Comparison of Two Types of Ideal Cascades for Asymmetric Separation Processes

The energy spectra of γ-rays in water, concrete, iron and lead are calculated by PALLAS- PL, SP-Br code for the plane perpendicular incidence. The calculation takes into account both annihilation and bremsstrahlung photons as well as Compton scattered ones as the secondary source.

Comparisons of energy spectra calculated by PALLAS were made with those of the moments method in water, iron and lead. In the PALLAS calculation the bremsstrahlung is neglected for the source energy of 6 MeV in iron because the influence of the bremsstrahlung on the energy spectrum is considered to increase for high energy photons. While for the case of inclusion of the bremsstrahlung source, a comparison of PALLAS calculations with experiments is made in transmitted dose through lead for a plane perpendicular 8-MeV source, resulting in good agreement.

Several examples of the calculated energy spectra in each material are presented at penetration distances of 0.5-, 1.0-, 2.0-, 4.0-, 7.0-, 10.0-, 20.0- and 40.0-mfp in 43 mfp depth for source energies of 0.1-     

Numerical Analysis of Separative Power of Isotope Centrifuges, (II)

It is found from numerical analysis that a strong influence is exerted on the separative efficiency of centrifuges by the thermal convection arising from the temperature difference prevailing between the end plates of a centrifuge drum—known as “Ekman suction”. The numerical method previously developed by Nakayama & Torii is used to compute the distributions of concentration resulting from considerations of both thermal convection and forced flow.

The effect of Ekman suction is represented by the parameter λ_E(≡(a²√E _ρpsV?T)/(16 lρDT₀)), different values of which were adopted in the calculations, as were other parameters such as λ(≡G_F/(?ηlρpD), G_F: feed rate) for the forced flow and θ representing the cut. The separative efficiency of an exemplified counter-flow type centrifuge is found to reach 58% when λ_e≒0.7, λ≒1.0 and θ≒O.3, with a product port radius r _p= 0.5.

It is also shown that the thermal convection in the Stewartson layer near the side wall of a centrifuge drum affects the separative, efficiency to relatively small but not negligible extent.     

Basic Characteristics of Centrifuges, (IV)

A method of numerically solving the convection-diffusion equation is presented for a binary isotopie gas mixture in the axisymmetric velocity field. A modified Newton's method is employed to perform the numerical integration without the assumptions that the pressure can be estimated from the rigid rotation model and the temperature of gas is uniform. A suitable form of the finite difference equation gives a computationally stable integration with reasonable representation of the molar concentration distribution of isotopie molecules in a rotating cylinder. The method includes a Gaussian elimination procedure which consists of the transformation of the Jacobian matrix to a triangular matrix followed by the backward elimination.

Computations are made on UF₆ gas in various centrifuges which have the openings for feed, product and waste on the end plates. Discussions are also presented on gas flows and separative efficiencies for the centrifuges which have baffle plates, skirting plates and bellows.     

Numerical Analysis of Separative Power of Isotope Centrifuges,(I)

A numerical method was developed to calculate the distribution of concentration of ²³⁵UF₆ in the rotating cylinder of a centrifuge. Satisfactory convergence was obtained by employing the formulation of convective terms devised for the computation of high Reynolds number flow. Moreover, the pressure diffusion term was linearized and approximated by a constant value, which significantly reduced the number of cases to be run on a computer. The results of numerical analysis for a centrifuge of counter-flow type are shown, and the effect brought upon the separative efficiency by changes in various parameters is discussed. The results of the present analysis are compared with those obtained from the existing theory, and the reasons for the discrepancy between the two results are explained. Finally, it is shown that the results of the numerical analysis agree well with the experimental data obtained previously by Beams et al.     

