pure gas near the wall, the problem is solved in two stages. First, the method of establishment is used to calculate the core of the flow, where the gas with the particles is flowing; under these circumstances, the parameters in the layer of pure gas are determined approximately; then simplified equations (of the type of the equations of the boundary layer) are used to find the distribution of the parameters in the zone of pure gas, and the flow in the core of the stream is refined. Examples of the calculation are given. Use of the method developed permitted establishing some of the special characteristics of the flow of a mixture of gas with particles in a Laval nozzle in the case of Stokes flow around the foreign particles.     

Void fraction,bubble velocity and bubble size in two-phase flow

Experiments were performed in atmosphereic vertical air-water flows, for void fractions between 0.25 and 0.75 (cross-sectional averages) and superficial liquid velocities of 1.3, 1.7 and 2.1 m/s. Local values of void fraction and bubble velocity as well as the bubble diameter were measured by means of a resistivity probe technique. Reliable values were obtained for the local void fraction over the entire range $\text{0 ≤ α ≤ 1}$. The void fraction profiles appeared to have a local maximum at the pipe center, local maxima close to the wall were obviously absent. The resistivity probes are shown to measure the velocity of the interface between the conducting and nonconducting phases, which equals the gas velocity only for low void fractions. The measured data for void fraction and bubble velocity were correlated by means of power law distribution functions, with exponents given by a function of the cross-sectionally averaged void fraction. The Sauter mean diameters for the bubble size spectra found, agree reasonably well with diameters predicted by a theoretical model based on the energy dissipation in the flow.     

Linear stability in the flow of a liquid film concurrent with a gas flow

The two-phase flow of liquid films are often encountered in practice, but the number of theoretical papers devoted to this problem is limited. The problem of the linear stability of a viscous liquid film subjected to a gas flow has been formulated in [1] and, in somewhat different form, in [2]. The linear stability of plane-parallel motion in films has been studied analytically in [1–8] for some limiting cases. The range of validity of the analytic approaches remains an open question. Therefore, an exact numerical analysis of flow stability over a fairly broad range is required. In the present paper a separate solution of the problem for the gas and the liquid is shown to be possible. The Orr-Sommerfeld equation has been integrated numerically, and the results are compared to the results of analytic calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–146, January–February, 1976.The author is grateful to É. É. Markovich for directing the work and to V. Ya. Shkadov for his interest in the work and many useful comments.