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The evaluation of multigroup constants in reactor calculations depends on several parameters. One of these parameters is the Dancoff factor which is used for calculating the resonance integral and flux depression in the resonance region in heterogeneous systems. In the current paper, a computer program (MCDAN-3D) is developed for calculating three dimensional black and gray Dancoff coefficients, based on Monte Carlo, escape probability and neutron free flight methods. The developed program is capable to calculate the Dancoff factor for an arbitrary arrangement of fuel and moderator pebbles. Moreover this program can simulate fuels with homogeneous and heterogeneous compositions. It might generate the position of Triso particles in fuel pebbles randomly as well. It could calculate the black and gray Dancoff coefficients since fuel region might have different cross sections. Finally, the effects of clad and moderator are considered and the sensitivity of Dancoff factor with fuels arrangement variation, number of TRISO particles and neutron energy has been studied. [ABSTRACT FROM AUTHOR]

Abstract: Various methods for solving the forward/adjoint equation in hexagonal and rectangular geometries are known in the literatures. In this paper, the solution of multigroup forward/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of equations is based on Galerkin FEM (GFEM) using unstructured triangle elements. Calculations are performed for both linear and quadratic approximations of the shape function; based on which results are compared. Using power iteration method for the forward and adjoint calculations, the forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for IAEA-2D, BIBLIS-2D and IAEA-PWR benchmark problems. Convergence rate of GFEM in linear and quadratic approximations of the shape function are calculated and results are quantitatively compared. A sensitivity analysis of the calculations to the number and arrangement of elements has been performed. [Copyright &y& Elsevier]

Abstract: In the present study, the neutron noise, i.e. the stationary fluctuation of the neutron flux around its mean value, is calculated in 2-group forward and adjoint diffusion theory for both hexagonal and rectangular reactor cores. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of equations is based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured triangle elements. Using power iteration method, forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for BIBLIS-2D and IAEA-2D benchmark problems and DONJON computer code. The dynamic calculations are performed in the frequency domain which leads to reducing the dimension of the variable space of the noise equations. The forward/adjoint noise in two energy group is obtained by assuming the neutron noise source as an absorber of variable strength type. The neutron noise induced by a vibrating absorber type of noise source is also obtained from the calculated adjoint Green''s function. Comparison of the calculated neutron noise at zero frequency with the results of static calculation, and utilizing the results of adjoint noise calculations are two different procedures to validate the neutron noise calculations. [Copyright &y& Elsevier]

Abstract: An improvement to the Direct Discrete Method (DDM), also known as the Cell Method, has been discussed. The improvement is based on a duality theorem between the primal and dual complexes. Also, the analog counterpart of the Integral operator has been derived in this paper. The multi-group neutron diffusion is then derived, directly in a discrete algebraic form, according to this procedure. A numerical example has shown that this method would yield a high order of convergence (approximately 4.6) if its parameters are adjusted suitably. Finally, the method is applied to the 2D IAEA benchmark problem, and has shown to yield accurate solutions with a reasonably low number of unknowns. [Copyright &y& Elsevier]

• Development of a Computer code for safety analysis of a nuclear reactor. • The Code works based on nodal discretization using MCNPX code. • The restrictions of previous methods in transient analysis have been removed. • The Code is capable to simulate the systems with time-varying geometry and cross sections. • Independency of the method of the code to the node size. This paper proposes a new method for solving the time-dependent neutron transport equation based on nodal discretization using the MCNPX code. Most valid nodal codes are based on the diffusion theory with differences in approximating the leakage term until now. However, the Monte Carlo (MC) method is able to estimate transport parameters without approximations usual in diffusion method. Therefore, improving the nodal approach via the MC techniques can substantially reduce the errors caused by diffusion approximations. In the proposed method, the reactor core is divided into nodes of arbitrary dimensions, and all terms of the transport equation e.g. interaction rates and leakage ratio are estimated using MCNPX. They are then employed within the time-dependent neutron transport equation for each node independently to compute the neutron population. Based on this approach, a time-dependent code namely MCNP-NOD (MCNPX code based on a NODal discretization) was developed for solving time-dependent transport equation in an arbitrary geometry considering feed backs. The MCNP-NOD is able to simulate multi-group processes using appropriate libraries. Several test problems are examined to evaluate the method. [ABSTRACT FROM AUTHOR]

Power reactor noise analysis is one of the most powerful tools in online monitoring and diagnostics of nuclear power reactors. Unfortunately, since such an analysis belongs to the non-linear “parametric excitation” realm, its theoretical aspects and relations have been mostly carried out after linearization. In this paper a general framework, i.e. the Ladder Expansion Method, is developed to convert such equations to a series of coupled linear equations, up to any desired accuracy. This method is then applied to the single mode random fluctuations of the absorption cross sections in a power reactor which is modelled by the multigroup diffusion equation with multiple delayed neutron groups. A system of coupled pseudo steady state diffusion equations has been derived as the result. The procedure of numerically solving such a system, using the Finite Element Method is described and the previously reported GFEM code, which is a Galerkin FEM based diffusion solver and Linear Power Reactor Noise analyzer for two dimensional geometries, has been generalized to accommodate the LEM to evaluate the higher order power reactor noise moments. Use of these moments in the Power Spectral Density of the flux and its derivatives, such as the detection rate, has shown that the value of the PSD at the main harmonic of the fluctuation deviates with the predictions of the conventional LPRN method. Moreover, the generation of super-harmonic modes in the PSD of the neutron flux distribution has been shown to follow naturally by using the developed LEM. Three numerical benchmarks show the correctness and accuracy of the developed method. Finally, the error introduced in the linearization process is quantified by comparing numerical results of the LPRN method with that of the LEM, and some of the general trends of this error have been identified. As a result, the expectation of validity of the linearization process in the “sufficiently small perturbation” region is confirmed. [ABSTRACT FROM AUTHOR]

Abstract: The time-dependent diffusion of neutrons in a spheroid as a function of the focal distance has been studied. The solution is based on an orthogonal basis and an extrapolation distanced related boundary condition for the spheroidal geometry. It has been shown that spheres and disks are two limiting cases for the spheroids, for which there is a smooth transition for the systems properties between these two limits. Furthermore, it is demonstrated that a slight deformation from a sphere does not affect the fundamental mode properties, to the first order. The calculations for both multiplying and non-multiplying media have been undertaken, showing good agreement with direct Monte Carlo simulations. [Copyright &y& Elsevier]

• Development of a computer code for safety analysis of a nuclear reactor in the presence of xenon oscillation. • The Code works based on nodal discretization using a MC code named MCSP. • The restrictions of previous methods in transient analysis have been removed. • The Code is capable to simulate the systems with time-varying geometry and cross sections. • Independency of the method of the code to the node size. In this paper a probabilistic methodology based on core nodalization is proposed to estimate the core power in the presence of xenon oscillation. A time-dependent Monte Carlo neutron transport code named MCSP-NOD is developed for dynamic analysis in arbitrary 3D geometries to simulate xenon oscillations as well as sub-critical condition with feedbacks. The new code is based on the approach adopted in MCNP-NOD which was previously introduced as a tool for core transient analysis using the MCNPX platform. As before, the core is divided into nodes of arbitrary dimensions, and all terms of the transport equation e.g. interaction rates, leakage ratio are estimated using the MC techniques. However, as a new option the concentration of iodine and xenon are also estimated which enables us to predict the oscillatory behavior of reactor power following poison oscillation. These quantities are then employed within the time-dependent neutron transport equation for each node independently to compute the neutron population. Simulations prove the robustness of the method. [ABSTRACT FROM AUTHOR]