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.     

Calculation of the stability of the flow in a circular pipe with injection

An experimental investigation of the transition of a laminar flow regime into a turbulent one has been carried out in [1] for a flow in a circular pipe which is organized due to injection through the porous lateral surface with a jammed leading end of the pipe. It was established as a result that injection leads to an increase in stability of the laminar flow regime and increases the Reynolds number of the transition to 10,000 instead of the value 2300 which is characteristic of flow in a circular pipe with impenetrable walls. A similar effect was discovered in [2], in which it was also obtained that the Reynolds number of stability loss under the action of injection can take values significantly larger than in pipes with impenetrable walls. The phenomenon of relaminarization of a turbulent flow in the initial section of a circular pipe under the action of injection has been experimentally detected at the entrance for relatively low Reynolds numbers in [3, 4]. Theoretical investigations of stability of flow with injection have been performed only for a plane channel [5, 6]. A calculation is made in this paper of the stability of a hydrodynamically developed flow in a circular pipe with injection through a porous lateral surface.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 82–86, May–June, 1984.     

Condensation of wet steam on a horizontal tube with additional droplet deposition

A theory is presented for condensation of downward flowing wet vapour on a horizontal tube. The vapour is assumed to consist of dry saturated vapour and uniformly distributed liquid droplets flowing independently of each other. In addition the droplets are assumed to be so large that they fall vertically on to the tube surface and are unaffected by the vapour flow around the cylinder. The results show that the heat transfer coefficients are extremely dependent on both the droplet mass flux and velocity as well as the steam velocity.     

Void fraction and pressure waves in a transient horizontal slug flow

The void fraction and the pressure waves in an air–water mixture flowing in the slug regime are experimentally investigated in a horizontal line. The test section is made of a transparent Plexiglas pipe with 26 mm ID and 26.24 m long, operating at ambient temperature and pressure. The flow induced transients are made by quickly changing the air or the water inlet velocity. The test grid has four operational points. This choice allows one to create expansion and compression waves due to the changes to the gas or to the liquid. Each experimental run is repeated 100 times to extract an ensemble average capable of filtering out the intrinsic flow intermittence and disclosing the void fraction and pressure waves’ features. The slug flow properties such as the bubble nose translational velocity, the lengths of liquid film underneath the bubble and the liquid slug are also measured. The objective of the work is two-fold: access the main characteristics of the void fraction and pressure waves and disclose the mechanics of the transient slug flow as described through the changes of the slug flow properties.     

Potential flow around a deforming bubble in a Venturi

The differential pressure between the entrance and throat of a Venturi will fluctuate if the liquid flowing through the Venturi contains bubbles. This paper reports computations of the pressure fluctuation due to the passage of a single bubble. The liquid is assumed inviscid and its velocity, assumed irrotational, is computed by means of a boundary integral technique. The liquid velocity at the entrance to the Venturi is assumed constant and uniform across the pipe, as is the pressure at the outlet. The bubble is initially far upstream of the Venturi and moves with velocity equal to that of the liquid. Buoyancy is neglected. If the bubble is sufficiently small that interactions with the Venturi walls may be neglected, a simple one-dimensional model for the bubble velocity is in good agreement with the full boundary integral computations. The differential pressure (taken to be positive) decreases when the bubble enters the converging section of the Venturi, and then increases to a value higher than for liquid alone as the bubble passes the pressure measurement position within the throat. The changes can be estimated using the one-dimensional model, if the bubble is small. The bubble is initially spherical (due to surface tension) but is perturbed by the low pressure within the Venturi throat. In the absence of viscosity, the bubble oscillates after leaving the Venturi. The quadrupole oscillations of the bubble are similar in frequency to those of a bubble in unbounded fluid; the frequency of the monopole oscillations is modified by the presence of the pipe walls. Numerical results for the frequency of monopole oscillations of a bubble in a uniform tube of finite length are in good agreement with analytic predictions, as is the computed drift of the oscillating bubble.     

Mixed convection in turbulent film boiling on a vertical ellipsoid under high and low velocity liquid

The theoretical study researched into heat transfer of turbulent film boiling on an isothermal ellipsoid under high and low velocity liquid. The flowing velocity of the saturated liquid at the boundary layer is determined by potential flow theory. The larger the eccentricity parameter is the smaller the mean Nusselt number will be. Besides, for the cases of turbulent film boiling under the flowing liquid, the increase in the Froude number will bring out an increase in the mean Nusselt number.     

