Abstract
We study axial core oscillations due to xenon poisoning in thermal neutron nuclear reactors with simple 1D models: a linear one-group model, a linear two-group model, and a non-linear model taking the Doppler effect into account. Even though nuclear reactor operators have some 3D computer codes to simulate such phenomena, we think that simple models are useful to identify the sensitive parameters, and study the efficiency of basic control laws. Our results are that, for the one-group model, if we denote the migration area by M 2 and by H the height of the core, the sensitive parameter is H/M. H being fixed, for the 2 groups model, there are still 2 sensitive parameters, the first one being replaced by M12+M22 where M12 denotes the migration area for fast neutrons and M22 the migration area for thermal neutrons. We show that the Doppler effect reduces the instability of xenon oscillations in a significant way. Finally, we show that some proportional/integral/derivative (PID) feedback control law can damp out xenon oscillations in a similar way to the well-known Shimazu control law [Y. Shimazu, Continuous guidance procedure for xenon oscillation control, J. Nucl. Sci. Technol. 32, 1159 (1995)]. The numerical models described in our paper have been applied to PWR.
Highlights
A lot of publications can be found in the literature on the problem of xenon oscillations in nuclear reactors [1,2,3,4,5,6,7,8,9,10].As reported in [1] xenon oscillations have occurred in Savannah River as early as in 1955
Axial core oscillations have been first studied with two zones lumped models, and by a one group diffusion model coupled to the evolution equations for xenon and iodine
We show that it is possible to derive a one-group model with the same behavior as our two-group model provided that, in the one-group model, the diffusion equation holds for the thermal neutron flux only and that the migration area is selected in an adequate way
Summary
A lot of publications can be found in the literature on the problem of xenon oscillations in nuclear reactors [1,2,3,4,5,6,7,8,9,10]. As reported in [1] xenon oscillations have occurred in Savannah River as early as in 1955. X e is the fission product with the highest capture cross section and that it can be produced either directly or via beta-decay of another fission product which is 15345I. Axial core oscillations have been first studied with two zones lumped models, and by a one group diffusion model coupled to the evolution equations for xenon and iodine. The first question is whether we should use a time dependent diffusion equation like in [11] or a stationary diffusion equation like in [1] and many other
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