EFFECT OF NOZZLE LENGTH-TO-DIAMETER RATIO ON ATOMIZATION OF TURBULENT LIQUID JETS ANU RANJAN OSTA

Transcription

1 EFFECT OF NOZZLE LENGTH-TO-DIAMETER RATIO ON ATOMIZATION OF TURBULENT LIQUID JETS By ANU RANJAN OSTA Master of Engineering in Applied Mechanics Bengal Engineering and Science University Howrah, India 2005 Bachelor of Mechanical Engineering University of North Bengal Darjeeling, India 2003 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December 2010

2 EFFECT OF NOZZLE LENGTH-TO-DIAMETER RATIO ON ATOMIZATION OF TURBULENT LIQUID JETS Thesis Approved By: Dr. Afshin J. Ghajar Dr. Khaled A. Sallam Dr. Frank W. Chambers Chair Dissertation Adviser Dr. Arland Johannes Dr. Mark E. Payton Outside Committee Member Dean of the Graduate College i

3 To my family, teachers and friends I am because they are Et Augebitur Scientia And Knowledge Will Be Increased (Daniel 12:4) ii

4 TABLE OF CONTENTS ACKNOWLEDGMENTS......v LIST OF TABLES......vi LIST OF FIGURES......vii NOMENCLATURE......xi Chapter Page ABSTRACT......xv I. INTRODUCTION 1.1 Background General Statement of the Problem Past studies and Brief Literature Review Introduction Effect of Nozzle Geometry on Jet Breakup Turbulent Jets in Still Air Turbulent Jets in Gaseous Crossflow Some Relevant Dimensionless Numbers and Terms Specific Objectives General Organization of the Report...12 II. EXPERIMENTAL SETUP 2.1 Introduction Liquid Injection System Crossflow Generation System Optical Setup Holography Holographic Microscopy Shadowgraphy...24 iii

5 2.4.4 X-ray Phase Contrast Imaging X-ray Phase Contrast Imaging Setup X-ray Image Normalization Calibration...31 III. JET BREAKUP IN STILL AIR 3.1 Introduction Flow Visualization Ligament Size and Distribution Ligament Séparation Distances Bubble Formation Spray Angle X-ray PTV...50 IV. JET BREAKUP IN CROSSFLOW 4.1 Introduction Test Conditions Flow Visualization Jet Surface Velocities Breakup Regime Transitions Onset of Breakup at the Upwind Surface Ligament Sizes along the Upwind Surface of Liquid Jet Breakup of Liquid Core...75 V. CONCLUSIONS AND FUTURE WORK 5.1 Summary Conclusions Future Work REFERENCES...97 APPENDIX A APPENDIX B APPENDIX C iv

6 ACKNOWLEDGEMENTS There are many people who have helped me on my way here and I take pleasure in thanking all of them. Their help made this thesis possible. I am thankful to my advisor, Dr. Khaled Sallam, whose encouragement, guidance and support from the initial to the final stages enabled me to develop and carry out this work to its present form. My gratitude to Dr. Afshin Ghajar, Dr. Frank Chambers and Dr. Arland Johannes for their invaluable assistance and suggestions, that made working on this thesis easy for me. Thanks in equal measure are due also to: Dr. Kamel Fezzaa who helped me with my experiments at APS, Argonne; to my fellow colleagues Jaiho Lee, Brian Miller and Ramprakash Sankarakrishnan who at some point helped me with my experimental work; Mr. Lee Clark who encouraged me to develop a liking for machining; to U.S. Department of Energy, Office of Science and NASA-EPSCoR for their support; and to all those people concerned whose names I am unable mention individually due to space restrictions. Lastly, I wish to thank my family who supported me in every possible way in this endeavor and to the almighty for his blessings. v

7 LIST OF TABLES Table Page 2.1 Equipment List Operating and initial conditions for jet in still air Spray angle for the present nozzle compared with previous results Flow field vector and particle velocity vector for PTV results Test conditions The coefficients in the C 1 (d lig /Λ) C 2 Vs (y lig / ΛWe 1/2 LΛ ) plot The coefficients in the breakup equation. 79 vi

8 LIST OF FIGURES Figure Number Page 1.1 Spray transition regions (Sallam, 2002) Effect of nozzle passage length on the liquid jet (McCarthy and Molloy, 1974) Nozzle geometry used by (a) Sterling and Sleicher (1975) and (b) Hiroyasu (2000) (both A and B) Pulsed-photographs of round liquid jets injected into still air for various L/d ratios, Wu et al (1995) Schematic of a turbulent liquid jet breakup in uniform crossflow Nozzle geometry of (a)wu et al. (1997), (b) Birouk et al. (2003), (c) Bellofiore et al. (2007), and (d) Lee et al. (2007) (a) Ligament Tip and (b) Base breakup (Sankarakrishnan et al., 2005) Diagrammatic sketch of a typical nozzle Schematic showing the liquid injection system Sketch of the Nozzle Geometry used in the present investigation Side elevation of the subsonic wind tunnel In-line digital holography setup (Miller et al., 2008) Co-ordinates system representing the digital hologram reconstruction process Digital in-line holographic microscopy setup (a) Digitally Recorded Hologram of the jet boundary and (b) Digital Reconstruction of the same vii

9 2.8 Diagram of the pin calibration, Lee et al. (2009) Digital in-line holographic microscopy experimental apparatus setup Lee et al. (2009) Shadowgraphy setup of a jet in crossflow Shadowgraph image of a turbulent jet from L/D = 10, D = 4 mm Transmission of an electromagnetic wave through a piece of matter of thickness d and complex refraction index n (El-Ghazaly et al., 2006) Schematic diagram of the x-ray experimental set-up (APS online resources) X-ray image of the jet showing (a) the surface ligaments and the bubble entrainment in the jet (b) simulation of air bubble in water and (c) simulation of a water droplet in air X-ray experimental setup A 400-Gold Grid, was used for spatial calibration where each period was 63.5 m X-ray imaging of turbulent liquid jet in still air at v j = 26 m/s for 0 d j 1.5 d j for (a) L/D = 10 D = 4 mm and (b) L/D = 40 D = 4 mm L/D = 10, D = 4 mm Nozzle injected into (a) Vented and (b) Non vented enclosures, from streamwise distance, y = 1.5dj to 3dj. Only the left-half portion of the jet is shown for clarity, with the jet motion in the vertically downward direction Liquid jet breakup for L/D = 40. (a) Map patched with high resolution x-ray images showing examples of spotted ligaments. (b) Zoom-in image with the edge of a ligament outlined in black lines Sketch of ligament showing the projected length (L lig ), diameter (d lig ) and area (A lig ) definitions Faeth and Sallam (2003) viii

10 3.5 Diagrammatic representation of the jet cross sectional plane showing a typical ligament location Ligament size distribution projected along the jet centre plane for (a) L/D = 10 and (b) L/D = Ligament size distribution along the stream wise direction for (a) L/D = 10 and (b) L/D = 40, D = 4 mm Diagrammatic representation of the ligament distribution mapping on the jet surface Ligament separation plot for L/D = 10, D = 4 mm (a) L, d1, d2 plot (b) L, d1 plot (c) L, d2 plot Ligament separation plot for L/D = 40, D = 4 mm (a) L, d1, d2 plot (b) L, d1 plot (c) L, d2 plot Surface efficiency parameter near the onset of breakup The x-ray jet image showing the surface ligaments and the bubble entrainment in the jet Bubble size variation along the streamwise direction for sub-atmospheric jet injection (a) X-ray PTV image above showing the seed particles inside a ligament and (b) the correlated velocity vectors (a) Shadowgraph of turbulent jet in crossflow L/D = 10 and D = 4 mm at We g = 330, u = 70 m/s, v j = 20 m/s, (b) Shadowgraph of turbulent jet in crossflow L/D = 40 and D = 4 mm at We g = 330, u = 70 m/s, v j =20 m/s The hologram of the turbulent jet (injected in the vertically downward ix

