Probabilistic model for determining the operational lifetime of rod-shaped absorbing elements of a VVÉR-1000 reactor

Abstract

The rules in [ 1] establish the limit of admissible probability of a serious accident with destruction of the core as 10-l x 1/(reactor.yr). Analysis of the reasons for unplanned stoppages of reactors reveals also a contribution from malfunctions in the control and shielding system (CSS) [2]. For this reason, increasing the lifetime of CSS elements is a mandatory condition for increasing both the overall operational safety of power reactors as well as the economic efficiency of a nuclear power plant. The estimation of the probability of malfunctioning of the equipment must be based on mathematical modeling of the kinetics of deformation and destruction of the most highly loaded elements operating in the core [3].The normal functioning of the control and shielding system largely depends on the technical state of the rod-shaped absorbing elements. The most important indicator of their working capacity is the working lifetime --the duration of operation up to the maximum admissible deformation or maximum admissible damage to the carrying structure. The absorbing elements employed in VVI~R-I000 reactors consist of a thin-walled tube --a shell, made of a structural alloy and filled with vibrationally compacted boron carbide powder --the absorber. The shell diameter is 8.2-9.6 ram, depending on the constructional implementation, and the nominal thickness of the wall is 0.5-0.6 mm. The lower and upper ends of the shell are closed by caps, welded to the shell by a circular seam. In the core the shell of an absorbing element is exposed at the bottom to fast neutrons with a flux density of up to 1.7-1018 sec-l.m -2 (E > 0.1 MeV) and thermal neutrons with a flux density of up to 1.1" 1018 sec -l"m -2, loading by contact pressure on the side of the swelling powder core, as well as heat and pressure cycling accompanying a change in the operating states of the reactor.Approximately 1000 absorbing elements are used in a VVI~R-1000 reactor during its period of operation. For this reason its operational lifetime is best calculated taking account of the statistical variance of the constructional, technological, and strength parameters.The mathematical model of plastic deformation and the damage to the cladding of an absorbing element, assuming that there are no technological defects and the distance from the weld seams is sufficiently large (greater than two diameters), is constructed on the basis of an analysis of the interaction of the core, which swells under the action of the thermal neutrons and is plastically compacted, at the bottom of the absorbing element in the section of length up to 500 mm from the bottom weld seam. In this case, it was determined that a powder core can be treated in the "hydrostatic" approximation, i.e., only the stress a 0 of hydrostatic compression need be taken into account. Then the equation expressing the equilibrium of the cladding and the core in a cylindrical coordinate system Orz can be written in the formwhere a z and a t are the axial and tangential stresses in the cladding; R and h are the...