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Transient jet impaction on a high speed moving surface Sarraf Shirazi, Alireza 2015

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Transient Jet Impaction On A High Speed Moving Surface  by Alireza Sarraf Shirazi  B.Sc., Sharif University of Technology, 2012  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in  THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES  (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  July 2015   © Alireza Sarraf Shirazi, 2015ii  Abstract  In the railroad industry liquid friction modifiers are applied on the rail track in the form of a liquid jet in order to reduce the friction and fuel consumption. In this application, the transfer efficiency of the liquid on the rail track is very important. To maximize the transfer efficiency, Newtonian and non-Newtonian transient liquid jet impingement on a dry moving surface was studied.   Five different water glycerin solutions with widely varying shear viscosities were used as Newtonian test liquids to isolate the effect of shear viscosity from other fluid properties. Furthermore, the effect of surface roughness on the impaction was investigated using four different roughness heights. The effects of jet velocity and surface speed were also studied. High speed imaging was performed to visualize the interaction between the jet and the moving surface. For surface roughness heights between 0.02 𝜇𝑚 and 0.64 𝜇𝑚, it was found that as the roughness increases, the jet becomes more prone to splash. It was also shown that increased jet and surface speeds trigger the splash.    The transient jet characteristics were also investigated for Newtonian liquids at different nozzle back pressures. It was found that at higher Reynolds and Weber numbers the transient jet breaks up downstream of the nozzle; However, it was shown that the Weber number has the dominant role in jet break-up compared to the Reynolds number. A numerical study was also undertaken to determine the drag force exerted on the plunger of the solenoid valve in the nozzle. The simulation results were in reasonable (16% on average) agreement with experiment.        iii  Preface   The authors of chapter 2 are Alireza Sarraf and Dr. Sheldon Green. Dr. Green identified and proposed the methods to prepare for the experimental investigations accomplished in chapters 3 and 4.    The authors of chapter 3 are Alireza Sarraf and Dr. Sheldon Green. Dr. Green and representatives from L.B. Foster®, found the need for an experimental study on the interaction of transient Newtonian and non-Newtonian liquid jets with a high speed moving surface. I identified the variables to be tested, e.g. liquid viscosity, surface roughness, jet and surface speeds, and also conducted the experiments and the results were analyzed with directions and supervision of Dr. Green.    The authors of chapter 4 are Alireza Sarraf and Dr. Green. Dr. Green suggested further investigation on the nozzle operation and the plunger motion and also controlling the application rate of the liquids applied on the rail track.        iv  Table of Contents  Abstract ........................................................................................................................................... ii Preface............................................................................................................................................ iii Table of Contents ........................................................................................................................... iv List of Tables ................................................................................................................................. vi List of Figures ............................................................................................................................... vii Acknowledgements ....................................................................................................................... xii Chapter 1: Introduction ................................................................................................................... 1 1.1 Friction control in the railroad industry ........................................................................... 1 1.2 Liquid Friction Modifiers ................................................................................................. 2 1.3 Application Methods of LFMs ......................................................................................... 2 1.4 Droplet Impaction On a Stationary/Moving Surface ....................................................... 3 1.5 Liquid Jet Impaction On a Stationary/Moving Surface ................................................... 6 1.6 Research Objectives ......................................................................................................... 9 Chapter 2: Experimental Setup and Methodology ........................................................................ 11 2.1 Test Liquids .................................................................................................................... 11 2.2 Solenoid Valve Actuation .............................................................................................. 12 2.3  Flow Rate Measurements ............................................................................................... 15 2.4 Measurement of Injection and Impaction Velocity ........................................................ 15 2.5  Blob Diameter Measurement ......................................................................................... 16 2.6 Experimental Apparatus for Low Speed Impaction Test ............................................... 16 2.6.1   Linear Traverse ........................................................................................................... 17 2.6.2    Projectile and the Impingement Surface .............................................................. 18 2.6.3    High Speed Imaging Setup ........................................................................................ 20 2.7 Experimental Apparatus for High Speed Impaction Test .............................................. 21 2.7.1    Spinning Disk ............................................................................................................ 21 2.8 Solenoid Plunger Position Measurement ....................................................................... 22 Chapter 3: Flow Rate Analysis ..................................................................................................... 25 v  3.1 Newtonian Test Liquids Flow Rate Measurements ....................................................... 25 3.2 Solenoid Actuation and Plunger Motion ........................................................................ 27 3.2.1    Experimental Method ................................................................................................ 27 3.2.2    Computational Model ................................................................................................ 31 3.2.3    Results of Simulation and Experiment ...................................................................... 33 3.2.3    Application Rate of LFMs ......................................................................................... 37 Chapter 4: Transient Jet Impaction on a Moving Surface ............................................................ 40 4.1 Flow Rate and Jet Characteristics Results...................................................................... 40 4.1.1   Newtonian Test Liquids.............................................................................................. 40 4.1.1.1   Flow Rate Test Results ........................................................................................ 40 4.1.1.2   Liquid Jet Diameter.............................................................................................. 42 4.1.1.3   Transient Jet Characteristics ................................................................................ 43 4.1.2   Liquid Friction Modifiers Test Results ...................................................................... 48 4.1.2.1   Flow Rate Test Results ........................................................................................ 48 4.1.2.2   Transient Jet Characteristics ................................................................................ 49 4.2   Effect of Surface Roughness on Transient Jet Impaction ................................................. 50 4.2.1   Newtonian Test Liquids.............................................................................................. 50 4.2.2    LFMs Test Results ..................................................................................................... 56 4.3 A Model for Jet Impingement ........................................................................................ 59 Chapter 5:   Conclusions and Recommendations ......................................................................... 66 5.1 Conclusions for Transient Jet Impaction on a Moving Surface ..................................... 66 5.2 Conclusions for Transient Jet Characteristics and Application Rate ............................. 67 5.3 Recommendations for Future Works ............................................................................. 68 Bibliography ................................................................................................................................. 69 Appendix A:   Newtonian Test Liquids Flow Rate As a Function of Duty Cycle ....................... 73     vi   List of Tables  Table 2-1: properties of Newtonian test liquids at 25°C .............................................................. 12 Table 2-2: properties of non-Newtonian liquids at 25°C .............................................................. 12 Table 2-3: Four stainless steel plate roughness measurements ..................................................... 19 Table 4-1: empirical fit parameters for flow rate results .............................................................. 42 Table 4-2: Steady state jet diameter measurements for different test liquids ............................... 43 Table 4-3: empirical fit parameters for LFMs’ flow rate results .................................................. 49               vii   List of Figures  Figure 1-1: Morphology of droplet impaction on a dry surface [15] .............................................. 4 Figure 1-2: Steady state jet impaction on a moving surface A) Deposition, B) Splash. Surface is traveling from left to right [10] ....................................................................................................... 8 Figure 2-1: Transmitted pulsed signal to the coil ......................................................................... 13 Figure 2-2: Cross section view of the nozzle ................................................................................ 14 Figure 2-3: Jet diameter measuring method.................................................................................. 