11 direction) in crossflow (taking place from left to right) for nozzle diameter 2 mm and (a) L/D = 20, (b) L/D = 40 shown for a distance of 20 jet diameters for We g = 170, u = 70 m/s Mean liquid surface velocities in the streamwise direction as function of streamwise distance from jet exit A simplified representation of the primary breakup process Jet breakup regime map of We LΛ q 1/n vs. We G Jet breakup regime map of (We LΛ ) m q 1/3 vs. We G Jet breakup regime map of We LΛ q 1/3 vs. Re LΛ Onset of Breakup against the Jet Weber number Ligament size vs. the streamwise distance on the upwind surface for different passage lengths Ligament size vs. the streamwise distance on the upwind surface for different radius of curvature Modified ligament size vs. the streamwise distance on the upwind surface for the different radius of curvature and passage lengths Plot of jet breakup time and breakup location against the crossflow Weber number The breakup length, y b /d j, as a function of the momentum flux ratio q, for L/D = 10, 20 and x

12 NOMENCLATURE A A lig A v A m BW c D d i d j d lig area Ligament projected area incident undisturbed EM wave outgoing EM wave Band width speed of light Inner diameter of the nozzle streamwise jet diameter at onset of drop formation. liquid jet diameter at jet exit. ligament effective diameter. FWHM Full width half maxima h I L L/D amplitude transmission function. Intensity Length of the nozzle passage Length/diameter ratio of the nozzle passage n i number of ligaments of size (d lig ) i q Flow momentum ratio, (ρ L v j 2 /ρ G u G 2 ) M Momentum flux ratio, (ρ G u G 2 / ρ L u L 2 ) MMD Mass median drop diameter of the spray. xi

13 n NA O refractive index Numerical Aperture Object beam Oh Ohnesorge number, μ L /(ρ L d j ζ ) 1/2 ph R R Number of photons Reference beam. Radius Re G Cross stream Reynolds number, (ρ G u G d j /μ G ) Re Ld Liquid jet Reynolds number, ( ρ L v j d j /μ L ) S circumferential length SMD Sauter Mean diameter t t * u u cap v We G Time. Characteristic time d j (ρ L /ρ G ) 1/2 /u G Cross stream velocity (in the horizontal direction) Capillary velocity Stream wise velocity (in the vertical direction) Crossflow Weber number, (ρ G d j u 2 G /ζ) We LΛ Jet Weber number, (ρ L Λv j 2 /ζ) x Δx y Crosstream distance (horizontal) Distance between neighboring pixels in x direction Downstream distance (vertical) xii

14 Δy Distance between neighboring pixels in y direction Greek Absorption index Deviation of the refractive index of the material from unity ε Surface breakup efficiency factor as defined in Eq (3.5) η λ μ 0 ξ ρ g ρ L ρ 1 Vertical distance of a point in the reconstruction plane Wavelength Length scale corresponding to ligament and drop size during primary breakup Molecular viscosity Absorption constant Horizontal distance of a point in the reconstruction plane Gas density Liquid density Distance between a point in the hologram plane and a point in the reconstruction plane. ζ η Surface tension Exposure time Angle defined in Fig 3.5 θ o θ R Phase of object beam Phase of reference beam xiii

15 Angular frequency Phase shift Λ Turbulence integral length scale, d j / 8 Subscripts b G i j L lig surf Free stream gas property End of the liquid core property Gas property Location of onset of breakup Jet exit property Liquid property Ligament properties Surface property xiv

16 ABSTRACT Breakup of liquid jets is of considerable interest motivated by its applicability in combustion and propulsion systems (CI and SI engines), and agricultural fertilizer/pesticide sprays, among others. Almost all of the practical liquid injectors introduce some degree of turbulence in the liquid jet leaving the injector passage and an intriguing question is the relative importance of the liquid turbulence, cavitation, and the aerodynamic forces in the breakup processes of fuel injectors. A better design of liquid fuel injector would reduce pollutants and increase the efficiency of liquid fuel combustion processes. An experimental study to investigate the effect of nozzle length to diameter ratio on the surface properties of turbulent liquid jets in gaseous crossflow and still air was carried out. Straight cavitation-free nozzles with length/diameter ratios of 10, 20 and 40 were used to generate turbulent liquid jets in gaseous crossflow. The present study was limited to small Ohnesorge number liquid jets (Oh < 0.01) injected in crossflow within the shear breakup regime (We G > 110). The diagnostics consisted of pulsed shadowgraphy, pulsed digital holographic microscopy and x-ray diagnostics. The x-ray tests were conducted at the Advanced Photon Source (APS) facility of Argonne National Laboratory. The test matrix was designed to maintain the same aerodynamic forces in order to isolate the effects of jet turbulence on the breakup process. The measurements included liquid jet surface properties, breakup location of the liquid xv

17 column as a whole, the breakup regime transitions, bubble size inside the jet and seeding particle displacement inside the jet structures. The results include the jet surface characteristics, the liquid column breakup lengths, bubble growth, and phenomenological analysis to explain the observed results. It is observed that for a jet breakup in crossflow the injector passage length does play a role in determining the breakup length as well as influence the characteristics of the jet upwind surface. The present results for jet breakup in still air also show that the ligament distribution follows an arrangement along the jet surface and bubble formation associated with the jet breakup as well. The x-ray diagnostic allowed the surface and internal topography of fuel jets to be visualized and the breakup mechanism in the dense-spray near-injector region to be revealed. xvi

18 CHAPTER I INTRODUCTION 1.1 Background Liquid jet atomization applications include combustion and propulsion systems, spray discharge systems for industrial and agricultural processes and in our daily life accessories such as hair and body sprays, among others. Jet atomization manifests itself in many ways in the nature around us and is important in many industrial processes, too such as spray breakup in aircraft propulsion systems, after-burners in jet engines, gas turbine combustors, ramjet engines, liquid rocket engines, diesel engines, spark ignition engines and agricultural sprays besides others. The rapid advancements in engine combustion technology have prompted the need for improving atomization quality which basically controls the air fuel mixing and dispersion of combustion products in combustion engines. A great deal of the present effort is directed at developing fuel nozzles to meet the requirements of staged combustion. This is helpful in obtaining reliable information about the fuel distribution and homogeneity in the combustor primary zone. It is known that for a cylindrical liquid jet, the perturbations initiated at or before the ejection nozzle grow and eventually cause the jet disintegration in a quiescent atmosphere. The disintegration process for turbulent liquid jets is brought about by the breakup of the ligaments which have been generated by the jet surface instabilities into 1

19 droplets. As pointed out by Reitz and Braco (1982) and Lin and Reitz (1998), the injector geometry influences the liquid-jet breakup while the turbulence and cavitation within the nozzle are factors which can decisively cause the breakup of the liquid jet. The experiments carried out by Wu et al. (1995) showed that the L/D ratio of the constant area section of the injector passage as well as the Reynolds number of the flow through the injector passage affected the onset of breakup along the surface of the liquid jet. The role played by the internal turbulence in the liquid jet can never be ruled out as a high degree of turbulence in a jet could initiate jet instability and be the driving mechanism in causing the jet to disintegrate earlier than it would due to the aerodynamic interplay alone. In most practical cases, however, one would expect the instability initiated by the turbulence to get amplified by the aerodynamic forces acting on the jet and that the cumulative effect causes the jet to disintegrate. Liquid jet breakup is illustrated in Figure 1.1 where it can be seen that the dense spray region for pressure atomization involves a liquid core and a dispersed flow mixing layer followed by the transition to dispersed flow region at the end of the jet. The present experimental work investigates the effect of the nozzle length to diameter ratio on the nature of liquid jets, the breakup lengths, ligament formation, their distribution and subsequent breakup into droplets as well as the flow inside turbulent structures constituting a turbulent liquid jet. Shadowgraphy, Digital Holographic Microscopy and X-ray phase contrast imaging diagnostics have been used to achieve this goal. 2

20 1.2 General statement of the problem The study of the effect of a plain orifice atomizer with a finite straight passage length on the breakup of turbulent liquid jet injected by it in uniform crossflow was motivated by its relevant application to fuel injection systems in jet engines where rapid fuel penetration, mixing with crossflow and sustainment of combustion are desired. In the absence of advanced measuring techniques that are capable of operating in the optically-challenging dense-spray near-injector region, knowledge of the primary breakup mechanisms is limited. The objectives of the present study were to conduct experimental observation of the atomization of turbulent jets in still air as well as in crossflow issued from nozzles with different length/diameter ratio. The observations would be analyzed using phenomenological theories. Nozzles having L/D ratios of 10, 20 and 40 were used as most practical injectors have L/D that falls between 0 and 40. It is hoped that by employing digital holography and x-ray diagnostics a good understanding of liquid jet atomization would be achieved, which could further be used in designing practical injection systems. 1.3 Past Studies and Brief Literature Review Introduction The present study is an extension of the previous studies carried out on turbulent round liquid jet in still air and uniform crossflow. Rayleigh (1878) in his classical paper had shown that the jet breakup is the consequence of hydrodynamic instability. Kuehn (1925), Weber (1931), DeJuhasz et al. (1932) and Lee and Spencer 3

