Transient two-phase flow of cryogenic fluid in a vertical transfer line during the cooldown process

The analytical and numerical modeling for prediction of the thermo-fluid parameters of the cooldown process of a vertical tube carrying cryogenic liquid are presented. Formulation of the problem is based on the flow patterns observed in the experimental studies. In this model the flow field consists of four distinct regions of fully liquid, inverted annular film boiling, dispersed flow film boiling, and fully vapor. For the fully liquid and fully vapor regions, the one-dimensional form of the mass, momentum, and energy conservation equations are used. For the two-phase regions, the volume-averaged, one-dimensional two-fluid model conservation equations are applied. In addition, a one-dimensional energy equation is formulated to determine the tube wall history. The numerical approximations are based on the finite difference technique. Calculation for inverted annular flow are based on a semi-implicit model while computations for the wall, fully liquid, and dispersed flow regions are performed explicitly. Comparison of calculated results with experimental data for water and liquid nitrogen are presented.