16 Figure 2-4: Linear traverse set-up [9] ........................................................................................... 17 Figure 2-5: A wooden carrier on which a steel plate with a desired roughness is mounted ......... 19 Figure 2-6: high speed imaging setup for low speed impaction test [12] ..................................... 20 Figure 2-7: Spinning disk setup schematic [12] ........................................................................... 22 Figure 2-8: Test set-up for obtaining plunger position by time .................................................... 23 Figure 2-9: Rod visualization with high speed camera, while the plunger is coming down (valve is being closed) a) the rod is immersed into the test liquid, b) rod is not immersed in the liquid; it could be observed that the fluid coming down makes the tip of rod distorted and blurry and hard to distinguish its motion ................................................................................................................ 24 Figure 3-1: Flow rate as a function of duty cycle for four different liquid tests at 20 psi nozzle back pressure. Frequency of actuation = 100 Hz .......................................................................... 26 Figure 3-2: Flow rate as a function of duty cycle for four different liquid tests at 40 psi nozzle back pressure. Frequency of actuation = 100 Hz .......................................................................... 26 Figure 3-3: Flow rate as a function of duty cycle for four different liquid tests at 60 psi nozzle back pressure. Frequency of actuation = 100 Hz .......................................................................... 27 Figure 3-4:  Rod position as a function of the time when there’s no fluid running through the nozzle ............................................................................................................................................ 28 viii  Figure 3-5: Rod position as a function of time for water glycerin 85% at different nozzle back pressures ........................................................................................................................................ 29 Figure 3-6: Rod position as a function of time for water glycerin 90% at different nozzle back pressures ........................................................................................................................................ 29 Figure 3-7: Rod position as a function of time for water glycerin 99.5% at different nozzle back pressures ........................................................................................................................................ 30 Figure 3-8: cross section of the geometry inside the nozzle ......................................................... 31 Figure 3-9: Axisymmetric domain of the solution ........................................................................ 32 Figure 3-10: Numerical and Experimental results of mass flow rate as a function of plunger position for water glycerin 90% at different nozzle back pressures ............................................. 33 Figure 3-11: Numerical and experimental results of hydrodynamic force as a function of plunger position for water glycerin 85% at different nozzle back pressures ............................................. 34 Figure 3-12: Numerical and experimental results of hydrodynamic force as a function of plunger position for water glycerin 90% at different nozzle back pressures ............................................. 35 Figure 3-13: Numerical and experimental results of hydrodynamic force as a function of plunger position for water glycerin 99.5% at different nozzle back pressures .......................................... 35 Figure 3-14: AP2 mass flow rate as a function of duty cycle with the solenoid actuation of 50 Hz....................................................................................................................................................... 37 Figure 3-15: AP2 application rate as a function of duty cycle with the solenoid actuation of 50 Hz for three different train speeds ................................................................................................ 38 Figure 3-16: spacing between liquid stitches applied on the rail track as a function of the frequency of solenoid actuation at the duty cycle of 0.5 for three different train speeds ............. 39 Figure 4-1: Newtonian test liquids flow rate results. Orifice diameter: 0.697 mm ...................... 41 Figure 4-2: Newtonian test liquids discharge coefficient as a function of Reynolds number ...... 41 Figure 4-3: Transient jet at 76 mm downstream of the tip of nozzle, a) WG 75 at 60 psi NBP, b) WG 90 at 60 NBP ......................................................................................................................... 44 Figure 4-4: Jet break-up/stable jet boundary 76 mm downstream of the nozzle (We vs. Re) ...... 45 ix  Figure 4-5: Transient jet evolution captured at 5 different frames from the tip of the nozzle to 75mm downstream for WG 85, We=2296, Re=128. Length of each frame = 15mm .................. 46 Figure 4-6: Transient jet evolution captured at 5 different frames from the tip of the nozzle to 75mm downstream for WG 75, We=1045, Re=275. Length of each frame = 15mm .................. 47 Figure 4-7 Mass flow rate results for commercial LFMs. Orifice diameter: 0.697 mm ............... 48 Figure 4-8: Transient jet visualization at 76 mm downstream of the nozzle for different LFMs, a) Hyb at 40 Psig NBP, b) AP2 at 40 Psig NBP, c) Simu at 40 Psig NBP, d) Hyb at 80 Psig NBP 49 Figure 4-9: different Newtonian liquid jet impingement on mirror surface test results for a) WG65, b) WG75, c) WG85, d) WG90, and e) WG99.5............................................................... 52 Figure 4-10: different Newtonian liquid jet impingement on smooth surface test results for a) WG65, b) WG75, c) WG85, d) WG90, and e) WG99.5............................................................... 53 Figure 4-11: different Newtonian liquid jet impingement on rough surface test results for a) WG65, b) WG75, c) WG85, d) WG90, and e) WG99.5............................................................... 54 Figure 4-12: different Newtonian liquid jet impingement on coarse surface test results for a) WG65, b) WG75, c) WG85, d) WG90, and e) WG99.5............................................................... 55 Figure 4-13: Three different LFMs impingement on smooth surface test results for a) AP2, b) Simu,  c) Hyb ................................................................................................................................ 57 Figure 4-14: Three different LFMs impingement on roughsurface test results for a) AP2, b) Simu, c) Hyb ................................................................................................................................. 58 Figure 4-15: droplet impaction modeling on a moving surface .................................................... 61 Figure 4-11: experimental results for five different water glycerin solutions, a) smooth surface, K=19200, k=0.5, b) rough surface, K=17600, k=0.9, c) coarse surface, K=13100, k=1, d) mirror surface, K=13700, k=1 .................................................................................................................. 64 Figure A-1: Flow rate as a function of duty cycle for WG 65 at different nozzle back pressures, Frequency of actuation = 50 Hz .................................................................................................... 74 Figure A-2: Flow rate as a function of duty cycle for WG 75 at different nozzle back pressures, Frequency of actuation = 50 Hz .................................................................................................... 75 x  Figure A-3: Flow rate as a function of duty cycle for WG 85 at different nozzle back pressures, Frequency of actuation = 50 Hz .................................................................................................... 75 Figure A-4: Flow rate as a function of duty cycle for WG 90 at different nozzle back pressures, Frequency of actuation = 50 Hz .................................................................................................... 76 Figure A-5: Flow rate as a function of duty cycle for WG 99.5 at different nozzle back pressures, Frequency of actuation = 50 Hz .................................................................................................... 76                  xi   Glossary  𝐷  Diameter [𝑚] 𝐷𝑗  Jet Diameter [𝑚] 𝐷𝑜  Orifice Diameter [𝑚] 𝑉  Velocity [𝑚. 𝑠−1] 𝑉𝑛  Normal Velocity [𝑚. 𝑠−1] 𝑉𝑡  Tangential Velocity [𝑚. 𝑠−1] 𝑅𝑒𝑛  Reynolds Number Based on Normal Velocity 𝑊𝑒𝑛  Weber Number Based on Normal Velocity 𝜎  Surface Tension [𝑁.𝑚−1] 𝜇  Viscosity [𝑃𝑎. 𝑠] 𝜌  Density [𝑘𝑔.𝑚−3] 𝐶𝑑  Discharge Coefficient ℎ  Lamella Thickness [𝑚] 𝐿  Lamella Length [𝑚] xii  Acknowledgements    First and foremost, I would like to express my sincere gratitude to my supervisor, Professor Sheldon I. Green, whose constant support, patience and guidance has been invaluable throughout the course of this research without which this thesis would have been impossible.  I would also like to acknowledge our sponsor company L.B. Foster® for their precious technical insights and guidance which made this work possible. In particular, I wish to thank Dave Elvidge, Don Eadie and John Cotter for all of their motivation and support to take this project forward.    I would like to extend my gratitude to my friends and colleagues, Ali Vakil, Hamed Ghasvari, Babak Mazhari, and Ehsan Zaman, and also the members of my research group, Yuchen Guo, Quinn Mulligan, and Hatef Rahmani for all their helps during my Master’s program.     Finally, it would be my pleasure to express my deepest gratitude to my parents and beloved brother, without whose love, encouragement, and sacrifice none of this have been possible. I will remain eternally in their debt.1  Chapter 1: Introduction  1.1 Friction control in the railroad industry   Rail transport is proved to be one of the most efficient and cost-effective forms of passenger and freight transportation in North America. The Canadian railway network, consists of more than 72,000 kilometers of track which annually transports more than 270 million tons of freight [1]. It will also continue to be highly efficient due to growing populations and their demand for transportation. Furthermore, fuel cost increase makes the use of trucks and air transport less efficient compared to that of the railway transportation. However, railroad industries such as LB Foster are consistently seeking novel methods to further enhance the efficiency of railroad transportation.   In order to further minimize the fuel consumption, railroad industries have found that by top of rail (TOR) friction control, i.e. applying a friction modifying agent on the wheel-rail interface, they can not only reduce the fuel consumption, but also lateral forces on the rail track and wheel-rail wear could be controlled [2]. Although it was found that TOR friction control substantially decrease the fuel consumption by 6% [3], it is considered to be a relatively novel procedure among world’s railroad industries as most of them don’t implement it in the field and research is still going on to further optimize this method.     