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JAEA Reports

Development of computer program for detailed thermal-hydraulic analysis in a fast reactor fuel subassembly (2); Incorporation of turbulence models

Ohshima, Hiroyuki; Ohshima, Hiroyuki; Imai, Yasutomo*

JNC-TN9400 2003-045, 74 Pages, 2003/06

JNC-TN9400-2003-045.pdf:3.05MB

As a thermal-hydraulic evaluation tool for fast reactor fuel subassemblies with high burn-up ratio, a numerical analysis system in which a subchannel analysis program and a detailed thermal hydraulic analysis program are utilized interractively is under development. This system enables us not only to clarify thermal hydraulic characteristics that cannot be revealed by experiments due to measurement difficulty but also to contribute to the rational safety design and assessment. This report describes the incorporation of turbulence models to the detailed thermal hydraulic analysis program SPIRAL-II and its verification study. In addition to the standard k-$$epsilon$$ two-equation model, Renormalization Group(RNG) k-$$epsilon$$ model and Algebraic Stress Model(ASM) were incorporated to SPIRAL-II as turbulence models. The former utilizes fewer empirical constants than the standard k-$$epsilon$$ model and is believed to be more accurate especially in low Reynolds number regions. The latter treats Reynolds stresses directly and therefore has applicability to anisotropic turbulent flow. It is common for three models that similar transport equations for turbulent kinetic energy k and dissipation rate $$epsilon$$ are discretized and solved by galerkin method. With respect to ASM, Daly-Harlow model is applied to the diffusion terms of the transport equations and algebraic expressions related to Reynolds stresses are solved by Newton-Raphson method using calculated k and $$epsilon$$. A wall function (Reichardt function) is applied to each model as the boundary condition treatment. A verification study of improved SPIRAL-II was carried out using three kinds of problems: turbulent flow between parallel walls, backstep facing turbulent and turbulent flow in a square duct. From these calculation results, the validity of the improved program was confirmed and prediction characteristics of each turbulent model were clarified.

JAEA Reports

Development of design window evaluation and display system (II); confermations of the basic performance of genetic algorism

Murakami, Satoshi*; Muramatsu, Toshiharu

JNC-TN9400 2003-038, 59 Pages, 2003/05

JNC-TN9400-2003-038.pdf:2.28MB

A large-scale sodium-cooled fast breeder reactor in feasibility studies on commercialized fast reactors which has a tendency of cosideration of thorough simplified and compacted system is being investigated, however special attention should be paid to thermohydraulic designs for a gas entrainment behavior from free surfaces, a flow-induced vibration of in-vessel components, a thermal shock for various structures due to to high-speed coolant flows, nonsymmetrical coolant flows, etc. in the reactor vessel. As thus a lot of thermal-hydraulic issues relate to each other complicatedly on the reactor designs, multiple-criteria decision-making on the understanding of relationship among thermal-hydraulic issues is indispensable to design the reactor efficiently. Genetic Algorithm (GA),which is one of the methods, for multjple-criteria decision-making, was applied to the typical simPle objective optimization problems and then was confirmed its basic performance. From the Analyses, the following results have been obtained: (1)In the unimodal optimization problem, it was confirmed that GA is capable of sufficient searching ability. (2)It was confirmed that GA can be also applied to the discrete optimization problems. (3)In the case of applying GA to the combinational optimization problem, the searching efficiency is improved better by increasing the number of experiment times than the maximum of generation. (4)In the case of applying GA to the multimodal optimization problem, the searching ability is improved by using the two genetic operators (i.e., the mutation, and the elite strategy)at the same time.

JAEA Reports

Modification of multi-dimensional sodium-water reaction analysis code: SERAPHIM and sensitivity analyses on the early stage of leakage

