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An experimental study on air-blast atomization of viscoelastic liquids Li, Larry Kin Bong 2006

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A N E X P E R I M E N T A L S T U D Y O N A I R - B L A S T A T O M I Z A T I O N O F V I S C O E L A S T I C L I Q U I D S by L A R R Y K I N B O N G L I B.A.Sc , The University of British Columbia, 2004 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D U A T E STUDIES (Mechanical Engineering) T H E U N I V E R S I T Y O F BRITISH C O L U M B I A September 2006 © Larry K i n Bong L i , 2006 ABSTRACT Motivated by the need to improve transfer efficiencies in spray coating, an experimental investigation into viscoelastic atomization using pre-formulated substitute test liquids is presented. These model liquids allowed for the decoupling of two common rheological phenomena: extension-thickening and shear-thinning. By maintaining similar values of surface tension, density, and rate-independent shear viscosity in the test liquids, and independently varying the extensional viscosity, the effect of elasticity was isolated and shown to act against the breakup of a spray issuing from a plain-jet air-blast atomizer operating at high aerodynamic Weber numbers (-1000). Flash photography revealed the presence of large-scale filamentary structures at breakup, which delayed discrete droplet formation until farther downstream of the atomizer where relative air-liquid velocities were reduced. Consequently, liquid elasticity led to an increase in the mean droplet size. This was confirmed by shadowgraphy measurements. Moreover, the hindering influence of elasticity on atomization was also supported by Particle Image Velocimetry measurements, which indicated that the elastic droplets, owing to their greater inertia, were better able to maintain their initial momentum. n T A B L E O F C O N T E N T S A B S T R A C T i i T A B L E O F C O N T E N T S i i i LIST O F T A B L E S v LIST O F FIGURES vi LIST O F S Y M B O L S vi i i A C K N O W L E D G E M E N T S xi 1 INTRODUCTION 1 1.1 Background and Literature Review 2 1.1.1 Newtonian Breakup 2 1.1.1.1 Liquid Jet Breakup in a Stationary Gas 3 1.1.1.2 Liquid Jet Breakup in a Co-flowing Gas 10 1.1.2 Non-Newtonian Rheology 21 1.1.2.1 Shear Behavior 22 1.1.2.2 Extensional Behavior 24 1.1.3 Viscoelastic Breakup 29 1.1.3.1 Capillary Jet Breakup 29 1.1.3.2 Atomization 31 1.2 Motivation and Objectives 36 1.2.1 Spray Coating 36 1.2.2 Railway Industry 37 1.2.3 Objectives 40 1.3 References 41 2 A N E X P E R I M E N T A L STUDY ON AIR-BLAST ATOMIZATION OF VISCOELASTIC LIQUIDS 52 2.1 Introduction 52 2.2 Motivation and Objectives 54 2.3 Test Liquids and Experimental Setup 54 2.3.1 Test Liquid Construction • 54 2.3.2 Test Liquid Characterization 56 iii 2.3.3 Air-blast Atomizer and Spray Setup 60 2.3.4 Particle Image Velocimetry 64 2.3.5 Flash Photography 70 2.3.6 Shadowgraphy 70 2.4 Viscoelastic Atomization Results 75 2.4.1 Breakup Visualization 76 2.4.1.1 Effect of Shear Viscosity 76 2.4.1.2 Effect of Elasticity 80 2.4.1.3 K E L T R A C K HiRail 82 2.4.2 Droplet Size Measurements 83 2.4.3 Mean Axial Centerline Droplet Velocity 96 2.4.3.1 Effect of Liquid Flow Rate 98 2.4.3.2 Effect of Shear Viscosity 101 2.4.3.3 Effect of Elasticity 102 2.4.3.4 Effect of Atomizing Air Pressure 103 2.5 References 105 3 CONCLUSIONS A N D RECOMMENDATIONS 110 APPENDIX A : Shear Viscosity Measurements 113 APPENDIX B: Surface Tension Measurements 115 APPENDIX C: Air-Blast Atomizer Drawings 123 APPENDIX D: M A T L A B Code for Compressible Duct Flow 132 APPENDIX E: PIV Measurements 136 APPENDIX F: Laser Timing Measurements 140 APPENDIX G: Droplet Size Measurements 143 APPENDIX H: Droplet Evaporation Calculations 167 iv L I S T O F T A B L E S Table 1.1: Ohnesorge' s [21 ] proposed regimes for the breakup of a liquid j et in stationary air 6 Table 1.2: Main factors affecting the air-blast atomization of Newtonian liquids.... 12 Table 2.1: Compositions and properties of elastic and inelastic test liquids at 25°C. 56 Table 2.2: Summary of droplet sizing results at Qi = 30, 60 ml/min, PA - 55.2 kPa.89 v L I S T O F F I G U R E S Figure 1.1: Figure 1.2: Figure 1.3: Figure 1.4: Figure 1.5: Figure 1.6: Figure 1.7: Figure 1.8: Figure 1.9: Figure 1.10: Figure 1.11: Figure 2.1: Figure 2.2: Figure 2.3: Figure 2.4: Figure 2.5: Figure 2.6: Figure 2.7: Figure 2.8: Figure 2.9: Figure 2.10: Figure 2.11: Figure 2.12: Figure 2.13: Figure 2.14: Appearance o f (a) idealized Rayleigh breakup and (b) actual capillary jet breakup as observed by high-speed photography 3 Classification of liquid jet breakup in stationary air as proposed by Ohnesorge [21] and Misse [24] 6 Classification of liquid jet breakup in stationary air as proposed by Reitz [23] 8 Schematic of a typical plain-jet air-blast atomizer 10 Classification of water jet breakup in co-flowing air by Farago and Chigier [73] 17 Photographs of water jet breakup in co-flowing air (Farago and Chigier [73]) 17 Variation of shear stress with shear rate for non-Newtonian materials.... 22 Variation of shear viscosity with time (at a constant shear rate) for non-Newtonian materials 23 Separation of liquid particles in simple extension 25 F M spray setup on a locomotive (Kelsan [142]) 38 F M spray setup on a HiRa i l maintenance vehicle (Kelsan [142]) 38 Trouton ratio as a function of Reynolds number for the elastic P E O liquids. (Reproduced from Mun ' s PhD thesis [22]) 58 Shear viscosity of K E L T R A C K H i R a i l at 25°C 59 The original air-blast atomizer before undergoing modification to have its rubber-duckbill cut off. 61 The modified air-blast atomizer used in most of the present work 62 Liquid and air supply connections to the air-blast atomizer 63 Schematic of the P IV setup 65 Sample P IV image of a water spray (one o f a pair) 65 Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs. 50 wt.% glycerin; Qi = 60 ml/min; PA = 55.2 kPa. 69 Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs. 100K P E O ; QL = 30 ml/min; PA = 55.2 kPa 69 Photograph of the shadowgraphy setup 71 Sample shadowgraph for droplet size measurements: (a) raw shadowgraph, (b) processed shadowgraph with liquid features identified and sized 71 Nine sampling locations for droplet size measurements (all at z = 152.4 73 mm Photographs of breakup for inelastic liquids having similar OL and pL, but different rjs: (a) water, (b) 80 wt.% glycerin, (c) 90 wt.% glycerin, (d) 99.5 wt.% glycerin. QL = 60 ml/min; PA = 55.2 kPa 78 PIV images showing the presence of oblique wave patterns: (a) water, (b) 50 wt.% glycerin, (c) 80 wt.% glycerin, (d) 100K P E O , (e) 300K P E O , and (f) K E L T R A C K H i R a i l . Field-of-view: 161.9 (H) x 163.5 (V) mm; QL = 60 ml/min; PA = 55.2 kPa; negative image 79 vi Figure 2.15: Figure 2.16: Figure 2.17: Figure 2.18: Figure 2.19: Figure 2.20: Figure 2.21: Figure 2.22: Figure 2.23: Figure 2.24: Figure 2.25: Figure 2.26: Figure 2.27: Figure 2.28: Figure 2.29: Figure 2.30: Figure 2.31: Figure 2.32: Figure 2.33: Figure 2.34: Figure 2.35: Figure 2.36: Figure 2.37: Sample mean Mie image used for determining the spray angle. Field-of-view: 161.9 (H) x 163.5 (V) mm; 80 wt.% glycerin; QL = 60 ml/min; PA = 55.2 kPa 80 Photographs of breakup for liquids having similar O~L, rjs, and pi, but different elasticities: (a) inelastic 50 wt.% glycerin, (b) 100K PEO, (c) 300K PEO, (d) 1000K PEO. QL = 60 ml/min; PA = 55.2 kPa 81 Photograph of breakup for KELT/RACK HiRail 82 D10, RMS, and N for water at QL = 30, 60 ml/min, PA = 55.2 kPa (x direction) 85 Dio, RMS, and T V for water at QL = 30, 60 ml/min, PA = 55.2 kPa (y direction) 85 Droplet volume distribution for water at QL - 30, 60 ml/min, PA = 55.2 kPa 86 DVR for water at QL = 30, 60 ml/min, PA = 55.2 kPa 86 Sketch of the partitioned spray cross-section used in droplet volume flux calculations 88 Mean Dw comparison at QL = 30, 60 ml/min, PA = 55.2 kPa 91 Droplet volume comparison at QL = 30, 60 ml/min, PA = 55.2 kPa 91 Droplet number comparison at QL = 30, 60 ml/min, PA = 55.2 kPa 92 Shadowgraphs of K E L T R A C K HiRail showing the presence of ligaments. 92 Cumulative volume distribution at QL = 30 ml/min, PA = 55.2 kPa 94 Cumulative volume distribution at QL = 60 ml/min, PA = 55.2 kPa 94 VMD comparison at QL = 30, 60 ml/min, PA = 55.2 kPa 95 Sample non-dimensional radial profile of the mean axial droplet velocity for water at QL = 60 ml/min, PA = 55.2 kPa 98 M A C L droplet velocity for water at QL= 30, 60 ml/min, PA = 55.2 kPa. 99 M A C L droplet velocity for 100K PEO at QL= 30, 60 ml/min, PA = 55.2 kPa 99 M A C L droplet velocity for K E L T R A C K HiRail at QL = 30, 60 ml/min, 100 M A C L droplet velocity for inelastic liquids at QL = 60 ml/min, PA = 55.2 kPa 101 Comparison of M A C L droplet velocity among inelastic and elastic liquids at QL = 60 ml/min, PA = 55.2 kPa 102 ALR and Mfor various PA ( K E L T R A C K HiRail at QL = 60 ml/min).... 104 M A C L droplet velocity for K E L T R A C K HiRail at QL = 60 ml/min (original air-blast atomizer with full rubber-duckbill) 104 vii L I S T O F S Y M B O L S a Mark-Houwink Exponent A Area ALR Air-liquid Mass Ratio B Deceleration Constant C Volume Concentration of Particle CCD Charged Coupled Device C A D Canadian Dollars dp Particle Diameter D Droplet Diameter Dj Liquid Orifice or Jet Diameter DVR Droplet Volume Ratio F M Friction Modifier g Gravitational Acceleration IP Image-pair (PIV) L Particle Length m Consistency Index in Power-Law Model m Mass Flow Rate M Momentum Flux Ratio M A C L Mean Axial Centerline MMD Mass Median Diameter n Power-law Index N Droplet Number Oh Ohnesorge Number PEO Polyethylene Oxide PIB Polyisobutylene PIV Particle Image Velocimetry ppm Parts Per Million Q Volumetric Flow Rate r Thickness of du Noiiy Ring viii R Radius of du Noiiy Ring Re Reynolds Number RMS Root-mean-square Deviation SMD Sauter Mean Diameter t Time TE Transfer Efficiency Tr Trouton Ratio u Velocity U Bulk Fluid Velocity Uc Mean Axial Centerline Droplet Velocity V Particle Velocity VMD Volumetric Median Diameter We Weber Number X Particle Position (or Radial Position) y Radial Position z Axial Distance From Atomizer Orifice zo Virtual Origin Greek A Finite Change e Extensional Strain 8 Uncertainty n Dynamic Viscosity (Instantaneous) It: Tensile Stress Growth Coefficient r Shear Strain y,j Strain Rate Tensor X Disturbance Wavelength Xmin Minimum Wavelength for Disturbance Growth X0pt Optimum Wavelength for Disturbance Growth M Dynamic Shear Viscosity (Newtonian) CO Total Error p Density o~app Apparent Liquid Surface Tension OE Normal Stress Difference <jjj Stress Tensor OL Liquid Surface Tension T Shear Stress Subscripts 0 Refers to Zero Shear Rate 1 Refers to x Coordinate 2 Refers to y Coordinate 3 Refers to z Coordinate 10 Refers to Arithmetic Mean A Refers to Atomizing Air E Refers to Extensional Deformation L Refers to Liquid N Refers to Droplet Number R Refers to Relative Air-liquid S Refers to Shear Deformation t Refers to Time u Refers to Velocity Miscellaneous Period above symbols denote temporal rate Bar above symbols denote average A C K N O W L E D G E M E N T S I wish to express my utmost gratitude to Professor Sheldon Green and Professor Martin Davy for their unending trust and technical guidance throughout this project. They epitomized the model supervisors by holding stimulating discussions and asking penetrating questions, through which I discovered that completing a Master's degree is not only about becoming familiar with a particular topic, but perhaps more so, it is to teach oneself how to learn. I will forever be indebted to Dr. Donald Eadie, Mr. Dave Elvidge, Mr. John Cotter, and others at Kelsan Technologies Corporation for their continual support over the years. Their devoted work ethic and meticulous research attitude have truly inspired me. I especially thank Don for sharing his professional wisdom during our discussions on career development. I am also grateful for Dave's valuable insights on polymer science, complex fluid rheology, and nozzle design. The office and technical staff in the Department of Mechanical Engineering deserve recognition for their ability to tackle day-to-day tasks with efficiency and courtesy. Special thanks are owed to Dan Dressier, Isabella L i , and Seth Gilchrist for the shared laughs (especially on our cottage trips); to my parents, Esther and Patrick, and brother, Timothy, for their daily support; and to Joyce for introducing me to the notion of fun. xi 1 I N T R O D U C T I O N Air-blast atomization, a process in which the kinetic energy of an externally-applied air jet is used to disintegrate a bulk liquid into droplets, has been the subject of many experimental investigations [1]. For Newtonian liquids, it is now known that the controlling liquid properties are the shear viscosity and surface tension [2]. Researchers have observed, however, that viscoelastic liquids are more difficult to atomize than Newtonian liquids [3,4]. Previous attempts to correlate the shear viscosity of viscoelastic liquids with the mean droplet size of their resulting sprays have failed [5-8]. Instead, because spray nozzles produce strong elongational flow fields [9], the significant extensional viscosity exhibited by viscoelastic liquids is expected to play an important role in controlling their breakup, though the physical mechanisms are generally not well understood [5,10,11]. Many paints and industrial coatings are non-Newtonian liquids that exhibit viscoelastic behavior [12], and they are often applied by air-blast atomizers during spray coating. The transfer efficiency in this process depends on spray characteristics such as droplet sizes and velocities. Accordingly, the present work aims to understand the effect of liquid elasticity on air-blast atomization in light of its significance to the spray coating process. The use of rheologically-ideal test liquids allows the extensional viscosity to be varied independently of the shear viscosity. Flash photography is employed to elucidate breakup details, while the velocities and sizes of the atomized liquids are quantified using Particle Image Velocimetry and shadowgraphy, respectively. This chapter presents a literature review on the breakup of Newtonian and viscoelastic liquids, and discusses the motivation and objectives behind the present work. I 1.1 Background and Literature Review In our attempt to understand the influence of liquid elasticity on air-blast atomization, it is helpful to review the major developments surrounding Newtonian and viscoelastic breakup under a variety of injection conditions. These conditions, in order of increasing complexity, are: classical capillary breakup, jet disintegration in a stationary gas, and atomization in a co-flowing gas or otherwise the conditions corresponding to air-blast atomization. This section is divided into three parts: the first focuses on Newtonian breakup, the second provides background information on non-Newtonian rheology, and the third is a literature review on the disintegration of viscoelastic liquids. 1.1.1 Newtonian Breakup When a bulk Newtonian liquid issues from a nozzle and into a gaseous medium (e.g. a liquid jet or sheet emerging into a stationary or co-flowing gas), oscillations and perturbations develop on its surface owing to the competition between disruptive and stabilizing forces. The disruptive forces are caused by the combined effects of hydrodynamic and aerodynamic instabilities; but under specific conditions of very low liquid jet velocity, capillary instabilities may also play an important role. Liquid surface tension and shear viscosity are generally regarded as the two major stabilizing forces; the former tends to pull the liquid into a form that exhibits minimum surface energy, while the latter opposes changes in liquid geometry. If the disruptive forces overcome the stabilizing forces, wave disturbances will amplify on the jet surface, leading to the breakup of the bulk liquid into droplets; this initial disintegration process is referred to as primary breakup. Large droplets produced in primary breakup may be unstable i f they exceed a critical size. In this event, they will undergo further disintegration into even smaller droplets through a process termed secondary breakup. Secondary breakup is driven by aerodynamic forces and resisted mainly by capillary forces. Consequently, the final droplet size distribution in a spray depends on both primary and secondary breakup. The phenomenon of Newtonian liquid jet breakup has been the subject of theoretical and experimental investigations for over a century [1,13,14]. The following highlights some of most significant contributions made in this field. 2 1.1.1.1 Liquid Jet Breakup in a Stationary Gas Over a century ago, Rayleigh [15] conducted one of the first theoretical studies of jet instability. He employed a linear stability analysis to predict the conditions under which laminar liquid jets would collapse when injected into a quiescent gas. Rayleigh concluded that an inviscid, round liquid jet (of diameter Dj) affected by capillary forces becomes unstable only to axisymmetric surface disturbances with wavelengths (X) greater than KDJ. That is, i f X exceeds the jet circumference, the disturbances will grow under the action of surface tension, terminating in the collapse of the liquid jet into droplets of uniform diameter, as illustrated in Figure 1.1a. In arriving at such a result, Rayleigh neglected aerodynamic interactions with the surrounding gas. He also predicted the existence of an optimum wavelength for fastest disturbance growth: XOPT = 4.5\Dj. Further, Rayleigh assumed a periodic breakup process, in which droplets formed were spherical and contained a volume equivalent to that of a cylindrical liquid column with diameter Dj and height 4.5\Dj (corresponding to XOPT). Therefore, the resultant droplet diameter (D) was predicted to be 1.89D/. D= 1 . 8 9 D (a) (b) F i g u r e 1.1: A p p e a r a n c e o f (a) i d e a l i z e d R a y l e i g h b r e a k u p a n d (b) a c t u a l c a p i l l a r y j e t b r e a k u p as o b s e r v e d b y h i g h - s p e e d p h o t o g r a p h y . 3 In an attempt to more accurately predict disturbance growth rates on a liquid jet's surface, Weber [16] extended Rayleigh's analysis [15] by accounting for the effects of liquid viscosity and relative velocity at the air-liquid interface (the ambient air was taken to be inviscid). It was assumed that any surface disturbances will cause rotationally symmetric oscillations on the liquid jet. Capillary forces may drive or dampen such disturbances depending i f X is greater or less than the minimum wavelength for disturbance growth (Xmi„), respectively. Weber concluded that increases in liquid viscosity will lengthen Xopt but leave Xmi„ unchanged from that of the inviscid Rayleigh [15] case: Xmin = nDj. This conclusion was verified by Haenlein's [17] experiments, which showed that for highly viscous liquids (JUL = 850 mPa-s), Xopt ranged from 30Dj to 40Dj (versus a value of 4.51 Dj predicted by Rayleigh). Moreover, Weber also demonstrated that aerodynamic interactions between the liquid jet and surrounding gas led to reductions in Xmin and Xopt. Although the inclusion of viscous and aerodynamic forces was an improvement over the work of Rayleigh [15], Weber's analysis [16] was still linear and did not predict the wide range of droplet sizes observed in the practical breakup of a liquid jet. As shown in Figure 1.1b, actual capillary jet breakup is characterized by pinch-off at the end of an intact liquid column, from which a stream of large droplets interspersed with smaller satellite droplets is produced. Satellite droplets are predicted only by higher-order analyses [18-20]. Many researchers, including Haenlein [17], Ohnesorge [21], Castleman [22], and Reitz [23], have since conducted experimental investigations on the breakup of liquid jets. Their efforts have led to the proposal of a number of different disintegration regimes. Each of these regimes reflects the appearance of the liquid jet at breakup and attempts to identify the dominant breakup mechanisms as injection conditions vary. 4 Ohnesorge [21] initially proposed three breakup regimes based on the relative importance of inertial, viscous, and capillary forces. By employing dimensional analysis, he showed that each regime could be classified by the magnitudes of the liquid Reynolds number (ReL) and the Ohnesorge number (Oh): p.U.D, Re 7 = / j Liquid Reynolds Number ML MI Oh = . = Ohnesorge Number where pL = liquid density U, = bulk liquid velocity in nozzle orifice Dj - liquid orifice diameter HL = dynamic shear viscosity (Newtonian) a, = liquid surface tension The liquid Reynolds number is a measure of the disruptive forces present within the bulk liquid. The Ohnesorge number (also known as the stability number or the viscosity group) is a ratio of the viscous to capillary forces. Ohnesorge [21] displayed his three breakup regimes on a graph of Oh versus ReL. This is reproduced in Figure 1.2 and described in Table 1.1. Note that for any given liquid type and nozzle orifice size, Oh remains constant, and increasing the jet velocity results in a horizontal translation along the ReL axis. 5 100000 Ret Figure 1.2: Classification of liquid jet breakup in stationary air as proposed by Ohnesorge [21] and Misse [24]. Table 1.1: Ohnesorge's [21] proposed regimes for the breakup of a liquid jet in stationary air. Breakup Regime Appearance and Proposed Mechanism(s) of Breakup Rayleigh Breakup (Regime I, Figure 1.2) Breakup is marked by the formation of radially symmetric perturbations on the liquid jet surface; these are driven by capillary forces. Aerodynamic effects are negligible. The jet breakup length and the jet velocity are linearly related. Droplet sizes are of order Dj. Sinuous Wave Breakup (Regime II, Figure 1.2) With increasing jet velocity, aerodynamic forces become progressively more important relative to capillary forces. The liquid jet oscillates about its axis, forming a sinuous wave structure, before eventually collapsing under the influence of aerodynamic (viscous and pressure) forces. 6 Breakup Regime Appearance and Proposed Mechanism(s) of Breakup Atomization (Regime III, Figure 1.2) This regime is marked by the complete and chaotic disintegration of the liquid jet immediately downstream of the nozzle. Droplet sizes are much smaller than Dj. The dominant breakup mechanisms in this regime are unknown. To ensure that his experimental data would fall into the appropriate breakup regimes, Miesse [24] discovered that he had to modify Ohnesorge's [21] original classification by shifting the boundary separating Regime II and III towards higher Rec, this is illustrated also in Figure 1.2. About two decades later, Reitz [23] set out to resolve some of the confusion that Miesse had caused with his modification of the Ohnesorge plot. Reitz examined diesel spray data collected by himself and others, including Giffen and Muraszew [25], and Haenlein [17]. He concluded that the breakup of a liquid jet in a stationary gas could indeed be divided into four regimes, as depicted in Figure 1.3. Reitz's classifications (the most commonly referenced today) resembled those of Ohnesorge's in that the Rayleigh and atomization regimes were both unchanged from before. In the intermediate Oh and ReL range, however, sinuous wave breakup (Regime II, Figure 1.2) was expanded into two separate regimes: first wind-induced and second wind-induced. In first wind-induced breakup [23], the destabilizing effects of surface tension are now augmented by aerodynamic interactions owing to the increased relative velocity at the air-liquid interface. The formation of wave disturbances on the liquid surface induces a non-uniform static pressure distribution around the jet - wave crests experience low pressures due to higher air velocities, while wave troughs experience relatively high pressures. This accelerates disturbance growth. Breakup of the liquid jet takes place many jet diameters downstream of the nozzle, and the resultant droplet sizes are comparable to the initial jet diameter. 