A nodal SN transport method for three-dimensional triangular-z geometry

A new nodal S_N transport method has been developed to perform accurate transport calculation in three-dimensional triangular-z geometry, where arbitrary triangles are transformed into regular triangles via a coordinate transformation. The transverse integration procedure is applied to treat the neutron transport equation in the regular triangle. The neutron angular distributions of intra-node fluxes are represented using the S_N quadrature set, and the spatial distributions of neutron fluxes and sources are approximated by a quadratic polynomial. The nodal-equivalent finite difference algorithm for 3D triangular geometry is applied to establish a stable and efficient iterative scheme. The present method was tested on four 3D Takeda benchmark problems published by the nuclear data agency (NEACRP), in which the first three problems are in XYZ geometry and the last one is in hexagonal-z geometry. The results of the present method agree well with those of the reference Monte-Carlo calculation method, the difference in k_eff being less than 0.1%. This shows that multi-group reactor core/criticality problems can be accurately and effectively solved using the present method.     

Vaporization and Surface Ionization of LaC2, CeC2, PrC2, NdC2, ThC2 and UC2

The Langmuir vaporization and the surface ionization of LaC₂, CeC₂, PrC₂, NdC₂, ThC₂ and UC₂ from a heated graphite filament have been studied mass spectrometrically. It was found that there were present small amounts of neutral and ionic metal dicarbide molecules in addition to neutral and ionic metal atoms in the LaC₂, CeC₂, PrC₂, ThC₂ and UC₂-C systems with the exception of NdC₂-C, where neither neutral nor ionic metal dicarbide molecules were observed. The reason for this exceptional behavior of the NdC₂-C system is explained by the very small vaporization coefficients, as estimated from the measurements of neutral MC₂/M ratios and ionic MC₂/M ratios.

From the measurements of the heats of vaporization, it was surmised that the ionization potential of Th measured by the surface ionization comparison technique might be too high.     

Charge and Mass Considerations for Plasma Velocity Measurements in Rotating Plasmas

Velocity of hydrogen plasmas rotating due to imposed E × B fields at the Maryland Centrifugal Experiment (MCX) (Ellis et al., Phys Plasmas 12:055704, 2005), where E is the electric field in the radial direction and B the magnetic field in the axial direction of a cylindrical configuration, has traditionally been measured using Doppler shifts of atomic spectra from impurity elements such as carbon. Ideally, the gyrocenter of trace particles rotates at the bulk plasma velocity, regardless of the charged state or trace particle mass. However, for sufficiently large applied |E/B| (or equivalently, a sufficiently large ratio of bulk plasma rotation frequency and particle gyrofrequency), charged particles may have gyroradii that depart significantly from quasi-circular orbits drifting about the B field axis. This effect is investigated numerically with a single particle code that includes scattering, as well as experimentally at MCX. Numerical findings are compared to experimentally measured Doppler shifts of singly inonized helium and oxygen, and doubly ionized carbon atoms.     

Seismic loads for crack stability assessment, in a review of leak-before-break (LBB) applicability

This study was performed to define the seismic loading conditions for use in the crack stability assessment of a BWR for the applicability of the leak-before-break (LBB) criterion. The LBB has been applied to the design of Class 1 piping in Japanese light-water reactors. Crack penetrated condition with detectable leak in the LBB applicability review is classified into the Level C service condition. Here an S₁-earthquake (maximum design earthquake) is currently assumed, rather than an S₂-earthquake (extreme design earthquake). In order to justify this assumption, the frequency of an S₁-earthquake occurring during coolant leakage due to crack propagation was determined. The frequency of coolant leakage from Class 1 piping must be less than that of the Level C service condition (2.5 × 10⁻² to 1 × 10⁻⁴ per year) in order to assume that an S₁-earthquake is appropriate. Accordingly, the frequency of coolant leakage from Class 1 piping was calculated using a probabilistic fracture mechanics (PFM). The results of this analysis indicate that the frequency of coolant leakage from Class 1 piping is less than the expected occurrence of an S₁-earthquake. As the results, it is concluded that the assumption of the seismic loading employed in an LBB applicability review should be appropriate.     