2  1.2 Liquid Friction Modifiers   TOR friction control is accomplished by liquid friction modifier (LFM). Kelsan Technologies Corporation is a huge center for developing suitable LFMs. The primary LFM they produce is a water based suspension of polymers and inorganic solids. This liquid friction modifier, KELTRACK®, is a non-Newtonian fluid showing shear thinning and viscoelastic behaviour [4,5]. Applying this liquid on the top surface of the rail results in fuel consumption reduction and also rail-wheel wear control and lateral forces decrease, and these are being accomplished without compromising traction and braking [6].  1.3 Application Methods of LFMs  Currently, in the railroad industries of North America, LFM is being applied from air-blast atomizers mounted underneath the locomotive to the top surface of rail track as the locomotive moves at high speed. The distance between the tip of the atomizer and the rail track top surface is approximately 76 mm and the LFM is atomized in the form of ligaments and droplets.  This application form has been found to be problematic in different aspects.  In order to obtain a suitable transfer efficiency of the LFM onto the rail track, the droplets and ligaments exiting from the atomizer should not be deflected by the cross wind on their way to impact the top surface of the rail track and also it is not desirable that a splash or rebound be observed after the impaction [7,8]. Air blast atomizers have been proved to be not sufficiently efficient in terms of transfer efficiency due to the high drag to inertia ratio of the droplets and ligaments they produce which elevates the deflection susceptibility of the LFM by the cross wind [9]. Furthermore, 3  sometimes the accessibility of the high volume and high pressure air supply to run these atomizers is challenging, and also the LFM rail coverage would be highly non-uniform by using these atomizers.   As applying LFMs using air-blast atomizers has been proved to be problematic and challenging, dispensing LFM by means of a continuous circular steady state liquid jet was offered as an alternative method and research has been conducted over the past few years to examine the resulting transfer efficiency [10, 11, 12]. The results show that the alternative method would lead to increase overall transfer efficiency of LFM on the rail track and also makes the resulting spraying system more simple and robust.   However, LFM application control is considered to be very important to the railroad industries. As two primary nozzle back pressures are currently being used in the field, therefore two main flow rates are always obtained. As a result, application rate cannot be regulated applying LFM by means of continuous liquid jet. Implementing a controllable on-off flow system using solenoid valve was offered in order to actively control the flow rate and therefore the application rate of the product. This method was examined thoroughly and the results in terms of transfer efficiency and application rate are brought in this thesis.    1.4 Droplet Impaction On a Stationary/Moving Surface  Many researchers have accomplished experimental and numerical analysis on Newtonian and non-Newtonian droplet impaction on a wet or dry stationary surface over more than 100 years. It has been proved that the droplet behaviour after 4  impaction is a challenging phenomenon depending on numerous parameters. Many researchers have investigated the effect of liquid properties, e.g. viscosity, surface tension and density, and also impact angle, surface roughness and wettability, and ambient gas pressure (or density) on the lamella spreading and threshold of splashing. Research accomplished by Rein [13], Rioboo et al. [14, 15], Jie Liu et al. [16], and Chandra et al. [17] are good examples in this area.              Rioboo et al. [15] classified the outcomes of droplet impaction on a dry surface into 6 different categories, which is shown in figure 1. He showed that the occurrence of each of these categories depends on the droplet velocity and diameter before impaction, surface tension, viscosity, roughness amplitude and wave length, and the wettability of the surface.       Figure 1-1: Morphology of droplet impaction on a dry surface [15] 5   Many researchers have found that surface roughness has huge impact on the outcome of the droplet impaction on a dry surface [18, 19, 20]. Mundo et al. [19] offered the parameter 𝐾 = 𝑂ℎ. 𝑅𝑒1.25 to characterize the transition from spreading to splashing at the atmospheric pressure which was a function of surface roughness. Range et al. [20] argued that the splashing threshold could be obtained in terms of the critical Weber number as a function of the surface roughness based on their experimental observation. Regardless of all the threshold models, all researchers have shown that increasing surface roughness cause the splashing threshold to decrease substantially. A thorough investigation and detailed review on the Newtonian droplet impaction outcome on a dry/wet surface was accomplished by Yarin [26] and Deegan [27].     Furthermore, many researchers have studied the effect of tangential velocity on the splashing threshold mostly by means of droplet impaction on an inclined or moving surface. Using a rotating dry disk, Mundo et al. [19] calculated the effective impingement angle of a Newtonian droplet to study its effect on the impaction behaviour by varying the rotating surface velocity.  Chen et al. [21] also have investigated droplet impaction on a rotating disk. They introduced a tangential Weber number based on the tangential velocity obtained by combining the disk rotational speed and the angle of droplet impaction, and investigated the effect of different tangential velocity on the impaction outcome. Moreover, Fathi et al. [22] and Povarov et al. [23] found that the tangential velocity has a substantial effect on the impaction outcome and splashing threshold.   Courbin et al. [24] reported that considerable tangential velocity causes an asymmetric splash to occur, i.e. the side of the lamella in the upstream direction of the impacting droplet spreads on the moving surface while the other side splashes. 6  In addition to make the same observation, Bird et al. [25] developed a physical mechanism for the impaction outcome according to the lamella growth rate.   Moreover, many researchers have investigated the impaction of a non-Newtonian droplet on a dry stationary/moving surface. Bartolo et al. [30] experimentally showed that non-Newtonian effects substantially change the contact line dynamics which leads to slowing down the lamella retraction after droplet impaction on a dry moving surface and the droplet rebound/splash could be completely inhibited as a result. They also provided a quantitative explanation for the slowing down of the contact line by polymers. Bergeron et al. [31] also showed that increasing elongational viscosity as a result of adding polyethylene oxide slows down the droplet spreading after impaction and inhibits splashing as a result. Crooks et al. [28] and Roux et al. [29] also obtained the same results showing that increasing elasticity makes the droplet more prone to deposit on the surface after impaction and prevent splashing.   1.5 Liquid Jet Impaction On a Stationary/Moving Surface  In contrast to the droplet impaction which researchers have been investigation for over a hundred years, a few researchers have studied jet impaction especially on a moving surface. Recent industrial applications such as ink-jet printing and surface coating have encouraged researchers to study the jet impaction outcome on a stationary/moving surface.  The majority of the investigations accomplished in this category is related to the liquid jet impingement on a stationary surface focusing on the hydraulic jump after the impaction and also heat transfer.   7  Liu et al. [32] that surface tension has a dominant role in stabilizing the hydraulic jumps in thin liquid sheets and leads to smooth jumps for low Weber numbers. Pagliara et al. [33] and Bejestan et al. [34] experimentally studied the effect of bed roughness on hydraulic jump and modified the governing equation by adding a coefficient to the Froude number which was found based on the experimental data.      As was mentioned, a few studies have been accomplished in the area of Newtonian or non-Newtonian liquid jet impingement on a high speed moving surface. Using five different surface roughness heights and seven different water-Glycerin solutions, Keshavarz et al. [35] experimentally studied the outcome of Newtonian circular jet impaction on a moving surface. They found that increasing the surface roughness decreases the splash threshold leading to an undesirable transfer efficiency of the liquid on the surface. They also found that the splash threshold is primarily governed by Reynolds number (defined using the jet and surface relative velocity) compared to the Weber number and the ratio of the surface velocity to the jet velocity.   Keshavarz et al. [36] also studied the effects of elasticity on the circular liquid jet impaction on a moving surface using twelve different samples of PEO solutions. They found that increasing elasticity substantially increase the splash threshold and also showed that the most primary dimensionless numbers are Reynolds and Deborah number compared to Weber number and jet pathline angle which play a small role in the impingement outcome. Moulson et al. [37] proved that lamella lift-off from the moving surface significantly depends on the surrounding air pressure and the detachment could be substantially suppressed by decreasing the surrounding air pressure which indicates that aerodynamic forces are a primary factor in determining the splash threshold.  8   Figure 1-2: Steady state jet impaction on a moving surface A) Deposition, B) Splash. Surface is traveling from left to right [10]   Conducting experiment on different Water-Glycerin solutions, Moulson [38] observed three viscosity regimes for lamella detachment in which splash is more likely to happen in the intermediate region. He explained that lamella stabilization in the low viscosity region is due to the high surface tension forces and high viscous dissipation is responsible for lamella stabilization in the high viscous region.     In experiments conducted with higher surface speeds Sterling [11] and Guo [12] proved that splash could be converted back to deposition by increasing the roughness height by a small value. For a particular jet and surface speed Guo [12] observed splash on a mirror polished surface whereas deposition was seen for two rougher surfaces under the same conditions.  9  1.6 Research Objectives   It has been proven that Applying LFM to the top surface of the railroad track is an effective way to reduce the fuel consumption and control the wheel-rail wear. The primary objective is to gain the maximum transfer efficiency, i.e. the percentage of total LFM which is applied onto the top surface of the rail track. Currently, railroad industries apply LFMs by means of air-blast atomizers. The transfer efficiency of such atomizers may  not be satisfactory due to the high drag to inertia ratio of the droplets and ligaments atomized by these types of nozzles which make them susceptible to the cross wind.  