Turbulent shear stress profiles in a bubbly channel flow assessed by particle tracking velocimetry

Particle tracking velocimetry (PTV) is applied to a bubbly two-phase turbulent flow in a horizontal channel at Re = 2 × 10⁴ to investigate the turbulent shear stress profile which had been altered by the presence of bubbles. Streamwise and vertical velocity components of liquid phase are obtained using a shallow focus imaging method under backlight photography. The size of bubbles injected through a porous plate in the channel ranged from 0.3 to 1.5 mm diameter, and the bubbles show a significant backward slip velocity relative to liquid flow. After bubbles and tracer particles are identified by binarizing the image, velocity of each phase and void fraction are profiled in a downstream region. The turbulent shear stress, which consists of three components in the bubbly two-phase flow, is computed by analysis of PTV data. The result shows that the fluctuation correlation between local void fraction and vertical liquid velocity provides a negative shear stress component which promotes frictional drag reduction in the bubbly two-phase layer. The paper also deals with the source of the negative shear stress considering bubble’s relative motion to liquid.     

Wall shear stress and void fraction in Poiseuille bubbly flows: Part II: experiments and validity of analytical predictions

In a companion paper, a simple analytical formulation has been established which provides the wall shear stress in laminar bubbly flows for idealised transverse void fraction distributions. In the present paper, this approach is applied to Poiseuille bubbly flows in circular ducts. New measurements of the void fraction profiles and wall friction angular distribution in a pipe are presented for a wide range of flow parameters. Approximating the void profiles by step-functions allows us to evaluate the wall friction with the above mentioned model. Results are shown to agree satisfactorily with measurements. Notably, negative wall shear stress and wall shear stress much higher than their single-phase flow counterpart at the same liquid flow rate are recovered. Therefore, the principal mechanisms responsible for friction modification are captured with this simple model.     

Heat transfer and interfacial drag in countercurrent steam-water stratified flow

Local condensation heat transfer coefficients and interfacial shear stresses have been measured for countercurrent stratified flow of steam and subcooled water in rectangular channels over a wide range of inclination angles (4–87°) at two aspect ratios. Dimensionless correlations for the interfacial friction factor have been developed that show that it is a function of the liquid Reynolds number only. Empirical correlations of the heat transfer coefficient, based upon the bulk flow properties, have also been set up for the whole body of data encompassing the different inclination angles and aspect ratios. These indicate that the Froude number as a dimensionless gas velocity is a better correlating parameter than the gas Reynolds number. As an alternative approach, a simple dimensionless relationship for the beat transfer coefficient was obtained by analogy between heat and momentum transfer through the interface. Finally, a turbulence-centered model has been modified by using measured interfacial parameters for the turbulent velocity and length scales, resulting in good agreement with the data.     

Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

Two-phase flow in inclined tubes with specific reference to condensation: A review

Tilting influences the flow patterns and thus the heat transfer and pressure drop during condensation in smooth tubes. However, few studies are available on diabatic two-phase flows in inclined tubes. The purpose of the present paper is to review two-phase flow in inclined tubes, with specific reference to condensation. Firstly, the paper reviews convective condensation in horizontal tubes. Secondly, an overview is given of two-phase flow in inclined tubes. Thirdly, a review is conducted on condensation in inclined tubes. It is shown for convective condensation in inclined tubes that the inclination angle influences the heat transfer coefficient. The heat transfer coefficient can be increased or decreased depending on the experimental conditions, and especially the flow pattern. Under certain conditions, an inclination angle may exist, which leads to an optimum heat transfer coefficient. Furthermore, this paper highlights the lack of experimental studies for the prediction of the inclination angle effect on the flow pattern, the heat transfer coefficient and the pressure drop in two-phase flows during phase change.     

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.     

Wall shear stress modified by bubbles in a horizontal channel flow of silicone oil in the transition region

We performed laboratory experiments on bubbly channel flows using silicone oil, which has a low surface tension and clean interface to bubbles, as a test fluid to evaluate the wall shear stress modification for different regimes of bubble migration status. The channel Reynolds numbers of the flow ranged from 1000 to 5000, covering laminar, transition and turbulent flow regimes. The bubble deformation and swarms were classified as packing, film, foam, dispersed, and stretched states based on visualization of bubbles as a bulk void fraction changed. In the dispersed and film states, the wall shear stress reduced by 9% from that in the single-phase condition; by contrast, the wall shear stress increased in the stretched, packing, and foam states. We carried out statistical analysis of the time-series of the wall shear stress in the transition and turbulent-flow regimes. Variations of the PDF of the shear stress and the higher order moments in the statistic indicated that the injection of bubbles generated pseudo-turbulence in the transition regime and suppressed drag-inducing events in the turbulent regime. Bubble images and measurements of shear stress revealed a correlated wave with a time lag, for which we discuss associated to the bubble dynamics and effective viscosity of the bubble mixture in wall proximity.     

