The effect of hydrodynamic friction on the stability of a wall layer in annular two-phase flow

This note is concerned with annulat flow in a vertical tube when the gas stream in the central portion of the tube is separated from the wall by an annular layer of liquid. The friction at the interface may have either a stabilizing or destabilizing effect on such a flow regime with respect to small disturbances of the interface. The liquid-layer thickness is assumed small, which permits direct use of the results of [1] in studying the stability. The analysis is applicable to laminar and developed turbulent gas motions; in both cases the motion in the liquid layer is assumed laminar.     

Simultaneous heat and mass transfer inside a vertical tube in evaporating a heated falling alcohols liquid film into a stream of dry air

A numerical study of the evaporation in mixed convection of a pure alcohol liquid film: ethanol and methanol was investigated. It is a turbulent liquid film falling on the internal face of a vertical tube. A laminar flow of dry air enters the vertical tube at constant temperature in the downward direction. The wall of the tube is subjected to a constant and uniform heat flux. The model solves the coupled parabolic governing equations in both phases including turbulent liquid film together with the boundary and interfacial conditions. The systems of equations obtained by using an implicit finite difference method are solved by TDMA method. A Van Driest model is adopted to simulate the turbulent liquid film flow. The influence of the inlet liquid flow, Reynolds number in the gas flow and the wall heat flux on the intensity of heat and mass transfers are examined. A comparison between the results obtained for studied alcohols and water in the same conditions is made.     

Numerical simulation of the modulated flow pattern for vertical upflows by the phase separation concept

The multiphase heat transfer could be enhanced by creating thin liquid film on the wall. The phase separation concept is called due to the separated flow paths of liquid and gas over the tube cross section to yield thin liquid film. Our proposed heat transfer tube consists of an annular region close to the wall and a core region, interfaced by a suspending mesh cylinder in the tube. The heat transfer tube is a multiscale system with micron scale of mesh pores, miniature scale of annular region and macroscale of tube diameter and length. Great effort has been made to link from micron scale to macroscale. The Volume of Fluid (VOF) method simulates air/water two-phase flow for vertical upflow. The three-dimensional system was successfully converted to a two-dimensional one by using three equivalent criteria for mesh pores. The non-uniform base grid generation and dynamic grid adaption method capture the bubble interface. The numerical results successfully reproduce our experimental results. The numerical findings identify the following mechanisms for the enhanced heat transfer: (a) counter-current flow exists with upward flow in the annular region and downward flow in the core region; (b) void fractions are exact zero in the core region and higher in the annular region; (c) the liquid film thicknesses are decreased to 1/6–1/3 of those in the bare tube section; (d) the gas–liquid mixture travels much faster in the annular region than in the bare tube; (e) three-levels of liquid circulation exists: meter-scale bulk liquid circulation, moderate-scale liquid circulation around a single-elongated-ring-slug-bubble, and microliquid circulation following the ring-slug-bubble tails. These liquid circulations promote the fluid mixing over the whole tube length and within the radial direction. The modulated parameters of void fractions, velocities and liquid film thicknesses in the annular region and three-levels of liquid circulation are greatly beneficial for the multiphase heat transfer enhancement.     

The motion of a closely-fitting sphere in a fluid-filled tube

Singular perturbation techniques are used to investigate the slow, asymmetric flow around a sphere positioned eccentrically within a long, circular, cylindrical tube filled with viscous fluid. The results apply to situations in which the sphere occupies virtually the entire cross section of the cylinder, so that the clearance between the particle and tube wall is everywhere small compared with both the sphere and tube radii. The technique is an improvement over conventional “lubrication-theory” analyses.Asymptotic expansions, valid for small dimensionless clearances, are obtained for the hydrodynamic force, torque and pressure drop for flow past a stationary sphere, as well as for the case of a sphere translating or rotating in an otherwise quiescent fluid. These expansions are employed to predict the macroscopic behavior of both a neutrally-buoyant sphere suspended in a Poiseuille flow, and a sedimenting sphere in a vertical tube.The results find application in capillary blood flow, pipeline transport of encapsulated materials, and falling-ball viscometers.     

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.     

Propagation of pressure waves in two-phase flow

We deal with a pressure wave of finite amplitude propagating in a gas and liquid medium or in the fluid in an elastic tube. We study the effects of pipe elasticity on the propagation velocity of the pressure wave. Pressure waves of finite amplitude progressing in the two-phase flow are treated considering the void fraction change due to pressure rise. The propagation velocity of the two-phase shock wave is also investigated, and the behavior of the reflection of the pressure wave at the rigid wall is analyzed and compared to that in a pure gas or liquid. The results are compared to experimental data of a pressure wave propagating in the two-phase flow in a vertical shock tube.     

