Statistical characterization and modelling of wavy liquid films in vertical two-phase flow

The motion of a wavy liquid, thin film falling under the action of gravity and of a co-current gas flow, was Investigated In a 2" diameter channel for a wide range of liquid and gas flow rates. The Reynolds number for the liquid phase was varied from 200 to 7500 and for the gas phase, from 0 to 113000. Since the nature of all processes observed In such a system are "random", It was necessary to use statistical means to describe this random wave process. By the use of a number of techniques for time series analysis, a broad range of Information on the characteristics of the waves was extracted from the film thickness data. The existence of three distinct classes of waves was established from this analysis, each with their characteristic dimensions (amplitude, shape, base length and separation distance) and celerity. One type is the small waves moving on the substrate; a second is the large wave structure and a third type are small waves moving on these large waves. Detailed statistical data were developed Including probability density and moments for the amplitude, location of maximum, minimum, separation time, base dimension, shape and celerity for each class. The variation of these statistical properties with liquid and gas rates and with location down the tube were established. Joint probability densities for certain important properties were also obtained. In order to develop much of this information, several new techniques of extracting the relevant data from the signals had to be developed involving special processing of the time series analysis and detailed interpretation of the stochastic process, h(t). A new technique for simultaneous measurement of local pressure and film thickness was developed. By measuring the spectral density of the wall pressure fluctuations and cross density between the pressure and film thickness definitive information on the gas-liquid interaction was obtained. These data were used to determine the distribution of liquid flow between waves and substrate and, for the first time, it is possible to understand the local flows in a wavy system such as this. The data also permitted definitive tests of existing theories. All were shown to be inadequate for both large and small waves. New theoretical approaches were developed to explain the process of wave motion. These included (1) introducing white noise perturbations into the equations of motion and (2) extending a theory originally proposed by Telles in which a shot noise model is assumed for the wave motion. In particular, this extension is shown to be the only theoretical description of wave motion that describes large wave behavior.