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Two-fluid model simulations of a bubbly vertical boundary layer with point injection are presented. A new bubble turbulence dispersion model, designed to be used with RANS type turbulence models, was formulated and compared with recent data of [1] and [2]. These data showed that bubble migration toward the wall is controlled by the coherent large scale liquid structures within the boundary layer. The model is based on the application of a kinetic transport equation, similar to Boltzmann’s equation, and the idea that by selectively removing bubbles from the liquid eddies within the boundary layer, bubble capture at the wall introduces a preferential direction of migration and/or nonhomogeneous, anisotropic dispersion. This is the first model capable of predicting all the types of void fraction profiles observed experimentally for point injection. It is shown that without this new model, two-fluid model simulations fail to predict the experimental data. In addition, a new physical interpretation of the data of [1] and [2] is presented, which strongly suggests that the quantity controlling bubble migration toward the wall and bubble dispersion, is the boundary layer drift parameter (i.e., the ratio of the bubble’s terminal velocity to the free-stream liquid velocity).

A new adaptive grid, 3-D FEM hydrodynamic shock (ie, HYDRO )code called PHASTA-2C has been developed and used to investigate bubble implosion phenomena leading to ultra-high temperatures and pressures. In particular, it was shown that nearly spherical bubble compressions occur during bubble implosions and the predicted conditions associated with a recent ORNL Bubble Fusion experiment [Taleyarkhan et al, Science, March, 2002] are consistent with the occurrence of D/D fusion.

In cavitation experiments with deuterated acetone, tritium decay activity above background levels was detected. In addition, evidence for neutron emission near 2.5 million electron volts was also observed, as would be expected for deuterium-deuterium fusion. Control experiments with normal acetone did not result in tritium activity or neutron emissions. Hydrodynamic shock code simulations supported the observed data and indicated highly compressed, hot (10 6 to 10 7 kelvin) bubble implosion conditions, as required for nuclear fusion reactions.

The accurate prediction of void fraction profiles near solid walls using the two-fluid model is still an unresolved issue. These profiles result from the combination of two factors: a) forces acting on the bubbles, and, b) geometric constraints imposed by their shape. We propose herein a two-fluid model that involves a particle-center-averaging procedure for the disperse phase, and a reinterpretation and postprocessing of the results obtained. This center-averaged approach averages the disperse phase (bubbles) based on a particle center indicator function, while using the standard phase indicator averaging for the continuous phase (liquid). The solution fields obtained are then postprocessed to introduce the geometry of the bubbles in order to recover the values that should be representative of measured fields. The key idea here is to separate the geometric aspect from the dynamic aspect of the problem into two independent, successive steps. The new model may be easily incorporated into existing two-fluid model codes. Results obtained with the new model showing agreement with experimental data (Moursali et al, 1995) are also presented.Copyright © 2002 by ASME

The fundamental and tenth harmonics were used to produce stable single-bubble sonoluminescence in water. By varying the phase difference between the harmonics, it was possible to enhance the sonoluminescence light emission by as much as a factor of 2.7 compared with single-frequency excitation. Absolute measurements of the bubble radius evolution were carried out using the two-detector technique. Unlike previous observations, these measurements and complementary fits of the Rayleigh-Plesset equation reveal that the maximum bubble radius does not change significantly with phase angle between the harmonics. Therefore, increased sonoluminescence intensity does not have to correlate with increases in maximum bubble radius prior to collapse. We believe that a more violent bubble collapse rate (driven by the very-high-frequency component) is responsible for the enhanced light emission under this type of mixed excitation. It was further found that the presence of the tenth-harmonic frequency component led to significant enhancements in the stability of the bubble undergoing sonoluminescence. This allowed the bubble to be driven at the fundamental frequency at 2.0 bars pressure amplitudes, which are significantly above often-reported thresholds of 1.4 bar itself, thereby leading to increased levels of light emission (by more than 250%).

