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Journal Articles

Development of crystallizer for advanced aqueous reprocessing process

Washiya, Tadahiro; Kikuchi, Toshiaki*; Shibata, Atsuhiro; Chikazawa, Takahiro*; Homma, Shunji*

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 7 Pages, 2006/07

The crystallization is an advanced and remarkable technology in the future reprocessing process, which requires safety and cost advantages. Japan Atomic Energy Agency (JAEA), Mitsubishi Materials Corporation and Saitama University have been developing an annular-type continuous crystallizer. This paper mainly discussed about this crystallizer design and its development. JAEA has considered following two application processes of the crystallization technology. One is a uranium crystallization process, which applied before the solvent extraction process to recover excessive uranium from dissolver solution and reducing the throughput in the later extraction process. In this process, highly concentrated dissolver solution (about 500g-HM/L) is fed to this crystallizer, and only uranium is crystallized. Another is a plutonium co-crystallization process, which consists of two crystallization steps and excludes extraction process, and thus it's expected to reduce the waste generation and to improve operation safety. In this process, plutonium is co-crystallized with uranium in the first step and separated from residual solution, then the crystals are dissolved into nitric acid solution and excessive uranium is crystallized in the second step. This residual solution is recycled to fuel dissolution process, thus it contributes to reduce nitric acid quantity consumption. For both crystallization processes, same crystallizer design can be applied; we have developed a continuous crystallization system to establish high process throughput and optimizing of the crystallization processes. In the design study of the crystallizer, an annular-type was selected as the most promising design. The fundamental data was obtained by scale-down test device with uranium conditions, and an engineering scale crystallizer was fabricated to confirm the system performance in engineering scale.

Journal Articles

Design study of mechanical disassembly system for FBR fuel reprocessing

Toya, Yuichi; Washiya, Tadahiro; Koizumi, Kenji; Morita, Shinichi

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 6 Pages, 2006/07

Japan Atomic Energy Agency (JAEA) has been leading feasibility study on commercialized fast reactor cycle systems in Japan. In this study, we have proposed a new disassembly technology by mechanical disassembly system that consists of a mechanical cutting step and a wrapper tube pulling step. In the mechanical tool system, high durability mechanical cutter cuts the wrapper tube (Slit-Cut (S/C) operation in circle direction), and then the wrapper tube is pulled out and removed from the fuel assembly. Then the fuel pins are cut (Crop-Cut (C/C) operation at entrance nozzle side) and the entrance nozzle is removed. The fuel pins are transported to the shearing machine in next process. The Fundamental tests were carried out with simulated FBR fuel pins and wrapper tube, and cutting performance and wrapper tube pulling performance has been confirmed by engineering scale. As the results, we established the disassembly procedure and the fundamental design of mechanical disassembly system.

Journal Articles

Verification of the plant dynamics analytical code CERES using the results of the plant trip test of the prototype fast breeder reactor MONJU

Nishi, Yoshihisa*; Ueda, Nobuyuki*; Kinoshita, Izumi*; Miyakawa, Akira; Kato, Mitsuya*

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 10 Pages, 2006/07

CERES is plant system analysis code for LMRs developed by the Central Research Institute of Electric Power Industry (CRIEPI). CERES has a function of calculating multidimensional flow in the plena of a coolant in addition to that in one-dimensional plant network calculation. To verify the CERES code, analyses were performed by using the result of the plant trip test from the partial power operation of the prototype FBR "MONJU" that had been executed in December, 1995. The verification work was performed as a joint research of CRIEPI and JAEA. (1)Analysis concerning the primary/secondary/auxiliary cooling system (the plenum in the reactor vessel (R/V) is modeled in R-Z 2-dimension). (2)Analysis concerning the flow pattern in the plenum of R/V (the plenum is modeled in 3-dimension). (3)Analysis concerning the flow pattern inside the IHX plenum (the plenum in the IHX is modeled in 3-dimension). Analytical results by the CERES code showed good agreement with the results of the test of the "MONJU". Fundamental abilities of the CERES as a plant dynamics calculation code had been verified through these analyses. Additionally, some characteristic flows in plena of "MONJU" became clear by these analyses.

