How to Scale the Air Demand of Low-Level Outlets? Comparison of Large-Scale Model and Prototype Data

Low-level outlets are a key safety feature of high-head dams. The high-speed water jet ejected from the gate leads to significant air transport out of the outlet tunnel. Consequently, air has to be supplied with a dedicated air vent to mitigate problems with gate vibration and cavitation. Current design recommendations are based on model tests and limited prototype data. Hydraulic, Froude-scaled models of air-water flows are subject to significant scale effects if limiting Reynolds or Weber numbers are not met. While limiting criteria for air entrainment on spillways and spillway aerator design are known, there is little knowledge on scale effects regarding the air demand of low-level outlets. Therefore, this paper investigates to what extent results from model tests can be up-scaled to prototypes to reduce design uncertainties.

The effect of different parameters, such as the contraction Froude number, loss coefficient of the air vent, tunnel length and slope, on relative air demand was studied in a hydraulic scale model at VAW, ETH Zurich. The model features a 0.2 m wide, 0.3 m high tunnel with a maximum total length of 20.6 m. A wide range of flow conditions was investigated with contraction Froude numbers from 10 to 45 and Reynolds numbers (based on specific discharge) up to 2.6∙10⁶. Existing prototype air demand data from literature were expanded with new measurements at three outlet structures in Switzerland featuring hydraulic heads of up to 113 m w.c. (max. Reynolds number ~3.3∙10⁷). In total, complete prototype data from six outlet structures were available for a comparison with model results.

The hydraulic model tests allowed to identify the effect of the contraction Froude number, the loss coefficient of the air vent, tunnel length and slope on the relative air demand. Considering these parameters results in a significant reduction of data scatter compared to existing design equations. The new prototype data significantly extend the range of observed relative air demand values at comparable Froude numbers. Only one of the prototype data sets can be reproduced with the model-based equation within ± 20% while others were underestimated by up to one order of magnitude. Geometric differences between model and prototypes as well as prototype data quality explain some of the observed differences. However, the data indicate that scale effects regarding the momentum transfer from the water to the air phase may be the reason for the remaining unexplained difference between model and prototype data.