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Hydrodynamics of circular free-surface long water jets in industrial metal cooling Seraj, Mohammad Mohsen 2011

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Hydrodynamics of Circular Free-surface Long Water Jets in Industrial Metal Cooling  by Mohammad Mohsen Seraj B.Sc., Amir Kabir University of Technology, Iran, 1994 M.Sc., Tarbiat Modarres University, Iran, 1997  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  February 2011 © Mohammad Mohsen Seraj  Abstract Control cooling in run-out table (ROT) is crucial in managing the properties of steel strip. However, industries still rely on experience and empirical methods due to the complexity and transient nature of cooling process. The associated flow features of ROT cooling received little attention in the literature. The main purpose of this research is to investigate systematically the hydrodynamics of long circular water jets impinging on fixed and moving plate with industrial scale. The fixed plate experiments showed that the impingement film and circular hydraulic jump were disturbed with surface waves and splattering. The experiments on moving plate with single impinging jet demonstrated the effect of jet flow rate and plate speed on wetting zone. For a given plate velocity, the size of wetting area increased according to jet Reynolds number. The moving impingement surface interferes with radial spreading film and the wetting front became noncircular. A new correlation for the radius of wetting front has been proposed. The effect of plate motion on liquid jets interactions were studied experimentally using multiple jets. Nonsplashing thick interaction film or thin upwash splashing fountain at the interaction zone were observed depending on process parameters. If the effect of plate motion was not promoted then the interaction flow structure was preserved similar to stationary plate. However, the moving plate could change the strong splashing fountain interaction flow to nonsplashing thick film depending on the velocity ratio of plate to jet for a given nozzle space. Higher plate speeds and/or lower jet flow rates are more likely to decrease splashing and change the fountain type interaction. Numerical simulations on stationary surface demonstrated that suggested velocity and pressure variation for short laminar jets may be adapted for long turbulent liquid jets if the gravity is considered. Generally, shear-stress transport k-ω model showed better performance after impingement. The moving plate simulations of single jet proved the distortion of the impingement zone. The shifted stagnation point produces noncircular impingement region and unsymmetrical spreading of impingement water film over the surface. Longitudinal negative velocity was occurred at higher plate velocity simulations which represent the backwash flow.  ii  Table of Contents Abstract.............................................................................................................ii Table of Contents ............................................................................................iii List of Tables ..................................................................................................vii List of Figures................................................................................................viii List of Symbols ..............................................................................................xiii Acknowledgements ........................................................................................ xv  Chapter 1 Introduction, Literature Review, and Research Scope.............. 1 1.1  Introduction.............................................................................................................1  1.2  Literature Review....................................................................................................5  1.2.1 Hydrodynamics of a Single Impinging Jet......................................................5 1.2.1.1 Impingement Zone ..........................................................................................6 1.2.1.2 Parallel Zone .................................................................................................10 1.2.2 Hydraulic Jump (HJ).....................................................................................11 1.2.3 Jet Instability and Splattering........................................................................13 1.2.4 Multiple Jets..................................................................................................14 1.2.4.1 Fountain Formation Region ..........................................................................16 1.2.4.2 Upwash Fountain Flow Region ....................................................................16 1.2.4.3 Multi Liquid Jets ...........................................................................................17 1.2.5 Moving Surface.............................................................................................18 1.2.6 Numerical Simulations..................................................................................23 1.3 Scope and Objective .............................................................................................25  Chapter 2 Experiment Facility and Setup................................................... 26 2.1  Apparatus ..............................................................................................................26  2.1.1 Water Supply System....................................................................................26 2.1.2 Flow Control .................................................................................................29 2.1.3 Nozzle Assembly ..........................................................................................29 2.1.4 Industrial Water Jet .......................................................................................29 2.2 Test Procedure ......................................................................................................31  iii  Chapter 3 Experiments on Stationary plate................................................ 33 3.1  Test Plate...............................................................................................................33  3.2  Test Procedure ......................................................................................................34  3.3  Data Analysis ........................................................................................................37  3.4  Pre-impingement...................................................................................................38  3.5  Flow Observation after Impingement ...................................................................39  3.6  Impingement Water Film......................................................................................41  3.7  Data Measurements...............................................................................................43  3.8  Progression of Water Front...................................................................................46  3.9  Frontal Velocities..................................................................................................49  3.10  Circular Hydraulic Jump (CHJ) ............................................................................53  3.11  Surface Waves and Splattering .............................................................................56  3.12  Summary and Conclusion .....................................................................................60  Chapter 4 Experiments on Moving Plate: Single Jet ................................. 61 4.1  Experimental Setup and Procedure.......................................................................61  4.2  Data Processing.....................................................................................................64  4.3  Flow Observation..................................................................................................66  4.4  Velocity of Test Plate............................................................................................70  4.5  Jet Flow Rate.........................................................................................................75  4.6  Hydraulic Jump Unsteadiness...............................................................................79  4.7  The Jump Radius...................................................................................................82  4.8  Wetting Front (HJ)................................................................................................90  Chapter 5 Experiments on Moving plate: Multiple Jets............................ 96 5.1  Introduction...........................................................................................................96  5.2  Experimental Setup and Procedure.......................................................................97  5.3  Data Processing...................................................................................................101  5.4  Experiments on Stationary Plate (H = 1.5 m).....................................................105  5.5  Experiments of Twin Jets on a Moving Plate (H = 1.5 m) .................................111  iv  5.5.1 Flow Observation........................................................................................111 5.5.2 10 and 15 L/min Jets Experiments ..............................................................115 5.5.3 Data Measurements (H = 1.5 m) ................................................................118 5.5.4 22 and 30 L/min Jets Experiments ..............................................................121 5.5.5 Data Measurements (22 and 30 L/min).......................................................124 5.5.6 Interaction Zone Transition.........................................................................126 5.6 Experiments with Three Nozzles on Stationary Plate (H = 1.5 m) ....................128 5.7  Experiments of Three jets on Moving Plate (H = 1.5 m) ...................................128  5.7.1 Flow Observation........................................................................................128 5.7.2 10, 15 and 22 L/min Jets Experiments ........................................................131 5.8 Experiments on Moving Plate with Lower Nozzle (H = 0.5 m).........................134 5.8.1 Experiments of Twin Jets on Moving Plate (H = 0.5 m)............................135 5.8.2 Data Measurements for Twin Jets (H =0.5 m) ...........................................137 5.8.3 Experiments of Three Jets on Moving Plate (H = 0.5 m)...........................140 5.8.4 Fountain Asymmetry ..................................................................................143 5.8.5 Data Measurements for Three Jets..............................................................144 5.9 Summary and Conclusion ...................................................................................144  Chapter 6 Numerical Simulations.............................................................. 146 6.1  Turbulent Flow Modeling ...................................................................................146  6.1.1 Two Equations k- Turbulent Model..........................................................148 6.1.2 Two Equations k- Turbulent Model.........................................................150 6.2 Volume of Fluid Method (VOF).........................................................................151 6.3  Numerical Simulations of Stationary Plate.........................................................152  6.3.1 Numerical Procedure ..................................................................................153 6.3.2 Domain, Boundary Conditions and Meshes ...............................................154 6.3.3 Impinging Jet ..............................................................................................157 6.3.4 Jet Axial Velocity .......................................................................................160 6.3.5 Frontal Propagation.....................................................................................161 6.3.6 Velocity at Impingement Zone ...................................................................163 6.3.7 Velocity in Wall (parallel) Zone .................................................................168 6.3.8 Pressure at Impingement Region ................................................................171 6.3.9 Heat Transfer Correlation ...........................................................................171 6.3.10 Hydraulic Jump...........................................................................................173 6.3.11 Jet Disturbances and Splattering.................................................................174 6.4 Numerical Simulation of Moving Plate ..............................................................175 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5  Geometry, Boundary Condition and Mesh .................................................176 Impingement Flow Spreading.....................................................................179 Wetting Front ..............................................................................................181 Impingement Zone on Moving Surface ......................................................183 Velocity in Symmetry Plane .......................................................................187 v  6.5  Conclusion ..........................................................................................................191  Chapter 7 Summary, Conclusions and Recommendations ..................... 192 7.1  Summary of the Results ......................................................................................192  7.1.1 Fixed Plate Experiments .............................................................................192 7.1.2 Moving Plate Test- Single Jet .....................................................................193 7.1.3 Moving plate Test-Multiple Jets .................................................................194 7.1.4 Numerical Simulations................................................................................195 7.2 Conclusions.........................................................................................................197 7.3  Recommendations and Future Works.................................................................198  Bibliography ................................................................................................. 201 Appendix A Flow Rate Measurement at Fixed Plate Tests ..................... 210 Appendix B Flow Rate and Plate Velocity Measurements at Moving Plate Tests: Single Jet .................................................................................. 212 Appendix C Flow Rate and Plate Velocity Measurements at Moving Plate Tests: Multiple Jets ............................................................................ 217 Appendix D Interaction Zones Measurements ......................................... 231  vi  List of Tables Table 1.1 Typical Geometry and Operating Parameters on ROT [4-5]..................................3 Table 1.2 Scaling Relations for CHJ.....................................................................................12 Table 2.1 Test and Jet Parameters (Test Plate at H = 1.5 m)................................................31 Table 3. 1 Average Jet Flow Rates on Fixed Plate Tests......................................................36 Table 3. 2 Jet Impingement Parameters on Stationary Plate ................................................38 Table 3.3 Radius of Transition to Turbulent Flow ...............................................................43 Table 3.4 Radius of Circular Hydraulic Jumps.....................................................................55 Table 3.5 Scaling Exponents for HJ Radius Circular Correlations on Fixed Surface ..........55 Table 3.6 Jets Splattering Parameters ...................................................................................58 Table 4.1 Experimental Parameters ......................................................................................64 Table 4.2 Average Nozzle Flow Rates and Plate Speeds with Changes ..............................65 Table 4.3 Average Plate Velocity Obtained from Films.......................................................66 Table 4.4 Average Radiuses of Hydraulic Jump Rj ..............................................................83 Table 4.5 Unknowns in Equation 4.7....................................................................................88 Table 4.6 Coefficient C of the Inner Radius Correlation......................................................88 Table 4.7 Coefficient C of the Outer Radius Correlation .....................................................89 Table 4.8 Radius Rj HJ from Kate’s Modeling and Present Experiments............................92 Table 5.1 Experimental Parameters for Two Nozzle Tests ..................................................98 Table 5.2 Experimental Parameters for Three Nozzle Tests ................................................98 Table 5.3 Average Nozzles Flow Rates and Plate Speeds with Variations in Twin Jets Tests ....................................................................................................................................100 Table 5.4 Average Nozzles Flow Rates and Plate Speeds with Variations in Tests in Three Jets ............................................................................................................................101 Table 6.1 Jet Parameters .....................................................................................................152 Table 6.2 Meshes before Impingement...............................................................................156 Table 6. 3 The Jet Impingement Parameters.......................................................................159 Table 6.4 Stagnation Pressure and Corrected Tsat' ..............................................................172 Table 6.5 Effect of Impingement Pressure on Heat Flux....................................................173 Table 6.6 Numerical Hydraulic Jump Radius (15 L/min)...................................................174 Table 6.7 a and b Dimensions in Moving Simulations.......................................................178  vii  List of Figures Figure 1.1 Run-out Table Cooling Systems [3] ......................................................................2 Figure 1.2 Circular Free-Surface Jet Impingement.................................................................7 Figure 1.3 Pressure and Velocity Variation along the Plate Surface (Modified from [21])...8 Figure 1. 4 Circular HJ on Stationary Surface due to Normal Impingement (b) Noncircular HJ due to Oblique Impingement (Vp = 0 for Fixed Plate and Vp  0 for Moving Surface) (c) Elliptical Impingement Region for Noncircular HJ ............................22 Figure 2. 