Gravity-driven film flow inside an inclined corrugated pipe: An experimental investigation of corrugation shape and tip width

Abstract

Fluorescence images were acquired in gravity-driven film flow through inclined corrugated pipes representing a range of corrugation shapes and tip widths. The film flow developed an identifiable statically deformed free surface with a wavelength similar to the substrate for most cases of corrugation shape and tip width. The amplitude and phase shift of the statically deformed free surface, as well as the steady-state film thickness, varied more with tip width than with corrugation shape. Transient fluctuations in the free surface elevation were examined for evidence of periodic traveling waves. In general, the film flow produced transient free surface fluctuations, and in many cases, periodic traveling waves with parameters that varied similarly with corrugation shape as with tip width. For flow conditions that produced positive phase shift, low amplitude, or minimal curvature of the statically deformed free surface, transient and periodic behavior were suppressed, supporting previous findings on the importance of the shape and position of the statically deformed free surface. An increase in corrugation tip width also reduced the transient and periodic response. These two findings implicate flow dynamics in the substrate trough as a leading factor in the development of transient and periodic behavior. Steady-state response and the existence of time-dependent behavior are influenced more by tip width than corrugation shape, in agreement with two-dimensional film flow over topography; however, transient fluctuation and periodic traveling wave parameters are similarly influenced by corrugation shape and tip width, which contrasts two-dimensional findings.