A Study on the Hydrodynamic Instability in Boiling Channels : 2nd Report, The Instability in Two Parallel Boiling Channels

Abstract

An investigation is carried out on the hydrodynamic instability in a system having two parallel boiling channels. The basic equations for the circulation flow rates and the driving heads are derived from the laws of conservation of mass, energy and momentum. The stability of equilibrium in a hydrodynamic system and the modes of vibration are discussed. As the result, the following facts are found. (a) A hydrodynamic system is always stable when the equilibrium of the system lies in the range of positive inclination of the characteristic curve for each channel and (b) always unstable when the equilibrium is in the range of negative inclination of the characteristic curve for each channel ; (c) when the equilibrium lies in the range of positive inclination for one channel and in one of negative inclination for the other channel, the system is either stable or unstable ; (d) there are two normal modes of vibration in the system having two parallel boiling channels. The first is a mode in which each channel vibrates in the same phase and the second is one in which each channel vibrates in the opposite phase ; (e) in the case of (b) the second mode is always unstable and a throttle or a pump in the downcomer is not effective to cause positive damping to the second mode, and (f) in the system with parallel channels there may be many equilibriums, so that non-uniform distributions of flow rates may occur.