1 Schematic of Pilot Scale Run-Out Table Apparatus ..........................................27 Figure 2.3 Experimental Setup (a) Spray Zone (b) Nozzle (Dimensions in mm) ................27 Figure 2.4 Header and Nozzles.............................................................................................28 Figure 2.5 Free Jet Surface (a) Disturbed (H = 1.5 m) (b) Smooth (H = 0.5 m)..................30 Figure 3.1 Fixed Test Plate Assembly and Four Perpendicular Directions..........................34 Figure 3.2 Experiment Setup for Stationary Plate ................................................................36 Figure 3.3 Experimental Results before Impingement (a) Jet Height (b) Jet Speed.............39 Figure 3.4 Sample Images from Development of Water Layer 15 L/min after Impingement (t = 0 Represents the Time of Impingement) .................................................40 Figure 3.5 Development of Water Layer (45 L/min) after Impingement (t = 0 Represents the Time of Impingement) ....................................................................................................41 Figure 3.6 Experimental Data of 15 L/min (a) Water Front Distance (b) Frontal Velocity .44 Figure 3.7 Experimental Data for 30 L/min (a) Water Front Distance (b) Frontal Velocity 45 Figure 3.8 Progression of Water Front on Hot Plate Q = 45 L/min, Tint = 860 °C, ∆Tsub = 50 °C [11] ..........................................................................................................................47 Figure 3.9 Progression of Water Front on Cold and Hot Plate (a) Hot Steel Plate, Tint = 860 °C, ∆Tsub = 5-70 °C (b) Hot Brass Plate, Tint = 300 °C, ∆Tsub = 50 °C [86] .............48 Figure 3.10 Frontal Velocity in Four Directions (15 L/min Experiments) ...........................49 Figure 3.11 Frontal Velocity in Four Directions (30 L/min Experiments) ...........................50 Figure 3.12 Frontal Velocity in Four Directions (45 L/min Experiments) ...........................51 Figure 3.13 Velocity Profiles along the Four Directions at Various Flow Rates .................52 Figure 3.14 Circular Hydraulic Jumps in a 15 L/min Experiment (a) Jump Evolution (the Time is Started after Impingement) (b) Single Roller (c) Double Roller .............................54 Figure 3.15 Radius of Circular Hydraulic Jump versus Jet Flow Rate.................................56 Figure 3.16 Surface Waves after Impingement (a) Spreading 15 L/min (b) Pattern 15 L/min (c) Pattern 30 L/min ....................................................................................................57 Figure 3.17 Splashing in a Series of Frame Sequence (a) 30 L/min (b) 45 L/min ................59 Figure 4.1 Pilot Scale Run-Out Table Apparatus .................................................................62 Figure 4.2 Moving Test Plate................................................................................................62 Figure 4.3 (a) Nozzles and Top Camera (b) Mesh and Lights..............................................63 Figure 4.4 Sample Impingement Flow of a 10 L/min Jet on a Moving Surface at 1.5 m/s ..68 Figure 4.5 Sample Impingement Flow of a 15 L/min Jet on a Moving Surface at 1.3 m/s...69 Figure 4.6 Sample Impingement Flow of a 30 L/min Jet on a Moving Surface at 1.0 m/s...69 Figure 4.7 Sample Impingement Flow of a 45 L/min Jet on a Moving Surface at 0.6 m/s...70  viii  Figure 4.8 Wetting Zones in all Experiments of 10 L/m Jets (a) Sample Photographs (b) Measured Inner and Outer Wetting Fronts ...........................................................................71 Figure 4.9 Wetting Zones in all the Experiments of 15 L/m Jets (a) Sample Photographs (b) Measured Inner and Outer Wetting Fronts......................................................................72 Figure 4.10 Wetting Zones in all the Experiments of 30 L/m Jets (a) Sample Photographs (b) Measured Inner and Outer Wetting Fronts......................................................................73 Figure 4.11 Wetting Zones in all the Experiments of 45 L/m Jets (a) Sample Photographs (b) Measured Inner and Outer Wetting Fronts......................................................................74 Figure 4.12 Wetted Zones in the Experiments of Plate Velocity of Vp = 0.6 m/s (a) Sample Photographs (b) Measured Inner and Outer Fronts (HJs) ..................................76 Figure 4.13 Wetted Zones in the Experiments of Plate Velocity of Vp = 1.0 m/s (a) Sample Photographs (b) Measured Inner and Outer Fronts (HJs)........................................77 Figure 4.14 Wetted Zones in the Experiments of Plate Velocity of Vp = 1.3 m/s (a) Sample Photographs (Rj is Jump Radius) (b) Measured Inner and Outer Fronts (HJs) .......78 Figure 4.15 Hydraulic Jumps of Jet of 10 L/min on a Vp = 0.6 m/s Moving Surface (a) Sample Images (b) Measured Inner and Outer Profiles of the Jumps of Sample Frames (c) Accumulated Measured Data of the Jumps of Sample Images.............................................80 Figure 4.16 Hydraulic Jumps of Jet of 45 L/min on a Vp = 1.0 m/s Moving Surface (a) Sample Images (b) Measured Inner and Outer Profiles of the Jumps of Sample Images (c) Accumulated Measured Data of the Jumps of Sample Images .......................................81 Figure 4.17 Average Radiuses of Hydraulic Jumps for Different Flow Rate Jets on a Moving Plate.........................................................................................................................83 Figure 4.18 (a) Radius of Hydraulic Jump at Different Velocity Ratios (a) 10 and 15 L/min Jets (b) 30 and 45 L/min Jets ......................................................................................86 Figure 4.19 Correlated and Experimental Radii of the Hydraulic Jumps.............................89 Figure 4.20 A Hydraulic Jump due to an Oblique Circular Liquid Jet Impinging on Moving Plate.........................................................................................................................91 Figure 4.21 Theoretical Profiles of the Noncircular HJ on a Moving Surface from Equation 4.16 (a) 10 L/min Jet (b) 30 L/min Jet ...................................................................91 Figure 4.22 HJ Profiles due to 10 L/min Jets ........................................................................94 Figure 4.23 HJ Profiles due to 15 L/min Jets ........................................................................94 Figure 4.24 HJ Profiles due to 30 L/min Jets ........................................................................95 Figure 4.25 HJ Profiles due to 45 L/min Jets ........................................................................95 Figure 5.1 Twin Liquid Free-surface Impinging Jets (1. Free Jet, 2. Impingement Zone, 3. Inner Wall Region, 4. Outer Wall Region, and 5. Interaction Region) ................................97 Figure 5.2 Experiment N = 2, H = 1.5 m, 10 L/min, Vp = 1.0 m/s (a) Sample Images Selected Frames (b) Measurements of Interaction Film from the Frames (c) Accumulated Data .....................................................................................................................................103 Figure 5.3 Data Processing at a Experiments N = 3, H= 1.5 m, 15 L/min, Vp = 0.6 m/s (a) Sample Images - Selected Frames (b) Measurements of the Interaction Film (c) Accumulated Data...............................................................................................................104 Figure 5.4 (a) Hydraulic Jump Interaction on a Stationary Surface - Top view (H =1.5 m) (1. Free Jet, 2. Inner Wall Jet, 3. Outer Wall Jet, 4. Hydraulic Jump, and 5. Int-Z)...........107 Figure 5.5 Wall Jets Separation at Int-Z of 10 L/min Jets...................................................108  ix  Figure 5.6 (a) Sample Images of HJs Interaction and Returning Flow on Stationary Surface (H = 1.5 m) (b) HJs Interaction for Two Adjacent Jets, 1. HJ and 2. Int-Z ..........109 Figure 5.7 Upwash Liquid Fountain in Adjacent Jets (N = 2, 22 L, H = 0.5 m) (a) Side View (b) The Interaction of Upwash Stream and HJs ........................................................110 Figure 5.8 Sample Images for Impingement Flow Development and Jet Interaction (N = 2, H = 1.5 m, 10 L/min, 1.5 m/s) (a) Top View (b) Front View .........................................113 Figure 5.9 Sample Images for Impingement Flow Development and Jet Interaction (N = 2, H = 1.5 m, 22 L/min, 1.0 m/s) (a) Top View (b) Front View .........................................114 Figure 5.10 The Interaction of 10 L/min Jets on the Moving Surface at Different Velocities (N = 2, H = 1.5 m) (a) Top View (b).................................................................117 Figure 5.11 The Interaction of 15 L/min Jets on a Moving Surface at Different Velocities (N = 2, H = 1.5 m) (a) Top View (b) Front View ..............................................................118 Figure 5.12 Data Measurements of Int-Z (N = 2, H = 1.5 m, 10, 15 L/min) (a) Vp= 0.6 m/s (b) Vp = 1.0 m/s (c) Vp = 1.5 m/s ................................................................................119 Figure 5.13 Wetting Front for Single and Twin 10 L/min Jets Experiments (H = 1.5 m, Vp = 1.5 m/s) (a) Inner Fronts (b) Outer Fronts .................................................................121 Figure 5.14 The Interaction of 22 L/min Jets on Moving Surface at Different Velocities (N = 2, H = 1.5 m) (a) Top View (b) Front View ..............................................................122 Figure 5.15 The Interaction of 30 L/min Jets on a Moving Surface at Different Velocities (N = 2, H = 1.5 m) (a) Top View (b) Front View ..............................................................123 Figure 5.16 Data Measurements of Int-Z (N = 2, 22, H = 1.5 m, 30 L/min) (a) Vp = 0.6 m/s (b) Vp = 1.0 m/s (c) Vp = 1.5 m/s ................................................................................125 Figure 5.17 Simple Schematic of Int-Z as a Control Volume ............................................127 Figure 5.18 Int-Z Alteration (N = 2, H = 1.5 m, 22 L/min, 1.5 m/s) ..................................127 Figure 5.19 Three jets Interaction on Stationary Surface - Top and Front views (H = 1.5 m) Q = 10 L/min (b) Q = 15 L/min (c) Q = 22 L/min (1. Free Jet, 2. Inner Wall Jet, 3. Outer Wall Jet, and 4. Upwash Fountain)...........................................................................129 Figure 5.20 Sample Images for Impingement Flows Development and Jets Interaction (N = 3, H = 1.5 m, 10 L/min, 1.0 m/s) (a) Top View (b) Front View......................................130 Figure 5.21 The Interaction of 10 L/min Jets on a Moving Surface at Different Velocities (N = 3, H = 1.5 m) (a) Top View (b) Front View ..............................................................132 Figure 5.22 The Interaction of 15 L/min Jets on a Moving Surface at Different Velocities (N = 3, H = 1.5 m) (a) Top View (b) Front View ............................................................133 Figure 5.23 The Interaction of 22 L/min Jets on a Moving Surface at Different Velocities (N = 3, H = 1.5 m) (a) Top View (b) Front View ..............................................................134 Figure 5.24 The Interaction of 10 L/min Jets on a Moving Surface at Different Velocities – Top View (N = 2, H = 0.5 m) ..........................................................................................136 Figure 5.25 The Interaction of 15 L/min Jets on a Moving Surface at Different Velocities – Top View (N = 2, H = 0.5 m) ..........................................................................................136 Figure 5.26 The Interaction of 22 L/min Jets on a Moving Surface at Different Velocities137 Figure 5.27 Data Measurements of Int-Z (N = 2, 10 L/min) ..............................................138 Figure 5.28 Data Measurements of Int-Z (N = 2, 15 L/min) ..............................................139 Figure 5.29 Data Measurements of Int-Z (N = 2, 22 L/min, Vp = 1.5 m/s)........................139 Figure 5.30 Interaction of 10 L/min Jets on a Moving Surface at Different Velocities - (N = 3, H = 0.5 m) (a) Top View (b) Front View ..................................................................141  x  Figure 5. 31 Interaction of 15 L/min Jets on a Moving Surface at Different Velocities - (N = 3, H = 0.5 m) (a) Top View (b) Front View ..................................................................142 Figure 5.32 The Interaction of 22 L/min Jets on Moving Surface Top View.....................143 Figure 5.33 Fountain Unsteadiness and Inclination during a Test (N = 3, H = 0.5 m, 10 L/min, Vp = 1.0 m/s) ...........................................................................................................144 Figure 6.1 Modeling (a) Flow Domain (b) Grid (Not to Scale)..........................................155 Figure 6.2 Gird Dependency (a) Jet Speed Deceleration near the Surface (b) Radial Velocities at Two Distances above the Plate Surface for SST 45 L/min Simulation .........157 Figure 6.3 Jet Computations before Impingement (a) Height (b) Axial Speed ..................158 Figure 6.4 Axial Velocity Profiles of 30 L/min at Different Level beneath the Nozzle in Turbulent Simulations (Not to Scale) (a) RKE (b) SST .....................................................159 Figure 6.5 Axial Jet Velocity Reduction above Surface a) 15, 30 and 45 L/min Jets (b) 15 L/min Jet at t = 0.6 and 4 s ..................................................................................................161 Figure 6.6 The Development of Thin 45 L/min Water Layer over Fixed Plate Surface at SST Turbulent Simulation ..................................................................................................162 Figure 6.7 Experimental and Numerical Frontal Velocities Uf (a) 15 L/min (b) 30 L/min (c) 45 L/min .........................................................................................................................163 Figure 6.8 Radial Velocity Profiles along Plate Surface in Stagnation Zone for 15L/min Jet Simulations (a) Laminar (b) Turbulent RKE (c) Turbulent SST ..................................165 Figure 6.9 Radial Velocity Profiles along Plate Surface in Impingement Zone for 15 L/min Long Jet Simulations (a) Laminar (b) Turbulent RKE (c) Turbulent SST...............167 Figure 6.10 Radial Velocity Profiles along Plate Surface in Impingement Zone for 30 L/min Long Jets Simulations (a) Turbulent RKE (b) Turbulent SST .................................168 Figure 6.11 Radial Velocity Profiles along Plate Surface in Impingement Zone for 45 L/min Long Jets Simulations (a) Turbulent RKE (b) Turbulent SST .................................168 Figure 6.12 Flow Velocity Parallel the Plate Surface for 15 L/min Jet Simulations ..........170 Figure 6.13 Velocity Parallel the Plate Surface for 45 L/min Jet Simulations ...................170 Figure 6.14 Pressure Distribution along the Plate Surface for 15, 30, and 45 L/min Jets ..172 Figure 6.15 Circular Jump Configurations at Jump Site in 15 L/min Numerical Simulations Shown by VOF Contours (a) No Roller (Turbulent SST) (b) One Roller (Turbulent RKE) .................................................................................................................174 Figure 6.16 Circular Jump Configurations during RKE 15 L/min Numerical Simulation .175 Figure 6.17 Computational Domain and Boundary Conditions of Moving Simulations (a and b are Given at Table 6.8)..............................................................................................177 Figure 6.18 Wetting Fronts for Two Grids (30 L/min, 1.3 m/s)..........................................178 Figure 6.19 VOF Contours at Q = 15 L/min, Vp = 1.3 m/s (a) Impingement Flow over Moving Surface: Red Color Shows Water (b) Wetting Front (HJ) at Symmetry Plane.....180 Figure 6.20 Wetting Front (a) 30 L/min Jets at Various Plate Speeds (b) Different Jet Flow Rates at 1.3 m/s Moving Plate ...................................................................................182 Figure 6.21 Velocity in Y Direction at Impingement Zone on 1.3 m/s Moving Plate (RKE Simulation)..........................................................................................................................184 Figure 6.22 Velocity in Y Direction at Impingement Zone for 30 L/min Jets....................184 Figure 6.23 Moving Impingement Surface (Point O is Impingement Point) .....................185 Figure 6.24 Velocities at 15 L/min Impingement Zone on Fixed and 1.3 m/s Moving Plates ...................................................................................................................................186 xi  Figure 6.25 Pressure at Impingement Zone ........................................................................186 Figure 6.26 Velocity at Y Direction along the Middle of Moving Plate Vp = 1.3 m/s .......188 Figure 6.27 Wetting Front over Moving Plate Vp = 1.3 m/s ...............................................188 Figure 6.28 Velocity at Y Direction of 30 L/min Jet along the Middle of Moving Plate ...190 Figure 6.29 Wetting Fronts of 30 L/min Jets on Moving Surface at Different Velocities..190  xii  List of Symbols A b B C d dimp dh e h h H f Fr  u / gS  Area of nozzle (m2) Major axis of elliptical impingement region (m) Dimensionless gradient of radial velocity Constants in jump radius relation Nozzle diameter (m) Impingement diameter(m) Jet diameter at distance h (m) Shift of stagnation point (m) Heat transfer coefficient (W/m2K) Distance from nozzle outlet (m) Nozzle-to-plate distance (m) Volume fraction of the fluid Froude number (h is flow layer thickness)  g k lo Nu = hd/k Pr = / p po  Gravity acceleration (m/s2) Turbulent kinetic energy (m2/s2) Onset of splattering (m) Nusselt number Prandtl number Pressure (N/m2) Ambient pressure (N/m2)  pstgn Q Qs Ave Q Q r rt R Rj Rj Re = Vd/ Re = Vimpdimp/ s S t Tw Tsat Tsub V (m/s) Vimp (m/s)  Stagnation pressure (N/m2) Jet flow rate (m3/s or L/min) Splattered flow rate (m3/s or L/min) Average jet flow rate (m3/s or L/min) Variation in jet flow rate (m3/s or L/min) Radial distance from impingement point (m) Radius of onset of turbulent flow (m) Radial distance of wetting front (m) Jump radius Variation in hydraulic jump (m) Jet Reynolds number Impingement Reynolds number jet-to-set space (m) Liquid layer thickness Time (s) Water temperature (C) Saturation temperature (C) Subcooling (C) Exit velocity or axial velocity (m/s) Impingement velocity  xiii  Vh Vp Vp Vy u uo u′ Ui Uf We  V 2 d /  X Y z  Weber Number x-coordinate y-coordinate Distance above the surface in vertical direction(m) Density (kg/m3) Kinematic viscosity (m2/s) Viscosity (N s/m2) eddy viscosity Thermal diffusivity (m2/s) Shear stress (N/ m2) Turbulent shear stress Surface tension (N/m) Splattering ratio Azimuthal angle Obliquity angle of jet Dissipation rate of turbulent kinetic energy (m2/s3) Specific dissipation rate (1/s) Kronecker delta  ρ    t  = k / cp  t        ij    We exp(  Jet velocity at distance h (m/s) Plate velocity (m/s) Variation in plate speed (m/s) Velocity in Y direction (m/s) Velocity in radial direction (m/s) Free-surface velocity (m/s) Velocity fluctuation (m/s) Velocity components (m/s) Frontal velocity (m/s)  0.971 H ) We d  Abbreviation HJ CHJ Int-Z SST RKE STDV  Scaling parameter for splashing  Hydraulic jump Circular Hydraulic jump Interaction zone Shear-stress transport k-ω turbulent model Realizable k- turbulent model Standard deviation  xiv  Acknowledgements First, my sincere and high appreciations go to my supervisor Prof. Mohamed S. Gadala for his academic guidance and his financial and personal support. His careful and thoughtful revisions greatly contributed to the preparation of this thesis. I am thankful to Prof. Ian Frigaard, and other my PhD. committee members, for helpful inputs and valuable discussions. I am also grateful to Prof. Matthias Militzer, the UBC ROT group members, and particularly Gary Lockhart. They provided me with use of the facility, helped with my experimental work, and gave great insight into this project. Thanks also to my friends at the FE-lab for sharing their knowledge and experiences. Special gratitude is given to my mother, my brothers, and my sister. They provided me with constant support and encouragement during my studies. Last but not least, I want to express my deepest appreciation to my wife, Masomeh, and my children, Taha and Sana. This work was not possible without their unlimited patience, co-operation, motivation and love. Finally, I would like to dedicate this research in loving memory of my late father Mohammad Seraj and my late brother Dr. Saeed Seraj.  