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  • Publication
    Open Access
    Piano-Key-Weirs as in-channel applications
    (Helmut-Schmidt-Universität / Universität der Bundeswehr Hamburg, 2023) ; ;
    Helmut-Schmidt-Universität / Universität der Bundeswehr Hamburg
    Tullis, Blake Paul
    With reduced footprint and excellent hydraulic performance, piano key weirs (PKW) have been gaining growing attention in the past two decades as a favorable up-to-date solution for the rehabilitation of spillways as well as in-channel applications. However, due to its complex geometry and flow characteristics, it has been challenging to find the optimal design that provides the best hydraulic efficiency. Within this dissertation, systematic experiments as well as numerical simulations have been conducted to investigate possible geometry optimizations and resulting influences on the hydrodynamic behaviour of PKWs. Based on comparative analysis between trapezoidal and rectangular piano key weirs with various key width ratios, trapezoidal plan forms are found to be more efficient especially for high relative upstream heads because of the larger outlet cross section; and less efficient for low relative heads due to the relative lack of total crest length. The influence mechanism of key width ratio on overall discharge capacity of the weir has been revealed and the optimal range of key width ratios have been determined. In addition, a new PKW configuration, which combines the advantages of both geometries (rectangular and trapezoidal) and improves the overall weir efficiency, is introduced. Moreover, a more detailed investigation on the downstream flow regime development was carried out using a large-scaled multi-cycle model. Compared to previous models, the downstream flow structure was observed to vary with actual model size and cycle number. A sufficient cycle number is found to be beneficial for a more stable downstream flow condition. Based on the results, a preliminary classification of the flow condition downstream of a PKW is provided with empirical equations proposed for the localization of aerated flow region. For a piano key weir with symmetrical trapezoidal plan form, the influences of varying model size and crest configuration on discharge capacity, downstream flow characteristics and energy dissipation are further examined. The correlation between crest shape, upstream total head and nappe behaviour is analyzed and critical conditions are identified. Related nappe instabilities and size scale effects in both upstream and downstream side of the weir crest are addressed. Based on experimental data, empirical equations are developed to accurately predict the discharge coefficients and downstream residual energies for similar PKW configurations. Last but not least, irregular piano key weir configurations with additional side extensions were also investigated via hybrid modelling. Comparative analysis shows that nappe collision between adjacent side walls has negligible influence on the side wall discharge. Instead, the nappe interaction between upstream apexes and side walls was noted to be the most critical factor limiting the side wall efficiency. Moreover, it was observed that the upstream apexes exhibited an equivalent head-discharge relationship to vertical linear weirs featuring the same crest, while the efficiency of downstream apexes as well as the side walls varied with key width ratio. With all these effects being taken into account, empirical approaches have been developed to estimate the discharge coefficients of such irregular configurations and facilitate their practical design.