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عنوان فارسی مقاله:
خواص طیفی فرآیندهای پویا در یک راکتور هسته ای
عنوان انگلیسی مقاله:
Spectral properties of dynamic processes in a nuclear reactor
سال انتشار : 2017
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مقدمه انگلیسی مقاله:
1. Introduction
The physical processes in a nuclear reactor (Duderstadt and Hamilton, 1976) depend on distribution of neutron flux, whose mathematical description is based on the neutron-transport equation (Hetrick, 1971; Stacey, 2007). The general view of this equation is integro-differential one, and the required distribution of neutrons flux depends on time, energy, spatial and angular variables. As a rule, the simplified forms of the neutron transport equation are used for practical calculations of nuclear reactors. The equation system that is known as a multigroup diffusion approach is mostly used for reactor analysis (Marchuk and Lebedev, 1986; Lewis and Miller, 1993; Sutton and Aviles, 1996; Cho, 2005) and is applied in most engineering calculation codes. Modern reactor simulations are actually based on transport calculations (see, for example, Smith and Rhodes, 2002; Sanchez, 2012; Boyd et al., 2014). In multiscale reactor-physics simulations diffusion models are derived and applied using sophisticated homogenization methodologies Sanchez (2009) which define parameters of the multigroup diffusion equations that enable one to take into account transport effects. The homogenization methodologies use solution of specially defined transport problems to generate homogenized cross sections for the multigroup diffusion equations. Most of current methodologies (see, for example, Sanchez (2009)) use k-eigenvalue transport problems to calculate averaging shape functions. Recently Dugan et al. (2016) developed advanced homogenization methods apply aeigenvalue transport problems. The standard methods of approximate solutions of nonstationary problems are used for modelling of the dynamics of neutron-physical processes. The most attention is paid to twolevel schemes with weights (h-method) (Ascher, 2008; LeVeque, 2007; Hundsdorfer and Verwer, 2003), the Runge–Kutta and Rosenbrock schemes (Butcher, 2008; Hairer and Wanner, 2010) are used. Let’s note a special class of methods for modelling of non-stationary neutron transport in diffusion multigroup approximation, which is connected with multiplicative representation of solution — space–time factorization methods and the quasistatic method (Chou et al., 1990; Dahmani et al., 2001; Dodds, 1976; Goluoglu and Dodds, 2001). The approximate solution is searched in the form of the product of two functions, one of which depends on time and is related to the amplitude, the second one (the shape function) describes the spatial distribution. It is difficult to check the accuracy of the approximate solution in such approach, in particular, while calculating the dynamic modes with complicated changes in neutron flux distribution. The processes occurring in a nuclear reactor are essentially nonstationary. The stationary state of neutron flux, which is related to the critical state of the reactor, is characterised by local balancing of neutron absorption and generation. This boundary state is usually described by solution of a spectral problem (Lambda Modesproblem, k-eigenvalue problem) provided that the fundamental eigenvalue (maximal eigenvalue) that is called k-effective of the reactor core, is equal to unity. In this case, the stationary neutron field is related with the corresponding eigenfunction. Calculations of k-effective of the reactor on the basis of the spectral Lambda Modes problem solution are obligatory for developing a new design of reactor installation.
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کلمات کلیدی:
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