To overcome this problem, using airless atomizers were suggested and many researchers studied the transfer efficiency of the steady state circular jet produced by these nozzles [10, 11, 12] and showed that it’s more efficient compared to the air-blast atomizers.   However, using these nozzles limits the application rate control in the field as only two main back pressure are being used to run the airless nozzles which results in merely two flow rates options. As application rate of LFM is significantly important to the railroad industries, implementing a controllable on-off flow system using solenoid valve was considered in order to actively control the flow rate and therefore the application rate of the product.   Hence, the first objective of the thesis is to study the impaction of the Newtonian and non-Newtonian transient jet, produced by this type of nozzle, on a high speed moving surface with different roughness heights and investigate the characteristics of the transient jet downstream of the nozzle. The second objective is to investigate on the hydrodynamic forces exerted on the plunger while the valve is operating in 10  order to gain better knowledge of the valve operation which leads to an efficient application rate regulation.                                 11  Chapter 2: Experimental Setup and Methodology  In this chapter, the test liquids and their properties and also devices used to conduct the experiment are thoroughly explained. Furthermore the details of experimental methods implemented to acquire the results are comprehensively discussed.   2.1 Test Liquids  Five different mixtures of water and glycerin were used as the Newtonian test liquids in order to isolate the viscosity effects on the tests, and also three non-Newtonian Hi-rail products were examined. The viscosity of the Newtonian test liquids was measured by a HAAKE VT550 viscometer and the surface tension measurements for all liquids were conducted by a Du Nouy ring apparatus at the temperature of 25°C. For the non-Newtonian liquids the relaxation time was measured by HAAKE CaBER 1 extensional rheometer. It was observed that the viscosity of the Newtonian solutions varied by three orders of magnitude while the difference of surface tension values among these solutions was negligible. The results of the surface tension and viscosity measurements for Newtonian liquids are presented in table 1 and table 2 shows non-Newtonian liquid properties.           12   Table 2-1: properties of Newtonian test liquids at 25°C Glycerin [wt%] Water [wt%] Viscosity [mpa.s] Surface tension [mN/m] Density [gr/𝒄𝒎𝟑] 65 35 12.8 68.4 1.14 75 25 28.4 67.7 1.20 85 15 87.4 64.3 1.22 90 10 154.7 62.2 1.24 99.5 0.5 809.3 62.0 1.27   Table 2-2: properties of non-Newtonian liquids at 25°C   Density [gr/𝒄𝒎𝟑] Viscosity [mpa.s] Surface tension [mN/m] Relaxation time [ms] Keltrack  1.083 Rate-dependent 33.04 927 Simulation product 1.024 Rate-dependent 33.74 766 Hybrid material 1.047 Rate-dependent 33.45 573   2.2 Solenoid Valve Actuation   A transient jet was produced by means of a PulsaJet AA10000AUH-104210, manufactures by spraying System Co., a commercial nozzle in which a solenoid actuated valve is located. A circuit was designed and built in order to actuate the solenoid valve with the desired frequency and duty cycle. A power supply with DC 13  24 Volts energized the magnetic coil and a signal generator was used to determine the desired frequency and duty cycle of actuation.   The signals transmitted to the coil are pulsed shape signals which could be characterized by duty cycle and frequency of actuation. Actuation frequency is the number of pulses generated per second and duty cycle is the ratio of signal on time to signal off time. Figure 2-1 illustrates the signal transmitted to the coil.       Figure 2-1: Transmitted pulsed signal to the coil       When there is no signal going through the solenoid the valve is closed and no flow exits from the orifice. As soon as the electric current is transmitted to the solenoid the coil gets energized and an electromagnetic force is exerted on the plunger in the upward direction. Consequently, the plunger moves upwards and lets the flow exit from the orifice.   14  When the pulse signal turns off, the coil gets de-energized and the plunger is forced to move downwards due to the force being exerted by the spring and again no flow exits from the orifice. A cross section view of the nozzle used in the experiment is demonstrated in figure 2-2. The solenoid valve can work with varied actuation frequencies up to 166 Hz. All the experiments were done with an orifice diameter of 0.697 mm.          Figure 2-2: Cross section view of the nozzle    15  2.3  Flow Rate Measurements   Mass flow rate measurements were conducted with the test liquids at different nozzle back pressures in order to obtain the volumetric flow rate and also the average velocity of the transient jet. The solenoid Valve was actuated with the desired frequency and duty cycle by means of a signal generator for one minute and the weight of the sprayed liquid was measured at the end. In the tests the duty cycle varied between 30% to 100% duty cycle and frequency varied between 1 Hz to 150 Hz in order to observe the effect of both parameters on the flow rate.    2.4 Measurement of Injection and Impaction Velocity   Due to non-circular and irregular shape of the transient jet, the average velocity was measured for each case which is regarded as the average velocity of injection. Having the average mass flow rate results for every nozzle back pressure and glycerine-water solution, volume flow rate could be derived based on the density data. For each nozzle back pressure and solution, the steady state jet diameter was measured using imaging method and regarded as the average diameter of the transient jets produced with different frequencies and duty cycles. Having the average diameter and average volume rate, the average velocity of the transient jet was determined. Figure 2-3 illustrates the diameter measuring method.   The velocity of impaction was measured by visualizing the tip of jet motion 76 mm downstream of the nozzle for each case using high speed images.   16   Figure 2-3: Jet diameter measuring method   2.5  Blob Diameter Measurement  In cases where a blob is formed at the tip of the transient jet downstream of the nozzle before impaction, the equivalent diameter of the blob was obtained based on the area calculation of the semi spherical blob whose image was captured by a high speed camera.    2.6 Experimental Apparatus for Low Speed Impaction Test         For low surface speeds up to 25 m/s a linear traverse, designed and built by Dan Dressler [9], was used which is a pneumatic energy powered system that accelerates a projectile to the desired velocity. A nozzle is mounted above and on the way of the projectile which is covered by a steel plate roughened with sand paper of different grits, to investigate the roughness height effect on the impaction. A high speed camera was triggered and provided high speed images of the impingement as the 1 mm 17  transient jet impacted on the surface. The details of this experimental setup are described further below.        2.6.1   Linear Traverse  As was mentioned in chapter 1, in field application the liquid is applied to the top surface of the rail track by means of the nozzles mounted underneath the locomotives. The nozzles apply LFM onto the stationary rail. As the mentioned condition is very difficult to be precisely replicated in lab, a linear traverse was used for providing a moving surface onto which the transient jet is applied by a fixed nozzle on the way of the moving projectile.     Figure 2-4 demonstrates the linear traverse set-up which consists of a 30 gallon air tank that is connected to a central air compressor and capable of supplying a maximum pressure of 100 psig, a solenoid actuated poppet valve connected to the tank, a 3 meter long 10 cm x 15 cm x 0.6 cm section of rectangular steel tubing, with the last meter of the tube being cut in half crosswise, and a stop mechanism.   Figure 2-4: Linear traverse set-up [9]  18  A wooden carrier base projectile on which a steel plate with the desired roughness height is mounted is inserted into a barrel. After the solenoid valve is activated with the desired frequency and duty cycle by the signal generator, the pressurized air in the tank is rapidly released (which is manually triggered) and forces the projectile to exit the barrel at a velocity dependent on the initial air pressure set in the tank. After exiting the barrel the projectile travels beneath the nozzle and the transient jet impacts onto the surface of the steel metal covering the projectile. At the end the projectile strikes an energy dissipation device and comes safely to a stop. Depending on the air pressure in the tank the projectile can travel with the speeds between less than 1 m/s to 25 m/s.    2.6.2    Projectile and the Impingement Surface  As was mentioned in chapter 1, many researchers studied the effect of surface roughness on the impaction of the Newtonian and Non-Newtonian droplets and circular jets on the surface [10, 11, 12, 19]. In this study the effect of surface roughness was investigated using three different grades of sand papers with different average roughness heights for the low speed test (and also four different grades for the high speed test with the spinning disk) by which the stainless steel plates were abraded. The roughness of the plates was measured in different directions on the surface using a commercial profilometer (three in vertical direction and three in horizontal direction for each plate) to average out the effects of randomness in roughness height distribution on the surface. Table 2-3 shows the resulting measured roughness heights for plates abraded by four different sand papers.      19  Table 2-3: Four stainless steel plate roughness measurements Surface Roughness height (𝝁𝒎) Type ID Horizontal Vertical Average Mirror #8 0.016 0.023 0.0195 Smooth P400 0.121 0.179 0.1500 Rough P60 0.364 0.542 0.4530 Course P30 0.563 0.713 0.6380   The wooden projectile acted as a light-weight carrier for the impingement surface which is a stainless steel plate. The dimension of the projectile is close to that of the barrel to minimize the air leakage and optimize the projectile shooting. In order to further ensure the tight seal inside the barrel, a 1/8” thick rubber sheet was mounted on the back of the projectile. The leading part of the projectile was shaped into a nose which made it aerodynamically efficient and also a barb was added underneath so that the projectile would be caught securely without being bounced back. The projectile used in the experiment is shown in figure 2-5.     