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Experimental Investigation of Effect of Viscosity on Aperiodic Bubbling from Submerged Capillary-Tube Orifices in Adiabatic Liquid Pools

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Experimental Investigation of Effect of Viscosity on Aperiodic Bubbling from Submerged Capillary-Tube Orifices in Adiabatic Liquid Pools Experimental investigation of effect of viscosity on aperiodic bubbling from submerged capillary-tube orifices in adiabatic liquid pools A Thesis Submitted to the Graduate School University of Cincinnati in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE (M.S.) in the Department of Mechanical and Materials Engineering of the College of Engineering and Applied Sciences (CEAS) by Aakash Deora Bachelor of Technology (Mechanical Engineering) G.B. Pant University, Pantnagar, India, 2013 Committee Chair: Dr. Milind Jog i ABSTRACT This thesis focusses on experimental investigation and subsequent regime mapping of the aperiodic bubbling from submerged capillary orifices through quiescent adiabatic liquids with varying viscosities. A high-speed and high-resolution digital camera is used to capture formation, departure, and coalescence of air bubbles in static liquids. Water and five glycerol-water mixtures with 36%, 48%, 65%, 77%, and 87% glycerol by volume are used to alter dynamic viscosity while keeping density and surface tension nearly the same. Five stainless steel orifices with diameter- 0.8 mm, 1 mm, 1.4 mm, 1.8 mm and 2.4 mm are used to vent compressed air through the liquids with air Reynolds number ranging from 100 to 1800. With increase in the flow rate, bubble frequency increases and beyond a critical value wake effect of the preceding bubble affects the formation and departure of trailing bubble. Due to this wake effect, trailing bubble rises faster and coalesces with the leading bubble. In this flow regime, fluid dynamics is conducive to coupling. With further increase in the flow rate, wake effect grows in strength and facilitates coalescence of two already coalesced bubbles. This regime is called quadrupling regime. For water, a tripling regime is also observed for orifice diameters 1 and 1.8 mm, where a single trailing bubble coalesces with a coupled bubble. Effect of viscosity on aperiodic bubbling is investigated using different glycerol-water solutions. Mathematical analysis of experimental data shows that Capillary number is an appropriate physical parameter for the characterization of different bubbling regimes. Effect of orifice diameter is also studied and for smaller orifice diameters, bubbles are seen to coalesce closer to ii orifices and coalescence takes place at larger Capillary numbers. For quadrupling, a high value of Ca is obtained for the smallest orifice and this is almost thrice the value for the largest orifice. A correlation between Capillary Number and non-dimensional orifice diameter is derived from the experimental data for the coupling regime; which can be used to predict transitional Ca values for liquids of varying viscosity. The correlation uses Morton Number to factor in the balance of forces i.e. viscous force, buoyancy and surface tension, in bubble dynamics to predict the transitional Ca. Similar effort was made to understand and analyze the experimental data in the quadrupling regime. However, due to the strong non-linear effect of viscous drag along with experimental limitation of analyzing both wake effect and inertia force of the surrounding liquid involved in this regime, it would require further experimentation with more glycerol solutions. This is recommended for future experimental investigation. iii ACKNOWLEDGEMENT I am indebted to Dr Milind Jog, my thesis advisor, for his guidance and valuable inputs throughout this experimental work. He has inspired me to pursue my academic endeavors with alacrity and honesty; and has also been a role model for me on being a wonderful person. I would also like to extend my heartfelt gratitude to Dr. Raj Manglik for countless in-depth and informative discussions which helped me in the proper analysis of my result. This work would have not been possible without his numerous insights into this experimental research. I have been very fortunate to have wonderful lab mates who were always ready to help with my experiments and kept my spirits up throughout the length of my stay in lab. I owe them all my gratitude and sincere love. Last, but the most important, to my family members who have always encouraged me to realize my dream by their unwavering support and love. My better-half, Nidhi, deserves the kudos for always inspiring me; being a true beacon of joy in my life and making sure I was at my intellectual best to pursue this research. iv TABLE OF CONTENTS ABSTRACT ii ACKNOWLEDGEMENT iv TABLE OF CONTENTS v LIST OF FIGURES vii LIST OF TABLES x