Experimental study of “laminar” bubbly flows in a vertical pipe

Measurement of bubbly two-phase flow parameters in a vertical pipe were performed. To keep the pipe Reynolds number below that for single-phase turbulent transition, a water-glycerin solution was used as the test liquid. Local void fraction and liquid velocity profiles along with the wall shear stress were measured by an electrochemical method. Experiments were made with bubbles of two different sizes. As the gas flow rate was increased, a gradual development of the liquid velocity profile from the parabolic Poiseuille flow to a flattened two-phase profile was observed. The evolution of the wall shear stress and of the velocity fluctuations were also quantified.Centre National de la Recherche Scientifique. Université Joseph Fourier, Institut National Polytechnique de Grenoble.     

Stability of flow of a thin layer of viscous magnetic liquid

The laminar flow of a thin layer of heavy viscous magnetic liquid down an inclined wall is examined. The stability and control of the flow of an ordinary liquid are affected only by alteration of the angle of inclination of the solid wall and the velocity of the adjacent gas flow. When magnetic liquids are used [1, 2], an effective method of flow control may be control of the magnetic field. By using magnetic fields of various configurations it is possible to control the flow of a thin film of viscous liquid, modify the stability of laminar film flow, and change the shape of the free surface of the laminarly flowing thin film, a factor which plays a role in mass transfer, whose rate depends on the phase contact surface area. The magnetic field significantly affects the shape of the free surface of a magnetic liquid [3, 4]. In this paper the velocity profile of a layer of viscous magnetic liquid adjoining a gas flow and flowing down an inclined solid wall in a uniform magnetic field is found. It is shown that the flow can be controlled by the magnetic field. The problem of stability of the flow is solved in a linear formulation in which perturbations of the magnetic field are taken into account. The stability condition is found. The flow stability is affected by the nonuniform nature of the field and also by its direction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 59–65, September–October, 1977.     

Investigation of a particulate flow containing spherical particles subjected to microwave heating

Microwave heating of a liquid and large spherical particles that it carries while continuously flowing in a circular applicator pipe is investigated. A three-dimensional model that includes coupled Maxwell, continuity, Navier–Stokes, and energy equations is developed to describe transient temperature, electromagnetic, and fluid velocity fields. The hydrodynamic interaction between the solid particles and the carrier liquid is simulated by the force-coupling method (FCM). Computational results are presented for the microwave power absorption, temperature distribution inside the liquid and the particles, as well as the velocity distribution in the applicator pipe and trajectories of particles. The effect of the time interval between consecutive injections of two groups of particles on power absorption in particles is studied. The influence of the position of the applicator pipe in the microwave cavity on the power absorption and temperature distribution inside the liquid and the particles is investigated as well.     

Numerical simulation of the flow in a conduit,in the presence of a confined air cushion

A rectangular conduit with a closed end has water flowing in/out at the other end. The water level at the open end has an imposed sinusoidal movement. When this level is higher than the ceiling of the conduit, a certain mass of air is trapped under the ceiling. In a previous article (T.D. Nguyen, La Houille Blanche, No. 2, 1990), it was supposed that this air is flowing out freely through the ceiling, so the relative pressure at the water surface is zero, and the water hammer at the dead end of the conduit was calculated when the conduit was thoroughly filled. In this article, it is supposed that the trapped air is compressed isothermally or adiabatically. The set of equations is resolved (water continuity and movement equations, air state equation) by supposing a regime of flow at each section (section submerged or not), a certain value for the air pressure and by using the sweep method to determine the water flow characteristics. The air volume calculated by iteration must converge, and the calculated regimes at each section (submerged or free) must agree with the supposed regimes. The simulation is performed first with a horizontal conduit then with an inclined conduit. As expected, adiabatic compression gives higher pressure than isothermal compression. The simulation shows also that when there is an air cushion, compared with the case when air is flowing out freely, the shock of the water hammer at the closed end of the conduit is significantly reduced. This method is aimed at calculating the flow with entrapped air in the inlet/outlet tunnel of a hydroelectric plant, or in sewer system pipe when a sudden discharge surge (due to turbin opening/closing or to urban storm) changes a previously free‐surface flow in a mostly full‐pipe flow, but with some air entrapped under the ceiling. Copyright © 1999 John Wiley & Sons, Ltd.     