21 (1933) carried out further studies related to turbulence in liquid jets. Laufer (1950) and Ranz (1956) also investigated the behavior of turbulent single phase jets and the role played by the jet exit conditions while Tennekes and Lumley (1972), Hinze (1975) and Schlichting (1979), reviewed and reported similar work. Phinney (1973), Hoyt and Taylor (1977), Reitz and Bracco (1982), subsequently studied pressure atomized sprays in still gases and also concentrated on visualization of the near-injector region of the flow. Arai et al. (1988), Hiroyasu et al. (1991) and Karasawa et al. (1992) showed that for supercavitating flows the jet breakup could be suppressed. More recently Ruff et al. (1989, 1991, 1992), Tseng et al. (1992), Wu et al. (1991, 1993, 1995), Faeth et al. (1991, 1995), Hsiang et al. (1993, 1995) and Sallam et al. (2002) applied pulsed shadowgraphy, pulsed holography and gamma ray absorption techniques to study the primary and secondary jet breakup properties for turbulent/non turbulent jets, their surface properties, their flow development, their mixing properties for different injector geometries and test conditions and came up with phenomenological analyses to explain their observations. The theories which attributed the jet disintegration solely to air friction were disproved by injecting the jets into evacuated chambers and achieving disintegration by varying the pressure only (Lee and Spencer, 1933). Changes in the nozzle s internal flow pattern caused by separation and cavitation exhibit hysteresis effects and the corresponding jets have short breakup lengths (Lin and Reitz, 1998). Fargo and Chigier (1992) classified the breakup into three main categories, (1) Rayleigh type breakup (2) Jet disintegration via the stretched sheet mechanism (membrane type ligaments) (3) Jet disintegration via fiber type ligaments that peel off the liquid gas interface. 4

22 Besides the above mentioned studies a number of researchers investigated different aspect of turbulent liquid jets both in still air as well as in crossflow as mentioned below: Sallam et al. (1999) studied the turbulent primary breakup of annular liquid jets in still air including ligament and drop formation and breakup. Marmottant and Villermaux (2004) experimented on the coaxial jet in still air and found that the jet suffers a capillary Plateau Rayleigh instability. Lasheras and Hopfinger (2000) stated that the momentum flux ratio M was the primary parameter which determined the length of the unbroken liquid core. Fuller et al. (2000) studied the effects of injection angle on the breakup processes of turbulent liquid jets in subsonic crossflow and defined a breakup regime parameter based on jet operating conditions. Bellofiore et al. (2007) carried out studies relating to liquid injection in a transverse airflow at high pressure and temperature which corresponded to the range of operating conditions of lean, premixed, prevaporized (LPP) gas turbines. Liquid jet trajectory, breakup location, liquid phase dispersion in the gas phase, jet atomization and evaporation were the parameters investigated Effect of Nozzle Geometry on Jet Breakup The effect of nozzle geometry on the jet breakup has been investigated by many researchers. Sterling and Sleicher (1975) compared the results of breakup of capillary jets at high jet velocities from nozzles with L/D = 0, 49, 96 and found the jet length to be in disagreement with the prevailing theories due to overestimation of the 5

23 aerodynamic factors. They proposed a modification to Weber s theory considering the effect of ambient fluid viscosity on the normal stresses at the jet surface. They indicated that the thicker boundary layer velocity profile would break up faster due to the convection of large wavelength instabilities into the free surface. For the second windinduced regime, McCarthy and Molloy (1974) explained the effects of injector geometry and internal flow conditions on the breakup of glycerol-water jets in still air and showed that for increasing L/D ratios, the roughness of the jet surface increased which resulted in the jet breakup changing from the varicose type to the secondary atomization type (see Figure 1.2). From the figure it is evident that the larger wave instabilities associated with the higher L/D nozzle caused significantly more atomization and erosion of the liquid core. Hiroyasu et al. (1982, 1991, 2000) studied high velocity jet breakup as encountered in diesel engines and observed that cavitation at the nozzle s entrance decreased the breakup length in general. This cavitation could be controlled by the jet velocity and the geometry of the nozzle entry, and for strong cavitation the flow reattachment in the nozzle resulted in increasing breakup lengths. The results were less pronounced for high pressure atmospheres (3 MPa) because the aerodynamic effects far outweighed the hydrodynamic instabilities. Arai et al. (1985) carried out similar tests for Reynolds numbers higher than 30,000 and observed that for L/D ratios up to 50, the breakup length increased with L/D because the strong turbulence created by separation at the nozzle entrance was reduced and the internal nozzle flow profile became fully developed. In the spray region, however, the increase in the nozzle aspect ratio caused separation and cavitation, 6

24 exhibiting hysteresis effects resulting in changes in the nozzle s internal flow pattern and the corresponding jets having short breakup lengths. The nozzle geometry used by Sterling and Sleicher (1975) and Hiroyasu et al. (2000) is shown in Figure 1.3 Wu et al. (1991, 1992, 1995) and Wu and Faeth (1993) observed the flow development at the jet exit (see Figure 1.4) by removing the boundary layer formed along the converging nozzle passage, and providing constant diameter variable length passage. They showed that the boundary layer generated along the injector passage walls led to jet surface instabilities. Zhang et al. (2005) investigated the influence of dissolved methane on fuel atomization for different L/D ratios and concluded that increasing the L/D ratio will lead to the increase in the residence time of fuels containing dissolved methane inside nozzles thus improve atomization Turbulent Jets in Still Air McCarthy and Molloy (1974) and Hiroyasu (1985, 2000) investigated the effects of injector geometry, internal flow conditions, and supercavitation on the breakup of turbulent jet in still air. Hoyt and Taylor (1977), Karasawa et al. (1992), Wu et al. (1993, 1995), Dai et al. (1998), Sallam et al. (2002, 2003), carried out studies on turbulent liquid jet breakup characteristics in still air related to drop and ligament sizes and velocities at onset and after turbulent primary breakup in bow sheets, primary and secondary breakup of round jets in still air, their breakup modes, and the jet surface properties. Ruff et al. (1989, 1990, 1991), Tseng et al.(1992), and Wu and Faeth (1993, 1995) also studied the liquid breakup properties at the surface of turbulent round liquid 7

25 jets in still gases using pulsed shadowgraphy and holography to observe the surface properties during liquid jet breakup and also drop formation properties after the breakup. Wu et al. (1992, 1995) assumed that the drop breakup at the liquid surface was a result of deformation of the liquid surface by turbulent eddies of comparable size which were in the inertial and large-eddy sub ranges of the turbulence spectrum Turbulent Jets in Gaseous Crossflow Breakup processes along the free surface of round turbulent liquid jets in uniform gaseous crossflow (see Figure 1.5) is of recent interest due to its importance in various industrial and natural processes. Recently Fuller et al. (1998), Aalburg et al. (2005), Sallam et al. (2006) investigated the breakup of turbulent liquid jets and the spray characteristics in uniform gaseous crossflow. Past work done on the turbulent breakup of liquid jets in still air showed a considerable aerodynamic effect on the jet breakup for liquid to gas density ratios of less than 500 (Wu and Faeth, 1993). Lee et al. (2007) carried out investigation on the breakup of fully turbulent liquid jet (L/D > 100) in crossflow and compared their results to the breakup of nonturbulent liquid jet (L/D = 0) in crossflow (Sallam et al., 2004) at conditions where liquid viscosity had negligible effect (Ohnesorge numbers were less than 0.12) and observed that the formation of ligaments and drops on the downwind side was enhanced by the presence of crossflow, which was due to a reduction in the pressure along the sides of the liquid jet. The onset of turbulent primary breakup was accelerated because of this reduction in pressure and it always occurred at some distance from the jet 8

