Development of a 1D model for the prediction of piano key weirs discharge capacity

Abstract

This master’s thesis enhances a 1D flow model named WOLF1DPKW, designed to pre- dict the discharge capacity of Piano Key Weirs (PKWs). These weirs hold paramount importance for dam safety, playing a pivotal role both socially and technologically within hydraulic infrastructures. The model is built upon the concept of two adjacent water lines crossing the PKW, exchanging water and lateral momentum. This allows for a 1D modeling approach. Prior to any parametric optimization, the preliminary outcomes of this model necessitate re- finement. Minimizing these discrepancies is the objective of this work, while maintaining a strong grounding in physics. After a brief introduction, the second chapter presents the existing model, identifies its weaknesses, quantifies errors, and outlines ideas for potential improvements. The main avenues explored are (1) the incline of the flow axis at the inlet, (2) a modification of the lateral crest discharge coefficient, (3) an adjustment of the alpha coefficient characteriz- ing lateral momentum exchange, and (4) a modification of the locations for lateral flux extraction and injection. Subsequently, a sampling of the provided database is conducted to maximize the rel- evance of statistical analyses. The fourth chapter showcases the outcomes of numerical simulations and the sen- sitivity analyses. To maintain a resolutely physics-based perspective, these results are examined using a hydraulic approach, allowing for both statistical and physical evalua- tion of their relevance for model enhancement. In conclusion, the findings of this research reveal that idea 1 is not retained, as a horizontal flow axis at the inlet yields better results than an inclined axis. Idea 2 highlights the significant influence of the lateral discharge coefficient at low flow rates, but not at high flow rates, where the model error reaches a maximum. Idea 3 reflects a similar trend to 2, with divergent behaviors observed in specific geometric configurations. Idea 4... (to be continued).