The two-phase natural circulation is induced by the density difference between the vapor and the liquid phase. The concept of the two-phase natural circulation is often adopted in designs of thermosyphon reboiler, solar collector and various cooling systems. In a two-phase natural circulation mode, various types of flow instabilities occur depending on the system geometry, fluid properties and the operating conditions, and often lead to abnormal behaviors such as limit cycle oscillations or premature burnout. That is, the self-sustained flow oscillations may cause mechanical vibrations of compenents, and affect the local heat transfer characteristics which can induce a boiling crisis.
In the present study, the time-averaged behavior and the density wave instability were predicted numerically for the three loop types;open loop, closed loop and semi-closed loop. The system pressure is constant in the open and the semi-closed loops, but it varies with the heat flux in the closed loop. The time-averaged equation was obtained by using the one-dimensional two-phase homogeneous equilibrium model, and the characteristic equation was derived by using the perturbation technique with linearizations. Heat flux, condenser liquid level(for the open loop), condenser and heater section lengths, loop height and the flow restrictions in the liquid-and two-phase regions were taken as parameters to examine the flow behavior. Effect of the inlet subcooling was also considered in the open and the semi-closed loops.
Stability criteria for the excursive and the density wave instabilities were obtained along with the variation of the steady liquid velocity with the heat flux for each loop.
For the open and semi-closed loops, excursive instability and density wave instability boundaries were shown on the instability map in the plane of $N_{\mbox{pch}}(Fr)^{1/2}{\mbox{vs}}N_{\mbox{sub}}$. It was found that examination of the density wave instability conditions is sufficient for the two-phase flow stability analysis. Both the stable region and the excursive instability region shift to the higher heat flux range with the higher condenser liquid level. The increase of the loop height results in a larger unstable region, and the stable region extends to the higher inlet subcooling range with the longer heater section. The system is stabilized with the increase of the liquid-phase restriction and/or with the decrease of the two-phase restriction.
In the closed loop, the dynamic instability boundary shows a convex shape in the plane of the heat flux vs. the condenser coolant temperature ($q_h$ vs $T_c$). the excursive instability dose not occur because the fluid inventory(charging level) remains constant in this loop. Flow becomes unstable as the charging level decreases. When the lengths and the vertical locations of the condenser and the heater sections are fixed, the system becomes unstable with the longer riser section. The systems is destabilized with the longer heater and condenser sections for the fixed heating rate. As for the open loop or the semi-closed loop, the systems is stabilized with the increase of the liquid-phase restriction or with the decrease of the two-phase restriction.
