Vertical air-entraining vortex at an intake

Air-entraining vortices at hydraulic intakes present significant challenges in engineering, leading to efficiency losses, structural vibrations, and potential operational instabilities. While previous research has explored these vortices, most studies have been limited to specific intake geometries and flow conditions, lacking a generalized predictive model. Additionally, due to the complex nature of air-core vortices, deriving a single universal theoretical formula remains elusive. Existing semi-empirical models are typically case-specific, and while numerical methods offer alternative solutions, they often require extensive computational resources and experimental calibration. By improving an analytical technique to forecast the profile of vertical air-entraining vortices across various intake configurations, this work seeks to overcome these constraints. The method improves on the semi-empirical formula for vertical non-air-entraining vortices (air-core vortex in suspension) that is already available. A trial-and-error solution method was created to predict vortex profiles with more precision since the air-core vortex height in air-entraining vortices cannot be measured directly. The available test data and the results of the present study are compared, and found to be in good agreement. This research identifies the following advancements: 1.A refined prediction model for the vertical air-entraining vortex profiles .By modifying the available formula for non-air-entraining vortices and incorporating empirical validation, the study establishes a reliable methodology for estimating air-entraining vortex profiles. The validation is based on experimental data from previous available studies, ensuring the proposed model accurately represents real-world vortex behavior. 2.Development of a practical chart and formula for engineers – The study provides a simplified chart that allows engineers to directly determine vortex parameters for downward-flowing intakes without requiring complex numerical simulations. 3.Validation using experimental data sets – The proposed methodology was examined and checked with test data for vertically flowing downward air-entraining vortices (h/S>1) at circular intakes. The results demonstrated a strong correlation between predicted and observed vortex profiles, confirming the accuracy and applicability of the refined model. The findings of this research offer a significant advancement in vortex prediction methodologies, providing engineers with a practical, validated, and computationally efficient tool for designing hydraulic intakes and mitigating vortex-related inefficiencies. By improving upon existing models and validating them against experimental data, this study enhances the ability to predict and control air-entraining vortices in real-world hydraulic applications