3D SPH modelling of hydraulic jump in a very large channel

Abstract

The formation of different undular hydraulic jumps in a very large channel is investigated and reproduced using a weakly-compressible XSPH scheme which includes a mixing-length turbulence model. An analysis of the ability and of the limits of the SPH method to reproduce undular hydraulic jumps is preliminarily performed on reference two-dimensional cases. The numerical description of the three-dimensional jump in a very large channel, where the hydraulic-jump front is trapezoidal and the lateral shock waves induce a large recirculation region along the side walls, is compared with experiments in a laboratory flume on two undular jumps at upstream Froude number equal to 3.9 and 8.3. Acoustic Doppler velocity measurements were compared with SPH instantaneous and time-averaged flow fields in order to evaluate whether the numerical method could help in having a clearer understanding of both hydraulic-jump development and lateral shockwave formation. The predicted free-surface elevations and velocity profiles show a satisfactory agreement with measurements and most of the peculiar features of the flow, such as the trapezoidal shape of the wave front and the flow separations at the toe of the oblique shock wave along the side walls, are qualitatively and quantitatively reproduced.

Keywords:

• Hydraulic jumps
• separated flows
• smoothed particle hydrodynamics models
• three-dimensional models
• turbulent flows

Acknowledgements

Part of the SPH simulations discussed in this article has been performed at the C.I.L.E.A. (Centro Interuniversitario Lombardo di Elaborazione Automatica) supercomputing centre in Segrate (Italy), under the grants assigned under the project LISA.