Takata, Takashi; Yamaguchi, Akira; Watanabe, Akira*

JNC-TN9400 2003-024, 129 Pages, 2003/04

JNC-TN9400-2003-024.pdf:9.72MB

Modification of the SERAPHIM code, which was developed to deal with the sodium-water reaction phenomena in a steam generator of the LMFR, has been carried out With regard to the reaction mechanism, the surface reaction model is improved. The hydrated effect on the reaction rate in the gas-phase reaction is estimated and the reaction product in the sodium-water reaction is investigated. The SERAPHIM code is also parallelized using the MPI (Message Passing Interface) method to apply to a large-scale simulation such as over one million nodes with a limited PC resource. The analysis region and the memory needed in the analysis are discrete in the SERAPHIM code. The execution time becomes approximately l7 times faster in case of 16 CPUs. The calculation of one million nodes can be available even in a PC cluster system with 1 GB memory. Sensitivity analyses of the surface reaction model in the beginning of the water vapor leakage are carried out and the following conclusion are obtained. 1)Gas region develops quickly in case of no chemical reaction. The pressure peak is obtained at an early stage of the leakage regardless of the chemical reaction. 2)The difference of the initial pressure strongly affects the development of the gas region and the flow-field. However,It is less influential on the maximum temperature. The maximum temperature depends not only on the chemical reaction characteristics such as the gas region and heat generation but also on the thermal-hydraulics characteristics in the multi-phase flow field. 3)Considering the evaporation of sodium hydroxide (NaOH), the maximum gas temperature of approximately 1200deg is observed in the analysis. In the standard state, the chemical reaction that produces a gas state sodium oxide and hydrogen gas from liquid sodium and water vapor is endothermic. In is concluded that the evaporation of sodium hydroxide is very important phenomena in the sodium-water reaction.

JAEA Reports

Numerical analysis of thermal stratification phenomena in upper plenum of a fast breeder reactor,1; Evaluation of thermal stratification phenomena near the region of flow holes

Suda, Kazunori; ; Yamaguchi, Akira

JNC-TN9400 2002-078, 108 Pages, 2002/12

JNC-TN9400-2002-078.pdf:7.96MB

Thermal stratification phenomena are observed in an upper plenum of liquid metal fast breeder reactors (LMFBRs) under reactor scram conditions, which give rise to thermal stress on structural components. Therefore it is important to evaluate characteristics of the phenomena in the design of the internal structures in an LMFBR plenum. To evaluate long-term characteristics of thermal stratification phenomena in a typical LMFBR upper plenum, numerical analysis was carried out with a multi-dimensional thermohydraulics code AQUA for a scram event from full power operation condition. Thereafter the numerical results were compared with extrapolated results of measured transient data on the 40% operation condition. From the thermohydraulic analysis by the AQUA code, the following results have been obtained. [Long-term characteristics of thermal stratification phenomena] (1)The cold fluid region near the inside inner barrel was expanded with accumulation of the cold fluid in the lower region of the plenum after 300 seconds from the reactor scram, so that the fluid from core flowed to the lower region of the upper plenum. The characteristics of axial temperature distributions in the upper plenum were similar to them at the 300 seconds. (2)The thermal stratification interface was located initially around intermediate position between upper and lower flow holes. And an another thermal stratification interface was formed around the inner barrel support plate after 300 seconds from the scram, so that the cold fluid accumulated in the lower region of the plenum. But the thermal stratification interface around the inner barrel support plate was disappeared by mixture and heat conduction of coolant of circumferential direction. The thermal stratification interface which was located below in the upper flow holes, rose to the upward position of the upper flow holes at the 720 seconds. (3)In annular gap region between the inner barrel and the reactor vessel wall, thermal ...

JAEA Reports

Numerical-simulation for gas entrainment from free surface (I); Calculation of free surface vortex in the cylinder“

Ito, Kei; ; Yamaguchi, Akira

JNC-TN9400 2002-054, 46 Pages, 2002/11

JNC-TN9400-2002-054.pdf:2.19MB

Design study is made on a large-scale sodium-cooled fast breeder reactor in the feasibility studies of the next generation reactors. In this design, coolant velocity in the upper plenum of reactor vessel is higher than conventional designs. Therefore special attention should be paid to gas entrainment behavior at the free surface. Gas entrainment due to a free surface vortex is particularly important, because it has downward velocity near the vortex center. The velocity is large enough to carry a gas bubble to the primary circuit, which connects to the core region. In this research, a free surface vortex test, conducted in Central Research Institute of Electric Power Industry, was numerically simulated, for the purpose of establishing an evaluation method of gas entrainment. VOF (Volume of Fluid) model of PLIC (Piecewise Linear Interface Calculation) type and CSF (Continuum Surface Force) model for surface tension are used to consider the free surface dynamics. As a result, it is noted that calculation accuracy of the vortex greatly depends on the mesh size in the analysis model. Required accuracy was obtained when the mesh size is 1/10 of the vortex scale length (i.e., radius where the tangential velocity reaches the maximum). Effect of surface tension was also investigated. It was cleared that higher surface tension coefficient tend to decrease the gas core dent of the vortex. In addition, 1$$^{st}$$ upwind scheme and 2$$^{nd}$$ upwind scheme was compared. It is concluded that the effect of numerical diffusivity is significant near the vortex center.

