Investigation of Drop Generation from Low Velocity Liquid Jets and its Impact Dynamics on Thin Liquid Films A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY (Ph.D.) in Mechanical Engineering of the College of Engineering and Applied Sciences by Sucharitha Rajendran September 2017 B.Tech., National Institute of Technology-Durgapur, 2010 M.S., University of Cincinnati, 2012 Committee Chair: Dr. Milind A. Jog Committee Member: Dr. Raj M. Manglik Committee Member: Dr. Kumar Vemaganti Committee Member: Dr. Woo Kyun Kim i ABSTRACT Drop generation from jet breakup and drop-impact on thin films are two key processes in many spray, coating and deposition applications which are experimentally and computationally investigated in this dissertation. A high-speed camera is used to capture the drop formation and its impingement on thin films and a modified volume of fluid (VOF) method is used to accurately simulate jet/film breakup. It is shown that the proposed modifications in interfacial property evaluations for VOF method provide accurate predictions of moving interface for highly viscous liquids. To understand the parameters governing uniform drop generation, a numerical study of the jet disintegration process, supplemented by experimental observations, is conducted. The simulations show that while an increase in viscous force offers greater resistance to propagation of the surface undulations thus resulting in stretching of the liquid jet, surface tension determines the radius of curvature of the pinch-off location. The interplay of these two forces leads to deviations from uniform drop generation and two different modes of liquid jet pinch-off that lead to satellite drop creation are observed. It is shown that the occurrence of these modes is governed by the liquid Morton number. A semi-empirical relation is proposed to predict the onset of the two modes. In most spray applications, the drops formed from a jet are incident on a target surface usually with a thin layer of liquid film. While viscous resistance to impact of the drop is offered by the film thus controlling drop spreading and crown formation, surface tension is noted to primarily govern the growth and eventual break-up of the ejected crown. An empirical relation for the onset of splash is obtained from high-speed image analyses of the drop-film interactions. Numerical simulation of the process indicates that the contribution of the target film and impacting drop in the creation of ejected crown depends on the film thickness. At low liquid film thickness, the liquid ii from the impacting drop primarily forms a jet that is ejected post-impact. For thicker films, the liquid layer absorbs a part of the energy from the impacting drop and thus the ejected jet is formed from both the impacting drop as well as the liquid layer. The temporal dynamics of deposition of Newtonian drops on thin films indicates that while surface tension and inertial forces govern resultant crown height, their contribution on crown diameter is not as significant. Viscosity is noted as the key factor that governs the crown diameter. In addition, experimental investigation of drop impact dynamics of shear thinning polymeric solution is carried out to understand the effects of solution rheology on the temporal dynamics. For aqueous solution of HEC 250 HHR, the apparent viscosity is low during initial impact (high shear rate) and this increases the likelihood of splashing compared to a Newtonian liquid with the same zero shear viscosity. High-speed images of drop impact on thin film of aqueous solution of PEO WSR 303 indicate that extensional viscosity also plays an important role in governing the post-impact behavior. iii iv ACKNOWLEDGMENTS I wish to express my most sincere gratitude and appreciation to those who have contributed to this work and to those who have been my support system throughout my academic journey. First, I am extremely grateful to my academic advisor, Dr. Milind A. Jog, and co-advisor Dr. Raj M. Manglik for their guidance and all the helpful brainstorming sessions. These discussions always helped me gain new insights into the problem and often I would come out looking at the problem in new light. Apart from this, I have often found myself being inspired by Dr. Jog and Dr. Manglik’s clarity in thinking – be it to resolve some tough numerical road blocks or to device better means of conceptual analysis. I would like to also thank my committee members, Dr. Kumar Vemaganti and Dr. Woo Kyun Kim for taking interest in my research and providing helpful suggestions and important insights. During my course of research, I have gotten to know some university staff members that I wish to express my gratitude to. Bo Westheider has helped me with setting up experiments and fixing multiple equipment for the different needs of the testing. Larry Schartman has helped me innumerable times to set-up and fix (and repeat) workstations for the different needs that arose. Luree Blythe and Barbara Carter have always been very approachable and helpful. I would also like to thank the very knowledgeable staff and consultants at OCC who helped with the many software and printing issues I’ve had over the years. Apart from working on my research, I was a part of the CEEMS (Cincinnati Engineering Enhanced Math and Science) fellowship and had the lovely opportunity to interact with students and teachers in their daily classroom lessons. I would like to thank Dr. Anant Kukreti, Julie Steimle, Debora Liberi and all the teachers for this experience. I have also been a part of the UC Simulation center and my interactions with Proctor and Gamble mentors and the projects I worked on have taught v me a lot. Working with both Dr. Joe Grolmes and Rakesh Gummalla has been a lovely learning experience. Dr. Brent Rudd and Fred Murrell’s enthusiasm to maintain the great working environment made it the experience marvelous. Apart from these two organizations, I would also like to thank the Education and Research Center’s (ERC) Pilot Research Program (PRP) for providing the initial funding for this project. The interest to pursue a PhD degree in Fluid and thermal science stems from Dr. Amarnath Mullick’s always cheerful motivation. I take this opportunity to thank him for encouraging me to pursue summer research fellowships during my under-graduation at NIT Durgapur, in addition to providing guidance to a very challenging and interesting senior year project. I appreciate the help and support provided by my colleagues at Thermal Fluid and Thermal Processing Laboratory. This was always a fun work environment. During my stay at Cincinnati, I have had the fortune of the company of some very good friends that have made this duration even more memorable: Deepak Saagar, An Fu, Wilma Lam, Sai Deogekar, Raghunandan Chilkuri, Srikirti Velaga, Amruta Dongonkar, Gautam Krothapalli, Santhosh Dungi, Suryanarayana Pappu, Anup Srikumar, Aditya Mantri, Sruti Jagabatulla, Vibhu Gautam, and many others. I would like to express my most sincere gratitude to Karthik Remella for not only being a pillar of support though everything, but also for being a constant source of inspiration and pushing me to always try harder. And finally, I am forever indebted to my parents, Rajendran and Jadila and to my brother Shashank, and to all my family for their unconditional love and support. Through times that have seemed discouraging and through those that were joyous, they have always shared an important part. They are my backbone. This work would not be a reality without them and I would like to dedicate this dissertation to them. vi TABLE OF CONTENTS Abstract ........................................................................................................................................... ii Acknowledgments........................................................................................................................... v Table of Contents .......................................................................................................................... vii Nomenclature .................................................................................................................................. x List of Figures ............................................................................................................................... xii List of Tables .............................................................................................................................. xvii 1 Chapter 1: Introduction ............................................................................................................ 1 1.1 Jet breakup and the resultant drop distribution ....................................................... 1 1.2 Drop impact dynamics ............................................................................................ 5 1.3 Scope of the current research .................................................................................. 9 2 Chapter 2: Modified Volume of Fluid method for two-phase flows ..................................... 12 1.4 Introduction ........................................................................................................... 12 1.5 Numerical Procedure ............................................................................................ 14 1.5.1 Governing Equations ................................................................................. 15