Drift-flux correlation for gas-liquid two-phase flow in a horizontal pipe

A drift-flux correlation has been often used to predict void fraction of gas-liquid two-phase flow in a horizontal channel due to its simplicity and practicality. The drift-flux correlation includes two important drift-flux parameters, namely, the distribution parameter and void-fraction-weighted-mean drift velocity. In this study, an extensive literature survey for horizontal two-phase flow is conducted to establish void fraction database and to acquire existing drift-flux correlations. A total of 566 data is collected from 12 data sources and 4 flow-regime-dependent and 1 flow-regime-independent drift-flux correlations are identified. The predictive capability of the existing drift-flux correlations is assessed using the collected data. It is pointed out that the drift velocity determined by a regression analysis may include a significant error due to a compensation error between distribution parameter and drift velocity. In this study, a simple flow-regime-independent drift-flux correlation is developed. In the modeling approach, the void-fraction-weighted mean drift velocity is approximated to be 0 m/s, whereas the distribution parameter is given as a simple function of the ratio of non-dimensional superficial gas velocity to non-dimensional mixture volumetric flux. The newly developed correlation shows an excellent predictive capability of void fraction for horizontal two-phase flow. Mean absolute error (or bias), standard deviation (random error), mean relative deviation and mean absolute relative deviation of the correlation are 0.0487, 0.0985, 0.0758 and 0.206, respectively. The prediction accuracy of the correlation is similar to the correlation of Chexal et al. (1991), which was formulated based on the drift-flux parameters by means of many cascading constitutive relationships with numerous empirical parameters.     

Three-dimensional evolution of wind waves from gravity-capillary to short gravity range

We report the first systematic laboratory observations of 3-D features of wind waves at early stages of wave field development. The experiments performed in the large IRPHE-Luminy wind-wave tank provided instantaneous reconstruction of the decimeter-scale water surface motions based on simultaneous imaging of the wave slopes in two perpendicular directions. Five essentially distinct regimes in the 3-D evolution of the dominant waves have been identified. Each regime is characterized by different types of 3-D wave patterns associated with specific ranges of wave scale and wave steepness. The likely scenario of the evolution and the possible physical mechanisms of the pattern formation are discussed.     

Measurements of thermally stratified pipe flow using image-processing techniques

The cross-correlation technique and Laser Induced Fluorescence (LIF) have been adopted to measure the time-dependent and two-dimensional velocity and temperature fields of a stably thermal-stratified pipe flow. One thousand instantaneous and simultaneous velocity and temperature maps were obtained at overall Richardson numberRi = 0 and 2.5, from which two-dimensional vorticity, Reynolds stress and turbulent heat flux vector were evaluated. The quasi-periodic inclined vortices (which connected to the crest) were revealed from successive instantaneous maps and temporal variation of vorticity and temperature. It has been recognized that these vortices are associated with the crest and valley in the roll-up motion.List of symbols A Fraction of the available light collected - C Concentration of fluorescence - D Pipe diameter - I Fluorescence intensity - L Sampling length along the incident beam - I ₀ Intensity of an excitation beam - I _c (T) Calibration curve between temperature and fluorescence intensity - I _ref Reference intensity of fluorescence radiation - Re _b Reynolds number based on bulk velocity,U _b D/v - Ri Overall Richardson number based on velocity difference,gDT/U ² - t Time - t Time interval between the reference and corresponding matrix - T Temperature - T ₁,T ₂ Temperature of lower and upper layer - T ^* Normalized temperature, (T–T ₁)/T - T _c (I) Inverse function of temperature as a function ofI _c - T _ref Reference temperature - T Temperature difference between upper and lower flow,T ₂ –T ₁ - U ₁ Velocity of lower stream - U ₂ Velocity of upper stream - U _b Bulk velocity - U _c Streamwise mean velocity atY/D=0 - U Streamwise velocity difference between upper and lower flow,U ₁–U ₂ - u, v, T Fluctuating component ofU, V, T - U, V Velocity component of X, Y direction - X Streamwise distance from the splitter plate - Y Transverse distance from the centerline of the pipe - Z Spanwise distance from the centerline of the pipe - Quantum yield - Absorptivity - vorticity calculated from a circulation - Kinematic viscosity - circulation     