An experimental investigation of pneumatic swirl flow induced by a three lobed helical pipe

This paper presents a discussion of the results and conclusions drawn from a series of experiments conducted to investigate the swirl flow that are generated by a three lobed helical pipe mounted within a laboratory scale pneumatic conveying rig. The experiments employed Laser Doppler Anemometry (LDA) to quantify the strength of the induced vortex formations and the decay rates of the observed downstream swirl flows over a range of Reynolds number in the turbulent regime. Instantaneous point velocity measurements were resolved in three directions across regular measurement grids transcribed across parallel planes located at four distances downstream of the swirl inducing pipe section. The equivalent axial, radial and tangential velocities were subsequently computed at these grids points. The degree of swirl measured across each measurement plane was expressed in terms of a defined swirl number.It was concluded that the three lobed helical pipe gave rise to a wall jet type of swirl whose rate of observed downstream decay is related to the Reynolds number of the upstream flow and the distance downstream of the swirl pipe. The decay rates for the swirl flows were found to be inversely proportional to the Reynolds number of the upstream flow. The swirl pipe was observed to create a redistribution of the downstream velocity field from axial to tangential, accompanied by a transfer of axial to angular momentum. The findings of this paper are believed to improve understanding to assist the selective use of swirl flow within lean phase particles pneumatic transport systems.     

Direct contact heat transfer between two immiscible liquids flowing in a horizontal concentric annulus

Direct contact heat transfer between water and a heat transfer oil was investigated under non-boiling conditions in co-current turbulent flow through a horizontal concentric annulus. The ratio of the inner pipe diameter to the outer pipe diameter (aspect ratio) κ = 0.730−0.816; total liquid velocity (mixture velocity) V_T = 0.42−1.1 m/s; inlet oil temperature T_oi = 38−94°C; oil volume fraction in the flowing mixture φ_o = 0.25−0.75 were varied and their effects on the overall volumetric heat transfer coefficient U_v were determined at constant interfacial tension of 48 dynes/cm.

It was found that, in each concentric pipe set, the overall volumetric heat transfer coefficient increased with increasing dispersed phase volume fraction at each constant mixture velocity and reached a maximum at around φ_o = φ_w ≈ 0.5. The maximum U_v values increased with increasing total liquid velocity and decreasing aspect ratio of the annulus. The volumetric heat transfer coefficient was also found to increase with increasing inlet oil temperature and increasing total liquid velocity but to decrease with length along the test section keeping all other parameters constant. Empirical expressions for the volumetric heat transfer coefficient were obtained within the ranges of the experimental parameters.     

Transition to turbulence on the initial section of a circular pipe

All the available data indicate that transition to turbulence in a circular pipe takes place within the initial section. This is confirmed by the conclusions of the linear theory of hydrodynamic stability, according to which the velocity profiles on the initial section of the pipe are unstable [1]. So far, however, there have been few investigations of initial-section flow at different values of the initial perturbation level ₀ at the pipe inlet and different values of the length to diameter ratio of the pipe 2/d. We have now investigated the transition to turbulence in the boundary layer on the initial section of a circular pipe for various ratios of the thickness of the layer to the radius of the pipe and various levels of initial turbulence. The transition point in the boundary layer was found experimentally, since at present there are no reliable methods of calculating it. In particular, the susceptibility problem has not been solved, i.e., the problem of the initial amplitude of the Tollmien—Schlichting wave, the development of which results in transition to turbulence. It may be assumed that the initial amplitude of this wave is determined by the interaction of higher-frequency waves on the section preceding its growth zone [2]. Moreover, different views are held concerning the mechanism of transition to turbulence at ₀ > 0.5%. At the same time, the results of the transition calculations for ₀ > 0.5% based on the three-parameter turbulence model [3] require experimental verification.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 52–56, July–August, 1985.     

Self-oscillation regimes in a liquid jet curtain separating gas regions with different pressures

The results of an experimental investigation of the self-oscillation regimes of liquid jet outflow into a plane channel with air injection in its dead end are presented. The effect of the volume of the cavity, or the air cushion, and its thickness (or channel width) on the flow is studied on a wide range of the gas injection rate and the liquid outflow velocity. The self-oscillation flow regimes are realized at a constant pressure of water in the supply tank and a constant mass flow rate of the air injected into the cushion. With increase in the air injection rate the self-oscillation regime realized at lower injection intensities is replaced by a higher-frequency regime. High-speed videofilming shows that the difference from the low-frequency regime consists in the absence of the direct interaction between the out flowing jet and the channel wall. It is found that in both low-frequency and high-frequency regimes the self-oscillation frequency and amplitude are independent of the cushion thickness but the moment of the regime changeover is determined by this parameter. It is established that there exists a threshold value of the cavity volume, behind which the low-frequency regime does not occur at any air injection rates.     

Regime change in a planar jet with a stepped velocity profile

Flows with a nearly stepped velocity profile are seen on the initial section of jets in experiments. The present article theoretically analyzes the stability and character of branching of secondary regimes in a planar submerged jet with a stepped velocity profile. The piecewise-constant form of the profile makes it possible to perform many of the calculations analytically. A mild excitation regime is discovered and the structure of the secondary regime is calculated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 43–47, November–December, 1984.The author expresses thanks to V. N. Shtern for his constant attention to the work and useful consultations.     

