International Journal of Multiphase Flow

Published by Elsevier BV

Print ISSN: 0301-9322


Two-phase critical flow
  • Article

August 1994


488 Reads


G.S. Lellouche
Understanding the heat and mass transfer phenomena occurring during critical flow of two-phase mixtures is of primary importance in the safety analyses of pressurized water, boiling water and liquid-metal-cooled nuclear reactors. It has been shown that during a blowdown incident, the critical flow rate of the two-phase mixture may be affected by a variety of parameters such as the fluid stagnation conditions, the configuration of the blowdown vessel, the length and diameter of the exhaust duct, the purity of the liquid and the local and frictional pressure losses in the flow channel. The complexity of the thermodynamic phenomena taking place during the blowdown process resulted in many studies which compare a particular theory with selected sets of experimental data. However, in the absence of an adequate theory which is applicable over the entire range of the parameters encountered in the nuclear industry, there is a tendency to rely on semi-empirical correlation of the existing data.The main objective of this paper is to provide a general review of two-phase critical flow from the viewpoint of the needs of thermal-hydraulic systems codes and to conduct a systematic evaluation of the existing data and theoretical models in order to quantify the validity, under various conditions, of several of the more widely used critical flow models. Ten different critical flow models have been formulated and tested in this study against an extensive set of data from critical flow experiments with water as the test fluid. Results of the present study are expected to enhance the understanding of the predictive capabilities and limitations of the critical flow models currently used in the power industry.

Measurements of two-phase mass flow rate: A comparison of different techniques

February 1982


108 Reads

The development of practical and accurate methods to measure two-phase mass flow rates is of prime interest to applied nuclear reactor safety research. This article summarizes a comparison and evaluation of four commonly used mass flow rate devices. The particular systems investigated include (a) the true mass flow meter (TMFM), (b) the radionuclide technique, (c) the combination of a free field drag disk-turbine meter-transducer (DTT) and a gamma densitometer, and (d) the combination of a venturi nozzle and a full flow turbine meter. The experiments were performed under similar conditions in steady-state steam-water flow. The flow direction upstream of the instruments was horizontal except for the last method. The pressures varied between 3 and 9 MPa, and the highest values of the mass flow rate, the quality were 5 kg/s and 90 per cent respectively. The test matrix included wave-, slug- and annular flow. The measuring techniques are described briefly and a classification is proposed, which is based on the different ways of mass flow rate evaluation. The experimental results show that the accuracy of some methods is distinctively dependent on phase distribution (flow regime). Simple calibration correlations were developed to account for these effects.

Characterization of diabatic two-phase flows in microchannels: Flow parameter results for R-134a in a 0.5mm channel

July 2006


105 Reads

Rémi Revellin






An optical measurement method for two-phase flow pattern characterization in microtubes has been utilized to determine the frequency of bubbles generated in a microevaporator, the coalescence rates of these bubbles and their length distribution as well as their mean velocity. The tests were run in a 0.5 mm glass channel using saturated R-134a at 30 °C (7.7 bar). The optical technique uses two laser diodes and photodiodes to measure these parameters and to also identify the flow regimes and their transitions. Four flow patterns (bubbly flow, slug flow, semi-annular flow and annular flow) with their transitions were detected and observed also by high speed video. It was also possible to characterize bubble coalescence rates, which were observed here to be an important phenomena controlling the flow pattern transition in microchannels. Two types of coalescence occurred depending on the presence of small bubbles or not. The two-phase flow pattern transitions observed did not compare well to a leading macroscale flow map for refrigerants nor to a microscale map for air–water flows. Time averaged cross-sectional void fractions were also calculated indirectly from the mean two-phase vapor velocities and compared reasonably well to homogeneous values.