NOMENCLATURE xi CHAPTER 1: INTRODUCTION 1 Motivation 2 Scope of Study 2 CHAPTER 2: LITERATURE REVIEW 4 CHAPTER 3: EXPERIMENTAL METHODS AND MATERIALS 9 CHAPTER 4: RESULTS AND DISCUSSION 12 Effect of viscosity on bubble shape, frequency and size 15 Double coalescence 18 Scaling and analysis for coupling regime 37 Quadrupling coalescence 43 Scaling and analysis for quadrupling regime 55 v Effect of viscosity on coalescence distance 59 CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS 62 REFERENCES 65 APPENDIX A 68 Transition values for coupling and quadrupling regimes for test liquids 68 APPENDIX B 72 Plots of transitional Ca for quadrupling regime for all test liquids 72 APPENDIX C 78 Coalescence distance for all the orifices 78 APPENDIX D 79 Uncertainty analysis 79 vi LIST OF FIGURES Page 3.1 Schematic diagram of experiment setup 11 4.1 Comparison of data obtained for water with 13 Gopal [14] (dO= 0.8, 1, 1.8, & 2.4 mm) 4.2 Bubble formation, growth, necking and pinching-off of air bubble through 14 dO= 1.8 mm in 17 cP GL solution 4.3 Comparison of bubble shape (at same flow rate, Q= 126 ccm and orifice 16 diameter dO= 1 mm) in (a) water (b) 3.5 cP GL solution (c) 6 cP GL solution (d) 17 cP GL solution (e) 72 cP GL solution and (f) 180 cP solution. 4.4 Translation of bubbles after coupling in 3.5 cP GL solution for dO= 0.8 mm 20 4.5 Coupling observed for dO=0.8 mm in 3.5 cP GL solution 21 4.6 Coupling closer to the orifice, dO= 1 mm, in 3.5 cP GL solution 22 4.7 Coupling away from the orifice tip, dO= 2.4 mm, in 3.5 cP GL solution 22 4.8 Coupling closer to orifice, dO= 0.8 mm, in 17 cP GL solution 24 4.9 Coupling away from the orifice, dO= 1.8 mm, in 17 cP GL solution 25 4.10 Coupling closer to orifice, dO= 0.8 mm, in 72 cP GL solution 26 4.11 Coupling away from the orifice, dO= 1.8 mm, in 72 cp GL solution 28 4.12 Coupling closer to orifice, dO= 0.8 mm, in 180 cP GL solution 29 4.13 Coupling away from the orifice, dO= 1.8 mm, in 180 cp GL solution 30 vii 4.14 Transitional Ca trend for coupling in water with change in orifice 31 diameter (on a log scale) 4.15 Ca for coupling transition in 3.5 cP GL solution with change in orifice 32 diameter (on a log scale) 4.16 Ca for coupling transition in 6 cP GL solution with change in orifice 33 diameter 4.17 Ca trend for coupling transition in 17 cP GL solution with change in 34 orifice diameter 4.18 Ca trend for coupling transition in 72 cP GL solution with change in 35 orifice diameter 4.19 Ca trend for coupling transition in 180 cP GL solution with change in 36 orifice diameter 4.20 Cumulative Ca trend as a function of dO/lc for all solutions 40 4.21 Power law fit of Ca vs normalized orifice diameter for all solutions 41 4.22 Comparing the experimental data with the predictions of proposed 42 Correlation 4.23 Quadrupling as observed in 6 cP GL Solution for dO= 0.8 mm at 46 28,44,64,82,97,137,167 ms 4.24 Quadrupling as observed in 6 cP GL Solution for dO= 1.8 mm at 47 viii 24,43,68,83,104,117 ms 4.25 Quadrupling as observed in 72 cP GL Solution for dO= 0.8 mm at ms 48 1,11,35,48,66,93,131,135 ms 4.26 Quadrupling as observed in 72 cP GL Solution for dO= 1.8 mm at 49 10,32,62,85,155,173 ms 4.27 Quadrupling as observed in 180 cP GL Solution for dO= 0.8 mm at 51-52 18,43,56,71,83,94,99,107,119,131,140 ms 4.28 Quadrupling as observed in 180 cP GL Solution for dO= 1.8 mm at 53-54 23,43,78,94,103,154,167,192 ms 4.29 Transitional Ca values for quadrupling in water-glycerol solutions 57 4.30 Comparing the experimental data with the predictions of proposed 58 power fit in the quadrupling regime 4.31 Representation of coalescence distance, hC, in coupling regime 59 4.32 Coalescence distance comparison for dO= 0.8 mm in all liquid solutions 60 4.33 Coalescence distance comparison for dO= 1.8 mm in all liquid solutions 61 ix LIST OF TABLES 3.1 Physical Properties of Test Liquids 10 x NOMENCLATURE do Orifice Diameter (mm) Va Air Velocity (m/s) Vw Wake velocity of the departed (previous) bubble (m/s) g Acceleration due to gravity (m/s2) FB Buoyancy force acting on the bubble (N) FI Inertia Force acting on the bubble (N) FD Drag force acting on the bubble (N) Fs Surface tension force acting on the bubble (N) f Bubble Frequency (1/s) hc Coalescence length (mm) Lc Capillary length (mm) Greek Symbols 3 ρa Air Density (kg/m ) 3 ρl Liquid density (kg/m ) µa Air Viscosity (kg/m-s) µl Glycerol solution Viscosity (kg/m-s) σ Liquid Surface Tension (N/m) xi Non-Dimensional Numbers ρ푎 푉푎 푑표 Reo Reynolds Number = µ푎 µ푙 푉푎 Ca Capillary Number = σ µ4 g Mo Morton Number = 3 ρ푙 σ xii xiii CHAPTER 1 Introduction Bubble dynamics has been a topic of great interest in the field of multiphase fluid flow for a long time with particular attention given to the forces controlling bubble formation, its rise in the quiescent liquid, and bubble coalescence.
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