Basic Characteristics of Centrifuges, (III)

A method of numerically integrating the Navier-Stokes equations is presented for axisymmetric compressible flows. A modified Newton's method is employed to determine the steady motion of gas in a rotating cylinder without the use of a time-consuming marching process with respect to time. A suitable form of the finite difference equations gives a computationally-stable integration with reasonable representation of the spatial characteristics of the flow. The method includes a Gaussian elimination procedure which consists of the transformation of the Jacobian matrix to a triangular matrix followed by the backward substitution. By using an auxiliary constant matrix algorithm, the method gives the solution within reasonably acceptable computation time.

As an example of the method, some features of solutions are presented for the steady flow of UF₆ gas in the centrifuges which have the openings for feed and withdrawal on the end plates.     

Optimum Cut of Separating Element as a Function of Total Separation Factor

Calculation of one of the SIMBATH experiments was performed using the SIMMER-II code. The experiments were intended to simulate the fuel pin disintegration, the molten materials relocation and following materials redistribution that could occur during core disruptive accidents assumed in fast breeder reactors. The calculation by SIMMER-II showed that the incorporated step-wise fuel pin disintegration model and the modified particle jamming model were capable of reproducing the course of materials relocation within the identified ranges of the parameters which governed the blockages formation, i.e. the characteristic radius of solid particles jamming and/or sieving out in the flow and the effective particle viscosity. In particular the final materials redistribution calculated by SIMMER-II very well reproduced the experiment. This fact made it possible to interpret theoretically the mechanisms of flow blockages formation and related materials redistribution.     

New Proposal for a Gas Centrifuge Rotating Differentially, (II)

Dry oxidation of spent ion exchange resin is one of the most effective methods to reduce radioactive waste volume and also to make the final waste form more stable. Thermo-gravimetric measurements were performed using cation exchange resins with or without Fe in either an ionized or unionized form to clarify the effect of metallic impurities on the resin oxidation.

The presence of an ionized Fe resulted in a considerable increase in the reaction rate constant, indicating that the Fe functioned as a catalyst. On the other hand, the unionized Fe showed no catalytic activity. Measurement of EPMA revealed that the ionized Fe was distributed uniformly throughout the resin particles, while the unionized one was distributed only on the surface of the resin particle.

Catalytic activity increased with ionized Fe concentration up to 0.5 mmol-Fe/g-dry resin, above which the activity tended to decrease. The X-ray diffraction study attributed this to Fe coagulation in the resin particle. Kinetic models for solid-gas reactions were also applied to the resin oxidation to evaluate catalytic activity quantitatively.     

Separation of Uranium Isotope by Plasma Centrifuge

A method of centrifugal separation of isotopes by electromagnetic means is presented. The principle proposed utilizes electromagnetic acceleration by the interaction between an electric current in a slightly ionized gas and an external magnetic field. The analysis shows that an azimuthal flow of 2.6 km/sec can be realized with a magnetic field of 200 gauss and an electric current of 1.5kA. The resulting centrifugal force is large enough to permit realization of a more compact concentration cascade than the conventional mechanical centrifuge.     

Theoretical Research on Gas-Centrifugal Separation for Uranium Enrichment

Studies are reviewed on the uranium hexafluoride gas isotope separation by centrifugation. A flow field in a centrifuge rotor is numerically determined by solving flow equations for compressible gas in strong rotation. The diffusion equation is also solved to determine the molar concentration distribution of the lighter isotope corresponding to the obtained flow field. A modified version of the Newton method is adopted to get the full solution in static state for these nonlinear equations.

Some numerical results are shown and compared with the experimental data made by Beams et al. and Zippe, and found to be in good agreement.     

