Kaichiro Mishima

Two-fluid model and hydrodynamic constitutive relations

Abstract Two-fluid formulation for two-phase flow analyses is presented. A fully three-dimensional model is obtained from the time averaging, whereas the one-dimensional model is developed from the area averaging. The constitutive equations for the interfacial terms are the weakest link in a two-fluid model because of considerable difficulties in terms of experimentation and modeling. However, these are of supreme importance in determining phase interactions. In view of this, the interfacial transfer terms have been studied in great detail both for the three- and one-dimensional models. New interfacial area, drag, virtual mass, droplet size and entrainment correlations are presented. In the one-dimensional model, a number of serious shortcomings of the conventional model have been pointed out and new formulations to eliminate them are presented. These shortcomings mainly arose due to the improper consideration of phase distributions in the transverse direction.

Droplet entrainment correlation in annular two-phase flow

Abstract The droplet entrainment from a liquid film by gas flow is important to mass, momentum, and energy transfer in annular two-phase flow. The amount of entrainment can significantly affect occurrences of the dryout and post-dryout heat flux as well as the rewetting phenomena of a hot dry surface. In view of these, a correlation for the amount of entrained liquid in annular flow has been developed from a simple model and experimental data. There are basically two different regions of entrainment, namely, the entrance and quasi-equilibrium regions. The correlation for the equilibrium region is expressed in terms of the dimensionless gas flux, diameter, and total liquid Reynolds number. The entrance effect is taken into account by an exponential relaxation function. It has been shown that this new model can satisfactorily correlate wide ranges of experimental data for water. Furthermore, the necessary distance for the development of entrainment is identified. These correlations, therefore, can supply accurate information on entrainment which have not been available previously.

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.

Theoretical Prediction of Onset of Horizontal Slug Flow

A criterion for the onset of a slug flow in a horizontal duct is derived theoretically. A potential flow analysis is carried out by considering waves of finite amplitude. The stability criterion is obtained by introducing the wave deformation limit and the “most dangerous wave” concept in the stability analysis. The present theoretical criterion for slug formation shows very good agreement with a large number of experimental data and with some empirical correlations.

Generation and Size Distribution of Droplet in Annular Two-Phase Flow

The mean droplet size and size distribution are important for detailed mechanistic modeling of annular two-phase flow. A large number of experimental data indicate that the standard Weber number criterion based on the relative velocity between droplets and gas flow predicts far too large droplet sizes. Therefore, it was postulated that the majority of the droplets were generated at the time of entrainment and the size distribution was the direct reflection of the droplet entrainment mechanism based on roll-wave shearing off. A detailed model of the droplet size in annular flow was then developed based on the above assumption. The correlations for the volume mean diameter as well as the size distribution were obtained in collaboration with a large number of experimental data. A comparison with experimental data indicated that indeed the postulated mechanism has been the dominant factor in determining the drop size. Furthermore, a large number of data can be successfully correlated by the present model. These correlations can supply accurate information on droplet size in annular flow which has not been available previously.

Flow regime transition criteria for upward two-phase flow in vertical narrow rectangular channels

In relation to the cooling system of high performance microelectronics, a high power research reactor with plate type fuels and plasma facing components of a fusion reactor, study of two-phase flow in a narrow rectangular channel has been paid considerable attention, recently. For the two-fluid model, direct geometrical parameters such as the void fraction should be used in flow-regime criteria. From this point of view, flow-regime transition criteria for vertical upward flows in narrow rectangular channels have been developed considering the mechanisms of flow-regime transitions. The basic concept of the present modeling followed the Mishima and Ishii model for vertical upward two-phase flows in round tubes. Newly developed criteria have been compared with the existing experimental data for air‐water flows in narrow rectangular channels with the gaps of 0.3‐17 mm. The present criteria showed satisfactory agreements with those data. Further comparisons with data for steam‐water in a rectangular channel at relatively high system pressures have been made. The results confirmed that the present flow-regime transition criteria could be applied over wide ranges of parameters as well as to boiling flow.

First Injection of Spallation Neutrons Generated by High-Energy Protons into the Kyoto University Critical Assembly

