An Analytical Model for Displacement Velocity of Liquid Film on a Hot Vertical Surface

Abstract

The downward progress of the advancing front of a liquid film streaming down a heated vertical surface, as it would occur in emergency core cooling, is much slower than in the case of ordinary streaming down along a heated surface already wetted with the liquid. A two-dimensional heat conduction model is developed for evaluating this velocity of the liquid front, which takes account of the heat removal by ordinary flow boiling mechanism.
In the analysis, the maximum heat flux and the calefaction temperature are taken up as parameters in addition to the initial dry heated wall temperature, the flow rate and the velocity of downward progress of the liquid front. The temperature profile is calculated for various combinations of these parameters. Two criteria are proposed for choosing the most suitable combination of the parameters. One is to reject solutions that represent an oscillating wall temperature distribution, and the second criterion requires that the length of the zone of violent boiling immediately following the liquid front should not be longer than about 1 mm, this value being determined from comparisons made between experiment and calculation.
Application of the above two criteria resulted in reasonable values obtained for the calefaction temperature and the maximum heat flux, and the velocity of the liquid front derived therefrom showed good agreement with experiment.