Numerical study of condensing a small concentration of vapour inside a vertical tube

The purpose of this study is to analyse the combined heat and mass transfer of liquid film condensation from a small steam–air mixtures flowing downward along a vertical tube. Both liquid and gas stream are approached by two coupled laminar boundary layer. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. The effects of a wide range of changes of three independent variables (inlet pressure, inlet Reynolds number and wall temperature) on the concentration at exit tube, local Nusselt and Sherwood numbers, film thickness, accumulated condensate rate and temperature are carefully examined. The numerical results indicate that in the case of condensing a small concentration of vapours from a mixture, the resistance to heat and mass transfer by non-condensable gas becomes very intense. The comparisons of average Nusselt number and local condensate heat transfer coefficient with the literature results are in good agreement.     

Local characteristics of upward gas-liquid flows

The results of two-phase flow structure measurements in an upward gas-liquid flow in a 86.4 mm i.d. tube by the electrochemical and conductivity techniques are presented. Measurements were made in bubble and slug flow regimes at liquid flow rates ranging from 0.2 to 2 m/s.The flow instability and ambiguity in a bubble regime at low velocities is shown to exist. Great discrepancy between measured wall shear stress values and those predicted by the Lockhart-Martinelli model are due to the nonuniform distribution of gas over the tube cross section. Measurements of intensity of wall shear stress and liquid velocity fluctuations in a two-phase flow are presented.     

Effect of surfactants on liquid loading in vertical wells

Most gas wells produce some amount of liquid. The liquid is either condensate or water. At high rates, the gas is able to entrain liquid to the surface; however, as gas well depletes, the liquid drops back in a gas well (called liquid loading) creating a back pressure on the reservoir formation. Addition of surfactants to the well to remove liquid is one of the common methods used in gas wells. Liquid loading in vertical gas wells with and without surfactant application was investigated in this study. Anionic, two types of amphoteric (amphoteric I and amphoteric II), sulphonate and cationic surfactants were tested in 2-inch and 4-inch 40-feet vertical pipes. Pressure gradient and liquid holdup are measured. Visual observation with a high speed camera was used to gain insight into the direction of foam flow in intermittent flow and foam film flow under annular flow conditions.Liquid loading is initiated when the liquid film attached to the wall in annular flow starts flowing downwards. Introduction of foam causes the gas velocity at which film reversal occurs to decrease; this shift increases with increasing surfactant concentration and it is more pronounced in 2-inch pipe than in 4-inch pipe. That is, the benefit of surfactants is much more pronounced in 2-inch pipe than in 4-inch pipe. The reason for postponement of liquid loading is reduction in the liquid holdup at low gas velocities which reduces the liquid holdup in foam flow compared to air-water flow. However, at higher gas velocities, the pressure drop in 2-inch compared to 4-inch pipe increases rapidly as the surfactant concentration increases. The selection of optimum concentration of the surfactant is a balance between the reductions in the gas velocity at which liquid loading occurs compared to increase in the frictional loss as the concentration increases. We provide guidelines about the selection of the surfactant concentration.Visual observations using high speed camera show differences in the behavior under foam flow conditions. Unlike air-water flow, the liquid film attached to the wall is replaced by thick foam capturing the gas bubbles. The type of roll waves which carry the liquid in 2-inch pipe is different than what was observed in 4-inch pipe. Compared to 4-inch pipe, the roll waves in 2-inch pipe are much thicker. This partly explains the differences in 2-inch versus 4-inch pipe behavior.     

Forced convective film condensation inside vertical tubes

A theoretical study of forced convective film condensation inside vertical tubes is presented. We propose a unified procedure for predicting the pressure gradient and condensation heat transfer coefficient of a vapor flowing turbulently in the core and associated with laminar or turbulent film on the tube wall. The analysis for the vapor flows is performed under the condition that the velocity profiles are locally self-similar. The laminar and turbulent film models equate the gravity, pressure and viscous forces, and consider the effect of interfacial shear. The transition from laminar to turbulent film depends not only on the liquid Reynolds number but also on the interfacial shear stress. In this work we also proposed a new eddy viscosity model which is divided into three regions: the inner region in liquid condensate near the wall; the interface region including both liquid and vapor; and the outer region for the vapor core. Comparisons of the theory with some published experimental data showed good agreement.     