7 In second wind-induced breakup [23], the intensified relative motion between the liquid jet and surrounding gas promotes the development of short-wavelength perturbations. Aerodynamic forces drag and strip ligaments and droplets directly off of the ruffled jet. Breakup takes place only several jet diameters downstream of the nozzle, and the resultant droplet sizes are much smaller than the initial jet diameter. Regime 1 Regime 2 Regime 3 Regime 4 •c O 1 10 100 1000 10000 100000 Figure 1.3: Classification of liquid jet breakup in stationary air as proposed by Reitz [23]. 8 In practice, there is no sharp demarcation between these clearly identified breakup regimes. Industrial hydraulic nozzles typically operate in the atomization regime (Regime 4, Figure 1.3). Unfortunately, the proposed mechanisms for atomization have generally been inconsistent [1,26]. Giffen and Muraszew [25], Chigier [27,28], and Cheremisinoff [29] have published extensive reviews on this subject. In particular, Chigier [28] suggested several possible triggering mechanisms for the initiation of disturbances on a liquid jet's surface: liquid supply pulsation, sharp-edged nozzle geometry causing flow separation, nozzle wall roughness, and turbulence and cavitation inside the nozzle and/or at the exit orifice. Once the surface disturbances have been triggered, further wave development depends primarily on aerodynamic interactions between the liquid and the ambient gas. Of the mechanisms proposed, the following combination has received the widest acceptance [26,28]: 1. Liquid Jet Turbulence. De Juhaz [30], Mehlig [31], Thiemann [32], and Schweitzer [33] suggested that liquid phenomena inside the nozzle, particularly radial velocity components in turbulent flow, ruffles the initially smooth liquid jet surface, thereby making it more susceptible to aerodynamic effects. 2. Aerodynamic Interaction. Castleman [27], after reviewing the work of Sauter [34], theorized that the relative motion between the outer liquid jet layer and the surrounding gas initiates the shedding of unstable ligaments from the bulk liquid. With increasing relative air-liquid velocity, the physical scales and life-times of these ligaments diminish; upon their collapse, smaller droplets are formed (in accordance with Rayleigh's theory). The importance of aerodynamic forces (viscous and pressure) to the atomization process was also supported by Weber [16], Scheubel [35], and Strazhewski [36]. 9 1.1.1.2 Liquid Jet Breakup in a Co-flowing Gas An alternative method for atomization is to expose a relatively slow moving liquid stream to the disruptive actions of a high-speed, co-flowing air jet. This method is known as air-blast or twin-fluid atomization. It is commonly achieved using air-blast atomizers of the plain-jet type, in which the liquid emerges from a round central orifice, surrounded by a high-speed annular air jet flowing in the same direction (co-axial) - an example is shown in Figure 1.4. This is incidentally a variation of the atomizer that is used in the present study. The advantages of air-blast atomization over hydraulic atomization, namely reduced droplet sizes at equivalent liquid supply pressures and enhanced air-liquid mixing, have led to its widespread use in industries such as combustion (liquid fuel injection in rockets, gas turbines, and furnaces) [37,38], spray drying [39,40], surface coating [12], and inhaled pharmaceuticals [41]. Atomizing Atomizing Air Liquid Air Exit Plane -Figure 1.4: Schematic of a typical plain-jet air-blast atomizer. 10 Experiments on the air-blast atomization of Newtonian liquids have been conducted by many researchers, including Nukiyama and Tanasawa [42], Lorenzetto and Lefebvre [43], Rizkalla and Lefebvre [44], Shanawany and Lefebvre [45], Mullinger and Chigier [46], Eroglu and Chigier [47], and others [48-58]. These investigations have produced numerous empirical correlations for predicting the mean droplet size. The mean droplet size is often defined by the Sauter Mean Diameter (SMD): SMD = Sauter Mean Diameter SMD represents the diameter of a droplet with a volume-to-surface area ratio equivalent to that of all the droplets in the entire spray. It is one of the most commonly used diameter moments because of its relevance to the rates of evaporation and combustion. Other diameters, such as the arithmetic mean diameter (D/o) or the volumetric median droplet (VMD), may also be used depending on the application. Although correlations for predicting the mean droplet size are useful in distinguishing the relative importance of specific liquid/air properties and injection parameters, they generally have little or no connection to the physics behind the air-blast atomization process. In fact, their application is usually limited to a particular atomizer design and scale, certain ranges of liquid/air properties and injection conditions, and Newtonian liquids. The main factors affecting the air-blast atomization of Newtonian liquids are summarized in Table 1.2. Emphasis is placed here on air-blast atomizers of the plain-jet type rather than the pre-filming type. 11 Table 1.2: Main factors affecting the air-blast atomization of Newtonian liquids. Factor Influence on Air-blast Atomization Atomizing Air Velocity (UA) and Relative Air-liquid Velocity (UR) Increasing the atomizing air velocity increases the relative velocity at the air-liquid interface (assuming the air is initially faster than the liquid), thereby promoting the development of wave instabilities on the liquid surface and aerodynamic form drag acting on any liquid protrusions. The mean droplet size has been found to be inversely proportional to UR (at constant ALR and up to sonic UA) [42-44,47-49,59,60]. Air-liquid Mass Ratio (ALR= rhA/mL ) Providing additional air for a given mL results in improved atomization. Golitzine et al [56] atomized water with air and observed an inverse variation of the mean droplet size with ALR (over an ALR range of 1.5 to 10). Anson [54] reported a similar relationship for ALR values between 20 and 30. Lefebvre [2] noted that for many air-blast atomizers acting on Newtonian liquids, atomization quality starts to decline as ALR is reduced to about four and deteriorates rapidly below an ALR of two. However, little improvement in atomization is gained by increasing the ALR above five because the air jet is too physically remote to interact with the liquid stream. Deficiencies in air flow rate and ALR (at constant m,) can be overcome by increasing UA (through a reduction in the outer diameter of the annular air jet) [43]. Atomizing Air or Gas Density (PA) By atomizing diesel fuel with helium and other gases, Lewis et al [61] reported that when the atomizing gas density was reduced to one-seventh of the value of air, the mean droplet diameter rose by a factor of approximately two, despite a slight increase in UA- Further, Lane [62] subjected individual water droplets (0.5 to 5.0 mm diameter) to high-speed air flows. His photographic evidence showed that the secondary droplets into which a main droplet was broken up became progressively smaller with increases in pA. 12 Factor Influence on Air-blast Atomization Dynamic Air Pressure (PAUA2) Kim and Marshall [49] employed a plain-jet air-blast atomizer with molten wax and air as the liquid and atomizing gas phases, respectively, to show that the mean droplet size decreases with increasing dynamic air pressure and ALR. By adjusting the atomizer scale (at equivalent air flow rates), Wiggs [63] suggested that the kinetic energy in the atomizing air, specifically the kinetic energy difference between the inlet air and resultant spray (i.e. surface energy due to the production of small droplets), was the most important factor in dictating the extent of atomization. This opinion was echoed by Lasheras et al [64] and Varga et al [65], who emphasized that i f the momentum flux ratio (M = PAUA2/PLUL) is on the order of or greater than unity, atomization is caused by the transfer of kinetic energy from the atomizing air to the liquid. Liquid Density (Pd By using geometrically similar air-blast atomizers of different dimensions, Lorenzetto and Lefebvre [43] reported that variations in liquid density (at constant ALR and UR) between approximately 800 and 2000 kg/m had little influence on the mean droplet size. The same conclusion was reached by Rizk and Lefebvre [57] over a similar liquid density range. Liquid Orifice Diameter (DJ) Lorenzetto and Lefebvre [43] found that for Newtonian liquids of low viscosity (kerosene or water: juL =. 1 mPa-s), variations in the liquid orifice diameter had almost no effect on the SMD (as measured by light scattering). Despite this, further tests performed on a more viscous liquid (p.i = 36 mPa-s) led to a marked dependence of SMD on the liquid orifice diameter; in fact, SMD oc Dj°5. For comparison, in pre-filming air-blast atomizers, a thicker liquid film tends to result in a coarser spray. Many investigators, including York et al [66], Hagerty and Shea [67], and Dombrowski and Johns [68] have noted that the mean droplet diameter is roughly proportional to the square root of the liquid film thickness. 13 Factor Influence on Air-blast Atomization Liquid Shear Viscosity (JUL) Liquid viscosity is a stabilizing force. Its increase extends the jet breakup length, impairs wave development on the liquid surface, lowers ReL and dampens turbulent velocity fluctuations in the liquid stream, and reduces the rate at which ligaments pinch-off so that droplet formation occurs farther downstream of the nozzle in regions of low relative air-liquid velocity. The mean droplet size increases with increasing liquid viscosity, as has been observed by many researchers including Nukiyama and Tanasawa [42] (water, gasoline, alcohol, heavy fuel oil), K im and Marshall [49] (wax melts), and Lorenzetto and Lefebvre [43] (water, kerosene). Liquid Surface Tension (OL) Surface tension can be deemed a stabilizing force in the context of its influence on the mean droplet size. Increasing the surface tension further opposes distortions of the liquid surface, impedes the growth of wave instabilities, and delays the onset of ligament and droplet formation. The result is an increase in the mean droplet size [42,44]. The influence of surface tension (between 24 and 73 mN/m) diminishes at large UR (> 140 m/s) and ALR (> 3.60) [43]. Liquid Turbulence Radial velocity components arising from turbulence in the liquid stream counteract the confining influence of capillary forces, thereby ruffling the initially smooth liquid surface and enhancing the effect of aerodynamic forces [4,30]. The process of air-blast atomization is complex and multi-staged [10], involving a number of forces alternately driving and suppressing the development of instabilities in and on the liquid. Of the mechanisms proposed, the wave theory has gained the widest acceptance among researchers. Mayer [69] postulated that as a bulk liquid interacts with a high-speed gas, waves develop on the free surface, the amplitudes of which will grow if their wavelengths exceed a critical value. At sufficiently large wave amplitudes, the liquid jet sheds ligaments that quickly collapse into droplets. Adelberg [70,71] suggested 14 that the waves may be triggered by the dynamic pressure of the air jet. Chigier [28] emphasized the importance of turbulence in the liquid and air streams since radial velocity fluctuations within the bulk liquid and large-scale eddy structures in the air jet can both combine to promote protuberance generation on the liquid jet's surface. This was also the conclusion from air-blast atomization experiments conducted by Lasheras and Hopfinger [72]. The wave theory has been experimentally verified by a number of researchers [57,59,73], most notably Dombrowski and his coworkers [68,74,75], whose high-speed photographs have consistently revealed the presence of waves on thin liquid sheets prior to their disintegration into ligaments and subsequently, droplets. Following the formation of stable droplets, air-blast atomization becomes essentially a transport process in which the following steps occur [58]: 1. Acceleration of droplets by the high-speed air jet and/or deceleration of droplets in recirculating flow. 2. Formation of a two-phase, liquid-gas spray, which undergoes spreading, and entrains ambient air. 3. Evaporation of liquid as a result of temperature and vapor pressure gradients between the droplet surface and surroundings. In his air-blast atomization experiments, Rizk [76] found that increasing the shear viscosity of a Newtonian liquid above approximately 15 mPa-s resulted in the absence of wave formation. Instead, liquid globules were formed at the nozzle orifice lip, from which ligaments were stretched in the downstream direction by the atomizing air. Rizk's experimental photographs revealed an atomization process resembling that proposed by Castleman [22]. Recall Castleman postulated that the interaction between the outer liquid jet layer and the surrounding atomizing air, together with the effect of viscous air drag, ruffles the initially smooth liquid surface and allows aerodynamic pressure forces to draw ligaments directly from the bulk liquid. These ligaments are stretched in the same direction as the atomizing air flow, such that their eventual collapse occurs in regions of lower relative air-liquid velocity. Consequently, the resultant droplets tend to be larger 15 than those formed from lower viscosity liquids. So far, there appears to be at least two major mechanisms governing the air-blast atomization process for Newtonian liquids: Mayer's [69] "wave theory" for low viscosity liquids (IUL< 15 mPa-s) and Casfleman's [22] "ligament" theory corresponding to high viscosity liquids (JUL> 15 mPa-s). Previously, Ohnesorge [21], Miesse [24], and Reitz [23] had shown that liquid jet breakup in a stationary gas could be classified according to the magnitude of the liquid Reynolds number and the Ohnesorge number. In air-blast atomization, however, none of these dimensionless representations capture the effects of the increased relative velocity at the air-liquid interface or the dynamic pressure in the air jet. By employing dimensional analysis on the breakup of liquid jets and droplets in quiescent and co-flowing gas, Farago and Chigier [73,77] were able to demonstrate the importance of the aerodynamic Weber number: pAUR2D, WeA- — Aerodynamic Weber Number The aerodynamic Weber number is a ratio of the destabilizing aerodynamic forces to the consolidating surface tension forces. By analyzing more than 1600 high-speed photographs, Farago and Chigier [73] identified four main regimes corresponding to the breakup of a round, Newtonian water stream by a high-speed annular air jet under conditions of ambient temperature and pressure. These regimes were classified according to the magnitudes of ReL and We A, as shown in Figure 1.5. Sample photographs depicting the appearance of the water jet in each regime have been reproduced Figure 1.6. 16 1 OE+05 1.0E+04 1 .OE+03 1.0E+02 1 OE-03 1.0E-02 1.0E+02 1.OE+03 Figure 1.5: Classification of water jet breakup in co-flowing air by Farago and Chigier [73]. Axisymmetric Non-axisymmetric Rayleigh Rayleigh Membrane-type Fiber-type Dj = 1 mm MM-Figure 1.6: [73]). Photographs of water jet breakup in co-flowing air (Farago and Chigier 17 As the velocity of the annular air jet increases so does WeA, which leads to a gradual progression across the different breakup regimes [73]: 1. Rayleigh Breakup (We±_< 25). The liquid jet collapses into discrete droplets without forming any ligaments, membranes, or fibers (to be described). The mean droplet diameter is on the order of the liquid jet diameter, while the maximum droplet diameter is about twice the liquid jet diameter. This regime can be further divided according to the magnitude of the aerodynamic Weber number: axisymmetric Rayleigh breakup (WeA < 15) and non-axisymmetric Rayleigh breakup (15 < WeA<25). a. Axisymmetric Rayleigh Breakup. Even at low air flow rates, the central liquid jet is accelerated and sheathed by the annular air. Helical structures, resembling those seen in the first wind-induced regime of Reitz [23], develop on the liquid jet. Nevertheless, the spatial distribution of ligaments and droplets around the jet remains fairly axisymmetric. Despite the name, this is a regime in which aerodynamic effects are important. b. Non-axisymmetric Rayleigh Breakup. This regime forms the boundary between classical Rayleigh breakup and the ensuing membrane-type breakup. The liquid jet is first accelerated by the high-speed annular air, thus reducing its diameter. The liquid jet's orientation is then determined by interactions between itself and the surrounding turbulent air structures. Wave development on the liquid surface is thought to be triggered by Kelvin-Helmholtz instabilities [78-80]. Aerodynamic forces continue to thin the liquid jet, but breakup itself is due to the Rayleigh mechanism. This regime may also be the operating mode in the final stages of membrane-type breakup and fiber-type breakup. 18 2. Membrane-type Breakup (25 < WeA_< 70). High annular air velocities flatten the initially round liquid jet into a thin sheet or membrane. Aerodynamic forces exerted on the membrane induce Kelvin-Helmholtz instabilities [79,80], leading to the development of surface waves. Liquid accumulates at the membrane edges, forming a thick frame that bounds a thin internal membrane. The diameter of the liquid frame is smaller than that of the emerging liquid jet. The liquid frame eventually collapses via the non-axisymmetric Rayleigh mechanism to produce large droplets, while the thin internal membrane bursts to form a multiplicity of smaller droplets. Mean droplet sizes are about one order of magnitude smaller than the initial liquid jet diameter. 3. Fiber-type Breakup (70 < WeA). Aerodynamic forces drag and strip small-scale ligaments or fibers from the crests of surface waves developed on the liquid jet. After detaching from the liquid core, these fibers collapse into discrete droplets by the Rayleigh mechanism; droplets formed at this stage are a few orders of magnitude smaller than the initial liquid jet diameter. Continuing on downstream, the liquid core accelerates under the influence of high-speed air. Aerodynamic forces drive wave growth on the liquid jet, leading to its disintegration into ligaments with lengths of about two to five times the initial liquid jet diameter. Additional fibers are striped from these ligaments; the diameters of these newly formed fibers increase with axial distance from the nozzle. Farther downstream, the remaining ligaments collapse to form intermittent plumes of small droplets and fibers, thereby generating periodic fluctuations in the droplet number-density of the spray. In general, droplets produced farther downstream are larger than those produced closer to the nozzle. 19 Farago and Chigier [73] observed that all of the different breakup regimes involved some degree of wave formation, wave development, or wavy jet breakup after a critical waveform was reached. Accordingly, they postulated that atomization is inherently an unsteady process, even i f the emerging liquid and air streams are both pulsation-free. In fact, they noted that the combination of high aerodynamic Weber numbers and low liquid Reynolds numbers (Re,J^]WeA <100) resulted in particularly strong spray pulsations. These pulsations were manifested as spatial and temporal fluctuations in the droplet number-density and liquid void-fraction of the spray. Farago and Chigier assigned such pulsating behavior to the regime of Super-pulsating Sub-mode (see Figure 1.5). 20 1.1.2 Non-Newtonian Rheology Rheology is the study of the deformation of materials under the application of shear and normal stresses. Non-Newtonian materials have microstructural orientations that depend on the kinematics of the imposed deformation. Because of this, their macroscopic properties can also be affected by deformation. For example, non-Newtonian fluids such as household paint and biological blood can exhibit time and rate-dependent shear viscosities. Additionally, non-Newtonian materials may also possess elastic properties. A viscoelastic material, as the name suggests, responds to an applied stress by exhibiting a combination of the classical linear behavior for fluids (Newton's law of viscosity) and solids (Hooke's law of elasticity). In this way, a viscoelastic material can dissipate (viscously) and store (elastically) energy, with the relative balance of each depending on the time scale of the imposed deformation as well as on the spectrum of relaxation times inherent to the composite material. There are a number of remarkable characteristics exhibited by viscoelastic materials that cannot be explained by shear (viscous) effects [81]. A notable example of such is the ability of viscoelastic liquids to develop extensional viscosities that are much higher than those observed in Newtonian liquids. The flow field produced by a spray nozzle is predominately extensional [9]. Therefore, in atomization, knowledge of a liquid's extensional properties becomes equally, i f not more, important than knowledge of its shear properties. For example, two liquids that behave identically in shear may atomize in totally different manners owing to slight differences in their extensional behavior [12]. In many paint and industrial coating formulations, small amounts of a high molecular weight polymer are added to increase the zero shear rate viscosity for improved anti-settling and sag resistance. However, the addition of these polymers also renders the overall liquid viscoelastic by changing its extensional properties, which can in turn profoundly affect the way it atomizes [5,81-83]. 21 1.1.2.1 S h e a r B e h a v i o r Many non-Newtonian liquids exhibit a non-linear relationship between shear stress (r) and shear rate (y), resulting in a rate-dependent shear viscosity (ns) as represented by the slope in Figure 1.7. The shear viscosity can be increasing (dilatant or shear-thickening) or decreasing (pseudoplastic or shear-thinning) functions of the instantaneous shear rate [84], and may additionally include a finite yield stress below which the liquid will not flow (plastic). The shear viscosity of a non-Newtonian liquid may also be time-dependent. A rheopectic liquid exhibits a limited increase in its shear viscosity as a function of time (at a constant shear rate), while a thixotropic liquid shows the opposite behavior. This is illustrated in Figure 1.8. Moreover, regardless of the nature of the liquid (Newtonian or non-Newtonian), the shear viscosity decreases with increasing temperature. It should be noted that viscoelastic materials exhibiting rate-independent and time-independent shear viscosities are still referred to as "non-Newtonian" simply to distinguish them from inelastic Newtonian materials. Shear Rate Figure 1.7: Variation of shear stress with shear rate for non-Newtonian materials. 22 Rheopectic Newtonian Thixotropic Time Figure 1.8: Variation of shear viscosity with time (at a constant shear rate) for non-Newtonian materials. Attempts at quantifying the shear viscosity of non-Newtonian liquids have been almost entirely empirical. Current molecular theories are vastly oversimplified and cannot describe accurately the complex molecular structure of real liquids to enable shear viscosity functions to be derived. So rheologists usually fit mathematical models to experimental shear flow data; Barnes et al [84] and Macosko [81] provide an extensive listing of such rheological models. The model used in the present work is the (Ostwald-de Waele) power-law model: T = m(j)" Power-law Model ns = m(y)"~l Power-law Model (explicit ns form) where r = shear stress m = consistency index f = shear rate (velocity gradient perpendicular to shear plane) n = power-law index ns = instantaneous dynamic shear viscosity 23 The power-law model is relatively straightforward in that it contains only two parameters: consistency index (m) and power-law index (ri). For shear-thinning liquids, n < 1, while for shear-thickening liquids, n > 1. For Newtonian liquids, ns is independent of f •> and n = 1. Although the power-law model is effective in predicting the shear flow behavior of many common liquids, deficiencies do exist at limiting / values. For example, for n < 1, the predicted shear viscosity decreases indefinitely with increasing shear rate, thereby requiring a liquid with infinite viscosity at rest and zero viscosity at an infinite shear rate. A real liquid has both a minimum and maximum shear viscosity determined by its physical chemistry at the molecular level. Consequently, the use of the power-law model is only valid across the range of shear rates to which the parameters m and n were fitted. 