On Axial Coherence of Interfacial Waves in Countercurrent Flow

Flooding is the limiting condition of stable countercurrent gas-liquid flow in columns and has been the subject of extensive research over a number of decades. An exhaustive review of the subject, as pertaining to unpacked columns, has been given by Bankoff and Lee.1 While a number of correlations exist in the literature to predict the onset of flooding, the topic of the mechanism of flooding has been debated and discussed widely in the recent literature. Briefly, there are two schools of thought on the flooding mechanism: (1) the formation and upward transport of large waves from the bottom of the column near the gas injection/liquid withdrawal point, and (2) the destabilization of the liquid film near the liquid inlet resulting in the formation of large waves. Direct visual evidence of formation of large waves at the liquid exit under flooding conditions has been reported by a number of researchers.2,3,4 However, this idea was opposed by Zabaras and Dukler.5 They measured the local instantaneous wall shear stress using an electrochemical method just below the liquid feed, as well as just above the liquid withdrawal point. They found that in all instances of countercurrent flow, including conditions along the flooding curve, the time-averaged wall shear stress was directed upward indicating that the velocity near the wall was downward. They also measured the instantaneous film thickness from two conductance probes located 0.053 m apart. Cross-correlation of these signals showed a well-defined peak at a measurable time delay even under flooding conditions. Zabaras and Dukler, therefore, concluded that waves were travelling downward even under flooding conditions and that they did not reverse direction at the flooding point. They explained the photographic observation of upward-travelling waves by McQuillan et al.3 as a transient phenomenon generated by the small depressurization used by McQuillan et al. to induce flooding. Thus, Zabaras and Dukler argued that the process of flooding was controlled by conditions that existed at the or just below the feed rather than at the liquid exit. Jayanti et al.6 attributed the existence of different mechanisms of flooding to the effect of tube diameter. In small diameter tubes, a coherent, ring-like wave could be formed around the inside wall of the tube which could then be transported upward by the gas. A flooding model, based on the formation of a large standing wave at the flooding point was developed by Shearer and Davidson.7 Jayanti et al. argued that such a wave would be very unstable in large diameter tubes and, hence, could not travel upward for long distances. Vijayan et al.8 conducted flooding experiments in tubes of 25, 67 and 99 mm inner dia. and confirmed visually the existence of upward travelling waves in the 25 mm dia. tube under flooding conditions. In the larger diameter tubes, the waves were observed to move only a short distance before collapsing. Similar behavior was also observed by Biage et al.9 in a duct of rectangular cross-section and by Watson and Hewitt10 in a tube of 82 mm internal dia. While there is, thus, a convergent view on the flooding mechanism, the careful experimental results of Zabaras and Dukler5 remain unexplained. Specifically, their observations that the wall shear stress always indicated a downward moving flow and that the film thickness measurements recorded no upward-moving waves need to be explained in a manner consistent with the recent visual observations of flooding mechanisms. Toward this end, film thickness measurements have been conducted under conditions in which different flooding mechanisms prevailed. The details of these studies and the results obtained are reported here.