Drop size measurements for annular two-phase flow in a 20 mm diameter vertical tube

As part of a study on the effect of tube diameter on the mean drop size and liquid film flow rate in annular two-phase flow, data was obtained for the vertical upflow of an air-water system in a 20 mm internal diameter tube, held at a pressure of 1.5 bar and ambient temperature. This complements data taken in earlier experiments on 10 and 32 mm tubes. Increases in the superficial gas velocity caused reductions in the mean drop size whilst increasing the liquid mass flux in all but the lowest gas velocity case, caused the drop size to rise. Comparisons were made between the current drop size data and that from a 10 mm and 32 mm internal diameter tube, for similar conditions of temperature and pressure. The current drop size measurements, which fall between those from earlier work, confirm the dependence of drop size on tube diameter. The performance of several drop size correlations have been tested. Because the correlations do not account for the influence of tube diameter, they fail to predict the drop size data accurately. The influence of gas and liquid flow rate on the measured film flow rate show trends similar to those seen in data from the 10 mm and 32 mm diameter tubes. Models, to calculate the entrained liquid mass flux were tested; good predictions were given.     

The identification of two distinct laminar to turbulent transition modes in pipe flows accelerated from rest

A study was undertaken to investigate transition in a pipe flow accelerated from rest. Experiments were carried out on a vertical tube under a constant head of liquid: flow was initiated by opening a solenoid valve. A wall shear stress probe used in the role of an event recorder identified two transition events, separated by the passage of a turbulent to laminar front and a period of laminar flow. Evidence suggests that the first comprises a laminar to turbulent interface arising from a natural stable/unstable front moving up the tube as local conditions become met, while the second is consequent upon the formation of a continuous turbulent structure carried down the tube from the inlet by the bulk flow. The paper provides a formal explanation of a phenomenon which is typical of that which is observed in starting pipe flows with a disturbed inlet.     

Experimental research on transient critical heat flux in vertical tube under oscillatory flow condition

The transient critical heat flux (CHF) experiments with forced sinusoidal inlet flow oscillation (oscillation period in 1–11 s, normalized amplitude of inlet flow oscillation in 0–3.0) were conducted in a vertical tube under low pressure condition. To analyze the triggering mechanism and aftermath of periodic dryout, the wall temperature fluctuation characteristics at the onset of periodic dryout and during post-periodic dryout were investigated. Under inlet flow oscillation condition, periodic dryout would be triggered at the wave trough of liquid film oscillation as wall heat flux far below the stable-flow CHF. The transient periodic dryout would give rise to temperature fluctuations on the tube wall, the amplitude of which increased with oscillation period and heat flux. The large wall temperature fluctuation during long-playing periodic dryout could significantly pre-trigger continuous dryout. The changing trends of the periodic dryout heat flux show a reasonable agreement with Okawa’s theoretical model, in which the liquid film oscillation was supposed be weakened by the axial mixing of liquid film. Moreover, the droplet entrainment at the oscillatory interface also has noticeable influence on the oscillation characteristics of liquid film. Based on the analysis of parameter effects on periodic dryout, a semi-empirical correlation was proposed to predict the periodic dryout heat flux under inlet flow oscillation condition.     

Gas displacement of viscoplastic liquids in capillary tubes

The displacement of viscoplastic liquids in capillary tubes by gas injection is examined. The viscoplasticity alters the flow kinematics and changes dramatically the amount of mass left attached at the tube wall as compared to the Newtonian case, studied experimentally by G.I. Taylor in 1961 [G.I. Taylor, Deposition of a viscous fluid on the wall of a tube, J. Fluid Mech. 10 (1961) 161–165]. Experiments with Carbopol aqueous solutions were performed for different flow rates. A recently proposed viscosity function for viscoplastic liquids was fitted to the rheological data of the Carbopol solutions. A new dimensionless rheological property – the jump number – arises in the dimensionless version of this viscosity function. The results show the effect of the viscoplastic character of the liquid on the free surface shape and on the thickness of the film of liquid left attached to the wall. This thickness decreases with the jump number and increases with the flow rate. It is also observed that there is a critical dimensionless flow rate below which the displacement is apparently perfect, i.e. there is no observable liquid left attached to the wall. This behavior is shown to be directly related to the fully developed flow far ahead the air–liquid interface.     

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.     

