"Applied Science, Faculty of"@en . "Mechanical Engineering, Department of"@en . "DSpace"@en . "UBCV"@en . "Moulson, Jeremy Bryce Taylor"@en . "2012-06-14T23:15:14Z"@en . "2012"@en . "Master of Applied Science - MASc"@en . "University of British Columbia"@en . "The impingement of a high-speed liquid jet on a moving surface and the resulting deposition or splash is important in a variety of technical and industrial processes. Of particular interest is the coating of the top-of-rail surface, in the rail road industry, with a thin film of viscoelastic liquid friction modifier, by liquid jet impingement, to control friction and reduce wear at the wheel-rail interface, thereby reducing fuel consumption and maintenance costs. For effective operation it is required that the fluid deposited by the jet adhere to the surface after impingement. \nAn experimental investigation into the effect of surrounding air pressure and fluid properties on liquid jet impingement on a moving surface was performed. The study was carried out with Newtonian liquids impacting smooth, dry surfaces. A variety of ambient air pressures, jet speeds, surface speeds, surface tensions, and liquid viscosities were studied. The interaction between the impinging jet and the moving surface was analysed through high-speed imaging. \nIt was observed that, as is the case for Newtonian droplet impact, the surrounding air pressure plays a crucial role in the splashing behaviour of jet impingement. There exists a threshold pressure below which splash does not occur. It is proposed that for certain impingement conditions lamella detachment from the surface occurs due to aerodynamic forces acting on the leading edge of the lamella, which destabilizes the balance between surface tension and fluid pressure forces. It was observed that both the Reynolds number and Weber number were salient to the occurrence of lamella detachment, with lamella detachment having a non-linear dependence on the Reynolds number. Lamella detachment was prone to occur for intermediate Reynolds numbers as the Weber number was increased, bounded by regions of deposition at higher and lower Reynolds numbers."@en . "https://circle.library.ubc.ca/rest/handle/2429/42498?expand=metadata"@en . "AN EXPERIMENTAL STUDY OF LIQUID JET IMPINGEMENT ON A MOVING SURFACE: THE EFFECTS OF SURROUNDING AIR PRESSURE AND FLUID PROPERTIES by Jeremy Bryce Taylor Moulson B.Eng., Carleton University, 2010 A THESIS SUBMITTED IN PARITIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in The Faculty of Graduate Studies (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) June 2012 \u00C2\u00A9 Jeremy Bryce Taylor Moulson, 2012 ii ABSTRACT The impingement of a high-speed liquid jet on a moving surface and the resulting deposition or splash is important in a variety of technical and industrial processes. Of particular interest is the coating of the top-of-rail surface, in the rail road industry, with a thin film of viscoelastic liquid friction modifier, by liquid jet impingement, to control friction and reduce wear at the wheel-rail interface, thereby reducing fuel consumption and maintenance costs. For effective operation it is required that the fluid deposited by the jet adhere to the surface after impingement. An experimental investigation into the effect of surrounding air pressure and fluid properties on liquid jet impingement on a moving surface was performed. The study was carried out with Newtonian liquids impacting smooth, dry surfaces. A variety of ambient air pressures, jet speeds, surface speeds, surface tensions, and liquid viscosities were studied. The interaction between the impinging jet and the moving surface was analysed through high-speed imaging. It was observed that, as is the case for Newtonian droplet impact, the surrounding air pressure plays a crucial role in the splashing behaviour of jet impingement. There exists a threshold pressure below which splash does not occur. It is proposed that for certain impingement conditions lamella detachment from the surface occurs due to aerodynamic forces acting on the leading edge of the lamella, which destabilizes the balance between surface tension and fluid pressure forces. It was observed that both the Reynolds number and Weber number were salient to the occurrence of lamella detachment, with lamella detachment having a non- linear dependence on the Reynolds number. Lamella detachment was prone to occur for intermediate Reynolds numbers as the Weber number was increased, bounded by regions of deposition at higher and lower Reynolds numbers. iii PREFACE The authors of Chapter 2 are Jeremy Moulson and Dr. Sheldon Green. Dr. Green identified the need to further understand the impingement behaviour of Newtonian liquid jet impingement on a moving surface. It was required to determine if the surrounding air pressure had an effect on the splashing behaviour of an impinging liquid jet. We also wanted to investigate the mechanism for lamella detachment and splashing. I built the experimental set-up and performed all the experiments. Dr. Green and I analysed the data and developed the model. A version of Chapter 2 has been submitted for publication: Moulson, J.B.T and Green, S.I., \u00E2\u0080\u009CThe Effect of Surrounding Air Pressure on Liquid Jet Impingement,\u00E2\u0080\u009D 2012. The authors of Chapter 3 are Jeremy Moulson and Dr. Sheldon Green. Dr. Green identified the requirement to investigate high velocity, low viscosity fluids for the 648 micrometer diameter nozzle and ensure it was consistent with previous works for smaller nozzle diameters. As well, Dr. Green thought it necessary to investigate low surface tension liquids within the same viscosity range to fully explore the effect of surface tension forces relative to viscous forces. The spread of the lamella was investigated for various combinations of jet velocity, surface velocity, and viscosity. I built the experimental set-up and performed all the experiments and measurements. Dr. Green and I analysed the data and interpreted the results. A version of Chapter 3 will be submitted for publication: Moulson, J.B.T, Kumar, P., and Green, S.I., \u00E2\u0080\u009CLiquid Jet Impingement: Influence of Fluid Properties and Jet Diameter,\u00E2\u0080\u009D 2012. iv TABLE OF CONTENTS ABSTRACT .................................................................................................................................................. ii PREFACE .................................................................................................................................................... iii LIST OF TABLES ....................................................................................................................................... vi LIST OF FIGURES .................................................................................................................................... vii LIST OF EQUATIONS ............................................................................................................................... ix NOMENCLATURE ..................................................................................................................................... x GLOSSARY ............................................................................................................................................... xii ACKNOWLEDGEMENTS ....................................................................................................................... xiii 1 INTRODUCTION ................................................................................................................................ 1 1.1 Propose of Research ...................................................................................................................... 1 1.2 Liquid Friction Modifiers.............................................................................................................. 2 1.3 Newtonian Droplet Impact ............................................................................................................ 2 1.4 Newtonian Liquid Jet Impingement .............................................................................................. 4 1.5 Research Objectives ...................................................................................................................... 7 1.6 Experimental Set-up and Methods ................................................................................................ 9 2 THE INFLUENCE OF SURROUNDING AIR PRESSURE ............................................................. 14 2.1 Influence of Surrounding Air Pressure and Surface Velocity ..................................................... 15 2.1.1 Jet Impingement Observations ............................................................................................ 15 2.1.2 Quantitative Results of Surrounding Air Pressure .............................................................. 19 2.2 A Model of Lamella Detachment ................................................................................................ 25 2.2.1 Model Development ............................................................................................................ 25 2.2.2 Model Comparison to Experiments .................................................................................... 28 2.3 Conclusions for the Effect of Surrounding Air Pressure ............................................................ 32 3 INFLUENCE OF FLUID PROPERTIES: VISCOSITY AND SURFACE TENSION...................... 33 3.1 Influence of Surface and Jet Velocities ....................................................................................... 33 3.2 Jet Impingement of Water-Glycerin Solutions ........................................................................... 34 3.2.1 Jet Impingement Observations for Water-Glycerin Solutions ............................................ 35 3.2.2 Quantitative Results of Water-Glycerin Solutions .............................................................. 36 3.3 Jet Impingement of Ethanol-Glycerin Solutions ......................................................................... 40 3.3.1 Jet Impingement Observations for Ethanol-Glycerin Solutions ......................................... 40 3.3.2 Quantitative Results of Ethanol-Glycerin Solutions ........................................................... 42 v 3.4 Summary and Discussion of Experimental Results .................................................................... 48 3.5 Lamella Spread ........................................................................................................................... 50 3.6 Conclusions for the Influence of Viscosity and Surface Tension ............................................... 52 4 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK ....................................... 53 4.1 Conclusions ................................................................................................................................. 53 4.2 Strength and Limitation of Thesis Research ............................................................................... 55 4.3 Potential Applications of Research Findings .............................................................................. 55 4.4 Recommendations for Future Work ............................................................................................ 56 5 REFERENCES ................................................................................................................................... 58 APPENDICES ............................................................................................................................................ 61 APPENDIX A: MASS FLOW RATES .................................................................................................. 61 APPENDIX B: EXPERIMENTAL SET-UP .......................................................................................... 68 APPENDIX C: FLUID PROPERTIES AND SOLUTION PREPARATION ........................................ 72 APPENDIX D: ADDITIONAL PARAMETERS ................................................................................... 74 D.1 Liquid Jet Impingement onto a Pre-Wetted Surface .................................................................... 74 D.2 Geometric Angle .......................................................................................................................... 77 D.3 Gravity Experiments .................................................................................................................... 80 vi LIST OF TABLES Table 1 Fluid properties of glycerin-water solutions at 25 \u00C2\u00BAC and 101kPa .................................. 11 Table 2 Fluid properties of glycerin-ethanol solutions at 25 \u00C2\u00BAC and 101kPa ............................... 12 vii LIST OF FIGURES Figure 1.1 Two possible outcomes of liquid jet impingement with a moving surface. .................. 4 Figure 1.2 Schematic diagram of liquid jet impinging on moving surface. ................................... 5 Figure 1.3 Detailed schematic diagram of experiment set-up. ..................................................... 10 Figure 1.4 Positioning of high speed video camera ...................................................................... 11 Figure 1.5 Mass flow rates of water-glycerin solutions. ............................................................... 13 Figure 2.1 Time evolution of jet impingement on a moving surface. ........................................... 16 Figure 2.2 Splashing behaviour of a viscous liquid jet at different ambient pressures. ............... 17 Figure 2.3 Effect of surface velocity on jet impingement............................................................. 18 Figure 2.4 Experimental results for pressure threshold ................................................................ 19 Figure 2.5 Dependence on fluid viscosity ..................................................................................... 20 Figure 2.6 Splashing behaviour of a low viscosity liquid jet ........................................................ 21 Figure 2.7 Dimensionless threshold pressure. .............................................................................. 23 Figure 2.8 Reynolds number of the air divided by the velocity ratio ........................................... 24 Figure 2.9 Schematic of the leading edge stagnation point. ......................................................... 26 Figure 2.10 Lamella detachment threshold pressure .................................................................... 31 Figure 3.1 Threshold jet velocity as a function of surface velocity .............................................. 34 Figure 3.2 Three viscosity regimes. .............................................................................................. 35 Figure 3.3 Splash chart of experimental results for water-glycerin solutions. ............................. 