1.1.2.2 Extensional Behavior In order to explain the ability of viscoelastic liquids to show remarkable resistance in extension, consider a simple polymeric system, similar to the one used in the present work: linear, flexible polymer chains in a homogenous, inelastic solvent at a concentration where minimal polymer-to-polymer entanglements are expected (i.e. "dilute" according to Flory's criteria [85]). The dilute regime is chosen to restrict the cause of any extensional viscosity development solely to polymer stretching and the associated slow relaxation response [86]. In almost all atomizers, the liquid encounters a flow path that includes some degree of convergence or contraction from a large diameter inlet tube to a fine exit orifice. The resultant velocity gradient is along the flow direction (i.e. acceleration). Because such a flow is irrotational except near solid boundaries, polymer chains within a liquid will experience extensional flow more often than shear flow. This promotes polymer stretching. To elaborate, imagine a polymer molecule in a rotational shear flow, where it tumbles around more like a rigid particle than a flexible coil. Polymer stretching is minimal, even when the shear rates are high [87]. Conversely, Figure 1.9 illustrates an extensional flow that involves stretching along streamlines. The liquid particles will separate more as the deformation proceeds. 24 Figure 1.9: Separation of liquid particles in simple extension. The deformation illustrated in Figure 1.9 is known as simple extension and is described by the following flow field: v, = e x, v2 = --ex2 v3 = --ex3 2 1 2 where v i ' v 2 ' v 3 ~ velocity components x, ,x2 ,x3 = displacement components s = extensional rate The particle trajectories are: x , ( r ) = x 1 ( o y x2(t) = x2(0)e -e x3{t)=x3{0)e~> -el Y Hence, the converging nozzle geometry produces regions of strong extensional flow, in which polymeric molecules are oriented and stretched in the flow direction [88]. Although Brownian motion prevents perfect orientation, it cannot instigate the tumbling 25 motion encountered in shear flows [89]. Moreover, i f air-blast atomizers are used, the additional sheathing action from the co-flowing air jet may contribute further to polymer stretching. So as Mannheimer [90] confirmed, the resistance of a polymer solution to flow in extension is highly dependent on the mechanical flexibility of the individual polymer chains. The strain rate and stress tensors for simple extension are as follows: '2s 0 0 " 0 - £ 0 Strain Rate Tensor in Simple Extension 0 0 -£ ~°ii 0 0 " 0 cr22 0 Stress Tensor in Simple Extension 0 0 Note that in contrast to shear flow, the principal stresses for extensional flow are in the same direction as those for the strain rate. For an isotropic liquid in simple extension, all shear stresses are zero and 022 = 035, by symmetry, so that the normal stress difference is: ° K = c r n _ c r 2 2 = °"ii -033 Normal Stress Difference When a liquid is suddenly exposed to an extensional flow field, normal stress development is described by the tensile stress growth coefficient, defined as: „:.M).£sM Tensile Stress Growth Coefficient For polymer melts, i f the initial extensional rate is too large, fracture may occur. Otherwise, for polymer solutions, stretching continues until the steady state value of the tensile stress growth coefficient is reached; this limiting value is known as the 26 extensional viscosity (Trouton [91]). The extensional viscosity is a measure of a material's resistance to deform continuously and permanently in extension. VE (^)= H m 1/7E (F> ^ )J Extensional Viscosity / ->» The results of extensional flow experiments are usually expressed using a ratio of the apparent extensional viscosity to the shear viscosity evaluated at equivalent values of the second invariant of the strain rate tensor. This is known as the Trouton ratio: Trouton Ratio (in simple extension [92]) According to the theory of linear viscoelasticity, the tensile stress growth coefficient is equal to three times the shear stress growth coefficient, and the extensional viscosity becomes equal to three times the zero shear rate viscosity. Therefore, the Trouton ratio for inelastic, Newtonian liquids is equal to 3. Moreover, for inelastic, shear-thinning liquids, the Trouton ratio is also equal to 3; this implies that the extensional viscosity actually decreases with the extensional rate - behavior known as extension-thinning. On the other hand, depending on the flexibility of the polymer [11,93], its molecular weight [82,94], and the concentration at which it is introduced [11,82,94], polymer solutions can exhibit Trouton ratios much higher than the Newtonian value of 3 - Trouton ratios exceeding 10 have been reported by Tirtaatmadja and Sridhar [95]. By using extensional rheometers of the filament stretching [95-97], contraction flow [4-6,98], and opposed-jet [3,11,82,93,94,99-102] types, rheologists have found that the extensional viscosity of polymer solutions is generally an increasing function of the extensional rate and the extensional strain; such behaviors are known, respectively, as extension-thickening and strain-hardening. Keller and Odell [103] attributed extension-thickening behavior to the physical re-orientation, uncoiling, and tensioning of the flexible polymer chains. However, once these macromolecules become fully uncoiled, typically ate «4.5 27 and above a critical s determined by the polymer [95], any further increases in the extensional rate or strain will have little influence on the extensional viscosity. Theoretical efforts to understand the effects of suspended macromolecules on the extensional viscosity have been published by Bird et al [104] and Batchelor [105,106]. Specifically, they predicted that an increase in the extensional viscosity can be achieved by allowing elongated particles, suspended in a Newtonian liquid, to re-orient along the extensional flow direction. Batchelor proposed the following expression for Y\E-where ?j0 = zero shear rate dynamic viscosity L = particle length dP = particle diameter C - volume concentration of particle As a crude approximation, assume that the elongated particles are substituted by polymer chains. Lldp for a randomly coiled polymer is roughly unity. But when a polymer is stretched in an extensional flow, L/dp can be much higher. Results from Mewis and Metzner's [107] extensional flow experiments using fiber suspensions with different volume concentrations and length-to-diameter ratios were in good agreement with Batchelor's theory. They reported a maximum Trouton ratio of 260 for L/dp of 586 at a volume concentration of about 1%. 3?7o o 28 1.1.3 Viscoelastic Breakup Research on the breakup of viscoelastic liquids has grown steadily over the past couple of decades. Much of it has been, and will continue to be for the unforeseeable future, experimental owing to the challenges faced in modeling such complex flow fields. Adding to this problem is the fact that the extension-thickening behavior exhibited by many viscoelastic liquids is dependent on kinematic conditions: extensional rate, extensional strain, flow geometry, and strain history. Therefore, formulating a constitutive equation that accurately predicts the extensional viscosity under atomization conditions is impossible given the capability, or lack thereof, of current measurement devices. This has not, however, precluded attempts by researchers to correlate an apparent extensional viscosity to spray properties such as the mean droplet size. The term "apparent" is used here to indicate that it is merely an indexing parameter, claiming in no way to be a true material property. The apparent extensional viscosity is reported by extensional rheometers that suffer from any number of fundamental deficiencies. These include, but are not limited to: 1) the inability to sustain steady state extensional rates [100], 2) the development of inhomogeneous flow fields involving both shear and extension [108], and 3) unknown extensional strain magnitudes [98]. Available literature on viscoelastic breakup can be divided into two categories: capillary jet breakup and atomization. The simplicity and easily understood boundary conditions surrounding capillary jet breakup have attracted several attempts at modeling. In contrast, almost all of the previous work relating to viscoelastic atomization has been experimental. 1.1.3.1 Capillary Jet Breakup Examination of the surface tension driven breakup of Newtonian jets began over a century ago with the linear stability analyses of Rayleigh [15] and Weber [16]; McCarthy and Molly [13] have published a detailed review. For viscoelastic jets, however, the use of a stability analysis is complicated by the need for a constitutive equation that accurately accounts for the additional stresses developed in a transient, extension-dominated flow field. Goldin et al [109] and Middleman [110] both used a linear 29 stability analysis to show that axisymmetric disturbances grew faster on viscoelastic jets than they did on Newtonian jets. Bousfield et al [111] employed a hybrid solution, one in which a linear analysis was applied at short downstream distances and a non-linear analysis was applied farther away so as to better predict the behavior of satellite droplets. They concluded that elasticity has essentially three effects on the stability of a jet: a delay in the onset of disturbance growth due to unrelaxed stresses produced within the nozzle, accelerated disturbance growth on the liquid surface, and enhanced filament stability in the final stages of breakup owing to normal stress development. The first and third effects promote jet stability while the second effect reduces it. Although the relative importance of each effect is difficult to assess independently, experimentalists generally agree that, compared with Newtonian jets, viscoelastic jets tend to be more stable. This is evidenced by their longer breakup lengths, fewer satellite droplets, and more pronounced filament stretching between the main droplets. Gordon et al [112] mechanically disturbed jets of aqueous Carbopol and Separan, and concluded that liquid elasticity enhances jet stability. Aqueous solutions of 0.1% Carbopol were inelastic, displaying a jet breakup pattern similar to that of water. However, the added elasticity in low (0.05%) concentration Separan jets retarded the growth of sinusoidal disturbances on the liquid surface. High (0.10%) concentration Separan jets did not display any sinusoidal disturbance growth at all, but instead collapsed from the outset to form a stream of main droplets connected to one another by long, slender filaments. Lenczyk and Kiser [113] and Mun et al [94] used aqueous solutions of Separan and Polyethylene oxide (PEO), respectively, at various concentrations and molecular weights to show that the jet breakup length increases with the extensional viscosity. Christanti and Walker [114] recognized that existing studies of the influence of elasticity on capillary jet breakup have often been limited by an inability to separate the effects of shear-thinning and extension-thickening. By employing a series of rheologically-ideal tests liquids, they were able to adjust the extensional viscosity independently of the rate-independent shear viscosity. Their photographic evidence confirmed that the elasticity 30 gained by increasing the molecular weight and/or concentration of a dissolved polymer can suppress satellite droplet formation as well as extend the jet breakup length. Additionally, liquid elasticity was shown to alter the shape at breakup from an inverted-cone attached to a droplet to the so-called "beads-on-string" structure, whereby main droplets are connected to one another through fine filaments. Christanti and Walker's results provided further evidence that extension-thickening is indeed the most significant rheological mechanism affecting the surface tension driven breakup of viscoelastic jets. 1.1.3.2 Atomization There is limited literature available on the atomization of viscoelastic liquids. In fact, only one group has cited the use of air-blast atomization: Mansour and Chigier [5] sprayed a series of aqueous Polyacrilamide and Xanthan gum solutions through a plain-jet air-blast atomizer, and measured the resultant SMD using a Phase Doppler Particle Analyzer. They found that liquid elasticity, namely the extensional viscosity as estimated by the contraction flow method, impaired atomization by inducing ligament stretching prior to the formation of droplets. These droplets were consequently larger than those formed from Newtonian liquids under similar injection conditions. Ligament stretching was believed to be caused by the development of elastic normal stresses. Moreover, the authors reported that for shear-thinning, inelastic liquids, the SMD correlated with the shear viscosity, just like in Newtonian liquids. However, an appropriate correlation could only be obtained by using the limiting value of the shear viscosity at high shear rates. On the other hand, for viscoelastic liquids, no correlation was found between any form of the shear viscosity and the SMD. Therefore, this suggests the potentially dominating role of the extensional viscosity in controlling breakup. Mansour and Chigier's [5] experimental procedures and results typify those of the majority of researchers who have investigated viscoelastic atomization. Aqueous polymer solutions are often used as test liquids because of their simplicity and ability to exhibit extensional viscosities proportional to the polymer molecular weight and concentration [5,82]. These liquids are then atomized and a set of indicators are chosen to represent the extent of atomization. Most commonly, this is a form of the mean 31 droplet size, though the spray angle [11] or jet breakup length [98] has been used in some cases. Collectively, the results indicate that liquid elasticity hinders atomization and increases droplet sizes; in fact, some researchers [6-8] have even successfully correlated the mean droplet diameter with the apparent extensional viscosity. The physical mechanisms behind these observations, however, have largely been ignored. This is unsurprising considering the complexity of the air-blast atomization process itself [2]. The most serious limitations common to almost all of the previous research efforts in viscoelastic atomization are listed below. 1. The use of test liquids exhibiting both shear-thinning and extension-thickening rheology can lead to deceptive results, especially when droplet size measurements are considered. For Newtonian liquids, it is known that the mean droplet size is well correlated with the shear viscosity. But for viscoelastic liquids, both the shear and extensional viscosities can affect the mean droplet size [6]. Consequently, any variation in atomization characteristics observed between test liquids can be misleading. Only two studies (Mun et al [3]; Hartranft and Settles [98]) have attempted to limit the variables between test liquids to just the extensional viscosity. 2. The atomization process subjects a liquid to very high rates of extension and shear. Only recently has there been significant progress made in the field of rheology to properly characterize the mechanical behavior of liquids under such conditions. In particular, the recognized difficulty in measuring the small tensile forces exhibited by dilute polymer solutions in an extensional flow field has been addressed somewhat by advents such as the Capillary Breakup Extensional Rheometer (CaBER) [96]. 3. Investigators typically perform extensional viscosity measurements on their polymer solutions before they are sprayed. However, of the investigators who were able to correlate an apparent extensional viscosity with the mean droplet diameter, few had taken into account the mechanical degradation that long 32 chain polymers can experience during pumping. Such degradation can significantly reduce polymer flexibility and the extent to which extension-thickening occurs [98]. Hence, the measured extensional viscosity may not be indicative of the value exhibited by the liquid during atomization. Research on viscoelastic atomization using conventional hydraulic atomizers constitutes the remaining bulk of the limited available literature. It has been known for quite some time that polymeric additives can suppress satellite droplet formation during atomization. This behavior has been exploited in many industrial applications. For example, Chao et al [115] and Johnson et al [116] discovered that by introducing high molecular weight polyisobutylene (PIB) into jet fuel at concentrations as low as 50 ppm, an anti-misting effect was established that reduced post-crash fire hazards. The effectiveness of flammability suppression increased with the molecular weight of the polymer, and was well correlated with the apparent extensional viscosity of the solution as measured by the ductless siphon method. Elsewhere in industry, Smolinski et al [7] and Marano et al [8] dissolved PIB in machining oil to suppress unwanted misting during metalworking operations. PIB molecular weights of 1.0 to 2.2 million were used at concentrations ranging from 0.1 to 1.0 wt.%. Under identical injection conditions, the mass median diameters of the PIB-oil solutions were 20 to 200% higher than those of pure mineral oil (at around 7-15 pm). This increase was attributed to a significant reduction in the number of droplets falling below 5 pm in diameter. The authors ascribed such behavior to the viscoelastic properties of the PIB solutions, namely the extensional viscosity. Moreover, increases in the mass median diameter were found to correlate linearly with the apparent extensional viscosity as predicted by the dumbbell kinetic theory. In agricultural pesticide sprays, small droplets are especially drift-prone and their release may have an adverse environmental impact. In view of this, Mun et al [3] added varying molecular weights of PEO into glycerin-water solvents and atomized the solutions using several agricultural (hydraulic) spray nozzles. They discovered that whenever a liquid 33 exhibits a detectable extensional viscosity, as measured by an opposed-jet rheometer, the VMD of the resultant spray increases while the percentage of fine droplets (< 105 um) formed decreases. A similar conclusion was reached by Dexter [6], who found that, by atomizing polymer solutions using a standard agricultural spray nozzle, the VMD correlated more strongly with the apparent extensional viscosity than with the shear viscosity. While attempting to improve the airless spray coating process, Hartranft and Settles [98] explored the role of elasticity in sheet atomization. Specifically, their experiments examined the behavior of dilute Polyacrilamide solutions when atomized under the high pressures (1.4-21 MPa) encountered in commercial airless sprayers. At a moderate atomizing pressure (3.7 MPa), flow visualization results revealed that the apparent extensional viscosity, as measured by the contraction flow technique, stabilized the liquid sheet by increasing the wavelength of surface disturbances. The size of the ligaments produced in primary breakup grew with the extensional viscosity. Unexpectedly, at the highest atomizing pressure (24 MPa), visual differences between the polymeric and Newtonian liquids were minimal. This was explained by the exceptionally high strain rates inside the nozzle, which had caused severe polymer degradation and an associated reduction in the extent of extension-thickening. Hartranft and Settles' findings were supported by those of Glass et al [12], who sprayed a set of industrial water-borne coatings, containing polymer thickeners of varying molecular weight, through a flat-fan atomizer. Their photographs showed that elasticity stabilized the liquid sheet and increased droplet sizes. Likewise, Stelter et al [97] employed flat-fan and pressure-swirl atomizers to evaluate the influence of viscoelastic properties on atomization. For sheet (flat-fan) atomization, liquid elasticity was shown to: 1) extend the sheet breakup length, thus stabilizing the sheet, 2) have no effect on the dimensions of ligaments produced from the sheet, 3) increase the SMD and Dio by retarding the pinch-off of ligaments into droplets, and 4) significantly reduce the contribution of small droplets (< 200 urn) to the droplet size distribution (e.g. VMD for polymer solutions was nearly three times that of Newtonian liquids). For pressure-swirl 34 atomization, liquid elasticity was shown to: 1) hinder the ability of the spray to form conical sheets (i.e. at high polymer concentrations, fully developed hollow-cone sprays could not be produced), and 2) increase the SMD and Dw-On a more fundamental note, Ferguson et al [9] investigated the influence of polymer type, molecular weight, and concentration on the atomization behavior of polymer solutions. Solutions containing low molecular weight polymers, such as Polyethylene glycol, were found to behave similarly to Newtonian liquids - the mass median diameter scaling with the steady shear viscosity to a power law. However, for solutions of high molecular weight polymers, such as those containing PEO or polyvinyl alcohol, the mass median diameter was not only a function of the shear viscosity, but also depended on, and could be correlated directly with, the polymer molecular weight and concentration. Because it is known that increasing the polymer molecular weight and concentration will enhance a liquid's elasticity [5,82], the authors concluded that the extensional viscosity must play a critical role in controlling breakup. Harrison et al [11] examined the influence of polymer rigidity on the cone angle of a spray produced by a swirl-type nozzle. Three test solutions were sprayed - each containing a polymer with a different rigidity. Their results showed that the spray produced from the solution containing the most flexible polymer, Polyacrilamide in this case, collapsed at the lowest concentration. This behavior was attributed to increases in extensional viscosity induced by the added polymer flexibility, which resulted in a more detrimental effect on atomization at equivalent concentrations. 35 1.2 Motivation and Objectives Motivated by a need to improve transfer efficiencies in spray coating, the present work aims to understand the influence of liquid elasticity on air-blast atomization. This section examines the current state of technologies used in the spray coating industry, and highlights some of the key reasons why research in this area should continue to progress. 1.2.1 Spray Coating Atomizers are routinely used in the surface coating process (i.e. spray coating), leading to the unavoidable, often costly, and environmentally damaging problem of overspray generation. Overspray refers to any liquid sprayed that does not adhere to the target surface, and is quantified by the transfer efficiency (TE), defined as the percentage of the total mass of solids in the liquid coating sprayed (i.e. excluding volatile components) that adheres onto the target surface [117]. Overspray is caused by the droplet-induced and/or externally-applied air jet (the latter only when air-blast atomizers are used) impinging on, and being redirected parallel to, the target surface. This air jet acts as a carrier medium for transporting small airborne droplets away from the target surface [118,119]. Larger droplets tend to possess sufficient inertia to cross aerodynamic streamlines [120], thus enabling them to deposit onto the target surface. Studies on the application of industrial coatings with conventional air-blast atomizers have revealed TEs on the order of 20 to 40% [121-124]. Although the adoption of high (liquid) volume-low (air) pressure nozzles and airless atomizers in recent years have improved TEs to about 65 to 80%> [121,125,126], many people still consider these figures to be unacceptably low. And despite success with electrostatic spraying technology [127-129], which further improves TEs to nearly 90%, the overall method remains hampered by the high costs, complexity, and safety hazards associated with its equipment. To bring about some perspective, an estimated 248 million liters of industrial coating was sold in Canada in 2004, amounting to roughly $2 billion (CAD) worth in sales [130]. 