The progress of the two-phase flow research has been divided into four stages in this series of the report. These periods are (I) 1948-1959, (II) 1960-1970, (III) 1971-1979, and (IV) 1980-1988. In this report, the development of analytical methods for flow instabilities in two-phase flow in periods (II),(III), and (IV) have been described. The development of the theoretical analysis in periods (II) and (III) are discussed based mainly on flow satability maps obtained by these analyses, and also the transition of the analytical methods are explained in relation to the rapid development of digital computer and the thermo-hydraulic simulation codes. In period (IV), the improvement of the modeling of fundamental equations and constitution equations and numerical calculation method as to the simulation codes is also described.

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The variety of multi-phase flow analysis capabilities in STAR-CD are explained here. These capabilities are classified into Lagrangian multi-phase, free surface(VOF) including cavitation models and Eulerian two-phase. Also some applications in engineering fields are introduced.

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A computational fluid dynamics analysis of the On-X^® bi-leaflet heart valve has been conducted. Unsteady blood flow in the hinge area was investigated using STORM/CFD2000. The Navier-Stokes equations were solved using a finite volume grid, and a PISO (pressure-implicit with splitting of operators) algorithm was employed to compute the pressure-velocity coupling. An alternating direction implicit(ADI) scheme was used to solve the set of linear algebraic equations. A moving grid methodology with a prescribed periodic motion was employed to simulate the opening and closing of the valve leaflet. Particular attention was paid to simulating the local flow inside the hinge socket of the On-X^® valve where experimental measurements are very difficult or impossible. The results show that local flow patterns and pressure distributions in the hinge area of the valve induce full wash-out during the opening and closing phases.

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A model for simulating breakup and coalescence of bubbles and liquid particles using DEM is introduced in multi-phase flow simulation. In addition, an approximation method for simulating numerous number of particles effectively is described. Numerical examples are next shown obtained by using a commercial flow simulation software “RFLOW”, in which the present model has been implemented.

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Introduction of multiphase capabilities of FLUENT, a general purpose heat transfer and fluid flow analysis software, is presented. FLUENT has several multiphase models, descrete phase model(DPM), mixture model, volume of fluid model (VOF), Eulerian multiphase models, and cavitation model. Each model is briefly described including applicability to the models.

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Numerical analysis and air-water test were performed in order to evaluate gas-liquid separation characteristics in a BWR steam separator. Centrifugal force and flow quality were simulated in the test. Simulation of plant operation conditions was not sufficient at low volumetric flux due to large effect of gravity force. Pressure loss coefficient agreed with the plant conditions within 10%. Carryover agreed well with plant conditions for a current separator but was under-estimated for a separator with small vane angle. Calculated gas-liquid behavior agreed well with plant condition data in the 1^st stage but calculated results over-estimated carryover. Combination of calculated results in the 1^st stage and simulation test results in the 2^nd and 3^rd stages gave good prediction for carryover.

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Numerical analysis and air-water test were performed in order to decrease pressure loss in a BWR steam separator. A current swirler and two low pressure-loss swirlers with a small swirl angle and with a small hub diameter were evaluated. Calculated results showed that the swirler with a small hub diameter had better gas-liquid separation than the swirler with a small swirl angle because of larger circumferential velocity and centrifugal force. It was also confirmed by the air-water simulation test. In case of the combination of the swirler with a small hub diameter and the current upper structure, the target of carryover was satisfied and its pressure loss was about 45% of the current separator. In case of a 3^rd stage high-swirl type, which had the same barrel diameter as the 2^nd stage pick-off ring diameter, carryover was as low as the current separator and pressure loss was about 60% of the current.

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Behavior of rising nitrogen (diamagnetic) bubbles in manganese chloride aqueous solution (paramagnet) is illustrated by an experiment and a numerical simulation. The bubbles obliquely rise toward the central axis under a high gradient magnetic field |grad(B²)|=254 T²/m(B=4.5T at the magnetic center). In this case, the outer region of the vessel has no bubbles above the oblique rising. On higher magnetic field, the rising velocity of the bubbles slows down and it stops under |grad(B²)|=314T²/m (B=5.0T at the magnetic center). Results of the numerical simulation agree with the experiment, and it gives a prediction of behavior of oxygen (paramagnetic) bubbles in the water (diamagnet).

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A ring-type obstacle, which simulated a spacer in Light Water Reactor or a flow obstruction supporting heat transfer tube, was set in an upward air-water two-phase flow within a vertical tube to investigate the effects of the obstacle on liquid film thickness. We measured the axial distributions of time varying liquid film thickness near the obstacle in the range of superficial water velocity of 0.06-1.6m/s and superficial air velocity of 0.5-36m/s and discussed the effects of the flow conditions and the distance from the obstacle on the liquid film thickness. The results are summarized as follows: (1) A reverse flow of liquid film has strong effects on the minimum film thickness near the obstacle. The axial distribution of the minimum film thickness near the spacer is different from that of the mean film thickness when the reverse flow of liquid film appears, however, these distributions are similar to each other when the reverse flow does not appear. (2) When the reverse flow appears, a liquid film may break down at the lower superficial air velocity as the superficial water velocity becomes higher.

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As one of the conveying methods for solid particles, there is a pneumatic conveyance using pipelines. In such a gas-solid two-phase flow in pipelines in the pneumatic conveyance, it is desirable to tranport particles with a fluid velocity as low as possible from the standpoint of saving energy for transportation, and preventing attrition of particles and abrasion of pipelines. However, in such operations, it is apt to stop eventually its movement due to the deposition of particles on the bottom wall of the pipe. As a result of this, it accompanies with a risk that its transportation becomes impossible. For this reason, it is far more important to study a limiting fluid velocity allowing steady state transport of particles, called the minimum transport velocity, than the investigation on its pressure drop. From such viewpoint in this paper an empirical equation to obtain the minimum velocity for coarse particles in fully developed flow region of a horizontal pipe for low pressure conveying type has been derived based on both model equation and actual transport experiment. In this experiment the particles conveyed is polyethylene pellets. The pipe diameters is 50mm and the pipe distance is about 10.0m. The above mentioned equation can arrange the data in this experiment with a considerably good accuracy, and Molerus’ equation agrees well with the present data.

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Accurate prediction of flow parameters in vertical upward gas-magnetic fluid two-phase flow in small diameter tubes is very important for developing a new energy conversion system. In this study, in order to find correlations applicable to such a flow, experiments have been conducted with a new test apparatus having 9 and 5 mm i.d. vertical tubes. To determine the effects of liquid properties, magnetic fluid, glycerin 68.3 wt % water solution (the same viscosity as that of the magnetic fluid) and tap water were used as the test liquid while air as the test gas. Flow regimes were observed with a high-speed video camera, and pressure drop and void fraction were measured with differential pressure transducer and constant current method, respectively. Experimental results of such flow parameters have been compared to study the effects of liquid properties and inside diameter of test tube. Moreover, the experimental results have been compared with the existing models and correlations. Additionally, some peculiar characteristics of air-magnetic fluid two-phase flow have been summarized.

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