Competition of roller rotation and horizontal crossflow to control the free surface cusp-induced air entrainment

Abstract

Efforts are made to delineate the dynamics of entrained gaseous cusps and flow of liquid films wrapped around a horizontal partially submerged rotating roller numerically. The solid roller is allowed to rotate across the gas–liquid interface with a fixed submergence ratio of 0.5 (equally immersed in both gaseous and liquid phases) and the gaseous phase is subjected to horizontal crossflow. The finite volume-based solver Gerris has been employed to track the interfacial configuration by using the volume of fluid (VOF) method. The combined influence of roller rotation (ω) and strength of crossflow (Reflow) on the wrapped film thickness and the structure of entrained cusp is demonstrated thoroughly for different gas–liquid pairs in order to understand the underlying physics. This study also includes the transient dynamics of liquid tip movement from the receding to advancing junction for various Reflow and gas–liquid pairs. Subsequently, the structure and rate of entrainment are also estimated, where the collapsible gaseous jet breaks into circular gaseous bubbles. Predictions are also made in order to establish the dependence of interfacial configuration on the Archimedes number (Ar). Finally, a theoretical model has been developed to elucidate both entrainment and wrapped film dynamics, which shows excellent agreement with the numerical results.

Numerical Simulation and Analytical Prediction on the Development of Entrained Air Filament Caused by the Combined Effect of Rotational Field and Free Stream Flow

“…The rotary drum is equally immersed in air and ink. Again, Figure b depicts the comparison of the width of the gaseous entrainment ( H *) for various crossflow velocities ( Re flow ) of the present model with the recently published literature (Panda et al). Panda et al analyzed the entrainment of the air cusp in a liquid pool caused by a partially submerged roller, which was allowed to rotate across the gas–liquid interface, and the gaseous phase was subjected to a steady free stream flow above the free surface.…”

“…Again, Figure b depicts the comparison of the width of the gaseous entrainment ( H *) for various crossflow velocities ( Re flow ) of the present model with the recently published literature (Panda et al). Panda et al analyzed the entrainment of the air cusp in a liquid pool caused by a partially submerged roller, which was allowed to rotate across the gas–liquid interface, and the gaseous phase was subjected to a steady free stream flow above the free surface. We compared the variation of H * with θ* predicted from the present model with that of Panda et al for the air–silicone oil fluid pair at ω = 20 rad/s for different Re flow .…”

“…(a) Comparison of the width of the film ( h ) with the findings of Yu et al and Rana et al . (b) Comparison of the width of the entrained cusp with that of Panda et al Copyright 2009, Elsevier, International Journal of Heat and Fluid Flow, Vol. 30, Yu, S. H.; Lee, K. S.; Yook, S. J., Film flow around a fast rotating roller, pp 796–803.…”

“…Panda et al analyzed the entrainment of the air cusp in a liquid pool caused by a partially submerged roller, which was allowed to rotate across the gas–liquid interface, and the gaseous phase was subjected to a steady free stream flow above the free surface. We compared the variation of H * with θ* predicted from the present model with that of Panda et al for the air–silicone oil fluid pair at ω = 20 rad/s for different Re flow . Hence, it is noticed that the findings of our model showed satisfactory agreement with the published article.…”

“…Furthermore, Ren et al carried out experiments on a steady flow past a partly immersed static drum and determined the critical value of the Froude number to differentiate “overtopping” and “nonovertopping” conditions. Most recently, Panda et al attempted numerically to describe the gas entrainment dynamics and wrapped film around a partly immersed (50% submergence ratio) drum across different gas–liquid interfaces with an additional effect of steady flow of air over the free surface.…”