Journal Articles

Applicability examination and evaluation of reactor dismantlement technology in the Fugen; Examination of double tubes cutting by abrasive water jet

Nakamura, Yasuyuki; Kikuchi, Koichi; Morishita, Yoshitsugu; Usui, Tatsuo*; Ogane, Daisuke*

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 9 Pages, 2006/07

It is necessary to clarify the dismantlement method of 224 double tubes arranging both pressure and calandria tubes concentrically in the reactor as a peculiar problem of Fugen, in the case of phased dismantlement of the reactor. The machine type cutting is desirable, considering the influence on the atmospheres because the double tubes consist of the zirconium alloy and zircalloy material radio activated highly. Besides, Cutting method has long standoff to cut the double tubes at a time for to be short the term of dismantlement. is desirable. Therefore, it was examined to confirm the applicability to the double tubes cutting by abrasive water jet (hereinafter referred to as AWJ) as the machine type cutting method that can take the standoff comparatively longer. As a result, We confirmed for possibility of cutting the double tubes at a time from inside and outside tube, and cutting thick slab by abrasive water jet. Besides, We confirmed for relationship of abrasive supply and cutting velocity, properties of secondly waste.

Journal Articles

Development of a slim manipulator type fuel handling machine for a commercialized fast reactor

Chikazawa, Yoshitaka; Usui, Shinichi; Konomura, Mamoru; Sadahiro, Daisuke*; Tozawa, Katsuhiro*; Hori, Toru*; Toda, Mikio*; Kotake, Shoji*

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 7 Pages, 2006/07

A seismic analysis has been performed showing that the seismic interaction between the UIS and the FHM can be avoided adopting gapless bearings at the FHM arm joint. An angular contact ball bearing is suitable for the new FHM since it can eliminate gaps by preload pressure. A major problem of the FHM bearings is lubrication since the contact pressure between steel rings and ball increases because of ball bearing. Additionally, FHM operating temperature is about 200 deg-C and normal grease is not applicable under argon gas with sodium vapor. A endurance test with 1/10 scale bearings in the air has been performed to show applicability of angular contact ball bearings to the FHM arm joint. The results with 20,000 cycle showed that bearings with combination of MoS$$_{2}$$ coating steel rings and ceramics balls can be tolerable as the FHM operating condition. A real scale bearing test in argon gas with sodium vapor has also been demonstrated to reveal bearing size and sodium vapor effects.

Journal Articles

One-loop operation of primary heat transport system in MONJU during heat transport system modifications

Goto, Takehiro; Tsushima, Hiroyuki; Sakurai, Naoto; Jo, Takahisa

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 13 Pages, 2006/07

MONJU is a prototype fast breeder reactor. Modification work commenced in March 2005. Since June 2004, MONJU has changed one-loop operation of the primary heat transport system with all of the secondary heat transport systems drained of sodium. Purposes of this change are to shorten the modification period and to reduce the cost incurred for circuit trace heating electrical consumption. Before changing condition, the following issues were investigated to show that this mode of operation was possible. The heat loss from the reactor vessel and the single primary loop must exceed the reactor core decay heat by an acceptable margin but the capacity of the preheater to keep the sodium within the primary vessel at about 200$$^{circ}$$C must be maintained. With regard to heat loss and core decay heat, the estimated heat loss in the primary system was in the range of 90-170kW in one-loop operation, and the calculated reactor decay heat was 21.2kW. Although the heat input of the primary pump was considered, it was clear that circuit heat loss greatly exceeded the core decay heat. As for the preheater, effective capacity was less than the heat loss. Therefore, the temperature of the reactor vessel room was raised to reduce the heat loss. One-loop operation of the primary heat transport system was able to be executed by means of these measures. The cost of electrical consumption in the power plant has been reduced by one-loop operation of the primary heat transport system. The modification period was shortened.

