A model for pressure loss, film thickness, and entrained fraction for gas-liquid annular flow

A two-component (air-water) annular flow model is presented requiring only flow rates, absolute pressure, temperature, and tube diameter. Film thicknesses (base film and wave height) are calculated from a critical film thickness model. Modeled pressure gradient is weighted by wave intermittency to compute average pressure gradient. Film flow rate and wave velocity are estimated using the universal velocity profile in the waves and a piecewise linear profile in the base film. For vertical flow, mean absolute errors for film thickness, wave velocity, and pressure gradient are 9%, 9%, and 19%, respectively. In horizontal flow, mean absolute errors for pressure gradient, base film thickness, and disturbance wave velocity are 17%, 10%, and 14%, respectively, on par with those from single-behavior models that require additional film thickness or other data as inputs.     

Turbulence modification in vertical upward annular flow passing through a throat section

Experimental studies on the turbulence modification in annular two-phase flow passing through a throat section were carried out. The turbulence modification in multi-phase flow due to the interactions between two-phases is one of the most interesting scientific issues and has attracted research attention. In this study, the gas-phase turbulence modification in annular flow due to the gas–liquid phase interaction is experimentally investigated. The annular flow passing through a throat section is under the transient state due to the changing cross sectional area of the channel and resultantly the superficial velocities of both phases are changed compared with a fully developed flow in a straight pipe. The measurements for the gas-phase turbulence were precisely performed by using a constant temperature hot-wire anemometer, and made clear the turbulence structure such as velocity profiles, fluctuation velocity profiles. The behavior of the interfacial waves in the liquid film flow such as the ripple or disturbance waves was also observed. The measurements for the liquid film thickness by the electrode needle method were also performed to measure the base film thickness, mean film thickness, maximum film thickness and wave height of the ripple or the disturbance waves.     

Time-dependent behaviour of the liquid film in horizontal annular flow

A crucial point still to be established in the prediction of the film thickness distribution in horizontal annular two-phase flow is the mechanism(s) for transporting liquid from the bottom to the top part of the tube. To resolve this issue, the time-dependent behaviour of the liquid film is studied. Wave characteristics such as velocity and frequency are measured around the circumference. It is inferred from the autospectral density functions of film thickness variation that disturbance waves play an important, but as yet unclear, role in the formation of a liquid film in the top part of the tube. A new mechanism, based on the shape of disturbance waves is proposed.     

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.     

Experimental study on axial development of liquid film in vertical upward annular two-phase flow

Accurate measurements of the interfacial wave structure of upward annular two-phase flow in a vertical pipe were performed using a laser focus displacement meter (LFD). The purpose of this study was to clarify the effectiveness of the LFD for obtaining detailed information on the interfacial displacement of a liquid film in annular two-phase flow and to investigate the effect of axial distance from the air–water inlet on the phenomena. Adiabatic upward annular air–water flow experiments were conducted using a 3 m long, 11 mm ID pipe. Measurements of interfacial waves were conducted at 21 axial locations, spaced 110 mm apart in the pipe. The axial distances from the inlet (z) normalized by the pipe diameter (D) varied over z/D = 50–250. Data were collected for predetermined gas and liquid flow conditions and for Reynolds numbers ranging from Re_G = 31,800 to 98,300 for the gas phase and Re_L = 1050 to 9430 for the liquid phase. Using the LFD, we obtained such local properties as the minimum thickness, maximum thickness, and passing frequency of the waves. The maximum film thickness and passing frequency of disturbance waves decreased gradually, with some oscillations, as flow developed. The flow development, i.e., decreasing film thickness and passing frequency, persisted until the end of the pipe, which means that the flow might never reach the fully developed state. The minimum film thickness decreased with flow development and with increasing gas flow rate. These results are discussed, taking into account the buffer layer calculated from Karman’s three-layer model. A correlation is proposed between the minimum film thickness obtained in relation to the interfacial shear stress and the Reynolds number of the liquid.     

Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part II: Analysis and comparison to models

Film thickness distributions in upward vertical air–water annular flow have been determined using planar laser-induced fluorescence (PLIF). Film thickness data are frequently used to estimate interfacial shear and pressure loss. This film roughness concept has been used in a number of models for annular flow of varying complexity. The PLIF data are presently applied to the single-zone interfacial shear correlation of Wallis; the more detailed model of Owen and Hewitt; and the two-zone (base film and waves) model of Hurlburt, Fore, and Bauer. For the present data, these models all under-predict the importance of increasing liquid flow on pressure loss and interfacial shear. Since high liquid flow rates in annular flow induce disturbance wave and entrainment activity, further modeling in these areas is advised.     