26 exit, approaching the jet exit at large jet Weber numbers. The breakup times of the turbulent liquid jets were smaller than those for nonturbulent liquid jets. Sallam et al. (2006) classified the turbulent jet breakup in gaseous cross flow into two major regimes known as aerodynamic breakup regime and turbulent breakup regime. Breakup properties of turbulent liquid jets in crossflow for different fluids and conditions including atomization of the liquid core have also been pursued by Wu et al. (1997), Cavaliere et al. (2003), Yoon (2005), Bellofiore et al. (2007), Birouk et al. (2003) and Mashayek and Ashgriz (2009). The nozzles used by (a)wu et al. (1997), (b) Birouk et al. (2003), (c) Bellofiore et al. (2007), and (d) Lee et al. (2007) are shown in Fig. 1.6 respectively. The above studies showed that jet disintegration occurs in two stages: (1) The disintegration of the liquid jet, termed as the primary breakup of liquid jet, and (2) the disintegration of the liquid droplets, termed the secondary breakup of the liquid droplets. The ligament formation and the breakup of ligaments into drops is shown in Figure Some Relevant Dimensionless Numbers and Terms The conditions for the liquid jet breakup are often characterized by certain dimensionless numbers which relate the forces tending to destabilize the jet to those forces tending to stabilize it. Usually the surface tension and liquid viscous forces attempt to stabilize the cross sectional area of the jet column by retarding the deformation of the jet against the prevailing aerodynamic forces and the internal turbulent kinetic energy of the jet. 9

27 (a) Ohnesorge Number (Oh): The Ohnesorge number ( L /(ρ L d j ζ) 1/2 ) represents the ratio of the viscous forces to surface tension forces. For primary breakup of liquid jets in gaseous crossflow, viscous effects become important when the Ohnesorge number exceeds 0.1 (Hsiang and Faeth, 1993). (b) Crossflow Weber Number (We G ): The crossflow Weber number ( ρ G d j u 2 /ζ) represents the ratio of the aerodynamic force of the crossflow to the surface tension force of the liquid jet. For small viscous effects (Oh <<1), the breakup regime transitions for the primary breakup of liquid jets in gaseous cross flow are solely controlled by the crossflow Weber number. (c) Reynolds Number (Re): It represents the ratio of the inertial forces to the viscous forces ( ρ L u j d j / L ) of the liquid jet. The turbulence of a liquid jet increases with increasing Reynolds number. (d) Capillary velocity (u cap ) : It is defined as ( (ζ/(ρ L d j )) ). The above quantities are linked through the relation Oh.Re = u j / u cap (1.1) (f) Nozzle: A nozzle is a device which facilitates the efficient conversion of pressure into flow energy (McCarthy and Molloy, 1974). The geometrical factors influencing the nozzle exit flow, (see Figure 1.8) are, (1) Contraction ratio (d/d) (2) Nozzle aspect ratio (L/D mean ) (3) Shape (Streamlining) of the nozzle interior (4) Smoothness of the nozzle interior 10

28 1.5 Specific Objectives The specific objectives of the present study were as follows: 1. To extend the past work done by Sallam (2004) for laminar liquid jets in uniform crossflow and Lee et al. (2007) for fully developed turbulent jets in uniform crossflow by considering nozzles with different Length/Diameter ratios. 2. Complete new measurements for different Length/ Diameter ratio nozzles, of the breakup length of the turbulent liquid jet breakup, the conditions at the onset of jet breakup, finding ligament /drop size and ligament /drop velocity distributions along the liquid surface. 3. Complete new measurements on the surface of turbulent jet in still air using x- ray phase contrast diagnostics and measure the ligament distribution along the jet surface and to identify the effects of dissolved gases on primary breakup. 4. To develop phenomenological analyses to interpret and correlate new measurements, in order to provide more understanding of the relation between the primary breakup processes and the jet turbulence. 11

29 1.6 General Organization of the Report This report is organized into five chapters. Chapter one covers the background, the problem statement, previous studies, and the specific objectives. Chapter two describes the experimental setup and the measuring techniques used. Chapter three gives results obtained from the jet in still air whereas Chapter four presents the result obtained by the jet breakup in crossflow. Finally, Chapter five presents the conclusions. 12

30 Figure 1.1 Spray transition regions (Sallam, 2002). Figure 1.2 Effect of nozzle passage length on the liquid jet (McCarthy and Molloy, 1974). 13

31 Figure 1.3 Nozzle geometry used by (a) Sterling and Sleicher (1975) and (b) Hiroyasu (2000) (both A and B). Figure 1.4 Pulsed-photographs of round liquid jets injected into still air for various L/d ratios, (Wu et al., 1995). 14

32 Figure 1.5 Schematic of a turbulent liquid jet breakup in uniform crossflow. Figure 1.6 Nozzle geometry of (a) Wu et al. (1997), (b) Birouk et al. (2003), (c) Bellofiore et al. (2007), and (d) Lee et al. (2007) 15

33 (a) (b) Figure 1.7 (a) Ligament Tip and (b) Base breakup (Sankarakrishnan et al., 2005). Figure 1.8 Diagrammatic sketch of a typical nozzle. 16

34 CHAPTER II EXPERIMENTAL SETUP 2.1 Introduction This chapter outlines the equipment and methodology used to carry out the experimental investigation. The experimental setup comprised the liquid injection system, the crossflow generation and the optical setup. The entire optical setup was mounted on a breadboard under the test section of the wind tunnel. The breadboard could be moved horizontally with a resolution of 0.5 mm. 2.2 Liquid Injection System Figure 2.1 depicts the primary liquid injection system. It consists of the nozzle assembly mounted flush with the wind tunnel test chamber s upper glass ceiling. The test liquid was contained within a cylindrical steel chamber with a diameter of 76.2 mm and a length of mm, constructed of Type-304 stainless steel. The liquid was injected using pressurized air vertically downward into the air crossflow flowing from left to right. The top part of the storage chamber is fitted with a top flange that is secured with eight screws to the cylindrical storage chamber and has two ports for the air lines and one port for the liquid fill line. The liquid fill line is connected to a ball valve that could be opened or closed after filling in the test liquid into the cylindrical chamber. The lower part of top flange is connected with a baffle. The bottom part of the cylindrical chamber 17

35 is fitted with a flange that contains the nozzle. The nozzle (shown in Figure 2.2) has a smooth rounded entrance to minimize cavitation effects followed by round constant area passage having length-to-diameter ratios of 10, 20 and 40. The liquid jet is injected by opening the solenoid valve using a pulse generator to admit high pressure air into the test chamber. 2.3 Crossflow Generation System The crossflow is generated using a subsonic wind tunnel manufactured by Engineering Laboratory Design Inc. It has a 16:1 contraction ratio with a test section cross sectional area of 0.3 x 0.3 m 2. The turbulence level in the test section is less than 0.25%. Variation in the test section velocity causes a wide range of crossflow Weber numbers to be achieved. Test section side-walls and floor are made of float glass for optical accessibility. The ceiling has a provision for mounting the test chamber and nozzle assembly supported by unistrut frames built around the test section. The side elevation of the wind tunnel is shown in Figure 2.3. A pitot static tube (United Sensors Model PDC-18-G-16-KL) is attached to the end of the test section in the centerline, extending into the section and is connected to an inclined tube 0 10 H 2 O manometer (Dwyer Model No Kit) though two clear plastic tubes. 2.4 Optical Setup For visualizing jet in crossflow the diagnostics adopted were Holography and Shadowgraphy while for the jet in still air x-ray phase contrast imaging was adopted. They are described next. 18

36 2.4.1 Holography Holography which is a technique whereby the interference pattern between a wave field scattered from the object after transmission through it and a coherent background, (called the reference wave) is recorded photographically (Schnars and Jeuptner (2002)), does not have the limitation of the depth of field and can be reconstructed at any distance normal to the 2D image plane. A sketch of digital in-line holography setup is shown in Figure 2.4. This technique was first invented by Gabor (1948) and later improved by Leith and Upatnieks (1962). Other research work in this field was done by Goodman and Lawrence (1967), Santagelo and Sojka (1995), Benatari et al. (1998), Sun et al. (2002, 2005), Javidi and Tajahuerce (2000), Meng and Pan (2003), Jeuptner et al. (2006), among others. Digital holography is unaffected by the non-spherical droplets and ligaments that are usually encountered very close to the injector exit, and often cause problems for other non imaging techniques such as PDPA. Depending on the angle between the reference wave and the object wave, in-line holography of zero reference angles and off-axis holography of non-zero angles exits. Mathematically the basic holographic process can be described as follows (Schnars and Juptner, 2002), The object wave is represented by O( x, y) o( x, y)exp( i ( x, y)) (2.1) o with o as real amplitude and o as phase. Similarly the reference wave is described by R( x, y) r( x, y)exp( i ( x, y)) (2.2) 19 R