36 Figure 3.4 Experimental results for impingement experiments .................................................... 38 Figure 3.5 Experimental results for water-glycerin. ..................................................................... 39 Figure 3.6 The three distinct flow regimes ................................................................................... 41 Figure 3.7 Experimental results for a solution of 0% EG and 20% EG ....................................... 43 Figure 3.8 Experimental results for a solution of 35% E-G and 40% E-G ................................... 43 Figure 3.9 Experimental results for a solution of 50% E-G and 63% E-G ................................... 43 Figure 3.10 Experimental results for a solution of 80% E-G and 90% E-G ................................. 44 Figure 3.11 Experimental data at a constant surface velocity of 5.5 m/s. .................................... 45 Figure 3.12 Experimental results at a constant surface velocity of 3.5 m/s .................................. 46 Figure 3.13 Experimental results at constant surface velocity of 7.5 m/s ................................... 47 Figure 3.14 Summary of experimental results .............................................................................. 48 viii Figure 3.15 Threshold points between deposition and lamella detachment. ................................ 49 Figure 3.16 Distance of the leading edge of the lamella ............................................................... 51 Figure 5.1 Mass flow rate for water-glycerin solutions ................................................................ 62 Figure 5.2 Mass flow rates for ethanol-glycerin solutions ........................................................... 62 Figure 5.3 Jet contraction ratio ..................................................................................................... 64 Figure 5.4 Jet velocity for water-glycerin solutions ..................................................................... 65 Figure 5.5 Jet velocity of ethanol-glycerin solution ..................................................................... 65 Figure 5.6 Discharge coefficients for water-glycerin solutions .................................................... 66 Figure 5.7 Experimental apparatus. .............................................................................................. 68 Figure 5.8 Vacuum generators and compressed nitrogen tank. .................................................... 69 Figure 5.9 Phantom\u00C2\u00AE V12.1 high speed video camera. ............................................................... 69 Figure 5.10 Screen shot of LabView program .............................................................................. 70 Figure 5.11 Viscosity of water-glycerin solutions ........................................................................ 73 Figure 5.12 Viscosity of ethanol-glycerin solutions ..................................................................... 73 Figure 5.13 Experimental results for impingement on pre-wetted surface ................................... 75 Figure 5.14 Impingement of a liquid jet on a pre-wetted surface ................................................. 75 Figure 5.15 The geometric angle is defined in the schematic diagram of jet impingement. ........ 77 Figure 5.16 Preliminary experimental results for geometric angle ............................................... 78 Figure 5.17 Geometric angle comparison ..................................................................................... 78 Figure 5.18 Experiments performed with an inverted apparatus .................................................. 80 ix LIST OF EQUATIONS Equation 2.1 .................................................................................................................................. 27 Equation 2.2 .................................................................................................................................. 27 Equation 2.3 .................................................................................................................................. 27 Equation 2.4 .................................................................................................................................. 27 Equation 2.5 .................................................................................................................................. 27 Equation 2.6 .................................................................................................................................. 28 Equation 2.7 .................................................................................................................................. 28 Equation 2.8 .................................................................................................................................. 29 Equation 2.9 .................................................................................................................................. 30 Equation 5.1 .................................................................................................................................. 61 Equation 5.2 .................................................................................................................................. 63 Equation 5.3 .................................................................................................................................. 63 Equation 5.4 .................................................................................................................................. 66 x NOMENCLATURE An Area of the nozzle exit Cd Discharge coefficient, ratio of actual mass flow rate to ideal mass flow rate CL Aerodynamic lift coefficient Dj Diameter of jet FA Aerodynamic force FAD Summation of adhesion forces FD Summation of detachment forces FN Normal force FS.T. Surface tension force h Lamella film thickness k Attachment length scale L Lamella length scale m& Mass flow rate Rea Reynolds number of air, a sja a VD \u00C2\u00B5 \u00CF\u0081 =Re Rej Reynolds number of liquid based on jet diameter, f jjf j VD \u00C2\u00B5 \u00CF\u0081 =Re Rl.e. Radius of lamella leading edge t Spread time T Atmospheric temperature Uair Velocity of the air xi Vj Velocity of impinging jet Vs Velocity of the surface W Control volume depth Wej Weber number of the fluid, f jjf j DD We \u00CF\u0083 \u00CF\u0081 2 = Greek Letters \u00CE\u00B4 Boundary layer thickness \u00CE\u00B8D Dynamic contact angle \u00CE\u00B8G Geometric angle of impingement \u00C2\u00B5a Air viscosity \u00C2\u00B5f Liquid viscosity \u00CF\u0081air Density of the air \u00CF\u0081f Density of the fluid \u00CF\u0083f Surface tension of the fluid \u00CE\u00BDf Kinematic viscosity of the fluid xii GLOSSARY E-G Ethanol - Glycerin LFM Liquid Friction Modifier NBP Nozzle Back Pressure TOR Top-of-Rail TE Transfer Efficiency \u00E2\u0080\u0093 ratio of liquid that adheres to the surface relative to the liquid emitted from the orifice. PSI Pounds per square inch W-G Water-Glycerin xiii ACKNOWLEDGEMENTS First and foremost I would like to extend my sincere gratitude to my graduate supervisor, Professor Sheldon Green. His never-ending support, guidance, and most importantly patience has made the past two years very intriguing, challenging, and enjoyable. For his critical analysis of my research and the constant encouragement to strive for my highest potential I am very grateful. I would like to thank the engineers from Kelsan Technologies Corporation, Dr. Don Eadie, David Elvidge, and John Cotter, for their interest, enthusiasm, and encouragement. As well, I would like to thank them for the opportunity to be involved in the industrial application of this research over the past year. It has been a very unique experience working with them and being involved in the direct application of academic research to a cutting edge industrial application and this experience has given me a very important perspective. I would also like to acknowledge the great support staff at UBC, particularly George Soong from the Pulp and Paper Centre for his constant assistance in all technical matters. I would also like to thank Markus Fengler for his advice in designing and constructing the experimental set-up and co-op student Michael Gosselin for assistance in the experimental set- up. For important discussions and critical review I thank the members of my research group at the Applied Fluid Mechanics Laboratory, specifically, Dr. Ali Vakil, George Sterling, and Fatih Damat. Finally, I would like to thank Kelsan Technologies Corporation and the Natural Science and Engineering Research Council of Canada for their financial support of this research. 1 1 INTRODUCTION 1.1 Propose of Research The impingement of a high-speed liquid jet on a moving surface and the resulting deposition or splash are important in a variety of technical and industrial processes including ink- jet printing, impingement cooling, and surface coating. The recent requirement to coat a moving surface with a liquid friction modifier (LFM) applied by a high speed jet has resulted in studies of the fundamental fluid physics of jet impingement, in order to maximize the proportion of liquid adhering to the surface following impingement. The aim of this research is to characterize the flow physics of a high velocity Newtonian circular liquid jet striking a horizontally moving smooth, solid, surface. It is desired to determine the flow regimes involved to be able to find a regime in which one hundred percent of the fluid being deposited onto the moving surface by the impinging jet remains on the surface after impingement. The parameters that have been thoroughly investigated in this study are the surrounding air pressure, the fluid viscosity, the fluid surface tension, the jet velocity, and the surface velocity. The geometric angle of impingement was also investigated. In determining the flow regimes of liquid jet impingement we are assisting an industrial partner, Kelsan Technologies Corporation, in the development of a system that will apply a liquid friction modifier onto the top of rail (TOR) surface, in the rail road industry, to control friction at the wheel-rail interface. Kelsan is an industry leader in the development of friction modifiers for the railroad industry. Rail transport is one of the most efficient methods for freight and passenger transportation and will remain so in the future. Therefore, this research is aimed 2 towards studying the parameters involved in liquid jet impingement to be able to determine regimes in which one hundred percent transfer efficiency of the LFM can be obtained. 1.2 Liquid Friction Modifiers The LFM of interest is a water based suspension of polymers and inorganics solids that displays non-Newtonian behaviour; shear thinning and viscoelastic [1] [2] . LFMs control the coefficient of friction at the wheel-rail interface and have been shown to reduce fuel consumption by 6-9% without compromising traction or braking [3] [4]. As well, the application of LFM reduces lateral forces on both the wheels and rail and therefore reduces maintenance costs. Currently, the industrial approach is to apply the LFM to the TOR surface by means of an atomized spray [3]. However, due to many effects, such as splashing and excessive deflection due to cross winds, the transfer efficiency of the atomized spray can be as low as 30-60% [5] [6] [7]. It has been proposed that liquid jets are the solution to this issue, as they are not as susceptible to crosswinds (high inertia) and offer the possibly of one hundred percent transfer efficiency. As well, it is possible to control the thickness of the applied layer by varying the jet speed, viscosity, or train speed. This could allow for the most efficient operating conditions to be determined. 1.3 Newtonian Droplet Impact An area of similar physics, droplet impact, has seen significant advancement in recent years. The physics of droplet impact on a stationary solid surface are somewhat understood, and are salient to numerous technical and industrial applications. Yarin [8] classifies droplet impact onto a solid surface into six distinct categories: deposition, prompt splash, corona splash, receding break-up, partial rebound, and complete rebound. For impact onto a smooth dry solid surface the 3 two classifications that are applicable are corona splash and deposition. Several researchers have shown that the splashing behaviour of droplets is dependent on many parameters including the viscosity, density, surface tension, and the normal component of the impact velocity [9] [10] [11]. Bird et al [11] demonstrated that for Newtonian droplet impact on a moving surface, both the normal and tangential velocities were of critical importance. It has been long speculated that the surrounding air has an influence on the splashing behaviour of droplets. In 1975, Povaro et al [9], demonstrated that the air boundary layer influences droplet impact. Entrapment of a small pocket of air underneath a liquid droplet after impaction with a dry smooth solid surface has been observed by several researchers [12] [13] [14]. Thoroddsen and Sakakibara [15] first speculated that air entrapment under the liquid droplet could be the reason for the fingering instability that is thought to cause splash, as the trapped air seeks to escape. Allen [16] suggested that this instability was in fact the Rayleigh- Taylor instability. However, the nature of the Rayleigh-Taylor instability implies that splashing should not be affected by changes in air pressure. In contrast to this prediction, Xu et al. proved experimentally that the surrounding gas pressure dramatically affects splash; there is a threshold pressure below which splash is suppressed completely [17] [18]. When a droplet strikes a surface a very thin layer of air is squeezed out from the gap between the liquid lamella and the surface. The substantial velocity difference at the interface between the two fluids could drive a Kelvin- Helmholtz instability, which Xu et al. have proposed to be the mechanism producing splash. Following on the work of Xu et al., Mishra et al. [19] have shown that by raising the surrounding gas pressure above one atmosphere, droplet splashing could be induced even at very low Reynolds numbers. 