Slip between the phases in two-phase water–oil flow in a horizontal pipe

This paper is devoted to slip phenomenon between the phases that occurs in unstable two-phase water–oil flow systems in a horizontal pipe. The emphasis is placed on the relation between the slip and the real (in situ) water fraction in a flowing mixture, as well as the substitute physical properties of the whole two-phase system. The experimental data collected throughout research served for the evaluation of the accuracy of the methods of real phase fraction in a water–oil flow system in horizontal pipes as they were referred to in the bibliography. Subsequently we have suggested the author indicate a method of determination of the fraction for two-phase liquid systems like O/W, W/O and W + O. In order to establish the specific equations, the drift-flux model has been used here.     

Structure of thin liquid films in gas-liquid horizontal flow

The structure of the liquid film in horizontal annular flow is studied visually using the refractive index matching technique. The liquid film is found to contain significant amount of air bubbles, which are continuously entrained, broken up and released by the rolling motion within the film. A new conceptual picture of the gas-liquid interface is presented.     

An analysis of holdup in horizontal two-phase gas-liquid flow

The Butterworth form of correlation for holdup in two-phase gas-liquid flow is justified theoretically for certain conditions. In addition, a wide range of experimental data were used to show that holdup data may be broadly classified into three major groups based on the flow pattern, and different relationships were found to represent the data in each group. Thus for slug and plug flow, the holdup is given by the Armand type of equation; for stratified flow the holdup is given by the theoretical equations which are derived while annular flow data are satisfactorily represented by a semi-empirical correlation.     

PIV space-time resolution of flow behind blast waves

An ultra-high speed, time-resolved particle image velocimetry (PIV) system is developed to measure velocity fields created by explosive detonators. When initiated into a gas, the detonators generate blast waves that propagate outwards from the origin of initiation at supersonic speeds. The PIV system consists of a custom eight-pulse Nd:YAG laser system and an ultra-high speed camera system comprising four dual-frame CCD cameras optically combined to share a single optic axis. The system is capable of sampling the flow field four times at up to 333 MHz or eight times at up to 8 MHz. System development is discussed, and preliminary application to the complex flow behind the blast wave from an exploding bridge wire detonator is demonstrated.     

Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup

Experimental data and correlations available in the literature for the liquid holdup ε_L and the pressure gradient ΔP_TP/L for gas-liquid pipe flow, generally, do not cover the domain 0 < ε_L < 0.06. Reliable pressure-drop correlations for this holdup range are important for calculating flow rates of natural gas, containing traces of condensate. In the present paper attention is focused on reliable measurements of ε_L and ΔP_TPIL values and on the development of a phenomenological model for the liquid-holdup range 0 < ε_L < 0.06. This model is called the “apparent rough surface” model and is referred to as the ARS model. The experimental results presented in this paper refer to air-water and air-water + ethyleneglycol systems with varying transport properties in horizontal straight smooth glass tubes under steady-state conditions. The holdup and pressure gradient values predicted with the ARS model agree satisfactorily with both our experimental results and data obtained from the literature referring to small liquid-holdup values 0 < ε_L < 0.06. Further, it has been shown that in the domain 38 < < 72 mPa m the interfacial tension of the gas-liquid system has no significant effect on the liquid holdup. The pressure gradient, however, increases slightly with decreasing surface tension values.     

A model for slug frequency during gas-liquid flow in horizontal and near horizontal pipes

Slug formation is an entry region phenomena. Waves form on a growing stratified film eventually blocking the gas to form a slug. The liquid level drops when the slug is swept away and the waves disappear. Then the film rebuilds its level in a time equal to the inverse frequency. The process is modelled and the results shown to be in agreement with experiment.     