Figure 2-5: A wooden carrier on which a steel plate with a desired roughness is mounted Nylon Sliders 20   2.6.3    High Speed Imaging Setup   In order to visualize the transient jet impingement on the moving surface a Vision Research Phantom v611 high-speed cine camera was used. The fast wide screen CMOS sensor in this camera facilitates imaging at extremely high resolutions and frame rates. In order to illuminate the field of view a 1kW high intensity incandescent light source was used and a light diffuser sheet was located between the light source and field of view to obtain an evenly illuminated background. A Navitar Zoom 7000 lens was used for visualization, and 800x600 resolution with 30,000 frames per second were implemented for all of the impaction tests with the linear traverse setup. Figure 2-6 demonstrates the high speed imaging setup.      Figure 2-6: high speed imaging setup for low speed impaction test [12]  21  2.7 Experimental Apparatus for High Speed Impaction Test  As was mentioned in section 2.5, the linear traverse setup could move the substrate only to speeds as high as 25 m/s. Since the trains are likely to travel with faster speed, high surface speed impingement tests are required to investigate the transfer efficiency of LFMs onto the surface. For this purpose a spinning disk setup was used.   2.7.1    Spinning Disk   A spinning disk was used to provide a very high speed surface onto which the transient jet impinges. The radius of the disk is 30 cm and the variable frequency drive (VDF) motor that supplies its power is capable of producing a maximum angular rate of 500-3000 rpm. Therefore, with the disk radius and the motor speed, a surface speed of 15-100 m/s could be achieved by the disk, which is well above the maximum train speed of even high speed trains (83 m/s or 300 km/hr).   The nozzle is mounted a distance 76 mm from the surface of the disk. This is the same separation as exists between the sprayer and the rail track in the field. Two halves of the spinning disk were polished by two different sand papers to facilitate the study of the effect of the roughness height on the transient jet impaction. Figure 2-7 shows a schematic of the spinning disk setup.   22   Figure 2-7: Spinning disk setup schematic [12]  Two high intensity light sources were used to illuminate the impingement location and a Vision Research’s Phantom v611 high-speed cine camera was used to capture high speed images of the impaction. The images were recorder at 30,000 frames per second and 500x500 resolution.   2.8 Solenoid Plunger Position Measurement  In order to investigate the transient jet behavior and study the flow rate results, the plunger response to the transmitted signal from the generator to the solenoid, and plunger position by time was required. In order to obtain the plunger position by time, a light carbon fiber rod with 0.15 mm diameter was attached to the plunger, so that its tip could be visualized by a high speed camera as the plunger moves with the desired frequency and duty cycle.   23  Due to presence of the transient jet between the lens and rod, the image of the rod became distorted due to the difference between the refraction index of the test liquid with that of the air, so the tip of the rod could not be visualized and distinguished properly. To solve this problem the same test liquid was provided inside a plexiglass tank into which the tip of the rod was immersed. Consequently, tip of the rod could be visualized and distinguished properly and its position as a function of time could be derived. Figure 2-8 demonstrates the mentioned setup and figure 2-9 shows the distorted image from the tip of the rod without immersing it into the test fluid.    Figure 2-8: Test set-up for obtaining plunger position by time   0.15 mm rod Nozzle Test Liquid 24             Figure 2-9: Rod visualization with high speed camera, while the plunger is coming down (valve is being closed) a) the rod is immersed into the test liquid, b) rod is not immersed in the liquid; it could be observed that the fluid coming down makes the tip of rod distorted and blurry and hard to distinguish its motion              25  Chapter 3: Flow Rate Analysis  It was mentioned that one of the primary reasons to use solenoid actuated valve in order to apply LFMs on the rail track is to control the application rate, i.e. the amount of LFM applied per distance of the rail track. Regulating the flow rate of the liquid along with the solenoid valve actuation and the plunger motion is investigated in this chapter.    3.1 Newtonian Test Liquids Flow Rate Measurements   Figures 3-1, 3-2, and 3-3 show the flow rate of four different water glycerin solutions at three different nozzle back pressures with respect to duty cycle of solenoid actuation while the frequency is fixed at 100 Hz. As could be observed, flow rate changes linearly with respect to duty cycle for all of the test liquids and nozzle back pressures. Consequently, changing the duty cycle could be regarded as a suitable way to regulate the flow rate and application rate of the liquid on the rail track.   26   Figure 3-1: Flow rate as a function of duty cycle for four different liquid tests at 20 psi nozzle back pressure. Frequency of actuation = 100 Hz    Figure 3-2: Flow rate as a function of duty cycle for four different liquid tests at 40 psi nozzle back pressure. Frequency of actuation = 100 Hz   00.511.522.533.540 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Mass flow rate (gr/s) Duty CycleWG 75WG 85WG 90WG 99.501234560 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Mass flow rate (gr/s)Duty cycleWG 75WG 85WG 90WG 99.527   Figure 3-3: Flow rate as a function of duty cycle for four different liquid tests at 60 psi nozzle back pressure. Frequency of actuation = 100 Hz   3.2 Solenoid Actuation and Plunger Motion  3.2.1    Experimental Method   In order to gain sufficient knowledge about jet characteristics and the flow inside the nozzle the motion of the plunger was observed as a function of time by means of a rod with the diameter of 0.15 mm which is attached to the plunger. The rod motion as a function of time was obtained using a high speed camera. To enhance the visualization, the tip of the rod was immersed into a plexiglass container filled with the test fluid.   012345670 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Mass flow rate (gr/s)Duty cycleWG 75WG 85WG 90WG 99.528  Figure 3-4 shows the rod motion as a function of time when there is no fluid running through the nozzle. Figures 3-5, 3-6, and 3-7 demonstrate the rod motion for water glycerin 85%, 90%, and 99.5% respectively, at three different nozzle back pressures. It could be observed that as the viscosity of the fluid or the nozzle back pressure increases, it takes longer for the plunger to move from fully closed to fully open position, which suggests that the hydrodynamic force exerted on the plunger by the fluid increases.     Figure 3-4:  Rod position as a function of the time when there’s no fluid running through the nozzle     0.050.150.250.350.450.550.650 0.2 0.4 0.6 0.8 1 1.2 1.4position (mm)time (ms)29   Figure 3-5: Rod position as a function of time for water glycerin 85% at different nozzle back pressures   Figure 3-6: Rod position as a function of time for water glycerin 90% at different nozzle back pressures   0.050.150.250.350.450.550.650 0.5 1 1.5 2 2.5 3position (mm)time (ms)20 psi40 psi60 psi0.050.150.250.350.450.550.650 0.5 1 1.5 2 2.5 3 3.5position (mm)time (ms)20 psi40 psi60 psi30   Figure 3-7: Rod position as a function of time for water glycerin 99.5% at different nozzle back pressures  There are three major forces exerted on the plunger while being opened, i.e. electromagnetic force, spring force, and hydrodynamic force. Electromagnetic force is generated by the energized coil when actuated by signal generator, and hydrodynamic force is exerted on the plunger by the test liquid which acts in the opposite direction of the electromagnetic force and slows down the plunger motion.   The tests were done with three different water glycerin solutions at three different nozzle back pressures. Rod motion as a function of time was obtained for all of these cases, based on which the total forces exerted on the plunger was obtained as a function of plunger position. Rod motion as a function of time was also determined when there was no fluid running through the nozzle, so the only forces exerted on the plunger would be electromagnetic force and the spring force. Consequently, the hydrodynamic force exerted on the plunger could be obtained for all of the cases.    0.050.150.250.350.450.550.650 1 2 3 4 5position (mm)time (ms)20 psi40 psi40 psi31    3.2.2    Computational Model   To supplement the experimental data, a computational model was developed. The model is intended to obtain hydrodynamic force exerted on the plunger and also determine whether the flow inside the nozzle could be regarded as a quasi-steady state flow.  Figure 3-8 shows the cross section of the geometry inside the nozzle. The dimensions are all in mm.     Figure 3-8: cross section of the geometry inside the nozzle  32  A structured quad mesh was generated to solve the flow inside the nozzle using Finite volume method with SIMPLE scheme in FLUENTTM. All the terms of the momentum equation were discretized according to the second order upwind method. The convergence criterion for the residual of continuity and momentum equations was set to be 10 −5. A grid convergence study was also performed to ensure that the results are mesh independent. The mesh was refined until the mass flow rate changed by less than 2%.  The flow regime was set to be laminar which is a suitable assumption because the Reynolds number values for all of the cases ranged between 1 and 129. The simulation was run under steady state condition for seven different positions of the plunger. Figure 4-9 shows the axisymmetric geometry and the domain of the solution.     Figure 3-9: Axisymmetric domain of the solution  The inlet and outlet of the nozzle were set with pressure boundary conditions and the walls were set to a no-slip boundary condition.     33  3.2.3    Results of Simulation and Experiment  As was mentioned, the simulation was run under steady state condition for seven different positions for three different water glycerin solutions and at three different nozzle back pressures. For all of the cases, mass flow rate and hydrodynamic force exerted on the plunger were obtained. To check if  the steady state results of the simulations agree well with those of the experiments, the flow rate was also measured experimentally at different plunger positions by using shim stock of different thicknesses, placed behind the plunger, to prevent the valve from fully opening (i.e., with the solenoid actuated, to hold the valve at different positions). Figure 3-10 shows the mass flow rate results of experiment and simulation for water glycerin 90% at three different nozzle back pressures.    