37 with r as real amplitude and R as phase. Both the waves interfere at the CCD sensor with the resulting intensity given by 2 * I( x, y) O( x, y) R( x, y) = ( O( x, y) R( x, y))( O( x, y) R( x, y)) (2.3) where * denotes the complex conjugate. For reconstructing the hologram the amplitude transmission is multiplied with the reconstruction (reference) wave, R ( x, y) h( x, y) (2.4) The recorded hologram could be described by the Fresnel Kirchhoff integral i (, ) 2 exp( i 1 ) h x y R x y 1 (, ) (, ) cos dxdy (2.5a) with ( x ) ( y ) d (2.5b) where h(x, y) is hologram function and ρ is the distance between a point in the hologram plane and a point in the reconstruction plane,, are coordinates on the hologram plane as shown in Figure 2.5. For numerically reconstructing the hologram, the discreet Fresnel Transform is employed using the convolution theorem. The image plane is then given by (, ) h ( x, y) R( x, y) g(,, x, y) dxdy (2.6) 20

38 exp i d ( x ) ( y ) i g (,, x, y) (2.7) d ( x ) ( y ) So Γ(, ) is calculated by first Fourier transforming (h R), followed by multiplication with the Fourier transform of g, and then taking an inverse Fourier transform of the resulting product. The optical setup consists of a light source which is two frequency-doubled Nd:YAG lasers (Spectra Physics model LAB SERIES , 532 nm wavelength, 7-10 ns pulse width duration, and up to 300 mj per pulse) that could be controlled to provide pulse separations as small as 100 ns, for double pulsed holography. The timing of the firing of the liquid jet and the firing of the optical system can be controlled by an eightchannel pulse generator (Quantum Composers, Model 9518) that has a 10 ns resolution and a control of delay ranging from sec. The beam is split using a polarized beam splitter cube. Identical polarization is then achieved by the use of a quarter wave plate and another polarized splitter cube. The resulting two beams are expanded and then collimated using a beam expander (objective lens + spatial filter) and convex lens combination. The object beam is made to pass through the object and after refraction, is combined with the reference beam via a non polarizing beam splitter plate, and the resulting interference pattern is then recorded on a CCD sensor. Magnification can be introduced by using a convex lens as relay lens after the object beam has passed through, the object and this magnified hologram then was recorded on the CCD sensor. The camera used was pco 2000 CCD camera manufactured by Cooke Corporation, having a 21

39 resolution of 2048 x 2048 pixel arrays, with pixel size 7.4 μm by 7.4 μm and running at 15 fps at full resolution. The recorded hologram is then reconstructed using a MATLAB program which solves the Rayleigh Sommerfeld formula for reconstruction of a wave field and is essentially based on the convolution type approach as discussed in Schnars and Juptner (1999, 2002). This is done with the use of the Fast Fourier Transform algorithm. The method of average intensity subtraction is used to suppress the DC term when reconstructing the hologram Holographic Microscopy A problem with using the relay lens for increasing magnification is that it works adequately for low levels of magnification but lens aberrations begins to present a problem at higher levels of magnification. The noise thus introduced poses a large problem for examining smaller details within the image. To visualize objects in such a situation with a very limited depth of focus due to the high magnification digital holographic microscopy is adopted as shown schematically in Figure 2.6. Holography does not have the limitation of the depth of focus and provides 3D images that can be reconstructed at any 2D plane. In the present holographic setup, ligaments and jet surface irregularities as small as 5 micron could be observed. Here the approach is much the same as the previous described setup except that only one beam expanded with an objective lens is used and then it is passed directly through the test section to the CCD. In order to obtain a high resolution in the reconstructed image the object has to be placed near to the objective lens and in order to have large field of view the object has to be 22

40 placed near the CCD. The necessary distance to obtain a resolution ', ' with the Fresnel approximation is ' = d /N x and ' = d'/n y (2.8) Here Δξ' (μm), ' (μm) is the resolution, λ (μm) is the wavelength of the light, d' (μm) is the recording distance from the object to the CCD, N is the number of pixels, and Δx (μm) by Δy (μm) is the pixel size. A sample hologram of the liquid jet surface and its reconstructed image is shown in Figure 2.7 (a) and (b), respectively. To apply physical dimensions to the images a calibration must be made to determine what length each pixel represents. The calibration target was the USAF 1951 resolution target which was used for ascertaining the resolution at a particular image reconstruction plane. However since the spatial resolution changes with reconstruction distance a target similar to Lee et al. (2009), consisting of four pins of diameter 0.5 mm placed diagonally at intervals of 2 mm in the spanwise and streamwise direction from each other was used, as shown in Figure 2.8. The length/pixel obtained by measuring the average pin diameter for each of the reconstructed respective pin image was plotted against the reconstruction distance and a spatial calibration fit curve was thus obtained. Similarly by plotting reconstruction distance separation versus the actual pin separation, the length/pixel calibration curve versus the actual distance from the CCD could be obtained. Digital magnification in the reconstruction process can be achieved either by changing the wavelength of the reference beam or the position of the reference beam point source. The entire digital holographic microscopy apparatus is similar to Lee et al. (2009) and the set up is shown in Figure

41 2.4.3 Shadowgraphy Shadowgraphy is a flow visualization diagnostic wherein the variations in the optical density and the non-uniformities in a transparent media like air, water, or glass is revealed after passing collimated beam through them. The non-uniformities in the transparent media (e.g. water) are revealed by the shadow formed, the differences in light intensity being proportional to the second spatial derivative of the media. This can be imaged on a screen or digitally recorded. Though the phenomenon of shadowgraph is as old as nature itself its scientific usage was demonstrated by Robert Hooke and later by Settles (2006) among others. A schematic representation is depicted in Figure The incident laser beam is expanded using objective lens, pinhole arrangement (spatial filter) and then passed through a collimating lens to provide a beam with uniform diameter of 2.5 inches approximately, which is then passed through the region of interest to be observed. After passing through the liquid jet region in the wind tunnel test section, this collimated beam passes through the relay lens and forms a real and inverted image of the object lying in the region of observation. The shadowgraphs are formed on the ground glass screen which is then recorded by a Nikon D70 camera as shown in Figure For double-pulse shadowgraphy, two laser light sources having different pulse energies controlled by using quarter wave plates are used in order to resolve the directional ambiguity of the image. The collimated laser beams with approximately same beam diameters are passed through the region under observation, with a very small time interval between them and the double pulsed image is then recorded by a CCD camera. 24

42 The distance traveled by the corresponding points such as a ligament base, on the two individual images or a single double exposed image, is then measured using the Sigma Scan software. This distance divided by the pulse interval gives the jet velocity (v j ). Shadowgraphy always gives the projected size of the droplets and the jet surface structures formed at the jet periphery, but any overlapping ligament or droplet information is lost due to obscurity by the larger structure. If recorded on a film (e.g. Polaroid), shadowgraphy gives the freedom of obtaining a very large field of view. Single-pulsed shadowgraphs, such as those shown in Fig. 2.11, can provide large field of view useful for investigating the breakup of the liquid column as a whole. The shadowgraphs have limited depth of field and so are not useful in observing very small droplets or ligaments X-ray Phase Contrast Imaging Phase contrast is the phenomenon that occurs when x-rays passing through a sample undergo refraction/propagation because of differences in sample absorption to produce interference effects thus yielding a contrast pattern. This is particularly sensitive to boundaries of phase media as it provides a contrast differentiation. Phase-enhanced techniques can in some cases (e.g. in the hard x-ray ( kev) regime) improve the image contrast by orders of magnitude. The natural edge enhancement that is observed in the images does not follow any linear behavior and so is unable to accurately indicate the thickness or density of the sample. To transform the observed intensity distribution of the images into a phase distribution by which the sample structure is more accurately reflected, phase retrieval of the images needs to be carried out. This would lead to 25