36 These included marine and automotive coatings that can contain toxic metals, isocyanates, and volatile organic compounds [130-132]. Therefore, long-term human exposure to the ensuing overspray may lead to serious health hazards, chief among them being lung cancer and central nervous system dysfunction [133-138]. As the environmental, financial, and health consequences owing to inadequate transfer efficiencies become increasingly clear, so does the need to better understand and improve the spray coating process. 1.2.2 Railway Industry Recently, spray coating has drawn growing interest from the railway industry, where railway operators are beginning to adopt the use of liquid friction modifiers (FM). KELTRACK™ [139-141], developed and marketed by Kelsan Technologies Corporation [142], is a line of aqueous liquid FMs that is applied on top of the railhead. After water evaporation, a dry thin film of F M material remains, controlling top-of-rail friction at an intermediate level while providing positive friction (versus creep) characteristics at the wheel-to-rail interface. Such positive friction behavior alleviates the frictional instability of roll-slip oscillations, which are responsible for the generation of curve squeal noise and short pitch corrugations [143,144]. In addition, F M application has also been demonstrated to reduce wheel and rail wear, lateral forces, and locomotive fuel consumption without adversely affecting train braking or traction [140,143,145,146]. K E L T R A C K is typically applied by air-blast atomizers mounted onboard locomotives and HiRail maintenance vehicles; these are shown in Figure 1.10 and Figure 1.11, respectively. In order to achieve effective friction control, it is currently known what volume of F M must be dispensed by Kelsan's air-blast atomizers per length of railroad track. But the exact amount of F M actually reaching the railhead, as opposed to the surrounding rail ties or train undercarriage, is unknown. Also unknown is the spatial distribution of F M in the spray, which can influence the uniformity of the resultant spray pattern on the railhead. This is believed to affect retentivity (the number of axle passes for which the F M film remains effective) and carry-down (the ability of the F M film to migrate down the track). 37 Moreover, F M spray nozzles that are mounted beneath locomotives can be exposed to significant crossflows because freight trains typically travel at speeds averaging 50 km per hour (and up to a maximum of about 100 km per hour in long stretches of straight track). Knowing the influence of such crossflows on F M spray trajectories would be valuable, especially considering the detrimental effects it can pose on the transfer efficiency. Further, crossflows have been observed to accelerate the deposition of fouling on nozzle orifices, which, i f left unattended, can accumulate to render the nozzle inoperable. Although it is now accepted practice for the nozzles to be periodically cleaned, this is generally a task that railway operators would rather avoid as it complicates train maintenance. Hence, Kelsan and its customers would benefit from improvements to the anti-fouling performance of the F M spray nozzles. 39 1.2.3 Objectives Many paints and industrial coatings are non-Newtonian liquids that exhibit viscoelastic properties [12]. Knowledge of their behavior, from the atomizer orifice to the target surface, is valuable towards optimizing the transfer efficiency in spray coating. The present work focuses on the air-blast atomization and subsequent aerodynamic transport of viscoelastic liquids. The surface impingement aspect is treated separately in Mr. Dan Dressier's M.A.Sc. thesis (also archived at UBC). Previous studies on viscoelastic atomization have been hampered by an inability to decouple shear-thinning and extension-thickening rheology. Additionally, information relevant to spray coating, such as droplet velocities and the influence of crossflows, were seldom provided. To this end, a major objective of the present work is to expand upon previous research efforts by addressing these aforementioned limitations. The numerous constituents in typical industrial coatings lead to highly coupled, and even deceptive, rheology. To understand these Theologically complex liquids, Glass [147] and Soules et al [148] pioneered the use of substitute test liquids in paint application research. The present work employs a series of rheologically-ideal test liquids belonging to the Boger class [83,149]. By maintaining similar values of surface tension, density, and rate-independent shear viscosity in the test liquids, and independently varying the extensional viscosity, the effects of elasticity on air-blast atomization are isolated and examined. Droplet sizes and velocities are measured using shadowgraphy and Particle Image Velocimetry, respectively. Application of liquid FMs in the railway industry is a unique case of spray coating, one that currently involves a plethora of unknowns. In view of this, another major objective of the present work is to evaluate the ability of Kelsan's air-blast atomizer to apply liquid F M onto the railhead. Only after evaluating the performance of Kelsan's existing air-blast atomizer can a future generation of improved spray nozzles be designed. 40 1.3 References 1. Lefebvre A H (1989). "Atomization and Sprays" Hemisphere Publishing. 2. Lefebvre A H (1980). Air-blast atomization. Progress in Energy and Combustion Science, 6:233-261. 3. Mun RP, Young BW, Boger D V (1999). Atomization of dilute polymer solutions in agricultural spray nozzles. Journal of Non-Newtonian Fluid Mechanics, 83:163-178. 4. Mansour A (1994). "The effects of non-Newtonian rheology and liquid turbulence on twin-fluid atomization" Ph.D Thesis, Carnegie Mellon University. 5. Mansour A and Chigier N (1995). 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Kalousek J and Johnson K L (1992). An investigation of short pitch wheel and rail corrugations on Vancouver mass transit system. Journal of Rail and Rapid Transit (PartF), 206:127-135. 145. Eadie DT and Hooper N E (2003). Top of rail friction control: lateral force and rail wear reduction in a freight application. International Heavy Haul Association Conference. Dallas, Texas, May 2003. 146. Cotter J, Eadie DT, Elvidge D, Hooper NE, Roberts J, Makowsky T, Liu Y (2004). Top of rail friction control with locomotive delivery on BC Rail: Reductions in fuel and greenhouse gas emissions. Presented at The American Railway Engineering and Maintenance of Way Association Conference and Expo. Nashville, Tennessee, September 2004. 147. Glass JE (1978). Dynamics of roll spatter and tracking, Parts I, II, & III. Journal of Coatings Technology. 148. Soules DA, Fernando RH, Glass JE (1988). Dynamic uniaxial extensional viscosity (DUEV) effects in roll application: Rib and web growth in commercial coatings. Journal of Rheology, 32(2):181-198. 149. Dontula P, Macosko CW, Scriven L E (1998). Model elastic liquids with water-soluble polymers. AIChE Journal, 44(6):1247-1255. 51 2 AN EXPERIMENTAL STUDY ON AIR-BLAST ATOMIZATION OF VISCOELASTIC LIQUIDS1 2.1 Introduction Air-blast atomization has been the subject of many experimental investigations [1-11], from which it is now known that the controlling liquid properties are the shear viscosity and surface tension. However, the majority of research in this area has focused on Newtonian liquids despite the recognized industrial importance of spraying non-Newtonian liquids, particularly those that exhibit viscoelastic properties. In the railway industry, for example, an increasing number of railway operators are adopting the use of liquid friction modifiers (FM) for controlling frictional instabilities at the wheel-to-rail interface. Air-blast atomizers are often used to apply these liquid FMs onto the rail head to derive benefits such as improved fuel economy and reduced wheel and rail wear, without adversely affecting train braking or traction [12-17]. However, like many paints and industrial coatings, liquid FMs also contain polymers and solids, thus making them viscoelastic [18]. As such, they are expected to atomize differently than Newtonian liquids owing to their ability to develop significant extensional viscosities when exposed to the extension-dominated flow fields generated by spray nozzles [19,20]. Rheologists have observed that the extensional viscosity exhibited by polymer solutions is usually an increasing function of the extensional rate and strain [21-23], behavior known respectively as extension-thickening and strain-hardening [24]. The maximum Trouton ratio (ratio of extensional to shear viscosity) for these solutions can be more than one order of magnitude greater than the Newtonian (inelastic) value of 3 [25]. Hence, liquid elasticity, through the extensional viscosity, will play an important role in controlling breakup. In viscoelastic atomization research, aqueous polymer solutions are commonly used as test liquids because they are easy to formulate [26] and can exhibit extensional viscosities proportional to the polymer molecular weight and concentration [21,22]. These liquids are then atomized and a set of indicators are chosen, such as the mean droplet diameter or the jet breakup length, to represent the extent of atomization. Collectively, researchers 'A version of this chapter will be submitted for publication in Atomization and Sprays. 52 have found that liquid elasticity impairs atomization and increases droplet sizes. For example, Mansour and Chigier [21] atomized a series of polymer solutions using an air-blast atomizer, and found that elasticity promoted ligament stretching prior to droplet formation. These droplets were consequently larger than those formed from Newtonian liquids under similar injection conditions. Ligament stretching was attributed to normal stress development owing to molecular reorientation. Mun et al [20] employed agricultural sprayers to assess the impact that polymer additives had on atomization quality. They discovered that whenever a liquid exhibits a detectable extensional viscosity, as measured by an opposed-jet rheometer, the mean droplet size of the resultant spray increases while the percentage of fine droplets (< 105 pm) formed decreases. Dexter [27] reported that the mean droplet diameter of a polymeric spray correlated more strongly with extensional viscosity than with shear viscosity. A similar conclusion was reached by Ferguson et al [19], who evaluated the influence of polymer type, molecular weight, and concentration on atomization. Harrison et al [28] examined the effect of polymer rigidity on the cone angle of viscoelastic sprays. They discovered that the spray produced from the solution containing the most flexible polymer in their study collapsed at the lowest concentration. Such behavior was attributed to increases in extensional viscosity induced by the added polymer flexibility, which caused a more detrimental effect on atomization at equivalent concentrations. Meanwhile, the ability of elasticity to suppress satellite droplet formation has attracted numerous industrial applications. For example, Chao et al [29] and Johnson et al [30] reported that by introducing high molecular weight polyisobutylene (PIB) into aircraft fuel, an anti-misting effect was established that minimized post-crash fire dangers. Smolinski et al [31] and Marano et al [32] added PIB in machining oil to suppress unwanted misting during metalworking operations. Under identical injection conditions, the mean droplet diameters of the elastic PIB-oil solutions were 20-200% higher than those of pure mineral oil. Finally, Hartranft and Settles [33], Glass et al [18], and Stelter et al [34] all concluded that elasticity stabilized liquid sheets formed from airless paint sprayers. 53 2.2 Motivation and Objectives The present work aims to understand the influence of liquid elasticity on air-blast atomization. Previous studies in this area have often relied on extension-thickening liquids that were also strongly shear-thinning. In order to systematically isolate and investigate the effect of elasticity, test liquids with common, rate-independent shear viscosities, but adjustable extensional viscosities were employed. Based on the work of Mun [22], these model elastic liquids belong to the Boger class [35] and were constructed by dissolving polyethylene (PEO) into a glycerin-water solvent. A series of inelastic liquids and an industrial F M (KELTRACK™ HiRail [12-17]) were also tested for comparison. Mean droplet velocities and sizes were measured using Particle Image Velocimetry (PIV) and shadowgraphy, respectively. Flash photography was used to elucidate breakup details. 2.3 Test Liquids and Experimental Setup This section begins with a description of the compositions and properties of the test liquids used, although the constituents in K E L T R A C K HiRail have been deliberately omitted for intellectual property reasons. Next, the air-blast atomizer and the accompanying liquid and air flow systems are detailed. Extensive literature exists on PIV and shadowgraphy, so for brevity, only an overview of these measurement techniques is presented. 2.3.1 Test Liquid Construction A total of nine test liquids were sprayed: three were model elastic, five were inelastic, and one was a commercial liquid F M ( K E L T R A C K HiRail). A l l of the test liquids were constructed, characterized, and sprayed at a room temperature of 25±1°C. When not in use, they were individually stored in air-tight containers to minimize evaporation, water absorption from the ambient air, and contamination. Table 2.1 summarizes the compositions and properties of the model elastic and inelastic test liquids. 54 To isolate the effect of elasticity on breakup, model elastic liquids (Mun [22]) with similar densities (PL), surface tensions (ar), and rate-independent shear viscosities (ns), but different extensional viscosities were employed. They were made by adding PEO (Sigma-Aldrich, Canada) into a water-glycerin solvent. PEO is a linear, flexible, and water soluble polymer. In the present study, the concentrations at which PEO was introduced corresponded to the dilute regime according to criteria set out by Flory [36]. Although water is a good solvent for PEO (Mark-Houwink exponent, a > 0.5 [36]), glycerin is not, implying that polymers within the composite solvent will have smaller coil sizes and a lower intrinsic viscosity. PEO with viscosity-average molecular weights (My) of 105, 3x105, and 106 g/mol was used to create three elastic liquids, each with a different My. These will be referred to as "100K PEO", "300K PEO", and "1000K PEO", respectively. They were prepared by gradually dissolving PEO powder into distilled water under gentle magnetic stirring over a 24 hour period. Because flexible polymers like PEO are susceptible to mechanical degradation [26,37], care was taken to avoid excessive agitation. Next, USP grade glycerin (99.5 wt.%, U N IQ EMA Australia) was added to raise the shear viscosity of each of the three elastic liquids to about 5 mPa-s. Due to the limited thermal stability of PEO [26], liquids were characterized and sprayed within 2 week of preparation, but after at least 48 hours since final PEO addition to allow for complete polymer solubility. The inelastic test liquids were constructed using glycerin and distilled water. Their rate-independent shear viscosities were adjusted by varying the relative glycerin concentration. In total, five inelastic liquids were prepared, with shear viscosities ranging from 0.9 mPa-s (distilled water) to 805.8 mPas (glycerin). 55 Table 2.1: Compositions and properties of elastic and inelastic test liquids at 25°C. PEO M v [g/mol] PEO [wt.%] Glycerin [wt.%] Distilled Water [wt.%] rjs [mPas] ai (Pre/Post-Spray) [mN/ml Pi [g/cm3] - 0 0 100 0.9 72.1/70.4 1.00 - 0 50 50 5.1 68.8/63.3 1.13 - 0 80 20 46.7 66.6/64.0 1.21 - 0 90 10 154.2 61.9/61.5 1.23 - 0 99.5 0.5 805.8 61.9/61.7 1.26 100000(100K) 0.60 32.4 67.0 4.8 62.0/60.4 1.08 300000 (300K) 0.05 44.35 55.6 5,1 61.7/60.4 1.11 1000000(1000K) 0.075 38.0 61.925 4.9 63.0/60.5 1.10 Measurement Uncertainty ±0.1 to ±5 ±0.1 ±0.001 2.3.2 Test Liquid Characterization Shear viscosities were measured using a H A A K E VT550 viscometer coupled to various concentric-cylinder sensors. A l l three of the elastic liquids exhibited shear viscosities of approximately 5 mPa-s (< 5% variation) at shear rates ranging from 100 to 1000 s"1. Likewise, the shear viscosities of the inelastic liquids were also constant over a similar range of shear rates, with the magnitudes increasing as a function of glycerin concentration. To assess the extent of PEO degradation caused by mechanical processes upstream of the atomizer, namely pumping and flow through supply lines, additional shear viscosity measurements were conducted on elastic samples collected after they had flowed through the spray system (air-blast deactivated). Results confirmed that the shear viscosities of the elastic liquids before and after flowing through the spray system were similar (see Appendix A), suggesting minimal PEO degradation. Thus, the shear viscosities measured before the spray tests were representative of those exhibited by the liquids during atomization. Equilibrium surface tensions were measured using a du Notiy ring; the measurement procedure and raw data can be found in Appendix B. Surface tensions ranged from 60.4 to 63.0 mN/ra, and 61.5 to 72.1 mN/m for the elastic and inelastic liquids, respectively. These values are consistent with published data [38,39] and confirm the fact that PEO is slightly surface active [40]. Although much care was taken in handling the test liquids, surface tension measurements before and after the spray tests (air-blast deactivated) 56 revealed a small but measurable drop (maximum of 5.5 mN/m or 8% for 50 wt.% glycerin); physical contamination was likely the cause. Previous research on air-blast atomization found that OL variations in the 60 to 70 mN/m range did not significantly affect the mean droplet size [6]. Moreover, at the high aerodynamic Weber numbers (-1000) in the present study, surface tension has only a weak influence on the development of interfacial instabilities on the liquid jet [11,41]. A s a result, the oi variations across the test liquids were considered insignificant. Liquid densities were measured using a standard 100 ml density cup. In their air-blast atomization experiments, Lorenzetto and Lefebvre [6] showed that liquid density variations between 0.8 to 2.0 g/cm had little influence on the mean droplet size. Thus, the relatively small density variations exhibited by the test liquids, owing to the different glycerin concentrations needed to achieve the desired shear viscosities, were considered insignificant. M u n [22] characterized the extensional behavior of the three elastic liquids using the Rheometrics R P X , a commercial extensional rheometer of the opposed-jet type (Fuller et al [42]). It must be emphasized, though, that like most extensional rheometers, the R F X reports an apparent extensional viscosity value owing to its inability to sustain a uniform strain and strain rate throughout the liquid sample. Moreover, the R F X also suffers from corrections pertaining to inertia [43] and viscous losses [44]. Nevertheless, despite these shortcomings, there is general support for the R F X ' s ability to reveal qualitative differences in elasticity for dilute polymer solutions [22,44,45]. R F X data extracted from Mun 's PhD thesis [22] revealed both the 300K and 1000K P E O liquids to be extension-thickening, as evidenced by increases in their Trouton ratios above the Newtonian value of 3. This is shown in Figure 2.1, where the Trouton ratio is plotted against the Reynolds number corresponding to the flow inside the opposed-jets. This Reynolds number is thus a measure of the apparent extensional rate. The maximum Trouton ratio recorded for the 300K and 1000K P E O liquids was around 5 and 11, respectively. This implies that the 1000K sample was more elastic than the 300K sample. 57 The 100K PEO liquid did not extension-thicken, which may suggest elasticity near or below the measurement threshold of the RFX. 12 10 nj or 1 6 3 o Newtonian Trouton Ratio: 3 • 100KPEO x 300K PEO A1000KPEO A A AAA A A * A A* A AA A A A A A A A A A A „ x r c * 5 0 ^ * * : , ™ X ^x x* - A - f • A . * X X * x*x -- x - - * » > X X 10 100 1000 Reynolds Number in Opposed-Jet of RFX 10000 Figure 2 .1: Trouton ratio as a function of Reynolds number for the elastic PEO liquids. (Reproduced from Mun's PhD thesis [22]) An industrial F M , K E L T R A C K HiRail, was also included in the spray tests. Its instantaneous shear viscosity was measured up to a shear rate of 32000 s"1 using a H A A K E HS1 viscometer (see Appendix A). The shear flow curve conformed to a power-law model, as shown in Figure 2.2, with power (n) and consistency indices (m) of 0.5214 and 3610.9 mPa-s", respectively. K E L T R A C K HiRail's equilibrium surface tension was 39.7 mN/m, and fell slightly to 39.5 mN/m after flowing through the spray system. Note that these OL values are far lower than those of the test liquids in Table 2.1. The density of K E L T R A C K HiRail is 1.09 g/cm3. Oscillatory shear experiments revealed K E L T R A C K HiRail to be elastic; from Appendix A: Figure A.3, its elastic modulus was comparable in magnitude to its viscous modulus over a frequency range of 58 0.01 to 10 Hz, resulting in a phase angle of roughly 45°. Although these measurements were conducted within the linear viscoelastic regime, where deformations are much smaller and slower than those expected in an atomizer, the results still confirm the elastic nature of K E L T R A C K HiRail. Moreover, in Appendix A : Figure A.4, the apparent extensional viscosity of K E L T R A C K HiRail is shown to increase with the extensional strain. These measurements were made on a commercial capillary breakup rheometer (ThermoHaake CaBER [46]). Attempts at measuring the extensional viscosities of the elastic PEO liquids were unsuccessful owing to their exceptionally low shear viscosities. 