xv  Chapter 1 Introduction, Literature Review, and Research Scope  1.1 Introduction The production of crude steel increased to above 1200 million metric tonnes in 2009 worldwide and continues to grow in 2010 [1]. Hot rolling is a recognized manufacturing method of flat steel production (e.g., steel strips) that is widely used in the automotive, construction, and manufacturing industries. Therefore, the quality of hot rolled steel strips is of great importance for many industries. However, in recent decades, the industries are under more pressure by escalating demand for a sustainable economy. For example, automakers are pressed to produce more fuel-efficient vehicles by reducing the overall weight by use of novel steels, aluminum, and other metal alloys. Indeed, steel companies have been asked for tailored steels (advanced high strength steel, or AHSS) having desirable mechanical properties such as strength, toughness, formability, and metallurgical properties such as microstructure and hardness. In oil and gas pipelines, higher pressure is accessible with larger diameter pipes using hot rolled AHSS steel, which furthermore decreases the required number of pump stations and operation costs. Nevertheless, the development of hot rolled AHSS steels requires more complex cooling systems such as accelerated cooling to reduce the final temperature. A typical hot rolling process starts with a continuous casting facility and is followed by a Run-out Table (ROT) and down coiler at the end. The hot strip passes through a rolling section to be sized and finished and then it is immediately moved along the ROT section to be cooled before coiling. Typically, the finishing hot rolling temperature is 800ºC to 950ºC and the coiling temperature is between 500ºC and 750ºC according to strip thickness and steel grade [2]. The coiling temperature and the cooling rate at the ROT have crucial roles in managing the steel  1  properties. Therefore, the precise control of strip temperature and cooling path is exercised by efficient cooling methods on the ROT to achieve the superior properties of AHSS steel. In ROT cooling, water impinging jets have been widely employed and next are air convection and radiation. Depending on the finishing temperature, strip speed and coiling temperature, the strip is cooled by the arrays of top and bottom cooling headers. Each header includes a set of free-surface circular jets in 1–2 jet lines or 1–2 large planar jets. Water is supplied to the headers from water banks at room temperature. The cooling methods on ROT are mainly classified as laminar cooling using circular jets, curtain cooling using planar jets, and spray cooling (Figure 1.1) [3]. In laminar cooling, a water bar exits a round tube nozzle and creates a circular area of a locally high cooling rate over a strip plate due to the increase of contact time of water with the hot strip; the jet penetrates the vapour layer over the hot surface by impact pressure. However, uneven heat transfer results over the width of the plate. Therefore, the nozzles should be closed as much as possible in a jet-line. In the water curtain method, water is issued from a large slot nozzle as a fluid sheet and a line of cooling is obtained along the entire width and this improves the uniformity of cooling [4]. Spray cooling covers a relatively large area but has low heat removal ability and requires high maintenance costs. Generally, at the runout table, the upper surface of a strip is cooled by the impingement of water bars and sheets. The lower surface is cooled by water sprays or jets. The typical geometry and operating parameters are shown in Table 1.1  Figure 1.1 Run-out Table Cooling Systems [3]  2  Table 1.1 Typical Geometry and Operating Parameters on ROT [4-5] Total length of accelerated Leading part of strip cooled 92 9 cooling zone (m) by quiescent air (m) Trailing part of strip in air Distance of top nozzle and 39 2.6 cooling zone (m) strip (m) Distance of bottom nozzle 0.05 Strip thickness (mm) 4-8 and strip (m) Exit temperature from Strip speed (m/s) 9.4 916 finishing mill (C) ......... ..... Coiling temperature (C) 556 Depending on the surface temperature, different boiling regimes may occur over the surface of the hot plate and thus the knowledge of boiling jet impingement is necessary to characterize the heat transfer on the ROT. Actually, an accurate prediction of the flow field and associated heat transfer in the boiling jet impingement poses significant problems. Boiling would create additional contributions to the turbulence within the fluid and it leads to a more complicated analysis that includes two-phase flow and boiling-induced mixing effects [6]. Moreover, operational conditions such as mill speed changes, gauge variation, jet-lines interaction, etc., produce non-symmetric cooling conditions spatially and directionally within the plate which lead to nonuniformity in mechanical properties and plate shape. Although various techniques to overcome these problems have been employed, they are essentially empirical and the results are sensitive to small variations in the geometry and the operational conditions (i.e., changing from mill to mill). Thus, ROT cooling is a highly complicated transient heat transfer process. The full scale modelling is a difficult task and significantly relies on the experimental data of boiling heat transfer. Modelling a ROT is based on developing expressions for local heat flux as function of operational parameters such as water temperature, strip velocity, surface temperature, water jet arrangement in cooling systems, and nozzle parameters (e.g., flow rate and height). Despite many efforts, there is still a lack of understanding and also a lack of a proper simulation of the process. Most available studies of boiling jet impingement in the literature are experiments of small scale laboratories where single water jet impinges on stationary test plates. Within these studies, the effect of such parameters as boiling regimes, jet velocity and diameter, nozzle-toplate distance, water temperature, plate initial temperature, etc., have been investigated. Reviews of boiling heat transfer studies using liquid jet impingement are available [7, 8]. The existing 3  works are restricted, in general, to specific boiling regimes or regions over the target surface and they also cover the limited range of operational parameters and experimental conditions. However, these provide insight to the factors governing the process for steel industries which cannot be easily observed and also correlating the relevant parameters. Indeed, these results do not reflect the true nature of mill operations and the applicability of these boiling heat transfer correlations to steel production is in doubt but the lack of literature forces one to incorporate these relationships into the available ROT models. Therefore, industries still rely greatly on operating experiences. This is not desirable when strict thermal control is very important for the uniformity of the product properties [9]. The experiment on moving test specimens by an array of water jets is very valuable in this regard but is scarcely found in the literature due to the complexity and technical problems when running the tests. Indeed, the flow field structure and boiling heat transfer mechanisms during jet impinging on high temperature moving surfaces are not well understood at present but are of great importance to the industries. The above discussion indicates the requirement for extensive systematic research on moving impingement surfaces for extending the understanding of jet impingement cooling in industrial conditions. The knowledge of both flow hydrodynamics and heat transfer of water jet impingement constitutes building blocks in such studies. At the University of British Columbia (UBC), a unique industrial pilot scale ROT facility has been built and developed for research on cooling processes as close as possible to ROT conditions by assessing the effect of relevant parameters on the cooling of hot moving plates in industrial conditions. Through more than a decade of work, the results have been implemented into an experimental database for the modelling of heat transfer on a real ROT in order to predict the refined microstructure; this guides the industries toward better control of the properties of the final product [e.g., 10-13]. The majority of studies on ROT have been focused on the heat transfer aspect of the problem and little attention has been paid to the hydrodynamics of long water jets with typical industrial geometric and fluid parameters impinging on moving plates. However, the flow structure of an impingement flow influences the heat transfer analysis. The local heat transfer coefficient between the spreading fluid and the substrate is found to be connected with the flow regime and flow field parameters. For example in the stagnation zone, the distribution of stagnation pressures along the wall influences the saturation temperature of cooling water and thus the heat transfer capability [14]. Moreover, the heat transfer coefficient is related to the flow  4  velocity gradient in the impingement zone [15]. Therefore, the current study is solely focused on the flow aspect of water jet cooling utilized at the ROT. The purpose of this research is to acquire the fundamental and overall understanding on the hydrodynamics of ROT processes by conducting the experiments at the UBC ROT facility on circular water jets impinging on an unheated plate but consistent with the conditions of heat transfer experiments and also by running numerical simulations of this industrial case.  1.2 Literature Review Jet impingement is a recognized cooling method in different industries ranging from glass manufacturing, electronic package cooling, paper drying, turbine blade cooling, metal making processes, etc. Liquid jet impingement has a remarkable capability to dissipate large amounts of heat and is of special interest in metal manufacturing [14]. Cooling jet impingement has been investigated by many researchers and has a comprehensive literature particularly on single jet impinging on stationary surfaces and extensive reviews are available (e.g., for liquid jets) [1617]. The impinging jets are classified mostly in terms of nozzle types (round or slot), nozzle geometry (orifice, tube, etc.), jet fluid (gas or liquid) and whether discharging into the same fluid (submerge or free-surface). The circular water jet on a ROT is a free-surface jet when impinging normally on dry strip surface from the first set of jet arrays but a water jet from following arrays impinging into the pool of water accumulating over the top surface is called a plunging jet. However, these two jets are commonly treated as free-surface jets with respect to the submerged type. This literature review concentrates on the hydrodynamics and nonboiling heat transfer of unsubmerged circular liquid jets unless otherwise mentioned since this type of jet is utilized in this study.  1.2.1 Hydrodynamics of a Single Impinging Jet The water jet after issuing from the nozzle outlet is accelerated and contracted due to gravity if the nozzle is not close to the target plate as in typical industrial setups. At the impingement surface, the jet velocity increases from the exit velocity V to the impingement velocity Vimp and the jet diameter decreases from the nozzle diameter d to the impingement diameter dimp. However, the increase of jet velocity is halted near the plate and the approaching jet slows down  5  and eventually becomes stagnant at the plate surface. The pressure along the surface beneath the jet is elevated accordingly. At the impingement region (Figure 1.2), the flow streamlines deflect and adjust to the plate surface. The impingement flow develops radially outward along the surface while the velocity recovers up to Vimp which may be noticeably more than the velocity V. Further downstream, the flow fully develops (i.e. u = u(r)) at the parallel (wall) region while thinning and losing velocity (Figure 1.2). The boundary layer is thin at the impingement region due to the impact of the incoming jet but gradually the viscous and thermal boundary layers penetrate into the radial mainstream flow and decelerate the spreading of thin liquid layer at the wall zone. The parallel flow in wall zone is similar to wall jet that issues from a nozzle parallel to the plate surface. Depending on the flow regime, the transition to the turbulent flow may take place where marked by the increase of liquid film thickness. The flow propagation may terminate with hydraulic jump as a sudden rise of the film thickness upon upstream and downstream conditions. The rapid deceleration of the fluid and the consequent degradation in heat transfer are associated with the hydraulic jump. Jet destabilization, breakup, and splattering of free-surface long liquid jet may have also occurred before impingement if the nozzle separation (H) is large. The nozzle builds the jet velocity profile and turbulence characteristics, as well as its contraction and then inclination to splattering or breakup. Each of these features can have a significant impact on the heat transfer characteristics of the jet, particularly in the impingement zone, and they are important in cooling jet impingement [17]. 1.2.1.1 Impingement Zone While the stagnation region is defined beneath the jet with the same size and the shape of the jet, the impingement zone extends up to a region where the effect of impingement disappears and the pre-impinging velocity and pressure are retained in the radial flow. Generally, the flow field can be divided into an inviscid outer region and an inner viscous boundary layer wall bounded region. The two regions are coupled through asymptotic way [19] at the jet impinging problem and the stagnation flow solution is found to be dependent primarily on the gradient of radial velocity near the stagnation point at r = 0 (point o at Figure 1.2). This plays an important role in heat transfer at this region as well [16]. The dimensionless gradient of radial velocity u at the stagnation point (or impingement point) is defined as  6  Figure 1.2 Circular Free-Surface Jet Impingement  B2  d (u / V ) d (r / d )  1.1 r0  and the velocity in the stagnation zone along the wall (z/d  0) is determined as [16]  u r  B( ) V d  r/d  0.5  1.2  The wall pressure p(r) near the stagnation point at inviscid flow just above the boundary layer (z/d  0) is given from Bernoulli equation p ( r )  po     V 2  2 imp   u (r ) 2    1.3  where po is the ambient pressure. Measurements of the wall pressure distribution p(r) have often been used to determine the velocity in the inviscid free stream u(r). Pressure increases as the approaching jet decelerates before impingement and is maximized at the stagnation point (stagnation pressure). Afterward, the wall pressure reduces radially to the pre-impinging pressure as the velocity increases along the plate. Therefore, the impingement zone is also called the gradient-based pressure region. The linear variation of velocity has been demonstrated experimentally; Stevens and Webb [20], for example, found a linear variation of velocity at different distances above the plate surface (z) for fully developed nozzles and obtained B ≈ 1.83 (in Eqn. 1.2) for a uniform jet 7  velocity. Different nozzle-types produced different magnitudes for the velocity gradient B and that resulted in different heat transfer characteristics in the stagnation zone [21] but the jet velocity profile is a major factor [17]. Liu and Lienhard’s analytical work [14] is notable since it considered the effect of surface tension as well. They found that the radial velocity approached Vimp at r ≈ d and changes nearly linearly when the effect of surface tension is negligible, as in many industrial applications. Figure 1.3 depicts the velocity and pressure variation in the impingement region. The maximum radial velocity gradient was found at the plate surface in the free stream above the boundary layer (z  0) which disappeared for z/d = 0.5. The value for B was then computed as 1.831 for a uniform jet. The axial jet velocity along the z-axis starts dropping at z/d = 0.5 and stagnating at the plate surface; this is also demonstrated experimentally [20] where the velocity u was found to be a function of f(r, z). Ochi et al [22] defined the impingement zone where velocity and pressure is proportional to the radius from the stagnation point, consistent with the above definitions. By using a circular water jet where d = 10 mm, the nozzle-to-plate distance of 25 mm (H/d = 2.5), and the jet velocity of 3 m/s, they measured the wall pressure and calculated the velocity along the plate surface and presented pressure and linear variations for velocity,  p  po r p(r )   1  0.61  pstgn  po d   2  1.4  Figure 1.3 Pressure and Velocity Variation along the Plate Surface (Modified from [21]) 8  u 1 r    V 1.28  d   1.5  where pstgn is the stagnation pressure which can be found from Bernoulli’s equation,  pstgn  po   1 2 Vimp 2  1.6  Ochi determined B as 1.5625. The thin boundary layer and high stagnation pressure provide a high heat transfer coefficient at the impingement zone and so the lowest surface temperature is maintained there. Therefore, the heat transfer at this region is important in cooling jet impingement. Theoretical and experimental studies [e.g., 23–25] show that the heat transfer is dependent on the gradient of mean radial velocity at the impingement zone. For example, the average Nusselt number Nu for a uniform surface temperature or heat flux wall is theoretically found as [16]  Nu   hd  f (Pr,..) Re1 / 2 B k  1.7  where h is heat transfer coefficient, k is thermal conductivity, Pr is the Prandtl number = / ( is kinematic viscosity and  is thermal diffusivity) and Re is the Reynolds number = Vd/. Constant heat transfer coefficient resulted for the isothermal surface. Different surface thermal conditions have also been investigated [26]. The aforementioned studies were mostly conducted with nozzles close to plates that produce laminar jets. For a long jet where the distance separation H/d is more than few nozzle diameters, the magnitude of B does not change significantly because viscosity tends to eliminate radial gradients in the bulk jet and a uniform jet velocity is obtained [27]. Stevens and Webb [13] found that the bulk velocity typically reached uniform within 5d downstream of the nozzle. Therefore, the heat transfer remains dependent on Re and B for a turbulent long jet. However, the turbulent intensity (e.g., u′/ V where u′ is the velocity fluctuation) is also important. Actually, the enhanced heat transfer for a high Re liquid jet is mainly of turbulence of free flow which results in the stronger dependence of Nu and to Re [28, 29]. The size of impingement zone influences the prediction of total heat removal from a hot surface by jet impingement due to the high transfer rate of this region as indicated above. In ROT modelling, the plate surface is divided into wetted and nonwetted regions and the impingement  9  and parallel zones are located at the wetted region. Different boiling regimes are assigned to each region mainly nucleate boiling of high heat flux to the impingement zone or single-phase convection [9]. Therefore, the demarcation of the impingement zone has a larger impact on the prediction of the total boiling heat transfer rate computed by an ROT model. Ochi sized this region as r/d1.28. However, Steven et al [30] measured it roughly as r / d  0.75 by experiments on a turbulent jet while Liu et al [23] estimated it as r / d  0.787 by heat transfer data for a laminar jet. Although it is larger than other predictions, the proposed size of impingement zone by Ochi has been implemented in the heat transfer analysis of the ROT because of using his correlations for boiling heat flux [4-5, 31-33]. 1.2.1.2 Parallel Zone Radial streamwise velocity is parallel to the surface at the parallel (wall) flow zone as the effect  of impingement vanishes. The flow velocity upon exiting the impingement region is accelerated to the jet impingement velocity but it is retarded and thinned at a larger radius downstream because of the growing viscous boundary layer into the fluid flow. The boundary layer may ultimately reach the free surface of the thin liquid sheet and subsequently the flow transforms into a viscous film with an increased bulk temperature. If the jet is laminar then the turbulence is developed downstream of impingement region and the thin film may become fully turbulent. However for a planar jet, the flow deceleration and thinning in the wall region does not occur and the thin boundary layer more likely remains beneath the outer inviscid flow that has constant thickness. Therefore, the heat transfer analysis of a circular jet is more complicated than a planar jet owing to radially different heat transfer mechanisms. Moreover, any turbulence in the incoming jet will disturb the free surface of the thin liquid layer and agitate splashing and a rapid transition to turbulent film flow. Principally, to model the free impingement liquid layer due to an axisymmetric jet, the parallel zone is divided into sub-regions with respect to viscous and thermal boundary layers extending into the liquid layer. Each region is demarcated over the surface and the liquid layer thickness is determined according to laminar and turbulence regimes [e.g., 34]. Also, the Nu number at different thermal surface conditions for every region is obtained [35, 36]. These subregions are also experimentally studied and satisfactory results were obtained [e.g. 37]. Heating up the liquid layer will reduce the heat transfer from hot substrate at the wall zone. In fact, the viscous effect of the surface and the reducing temperature difference between  10  thin liquid film and the surface decrease the cooling performance. Therefore, surface temperature is nonuniform along the impingement and parallel zones over the surface due to single jet impingement.  1.2.2 Hydraulic Jump (HJ) After the impingement flow spreads out radially into a thin liquid sheet, the layer thickness may abruptly increase forming a jump (HJ). The HJ characterizes a region of decreasing the average flow velocity and elevating the flow turbulence where the free-surface and boundary layer are distorted and then separation and backflow (negative velocity) results [33, 39]. The high local turbulence at HJ can be utilized for mixing fluids and oxygenating water but energy dissipation at the jump and slow motion liquid layer after the jump reduces the heat transfer rate downstream. Indeed, the HJ place is marked with a sharp reduction in flow velocity and in a heat transfer coefficient or Nu number at the jump and also decreasing heat removal after the jump [40]. Therefore, the control of HJ is important in thermal design. The circular hydraulic jump (CHJ) is obtained from the axisymmetric jet impingement, which is different from the planar HJ at the open channel. A one-dimensional moment balance successfully describes the planar HJ but fails for the CHJ. The CHJ is governed by jet parameters such as the Re and We numbers ( We  V 2 d /  where  is surface tension) and upstream conditions (e.g., flow velocity profile and flow regime) and downstream conditions such as layer thickness after the jump and Froude number  Fr  u / gS where S is liquid layer depth and also fluid properties such as viscosity [38]. The CHJ is usually unstable and is accompanied by surface waves. Surface tension influences the jump configuration and instability but has a negligible effect on locating the jump [38, 41-42]. The CHJ location can be controlled by drainage conditions (e.g., free plate border or barrier). For example, different jump sizes and shapes are managed by adjusting the liquid thickness after the jump using a lip around the edge (outer rim) of the plate [38, 43]. Flow boiling is vulnerable to the HJ because boiling acts like a flow obstruction and the steel strip edges should be free to not impose more restriction downstream. Various aspects of the CHJ have been investigated. However, the flow structure at the vicinity of the CHJ is complex and is still a subject for research. One of the early and more important theoretical works was done by Watson [44]. He divided the impingement flow into  11  sub-regions and used a momentum balance to delineate the regions before and after the jump by assuming a uniform flow velocity and no width for the jump and disregarded the gravitational pressure gradient and skin friction at the jump. The radius of the CHJ was found based on the jet Re number at the impingement point and layer thickness right after the jump. Subsequently, other researchers tried to modify his work and study the flow structure at the jump in detail using viscous flow over the boundary layer [e.g. 45]. Bohr et al [46] matched theoretically two regions of the supercritical and subcritical regions through a shock (jump), which attributed to CHJ for radial flow with the free surface. Godwin [47] assumed the jump is where the viscous boundary layer reaches the free surface. The CHJ has been also extensively studied experimentally and numerically [for instance, see refs. 48–51]. The quantitative estimate of the CHJ was also carried out through consideration of relevant parameters such as Q (jet flow rate m3/s),  (kinematic viscosity m2/s), H (m), d (m), g (gravity m/s2),  (surface tension N/m), etc. Using dimensional analysis, the radius of the CHJ Rj for viscous flow may be scaled:  R j  Q  d  H  g   ....  