Rotation effects on a fully-developed turbulent pipe flow

A fully-developed turbulent pipe flow is allowed to pass through a rotating pipe section, whose axis of rotation coincides with the pipe axis. At the exit end of the rotating section, the flow passes into a stationary pipe. As a result of the relaxation of surface rotation, the turbulent flow near the pipe wall is affected by extra turbulence production created by the large circumferential shear strain set up by the rapid decrease of the rotational velocity to zero at the wall. However, the flow in the most part of the pipe is absent of this extra turbulence production because the circumferential strain is zero as a result of the solid-body rotation imparted to the flow by the rotating pipe section. The combined effect of these two phenomena on the flow is investigated in detail using hot-wire anemometry techniques. Both mean and turbulence fields are measured, together with the wall shear and the turbulent burst behavior at the wall. A number of experiments at different rotational speeds are carried out. Therefore, the effects of rotation on the behavior of wall shear, turbulent burst at the wall, turbulence production and the near-wall flow can be documented and analysed in detail.     

Electroviscous effects in steady fully developed flow of a power-law liquid through a cylindrical microchannel

Electroviscous effects in steady, fully developed, pressure-driven flow of power-law liquids through a uniform cylindrical microchannel have been investigated numerically by solving the Poisson–Boltzmann and the momentum equations using a finite difference method. The pipe wall is considered to have uniform surface charge density and the liquid is assumed to be a symmetric 1:1 electrolyte solution. Electroviscous resistance reduces the velocity adjacent to the wall, relative to the velocity on the axis. The effect is shown to be greater when the liquid is shear-thinning, and less when it is shear-thickening, than it is for Newtonian flow. For overlapping electrical double layers and elevated surface charge density, the electroviscous reduction in the near-wall velocity can form an almost stationary (zero shear) layer there when the liquid is shear-thinning. In that case, the liquid behaves approximately as if it is flowing through a channel of reduced diameter. The induced axial electrical field shows only a weak dependence on the power-law index with the dependence being greatest for shear-thinning liquids. This field exhibits a local maximum as surface charge density increases from zero, even though the corresponding electrokinetic resistance increases monotonically. The magnitude of the electroviscous effect on the apparent viscosity, as measured by the ratio of the apparent and physical consistency indices, decreases monotonically as the power-law index increases. Thus, overall, the electroviscous effect is stronger in shear-thinning, and weaker in shear-thickening liquids, than it is when the liquid is Newtonian.     

Visualisation and modelling studies of churn flow in a vertical pipe

Churn flow is an important flow regime intermediate between slug flow and annular flow. A feature of this regime is the occurrence of very large waves travelling upwards over a liquid film substrate which may intermittently travel downwards. These waves are often formed close to the liquid inlet where their behaviour is usually difficult to observe. This paper describes a series of experiments using a test section with a specially constructed transparent liquid inlet. High-speed video recordings show clearly the process of wave formation and analysis of the recordings gave data on wave frequencies and typical velocities. Also, predictions of velocity and distance travelled by the waves were obtained via the application of a simple mathematical model that takes into account the forces acting on a circumferentially coherent wave.     

Flow of elastico-viscous liquids in channels under the influence of a periodic pressure gradient,part 1

Summary The flow of a non-Newtonian incompressible liquid in a straight pipe of circular cross-section under the influence of a periodic pressure gradient is investigated; the viscous and elastic properties of the liquid are defined in terms of a spectrum of relaxation times. Such a flow is of interest to the experimentalist, because the flow could be readily attained and controlled in practice. A solution is obtained which determines the variation in the mean-square velocity over the section of the pipe. In the numerical illustrations given, it is shown that the general nature of the flow is similar to that of a purely viscous liquid of constant viscosity, a high peak of average velocity occurring near the wall of the pipe. However, it is shown that elasticity of the type considered could strongly affect the value and position of this peak of the average velocity.     

Measurements of local velocities inside thin liquid films in horizontal two-phase flow

A new experimental facility based on Laser Doppler anemometry permits accurate local measurements in a horizontal pipe. Measurements of the axial velocity component in the liquid layer of the atomization/stratified flow regime are reported. The new information includes time-averaged local velocities, RMS values, probability density distributions, and power spectra. Elimination of velocity bias and calculation of velocity spectra is accomplished by a recently developed “signal reconstruction” algorithm. The data suggest that only in the vicinity of the solid surface (sublayer) does the liquid motion resemble the well-known behavior of single phase flow. Beyond that, the flow field is strongly influenced by the wavy gas/liquid interface and by the apparently intensive energy transfer from the very fast moving gas to the liquid layer.