Experimental investigation of the global instability of plane sheet flows

Abstract

A global stability investigation of two-dimensional vertical liquid sheet flows is experimentally carried out. The motivation is that previous investigations addressed the study of the local absolute/convective character of such flows, thus they are not able to predict the actual critical flow Weber number corresponding to sheet rupture. The objective of the paper is twofold: first, the link between local absolute and global instabilities is investigated and the measured length of the absolute instability region is correlated with the non-parallelism parameter (sheet slenderness ratio which is the reciprocal of the Froude number); then, a criterion to predict the flow Weber number value at sheet rupture is given for which the critical Weber number is correlated with Froude and Reynolds numbers. Tests are carried out on liquid (low-concentration water solutions of surfactants and low-viscosity motor oil) sheets issuing from a nozzle with a long horizontal exit section in still air under the gravitational field. A major goal of the experiments is the determination of the vertical location where the local Weber number equals unity, because this yields the length of the absolute instability region. This location is determined by observing the standing sinuous waves generated by an obstacle placed normally to the sheet, and by measuring the angle between the tangent to the wave at the obstacle and the vertical direction for the minimum liquid flow rate necessary to maintain the sheet stable (global instability onset).