1.8  and the relationship between the parameters of interest can be obtained by determining the exponents in Equation 1.9 using the  theorem [52]. The jet flow rate Q and viscosity  are demonstrated to play an important role is sizing the CHJ [44, 47, and 53]. Some correlations, for example, for the radius of the CHJ are presented in Table 1.2 from literature.  Table 1.2 Scaling Relations for CHJ research  Rj (m)   Bohr et al [46]  theory  Q 5 / 8 3 / 8 g 1 / 8  Brechet et al [53]  theory  Q 2 / 3 1 / 3 H 1 / 6  Brechet et al [53]  experiment  Q 0.703 0.295  theory  Q1 / 3 1 / 3  Godwin [47]  12  1.2.3 Jet Instability and Splattering When a liquid jet is discharged from a nozzle far from the target plate (H/d >> 1), the jet turbulence and air drag produce surface roughness, develop disturbances along the jet surface, and cause jet instability and splattering [54]. Jet instability or breakup disrupts the liquid jet before impingement and splattering reduces the water flow and the residence time of the water sheet over the plate after impingement. The jet surface disturbances transfer into the impingement flow and if the disturbances’ amplitude is large enough, then splashing from surface of thin radial liquid layer occurs. In general, the droplets migrated from free surface do not go back to the liquid layer but stay airborne [55]. Therefore for thermal efficiency, the jet instability and splattering for long liquid jet should be avoided. When the nozzle height (H) is small (a few nozzle diameters or less) i.e. a short jet, breakup and splattering is not an issue. Generally, the heat transfer at the impingement zone is not influenced by splattering independently because it is encountered downstream at parallel zone and then abovementioned results for impingement zone hydrodynamics and heat transfer are valid. The splattering depends on the nozzle diameter and flow rate (or jet Reynolds and Weber numbers) and excited by jet disturbances; surface tension is an important parameter in splattering [54]. The jet instability is linked to the specific design for nozzle. A sharp-edge orifice with a high contraction is suitable to produce a uniform velocity profile or an unsplattered laminar jet. A fully developed turbulent jet with a relatively flat velocity profile could be obtained by a tube nozzle with no contraction which is susceptible to splattering [18]. Errico’s [55] observations show that the splattering occurs at narrow band downstream of the impingement zone and no more splattering takes place beyond there. The departure radius was estimated as r/d  4.5. He experimentally showed that the jet disturbances govern the splattering. Lienhard et al. [54, 56–57] measured the speed and size of droplets by phase-doppler and proposed a model for the splattering of a long fully turbulent liquid jet issued from the pipe type of nozzles. They measured splattering ratio , defined by    Qs Q  1.9  where Q is flow rate of incoming jet and Qs is the splattered flow rate. The amplitude of jet surface disturbances is related to the rate of splattering. A scaling parameter χ is defined  13    We exp(  0.971 H ) We d  1.10  which relates the disturbances amplitude to fraction of splattering [56]    0.258  7.85  105   2.51  109  2  1.11  as a larger value for ξ should be obtained for larger disturbance amplitudes. Equation 1.12 is valid over the range of 1000 < We < 5,000, H/d < 50 and 4400 < χ < 10,000. The model fails for larger H/d values and is not relevant for the low Weber number jets. Bhunia et al.’s [56] observations demonstrated that the pre-impingement splattering is a function of jet length (H/d) and surface tension (Wej) but not of the Re number. The onset of splattering (lo) where at least 5% of the incoming jet is splattered before hitting the plate was correlated as  l0 130  d 1  5  10 7We2  1.12  In ROT, the nozzles are far from the steel strip, typically H ≥ 1200 mm, and the water jets are as long jets. Large circular pipe type nozzles are also employed (d  20 mm). Although the jet velocity profile is most likely flattened and approaches uniformity before impingement, splattering and jet breakup are two issues that should be noted. Observations on mill production (ROT) show jet splashing at pre-impingement [33]. Jet interaction may happen among closelyspaced nozzles in a jet-line  1.2.4 Multiple Jets Single jet cooling efficiently dissipates the heat at the stagnation point and the neighbourhood where the local temperature decreases greatly but the temperature increases downstream in the parallel zone and nonuniform heat transfer rate is imprinted spatially over the surface. The local heat transfer coefficient varies like a bell-shape radially which has a peak at stagnation point and decreases rapidly outward. Second maxima may occur if the flow regime changes to turbulent in the parallel (wall) region [23]. Therefore, if the heated surface is large, as in many industrial applications, then multiple jets have to be utilized to improve the global cooling over the entire surface by creating multi-stagnation zones although the heat transfer is still not uniform over  14  whole surface. However, a reasonable uniformity of heat transfer and a high average heat transfer coefficient over the surface is attainable by adjusting the flow rate and geometrical aspects for jet array such as jet-to-jet spacing, jet-to-plate separation, jet-lines distances, crossflow, etc. The improved uniformity of surface temperature is particularly desirable in industrial cooling such as ROT to establish proper homogeneity in steel strip properties. The spatial arrangement of nozzles at a jet array (e.g., in-line, staggered, and hexagonal) and geometrical parameters highly influence the flow characteristics and heat transfer of multiple impinging jets. Generally, the important factors are, but not limited to, interjet spacing, nozzle geometry [58–60], nozzle-to-surface distance [61–63], wall jet interaction [64–65], and other factors such as turbulence and entrainment [66–68], drainage [65, 69], and cross flow [70]. The impingement jet flow from the middle jets in a jet array spreads outward interfering with the neighbour jets flow and forming a cross-flow across the heated surface which may prevent the jets from touching the target surface. Moreover, the cross flow is heated up by passing over the heated surface and this warmer flow mixes with the fresh impingement flow of the other jets reducing the temperature difference between the impingement plate and the coolant [67, 69]. Therefore, crossflow deteriorates heat transfer rate especially at the outer jets at the edge of the array and but helps uniformity. A considerable portion of existing literature on multiple jets deals with wall jet interactions due to twin power lift jets in VTOL (vertical takeoff and landing) of aircraft. Multiple jets also have been investigated in other areas. For example, jet arrays are utilized for increasing heat dissipation in electronic packages. Controlling flow-induced vibration in jet arrays is important for reducing acoustic resonance, etc [71]. Following the above studies, the flow in an arrangement of multiple submerged air jets can be characterized, in general, by dividing the domain into these individual regions: 1) lift or free jet flow, 2) jet impingement region, 3) inner wall jet region, 4) outer wall jet region, 5) wall interaction stagnation line, 6) fountain formation region, 7) fountain upwash flow region, and 8) entrainment. The free jets are commonly called parent jets in the literature. The free jet, impingement, and wall jet regions are also seen in single jet impingement. But, fountain formation and upwash fountain regions are characteristic of multi-jet systems. The two regions of fountain formation and upwash fountain are further explained in more detail.  15  1.2.4.1 Fountain Formation Region The wall jet from each jet meets the other wall jet from the adjacent jet and forms stagnation  which produce upward deflections of the wall fluids. The individual wall jets come in contact along a line in collision zone which called interaction stagnation line or dividing line. The interaction stagnation line is briefly termed the stagnation line hereafter. Any change in nozzle positions (e.g., jet-to-jet and jet-to-plate spaces) change significantly the flow pattern and properties of the fountain formation zone [70]. The characteristics of stagnation line are strongly dependant upon the relative momenta of opposing individual wall jets [66, 72]. If the twinimpinging vertical jets have equal strength or momentum (i.e., issue from equal nozzle diameter so that the stagnation line is straight and equidistant from each jet center everywhere (equal jets). Any differences results in unequal jets and the fountain shifts and leans along interjet distance toward the weaker jet. The lower the jets’ momentum ratio, the larger curvature is at the stagnation line [73]. For a pair of two-dimensional colliding wall jets, the location of the stagnation region is determined from the place of equal maximum total pressure in each wall jet layer. For a pair of circular jets impinging vertically with equal momentum it is given as [72]  r2  V2   d 2    .  r1  V1   d1   1.13  where indices 1 and 2 denote the two jets, r is the radial distance of stagnation line from impingement point, V is the jet velocity, and d is the jet diameter. 1.2.4.2 Upwash Fountain Flow Region The opposing wall jets are separated along the stagnation line but finally merge fully together  while accelerating spatially into surroundings which generate an asymmetric, in general, upwash fountain. The strength of the parent jets strongly governs the direction and strength of the fountain. Two equal jets generate a vertical and centered fountain but if they are unequal jets, the fountain will be inclined toward the weaker jet. The larger the jet momentum ratio, the bigger the inclination angle will be [66]. The flow field of a fan-shaped upwash fountain is rather complex. Actually, distinct features in this region are presented with respect to other free flows. It involves the turbulent mixing rate much higher than other free turbulent flows. Although remarkable threedimensional, it is generally symmetric in mean characteristics [72, 74]. But, the instantaneous  16  velocity field is highly asymmetric with large eddies and the location of stagnation region between the two jets is displacing randomly. The upwash fountain is highly unsteady and very sensitive to small imbalances between the jets and may easily become unstable [73]. 1.2.4.3 Multi Liquid Jets Wall jet interactions induced by twin air jets have been the subject of many research studies in  relation to the VTOL of an aircraft and cooling of electronic packages [for instant, 58, 69, 7273]. Despite a noticeable desire in industries to study the flow field and heat transfer of liquid jet interactions, little attention has been paid to multiple wall liquid jets due to free surface water jets and the associated upwash fountain comparison to air jets [Among the few available, see: 61–63, 74]. The jet-to-jet interaction is not an issue for multi-liquid jet systems if the nozzle-tonozzle is not very small. Air entrainment and suckdown are also not important in opposition to air jets. Pan and Webb [61] examined the effect of jet-to-set space (s/d) for two configurations of free surface jet arrays (staggered, in-line) in the range of 2  s/d  8. The stagnation heat transfer coefficient at the central jet was determined to be independent of s/d and array arrangement. Moreover, different interjet flow interactions induced by jet array configurations were found to be unimportant for local heat transfer beneath the central jet. In addition to the stagnation point, a significant increase in the heat transfer rate occurred midway along the interjet distance that is attributed to jets interaction. The position of this secondary maximum depends on the flow from adjacent jets and the jet-to-plate spacing (H/d) but usually is at an equal distance from the two jets (see also [59] for air jets). Womac et al. [74] also found negligible effect of H/d on heat transfer for two arrays of 22 and 3  3 circular jets for range of 5  H/d  10. But nozzle space s/d is influential; smaller the jet space s/d, higher the heat transfer rate is obtained. Generally, the effect of nozzle configuration (nozzle geometry, H/d, s/d, etc.) on flow and heat transfer characteristics is more pronounced at smaller H/d. A fully flooded (submerged) flow is obtained when the nozzle is close to the plate. For example, Pan et al. [61] found that the flow around the central jet was changed from confined and submerged to a free surface jet flow as the jet-to-plate distance H/d increased from 2 to 5. Changing the nozzle-to-nozzle spacings (s/d) in one jet array also affects the flow over impingement surface. Slayzak et al. conducted experiments on two planar water jets [62] and two jet lines of attached circular water jets together [63]. They found enhanced heat transfer at the fountain place  17  between the two planar jets or two jet-lines. The elevation of the heat transfer coefficient due to jet-line interactions is comparable with the counterpart at the impingement region. The location of the interaction zone shifts from the median toward the weaker jet if the jet velocities are not equal between the two jets. Ishigai et al. [75] investigated the hydraulic jump (HJ) and the interaction zone due to laminar round water jets by measuring the liquid layer thickness. These two domains are similar because basically they are both the consequence of two radial flows interfering. A thin liquid film interferes with a thick layer at the jump and the thin wall film interacts with the other wall film at the interaction zone. Various types of HJs ranging from stable and smooth to unstable and air entrainment were obtained by changing the Fr number which is defined based on the film thickness. Interestingly, the increase and decrease in heat transfer after the HJ was obtained. The enhanced heat removal is attributed to the HJ occurrence before the transition of flow to turbulent. However, the heat transfer coefficient decreased at a large radius and ultimately the heat transfer is less than the jet flow downstream of the jump. Different types of interactions between the two equal water jets are also classified in terms of the Fr number. The different heat transfer characteristics of the interaction zone are also found in accordance with inference film classification according to the Fr number but the Re Number based on the radius from the center of the jet is also important.  1.2.5 Moving Surface The flow hydrodynamics and attributed heat transfer of a jet impinging on a moving target surface has been the subject of relatively few research studies compared to stationary surfaces. Chen et al [76] conducted experiments on stationary and moving surfaces using heated and unheated conditions by a circular water jet. The moving cold impingement surface dealt with the dividing impingement flow differently at two sides of the impingement point. Generally, the liquid film spreads over the surface under the balance of surface tension, viscosity, gravity and inertia forces. The flow development is facilitated in the motion direction by plate movement but is restricted in the opposite side where the flow is entrained. Therefore, unsymmetrical wetted area is obtained over the moving plate respect to circular wetting area around impingement point over fixed plate. The size of wetted zone is according to the jet Reynolds number. The heated plate was tested at two surface temperatures of 88ºC and 240ºC. Enhanced heat transfer results after the jet in motion direction due to stretched wetting area over the surface; it then resulted in 18  an unsymmetrical cooling zone. The maximum heat transfer coefficients are comparable at stationary and moving cases because the heat transfer mechanism is the same at stagnation point and the plate velocity was not high (0.5 m/s) compared to the jet velocity (2.3 m/s). The maximum heat flux was at front of cooling zone when the plate comes first in contact with coolant. However, the overall heat transfer efficiency improved noticeably at higher surface temperature due to boiling. Other experimental work on moving surfaces are available [77–78] . Zumbrunnen et al. [79-81] experimentally and analytically studied the cooling of an unsubmerged planar liquid jet and found a strong effect of surface motion on flow and heat transfer when the surface velocity exceeded the jet velocity. If the plate motion is about half the jet velocity then the high heat transfer coefficient does not shift from beneath the nozzle. For a parallel mainstream velocity and plate speed, the flow near the moving surface has a higher velocity than the unaffected bulk of fluid far from the surface but on other side of the impingement line, the flow at the affected part near the moving surface has an opposite velocity to the mainstream flow. At the jet centerline the flow has zero velocity except near the wall that is moving with the plate. Therefore, unsymmetrical flow velocity profiles are induced at impingement flow by a moving surface and then different influences on heat transfer due to plate motion take place at two sides of the impingement line. Surface temperature typically decreases in the direction of motion. The faster the plate movement, the higher the difference in velocities is over the moving surface. In case of a boiling film (i.e., a stable vapour layer over the surface), the importance of effective heat transfer mechanisms in and opposite direction is dependant on plate velocity besides water and plate temperature. Radiation at the vapour layer can be ignored at higher plate speeds parallel to the flow except for very hot plates. However, it is important in the case of opposite plates and flow velocities and even for slow moving plates. Therefore, the correlations of film boiling on a fixed plate do not provide an accurate estimation of heat flux on a high velocity moving plate. The thermal condition of the plate is influential on the evaluation of plate motion effect on heat transfer as well. Multiple water jets cooling a hot moving plate have been recently investigated at the ROT UBC facility [13, 82–84]. The results from experiments on inline array jets show that the secondary high heat flux occurs midway between adjacent jets when the spacing between jets decreases and it disappears at a larger jet space. However, the effect of nozzle space(s) is found to be insignificant on the peak of heat transfer coefficient in the impingement zone. Actually, the  19  maximum heat transfer is not coincident with the impingement point on the moving surface [83]. The experiments with two jet-line (inline and stagger) arrays demonstrate the effect of smaller inter-line distances on improving the heat transfer uniformity. However, the cooling efficiency was found to be unaffected by array configurations for same plate speed, jet line spacing and flow rate. Nozzle configuration has a strong effect on the surface temperature uniformity [84]. As a result, the spacing of circular nozzles at in-line jets should be adjusted accordingly to cover a larger portion of the strip width by impingement zones and almost uniform temperature is obtained. Generally, the effect of plate motion is not confined to the region close the plate surface and it penetrates into the bulk of a thin liquid largely in addition of the vapour layer in case of boiling. When the plate speed surpasses the jet velocity (as in many industrial applications) then it is involved strongly in boundary layer development in the vapour and liquid layers above the hot surface, especially away from the jet [79]. Indeed, a high speed moving plate could reverse the velocity of the bulk flow even at the impingement zone depending on the ratio of plate velocity to jet velocity. Therefore, the plate motion