JAEA Reports

Analytical study on thermal-hydraulics of gas cooled fast reactors

Ohshima, Hiroyuki; Nishimura, Motohiko*

JNC-TN9400 2002-072, 97 Pages, 2002/08

JNC-TN9400-2002-072.pdf:3.85MB

A feasibHity study has been carried out at JNC to construct new design concepts of commercialized fast reactors. This report describes two kinds of numerical investigations related to thermal-hydraulics of gas-cooled fast reactors of which design studies are being performed as part of the feasibility study. A series of thermal hydraulic analyses was carried out using multi-dimensional analysis program AQUA in order to confirm the heat removal capability of the helium-gas-cooled fast reactor with a coated-particle-type fuel assembly design under a rated power operation, a low power/low flow and an accident conditions. The calculation results indicates that the lateral gas flow which is indispensable for normal heat removal in the fuel particle region is kept under each calculation condition and the maximum temperature does not exceed the tentative design limitation as far as the inlet surface permeability is uniform. Only in the case of high pressure and very low flow rate, a possibility that local high temperature region exceeding the design limitation appears may not be denied due to upward flow driven by buoyancy force. Improvement on knowledge of gas property functions in high temperature and pressure drop correlations are required for more accurate analysis. Natural circulation decay heat removal characteristics of the CO$$_{2}$$ gas cooled fast reactor are examined using a one-dimensional nuclear-thermal-hydraulics network analysis code, MR-X equipped with correlations for the core thermal-hydraulics of gas cooled fast reactors. Simulation parameters are the shutdown time of steam generators (SGs), restart time of gravitational water feed to the SGs, and flow rate of the feed water. It was predicted that the reactor satisfied limitation of the maximum cladding temperature under the realistic operation condition of SGs with the shutdown time of 30 s and the restart time of 20 min. Moreover, the cladding temperature still satisfied the limitation, even ...

JAEA Reports

Thermal-hydrauhc analysis of cover gas region in steam generator of MONJU

Ito, Kei; ; Yamaguchi, Akira; *

JNC-TN9400 2002-042, 51 Pages, 2002/06

JNC-TN9400-2002-042.pdf:2.17MB

The upper region of steam generator is filled with argon cover gas. The cover gas is expected to constitute a complex natural circulation derived by heat exchange with cold feed water tubes, hot steam tubes, other structures and sodium surfaces. It is one of important issues to make clear the gas temperature distribution for a detail thermal-hydraulic evaluation in a steam generator. In this study, a cylindrical two-dimensional (2-D) code (MSG code) was applied to the whole region analysis of the Monju steam generator involving the cover gas region. In order to confirm the analysis accuracy, the 2-D results was compared with three-dimensional (3-D) results calculated by the FLUENT code, which has employed unstructured mesh for each tube, and both results were compared with measured temperature of the shell. In addition, a sensitivity of heat transfer coefficients to the shell temperature was been evaluated by the 3-D analysis. As a result, the cover gas temperature distribution by the 2-D analysis showed good agreement with the result by the 3-D analysis. In addition, it was confirmed that heat conductive coefficient has negligible effects on the shell temperature.

JAEA Reports

None

; *; Yamaguchi, Akira

JNC-TN9400 2002-022, 96 Pages, 2002/06

None

JAEA Reports

Thermal-hydraulic Analysis for the LBE-cooled natural circulation reactor; Development of the MSG-COPD code and application to the system analysis

*; ; ;

