Numerical Understanding of Free Surface Vortex Driven by Rotational Field Inside Viscous Liquid

Abstract

The present study established the genesis of free surface vortex inside a viscous liquid using a rotating cylindrical disc immersed in the liquid. The longitudinal axis of the disc is kept normal to the nominal interfacial plane and its rotation is characterized in terms of Froude number (1.50–4.49). This configuration is simulated using a grid-based volume of fluid technique in the air and high viscous polybutene pair. A dip in nominal interface profile is observed at low disc rotations (Froude number ≈ 1.50), however, the gradual progress of the rotational inertia (Froude number > 1.50) has resulted in elongation of the interface in the form of a free surface vortex progressing inside the liquid. The transient progress of vortex depicts bullet nose like interface tip during the early stages, which grows in the outward radial direction along with its downward motion due to the centrifugal effect of the surrounding liquid. The initial submergence ratio of the disc and its radius are shown as the important parameters governing the entrainment rate and shape of the vortex profiles. The physical understanding behind the formation of the vortex is revealed using axial and crosswise circulations of the surrounding liquid.