4 1.4 Newtonian Liquid Jet Impingement Liquid jet impingement onto a moving substrate is a very interesting, complex, multiphase, fluid mechanics problem. Free impinging liquid jets are widely used in many industrial applications; steel making, ink-jet printing, agricultural spraying, heating/cooling, and surface coating. Experimental, numerical, and analytical studies have provided a vast amount of information; however, the majority of the work is concerned with parameters involved with heat transfer. However, with the recent requirement to increase the amount of liquid adhering to the surface after jet impingement, studies of the fundamentals of the fluid physics have begun. For jet impingement onto a stationary surface the initial inertia of the radial flow is dissipated by viscous forces and a hydraulic jump may be generated [20]. For stationary impingement no lamella detachment occurs, and any fluid leaving the surface is by droplet spattering, which is believed to be caused by turbulence and surface instabilities in the jet [21]. When a surface velocity is incorporated in this situation it is observed that under certain conditions the lamella detaches from the surface, Figure 1.1. This detached lamella configuration is stable and is sustained in the detached configuration by aerodynamic forces. Figure 1.1 Two possible outcomes of liquid jet impingement with a moving surface are lamella detachment (a) and deposition (b). 5 Gradeck et al. [22] numerically and experimentally investigated the flow field of an impinging jet of water on a moving substrate for various combinations of jet velocity, surface velocity, and nozzle diameters. Fujimoto et al. [23] investigated the flow characteristics of a circular water jet impinging onto a moving substrate covered with a thin film of water. However, these researchers were interested in relatively large nozzle diameters and low surface and jet velocities compared to the current work. For high speed jet impingement on a moving surface it has been shown that among the important parameters are fluid viscosity, surface tension, and the normal and tangential velocity. Figure 1.2 defines parameters involved. Vs Rlamella Dj/2 Vj y x Uair Figure 1.2 Schematic diagram of liquid jet impinging on moving surface. Relative geometric parameters are defined in the figure. For high speed jet impingement, Keshavarz et al [24] showed that for liquid jet impingement with a moving surface viscous forces are more important than surface tension forces and therefore the Reynolds number is an important parameter in determining the result of impingement. Keshavarz found a threshold Reynolds number based on the jet diameter of 325 between deposition and splash, with deposition occurring at the lower Reynolds numbers. We recall here that the Reynolds number is defined as: 6 f jjf j DV \u00C2\u00B5 \u00CF\u0081 =Re In experiments conducted on elastic liquids, Keshavarz et al. [24] found a similar clear threshold between splash and deposition, but in this case the threshold was a function of both the Reynolds and Deborah numbers. Owing to differences between his experimental device and Keshavarz\u00E2\u0080\u0099s, Kumar [25] was able to study higher Reynolds number impingement than could Keshavarz. Kumar found that in addition to the lower threshold for splash, there is an upper Reynolds number threshold above which the jet deposits. Kumar [25] showed that splashing is inhibited for low and high viscosity but lamella detachment and splash occurs for intermediate values of the viscosity. This result appears to be counter-intuitive as one might expect that a fluid with increased viscous dissipation would be less prone to splashing. Kumar proposed that this non-linear dependence of splash on viscosity is due to the balance between the inertia (promotes splash), viscous (inhibits splash), and surface tension (inhibits splash) stresses. The lamella thickness is proportional to the square root of the viscosity and therefore a lower viscosity fluid has a thinner lamella. Surface tension stresses can be approximated by \u00CF\u0083/h, where \u00CF\u0083 is the surface tension and h is the lamella thickness. Therefore, a lower viscosity fluid with its thinner lamella has a higher surface tension stress adhering it to the surface. In the low viscosity regime surface tension is dominant and acts to stabilize the lamella whereas in the high viscosity regime the viscous dissipation dominates and stabilizes the lamella. For intermediate values of the viscosity inertia is dominant and therefore the lamella breaks up and splash occurs. However, Kumar's model cannot be used to explain why lamella detachment can be suppressed by reducing the surrounding air pressure. Arzate and Tanguy [26] studied the hydrodynamics of jet coating at high surface speeds and investigated the influence of the air pressure forces on the jet, 7 however they were primarily concerned with the deflection of low Reynolds number jets impinging on high speed surfaces and did not observe lamella detachment. 1.5 Research Objectives The use of liquid friction modifiers in the railroad industry is an effective means of controlling the friction at the wheel-rail interface and thereby reducing the fuel consumption and lateral forces on the interface. The proposed application method utilizing liquid jet impingement will impinge the top of rail surface with the non-Newtonian product from nozzles located 8 cm from the top-of-rail surface. The aim is for the product to be transferred down the train by the wheels as they roll over the applied product. In order to maximize this secondary transfer it is required that the majority of the sprayed product remains on the rail so as to maximize the transfer efficiency. The issues arising for the lamella detaching and splashing are loss of product and a detached lamella is susceptible to destabilization and loss of product by cross winds. Behfarshad et al. [27] showed experimentally that for a perpendicular impinging jet up to 50% of the product can be lost if the lamella detaches and splashes. These experiments did not incorporate cross winds. Therefore, it is desired that the impinging LFM jet deposit and fully adhere to the surface in order to obtain one hundred percent transfer efficiency. The initial primary objective of this research work was to investigate whether the surrounding air pressure had an impact on the splashing behaviour of liquid jet impingement with a moving surface as had been seen for droplet impact onto stationary surfaces. The secondary objective was to study how the fluid properties influenced the behaviour of an impinging jet. Also studied briefly were the influence of the geometric angle of the impinging jet 8 relative to the surface, the influence of the gravitational force, and the influence of a pre-wetted surface. These research objectives were achieved by systematically studying the outcome of liquid jet impingement on to a moving surface for a variety of liquid solutions, various concentrations of both water-glycerin and ethanol-glycerin, for various jet velocities, surface velocities, ambient air pressures, and geometric angles. In Chapter 2 the effect of the surrounding air pressure is discussed in detail and the experimental results from this study are presented. A physical model that was developed based on experimental observations is presented and discussed and the model is in qualitative agreement with the experimental results obtained. Dimensional analysis was performed and resulted in a collapse of the pressure threshold curves. In Chapter 3 the influence of fluid properties, fluid viscosity and surface tension, is discussed in detail. These studies were conducted at a constant nozzle diameter of 648 microns for various surface velocities and fluid solutions. This chapter discusses the influence of the Reynolds number and Weber number on jet impingement with a moving surface. As well, the characteristics of the lamella formed during the impingement of a Newtonian liquid jet onto a moving surface are discussed. This section displays experimental results for lamella spread as a function of jet velocity, surface velocity, and fluid viscosity. In Appendix D the effect of angling the jet relative to the surface was investigated and the experimental results are displayed. The effect of a pre-wetted surface was experimentally investigated and preliminary results are displayed in this section. 9 1.6 Experimental Set-up and Methods To study the role of the surrounding air on the perpendicular impingement of a circular liquid jet with a horizontal moving surface, an experimental set up was constructed that allows for all parameters of the interaction to be precisely controlled. The interaction of a 564 micrometer diameter1, liquid jet impinging onto a horizontally moving, dry, smooth, polished spring-steel surface was observed using a Phantom V12.1 high-speed camera recording at 11000 frames per second and a resolution of 800 x 600 pixels. From the captured high-speed images it was possible to qualitatively determine the lamella characteristics for a particular set of conditions. For various combinations of liquid viscosities, jet velocities, surface velocities, and ambient air pressures the thresholds between lamella detachment and deposition were determined experimentally by systematically increasing specific parameters; either air pressure or jet velocity. The highest air pressure or jet velocity at which the leading edge of the lamella did not detach from the surface was classified as the threshold. Multiple experiments were performed in the vicinity of the thresholds as near the threshold the lamella is very sensitive to destabilization. The experimental set-up is shown schematically in Figure 1.3 and 1.4. The vacuum chamber, which was constructed specifically for these experiments, allows for precise control of the ambient air pressure by use of vacuum generators which utilize the Venturi effect to create a low pressure region and therefore result in air from the chamber being evacuated. Contained with-in the vacuum chamber were the instrumentation required to impinge a steady liquid jet onto the moving surface. These include a modified Makita\u00C2\u00AE belt sander, which rotated a continuous 7.5 cm wide metal belt, a nozzle with a converging tip of 648 micrometers, pressured flow lines, a pressure transducer to record the nozzle back pressure, and a flow interrupter. 1 Jet contracts upon expulsion from orifice, for Reynolds number above 100, jet contraction ratio is 0.87. 10 Figure 1.3 Detailed schematic diagram of experiment set-up. The impingement of the liquid jet with the moving surface was captured through high-speed imaging. The flow interrupter was incorporated in order to remove the initial condition of the jet at start-up which was unsteady and susceptible to break-up. Once the jet had stabilized the flow interrupter was retracted and a stable jet impinged on the surface. The nozzle was vertically offset by 10 cm from the surface however, for low viscosity liquids ( cPf 5\u00E2\u0089\u00A4\u00C2\u00B5 ) this distance had to be reduced to avoid jet break-up as described in [21]. High nozzle back pressures were created by means of a bladder accumulator that was pressured by a compressed nitrogen tank which yielded jet velocities in the range of 5 \u00E2\u0080\u0093 40 ms-1.The lower limit of this range is constrained by Plateau-Rayleigh instabilities. The jet velocities were measured from an empirical correlation between the nozzle back pressure and the gravimetric flow rate, which was experimentally 11 measured over a 30 second interval. The surface velocities of the metal belt were in the range of 0 \u00E2\u0080\u0093 8 ms-1 and measured using the Phantom V12.1 high speed camera. Figure 1.4 Positioning of high speed video camera and backlighting in experimental set-up Table 1 Fluid properties of glycerin-water solutions at 25 \u00C2\u00BAC and 101kPa Fluid (wt % glycerin-water) Dynamic Viscosity [mPa\u00E2\u0088\u0099s] Density [kg/m3] Surface Tension [mN/m] 0 0.9 1000 72.1 10 1.15 1026.1 71.3 20 1.56 1052.2 70.5 30 2.135 1078.3 69.7 40 3.28 1104.4 68.9 50 5.11 1130.5 68.1 60 9.00 1156.6 67.3 65 12.45 1169.6 66.9 70 18.40 1182.7 66.5 75 28.45 1195.7 66.1 80 46.47 1208.8 65.7 85 83.5 1221.8 65.3 90 164 1234.9 64.9 100 947 1261.0 64.1 12 To investigate the effect of surface tension it was desired to use a Newtonian test fluid that would be able to match the viscosity of the water-glycerin solutions but have much lower surface tension. Thus ethanol-glycerin solutions were used that can be made to match viscosity with water-glycerin but have one third of the surface tension. Table 2 details the fluid properties of the ethanol-glycerin solutions used in these experiments. Table 2 Fluid properties of glycerin-ethanol solutions at 25 \u00C2\u00BAC and 101kPa Fluid (wt % glycerin-ethanol) Dynamic Viscosity [mPa\u00E2\u0088\u0099s] Density [kg/m3] Surface Tension [mN/m] 0 1.41 789.9 22.2 5 2.04 823.9 22.3 10 2.67 854.7 22.5 15 2.90 884.9 22.8 20 3.12 914.0 23.1 25 3.92 942.3 23.6 30 4.72 969.6 24.1 40 8.41 1021.6 25.6 50 15.6 1070.1 27.7 60 65 29.5 47.0 1114.9 1136.0 30.8 32.8 70 58.1 1156.2 35.2 80 131 1193.9 41.7 90 317 1228.0 50.7 100 947 1261.0 64.1 The liquid parameters, Tables 1 and 2, can be combined into two dimensionless groups, fjjf VD \u00C2\u00B5\u00CF\u0081=Re and \u00CF\u0083\u00CF\u0081 2jjf VDWe = . The Reynolds number represents the ratio between inertial and viscous forces, and the Weber number represents the ratio between inertial and surface tension forces. The current experiments concentrate on flow regimes of 10 < Re < 10000 and 200 < We < 10000. The viscosities of the water-glycerin and ethanol-glycerin solutions used were determined using a Kinexus rotational rheometer at a temperature of 25\u00C2\u00B0C and were within 2% of values found in literature [28] [29]. The surface tensions of the fluids were determined using a Du Nouy 13 ring apparatus at a temperature of 25\u00C2\u00B0C [24]. The surrounding air pressure was determined using an Omegadyne Inc. PX209-39VACI pressure transducer. The velocity of the jet was determined through mass flow rate measurements over a span of 30 seconds for constant nozzle back pressures ranging from 1 to 200 PSI. The back pressure was measured by a WIKA A-10 pressure transducer. The average jet velocity was then calculated from the mass flow rate by dividing by the density of the solution and the cross- sectional area of the jet. The cross-sectional area of the jet was measured for various Reynolds numbers using the Phantom V12.1 high speed camera and compared to jet diameter measurements from Keshavarz et al [24]. Figure 1.5 shows the jet velocity plotted against nozzle back pressure for a selected sample of water-glycerin solutions. Detailed calculations and data can be found in the Appendix. Figure 1.5 Mass flow rates of water-glycerin solutions with a nozzle diameter of 648 microns. 