The Determination of Wall Friction for Vertical and Horizontal Two-Phase Bubbly Flows

Abstract

The one-dimensional momentum equation without slip is applied to the bubbly flow of air-water mixtures in pipes for Reynolds numbers in excess of 105 . The equation is integrated along the pipe so that pressure measurements made over a finite length of pipe may be used to determine the surface friction factor. The critical void fraction for the flow is found to characterize the flow. The results show a variation of friction factor with Reynolds number similar to that found in single-phase flows but with values approximately 10 percent greater, provided the critical void fraction is less than 0.85. For larger values, it is found that the results indicated lower values of the friction factor which depart from the general trend of the rest of the data. Similar effects were observed for both vertical and horizontal flows.