Structure of the nonisothermal swirling gas-droplet flow behind an abrupt tube expansion

Flow structure and heat and mass transfer in a swirling two-phase stream is numerically modeled using the Reynolds stress transport model. The gas phase is described by the 3DRANS system of equations with account for the inverse influence of particles on the transport processes in the gas. The gas phase turbulence is calculated using the Reynolds stress transport model with account for the presence of disperse particles. The two-phase nonswirling flow behind an abrupt tube expansion contains a secondary corner vortex which is absent from the swirling flow. The disperse phase is redistributed over the tube cross-section. Large particles are concentrated in the wall region of the channel under the action of the centrifugal forces, while the smaller particles are in the central zone of the chamber.     

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.     

Magnetic field effect on heat transfer and fluid flow characteristics of blood flow in multi-stenosis arteries

Heat and fluid flow characteristics of blood flow in multi-stenosis arteries in the presence of magnetic field is considered. A mathematical model of the multi-stenosis inside the arteries is introduced. A finite difference scheme is used to solve the governing equations in terms of vorticity-stream function along with their boundary conditions. The effect of magnetic field and the degree of stenosis on wall shear stress and Nusselt number is investigated. It was found that magnetic field modifies the flow patterns and increases the heat transfer rate. The severity of the stenosis affects the wall shear stress characteristics significantly. The magnetic field torque will increase the thermal boundary layer thickness and the temperature gradient in the streaming blood, and hence increasing the local Nusselt number     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.     

Drag reduction and heat transfer in surfactant solutions with excess counterion

We present the results of a study of turbulent drag reduction in a small circulating loop using surfactant solutions with excess counterion. In addition, these solutions were used in measurements of heat transfer, both in pipe flow and in an impinging jet. Both frictional drag and heat transfer were reduced in the pipe flow experiments. Measurements of heat transfer in the impinging jet revealed a dependence on the molar concentration ratio of the counterion. When the counterion was added at a molar concentration 30 times higher than that of the surfactant, the resulting surfactant solution did not reduce the rate of heat transfer in the impinging jet. By using this surfactant system in an impinging jet, we show both a reduction in pipe friction and normal heat transfer potential in a circulating heat exchange system. In order to investigate this difference in heat transfer between pipe flows and impinging jet flows, a comparison was made of the wall shear stress between these two flow regimes. The estimated wall shear stress was of the same order in both flows, and thus was not considered to be the primary cause of the difference in heat transfer. It is instead suggested that the micellar structure of the surfactant is influenced by a compressive deformation of the impinging flow in a manner that is different from the shear deformation observed in pipe flow.     

Experimental study on near wall transport characteristics of slug flow in a vertical pipe

In this work, the wall shear stress and the mass transfer coefficient of the gas–liquid two-phase upward slug flow in a vertical pipe are investigated experimentally, using limiting diffusion current probes and digital high-speed video system. In experiments, the instantaneous and averaged characteristics of wall shear stress and mass transfer coefficient are concerned. The experimental results are compared with the numerical results in previous paper of the authors. Both experiment and numerical simulation show that the superficial gas and liquid velocities have an obvious influence on the instantaneous characteristics of the two profiles. The mass transfer coefficient has characteristics similar to the wall shear stress. The instantaneous wall shear stress and mass transfer coefficient profiles have the periodicity of slug flow. The averaged wall shear stress and mass transfer coefficient increase with increased superficial gas velocity. However, there is inconsistency in the variation trends of the averaged wall shear stress and mass transfer coefficient with superficial liquid velocity between experimental result and numerical simulation result, which can be attributed to the difference in flow condition. Moreover, the Taylor bubble length is also another impacting factor. The experimental and numerical results all shows that the product scale can not be damaged directly by the flow movement of slug flow. In fact, the alternative forces and fluctuations with high frequency acting on the pipe wall due to slug flow is the main cause for the slug flow enhanced CO₂ corrosion process.     

An investigation on near wall transport characteristics in an adiabatic upward gas–liquid two-phase slug flow

The near-wall transport characteristics, inclusive of mass transfer coefficient and wall shear stress, which have a great effect on gas–liquid two-phase flow induced internal corrosion of low alloy pipelines in vertical upward oil and gas mixing transport, have been both mechanistically and experimentally investigated in this paper. Based on the analyses on the hydrodynamic characteristics of an upward slug unit, the mass transfer in the near wall can be divided into four zones, Taylor bubble nose zone, falling liquid film zone, Taylor bubble wake zone and the remaining liquid slug zone; the wall shear stress can be divided into two zones, the positive wall shear stress zone associated with the falling liquid film and the negative wall shear stress zone associated with the liquid slug. Based on the conventional mass transfer and wall shear stress characteristics formulas of single phase liquid full-pipe turbulent flow, corrected normalized mass transfer coefficient formula and wall shear stress formula are proposed. The calculated results are in good agreement with the experimental data. The shear stress and the mass transfer coefficient in the near wall zone are increased with the increase of superficial gas velocity and decreased with the increase of superficial liquid velocity. The mass transfer coefficients in the falling liquid film zone and the wake zone of leading Taylor bubble are lager than those in the Taylor bubble nose zone and the remaining liquid slug zone, and the wall shear stress associated falling liquid film is larger than that associated the liquid slug. The mass transfer coefficient is within 10⁻³ m/s, and the wall shear stress below 10³ Pa. It can be concluded that the alternate wall shear stress due to upward gas–liquid slug flow is considered to be the major cause of the corrosion production film fatigue cracking.     