JNC-TN9400 2002-013, 62 Pages, 2002/05

JNC-TN9400-2002-013.pdf:1.86MB

Thermal-hydraulic analysis for the Lead-Bismuth eutectic (LBE)-cooled natural circulation reactor has been conducted by using a combined plant dynamics code (MSG-COPD). MSG-COPD has been developed to consider the multi-dimensional thermal-hydraulics cffect on the plant dynamics during transients. Plant dynamics analyses for the LBE-cooled STAR-LM reactor, which has been designed by Argonne National laboratory in U.S.A., have been performed to understand the basic thermal-hydraulic characteristics of the natural circulation reactor. As a result, it has been made clear that cold coolant remains in the lower plenum by the thermal stratification in case of the ULOHS condition with a severe temperature gradient at the stratified surface in the lower plenum. In addition, the flow-redistribution effect in a core channels by the buoyancy force has been evaluated for a candidate LBE-cooled FBR plant concept (LBE-FR), which has been designed by JNC. A linear evaluation method for the flow-redistribution coefficient is proposed for the LBE-FR, and compared with the multi-dimensional results by MSG-COPD. In conclusion, the method shows sufficient performance for the prediction of the flow-redistribution coefficient for typical lateral power distributions in the core.

JAEA Reports

Numerical investigation on thermal striping conditions for a tee junction of LMFBR coolant pipes (VI); Numerical evaluations of arched-vortex characteristics in non-isothermal fields

*;

JNC-TN9400 2002-011, 37 Pages, 2002/05

JNC-TN9400-2002-011.pdf:5.36MB

Numerical analyses for turbulence thermal mixing, the aim of which is to evaluate relationship between hydrodynamics and temperature distribution of an archedvortex, were carried out using the direct numerical simulation code DINUS-3. From the analyses, the following results have been obtained: (1)Transportation period of the arched-vortex and distance between the arched--vortices were kept constant in isothermal and non-isothermal conditions. (2)The transportation period of afched-vortex was decreased with increasing Reynolds number under the condition of the constant flow velocity ratio between both coolant pipes. (3)One of the main reasons for this behavior was considered that the motion of the cold fluid flowing out of the branch pipe was restricted by the difference of fluid density between the branch and the main pipes. The amplitudes of the cross flow velocity fluctuation in the leg region of the arched-vortex were larger than those under isothermal condition. (4)It was confirmed that the arched-vortex consists of two kinds of vortexes, i.e., a longitudinal vortex generated by a shear motion at the top of the arched-vortex, and a horizontal vortex by shedding motion at both sides of the branch jet flow.

JAEA Reports

Study on in-vessel thermohydraulics phenomena of sodium-cooled Fast reactors (II); Numerical investigations on proprieties of R/V upper plenum separation

; *; Yamaguchi, Akira

JNC-TN9400 2001-129, 51 Pages, 2002/03

JNC-TN9400-2001-129.pdf:8.76MB

A large-scale sodium-cooled fast breeder reactor investigated in the feasibility studies on commercialized fasat reactors has a tendency of consideration of thorough simplified and compacted system designs to realize drastic economical improvements. Therefore, special attention should be paid to thermohydraulic designs for gas entrainment behavior from free surfaces, a flow-induced vibration of in-vessel components, thermal shock for various structures due to high-speed coolant flows, nonsymmetrical coolant flows, etc. in the reactor vessel. In-vessel thermohydraulic analyses were carried out using a multi-dimensional code AQUA to contribute to a planning of water scaled-model experiments for the separated upper plena of the reactor vessel. From the analysis, the following results were obtained. (1)It can be considered that there is little effect of volumetric flow rate between the upper plenum and the free surfase plenum on hydrodynamic characteristics in the whole upper plenum. Because the affected area is limited in the neighborhood of gaps of hot/cold leg pipes. (2)Change in flow velocity components is limited around the outer wall of hot leg pipes if the gap width of the dipped plate and penetrating components changes. From the above results, it was concluded that the assumption seems to be valid that the free surface plenum hydrodynamic characteristics is independent of the upper plenum flows. However it is necessary to consider jet effects due to the hot leg intake flows affecting vortex concentrations in the upper plenum.