Figure 3-10: Numerical and Experimental results of mass flow rate as a function of plunger position for water glycerin 90% at different nozzle back pressures 00.511.522.533.544.550 0.1 0.2 0.3 0.4 0.5 0.6Mass flow rate (gr/s)plunger position (mm)20 psi Simulation20 psi Experiment40 psi Simulation40 psi Experiment60 psi Simulation60 psi Experiment34  As can be observed in Figure 3-10, the numerical results agree well with experiments, with a maximum error of 8.1%. The fact that for all plunger positions the simulations systematically under-predict the experimental flow rates is possibly due to numerical dissipation.  It is also noteworthy to mention that as back pressure increases the corresponding percentage error between numerical and experimental results increases as well.   Figures 3-11, 3-12, and 3-13 show the numerical and experimental results for hydrodynamic force exerted on the plunger for three different water glycerin solutions at three different nozzle back pressures.    Figure 3-11: Numerical and experimental results of hydrodynamic force as a function of plunger position for water glycerin 85% at different nozzle back pressures   00.511.522.50 0.1 0.2 0.3 0.4 0.5 0.6Hydrodunamic force (N)plunger position (mm)20 psi Simulation20 psi Experiment40 psi Simulation40 psi Experiment60 psi Simulation60 psi Experiment35   Figure 3-12: Numerical and experimental results of hydrodynamic force as a function of plunger position for water glycerin 90% at different nozzle back pressures   Figure 3-13: Numerical and experimental results of hydrodynamic force as a function of plunger position for water glycerin 99.5% at different nozzle back pressures  00.511.522.530 0.1 0.2 0.3 0.4 0.5 0.6Hydrodynamic Force (N)plunger position (mm)20 psi Simulation20 psi Experiment40 psi Simulation40 psi Experiment60 psi Simulation60 psi Experiment00.511.522.533.544.50 0.1 0.2 0.3 0.4 0.5 0.6Hydrodynamic foce (N)Plunger position (mm)20 psi Simulation20 psi Experiment40 psi Simulation40 psi Experiment60 psi Simulation60 psi Experiment36  According to experimental and numerical results, it could be observed that for all of the cases the hydrodynamic force decreases as the plunger moves towards its fully closed position. Although the difference between experimental and numerical results are more than that of the flow rate, they have a similar trend for all of the cases. The primary reason for the higher difference is that for numerical analysis of the hydrodynamic force as a function of plunger position it was assumed that the flow could be regarded as a quasi-steady state flow. This assumption is reasonable when the velocity of the plunger is negligible compared to the velocity of the fluid running through the nozzle. The typical plunger velocities are 0.2 m/s, 0.18 m/s, and 0.16 m/s for water glycerin 85%, 90%, and 99.5% respectively. However the typical velocity ratios of the plunger and its surrounding fluid are 0.08, 0.12, and 0.81 for water glycerin 85%, 90%, and 99.5% respectively which indicates that assuming quasi-steady state regime for water glycerin 99.5% running through the nozzle is not suitable.   From Figures 3-11, 3-12, and 3-13 it also could be observed that as the viscosity of the test liquid increases, the difference between numerical and experimental results increases as well. The average difference between the experimental and numerical results for water glycerin 85%, 90%, and 99.5% are 15%, 18%, and 27% respectively. The reason is that at a fixed nozzle back pressure, the velocity of the fluid with higher viscosity is lower and more comparable to the velocity of the plunger; Therefore, the quasi-steady state assumption becomes less reliable.     37  3.2.3    Application Rate of LFMs  Similar to Newtonian liquid tests, LFM flow rate could be regulated by changing the duty cycle of the solenoid actuation and the spacing between the LFM stitches applied on the rail track could be controlled by changing the frequency.  Figure 3-14 shows the mass flow rate of AP2 as a function of duty cycle at three different nozzle back pressures with the solenoid actuation frequency of 50 Hz.     Figure 3-14: AP2 mass flow rate as a function of duty cycle with the solenoid actuation of 50 Hz  Figure 3-15 shows the application rate of AP2 as a function of duty cycle for three different train speeds at 40 psi nozzle back pressure with the solenoid actuation frequency of 50 Hz. The figure demonstrates how the application rate of LFM can be regulated by changing the duty cycle.   00.511.522.530 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Mass flow rate (gr/s)Duty cycle20 psi40 psi60 psi38   Figure 3-15: AP2 application rate as a function of duty cycle with the solenoid actuation of 50 Hz for three different train speeds  Spacing between the stitches of the applied LFM on the rail track could be regulated by changing the frequency of solenoid actuation.  Figure 3-16 shows the spacing as a function of the frequency at a duty cycle of 0.5 for three different train speeds.   0501001502002500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Application rate (gr/mile)Duty cycle30 mile/hr60 mile/hr90 mile/hr39   Figure 3-16: spacing between liquid stitches applied on the rail track as a function of the frequency of solenoid actuation at the duty cycle of 0.5 for three different train speeds  As a conclusion, the application rate of the LFMs applied on the rail track at different train speeds can be controlled by changing the duty cycle of the solenoid valve. This concepts represents an improvement over the current application technique which involves a fixed nozzle geometry and only two nozzle back pressures available at which LFMs could be applied. In addition, spacing between the stitches of the applied LFM on the rail track can be adjusted by changing the frequency of solenoid actuation.     00.511.522.50 20 40 60 80 100 120 140 160 180Spacing (m)Frequency (Hz)30 mile/hr60 mile/hr90 mile/hr40  Chapter 4: Transient Jet Impaction on a Moving Surface   4.1 Flow Rate and Jet Characteristics Results In this section, the flow rate results for Newtonian and non-Newtonian liquid tests and also transient jet characteristics downstream of the nozzle are brought and discussed.  4.1.1   Newtonian Test Liquids  4.1.1.1   Flow Rate Test Results      Flow rate tests were conducted with the plunger at its fully open position with different water-glycerine solution and the results are presented in figure 4-1. The liquid properties information can be found in table 2-1. A power law was fit to the flow rate data of each solution and the result is presented in table 4-1 in the form of 𝑄 = 𝑎(∆𝑃)𝑘. As was expected, at each back pressure, as the viscosity increases the flow rate decreases due to more viscous losses at the orifice.     Calculating discharge coefficient at different Reynolds numbers is a popular way of characterizing the flow rate behaviour through the nozzle. The results are shown in figure 4-2. As could be observed, for low Reynolds numbers, the discharge coefficient has a small value and increases as Reynolds number rises. In addition, a power curve was fitted to every set of data. It is observed that at very low Reynolds numbers, the discharge coefficient is proportional to 𝑅𝑒0.5 and as Reynolds number increases, the power value decreases. These results are consistent with the study done by Hollingshead [45].  The discharge coefficient rises to a nearly constant value 41  of 0.8 for water-glycerin 65%. The reason is that viscous losses are more dominant at low Reynolds numbers [39].     Figure 4-1: Newtonian test liquids flow rate results. Orifice diameter: 0.697 mm   Figure 4-2: Newtonian test liquids discharge coefficient as a function of Reynolds number   0.111010010 100mass Flow rate (gr/s)Nozzle back pressure (psig)WG 65WG 75WG 85WG 90WG 99.5Power (WG 65)Power (WG 75)Power (WG 85)Power (WG 90)Power (WG 99.5)y = 0.342x0.1156y = 0.2093x0.19y = 0.1069x0.3197y = 0.078x0.3954y = 0.0604x0.493700.10.20.30.40.50.60.70.80.90.1 1 10 100 1000 10000CdReWG 65WG 75WG 85WG 90WG 99.5Power (WG 65)Power (WG 75)Power (WG 85)Power (WG 90)Power (WG 99.5)42  Table 4-1: empirical fit parameters for flow rate results  Test Liquid a k 𝑹𝟐 WG 65 0.9087 0.5653 0.9997 WG 75 0.6651 0.6172 0.9993 WG 85 0.3018 0.7348 0.9996 WG 90 0.1575 0.8267 0.9989 WG 99.5 0.0218 0.9876 0.9991   It could also be observed from figure 4-2 that no cavitation occurred for the tests conducted in the experiment as the discharge coefficient is constantly increasing as Reynolds number rises for each solution.    4.1.1.2   Liquid Jet Diameter   Steady state liquid jet diameters for five different water-glycerin solutions and seven back pressures were visualized and measured. It was observed that the results were independent of nozzle back pressure for all of the tests. The results are presented in table 4-2, which shows the average 𝐷𝑗 𝐷0⁄  for all five different test liquids.   It was observed that for high Reynolds numbers 𝐷𝑗 𝐷0⁄  ratio is close to 0.87, but for low Reynolds numbers the ratio increases. These results are consistent with the research done by Middleman [40]. Having the results for steady state jet diameter, density, and average mass flow rate for transient operation, the average velocity could be calculated.     43  Table 4-2: Steady state jet diameter measurements for different test liquids Test liquid Average jet diameter (𝑫𝒋) [mm] 𝑫𝒋 𝑫𝟎⁄  Characteristic Reynolds number WG 65 0.6049 0.868 1185.52 WG 75 0.6084 0.873 486.77 WG 85 0.6098 0.875 112.43 WG 90 0.6168 0.885 47.19 WG 99.5 0.6349 0.911 2.35   4.1.1.3   Transient Jet Characteristics  All impingement test were done with transient jets produced with 100 Hz actuation frequency and duty cycle of 0.5. In order to efficiently investigate the physics of transient jet impaction on a moving surface, sufficient knowledge of transient jet characteristics is required. It was found that under certain conditions, the transient jet breaks up on its way to reach the surface. However, if it doesn’t break up, a blob of liquid forms on the tip of the transient jet. Figure 4-3 shows transient jet under the two mentioned conditions.    Many researchers have studied the breakup of a liquid jet that is injected into a stagnant gas from a circular nozzle orifice and the precise mechanisms of the jet breakup are still being researched [41, 42, 43]. However jet breakup studies have been mostly done on circular liquid jet injected to a stagnant gas and few studies are known which investigated the transient jet breakup moving through the air. Most primary dimensionless numbers that are effective in circular jet breakup are Reynolds and Weber number [42].    44                                                          Figure 4-3: Transient jet at 76 mm downstream of the tip of nozzle, a) WG 75 at 60 psi NBP, b) WG 90 at 60 NBP   In order to gain more knowledge about the transient jet characteristics the effect of Weber and Reynolds number on the jet break-up is shown in figure 4-4. As could be observed from the figure, Weber number has the dominant role in jet break-up results compared to Reynolds number, e.g. as is shown in Figures 4-5 and 4-6, it was observed that at 75 mm downstream of the nozzle transient jet at higher Reynolds numbers is stable with a blob forming on its tip whereas the jet breaks up at a lower Reynolds number and higher Weber number. This visualization proves that Weber (a) (b) 1 mm 1 mm 45  number has the primary role on the transient jet break-up outcome downstream of the nozzle.     