has an additional effect on the distribution of the heat transfer coefficient over the entire surface in cooling jet impingement with different impacts on the regions parallel and opposite to surface motion direction. In analytical investigations, generally, the plate speed was lower than the mainstream flow. The flow was parallel to the plate motion (considering only wall zone without effect of impingement), surface temperature was constant, and laminar flow was considered. These efforts also reveal the crucial effect of the velocity ratio of the plate to jet on the Nu number and the friction coefficient [85] but beneficial to cooling planar jet impingement partially. In axisymmetric free-surface jet impingement, the surface motion involves the propagation of radial flow in all directions upstream and downstream, causing more complication. The expanding radial liquid sheet is not symmetric along the plate at two sides of the impingement point. This makes the study of moving plate under circular jets harder than for planar jets. The spreading of impingement flow in the opposite direction of the motion is restricted over the surface and the front of liquid film is thickened. The moving surface is delineated into wetting and non-wetting regions. This thick front (wetting front) is similar to the hydraulic jump as a sudden thickness increase of the impingement film where connected two regions. It is common to treat the wetting front similar to the HJ. This HJ or wetting front is not  20  circular but its position is important in cooling jet impingement. The peak of heat flux occurs at the wetting front [86]. According to the wetted and non-wetted regions, different boiling regimes are demarcated over the hot surface which each has its own heat transfer mechanism. Therefore, any study on the wetting zone on the moving surface due to a round impingement jet is valuable to industry. The literature on circular liquid jet impingement on moving surface is very limited. Recently, Gradeck et al. [87] experimentally and numerically studied the HJ (wetting front) due to round water jet on a plastic strip stretched between two rollers as the moving surface. Limited results were reported. The k-e simulations were performed at three velocity ratios and the wetting fronts found close to the experimental data. His work is discussed more in chapter 4. More recently, Kate et al. theoretically and experimentally [88] investigated a noncircular hydraulic jump from an oblique circular water jet. The jet obliquity distorts the contour of the HJ on a stationary plate and makes it noncircular. The impingement zone is no longer circular but is elliptical and the stagnation point does not coincide with the geometrical center of the jet. The eccentric stagnation point as the source of radial flow is shifted from beneath the jet to ahead of the impingement point over the surface. Therefore, the flow loses radial symmetrical spreading with respect to the impingement point and then the impingement flow is three-dimensionally complicated. Consequently, a noncircular shape is obtained for the HJ. Later, a study [89] notes the similarity of the noncircular HJ due to an oblique laminar water jet and the wetting front of impingement flow over the infinite horizontal continuous moving surface. Using this conjecture, the relationships for major and minor axes of the elliptical impingement zone and the shift of the stagnation point were presented (Figure 1.4). The radius of HJ was obtained based on Bohr et al [46] correlation for CHJ (Table 1.2). These equations for normal impingement are as below [89]  e  d Vp 2 V  d b 2   V 1  p   V   1.14 2  1.15  21     Figure 1. 4 Circular HJ on Stationary Surface due to Normal Impingement (b) Noncircular HJ due to Oblique Impingement (Vp = 0 for Fixed Plate and Vp  0 for Moving Surface) (c) Elliptical Impingement Region for Noncircular HJ     2 d R j  c 8    5/8    1          V 3    2 2    V  Vp   3 / 8 g 1 / 8 2     cos    V   V 2  V p2     1.16  where V (m/s) is jet velocity as it falls on the surface (the nozzle is close to the target plate), Vp (m/s) is velocity of the moving surface, and d (m) is the jet diameter. The minor axis of the impingement region is the jet radius d/2 (Figure 1.4c) and O is the impingement point beneath  22  the nozzle. The magnitude of the constant c in Equation 1.16 depends on velocity profiles. For example, c is 0.73 for a parabolic profile and 0.85 is for a 5th order profile [88]. Kate extended his experimental investigation to twin circular water jets [90] and studied the jet-to-jet interaction and the HJ’s interference over a fixed surface. The interaction of HJ of adjacent water jets on moving impingement surface is yet to be reported. Kate’s work is discussed in detail in chapters 4 and 5 where the experimental data from this study are compared with above equations.  1.2.6 Numerical Simulations Computational modeling is important for optimizing and tuning the properties of final products in industrial processes. Flow details such as velocity and pressure variation and temperature changes can be drawn using steady and unsteady simulations especially at regions where the measurement is difficult and expensive such as blade tip at gas turbine [91-92]. Computational fluid dynamics (CFD) is also the first choice in studying flow and heat transfer of cooling jet impingement. Despite many studies, jet impingement remains an active subject of research due to its complicated fluid dynamics and its industrial importance. Turbulent modeling of jet impingement on a stationary surface is difficult because of strong streamline curvature, flow recirculation, pressure gradient, boundary layer development, etc. In fact, a cooling jet impingement serves as an important test case to validate the turbulent modeling. The majority of publications on the numerical assessment of jet impingement focused on single submerged jet impinging on stationary surface and free surface jets attracted little attention. Flow structure and thermal field of liquid free surface impinging on fixed substrate has been investigated by Fujimoto et al [93-94] and Tong [95]. The numerical results on velocity, pressure in impingement and parallel zones were validated by Stevens and Web [15] and Liu and Lienhard [14, 27]. Impingement plate motion raises the level of complexity by adding a shear region to the above features for jet impingement. Relatively few studies have evaluated the effect of plate motion on jet impingement despite great importance to industries [96]. Also, most of the available publications on moving plates are dealt with slot (planar) nozzles. Huang et al [97] numerically investigated heat transfer beneath a turbulent planar air jet impinging on a moving surface with a crossflow. Increasing or decreasing the Nu number depends on the direction of  23  surface motion at higher plate speeds. Chen et al [98] considered convective heat transfer from moving isothermal and isoflux surfaces due to multiple submerged air jets in laminar regime. More uniformity was obtained but total heat transfer decreased. The results suggested that neglecting plate motion might cause the overestimation of heat transfer. Chattopadhayay et al. [99] preformed the Large-Eddy-Simulation (LES) for heat transfer of slot turbulent jet array for 500 < Re < 3000. A more uniform distribution of the average Nu obtained over the surface but total heat transfer decreased at higher plate velocity similar to Chen’s results. They [100] also employed LES for laminar planar jet impinging on moving surface and came to same result as [99]. LES also examined for simulation of flow field due to turbulent low Re number slot jet impinging of on moving surface of constant temperature [101]. Different turbulent models have been applied for impingement flow including low computational cost models such as k- and k- models, intermediate cost such as LES, or high cost models such as direct numerical simulation (DNS). To assess the details of complex flow such as jet impingement, DNS is certainly a good approach but it is very expensive due to resolving all eddy scales. The total numerical nodes needed for simulation of all scales of turbulent flow in the order of Re 9/4 [101]. Large eddies are resolved exactly in LES method but smaller ones are modeled. LES needs a fine mesh particularly for high Reynolds numbers wallbounded flows to resolve the dominant small-scale structure in the near-wall regions. The high level methods (DNS, LES, etc) are still the subject of research and they need more effort to become as a design and optimization tool [101]. Moreover, the employment of these methods to application problems requires high computational effort and equipment. The studies on low cost models such as k- model demonstrate that the standard turbulence models are not very accurate for cooling jet impingement particularly at stagnation zone [102–103] but their performance improved by appropriate corrections to these models such as wall treatment [104–105]. A recent development of k- turbulence model (Stress transport SST) demonstrates satisfactory prediction of near wall flow of jet impingement [106-108]. In general, varying degree of success was reported for the proposed turbulent models in cooling jet impingement. Indeed, no unique turbulent model is found to predict accurately the flow field and heat transfer of cooling jet impingement over whole surface [96]. It is revealed that the prediction of each turbulent model is largely influenced by gird distribution and numerical schemes used in spatial discretization [109]. Therefore, the improved versions of the k- and then the k- models are widely used for 24  industrial flow due to reasonable accuracy and less requirements for computational budget for predicting the overall features of hydrodynamics and heat transfer of the problem. For example, Gradeck et al [86] utilized a k- turbulent model in numerical simulation of the noncircular HJ over moving surface with reasonable agreement with their experimental data. Cho et al. [103] numerically investigated an ultra high flow rate bank of water jet arrays in a ROT application using k- turbulent model exploring flow depth and patterns. Computational studies on circular jet(s) impinging on moving surface is limited and overweighed by experimental studies.  1.3 Scope and Objective The above review of literature indicates that a comprehensive study on the hydrodynamics of free surface liquid single/multiple jets impinging on stationary and moving surfaces has not been conducted yet for a wide range of jet flow rates, nozzle geometrical aspects and plate speeds in an industrial scale. The scope of this study is to investigate the hydrodynamics of circular liquid free surface jet impingement by conducting experiments at the UBC ROT-Pilot facility and to investigate possible and efficient ways for the numerical simulation of the problem. This research aims at understanding certain overall flow features of long round water jet impingement relevant to industries and finding a systematic approach for the numerical modeling of the problem. These goals are achieved through the following objectives/steps: 1- Studying the single impinging water jet and the spreading wetting front on a fixed plate. 2- Assessing the effect of plate motion on wetting front due to a single impinging water jet. 3- Investigating the interaction of two and three in-line water jets on a stationary plate, particularly in the interference zone and the interaction of hydraulic jumps. 4- Evaluating the plate motion influence on interaction zone and interfering hydraulic jump due to twin or triple in-line circular water jets. 5- Performing transient numerical simulations to examine the flow structure and to map the velocity and pressure profiles of impingement flow due to long impinging jet on fixed and moving surface. This also evaluates the results of experimental and analytical studies on short jets for long turbulent water jets and the effect of plate motion on bulk mainstream flow.  25  Chapter 2 Experiment Facility and Setup  2.1 Apparatus All experiments in this work were conducted on a developed industrial scope run-out table facility at the University of British Columbia. The run-out table apparatus is shown schematically in Figure 2.1. It has the following sections: furnace, acceleration zone, spray zone, and deceleration zone. The main components that were used to carry out the experiments, in general, include: a test bed (carrier), a hydraulic torque motor (to move the test bed by a chain conveyor through the spray section at a prescribed speed), a series of water nozzles above the spray zone, a water pipe system (consisting of pipes, headers, flowmeters, globe valves, hoses, etc., to deliver the water from the upper water storage tank to the nozzles), and test plate. A hydraulic power unit at the end of the deceleration zone drove the torque motor. The tracks provided a bed for the chain conveyor and the carrier. They also suppressed the test plate velocity fluctuations. The experiments on fixed plate were run at spray zone. The furnace was not used and the experiments were conducted under room temperature. Figure 2.2(a) schematically shows a front view of spray section. The main parts are the upper tank, circular nozzles, test plate, lower tank and a pump.  2.1.1 Water Supply System The water supply system consists of the upper and lower tanks, two headers, the top six nozzles in two jet-lines, the bottom nozzle, a centrifugal pump, pipes, fitting, elbows, solenoid valves for directing water toward headers, globe valves, flowmeters, hoses, etc. The system is mounted on a heavy and rigid frame tower.  26     Figure 2. 1 Schematic of Pilot Scale Run-Out Table Apparatus  Figure 2.2 Experimental Setup (a) Spray Zone (b) Nozzle (Dimensions in mm)  27  The upper tank was constructed at the top of the 6.5 m high rigid tower as a water reservoir with internal heaters to control the water temperature and provide sub-cooled water for heat transfer experiments. The maximum capacity of the tank is 1350 liters. The lower tank is an open tank placed on the ground beneath the test plate. It is fed by city water and used for collecting effluent from the experiment. The leveler sets the water level inside the tank to control the pump operation. A piping system connects the two tanks through the main supply line. A centrifugal pump rated to deliver 170 US GPM at 185 FT of head recirculates water to the overhead tank which keeps the water level constant in the tank and hence maintains a uniform flow rate. Water is, then, delivered to the nozzles through pipes and headers at the required flow rates. The flow rate may be up to 90 L/min per nozzle. The pump is checked under steady operation at four different flow rates of 15, 21, 30 and 45 L/min before and while running the experiments and no noticeable changes in discharge rates were detected. The industrial scale headers are two hollow cylinders located before the nozzles. Their purpose is to decrease flow turbulence (Figures 2.2a and 2.3). Three nozzles are attached externally to each header. The current experiments were performed with unheated room temperature city water.  Figure 2.3 Header and Nozzles  28  2.1.2 Flow Control One hand operated globe valve and flow meter are mounted between the header and each nozzle to regulate and measure the flow rate at each nozzle exit separately (Figure 2.3). Flow rates are recorded at certain times during each experiment and are then used to find the time average and standard deviation of the flow rate over the total time of the experiment. The calibration is also checked frequently using a bucket and a stopwatch. The differences were ranging from -1 to 5 percent.  2.1.3 Nozzle Assembly The 19 mm / 0.75 inch inner diameter circular tube nozzles in the shape of a shepherd’s hook, shown schematically in Figure 2-2b and 2-3, were supplied by a steel company. After the flow meter, water passes into a hose attached to the nozzle. The hose is long enough to minimize valve and flow meter effects on the flow. The nozzle is made of a steel tube with a semi-circular curve between the two straight parts (Figure 2.2b). The diameter of the nozzle is measured using vernier gauges (0.1 mm). The total length of the nozzle is bigger than entrance length of the flow inside the tube for all flow rates [52]. Turbulent fully developed flow condition could be achieved at the end of the pipe line in this system using long, large diameter lines. However, the headers and the contracting nozzle influence the level of turbulence before the nozzle exit. Considering the range of the jet Reynolds numbers (Table 2.1), the resultant liquid jet discharging from the nozzle may be fully turbulent at the nozzle exit. However, the impinging water jet surface will be greatly disturbed thereafter and the jet is fully developed before impingement.  2.1.4 Industrial Water Jet The nozzle standoff distance is adjustable from 0.5 to 2 m in the UBC facility but a fixed height of 1.5 m from the test plate was chosen in the performed experiments on moving and stationary plates. The water jet in this study has a ratio H/d ≈ 79 and is considered a long liquid jet. However, the nozzles were lowered to 0.5 m above the test plate at some multi-nozzles test to increase velocity ratio between the moving plate and jet; this is discussed in details in chapter 5.  29  Figure 2.4 Free Jet Surface (a) Disturbed (H = 1.5 m) (b) Smooth (H = 0.5 m) A sharp-edged nozzle orifice is suitable to produce a uniform velocity profile or laminar jet, while fully developed turbulent jet with a relatively flat velocity profile can be attained by a tube nozzle at the end of the supply line. However, long distant between the nozzle outlet and target plate provides enough time for impinging jet to overcome the exit condition and becomes fully developed turbulent [57]. The jet surface is not smooth and is completely disturbed in these experiments (Figure 2.4). The free jet in moving downward is a motion under gravity acceleration. At any time t before impingement, the jet tip distance h from the nozzle outlet may be found analytically from  h  1 2 gt  V  t 2  2.1  The jet discharge velocity V (m/s) and jet diameter d (m) at the nozzle outlet may be related to that at any height h below the nozzle using mass and momentum conservation:  Vh  V 2  2 gh dh  d  2.2  V Vh  2.3  30  where g (m/s) is gravitational acceleration, h (m) is the distance from the nozzle and Vh (m/s) and dh (m) are jet velocity and diameter at distance h, respectively. It should be noted that the circular thinning and acceleration of the water jet induced by gravity are significant here. For a 15 L/min water jet, for example, the impingement velocity Vimp is 6 times greater than at the nozzle exit, and the jet diameter d is decreased by 60 percent at the test plate surface at H = 1.5 m (Table 2.1). Jet exit velocity was assumed to be uniform across the area of the nozzle and can be found from the volumetric flow rate Q and the circular cross sectional area of nozzle outlet A  d 2 / 4 , as  V  Q A  2.4  The volumetric flow rate Q is simply denoted as “flow rate Q” for simplicity thereafter.  2.2 Test Procedure Briefly, the water is supplied from the city line to the lower tank and is accumulated in the upper tank by a centrifugal pump through a main supply line. The water then flows down toward the headers and nozzles. After releasing water normally onto the test plate secured to a test bed (carrier), the impingement water spreads radially over the target plate surface, and falls freely from the plate edges into the lower tank. The water was collected in the lower storage tank to be recirculated with the centrifugal pump in a closed loop. Two high definition camcorders (Sony HDR-SR7) were used to record Table 2.1 Test and Jet Parameters (Test Plate at H = 1.5 m) d (mm)  19  Q (L/min)  V (m/s)  Re  We  dimp (mm)  Vimp (m/s)  Reimp  10  0.5878  11,126  90  6.236  5.457  33,890  15  0.8817  16,690  203  7.61  5.49  41,666  22  1.2923  24,478  435  9.149  5.577  50,832  30  1.7635  33,380  811  10.565  5.704  60,032  45  2.6452  50,068  1823  12.579  6.035  75,627  31  the experiments in 1080i format and at 120 frames per second. Two 1000 W Tota high stand up powerful lights were also used for illumination and increasing the films quality. The flow rates and test plate velocities were monitored and recorded using the software: Data Acquisition System Laboratory (DASYLab). Flow rates of the water nozzles were controlled by individual globe valves. Before each scheduled experiment date, it was necessary to check the turbine flowmeters to ensure accurate readings. Test plate velocities, on the other hand, were controlled by governing the input voltage signal manually to be proportionate to the control valve of the hydraulic power unit. The experiments on fixed plate were run at spray zone and other parts of the apparatus were not used. But, moving plate was displaced along the tracks by the motor and passed through spray zone and cut the water jets columns issued from the top nozzles. Actually, different procedures were taken for experiments on stationary and moving plate. The test plates were also different. Therefore, the procedure for each series of tests and data processing will be explained separately in each chapter next.  32  Chapter 3 Experiments on Stationary Plate  In this chapter, the impingement flow over the stationary plate due to long turbulent water jets is experimentally studied and reported. Three jet flow rates of 15, 30 and 45 L/min issued from single round nozzle of 19 mm diameter (denoted by ‘d’) at H = 1.5 m at these experiments. The impinging water jet was turbulent due to large jet Re number and large nozzle-to-plate distance (Table 2.1). The experiments were done at spray zone of ROT facility which was explained in Chapter 2.  