Application of Mixing Length Theory to Wavy Turbulent Liquid—Gas Interface

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Abstract
A fully developed and adiabatic two-phase annular model with liquid entrainment is derived for flow in a pipe with negligible gravity effects. The model is based upon application of the single phase mixing length theory to a wavy liquid-gas interface. The model subdivides the flow cross section into three regions: a liquid film, a gas core of constant density, and a transition wavy layer between them. The combination of a constant velocity and a density varying exponentially with distance from the wall is employed in the transition layer. This approach plus appropriate logarithmic velocity distributions in the liquid film and gas core make it possible to specify the two-phase pressure drop, volume fraction, wave velocity, and thickness of the liquid film and transition layer. The liquid entrainment is obtained in terms of the exponent of the density profile in the transition layer, and interface stability considerations are used to express this entrainment parameter semiempirically in terms of an apparent Weber number and density ratio. Comparisons of the model are made with air-water and steam-water test data, and the results generally are satisfactory over a wide range of conditions and for all the important characteristics of this flow pattern.

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