Hydration Model for Evaluation of Thermodynamic Activities in Nitric Acid-Nitrate-Water System

Modeling was carried out on activities of components in the nitric acid-nitrate-water ternary system in order to examine details of the chemical reactions in reprocessing solutions. To modify our earlier “Hydration Model”, the ternary system was regarded as the mixed solution of two kinds of cluster molecules which were dominant associated molecules in the nitric acid-water system and nitrate-water system, respectively. Activities in the ternary system were calculated from those in the two binary systems taking into account the change of entropy and enthalpy during mixing. The entropy term was calculated assuming ideal mixing. The enthalpy term was calculated assuming that the nitric acid cluster would be influenced by one nitrate cluster as if there were m _s /m _na numbers of nitric acid clusters, where m _s and m _na were the numbers of water molecules in nitrate and nitric acid cluster molecules, respectively.

The model was able to predict activities of nitric acid, water and nitrate. Its use was verified for the activities of nitric acid and water provided phase separation did not occur. The verification for nitrate activity was not carried out, however, the model should be suitable.     

Fuel Temperature Coefficients of Reactivity for Heavy-Water-Moderated,Cluster-Type Fuel Lattices

Temperature coefficients of reactivity have been measured up to 600°C on cluster-type UO₂ fuel for three kinds of ²³⁵U enrichment and on a hollow cluster of sus-cladding tubes by using a hot He gas loop in a heavy-water-moderated, pressure-tube-type critical assembly. A new experimental method has been developed which accurately eliminates the reactivity disturbance caused by heat leakage in the measurement of an extremely small change in reactivity. The fuel (fuel pellet, cladding land pressure-tube) temperature coefficients of reactivity obtained for the temperature range below 300°C are +1.00±0.04, ?3.48±0.13 and - 6.36±0.25 in the unit of l0^-5% Δk/k.°C for 0.2%, 0.7% and 1.5%²³⁵U enrichment, respectively. In the higher temperature region above 300°C, each coefficient shifts to positive side by about 2x10^-5 Δk/k.°C. Temperature coefficient of reactivity for the hollow cluster of sus-cladding tubes (cladding and pressure-tube) has a large constant value with positive sign, + (6.42±0.26) x 10^-5 Δk/k.°C, all through the temperature range. A calculational model to analyze a hot-loop-type measurement of temperature coefficients with use of WIMS-D code was proposed and could be successfully applied to the present measurement.     

Effect of Gamma Radiation on Silica Gel, (II)

Radiolysis of N₂O adsorbed on silica gel degassed at 200, 450 and 600°C has been studied to investigate the behavior of electrons on the gel surface. The G-value of nitrogen as the major radiolytic product increases with an increase of N₂O concentration adsorbed approaching a plateau value which depends on degassing temperature of the gel prior to irradiation. By the competitive electron scavenging of N₂O with several electron scavengers, such as CCl₄, SF₆ and nitrobenzene, initial yield of electrons G (e ^?), and relative rate constant for reaction of electrons with scavenger to that with N₂O, k _s /k _N2O, have been obtained. The G (e ^?) is 3.8 and 2.0 for the gel degassed at 200 and 600°C respectively. In the former gel, the value of k _s /k _N2O is comparable with that in aqueous system, while in the latter, with that in non-polar hydrocarbon such as neopentane. The observed difference may be attributed to the presence of silanol groups and residual water which facilitate some form of hydration of electrons on the gel degassed at low temperature. Despite of the complexity of the heterogeneous system, Hammett's relationship is observed among the reactions of electrons with monosubstituted derivatives of benzene, providing the reaction constant ρ as 2.8.     

Isotope effect and hydrogen content dependence on the heat capacity and thermal conductivity of zirconium hydride and deuteride

Zirconium (Zr) hydride and deuteride are considered as candidates of neutron reflector materials in fast reactors (FRs). Thus, it is important to evaluate their fundamental physical and chemical properties. In this study, we prepared ?-phase Zr deuteride (?-ZrD_1.90), whose physical properties have been investigated and also the heat capacity (C_P) and thermal conductivity (κ) have been measured from room temperature to 673 K. The obtained data were compared with the literature data of δ-phase Zr hydride (δ-ZrH_1.66), ?-phase Zr hydride (?-ZrH_1.94), and deuteride (?-ZrD_1.95). Both C_P and κ of ?-ZrD_1.90 were higher than those of δ-ZrH_1.66. The higher C_P of ?-ZrD_1.90 than that of δ-ZrH_1.66 is mainly due to the smaller vibration frequency of deuterium atoms than that of hydrogen atoms. On the other hand, the higher κ of ?-ZrD_1.90 than that of δ-ZrH_1.66 is due to the larger hydrogen isotope content of ?-ZrD_1.90 than that of δ-ZrH_1.66. The data reported here would be useful when Zr hydride and deuteride are installed into FRs.     