Pressure Recovery in Diffuser for Discharge Flows from Gas Centrifuges Rotating at High Mach Numbers

This paper deals with the irradiation effects on the thermal shock resistance Δ = σ_tk/Eα (σ_t : tensile strength, k: thermal conductivity, E: Young's modulus, α: thermal expansivity) and the thermal shock fracture toughness ?=K_Ick/Eα (K_Ic : fracture toughness value of mode I) in addition to other mechanical properties such as the diametral compressive strength and fracture toughness of two kinds of near isotropic graphite neutron irradiated at 750～1,000°C to a dose of (1.1 ～ 1.5)10²¹ n/cm² (>29 fJ). One of the graphite specimen is an isostatically molded graphite IG-11 with fine grain petroleum coke and the other is a binderless molded graphite HCB-18 which was prepared using mesophase pitch carbon with very fine grain size. These measurements are carried out by means of disk testing method developed by us. Results show that both the thermal shock resistance and the thermal shock fracture toughness of the two kinds of graphite after irradiation decrease considerably in contrast with increasing trends of the usual mechanical strengths.     

Si同位素分离单机供料流量的优化

介绍了二元和多组分同位素混合物的分离功率表达式。以SiHCl3（硅氯仿）为工作气体,在分离装置上进行单机分离实验,得到了供料流量与各分离性能参数之间的关系。结果表明,当供料流量在20克每小时附近时,单机分离性能最佳。     

Numerical Analysis of Flow of Binary Gas Mixture with Large Mass Difference in Rotating Cylinder

A numerical analysis is presented of the flow of a binary gas mixture of UF₆ and N₂ in a rotating cylinder. The equations for flow and the diffusion equation are solved simultaneously for the binary mixture in static state, taking account of viscosity and compressibility, using a modified version of the Newton method, commonly applied to rotating fluid flow. An appropriate model is assumed for a centrifuge provided with scoop and baffle plate. Computations are carried out with the N₂ to UF₆ mixing ratio adopted as parameter.

At small values of mixing ratio, the pressure distribution of UF_C in the radial direction is little influenced by the presence of N₂. The N₂ pressure distribution is close to that at equilibrium of N₂ itself in zones inside cylinder of relatively slow gas travel. In the zones of faster gas travel, conversely, the N₂ pressure distribution deviates from that of its equilibrium and approaches that of UF₆.

The pressure distribution of UF₆, on the other hand, is strongly influenced by the presence of N₂ when the mixing ratio is above 0.2. The resulting radial distribution along a section close to the exit scoop presents a peculiar concave configulation with a shallow valley appearing in the intermediate zone, and this significantly lowers the concentration of UF₆ extracted through the scoop. The separation efficiency obtained between the two gases is extremely low, but this is due to the mass flow rate having been chosen to optimize the separation efficiency between UF₆ isotopes.     

Use of Neural Network for the Simulation of a Gas Centrifuge

The prediction by a mathematical model of the separation of uranium isotopes using a gas centrifuge process is a hard task. The gas motion can be described by analytical or numerical solutions of the system of equations defined by the equation of continuity, the Navier-Stokes equation and the equation of energy. However, these calculations cannot be performed for actual centrifuges.

Neural networks are an alternative for modelling complex problems that show too many difficulties to be solved by phenomenological models.

The authors propose the use of neural networks for the simulation and prevision of the separative and operational parameters of a gas centrifuge separating uranium isotopes. The results from the uranium separation experiments (Zippe data) are compiled and presented to the neural network in the learning and testing processes. The prediction using the neural network model shows good agreement with the experimental data.     

Additive Property of Separative Power

A separative power of a separating element, whose heads and tails separation factors are α and β is expressed by φ _b (α, β)= [α(β-1)1n α-(alpha;-1) in β]/(α β-1) for the unit flow of the desired material and φ _a (α, β) (≡ φ _b (β, α) for that of undesired material. The additive properties of the functions φ _b and (φ _a were demonstrated by calculations of various types of ideal cascades, but the origin of the property is not obvious. The present study has furnished the mathematical basis of the additivity based on the special functional equation. First, for symmetric processes (α, β), the functional equation which describes the function representing the quality of separation f(α, α) concerning the desired material was obtained and solved to give the functional form of f(α, α,). The result was extented to the function f(α, β) representing the quality of asymmetric separation (α, ≠ β). The derived function f(α, β) was demonstrated to be equal to φb(α, β)and it was verified that functions φb(α, β) and φ _a (α, β) have the additive property in themselves.     

