Statistical analysis of measured and computed thickness and interfacial temperature of free-falling turbulent liquid films

Abstract

This study examines the evolution of film thickness and interfacial temperature in turbulent, free-falling water films that are subjected to sensible heating. Measured temporal records of film thickness and interfacial temperature are subjected to thorough statistical analysis to understand the influence of interfacial waves on the distribution, periodicity and interdependence of these two parameters. A computational model of the film is constructed and its predictions subjected to similar statistical analysis. The statistical tools employed in this study include probability density, auto-covariance, cross-covariance, auto-spectrum and cross-spectrum. Probability density of film thickness shows an increase in substrate thickness and amplitude with increasing Reynolds number, while auto-covariance of thickness captures dominant frequencies corresponding to the large waves. Cross-covariance of film thickness and interfacial temperature difference captures a clear phase shift between the two parameters, with the temperature reaching a maximum in the relatively thin film region between the substrate and wave peak. Statistical results for both parameters exhibit clear dependence on axial location in the thermal entrance region, and point to fully developed wave structure downstream. The statistical results based on computed film thickness and interfacial temperature difference agree well with the results based on the measured, which demonstrates the effectiveness of the adopted computational tools at predicting the complex transport phenomena associated with wavy liquid–vapor interfaces.