Observations on waveforms of capillary and gravity-capillary waves

Due to extreme conditions in the field, there has not been any observational report on three-dimensional waveforms of short ocean surface waves. Three-dimensional waveforms of short wind waves can be found from integrating surface gradient image data (Zhang 1996a). Ocean surface gradient images are captured by an optical surface gradient detector mounted on a raft operating in the water offshore California (Cox and Zhang 1997). Waveforms and spatial structures of short wind waves are compared with early laboratory wind wave data (Zhang 1994, 1995). Although the large-scale wind and wave conditions are quite different, the waveforms are resoundingly similar at the small scale. It is very common, among steep short wind waves, that waves in the capillary range feature sharp troughs and flat crests. The observations show that most short waves are far less steep than the limiting waveform under weak wind conditions. Waveforms that resemble capillary-gravity solitons are observed with a close match to the form theoretically predicted for potential flows (Longuet-Higgins 1989, Vanden-Broeck and Dias 1992). Capillaries are mainly found as parasitic capillaries on the forward face of short gravity waves. The maximum wavelength in a parasitic wave train is less than a centimeter. The profiles of parasitic wave trains and longitudinal variations are shown. The phenomenon of capillary blockage (Phillips 1981) on dispersive freely traveling short waves is observed in the tank but not at sea. The short waves seen at sea propagate in all directions while waves in the tank are much more unidirectional.     

Liquid-phase axial mixing in two-phase horizontal pipe flow

The liquid-phase axial dispersion coefficient and volume-averaged fractional phase hold-ups have been measured in two-phase horizontal pipe flow. Radioactive ^99mTc—technetium-99 metastable—(as an aqueous solution of sodium pertechnate) was used as a tracer. The pulse technique with two-point measurement was employed. Superficial gas (air) and liquid (water) velocities were varied in the range 20–2300 and 30–800mm/s, respectively. The flow regimes covered were bubbly, elongated bubbly, stratified, wavy and slug. Experiments were also performed using single-phase pipe flow. The liquid-phase dispersion coefficient has been shown to depend upon the flow regime and the superficial gas and liquid velocities.     

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines. Friction factors play an important role in the accurate calculation of pressure drop. Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall, gas-wall and interfacial friction in two-phase pipe flow.However most of them are empirical correlations found under special experimental conditions. In this paper by modification of a friction model available in the literature, an improved semiempirical model is proposed. The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved. Pressure gradient and velocity profiles are validated against experimental data. Using the improved model, the pressure gradient deviation from experiments diminishes by about 3%; the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.     

Experimental study of gas-liquid slug flow in a small-diameter vertical pipe

Experimental investigation of upward gas-liquid slug flow in a vertical pipe in 15 mm ID has been carried out. The electrochemical method which permits the determination of the value and direction of instantaneous wall shear stress as well as the mean and fluctuating components of the liquid velocity is used for measurements. It is shown that the change of the sign of the velocity near the wall usually occurs at the moment of slug passage; the time-averaged wall shear stress at low liquid velocities is significantly lower than the value obtained by means of common prediction methods. The results of measuring of the local void fraction. liquid velocity and components of liquid velocity fluctuations are presented. The time-dependent behavior of the instantaneous hydrodynamic characteristics is described.     

Bifurcation mechanism of interfacial electrohydrodynamic gravity-capillary waves near the minimum phase speed under a horizontal electric field

We investigate the evolution of interfacial gravity-capillary waves propagating along the interface between two dielectric fluids under the action of a horizontal electric field. There is a uniform background flow in each layer, and the relative motion tends to induce Kelvin–Helmholtz(KH) instability. The combined effects of gravity, surface tension and electrically induced forces are all taken into account. Under the short-wave assumption, the expansion and truncation method of Dirichlet-Neumann(DN) operators is applied to derive a reduced dynamical model. When KH instability is suppressed linearly by a considerably large electric field, our numerical results reveal that in certain regions of parameter space, nonlinear symmetric traveling wave solutions can be found near the minimum phase speed. Additionally, the detailed bifurcation structures are presented together with typical wave profiles.     

