Analytical prediction of the hydraulic jump detachment length in front of mounted obstacles in supercritical open-channel flows

Lorris Gond (1) , Gaële Perret (1) , Emmanuel Mignot (2) , Nicolas Rivière (2)

1 LOMC - Laboratoire Ondes et Milieux Complexes
2 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique

Detached hydraulic jumps are major features of supercritical open-channel flows interacting with emerging obstacles. Such a flow pattern exhibits strong similarities with shock waves detached in front of bluff bodies in supersonic aerodynamic flows. This paper aims at evaluating the capacities of an analytical model, adapted from supersonic aerodynamics, to predict the hydraulic jump detachment length. The analytical predictions are compared to the measured hydraulic jumps from two experiments: (i) a uniform supercritical open-channel flow that skirts a mounted and emerging obstacle (with a horseshoe vortex) and (ii) a mounted and emerging obstacle moving at constant velocity in water at rest (without a horseshoe vortex). Moreover, numerical calculations of supercritical flow skirting emerging obstacles are undertaken, with a free-slip condition at the bed to remove the horseshoe vortex, while keeping the detached hydraulic jump. The comparison of the detachment lengths of these experimental, analytical, and computed hydraulic jumps reveals that two types of detachment lengths can be defined. The detachment length visible on experiments corresponds to the toe of the hydraulic jump, while the detachment length predicted by the analytical model rather corresponds to the location of flow regime transition from the supercritical to subcritical regime. The present work thus validates the analytical model for predicting the location of flow regime transition (for configurations without a horseshoe vortex) but not for predicting the toe of the hydraulic jump. We finally confirm the strong connections between two distinct phenomena: a hydraulic jump in water flow and a shock wave in gas flow.

Domaines: Mécanique des fluides [physics.class-ph]

Lorris Gond, Gaële Perret, Emmanuel Mignot, Nicolas Rivière. Analytical prediction of the hydraulic jump detachment length in front of mounted obstacles in supercritical open-channel flows. Physics of Fluids, 2019, 31 (4), pp.045101. ⟨10.1063/1.5085744⟩. ⟨hal-02381377⟩