Stability analysis of a closed thermosyphon model

Closed two-phase thermosyphon stability is analyzed as a function of the heat input, liquid filling, viscosity, density, capillary number and two-phase flow Grashof number. It is shown that for small liquid fillings there is a one-to-one correspondence between the heat input and the corresponding steady-state solution, and that for larger fillings there is a stable and an unstable solution possible for each heat input. A turning point is indicated at the maximum heat input at which one of the eigenvalues of the linear stability analysis is zero. It is found that the steady operation of the thermosyphon is insensitive to the vapor-to-liquid viscosity ratio and the thermosyphon length, and very sensitive to vapor-to-liquid density ratio. Upper limits for the heat input are found for large fillings near the steady-state operating conditions. It is also shown that a linear analysis grossly underestimates the transient behavior of the thermosyphon behavior.