Analytical study of coupled neutronic and thermodynamic instabilities in a boiling channel

Linear stability analysis in the frequency domain is performed to reveal the basic mechanism of coupled nuclear-thermal instabilities in a boiling channel. It is found that the Ledinegg instability will not occur due to the coupling of the void-reactivity feedback and the hydrodynamic feedback. Besides the phase-change number N_p and Jacob number Ja, the Froude number Fr and the fuel-time-constant τ_M are found to be the parameters determining the density-wave instability. It is also found that the Froude number effect on the density-wave stability becomes stronger when the void-reactivity feedback is involved, and that the lower the Fr number the less stable the system. The result reveals that there exists a region in which the void-reactivity feedback loop is unstable, and this has a strong effect on the stability of the system. A non-dimensional fuel-time-constant number is proposed, with which the stability boundary is better presented in the range of Froude numbers of interest.