This chapter is devoted to deriving and using microstructural information to find constitutive equations, giving relationships between certain average quantities and the average fields. The physical situation is one in which corpuscular models can be highly useful in motivating the forms of the constitutive equations. In effect, the study of the mechanics of multicomponent fluids necessitates the study of the form of the momentum exchange term and the stress in the momentum equation. The study of these terms is aided by a physically appropriate corpuscular model, consisting of solutions for flows in this model, which are sometimes exact but usually approximate. Once these solutions are found, they can be averaged to find the force of interaction in the continuum equations.

The spherically-symmetric problem of the oscillations of a gas bubble in the center of a spherical flask filled with a compressible liquid that is excited by pressure oscillations on the flask wall is considered. A generalization of the Rayleigh-Plesset equation for a compressible liquid is given in the form of two ordinary difference-differential equations that take into account the pressure waves which are reflected from the bubble and those that are incident on the bubble from the flask wall. The initial value problem for the initiation of bubble oscillations due to flask wall excitation and for the evolution of these oscillations is considered. Linear and non-linear periodic bubble oscillations are analyzed analytically. Non-linear resonant and near-resonant solutions for the bubble nonharmonic oscillations, which are excited by harmonic pressure oscillations on the flask wall, are obtained. The influence of heat transfer phenomena on the bubble oscillations is analysed.

A one‐dimensional hydrodynamic shock (HYDRO) code was developed to numerically evaluate the conservation equations of each phase during bubble growth and collapse. This code includes the Mie–Gruniesen equations of state and Born–Mayer potential functions, which are known to be valid for highly compressed fluids. In particular, for acetone these equations of state are based on the shock wave adiabat data, and they implicitly specify the effect of the induced radiation field and the dissociation and ionization processes that take place during plasma formation within imploding bubbles. Moreover, relevant energy losses and the effect of both molecular and electron conductivity were taken into account, and the resultant HYDRO code allowed for the evaluation of shock wave interaction using the well‐established Godunov numerical technique. Bubble dynamics were studied in deuterated acetone for conditions typical of those in our experiments. It was found that highly compressed conditions suitable for thermonuclea...

The entrainment of non-condensible gases by a plunging liquid jet impacting a liquid pool is related to some important practical problems. For example, the absorption of greenhouse gases into the ocean has been hypothesized to be highly dependent upon the air carryunder that occurs during breaking waves, which represent a type of plunging jet Monahan, 1991; Kerman, 1984. Other applications include some type of liquid/gas chemical reactors. In order to enhance the reaction rate, a jet of liquid entrains the surrounding gas reactant forming a two-phase jet. The reaction rate is enhanced because of the increase of the interfacial area density and the pseudo-turbulence produced by the entrained gas bubbles.

This chapter presents material on the use of multidimensional two-fluid models for the analysis of phase distribution and phase separation phenomena. In particular, the analysis of lateral phase distribution for bubbly upflows and downflows in pipes and in more complex geometry conduits, is presented. In addition, the analysis of phase separation in a horizontal tee is discussed for stratified two-phase flow. It is shown that accurate mechanistic predictions of two-phase flows can be performed using multidimensional two-fluid models and appropriate computational fluid dynamic (CFD) numerical techniques.

This chapter presents data and a one-dimensional two-fluid model analysis of pressure and void waves. Both linear and nonlinear analysis are performed. The analytical linkage between standing and propagation pressure waves, as well as critical flow, is developed. The well-posedness of a two-fluid model is found to be determined by the void wave eigenvalues, which are, in turn, determined by the closure conditions. Moreover, the criterion for the formation of void shocks and solitons is given. It is shown that wave propagation phenomena may be quite sensitive to the closure laws used in the two-fluid models. As a consequence pressure and void wave data are very useful for two-fluid model assessment.