Fracture toughness characterization of irradiated, low upper shelf welds

A data base of J − R curve trends is being established for irradiated, light-water reactor pressure vessel steels of low upper shelf toughness. R-curve trends have been developed for several welds made with Linde 80 flux and containing a high copper impurity which enhances the sensitivity to irradiation embrittlement. Tests were conducted using compact toughness specimens of 12.5 mm to 100 mm thickness. These data provide the materials properties necessary for a tearing instability analysis of postulated accident conditions in certain commercial power reactors. Irradiation decreased the level of the R curve significantly in most cases. Furthermore, the average value of tearing modulus (T_avg) was a more discriminating indicator of toughness degradation than the crack initiation toughness (J_Ic). Temperature-dependent correlations between the R-curve parameters (J_Ic, T_avg) and Charpy-V (C_v) upper shelf energy have been suggested here and in other programs. This finding could enhance the significance of C_v reactor surveillance data with respect to structural integrity. However, J_Ic and T_avg have demonstrated an inverse relationship with temperature which is not reflected in C_v upper shelf energy and this must be taken into account in the development of correlations.     

Transmission probability method for solving neutron transport equation in three-dimensional triangular-z geometry

This paper presents a transmission probability method (TPM) to solve the neutron transport equation in three-dimensional triangular-z geometry. The source within the mesh is assumed to be spatially uniform and isotropic. At the mesh surface, the constant and the simplified P₁ approximation are invoked for the anisotropic angular flux distribution. Based on this model, a code TPMTDT is encoded. It was verified by three 3D Takeda benchmark problems, in which the first two problems are in XYZ geometry and the last one is in hexagonal-z geometry, and an unstructured geometry problem. The results of the present method agree well with those of Monte-Carlo calculation method and Spherical Harmonics (P_N) method.     

International Symposium on Isotope Separation and Chemical Exchange Uranium Enrichment

From the viewpoint of nuclear criticality safety, it is important to comprehend the reactivity of fuel solutions induced by oscillatory movements such as earthquakes. This paper intends to figure out the reactivity of a fuel solution system with a free surface formed by oscillation by evaluating the fluctuation of the neutron multiplication factor (k _eff ) obtained from a static calculation. To fulfill this intension, criticality calculations with reflecting fluid calculation results have been carried out. In the fluid calculations, the finite volume method and the volume of fluid (VOF) method have been applied in tracking the free surface formed by oscillation. The continuous energy Monte Carlo calculation method has been applied in the criticality calculations. As a result, it has been found that the variation patterns of the k _eff and those of the shape of fuel solutions are classified according to oscillation frequency and the ratio of solution height to the width of the tank (H/L). If a sloshing motion is generated, the k _eff fluctuates widely and has a threshold, with which we can classify the fluctuation type of the k _eff , despite the kind of reflector. If H/L is above the threshold, i.e., H/L =0.4, the k _eff fluctuates to a value below that obtained in the resting state. On the contrary, if H/L is below the threshold, the k _eff fluctuates to a value above that obtained in the resting state. This result implies the criticality calculation for a fuel solution with a free surface using the Monte Carlo method may give a slightly smaller threshold than using other approaches.     

Development of Discrete Ordinates SN Code in Three-Dimensional (X,Y, Z) Geometry for Shielding Design

A discrete ordinates transport code ENSEMBLE in (X, Y, Z) geometry has been developed for the purpose of shielding calculations in three-dimensional geometry. The code has some superior features, compared with THREETRAN which is the only code of the same kind so far developed. That is, the code can treat higher order anisotropic scattering and employs a coarse mesh rebalancing method. Moreover it has a negative flux fix-up routine using a variable weight diamond difference equation scheme and has a ray-effect fix-up option using a fictitious source based on S_N→P_N-1 conversion technique. Formulations for these advanced features in three-dimensional space have been derived.

As the demonstration of the capabilities of the code, several numerical analyses and an analysis of an annular duct streaming experiment in JRR-4 at Japan Atomic Energy Research Institute, have been performed.