14 2 THE INFLUENCE OF SURROUNDING AIR PRESSURE The primary objective of this work is to experimentally investigate whether the surrounding air pressure influences the splashing behaviour of liquid jet impingement on a moving surface and to measure the critical pressure thresholds. The interaction of a 564 micrometer diameter, liquid jet impinging onto a horizontally moving, dry, smooth, polished spring-steel surface was observed using a Phantom V12.1 high- speed camera recording at 11000 frames per second. From the captured high-speed images it was possible to qualitatively determine the lamella characteristics for a particular set of conditions. It was observed that detachment of the lamella from the surface is fully suppressed below a specific ambient air pressure. For various combinations of liquid viscosities, jet velocities, and surface velocities the air pressure at which lamella detachment is suppressed was determined experimentally by systematically decreasing the ambient air pressure inside a vacuum chamber. The highest air pressure at which the leading edge of the lamella did not detach from the surface was classified as the threshold air pressure. Multiple experiments were performed in the vicinity of the threshold pressure as near the threshold the lamella is very sensitive to destabilization. The liquid parameters, Table 1, can be combined into two dimensionless groups, fjjf VD \u00C2\u00B5\u00CF\u0081=Re and \u00CF\u0083\u00CF\u0081 2jjf VDWe = . The current experiments concentrate on flow regimes of 100 < Re < 10000 and 300 < We < 10000. 15 2.1 Influence of Surrounding Air Pressure and Surface Velocity 2.1.1 Jet Impingement Observations A time series of a liquid jet impinging on a moving surface is shown in Figure 2.1. This series of images shows the initial impingement of the jet and the subsequent radial and downstream spread of the deposited liquid. In these images both upstream and downstream lamella can be seen clearly. In subsequent discussions only the behaviour of the upstream lamella will be mentioned, and henceforth it will be referred to simply as the lamella. At a certain time during the transient development of the lamella, the leading edge of the lamella detaches from the surface. For the particular set of conditions shown in Figure 2.1 the average time to lamella detachment was 2.07\u00C2\u00B10.2 ms over a sample of 25 experiments conducted under constant conditions. When the leading edge of the lamella detaches from the surface, the angle of the detached lamella relative to the surface increases with time until it reaches a steady state angle relative to the surface. Experiments were conducted in which the surface normal was parallel to gravity or anti-parallel to gravity. In both cases the lamella detachment was the same to within experimental error. 16 Figure 2.1 Time evolution of jet impingement on a moving surface. For the conditions shown in the series of images the jet velocity is 8.0 ms-1, the surface velocity is 5.5 ms-1, the liquid viscosity is 15.6 cP, and the ambient air pressure is 101 kPa. In these experiments it was desired to investigate whether the surrounding air pressure played a role in the detachment behaviour of the liquid lamella. Through high-speed imaging it was observed experimentally that if the ambient air pressure is reduced below a specific threshold value detachment of the lamella from the surface is inhibited. Figure 2.2 shows jet impingement for a particular jet and surface condition, as a function of the surrounding air pressure2. Interestingly, at low pressures no lamella detachment occurs and as pressure is increased the lamella begins to detach from the surface and lamella detachment is initiated. 2 The air temperature was held constant in these experiments. As the air viscosity and liquid surface tension are only very weak functions of the air pressure, the air viscosity and surface tension were nearly constant in the experiments. Therefore, varying the air pressure is equivalent to varying only the air density. 17 Figure 2.2 Splashing behaviour of a viscous liquid jet (18.3 mPa\u00C2\u00B7s) during impingement onto a smooth dry moving surface at different ambient pressures. As the surrounding gas pressure is lowered, at the same jet and surface conditions, splash is inhibited. The velocity of the jet is 14.0\u00C2\u00B10.3 ms-1 and the velocity of the surface is 7.5\u00C2\u00B10.2 ms-1. For this combination of velocities, the threshold pressure is 37 \u00C2\u00B1 5kPa. The detached lamella spreads farther than it did prior to detachment owing to the dramatically reduced viscous force acting on the lamella underside. It was observed in all cases of velocity ratios and liquid viscosity that lamella detachment can be suppressed by reduction in 18 ambient air pressure. Therefore, as for droplet impact, the surrounding air plays a significant role in the behaviour of liquid jet impingement onto a moving surface. However, reduction in the surrounding air pressure is not the sole method observed for suppressing lamella detachment. The velocity of the surface has been seen to have a significant effect on the lamella detachment behaviour of an impinging jet. At low surface velocity lamella detachment does not occur, to the limiting case of a hydraulic jump formation on a stationary surface, as has been studied by other researchers for large diameter nozzles and low velocities [22] [23]. At higher surface velocities the lamella detaches from the surface, as can be observed in Figure 2.3 for a condition of the same jet speed, ambient air pressure, and liquid viscosity. Figure 2.3 Effect of surface velocity on jet impingement. In both images the jet velocity is 13 ms-1 and the fluid is 65% wt glycerin in water. The surface is moving left to right and the velocity of the surface in image a and image b are 2.6 ms-1 and 7.5 ms-1, respectively. These figures clearly show that lamella detachment is affected by the surface velocity. 19 2.1.2 Quantitative Results of Surrounding Air Pressure We experimentally determined the surrounding air pressure below which lamella detachment from the surface was completely suppressed. The main experimental results are summarized in Figure 2.4 for the threshold ambient air pressure as a function of both jet and surface velocity and in Figure 2.5 for threshold ambient air pressure as a function of liquid viscosity. Note that in Figure 2.4 the threshold air pressure is a strong function of the jet velocity at low jet velocities and only a weak function of jet velocity at high jet velocities. This plateau behaviour was observed for both surface velocities studied. It is also noted that the threshold air pressure increases with a decrease in the surface velocity. Figure 2.4 Experimental results for pressure threshold between lamella adhesion and lamella detachment for a solution of 70% glycerin in water which has a viscosity of 18.3 cP. The figure displays the threshold ambient air pressure as a function of jet velocity and surface velocity. Below the threshold pressure lamella detachment is fully suppressed. 20 Additionally, it can be noted from the experimental results for threshold air pressure as a function of liquid viscosity that the threshold pressure has a non-linear dependence on the liquid viscosity. Lamella detachment was not observed for the extremities of the viscosity range; solutions of 80% or more glycerin, \u00C2\u00B5=47 mPa\u00C2\u00B7s, and 30% or less glycerin, \u00C2\u00B5=2.14 mPa\u00C2\u00B7s. The pressure threshold decreases with increased viscosity at low liquid viscosity, however, as the liquid viscosity is increased above about 8 mPa\u00C2\u00B7s the detachment threshold pressure increases as well. Figure 2.5 Dependence on fluid viscosity. The graph shows the pressure thresholds below which lamella detachment is suppressed. In all cases the surface and jet velocities were maintained at 7.5 \u00C2\u00B10.2 m/s, and 16.5 \u00C2\u00B10.5 m/s, respectively. We believe that for the extremities of the viscosity range only air pressures above 100 kPa would be sufficient to cause detachment. The results of Mishra et al. [19], Xu et al. [17] [18], Kumar [25] and the current work clearly imply the existence of three viscosity regimes. 21 Figure 2.6 shows the behaviour of a low viscosity liquid jet under increasing ambient air pressure. Figure 2.6 Splashing behaviour of a low viscosity liquid jet. The jet is a solution of 40 % glycerine, viscosity of 3.2 mPa\u00E2\u0080\u00A2s, with a jet velocity of 9.5 \u00C2\u00B10.5 m/s. In all images the surface moves from left to right at a velocity of 7.5 \u00C2\u00B10.2 m/s. The transition from deposition to lamella detachment for this case lies between an ambient pressure of 40 and 43 kPa. 22 The experimental results (including some not documented here) have shown that the lamella detachment behaviour is a function of many parameters: ( )jsjairairfff DVVf ,,,,,,, \u00C2\u00B5\u00CF\u0081\u00CF\u0083\u00CF\u0081\u00C2\u00B5 Dimensional analysis determines the dimensionless groups to be: jet ofnumber ReynoldsRe:1 ==\u00E2\u0088\u008F j f jjf DV \u00C2\u00B5 \u00CF\u0081 =\u00E2\u0088\u008F air jsair DV \u00C2\u00B5 \u00CF\u0081 :2 Rea= Reynolds number of air jet ofnumber Weber : 2 3 ==\u00E2\u0088\u008F j f jjf We VD \u00CF\u0083 \u00CF\u0081 4 : Velocity Ratio j s V V \u00E2\u0088\u008F = RatioViscosity :5 =\u00E2\u0088\u008F f air \u00C2\u00B5 \u00C2\u00B5 The results of Figures 2.4 and 2.5 may be combined into a single graph by plotting 1 2 4 1vs \u00E2\u0088\u0092\u00E2\u0088\u008F \u00E2\u0088\u008F \u00E2\u0088\u008F . This combination of dimensionless groups provides good collapse of the experimental results, as seen in Figure 2.7. As the magnitude of the Reynolds number of the air is fairly small ( 300Re \u00E2\u0089\u00A4a ), it is plausible that both the air viscosity and air density play a role in splash. 23 Figure 2.7 Dimensionless threshold pressure as a function of dimensionless jet velocity. Two features of Figure 2.7 are noteworthy. At low Reynolds numbers, which correspond to low jet velocities, 1 2 4 \u00E2\u0088\u0092\u00E2\u0088\u008F \u00E2\u0088\u008F increases sharply, which implies that only very high ambient air pressures would be sufficient to detach the lamella. At high Reynolds numbers the curve seems to approach an asymptotic value greater than zero. This implies for a surface at rest, even extremely high jet velocities cannot produce lamella detachment. Using the same dimensionless parameters, 12 4 1vs\u00E2\u0088\u0092\u00E2\u0088\u008F \u00E2\u0088\u008F \u00E2\u0088\u008F , experimental pressure thresholds for two other concentrations of water-glycerin (60% WG and 65% WG) have been plotted against the Reynolds number of the jet in Figure 2.8. Additionally, the viscosity thresholds shown in Figure 2.5, which were determined at constant jet and surface velocity, are plotted as Reynolds number of the air divided by the velocity ratio against Reynolds number of 24 the jet. Interestingly, the curves collapse onto the threshold curve of the 70% glycerin in water curve. Each point is a pressure threshold that has been determined by systematically increasing the ambient air pressure until lamella detachment occurs. Therefore, lamella detachment occurs above the curve and deposition occurs below the curve. Figure 2.8 Reynolds number of the air divided by the velocity ratio plotted against Reynolds number of the jet. Plotting the experimental data with these dimensionless groups provides good collapse of the data. Lamella detachment is suppressed below the curve. 25 2.2 A Model of Lamella Detachment 2.2.1 Model Development For droplet impact onto a stationary surface, Xu et al. have suggested that the driving mechanism of splashing is the Kelvin-Helmholtz instability. For jet impingement on a moving surface the conditions also exist for the Kelvin-Helmholtz instability to occur. However, this instability is not thought to be the driving mechanism for lamella detachment since the conditions for the Kelvin-Helmholtz instability are satisfied for all ranges of surface velocity, whereas lamella detachment is suppressed at low surface velocities. Consistent with the observed dependence of lamella detachment on surface velocity and surrounding air pressure, we propose here that lamella detachment is caused by the aerodynamic force lifting the liquid off the surface, destabilizing the balance between surface tension and fluid pressure. Once the leading edge of the lamella detaches from the surface, the air boundary layer on the moving surface forms a stagnation point on the underside of the lamella that supports the detached lamella. The detached lamella configuration is stable. It has been observed that lamella detachment is initiated at the leading edge and therefore the relevant forces in determining lamella detachment can be analyzed at this location through a force balance in the vertical (y) direction. Figure 2.9 is a diagram showing the relevant forces acting on the leading edge of the lamella in the vertical direction in a two dimensional plane. 26 Figure 2.9 Schematic of the leading edge stagnation point. The image shows the relevant forces acting on the two dimensional control-volume around the stagnation point at the leading edge of the lamella. For clarity, the viscous, gravitational, and inertial forces acting on the control volume are not shown. This force balance analysis requires several assumptions to be made: \u00E2\u0080\u00A2 A two dimensional analysis can be used to approximate the interaction because the relevant length scale is the thickness of the lamella, which is much smaller than the radius of curvature of the lamella in the plane of the surface. \u00E2\u0080\u00A2 Since the leading edge of the lamella is the location of the liquid stagnation point, and since in this region the fluid flow is largely parallel with the surface, the inertial and viscous forces in the vertical direction in this region are negligible. \u00E2\u0080\u00A2 The influence of gravity is negligible (shown experimentally with an inverted apparatus). \u00E2\u0080\u00A2 Due to the low velocity of the liquid near the lamella leading edge, the local velocity of the air (not the differential velocity between the air and the liquid) is the relevant variable for predicting the aerodynamic force. 