Roll waves in falling films: An approximate treatment of the velocity field

Wavy flows, an important aspect of falling film absorption in refrigeration systems, are difficult to describe analytically because of their transitional regime. Within the wavy-laminar flow regime, high-frequency capillary waves are known to exist below a Reynolds (Re) number of 200. Above the critical Re, inertial waves driven by gravity, known as roll waves, can exist. These low-frequency waves, observed in an experimental absorber, were identified via image-processing studies of the falling film. A frequency analysis (fast Fourier transformation - FFT) of the film thickness trace in time yielded a wave frequency corresponding to roll waves at the given Re. A hydrodynamic description of this flow regime was then obtained from the literature. The flow equations provided by this model were solved for various wave parameters at different Reynolds numbers. The results from the solution were then extended using Fourier series expansions and continuity at each point to yield the complete periodic velocity field.