1000 'i r r i • i r i i i i ~ i i ~ i i i i i i i i i i i i i r~r~i 1 -| I I I I M i l l I I I I I I I I | I I I I I i I I j 100 1000 10000 100000 Shear Rate [s 1] Figure 2.2: Shear viscosity of K E L T R A C K HiRail at 25°C. 59 2.3.3 Air-blas t Atomizer and Spray Setup The air-blast atomizer used is of the external-mix, plain-jet design. It is based on a commercial paint sprayer and is currently employed by a number of railway operators for applying liquid F M . The original atomizer made use of a rubber-duckbill (see Figure 2.3) to prevent excessive F M from dripping out of the otherwise open liquid orifice and clogging the atomizer. However, most of the present research was conducted using a modified version of this original atomizer, one which had the tip of the rubber-duckbill removed. This was done to overcome the challenges in calculating the liquid velocity and Reynolds number caused by the variable, elliptical flow area of the duckbill. Reliably measuring this area was difficult due to the flexible nature of rubber and visual hindrance imposed by the liquid stream. Removing the duckbill altogether was considered, but owing to the desire to maintain the same annular air orifice area, only the tip was cut off flush with the exit plane of the atomizer. Figure 2.4 shows the modified atomizer geometry; full engineering drawings of each component can be found in Appendix C. The inner diameter of the round liquid orifice (Dj) is 1.37 mm. The annular air orifice has inner (£),) and outer diameters (D0) of 4.06 mm and 4.72 mm, respectively, for an air gap of 0.33 mm. In order to keep its orifices clean, this atomizer employs the use of purge air. Five diametrically-opposed holes (see Figure 2.4) were drilled into the atomizer body and through to the internal air flow paths so that a portion of the incoming supply air can be diverted outside the atomizer. By means of an external shroud, the diverted air was aimed back at the atomizer orifices to clear away residual liquid buildup. Although effective in practice, this geometry complicates the calculation of the atomizing air velocity under sub-sonic conditions owing to the unknown mass fraction split between the purge air and atomizing air. 60 Annular Air Orifice 5 Liquid Orifice: Rubber-duckbill with Variable Elliptical Flow Area Figure 2.3: The original air-blast atomizer before undergoing modification to have its rubber-duckbill cut off. Sprayed liquids were collected in a tray placed approximately 1 m below the atomizer. The liquid flow was supplied by a gear pump, and measured using a graduated cylinder and stopwatch; this was confirmed during the spray tests with continuous balance readings. The air flow rate was monitored using a rotameter, and verified by solving the compressible duct flow equations using MATLAB® and input from pressure drop measurements made along the air line (see Appendix D for computer program). Liquid and air supply connections to the atomizer were made with flexible polyethylene tubing to minimize vibration transfer. Spray tests were conducted at a room temperature of 25±1°C and in atmospheric, stagnant air. Sketches of the liquid and air supply connections are shown in Figure 2.4. 61 Incoming Incoming Supply Air L , < l u ' d Supply Air Figure 2.4: The modified air-blast atomizer used in most of the present work. 62 Gear Pump HX—Q—CX-Valve Filter + Water Trap Air Rotameter Air-blast Atomizer Pressure Gauge Collection Tray ~1 m Compressed Air Supply Pressure Regulator / P r e s s u r e Regulator Figure 2.5: Liquid and air supply connections to the air-blast atomizer. 63 2.3.4 Particle Image Velocimetry Particle Image Velocimetry (PIV) is a non-intrusive, optical-based measurement technique used to obtain instantaneous whole-field velocities in a two dimensional plane. Its principles and development over the past twenty years have been described and reviewed by Adrian [47], Keane et al [48], and Raffel et al [49]. The general idea is to illuminate tracer particles in a flow field with two short pulses of a planar light sheet, during which two corresponding images are recorded over a known time separation. These image-pairs (IP) are then divided into interrogation areas (IA) and processed by a cross-correlation algorithm to obtain the average particle displacement in each IA. By knowing the time separation over which this displacement occurs, the average velocity is calculated; this procedure is then applied to every IA in the image domain to produce an entire velocity field. In the present application of PIV, the tracer particles were simply droplets produced by the atomizer. Appendix E outlines the experimental setup and procedures. In brief, a dual-head, frequency-doubled N d : Y A G laser (532 nm; max. 120 mJ per 5 ns pulse) was used to double-pulse a vertical laser-sheet, 1 mm in thickness, through the spray centerline. Image-pairs were recorded with a digital CCD camera ( R E D L A K E MegaPlus® ES1.0; 1008 (H) x 1018 (V) pixel; 8 bits) coupled to a Y A S H I C A 50 mm lens (F/4), producing a typical field-of-view of 161.9 (horizontal) x 163.5 (vertical) mm. The laser pulses were synchronized to the CCD camera through a pulse generator, while the laser-sheet optics were mounted on a linear rail to ensure consistent alignment. A l l of the experiments were performed in a dark room to minimize optical noise from ambient lighting. Figure 2.6 illustrates the PIV setup and Figure 2.7 is a sample PIV raw image of a water spray (one of a pair). 64 P I V Laser Figure 2.6: Schematic of the P I V setup. 163.5 mm Figure 2.7: Sample P I V image of a water spray (one of a pair). 65 The time separation between the two laser pulses was 38 ps. This value was chosen based on considerations such as resolvable spatial resolution, adequate droplet number-density, and velocity dynamic range. Image-pairs were processed using an adaptive-correlation algorithm embedded in Dantec's FlowManager software [50]. Adaptive-correlation improves upon conventional cross-correlation by allowing successive size reductions and offsets in the IA over multiple evaluation iterations. The amount by which an IA is offset is determined from an initial velocity estimate calculated by using cross-correlation. The result is increased spatial resolution without sacrificing velocity dynamic range. More importantly, in sprays, where droplet sizes and number-densities are often non-uniform, an adaptive algorithm increases the number of true correlations by relaxing the minimum droplet number requirement of 10 per IA such that it applies instead to the initial IA, which can be made large to capture more droplets. Image-pairs were processed using an initial IA size of 64 (H) x 128 (V) pixels, corresponding to 10.28 x 20.56 mm in physical space. A single iteration step was applied to arrive at a final IA size of 32 x 64 pixels or 5.14 x 10.28 mm. The horizontal and vertical IA overlaps were 75% and 50%, respectively. The resultant raw vector maps were subjected to a validation procedure to detect and replace spurious velocity measurements. This involved firstly a velocity range validation that rejected vectors under the following criteria: radial velocities exceeding 15 m/s and axial velocities above 100 m/s or below 0 m/s (i.e. upstream towards the atomizer). These criteria were selected by carefully examining numerous raw vector maps, in which the velocity bounds were gradually narrowed from initially large values until a majority of the unphysical vectors (having unrealistically large velocities) situated outside the spray boundaries were rejected. Of course, care was taken not to eliminate vectors of reasonable magnitude and direction appearing within the spray boundaries. Next, a moving average filter was applied to identify vectors that deviate by more than a prescribed amount from the average of the adjacent ( 3 x 3 window) vectors. Vectors detected as spurious were then replaced with the local average of the (accepted) adjacent vectors. Using this validation procedure, the typical number of vectors replaced was less than 10% of the total vectors lying within the spray boundaries. However, these did not 66 include vectors that were less than 30 mm (6AD„) downstream from the atomizer because the spray was too optically dense in this area, which produced excessive pixel saturation and led to poor correlation quality. To avoid peak-locking effects, droplet image diameters were verified to be more than 2 pixel-pitches wide [49]. The total relative uncertainty (cou) associated with a PIV velocity measurement can be calculated by summing the variances of the known error sources [51]: temporal error, scale error, peak location error. These are expressed in the following equation: to' = AX + (8 ^ scale scale 2 f + (1) Temporal error is caused by the uncertainty (8 t) in determining the exact time separation (At) between the two laser pulses, and it was measured to be negligible (less than 0.026% - see Appendix F for laser timing tests). Scale error is due to the uncertainty (8scale) in transforming the camera pixel coordinates to physical dimensions ( scale ), and its contribution was 0.1%). Peak location error arises from the uncertainty (8X) in locating the displacement peak ( A X ) within the correlation plane. Most modern correlation algorithms can achieve sub-pixel resolution by least squares fitting a 2-dimensional Gaussian function to the displacement peak. For experimentally recorded images, a 8X value of ±0.1 pixel is widely accepted [48,49,52]. Because a major contribution to cou now comes from the peak location error (on order of 1% vs. <0.1% for temporal and scale error), the uncertainty in the measured velocity for any reasonable At becomes independent of AX, and at an image conversion factor of 6.23 pixel/mm is equal to ±0.42 m/s. This implies that the total relative uncertainty associated with measured droplet velocities of say 10 m/s and 50 m/s is 4.2% and 0.85%, respectively. Time and length scales within a spray vary considerably depending on their spatial locations, leading to difficulties in extracting velocity information of the entire spray from a series of image-pairs captured over a set time separation. This is because the 67 relative uncertainty in locating the displacement peak varies over the spray domain and is highest near the spray boundaries where droplets travel at low velocities and undergo small displacements. As a result, the time separation of 38 us chosen for the ensuing tests was optimized for resolving axial droplet velocities at the spray centerline. For proper statistical representation of the spray, a sufficient number of image-pairs must be acquired. Preliminary testing has revealed that a minimum of 70 IP are needed in order to stabilize the mean axial centerline (MACL) droplet velocity to within experimental uncertainty; this convergence criterion was valid for all the test liquids and at every injection condition. Samples of the convergence of the M A C L droplet velocity along with its root-mean-square (RMS) deviation are shown in Figure 2.8 and Figure 2.9 (see Appendix E for additional samples). Therefore, to obtain an accurate representation of the dynamic behavior of the spray while complying with time and data storage limitations, 100 image-pairs were captured for each test run. These were ensemble-averaged at identical measurement locations, for which a 95% confidence interval, based on the z-normal distribution, was computed. This sampling methodology led to expected statistical uncertainties of about 3 to 5%, and confidence intervals ranging from approximately ±0.5 to ±3 m/s. 68 10 IP Mean + 10 IP RMS 20 IP Mean + 20 IP RMS - - - 50 IP Mean + 50 IP RMS — - 70 IP Mean + 70 IP RMS 100 IP Mean —I—100 IP RMS 50 wt.% Glycerin: 60 ml/min Atomizing Air Pressure: 55.2 kPa 20 40 60 80 100 120 Downstream Distance from Atomizer [mm] 140 160 Figure 2.8: Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs. 50 wt.% glycerin; QL = 60 ml/min; PA - 55.2 kPa. -10 IP Mean -20 IP Mean 50 IP Mean 70 IP Mean -100 IP Mean -10 IP RMS 20 IP RMS 50 IP RMS 70 IP RMS -100 IP RMS 100KPEO: 30 ml/min Atomizing Air Pressure: 55.2 kPa 95% Confidence Interval Shown RMS 20 40 60 80 100 120 Downstream Distance from Atomizer [mm] 140 160 Figure 2.9: Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs. 100K P E O ; QL = 30 ml/min; PA = 55.2 kPa. 69 2.3.5 Flash Photography A high intensity P A L F L A S H 500 light source and the previously mentioned PIV camera were used for imaging spray breakup details. A typical backlit setup was used, in which the spray was situated between the light source and camera such that liquid droplets and ligaments appeared dark on a bright background [53]. 2.3.6 Shadowgraphy Droplet sizing was attempted using an optical technique in which high-resolution, backlit photographs (shadowgraphs) of the spray were analyzed. This technique, referred to as shadowgraphy, has been used in various forms over the past fifty years [54-56]. Appendix G describes in detail the calibration, image analysis, and measurement procedures. Basically, a high intensity light source with a short pulse duration ( P A L F L A S H 500) was used to illuminate and "freeze" droplets in mid-flight while a camera (PCO Pixelfly digital CCD; 1360 (H) x 1024 (V) pixel; 12 bit), situated directly opposite to the light source, captured shadowgraphs through a far-field microscope (Navitar 12X zoom). The camera position was adjusted using a 3-axis traverse with an accuracy of 10 um in the radial directions (x, y) and 25 um in the axial direction (z). Figure 2.10 is a photograph of the experimental setup. Figure 2.11 is a sample shadowgraph of a water spray, in which the presence of droplets both inside and outside (i.e. beyond the depth-of-field) the measurement volume can be clearly discerned. 70 F i g u r e 2.10: P h o t o g r a p h o f the s h a d o w g r a p h y se tup . . * (a) (b) F i g u r e 2.11: S a m p l e s h a d o w g r a p h f o r d r o p l e t s ize m e a s u r e m e n t s : (a) r a w s h a d o w g r a p h , (b) p r o c e s s e d s h a d o w g r a p h w i t h l i q u i d f ea tu res i d e n t i f i e d a n d s i z e d . 71 The measurement volume is defined by the camera's field-of-view and depth-of-field. In order to resolve droplets as small as 10 urn in diameter, an image conversion factor of 0.525 pixel/um was required, which produced a field-of-view of 2.58 (H) x 1.94 (V) mm. A minimum droplet diameter of 10 pm was chosen because droplets that are any smaller will evaporate quickly and represent only a small fraction of the total liquid volume in the spray. The depth-of-field was estimated by traversing a transparent slide, on which a circle of known diameter was printed, along the camera axis and through the measurement volume. The depth-of-field was measured to be about 1 mm. Recorded shadowgraphs were processed digitally using a multi-step thresholding algorithm (La Vision, SizingMaster software), through which droplets situated within the measurement volume were differentiated from the background and from out-of-focus droplets based on contrast differences (see Appendix G for details on this thresholding procedure). Deciding whether or not a droplet is in focus is subjective. To this end, through a meticulous trial-and-error process, it was ensured that only droplets lying within the abovementioned measurement volume were accepted for size calculations. Droplets were sized by having their occupied areas on the shadowgraphs computed, from which equivalent spherical diameters were assigned based on the image conversion factor. In the present study, droplet sizing results are presented using the arithmetic mean diameter (Dw) and the volumetric median diameter (VMD), both measured at nine spatial locations in spray, as depicted in Figure 2.12. Due to light attenuation effects, all of the shadowgraphs were recorded at a downstream distance (z) of 152.4 mm from the atomizer exit plane. In this far region, the local droplet Weber number was on the order of 10"2, even for the larger droplets, which meant that secondary atomization was not expected. Due to the non-volatile nature of the test liquids and the moderate temperature (25°C) at which experiments were conducted, evaporation effects were negligible (see Appendix H for evaporation model). 72 Atomizer = 152.4 mm -g Figure 2.12: Nine sampling locations for droplet size measurements (all at z = 152.4 mm). 7 3 The DJO at each of the nine sampling locations was averaged together on a droplet number-weighted basis to provide a single indicator (Z) 1 0) of atomization quality for the entire spray. Although each shadowgraph represents a spatial-average, instantaneous-time measurement, multiple images were recorded and analyzed to provide time-average statistics. Preliminary testing has revealed that with the present optical setup, approximately 100 shadowgraphs were required at each sampling location in order to measure Dio and VMD to within 5% repeatability. Depending on the test liquid and flow rate, anywhere from 500 to 2000 droplets were analyzed at each sampling location. Assuming high-quality images are captured and proper calibration procedures are performed, the accuracy of the shadowgraphy technique is limited by the number of pixels a droplet occupies in the image. In this sense, it is advantageous to use a very small field-of-view in order to allocate as many pixels as possible to a single droplet. However, given the need to acquire a sufficient number of droplets for reliable statistics, a compromise is usually made that allows for the mean droplet diameter to span at least 20 pixels. The uncertainty in droplet size measurements, as estimated from imaging a series of calibration spheres, is on the order of 3 to 5% for droplet diameters greater than 30 um, and about 5 to 10% for droplet diameters nearing the low end of the measurement threshold of lOum [57]. 74 2.4 Viscoelastic Atomizat ion Results The experiments were conducted at two liquid flow rates (QL), 30 and 60 ml/min [±1.1 ml/min], which produced velocities inside the liquid orifice of UL = 0.34 and 0.68 m/s [±0.012 m/s], respectively. Unless otherwise noted, the atomizing air pressure (PA) was kept constant at 55.2 kPa [±3.4 kPa], corresponding to a total mass flow rate (rhA) of 2.31xl0"3 kg/s [±3.33xl0"5 kg/s]. As alluded to earlier, because this atomizer employs purge air, and at PA = 55.2 kPa has not reached choked conditions, the exact mass fraction of the total incoming air flow going into the annular orifice, where the most effective atomization takes place, was unknown. As a general estimate, owing to the comparable flow areas of the annular orifice (AALNMJZLNG , see Figure 2.4) and the five purge air holes (AMGE), it is reasonable to assume that the total incoming air flow is split proportionally to these respective areas. ^momizmg I Spurge =1-16 and so the atomizing air velocity was UA = 226.7 m/s [±6.1 m/s]. It should also be mentioned that the effective area through which the purge air flows just before contacting the atomizer orifices is actually larger than both A and AATOMI!I (in fact, about 45 times larger). Consequently, the purge air velocity is much lower than the atomizing air velocity and should not affect atomization. In the present study, the liquid Reynolds number (ReL) varied between 5.8 ( K E L T R A C K HiRail) and 928 (water), while the aerodynamic Weber number (WeA) exceeded 1000 for all test conditions. The air-liquid mass ratio (ALR) and the momentum flux ratio (M) ranged from 1.1 to 7.0 and 126 to 2322, respectively. The characteristic shear viscosity used in calculating the ReL for K E L T R A C K HiRail was chosen based on the wall shear rate (y) experienced inside the liquid orifice; for a non-Newtonian liquid with a power-law index, n, this is given by [24]: (2) 75 Although the action of the atomizing air will subject the liquid to additional shear, it is difficult to estimate the extent of this effect owing to the complex flow fields. As such, the characteristic shear viscosity calculated based on the instantaneous wall shear rate should only be taken as an approximation. 2.4.1 Breakup Visualization A qualitative description of the breakup patterns exhibited by the test liquids in Table 2.1 and K E L T R A C K HiRail is presented in this section. The goal is to compare the breakup features of these various liquids, and to observe changes induced by differences in the shear viscosity and elasticity. The liquids were atomized at QL = 60 ml/min and PA = 55.2 kPa. 2.4.1.1 Effect of Shear Viscosity Figure 2.13 captures the effect of increasing shear viscosity in a set of inelastic liquids. A rise in ns by two orders of magnitude from 0.9 mPa-s (water) to 154.2 mPa-s (90 wt.% glycerin) resulted in visibly larger droplets. This observation is consistent with previous Newtonian droplet size measurements [6,20]. Furthermore, water, 50 wt.% glycerin (Figure 2.16a), and 80 wt.% glycerin demonstrated a disintegration pattern resembling Chigier and Farago's "super-pulsating sub-mode" [9]. The appearance of this mode is marked by an extremely short jet breakup length, combined with periodic pulsations that lead to temporal and spatial fluctuations in the droplet number-density within the spray. In fact, this pulsating behavior can be seen more clearly in the PIV images in the form of oblique wave patterns. These are shown in Figure 2.14 for inelastic, elastic, and F M liquids all at the same injection condition. Note that these are planar images representing only a two dimensional slice of the spray. The oblique wave patterns were very apparent in the inelastic liquids, but were not so pronounced in the elastic PEO liquids and K E L T R A C K HiRail. 76 Another observation from Figure 2.14 is that the spray angle (full) appears to be insensitive to liquid type. Inspection of the mean PIV (Mie) images confirmed that the spray angle was not only insensitive to liquid type, but also to the liquid flow rate (between 30 and 60 ml/min). The spray angle was measured to be 28±1°. Figure 2.15 shows a sample mean Mie image used for determining the spray angle. Focusing back on the breakup photographs in Figure 2.13, by increasing the shear viscosity to 805.8 mPa-s (99.5 wt.% glycerin), a "rope-like" pattern was observed. The liquid stream remained intact and underwent erratic excursions away from its centerline. Radial motions appear to be induced by large-scale turbulent structures. 77 Figure 2.13: Photographs of breakup for inelastic liquids having similar aL and pL, but different J/ s: (a) water, (b) 80 wt.% glycerin, (c) 90 wt.% glycerin, (d) 99.5 wt.% glycerin. QL = 60 ml/min; PA = 55.2 kPa. 7 8 Figure 2.14: PIV images showing the presence of oblique wave patterns: (a) water, (b) 50 wt.% glycerin, (c) 80 wt.% glycerin, (d) 100K PEO, (e) 300K PEO, and (f) KELTRACK HiRail. Field-of-view: 161.9 (H) x 163.5 (V) mm; QL = 60 ml/min; PA = 55.2 kPa; negative image. 79 Figure 2.15: Sample mean Mie image used for determining the spray angle. Field-of-view: 161.9 (H) x 163.5 (V) mm; 80 wt.% glycerin; QL = 60 ml/min; PA = 55.2 kPa. 2.4.1.2 Effect of Elasticity Figure 2.16 captures the effect of increasing elasticity in liquids exhibiting comparable surface tensions, densities, and rate-independent shear viscosities. 50 wt.% glycerin is included here because its tjs along with its oi and pi were similar to those of the elastic PEO liquids, allowing comparisons to be made with a completely inelastic baseline. As mentioned earlier, 50 wt.% glycerin disintegrated in a manner similar to water, collapsing into a multiplicity of small droplets almost immediately downstream of the atomizer. In contrast, all three of the elastic PEO liquids displayed filamentary structures containing large-scale ligaments. The physical scale of these ligaments increased with PEO molecular weight, and hence elasticity. For 100K and 300K PEO, spherical droplets were often observed at the ends of the ligaments, indicating the onset of pinch-off. The ligaments appear to have experienced significant stretching at high elongational rates; these high rates-of-strain were deduced from the short time-scales inherent to the atomization process. As a result, it is believed that, through molecular reorientation and stretching, the extension-thickening behavior exhibited by these elastic ligaments induced additional tensile stresses in their cross-sections, which enhanced their stability against capillary forces. Discrete droplet formation was delayed until farther downstream where relative air-liquid velocities were reduced. So, in agreement with findings of Mun et al [20] and Mansour and Chigier [21], liquid elasticity is predicted to increase droplet sizes. 80 Figure 2.16: Photographs of breakup for liquids having similar aL, ns, and pL, but different elasticities: (a) inelastic 50 wt.% glycerin, (b) 100K P E O , (c) 300K P E O , (d) 1000K P E O . QL = 60 ml/min; PA = 55.2 kPa. 8 1 2.4.1.3 K E L T R A C K HiRai l Figure 2.17 shows the breakup pattern of K E L T R A C K HiRail. Note the presence of large-scale ligaments, filamentary structures, and a membrane (center of image). Because K E L T R A C K HiRail is opaque, it imaged to a higher contrast than the transparent solutions of PEO and glycerin. With this optical inconsistency in mind, there are indeed similarities between the breakup patterns of K E L T R A C K HiRail and 300K PEO (Figure 2.16c). Although one exceptional difference is that the onset of ligament pinch-off is more apparent in 300K PEO than in K E L T R A C K HiRail. This may be related to the reduced surface tension of K E L T R A C K HiRail. Figure 2.17: Photograph of breakup for K E L T R A C K HiRail. QL = 60 ml/min; PA = 55.2 kPa. 82 2.4.2 Droplet Size Measurements Assuming Stokes flow, the aerodynamic relaxation time of a droplet increases with the square of its diameter. Therefore, in spray coating, the diameter of a droplet is one of the main factors determining whether it will deposit onto the target surface or be carried away by the surrounding air jet. In view of this, droplet size measurements were performed on three inelastic liquids (water, 50 wt.