Flooding prediction of counter-current flow in a vertical tube with non-axisymmetric disturbance waves

A three-dimensional wave calculation is performed to investigate the growth of the non-axisymmetric disturbance wave for counter-current flow in a vertical pipe. The calculation is based on inviscid Kelvin-Helmholtz instability with the additional consideration of the azimuthal component of the long wavelength disturbance wave. Recognizing that the onset of flooding originates from the complicated interaction between gas flow and a wavy interface, the critical relative velocity prediction for interfacial instability is utilized to obtain an empirical formula for flooding predictions through correlations with the available experimental data. Compared with predictions based on the axisymmetric wave assumption, the present calculations reveal that the azimuthal propagation of the disturbance wave can significantly increase the interfacial stability. As a result, predictions for the onset of flooding based on the three-dimensional wave approach are found to agree better with the experimental data than that based on axisymmetric assumption. Effects of the tube diameters on interfacial instability are investigated, which becomes a crucial factor in determining the incipient flooding conditions when the diameter is small.