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.

Self organization of granular flow by basal friction variation: Natural jump, moving bore, and flying avalanche

“…At θ ≈ 32° (Figure 5), the increase in flow velocity is sufficient for a transition from subcritical to supercritical state at the crossover from R A to S A 2 . A similar transition, conventionally termed as hydraulic drop, is reported by Dhar et al (2021) 20 during water flow over an obstacle.…”

“…A similar transition, conventionally termed as hydraulic drop, is reported by Dhar et al (2021) 20 during water flow over an obstacle. accumulation upstream of rough surface (S A1 ) ceases and the "moving bore phenomenon" is no longer exhibited.…”

“…In order to obtain the depth over R A , we adopt the methodology of forward and backward integration as has been previously done for granular jump 9 and hydraulic jump over obstacles. 20 This is because the jump is characterized by a discontinuity with an abrupt change in bed thickness and velocity. 8,9,12 Thus (Equation 12) is integrated forward from the beginning of R A and backward from the end of R A till the jump location, where the following Belanger-like equation 12,27 (Equation ( 13)) is satisfied.…”

“…During granular jump, we integrate Equation () forward over S A 1 and S A 2 since Figures 5 and 8B shows that the flow depth attains critical depth twice. In order to obtain the depth over R A , we adopt the methodology of forward and backward integration as has been previously done for granular jump 9 and hydraulic jump over obstacles 20 . This is because the jump is characterized by a discontinuity with an abrupt change in bed thickness and velocity 8,9,12 .…”

Experimental, numerical and analytical evaluation of j × B -thrust for fast-liquid-metal-flow divertor systems of nuclear fusion devices

“…A different formulation was used to study the effect of viscous shear on free surface flows and the generation of natural hydraulic-jump-like discontinuities [31]. More recently, SFSFM was reformulated to understand the effect of channel inclination on flows [32][33][34][35]. The specific approach followed in this article is presented in [36], with variations added to describe j × B-forces in the flow.…”