A spectral turbulent cascade-transport model was developed and applied to single-and two-phase turbulent uniform shear flows. This model tracks the development of the turbulent kinetic energy spectrum by splitting the turbulent kinetic energy into wave number bins. A separate transport equation accounts for the spectral production, dissipation and transport terms and is solved for each wave number bin. The predicted evolution of the turbulence level, turbulent production and turbulent dissipation is shown to be consistent with experimental data for turbulent uniform shear flows. The shear rate in the various experiments ranges from 12.9 to 46.8 s− 1 for air flows, 0.96 to 1.23 s−1 for water flows and was 2.9 s− 1 for bubbly two-phase air/water flow.

The four year research program, entitled The Continuum Modelling of Two-Phase Systems,'' is intended to advance the state-of-the-art in the two-fluid modeling of steady and transient two-phase flows. During the report period (i.e., the first year) our efforts have focused on the question of well-posedness, that is, the modeling of those closure conditions which yield systems of equations having real eigenvalues, and the implications of having complex eigenvalues. To this end, void wave phenomena were investigated, since the void wave eigenvalues are the ones which become complex, thus leading to ill-posedness. The most significant technical publications that have resulted from the research performed during the report period are attached to this letter. 13 refs.

HYDRO code model of the spherically symmetric motion for a vapor bubble in an acoustically forced liquid is presented. This model describes cavitation bubble cluster growth during the expansion period, followed by a violent implosion during the compression period of the acoustic cycle. There are two stages of the bubble dynamics process. The first, low Mach number stage, comprises almost all the time of the acoustic cycle. During this stage, the radial velocities are much less than the sound speeds in the vapor and liquid, the vapor pressure is very close to uniform, and the liquid is practically incompressible. This process is characterized by the inertia of the liquid, heat conduction, and the evaporation or condensation of the vapor. The second, very short, high Mach number stage is when the radial velocities are the same order, or higher, than the sound speeds in the vapor and liquid. In this stage high temperatures, pressures, and densities of the vapor and liquid take place. The model presented herein has realistic equations of state for the compressible liquid and vapor phases, and accounts for nonequilibrium evaporation/condensation kinetics at the liquid/ vapor interface. There are interacting shock waves in both phases, which converge toward and reflect from the center of the bubble, causing dissociation, ionization, and other related plasma physics phenomena during the final stage of bubble collapse. For a vapor bubble in a deuterated organic liquid e.g., acetone, during the final stage of collapse there is a nanoscale region diameter 100 nm near the center of the bubble in which, for a fraction of a picosecond, the temperatures and densities are extremely high 10 8 K and 10 g/cm 3 , respectively such that thermonuclear fusion may take place. To quantify this, the kinetics of the local deuterium/deuterium D/D nuclear fusion reactions was used in the HYDRO code to determine the intensity of the fusion reactions. Numerical HYDRO code simulations of the bubble implosion process have been carried out for the experimental conditions used by Taleyarkhan et al. Science 295, 1868 2002; Phys. Rev. E 69, 036109 2004 at Oak Ridge National Laboratory. The results show good agreement with the experimental data on bubble fusion that was measured in chilled deuterated acetone. © 2005 American Institute of Physics. DOI: 10.1063/1.2104556

Time spectra of neutron and sonoluminescence emissions were measured in cavitation experiments with chilled deuterated acetone. Statistically significant neutron and gamma ray emissions (with more than 25 standard deviation accuracy) were measured with a calibrated liquid‐scintillation detector. The neutron and sonoluminescence emissions were found to be time correlated over the time of significant bubble cluster dynamics. The neutron emission energy was at and below 2.45 MeV and the neutron emission rate was up to ∼400 000 n/s. Measurements of tritium production were also performed and these data implied a neutron emission rate due to D‐D fusion which agreed with what was measured. In contrast, control experiments using normal acetone did not result in statistically significant tritium activity, or neutron or gamma ray emissions. The talk will highlight significant details of the acoustic chamber design, characterization and qualification along with the nuclear data obtained.