3.1 Test Plate The target plate was a square Plexiglas sheet of 17″×17″ (430×430 mm) with a thickness of ¾″ (18 mm). Co-centered circles were marked and painted on the back side of the plate to facilitate measurement of water spreading over the plate. The circles were located at 0.25″ or 0.5″ (6.36 to 12.7 mm) radial intervals, depending on whether they were close to the stagnation zone or downstream, respectively. For better image quality in photography, another Plexiglas sheet (18″×18″) painted white was placed beneath the test plate as a background and fixed to it by silicon glue. These two plates were supported by a 20″×20″× ¾″ (508×508×19mm) Plexiglas sheet that rested on the carrier. This plate was used to horizontally level the top plates using four adjustable screws mounted at its edges. The arrangement was such that an axisymmetric flow expansion around the test plate center would be achieved. The two-track carrier along the table provided a test bed for the target plate under the nozzle. Figure 3.1 shows the test plate assembly.  33  Figure 3.1 Fixed Test Plate Assembly and Four Perpendicular Directions  3.2 Test Procedure Prior to running the experiment, the carrier was moved beneath the nozzle. The stack of three plates was then placed on the carrier and levelled using a level and adjustment of screws. The pump started to deliver water to the nozzle from the overhead tank while the flow rate was recorded. After attaining a desirable flow rate by regulating the globe valve before the nozzle, the center of the plate was set directly beneath the nozzle axis. The Sshapes diverting pipe was then turned inward manually to divert the jet off from the test plate and bypass the water flow to the lower tank. Depending on the flow rate, it took 3-5 minutes to achieve steady flow with no air bubbles at the nozzle exit. In the meantime, the wet top surface of the test plate was cleaned and dried, and the cameras were prepared and made ready for filming. Two high definition camcorders capturing 120 frames per second were used to take films in AVCHD video format; one to observe the jet column from the nozzle outlet down to the plate before impingement and the other focused at the target plate to capture water flow following impingement. In addition, two wooden boards painted black were placed behind the nozzle down to the plates to provide a dark background for better contrast in videos and to prevent unwanted extra light from the backside of the apparatus degrading the film quality (Figure 3.2). Also, two Tota lights with variable height and lighting angle stands are used to provide focused illumination;  34  the one light set for the jet coming downward after exiting the nozzle and another zoomed on the test plate. Consequently, the surface of the traveling water jet is distinguished more clearly from surrounding air pre-impingement and sufficient brightness is available to observe disturbances of the free-surface and expanding water flow over the plate surface after impingement. Each experiment started when the recorded flow rate was appropriately steady. The experiment is started by diverting the pipe quickly outward and allowing the jet to fall downward onto the plate while simultaneously starting the camcorders. The water jet impacted the target plate and a thin water sheet formed around the impingement point and developed radially over the top surface of the test plate. Circular hydraulic jump developed depending on the jet condition. The flow left the plate edges and dropped freely into the lower tank, thus continuously supplying water to the upper tank by the pump. The diverting pipe is then returned to its initial position at the end of each experiment. The flow rate readings are saved in a file for each experiment, whereas the two HD video files are stored in the hard disks of the camcorders. The experiments were performed in room temperature and ambient pressure. Air temperature is measured using a lab mercury thermometer. The water temperature inside the upper tank is measured and shown digitally on a controller board. The water temperature is checked inside the bottom tank using a lab thermometer; city water is fed into the lower tank if the water temperature differed by more than 2-3 °C. The nozzle height is 1.5 m with -2 to +1 cm variation. Room temperature is usually 23±2 °C for different experiments. To ensure repeatability, reduce the effect of randomness and have statistically more accurate results for such a turbulent jet flow rate, the readings are repeated and recorded for around 40 times for each flow rate. Table 3.1 shows time average flow rate and associated standard deviations for the present experiments. The flow rates for 45 L/min experiments changed from 44.1 to 47.2 l L/min. The information for each repetition is available in Appendix A.  35  Table 3.1 Average Jet Flow Rates on Fixed Plate Tests Flow rate Q (L/min)  Exp No.  Ave Q (L/min)  STDV (L/min)  15  46  15.033  30  41  30.095  0.358112 0.418066  45  36  NA  NA  Figure 3.2 Experiment Setup for Stationary Plate  36  3.3 Data Analysis The video files are assessed frame-by-frame and proper frames to illustrate the water impingement spreading were chosen for post-processing the experimental data. The frames were saved using Sony’s Picture Motion Browser software. The image processing software known as Matrox Inspector 8.0 is used to analyze the selected frames sequentially and to measure and extract the data (or in subsequent time intervals of 1/120 sec). The height of the jet tip from nozzle outlet is determined before impingement. The distance of the water flow front is measured after impingement. In this way, two data sets (h, t) and (r, t) are obtained for before and after impingement, respectively. To check the symmetrical evolution of water flow around impingement point, the measurement procedure is repeated in four mutual directions 0°, 90°, 180° and 270° (Figure 3.1). These data sets are used to find jet speed before impingement and the radial velocity of the water front (parallel to plate surface) after impingement. Some points with known coordinates were used to check the accuracy of calibration. The difference between the measurements and the known coordinates were fount to less than 0.3 mm. Different functions are examined to fit curves to the velocity profiles. The diameter of the jet just above the plate was measured in at least 5 selected frames of each experiments and an average value is obtained from accumulated data for each flow rate. The formation of hydraulic jumps is assessed and their radial positions were measured. Precise measurement at the first frame after impingement is difficult and the obtained data from those frames were scattered. Actually, water flow is highly disturbed due to the effect of impacting on the plate and the wetting front of spreading water over the plate is not easily distinguishable after the impingement point. Hence, the first frames in some experiments have been ignored where the data are highly dispersed. The diameters of the jets above the plate surface were measured in all experiments. The average measurement of jet impingement diameter for 40 runs of 15 L/min, 20 runs of 30 L/min and 20 runs of 45 L/min are shown in Table 3.2 with associated standard deviations.  37  Table 3.2 Jet Impingement Parameters on Stationary Plate Vimp Q dimp(mm) (L/min)  (m/s)  15  8.82 (± 0.5)  5.496  30  11.105 (± 0.25)  5.704  45  13.314 (± 0.81)  6.04  3.4 Pre-impingement While developing toward the test plate and before impingement, the distance of the free jet tip from the nozzle outlet is measured (jet height h) and the corresponding speed of the jet is found. The experimental jet height and speed are compared with theoretical ones in Figure 3.3 for different flow rates. In the figure, the experimental points are obtained from the fitted curve to the accumulated experimental data. It is noted that, the analytical values of the jet tip height are higher than the measured ones. The discrepancy between analytical and experimental values grows in time and with flow rate (Re number). The jets in experiments took longer time to reach the plate than the time expected from the equations 2.1 and 2.2. The discrepancy is due to the neglect of air resistance in deriving the equations and to the development of higher turbulence levels. The average difference between analytical and 15 L/min experimental results is less than %9 for the heights and less than %8 in velocities at the same time. The average delay of the jet in reaching the plate is %7.7 for 15 L/min, %11.4 for 30 L/min and %9.6 for 45 L/min but the impingement velocities are almost the same as predicted analytically one for all experiments (Table 3.2).  38  Figure 3.3 Experimental Results before Impingement (a) Jet Height (b) Jet Speed  3.5 Flow Observation after Impingement Figures 3.4 and 3.5 illustrate the typical evolution of the water sheet around the impingement point for 15, and 45 L/min, respectively. At first, it is observed that (Figure 3.4) a thin water layer was steadily developing (e.g. frame 4). Then, water flow was suppressed, the front starts to be rugged and scalloping began; the flow started to feel the plate surface effect. The spreading of the edge of the water flow slowed down but the rugged fingering increased (e.g. frames 12-14, 18) and the water sheet thickness started to increase at the front (e.g. frame 18). Following the above mentioned stage the circular waves began traveling over the surface giving new momentum to the front (e.g. frame 18, 45). Thereafter, the edge growth was retarded but crenations expedited; moving circular humps initiated from the impingement zone and extended through the parallel flow (wall) zone. In the meantime, the thickening of edge border became noticeable where the circular hydraulic jumps formed (e.g. frame 45) and the flow development beyond the circular hydraulic jump was impeded. The motion of the wetting front, interestingly, was not monotonically outward and it was stagnant during a few milliseconds and moved 39  backward slightly in harmony with the waves. Mild splashing was detected at the time of impingement only at the lower flow rates. However in 45 L/min experiment (Figure 3.5), the jet hit the plate with noticeable splashing and the spreading water layer was very chaotic at the beginning. The water layer was monotonically spreading over the plate surface and the suppression was not observed similar to the case of 15 L/min experiments. The water flow slowed down near the plate edges and it finally covered the plate surface. In the case of 45 L/min, the propagating disturbances were seen earlier than 15 L/min case and were not like the circular waves. They had irregular and intermittent circular shapes, which disturbed the stretching thin water layer. No hydraulic jumps were detected on the test plate for the experiments of 30 and 45 L/min due to plate size; the jump radius was beyond the test plate size with free edges in these cases.  Figure 3.4 Sample Images from Development of Water Layer 15 L/min after Impingement (t = 0 Represents the Time of Impingement)  40  Figure 3.5 Development of Water Layer (45 L/min) after Impingement (t = 0 Represents the Time of Impingement)  3.6 Impingement Water Film The water film after covering the plate surface is disturbed. However, to assess the possibility of changing flow regime from laminar to turbulent after impingement, the suggestive relations 3.1 and 3.2 for position of the transition by Lienhard [18] and Azuma [37], respectively, are considered.  rt  1200 Re  0.422 d  3.1  rt  730 Re  0.315 d  3.2  where rt is the radius of alteration to turbulent. These correlations were developed for short water jets where the nozzle is close to the target plate (typically H/d < 1) and for laminar free water jets with smooth and disturb-free jet surface. The jets were discharged from orifice types of nozzles and laminar impingement flow fully developed over the surface and the fluid layer thickness increased after transition (steady condition).  41  According to the predictions by both correlations (Table 3.3), the laminar impingement flow turns to turbulent beyond the plate size for all flow rates (the plate size is r/d = 11.3). The above two equations give different radii for the onset of turbulence with larger values from Azuma’s relation. As a result, the flow regime remained unchanged laminar over the test plate which contradicted the wavy surface and disturbed impingement water film. However, if the effect of gravity on our long jets is taken into account, then the above equations can be used with an adapted jet diameter and Reynolds number (dimp, Reimp) which give better results for rt /dimp (Table 3.3). The plate borders are placed at r /dimp ≈ 24.5 for 15 L/min and r /dimp ≈ 19.5 for 30 L/min and r /dimp ≈ 16.5 for 45 L/min. The transition to turbulent now occurs inside the plate borders according to Lienhard’s relation while it lies outside the plate edges by Azuma’s suggestion. The observations clearly showed the waves initiated from impingement region and disturbed the water film downstream. Rao et al [111] experimentally showed that these radial surface streaks can agitate the transition even for laminar impingement at jet flow rate as low as 4.5 L/min due to smooth water jet issued from an orifice (H/d < 15). The growth and breakdown of wave altered the flow structure of the thin impingement film and influenced the flow velocity locally. In the performed experiments, the thickening of the water film happened at the water front (not before) and was related to the jump occurrence for 15 L/min experiments. The frontal congealing is not observed for 30 and 45 L/min jets over the plate surface. The flow over plate surface is clearly not laminar for higher flow rates and round humps were seen travelling over the free-surface frequently. Therefore, these correlations which developed for steady laminar flow with no jet surface disturbance are not applicable to the transient conditions of the current experiments.  42  Table 3.3 Radius of Transition to Turbulent Flow Equation  3.1  3.2  15 L/min  30 L/min  45 L/min  Re  16,690  33,380  50,068  rt /d  19.83  14.8  12.47  Reimp  41,666  60,032  75,632  rt /dimp  13.48  11.55  10.48  Re  16,690  33,380  50,068  rt /d  34.14  27.44  24.15  Reimp  41,666  60,032  75,632  rt /dimp  25.59  22.81  21.21  3.7 Data Measurements The measurements of the distance and velocity of the water sheet front in the first 5 experiments of 15 L/min and 30 L/min cases, for example, in the 0°, 90°, 180° and 270° directions are shown in Figures 3.6 and 3.7, respectively. The radius of wetting front was sharply growing parallel to the surface initially after impingement but the retardation occurred later which is evident from the flattening of the growth of radial distances in all directions (Figures 3.6a, 3.7a). As shown in the figures, the plots are similar for 15 and 30 L/min jets and the repeatability of these experiments is good. The experimental data however, are scattered initially after the jet hits the test plate but the trend is similar in all four directions. Actually, the front of water was not clearly visible at the incident of impingement (first frame in the film) and then the measurements were scattered initially after impingement. The scattering of the data increased for higher flow rates and extended further away from the impingement point (Figure 3.7). Accordingly, the frontal velocity (Figure 3.6b, 3.7b) steadily decreased with the increase of the radial distance [112].  43  Figure 3.6 Experimental Data of 15 L/min (a) Water Front Distance (b) Frontal Velocity 44  Figure 3.7 Experimental Data for 30 L/min (a) Water Front Distance (b) Frontal Velocity 45  3.8 Progression of Water Front During cooling water jet impingement, the position of wetting front over the high temperature surface is important because the maximum heat flux is usually located in the vicinity of the wetting front and the sudden changes occur in surface temperature and heat flux during the passing of the wetting front [23, 24]. After impingement, the wetting front does not start spreading immediately over the hot surface. However, the residence of water front in impingement region does not occur on the unheated plate as seen in present experiments on stationary plate. This delay time along with the subcooling of water (∆Tsub=Tsat - Twater) and jet velocity influence the velocity of wetting front motion and the pattern of propagation. Therefore, the frontal spreading of water impingement on cold and hot plates are different and different rate of progression is expected. The frontal spreading of impingement water over heated and unheated surface are studied here for sake of comparison. The fitted curves to our accumulated data in four directions from the present tests were obtained. In addition, the measurements of wetting front of cooling water over a hot stationary steel plate are used. The heat transfer experiments were previously conducted at this apparatus using same nozzle (d, H) and same range of flow rates (Q) and reported in reference [11]. The initial plate temperature was about 860 °C and subcooling was 5 to 70 °C. Figure 3.8 shows the wetting front progressions over hot plate at a 45 L/min experiment and ∆Tsub = 50 °C. The comparison between cold and hot plate at each jet flow rate is depicted at Figure 3.9. The frontal radius is normalized with nozzle diameter. The delay time for lower subcooling (∆Tsub = 5-40 °C) is too long (60 sec for example). Therefore, the data of hot plate tests were reproduced and corrected against the delay time for lower sub-cooling (shown on separate plot). After the front started propagation (ignoring delay time), the water stream was developing over the surface radially outward in a similar manner for hot and cold plates but with dissimilar rates. Apparently, the mechanisms for front spreading on cold and hot plate are different. Thermal properties and heat transfer conditions have major effect on radial propagation of water front on hot plate but surface condition and jet flow rate are important for cold plate. To examine the effect of different material, the reproduced data obtained from Monde [86] on hot brass plate with initial temperature of 300 °C and 50 °C subcooling and 5 m/s jet velocity is also included (Figure 3.9b). Again  46  comparable profile for expansion of water flow is found but Monde [86] reported sudden changes in wetted propagation on steel surface in the same thermal conditions. Figure 3.9 illustrates the typical comparison of water front motion on hot and cold plate but caution should be made considering different physics of the two cases. Preliminary tests on steel plate which used in heat transfer experiments revealed similar flow spreading to what observed over the Plexiglas but with different rate of propagation of wetting front.  Figure 3.8 Progression of Water Front on Hot Plate Q = 45 L/min, Tint = 860 °C, ∆Tsub = 50 °C [11]  47  Figure 3.9 Progression of Water Front on Cold and Hot Plate (a) Hot Steel Plate, Tint = 860 °C, ∆Tsub = 5-70 °C (b) Hot Brass Plate, Tint = 300 °C, ∆Tsub = 50 °C [86] 48  3.9 Frontal Velocities The frontal velocities in four directions parallel to the impinging surface are drawn from a total of 30 experiments for 15 L/min (Figure 3.10). The measured front velocities vary erratically up to r/d ≈ 4, (1-2 frames after impingement) but reasonable repetition of results is observed beyond r/d = 5 for all directions. The comparison of the velocities in the four directions indicates that the growth of the water sheet is not always axisymmetric at first but symmetric behaviour is detected for all directions after around r/d ≈6; this is partly attributed to jet tip distortion by diverting pipe.  Figure 3.10 Frontal Velocity in Four Directions (15 L/min Experiments)  49  In the same way, normalized frontal velocities over the target surface are obtained from 20 experiments of 30 and 45 L/min each (Figures 3.11 and 3.12, respectively). The scatter in velocity data is increased with the flow rates but similar profiles in velocity decreasing are obtained in all directions. Jet unsteadiness is important here and it is noted that the impingement point doesn’t usually coincide with the plate center. A maximum offset of about 13 mm is observed in 15 L/min experiments for example. It is larger in 30 and 45 L/min experiments [113].  