% and 80 wt.% glycerin), two elastic liquids (100K and 300K PEO), and K E L T R A C K HiRail. The results for water are presented and discussed first because they are the simplest to understand. Radial Dio profiles for water are shown in Figure 2.18 and Figure 2.19 corresponding to the x and y radial directions (see Figure 2.12 for position reference), respectively. Also included on these plots are the RMS deviation of the D\o and the droplet number (JV) at each sampling location. Error bars on the Dio symbols represent the 95% confidence interval as computed using the z-normal distribution. Several observations can be made at this point. Higher Dio values were measured near the spray periphery. This observation has been reported by other researchers [34,41,58,59]. Eroglu and Chigier [8] noted from their air-blast atomization research that the flapping motion of the unstable liquid jet can launch droplets radially away from the spray centerline. Thus, larger droplets are expected to continue farther along in their initial trajectory owing to their increased inertia [58]. Although the air-blast atomizer used in the present work did not incorporate swirl in its design, high-speed videos captured of water and other liquids revealed swirling motions in the spray as evidenced by helical droplet trajectories. The origin of these swirling motions is unclear but the resultant centripetal forces may cause larger droplets to migrate farther towards the spray periphery than smaller droplets. The RMS deviation of the Dw also exhibited higher values near the spray periphery, though this was attributed mainly to reduced droplet numbers. The Dio at each sampling location rose by about 10 to 15% as the liquid flow rate increased from 30 to 60 ml/min. This result was expected since it is well established that reducing the ALR (from 2.48 to 1.24 in this case) leads to larger droplets [2]. It should be 83 emphasized, however, that because the liquid velocity (UL < 1 m/s) was two orders of magnitude lower than the atomizing air velocity (UA - 226.7 m/s), even a doubling of the liquid flow rate produced only a minor change in the relative velocity at the air-liquid interface. Consequently, the observed increase in droplet size was not attributed to changes in the relative air-liquid velocity, but rather to the increased momentum in the liquid stream; by doubling the liquid flow rate (30 to 60 ml/min), the momentum flux ratio reduced from 539 to 135. From the work of Eroglu et al [60], it has been shown that increasing the momentum in the liquid stream results in a longer jet breakup length and, hence, larger droplets. Although values of D/o were fairly symmetric with respect to the spray centerline, the spatial distribution of N and the droplet volume (Figure 2.20) displayed obvious asymmetries. For example, from inspection of Figure 2.18, the value of TV at JC = 25.4 mm and QL = 30 ml/min was only one-third of the corresponding value at x = -25 A mm. Similarly, in Figure 2.20, the droplet volume measured at x = 25A mm and QL = 30 ml/min was less than half of the corresponding value at x = -25.4 mm. In general, the spray appears to be skewed significantly towards the negative x and negative y directions. Although skewness was observed in the breakup visualization photographs and the PIV images, the extent there was very minor at less than 2° off-axis. These observed asymmetries are actually quite common in atomizers of such small dimensions and have been reported to varying degrees elsewhere [58,61,62]. They are presumably the result of geometric asymmetries in the atomizer orifices. The atomizer used was manufactured using standard machining practices, in which even a strict tolerance of ±0.03 mm (~ ±0.001 inches) can skew the alignment of the central liquid tip enough to cause a 10% variation in the annular air gap. Moreover, optical and vernier-caliper measurements confirmed the presence of some eccentricity in the present annular air orifice. The magnitude of this eccentricity, however, was difficult to quantify accurately because of the erratic dimensions of the flexible rubber-duckbill base - a rough estimate of 0.10 mm is reasonable. 84 50 45 40 35 ^ 30 c o i 2 5 Q 20 15 10 —•— D10 (60 ml/min) —*— D10 (30 ml/min) _ H _ n n o / e n ~ . i / M : « \ _ ji _ D i n e / o n - -m - r \ i v i o ^ u u M I I M I I I I I ; - • a - N (60 ml/min) - • A - N (30 ml/min) n ^  ^  3^  ^ „. ^ *~ " ~- — N A — ~ ~~ S N \ • „ N . V - - * - - v A " • -1 nl -30 -20 20 3000 2500 0) E 3 O Q . O Q 1000 30 - 1 0 0 1 0 Radial Position: x [mm] Figure 2.18: Dm RMS, and TV for water at QL = 30,60 ml/min, PA = 55.2 kPa (JC direction). 50 45 40 35 30 c" o o 25 E S 20 15 1 0 -30 - H » — D 1 0 ( 6 0 ml/min) — * — D 1 0 ( 3 0 ml/min) _ m - D M C /cn m i f m ; n \ . ^ . D M C /QO m l / m l n X - - B - N ( » j y u u llllfllllli/ *•* I M V I U i i i i / r i r u i / 6 0 ml/min) - -A - N ( 3 0 ml/min) n " " — ~ ~ y " - " T \ s y zf — "x N \ h"" . — \ \ m . *• • -* ~ \ ID * - i -20 20 3000 2500 2000 1500 1000 0) .o E 3 4) Q. O o 30 - 1 0 0 1 0 Radial Position: y [mm] Figure 2.19: D,0, RMS, and T V for water at QL = 30,60 ml/min, PA = 55.2 kPa 0 direction). 85 1.25E+08 O.OOE+00 -10 0 10 Radial Position: x, y [mm] Figure 2.20: Droplet volume distribution for water at QL = 30,60 ml/min, PA = 55.2 kPa. 3.5 (0 CC a> E 3 o > a 2 a 2.5 1.5 0.5 -30 —•-x Direction - 0 - y Direction -20 20 -10 0 10 Radial Position: x, y [mm] Figure 2.21: DVR for water at QL = 30,60 ml/min, PA = 55.2 kPa. 30 86 The observed asymmetric behavior may possibly be due to another cause. A misaligned liquid tip creates an eccentric annular air orifice, which causes the emerging liquid stream to deflect towards a preferential direction due to pressure differences in the air. In other words, the spatial distribution of liquid around the circumference of the liquid orifice becomes non-uniform. However, owing to the high relative air-liquid velocities, a similar droplet size distribution is produced everywhere locally, regardless of tangential position. These droplets are then transported downstream in a manner that still reflects the initial non-uniform liquid volume distribution. In this way, the Dio values can remain spatially symmetric, while N and the droplet volume become dependent on tangential position. To support the quantitative accuracy of the droplet size measurements, the droplet volume ratio (DVR), defined as the local ratio of the droplet volume at Qi = 60 ml/min to the equivalent value at Qi = 30 ml/min, is plotted in Figure 2.21. If the droplet volumes reported in Figure 2.20 were meaningful, then a DVR value of 2 should be expected at every sampling location. Results indicate that DVR values were within approximately 20% of the expected ratio of 2. This level of variation is unsurprising given that the spatial distribution of liquid within the spray probably shifts as the liquid flow rate is changed. The global droplet volume ratio, DVRglobal, was 2.08, which is within 5% of the expected value. To further substantiate the quality of the measurements, the volume flux at each sampling location was calculated using data provided by PIV velocity measurements (presented in the following sections). These fluxes were then used to provide a crude estimate of the liquid flow rate, to which balance measurements were compared. To begin, the droplet number concentration (CN) at each sampling location (/) was calculated based on the measurement volume dimensions stated in Section 2.3.6: CH ' « 1 measurement volume (3) 87 CN was multiplied by the mean axial droplet velocity (LO at the spatial center of each measurement volume to obtain the droplet number flux (FIUXN): FluxN=CNI-UI (4) FIUXN at each sampling location was assumed to flow through predefined areas in the spray cross-section, as sketched in Figure 2.22. Measurements at radial distances of 0 mm (centerline), 12.7 mm, and 25.4 mm were assigned cross-sectional areas of Al, A2, and A3, respectively. Figure 2.22: Sketch of the partitioned spray cross-section used in droplet volume flux calculations. The resultant droplet number flow rate (#/s) was converted to a liquid volume flow rate (ml/s) by multiplying it with the volume of a droplet having a diameter equal to the local volume mean diameter. The total liquid flow rate in the spray was then computed by summing up the contributions from the nine sampling locations. The estimated flow rate for water was 58.5 ml/min and 29.6 ml/min, compared with actual balance measurements of 60 ml/min and 30 ml/min, respectively. 88 There were a number of underlying approximations made in the above calculation, some more valid than others. The one that is most likely to draw criticism is the assumption that very little liquid volume is distributed beyond a radial distance of 25.4 mm, when in fact Figure 2.20 shows the droplet volumes to be largest near the spray peripheries. The weakness in this assumption, however, is alleviated somewhat by recognizing that the mean axial droplet velocity at a radial distance of 25.4 mm was only a fifth of its value at the spray centerline (see Appendix E). A l l things considered, this crude estimate of the liquid flow was meant to be just that, and arriving at a result that is within even 50% of the actual flow rate is already encouraging. The Dw, total droplet volume, and total N at the two liquid flow rates are plotted in Figure 2.23, Figure 2.24, and Figure 2.25, respectively, for comparison among all the test liquids. Moreover, Table 2.2 lists the D 1 0 , total droplet volume, total N, global DVR, and estimated flow rate. The remainder of the droplet sizing results, including number and cumulative volume distributions, can be found in Appendix G. Most of the test liquids exhibited qualitative Dio characteristics resembling those of water, in that the Dio increased with radial position and liquid flow rate. Inspecting the N and droplet volume distributions for the glycerin and PEO solutions shows that the previously observed asymmetries are less apparent at higher shear viscosities and elasticities. Table 2.2: Summary of droplet sizing results at QL = 30,60 ml/min, PA = 55.2 kPa. Liquid Qi [ml/min] Ao [um] Total N Total Liquid Volume [um3] DVRgi0bal Estimated QL [ml/min] Water 30 30.1 10712 2.92E+08 2.08 29.6 60 33.8 15249 6.09E+08 58.5 50 wt.% Glycerin 30 30.3 7142 2.08E+08 2.59 18.2 60 33.1 14057 5.38E+08 49.9 80 wt.% Glycerin 30 29.4 5971 1.69E+08 1.77 14.5 60 30.9 9177 2.99E+08 26.3 100K PEO 30 29.1 6785 1.97E+08 2.65 21.0 60 33.1 9778 5.22E+08 45.1 300K PEO 30 31.5 4545 1.88E+08 2.27 17.8 60 34.9 5943 4.28E+08 30.7 KELTRACK HiRail 30 37.6 3178 3.50E+08 1.82 25.7 60 40.7 3928 6.38E+08 36.9 89 When comparing the results of water to those of 50 wt.% and 80 wt.% glycerin, one would expect the glycerin solutions to exhibit larger droplet sizes owing to their higher shear viscosities. This was, however, not observed in the present study. By examining Table 2.2 or Figure 2.23, Z)10 for all of the inelastic glycerin liquids and also the elastic PEO liquids were nearly the same as or slightly lower than the value for water (maximum variation of approximately 5% and 10% at Qi = 30 and 60 ml/min, respectively). Such behavior contradicts previous findings [1,2,6,20], including those inferred from breakup visualization in Section 2.4.1, where droplet sizes of the inelastic and elastic liquids were shown to increase with shear viscosity and elasticity, respectively. The unphysical £>10 behavior is speculated to be due to a statistical artifact. Because large droplets contain most of the liquid volume, they are relatively few by number. Therefore, the probability for a large droplet to pass through the spatially-fixed measurement volumes is lower than that for a small droplet. To put it another way, because the total cross-sectional area of the measurement volumes is small relative to that of the spray, the likelihood of an odd large droplet passing through, as opposed to between, the sampling locations is low. The implication is that results for the viscous glycerin and elastic PEO liquids may be representative of only the smaller droplet size classes. Support for this hypothesis can be found by examining the droplet volume (Figure 2.24) and number plots (Figure 2.25). At equivalent liquid flow rates, an increase in shear viscosity from 0.9 to 46.7 mPa-s (water -> 50 wt.% -> 80 wt.% glycerin) led to a reduction in the droplet volume and number. The same behavior was demonstrated by the PEO liquids through an increase in elasticity (50 wt.% glycerin -> 100K PEO -> 300K PEO). Since both shear viscosity and elasticity increases have been known to suppress satellite droplet formation [1,2,20,27,29-32], it is believed that the Dw and droplet volume discrepancies were attributed to a statistically-induced exclusion of the larger droplets, rather than the smaller droplets. This effect may be combined with the possibility that the spatial coverage of the sampling locations was inadequate, thereby allowing a significant number of the larger droplets traveling beyond a radial distance of 25.4 mm to be ignored. 1 90 D,0 [micron] Figure 2.23: Liquid Flow Rate [ml/min] Mean D10 comparison at QL = 30,60 ml/min, PA = 55.2 kPa. 7.00E+08 6.00E+08 5.00E+08 4.00E+08 Droplet Volume [micron3] 3.00E+08 2.00E+08 1.00E+08 0.00E+00 Liquid Flow Rate [ml/min] Figure 2.24: Droplet volume comparison at QL = 30,60 ml/min, PA = 55.2 kPa. 91 18000 16000 14000 12000 10000 Droplet Number 8000 6000 4000 2000 Liquid Flow Rate [ml/min] Figure 2.25: Droplet number comparison at QL = 30,60 ml/min, PA = 55.2 kPa. Owing to the expected presence of ligaments in the shadowgraphs of the elastic PEO liquids and K E L T R A C K HiRail, the centricity filter in the sizing algorithm was purposely relaxed for these liquids. There were, however, virtually no ligaments observed in the shadowgraphs of 100K and 300K PEO; the ligaments depicted in Figure 2.16 had presumably collapsed under capillary forces by the time they reached z = 152.4 mm. In contrast, K E L T R A C K HiRail displayed ligaments on several occasions; they were in various shapes, sizes, and orientations, often interspersed with smaller droplets, as shown below in Figure 2.26. Figure 2.26: Shadowgraphs of K E L T R A C K HiRai l showing the presence of ligaments. 92 D 1 0 values for K E L T R A C K HiRail were higher than that of the other test liquids by about 25% and 20% at QL = 30 and 60 ml/min, respectively. This result agrees with the expectation that elasticity increases droplet sizes. However, due to the presence of ligaments in the two-dimensional shadowgraphs, the equivalent spherical diameters reported for K E L T R A C K HiRail require careful interpretation. For instance, imagine a ligament shaped like a cylinder. If this ligament is imaged with its axis facing the camera, the resultant shadowgraph reveals a circular object and the sizing algorithm attempts to assign an equivalent diameter not knowing that this ligament may have an aspect ratio much larger than unity. Consequently, the reported diameter tends to underestimate the actual ligament volume. Conversely, i f a thin membrane is imaged with its plane facing the camera, then the reported diameter tends to overestimate the actual volume. These biases aside, it is believed that because a large fraction of the total K E L T R A C K HiRail volume resided in the form of ligaments, as opposed to spherical droplets, the probability of them (or a section of each ligament) appearing clearly enough within the measurement volumes to be recognized and sized was comparatively higher than that of the glycerin and PEO droplets. Additionally, there could also have been a re-distribution of the K E L T R A C K HiRail volume within the spray boundaries that allowed for more droplets and ligaments to pass through the sampling locations. Altogether, these effects are thought to have contributed to the higher £>10 values. Support for this hypothesis can be found in the droplet volume measurements (Figure 2.24), which show K E L T R A C K HiRail to have values comparable to those of water; the slight overshoots may be related to biases introduced from imaging ligaments in various orientations. In view of the proposed statistically-induced exclusion of the larger droplets (containing the bulk of the liquid volume) as the cause of the unphysical DW values, it is more appropriate to employ a representative diameter based on the droplet volume than on the droplet number. Hence, the volumetric median diameter (VMD) is considered. Figure 2.27 and Figure 2.28 depict the cumulative volume distributions of the test liquids at QL = 30 and 60 ml/min, respectively, while Figure 2.29 summarizes the corresponding VMD values. 93 Droplet Diameter [micron] Figure 2.27: Cumulative volume distribution at QL = 30 ml/min, PA = 55.2 kPa. N N N n N <vN K . N 6^ r> ^ rJS ^ K N n * - o-N K S <•> r-S O-N n N kN / l N O N O N Droplet Diameter [micron] Figure 2.28: Cumulative volume distribution at QL = 60 ml/min, PA = 55.2 kPa. 94 •Water 60 30 Liquid Flow Rate [ml/min] Figure 2.29: VMD comparison at QL = 30,60 ml/min, PA = 55.2 kPa. From Figure 2.27 and Figure 2.28, it is apparent that the elastic PEO liquids and K E L T R A C K HiRail both have a greater percentage of their volumes residing in large droplets than the inelastic glycerin liquids and water. Although the VMD for 50 wt.% and 80 wt.% glycerin did not differ significantly from that of water, the VMD for 100K PEO, 300K PEO, and K E L T R A C K HiRail all exhibited notable increases above the values for the inelastic glycerin liquids and water, as shown in Figure 2.29. It is reminded that the quantitative accuracy of these V M D values is still suspect owing to the exclusion of a significant fraction of the total liquid volume in the measurements. Even so, it is apparent that the VMD is more responsive to changes in the droplet size than fhe£) 1 0 . 95 2.4.3 Mean Axial Centerline Droplet Velocity In spray coating, a droplet's impingement behavior is strongly dependent on the normal velocity at which it strikes a surface [63,64]. Accordingly, the M A C L droplet velocity is presented here as a function of the downstream distance from the atomizer orifice (z). In the near region of the spray, the droplets, regardless of their size, are slower than the carrier air jet and will accelerate under the influence of viscous and pressure forces. However, the magnitude of this acceleration depends, in part, on the droplet size. Smaller droplets will experience stronger accelerations because of their higher drag-to-momentum ratios. For simplicity, i f Stokes' drag law is applied, then the acceleration of a droplet is inversely proportional to the square of its diameter. In our tests, droplet velocities in the near region could not be resolved because the spray was too dense. Eventually, the droplets will reach a peak velocity as the relative velocity between them and the carrier air is reduced. Larger droplets, owing to their increased inertia, tend to overshoot the velocity of the carrier air [41], while the smaller droplets are able to relax quickly, following the air with minimal overshoot. Because the overshoot for large droplets occurs at relatively far downstream distances and after the carrier air velocity has had an opportunity to decay, the peak velocities reached are generally lower than those of smaller droplets. Farther downstream, larger droplets can better preserve their initial momentum, traveling longer distances before eventually settling to the carrier air jet velocity. In the sections to follow, PIV results are presented on plots of the M A C L droplet velocity versus z. Included on these plots are the 95% confidence interval as computed using the z-normal distribution with 100 independent observations (image-pairs), and the RMS deviation. The overall trend shows the M A C L droplet velocity and its RMS decaying with increasing z. Often, a velocity plateau was observed at 30 < z < 40 mm, indicating a transition between droplet acceleration and deceleration. Results for 90 wt.% glycerin, 99.5 wt.% glycerin, and 1000K PEO are not shown because these liquids did not adequately atomize, producing far too few droplets for proper PIV correlations. As 96 mentioned earlier, owing to excessive pixel saturation and large-scale ligament formation, data nearest to the atomizer (z < 30 mm or 6AD0) were deemed unreliable and rejected; thus, only results for z > 30 mm are shown. The apparent asymmetries in the droplet volume distribution observed earlier were absent in the PIV images. The mean axial droplet velocities (U) were fairly symmetric with respect to the spray centerline. Radial profiles of U became self-similar past a certain downstream distance from the atomizer, and displayed a typical Gaussian distribution; a sample of the non-dimensional axial velocity profile is shown in Figure 2.30 for water at QL = 60 ml/min (additional samples can be found in Appendix E). A l l of the other test liquids exhibited a similar profile, zo refers to the virtual origin and was found by fitting the following linear correlation function to the droplet deceleration curve: Uc is simply the M A C L droplet velocity at the z axial station, while B is the deceleration constant. The shape of the non-dimensional axial velocity profiles was consistent with the results of Vega et al [58], who used a Phase Doppler Particle Analyzer to measure the axial velocity of water droplets produced from an air-blast atomizer. Also plotted on Figure 2.30 is the non-dimensional axial velocity profile of a round, single-phase turbulent jet as measured using a laser-Doppler anemometer (Hussein et al [65]). To assess the influence of the atomizer orientation on droplet velocities, several PIV tests were conducted with the atomizer rotated at random tangential positions. No significant differences in mean droplet velocities were found. The effects of QL, shear viscosity, elasticity, and PA on the M A C L droplet velocities are now discussed. UA_l z \ (5) o J 97 Figure 2.30: Sample non-dimensional radial profile of the mean axial droplet velocity for water at QL = 60 ml/min, PA = 55.2 kPa. 2.4.3.1 Effect of Liquid Flow Rate For all of the liquids tested, the M A C L droplet velocity was found to be insensitive to liquid flow rate variations between 30 and 60 ml/min. Figure 2.31, Figure 2.32, and Figure 2.33 depict this observation for sample inelastic (water), elastic (100K PEO), and K E L T R A C K HiRail liquids, respectively. For brevity, only results at the higher flow rate of QL = 60 ml/min are shown from this section onwards. 98 80 z [mm] Figure 2.31: M A C L droplet velocity for water at QL= 30,60 ml/min, PA = 55.2 kPa. 160 160 Figure 2.32: 80 z [mm] M A C L droplet velocity for 100K P E O at QL= 30,60 ml/min, PA = 55.2 kPa 99 160 Figure 2.33: M A C L droplet velocity for K E L T R A C K HiRail at QL = 30,60 ml/min, PA = 55.2 kPa. 100 2.4.3.2 Effect of Shear Viscosity In Figure 2.34, the effect of shear viscosity on the M A C L droplet velocity for a series of inelastic liquids (water, 50 wt.% and 80 wt.% glycerin) is shown. The most viscous liquid, 80 wt.% glycerin (rjs = 46.7 mPa-s), demonstrated lower droplet velocities than both water (rjs= 0.9 mPa-s) and 50 wt.% glycerin (//$= 5.1 mPa-s) at 30 < z < 60 mm. Lorenzetto and Lefebvre [6] have noted that increasing the shear viscosity leads to larger droplets. It is hypothesized that here the larger 80 wt.