Direct contact evaporation of nearly saturated R 114 in water

January 1996


30 Reads

This paper reports the results of an experimental investigation on direct contact boiling of immiscible liquids. The continuous phase, water, is under stagnant conditions, while the dispersed one, Freon 114, is injected in the test section with different velocity and thermodynamic conditions through a nozzle. The injection system has been designed to vary the quantity of injected refrigerant and/or the liquid injection velocity. The test section is a Plexiglas vertical cylinder 72 mm i.d., 2.0 m long. Experimental data are obtained from high-speed movies of the continuous phase level during and after the Freon 114 injection, as well as from the movies of the rising boiling dispersed phase (injected under nearly saturation conditions). Vaporization rate has been characterized as a function of thermal hydraulic conditions (i.e. water temperature, system pressure and Freon mass flow rate). Direct contact boiling efficiency was derived by the evaluation of the fraction of Freon that did not undergo the boiling process during the transit in the test section.

Subcooled flow boiling of R-134a in vertical channels of small diameter

August 2007


43 Reads

Subcooled flow boiling heat transfer for refrigerant R-134a in vertical cylindrical tubes with 0.83, 1.22 and 1.70 mm internal diameter was experimentally investigated. The effects of the heat flux, q″ = 1–26 kW/m2, mass flux, G = 300–700 kg/m2 s, inlet subcooling, ΔTsub,i = 5–15 °C, system pressure, P = 7.70–10.17 bar, and channel diameter, D, on the subcooled boiling heat transfer were explored in detail. The results are presented in the form of boiling curves and heat transfer coefficients. The boiling curves evidenced the existence of hysteresis when increasing the heat flux until the onset of nucleate boiling, ONB. The wall superheat at ONB was found to be essentially higher than that predicted with correlations for larger tubes. An increase of the mass flux leads, for early subcooled boiling, to an increase in the heat transfer coefficient. However, for fully developed subcooled boiling, increases of the mass flux only result in a slight improvement of the heat transfer. Higher inlet subcooling, higher system pressure and smaller channel diameter lead to better boiling heat transfer. Experimental heat transfer coefficients are compared to predictions from classical correlations available in the literature. None of them predicts the experimental data for all tested conditions.

Flow pattern of air–water and two-phase R-134a in small circular tubes

July 2001


154 Reads

Experimental investigation of two-phase flow patterns for refrigerant R-134a and air–water in horizontal tubes with inside diameter from 1.0 to 3.0 mm was performed. The air–water test results agree very well with previous work. However, R-134a flow leads to a shift in the slug to annular transition to lower value of gas velocity. The locations of bubble to plug and slug flow transition are also significantly affected by the working fluids properties. We concluded that, in addition to buoyant force and turbulent fluctuations, surface tension force is also an important parameter for flow pattern determination in small tubes. Surface tension force causes the system to act to minimize its interfacial area. It tends to keep bubbles retaining its circular shapes and also to keep the liquid holdup between the tube walls to retard the transition from slug to annular. Since the surface tension of air–water is much larger than that of R-134a, it makes the intermittent to bubble flow transition occurs earlier for air–water than for R-134a. And also leads to a shift in the slug to annular transition to lower value of gas velocity for R-134a.

Radial penetration of a viscous liquid into a planar anisotropic porous medium. International Journal of Multiphase Flow, 14(2), 203-15

March 1988


132 Reads

The equations describing the radial encroachment of a viscous liquid into a homogeneous, anisotropic porous medium are formulated and solved by two approximate methods. An analytical approximation is in good agreement with a finite element numerical solution, provided the angular component of the pressure gradient in an elliptical coordinate system is small. In the specific case where one of the principal flow directions is perpendicular to the flow plane, treatment of experimental flow data in accord with the analytical approximation determines the principal in-plane permeabilities and the degree of in-plane anisotropy. In the general case, the analysis yields effective permeabilities that are functions of the principal permeabilities and the orientation of the principal coordinate system.

Heat transfer augmentation by coiled wire inserts during forced convection condensation of R-22 inside horizontal tubes

June 1998


59 Reads

In the present work, heat transfer augmentation by coiled wire inserts during forced convection condensation of R-22 inside horizontal tubes has been studied. The test-condenser consisted of four separate coaxial double pipe test sections assembled in series. It was a counterflow heat exchanger where R-22 condensed inside the inner tube by rejecting heat to the coolant water flowing in the annulus. Coiled wires with three different wire diameters of 0.65, 1.0 and 1.5 mm and three different coil pitches of 6.5, 10.0 and 13 mm were made and used in full length of test-condenser. The use of helically coiled wires were found to increase the condensing heat transfer coefficients by as much as 100% above the plain tube values on a nominal area basis.