Figure 4-4: Jet break-up/stable jet boundary 76 mm downstream of the nozzle (We vs. Re)           101001000100001 10 100 1000 10000WeReJet break-upStable jet with blob46   a) 0.3 ms  b) 0.7 ms  c) 1.1 ms  d) 1.4 ms  e) 1.8 ms  f) 2.1 ms  g) 2.5 ms  h) 2.9 ms  i) 3.3 ms  j) 3.7 ms  k) 4.2 ms  l) 4.6 ms  m) 4.9 ms  n) 5.2 ms  o) 5.5 ms Figure 4-5: Transient jet evolution captured at 5 different frames from the tip of the nozzle to 75mm downstream for WG 85, We=2296, Re=128. Length of each frame = 15mm 47    a) 0.6 ms  b) 1.2 ms  c) 1.8 ms  d) 2.4 ms  e) 3 ms  f) 3.6 ms  g) 4.2 ms  h) 4.8 ms  i) 5.4 ms  j) 5.9 ms  k) 6.5 ms  l) 7.1 ms  m) 7.5 ms  n) 8.1 ms  o) 8.7 ms Figure 4-6: Transient jet evolution captured at 5 different frames from the tip of the nozzle to 75mm downstream for WG 75, We=1045, Re=275. Length of each frame = 15mm 48  4.1.2   Liquid Friction Modifiers Test Results In this section results of flow rate tests and also transient jet characteristics are presented and discussed.    4.1.2.1   Flow Rate Test Results   Flow rate tests were conducted with the plunger at its fully open position with three different types of commercial LFMs and the results are brought in figure 4-7. The liquid properties information could be found in table 2-2. Power law fit was accomplished for the flow rate data of each solution and the data are brought in table 4-3 in the form of 𝑦 = 𝑎(∆𝑃)𝑘. All tests were done with orifice diameter of 0.697 mm.    Figure 4-7 Mass flow rate results for commercial LFMs. Orifice diameter: 0.697 mm 11010 100Mass flow rate (gr/s)Nozzle back pressure (Psig)AP2SimuHybPower (AP2)Power (Simu)Power (Hyb)49  Table 4-3: empirical fit parameters for LFMs’ flow rate results  Test Liquid a k 𝑹𝟐 AP2 0.1149 0.827 0.9995 Simu 0.1035 0.8356 0.9997 Hyb 0.0857 0.8611 0.9989  4.1.2.2   Transient Jet Characteristics  In contrast to Newtonian liquids, transient jets produced by LFMs which are non-Newtonian liquids, were stable with a blob forming on the tip of jet as it moves through the ambient air, except for Hybrid Material at the maximum nozzle back pressure (80 psi) where the transient jet breaks up on its way. Figures 4-11a to 4-11d shows the transient jet under different conditions for three LFMs tested.         Figure 4-8: Transient jet visualization at 76 mm downstream of the nozzle for different LFMs, a) Hyb at 40 Psig NBP, b) AP2 at 40 Psig NBP, c) Simu at 40 Psig NBP, d) Hyb at 80 Psig NBP (a) (b) (c) (d) 50  Figures 4-8a, 4-8b, and 4-8c show transient jets for Hyb, AP2, and Simu respectively, all at 40 psig nozzle back pressure and 76 mm downstream of the nozzle where jets are stable and a blob forms at the tip of the jet. On the other hand, Figure 4-8d illustrates the only condition under which the jet breaks up for all of tests done with commercial LFMs, which is Hyb at 80 psig nozzle back pressure. All the transient jets were produced at 100 Hz frequency actuation and a duty cycle of 0.5.    4.2   Effect of Surface Roughness on Transient Jet Impaction  In this section transient jet impingement on the moving surface using linear traverse and spinning disk setup for Newtonian test liquids and also three types of commercial LFMs (AP2, Simulation Product (Simu), and Hybrid Material (Hyb)) are presented and discussed.    4.2.1   Newtonian Test Liquids   Five Newtonian test liquids with different viscosities were used to perform the transient jet impingement test on a high-speed moving surface on four different stainless steel plates with different roughness heights in order to study the effect of surface roughness on the impaction outcome. All tests were done with 100 Hz frequency actuation and duty cycle of 0.5. The 0.697 mm orifice was used for all of the tests. As was mentioned in section 2.4, the velocity of impaction was measured using high speed images captured from the tip of the transient jet 76 mm downstream of the nozzle.   51  Impingement test results on mirror surface (0.0195 𝜇𝑚), smooth surface (0.1500 𝜇𝑚), rough surface (0.4530 𝜇𝑚), and coarse surface (0.6380 𝜇𝑚) are shown in Figure 4-9, Figure 4-10, Figure 4-11, Figure 4-12, respectively. These experiments were performed on air cannon test setup (for the surface speeds up to 25 m/s) and spinning disk test setup (for speeds above 25 m/s up to 75 m/s) and the combined results obtained by means of both setups are brought in the Figures 4-6 to 4-9. In all of the graphs every scatter point represents one single test result and its colour demonstrates the impaction outcome under that particular condition; i.e. the colour is red in case of splash and is green in case of deposition after impaction.    As could be observed from Figures 4-9a to 4-12a and Figures 4-9b to 4-12b at all surface and jet speeds splash was achieved for WG 65 and WG 75 on all four surface roughness heights. On the other hand, Figure 4-10e and Figure 4-11e shows deposition was achieved at all surface and jet speeds for WG 99.5 on the smooth and rough surfaces.   Another interesting result is that at same jet and surface speeds, transient jet is more prone to splash on the mirror surface compared to smooth and rough surfaces, and splash threshold decreases as the roughness height increases above the smooth surface. This result suggests that a minimum roughness height is necessary for deposition on the surface, but if the roughness goes above that minimum, the splash threshold starts to decrease as the roughness height increases.         52            010203040506070800 10 20 30Surace speed (m/s)Jet Speed (m/s)Splash010203040506070800 5 10 15 20 25Surface Speed (m/s)Jet Speed (m/s)Splash(a) (b) 010203040506070800 5 10 15 20Surface Speed (m/s)Jet Speed (m/s)010203040506070800 5 10 15Surface Speed (m/s)Jet Speed (m/s)010203040506070800 1 2 3 4Surface Speed (m/s)Jet Speed (m/s)DepositionSplash(c) (e) Figure 4-9: different Newtonian liquid jet impingement on mirror surface test results for a) WG65, b) WG75, c) WG85, d) WG90, and e) WG99.5 (d) 53          (a) (b) (c) (e) Figure 4-10: different Newtonian liquid jet impingement on smooth surface test results for a) WG65, b) WG75, c) WG85, d) WG90, and e) WG99.5 (d) 010203040506070800 10 20 30Surface Speed (m/s)Jet Speed (m/s)Splash010203040506070800 5 10 15 20 25Surface Speed (m/s)Jet Speed (m/s)Splash010203040506070800 5 10 15 20Surface Speed (m/s)Jet Speed (m/s)010203040506070800 5 10 15Surface Speed (m/s)Jet Speed (m/s)010203040506070800 1 2 3 4Surface Speed (m/s)jet Speed (m/s)Deposition54          (a) (b) (c) (d) 010203040506070800 10 20 30Surface Speed (m/s)Jet Speed (m/s)Splash010203040506070800 5 10 15 20 25Surface Speed (m/s)Jet Speed (m/s)Splash010203040506070800 5 10 15 20Surface Speed (m/s)Jet Speed (m/s)010203040506070800 5 10 15Surface Speed (m/s)Jet Speed (m/s)010203040506070800 1 2 3 4Surface Speed (m/s)Jet Speed (m/s)Deposition(e) Figure 4-11: different Newtonian liquid jet impingement on rough surface test results for a) WG65, b) WG75, c) WG85, d) WG90, and e) WG99.5  55          (a) (b) 010203040506070800 10 20 30Surface Speed (m/s)Jet Speed (m/s)Splash010203040506070800 5 10 15 20 25Surface Speed (m/s)Jet Speed (m/s)Splash010203040506070800 5 10 15 20Surface Speed (m/s)Jet Speed (m/s)010203040506070800 5 10 15Surface Speed (m/s)Jet Speed (m/s)010203040506070800 1 2 3 4Surface Speed (m/s)Jet Speed (m/s)(e) Figure 4-12: different Newtonian liquid jet impingement on coarse surface test results for a) WG65, b) WG75, c) WG85, d) WG90, and e) WG99.5  (d) (c) 56  The results also shows that for each surface roughness and test liquid, as surface speed or jet speed increases, the jet is more prone to splash after impaction. Furthermore, for non-smooth surfaces, as the roughness height is increased the propensity of the jet to splash also increases. It is noteworthy to mention that the experiments were repeated many times specially near the thresholds where transition from deposition to splash was observed and the consistency of the results was ensured.  4.2.2    LFMs Test Results  Three different types of commercial LFMs were used to perform the transient jet impingement test on a moving surface on two different stainless steel plates with different roughness heights in order to investigate the effect of surface roughness on the impaction outcome. All tests were done with 100 Hz frequency actuation and duty cycle of 0.5. The 0.697 mm orifice was used for all of the tests.   Impingement test results on smooth surface and rough surface are shown in Figure 4-13 and Figure 4-14 respectively. These experiments were performed on air cannon test setup for the surface speeds up to 25 m/s.  It could be observed from the figures that deposition was achieved for all surface and jet speeds with Simu which offers the best transfer efficiency compared to the other two LFMs. Deposition was also achieved for AP2 transient jet at all surface and jet speeds on smooth surface, whereas splash was observed at high surface and jet speeds on the rough surface.   57                          0510152025300 5 10 15Surface Speed (m/s)Jet Speed (m/s)Deposition0510152025300 2 4 6 8 10 12Surface Speed (m/s)Jet Speed (m/s)Deposition0510152025300 2 4 6 8 10Surface Speed (m/s)Jet Speed (m/s)(a) (b) (c) Figure 4-13: Three different LFMs impingement on smooth surface test results for a) AP2, b) Simu,  c) Hyb      58   (a)  (b)  (c) Figure 4-14: Three different LFMs impingement on roughsurface test results for a) AP2, b) Simu, c) Hyb 0510152025300 5 10 15Surface Speed (m/s)Jet Speed (m/s)0510152025300 5 10 15Surface Speed (m/s)Jet Speed (m/s)Deposition0510152025300 2 4 6 8 10Surface Speed (m/s)Jet Speed (m/s)59  Hybrid material proved to be the least efficient in terms of transfer efficiency compared to other two LFMs, as splash was observed at the same surface and jet speeds for which deposition was observed with AP2 and Simu. It could be attributed to the lower relaxation time of Hyb compared to AP2 and Simu, as it’s been proved experimentally both for droplets [28] and circular jets [36] that Deborah number has a primary role on the impingement outcome. It is noteworthy to mention that similar to Newtonian liquid tests results, the jet is more prone to splash on the rough surface compared to the smooth one.        4.3 A Model for Jet Impingement   Courbin et al. [24] reported that if the impaction surface has a tangential velocity, asymmetric splash occurs, and in particular the side of the lamella in the upstream direction of the impacting droplet spreads on the moving surface while the other side splashes.   Bird et al. [25] developed a model for the spherical droplet impaction outcome on a moving surface. Figure 4-15 shows a schematic of their model. The lamella is the portion of the droplet that contacts the moving substrate and is transferred into a film with thickness ℎ and length 𝐿 (region **). Film deformations increase the interfacial surface area and is prompted by surface or gas-related perturbations [25]. According to their model, the film becomes unstable and leads to splash when the kinetic energy of the film relative to the surroundings substantially exceeds the surface energy which prevents deformations.  