Takashi Hibiki

Thermo-fluid dynamics of two-phase flow

Part I Fundamental of two-phase flow.- Introduction.- Local Instant Formulation.- Part II Two-phase field equations based on time average.- Basic Relations in Time Average.- Time Averaged Balance Equation.- Connection to Other Statistical Averages.- Part III. Three-dimensional model based on time average.- Kinematics of Averaged Fields.- Interfacial Transport.- Two-fluid Model.- Interfacial Area Transport.- Constitutive Modeling of Interfacial Area Transport.- Hydrodynamic Constitutive Relations for Interfacial Transfer.- Drift Flux Model.- Part IV: One-dimensional model based on time average.- One-dimensional Drift-flux Model.- One-dimensional Two-fluid Model.- Two-Fluid Model Considering Structural Materials in a Control Volume.

Some characteristics of air-water two-phase flow in small diameter vertical tubes

Abstract Flow regime, void fraction, rise velocity of slug bubbles and frictional pressure loss were measured for air-water flows in capillary tubes with inner diameters in the range from 1 to 4 mm. Although some flow regimes peculiar to capillary tubes were observed in addition to commonly observed ones, overall trends of the boundaries between flow regimes were predicted well by Mishima-Ishiis model. The void fraction was correlated well by the drift flux model with a new equation for the distribution parameter as a function of inner diameter. The rise velocity of the slug bubbles was also correlated well by the drift flux equation. The frictional pressure loss was reproduced well by Chisholms equation with a new equation for Chisholms parameter C as a function of inner diameter.

One-Dimensional Drift-Flux Model and Constitutive Equations for Relative Motion Between Phases in Various Two-Phase Flow Regimes

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the kinematic constitutive equation for the drift velocity has been studied for various two-phase flow regimes. The constitutive equation that specifies the relative motion between phases in the drift-flux model has been derived by taking into account the interfacial geometry, the body-force field, shear stresses, and the interfacial momentum transfer, since these macroscopic effects govern the relative velocity between phases. A comparison of the model with various experimental data over various flow regimes and a wide range of flow parameters shows a satisfactory agreement.

Axial interfacial area transport of vertical bubbly flows

Abstract Recently, the concept of the interfacial area transport equation has been proposed to develop the constitutive relation on the interfacial area concentration in relation to the modeling of the interfacial transfer terms in the two-fluid model. Accurate data sets on axial development of local flow parameters such as void fraction, interfacial area concentration, interfacial and liquid velocities and turbulence intensity are indispensable to verify the modeled source and sink terms in the interfacial area transport equation. From this point of view, local flow measurements of vertical upward air–water flows in a round tube with an inner diameter of 50.8 mm were performed at three axial locations of z/D=6.00, 30.3 and 53.5 as well as 15 radial locations from r/R=0–0.95 by using the double-sensor probe and the hotfilm probe. In the experiment, the superficial liquid velocity and the void fraction ranged from 0.491 to 5.00 m/s and from 4.90% to 44.2%, respectively. The flow condition covered extensive region of bubbly flows including finely dispersed bubbly flow as well as bubbly-to-slug transition flow. The combined data from the double-sensor probe and the hotfilm probe give near complete information on the time averaged local hydrodynamic parameters of two-phase flow. This data can be used for the development of reliable constitutive relations which reflect the true transfer mechanisms in two-phase flow.

Some characteristics of gas-liquid flow in narrow rectangular ducts

Abstract Flow regime, void fraction, slug bubble velocity and pressure loss were measured for rectangular ducts with a narrow gap and a large aspect ratio. The neutron radiography technique was used to visualize the flow and the void fraction was obtained by image processing. The void fraction was well-correlated by the drift flux model with the existing correlation for the distribution parameter, which was about 1.35. Similar results were obtained for the slug bubble velocity, however the distribution parameter was in the range 1.0–1.2. The frictional pressure loss was well-correlated by the Chisholm-Laird correlation. In collaboration with previously obtained data, it was found that the Chisholms parameter C , however, changed from 21 to 0 as the gap decreased.

One-group interfacial area transport of bubbly flows in vertical round tubes

Abstract In relation to the development of the interfacial area transport equation, the sink and source terms in an adiabatic bubbly flow system were modeled based on the mechanisms of bubble–bubble and bubble–turbulent eddy random collisions, respectively. The interfacial area transport mechanism was discussed based on the derived model. One-dimensional interfacial area transport equation with the derived sink and source terms was evaluated by using the area averaged flow parameters of adiabatic air–water bubbly flows measured in 25.4 mm and 50.8 mm diameter tubes. The flow conditions of the data set covered most of the bubbly flow regime, including finely dispersed bubbly flow (inlet superficial gas velocity: 0.0414–3.90 m/s, superficial liquid velocity: 0.262–5.00 m/s, void fraction: 1.27–46.8%). Excellent agreement was obtained between modeled and measured interfacial area concentrations within the average relative deviation of 11.6%. It was recognized that the present model would be promising for the interfacial area transport of the examined bubbly flows.

