Author(s): Benjamin Hohermuth; Robert M. Boes; Stefan Felder

Linked Author(s): Benjamin Hohermuth

Keywords: High-velocity flows; Phase-detection conductivity probes; Prototype conveyance structures; Scale effects; Spillway flows

Abstract: Air-water flows commonly occur in hydraulic structures such as spillway chutes and low-level outlets. In these high-velocity flows, air entrainment is a dominant feature and must be considered for a sound design of these safety-relevant appurtenant structures of reservoir dams. Numerous fundamental studies have shed light on the entrainment process, micro- and macroscale air-water flow properties as well as two-phase turbulence since the landmark publication of Straub and Anderson in 1956. Detailed design guidelines were developed for smooth and stepped spillways as well as low-level outlets. However, due to their empirical nature, most of these guidelines are limited to specific cases studied in laboratory scale models. Consequently, scale effects remain a common issue in air-water flow research as they possibly affect the extrapolation of laboratory-scale mass and momentum transfer processes to prototype scale. While Reynolds numbers exceed 10⁷ to 10⁸ in prototypes, most laboratory studies have been conducted at 10⁴ to 10⁶. Data for Reynolds numbers in the order of 10⁷ are scarce and a thorough validation of air-water flow research is thus missing. In the present study, we acquired unique data of detailed air-water flow properties in a prototype tunnel chute with Reynolds numbers up to 2.2∙10⁷. To this end, an array of 16 double-tip conductivity phase detection probes was installed towards the downstream end of the 38° tunnel chute at the 225 m high Luzzone Dam in Switzerland. The measured raw voltage signal was post-processed using the recently developed adaptive window cross-correlation technique to obtain air concentration, particle frequency and particle chord times as well as interfacial velocity time series. Additional statistical analyses allowed to uncover information on the droplet size distribution in the spray flow region. The results indicate that the air concentration distribution compares well with existing semi-empirical advection diffusion equations. The time-averaged velocity distribution follows the typical power law distribution previously observed for laboratory scale data. Bulk properties of engineering interest such as the depth-averaged and bottom air concentrations and the Darcy Weisbach friction factor are within predictions of empirical relations developed for laboratory-scale data. This finding is important since it suggests that laboratory-scale design approaches can be applied to prototype-scale structures up to at least 2.2∙10⁷. However, the measured droplet size distributions revealed significantly smaller particle sizes compared to laboratory-scale data, supporting our working hypothesis. For the studied flows, the particle size showed a continuous decrease with increasing bulk Reynolds numbers up to 2.2∙10⁷. This finding may have important implications for mass and momentum transfer processes such as air demand in outlet structures or flow oxygenation in energy dissipators.

DOI: https://doi.org/10.3850/IAHR-39WC252171192022119

Year: 2022