Discrete Element Simulation of Granular Flow in 2D and 3D Hoppers: Dependence of Discharge Rate and Wall Stress on Particle Interactions

March 1995


99 Reads

Discrete element Newtonian dynamics simulations have been carried out of filling and discharge under gravity of non-cohesive discs (in two dimensions) and spheres (in three dimensions) from model hoppers. The current model improves that developed previously by us (Langston et al., 1994) in several respects. We introduce a continuous and gradual hopper filling method, a more realistic normal-tangential interaction between the particles, particle size polydispersity, and the model is extended from two to three dimensions (3D). The hopper discharge rate has been computed as a function of material head height, outlet size and the hopper half-angle. The model results are, in general, in very good agreement with established literature empirical predictions. The hopper wall stresses have been compared in the static state after filling and in the dynamic state during discharge. Generally there is encouraging agreement with predictions from the continuum differential slice force balance method, with significant improvements over our previous work. We have also observed, for the first time in a discrete element simulation of hoppers, the appearance of rupture zones within the material and associated wall stress peaks where the rupture zones intersect with the hopper wall. We consider that the current model is more successful than the previous one because the particle interactions include a much greater level of frictional “engagement” at low loads, with less variation at high loads.

Fundamentals of migrating multi-block lattice Boltzmann model for immiscible mixtures in 2D geometries

October 2010


35 Reads

This paper proposes an extension scheme for the application of the single phase multi-block lattice Boltzmann method (LBM) to the multiphase Gunstensen model, in which the grid is refined in a specific part of the domain where a fluid–fluid interface evolves, and the refined grid is free to migrate with the suspended phase in the flow direction. The method is applicable to single and multiphase flows, and it was demonstrated by simulating a benchmark single phase flow around a 2D asymmetrically placed cylinder in a channel and for investigating the shear lift of 2D neutrally buoyant drop in a parabolic flow.

The influence of particle rotation on wake stability at particle Reynolds numbers, ReP < 300 - Implications for turbulence modulation in two-phase flows

August 1998


14 Reads

The influence of particle rotation on the stability of the grain wake is investigated experimentally for particle Reynolds numbers less than 300. Particle rotation may be present in most industrial and geophysical two-phase flows and imparts significant differences to the structure of the wake when compared to cases where no rotation is present. An oil-filled flume has been used to investigate the dimensions of the wake region and frequency of wake eddy shedding for isolated, spherical and spheroidal particles at rotation rates up to 10 revolutions/second. A parameter, β, is defined which expresses the ratio of the peripheral surface velocity of the particle to the relative velocity between the two phases. For both shaped particles, the wake is destroyed and absent at β>0.5, whilst the size of the wake region is significantly smaller for 0<β<0.5 when compared to the wake dimensions at zero rotation. At 0<β<0.5 for the spherical grain, the frequency of eddy shedding is modulated and equal to the rotation rate, w, whilst for spheroidal grains this frequency is 2w as alternate wakes are shed into the flow as the particle adopts two oblate and prolate orientations in each revolution. At greater rotation rates, an increasingly dominant shear layer is formed on the underside of the grain and generated by fluid being dragged over the rotating particle and sheared against the freestream flow beneath the particle. Where the wake region is destroyed through particle rotation (β>0.5), turbulence enhancement in the freestream may still be present due to the generation of this lower shear layer. This work suggests that a principal mechanism of turbulence enhancement by large grains in two-phase flows involves the influence of particle rotation. If particle rotation is present, turbulence enhancement may occur at much lower particle Reynolds numbers than previously assumed, and at higher rotation rates turbulence enhancement of the freestream flow may occur in the absence of the wake region. Previous numerical modelling of two-phase flows which invokes wake instability to explain turbulence enhancement in the absence of rotation, may therefore require modification.