Figure 3.11 Frontal Velocity in Four Directions (30 L/min Experiments)  50  Figure 3.12 Frontal Velocity in Four Directions (45 L/min Experiments)  Fitted profiles of velocity for various flow rates in the four directions are shown in Figure 3.13. The velocities are measured in the parallel flow zone and outside of the impingement zone (e.g. r/d >1). The frontal velocity increased with the flow rate. The frontal velocity decreased steadily for all flow rates as the wetting front cover larger area over the test plate. However, the propagation of 15 L/min jet retarded more because of hydraulic jump and different expansion of water layer as shown at Figures 3.4, 3.5. The hydraulic jump and flow retardation didn’t occur for the higher flow rates over the plate test surface. On the other hand, the free-surface disturbances such as waves were intensified in the developing flow as the flow rates increased.  51  Figure 3.13 Velocity Profiles along the Four Directions at Various Flow Rates  A single profile could be established for each flow rate by averaging the velocities in the four directions. The maximum R-square of fitted curves with the magnitude of 0.92 obtained along 0° direction of 15 L/min case and the minimum value of 0.7 delivered in the 270° direction of 45 L/min case. The R-square has the highest magnitude for 15 L/min experiments in all four directions and the least values have been obtained for 45 L/min. Again this illustrates the intrinsic unsteadiness of the flows at higher flow rate.  52  3.10 Circular Hydraulic Jump (CHJ) The circular hydraulic jump (CHJ) configuration is investigated for 15 L/min experiments at first. No jumps occurred within the plate surface for 30 and 45 L/min cases. The formation of the CHJ is consequence of front thickening of thin water film after impingement, as illustrated in Figure 3.14a. The place and shape of CHJ were variable after formation and it did not have same radius in different directions; the jump was not symmetric entirely around the center of the plate. The jump front was rugged especially during creation and it was configured after formation with no rollers or with one roller (Figure 3.14b) or sometimes with two rollers (Figure 3.14c). The CHJ was unsteady and moved back and forth due to jet condition (e.g. high Re and oscillating impingement point). The disturbances caused the fluctuations at the free-surface and then difficulty in the measurement of water layer thickness. Therefore, the film thickness was not measured. In addition, changeable depth after the jump influenced its profile [38, 39]. Here, the water after fully covered the plate surface freely dropped from the plate edges with no barriers (as in industrial run-out table). Therefore, the thickness of water downstream the jump has no controlling effect on the jump; the thickness layer is adjustable using a rim at the outer border of the plate which is a known way to change the jump radius and examine the jump instability [38, 53]. According to measurements in all 15 L/min tests, the minimum radius for the circular jump was between 156 and 178 mm and the maximum radius was 187-215 mm, giving an average of 167 to 195 mm and a maximum standard deviation of 6 mm [113]. Following the 30 and 45 L/min tests, the CHJ radius was measured for a range of flow rate Q = 5 – 45 L/min on a new test plate which was prepared for moving tests and is large enough for HJ formation at higher Q . Due to jump instability, the measurements were repeated many times and the average values shown in Table 3.4 Stevens and Webb [30] presented a correlation for circular jump (equation 3.3) based on experiments with pipe nozzle diameter (2.2 < d < 8.9 mm), Reynolds number (2000 < Re < 50,000) and nozzle stand-off distance (z/d < 7):  Rj d   0.0061Re0.82  3.3  53  here, Rj is the radius of the jump. Although the average error was determined to be 15% over the full range of the experimental data, the correlation shows rather poor agreement with Watson model [44]. Due to the relatively high uncertainty, the correlation 3.3 yields a crude estimation of the jump location for axisymmetric jets. The relation 3.3 overestimates the CHJ radius in the present experiments (Table 3.4) and the discrepancies increased with flow rate (Q). Higher jet flow rates, disturb more the impingement flow and smaller jump, in general, was obtained respect to undisturbed water layer. Our measurements are also not very accurate due to jump front instability. The uncertainties in the present measurements are also included in Table 3.4.  Figure 3.14 Circular Hydraulic Jumps in a 15 L/min Experiment (a) Jump Evolution (the Time is Started after Impingement) (b) Single Roller (c) Double Roller  54  Table 3.4 Radius of Circular Hydraulic Jumps experiments Stevens [30] Q Re Rj /d Rj /d (L/min) 5  5,563  5.517 (-7.82% – 15.9%)  7.186  10  11,126  9.06 (-8.6% - 7.5%)  12.69  15  16,690  10.289 (-4% - 5.9%)  17.69  21  23,361  13.72 (-6.9% - 8.2%)  23.308  30  33,380  14.9 (-4.83% - 2%)  31.23  45  50,068  16.54 (-6.74% - 5.7%)  43.55  Table 3.5 Scaling Exponents for HJ Radius Circular Correlations on Fixed Surface Exp Bohr et Brechet et al Brechet et al Godwin Stevens Parameter Eq 3.4 al [46] [53]- theory [53]- experiment [47] et al [30] Flow rate Q  0.5165  5/8  2/3  0.703  1/3  0.82  Viscosity   -----  -3/8  -1/3  -0.295  -1/3  -0.82  Gravity g  -----  -1/8  -1/6  -----  -----  -----  Height H  -----  0  -1/6  0  -----  ----  Most of the available correlations for CHJ available in literature have been developed for short jets (e.g. H/d < 7) and were not for predicting the jump location for our long water jets with H/d=79. Therefore, a new correlation based on jet flow rate Q (m3/s) and nozzle diameter is found which correlated the present experimental data within  10%:  Rj d   749.45Q 0.5165  3.4  Table 3.5 show the comparison of some correlations available in the literature and the relation 3.4 similar to Table 1.2. Figure 3.15 illustrates the present experimental data along with other theoretical and experimental data. The experimental data are in good agreement with theoretical prediction by Bohr et al [46] and Kate et al [88]. Brechet’s theory [53] underestimates the CHJ radius for these long water turbulent jets.  55  Figure 3.15 Radius of Circular Hydraulic Jump versus Jet Flow Rate  3.11 Surface Waves and Splattering Before impingement, the turbulence was fully developed within the studied jets at the long separation distance of the nozzle and the plate [18]. The disturbances along jet surface were detected as shown in Figure 2.4. Higher frequency disturbances were observed along 45 L/min jet. These disturbances were carried to the impingement flow. The concentric waves over the free-surface abruptly appeared at some radial distance (usually near impingement region as shown in Figure 3.16a), grew radially downstream and collapsed within the water layer over plate surface. The surface waves were traveling over the free-surface with a speed much faster than average velocity of the flow and the wave speed increased with the flow rate. Although the camcorder couldn’t capture appropriately the waves’ evolution with fast and variable growth rate, the pattern of waves can be seen. Figure 3.16a illustrates the surface wave propagation upstream the HJ at a 15 L/min. The waves were, in general, circular in 15 and 30 L/min cases (Figures 3.16b, c) but irregular for 45 L/min (Figure 3.5). For higher flow rate, more frequent and intensified waves are developed which disturbed highly the water film (30 and 45 L/min tests). According to observations at all tests, the surface waves were in harmony with surface disturbances over the surface of liquid jet. These disturbances developed as  56  undulation over the surface of impinging jet and then carried into the impingement flow appeared as the surface wave and amplifying the film flow. This is reported in the literature as well [56, 114]. The frequency of surface wave is linked to the disturbance period along the incoming jet surface. The waves passed the HJ at 15 L/min and usually break and cell-type structure was formed locally (Figure 3.16b) which is an indication for lower flow speed and degraded heat transfer capability. The above behaviour of surface waves triggers transition to turbulence in laminar flow regime and may be exploited to enhance the heat transfer for laminar jets impingement. The Q variation also influenced jet unsteadiness. However the experiments were run after the recorded jet flow rate showed least changes.  Figure 3.16 Surface Waves after Impingement (a) Spreading 15 L/min (b) Pattern 15 L/min (c) Pattern 30 L/min  57  Surface tension is dominant for our low Weber number jets (see Table 3.6) where the turbulence is damped effectively and splashing is expected. Splattering is associated with moving surface waves and is unwanted in heat transfer because it wastes the cooling fluid. Lienhard et al [55] suggested equation 3.5 based on the scaling parameter χ (  We exp(  0.971 H ) ) for characterizing the disturbances amplitude over the range of We d  1000 < We < 5,000, H/d < 50 and 4400 < χ < 10,000:    0.258  7.85  105   2.51  109  2  3.5  The model fails for larger H/d and is not relevant for the low Weber number jets. Thus, its application to lower flow rates especially 15 L/min jet with high magnitude of χ is doubtful (Table 3.6). The model predicts considerable amount of splattering ξ = 0.3 for the 45 L/min jet. However for 30 L/min jet, the small splattering fraction of 0.02 is inferred from their experimental data [57]. The comparable observation on frequency and amount of the splashing among all experiments of different flow rates on stationary plate revealed that the most reoccurrence splattering happened for 45 L/min jet which is far higher than for 30 L/min jet (Figure 3.17). No splashing was observed for the 15 L/min jet in general.  Table 3.6 Jets Splattering Parameters Q l0 Wed χ d (L/min) 15  202  44600  127  30  808  12006  98  45  1817  10987  49  58  Figure 3.17 Splashing in a Series of Frame Sequence (a) 30 L/min (b) 45 L/min At pre-impingement, splattering was modeled also by the onset of splattering (lo) where at least 5 percent of the incoming jet is splattered before hitting the plate was predicted Bhunia et al [57]  l0 130  d 1  5  10 7 We 2  3.6  Accordingly, splattering more than 5 percent is expected just from 45 L/min jet (Table 3.6) before impacting the plate. This is consistent with the observation in the present experiments. Splashing was frequently detected at 45 L/min experiments and was seldom 59  occurred at 15 and 30 L/min experiments. Precise measurement, however, is needed to determine the percentage of splattering before and after impingement.  3.12 Summary and Conclusion The experiments of 15, 30 and 45 L/min long turbulent jets impinging on stationary plate demonstrate the developing of disturbances along the jet surface which carries into the impingement flow as surface waves. These travelling waves over the free surface disturb the thin water layer and agitate splashing. The existing relations 3.1, 3.2 for the radius of onset of turbulence basically developed for short and laminar jet and the applicability of these correlations to long industrial jets is questionable. The configuration and place of CHJ is variable due to jet conditions. The CHJ expanded whenever the surface waves reached to the jump front and created unsymmetrical jump around the plate center. A simple correlation for radius of CHJ is developed in term of jet Q for the long liquid jets.  60  Chapter 4 Experiments on Moving Plate: Single Jet  In this chapter, the series of experiments explained were conducted on a moving plate using the UBC pilot-scale apparatus with typical industrial geometry and parameters. The velocity of the moving test surface and the flow rates of the long water circular jet issued from a single nozzle were changed systematically to study the hydrodynamics of the water flow spreading over the moving surface and to explore the effect of these parameters on the wetting front or the hydraulic jump that occurred on the moving surface. The experimental procedure and results are provided in detail.  4.1 Experimental Setup and Procedure The run-out table apparatus is shown in Figure 4.1. This facility was explained in section 2.1. The test plate used for these experiments is illustrated in Figure 4.2. Long plate is needed for the impingement flow to develop and settle down. Therefore, the plate dimensions were chosen according to the plate velocities, dimension limit at the facility and the experience gain from the tests on a fixed plate. The plate is 1.88 m / 74 inches long and 0.508 m / 20 inches wide. A 0.0127 m / 0.5 inch thick segment of MDF was used as the base material where each end had 0.3 m / 12 inches painted white to allow for measurement referencing. A 0.0191 m / 0.75 inch thick piece of Plexiglass with the same length and width dimensions as the MDF was put on top of the MDF to provide a durable finish. The interface between the Plexiglass and MDF was sealed against water damage using Shellac.  61     Figure 4.1 Pilot Scale Run-Out Table Apparatus  Figure 4.2 Moving Test Plate     To begin the experiment, the test plate was located at the start of the acceleration zone to allow for a steady velocity when the plate entered the spray zone. The water jet was impinged perpendicular to the plate from the tube water nozzles that were aligned vertically. Two high definition camcorders (Sony HDR-SR7) were used to record the experiments in 1080i format and at 120 frames per second. The water flow development and the formation of circular hydraulic jump (HJ) over the top surface of the plate were filmed by both a top camera placed near the nozzles (Figure 4.3a) and another camera positioned in front of the end of the tracks in the deceleration zone. After the spray zone, where the experiment was recorded, a deceleration zone of 5 m allowed the test plate to stop unharmed. Due to the length of the deceleration zone used to securely stop the test plate at the end of the track, experiments faster than 1.5 m/s could not be safely conducted. The furnace was not utilized in any of these experiments and the experiments were run at room temperature. The water was issued from the nozzles 5-10 minutes  62  before starting the first experiment to maintain a steady flow with no air bubbles. It has been reported that the HJ from the air-liquid jet will occur at a larger radius [115]. The flow rates were 10, 15, 30, and 45 L/min while the test plate velocity was in the range of 0.3, 0.6, 1.0, 1.3, and 1.5 m/s. The vertical distance between the water nozzle and the test plates was fixed at a height of 1.5 m. A single nozzle was utilized for these tests. Each experiment is represented by a set of parameters: the water jet flow rate and the plate’s velocity. 14 series of experiments are summarized in Table 4.1. The experiments were repeated several times for each experimental set, usually a minimum of 10 successions or more, to ensure accurate and repeatable experimental results. The impingement Reynolds number Reimp is also shown in Table 4.1, and is defined based on the impingement velocity and diameter. High magnitudes of Reimp show that the impingement flow spreading over the plate surface is turbulent.  Figure 4.3 (a) Nozzles and Top Camera (b) Mesh and Lights  63     Table 4.1 Experimental Parameters Flow rates Q (L/min)  Reimp  10  33,890  0.6  1.0  1.5  15  41,666  0.3  0.6  1.0  30  60,032  0.6  1.0  1.3  45  75,623  0.6  1.0  1.3  Plate velocity Vp (m/s)  1.3  1.5  4.2 Data Processing Assessments of the recorded films were done frame-by-frame using Matrox Inspector program. The frames were saved and chosen after the HJ formed by Sony’s Picture Motion Browser software. For scaling the frames extracted from the film of every experiment, a wire mesh was placed in-between the water nozzles and the test plate. The wire mesh consisted of 0.0254 m / 1 inch squares and was picked up by the high speed camcorder which was facing downward, normal to the mesh and plate (Figure 4.3b). Using the reference squares, points on the wire mesh were used for calibration by the image processing software. The round water jets were turbulent and jet unsteadiness was also inevitable due to the long distance between the nozzle and the moving plate [57]. Also, the shape and place of HJ is not stable after formation. Therefore 3-5 frames per film were selected to capture the HJ during each unsteady experiment. The collected data was used to represent the wetted zone and HJ in each experiment. Jet instability was more pronounced for 30 and 45 L/min jets. Depending on plate velocity and flow rate, 30-70 points were used to locate the inner and outer front of the wetting zone, each separately. The HJ width was embedded between the inner and outer fronts and is not negligible. Table 4.2 shows the time average nozzle flow rate (Q) and the time average plate velocity (Vp) during repeat tests for each set of experiments. For each series of experiments, the variation of Q and Vp during all repetitions is found as Q and Vp and then the average of these variations compared with nominal magnitude of Q and Vp, respectively, and present in percentage in 4th and 6th columns of the Table 4.2. During the  64  experiments, the average flow rate did not exceed 6.2% of the nominal Q and the average plate velocity usually varied between -5% to +10% with respect to the nominal Vp, but it was larger for experiments on slower plates (0.3 and 0.6 m/s). In tests with smaller plate speeds, it was more difficult to establish steady plate motion because of a larger speed fluctuation. It was noted that the velocity had to increase sharply to around 0.6 m/s or more to overcome the static friction of the chains to start the experiment. After that, the velocity was decreased and maintained at the desired magnitude. Keeping a steady velocity in displacing the plate was not an easy task. Variable jet flow rate and/or velocity of the plate during the experiment influenced the hydrodynamics of impingement water flow over the surface and increased HJ unsteadiness. Detailed information of each repetition is available in the Appendix A. Occasionally, the flow rate was also checked manually with a bucket and timer. The plate speed was also checked with camera filming (Table 4.3) and very close results were obtained with respect to the recorded speeds.  Table 4.2 Average Nozzle Flow Rates and Plate Speeds with Changes Ave Vp Vp % Flow rate Plate velocity Ave Q Q % (L/min) (m/s) (L/min) (L/min) (m/s) (m/s) 10  15  30  45  0.6  10.141  6.18  0.614  16.67  1.0  10.257  4.77  1.007  10.43  1.5  10.203  5.25  1.53  5.53  0.3  15.075  4.02  0.305  14.24  0.6  15.303  3.74  0.589  10.3  1.0  15.527  2.92  1.051  10.9  1.3  15.028  3.69  1.292  6.15  1.5  15.475  4.19  1.523  5.26  0.6  30.774  4.707  0.59  12.82  1.0  30.481  4.714  1.017  5.8  1.3  30.24  4.69  1.339  8.28  0.6  46.58  3.61  0.613  13.33  1.0  46.027  1.95  1.002  5.6  1.3  45.741  1.71  1.29  6.08  65  Table 4.3 Average Plate Velocity Obtained from Films Plate speed (m/s) Flow rate (L/min) 15 30 45  0.3  0.6  1  1.3  0.298 -----------  0.594 0.586 0.609  1.057 1.0197 1.0291  1.31 1.364 1.297  4.3 Flow Observation In stationary plates, the approaching water jet hits the plate and the impingement flow advances radially outward and symmetrically with respect to the impingement point over the surface. The impingement point is fixed and unique. However, the moving plate cuts the jet column and passes through it along the middle line of the surface. During the experiments, every point on the middle line passes beneath the jet successively and it is instantaneously considered as the impingement point. Therefore, the impingement point is not unique over the moving surface. Actually, the development of impingement radial flow due to the circular free-surface jet is no longer symmetric on a moving surface and it is treated differently before and after the moving impingement point depending on the direction of movement. The impingement water layer is assisted to expand after the jet where the concurrent flow takes place while the propagation of the liquid sheet is opposed in developing ahead of the jet where the countercurrent flow occurs. Sample images of the flow evolution of jet impingement over a moving test plate for different jet flow rates and plate velocities are shown in Figures 4.4 to 4.7. The flow rate increases from 10 to 45 L/min but the plate velocity decreases from 1.5 to 0.6 m/s, respectively. The direction of plate motion is illustrated in the figures and the time is measured from the start of impingement. Generally, the impingement free-surface water flow is initially expanding symmetrically around the moving impingement point after the jet impacts the moving plate from the front end. But soon afterwards, the flow felt the motion of the surface gradually while the white background section of the plate cuts the jet. The ragged edge of liquid film appears in front and enlarges radially outward, but not  66  circularly, around the moving impingement point and tailing downstream. The wetted zone is elongated in the motion direction and extended downstream, but constrained transversely. Afterwards, the wetted front thickens and consequently the HJ is detected ahead of the jet where the flow lost momentum due to viscosity, inertia, and surface tension effects. The HJ at the wetted front is established after the jet leaves the front white section of the test plate. Thereafter, the HJ travels in the middle part of the plate but is not stable in shape and place. At the end, the jet enters the rear white part of the plate and then leaves it. The large distance between the nozzle outlet and the plate surface enhanced the disturbances over the surface of turbulent incoming jets which then transferred to the impingement flow. Subsequently, travelling waves over the free-surface of developing flow and splattering were two prevailingly observed features. Splashing of water droplets occurred frequently from the free-surface and the front HJ which is governed by surface tension (e.g., Figures 4.5, 4.6 and 4.7). Air entrainment in the HJs was detected in experiments with higher jet flow rates of 30 and 45 L/min. Nearly round surface waves were also observed down to the impingement point and were detected in all experiments. Although disturbances were observed on the surface of the jet columns at all flow rates, experiments with higher jet flow rates (30 and 45 L/min) produced more intensified waves with higher frequencies at the impingement flow upstream and downstream which agitated the splashing (Figures 4.6 and 4.7). Despite more HJ instability and wavier impingement flows in higher flow rate experiments, the advancement of the water layer and HJ formation were similar for all flow rates and plate velocities as shown in Figures 4.4-4.7. The initial wetness of the target surface influenced the movement of the water front. The wetted zone did not turn back quickly to a symmetrical shape when the plate stopped beneath the jet. It was noted that the wetted front tailing downstream took time to form a circle which is an indication of a wet surface. Therefore, the plate surface was cleaned and dried after each experiment by a warm compressed air spray before beginning the next experiment. Figures 4.4-4.7 exhibit that the wetted zone spans the area around the impingement point and is proportional to the jet flow rate and the test surface velocity. The wetted front, for example, did not reach the sides of the plate and shrunk more 67  toward the impingement point for lower flow rates and higher plate speeds (Figures 4.4 and 4.5). On the other hand, water reached the plate edge sides and fell into lower tanks for higher flow rates and smaller plate speeds (Figures 4.6 and 4.7). Therefore, the jet flow rate (jet Re) and the plate velocity are both key parameters to the shape and size the wetted zone although fluid properties and surface conditions are also important. In the following, the effect of test surface velocity and jet flow rate will be assessed.  