At the Kyoto University Research Reactor Institute, the world’s first injection of spallation neutrons generated by high-energy proton beams into a reactor core was successfully accomplished on March 4, 2009. By combining the fixed field alternating gradient (FFAG) accelerator with the A-core (Fig. 1) of the Kyoto University Critical Assembly (KUCA), a series of accelerator-driven system (ADS) experiments were carried out by supplying spallation neutrons to a subcritical core through the injection of 100MeV protons onto a tungsten target of 80mm diameter and 10mm thickness. In these experiments, the proton beams from the FFAG accelerator were generated at 30Hz repetition rate and 10 pA current. The neutron intensity generated at the tungsten target was around 1 10 s . The objective of these experiments was to conduct a feasibility study on ADS from the viewpoint of reactor physics, in order to develop an innovative nuclear reactor for a high-performance transmutation system with a capability of power generation or for a new neutron source for scientific research. The A-core employed in the ADS experiments was essentially a thermal neutron system composed of a highly enriched uranium fuel and a polyethylene moderator/reflector. In the fuel region, a unit cell is composed of a 93% enriched uranium fuel plate 1/1600 thick and polyethylene plates 1/400 and 1/800 thick. In these ADS experiments, three types of fuel rods designated as the normal, partial, and special fuels were employed. From the reason of the safety regulation for KUCA, the tungsten target was located not at the center of the core but outside the critical assembly, and the outside location was similar to that in previous experiments using 14MeV neutrons. As in previous ADS experiments with 14MeV neutrons, the introduction of a neutron guide and a beam duct is requisite to lead the high-energy neutrons generated from the tungsten target to the center of the core as much as possible. The detailed composition of the normal, partial, and special fuel rods, the polyethylene rod, the neutron guide, and the beam duct was described in Refs. 3–5). To obtain the information on the detector position dependence of the prompt neutron decay measurement, neutron detectors were set at three positions shown in Fig. 1: near the tungsten target (position (17, D); 1=200 BF3 detector) and around the core (positions (18, M) and (17, R); 100 He detectors). The prompt and delayed neutron behaviors (Fig. 2), which were an exponential decay behavior and a slowly decreasing behavior, respectively, were experimentally confirmed by observing the time evolution of neutron density in ADS. These behaviors clearly indicated that neutron multiplication was caused by an external source: sustainable nuclear chain reactions were induced in the subcritical core by spallation neutrons through the interaction of the tungsten target and the proton beams from the FFAG accelerator. In these kinetic experiments, subcriticality was deduced from the prompt neutron decay constant by the extrapolated area ratio method. The difference between the measured results of 0.74% k=k and 0.61% k=k at the positions (17, R) and (18, M) in Fig. 1, respectively, from the experimental evaluation of 0.77% k=k, which was deduced from the combination of both the control rod worth by the rod drop method and its calibration curve by the positive period method, was within 20%. Note that the subcritical state was attained by the full insertion of C1, C2, and C3 control rods into the core. The thermal neutron flux distribution was estimated through the horizontal measurement of the In(n, )In Atomic Energy Society of Japan Corresponding author, E-mail: pyeon@rri.kyoto-u.ac.jp Present address: SR Center, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu-shi, Shiga 527-8577, Japan Present address: Institute of Nuclear Safety System, Incorporated, 64, Sata, Mihama-cho, Mikata-gun, Fukui 919-1205, Japan Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 46, No. 12, p. 1091–1093 (2009)

The effect of flow direction and magnitude on CHF for low pressure water in thin rectangular channels

Abstract Critical heat flux (CHF) at low flow condition can become important in an MTR-type research reactor under a number of accident conditions. Regardless of the initial stages of these accidents, a condition which is basically the decay heat removal by natural convention boiling can develop. Under such conditions, burnout may occur even at a very low heat flux. In view of this, the CHF at low-flow-rate and low-pressure conditions has been studied for water flowing in thin rectangular channels. Experiments were carried out with two types of rectangular test sections, namely, the one heated from one wide side and the other heated from two opposite sides. In order to observe the effects of gravity, CHF was measured both in upflow and downflow. The CHF at complete bottom blockage was also studied. The results indicate that burnout can occur at a much lower heat flux than pool-boiling CHF or than predicted by the conventional correlations. There was observed a minimum CHF at complete bottom blockage and at very low downflow. The low CHF at very low downflow appears to be due to the stagnation of the bubble in the heated section. This fact indicates that special care should be taken in analyzing the boiling phenomenon which occurs when the coolant flow is very low in a low pressure system.

Critical heat flux prediction for saturated flow boiling of water in vertical tubes

Abstract This study presents a new analytical model for the prediction of the critical heat flux (CHF) in water saturated flow boiling in round vertical and uniformly heated pipes. The CHF is assumed to occur in annular flow when the liquid film vanishes at the exit section of the heated channel. Channel pressure drop is calculated using the Friedel correlation. Liquid film flow rate is obtained by a balance of liquid entrainment and droplet deposition. Two mechanisms are considered in the calculation of the entrainment: liquid–vapour interfacial waves and boiling in the liquid film. The model CHF prediction values are compared with a data set of 5159 selected experimental points for water, showing a good agreement both in precision and in accuracy for liquid quality in the range 0.2–1.0.

Effect of channel geometry on critical heat flux for low pressure water

Abstract The main difficulty in interpreting critical heat flux (CHF) at low velocity and pressure conditions arises from the fact that the burnout phenomenon under such conditions is vulnerable to the effect of buoyancy and flow instabilities. This study is intended to provide some systematic understanding on CHF at low velocity and pressure conditions. Data obtained in the previous experiments for water in an annulus, rectangular ducts and a round tube are briefly reviewed and augmented in collaboration with existing data and correlations to extract more generic information. The effect of channel geometry on CHF is then discussed. The effect of channel geometry turned out to be remarkable at intermediate mass velocities. The difference in CHF at these mass velocities between a round tube and the other channel geometries was attributed mainly to the existence of an unheated wall which cause a non-uniform distribution of liquid film.