As a result of these analyses, confirmation has been obtained for the prospect of applicability of ENSEMBLE to practical shielding design.     

Recent Results in JT-60 Advanced Experiment JT-60 Team,JAERI (Presented by Naoyuki MIYA)

Major efforts in the recent JT-60 experiments have been concentrated on the improved confinement of plasmas with profile control and on the steady state operation study. Peaked density profiles were produced with the successive pellet injection. The energy confinement time was improved by 40% as large as that with the gas fuelled discharges. The fusion products n _e(0)τET _i(0)reached 1.2 × 10²⁰m^?3·s·keV, which was twice that of gas fuelled discharges. High-β_p, plasmas were obtained in low-I _p discharges with improved confinement and a high ion temperature T _i, (0) of 12 keV. The bootstrap current reached 80% of the total plasma current at β_p=3.2. The new concept of a steady-state tokamak power reactor has been proposed on the basis of this result. The maximum current drive efficiency ηCD of 3.4 × 10₁₉m^?2·MA/MW was obtained in the LH current drive experiments. Helium ash exhaust experiments using He-beam injection into H⁺ plasmas showed promising results for α-particle exhaust in a fusion power reactor.     

Ab initio Quantum Chemical Study on Charge Distribution and Molecular Structure of Uranyl (VI) Species with Raman Frequency

Ab initio molecular orbital calculation was performed for uranyl (VI) monomer and dimer complexes with some water molecules and/or hydroxide ions. The Raman active frequencies were calculated for each complex after structural optimization in vacuum state, and investigated the molecular structure and the charge distribution. For uranyl monomer, the calculated Raman frequencies for uranyl with 5 or 6 water molecules show good agreement with experimental Raman frequencies for uranyl hydrates. On the contrary, the calculation underestimates the Raman frequency in case of hydroxide ions in uranyl complex. The calculation models for uranyl dimer were made from [UO₂(H₂O)₅]²⁺, then the hydroxide ions bridging model, [(UO₂)₂(OH)₂(H₂O)₆]²⁺, is more stable than water molecules bridging, [(UO₂)₂(H₂O)₈]⁴⁺, and the theoretical Raman frequency and uranyl bond lengths have the good coincidence with those of experiments. The calculated uranyl bond length of dimer is slightly longer than that of monomer. Also, the charge of oxygen atom in uranyl shows larger change than that of uranium atom between dimer and monomer. And this charge distribution is mostly influenced by the charge donation of ligands. If only same ligands are surrounding, the number of ligands influenced this charge distribution.     

A parametric study and a guide chart to avoid condensation-induced water hammer in a horizontal pipe

An experimental and analytical studies on the condensation-induced water hammer (CIWH) for steam-water countercurrent flow in a nearly horizontal circular pipe have been performed. A total of 17 experimental data for the onset of slugging, which is assumed to be the precursor of the CIWH, have been obtained for various flow rates of water. Incorporating the most recent correlations of interfacial heat transfer and friction factor developed for a circular geometry and using an improved criterion of transition from stratified to a slug flow, two existing analytical models to predict lower and upper bounds for CIWH have been upgraded. Applicability of the present as well as existing CIWH models has been tested by comparison with two sets of CIWH data. The result of this comparison shows that the applicability of the present as well as existing models is reasonably good. Based on the present models for CIWH, a computer code entitled as ‘KAIST-CIWH’ has been developed and sample guide charts to find CIWH free regions for a given combination of major flow parameters in a long horizontal pipe have been presented along with the results of parametric studies of major parameters (D, P, T_f,in, and L/D) on the critical inlet water flow rate (W_f,in)_crit for both lower and upper bounds. In addition, two simple formulas for lower and upper bounds that can be used in an emergency for quick results have been presented.     

Energy Dependence of MeV He+ Ion-Induced Re-Emission of Hydrogen Isotopes Implanted into Graphite

The energy dependence of MeV He⁺ ion-induced re-emission of hydrogen isotopes (H and D) implanted into graphite has been measured by means of the elastic recoil detection (ERD) technique in order to clarify the collision process for the ion-induced detrapping. The experimental re-emission profiles have been analyzed by solving the mass balance equations, in which the ion-induced detrapping cross section σ _d and the rate constants of the retrapping Σ ^T and local molecular recombination K between an activated hydrogen atom and a trapped one are taken into account. The values of σ _d and K/Σ _T have been determined from the best-fit analytical solution to the experimental re-emission profiles. It has been found that the average values of σ _d and K/Σ _T for H are twice as large as those for D, which is the so-called isotope effect.

