Rankine Vortex Formation during Draining: A New Twin Port Suppression Strategy

Abstract

This paper reveals the results of a study of vortex air core formation (Rankine vortex) when a rotated liquid (water) column in a cylindrical vessel is drained through two ports located at equal eccentricity (e) at the vessel base (diameter, d_1and d_2) simultaneously; d_1is fixed whereas d_2 is varied. Just before draining, a rotation (n rpm) is provided to the liquid column in controlled conditions. As draining progresses, when the liquid level reaches certain height called critical height (h_c), initially a surface dip forms which further develops in to a vortex extending down till the drain port. Results show that critical height increases as the fluid rotation rate increases at the lowest eccentricity. But, at higher eccentricities, h_c, exhibits more or less an increasing-decreasing trend in most of the cases studied. Critical height is observed to be minimum for the largest value of d_2 (equal to d_1) irrespective of the values of the speed of fluid rotation, liquid initial height and port eccentricity. To particularly note, at the highest eccentricity, vortex formation is found to be completely suppressed for all values of port diameter (d_2) and initial fluid rotation (n) as indicated by the near-zero critical height values. The tangential velocity measurements using Particle Image Velocimetry are also reported. PIV results obtained for certain cases with induced fluid rotation (normal draining and faster draining) correlate well with the changes in the efflux (axial) velocity (deduced analytically) in these cases studied. The tangential velocity along radial direction obtained (PIV) also indicated the type of vortex formed in normal and faster draining cases. Video visualization of vortex formation carried out reveals that, vortex air core switching takes place between the drain ports maintaining an arched or curvilinear surface profile apart from demonstrating the nature of outlet flow discharge. All the vortex air core formation studies so far carried out were invariably with single drain port except the preliminary novel study by the same author group and the present study is a detailed extension of that novel study.

Keywords

• Vortexing; Twin drain ports; Liquid draining; Critical height; Time of emptying; PIV; Flow visualization.