Instability of Radial Liquid Sheet Flow

In this paper, the stability of a radial liquid sheet is described experimentally and theoretically. The liquid sheet was formed by the release of a radial liquid film flowing on a disk from the edge of the disk to still air. When the Reynolds number was large, a concentric disturbance wave (D wave) appeared and grew downstream on both free surfaces of the liquid sheet. To clarify the cause of the D wave, its frequency was measured by a laser beam reflection method and the cross section of the wavy liquid sheet was observed by the laser-induced fluorescence (LIF) method. Temporal and spatial linear stabilities of the liquid sheet were also investigated. The frequency and wavelength of the D wave and the phase difference between the D waves on the two liquid surfaces agreed well with those of the disturbance predicted using the stability theory. This means that the D wave on the liquid surface is caused by unstable disturbance, which is attributable to the inflectional velocity distribution of the liquid sheet. It was also found that Gaster's simplified equation, which transforms the temporal growth rate to a spatial one in the stability theory, is inadequate for a disturbance with a high growth rate.