以七氟丙烷为介质离心分离碳同位素

以七氟丙烷（C₃HF₇）为分离介质,通过气体离心法研究碳同位素的分离制备。利用国产气体离心机开展单机离心分离实验,通过气体质谱仪分析C₃HF₇样品,计算不同工况条件下的分离系数和单机分离功率,分离系数可达1.12。在单机实验结果的基础上,采用相对丰度匹配级联（MARC）模型,对富集¹³C的生产进行级联计算。选取分离功率最大的实验工况作为计算参数,通过三次级数分别为30、60、75的级联分离,可以将¹³C的丰度从天然丰度富集至30%以上。综合考虑单机实验和级联计算的结果,以C₃HF₇为介质离心分离碳同位素可行。     

气体扩散法分离二氧化碳实验研究

随着碳13呼气检测实验的推广和普及,碳13同位素产品的市场需求呈上升趋势.为探索碳13同位素的工业化分离方法,开展以二氧化碳为介质分离碳同位素的气体扩散分离实验研究.根据二氧化碳的平均自由程,使用平均孔径55～65 nm的有机高分子多孔膜作为分离膜,并开发了单级分离装置.通过单级扩散分离实验,探究分离膜层数和膜前压强对...     

Simple Formulae for Analyzing Matched Abundance Ratio Cascade with Constant Separation Factors for Multi-Component Isotope Separation

After the ratification of START-I the question of how to dispose safely and effectively of excess weapons plutonium, of which there is estimated to be about 501 in the USA and 501 in Russia, has become an important international issue. One of the most likely options is the proposal to use the excess weapons plutonium as MOX fuel in commercial LWRs. This paper evaluates fuel material flow and fuel cycle costs when weapons-grade plutonium is mixed with reactor-grade plutonium to fabricate the MOX fuel and to be recycled in Japanese commercial LWRs.

The results show the MOX fuel using weapons- and reactor-grade mixed plutonium facilitates multiple recycling, because the weapons-grade plutonium improves the isotopic composition of the MOX fuel working like a “purifier” of the degraded recycled plutonium. And they also indicate that it might be an economically realistic method in Japan to use the excess weapons plutonium in the commercial LWRs as MOX fuel if the fabrication cost and the reprocessing cost of MOX fuel are moderate compared to those of UO₂ fuel, assuming the MOX powder using weapons-grade plutonium would be provided free of charge.     

气体扩散法生产硼-10同位素的经济性分析

10 B同位素在中子屏蔽和探测中有重要的作用,目前大规模生产硼同位素的方法主要是化学交换精馏法.随着10 B市场需求的增加,在国产化取代进口的背景趋势下,探索硼同位素分离方法的优化和创新有重要意义.本研究分析了气体扩散法用于10 B同位素分离的经济性,并根据市场实际情况估算产品成本.首先分析以B F3为介质的单级扩散分...     

Pressure Recovery in a Diffuser for Gas Centrifuge

The pressure recovery of supersonic flow at very low density was studied in a vane-island type diffuser for gas centrifuge.

A tester of diffuser with a rapidly rotating cylinder was used in experiments. Wall static pressures were measured at many points in the diffuser to observe the static pressure distribution. The change of pressure distribution with back pressure and the effect of flow rate were investigated. Pressure distribution showed that the pressure recovery occurred in the converging section. The pressure ratio increased linearly with the back pressure in this experimental range and the effect of flow rate was not observed.

A numerical analysis of the pressure recovery in the channel section of the diffuser was made by applying the finite difference method to the slender-channel equations. The pressure distribution obtained in experiments could be explained as a result of supersonic compression with reverse flow.