一维特征线法中子输运程序开发及验证

为探讨两维/一维综合法堆芯分析方法,本文基于特征线法研制了一维中子输运程序--PEACH-1D.不同于通常的平源近似特征线方法,PEACH-1D可对子区的中子源项作线性近似;程序运用指数函数插值表和渐近源外推技术来加速计算过程.相关数值结果表明,PEACH-1D具有很高的计算精度和效率,线性源近似的特征线法具备处理较粗网格的能力,值得推广.     

基于CAD技术的特征线中子输运计算程序开发

特征线方法(Method of Characteristics,MOC)能否应用于复杂几何关键在于能否将特征线方法与有效的几何处理方法结合起来。本文在菱形差分特征线理论基础上,基于FDS团队自主研发的核与辐射输运计算自动建模软件MCAM的几何处理引擎,研发了基于CAD技术的特征线中子输运计算程序,并利用相关基准例题对程序进行了数值验证,其结果与参考值吻合良好,表明本文方法和程序的可行性、正确性与可靠性。     

Transmission probability method based on triangle meshes for solving unstructured geometry neutron transport problem

In the advanced reactor, the fuel assembly or core with unstructured geometry is frequently used and for calculating its fuel assembly, the transmission probability method (TPM) has been used widely. However, the rectangle or hexagon meshes are mainly used in the TPM codes for the normal core structure. The triangle meshes are most useful for expressing the complicated unstructured geometry. Even though finite element method and Monte Carlo method is very good at solving unstructured geometry problem, they are very time consuming. So we developed the TPM code based on the triangle meshes. The TPM code based on the triangle meshes was applied to the hybrid fuel geometry, and compared with the results of the MCNP code and other codes. The results of comparison were consistent with each other. The TPM with triangle meshes would thus be expected to be able to apply to the two-dimensional arbitrary fuel assembly.     

A new three-dimensional method of characteristics for the neutron transport calculation

The method of characteristics (MOC) is a very flexible and effective method for the neutron transport calculation in a complex geometry. It has been well developed in two-dimensional geometries but meets serious difficulty in three-dimensional geometries because of the requirements of large computer memory and long computational time. Due to the demand related to the advanced reactor design for complex geometries, an efficient and flexible three-dimensional MOC is needed. This paper presents a modular ray tracing technique to reduce the amount of the ray tracing data and consequently reduce the memory. In this method, the object geometry is dissected into many cuboid cells by a background mesh. Typical geometric cells are picked out and ray traced, and only the ray tracing data in these typical cells is stored. Furthermore, the Coarse Mesh Finite Difference (CMFD) acceleration method is employed to save computing time. Numerical results demonstrate that the modular ray tracing technique can significantly reduce the amount of ray tracing data, and the CMFD acceleration is effective in shorting the computing time.     

Spherical harmonics method for neutron transport equation based on unstructured-meshes

Based on a new second-order neutron transport equation, self-adjoint angular flux (SAAF) equation, the spherical harmonics (PN) method for neutron transport equation on unstructured-meshes is derived. The spherical harmonics function is used to expand the angular flux. A set of differential equations about the spatial variable, which are coupled with each other, can be obtained. They are solved iteratively by using the finite element method on unstructured-meshes. A two-dimension transport calculation program is coded according to the model. The numerical results of some benchmark problems demonstrate that this method can give high precision results and avoid the ray effect very well.     

NODHEX: A 2-D diffusion code based on the nodal expansion method in hexagonal geometry and its validation

A 2-D neutron diffusion theory computer code NODHEX for hexagonal geometry has been developed. The nodal algorithm is based on the nodal expansion method proposed by Lawrence. The nodal equation formulation is accomplished by using a second-order polynomial approximation for the flux. The equations include additional terms of discontinuity which occur in the expression of transverse leakage for the hexagonal geometry, unlike the nodal equations (using a second-order polynomial approximation) formulated by Lawrence. The code has been validated by comparing its predictions for the SNR-300 and VVER-1000 benchmarks with the results of other standard computer codes like DIF3D and SNAP. The inclusion of the additional terms of discontinuity is found to improve the predictions relative to Lawrence's predictions, though the same second-order polynomial approximation was used for solving the nodal equations.     

