Impinging jet flow and hydraulic jump on a rotating disk

• Published in: Journal of fluid mechanics Vol. 839; pp. 525 - 560
• Main Authors: Wang, Yunpeng, Khayat, Roger E.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.03.2018
• Subjects: Boundary layers; Film thickness; Flow rates; Flow velocity; Free surfaces; Height; High flow; Hydraulic jump; Hydraulics; Inertia; Jet flow; JFM Papers; Kinematics; Navier-Stokes equations; Reynolds number; Rotating disks; Rotation; Shear stress; Spin coating; Surface flow; Theory; Thin films; Velocity; Viscosity; Wall shear stresses; boundary layer structure; capillary flows; interfacial flows (free surface)
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2018.43

The free-surface flow formed by a circular jet impinging on a rotating disk is analysed theoretically. The study explores the effects of rotation and inertia on the thin-film flow. Both boundary-layer height and film thickness are found to diminish with rotation speed. A maximum film thickness develops in the supercritical region, which reflects the competition between the convective and centrifugal effects. Unlike the flow on a stationary disk, an increase in the wall shear stress along the radial direction is predicted, at a rate that strengthens with rotating speed. Our results corroborate well existing measurements. The location and height of the hydraulic jump are determined subject to the value of the thickness at the edge of the disk, which is established first for a stationary disk based on the capillary length, and then for a rotating disk using existing analyses and measurements in spin coating. The case of a stationary is revisited in an effort to predict the location and height of the jump uniquely. The formulated value of the height at the edge of the disk seems to give excellent results for a jet at moderately high flow rate (or low viscosity) where the jump structure is well identifiable in reality.