A simple SPH model of a free surface water wave pump: waves above a submerged plate

ABSTRACT

In this work, the SPH method is used in 2D to evaluate the pump characteristics of free surface water waves above a submerged plate. The configuration considered here consists of an infinite wave train reaching a rectangular plate of length $2l_p$ and thickness $t_p$ submerged $d_p$ under the undisturbed water level. The numerical method is validated against experimental results with good agreement. The mean Eulerian mass flux $⟨\rho u⟩$ is evaluated in the simulation and outlines the importance of the wave mass transport in the circulation around the submerged plate. It is observed an increase of the mass flux in the surface layer (wave mass transport) as predicted by the water waves linear theory. The incident wave frequency and height are varied and the flow rate is evaluated and compared to the linear model. To study the pump response, a gate valve is placed at the center position under the submerged plate. The fully open gate configuration corresponds to the experimental case. Pump curves are provided. The maximum dynamic pressure efficiency is evaluated to be $\approx 10\mathrm{\%}$ for the present configuration.

KEYWORDS:

• SPH method
• pump
• water waves
• linear potential theory

Acknowledgments

The authors would like to thank Alex Ghaïtanellis, Martin Ferrand, Alexis Hérault, and Gaële Perret for their useful comments and interest in the project.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Note that this value is not important. It should be close enough to the paddle to not be affected by the surface curvature. For monochromatic wave, we consider this as sufficient. If one wants to absorb irregular waves, this should be fixed to typically 3 particle size.

² In certain cases, as outline in Carmigniani (2017) Section 3.2, the wave mass transport might decrease above the plate and become negative.