CALIPSO—A computer code for the calculation of the thermodynamics, fluiddynamics and geometry changes following pin failure

The computer code CALIPSO calculates the thermodynamics and fluid-dynamics of fuel, fission gas and coolant as well as changes in geometry subsequent to pin failure in an anticipated liquid-metal fast breeder reactor (LMFBR) accident. In the documented version, CALIPSO is well suited for the analysis of the out-of pile SIMBATH experiments carried out at Kernforschungszentrum Karlsruhe (KfK) which simulate the above-mentioned accident with thermite technology. In two-dimensional geometry the fuel pin and its associated coolant channel, initially separated by the fuel cladding are treated as a single fluid domain. The conservation equations of mass, momentum and energy are solved separately for each component. The transient evolution of the temperature profile in the cladding is modeled in detail, thus permitting the analysis of various phase transition processes (melting, freezing and clad failure propagation). The coolant channel has a variable cross section and it is surrounded by an outer channel wall for single pin experiment analysis. Axially the coolant channel is connected to a simplified model of the whole sodium loop.     

Solution of the neutron transport problem with anisotropic scattering in cylindrical geometry by the decomposition method

An analytical solution has been obtained for the one-speed stationary neutron transport problem, in an infinitely long cylinder with anisotropic scattering by the decomposition method. Series expansions of the angular flux distribution are proposed in terms of suitably constructed functions, recursively obtainable from the isotropic solution, to take into account anisotropy. As for the isotropic problem, an accurate closed-form solution was chosen for the problem with internal source and constant incident radiation, obtained from an integral transformation technique and the F_N method.     

基于离散纵标法的三维耦合燃耗与活化计算方法的发展

燃耗与活化分析在反应堆的燃耗管理与辐射屏蔽设计分析中起关键性的作用.基于一维、二维的输运程序的燃耗与活化分析方法难以解决复杂几何和强烈各向异性散射问题.本文通过耦合三维离散纵标(SN)方法粒子输运程序以及指数欧拉法活化计算程序,发展了快速精确的三维耦合燃耗与活化计算方法.该方法考虑了共振自屏效应动态修正,并采用重要核素...     

A spherical harmonics—Finite element discretization of the self-adjoint angular flux neutron transport equation

The spherical harmonics (P_N) method is widely used in solving the neutron transport equation, but it has some disadvantages. One of them comes from the complexity of the P_N equations. Another one comes from the difficulty of dealing with the vacuum boundary condition exactly. In this paper, the P_N method is applied to the self-adjoint angular flux (SAAF) neutron transport equation and a set of P_N moments equations coupled with each other are obtained. An iterative method is utilized to decouple them and solve them moment by moment. The corresponding vacuum boundary condition is derived based on the Marshak boundary condition. The spatial variables are discretized on unstructured-meshes by use of the finite element method (FEM). The numerical results of several problems demonstrate that this method can provide high precision results and avoid the ray effect, which appears in the discrete ordinate (S_N) method, with relatively high computational efficiency.     

A finite element method for neutron transport—VI. Upper and lower bounds for local characteristics of solutions

Finite element methods for neutron transport are being developed because they have the potential to achieve the full geometrical flexibility of the Monte Carlo method, and they are faster in computing global solutions. It is shown that the finite element method also shares with Monte Carlo the capability to bracket local characteristics of a solution, such as the reaction rate for a small locality. The bracketing bounds for the Monte Carlo method have a statistical error, whereas these bounds are rigorous for the finite element method. The latter bounds for a locality of a system are obtained by a bi-variational method with the aid of an associated system.For cell problems very tight bounds can be computed, but in deep-penetration problems for shields there are some difficulties to be overcome. Reasons are advanced for the difficulties.     

A multigroup finite-element solution of the neutron transport equation—I: X-Y geometry

The result of extending a variational finite element method of solving the neutron transport equation, to energy dependence, is reported. Detailed results are given, in the form of tables and graphs, of P₁ and higher-order transport solutions to a number of benchmark problems in X-Y geometry. The accuracy and flexibility of the method are demonstrated. Some suggestions are made for the future development of the computer implementation of the method.     

3D neutron diffusion computational code based on GFEM with unstructured tetrahedron elements: A comparative study for linear and quadratic approximations

In the present study, the comparison between the results obtained from the linear and quadratic approximations of the Galerkin Finite Element Method (GFEM) for neutronic reactor core calculation was reported. The sensitivity analysis of the calculated neutron multiplication factor, neutron flux and power distributions in the reactor core vs. the number of the unstructured tetrahedron elements and order of the considered shape function was performed. The cost of the performed calculation using linear and quadratic approximation was compared through the calculation of the FOM. The neutronic core calculation was performed for both rectangular and hexagonal geometries. Both the criticality and fixed source calculations were done using the developed GFEM-3D computational code. An acceptable accuracy with low computational cost is the main advantage of applying the unstructured tetrahedron elements. The generated unstructured tetrahedron elements with Gambit software were used in the GFEM-3D computational code via a developed interface. The criticality calculation was benchmarked against the valid data for IAEA-3D and VVER-1000 benchmark problems. Also, the neutron fixed source calculation was validated through the comparison with the similar computational code. The results show that the accuracy of the calculation for the both linear and quadratic approximations improves vs. the number of elements. Quadratic approximation gives acceptable results for almost all considered number of the elements, while the results obtained from the linear approximation have good accuracy for only high number of the elements.     