A seminal discovery related to detection of nuclear emissions during acoustic inertial confinement fusion with deuterated acetone has been reported in Science (3/8/2002 issue). Nuclear emissions we measured included 2.5‐MeV neutrons and tritium as would be expected from deuterium–deuterium nuclear fusion. These unmistakable statistically significant signatures were measured under conditions commensurate with degassed rapid condensation‐induced implosion conditions only with the test fluid deuterated acetone. In these experiments bubble clusters are nucleated in tensioned degassed liquids with neutrons at the nanoscale level and are then made to grow by a factor of ∼100 000 in size to the mm scale prior to implosive collapse. Similarly conducted control experiments with natural acetone did not result in any statistically significant nuclear emissions. Shock code simulations (discussed in a companion talk) corroborated these observations and provided insights into the physics of the overall process. Since the recent announcement of this discovery several world‐wide researchers have contacted the authors for further clarifications in a variety of areas. The presentation will discuss these issues and questions, and will provide relevant explanations with supporting evidence.

In cavitation experiments with deuterated acetone, statistically significant tritium decay activity above background levels was detected. In addition, evidence for statistically significant neutron emissions near 2.5 MeV was also observed, as would be expected for deuterium–deuterium fusion. Control experiments with normal acetone did not result in tritium activity or neutron emissions. Hydrodynamic shock code simulations supported the observed data and indicated compressed, hot (106–107 K) bubble implosion conditions, as required for thermonuclear fusion reactions. Separate experiments with additional fluids are under way and results appear to support those observed with acetone. Scalability potential to higher yields, as well as evidence for neutron−tritium branching ratios are presented.

The spherically symmetric problem of the oscillations of a gas bubble in the center of a spherical flask filled with a compressible liquid that is excited by pressure oscillations on the flask wall is considered. A generalization of the Rayleigh–Plesset equation for a compressible liquid is given in the form of two ordinary difference‐differential equations that take into account the pressure waves that are reflected from the bubble and those that are incident on the bubble from the flask wall. The initial value problem for the initiation of bubble oscillations due to flask wall excitation and for the evolution of these oscillations is considered. Linear and nonlinear periodic bubble oscillations are analyzed analytically. Nonlinear resonant and near‐resonant solutions for the bubble nonharmonic oscillations, which are excited by harmonic pressure oscillations on the flask wall, are obtained. The influence of heat transfer phenomena on the bubble oscillations is analyzed.

Advances in the analysis of the linear stability of ventilated and unventilated boiling channels are presented. It is also shown that the entire closed loop transfer function matrix must be considered when evaluating the linear stability margin of a Multi-Input/Multi-Output (MI/MO) system such as a boiling water nuclear reactor (BWR). An analysis is also presented of finite amplitude instability modes. It is shown that a boiling channel can exhibit both subcritical and supercritical bifurcations.

Calcul de la force s'exercant sur une sphere unique en accelation par rapport a un fluide non visqueux soumis a une deformation pure et une rotation loin de la sphere. Cette force consiste en trois parties: la force de gradient de pression et une force de non trainee qui consiste en une force de masse virtuelle et une force de portance

Analysis of light water nuclear reactor loss-of-coolant accidents (LOCA) requires that one be able to accurately calculate how two-phase flows split in complex, branching conduits. This paper is intended to provide a more thorough understanding of phase separation phenomena in such systems. In particular, detailed experiments have been performed with air/water mixtures in vertical wyes and tees to provide a data base for the development and verification of analytical models. The dependence of phase separation on different parameters, such as inlet quality, mass flux and separation angle, is discussed.

An experimental and analytical study of phase separation for impacting two-phase flows in branching conduits has been performed. The resulting analytical model is applicable to impacting flows in wyes and tees for various inlet flow regimes. This model is based on a dividing-streamline concept, and it assumes that there is a “zone of influence” for each of the two phases which is bounded by the conduit wall and the dividing streamlines. Good agreement was obtained between model predictions and the experimental results from this study and others.