Experimental studies on critical heat flux in vertical tight 37-rod bundles using freon-12

October 2005


50 Reads

The design of tight-lattice pressurized water reactors requires the knowledge of CHF in tight rod bundles. Experimental investigations on CHF behavior in tight hexagonal 37-rod bundles were performed by using the model fluid Freon-12. About 400 CHF data points have been obtained in a range of parameters: pressure 1.0–2.7 MPa, mass flux 1.4–4.5 Mg/m2 s and bundle exit steam quality −0.4 to +0.2. It is found that the effect of different parameters on CHF in the tight rod bundle is similar to that in tube geometries. The present test results agree also quantitatively well with the CHF data obtained in tubes of comparable hydraulic diameters. Some in the open literature well known CHF correlations proposed for rod bundles under-predict the test results significantly.

Comprehensive experimental investigation of the hydrodynamics of larg-scale, 3D, oscillating bubble plumes

October 2006


56 Reads

An extensive study of the most important hydrodynamic characteristics of fairly large-scale bubble plumes was conducted using several measurement techniques and a variety of tools to analyze the data. Particle image velocimetry (PIV), double-tip optical probes (OP) and photographic techniques were extensively applied to measure bubble and liquid velocities, void-fraction and bubble sizes. PIV measurements in a vertical plane crossing the centre of the injector provided the instantaneous velocity fields for both phases, as well as hydrodynamic parameters, such as the movement of the axis of the plume and its instantaneous shape. Statistical studies were performed using image processing to determine the distribution of the apparent instantaneous plume diameter and centreline position. An important finding was that there is little instantaneous spreading of the bubble plume core; the spreading of the time-averaged plume width (as measured from the time-averaged void-fraction and time-averaged liquid velocity fields) is largely due to plume meandering and oscillations. The liquid-phase stress tensor distributions obtained from the instantaneous velocity data indicate that, for the continuous phase, these stresses scale linearly with the local void-fraction in the range of 0.5% < α < 2.5%. The bubbles were found to be ellipsoidal, with shape factor e ≈ 0.5.

Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet

May 2007


1,037 Reads

Numerical simulations are carried out to describe the dense zone of a spray where very little information is available, either from experimental or theoretical approaches. Interface tracking is ensured by the level set method and the ghost fluid method (GFM) is used to capture accurately sharp discontinuities for pressure, density and viscosity. The level set method is coupled with the VOF method for mass conservation.The level set–VOF coupling is validated on 2D and 3D test cases. The level set–ghost fluid method is applied to the Rayleigh instability of a liquid jet. Preliminary results are then presented for 3D simulation of the primary break-up of a turbulent liquid jet with the level set–VOF–ghost fluid method.

Flow boiling critical heat flux of FC-72 from flush-mounted and protruded simulated chips in a vertical rectangular channel

March 2000


36 Reads

Experiments on flow boiling heat transfer and critical heat flux (CHF) of the dielectric coolant FC-72 are carried out for four in-line simulated electronic chips of 10 mm × 10 mm, for both flush-mounted and protruded chips on one wall of a vertical rectangular channel. The fluid velocity and subcooling are varied from 4.2 to 78 cm/s (ReL=1.0×103 to 3.0 × 104), and from 15 to 33°C, respectively. The fully-developed nucleate boiling regime is not affected by changes in flow velocity and subcooling, whereas the surface temperatures decrease with increasing flow velocity and subcooling in the partial boiling regime. CHF generally increases with the degree of subcooling and with velocity at higher inlet velocities, but velocity has little effect at values less than 20 cm/s. The surface temperatures for the flush-mounted chips are lower than those for protruding chips, and the CHF data for the flush-mounted chips are higher than those for protruding chips; the differences between these two cases increase with increasing velocity.

Steam-water void fraction for vertical upflow in a 73.9 mm pipe

July 1986


38 Reads

Forced flow and natural circulation void fraction data are presented for steam-water upflow in a 73.9 mm pipe. Nondevelopment apparent in some of the data is due to bubble retardation at a nearby upstream bend. Through the use of suitable approximations, a previous analysis of distributed and annular flow voidage has provided a simple but accurate predictive method for the “developed flow” component of the data.

