Modulation of viscous planar jump by an obstacle in the flow path—Interrogation through shallow water equations and numerical analysis

Abstract

The paper investigates a planar hydraulic jump during a thin film flow over a two-dimensional obstacle spanning the entire width of a horizontal channel. The shallow water analysis supported by numerical simulations identifies a hydraulic drop and simultaneous jump-drop-jump phenomenon under certain flow conditions. A hydraulic drop although observed for flow over obstacles in the macro-domain has never been reported for a thin film flow. The study, thus, establishes the efficacy of shallow water analysis which, with a novel solution methodology, predicts jump and drop characteristics over obstacles with much less computational effort compared to computational fluid dynamics based simulations. In addition, analytical expressions for jump efficiency and head loss across jump along with energy dissipation analysis are provided for a viscous jump. The numerical simulations reveal recirculation zones close to the channel floor and at the free surface, and the energy dissipation analysis provides a quantitative criterion for formation of recirculation zone pair. The observations are consolidated as a phase diagram which characterizes a myriad of free surface profiles based on operating and geometrical parameters.