A finite element method for neutron transport—III. Two-dimensional one-group test problems

The even-parity transport equation for an isotropic scattering medium is applied using a maximum principle to determine the angular flux in a square lattice cell with a cylindrical fuel element, a square isotropic source in a corner of an absorbing shield and a dog-leg duct through an absorbing shield. The finite element solutions obtained are compared with an exact solution for the cell, and benchmark results for the square source and duct problem. The accuracies achieved for the fluxes in the cell problem are everywhere better than 0.75% and high accuracy is achieved for the other test problems. The linear elements, used for the spatial dependence of the angular flux in conjunction with a spherical harmonic expansion for the angular dependence, provide a flexible means of treating awkward geometries. At present the equations are assembled and solved using the UNCLE code, which uses direct Gaussian elimination. This process limits the speed of the finite element method to about 1/3 of the Fletcher finite difference spherical harmonics method for the square source problem. This latter method is, however, limited to systems with geometries defined by co-ordinate surfaces, whereas the finite element method can be used for any region that can be triangulated.     

A multi group finite-element solution of the neutron transport equation—II: R-Z geometry

The extension of a variational finite-element method of solving the neutron transport equation, to include multigroup-energy dependence in R-Z geometry, is evaluated. The method is implemented in a computer program called felicit. The solutions obtained by means of felicit to a number of axisymmetric test problems are given in numerous tables and graphs. A comparison is made between felicit, exact solutions and solutions obtained by other transport techniques. The ability of the method to handle problems characterized by difficult geometries is demonstrated; in particular by considering a fixed-source problem in a model Tokamak configuration.     

Spectral Green's function method for neutron transport: isotropic,forward, and backward scattering in 1-D slab geometry

Numerical solutions of one-group and one-dimensional neutron transport problems are reported for isotropic, forward, and backward scattering. Numerical solution is carried out by using two different methods, the SGF “ spectral Green's function ” method and the DD “ diamond-difference” scheme, to test the accuracy of the results. Results of cell-edge scalar fluxes obtained for both methods are presented in the tables.     

Development and validation of the code COUPLE3.0 for the coupled analysis of neutron transport and burnup in ADS

The analysis of the fuel depletion behavior is critical for maintaining the safety of accelerator-driven subcritical systems(ADSs). The code COUPLE2.0 coupling 3-D neutron transport and point burnup calculation was developed by Tsinghua University. A Monte Carlo method is used for the neutron transport analysis, and the burnup calculation is based on a deterministic method. The code can be used for the analysis of targets coupled with a reactor in ADSs. In response to additional ADS analysis requirements at the Institute of Modern Physics at the Chinese Academy of Sciences, the COUPLE3.0 version was developed to include the new functions of(1) a module for the calculation of proton irradiation for the analysis of cumulative behavior using the residual radionuclide operating history,(2) a fixed-flux radiation module for hazard assessment and analysis of the burnable poison, and(3) a module for multi-kernel parallel calculation, which improves the radionuclide replacement for the burnup analysis to balance the precision level and computational efficiency of the program. This paper introduces thevalidation of the COUPLE3.0 code using a fast reactor benchmark and ADS benchmark calculations. Moreover,the proton irradiation module was verified by a comparison with the analytic method of calculating the210 Po accumulation results. The results demonstrate that COUPLE3.0 is suitable for the analysis of neutron transport and the burnup of nuclides for ADSs.     

基于离散纵标输运计算方法的三维燃耗程序发展研究

为了精确描述和分析具有强烈各向异性中子注量率空间分布的反应堆燃耗过程,本文实现了三维SN 输运计算与燃耗计算的耦合,发展了相应的三维输运燃耗耦合计算程序.该程序系统采用接口程序自动耦合三维SN输运计算程序和同位素燃耗计算程序的方法实现对三维中子学计算模型的精细燃耗计算,获得燃料同位素成分、燃耗反应性、中子注量率空间分布等参数随燃耗时间的变化量.采用IAEA 基准校核例题对程序系统进行了校核,计算结果初步证明了所开发的三维燃耗程序系统的正确性.     

ARARAT — A computer code for thermal design of cooling towers

A computer program is presented for thermal and hydraulic design of cooling towers. Options have been provided for the evaluation of cooling tower size and performance curves by applying a basic physical model of heat and mass transfer.The solution is conducted by multiple iteration, in which iteration loops are mutually inclusive. Both film and spray-filled cooling towers are considered with either induced or natural air circulation.Numerical solutions are presented to a number of natural draft cooling towers which serve present nuclear or conventional power plants.