% glycerin droplets were unable to accelerate to as high of a peak velocity owing to their reduced drag-to-momentum ratios. For z > 60 mm, the M A C L droplet velocities of all the inelastic droplets converged to a common decay, suggesting that they have relaxed sufficiently to the carrier air jet velocity. From breakup visualization in Section 2.4.1, the droplet sizes of these inelastic liquids were shown to increase with shear viscosity. Consequently, a common M A C L droplet velocity decay implies that droplet sizes and velocities were uncorrelated for these inelastic liquids at far downstream distances. 60 50 -Water -50 wt.% Glycerin -80 wt.% Glycerin -m— Water (RMS) • -A — 50 wt.% Glycerin (RMS) -*—80 wt.% Glycerin (RMS) 0 20 40 60 80 100 120 140 160 z [mm] F i g u r e 2 .34 : M A C L d r o p l e t v e l o c i t y f o r i ne l as t i c l i q u i d s a t QL = 60 m l / m i n , PA = 55.2 k P a . 101 2.4.3.3 Effect of Elasticity Figure 2.35 compares the M A C L droplet velocity of 50 wt.% glycerin to that of the two elastic PEO liquids. A l l three of these liquids exhibited similar shear viscosities, surface tensions, and densities; they differed primarily through elasticity. As noted from Figure 2.34, the behavior of the 50 wt.% glycerin droplets can be taken as representative of the carrier air velocity in the far region of the spray (z > 60 mm). Over the entire downstream distance range examined, elastic PEO droplets were consistently faster than the inelastic 50 wt.% glycerin droplets. This suggests that the elastic droplets, owing to their significantly greater size and inertia, were better able to maintain their initial momentum against decelerating drag forces and were unable to relax fully to the carrier air jet velocity within the image domain. For z > 60 mm, the more elastic 300K PEO liquid exhibited higher droplet velocities than the 100K PEO liquid; the magnitude of this difference was about 2 to 3 m/s. However, at 30 < z < 60 mm, droplet velocities for the two elastic PEO liquids were statistically similar. 60 50 -50 wt.% Glycerin -100K PEO -300KPEO -KELTRACK HiRail -50 wt.% Glycerin (RMS) 100KPEO (RMS) -300KPEO (RMS) - KELTRACK HiRail (RMS) 80 100 120 140 160 z [mm] Figure 2.35: Comparison of MACL droplet velocity among inelastic and elastic liquids at QL = 60 ml/min, PA = 55.2 kPa. 102 Further, results indicate that the elastic PEO droplets out-accelerated the 50 wt.% glycerin droplets at 30 < z < 60 mm, which seems counterintuitive given their expected size difference and may instead be attributed to artifacts or biases in the correlation algorithm owing to the presence of ligaments. Nevertheless, farther downstream at z > 60 mm, the majority of the elastic ligaments have already collapsed, and so data in this far region is more reliable. Figure 2.35 also depicts the M A C L droplet velocity decay for K E L T R A C K HiRail. For z > 60 mm, K E L T R A C K HiRail droplets were faster than the 50 wt.% glycerin droplets and behaved similarly to the 100K PEO droplets, which again, may be indicative of larger droplets with slower relaxation scales. 2.4.3.4 Effect of Atomiz ing A i r Pressure The effect of atomizing air pressure was examined separately using the original air-blast atomizer with the full rubber-duckbill. This configuration is of industrial importance because it is used by railway operators for F M application. In view of this, only results for K E L T R A C K HiRail are presented. Again, the M A C L droplet velocity was found to be insensitive to liquid flow rate variations; only results at QL = 60 ml/min are shown for brevity. Atomizing air pressures were varied from the initial PA = 55.2 kPa up to PA = 193.1 kPa in 27.6 kPa increments. Figure 2.36 shows the explored ranges of the ALR and M. As depicted in Figure 2.37, the M A C L droplet velocity increased with the atomizing air pressure. The RMS deviation of the M A C L droplet velocity also increased with atomizing air pressure; this was likely due to enhanced turbulent fluctuations, and the production of smaller droplets, which were better able to follow those fluctuations. 103 a. u. E 3 400 350 300 250 200 c a> E 150 o 100 50 - B - Momentum F —•-Air-liquid Ma -lux Ratio ss Ratio 2.5 1.5 cs QC CO IS) cs 2 "D 3 0.5 50 200 250 Figure 2.36: 100 150 Atomizing Air Pressure [kPa] ALR and M for various PA (KELTRACK HiRail at QL = 60 ml/min). 90 80 70 60 (A 1 O ° 50 4) > 0) a. 40 s Q O 30 < s 20 10 P = 55.2 kPa P = 82.7 kPa P = 110.3 kPa P= 137.9 kPa P= 165.5 kPa P= 193.1 kPa - — P = 55.2 kPa(RMS) - » - P = 82.7 kPa (RMS) I (RMS) i (RMS) i (RMS) i (RMS) 110.3 kPa( 137.9 kPa I 165.5 kPa ( 193.1 kPa I RMS 20 40 60 80 z [mm] 100 120 140 160 Figure 2.37: M A C L droplet velocity for K E L T R A C K HiRail at QL = 60 ml/min (original air-blast atomizer with full rubber-duckbill). 104 2.5 References 1. Lefebvre A H (1989). 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The effects of polymer concentration and molecular weight on the breakup of laminar capillary jets. Journal of Non-Newtonian Fluid Mechanics, 74:285-297. 46. Rodd LE , Scott TP, Cooper-White JJ, Mckinley G H (2004). Capillary break-up rheometry of low-viscosity elastic fluids. Applied Rheology, 15(l):12-27. 47. Adrian RJ (2005). Twenty years of particle image velocimetry. Experiments in Fluids, 39(2)A59-\69. 48. Keane RD and Adrian RJ (1992). Theory of cross-correlation analysis of PIV images. Applied Scientific Research 49(3): 191-215. 49. Raffel M , Willert C, Kompenhans J (1998). "Particle Image Velocimetry: A Practical Guide" Springer: Germany. 50. Westerweel J, Dabiri D, Gharib M (1997). The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings. Experiments in Fluids, 23:20-28. 51. Cater J and Soria J (2001). PIV measurements of turbulent jets. Proceedings from the 4th International Symposium on Particle Image Velocimetry, Gottingen, Germany, September 17-19. 52. Soria J (1996). An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Experimental Thermal and Fluid Science, 12:221-223. 108 53. Chigier N (1991). Optical imaging of sprays. Progress in Energy and Combustion Science, 17:211-262. 54. Chigier N (1983). Drop size and velocity measurement. Progress in Energy and Combustion Science, 9:155-177. 55. Ow CS and Crane R l (1981). Pattern recognition procedures for a television-mini computer spray droplet sizing system. Journal of Energy, 119-123. 56. Simmons HC and Lapera DJ (1969). A high-speed spray analyzer for gas turbine fuel nozzles. Proceedings from the ASME Gas Turbine Conference, Cleveland, Ohio. 57. Dr. Steve Anderson, LaVision Inc.: Personal communication. 58. Vega de M , Rodriguez P, Lecuona A (2000). Mean structure and droplet behavior in a coaxial airblast atomized spray: self-similarity and velocity decay functions. Atomization and Sprays, 10:603-626. 59. Karl JJ, Huilier D, Burnage H (1996). Mean behavior of a coaxial air-blast atomized spray in a co-flowing air stream. Atomization and Sprays, 6:409-433. 60. Eroglu H, Chigier N , Farago Z (1991). Coaxial atomizer liquid intact lengths. Physics of Fluids A, 3(2):303-308. 61. Sankar SV, Brena de la Rosa A, Isakovic A , Bachalo WD (1991). Liquid atomization by coaxial rocket injectors. AIAA Paper, 91-0691. 62. Hardalupas Y and Whitelaw JH (1994). Characteristics of sprays produced by coaxial air-blast atomizers. Journal of Propulsion and Power, 10(4):453-458. 63. Rein M (1993). Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dynamic Research, 12(2): 61-93. 64. Chandra S and Avedisian CT (1991). On the collision of a droplet with a solid-surface. Proceedings of the Royal Society of London Series A, 432(1884): 13-41. 65. Hussein JH, Capp SP, George W K (1994). Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet. Journal of Fluid Mechanics, 258:31-75. 109 3 C O N C L U S I O N S A N D R E C O M M E N D A T I O N S A series of elastic and inelastic test liquids, along with K E L T R A C K HiRail, were sprayed through a commercial air-blast atomizer at ALR ranging from 1.1 to 7.0, M ranging from 126 to 2322, and WeA exceeding 1000. Through the use of pre-formulated, substitute test liquids belonging to the Boger class, the rheological effects of extension-thickening were decoupled from those of shear-thinning. Liquid elasticity was shown to impair atomization by promoting the development of large-scale filamentary structures at breakup. The additional normal stresses induced in these elastic structures enhanced their stability against capillary forces, which delayed droplet formation until farther downstream where relative air-liquid velocities were reduced. Consequently, elasticity led to an increase in droplet sizes. This was confirmed through qualitative increases in the VMD as measured by shadowgraphy. Although the quantitative accuracy of the droplet size measurements was confirmed for water by the agreement between liquid flow rate estimates, based on volume flux calculations, and their actual values, the results for viscous-inelastic (ns > 1 mPa-s) and all of the elastic test liquids (including K E L T R A C K HiRail) were inconsistent with previously published results. The cause of this discrepancy is speculated to be due to the statistically-induced exclusion of the larger droplets from the measurement volume. In the past, researchers who have successfully applied shadowgraphy had often investigated the atomization of liquid fuels, which have shear viscosities near that of water and are inelastic. However, in order to account for the larger droplets produced in the atomization of viscous-inelastic (ns> 1 mPa-s) and elastic liquids, shadowgraphy may not be the most suitable tool given the limited range of droplet diameters that can be imaged and sized. Future tests should involve extending the sampling locations to farther radial distances in an attempt to capture a greater number of the larger droplets. In the present study, droplet size measurements were limited to a nearest axial plane of z = 152.4 mm because of light attenuation effects. The use of a high-powered laser combined with a beam expander would mitigate this effect and allow for measurements 110 to be made closer to the atomizer exit plane. In this way, the spatial distribution of the droplet size and volume can be measured as a function of the axial distance. In spray coating, this information could be useful in determining the ideal atomizer-to-target separation distance for optimal spray uniformity. Moreover, in order to mitigate overspray in spray coating, the droplet diameter class that is most important would be near the lower measurement threshold of 10 urn. This is because smaller droplets have a shorter aerodynamic relaxation time and lower inertia, implying that they are more susceptible to be transported away by the surrounding air jet. Hence, future droplet sizing attempts should be carried out with a reduced field-of-view (increased resolution) so as to better resolve the smaller droplet size classes. Asymmetries were observed in the spatial distribution of liquid volume around the spray centerline. These were believed to be due to asymmetries in the atomizer geometry. To ensure repeatable measurements in the future, it is recommended that the rubber-duckbill (in half or full form) be removed altogether. Each air-blast atomizer that is to be used for research purposes should be meticulously checked using an optical microscope to ensure symmetry. Additionally, the air-blast atomizer should also incorporate separate flow paths for the atomizing air and purge air. This way, atomizing air velocities and flow rates can be calculated more accurately, while allowing the purge air to be deactivated in laboratory environments. Oscillatory shear and extensional viscosity measurements on K E L T R A C K HiRail confirmed that it was indeed elastic. This is consistent with observations from breakup visualization, in which K E L T R A C K HiRail atomized in a manner similar to the elastic liquids, in particular, 300K PEO. The presence of K E L T R A C K HiRail ligaments at far downstream distances (z « 152.4 mm) was attributed to its low surface tension and high elasticity. PIV results showed the M A C L droplet velocities decreasing with z. For all of the test liquids, variations in liquid flow rate from 30 to 60 ml/min (ALR variation between 2.5 to 1.1) had no effect on the M A C L droplet velocities. For inelastic liquids at 30 < z < 60 111 mm, a higher shear viscosity led to reduced droplet velocities. This was explained by the presence of larger droplets with lower drag-to-momentum ratios. Results for elastic liquids at the same downstream distance range were unreliable due to the presence of ligaments. However, farther downstream, elastic droplets, owing to their significantly greater size and inertia, were better able to preserve their initial momentum by demonstrating velocities higher than that of the underlying carrier air jet. M A C L droplet velocities for all of the inelastic liquids converged at far downstream distances, indicating relaxation to the carrier air jet velocity. This result also indirectly implies that droplet sizes and velocities were uncorrelated at far downstream distances for these inelastic liquids. Finally, the effect of atomizing air pressure was investigated by atomizing K E L T R A C K HiRail through a rubber duck-bill equipped air-blast atomizer. Results showed that the M A C L droplet velocities, along with their RMS deviations, increased with atomizing air pressure up to a maximum of 193.1 kPa. 112 A P P E N D I X A : S h e a r V i s c o s i t y M e a s u r e m e n t s 1000 * mm—• «— J J ... L 1 . . . . . 1 1 o 50 wt.% Glycerin » 80 wt.% Glycerin • 90 wt.% Glycerin • 99.5 wt.% Glycerin • 100KPEO Pre-Spray -100KPEO Post-Spray • 300K PEO Pre-Spray • 300K PEO Post-Spray » 1000K PEO Pre-Spray . . . —• mmmn f t f t t f t m t t tm 00 >©<: 1! r * * • * n 0-— 100 o a c a - 10 Figure A . l : Shear Rate [1/s] Rate-independent shear viscosities of elastic and inelastic test liquids at 25°C. 113 100.00 10.00 « OL TJ O s 1.00 0.10 0.01 10.00 0.10 1.00 Frequency [Hz] Figure A.3: Oscillatory profile of K E L T R A C K HiRail at 25°C (5% strain) 100 to 0. w o o ra c o '(/> c X Ul c £ ra a. a. < 6 8 Extensional Strain 10 Figure A.4: Apparent extensional viscosity of K E L T R A C K HiRail at 25°C as measured using a Capillary Breakup Extensional Rheometer (CaBER) 114 APPENDIX B: Surface Tension Measurements The equilibrium surface tension of the test liquids were measured using a CSC Scientific Cenco du Notiy ring. Figure B . l depicts this instrument, which was generously loaned from the UBC Mining Department (Ms. Sally Finora, smf@,mining. u be. ca). The du Noiiy ring reports an apparent surface tension value by measuring the maximum force required to pull a submersed Pt-Ir ring out beyond the free surface of the liquid. Figure B.l: du Notiy ring apparatus Calibration of the instrument was performed according to the procedures set out in the operator's manual. This involved progressively loading the ring with known masses while comparing the reported surface tensions with their apparent values calculated based on an ideal force balance for the ring. Table B . l is a sample set of calibration values. Calibration and all of the measurements were performed at a room temperature of 25±1°C. The apparent surface tension was calculated by: _ (mass on ring\gravitational acceleration) a p p 2 x (ring circumference) 115 The factor of 2 in the denominator of the above formula is to account for the two (inner and outer) wetted perimeters of the ring. The ring circumference was 5.992 cm. Table B.l: Sample calibration values for surface tension measurements Mass placed on ring [g] Dial reading [mN/m] Apparent surface tension (aapp) [mN/m] 0 0 0 0.0346 3.2 2.8 0.1346 10.5 11.0 0.2346 18.8 19.2 0.2846 22.6 23.3 0.5346 43.4 43.8 0.6346 51.5 51.9 0.7346 60.1 60.1 0.7846 64.7 64.2 The calibration was verified regularly against measurements of distilled water, of which the surface tension is known to be 72.0 mN/m at 25°C [White F M (1999). "Fluid Mechanics" 4 t h ed, McGraw Hill]. To begin a measurement, approximately 100 ml of liquid was placed in a beaker. The diameter of this beaker should be at least three times that of the ring in order to minimize errors introduced by the proximity of the beaker walls. Here, we used a beaker that was 5 cm in diameter. To ensure accurate results, the ring was rinsed with distilled water and then flamed to rid it of any residual oils and contaminants. Next, the ring was fully submersed below the free surface of the liquid, and then gradually pulled out. As the ring travels above the free surface, a lamella forms, which tears only when a sufficiently large force has been exerted on the ring; this maximum pull force was used to calculate the apparent surface tension. 116 The original surface tension calculations were derived based on theories that applied to rings of infinite diameter and did not consider the added weight of liquid lifted due to the proximity of one side of the ring to the other. As a result, Adamson [Adamson A W (1990). "Physical Chemistry of Surfaces" Wiley: New York, Chapter 2] proposed the following correction factor (Fcorrection) for the apparent surface tension: {Fcorrecllon -0-725) 2 = ^'°llv}CTaPP -1.679^1 + 0.04534 [2xR) Ap g \RJ where aapp = apparent surface tension Ap = pljquicl - pair = density difference between liquid and air g = gravitational acceleration r = ring thickness R = ring radius To assess the extent of physical contamination, the test liquids' surface tensions were measured both before and after they were pumped through the spray system (air-blast deactivated). PEO is only mildly surface active and its addition did not significantly affect the surface tensions of the underlying solvents. Because of this, dynamic surface tension measurements were deemed unnecessary for the PEO solutions. However, KELTRACK™ HiRail, like many paints and industrial coatings, contains surfactants in its formulation and may exhibit a dynamic surface tension owing to the finite time scale associated with surfactant transport to newly generated interfaces. At the present time, there is no equipment available at U B C capable of measuring dynamic surface tensions. The measurement uncertainty, as specified by the du Notiy ring manufacturer (Cenco), is ±0.1 mN/m. Table B.2 lists the surface tension data for all of the test liquids at a room temperature of 25±1°C. 117 Table B.2: Surface tension data for all test liquids at 25°C (including K E L T R A C K Trackside and Xanthan gum solutions) Liquid Apparent Equilibrium Surface Tension [niN/m] Correction Factor from Adamson 1990 (Chapter 2) Corrected Equilibrium Surface Tension [mN/m] Mean Equilibrium Surface Tension (Standard Deviation) fmN/ml Distilled Water (fresh from PPC supply) 76.7 0.938770503 72.00 72.0 (0) 76.7 0.938770503 72.00 76.7 0.938770503 72.00 Distilled Water (Pre-Spray) 76.8 0.938867096 72.10 72.1 (0.058) 76.9 0.938963646 72.21 76.8 0.938867096 72.10 Distilled Water (Post-Spray) 75.2 0.937316328 70.49 70.4 (0.058) 75.1 0.937219029 70.39 75.1 0.937219029 70.39 50 wt.% Glycerin (Pre-Spray) 74.4 0.927944926 69.04 68.8 (0.814) 74.9 0.92839431 69.54 73.3 0.92695276 67.95 50 wt.% Glycerin (Post-Spray) 68.0 0.922102332 62.70 63.3 (0.968) 68.0 0.922102332 62.70 69.7 0.92367103 64.38 80 wt.% Glycerin (Pre-Spray) 72.0 0.921392278 66.34 66.6 (0.429) 72.8 0.922085654 67.13 72.1 0.921479084 66.44 80 wt.% Glycerin (Post-Spray) 69.3 0.91903384 63.69 64.0 (0.484) 69.4 0.919121701 63.79 70.2 0.919823158 64.57 Liquid Apparent Equilibrium Surface Tension [mN/m] Correction Factor from Adamson 1990 (Chapter 2) Corrected Equilibrium Surface Tension [mN/m] Mean Equilibrium Surface Tension (Standard Deviation) |niN/m| 90 wt.% Glycerin (Pre-Spray) 67.5 0.916469565 61.86 61.9 (0.685) 68.3 0.91716915 62.64 66.9 0.915943195 61.28 90 wt.% Glycerin (Post-Spray) 66.9 0.915943195 61.28 61.5 (0.195) 67.1 0.916118813 61.47 67.3 0.916294269 61.67 100K PEO (Pre-Spray) 66.9 0.923947188 61.81 62.0 (0.249) 67.4 0.924426802 62.31 67.1 0.924139172 62.01 100K PEO (Post-Spray) 65.3 0.922404592 60.23 60.4 (0.285) 65.3 0.922404592 60.23 65.8 0.922887945 60.73 300K PEO (Pre-Spray) 66.5 0.921823737 61.30 61.7 (0.346) 66.9 0.922201167 61.70 67.2 0.922483767 61.99 300K PEO (Post-Spray) 65.3 0.920687077 60.12 60.4 (0.260) 65.8 0.921161486 60.61 65.7 0.921066696 60.51 1000K PEO (Pre-Spray) 68.1 0.923909216 62.92 63.0 (0.453) 68.7 0.924474264 63.51 67.8 0.92362609 62.62 Liquid Apparent Equilibrium Surface Tension [mN/m] Correction Factor from Adamson 1990 (Chapter 2) Corrected Equilibrium Surface Tension [mN/m] Mean Equilibrium Surface Tension (Standard Deviation) [mN/ml 1000K PEO (Post-Spray) 65.7 0.921632788 60.55 60.5 (0.098) 65.6 0.921537365 60.45 65.5 0.921441895 60.35 KELTRACK HiRail (Pre-Spray) 44.0 0.900142064 39.61 39.7 (0.545) 43.6 0.89970917 39.23 43.5 0.899600778 39.13 44.6 0.900789408 40.18 44.9 0.901112187 40.46 43.7 0.899817494 39.32 KELTRACK HiRail (Post-Spray) 44.2 0.900358111 39.80 39.5 (0.405) 43.3 0.899383793 38.94 44.2 0.900358111 39.80 44.0 0.900142064 39.61 Glycerin (Pre-Spray) 66.9 0.914537371 61.18 61.9 (0.686) 67.8 0.915313308 62.06 67.1 0.914710076 61.38 67.6 0.915141151 61.86 68.7 0.916086095 62.94 Glycerin (Post-Spray) 67.0 0.914623743 61.28 61.8 (0.472) 67.4 0.914968838 61.67 68.1 0.915571252 62.35 67.1 0.914710076 61.38 67.9 0.915399329 62.16 Liquid Apparent Equilibrium Surface Tension [mN/m] Correction Factor from Adamson 1990 (Chapter 2) Corrected Equilibrium Surface Tension [mN/m] Mean Equilibrium Surface Tension (Standard Deviation) [mN/ml For KELTRACK HiRail, the extent of batch-to-batch variation was assessed by testing two additional samples. The mean surface tension among the three samples was 39.6 mN/m with a combined standard deviation of 1.87 mN/m. K E L T R A C K H i R a i l (Ba tch B ) 45.7 0.901970055 41.22 41.9 (0.492) 46.1 0.902397432 41.60 47.0 0.903355288 42.46 46.9 0.903249114 42.36 46.3 0.902610736 41.79 46.8 0.903142877 42.27 K E L T R A C K H i R a i l (Ba t ch C ) 40.8 0.896648339 36.58 37.2 (0.768) 41.2 0.897088934 36.96 41.7 0.897638096 37.43 42.5 0.89851314 38.19 42.2 0.898185516 37.90 40.4 0.89620661 36.21 0.05 w t .% X a n t h a n Gum 77.1 0.939156615 72.41 72.5 (0.059) 77.2 0.939253034 72.51 77.2 0.939253034 72.51 0.10 w t .% X a n t h a n Gum 77.8 0.939830642 73.12 71.9 (1.328) 76.8 0.938867096 72.10 75.2 0.937316328 70.49 Liquid Apparent Equilibrium Surface Tension [mN/m] Correction Factor from Adamson 1990 (Chapter 2) Corrected Equilibrium Surface Tension [mN/m] Mean Equilibrium Surface Tension (Standard Deviation) [mN/ml For completeness, additional formulations of KELTRACK were also tested. KELTRACK Trackside Freight 45.9 0.902183872 41.41 41.41 (0.190) 46.1 0.902397432 41.60 45.7 0.901970055 41.22 KELTRACK Trackside LT (Low Temp) 43.1 0.899166538 38.75 37.56 (1.281) 40.4 0.89620661 36.21 42.0 0.897966756 37.71 KELTRACK Trackside Transit 43.6 0.89970917 39.23 38.69 (0.467) 42.7 0.898731212 38.38 42.8 0.898840146 38.47 APPENDIX C: Air-Blast Atomizer Drawings Air S h r o u d Assembly Scalei NTS Dotei OCT 07 2005 123 01.0530— 01.3930— SECTION A-A All Dimensions In Inches Part Namei Air Shroud Part No.' 1 of 8 Scale* NTS Datei OCT 07 2005 124 AU Dimensions in Inches P a r t Namei Retain ing Ring P a r t N0.1 2 o f 8 Scale i NTS Datei DCT 07 2005 -0O.