An analytical model for vortex at vertical intakes

Abstract

In the present paper, free surface vortex formation at intakes is investigated analytically. By assuming a spiral form for vortex streamlines, continuity and momentum equations were integrated and solved in a vortex flow domain. From this solution, velocity and pressure distributions were found above the intake under vortex action. An equation for the water surface profile was also found and compared with another research. By considering that in an air core vortex, pressure at the intake entrance drops to zero, a relationship was found for critical submerged depth and verified by experimental data and another analytical equation. It was concluded that the results of the proposed spiral analytical model had good agreement with the experimental data. HIGHLIGHTS Analytical analysis of free surface vortex phenomenon over a vertical intake in the reservoir.; Solving 3D Navier-Stokes equations analytically for a swirling flow.; Predicting the critical submergence at a vertical intake.; Extracting pressures and velocities analytically using spiral theory.; Comparing obtained analytical results with previous experimental and analytical results.;

Keywords

• critical submerged depth
• free surface
• navier-stokes equations
• pressure and velocity distributions
• spiral vortex flow