43 information about the shape and thickness of the object and the internal composition of the sample. Wilkins et al. (1996) describes the phase contrast imaging principles in detail. When an x-ray beam passes through a matter (sample), some absorption of photons occurs along with some scattering of photons from the beam which results in a phase shift and the reduction in the intensity of the beam known as attenuation. This creates very small variations in the speed and direction of x-rays (refraction/propagation) because of the differences in sample absorption and produces interference effects at the boundaries which reveal a significant contrast. The amount of absorption depends on the thickness and density of the sample which may be related to features and structure within the sample. After interaction with the sample, the x-ray s wave field propagates in free space and its different components having been diffracted by the sample start to overlap and interfere, giving rise to a contrasted pattern of light and dark fringes around the edges of features. Figure 2.12 depicts the transmission of an electromagnetic wave through a piece of matter of thickness d and complex refraction index n. Following the description shown in El-Ghazaly et al. (2006) the refractive index of the x- ray could be represented by n( ) = 1 - ( ) + i ( ) (2.9) where Re{n( )} = 1 - ( ) is refraction of the wave of angular frequency, ( ) is the deviation of the refractive index of the material from unity and Im{n( )} = ( ) is the attenuation of the x-ray s known as the absorption index. The measured x-ray intensity and the mass of liquid in the path of the beam is given by Powell et al. (2003) I / I 0 = exp { 0 M L } (2.10) 26

44 where I and I 0 are the transmitted and incident x-ray intensities, respectively, M L is the mass of liquid in the path of the x-ray beam, and 0 is the absorption constant. Demonstrating the transmission of an electromagnetic wave through a piece of matter of thickness d, we can represent the undisturbed wave propagation in x-direction by A v = A 0 exp{i[ t-k v d]} where k v = /c (2.11) The amplitude of the outgoing wave behind the object is represented by A m = A 0 exp{i[ t-k m d]} where k m = n/c (2.12) Comparing equations 2.11 and 2.12, we can say the transmitted wave suffers a phase shift = ( /c) ( )d (2.13) relative to the undisturbed wave, and an attenuation A m / A v = exp{( /c) ( )d } (2.14) Any rapid variations in the refractive index or thickness of the sample will be imaged as sharp losses (variations) in intensity at the corresponding points in the image. This allows high-speed and high resolution visualization of the surface and internal topography of fuel jets to be visualized and the breakup mechanism in the dense-spray near-injector 27

45 region to be revealed as in Lin et al. (2008). This is desired because all of the conventional diagnostics using diffraction, exciplex fluorescence, and pulsed laser methods used to study dense sprays have been limited by the scattering of light from the droplets surrounding the relatively dense spray core region as well as the optical inaccessibility of the spray core region itself X-ray Phase Contrast Imaging Setup The tests were conducted at the Advanced Photon Source (APS) facility of Argonne National Laboratory at XOR 32-ID beamline. The setup was similar to Vabre et al. (2009), shown in Figure The undulator source, produces a collimated x-ray beam in a wide energy range (1-100 kev) which has high brilliance, small size, broad energy spectrum and flexible time structure (hybrid-singlet mode) necessary for this white-beam ultra-fast imaging technique. The undulator gap is set to 20 mm, most of the intensity is located within the first harmonic at 9 kev, with a peak brilliance of ~ ph/s/mrad 2 /mm 2 / 0.1% BW, and a natural bandwidth of 0.3 kev FWHM. The sample stage is placed at a distance of 40 m downstream from the source. The transmitted x-rays are converted into visible light (434 nm) by a fast scintillator crystal (LYSO:Ce, with a 40 ns decay time). The sample-scintillator distance, is adjusted so as to correspond to an optimized defocus value for Fresnel propagation contrast and spatial resolution and was set to 50 cm. The CCD camera (Sensicam from Cooke Corp., 1024x1024 pixels and 6.7 µm pixel size) is coupled to the scintillator using a microscope objective (X5, NA = 0.14) and a 45º mirror and records the images at a high speed. The effective pixel size, matched to the available x-ray beam size was 1.3 µm, and the field of view was 1.3x1.7 mm 2. The 28

46 pulsed nature of the x-ray beam combined with an adequate shuttering and timing of the setup provided an effective exposure time of 150 ps for each image. In addition to some weak absorption effect, the contrast in the recorded images with this propagation-based imaging technique comes from a phase affect. After interaction with the sample, the x-ray s wave field propagates in free space and its different components having been diffracted by the sample starts to overlap and interfere, giving rise to a contrasted pattern. This contrast depends on the Laplacian of the phase shift undergone by the beam upon its passage through the sample, Wilkins et al. (1996). As a consequence, this technique is most sensitive to boundaries and interfaces between materials with different refraction index or abrupt thickness variations, which are greatly enhanced. Also, due to refraction and for the same interface, different curvatures will have very distinct "signature" contrasts. For instance, a bubble (gas surrounded by liquid) will have a dark/bright outer edge whereas a droplet (liquid surrounded by gas) will have an opposite boundary contrast (bright/dark) as illustrated in the simulations shown in Fig This allows the surface and internal topography of fuel jets to be visualized and the breakup mechanism in the dense-spray near-injector region to be revealed. The experimental apparatus is shown in Fig The test liquid was contained within a cylindrical liquid supply stainless steel chamber. The turbulent round liquid jet was injected vertically downward through the nozzle by using a pressure feed system through a solenoid valve i.e. air at psi (from a pressurized air tank), into a collecting bucket. A baffle at the air inlet prevented undesirable mixing between the air and the test liquid. 29

47 X-ray Image Normalization The phase contrast images (IMAGE) obtained with the jet flow need to be normalized in order to exhibit the contrast/intensity gradients more efficiently. This is achieved by recording a background image without the jet under the same lightning conditions as the rest of the images. This is denoted as BRIGHT. A similar background image obtained in the absence of all ambient lightening is also obtained and is denoted as DARK. Then by following the given algorithm the normalization process is accomplished. If both BRIGHT and DARK images are specified IMAGE = scale * (IMAGE - DARK) / (BRIGHT - DARK) If only BRIGHT image is specified IMAGE = scale * IMAGE / BRIGHT If only DARK image is specified IMAGE = IMAGE DARK Scale is a number to scale resulting binary image back to the 255 grayscale value after division by BRIGHT. In some cases the uniformity of illumination cannot be maintained due to uncontrollable reasons resulting in some degree of brightness towards the image borders after normalization. Once the images have been normalized, the surface topography is zoomed to visualize the surface dynamics, measurements are carried out with respect to the ligament size and their surface distribution. 30

48 Calibration A 400-Gold Grid, shown in Figure 2.16 was used for spatial calibration where each period was 1 inch / 400, which is 63.5 µm. The results obtained are discussed in the next chapter. 31

49 Figure 2.1 Schematic showing the liquid injection system. Figure 2.2 Sketch of the nozzle geometry used in the present investigation. 32

50 Figure 2.3 Side elevation of the subsonic wind tunnel. 33

51 Figure 2.4 In-line digital holography setup (Miller et al., 2008). Figure 2.5 Coordinates system representing the digital hologram reconstruction process. 34

52 Figure 2.6 Digital in-line holographic microscopy setup. (a) (b) Figure 2.7 (a) Digitally recorded hologram of the jet boundary and (b) Digital reconstruction of the same. 35

53 Figure 2.8 Diagram of the pin calibration, (Lee et al., 2009). 36

54 Cylindrical chamber Figure 2.9 Digital in-line holographic microscopy experimental apparatus setup (Lee et al., 2009). 37

55 Injection Figure 2.10 Shadowgraphy setup of a jet in crossflow. Crossflow Figure 2.11 Shadowgraph image of a turbulent jet from L/D = 10, D = 4 mm. 38

56 Figure 2.12 Transmission of an electromagnetic wave through a piece of matter of thickness d and complex refraction index n (El-Ghazaly et al., 2006). Figure 2.13 Schematic diagram of the x-ray experimental set-up, (APS online resources). 39

57 Figure 2.14 X-ray image of the jet showing (a) the surface ligaments and the bubble entrainment in the jet (b) simulation of air bubble in water and (c) simulation of a water droplet in air. 40

