A delay theory for boiling flow stability analysis

An analysis of density-wave instabilities in boiling channels based on delay equations is presented. A two-dimensional mapping is derived from the flow conservation equations by assuming constant transport delays along the different parts of the channel. The simplicity of the final equation allows the fully analytical treatment of the system dynamics, both linear and non-linear, valid for high inlet subcoolings. Hopf bifurcations, subcritical and supercritical, could be identified and treated using perturbation methods. The derivation of a fully analytical criterion for Hopf bifurcation transcription was applied to determine the amplitude of limit cycles and the maximum allowed perturbations necessary to break the system stability.