JAEA Reports

Study on in-vessel Thermohydralics phenomena of sodium-cooled fast reactors (I); Numerical investigation for the Rationalization of Hydrodynamics in the upper plenuln

; *; Yamaguchi, Akira

JNC-TN9400 2001-117, 60 Pages, 2002/02

JNC-TN9400-2001-117.pdf:7.06MB

A large-scale sodium-cooled fast breeder reactor in feasibility studies on commercialized fast reactors has a tendency of consideration of thorough simplified and compacted system designs to realize drastic economical improvements. Therefore, special attention should be paid to thermohydraulic designs for a gas entrainment behavior from free surfaces, a flow-induced vibration of in-vessel components, a thermal shock for various structures due to high-speed coolant flows, nonsymmetrical coolant flows, etc. in the reactor vessel. In-vessel thermohydraulic analyses were carried out using a multi-dimensional code AQUA to understand the thermohydraulic characteristics in the upper plenum, and to investigate suitable in-vessel structure for the elimination of gas entrainment possiblity. From the analysis, the following results were obtained. (1)It is difficult to rationale in-vessel flow patterns through adjustments of porous ratio and pressure loss for a hold down plate and baffle plates installed in an upper core structure. (2)Dummy plug insertion to a slit of the upper core structure is one of effective measures to stabilize in-vessel flow patterns. (3)Flow guide devices such as a baffle ring and a partial inner barrel are also effective measures to eliminate impinging jet to a dipped plate (D/P) and to reduce horizontal flow velocity components at free surface. (4)Installations of labyrinth structures to a R/V - D/P gap is successful for decreasing of free surface horizontal flows. (5)Gap closing of an in-vessel fuel pot and two cold trap components has the effects of reductions for free surface horizontal flows and for the difference of free surface levels. Following future investigations are important preventive measures against the gas entrainment from the free surface. (1)Flattening of spatial axial velocity distributions at the R/V - D/P gap. (2)Alleviation measures of vortex concentration at free surface. (3)Separation measures of 3-dimensional vortex distributi

JAEA Reports

0xygen concentration diffusion analysis of Lead-Bismuth-Cooled, natural-circulation reactor

Ito, Kei;

JNC-TN9400 2001-102, 49 Pages, 2001/12

JNC-TN9400-2001-102.pdf:3.02MB

The feasibility study on fast breeder reactors in Japan has been conducted at JNC and related organizations. The Phase-I study has finished in March, 2001. During the Phase-I activity, 1ead-bismuth eutectic coolant has been selected as one of the possible coolant options and a medium-scale plant, cooled by a lead-bismuth natural circulation flow was studied. 0n the other side, it is known that lead-bismuth eutectic has a problem of structural material corrosiveness. It was found that oxygen concentration control in the eutectic plays an important role on the corrosion protection. In this report, we have developed a concentration diffusion analysis code (COCOA:COncentration COntrol Analysis code) in order to carry out the oxygen concentration control analysis. This code solves a two-dimensional concentration diffusion equation by the finite differential method. It is possible to simulate reaction of oxygen and hydrogen by the code. We verified the basic performance of the code and carried out oxygen concentration diffusion analysis for the case of an oxygen increase by a refueling process in the natural circulation reactor. In addition, characteristics of the oxygen control system was discussed for a different type of the control system as well. It is concluded that the COCOA code can simulate diffusion of oxygen concentration in the reactor. By the analysis of a natural circulation medium-scale reactor, we make clear that the ON-OFF control and PID control can well control oxygen concentration by choosing an appropriate concentration measurement point. In addition, even when a trouble occurs in the oxygen emission or hydrogen emission system, it observes that control characteristic drops away. It is still possible, however, to control oxygen concentration in such case.

JAEA Reports

Thermal-hydraulic analysis in local fuel region of helium gas-cooled fast breeder reactor with coated-particle-type fuel

; Ohshima, Hiroyuki

JNC-TN9400 2001-101, 85 Pages, 2001/06

JNC-TN9400-2001-101.pdf:2.53MB

Feasibility Study is being carried out at JNC to generate new concepts for commercialized fast breeder reactors. In this study, a helium gas-cooled reactor with coated-particle-type fuel is proposed, as one of the candidates for fast breeder reactors. Each fuel assembly has a compartment of an annular duct shape and the annular space of the compartment is filled with coated-particle-type fuels. The assessment of heat removal capability of coolant flowing in the coated-particle-fuel region and the endurance of fuel particle is one of the important issues in the reactor safety. In the present study, a thermal-hydraulic analysis was carried out in order to clarify flow and temperature fields in a local coated-particle-fuel region as well as in-particle temperature distributions. The FLUENT code was applied to this numerical analysis and the simulations were performed using five face-center cubic unit cells, which were combined with one another in the flow direction. Through the analysis, it was confirmed that the extreme temperature peak in coolant did not appear in the local Coated-particle-fuel region and the temperature in a coated fuel particle rises along the flow direction almost linearly except fuel core region. With respect to the surface temperature of a coated fuel particle, the maximum and the minimum temperatures appear at the downstream and the upstream contact points with neighboring particles, respectively. Further, the calculation results by FLUENT were compared with Ergun's correlation in order to verify the applicability of it to the pressure drop estimation in the coated-particle-fuel region. The friction coefficient estimated by FLUENT agreed with that by Ergun's correlation with errors from -11% to 20% for 2 $$leq$$ Re $$leq$$ 154.