Velocity field in isothermal turbulent bubbly gas-liquid flow through a pipe

Velocity field was measured by laser Doppler velocimetry in isothermal, turbulent bubbly gas-liquid flow through a 26.6 mm inner diameter vertical pipe. The measurements were made about 33 diameters downstream from the pipe entrance, gas injection being just upstream of the entrance. The gas phase radial distribution at the measurement plane exhibited influence of the injection device in that higher gas fraction existed in the central region of the pipe. For comparison, velocity field was also measured in isothermal, turbulent single-phase liquid flow through the same pipe at the same axial plane. Measured were the radial distributions of liquid mean axial and radial velocities, axial and radial turbulent intensities, and axial Reynolds shear stress. The radial distributions of gas bubble mean axial velocity and axial velocity fluctuation intensity were also measured by LDV. A dualsensor fiberoptic probe was used at the same time to measure the radial distributions of gas fraction, bubble mean axial velocity and size slightly downstream of the LDV measurement plane.List of Symbols an average gas bubble diameter - f, f _TP friction factor, friction factor for gas-liquid flow - k _L liquid turbulent kinetic energy - , gas, liquid mass flow rate - R inner radius of pipe - r, {sitR}^* radial coordinate; nondimensional radial coordinate (=r/R) - Re _L liquid Reynolds number - U _G mean axial velocity of gas bubble - U _L mean axial velocity of liquid - U _LO mean axial velocity for flow at the total mass velocity with properties of the liquid phase - u _L ⁺ nondimensional mean axial velocity of liquid in wall coordinate - friction velocity - axial velocity fluctuation intensity of liquid - axial velocity fluctuation intensity of gas bubbles - V_L mean radial velocity of liquid - v _L radial velocity fluctuation intensity of liquid - (uv)_L single-point cross-correlation between axial and radial velocity fluctuations of liquid ( axial Reynolds shear stress) - T _in mean liquid temperature at test section inlet - x flow quality - y normal distance from wall - y ⁺ nondimensional normal distance from wall in wall coordinate (=yu/v_L) - _G gas phase residence time fraction - _L rate of dissipation in the liquid - _L Kolmogorov length scale in the liquid - _L liquid kinematic viscosity - _L characteristic turbulence length scale in the liquid - _G, _L density of gas, liquid - _m gas-liquid mixture density This work was partly supported by National Science Foundation, Thermal Transport and Thermal Processing Program, Chemical and Thermal Systems Division, under Grant No. CTS-9411898.     

Laser velocimetry measurements in a horizontal gas-solid pipe flow

This paper presents laser measurements of particle velocities in a horizontal turbulent two-phase pipe flow. A phase Doppler particle analyzer, (PDPA), was used to obtain particle size, velocity, and rms values of velocity fluctuations. The particulate phase consisted of glass spheres 50 m in diameter with the volume fraction of the suspension in the range _p=10^-4 to _p=10^-3. The results show that the turbulence increases with particle loading.List of symbols a particle diameter - C _va velocity diameter cross-correlation - d pipe diameter - Fr ² Froude number - g gravitational constant - p(a) Probability density of the particle diameter - Re pipe Reynolds number based on the friction velocity - T characteristic time scale of the energy containing eddies - T _L integral scale of the turbulence sampled along the particle path - u, U, u characteristic fluid velocities: fluctuating, mean and friction - v characteristic velocity of the paricle fluctuations - f expected value of any random variable f - f¦g expected value of f given a value of the random variable g - _p particle volume fraction - _p particle response time - absolute fluid viscosity - v kinematic fluid viscosity - _p, _f densities, particle and fluid - _a ² particle diameter variance - _va ² velocity variance due to the particle diameter variance - _vT ² total particle velocity variance - _vt ² particle velocity variance due to the response to the turbulent field     

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.     

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.