Parallel channel instabilities in boiling water reactor systems: boundary conditions for out of phase oscillations

In this paper we study the boundary conditions during out of phase oscillations, in a system formed by two parallel channels coupled to multimodal neutron kinetics. The fact that the pressure drop can change with time, but remains the same in all the parallel channels, leads us to analytical integration of the time derivative term of the channel momentum equation, in order to get a dynamic equation for the inlet mass flux to each channel. From these inlet mass flux dynamic equations plus the appropriate boundary conditions, we have obtained the expression of the time dependent common pressure drop to all the channels. Finally the oscillations in the pressure drop and in the inlet mass flux to the channels have been investigated when out of phase oscillations take place.