It has been shown that the experimental values of σ _d and their energy dependence agree well with the theoretical ones, which are calculated using the power-law approximations for Thomas-Fermi potential, on the assumption that the ion-induced detrapping of hydrogen isotopes takes place due to elastic displacement collisions with energetic carbon recoils produced by incident MeV He⁺ ions.     

Structural and Electrochemical Studies on Uranium(VI) Nitrato Complex with n-Octyl(phenyl)-N,N-Diisobutylcarbamoylmethylphosphine Oxide in Non-aqueous Solvents

The structure of uranyl nitrato complex with CMPO [n-Octyl(phenyl)-N,N-diisobutylcarbamoylmethylphosphine oxide] in solid state and in non-aqueous solvents without containing free CR/IPO has been studied by using IR spectrophotometer, ¹³C- and ³¹P-NMR. The carbonyl(vcO) and phosphoryl(vpO) stretching bands of coordinated CMPO were observed at lower wavenumber than the corresponding bands of free CMPO in both the states. The ¹³C and ³¹P peaks assigned to the carbonyl carbon and phosphoryl phosphine of coordinated CMPO was detected in the lower field than that of free CMPO. From these results, it was concluded that the uranyl nitrato complex with CMPO in both the states has the structure with two nitrate and one CMPO coordinated as bidentate in the equatorial plane of uranyl ion, i.e., UO₂(NO₃)₂·CMPO. Furthermore, the electrochemical studies of UO₂(NO₃)₂·CMPO complex in CH₃CN have been carried out using cyclic and normal pulse voltammetric methods. It was found that the UO₂(NO₃)₂·CMPO complex is reduced to U(V) complex at around ?1.22V vs. Fc/Fc⁺ (ferrocene/ferrocenium) and that the resulting reductant is oxidized to U(VI) at around +0.04V vs. Fc/Fc⁺.     

Measurements of Natural Frequency and Damping Constant of Single Steam Bubble Oscillating in Water

The natural frequency f_n and damping constant δ of a bubble in liquid have been determined by observing the resonance of the bubble to forced oscillation. The bubble was retained under a rigid plate horizontal disk, and the oscillation was applied by underwater speaker. The applied frequency f was kept constant while letting the bubble increase its volume and vary its radius R. Bubble resonance was detected by observing wrinkles appearing on the bubble due to surface waves. Resonance curves relating the amplitude of bubble radius variation to the intensity of applied oscillation is derived theoretically.

Good agreement was seen between the data obtained from experiment and the theoretically derived resonance curves at test to the validity of the method proposed of determining fⁿ and δ from bubble resonance. The values of δ and of the resonant bubble radius R_o of large steam bubbles (8.5 mm>R>11.5 mm) in water were determined at f =270, 290 and 358 Hz. The results support the assumption that for large bubbles the value of f_n is little influenced by the exchange of mass between liquid and gaseous phases through evaporation and condensation accompanying bubble pressure oscillation. On the other hand, δ is found to be one order of magnitude higher than calculated for steam bubbles without taking into evaporation and condensation the interphase exchange of mass. The effect brought on δ by the interphase mass exchange can be taken into account by adding a new constant δ_pn to the terms constituting the total damping constant.     

Seismic response analysis of embedded structure at Hualien, Taiwan

Predictive and correlative analyses of the forces vibration tests (‘FVT’ for short, hereafter:) and seismic response of the large-scale embedded structure were performed as one of the analytical phases of an international large-scale seismic test (LSST) program (Tang et al., 1991) at Hualien, Taiwan. Consequently, the following was clarified; (1) FVT analysis using unified ground model (UMFVT2) predicted the fundamental system frequency (ƒ₀) about 20% higher than the test. (2) After careful investigation on several items cited as the presumed causes of (ƒ₀) discrepancy between the test and the prediction, it was attributed to the V_s of the backfill, and best correlated ground model (BCFVT2) was formed, based on it. (3) Seismic response analysis using BCFVT2 brought a bit better agreement with the observation than using UMFVT2, but from another viewpoint, both analysis results agreed fairly well with the observation, indicating that backfill V_s does not affect seismic response so much as during FVT.