Analytical, Numerical, and Computational Methods to Analyze the Time to Empty Open, Closed, and Variable-Topped Inverted Bottles
Available at: https://digitalcommons.calpoly.edu/theses/2611
Date of Award
MS in Mechanical Engineering
College of Engineering
College of Engineering
Recent unexpected experimental observations of the emptying of inverted bottles with perforations has generated interest in modeling and simulation of this phenomenon. It was observed that as a perforation, i.e., a small hole at the "top" of the inverted bottle, is added and enlarged, the overall emptying time first increases to a maximum value and then decreases until it reaches a lower limit. The change in emptying time is associated with a transition from jetting, where only water exits the neck, to glugging, a competition between air and water flows at the neck of the bottle.
This paper develops analytical and numerical models to predict emptying time and liquid height as a function of time which capture the jetting-to-glugging transition. When qualitatively compared to experimental data using a bottle with neck diameters of 12.7 mm, 25.4 mm, and 38.1 mm and bottle diameter of approximately 355 mm (equating to several hundred to several thousand seconds to drain) a favorable agreement is observed. These models attempt to explain the transition in terms of a competition between liquid and bubble velocities at the bottle neck and build on an existing model of glugging available in the literature.
The paper also explores the first steps taken toward simulation of bottle emptying using a commercial CFD package (Fluent) to simulate draining for a smaller bottle of neck diameter 21.6 mm and bottle diameter of 62.2 mm. The Fluent simulations are used to further elucidate the jetting-to-glugging transition mechanism by simulating emptying with and without perforations. CFD results reported are limited to a few select large perforation diameters. Specifically, a 4 mm perforation taking 15 hours to simulate and 6 mm perforation taking 5 hours to simulate. Despite the lengthy simulation times, both capture only the approximate 2 seconds required to drain the bottle, but demonstrate the effect of the perforation on emptying time. Smaller perforations on the order of 1 mm, which would align with the experimentally determined maximum emptying time would require unfeasibly long simulations for present resources as dictated by required low Courant numbers. Future work with greater computational capability will further expand upon the simulations conducted in this work.