The conservation equations for one-dimensional two-phase flow are derived from first principles. The effects of the radial distributions of velocities, enthalpies, and void fraction are taken into account through the use of correlation coefficients. Several simplified separated-flow model formulations that have appeared in the literature are derived from these equations by specializing the values of the correlation coefficients. The equivalence of these formulations under certain assumptions is demonstrated. Finally, new Lagrangian forms of the conservation equations, written in terms of the velocities of the center of mass, momentum, and energy are presented.

An analytical model for the long-term emergency core cooling (ECC) of a boiling water nuclear reactor (BWR) has been developed. This one dimensional drift-flux model, is an extension of a previous study by Lahey and Kamath [1]. It considers both subcooled and bulk boiling in the core, allows the drift-flux parameters, C 0 and V g j , to be functions of void fraction (α), and can accommodate both broken and intact jet pump seals. The results of this analytical model compare well with data from simulated full scale BWR fuel rod bundles, and experiments in the PCE facility at RPI. It has been found that the unlikely failure of jet pump seals can have a detrimental effect on the long term cooling capabilities of a BWR/4.

Models for predicting single- and two-phase pressure drop in wyes and tees have been developed and compared to air/water and steam/water data. It is shown that the model previously proposed by Saba and Lahey [1] can be used to predict the observed pressure drops in tees; however, it is not always reliable for wyes.

The influence of parallel channel effects (PCE) on the effectiveness of the emergency core cooling systems in a boiling water nuclear reactor (BWR) was experimentally investigated. Specifically, the effectiveness of the core spray cooling system and the low-pressure coolant injection system during the emergency core cooling of a simulated 218-BWR/4 was studied. Experiments simulating conditions after a hypothetical design basis loss-of-coolant accident were performed in a special PCE test section in which Freon-114 was used as the working fluid. A detailed scaling analysis was performed to allow real-time simulation of the bypass leakage inflow, reflood rate, countercurrent flow limitation core decay heat, and the size of postulated jet pump breaks. It was found that BWR core cooling could be adversely affected by postulated failure of the jet pump seals by observing the parallel channel effects.

The radial distribution of the volumetric vapour (or void) fraction in steady, fully developed turbulent two-phase flow is described for vertical low-quality bubbly flows in a circular pipe. The analysis is based on the phasic equations of conservation of momentum in the axial and radial directions. Mixing-length theory is used to model the turbulent stresses in the continuous phase. The predicted flow structure shows three distinct regions. The ‘outer’ region, that is, the region away from the wall and the centre-line, has a uniform void distribution. For upflow, a bubble layer is predicted near the wall, while for downflow, vapour coring is predicted, with a peak in void fraction at the centre-line. These predictions are in agreement with observed void profiles.

Experiments were performed to study phase separation and distribution phenomena in a 2-D test section. The conditions tested were intended to simulate the “chimney effect” that may occur during reflood in a pressurized water nuclear reactor (PWR) core after a hypothetical loss-of-coolant accident (LOCA). Such flow situations may enhance the cooling of the higher powered assemblies during reflood. The countercurrent two-phase flow conditions expected in a PWR were simulated using air/water in a special 2-D test section having two inlet and two outlet ports. The void fraction distribution across the test section was measured with a γ-ray densitometer for different flow conditions, including various flow rates, flow qualities and flow splits between the four ports. These flow conditions were run for cases with and without vertical rods mounted inside the test section. These rods were intended to simulate the effect of the lateral resistance to the flow due to fuel rods in a PWR core. It was found that the presence of the rods dramatically reduced the degree of recirculation observed. A variety of flow regimes were observed, including regions of single-phase water and air, and bubbly, slug and churn—turbulent flows. It is felt that these data form an excellent basis for the assessment of multidimensional two-fluid models of two-phase flow.

Dispersion and attenuation was measured for standing waves in a vertical waveguide filled with a bubbly air/water mixture. The propagation speed of pressure pulses was also measured. The data were compared with a two-fluid model for a range of values of the virtual volume coefficient, CVM. The experimentally determined CVM was found to be a function of global void fraction (〈α〉). Moreover it was noted that this CVM was less strongly related to void fraction than those proposed by Zuber (1964) and Van Wijngaarden (1976).