Finite-amplitude stability analysis of liquid films down a vertical wall with and without interfacial phase change

The generalized kinematic equation for film thickness, taking into account the effect of phase change at the interface, is used to investigate the nonlinear stability of film flow down a vertical wall. The analysis shows that supercritical stability and subcritical instability are both possible for the film flow system. Applications of the result to isothermal, condensate and evaporate film flow show that mass transfer into (away from) the liquid phase will stabilize (destabilize) the film flow. Finally, we find that supercritical filtered waves are always linearly stable with regard to side-band disturbance.     

The effect of surfactants on air–water annular and churn flow in vertical pipes. Part 1: Morphology of the air–water interface

In this work, the influence of surfactants on air–water flow was studied by performing experiments in a 12 metre long, 50 mm inner diameter, vertical pipe at ambient conditions. High-speed visualisation of the flow shows that the morphology of the air–water interface determines the formation of foam. The foam subsequently alters the flow morphology significantly. In annular flow, the foam suppresses the roll waves, and a foamy crest is formed on the ripple waves. In the churn flow regime, the flooding waves and the downwards motion of the liquid film are suppressed by the foam. The foam is transported in foam waves moving upwards superposed on an almost stagnant foam substrate at the pipe wall. Foam thus effectively reduces the superficial gas velocity at which the transition from annular to churn flow occurs. These experiments make more clear how surfactants can postpone liquid loading in vertical pipes, such as in gas wells.     

Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part I: Methods and data

Most approaches to the modeling of annular flow require information regarding the thin liquid film surrounding the central gas core. This film is hypothesized to present a rough surface to the gas core, enhancing interfacial shear and pressure loss, with the roughness closely linked to the height of the film. This height is typically obtained from conductance probe measurements. The present work used planar laser-induced fluorescence to provide direct visualization of the liquid film in upward vertical air–water annular flow. Images were processed to produce the distribution of film heights. The standard deviation and average film thickness are found to be an increasing function of liquid flow and a decreasing function of gas flow, with the standard deviation approaching 0.4 times the average at sufficient liquid flow.     

Experiments on the flow of a thin liquid film over a horizontal stationary and rotating disk surface

Experiments on characterization of thin liquid films flowing over stationary and rotating disk surfaces are described. The thin liquid film was created by introducing deionized water from a flow collar at the center of an aluminum disk with a known initial film thickness and uniform radial velocity. Radial film thickness distribution was measured using a non-intrusive laser light interface reflection technique that enabled the measurement of the instantaneous film thickness over a finite segment of the disk. Experiments were performed for a range of flow rates between 3.0 lpm and 15.0 lpm, corresponding to Reynolds numbers based on the liquid inlet gap height and velocity between 238 and 1,188. The angular speed of the disk was varied from 0 rpm to 300 rpm. When the disk was stationary, a circular hydraulic jump was present in the liquid film. The liquid-film thickness in the subcritical region (downstream of the hydraulic jump) was an order of magnitude greater than that in the supercritical region (upstream of the hydraulic jump) which was of the order of 0.3 mm. As the Reynolds number increased, the hydraulic jump migrated toward the edge of the disk. In the case of rotation, the liquid-film thickness exhibited a maximum on the disk surface. The liquid-film inertia and friction influenced the inner region where the film thickness progressively increased. The outer region where the film thickness decreased was primarily affected by the centrifugal forces. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. At high rotational speeds, spiral waves were observed on the liquid film. It was also determined that the angle of the waves which form on the liquid surface was a function of the ratio of local radial to tangential velocity.     

Do huge waves exist in horizontal gas-liquid pipe flow?

Huge waves are periodic interfacial structures which are observed in vertical co-current gas-liquid two-phase flow under churn and the transition between churn and annular flows. Published data examining vertical gas-liquid flow indicate that a huge wave has either a continuous gas core surrounded by a large-scale interfacial wave or a core with a highly-agitated mixture of gas and liquid.Employing a Wire-Mesh Sensor (WMS), the spatio/temporal investigation of high flow rate horizontal air-water flow divulged some recurrent liquid structures (one may call pseudo-slugs) analogous to huge waves of (vertical) churn flow. In both cases, the blow-through (penetration of gas into the liquid structure) was the most manifest feature.Different qualitative and quantitative methods were employed to compare the behavior of pseudo-slug to churn flow. The quantitative measures included Probability Density Function analysis (PDF), distribution coefficient in drift flux model, structural velocity, core average velocity, interfacial friction factor, and slippage number. Both flow regimes demonstrated similar behavior.     