27 \u00E2\u0080\u00A2 Since the air boundary layer thickness (\u000F~3000 \u0012\u0013) is much larger than the lamella thickness \u0014\u00E2\u0084\u008E\u0016\u0017\u0018\u0019\u0016\u0016\u0017~40\u0012\u0013\u001B, the local velocity of the surrounding air may be approximated by the velocity of the surface, sair VU \u00E2\u0089\u0088 . Given these assumptions we may write the force balance in the vertical direction, taking W to be the length scale into the page. DTSNyA FFF \u00CE\u00B8sin.., =+ Equation 2.1 Where, 22 22 , LsairLairair yA WLCVWLCUF \u00CF\u0081\u00CF\u0081 \u00E2\u0089\u0088= Equation 2.2 Wk r WkPF lN \u00CF\u0083 \u00E2\u0089\u0088\u00E2\u0089\u0088 Equation 2.3 DTS WF \u00CE\u00B8\u00CF\u0083 sin.. = Equation 2.4 From Equations 2.1-2.4 the following criterion for lamella detachment is given: D Lsair AD D r kLCV F F \u00CE\u00B8\u00CF\u0083 \u00CF\u0083\u00CF\u0081 sin 2 1 2 + \u00E2\u0089\u0088 Equation 2.5 Hence, 1> AD D F F , lamella detachment 1< AD D F F , lamella adhesion 28 The purpose of the model is to be able to theoretically predict the pressure threshold below which lamella detachment is suppressed. Equation 2.5 can be rearranged, with 1= AD D F F , to give an expression for the density of the air at the threshold. \u00EF\u00A3\u00BE \u00EF\u00A3\u00BD \u00EF\u00A3\u00BC \u00EF\u00A3\u00B3 \u00EF\u00A3\u00B2 \u00EF\u00A3\u00B1 \u00E2\u0088\u0092\u00E2\u0089\u0088 r k LCV D Ls air \u00CE\u00B8 \u00CF\u0083\u00CF\u0081 sin 2 1 2 Equation 2.6 Incorporating the ideal gas law the threshold air pressure can be determined. \u00EF\u00A3\u00BE \u00EF\u00A3\u00BD \u00EF\u00A3\u00BC \u00EF\u00A3\u00B3 \u00EF\u00A3\u00B2 \u00EF\u00A3\u00B1 \u00E2\u0088\u0092\u00E2\u0089\u0088 r k LCV RTP D Ls T \u00CE\u00B8 \u00CF\u0083 sin 2 1 2 Equation 2.7 2.2.2 Model Comparison to Experiments The relationship for the threshold ambient air pressure derived in the previous section will be compared to the experimental results. As there are many geometric parameters (L, k, r, \u00CE\u00B8D), several assumptions as to the value of these parameters must be made to further develop this model as the scientific knowledge in this area not sufficient to fully describe the relevant geometry. The first parameter which must be defined is the dynamic contact angle, \u00CE\u00B8D. It is usually assumed that the dynamic contact angle is a function of the contact-line speed, U, and fluid properties [30], ( ),...,,, 321 \u00CF\u0087\u00CF\u0087\u00CF\u0087\u00CE\u00B8 UfD = , This implicitly assumes that the dynamic contact angle is independent of the impaction velocity of the jet or the bulk fluid flow. However, recent experiments at surface velocities up to 15 ms-1 29 have shown this assumption is invalid and proved there is a nonlocal influence of the flow on the dynamic contact angle [30] [31]. The dynamic contact angle approaches a maximum dynamic contact angle, max,D\u00CE\u00B8 , which is generally less than 180\u00C2\u00B0 for spreading on a moving surface [32]. Blake et al. [33] provide a good detailed review of the dynamic contact angle. Knowing that the dynamic contact angle increases with jet and surface velocity [34] [31] [35] [36] we will approximate the dynamic contact angle by the following relationship which follows a similar trend to that observed experimentally by several researchers [23-28]. 3 max, max,: \u00EF\u00A3\u00B7\u00EF\u00A3\u00B7 \u00EF\u00A3\u00B8 \u00EF\u00A3\u00B6 \u00EF\u00A3\u00AC\u00EF\u00A3\u00AC \u00EF\u00A3\u00AD \u00EF\u00A3\u00AB \u00E2\u0088\u0092 \u00E2\u0088\u0092 s j SD DD V V \u00CE\u00B8\u00CE\u00B8\u00CE\u00B8\u00CE\u00B8 Equation 2.8 max,D\u00CE\u00B8 is a function of the surface velocity and liquid viscosity. It should be noted that there are several correlations for the dynamic contact angle as a function of the capillary number, \u00CF\u0083\u00C2\u00B5 /VCa = ,based on the experimental results of Hoffman [37]. However, since the interface velocities were very small and Blake et al. [38] have shown that there is a change in the physical mechanism of the advancing contact line at velocities greater than 7 cms-1 these correlations cannot be applied to the current work. From [33] a value of the maximum dynamic contact angle at high surface speed can be obtained from experimental data to be approximately 160\u00C2\u00B0 for an intermediate viscosity water- glycerin solution. The term \u00EF\u00A3\u00BE \u00EF\u00A3\u00BD \u00EF\u00A3\u00BC \u00EF\u00A3\u00B3 \u00EF\u00A3\u00B2 \u00EF\u00A3\u00B1 \u00E2\u0088\u0092 r k D\u00CE\u00B8sin in Equation 2.7 cannot be approximated simply. However, based on geometric considerations, it is apparent that r k will be strongly dependent on 30 \u00CE\u00B8D. Therefore, to further develop this model of lamella detachment we will assume that { } DDD Cf r k \u00CE\u00B8\u00CE\u00B8\u00CE\u00B8 sinsin == \u00EF\u00A3\u00BE \u00EF\u00A3\u00BD \u00EF\u00A3\u00BC \u00EF\u00A3\u00B3 \u00EF\u00A3\u00B2 \u00EF\u00A3\u00B1 \u00E2\u0088\u0092 . Thus, Equation 2.7 becomes: D Ls T C LCV RTP \u00CE\u00B8\u00CF\u0083 sin 2 1 2 \u00E2\u0089\u0088 Equation 2.9 For a solution of intermediate viscosity, such as 70% glycerin in water, the length scale, L, can be approximated by 2h and the aerodynamic lift coefficient, CL, will be set equal to unity. It has been assumed that the thickness of the lamella at detachment is proportional to the boundary layer thickness, tch \u00CE\u00BD1\u00E2\u0089\u0088 , which is a commonly used assumption in modelling lamella thickness3. The relevant time scale, t, in the jet impingement problem was taken as j j D t V= and the proportionality constant 1c was set to 1.Incorporating these approximations and performing a least square fit of our model to the experimental results for the ambient air pressure thresholds for intermediate viscosity liquids we found that 031.0=C . The model predictions are compared with the experiment in Figure 2.10. Both the model and experiment are characterized by a detachment threshold air pressure that decreases strongly with jet velocity at low velocities, but only weakly at higher jet velocities. The model and the experiments are consistent in also having a detachment threshold that increases as the surface velocity decreases. The differences between the model and the experiment may arise from the crude approximations of the dynamic contact angle, constant aerodynamic lift coefficient and approximations of the geometric parameters. 3 de Ruiter et al. [42] have shown that the lamella thickness is a more complex function of many parameters including the viscosity, velocity, surface tension, and time. 31 Figure 2.10 Lamella detachment threshold pressure as a function of jet velocity and surface velocity. The curves are the predicted pressure thresholds as a function of jet velocity and surface velocity. Here the constant C in equation 2.9 is C=0.031. This model predicts detachment for the intermediate viscosity liquids. We postulate that at low liquid viscosity the lamella is stabilized by high surface tension forces which are a result of the thinness of the lamella. At high liquid viscosities high viscous dissipation produces a thick lamella. The high shear forces in the lamella may reduce the dynamic contact angle of the liquid, increasing the component of the surface tension adhering the liquid to the surface. As well, at high liquid viscosity the lamella geometry is not consistent with the lamella geometry in the intermediate range. Therefore, many of the geometric assumptions made may not apply to high viscosity liquids. As with many fields of research, advancement is motivated by technological needs and therefore the scientific background of this area is limited. With further advancement the model 32 proposed could be further developed to account for the geometric parameters and tighten up the assumptions made. As well, quantities such as the dynamic contact angle and aerodynamic lift coefficient can be known with more precision which would increase the robustness of the model. 2.3 Conclusions for the Effect of Surrounding Air Pressure From the experimental investigation into the effect of surrounding air pressure on liquid jet impingement with a moving surface the following can be concluded: \u00E2\u0080\u00A2 Lamella detachment can be fully suppressed by reducing the surrounding air pressure, which shows that aerodynamic forces are important in determining the outcome of liquid jet impingement on a moving surface \u00E2\u0080\u00A2 Surface velocity plays a critical role in the splashing and detachment behaviour of liquid jet impingement; lamella detachment does not occur for a stationary surface but is initiated with increased surface velocity \u00E2\u0080\u00A2 Measurements of the lamella detachment air pressure threshold collapse well on a normalized Reynolds number of air versus Reynolds number of jet graph \u00E2\u0080\u00A2 The model developed based on experimental observation and data is in qualitative agreement with the experimental results \u00E2\u0080\u00A2 Three viscosity regimes are evident with lamella detachment and splashing most likely to occur in the intermediate regime; low viscosity regime the lamella is stabilized by high surface tension forces and the high viscosity regime the lamella is stabilized by high viscous dissipation 33 3 INFLUENCE OF FLUID PROPERTIES: VISCOSITY AND SURFACE TENSION The three viscosity regimes observed by Xu et al. [18] [17], Kumar et al. [25], and in the previous chapter were further investigated with 25 solutions of varying viscosity and surface tension. The full range of water-glycerin solutions with a 648 \u00C2\u00B5m nozzle was investigated at an ambient air pressure of 101 kPa. As well, the three viscosity regimes were investigated with solutions of ethanol-glycerin which have comparable viscosities and densities to the water- glycerin solutions with approximately one third the surface tension. 3.1 Influence of Surface and Jet Velocities Experiments were carried out with the 648 \u00C2\u00B5m nozzle and a jet liquid of 70% glycerin in water at the ambient air pressure of 101 kPa. The surface velocity was fixed and the jet velocity was systematically varied. As seen in Figure 3.1, for low surface velocities no lamella detachment was observed whereas at higher surface velocities there was a transition to lamella detachment and splashing as the jet velocity was increased. However, at low jet velocity deposition always occurred. 34 Figure 3.1 Threshold jet velocity as a function of surface velocity. The figure shows the splash threshold as a function of both jet and surface velocities for a solution of 70% glycerin in water. It can clearly be observed that as the surface velocity is increased the critical jet velocity decreases drastically. If the curve is extrapolated it can be seen that for the limiting case of zero surface velocity no lamella detachment would occur. It is likewise clear that the splash threshold occurs at a non-zero jet velocity even at very high surface velocities. As can be seen in the figure, lamella detachment and splashing is a strong function of both the jet and surface velocities with the lamella not detaching at low surface velocity. Knowing this, further experiments into the effects of fluid viscosity and surface tension were performed at constant surface velocity to reduce the parameter space being investigated. 3.2 Jet Impingement of Water-Glycerin Solutions Jet impingement experiments performed with 15 different water-glycerin solutions verified the three viscosity regimes observed by Kumar et al. [25] at the larger nozzle diameter of 648 \u00C2\u00B5m. Kumar studied nozzle diameters of 200 and 400 micrometers. The viscosities of the solutions ranged from 1 cP to 1000 cP (0% W-G to 100% W-G). The liquid parameters can be combined into two dimensionless groups, fjjf VD \u00C2\u00B5\u00CF\u0081=Re and \u00CF\u0083\u00CF\u0081 2jjf VDWe = . The current 35 experiments concentrate on flow regimes of 10 < Re < 10000 and 200 < We < 10000. Lower Weber numbers could not be obtained as the surface tension of these fluids was approximately constant and the jet was susceptible to break up at low jet velocity due to Plateau-Rayleigh instabilities. 3.2.1 Jet Impingement Observations for Water-Glycerin Solutions Figure 3.2 displays the flow characteristics of each of the three viscosity regimes for water-glycerin solutions. Figure 3.2 Three viscosity regimes are evident in the above figure. In all cases the jet velocity was 12.1 ms-1, the surface velocity was 5.5 ms-1, and the air pressure was 101kPa. The viscosity was, (a) 2.155 mPas, (b) 8.995 mPas, and (c) 47 mPas. Fluid viscosity plays a very significant role in the splashing behaviour of liquid jet impingement. In the low and high viscosity regime, the lamella does not detach from the surface and complete deposition occurs. In the intermediate viscosity regime the lamella is most prone to detachment and at all but low jet velocities lamella detachment is observed. The detached lamella spreads further due to significantly reduced viscous forces acting on the lamella underside. Once detached the lamella is sustained in the detached configuration by aerodynamic forces. Droplets form on the rim of the detached thin liquid sheet. These droplets can be separated from the rim by either aerodynamic forces or due to high inertial forces. It is also observed that the lamella spread further in the low viscosity regime than the high viscosity regime due to lower viscous dissipation. As well, the lamella thickness is much larger in the high 36 viscosity regime than the low viscosity regime due to continuity. As viscosity is increased the lamella thickness is increased and the lamella spread is decreased. 3.2.2 Quantitative Results of Water-Glycerin Solutions The experimental data from this study of water-glycerin solutions is presented as jet velocity against the liquid viscosity in Figure 3.3. It is seen that lamella detachment and splashing only occurs in the intermediate viscosity range. The lamella adheres to the surface in the high and low viscosity regimes. Figure 3.3 Splash chart of experimental results for water-glycerin solutions at a surface velocity of 5.5 ms-1 and ambient air pressure of 101 kPa. This chart shows the three regimes of viscosity, with lamella detachment and splashing prone to occur in the intermediate regime. Complete deposition is achieved in the low and high viscosity regimes. It can be concluded that lamella detachment is completely suppressed at viscosity lower than 3 cP and greater than 40 cP with lamella detachment occurring between. This result is in 37 good agreement with Kumar et al. [25] who has previously investigated the three viscosity regimes for smaller jet diameters and the previous chapter. At sufficiently low jet velocity, 15 \u00E2\u0088\u0092\u00E2\u0089\u00A4 msV j , lamella adhesion is observed in all cases, however, the flow rate of the liquid is sufficiently low that the liquid is convected downstream by the moving surface prior to spreading far radially and only a small toe is seen to form upstream of the impingement point. The jet velocity corresponds to a velocity ratio of one or less, 1\u00E2\u0089\u00A4 s j V V . There may be a vertical component of momentum in the leading edge of the toe that prevents detachment since the flow in the leading edge would not be fully parallel to the surface. As the jet velocity is increased the liquid spreads further upstream and lamella detachment occurs. At the lower viscosity threshold there appears to be a critical viscosity below which lamella detachment is inhibited. The experimental data can be plotted in dimensionless form as the Weber number and the Reynolds number. Plotting the results in this manner shows the relative influence of viscous forces to surface tension forces. This has been done in Figure 3.4. In the figure the data are arranged in parallel lines of slope 2 on the log-log plot. Each line represents a particular concentration of glycerin in water, with lower concentrations of glycerin solutions represented by lines to the lower right. Each point along the line represents a test conducted at a particular jet velocity; higher velocities are represented by points to the upper right of each line. 38 Figure 3.4 Experimental results for impingement experiments at a constant surface velocity, \u001C\u001D = \u001F. \u001F !