Journal Articles

Methodology of local instantaneous interfacial velocity measurement in multi-dimensional two-phase flow

Shen, X.*; Mishima, Kaichiro*; Nakamura, Hideo

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 8 Pages, 2006/07

Since the transport of momentum, heat and mass tightly links with local interfacial characteristics it is essential to know the local interfacial parameters in various two-phase flows. The interfacial velocity plays a determinant role in determining the other interfacial parameters such as the interfacial area concentration and so on. It is accordingly one of the most important parameters in analyzing two-phase flow. However, it also is one of the most difficult parameters to measure up to now. Based on the application of the interfacial measurement theorem to several four-sensor probes, the present study established a theoretical foundation of the measurement method for the local instantaneous interfacial velocity in multi-dimensional two-phase flow by using three independent four-sensor probes. Since we can find three independent four-sensor probes in a multi-sensor probe, which has more than four sensors, by sharing the sensors of the first four-sensor probe with the sensors of the others, a five- or six-sensor probe including at least one set of three four-sensor combinations was recommended to measure the local instantaneous interfacial velocity, interfacial area concentration and so on in multi-dimensional two-phase flow. A six-sensor probe was developed and employed in the practical measurement in an air-water multi-dimensional two-phase flow in a pool. The six-sensor probe measurements were checked against the gas flow rate measurement using a rotameter and a manometer. The comparing results were very satisfactory.

Journal Articles

Two-dimensional optical measurement of waves on liquid lithium jet simulating IFMIF target flow

Ito, Kazuhiro*; Ito, Taro*; Kukita, Yutaka*; Koterazawa, Hiroyuki*; Kondo, Hiroo*; Yamaoka, Nobuo*; Horiike, Hiroshi*; Ida, Mizuho; Nakamura, Hideo; Nakamura, Hiroo; et al.

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 6 Pages, 2006/07

Waves on a liquid-lithium jet flow, simulating a proposed high-energy beam target design, have been measured using an optical technique based on specular reflection of a single laser beam on the jet surface. The streamwise and spanwise fluctuations of the local free-surface slope were least-square fitted with a sinusoidal curve to makeup the signals lost due to the constriction in the optical arrangement. The waveform was estimated with an assumption that wave phase speed can be calculated using the dispersion relation for linear capillary gravity waves. The direction of propagation on the jet surface was also evaluated so that the wave amplitudes, calculated by integral of slope angle signal, agree consistently in streamwise and spanwise direction. These measurements and analyses show that the waves at the measurement location for a jet velocity of 1.2 m/s can best be represented by oblique waves with an inclination of 0.32 rad, a wavelength of 4.2 mm and a wave amplitude of about 0.06 mm.

Journal Articles

Development program of IS process pilot test plant for hydrogen production with high-temperature gas-cooled reactor

Iwatsuki, Jin; Terada, Atsuhiko; Noguchi, Hiroki; Imai, Yoshiyuki; Ijichi, Masanori; Kanagawa, Akihiro; Ota, Hiroyuki; Kubo, Shinji; Onuki, Kaoru; Hino, Ryutaro

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 8 Pages, 2006/07

JAEA has been conducting the HTTR project from the view to establishing technology base on HTGR and also on the IS process. Based on the test results and know-how obtained through the bench-scale tests, a pilot test plant that can produce hydrogen of about 30 Nm$$^{3}$$/hr is being designed. The test plant will be fabricated with industrial materials such as glass coated steel, SiC ceramics etc, and operated under high pressure condition up to 2 MPa. The test plant will consist of a IS process plant and a helium gas (He) circulation facility (He loop). In parallel to the design study, key components of the IS process such as the sulfuric acid (H$$_{2}$$SO$$_{4}$$) and the sulfur trioxide (SO$$_{3}$$) decomposers working under-high temperature corrosive environments have been designed and test-fabricated to confirm their fabricability. Also, other R&D's are under way such as corrosion, processing of HIx solutions. This paper describes present status of these activities.