This paper presents an analytical model for the determination of the cross-sectionally averaged transient mass flux of a two-phase fluid flowing in a conduit instrumented by a Drag-Disk Turbine Transducer (DTT) Rake and a multibeam gamma densitometer. Parametric studies indicate that for a typical blowdown transient, dynamic effects such as rotor inertia can be important for the turbine-meter. In contrast, for the drag-disk, a frequency response analysis showed that the quasisteady solution is valid below a forcing frequency of about 10 Hz, which is faster than the time scale normally encountered during blowdowns. The model showed reasonably good agreement with full scale transient rake data, where the flow regimes were mostly homogeneous or stratified, thus indicating that the model is suitable for the analysis of a DTT rake.

Phase separation phenomena in a two-phase (air/water) mixture flowing through a plexiglas tee test section was measured. R was found that eren for low inlet flow qualities (≤1%) the degree of phase separation was quite pronounced, with the gas phase preferentially separating into the branch. Using these data a physically-based empirical model was developed with which to calculate the phase distribution of a subsonic, two component, two-phase mixture in the downstream branches of a branching conduit. The model appears to correctly prcdict the observed phase separation in horizontal and vertical wyes and tees (having a horizontal branch). Moreover, aithough there is no data available for high pressure steam/water conditions, the predicted trends appear to be reasonable. The model described in this paper is only considered to be valid for small conduits and mass withdrawal ratios ( G 3 A 3 G 1 A 1 ) greater than 0.3.

A closed-loop analysis of phase distribution is presented. This analysis is based on the use of a two-fluid model. It is shown that the treatment of the turbulence distribution in the continuous phase is crucial if accurate predictions are to be made. A K-κ model is used to model turbulence in this study. Finally, recommendations are made as to how the state-of-the-art can be advanced.

A state-of-the-art one-dimensional thermal-hydraulic model has been developed to be used for the linear analysis of nuclear-coupled density-wave oscillations in a boiling water nuclear reactor (BWR). This model accounts for phasic slip, distributed spacers, subcooled boiling, space/time-dependent power distributions and distributed heated wall dynamics. In addition to a parallel channel stability analysis, a detailed model was derived for the BWR loop analysis of both the natural and forced circulation modes of operation. The model for coolant thermal-hydraulics has been coupled with the point kinetics model of reactor neutronics. Kinetics parameters for use in the neutronics model have been obtained by utilizing self-consistent nodal data and power distributions. The computer implementation of this model, NUFREQ-N, was used for the parametric study of a typical BWR/4, as well as for comparisons with existing in-core and out-of-core data. Also, NUFREQ-N was applied to analyze the expected stability characteristics of a typical BWR/4.

A novel new ensemble cell averaging technique has been used to derive various interfacial forces and Reynolds stresses for inviscid two-fluid models of two-phase. New terms, not seen in the spatially averaged conservation equations, have been found. Moreover, deficiencies inherent in spatial averaging techniques have been demonstrated.

The Pulsed Photon Activation (PPA) technique for the non-intrusive measurements of single and two-phase flows in a horizontal pipe was developed. The advantages of PPA over pulsed neutron activation (PNA) are discussed. Fluid velocity determinations using such a technique were carried out. An interesting subregion of the horizontal annular flow regime was found to have twin-peak PPA activation time profiles. These twin peaks were confirmed to be associated with the film flows on the upper and lower parts of the horizontal pipe, using the directionality of the PPA bremsstrahlung tagging beam. Film thickness measurements around the circumference of horizontal annular flows were also carried out using a resistivity needle probe and analytical models involving droplet exchange and secondary vapor flow pattern were compared with the experimental data.

