The Effect of Aeration on Energy Dissipation in Plunge Pools

Plunge pools are energy dissipation structures in hydropower installations which dissipate the excess energy of spillways. It is usually assumed, that the energy of the highly aerated falling water jet is dissipated as turbulence. During the impact of the water jet, high transient pressures are generated which can cause erosion of the plunge pool bed.

Researchers noted that the energy dissipation in model scale plunge pools appeared to be significantly smaller than at full scale. This was attributed to the aeration content, which was higher at full than at model scale due to the higher Weber-Nr. No explanation of an energy dissipation mechanism was however given.

The high air content of the aerated flow, in combination with the high transient pressures generated by the jet impact, suggests that the compression of air bubbles during the impact of a water could be of importance. Experiments reported in the literature showed that under impact velocities of around 22 m/s, the air bubbles below the impact point are compressed to around ¼ of their original volume. In the plunge pool, the air bubbles are then transported from the pressurized zone below the impacting je into the free stream, where they expand.

At Southampton University, a thermodynamic model was developed to analyse the effects of compression and expansion of air bubbles. The analysis showed, that the flow of water-air mixtures can be compressible, and that pressure fluctuations due to a dynamic response can occur. The model also indicated, that a significant amount of the total energy of a plunging jet can be absorbed by air compression. During subsequent expansion, 2/3 of the energy required for compression will be radiated out normal to the flow direction, this energy being lost to the flow. This led to an energy dissipation rate of 2.0 % for a jet velocity of 6 m/s, and 18% for a jet velocity of 24 m/s. Due to the non-linear compressibility of the air, the energy dissipation ratio increases exponentially with the air content and pressure magnitude. This implies, that energy dissipation at model scale will be disproportionally smaller.

The thermodynamics of an aerated impinging jet, which is currently neglected, can therefore have a significant effect on energy dissipation. The modelling of energy dissipation in plunge pools would require a combined hydrodynamic and thermodynamic model.