Journal Articles

Study on transient void behavior during reactivity initiated accidents under low pressure condition; Development and application of measurement technique for void fraction in bundle geometry

Satou, Akira; Maruyama, Yu; Asaka, Hideaki; Nakamura, Hideo

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 8 Pages, 2006/07

Series of out-of-pile experiments to obtain the knowledge on the transient void behavior during reactivity initiated accidents are in progress at JAEA. In the present series of experiments, the transient void behavior in a test section of 2$$times$$2 bundle geometry under atmospheric pressure condition was measured using an impedance technique. The measuring areas and the arrangement of electrodes for the impedance technique were defined on the basis of numerical analyses and scaled model experiments. The comparison was made between the impedance and differential pressure techniques for steady boiling experiments to estimate the accuracy of the impedance technique. The impedance technique showed a good agreement with the void fraction estimated from the differential pressure. The transient void behavior in the bundle geometry was measured using the impedance technique. It was clarified that the transient void behavior depends on both the subcooling of inlet water and the heat generation rate of simulated fuel rod. Local void fraction was influenced by the ratio of flow area to heat transfer area of the simulated fuel rod.

Journal Articles

Experimental investigation of evaporation behavior of polonium and rare-earth elements in lead-bismuth eutectic pool

Ohno, Shuji; Miyahara, Shinya; Kurata, Yuji; Katsura, Ryoei*; Yoshida, Shigeru*

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 7 Pages, 2006/07

Equilibrium evaporation behavior was experimentally investigated for polonium ($$^{210}$$Po) in liquid lead-bismuth eutectic (LBE) and for rare-earth elements gadolinium (Gd) and europium (Eu) in LBE to understand and clarify the transfer behavior of toxic impurities from LBE coolant to a gas phase. The experiments utilized the "transpiration method" in which saturated vapor in an isothermal evaporation pot was transported by inert carrier gas and collected outside of the pot. While the previous paper ICONE12-49111 has already reported the evaporation behavior of LBE and of tellurium in LBE, this paper summarizes the outlines and the results of experiments for important impurity materials $$^{210}$$Po and rare-earth elements which are accumulated in liquid LBE as activation products and spallation products. In the experiments for rare-earth elements, non-radioactive isotope was used. The LBE pool is about 330-670 g in weight and has a surface area of 4cm$$times$$14cm. $$^{210}$$Po experiments were carried out with a smaller test apparatus and radioactive $$^{210}$$Po produced through neutron irradiation of LBE in the Japan Materials Testing Reactor (JMTR). We obtained fundamental and instructive evaporation data such as vapor concentration, partial vapor pressure of $$^{210}$$Po in the gas phase, and gas-liquid equilibrium partition coefficients of the impurities in LBE under the temperature condition between 450 and 750$$^{circ}$$C. The $$^{210}$$Po test revealed that Po had characteristics to be retained in LBE but was still more volatile than LBE solvent. A part of Eu tests implied high volatility of rare-earth elements comparable to that of Po. This tendency is possibly related to the local enrichment of the solute near the pool surface and needs to be investigated more. These results are useful and indispensable for the evaluation of radioactive materials transfer to the gas phase in LBE-cooled nuclear systems.

Journal Articles

Reaction, transport and settling behavior of lead-bismuth eutectic in flowing liquid sodium

Miyahara, Shinya; Ohno, Shuji; Yamamoto, Nobuhiro; Saito, Junichi; Hirabayashi, Masaru

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 7 Pages, 2006/07

The experimental study has been carried out to investigate reaction, transport and settling behavior of lead-bismuth eutectic (LBE) in flowing liquid sodium. In the test, 168 g of LBE were poured into flowing sodium from the top of a vertical-type sodium loop which contained 23.2 kg of sodium. The initial temperature of LBE and sodium was 673 K. The flow rate and the maximum velocity of sodium in the loop were controlled and measured at 20 dm$$^{3}$$/min and 1 m/sec, respectively, using an electro-magnetic pump and an electro-magnetic flow meter. The sodium loop has a settling chamber at the lower part to investigate the concentration decrease behavior of solid particle reaction products in the sodium due to the settling effect. The concentration was measured by sodium sampling from the 11 positions of the loop during the experiment and its post-test chemical analysis. The temperature changes at the various parts of the loop were also measured during the experiment by thermo-couples attached on the outer surface of the loop. Ultrasonic detectors were attached on the outer surface of the loop below the position of a LBE pour nozzle to demonstrate the utility as a leak detector.