\u001D\"#, and ambient air pressure, P=101 kPa. These results clearly show that there is a distinct Reynolds number regime in which lamella detachment and splashing can occur. There are no clear linear boundaries separating the lamella detachment region from the deposition region. The boundary forms a skewed parabola in which lamella detachment occurs above with deposition below. For low Reynolds number flows, lamella detachment does not occur even at high Weber numbers. The same is true for high Reynolds number jets, where increasing the Weber number does not lead to lamella detachment. Increasing the Weber number in the intermediate Reynolds number regime promotes lamella detachment. In the intermediate Reynolds number regime, deposition occurs at velocity ratios less than one or Weber numbers less than 300. The majority of the experiments were conducted at a constant surface velocity of 5.5 ms-1, however, an investigation into the impingement of jets of various liquid viscosities was 39 conducted at a low velocity surface. Figure 3.5 plots the Reynolds number against the Weber number for the impingement experiments on a surface moving at 2.3 ms-1. Figure 3.5 Experimental results for water-glycerin solutions for a constant surface velocity of 2.3 ms-1 and ambient air pressure of 101 kPa. As can be seen in the figure, at this low surface velocity lamella detachment does not occur due to reduced aerodynamic forces. For the full range of Reynolds numbers lamella detachment does not occur at the reduced surface velocity. In the intermediate Reynolds number regime, in which lamella detachment is most prone to occur, increasing the Weber number did not lead to detachment at the lower surface velocity. This is consistent with previous studies on the effect of surface velocity. Lamella detachment does not occur at low surface velocity because there is not sufficient aerodynamic force to lift the liquid lamella from the surface. The aerodynamic force is proportional to the square of the surface velocity and therefore at low surface velocity the aerodynamic force acting on the lamella is also small. In addition, at higher jet velocity a 40 hydraulic jump is observed to form on the surface. This occurs as at the higher jet flow rates the liquid is not convected downstream at a high enough rate to prevent liquid build up. 3.3 Jet Impingement of Ethanol-Glycerin Solutions To investigate the influence of surface tension on the three viscosity regimes and splashing behaviour of liquid jet impingement an experimental study was conducted with eleven solutions of various concentrations of glycerin in ethanol varying from 0% to 100% glycerin in ethanol. The surface tension of these solutions was approximately one third of the surface tension of the water-glycerin solutions allowing for the influence of surface tension to be studied well the viscosity was held constant. The liquid parameters can be combined into two dimensionless groups, fjjf VD \u00C2\u00B5\u00CF\u0081=Re and \u00CF\u0083\u00CF\u0081 2jjf VDWe = . The current experiments concentrate on flow regimes of 10 < Re < 10000 and 400 < We < 20000. Weber numbers below 400 could not be obtained in this study as the surface tension was low and the jet was susceptible to break-up at low jet velocities due to the Plateau-Rayleigh instability. 3.3.1 Jet Impingement Observations for Ethanol-Glycerin Solutions The flow regimes observed are depicted in Figure 3.6. Each image is representative of the characteristics of the lamella in that regime. 41 Figure 3.6 The three distinct flow regimes observed experimentally are shown. (a) is a jet of 100% ethanol (\u00C2\u00B5=1.341 cP), (b) is a jet of 20% Ethanol-80% Glycerin (\u00C2\u00B5=131 cP), and (c) is a jet of 50% Ethanol-50% Glycerin (\u00C2\u00B5=15.6 cP). In all cases the jet velocity is #$. \u001F \u00C2\u00B1 &. \u001F !\u001D\"# and the surface is moving from left to right at a velocity of \u001F. \u001F \u00C2\u00B1 &. ' !\u001D\"#. The three flow regimes can clearly be seen, (a) and (b) show lamella adhesion to the surface with the non-continuous fluid phase at high Reynolds and Weber numbers. While, (c) shows lamella detachment and splashing at intermediate Reynolds numbers. In the high viscosity regime, consistent with water-glycerin solutions, lamella detachment does not occur and deposition is observed for all jet velocities and surface velocities studied. The lamella spread is inhibited by high viscous dissipation and due to continuity the lamella thickness is significantly larger than the lamella thickness of the low viscosity fluids. There is significant build-up of fluid at the rim of the lamella and there is potentially a region of recirculation in the rim as observed for high viscous coating flows [30]. In the low viscosity regime, consistent with water-glycerin solutions, the lamella adhered to the surface and lamella detachment was not observed. The lamella spreads further in this regime than in the high viscosity regime and the thickness of the film is reduced. An interesting observation from high-speed imaging of the flow characteristics of the low viscosity, low surface tension regime is that although the lamella is adhering to the surface the liquid phase is non- continuous. This is due to small droplets being emitted from the leading edge of the lamella. This phenomenon has been called droplet spattering. It is postulated that this occurs for low surface tension solutions of low viscosity because the viscous dissipation is not sufficient to balance the 42 initial inertia of the jet. When the fluid reaches the rim of the lamella it has retained sufficient momentum to overcome the surface tension forces restraining fluid from leaving the continuous phase. This description is supported by experimental evidence as at high jet velocities droplets can be seen forming on the rim of the lamella for the water-glycerin solutions, however, they are restrained by the higher surface tension forces. As well, droplet spattering can be suppressed for the ethanol-glycerin solutions by reducing the velocity of the jet and therefore the initial inertia of the fluid. Similar to the water-glycerin solutions lamella detachment and splashing is most prone to occur in the intermediate viscosity regime. Lamella adhesion was not observed even at the minimum jet velocities, as had been seen for the water-glycerin solutions. The detached lamella spreads further for ethanol-glycerin solutions due to the reduced surface tension forces and far more droplets broke off the detached thin sheet. These droplets are in general smaller in diameter than the droplets that break off the detached lamella for water-glycerin solutions. The change in droplet diameter is due to lower surface tension forces. Subjected to an equivalent pressure across the interface the radius must be smaller to satisfy the normal stress balance across the interface. 3.3.2 Quantitative Results of Ethanol-Glycerin Solutions Figure 3.7-10 present the dimensional experimental data for a select sample of ethanol- glycerin solutions plotted as jet velocity against surface velocity. These figures show the experimental test points and the resulting deposition, lamella detachment, or droplet spattering that occurs under those conditions. 43 Figure 3.7 (a) experimental results for a solution of 0% EG and (b) experimental results for a solution of 20% EG for various combinations of jet and surface velocity. Figure 3.8 (a) experimental results for a solution of 35% E-G and (b) experimental results for a solution of 40% E- G for various combinations of jet and surface velocity. Figure 3.9 (a) experimental results for a solution of 50% E-G and (b) experimental results for a solution of 63% E- G for various combinations of jet and surface velocity. 44 Figure 3.10 (a) experimental results for a solution of 80% E-G and (b) experimental results for a solution of 90% E- G for various combinations of jet and surface velocity. The high viscosity liquids were not observed to detach regardless of surface velocity. As well, the low viscosity liquids exhibited droplet spattering and deposition dependent on the velocity of the surface. Figure 3.10a is a good representation of the effect of surface velocity as all three of the flow regimes are represented. This figure shows the experimental results for impingement experiments for a solution of 80% ethanol-20% glycerin. At surface velocities higher than 5.5 ms-1 the lamella was observed to detach from the surface. For a surface velocity of 3.5 ms-1 the lamella adhered to the surface, however, droplet spattering occurred and therefore the fluid phase was not continuous. At the low surface velocity of 2.5 ms-1 clean deposition occurred. This figure clearly shows the influence of surface velocity. The experimental data can be plotted in dimensionless form as the Weber number and the Reynolds number. This has been done in Figure 3.11. In the figure the data are arranged in parallel lines of slope 2 on the log-log plot. Each line represents a particular concentration of glycerin in ethanol, with lower concentrations of glycerin solutions represented by lines to the lower right. Each point along the line represents a test conducted at a particular jet velocity; higher jet velocities are represented by points to the upper right of each line. 45 Figure 3.11 Experimental data for 10 different ethanol-glycerin solutions showing regions of splash and deposition at a constant surface velocity of 5.5 ms-1. Consistent with the results of the water-glycerin solutions impacting onto a surface moving at 5.5 ms-1 lamella detachment only occurs at intermediate Reynolds numbers. However, at intermediate Reynolds numbers, deposition does not occur at low Weber numbers, as it does for the water-glycerin solutions. Weber numbers below 400 could not be achieved with the ethanol-glycerin solution due the low surface tension of the solutions. Therefore, the low Weber number boundary of 300 in the intermediate Reynolds number regime could not be verified for the ethanol-glycerin solutions. In the higher Reynolds number region increasing the Weber number results in droplet spattering as inertial forces are increased relative to surface tension forces. 46 Impingement experiments with ethanol-glycerin solutions were conducted at two other surface velocities, 3.5 ms-1 and 7.5 ms-1. The experimental results are plotted in dimensionless form as Reynolds number against Weber number in Figure 3.12 and 3.13. Figure 3.12 Experimental results of ethanol-glycerin solutions at a constant surface velocity of 3.5 ms-1 at an ambient air pressure of 101 kPa 47 Figure 3.13 Experimental results of ethanol-glycerin solutions at constant surface velocity of 7.5 ms-1 at an ambient air pressure of 101 kPa For different surface velocities it is clear that the same Reynolds number regimes occur with lamella detachment only occurring at intermediate Reynolds numbers. Again the lower Weber number boundary is not observed at it was not possible to obtain Weber numbers below 400 for the ethanol-glycerin solutions. There is a slight shift in the lower Reynolds number boundary with changes in the surface velocity. However, the main difference is the prevalence of droplet spattering at high Reynolds numbers and high Weber numbers. Droplet spattering can be suppressed at lower surface velocities. As well, the range of Reynolds numbers prone to lamella detachment is narrower at lower surface velocities. 48 3.4 Summary and Discussion of Experimental Results From the experimental investigation into the impingement of a high velocity jet on a moving substrate it is clear that the viscosity, surface tension, jet velocity and surface velocity effect the resulting deposition or lamella detachment at a constant ambient air pressure of 101 kPa. The results of the water-glycerin and ethanol-glycerin experiments are plotted together as Reynolds number against Weber number for a constant surface velocity of 5.5 ms-1 and ambient air pressure of 101 kPa in Figure 3.14. Figure 3.14: Summary of experimental results at a constant surface velocity of 5.5 ms-1, and a constant nozzle diameter of 648 \u00C2\u00B5m. The predominant difference in the lower surface tension fluids is the situation where the lamella adheres to the surface but droplet are still being emitted resulting in a non-continuous fluid phase. However, it can be seen that the results of both water-glycerin and ethanol-glycerin solutions are consistent in the three viscosity regime behaviour. 49 Similar Reynolds number regime behaviour occurs for both ethanol-glycerin and water- glycerin solutions. However, the upper threshold transition from lamella detachment back to deposition at high Reynolds numbers occurs at lower Reynolds numbers for the ethanol-glycerin solutions than for the water-glycerin solutions. This could be due to the occurrence of droplet spattering for the ethanol-glycerin solutions at high Weber numbers. This region is high Reynolds and high Weber numbers implying that inertial forces are dominate over both viscous and surface tension forces. The inertial forces relative to surface tension forces could be the reason that droplet spattering is seen to occur in this region. Figure 3.15 Threshold points between deposition and lamella detachment. Lamella detachment occurs in the intermediate Reynolds number regime (300 < Re < 2500) as the Weber number is increased above 250. Dashed line represents spline fit of water-glycerin thresholds. 50 The thresholds between deposition and lamella detachment have been isolated for the different combinations of liquids and various surface velocities. These thresholds are plotted as Reynolds number against Weber number in Figure 3.15. The threshold between deposition and lamella detachment is non-linearly dependent on the Reynolds number. At Reynolds numbers, below 270, deposition is achieved at the full range of Weber numbers. At intermediate Reynolds numbers (300< Re < 2500) lamella detachment is initiated with increased Weber numbers. Moreover, at high Reynolds numbers, Re>2500, deposition occurs for the full range of Weber numbers however droplet spattering occurs at high Weber numbers. Deposition is always achieved at Weber numbers less than 250 regardless of Reynolds number. There is good agreement between the thresholds for the ethanol-glycerin and water-glycerin solutions at different surface velocity with the exception of the lower surface velocity of 3.5 ms-1 which is in agreement with lamella detachment not occurring on sufficiently slow moving surfaces as the regime in which detachment occurs is becoming narrower with decreased surface velocity. The right side of the threshold curve has a slope of 2 which indicates that the threshold is a strong function of the liquid viscosity and there is a critical viscosity below which lamella detachment is suppressed. 