58 Figure 2.15 X-ray experimental setup. Figure 2.16 A 400-Gold Grid, was used for spatial calibration where each period was 63.5 m. 41

59 Table 2.1. Equipment List Component Manufacturer Model Description CCD Camera PCO. Imaging Cooke Corp. PCO x2048 pixels CCD Sensor Focusing Lens Nikkon D-AF Micro Nikkon 105 mm f/2.8 Nd:YAG Laser Spectra Physics Quanta-Ray Lab nm wavelength Optical Table Newport Corp Lab legs RL-2000 Flat mirror Newport Corp BD VIS 1 dia. POL Cubeport Corp. Beamsplitter Newport Corp 10BC16PC 532 nm Tp/Ts= 1000:1,25,4 mm Objective Lens Newport Corp M -20X, 0.4 Microscope, 20x Convex Lens Newport Corp KPX226AR.14 Quarter wave plate Thor Labs WPMH05M-532 Flat Mirror, Pyrex Thor Labs 30D10ER.1 Plate Beam Splitter Thor Labs BSW13 3 dia., 150 mm. (focal length) AR Coated, λ/2 = 532 nm 3 dia., R>93% 1 Dia., 50:50 42

60 CHAPTER III JET BREAKUP IN STILL AIR 3.1 Introduction The surface properties of a turbulent liquid jet injected in still air from nozzles with two different L/D ratios were observed. Highly energetic and penetrating x-ray beam was used to observe the ligaments sizes and distributions on turbulent liquid jets injected from two injectors with L/D = 10 and 40. The test matrix, Table 3.1, included testing two injectors with a smooth entry (to minimize cavitation) with length-to-diameter (L/D) ratio of 10 and 40 and was designed to isolate the effects of jet turbulence due to the nozzle passage length on the jet breakup process. The experimental apparatus has been discussed in the previous chapter (shown in Figs. 2.1, 2.2, 2.13 and 2.15). The data reduction methods were similar to previous work on breakup of turbulent jets in still air, Wu et al. (1995) and Lee et al. (2007). In the present work all the uncertainties in the measurements carried out were taken to be those for the 95% confidence level. 3.2 Flow Visualization An important objective of the present investigation was to visualize the surface of the turbulent liquid jet using x-rays as opposed to other competing diagnostics 43

61 such as shadowgraphy and digital holography (Osta and Sallam 2010). X-ray visualization is essentially a 3 dimensional jet surface topology projected on a 2 dimensional image revealed by the intensity variations. To visualize the breakup of the liquid jet in the near-injector region, a spray map was constructed with several highresolution images to overcome the small field of view used in the present study (1.3x1.7 mm 2 ). Figure 3.1 shows the patched x-ray images of turbulent liquid jet in still air at v j = 26 m/s from 0 d j 1.5 d j for L/D = 10 and L/D = 40, D = 4 mm. Figure 3.2 shows the patched x-ray images of L/D = 10, D = 4 mm nozzle injected into (a) atmospheric and (b) sub atmospheric enclosures. By zooming on the surface topography obtained in the x-ray images, measurements were made with respect to the ligament sizes and their spatial distribution. Ligaments were identified if they had a uniform density inside it (grayscale value), a darker boundary surrounded by a lighter background (simulation results). Some typical ligaments are outlined in black thick lines in Figure 3.3. Another condition that was adhered to was the length/(base diameter) ratio of the structures had to be greater than or equal to Ligament Size and Distribution The formation of ligaments close to the jet exit for large L/D ratios was discussed in Wu et al. (1991, 1992, and 1995) and Wu and Faeth (1993), and it takes place when a region of vorticity thickness develops near the jet surface. A diagrammatic sketch of a typical ligament (Sallam and Faeth, 2003) is shown in Figure 3.4. Ligaments were considered as approximately cylindrical and were represented by their average diameters. To find the ligament size, as shown in Figure 3.4, first the geometrical 44

62 alignment of the ligaments on the jet surface was identified. The ligament projected length was measured as L lig. The ligament effective diameter d lig was calculated from the measured ligament projected length L lig and the ligament projected area on the image A lig as d lig =A lig / L lig (3.1) It is an approximate representation of the ligament size. The ligament size was measured manually using the SigmaScan software as discussed previously. The circumferential position of ligament at any location y along the jet centerline having radius R was estimated as depicted in Figure 3.5. R was calculated by averaging the minimum and the maximum radius of the jet in the respective images. The circumferential length, S, corresponding to an angle could be calculated as S = R (3.2) where is given by = sin -1 (x/r) (3.3) The plot of the ligament distribution along the streamwise direction is shown in Figure 3.6 where the dashed gridlines mark the individual field of views of each x-ray image. The size of the circles corresponds to the ligament diameter. It is hard to confirm whether the ligaments are formed along ridges because of the limited field of view of each image and more importantly because the ligaments located at both the front and the back surfaces are indistinguishable from the present x-ray images. By increasing the field 45

63 of view one would still have only a 2D projection and the only way to distinguish the front from the back is to employ 3D tomography which is not currently possible in these short time scales. A quantity denoting the mean ligament diameter was calculated as shown in Eq. (3.4) ~ d lig = d 3 2 lig / d lig (3.4) for each streamwise interval, averaged and was plotted against y b /d j as shown in Fig The ligament diameters increased streamwise for the longer nozzle passage. The amount of counted ligaments varied from /image, and there were two image sets per nozzle for each injection condition. 3.4 Ligament Separation Distances In order to investigate the relationship between a ligament size and its separation distance from its neighbors, the ligaments located peripherally along the right or the left edges were considered and their separation distance, L, was determined according to Figure 3.8 by: L = (S 2 +y 2 ) (3.5) where y and s are the vertical and circumferential distance between those two ligaments. Whether the neighboring ligament is located on the front or the back surface, Eq. (3.5) will still be valid. Due to the indistinguishability of the surfaces (front or the rear) on which the ligaments are formed, Eq. (3.5) would be practically correct only when considering the peripheral ligament as the reference ligament, since the distances of the 46

64 neighbours situated on either the front surface or the rear would be the same. For a nonperipheral reference ligament the value of L would be inaccurate due to surface ambiguity of ligament location. A plot between a peripheral ligament (diameter d 1 ) and its neighbors (diameter d 2 ) and the corresponding distance L between them is shown in Figure 3.9 for L/D = 10, 4 mm and in Figure 3.10 for L/D = 10, 4 mm. The increase in L with increasing ligament diameters is suggestive that separation of the ligaments is influenced by the ligament sizes. This suggests that the creation of a ligament at a particular location reduce the amount of turbulent kinetic energy available to create more ligaments nearby. In order to investigate the rates of breakup, the present x-ray images were used to measure a surface breakup efficiency factor, ε, defined as an area ratio (ie. the total ligament cross sectional area in a particular region to the total area of the region) in the stream wise direction which could be is represented by ε as follows. ε = n i (( /4)d lig 2 ) i /A (3.6) where the limit ε = 1 represent conditions where ligaments are formed in continuous manner all over the liquid jet surface. Here the middle two rectangular gridline regions corresponding to those shown in Figure 3.6 were considered. The plot of ε as a function of streamwise distance for the L/D = 10 and 40 is shown in Figure The relatively large ligament separation distances measured in the present study suggest that generally ε << 1. The surface breakup efficiency factor is small for the two injectors as expected. The longer passage length nozzle has a higher surface breakup rate supported by the fact that it has a larger magnitude of surface activity following from the results of Figure 3.6. The 47

