The effect of substrate amplitude and wavelength on gravity-driven film flow inside an inclined corrugated pipe

Abstract

An experimental investigation was conducted to determine the effect of substrate amplitude and wavelength on gravity-driven film flow inside an inclined corrugated pipe. Nine different geometries were examined, with substrate amplitude and wavelength varied independently. A statically deformed free surface occurred for all conditions. The amplitude of the statically deformed free surface depended on substrate amplitude and wavelength, with phase shift unaffected by changes in substrate geometry for many conditions under investigation. Fluctuations in free surface elevation were enhanced at low substrate amplitude and intermediate substrate wavelength. Notable reductions in transient free surface behavior were observed for conditions that resulted in a positive phase shift. Transient free surface behavior developed into periodic traveling waves without applied external forcing. Frequency selection for traveling waves was strong, and traveling waves were detected for a majority of the conditions examined. The frequency, phase velocity, and wavelength of the traveling waves showed a potential dependence on substrate geometry; however, there were ranges of substrate amplitude and wavelength for which traveling wave characteristics remained unaffected by changes in substrate geometry. An examination of the amplitude of the statically deformed free surface and transient free surface fluctuations revealed that waviness is a potentially suitable method for combining the effects of substrate amplitude and wavelength on film flow in corrugated pipes. The comparison of amplitudes highlighted a possible link between the statically deformed free surface and the emergence of transient behavior and traveling waves. Length scales proposed in our original work showed promise for characterizing some results.