Studying disturbance waves in vertical annular flow with high-speed video

In many annular two-phase gas–liquid flows, large disturbance waves propagate liquid mass. These waves are important for modeling of gas-to-liquid momentum transfer and liquid film behavior. High-speed videos of vertical upflow have been analyzed to extract individual and average wave data. Two types of structures, coherent waves and piece waves, have been identified in these flows. Velocities, lengths, and temporal spacings of individual waves and average velocities, lengths, frequencies, and intermittencies have been studied as functions of both gas and liquid flow rates. Velocity and frequency increase with liquid and gas flow rates, length decreases with increasing gas flow and increases with increasing liquid flow, and intermittency is predominantly an increasing function of liquid flow.     

Downwards co-current annular flow

This paper summarizes a study of the characteristics of downwards annular two-phase flow. The measurements reported are of film thickness, wave velocity and frequency, local pressure fluctuations, pressure gradient and liquid entrainment. The most important new feature of the work is the use of continuous data recording with either on-line or off-line statistical analysis. Experiments were carried out with air-water flows in tubes of 3.18 and 3.82 cm bore. It is shown that the interfacial characteristics of the flow may require at least 5 m for full development at some flow rates and most measurements were carried out with an entrance region of this length. It is also shown that the pressure fluctuations, characteristic of this two-phase flow regime, are primarily due to pressure surges caused by disturbance waves in the system passing through the exit device. A new regime map is proposed, based on experimental evidence, in which several distinctive types of interfacial behaviour are noted.     

Study of gas-sheared liquid film in horizontal rectangular duct using high-speed LIF technique: Three-dimensional wavy structure and its relation to liquid entrainment

The flow of a liquid film sheared by high velocity gas stream in a horizontal rectangular duct was investigated using a high-speed laser-induced fluorescence technique. Measurements of local film thickness were resolved in both longitudinal and transverse coordinates with high spatial and temporal resolution. It was found that the generation of fast and slow ripples by the disturbance waves was qualitatively the same as it was observed earlier in completely different conditions. The transverse size and curvature of the disturbance waves and ripples were measured. A relationship between the three-dimensional structure of ripples on top of disturbance waves and the two mechanisms of liquid entrainment, known as ‘bag break-up’ and ‘ligament break-up’, is proposed.     

The effect of pipe diameter on the structure of gas/liquid flow in vertical pipes

Experimental work on two-phase vertical upward flow was carried out using a 19 mm internal diameter, 7 m long pipe and studying the time series of cross-sectional average void fractions and pressure gradient which were obtained simultaneously. With the aid of a bank of published data in which the pipe diameter is the range from 0.5 to 70 mm, the effect of pipe diameter on flow characteristics of two-phase flow is investigated from various aspects. Particularly, the work focuses on the periodic structures of two-phase flow. Average film thicknesses and the gas flow rate where slug/churn and churn/annular flow transitions occur all increase as the diameter of the pipe becomes larger. On the other hand, the pressure gradients, the frequencies of the periodic structures and the velocities of disturbance waves decrease. The velocity of disturbance waves has been used to test the model of Pearce (1979). It is found that the suggested value of Pearce coefficient 0.8 is reasonable for lower liquid flow rates but becomes insufficient for higher liquid flow rates.     

Liquid film circumferential asymmetry prediction in horizontal annular two-phase flow

This study considers the prediction of the degree of asymmetry in the circumferential distribution of the liquid film in the tube cross section of horizontal annular gas–liquid two-phase flow, endemic of the lower region of this flow regime near the stratified-wavy flow transition boundary. Focusing on disturbance waves as the predominant mechanism for transporting the liquid in the annular film from the bottom to the top of the tube to counterbalance the draining effect of gravity, a new prediction method for the degree of asymmetry in the annular liquid film is proposed that outperforms existing correlations. Flow pattern maps for horizontal gas–liquid two-phase flow of frequent use in the design of evaporators and condensers can thus be explicitly updated to account for both symmetric and asymmetric annular flows. The underlying experimental database contains 184 measured liquid film circumferential profiles, corresponding to 1276 local liquid film thickness measurements collected from 15 different literature studies for tube diameters from 8.15 mm to 95.3 mm.     

Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow

The study considers algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow, focusing in particular on momentum and heat transfer (so-called ‘convective boiling’) through the annular liquid film. In contrast with single-phase wall-bounded flow theory, shear-driven annular liquid films are assumed here to behave as fluid-bounded flows, mostly interacting with the shearing gas-entrained droplets core flow. Besides providing velocity and temperature profiles through the liquid film, the turbulence model proposed here predicts key parameters such as the average liquid film thickness, the void fraction and the convective boiling heat transfer coefficient with accuracies comparable or better than those of leading design correlations. This turbulence model is part of a unified annular flow modeling suite that includes methods to predict the entrained liquid fraction and the axial frictional pressure gradient. The underlying heat transfer database covers nine fluids (water, two hydrocarbons and six refrigerants) for vertical and horizontal tubes of 1.03-14.4 mm diameter and pressures of 0.1-7.2 MPa. Importantly, this study shows that there appears to be no macro-to-microscale transition when it comes to annular flow. Simply better physical modeling is required to span this range.     

A two-phase model for laminar film condensation from steam-air mixtures in vertical parallel-plate channels

Detailed results are presented for laminar film condensation from steam-air mixtures flowing downward in vertical flat-plate channels. The mixture flow is laminar and saturation conditions prevail at the inlet. A fully coupled implicit numerical approach is used that achieves excellent convergence behavior, even for high inlet gas mass fractions. The detailed results include velocity, temperature, and gas mass fraction profiles, as well as axial variations of film thickness, pressure gradient and Nusselt number. The effects of a wide range of changes in the four independent variables (the inlet-to-wall temperature difference and the inlet values of gas concentration, Reynolds number, and pressure) on the film thickness, axial pressure gradient, and the local and average Nusselt numbers are carefully examined. It was found that increases in inlet concentration of noncondensable gas caused significant decreases in the film thickness, local Nusselt number, and axial pressure gradient. An analytical solution for the film thickness and velocity field at the end of condensation path was developed and shown to be the asymptotic value of the numerical results for large distances along the channel.     

Wave regimes of ascending flow of a thin layer of a viscous liquid in contact with a gas

The flow of a liquid in thin layers is one of the hydrodynamic problems of chemistry and heat engineering. The large surface area of films and their small thickness make it possible to accelerate thermal, diffusive, and chemical processes at the gas-liquid boundary.Theoretical studies of liquid flow in a vertical descending thin layer are presented in [1–4]. In this paper we study ascending wave flows of a liquid in a thin vertical layer in contact with a gas, i.e., flows in the direction opposite the action of the force due to gravity, with account for the action of the gas on the liquid surface. Such motions are encountered when oil is extracted from strata that are saturated with gas. At some distance from the stratum the oil and gas separate: the gas travels at high velocity inside the pipe, occupying a considerable portion of the pipe, and the liquid is displaced toward the pipe walls, forming a thin film. In certain cases a wave-like interface develops between the oil and gas that travels with a velocity greater than that of the liquid but less than the average gas velocity. Similar phenomena are observed in high velocity mass exchangers.We examine the effect of the gas for both laminar and turbulent flow.Studies that neglect the effect of the gas flow on the liquid show that for waves on the film surface whose lengths are considerably longer than the average thickness of the layer, the liquid motion in the film is described by boundary layer equations in which account is taken of the mass force, i.e., the force due to gravity. With some approximation, we can assume that in accounting for the effect of the gas on the liquid the liquid flow is described by these same equations.     

The effect of total reflection in PLIF imaging of annular thin films

Planar laser-induced fluorescence (PLIF) imaging techniques are increasingly used to study wavy annular flows in vertical and horizontal pipes. We present a ray-tracing study that analyzes the imaging properties of the PLIF technique for uniform and wavy annular films. Part of the emitted fluorescence will hit the water–air interface at angles greater than the critical angle of total reflection. As a consequence, PLIF imaging probes the film twice: From bottom to top and then again from top to bottom. Deflected fluorescence widens PLIF images of uniform films by about 30%. Surface waves further increase the contribution of deflected rays to the overall signal. At the steep slopes of large amplitude axial waves, total reflection might widen PLIF signals by up to a factor of two.