Two-group interfacial area transport equations at bubbly-to-slug flow transition

Abstract In relation to the development of the interfacial area transport equation, the basic concept of two-group interfacial area transport equations was demonstrated. This study focused on (1) the formulation of the two-group interfacial area transport equations, (2) the classification of bubble interactions between spherical/distorted bubbles and cap/slug bubbles, (3) the categorization of basic mechanisms of bubble coalescence and breakup, (4) the preliminary modeling of sink and source terms in the interfacial area transport equation, (5) the construction of several data sets at bubbly-to-slug flow transition by assuming the shape of a cap bubble, and (6) the validation of the two-group interfacial area transport equations by means of the data sets at the bubbly-to-slug flow transition. Excellent agreement was obtained between predicted and measured interfacial area concentrations within the average relative deviation of ±3.61% for seven data sets. It was expected that this preliminary work would serve to show the capability of the two-group interfacial area transport equations as well as to understand the basic behavior of the interfacial area transport at the transition from bubbly to slug flow.

Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow

Double sensor probe and hotfilm anemometry methods were developed for measuring local flow characteristics in bubbly flow. The formulation for the interfacial area concentration measurement was obtained by improving the formulation derived by Kataoka and Ishii. The assumptions used in the derivation of the equation were verified experimentally. The interfacial area concentration measured by the double sensor probe agreed well with one by the photographic method. The filter to validate the hotfilm anemometry for measuring the liquid velocity and turbulent intensity in bubbly flow was developed based on removing the signal due to the passing bubbles. The local void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter, liquid velocity, and turbulent intensity of vertical upward air–water flow in a round tube with an inner diameter of 50.8 mm were measured by using these methods. A total of 54 data sets were acquired consisting of three superficial gas flow rates, 0.015–0.076 m s−1, and three superficial liquid flow rates, 0.600, 1.00, and 1.30 m s−1. The measurements were performed at the three locations: L/D=2, 32, and 62. This data is expected to be used for the development of reliable constitutive relations which reflect the true transfer mechanisms in two-phase flow.

Development of one-group interfacial area transport equation in bubbly flow systems

Abstract To finalize one-dimensional one-group interfacial area transport equation in bubbly flow systems, this study has conducted the developments of (I) refined sink and source terms of the interfacial area concentration based on mechanisms of bubble–bubble and bubble–turbulent eddy random collisions, (II) the correlations of two adjustable variables in sink and source terms, and (III) the correlation of the initial interfacial area concentration. The finalized one-dimensional one-group interfacial area transport equation has been validated by 55 data sets taken in extensive adiabatic air–water bubbly flow conditions in four different vertical pipes (pipe diameter: 25.4–50.8 mm). The flow conditions of the data sets cover most of the bubbly flow regime, including finely dispersed bubbly flow and partly bubbly-to-slug transition flow (superficial gas velocity: 0.0144–4.88 m/s, superficial liquid velocity: 0.262–5.00 m/s, void fraction: 0.0124–0.443, interfacial area concentration: 22.1–1085 m −1 ). Excellent agreement is obtained between predicted and measured interfacial area concentrations with an average relative deviation of ±11.5%. Detailed discussions have been made on (i) the sensitivity analysis to the adjustable variables in the sink and source terms, (ii) the predominant term, (iii) the sensitivity analysis to the initial bubble size, and (iv) the comparison with TRAC-P code.

Distribution parameter and drift velocity of drift-flux model in bubbly flow

Abstract In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for bubbly flow regime. The constitutive equation that specifies the distribution parameter in the bubbly flow has been derived by taking into account the effect of the bubble size on the phase distribution, since the bubble size would govern the distribution of the void fraction. A comparison of the newly developed model with various fully developed bubbly flow data over a wide range of flow parameters shows a satisfactory agreement. The constitutive equation for the drift velocity developed by Ishii has been reevaluated by the drift velocity calculated by local flow parameters such as void fraction, gas velocity and liquid velocity measured under steady fully developed bubbly flow conditions. It has been confirmed that the newly developed model of the distribution parameter and the drift velocity correlation developed by Ishii can also be applicable to developing bubbly flows.