Abstract

A thin falling film is well suited to simultaneous heat and mass transfer because of the small thermal resistance through the film and because of the large contact surface achievable at low flow rates. The film enters as a smooth laminar flow and quickly transitions into small-amplitude wavy flow. The waves grow in length and amplitude and are identified as roll waves. This flow regime is termed “wavy-laminar flow,” and modern heat and mass transfer equipment operate in this complicated transition regime. Research published in open literature has shown the mass flow rate in the roll waves to be about 10 to 20 times greater than that in the laminar substrate. As the film fully develops, the waves grow in mass and the film substrate thins because fluid is swept from the substrate by the secondary flows of the roll wave.

Many studies have been conducted to measure and correlate the film thickness of wavy-laminar flows. Literature data show that Nusselt’s theory for smooth laminar flow can over predict the film thickness by as much as 20% for certain wavy-laminar flow conditions. The hydrodynamics of falling films were therefore studied to measure the film thickness of a free-surface falling film and to better understand the parameters that affect the variations of the film thickness.

A flow loop was set up for measuring the thickness, wave amplitude, and frequency of a film during hydrodynamic flow. Decreasing the pipe diameter caused the amplitude of the wavy flow to diminish. Measurements monitored from stations along the falling film showed a thinning of film thickness. Fully developed flow required large starting lengths of about 0.5 m. The film thickness increases as the Reynolds number (Re) increases. Increasing the Kapitza number (Ka) causes a decrease in the film thickness. Regression analysis showed that the Re and Ka numbers described the data trends in wavy-laminar flow. Rather than correlating the Re number in discrete ranges of the Ka number as earlier researchers have done, this research made the Ka number an independent regression variable along with the Re number. The correlation explains 96% of the total variation in the data and predicts the experimental data within an absolute average deviation of ±4.0%. The correlation supports the calculation of a fully developed film thickness for wavy-laminar falling films.

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