3.5 Lamella Spread To investigate the lamella geometry, the lamella leading edge spread was measured for a range of liquid viscosity, jet velocity, and surface velocity. The relevant geometry is presented in Figure 1.2. The distance being measured is the distance from the impingement point of the jet to the leading edge of the lamella. The results of this study are presented in dimensionless form as 51 jD R against Re s j V V in Figure 3.16. Plotting the spread data in this manner displays the effects of inertial to viscous forces on the spread distance of the leading edge of the lamella. Figure 3.16 Experimental results showing the distance of the leading edge of the lamella relative to the impingement point of the jet. As shown in Figure 3.16 the spread of the lamella is a strong function of the Reynolds number. At low Reynolds numbers the lamella spread is small and as the Reynolds number is increased the lamella spread increases as well. Also, increasing the surface velocity will decrease the lamella leading edge distance for a constant viscosity and jet velocity. This curve collapse implies that the Weber number and therefore surface tension forces are not important in the 52 spread of the lamella which is as expected as lamella spread should be a function of the inertial and shear forces. 3.6 Conclusions for the Influence of Viscosity and Surface Tension From the experimental investigation into the influence of liquid viscosity and surface tension on liquid jet impingement on a moving surface the following can be concluded: \u00E2\u0080\u00A2 Consistent with [25] and [18] there are three viscosity regimes with lamella detachment and splashing being most prone to occur in the intermediate regime \u00E2\u0080\u00A2 Solutions of low surface tension display similar behaviour as those with higher surface tension, the three viscosity regimes have similar thresholds \u00E2\u0080\u00A2 Deposition occurs for all Reynolds numbers below a Weber number of 250 \u00E2\u0080\u00A2 Increasing Weber number in intermediate Reynolds number regime promotes lamella detachment \u00E2\u0080\u00A2 Viscosity is a significant parameter when determining the outcome of liquid jet impingement \u00E2\u0080\u00A2 Fluid phase is non-continuous in low viscosity regime for ethanol-glycerin solutions as droplets are emitted due to low surface tension \u00E2\u0080\u00A2 Lamella leading edge spread is a function of the Reynolds number and velocity ratio 53 4 CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK 4.1 Conclusions An experimental investigation into the effect of surrounding air pressure on liquid jet impingement on a moving surface was performed. The study was carried out with Newtonian liquids impacting smooth, dry surfaces. A variety of jet speeds, surface speeds, and liquid viscosities were studied at different ambient air pressures. The interaction between the impinging jet and the moving surface was observed through high-speed imaging. The key findings are: \u00E2\u0080\u00A2 Lamella detachment can be fully suppressed by reducing the surrounding air pressure, which shows that aerodynamic forces are important in determining the outcome of liquid jet impingement on a moving surface \u00E2\u0080\u00A2 Surface velocity plays a critical role in the splashing and detachment behaviour of liquid jet impingement; lamella detachment does not occur for a stationary surface but is initiated with increased surface velocity \u00E2\u0080\u00A2 Measurements of the lamella detachment air pressure threshold collapse well on a normalized Reynolds number of air versus Reynolds number of jet graph \u00E2\u0080\u00A2 The model developed based on experimental observation and data is in qualitative agreement with the experimental results \u00E2\u0080\u00A2 Three viscosity regimes are evident with lamella detachment and splashing most likely to occur in the intermediate regime; low viscosity regime the lamella is stabilized by high surface tension forces and the high viscosity regime the lamella is stabilized by high viscous dissipation 54 An experimental study into the effect of fluid properties, viscosity and surface tension, on the outcome of Newtonian liquid jet impingement on a moving surface was conducted. A variety of liquid viscosities, surface tensions, surface velocities, and jet velocities were studied at a constant ambient air pressure of 101 kPa. The interaction between the impinging jet and the moving surface was observed through high speed imaging. The key findings of this study are: \u00E2\u0080\u00A2 Consistent with [25] and [18] there are three viscosity regimes with lamella detachment and splashing being most prone to occur in the intermediate regime and therefore viscosity is a significant parameter in the outcome of liquid jet impingement on a moving surface \u00E2\u0080\u00A2 Solutions of low surface tension display similar behaviour as those with higher surface tension, the three viscosity regimes have similar thresholds \u00E2\u0080\u00A2 Deposition occurs for all Reynolds numbers below a Weber number of 250 \u00E2\u0080\u00A2 Both the Reynolds number and Weber number are salient to the occurrence of lamella detachment, with lamella detachment having a non-linear dependence on the Reynolds number. Lamella detachment is prone to occur for intermediate Reynolds numbers as the Weber number is increased, bounded by regions of deposition at higher and lower Reynolds numbers. \u00E2\u0080\u00A2 Fluid phase is non-continuous in low viscosity regime for ethanol-glycerin solutions as droplets are emitted due to low surface tension \u00E2\u0080\u00A2 Lamella leading edge distance spread is a function of the Reynolds number and velocity ratio 55 4.2 Strength and Limitation of Thesis Research This experimental research investigation has yielded several important findings that further the understanding of liquid jet impingement on a moving surface. Integral was the finding that the surrounding air pressure has an influence on the splashing behaviour of an impinging jet. This finding provides an important parameter that will need to be included in future work in this area as the influence of the surrounding air is dependent on many parameters including the geometry of the lamella. Also important was the finding that the low surface tension ethanol- glycerin solutions demonstrate the same three viscosity regime behaviour as do the water- glycerin solutions. Moreover, it was found that incorporating a geometric angle can inhibit splash at high jet velocities. All these findings provide useful information for potential applications. The limitations of this research work are due to the low surface velocities that were capable of being studied and the unknown lamella geometry. Also the assumptions made in regards to the lamella geometry and dynamic contact angle result in the model developed in Chapter 2 not being as robust as would be desirable. 4.3 Potential Applications of Research Findings The results of this experimental investigation are of significant importance for the application of liquid friction modifiers by high speed liquid jets on to the top-of-rail surface in the rail road industry. It is important for industrial applications to understand the fluid physics of liquid jet impingement. The discovery that a geometric angle of impingement can suppress lamella detachment and splashing has already been incorporated in a current industrial system. 56 As well, the discovery that a reduction in surrounding air pressure can suppress lamella detachment completely is important for future developments in the field as it offers a method in which to ensure one hundred percent transfer efficiency. Although impractical in the railroad industry to incorporate a device to reduce the surrounding air pressure at the impingement location, there are applications for surface coating in which the environment can be more precisely controlled. Since the thickness and width of the deposited liquid is a function of the fluid properties, jet velocity, and surface velocity, all of which can be precisely controlled, liquid jet impingement could be utilized as a means of stripe coating, surface coating, or cooling/heating surfaces. Incorporating a low vacuum environment splashing and air entrainment would not be an issue. Therefore one hundred percent transfer efficiency with no surface fouling could be achieved. 4.4 Recommendations for Future Work To further advance the understanding of liquid jet impingement on a moving surface the following areas should be further investigated: \u00E2\u0080\u00A2 The exact characteristics of the lamella geometry; lamella thickness, lamella rim thickness, and lamella spread \u00E2\u0080\u00A2 An experimental investigation into the value of the dynamic contact angle as a function of surface velocity, jet velocity, and liquid viscosity for a high speed moving surface \u00E2\u0080\u00A2 Further understanding of the non-linear dependence of lamella detachment on the liquid viscosity \u00E2\u0080\u00A2 Jet impingement on a moving surface coated with a thin film of liquid 57 \u00E2\u0080\u00A2 The effect of lamella geometry on lamella detachment behaviour \u00E2\u0080\u00A2 The influence of the viscosity of the surrounding gas \u00E2\u0080\u00A2 An analysis of moving the nozzle rather than the surface as would be seen in real application of spraying the top-of-rail surface from the moving train 58 5 REFERENCES [1] J. 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Eadie, \"Elastic Liquid Jet Impingement on a High Speed Moving Surface,\" AIChE J, in press. 61 APPENDICES APPENDIX A: MASS FLOW RATES An important parameter of this investigation that could be precisely varied was the velocity of the liquid jet. The jet velocity could be controlled precisely by setting the nozzle back pressure. This was done by pressurizing the liquid in a bladder accumulator that was pressurized by a compressed nitrogen tank. This allowed the back pressure to be set accurately in the range of 0 to 200 PSI. The jet velocity was determined, as a function of the nozzle back pressure, by performing mass flow rate experiments in which the nozzle back pressure was set at a constant value and the fluid being emitted from the nozzle was captured in a beaker over a 30 second interval. The captured fluid was then weighed using a PT Ltd. high precision scale which had an accuracy of \u00C2\u00B10.005 g. The mass of the captured fluid was divided by the time elapsed during the fluid capture to determine the average mass flow rate for that particular nozzle back pressure and fluid. t m m \u00E2\u0088\u0086 \u00E2\u0088\u0086 =& Equation 5.1 Figure 5.1 shows the relationship between mass flow rate and nozzle back pressure for water- glycerin solutions for a nozzle size of 648 \u00C2\u00B5m. Figure 5.2 displays the mass flow rates as a function of the nozzle back pressure for a sample of ethanol-glycerin solutions with a 648 \u00C2\u00B5m nozzle. 62 Figure 5.1 Mass flow rate for water-glycerin solutions as a function of the nozzle back pressure Figure 5.2 Mass flow rates for ethanol-glycerin solutions as a function of the nozzle back pressure 63 From the mass flow rate, the velocity of the jet can be determined by dividing the mass flow rate by the area of the jet and the density of the fluid as shown below. jjf VAm \u00CF\u0081=& Equation 5.2 2 4 jf jf j D m A mV pi\u00CF\u0081\u00CF\u0081 && == Equation 5.3 When fluid is expelled from an orifice the jet contracts and the jet diameter is therefore not equal to the nozzle diameter (except for low Reynolds number flow where the jet can expand slightly). As the Reynolds number increases the contraction ratio approaches a limiting value of approximately 0.87. The jet diameter was measured using the Phantom V12.1 high speed video camera at high magnification with a measurement accuracy of \u00C2\u00B110 \u00C2\u00B5m. This result agrees very closely with the contraction ratio measurements of Kesharvez et al. [24] and the findings of Middleman [39] [40]. Shown in Figure 5.3 are the experimental results of Kesharvez et al. for contraction ratio as a function of the Reynolds number. 64 Figure 5.3 Jet contraction ratio, which is a measure of the jet diameter to the diameter of the nozzle, as a function of the Reynolds number [24] From equation 5.3 the jet velocity can be calculated for each back pressure from the experimental data collected by gravimetric flow rates. Figure 5.4 displays the jet velocity as a function of the nozzle back pressure for water-glycerin solutions. Figure 5.5 shows the jet velocity as a function of the nozzle back pressure for the ethanol-glycerin solutions used in this experimental study. 