Journal Articles

Development of the ISI device for fast breeder reactor MONJU reactor vessel

Tagawa, Akihiro; Ueda, Masashi; Yamashita, Takuya

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 8 Pages, 2006/07

In-service inspection (ISI) is carried out to confirm the integrity of the main components of the Fast Breeder Reactor (FBR) "MONJU". The weld-joints are examined by using an inspection device which has a glass fiber scope for visual examination and a horizontally polarized shear (SH) wave electromagnetic acoustic transducer (EMAT) for volumetric testing. The ambient temperature during the inspection is 200 $$^{circ}$$C and the irradiation field is 10 Sv/hr. A new inspection device has been developed in order to improve the visual test performance, volumetric test performance and controllability of the inspection device reflecting the experience of the original test. In this paper, detail of the new inspection device and the test results of sensors such as the CCD camera, EMAT and bead sensor are reported. The paper also reports on the CCD camera cooling system and other components.

Journal Articles

Numerical analysis on air ingress behavior in GTHTR300H

Takeda, Tetsuaki; Yan, X.; Kunitomi, Kazuhiko

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 5 Pages, 2006/07

Japan Atomic Energy Agency (JAEA) has been developing the analytical code for the safety characteristics of the HTGR and carrying out design study of the gas turbine high temperature reactor of 300 MWe nominal-capacity for hydrogen production, the GTHTR300H (Gas Turbine High Temperature Reactor 300 for Hydrogen). The objective of this study is to clarify safety characteristics of the GTHTR300H for the pipe rupture accident. A numerical analysis of heat and mass transfer fluid flow with multi-component gas mixture has been performed to obtain the variation of the density of the gas mixture, and the onset time of natural circulation of air. From the results obtained in this analysis, it was found that the duration time of the air ingress by molecular diffusion would increase due to the existence of the recuperator in the GTHTR300H system.

Journal Articles

Two-dimensional optical measurement of waves on liquid lithium jet simulating IFMIF target flow

Ito, Kazuhiro*; Ito, Taro*; Kukita, Yutaka*; Koterazawa, Hiroyuki*; Kondo, Hiroo*; Yamaoka, Nobuo*; Horiike, Hiroshi*; Ida, Mizuho; Nakamura, Hideo; Nakamura, Hiroo; et al.

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 6 Pages, 2006/07

no abstracts in English

Journal Articles

Analytical study on micro-indentation method to integrity evaluation for graphite components in HTGR

Sumita, Junya; Hanawa, Satoshi; Shibata, Taiju; Tada, Tatsuya; Iyoku, Tatsuo; Sawa, Kazuhiro

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 8 Pages, 2006/07

An analytical study on micro-indentation method to integrity evaluation for graphite components was carried out. The indentation method is used as simplicity test to measure mechanical properties of materials. This method is thought to be applicable to evaluate the residual stress from the relationship between indentation load and indentation depth. In this study, in order to confirm the applicability of the micro-indentation method for lifetime evaluation of the graphite component, indentation load-depth behavior under stress/strain condition was evaluated taking account of the specified minimum ultimate strength of IG-110 graphite. Moreover, analytical investigations of indentation load-depth behavior for oxidized graphite and oxidized graphite with residual strain were also carried out. As a result, it can be said that the indentation method is potentially applicable to evaluate the integrity of graphite components.