Detached direct numerical simulations of turbulent two-phase bubbly channel flow

DNS simulations of two-phase turbulent bubbly channel flow at Re_τ = 180 (Reynolds number based on friction velocity and channel half-width) were performed using a stabilized finite element method (FEM) and a level set approach to track the air/water interfaces.     

Turbulent flow structure and bubble distribution in an axisymmetric nonisothermal impinging gas-liquid jet

The flow structure of a bubbly impinging jet in the presence of heat transfer between the two-phase flow and the surface is numerically investigated on the basis of the Eulerian approach. The model uses the system of Reynolds-averaged Navier–Stokes equations in the axisymmetric approximation written with account for the inverse effect of the bubbles on the average and fluctuating flow parameters. The influence of the gas volumetric flow rate ratio and the dimensions of the bubbles on the flow structure in a gas-liquid impinging jet is studied, In the presence of gas bubbles the liquid velocity is higher than the corresponding value in the single-phase flow. A considerable, more than twofold, anisotropy between the axial and radial turbulent fluctuations in the gas-liquid impinging jet is shown to exist. An addition of air bubbles leads to a considerable growth in the liquid velocity fluctuations in the two-phase flow (up to 50% compared with the single-fluid liquid impinging jet). An increase in the disperse phase dimensions leads to intensification of turbulence of the liquid.     

Two-phase non-linear model for blood flow in asymmetric and axisymmetric stenosed arteries

The pulsatile flow of a two-phase model for blood flow through axisymmetric and asymmetric stenosed narrow arteries is analyzed, treating blood as a two-phase model with the suspension of all the erythrocytes in the core region as the Herschel-Bulkley material and plasma in the peripheral layer as the Newtonian fluid. The perturbation method is applied to solve the resulting non-linear implicit system of partial differential equations. The expressions for various flow quantities are obtained. It is found that the pressure drop, plug core radius, wall shear stress increase as the yield stress or stenosis height increases. It is noted that the velocity increases, longitudinal impedance decreases as the amplitude increases. For asymmetric stenosis, the wall shear stress increases non-linearly with the increase of the axial distance. The estimates of the increase in longitudinal impedance to flow of the two-phase Herschel-Bulkley material are significantly lower than those of the single-phase Herschel-Bulkley material. The results show the advantages of two-phase flow over single-phase flow in small diameter arteries with stenosis.     

Research on heat transfer of two-phase dispersed flow in narrow annular channel

Narrow channel heat transfer technique is a new developing heat transfer technique in recent years. As the temperature of droplet, steam and wall are decided by forced convection heat transfer between the steam and the wall, between the droplet and the wall, between the steam and the droplet and radiation heat transfer, which makes heat transfer mechanism of dispersed flow be difficultly interpretative. Dispersed flow in narrow annular channel is analyzed in the paper, investigating the influence of all kinds of heat transfer processes on dispersed flow, building annular channel dispersed flow model using thermodynamic non-equilibrium model. Calculation results show heat transfer is mainly controlled by heat transfer process between steam and wall. When temperature is low, radiation can be ignored on heat transfer coefficient calculation. The calculation of model can provide a reference for engineering application of steam generator, refrigeration system and so on.     

Effect of void fraction and friction factor models on the prediction of pressure drop of R134a during downward condensation in a vertical tube

The theoretical flow models of homogeneous and separated flow are applied to in-tube condensation to predict the pressure drop characteristics of R134a. The homogeneous flow model is modified by ten different dynamic viscosity correlations and various alternative correlations of total, frictional and momentum pressure drops to take account of the partial condensation inside the tube. Numerical analyses were performed to determine the average and local homogeneous wall shear stresses and friction factors by means of a CFD program. The equivalent Reynolds number model is modified by six different two-phase friction factors to determine the total condensation pressure drop in the separated flow model. The refrigerant side total pressure drops, frictional pressure drops, friction factors and wall shear stresses are determined within a ±30% error band. The importance of using the alternative total, momentum and frictional pressure drop correlations for the homogeneous flow model is also shown.     

Unsteady compressible boundary layer flow over a circular cone near a plane of symmetry

An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either inflow or outflow in the presence of suction. The flow is assumed to be steady at time t=0 and at t>0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer approximations have been solved by using an implicit finite-difference method. It is found that suction plays an important role in stabilising the fluid motion and in obtaining unique solution of the problem. The effect of the cross flow parameter is found to be more pronounced on the cross flow surface shear stress than on the streamwise surface shear stress and surface heat transfer. Beyond a certain value of the cross flow parameter overshoot in the cross flow velocity occurs and the magnitude of this overshoot increases with the cross flow parameter. The time variation of the streamwise surface shear stress is more significant than that of the cross flow surface shear stress and surface heat transfer. The suction and the total enthalpy at the wall exert strong influence on the streamwise and cross flow surface shear stresses and the surface heat transfer except that the effect of suction on the cross flow surface shear stress is small.