Study on the deformation and departure of a bubble attached to a wall in D.C./A.C. electric fields

February 1998


66 Reads

In order to investigate the effects of electric fields on the behavior of a bubble attached to a wall, basic experiments on the deformation and departure of a bubble are carried out under d.c./a.c. applied voltages. In the present study, three types of electrodes are used, to examine the bubble behavior by the nonuniformity of the electric field. For a d.c. electric field, as the applied voltage increases the bubble attached to a wall is more extended in the direction parallel to the imposed electric field, thus the aspect ratio and the contact angle also increase. The bubble departure volume in a nonuniform electric field decreases continuously, while that in a uniform electric field is nearly constant. The present results by the d.c. electric field show that the bubble behavior is significantly affected by the degree of the in omogeneity of the electrode configuration. For an a.c. electric field, as a preliminary analysis, a general theory on an equivalent dynamic system is extended to derive the bubble oscillation frequency. The analysis predicts that the bubble departure occurs near a resonant frequency. It is observed that the departure process of a bubble in the a.c. electric field is associated with the bubble oscillation which is composed of three different regions. Near the critical voltage, the bubble departure volume drops suddenly. It is also found that the reduction of the bubble departure volume by the a.c. electric field is more effective than in the d.c. electric field case.

Experimental studies on two-phase flow patterns aboard the Mir space station

November 2001


49 Reads

A series of experiments on two-phase gas–liquid flow patterns in a test tube with a length of 356 mm and an inside diameter of 10 mm were performed aboard the Mir Space Station in August 1999. Carbogal and air were used as the liquid and the gas phase, respectively. In the present paper, the experimental results at the background microgravity environment of the Mir Space Station (no more than 10−5g) were reported. Five kinds of flow patterns, namely dispersed bubble flow, bubble flow, slug flow, slug–annular transitional flow, and annular flow, were observed in the space experiment. Due to the small length-to-diameter ratio of the test tube used in the present study, the observed flow patterns should be considered to be developing ones. The experimental results were compared with the model proposed previously which accounts for the entrance effects on the flow pattern transitions. A good agreement between the predictions and the experimental data was obtained. Some widely used models developed based on the analysis of fully developed two-phase flow at microgravity were also compared with the present data in order to make evaluations of these models and to have some insights on the flow evolution.

Plane two-phase stagnation-point flow above a stretching sheet

September 1988


7 Reads

The steady-state two-dimensional flow which takes place in a half space of two-phase suspension bounded by an infinite stretching sheet is investigated. This problem is used as a vehicle for the study of certain aspects of two-phase stagnation-point flow. Attention is focused on the singularity in the particle-phase density distribution in the vicinity of the stagnation point predicted by certain existing theories. It is found that the inclusion of a particle-phase pressure gradient in the governing equations eliminates singular behavior in the particle-phase density distribution and makes possible the calculation of stagnation-point solutions throughout the entire range of inverse Stokes numbers.

A New Formula for the Pressure Recovery in an Abrupt Diffusor

April 1989


37 Reads

A new formula for the pressure recovery in an abrupt expansion based on the superficial velocities of the two phases is proposed. Its predictive accuracy and that of other models from the literature are compared with new experimental data from stationary two-phase flow experiments in a diffusor with a very steep opening contour. Only the new model exhibits good agreement between predicted and measured experimental steam-water and air-water data. Furthermore, the new formula is verified by experimental data of other authors obtained with different expansion geometries and flow conditions.

Stochastic modelling of the effects of liquid droplet collisions in impinging streams absorbers and combustors

March 1991


42 Reads

A stochastic model based on the Boltzmann kinetic equation and employing the comprehensive treatment of the dynamics of binary droplet collisions is suggested to describe the droplet size and spatial distribution in dense spray. The model is valid for highly non-equilibrium impinging sprays in which the inertia of the droplets is very high and dynamic coupling with the gas is low. A Monte Carlo simulation procedure is developed for the solution of the kinetic equation. A model is used to analyse the absorption of a gas in a liquid spray in an impinging streams absorber. It is demonstrated that droplet collisions result mainly in coalescence, and reduce the overall droplet concentration and the interphase area in the reactor. The results of the analysis of the vaporization of a pentane spray in an impinging streams combustor are presented. It is shown that while droplet collisions reduce the vaporization rate by deflecting droplets out of the reactor and by coalescence, collision-induced fragmentation strongly affects the droplet size distribution and increases the fuel vaporization rate. The obtained results indicate that in the high velocity combustion of light fuels the collision-induced fragmentation of fuel droplets has a profound effect on the droplet size and spatial distribution.