60  The relative kinetic energy and the surface energy will scale as 𝜌(𝑉𝑙 − 𝑉𝑡)2𝐿2ℎ and 𝜎ℎ𝐿 respectively, where 𝑉𝑙 is the lamella speed and 𝑉𝑡 is the tangential speed of the substrate. So according to their model, splash occurs when:  𝜌(𝑉𝑙−𝑉𝑡)2𝐿𝜎≥ 𝐶 ≫ 1                                                                                                    (1)  where the value of C is a function of the surface and the  surrounding air properties. To achieve a criterion which involves the governing dimensionless numbers, i.e. 𝑅𝑒,𝑊𝑒, and velocity ratio, many assumptions were considered in their modeling. First, according to conservation of mass, the volume of region * and region ** should be equal.   Another assumption is that the thickness of lamella is proportional to the momentum boundary layer thickness in the liquid, i.e. ℎ = 𝑐1√νt where 𝑐1 is a constant of order 1. It was also assumed that the time at which splash occurs, 𝑡𝑐, is when a distinct lamella is achieved, i.e. when 𝐿 grows at the same rate or faster than 𝑎. With this assumption, the approximation (𝑡𝑐) ≈ 𝑎(𝑡𝑐) is derived which gives 𝑡𝑐 the value ν𝑉𝑛2 where 𝑉𝑛 is the normal velocity of the droplet. The final splash criterion is derived to be: 𝑊𝑒𝑛𝑅𝑒𝑛12 [1 − 𝑘𝑉𝑡𝑉𝑛𝑅𝑒𝑛−12]2≥ 𝐾                                                                                   (2) Where 𝑅𝑒𝑛 =𝑉𝑛𝑅ν , 𝑊𝑒𝑛 =𝜌𝑉𝑛2𝑅𝜎 and k and K are scaling factors. The value of K should depend primarily on the surface roughness height. 61   According to the model, in the case that the surface is not moving, i.e.  𝑉𝑡𝑉𝑛= 0 splash will occur when 𝑊𝑒𝑛𝑅𝑒𝑛12 ≥ 𝐾 which is consistent with the previous studies on droplet impaction on a stationary surface [44, 45]. In these studies, it was also proved that the value of 𝐾 decreases as the roughness height of the surface increases, meaning that the droplet will be more prone to splash.       Figure 4-15: droplet impaction modeling on a moving surface  Bird et al. [25] successfully implemented the aforementioned model on a Newtonian droplet impaction on a moving surface. However, the effect of surface roughness was not investigated.   We investigate here whether transient jet impaction on a moving surface could also be modeled using this criterion. Specifically, we will consider transient jets for which jet break-up is not observed. For such jets a blob of fluid is formed at the tip of the jet, which is very approximately spherical. It is hypothesized that splash is 62  governed by this blob because if splash occurs it happens shortly after impaction, before the thin part of the transient jet following the blob reaches the surface.   Figure 4-11 demonstrates the experimental results for five different water-glycerin solutions and four different surface roughness heights, under circumstances that a blob is formed at the tip of the transient jet when impacting the surface, following the scaling obtained using equation (2). The horizontal axis is nondimensionalized as 𝑉𝑡𝑉𝑛𝑅𝑒𝑛−12, and the vertical axis as 𝑊𝑒𝑛𝑅𝑒𝑛12𝐾 . The blob velocity and diameter are obtained based on high speed images as was explained in sections 2.4 and 2.5.    63     (b) 00.20.40.60.811.20 2 4 6 8 10 12Axis TitleAxis TitleThreshold lineSplashDeposition00.10.20.30.40.50.60.70.80.910 2 4 6 8 10 12Axis TitleAxis Titlethreshold lineSplashDeposition(a) 64   (c)   (d) Figure 4-11: experimental results for five different water glycerin solutions, a) smooth surface, K=19200, k=0.5, b) rough surface, K=17600, k=0.9, c) coarse surface, K=13100, k=1, d) mirror surface, K=13700, k=1 00.20.40.60.811.21.40 2 4 6 8 10 12Axis TitleAxis TitleThreshold lineSplashDeposition00.20.40.60.811.21.40 2 4 6 8 10 12Axis TitleAxis TitleThreshold lineSplashDeposition65  As could be observed from Figure 4-11, the model prediction agrees well with the experimental data for all surface roughness heights. According to previous studies it is expected that k is in the order of one and K to be much greater than one, between 1180 and 19200 which agrees with the results obtained here [19, 25, 44]. It is further observed that 𝐾 decreases as the roughness height increases (except for the case of impaction on a smooth surface), which is consistent with previous studies on the effect of surface roughness on impaction outcome [19, 44]. It is also noteworthy to mention that the experiments were repeated many times specially near the thresholds where transition from deposition to splash was observed and the consistency of the results was ensured.  However, the value of 𝐾 for the mirror-smooth surface is found to be considerably more than that of “smooth” and “rough” surfaces, which implies that the droplet is more prone to splash on mirror surfaces compared to the other two. This is an interesting result which was not obtained before in the studies done on surface roughness effect on droplet impaction on a stationary or moving substrate.                66  Chapter 5:   Conclusions and Recommendations   5.1 Conclusions for Transient Jet Impaction on a Moving Surface  An experimental study was performed to investigate the interaction of Newtonian and non-Newtonian transient liquid jets on a high speed dry moving surface. The effect of surface roughness, jet speed, and surface velocity were examined on the impaction outcome using five different water glycerin solutions to isolate the effect of shear viscosity from other properties of the fluid. High speed imaging was performed to visualize the interaction between the jet and the moving surface. The key findings of this study are as follows:    In the range of 0.15 to 0.64 𝜇𝑚 roughness heights, as the roughness increases the jet is more prone to splash, whereas splash is more likely to occur on the mirror surface compared to smooth and rough surfaces.   As the viscosity of the liquid decreases, the jet is more prone to splash after impaction.   Splash was observed to be more likely for higher surface and jet speeds.   The transient jet impaction outcome was modeled as being similar to a spherical droplet impaction, under conditions where a blob forms at the tip of the transient jet. With appropriate fitting of constants, the theory was in good agreement with the experiments.   The tested commercial LFMs were found to have a satisfactory transfer efficiency and deposited well on the surface for a wide range of jet and surface velocities on both rough and smooth surfaces except for the Hybrid material 67  whose transfer efficiency was proved to be lower than that of AP2 and Simulation Product.  5.2 Conclusions for Transient Jet Characteristics and Application Rate  An experimental study was performed to investigate the effect of jet speed and liquid viscosity on the transient jet evolution from the tip of the nozzle to further downstream where it impacts on the surface. Furthermore, numerical and experimental studies were accomplished to obtain the drag force exerted on the plunger of the solenoid valve in the nozzle. The key findings of this study are as follows:   At high Reynolds and Weber numbers the jet breaks up downstream of the nozzle. However it was proved that in the range of Reynolds and Weber number tested (Reynolds and Weber ranging from 1 to 1500, and 10 to 7200 respectively) the Weber number has the dominant role in determining the outcome of the transient jet downstream of the nozzle.  At sufficiently low Reynolds and Weber numbers a blob forms at the tip of the transient jet.  Numerical results for drag force exerted on the plunger is in reasonable agreement with experiments, which suggests that the flow inside the nozzle could be regarded as a quasi-steady state flow.   As the plunger moves closer to the closed position, the corresponding drag force decreases.  68   At a fixed plunger position, the drag force increases as the viscosity of the test liquid or nozzle back pressure increases.    The application rate of the LFMs applied on the rail track could be efficiently regulated by changing the duty cycle of the solenoid actuation.    5.3 Recommendations for Future Works  To further extend the knowledge of liquid jet impaction on a dry moving surface and also transient jet characteristics the following areas should be investigated:   More detailed investigation on the effect of surface roughness on liquid jet and moving surface interaction, especially for mirror finish surface.  Conducting experiment with broader range of jet and surface speeds.   More detailed study of transient jet characteristics with broader range of duty cycle and frequency of actuation, and also simulating the transient jet evolution downstream of the nozzle.  Effect of elasticity and other non-Newtonian properties on transient jet evolution and also its impingement on a high speed moving surface.      Investigation on the effect of duty cycle and frequency of actuation on the impaction outcome.  69   Bibliography   [1] Cotter, J., Eadie, D.T., Elvidge, D., Hooper, N., Robert, J., Makowsky, T., Liu, Y., 2005, Top of Rail Friction Control: Reductions in Fuel and Greenhouse Gas Emissions. 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P., Reitz, R.D., 1998, DROP AND SPRAY FORMATION FROM A LIQUID JET, Annual Review of Fluid Mechanics, 30: 85-105.  [43] Reitz, R. D., Bracco, F.V., 1986, Mechanisms of breakup of round liquid jets. The Encyclopedia of Fluid Mechanics, ed. N Cheremisnoff, 3:233–49. Houston: Gulf.  [44] Stow, C. D., Hadfield, M. G., 1981, An experimental investigation of fluid-flow resulting from the impact of a water drop with an unyielding dry surface. Proc. R. Soc. A 373 419–41.   73                           Appendix A:   Newtonian Test Liquids Flow Rate As a Function of Duty Cycle  Figures A-1 to A-5 show the results of flow rate as a function of duty cycle at the actuation frequency of 50 Hz for five different Newtonian test liquids. The uncertainty of flow rate results is ±0.05 𝑔𝑟𝑠. 74    Figure A-1: Flow rate as a function of duty cycle for WG 65 at different nozzle back pressures, Frequency of actuation = 50 Hz       0123456780 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flow rate (gr/s)Duty cycle20 psi40 psi60 psi75   Figure A-2: Flow rate as a function of duty cycle for WG 75 at different nozzle back pressures, Frequency of actuation = 50 Hz    Figure A-3: Flow rate as a function of duty cycle for WG 85 at different nozzle back pressures, Frequency of actuation = 50 Hz 012345670 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flow rate (gr/s)Duty cycle 20 psi40 psi60 psi00.511.522.533.544.550 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flow rate (gr/s)Duty cycle20 psi40 psi60 psi76   Figure A-4: Flow rate as a function of duty cycle for WG 90 at different nozzle back pressures, Frequency of actuation = 50 Hz    Figure A-5: Flow rate as a function of duty cycle for WG 99.5 at different nozzle back pressures, Frequency of actuation = 50 Hz 00.511.522.533.540 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flow rate (gr/s)Duty cycle20 psi40 psi60 psi00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flow rate (gr/s)Duty cycle20 psi40psi60 psi

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