JAEA Reports

Development of computer program for detailed thermal-Hydraulic analysis in a fast reactor fuel subassembly (1)

Ohshima, Hiroyuki; Imai, Yasutomo*

JNC-TN9400 2001-064, 90 Pages, 2001/06

JNC-TN9400-2001-064.pdf:2.06MB

As a thermal-hydraulic evaluation tool for high performance fast reactor fuel subassemblies, with high burn-up fuel, a numerical analysis system in which a subchannel analysis program and a detailed thermal hydraulic analysis program are utilized interactively is under development, This system enables us to clarify thermal hydraulic characteristics that cannot be revealed by experiments due to the measurement difficulty and to contribute to rational safety design and assessment. This report describes the first step of development and verification study of the detailed thermal hydraulic analysis program SPIRAL-II. SPIRAL-II adopts the finite element method from thc viewpoint of the advantage to treat precisely complicated geometry. Conservation equations of mass and momentum were discretized by Bubnov-Galerkin method. At the same time, one can choosc streamline upwind Petrov-Galerkin method or a balancing tensor diffusivity method for calculation stabilization. Semi-implicit solution scheme (fractional step method) developed by Ramaswamy is used for time integration. As the pressure equation matrix solver, ICCG or Gaussian elimination is applied. With respect to the turbulence model, k-$$varepsilon$$ two equation model was implemented. As to the type of calculation element, 1st/2nd order hexahedron element and 1st order pentahedron clement are available. A verification study of SPIRAL-II was carried out using the following problems: (1)2-dimensional flow in duct (laminar and turbulent flow), (2)Cavity flow, and (3)Backstep facing flow (laminar and turbulent flow) The predicted velocity profiles in the case (1)agreed with theoretical ones in both laminar and turbulent flow. In the cases of (2) and (3), it was confirmed that the SPIRAL-II has the prediction accuracy that is almost equivalent to the higher-order finite difference method.

JAEA Reports

MSV:Multi-Scaler Viscosity Model of Turbulence

Kriventsev, V.

JNC-TN9400 2001-053, 38 Pages, 2001/04

JNC-TN9400-2001-053.pdf:1.31MB

Multi-Scale Viscosity (MSV) model is proposed for estimation of the Reynolds stresses in turbulent fully-developed flow in a wall-bounded straight channel of an arbitrary shape. We assume that flow in an "ideal" channel is always stable, i.e.laminar, but turbulence is developing process of external perturbations cased by wall roughness and other factors. We also assume that real flows are always affected by perturbations of any scale lower than the size of the channel. The turbulence can be modeled in form of internal or "turbulent" viscosity increase. The main idea of MSV can be expressed in the following phenomenological rule: A local deformation of axial velocity can generate the turbulence with the intensity that keeps the value of local turbulent Reynolds number below some critical value. Here, local turbulent Reynolds number can be defined in two different ways: (1)as a product of value of axial velocity deformation for a given scale and generic length of this scale divided by accumulated value of laminar and turbulent viscosity of lower scales (2)as a ratio of the difference between total kinetic energy and "flat-profile" kinetic energy to the work of friction forces In MSV, the only empirical parameter is the critical Reynolds number that is estimated to be around 100 in the former case and about 8.33 in the later. MSV model has been applied to the fully-developed turbulent flows in straight channels such as a circular tube and annular channel. Friction factor and velocity profiles predicted with MSV are in a good agreement with numerous experimental data. The MSV model can be classified as "zero-order" integral model of turbulence. Because of simplicity, MSV can be easily implemented for calculation of fuIly-developed turbulent flows in straight channels of arbitrary shapes including fuel assemblies of nuclear reactors. The intent of this report is to summarize the progress made in the development of the model of turbulence. Since the final ...

16 (Records 1-16 displayed on this page)
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