The Enhancement of the Physical Absorption of Gases in Aqueous Activated Carbon Slunies

January 1996


26 Reads

The enhancement of the gas-liquid mass transfer rates in aqueous slurries containing small activated carbon particles was studied in a semi-batchwise operated stirred cell absorber with a plane interface. The maximum observed enhancement factors for absorption of propane, ethene and hydrogen in the aqueous slurries were 3.6, 3.3 and 2.0, respectively. It was shown that for our results and those reported in the literature the maximum enhancement factor, Emax, decreases with increasing liquid side gas-liquid mass transfer coefficient, kl. From all the experimental data the following relationship is found: although different types of activated carbon particles and differences in sizes were used by the various research groups. To describe these results a simple theory is presented.

Air entrainment by a plunging jet: The dynamical roughness concept and its estimation by a light absorption technique

September 2002


118 Reads

Air entrainment by plunging jets and the consequent production of bubbles play an increasing role in industrial and environmental applications. Generally, air entrainment can be seen as the consequence of two complementary mechanisms: (1) the interfacial shear along the liquid jet interface which drags down an air boundary layer and (2) the air entrapment process at the point of impact of the plunging jet with the receiving pool. The latter process is usually dominated by growing interfacial disturbances travelling on the jet. The great variety of these disturbances is represented by the concept of dynamic interfacial roughness of which a definition is provided and justified. To measure this quantity, an easy-to-use optical technique is designed. The dynamic interfacial roughness and the ability to entrap air by a plunging jet are found to depend on the hydrodynamical noise applied to the jet. The optical technique is presented as a very simple tool to optimally devise the internal design of nozzles and then, to control air entrainment.

Measurement and prediction of solid sphere trajectories in accelerated gas flow

April 1997


11 Reads

Trajectories are measured and compared with computed trajectories of solid particles with a diameter of 1–2 mm in downward gas flow near a solid cylinder with a diameter, dc, of 25 mm. The Reynolds number based on dc has been varied from 3000–13,000. The particle Reynolds numbers, based on the relative velocity |UG − Up|, ranged from 0 to 2000. Of all forces other than gravity, drag is dominant, although the pressure gradient and added mass forces for Rec > 10,000 have the same order of magnitude. The Basset force can be neglected. The correlation [3], originally derived by Sridhar and Katz (1995) for the lift force coefficient of bubbles, has been found to be appropriate for freely moving solid particles with shear number less than 0.04.

The accelerated motion of rigid bodies in non-steady Stokes flow

February 1990


29 Reads

The force and torque acting on an accelerating rigid body of arbitrary shape, moving at low Reynolds number through a fluid at rest in infinity, are considered. The expressions found for the force due to pure translation and the torque due to pure rotation of the body each include three tensors which relate the acceleration and velocity to the force and the torque. In the case of combined translation and rotation, three “coupling tensors” are added to each of the above expressions. These expressions are extended for the case of a particle, immersed in a quiet fluid and acted upon by an impulse. Generalized Faxen's theorems are derived for non-steady flows which do not vanish in infinity. Finally, the effect of non-zero initial velocity of the fluid and the body is considered. The stop distance is shown to depend linearly on the initial velocity of the body through a displacement tensor which consists of the traditional quasi-stationary term and an additional tensor. This additional tensor depends on the geometry of the body and on the initial velocity field of the fluid. It is infinite if the kinetic energy of the initial field is infinite. Likewise, the expression for the force acting on the body contains an additional term which depends on time, on the geometry of the problem and on the initial velocity field.

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