Analysis of Velocity Profiles and Power Prediction for Single-Stage Gravitational Vortex Water Turbine (GVWT)

The gravitational vortex water turbine (GVWT) is a promising technology for low-head hydropower applications; however, its internal flow structure and hydrodynamic basis for multistage runner placement remain insufficiently understood. A GVWT primarily consists of an inlet channel, vortex-forming basin, and runner installed within the vortex-forming basin. This study focuses on the inlet-channel notch angle configuration and its influence on the conical basin flow field, single-stage power prediction, and residual flow criteria for second-stage runner placement. This study investigated the velocity profiles and power prediction of a single-stage GVWT in two conical basin configurations, namely, Basin A (conical basin with 0° inlet-channel notch angle) and Basin B (conical basin with 19° inlet-channel notch angle), with the aim of deriving design-relevant guidance for multistage implementation. Computational fluid dynamics (CFD) simulations were performed to examine vortex formation and the distributions of tangential, axial, and radial velocities before and after runner installation. The results show that Basin B produces a more symmetric and vertically coherent vortex, along with a more uniform tangential velocity distribution, smoother axial flow, and reduced radial diffusion compared with Basin A. These characteristics create a favorable hydrodynamic environment for energy extraction. A semiempirical power prediction model was developed using Buckingham pi analysis and evaluated as a practical design tool using experimental data for a 10 cm propeller runner installed at different depths. The model reproduced the experimental trend well, with deviations of approximately 2% across the tested runner depths. Downstream flow analysis further showed that significant tangential kinetic energy remained below the first-stage runner, indicating that the lower basin retained sufficient hydrodynamic quality for evaluating second-stage runner placement. Based on the combined velocity and kinetic-energy distributions, the region z/H = -0.9 to -0.8 was identified as the most suitable location for second-stage runner installation because it offers high residual tangential energy, moderate axial energy, reduced radial diffusion, and improved submergence, providing a depth-based design criterion for multistage GVWT systems. Therefore, this study provides a hydrodynamics-based design framework for predicting the single-stage GVWT performance and identifying suitable second-stage runner placements in multistage systems.