Application of diffusion approximation in the calculations of reactor with cavities

Abstract

The importance of calculation of radiation fields inside in-reactor cavities is associated with the necessity to simulate the emergency modes in fast breeder reactors (FBR), as well as reactor states with different coolant levels in special dedicated channels of passive feedback devices in lead-cooled fast reactors (LFR) of BREST type or in sodium cavities in sodium-cooled fast reactors (SFR). The Last Flight (LF) method (Bell and Glesston 1974, Davison 1960, DOORS3.2 1988, Mynatt et. al. 1969, Rhoades and Childs 1988, Rhoades and Sipmson 1997, SCALE 2009, Voloschenko et. al. 2012), or the method of the unscattered component is widely known and is commonly used in computer codes based on the method of spherical harmonics for obtaining solution in a gas medium at a certain distance from the calculated volume domain (DORT (Rhoades and Childs 1988), TORT (Rhoades and Sipmson 1997) and others (SCALE 2009)). The practice of its application (DOORS3.2 1988) demonstrated that acceptable results are achievable at considerable distances from the surface separating dense and gas media (more than two meters). Obtaining high-quality solution is not guaranteed for cavities within the calculation area. In addition, it is desirable to implement the cavities calculation methodology within the framework of the approximations used in reactor calculations introducing certain specific features. In particular isotropy of the neutron flux density and the necessity of forced introduction of a “conditional” calculation cell on the boundary surface of the void cavity are assumed in the diffusion approximation. If the LF method is oriented on the connection of the source point with the detection point, then it is necessary to determine in the calculation of neutron field in the cavities the neutrons escaping the surface area of the source and neutrons reaching a certain surface area of the cavity. In order to solve the problem, the authors suggested using the approximate solution presented in the paper. Thus, an algorithm for calculation of in-reactor cavities using the diffusion approximation was developed and implemented by the authors.