Linear stability analysis on instabilities of in-phase and out-of-phase modes in boiling water reactors

An analytical model is proposed to study the two-phase flow instabilities of in-phase and out-of-phase modes in boiling water reactors. This model, developed far parallel boiling channels with the void-reactivity feedback loop, takes into consideration the interaction between channels with different void fraction variations. Linear stability analysis in the frequency domain is performed to reveal the mechanisms of the instability. Stability boundaries for the system are obtained on the stability map. In the case of parallel two channels, two types of stability boundaries are found to exist on the stability map; one for the instability of the in-phase made and the other for that of the out-of-phase mode respectively. It is found that the interaction between channels affects the instability of the out-of-phase mode. For a certain range of the void-reactivity coefficient, the void-reactivity feedback loop is found to be unstable in a certain region on the stability map; which has an effect an the stability of the in-phase mode. Froude number is important to the stability of the system, especially to the instability of the in-phase mode.