65 large scatter of the data due to the sampling limitation, however, renders the results for the two injectors indistinguishable. Further studies are needed to clarify if there an effect of the injector L/D ratio on the rates of breakup. A close-up view of the upstream jet surface is suggestive of the fact that the nozzle passage length as well as entrance curvature are some of the factors that could be designed to improve atomization quality in fuel injectors. The sample size of the ligaments measured was approximately 170 ligament pairs per injector. 3.5 Bubble Formation Presence of bubbles in the jet was observed for the nozzle L/D = 10 as shown in Figure 3.12 when injected in sub atmospheric pressure, but were absent when injected in atmospheric pressure. The sub atmospheric conditions were achieved by enclosing the flow field around the jet with transparent plastic having a diameter of 6 inches. Perforating small holes into the walls of this plastic enclosure ensured atmospheric conditions at the flow field inside the plastic enclosure. Since these bubbles showed up further down streamwise from the nozzle exit and were absent closer to the exit, it is reasonable to conclude that the bubbles are caused by the dissolved gases (air) in the liquid jet which suffered expansion and appeared as bubbles in the low pressure region. Sudden development of low pressure region would result in super saturation of the dissolved gasses and set in the bubble growth whereas turbulence would cause conditions favorable for bubble growth. Hiroyasu et al. (1991) describes the cavitation number of the internal flow inside the nozzle as K c = (P L -P v ) /{ (1/2)ρ L v L 2 } (3.7) 48

66 where P L is the pressure inside the nozzle at the cavitation location, P v is the vapor pressure of water, and v L is the velocity of liquid inside the nozzle (~ jet velocity). K c > 1 would indicate absence of cavitation, K c < 1 indicates existence of fixed cavitation, and K c < 0 indicates strong cavitation. Sou et al. (2007) defined the cavitation number in terms of the difference between the atmospheric pressure and the vapor pressure. For the present test conditions the existence of cavitation inside the nozzle is unlikely, because by taking the values of P L = 573 kpa (injection pressure), P v = 18 mm Hg, v L = 30 m/s, corresponding to the given test conditions, the value obtained for K c is Absence of bubbles for the same test condition, for both the nozzles, carried out in atmospheric pressure enclosure, strongly suggests the absence of cavitation. Thus cavitation as the cause for jet breakup is ruled out. The growth of bubble size along the streamwise direction for an upstream pressure range of 573 kpa for the nozzle L/D = 10, D = 4 mm, is shown in Fig The equation of the fit was D b /d j = (Y/d j ) 0.33 (3.8) where D b is the bubble diameter, d j is the jet diameter, and Y is the downstream distance. The correlation coefficient was This low value was due to sampling limitations. It also suggests that the present correlation is lacking other flow parameters (e.g. the nozzle geometrical factors, L/D, R/D). 3.6 Spray Angle The jets issuing out of the nozzle were observed to diverge. The mean divergence of the jets were measured and the spray angle calculated and compared with 49

67 those of Sou et al. (2007), Wu et al. (1983) and Shimizu et al. (1984) as described in Table 3.2. Taking into account the above mentioned studies including those of Reitz and Bracco (1982) and Hiroyasu (2000), the spray angle is observed to depend on fluid density ratio (ρ G / ρ L ), ambient gas pressure ( P amb ), injection velocity (v j ), type of the nozzle inlet (R/D), and the passage length (L/D). The jet angle was measured by measuring the jet diameter at different streamwise distances, manually and then calculating the mean slope of the jet surface boundary. A minimum of four sets of composed images for each nozzle at a particular injection condition were used and the mean angle was determined. 3.7 X-ray PTV The flow inside the ligaments and jet peripheral structures was investigated by double-pulsed x-ray phase-contrast imaging. Silver coated glass spheres having 8-12 μm diameters were used as seeding particles. The camera pixel size was 1.34 μm and the time between the exposures was 3.7 μs. The images were normalized and filtered as mentioned previously and the region of particle activity was identified. The seeded particles inside a typical ligament are shown in Fig. 3.14a. In order to visualize the flow behavior inside the ligament region the particle displacements in the flow direction were tracked and measured and the individual particle velocity calculated from them. The mean flow was then determined by averaging all the individual particle velocities. The mean flow was then subtracted from the velocity vector of each particle to give the resulting relative velocities, which were then plotted on the image as shown in Fig. 3.14b. Table 3.13 shows an example of the respective velocity vectors depicted in Fig A circulation 50

68 inside the ligament was observed for most of the cases. However this method only gives the projected speed on the plane perpendicular to the x-ray beam. In order to come up with a predictive flow pattern inside the ligaments more data and a good map of the flow is needed. This present demonstration thus shows that this technique will be successful in mapping the flow pattern inside the liquid ligaments at different streamwise locations along a liquid jet. Table 3.1. Operating and Initial conditions for Jet in Still air. Parameters Nozzle diameter (m) Nozzle entrance curvature (R/D) 1.2 Nozzle passage length (L/D) 10, 40 Density of gas, air (ρ air ) kg/m Dynamic viscosity of gas, air (μ air ) - Ns/m E-05 Surface tension of test liquid, water (ζ w ) N/m Density of test liquid, water. (ρ w )-kg/m Dynamic viscosity of test liquid (μ w ) Ns/m E-04 Jet Weber Number (We LD ) 50,700 Jet Velocity (V j ) m/s 26 `- 30 Jet Reynolds Number (Re LD ) ,000 Ohnesorge Number (Oh)

69 Table 3.2 Spray angle for the present nozzle compared with previous results. Researcher Present : L/D = 10 at 0.57 MPa L/D = 10 at 0.66 MPa Present : L/D = 40 at 0.69 MPa L/D = 40 at 0.34 MPa (Spray angle) (degrees) Sou et al L/D = 4 ~0.75 Remarks Straight rounded entry nozzles with L/D = 10 and 40, D = 4 mm, ρ G / ρ L = D nozzle, Sharp inlet, D = 4mm, p < 1 MPa, Cavitation Length (L cav = 0) Wu et al L/D = 4 (for ρ G / ρ L ~ ) Shimizu et al L/D = 4 L/D = 50 ~1.5 ~2.5 ~2.5 Constant diameter tube, D = 3.43 m, Injection velocity = m/s, ρ G / ρ L = 0 to 0.08, p < 1 MPa. Sharp edged nozzle, D = 0.3 mm, Injection velocity = 120 m/s, p = 1 MPa. Table 3.3 Flow field vector and particle velocity vector for PTV results. Mean flow vector Particle velocity vector Remarks (-2.08) i + (-16.64) j 2.08 i 0.62 j 2.08 i 0.26 j 8.99 i 9.73 j i 4.27 j i j 2.44 i j pixel size = 1.34µm Δt = 3.68µs (Fig. 3.14) 52

70 (a) (b) Figure 3.1 X-ray imaging of turbulent liquid jet in still air at v j = 26 m/s for 0 dj 1.5 d j for (a) L/D = 10, D = 4 mm and (b) L/D = 40, D = 4 mm. 53

71 (a) (b) Figure 3.2 L/D = 10, D = 4 mm nozzle injected into (a) vented and (b) non vented enclosures from streamwise distance, y = 1.5dj to 3dj. Only the left-half portion of the jet is shown for clarity, with the jet motion in the vertically downward direction. 54

72 (a) (b) Figure 3.3 Liquid jet breakup for L/D = 40. (a) Map patched with high resolution x-ray images showing examples of spotted ligaments. (b) Zoom-in image with the edge of a ligament outlined in black lines. Figure 3.4 Sketch of ligament showing the projected length (L lig ), diameter (d lig ) and area (A lig ) definitions (Faeth and Sallam, 2003). 55

73 Figure 3.5 Diagrammatic representation of the jet cross sectional plane showing a typical ligament location. (a) (b) Figure 3.6 Ligament size distribution projected along the jet centre plane for (a) L/D = 10 and (b) L/D =

74 (a) (b) Figure 3.7 Ligament size distribution along the stream wise direction for (a) L/D = 10 and (b) L/D = 40, D = 4 mm. Figure 3.8 Diagrammatic representation of the ligament distribution mapping on the jet surface. 57

75 (a) (b) (c) Figure 3.9 Ligament separation plot for L/D = 10, D = 4 mm (a) L, d1, d2 plot (b) L, d1 plot (c) L, d2 plot. 58

76 (a) (b) (c) Figure 3.10 Ligament separation plot for L/D = 40, D = 4 mm (a) L, d1, d2 plot (b) L, d1 plot (c) L, d2 plot. 59

77 Figure 3.11 Surface efficiency parameter near the onset of breakup. Figure 3.12 The x-ray jet image showing the surface ligaments and the bubble entrainment in the jet. 60

78 Figure 3.13 Bubble size variation along the streamwise direction for sub-atmospheric jet injection. 61

79 (a) (b) Figure 3.14 (a) X-ray ptv image above showing the seed particles inside a ligament and (b) the correlated velocity vectors. 62