by Adrien Bourgoin, R&D Engineer
Photo by Jeremiah Castro from FreeImages
Numerical modelling hardly assesses the involved physical phenomena. Most of the numerical approaches used in engineering assume flows to be monophasic, and lead to an overestimation of pressure at the impact point. Eulerian methods do not suit fluid displacement estimation, due to their immobile degrees of freedom. That is why such flows are still mostly studied experimentally .
In  a weir water jet was modelled with an experimental set-up representing a 9 meters waterfall. A Photogrammetry method allows the reconstitution of the three-dimensional water jet shape from a series of photographs. For a flow rate range from 0.075 m3/s to 0.220 m3/s, Bercovitz established a waterfall profile defined by:
where z is the vertical ascending coordinate, x is the stream-wise coordinate, and H is the head over the crest.
Although accurate, this approach remains expensive and long-winded. Thanks to its Lagrangian nature, the Smoothed Particle Hydrodynamics (SPH)  method could be a relevant candidate for those kinds of applications . Very recently, air entrainment has even been introduced with this approach , which could also lead to better estimations of the pressure at the impact point.
A monophasic incompressible model is used here, only the jet shape is investigated. The experimental setup from  was reproduced with a flow rate of 0.1 m3/s.
Fig. 1 shows the comparison of the waterfall lateral profiles, obtained with the numerical solver and the analytical profile defined in . Extracted after 15s of physical time, this result shows a good cohesion with literature.
 Y. Bercovitz, W. Barrey, F. Lebert, and C. Buvat. Envelope trajectory of water jet issuing from a thin weir obtained by photogrammetry. 2018.
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