Flooding correlation based on the concept of hyperbolicity breaking in a vertical annular flow

Flooding is classified into exit flooding and entrance flooding depending on the positions at which it is initiated. It is postulated that flooding may result from the instabilities of roll waves and the stationary wave generated at the entrance and the exit respectively. Based on the two-fluid model, the neutral stability condition for wave instabilities is derived by studying hyperbolicity breaking near a singular point in two-phase flow. It turns out to be a type of onset condition of Helmholtz instability; the critical relative velocity depends on the void fraction derivative of the interfacial pressure force as well as on the void fraction and density ratio. In order to obtain information on the interfacial pressure force, a Korteweg-de Vries solitary wave is studied with the assumption that its wavenumber is the same as that of the fastest-growing sine wave. Predictions by the correlations for entrance flooding and exit flooding are in good agreement with experimental data. Also, the present model is able to consider the effect of the test section length on flooding.