Periodic Homogeneization Techniques As a Way to Account for Surface Roughness in a Confined Air Flow

Abstract

The motivation of the study is concerned with high speed winding of plastic films (i.e. PET). During this process, some air is entrapped between the first wrap and the roll being wound. It is well known that the residual air layer between the plastic layers has a strong influence on the internal stress state within the roll. The surface roughness of the film plays an important role on these aerodynamic effects and consequently on the internal stress. Nevertheless, the mechanisms involved are not clarified yet. As a first step, an experimental study was conducted with the aim of characterizing the global flow kinetics of an air layer squeezed between a plastic film sample and a smooth substrate. In so doing, a new parameter was defined: some sort of a “dynamic roughness coefficient”. Nevertheless, the correlation between this parameter and those which describe the topography of a film surface (static) needed to be established. Using the tools of 3D roughness measurements, it was observed that the heights of the peaks and the mean distances between them are of the same order of magnitude as the average distance between the opposite surfaces. We therefore assimilated the surface topography to a periodic array of cylinders of known dimensions, their spatial period and their height being of the same order as the interlayer distance. In such conditions, the air flow squeezed in the space confined between the two surfaces is studied by using an approach based on periodic homogeneization techniques. The first tendencies indicate that a good qualitative agreement exists between the global experimental data and the theoretical results.