&25O-H?)O,250Oh I 0,0710 T 0.1300 0.2810 I 0.0352 -0,0435 -0.0475 0.0298-0.1250-1 SECTION A - A AU Dimensions in I n c h e s P a r t Nanei A i r Cap P a r t No.! 3 o f 8 S c a l e : NTS D a t e i DCT 07 2005 BOLT CIRCLE - 0O.E637 00,1600 00,3675 00,0480 - 6 HDLES THRU ALL EQUAL SPACING 0,0345-SECTION A -A AU Dimensions in Inches P a r t Name: W a s h e r P a r t No,; 4 o f 8 Sca le : NTS Date: rjCT 07 2005 AU Dimensions in I n c h e s P a r t Nane: Duckb i l l S c a l e : NTS P a r t N o ; 5 o f 8 D a t e : OCT 07 2005 to oo All Dimensions In Inches Part Name' Fluid Cap Par-t No.i 6 of 8 Scalei NTS Date. OCT 07 3005 129 8 HDLES THRU ALL EQUAL SPACING SECTION A - A All Dimensions in I n c h e s P a r t Name: G a s k e t P a r t No,: 7 o f 8 S c a l e : NTS D a t e : DOT 07 2005 FLOW ("0.0394 5 HOLES EQUAL SPACING <*'/////' ///////// SECTION B-B AH Dimensions In Inches Par t Namei Atomizer Body Par t No.i 8 of 8 Scale' NTS Datei OCT 07 2005 APPENDIX D: MATLAB Code for Compressible Duct Flow % comppressuredrop.m % % 1 dimensional compressible duct flow with friction (non-isentropic) and no area change % -- — % Program to calculate the air mass flow rate through a circular duct, taking into % account compressibility effects and assuming either an isothermal or adiabatic process clc; format long; D=4.318E-03; % Air hose ID [m] Pl_psia=40.7; % Upstream static pressure [psia] P2_psia=22.7; % Downstream static pressure [psia] L=3.96; % Air hose length [m] R=287; % Universal gas constant [mA2/(sA2*K)] k=l .4; % Ratio of specific heats for air T=300; % Temperature [K] f=0.0233; % Average friction factor along hose length (drawn plastic tubing %e = 0.0015E-3 m) Pl=Pl_psia*6894.75728; % Upstream static pressure [Pa] P2=P2_psia*6894.75728; % Downstream static pressure [Pa] A=(pi/4)*(DA2); % Air hose area [mA2] reply = input('Do you wish to perform an isothermal or adiabatic analysis? i/a [i]:','s'); if isempty(reply) reply = T; end if reply =='i' %==================================== % Isothermal case (use Equation 9.73 in F.M. White) --> no need to iterate disp('l-D Compressible Duct Flow with Friction (No area change): Isothermal Analysis'); term 1 =(f*L/D)+2*log(P 1 /P2); mdot_isotheirnal=(((PlA2-P2A2)/(R*T*tenril))A(0.5))*A % Air mass flow rate thru air % hose [kg/s] disP('============—============—============'); rhol=Pl/(R*T) % Air density at Point 1 [kg/mA3] Vl=mdot_isothermal/(rhol *A) % Air velocity at Point 1 [m/s] Mai =V 1 /((k*R*T)A0.5) % Mach number at Point 1 132 % Check Mach number at Point 2 for choking disp('= rho2=P2/(R*T) % Air density at Point 2 [kg/mA3] V2=mdot_isothermal/(rho2*A) % Air velocity at Point 2 [m/s] Ma2=V2/((k*R*T)A0.5) % Mach number at Point 2 ifMa2<(l/kA0.5) disp('Good! State 2 is not choked, therefore the solution is accurate'); else disp('Warning! State 2 is choked: inaccurate solution') end else % Adiabatic case —> iteration required; let's begin by applying the adiabatic, % frictional relations from Equation 9.66 and 9.67 in F.M. White string = ['']; disp(string); dispC ^ — = — ^ — — •); disp('l-D Compressible Duct Flow with Friction (No area change): Adiabatic Analysis'); init_Mal=0.14; % Initial guess for Mai init_Ma2=0.26; % Initial guess for Ma2 Mal=init_Mal; Ma2=init_Ma2; delta_fLD=f*L/D; T1=T; % Define temperature at Point 1 (Recall T l not equal to T2 since % adiabatic process, not isothermal) for m=l: 10000 flag=0; while Ma2<0.4 while Mal<0.2 Mai Ma2 fLDl =( 1 -Mai A2)/(k*Mal A2) + (k+1 )/(2*k)*log((k+l )*(Mal A2)/(2+(k-1 ) * M a l A2)); fLD2=(l-Ma2A2)/(k*Ma2A2) + (k+1 )/(2*k)*log((k+l)*(Ma2A2)/(2+(k-l )*Ma2A2)); iter_delta_fLD=fLD 1 -fLD2; if (iter_delta_fLD< 1.001 *delta_fLD) if(iter_delta_fLD>0.999*delta_fLD) flag=l; break end end Mal=Mal+0.0001; end ifflag==l 133 break end Mal=init_Mal; Ma2=Ma2+0.0001; end Pstar l=Pl/((((k+l )/(2+(k-l )*Mal A2))A0.5)/Mal); % Pstar 1 and Pstar2 should actually be the same; we use different nomenclatures % for them just as comparison criterion Pstar2=P2/((((k+1 )/(2+(k-1 )*Ma2A2))A0.5)/Ma2); if(Pstarl<1.001*Pstar2) if(Pstarl>0.999*Pstar2) disp('================================================'); disp('Solution converged!'); break end end Mal=Mal+0.0001; end Mai Ma2 iterdeltaJLD delta_fLD Pstarl % Pstarl and Pstar2 should be the same since there is only one % Pstar (constant reference value) for adiabatic flow; the stagnation % pressure and density decrease continually along the duct due to % non-isentropic losses (friction) and as such are not used as % reference properties Pstar2 Tstar=T 1 /((k+1 )/(2+(k-1 )*Mal A2)) % Tstar is also a constant reference property % in adiabatic duct flow with friction Tl T2=Tstar*((k+l)/(2+(k-l )*Ma2A2)) Vl=Mal *sqrt(k*R*Tl) % At Point 1 rhol=Pl/(R*Tl) % At Point 1 V2=Ma2*sqrt(k*R*T2) % At Point 2 rho2=P2/(R*T2) % At Point 2 mdot_adiabatic_l =rho 1 * A* V1 % At Point 1 mdot adiabatic 2=rho2*A*V2 % At Point 2 end 134 Sample Comparison: Rotameter vs. Compressible Duct Flow Calculation • To confirm rotameter readings by computing the air mass flow rate based on the pressure drop along a given length of hose (see Figure D. l ) . o 1-dimensional compressible duct flow with friction but no area change, o Re = 37863; e/Dhme = 0.000347 for drawn plastic tubing friction factor = 0.0233 from Moody chart. Because the flow is still subsonic, one may ignore compressibility effects and rely on the Moody chart for estimating the friction factor with acceptable accuracy, o Rotameter reading (pressure corrected): 0.002311 kg/s Solenoid • Quick Regulator Valve Rotameter Disconnect : IMT. 8 0 p s i8 — K — t > - o — T 7 Filter wl Water Trap 4 0 ~ p s i g 5 ! f p s j g Nozzle 40 psig 3$ psig 34 psig .50.5 psig 26 psig \ ^ Figure D.l: Spray lab air supply (version 1) - Polyethylene air hose: 0.25" OD, 0.17" ID 38 psig -> 34 psig over 87" 26 psig 8 psig over 156" Isothermal (T=300K) rhol =4.220 kg/m* VI =32.331 m/s Mai =0.0931 rho2 = 3.900 kg/m3 V2 = 34.987 m/s Ma2 = 0.101 mdot_isothermal = 0.00199 kg/s (14% less than rotameter reading) rhol =3.259 kg/m3 VI =51.304 m/s Mai =0.148 rho2 = 1.818 kg/m3 V2 = 91.985 m/s Ma2 = 0.265 mdot_isothermal = 0.00245 kg/s (6% more than rotameter reading) Adiabatic (T1=300K) rhol =4.220 kg/m3 VI =32.150 m/s Mai = 0.0926 Tl =300K rho2 = 3.901 kg/m3 V2 = 34.749 m/s Ma2 = 0.100 T2 = 299.9 K mdot_adiabatic = 0.00199 kg/s (14% less than rotameter reading) rhol =3.259 kg/m3 VI =51.384 m/s Mai =0.148 T l =300K rho2= 1.835 kg/m3 V2 = 91.191 m/s Ma2 = 0.264 T2 = 297.2 K mdotadiabatic = 0.00245 kg/s (6% more than rotameter reading) APPENDIX E: PIV Measurements 20 40 60 80 z [mm] 100 120 140 160 Figure E . l : Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs (water at QL = 60 ml/min, PA = 55.2 kPa). -10 IP Mean -20 IP Mean 50 IP Mean 70 IP Mean -100 IP Mean —i—10 IP RMS - + - 20 IP RMS + 50 IP RMS —t— - 70 IP RMS —t—100 IP RMS Water: 30 ml/min Atomizing Air Pressure: 55.2 kPa 20 40 60 100 120 140 160 80 z [mm] Figure E.2: Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs (water at QL = 30 ml/min, PA = 55.2 kPa). 136 80 100 120 140 160 z [mm] Figure E.3: Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs (50 wt.% glycerin at QL = 30 ml/min, PA = 55.2 kPa). 160 Figure E.4: Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs (80 wt.% glycerin at QL = 60 ml/min, PA = 55.2 kPa). 137 20 40 60 80 z [mm] 100 120 140 160 Figure E.5: Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs (80 wt.% glycerin at QL = 30 ml/min, PA = 55.2 kPa). 20 40 60 100 120 140 160 80 z [mm] Figure E.6: Sample M A C L droplet velocity plot showing statistical convergence above 70 image-pairs (100K P E O at QL = 60 ml/min, PA = 55.2 kPa). 138 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 Radial Position [mm] Figure E.7: Radial profile of the mean axial droplet velocity for water at QL = 60 ml/min, PA = 55.2 kPa. Figure E.8: Non-dimensional radial profile of the mean axial droplet velocity for 50 wt.% glycerin at QL = 60 ml/min, PA = 55.2 kPa. 139 APPENDIX F: Laser Timing Measurements The temporal error associated with a PIV velocity measurement is due to the uncertainty in determining the exact time separation between the image-pair exposures, which is in turn dictated by the timing between the two laser pulses. To this end, the temporal accuracy and precision of the PIV laser system (New Wave Gemini 15 Hz; dual-head; frequency-doubled; 532 nm; 5 ns pulse duration) were investigated. In terms of equipment, a digital phosphorus oscilloscope scope was used (Tektronix TDS3014B) to acquire voltage data provided by a photodiode assembly (THORLABS DET210). The experimental setup is shown in Figure F . l . Figure F . l : Photodiode setup for measuring the time separation between laser pulses. 140 The measurement uncertainty of the photodiode was ±1 ns. The oscilloscope was set to acquire data at 100 MHz, resulting in a sampling period of 10 ns. Thus, the limiting temporal resolution of this measurement system was 10 ns. Because the time separations typically employed in PIV experiments are on the order of microseconds, this resolution was deemed acceptable. Figure F.2 and Figure F.3 show laser timing diagrams for a set time separation of 30 (xs and 40 us, respectively. The laser pulse duration was approximately 5 ns, which was shorter than the sampling period of the oscilloscope. Therefore, laser emission events were recorded as single data point peaks. In all cases, the set time separation agreed perfectly with the measured time separation (repeatability of 100%). Consequently, the temporal error contribution to the total relative uncertainty in a PIV velocity measurement is: £_Mi2/£_ 0.026% At 38 jus where St = uncertainty in time separation between laser pulses Ar = time separation between laser pulses (typically 38 (as in the present study) 141 1.2 I 0.8 O n O) 0.6 w c o (0 0.4 E hi i_ 0) CO 0.2 ra 30.000 ±0.010 MS -0.2 -0.000010 -0.000005 0.000000 0.000005 0.000010 0.000015 0.000020 0.000025 0.000030 0.000035 0.000040 Time [s] Figure F.2: Laser emission timing for a At setting of 30 fis 1.2 £ 0.8 o £ . «) §> 0.6 w c o in 0.4 I LU L_ o 8 0.2 40.000 ±0.010 ijs -0.2 -0.000040 -0.000020 0.000000 0.000020 Time [s] 0.000040 0.000060 0.000080 Figure F.3: Laser emission timing for a At setting of 40 us 142 APPENDIX G: Droplet Size Measurements — • — D10 (60 ml/min) —*— D10 (30 ml/min) - I M V I U \ w l l l l f l l l l l i y I M V I V J - • a - N (60 ml/min) N(3( ^tJU II I If • • III If ) ml/min) Cl r ^ ^ T \ - -i- - — " T \ \ A - " ~ 1 — — _ \ \ • . * - -' , ' \ • - _ ~ ~ - . • - - . . " "1 • -, - -A -30 -20 20 0) E a; a. o 30 -10 0 10 Radial Position: y [mm] Figure G.2: D,0, RMS, and N for water at QL = 30, 60 ml/min, PA = 55.2 kPa (v direction). 143 O.OOE+00 -30 -20 20 30 -10 0 10 Radial Position: x, y [mm] Figure G.3: Droplet volume distribution for water at QL = 30,60 ml/min, PA = 55.2 kPa r" —o-x Direction -e-y Direction 0 4 -30 -20 20 -10 0 10 Radial Position: x, y [mm] Figure G.4: DVR for water at QL = 30,60 ml/min, PA = 55.2 kPa. 30 144 60 , Droplet Diameter [micron] Figure G.5: Droplet number distribution for water at QL = 60 ml/min, PA = 55.2 kPa. Droplet Diameter [micron] Figure G.6: Cumulative volume fraction for water at QL = 60 ml/min, PA = 55.2 kPa. 145 60 50 Droplet Diameter [micron] Figure G .7: Droplet number distribution for water at QL = 30 ml/min, PA = 55.2 kPa. Droplet Diameter [micron] Figure G.8: Cumulative volume fraction for water at QL = 30 ml/min, PA = 55.2 kPa. 146 50 45 40 35 c" 30 s u E 25 20 15 10 5 0 I I —•—D10(60 ml/min) —*—D10 (30 ml/min) - RMS (60 ml/min) - * - RMS (30 ml/min) - -a- N (60 ml/min) - - A - N (30 ml/min) _ -t • m ft-.---. . " * -* - " 3000 2000 CU n E 3 1500 ^ 0) a. o -30 -20 20 30 Figure G.9: -10 0 10 Radial Position: x [mm] D,0, RMS, and N for 50 wt.% glycerin at QL = 30,60 ml/min, PA = 55.2 kPa (.v direction). 50 45 40 35 ^ 30 o 1 2 5 o Q 20 15 10 5 0 —•— D10 (60 ml/min) —*— D10 (30 ml/min) - • - RMS (60 ml/min) - * - RMS (30 ml/min) - -a- N (60 ml/min) - N (30 ml/min) ^ - • ^ ~ ~ - —t >-A- . . • a . & • • - • - - V v ^ 3000 2500 2000 k_ 0) J3 E 3 1500 J « a. o 1000 500 -30 -20 20 30 -10 0 10 Radial Position: y [mm] Figure G.10: D,0, RMS, and N for 50 wt.% glycerin at QL = 30,60 ml/min, PA = 55.2 kPa (y direction). 147 1.00E+08 | -•-x Direction (60 ml/min) -e-y Direction (60 ml/min) - * - x Direction (30 ml/min) - A - y Direction (30 ml/min) 0.00E+00 -I 1 1 1 1 1 1 -30 -20 -10 0 10 20 30 Radial Position: x, y [mm] Figure G . l l : Droplet volume distribution for 50 wt.% glycerin at QL - 30,60 ml/min, PA = 55.2 kPa. 4 T — - i T i i r i 148 60 -| Droplet Diameter [micron] Figure G.13: Droplet number distribution for 50 wt.% glycerin at QL = 60 ml/min, PA = 55.2 kPa. 100 -| Droplet Diameter [micron] Figure G.14: Cumulative volume fraction for 50 wt.% glycerin at QL = 60 ml/min, PA = 55.2 kPa. 149 60 50 40 cu . Q E 3 Droplet Diameter [micron] Figure G.15: Droplet number distribution for 50 wt.% glycerin at QL = 30 ml/min, PA = 55.2 kPa. 100 Droplet Diameter [micron] Figure G.16: Cumulative volume fraction for 50 wt.% glycerin at QL = 30 ml/min, PA = 55.2 kPa. 150 50 45 40 35 „ 30 c o 1 2 5 Q 20 15 10 5 0 -30 —"—D10 (60 ml/min) —•—D10 (30 ml/min) ™" I A I V I O \KJ\J l l l i n i l l l l / "* I M V I U - - a - N (60 ml/min) -*-N(3( 1 l l l / l MM 1/ ) ml/min) a- - - t - • " . - - * I -20 -10 0 10 Radial Position: x [mm] 20 3000 2500 2000 tU •Q E 3 Z 1500 * . _» a p 1000 500 30 Figure G . 1 7 : Dl0, RMS, and TV for 80 wt.% glycerin at QL = 3 0 , 60 ml/min, PA = 55.2 kPa (x direction). 50 45 40 35 -30 ——D10 (60 ml/min) • - RMS (60 ml/min) • a - N (60 ml/min) -*— D10 (30 ml/min) * - RMS (30 ml/min) • - A - N (30 ml/min) -20 3000 2500 -10 0 10 Radial Position: y [mm] Figure G . 1 8 : Dw, RMS, and N for 80 wt.% glycerin at QL = 3 0 , 6 0 ml/min, PA = 55.2 kPa (y direction). 151 1 .OOE+08 -•-x Direction (60 ml/min) -e-y Direction (60 ml/min) - ± - x Direction (30 ml/min) -A-y Direction (30 ml/min) 7.50E+07 c o u I tu § 5.00E+07 -0.00E+00 -30 -20 -10 0 10 Radial Position: x, y [mm] 20 30 Figure G.19: Droplet volume distribution for 80 wt.% glycerin at QL = 30,60 ml/min, PA = 55.2 kPa. -30 -20 20 -10 0 10 Radial Position: x, y [mm] Figure G.20: DVR for 80 wt.% glycerin at QL = 30,60 ml/min, PA = 55.2 kPa. 152 60 50 40 Droplet Diameter [micron] Figure G.21: Droplet number distribution for 80 wt.% glycerin at QL = 60 ml/min, PA = 55.2 kPa. Droplet Diameter [micron] Figure G.22: Cumulative volume fraction for 80 wt.% glycerin at QL = 60 ml/min, PA = 55.2 kPa. 153 60 50 40 E 30 20 10 I  III ILI L J UL N n*" n.*" <J> /^ ^ oN r>N exN <v~- ^ tS A »N ^ cN -N ,A oN k> t> cN oN c\K Droplet Diameter [micron] Figure G.23: Droplet number distribution for 80 wt.% glycerin at QL = 30 ml/min, PA = 55.2 kPa. J— f 1 V I c o o 2 u. o £ 3 o > * * n> * * * * AN <bN * ^ ^ <1> & ^ ^ NfeN ^ k?»N & j> rtf- ^ & & & Droplet Diameter [micron] Figure G.24: Cumulative volume fraction for 80 wt.% glycerin at QL = 30 ml/min, PA = 55.2 kPa. 154 50 45 40 35 c 3 0 o o I 2 5 Q 20 15 10 5 0 —•— D10 (60 ml/min) —*— D10 (30 ml/min) _ JM _ DUO fCf\ m|/mln\ _ ,4. _ DMC /Of\ ml/min\ - • a - N ( io \ u v I I I I M I I I I I / 60 ml/min) » 1 \ I V I \ J I ^ J U 1111/ 11 111 - -a - N (30 ml/min) ————4 1 1 a. ^ • A - -A - TT B" - ' — •> * • * ' " - ^ ^—^ 3000 2500 E 3 a p -30 -20 20 30 -10 0 10 Radial Position: x [mm] Figure G.25: D,0, RMS, and N for 100K PEO at QL = 30,60 ml/min, PA = 55.2 kPa (x direction). 50 45 40 35 30 —•—D10 (60 ml/min) —*—D10 (30 ml/min) - • - RMS (60 ml/min) - * - RMS (30 ml/min) - • a - N (60 ml/min) N (30 ml/min) 2000 1500 1000 n E 3 a. p -10 0 10 Radial Position: y [mm] Figure G.26: Dl0, RMS, and N for 100K PEO at QL = 30,60 ml/min, PA = 55.2 kPa (v direction). 155 1.00E+08 c s o I 0) E 3 o > » Q. O 7.50E+07 5.00E+07 2.50E+07 O.OOE+00 -x Direction (60 ml/min) -x Direction (30 ml/min) -y Direction (60 ml/min) -y Direction (30 ml/min) -10 0 10 Radial Position: x, y [mm] 30 Figure G.27: Droplet volume distribution for 100K P E O at QL = 30,60 ml/min, PA = 55.2 kPa. -30 -20 -10 0 10 Radial Position: x, y [mm] Figure G.28: DVR for 100K P E O at QL = 30,60 ml/min, PA = 55.2 kPa. 156 60 50 -Droplet Diameter [micron] Figure G.29: Droplet number distribution for 100K P E O at QL = 60 ml/min, PA = 55.2 kPa. Droplet Diameter [micron] Figure G.30: Cumulative volume fraction for 100K P E O at QL = 60 ml/min, PA = 55.2 kPa. 157 Illllllllllllll I • l_J_ ^ KN <A nN ^ r> aS oN nN ^ <A oN c> oN nN oN kN tN ci> /A o> nN rN Droplet Diameter [micron] Figure G.31: Droplet number distribution for 100K P E O at QL = 30 ml/min, PA = 55.2 kPa. 100 90 80 70 60 o o 2 50 u. 0) E = 40 o > 30 20 10 0 r -* k> <V <S- k?> N« <V N« r$> r{V rj? rjO >^ >^ Droplet Diameter [micron] Figure G.32: Cumulative volume fraction for 100K P E O at QL = 30 ml/min, PA = 55.2 kPa. 158 50 45 40 35 „ 30 c o I 2 5 © Q 20 15 10 B- -_A=. -•—D10(60 ml/min) • - RMS (60 ml/min) • B - N (60 ml/min) —*—D10(30 ml/min) - * - RMS (30 ml/min) N (30 ml/min) 3000 2500 .o E 3 a> Q. p 1000 500 -30 -20 20 30 -10 0 10 Radial Position: x [mm] Figure G.33: D,0, RMS, and TV for 300K P E O at QL = 30,60 ml/min, PA = 55.2 kPa (x direction). 50 45 40 35 „ 30 c p E w o Q 20 15 10 5 0 — — D10 (60 ml/min) —*— D10 (30 ml/min) • • • P M Q tRC\ m l / m i n i - A - R M R flf) m l / m i n i - • a - N(C >0 ml/min) - • a - N (30 ml/min) * . . . - • " A - -- 1 1 % "- - - ". " - * " ' - ** * _ - & - -o- ^ a -| 2000 1500 1000 n E 3 a. o Q 4- 500 -30 -20 20 30 -10 0 10 Radial Position: y [mm] Figure G.34: Dl0, RMS, and TV for 300K P E O at QL = 30, 60 ml/min, PA = 55.2 kPa (y direction). 159 1.00E+08 7.50E+07 c o L -o ! I 5.00E+07 3 O > CL O Q 2.50E+07 O.OOE+00 -30 1 1 1 -•-x Direction (60 ml/min) -B-y Direction (60 ml/min) -A—x Direction (30 ml/min) -*-y Direction (30 ml/min) -20 20 30 -10 0 10 Radial Position: x, y [mm] Figure G.35: Droplet volume distribution for 300K P E O at QL = 30, 60 ml/min, PA = 55.2 kPa. -30 -20 -10 0 10 Radial Position: x, y [mm] Figure G.36: DVR for 300K P E O at QL = 30,60 ml/min, PA = 55.2 kPa. 160 K K N . N N „ \ . \ «.N - N . \ „ N _ \ - \ . \ - \ - \ . N , \ R \ „ \ J\ _ N - \ K K A » S A ( S T N / A < A Q N <~N Droplet Diameter [micron] Figure G.37: Droplet number distribution for 300K P E O at QL = 60 ml/min, PA = 55.2 kPa. 100 90 80 70 60 o o 2 50 u. 0) E 2 40 o > 30 20 10 0 r-r" JT _r i \ K \ nN. _\ . \ . \ , \ _K _N .S n \ - \ i> (N «N O."1 ^ ^ n"1 ^ ^ h"> ^ t,"1 tt1 ^ Droplet Diameter [micron] Figure G.38: Cumulative volume fraction for 300K P E O at QL = 60 ml/min, PA = 55.2 kPa. 161 60 50 -40 <D n E 3 z 30 «-< a Droplet Diameter [micron] Figure G.39: Droplet number distribution for 300K P E O at QL = 30 ml/min, PA = 55.2 kPa. Droplet Diameter [micron] Figure G.40: Cumulative volume fraction for 300K P E O at QL = 30 ml/min, PA = 55.2 kPa. 162 D10 [micron] D 1 0 [micron] ON Droplet Number Droplet Number 1.50E+08 i -•-x Direction (60 ml/min) -B-y Direction (60 ml/min) -*—x Direction (30 ml/min) -A-y Direction (30 ml/min) 1.25E+08 -§ 1.00E+08 -o E o | 7.50E+07 2 5.00E+07 Q 2.50E+07 - -0.00E+00 -30 -20 -10 0 10 Radial Position: x, y [mm] 20 30 Figure G.43: Droplet volume distribution for K E L T R A C K HiRail at QL = 30,60 ml/min, PA = 55.2 kPa. 0.5 -0 -I 1 1 1 1 1 1 -30 -20 -10 0 10 20 30 Radial Position: x, y [mm] Figure G.44: D VR for K E L T R A C K HiRail at QL = 30,60 ml/min, PA = 55.2 kPa. 164 60 50 40 E 3 30 a. o 20 10 ^ * ^ * * * * a* * * ^ ^ nt> N * ^ ^ & f & & ^ ^ & ^ & ^ ^ ^ ^ ^ Droplet Diameter [micron] Figure G.45: Droplet number distribution for K E L T R A C K HiRail at QL = 60 ml/min, PA = 55.2 kPa. 100 90 80 70 60 o •3 U 2 50 LU 0) E = 40 o > 30 20 10 0 ^ * * * * ^  * ^  * «fr ^  ^  ^ £ f ^ # f & & ^ $ ^ ^ ^ ^ ^ & ^ ^ Droplet Diameter [micron] Figure G.46: Cumulative volume fraction for K E L T R A C K HiRail at QL = 60 ml/min, PA = 55.2 kPa. jr JT 1 ,1 Jr 165 60 50 40 0) E 3 30 o a. o Q 20 10 JlllLLUli mi nil II n i JL__L N K \ n \ «N fcN oN /.N oN oN ~.\ -\ ^ oN ^ (N t.N A „K K N i> ^ ^ A"> C \ N \ <V N h <o \ <b % sO ^ ^ <b ^ ^ S % < \ N % N C ) ^ ^ ^ | i ^\ >^ ^) Droplet Diameter [micron] Figure G.47: Droplet number distribution for K E L T R A C K HiRail at QL = 30 ml/min, PA = 55.2 kPa. 100 90 80 70 E c 60 o o 2 50 u. <u E = 40 o > 30 20 10 0 ^ * o> * * * * * * * & s <j> J> & & <> & & <f & <v>N tfN & ^ ^ & Droplet Diameter [micron] Figure G.48: Cumulative volume fraction for K E L T R A C K HiRail at QL = 30 ml/min, PA = 55.2 kPa. r l " " Ji 166 APPENDIX H: Droplet Evaporation Calculations The effect of diffusional evaporation on the droplet size distribution was assessed by solving the diffusion equation (see equation [1.0]). In short, the difference between the partial pressure of water vapor at far-field and that corresponding to saturation on the droplet surface is the driving force behind water transport. The following assumptions were made in the analysis: o Liquid: Water. o Uniform temperature on the droplet surface and at far-field: 298K (25°C). o Relative droplet-air slip velocity = ~0 (fully relaxed far downstream), o Kn « 1 (i.e. Continuum Regime). The rate of change of the droplet diameter due to diffusional evaporation is (Seinfeld and Pandis, p.652): dDk _ 4D„ M, dt DkPv v-(c -C * ) \ oc surface / [1.0] Dv = Modified diffusivity of water vapor in air accounting for non-continuum effects jum Mv = Molecular weight of water (H2O) Dk = Diameter of the k t h droplet \jjm] Cx = Water vapor concentration at far-field g mol H20 pv = Density of water g cm mol H20 cm3 C surface Water vapor concentration on droplet surface molH2Q cm 167 Equation [1.0] neglects other processes that may also alter the droplet size distribution, such as coalescence. Water vapor concentrations on the droplet surface and at far-field are taken to remain constant during the time in which evaporation occurs. Moreover, this analysis does not account for heat absorbed during the evaporation process (i.e. uniform temperature is assumed both on the droplet surface and at far-field). The diffusivity of water vapor in air is a function of both temperature and pressure. D„ is given as (Seinfeld and Pandis, p.801): Equation [1.1] represents a modified diffusivity accounting for free-molecular effects, in which the continuum-limit diffusivity (pv) is used: A . = [1.1] 2Dv(2xMry 0.211 r T P I 273 N 1.94 0.21 If 298 1.94 (l08)= 0.25x10 8 V™2 [1.2] 273 5 T = Temperature [K] P= Pressure [atm] 168 Substituting Equation [1.1] and [1.2] into [1.0] and integrating from time = 0 to t gives the following quadratic equation for the droplet diameter, Dk: AD..M, Pv -ic -C , )t + \ x surface / D, \2nM„ •°- + 2DJZ^L{D0) 2 v RT = 0 [1.3] D0 = Initial diameter of the k t h droplet \pm] Two sample droplet distributions were allowed to evolve with time in different relative humidity levels. Variations in the arithmetic mean diameter (Dio) are shown below in Figure H . l and Figure H.2. 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Elapsed Time [s] Figure H. l . Dl0 variation due to diffusional evaporation. 169 25.6 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Elapsed Time [s] Figure H.2. D,0 variation due to diffusional evaporation. PIV data of the mean axial centerline (MACL) droplet velocity (Uc) were used to estimate the droplet residence time with the assumption that in the region of interest (70 < z < 210 mm), droplet sizes and velocities were uncorrelated. Droplet velocities were fitted to Equation [1.4], where zQ is the virtual origin. Figure H.3 and Figure H.4 depict the agreement between experimental and correlated results. ^ = Uc=^-= , 2 - 8 0 1 4 3 i [1-4] dt z-z0 z-{- 24.101 lx lO - 3 ) 170 Comparison of Experimental and Predicted MACL Droplet Velocites 101 i i i : i— i i i 20 40 60 80 100 120 140 160 Downstream Distance [mm] Figure H.3. Mean axial centerline droplet velocity. Water; QL = 60 ml/min; PA = 55.2 kPa. Comparison of Predicted and Experimental MACL Droplet Velocities Predicted MACL Droplet Velocity [m/s] Figure H.4. Mean axial centerline droplet velocity correlation. Water; QL = 60 ml/min; PA = 55.2 kPa. Equation [1.4] was integrated between 70 < z < 210 mm to obtain a droplet residence time of 8.2 ms. From inspection of Figure H . l and H.2, Dio was not significantly affected by evaporation (for all relative humidity values plotted) during this time interval. For example, assuming a worst-case scenario of 40% relative humidity (Sahara desert or dry winter), the Dio decreased only by about 0.5 (am over 8.2 ms. The relative humidity within a spray is probably near saturation (100%). This, coupled with the short droplet residence times, supports our original assumption that diffusional evaporation effects for non-volatile droplets existing in self-similar temperatures are indeed minor. Turning our attention now to individual droplets: Figure H.5 shows the influence of diffusional evaporation on isolated droplets having different initial diameters at an ambient relative humidity of 40% and T- 25°C. 14 I 12 10 _L 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 . Elapsed Time [s] Figure H.5. Influence of diffusional evaporation on individual droplets. Far-field relative humidity: 40%. 172 

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