65 Figure 5.4 Jet velocity for water-glycerin solutions as a function of the nozzle back pressure Figure 5.5 Jet velocity of ethanol-glycerin solutions as a function of nozzle back pressure 66 A common way to characterize the behaviour of a nozzle is the discharge coefficient. The discharge coefficient is defined as the ratio of actual mass flow rate to ideal mass flow rate. The relationship for discharge coefficient is given in Equation 5.4. PA m m mC fn actual ideal actual d \u00E2\u0088\u0086 == \u00CF\u00812 & & & Equation 5.4 Where actualm& is the actual mass flow rate and idealm& is the ideal mass flow rate. The discharge coefficient for solutions used was calculated as a function of the Reynolds number and is plotted for water-glycerin solutions in Figure 5.6. Figure 5.6 Discharge coefficients for water-glycerin solutions as a function of the Reynolds number The value of the discharge coefficient is strongly dependent on the Reynolds number. It varies nearly linearly with Reynolds number at low Reynolds numbers then becomes nearly constant at higher Reynolds numbers before decreasing slightly at high Reynolds numbers. This 67 dependence on Reynolds number is due to viscous losses being more dominant at lower Reynolds numbers. Kesharvez et al. [24] and Kumar et al. [25] have observed similar trends for the discharge coefficient as a function of Reynolds number. As well, Lefebvre [41] observed the same behaviour for round orifices discharging fluid into ambient gas. 68 APPENDIX B: EXPERIMENTAL SET-UP In order to investigate the effect of the surrounding air pressure on liquid jet impingement with a moving surface an experimental set-up had to be designed and constructed that allowed for precise control of the many parameters involved. These parameters include the atmospheric air pressure, the nozzle back pressure, the velocity of the surface, the height of the nozzle from the surface, and the orientation of the jet relative to the surface. The challenge involved constructing a chamber where the atmospheric air pressure could be varied while automatically controlling the system enclosed (Figure 5.7 (b)). A vacuum chamber was constructed that incorporated a self-sealing door and vacuum was created by the use of vacuum generators (Figure 5.8 (a)) which utilize the Venturi effect to produce very low static pressures. The fluid was pressurized in a bladder accumulator which was pressurized by compressed nitrogen from a compressed nitrogen cylinder (Figure 5.8 (b)). Figure 5.7 (a) shows the National Instruments DAQ, relays, circuits, and power supplies used in the experimental set-up. Figure 5.7 (a) National Instruments DAQ, power supplies, and circuitry used to automate the system and record pressures. (b) Frontal view of vacuum chamber. Brackets, nozzle, moving surface, and pressure transducers can be seen. This experimental apparatus was designed and constructed for these experiments. a b 69 Figure 5.8 (a) Vacuum generators that created low atmospheric pressures by utilizing the Venturi effect, attached to a compressed air line. (b) Compressed nitrogen tank and control valves. Figure 5.9 Phantom\u00C2\u00AE V12.1 high speed video camera and Navitar\u00C2\u00AE ZOOM 6000 high magnification lens used in this experimental investigation. a b 70 Figure 5.10 Screen shot of LabView program command window to control experiment A program was produced in the LabView software package that allowed for the control of the interaction and the ability to capture the impingement at a very short duration of video so as to maximize the frame rate and resolution which were set at 11000 frames per second and 600 x 800 pixels, respectively. The exposure time was set at 10 \u00CE\u00BCs. The program recorded the signals from the line pressure transducer and the vacuum pressure transducer and converted the signal to PSI by multiplying by calibration constants. As well, relays were incorporated that permitted the control of the light, belt, nozzle solenoid valve, and flow interrupter solenoid through LabView. The automation increases the repeatability of the experiments. To capture the interaction, the Phantom V12.1 high speed camera (Figure 5.9) was triggered automatically by emitting a 5 V signal from the DAQ through the trigger cable which was connected to a port on the back of the camera. The LabView program ran the full 71 experiment at a specified ambient air pressure through a sequence of events which were timed precisely incorporating the transient behaviour of each device being operated. Figure 5.10 is a screen shot of the LabView control panel. It can be seen that the program recorded the nozzle back pressure and ambient air pressure over time and at the moment of triggering. The experiment was initiated by clicking the sequence button, in the top left of the screen, which then turned on all the equipment at the precise time to capture the interaction of the jet impinging upon the surface. As it was observed that the starting transient of the jet could affect the impingement behaviour a flow interrupter was incorporated in the design which allowed for the jet to stabilize and was then retracted by a solenoid actuator to allow for a steady jet to cleanly impinge the moving surface. The surface was constructed from blue tempered polished spring steel which was spot- welded and annealed into a continuous 7.5 cm wide belt. The polished metal surface was thoroughly cleaned between experiments to eliminate the possibility of experiment fouling by a contaminated surface. As well, all parts near the rotating surface were cleaned prior to each experiment to ensure droplets or particles did not come in contact with the surface during an experiment and to avoid fluid buildup. The height of the nozzle from the surface was nominally set at 10 cm vertically above the surface for most cases, however, this height was reduced for experiments involving low viscosity jets to avoid jet break up due to Plateau-Rayleigh instabilities as explained in [20]. To create a vacuum the door with the O-ring seal was placed against the frontal flange and the compressed air was turned on to 90 PSI then slight pressure was applied to the door to engage the self-sealing process. The level of vacuum was set through quarter turn values located 72 at the front of the chamber that controlled the flow rate of air into and out of the chamber. This allowed for the ambient pressure to be set to a specific value to an accuracy of \u00C2\u00B1 0.5 kPa, once steady state had been achieved. APPENDIX C: FLUID PROPERTIES AND SOLUTION PREPARATION The properties of the test solutions were required to be known to a high precision as the viscosity, surface tension, and density of the Newtonian test solutions are important. The viscosity of the test solutions were determined experimentally using a Kinexus rotational rheometer and compared to values found in literature. It should be noted that the viscosity of Newtonian fluids is highly dependent on temperature and therefore the laboratory room temperature was recorded and was approximately 298 \u00C2\u00B12 K through the duration of the experiments. The experimental results from the Kinexus rheometer are shown in Figure 5.11 and Figure 5.12 for the water-glycerin and ethanol-glycerin solutions, respectively. It is evident from the viscosity results that the viscosity of the solutions is a strong function of the percent of glycerin and therefore much care was taken when preparing the solutions. The solutions were prepared by first combining glycerin and either water or ethanol to the correct mass percentage, using syringes to ensure that the exact mass ratio was achieved. This procedure enabled the accuracy of the mass percentage solutions to be \u00C2\u00B10.5 g. The solutions were then mixed for one hour by a twin impeller mixer to ensure the proper mixing of the two fluids. To check that the mixing time was indeed sufficient rheometry was performed on samples of the same mass percentage solutions that had been mixed for various time intervals. It was determined from this analysis that one hour would be the appropriate mixing time. 73 Figure 5.11 Viscosity of water-glycerin solutions at 25\u00C2\u00B0C and 101 kPa Figure 5.12 Viscosity of ethanol-glycerin solutions at 25\u00C2\u00B0C and 101 kPa 74 APPENDIX D: ADDITIONAL PARAMETERS In addition to the parameters investigated in the previous chapters (air pressure, surface velocity, jet velocity, viscosity, surface tension) further studies were conducted on the influence of the geometric angle of impingement, the influence of gravity, and the influence of a pre- wetted surface. D.1 Liquid Jet Impingement onto a Pre-Wetted Surface To investigate the influence of a liquid jet impinging onto a pre-wetted surface a series of experiments were performed in which a liquid jet was impinged onto a moving surface that had been coated with a thin film (hfilm\u00E2\u0089\u00882-5\u00C2\u00B5m) of the same fluid. These experiments were performed with a solution of 65% glycerin in water at an ambient air pressure of 101 kPa for various jet speeds and two surface speeds of 5.5 m/s and 7.5 m/s. Figure 5.13 details the results of the experimental investigation. It was observed that deposition occurred for the full range of jet velocities studied at surface velocities of 5.5 m/s and 7.5 m/s. It is interesting to note that for similar conditions of a jet of 65% glycerin in water impinging on to a dry moving surface, lamella detachment and splashing would occur. Figure 5.14 displays a direct comparison of the splashing behaviour of an impinging jet for the two different surface conditions. 75 Figure 5.13 Experimental results for impingement of a jet of 65% glycerin in water on a moving surface pre-wetted with a thin film of 65% glycerin in water. It is interesting to note that deposition was obtained at the full range of jet velocities and surface velocities studied. For comparison similar conditions for a dry surface would result in lamella detachment and splashing. Figure 5.14 Impingement of a liquid jet of 65% glycerin in water on a surface moving at 7.5 m/s from left to right. In both images the velocity of the jet is 18 m/s. Image a shows the jet impinging onto a dry surface and image b shows the jet impinging onto a surface that has been pre-wetted with a very thin film of the same liquid, 65% glycerin in water. It is interesting to note that the dry surface results in lamella detachment and splashing whereas impingement onto the wetted surface results in deposition. 76 The exact mechanism for lamella detachment is not yet fully understood, however, it is thought that the reason the lamella does not detach from the surface for the condition where the surface is pre-wetted with a thin film is due to a reduction in the velocity gradient as the presence of the thin film allows slip at the interface between the lamella and the thin film. The reduced velocity gradient results in lower shear forces at the interface which reduce the dynamic contact angle and therefore increase the vertical component of surface tension adhering the lamella to the surface. Further experimental work is required to be performed prior to an exact description and full understanding of the mechanism of lamella adhesion during jet impingement on to a pre- wetted moving surface. However, this offers the ability to externally alter the interface condition onto which the liquid jet is impinging for the possibility of complete deposition in the intermediate viscosity range. 77 D.2 Geometric Angle A preliminary experimental study was conducted on the influence of the geometric angle of impingement on the behaviour of jet impingement onto a moving surface. This preliminary study was performed for a range of geometric angles from 20\u00C2\u00B0 to 90\u00C2\u00B0, with 90\u00C2\u00B0 being perpendicular impingement. Figure 5.15 shows the definition of the geometric angle. Figure 5.15 The geometric angle is defined in the schematic diagram of jet impingement. The liquid used was a solution of 70% glycerin in water and the impingement tests were performed at an ambient air pressure of 101 kPa and a surface velocity of 7.5 m/s. Figure 5.16 shows the experimental results obtained in this study plotted as Reynolds number of the jet against the geometric angle and Figure 5.17 shows a visual comparison between two jets impinging at different geometric angles. 78 5.16 Preliminary experimental results for jet impingement with a geometric angle plotted as geometric angle against the Reynolds number. It can be concluded that lamella detachment can be suppressed by incorporating a geometric angle of impingement. Figure 5.17 Comparison of jet impingement on a moving surface for extremities of geometric angle range tested. The fluid is a solution of 70% glycerin in water and the ambient air pressure is 101 kPa. The velocity of the jet and the velocity of the surface, in both images, is 18 m/s and 7.5 m/s, respectively. It can clearly be seen in (a) that the lamella is detached from the surface and in (b) the lamella adheres to the surface and splashing is inhibited. 79 The results of this study indicate that the detachment behaviour of an impinging jet is a strong function of the geometric angle. At 90\u00C2\u00B0 lamella detachment occurs at a Reynolds number of approximately 270 however at an angle of 30\u00C2\u00B0 lamella detachment does not occur in the range of Reynolds numbers studied, up to 1200, which implies that lamella detachment and splashing is inhibited for lower geometric angles. The mechanism for lamella detachment being inhibited by reducing the geometric angle could be the cause of several factors. With reduced geometric angle the momentum vector approaches surface parallel which reduces the momentum in the upstream lamella. With a geometric angle other than 90\u00C2\u00B0 it can no longer be assumed that the free stream lamella velocity close to the impingement point is equal to the jet velocity in all directions. It was observed experimentally for reduced geometric angles that the leading edge spread was significantly reduced to the limit of essentially no upstream spread at low geometric angles. The reduced upstream lamella velocity due to the direction of the momentum vector could result in a lower dynamic contact angle and therefore a larger vertical component of the surface tension force adhering the lamella to the surface as the dynamic contact angle is a function of the local fluid flow. As well, with the reduced leading edge spread observed for jet impingement at geometric angles less than 90\u00C2\u00B0, decreased geometric angle resulting in decreased spread could inhibit lamella detachment. These changes in lamella geometry affect the balance of forces acting on the lamella and therefore by decreasing the geometric angle lamella detachment is suppressed. Moreover, at sufficiently low geometric angles, Figure 5.17 (b), there would be a vertical component of inertia acting on the leading edge of the small lamella and therefore suppressing detachment. 80 D.3 Gravity Experiments In order to properly analyze the experimental data it was deemed necessary to determine if the behaviour of an impinging jet on a moving surface and the steady state lift off was influenced by gravitational forces. To verify that gravity did not play a role, as was assumed, experiments were run with an inverted apparatus. These experiments were performed for ten test cases with a solution of 65% glycerin in water which had been observed to result in lamella detachment and splashing at surface velocities above 3 m/s and jet velocities above 5 m/s. An example is shown in Figure 5.18 for a situation of constant viscosity, surface velocity, jet velocity, and atmospheric air pressure with gravity being inverted. Figure 5.18 Experiments performed with an inverted apparatus proved that gravity had a negligible effect on the behaviour of a liquid jet impinging a moving surface. The image on the left is the situation with the inverted apparatus and therefore the gravitational vector is in the opposite direction to the image on the right which is in the normal configuration. In both cases the velocity of the jet was 17.5 m/s, the surface velocity was 5.5 m/s, and the fluid is a solution of 65% glycerin in water. 81 This series of experiments proved that the effect of gravitational forces on liquid jet impingement is negligible. The only observable difference was with the inverted apparatus droplets were more susceptible to break off from the rim of the detached lamella due to the additional body force acting on the droplets and the leading edge of the detached lamella curves more sharply due to the additional body force of gravity."@en . "Thesis/Dissertation"@en . "2012-11"@en . "10.14288/1.0072835"@en . "eng"@en . "Mechanical Engineering"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "Attribution-NonCommercial-NoDerivatives 4.0 International"@en . "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en . "Graduate"@en . "An experimental study of liquid jet impingement on a moving surface : the effects of surrounding air pressure and fluid properties"@en . "Text"@en . "http://hdl.handle.net/2429/42498"@en .