Classification and modeling of flooding according to the type of vertical tube-end geometries

Abstract

In order to study the effect of tube-end geometry on flooding data classification, and experimental & analytical work have been performed. The first is to build flooding database and classify its data by means of entropy-minimax principle. The second step is to develop an analytical model which is applicable to the both of entrance and exit flooding. The last one is to perform experiments for validation. Flooding data are partitioned according to the type of the entrance and exit geometry by applying entropy-minimax principle. It is found that the effects of exit and entrance geometry on flooding are dominant in the low and high liquid velocity region, respectively. Two flooding correlations having the second order polynomial form are suggested with $\pm\,20$\% uncertainty bands for smooth exit and sharp exit geometries, respectively. It is found that flooding gas velocities predicted by most previous correlations are close to those predicted by the smooth exit correlation. Flooding is classified into the exit flooding and the entrance flooding depending on the positions at which flooding 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 the wave instabilities is derived by studying hyperbolicity breaking near a singular point in two-phase flow. It turns out to be a type of the onset condition of Helmholtz instability; the critical relative velocity depends on the void fraction derivative of the interfacial pressure force as well as void fraction and the 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 wave number is the same as that of the fastest growing sine wave. Predictions by the correlations for the entrance flooding and the exit flooding are in good agreement with e...