Studies on two-phase co-current air/non-Newtonian shear-thinning fluid flows in inclined smooth pipes

In this work, co-current flow characteristics of air/non-Newtonian liquid systems in inclined smooth pipes are studied experimentally and theoretically using transparent tubes of 20, 40 and 60 mm in diameter. Each tube includes two 10 m long pipe branches connected by a U-bend that is capable of being inclined to any angle, from a completely horizontal to a fully vertical position. The flow rate of each phase is varied over a wide range. The studied flow phenomena are bubbly flow, stratified flow, plug flow, slug flow, churn flow and annular flow. These are observed and recorded by a high-speed camera over a wide range of operating conditions. The effects of the liquid phase properties, the inclination angle and the pipe diameter on two-phase flow characteristics are systematically studied. The Heywood–Charles model for horizontal flow was modified to accommodate stratified flow in inclined pipes, taking into account the average void fraction and pressure drop of the mixture flow of a gas/non-Newtonian liquid. The pressure drop gradient model of Taitel and Barnea for a gas/Newtonian liquid slug flow was extended to include liquids possessing shear-thinning flow behaviour in inclined pipes. The comparison of the predicted values with the experimental data shows that the models presented here provide a reasonable estimate of the average void fraction and the corresponding pressure drop for the mixture flow of a gas/non-Newtonian liquid.     

Natural convection flow with solidification between two vertical plates filled with a porous medium

Quasi-steady solidification between two vertical flat plates filled with a saturated porous medium has been investigated. The medium is homogeneous and isotropic. The convection flow of liquid takes place in the porous medium in the variable space between the two walls. One of the vertical walls is set to a temperature lower than the solidification temperature of the medium and therefore a frozen crust is formed on this wall. The second wall has a high temperature then the fusion temperature of the medium. The problem has been simplified by assuming laminar flow and the Brinkman and the Oberbeck–Bousinesq’s approximations. The results are presented in terms of the velocity for different properties of the porous medium. Various velocities are displayed in dependence of the Rayleigh and Darcy numbers. The study indicates that asymmetric boundary conditions have an important effect on the temperature and flow field. In addition, the growth of the thickness of the frozen layer with time has been derived from a simple analytical solution of the interface energy equation.     

Study of local hydrodynamic characteristics of upward slug flow

Results of an experimental study of local velocity, fluctuation and void fraction profiles in liquid plugs of an upward vertical gas-liquid flow as well as of wall shear stress distribution both under gas slugs and in liquid plugs, are presented. The conditional sampling technique allowed to obtain instantaneous profiles of the above hydrodynamical quantities, which illuminated the real physical picture of the flow in a liquid plug. The toroidal vortex adjacent to the bottom of a gas slug is shown to determine significantly the development of the flow in a liquid plug. The intensity of this vortex is determined only by the relative velocity of the gas bubble with respect to the liquid.     

Effects of a countercurrent gas flow on falling-film mode transitions between horizontal tubes

A liquid film falling between horizontal tubes is known to take the form of droplets, jets or sheets, depending on the liquid flow rate; the form of the flow is the so-called “falling-film mode”. Although previously neglected in studies of mode transition, a countercurrent gas flow often exists in falling-film heat exchangers, and its effect on the liquid flow might be important: it could impact the flow regime, lead to local “dryout,” and decrease the heat transfer rate. Experiments are conducted to explore the effects of a countercurrent gas flow and liquid feeding length on falling-film mode transitions for a liquid flowing over horizontal tubes. The effects on mode transition are shown to depend on fluid properties and are explained in terms of unsteadiness and film thickness. In general, transition hysteresis is reduced with an increasing gas velocity. A correlation is developed to predict the countercurrent gas flow effects on falling-film mode transitions. The liquid feeding length can affect mode transitions in quiescent surroundings and when a countercurrent gas flow imposed.     

Dynamic fluid flow behaviour of a tank draining through a vertical tube

This paper describes the unsteady draining of a sealed tank partially filled with water. The water discharges via a vertical tube into an open tank at atmospheric conditions. The air inflow, compensating for the volume of the discharged liquid, enters the system in an oscillatory manner, much like the “gulping” seen in an upended beer bottle. A mathematical model, based closly on that derived by Dougall & Kathiresan [Chem. Engng Commun. 8, 289–304 (1981)], has been applied to predict the pressure fluctuations in the closed tank. The rate of water discharge from the tank has been predicted and gives a much closer agreement with experimental results than a prediction based on a steady counter-current flooding limitation approach. A drift flux model has been used to describe the two-phase flow effect in the tube and the Wallis flooding criterion has been modified for use in the slug flow regime to describe the boundary conditions at the bottom of the tube. The pressure fluctuations in the sealed tank have been measured and compared with results obtained from the mathematical prediction for a variety of tube diameters.