An exact analytical solution, based on the method of characteristics, has been obtained for the spatial and temporal variation of vapor volumetric (void) fraction in a depressurizing pool. Numerical evaluations have shown that the axial void profile is strongly dependent on the drift velocity formulation, and that wall heat flux plays only a minor role in the pool swell transient.

This paper presents a study on the effect of fuel rod dynamics on BWR Stability Margin. Specifically, Boiling Water Nuclear Reactor (BWR) stability predictions using lumped parameter fuel rod models were compared with those using a more detailed distributed parameter nuclear fuel rod model, in which radial variations in power generation were considered. It was found that, when nuclear feedback mechanisms were neglected, both models predicted similar stability margins. However, significantly different margins were obtained when void-reactivity feedback was considered. It was further found that the radial power distribution in a nuclear fuel rod, and the void reactivity coefficient, can have a significant impact on predicted stability margins. This study implies that the nuclear fuel must be accurately modeled in the linear stability analysis of BWR channels, and that simplified fuel dynamics models can lead to large non-conservative errors in the predicted stability margin.

A mathematical model has been developed for the linear stability analyses of a system of ventilated parallel boiling channels. The model accomodates phasic slip, nonuniform power distribution, local losses, heater wall dynamics, channel-to-channel (radial) power skews, discrete or continuous ventilation between the channels, turbulent mixing between the channels, various donor-cell options for the lateral transport of energy and momentum, and a transverse momentum equation. A special matrix reduction algorithm was developed to efficiently solve the system of linearized, Laplace-transformed, nodal equations. A parametric study revealed that phasic slip, axial power distribution, heater wall dynamics, local losses, lateral ventilation, and radial power skew can have a significant effect on the stability characteristics of the system [5]. Comparisons were made with the available experimental data, and good agreement was achieved.

Local void fraction measurements were made with a Karlsruhe type impedance probe. The probe was operated at radio frequency to minimize sensitivity to liquid phase resistivity. Two types of signal thresholding were used: level and derivative. A dual beam X-ray system was used as a calibration standard for the radio frequency excited impedance probe. Calibration was performed in vertical air/water flows. Derivative thresholding was found to be preferable to level thresholding, however, in both schemes hydrodynamic and surface tension effects were observed below a liquid superficial velocity of 0.5 m/s. Table salt (NaCl) was added to the water to verify the probe's response to changing water resistivity. Derivative thresholding appeared to work quite well but level thresholding was found to be inadequate due to the change in capacitance.

Phase separation in dividing T- and Y-junctions was investigated experimentally and analytically in this study. New air/water phase separation data are presented for three horizontal test sections (a T-junction, a 45° Y-junction and a 135° Y-junction). Emphasis was placed on low extraction rates through the side branch. A phenomenological model was developed which was based on the idea of dividing streamlines in which centrifugal and interfacial drag forces were assumed to be dominant. Comparisons between model predictions and the available data, corresponding to different flow regimes, pressures, fluid properties, inlet flow rates and qualities and extraction rates, showed good agreement thus supporting the assumptions inherent in the model.

The process of determining appropriate constitutive equations for multidimensional time averaged two-phase flow equations is studied from the point of view of starting from general principles, and proceeding to specific constitutive equations which contain known physical effects. Energetic effects and phase change are not considered. Models are given for the interfacial momentum transfer, the laminar and turbulent (Reynolds) stresses, and the pressure differences between the phases, and between a given phase pressure and the interfacial average pressure.

A two-fluid model is presented that can be used to predict the celerity and attenuation of small-amplitude harmonic disturbances in bubbly two-phase flow. This frequency-dependent relationship is then used to predict the propagation of small-amplitude pressure perturbations through the use of Fourier decomposition techniques. Predictions of both standing waves and propagating pressure perturbations agree well with existing data. The low and high-frequency limits of the celerities predicted by the model are examined and their relationship to critical flow rate is demonstrated. Some limitations of the interfacial pressure model employed in conventional critical flow analysis are exposed and the implications to the prediction of critical flow rate are discussed.