Semi-empirical correlation for counter-current flow limitation at the upper or lower end of sharp-edged vertical pipes

A semi-empirical correlation for CCFL (counter-current flow limitation) in vertical pipes was derived from one-dimensional momentum equations. Available correlations such as the empirical correlations proposed by Wallis (1969) and Zapke and Kröger (1996) can be deduced from the derived fundamental functional form of the semi-empirical correlation in limiting flow conditions. Comparisons between the semi-empirical correlation with available experimental data of CCFL taking place at the sharp-edged lower end of a vertical pipe showed that the correlation is applicable for various fluid properties and pipe diameters. The fundamental functional form of the correlation was also transformed so as to express the characteristics of CCFL occurring at the sharp-edged upper end of a vertical pipe. The present fundamental functional form of CCFL correlation is useful not only to express CCFL data but also to understand how relevant parameters play their roles in the CCFL characteristics.