Journal Articles

Development of water radiolysis code for the JMTR IASCC test loop

Hanawa, Satoshi; Sato, Tomonori; Mori, Yuichiro; Ogiyanagi, Jin; Kaji, Yoshiyuki; Uchida, Shunsuke*

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 9 Pages, 2006/07

no abstracts in English

Journal Articles

Comprehensive cost estimation method for decommissioning

Kudo, Kenji; Kawatsuma, Shinji; Rindo, Hiroshi; Watabe, Kozo; Tomii, Hiroyuki; Shiraishi, Kunio; Yagi, Naoto; Fukushima, Tadashi; Zaitsu, Tomohisa

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 8 Pages, 2006/07

Japan Atomic Energy Research Institute (JAERI) played a leading role in basic research in the field of atomic energy research and development, while Japan Nuclear Cycle Development Institute (JNC) did a major role in FBR cycle development and high level waste disposal. Following the Government's decision in December 2001, JAERI and JNC was merged as of October 1st, 2005. The new organization, Japan Atomic Energy Agency (JAEA), is an institute for comprehensive R&D for atomic energy, and is the largest research and development institute among Governmental R&D organizations. Its missions are basic research on atomic energy, R&D for nuclear fuel cycle, decommissioning of own facilities and disposal of waste, contribution to safety and non-proliferation, etc. The JAEA owns a number of nuclear facilities: research reactors such as JRR-2 and Joyo, prototype reactors such as ATR "Fugen" and FBR "Monju", fuel cycle plants such as Uranium Enrichment Demonstration Plant at Ningyo-Toge, MOX fuel plants at Tokai, Reprocessing Plant at Tokai, and Hot Laboratories such as JRTF and FMF. As a part of preparation of the mergence, JNC and JAERI have jointly developed a comprehensive cost estimation method for decommissioning, based on decommissioning and refurbishing experiences of JAERI and JNC. This method involves more estimation parameters from typical decommissioning activities than before, so as to make it more reliable. JAERI and JNC have estimated the total cost for decommissioning by using this method, and concluded that the cost would be 600 billion yen (approx. 5 billion USD).

Journal Articles

In-pile SCC growth behavior of type 304 stainless steel in high temperature water at JMTR

Kaji, Yoshiyuki; Ugachi, Hirokazu; Tsukada, Takashi; Matsui, Yoshinori; Omi, Masao; Nagata, Nobuaki*; Dozaki, Koji*; Takiguchi, Hideki*

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 7 Pages, 2006/07

Irradiation assisted stress corrosion cracking (IASCC) is one of the critical concerns when stainless steel components have been in service in light water reactors (LWRs) for a long period. In general, IASCC can be reproduced on the materials irradiated over a certain threshold fluence level of fast neutron by the post-irradiation examinations (PIEs). In the research field of IASCC, mainly PIEs for irradiated materials have been carried out, because there are many difficulties on SCC tests under neutron irradiation. Hence we have embarked on a development of the test technique to obtain information concerning effects of applied stress level, water chemistry, irradiation conditions, etc. In-pile IASCC growth tests have been successfully carried out using pre-irradiated type 304 stainless steel at JMTR. In the paper, results of the in-pile SCC growth tests will be discussed comparing with the result obtained by PIEs from a viewpoint of the synergistic effects on IASCC.

Journal Articles

Study on applicability of numerical simulation to evaluation of gas entrainment from free surface

Ito, Kei; Sakai, Takaaki; Ohshima, Hiroyuki

Proceedings of 14th International Conference on Nuclear Engineering (ICONE-14) (CD-ROM), 8 Pages, 2006/07

An onset condition of gas entrainment (GE) due to free surface vortex has been studied to establish a high coolant velocity fast breeder reactor. In this research, to evaluate the applicability of the numerical simulation to the GE phenomena, numerical simulations were conducted on the basic experimental apparatus of the GE. As a result, traveling behavior of free surface dent, frequency of vortex generation and vortex growing behavior were accurately simulated, although the GE itself was not completely reproduced due to a lack of enough grid partition. In addition, several parameters, such as a free surface level and suction velocity, were numerically examined to evaluate their influence on the GE. The tendencies that lower free surface level or larger suction velocity enhance occurrence of the GE could be simulated. These simulation results implied that the numerical simulation method is enough applicable to the evaluation of the GE.

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