Figure 4.4 Sample Impingement Flow of a 10 L/min Jet on a Moving Surface at 1.5 m/s  68  Figure 4.5 Sample Impingement Flow of a 15 L/min Jet on a Moving Surface at 1.3 m/s  Figure 4.6 Sample Impingement Flow of a 30 L/min Jet on a Moving Surface at 1.0 m/s 69  Figure 4.7 Sample Impingement Flow of a 45 L/min Jet on a Moving Surface at 0.6 m/s  4.4 Velocity of Test Plate The effect of the velocity of a moving surface on a wetted zone and HJ can be studied through a series of experiments of fixed jet flow rates and changing plate velocities. Figures 4.8 to 4.11 illustrate the sample images of wetted areas created on a moving surface of 0.3-1.5 m/s from fixed jet flow rates of 10 to 45 L/min and the corresponding measured inner and outer wetted fronts. The measured data is scaled by the nozzle diameter (d). The origin of the Cartesian coordinate XY system over the plate surface (Figure 4.9a) is set on the impingement point and is determined by a plus sign in the plots. Motion direction is downward along the Y axis. The figure of each flow rate reveals that if the plate velocity increases, then the radius of wetted front decreases and a smaller wetted zone is obtained. For each flow rate, a faster moving plate (Vp ≥ 1 m/s) drags the HJ toward the impingement point and restricts the wetted zone closer around it. In 30 L/min jet experiments, for example, the maximum jump radius along the impingement line (Y-axis) is 11.5d on a 0.6 m/s moving plate, and while it is about 8d on a 1.3 m/s plate. This can also be seen from Figures 4.4 and 4.5, where the effect of  70  surface motion is promoted. On the other hand, a larger wetted zone occurred over a slower moving plate (Vp < 1 m/s) for each flow rate where HJ was allowed to move further away from the impingement point. For example, for a 15 L/min jet, as shown in Figure 4.9, the wetted zone spans a larger area over the surface of a slow moving plate and the jump front reached the edges of the plate; however, this did not happen in fast moving plate experiments. Therefore, the velocity of the impingement surface has a significant effect on the shape and size of the wetted area around the impingement point. It also impacts the profile and place of the HJ. Higher plate velocities bend the HJ more around the impingement point, but lower surface speed decreases the curvature of the HJ profile. This is the same for inner and outer fronts of the HJ.  (a)  (b) Figure 4.8 Wetting Zones in all Experiments of 10 L/m Jets (a) Sample Photographs (b) Measured Inner and Outer Wetting Fronts  71  (a)  (b) Figure 4.9 Wetting Zones in all the Experiments of 15 L/m Jets (a) Sample Photographs (b) Measured Inner and Outer Wetting Fronts  72  (a)  (b) Figure 4.10 Wetting Zones in all the Experiments of 30 L/m Jets (a) Sample Photographs (b) Measured Inner and Outer Wetting Fronts  73  (a)  (b) Figure 4.11 Wetting Zones in all the Experiments of 45 L/m Jets (a) Sample Photographs (b) Measured Inner and Outer Wetting Fronts  74  4.5 Jet Flow Rate The jet velocity or jet flow rate also plays an important role in the creation of a wetted zone and HJ over a moving surface. Figures 4.12-4.14 display sample images of water flow and measured data from the experiments of various jet flow rates on a moving plate with constant velocity. In the series of 0.6 m/s moving plate experiments (Figure 4.12b), for example, the average radius of the measured outer front along the impingement line is 6.8d for a 10 L/min jet and it increases to 8.4d, 11.6d, and 13.4d for 15, 30, and 45 L/min jets, respectively. Similarly, the jump radius increases according to the jet flow rate in the series of experiments on 1.0 and 1.3 m/s moving surfaces (Figures 4.13 and 4.14). This same trend is detected for inner fronts. As seen in Figures 4.12a-4.14a, for each velocity of the moving plate, the size of the wetted zone increases proportionally with the jet flow rate. Conversely, the HJ curves more around the impingement point when the jet flow rate is reduced. Therefore, the effect of plate motion is suppressed with higher flow rates while the impingement water covers a larger area over the moving surface. Actually, both jet flow rates and impingement surface velocities are important in sizing the wetted zone around the impingement point and in finding the HJ radius along the impingement line (Figure 4.14).  75  (a)  Figure 4.12 Wetted Zones in the Experiments of Plate Velocity of Vp = 0.6 m/s (a) Sample Photographs (b) Measured Inner and Outer Fronts (HJs)  76  (a)  (b) Figure 4.13 Wetted Zones in the Experiments of Plate Velocity of Vp = 1.0 m/s (a) Sample Photographs (b) Measured Inner and Outer Fronts (HJs)  77  (a)  (b) Figure 4.14 Wetted Zones in the Experiments of Plate Velocity of Vp = 1.3 m/s (a) Sample Photographs (Rj is Jump Radius) (b) Measured Inner and Outer Fronts (HJs)  78  4.6 Hydraulic Jump Unsteadiness The spreading liquid film has a wavy free-surface initiated from disturbances along the surface of the jet column at pre-impingement (see the jet columns in Figures 4.4-4.7). It was noted that the HJ as the front of developing impingement flow, was pushed forward in harmony with the surface waves and delivered fresh momentum and then pulled backward by the moving surface when it spent its momentum. Indeed, the wetting fronts were unstable during each experiment and more than one frame from the film of each experiment was needed to locate it accurately. Figures 4.15(a) and 4.16(a) illustrate sample frames taken from one experiment film for 10 and 45 L/min jets, each when the plate was displaced by velocities of 0.6 and 1.0 m/s, respectively. These recurrent tests had the least deviation and the closest averages in the plate velocity and the jet flow rate during the experiments with respect to the nominal magnitudes of these parameters. The measured points along the inner and outer fronts from each frame are also plotted in parts (b) and all data points together from all frames during the test in parts (c). The impingement point is set as the origin of the coordinate XY system (Figure 4.16a). As shown in parts (a) and (b) of the figures, the HJ is less unsteady with a fairly smooth face for the least jet flow rate: 10 L/min, compared to the highly unsteady HJ with an uneven face for the largest jet flow rate: 45 L/min. The wetting front during each test was not the same and it was sometimes unsymmetrical with respect to the middle line of the plate. These HJ characteristics were detected in all experiments of 10 and 45 L/min jets and on all moving plate velocities. Also, the jump front was even in 15 L/min jets on 0.3 m/s moving plate experiments, but uneven for higher plate velocity tests and in all 30 and 45 L/min experiments. Hence, the HJ in these transient experiments could not be accurately taken from just one shot of each experiment film. On the other hand, the accumulated data could be used to construct the smoothed profiles to represent the HJ during each experiment repetition (parts c). The fitted curves are 4th or higher order polynomials which were found by the least-squares method. In this way, the obtained HJ profiles could be compared among the repeated experiments for each set of experimental parameters. Again, the HJ profile geometry was dependent on the jet flow rate and the velocity of the moving surface.  79  Figure 4.15 Hydraulic Jumps of Jet of 10 L/min on a Vp = 0.6 m/s Moving Surface (a) Sample Images (b) Measured Inner and Outer Profiles of the Jumps of Sample Frames (c) Accumulated Measured Data of the Jumps of Sample Images 80  Figure 4.16 Hydraulic Jumps of Jet of 45 L/min on a Vp = 1.0 m/s Moving Surface (a) Sample Images (b) Measured Inner and Outer Profiles of the Jumps of Sample Images (c) Accumulated Measured Data of the Jumps of Sample Images 81  As shown in Figure 4.17, for each jet velocity (flow rate), a faster moving plate decreases the radius Rj proportionally. Although it is not shown, linear lines were fitted well to our data for each jet flow rate. On other hand, Rj increases with jet flow rate in experiments of constant velocity plate motion. This demonstrates that the wetting size is in direct relation with both jet and plate velocities. The HJ is not circular over the moving impingement surface and has a variable radius around the impingement point. The HJ radius along the middle line at the Y-axis is denoted as Rj (Figure 4.16a) where the jump curvature is minimum. The distances of the inner and outer wetting fronts at the middle line of the plate were measured in every experiment and the average Rj among all repetitions for each set of experiment was obtained (Table 4.4). Moreover, the change in the radius, Rj, during each repeated test as an indication of jump instability and the average of Rj for each series of experiments were calculated. The jump width, which is the difference of outer and inner radii, was also computed (Table 4.4). These quantities are expressed in the table in terms of nozzle diameter. More details are available in Appendix B for each repetition. Although the data for Rj are a little scattered, Rj generally increases with jet flow rate especially for 30 and 45 L/min jets, which is in agreement with the higher jump unsteadiness for the higher jet flow rate tests. A comparison of Tables 4.2 and 4.4 exhibits that Rj is usually larger according to the higher variability of jet flow rates and the velocity of the surface during the experiment. This is the same for jump width.  4.7 The Jump Radius On a stationary surface, the circular HJ radius depends on parameters such as jet flow rate Q, nozzle diameter d, drop height H, gravity g, fluid properties density ρ, viscosity μ, and surface tension σ [18, 38]. But on a moving plate, as demonstrated in our experiments, the velocity of the impingement surface Vp is also important in shaping the geometry of the non-circular HJ. Accordance to previous studies [53, 87, 89] and our experiments, the HJ radius Rj on a moving plate, in general, is a function of the parameters Q, Vp, d, H, ρ, μ, σ and g. Using dimensional analysis and scaling law [52]:  82  Table 4.4 Average Radii of hydraulic Jump Rj Flow rate Q (L/min) 10  15  30  45  Inner radius  Outer radius  Plate velocity Vp (m/s)  Rj /d  Rj /d  Rj /d  Rj /d  Jump width /d  0.6  5.708  0.79  6.891  0.71  1.183  1.0  4.518  0.57  5.897  0.61  1.379  1.5  3.524  0.51  4.705  0.4  1.181  0.3  9.342  0.36  10.366  0.41  0.82  0.6  7.166  0.37  8.442  0.4  1.28  1.0  5.982  0.43  7.246  0.34  1.29  1.3  5.375  0.36  6.583  0.31  1.2  1.5  4.636  0.75  5.728  0.59  1.11  0.6  10.087  0.72  11.641  0.64  1.556  1.0  7.561  0.61  9.061  0.73  1.5  1.3  6.592  0.73  8.126  0.57  1.534  0.6  12.108  1.2  13.43  1.1  1.323  1.0  9.735  0.98  11.324  1.19  1.529  1.3  8.131  1.17  9.826  0.94  1.7     Figure 4.17 Average Radii of Hydraulic Jumps for Different Flow Rate Jets on a Moving Plate  83  R j  C. Q  V p d  H        g   4.1  This is the general relation for the HJ radius in terms of the 8 parameters for which the coefficient C and the exponents α, β, γ, δ, η, ε, ξ,  are unknowns. Using the respective dimensions substituted for each term, Equation 4.1 can be rewritten as  Rj d  C(  Q  Vp d  H  d  gd 3  2  ) ( ) ( ) ( 2 ) ( )  d d  2  4.2  Here, the HJ radius is function of five nondimensional terms for which the constant C and the exponents α, β, γ, ξ and  have to be found empirically. The first term includes the jet flow rate Q, the second surface velocity Vp, and the third the nozzle specifications H and d. The last two groups contain gravity g, surface tension, and fluid properties  and , which are constant for a specific nozzle diameter and fluid. Therefore, Rj may be modeled with less parameters and dimensionless groups in our experiments. For example, if the 7 parameters Q, Vp, d, H, ρ, μ, and σ are considered, then 4 Π groups may be found using the Buckingham Pi theorem [52]. It may be shown that the above first 4 nondimensional groups may be obtained and they can be rearranged as:  Rj d  C(  Vp d 2 Q  ) (  d  H  d 3  ) ( ) ( 2 ) d Q Q   4.3  or  Rj d  C(  Vp V  ) Re  (  H  ) We d  4.4  Here, Rj is defined by the following parameters: the velocity ratio Vp/V (where V is the nozzle exit velocity), Reynolds number Re, Weber number We, and the height ratio H/d. Recently, Gradeck et al. [87] conducted experiments on a moving plastic strip (conveyor belt) to study the HJ forming from a normal impinging circular water jet. Although a series of experiments with different jet velocities and surface speeds were conducted, limited results were reported. The nozzles diameters were 17 and 20 mm but the nozzle was close to the surface. Gradeck correlated their experimental data for the radius Rj as below which fitted with more than ±20% error [87]  84  Rj V   1.0033 p  d V   0.44  H   d   0.607  Re 0.0073 We  0.058  4.5  This correlation is applied to the ranges of 0.42 < Vp/V < 5.1, 6,800 < Re < 36,900, 39 < We < 1,162, and 3.9 < H/d < 8.82 where Rj /d ranged from 1.04 to 6.64. Our 10 and 15 L/min jet experiment conditions are almost within the above ranges but not those experiments with jets of 30 and 45 L/min. However, this is important to mention that the exponent of the velocity ratio (Vp/V) is positive in the reported relation by Gradeck [87]. But this means that at a given jet flow rate and specific nozzle (d, H), a higher plate velocity will increase Rj while apparently it should decrease. Therefore, it is supposed that it is a typo and the exponent of the velocity ratio is adjusted to be negative with the same value as shown above. The relation 4.5, thus, is different from what reported [87] in this regard. It is the only available correlation found in the literature for noncircular HJ. However, Rj /d is mostly above 6 in our experiments and H/d is 79. Moreover, Gradeck et al. did not distinguish between the inner and outer front whereas a clear HJ width was observed in their experiments. Figures 4.18a and b show the comparison of our measured Rj with relation 4.5 for lower jet flow rates (10 and 15 L/min) and higher jet flow rates (30 and 45 L/min), respectively. Relation 4.5 noticeably overestimates our experimental data for the HJ location. Generally, the jump occurs close to the impingement point in Gradeck’s experiments over the limited axial dimension of the strip while the impingement surface at the present experimental conditions provide a long enough moving surface where the jump can occur far before of the impingement point. Gradeck et al. assumed a 2nd degree polynomial fit to construct their jump profiles while the fitted curves to our HJ profiles such as in Figures 4.15 and 4.16 are usually of 4th-6th degree polynomials. Quadratic fitting does not provide an accurate fitting to represent the HJ profiles in our experimental conditions because they predict larger Rj values. Moreover, the nozzle in Gradeck et al.’s experiments was close to the surface (H/d = 0.11 for example) while in the present experiments the ratio of H/d is equal to 79. In short jets, the impinging jet had a smooth surface and the impingement flow was not disturbed over the surface and thus an almost  85     Figure 4.18 (a) Radius of Hydraulic Jump at Different Velocity Ratios (a) 10 and 15 L/min Jets (b) 30 and 45 L/min Jets steady condition was attainable in Gradeck’s experiments. Here in the present experiments, apparent surface disturbances on jet column surfaces were observed even for 10 L/min jets which carried into the impingement flow and caused a wavy freesurface, splashing, and instability in the HJ shape and location. Also, the method for finding Rj values in Gradeck’s work was not explained. In the present experiment, we used the average Rj resulting from the total frames extracted from all repeated tests for every series of experiments. Therefore, the correlation 4.5 of Gradeck is considered not applicable to the present industrial scale water jet experiments [116]. As discussed above, the relevant physical parameters are the jet flow rate, the plate velocity, and the nozzle specifications in our industrial experiments. Therefore, the HJ radius may be simply scaled as shown below where the fluid properties ρ and μ are condensed into kinematic viscosity ,  R j  Q  V p d  H      4.6  In a similar way as mentioned above, the Rj is correlated with 3 non-dimensional terms,   Q   Vpd   C   d  d      Rj    4.7  In the above analysis, surface tension does not appear in the correlation because it is the only term that has the dimension M and the effect of the surface tension on the 86  radius of the circular HJ is assumed to be small, although it had a critical role in jump instability, especially for small radii [38, 41-42]. The nozzle diameter and height were fixed in these experiments such that the term H/d was constant. Hence, the above correlation for our experiments is reduced to the simple form equation 4.7. Using the measured Rj value (Table 4.4), the exponents α and β and the coefficient C are determined graphically by a least-squares method (Tables 4.5, 4.6 and 4.7) The correlations for the inner and outer front of the HJ formed on the moving surface are obtained as:  Inner front:  Outer front:  0.4291 Rj  Vpd   Q     7.860409   d   d     Rj  Q   6.460432   d  d   0.3855   Vp d        0.4462  4.8  0.3632  4.9  where the ranges of the main parameters are: the jet flow rate Q = 1.667 – 7.5 m3/s (1045 L/min), the velocity of the surface Vp = 0.3 – 1.5 m/s, the nozzle exit diameter d (m), and the kinematic viscosity  (m2/s) . As seen from the correlations, higher jet flow rates result in larger Rj values while an increase of plate velocity decreases Rj. The above correlations are applicable in the following ranges for non-dimensional terms: 11,150  Re  50, 170 90  We  1820  4.10  0.227  Vp/V  2.55 H/d = 79 The radii of all the HJs in all the experiments are correlated by the above relations within 7% error for the inner and outer fronts (Figure 4.19).  87  Table 4.5 Unknowns in Equation 4.7 C  Α  β  Inner  7.860409  0.4291  -0.4462  Outer  6.460432  0.3855  -0.3632  Table 4.6 Coefficient C of the Inner Radius Correlation Q (m3/s) 1.667e-4  2.5 e-4  5 e-4  7.5 e-4  Vp (m/s)  Rj / d  Q/ v.d  Vp. d / v  C = (Rj /d) / [ (Q/ d.v) α  (Vp.d/ v)β) ]  0.6  5.708  8685.079  11287.129  7.491811614  1.0  4.518  8685.079  18811.881  7.447665918  1.5  3.524  8685.079  28217.822  6.961078251  0.3  9.342  13027.619  5643.5644  7.562663798  0.6  7.166  13027.619  11287.129  7.903861524  1  5.982  13027.619  18811.881  8.287425919  1.3  5.375  13027.619  24455.446  8.370966067  1.5  4.636  13027.619  28217.822  7.695843601  0.6  10.087  26055.237  11287.129  8.263400807  1  7.561  26055.237  18811.881  7.780293416  1.3  6.592  26055.237  24455.446  7.624945347  0.6  12.108  39082.856  11287.129  8.335218332  1  9.735  39082.856  18811.881  8.416958184  1.3  8.131  39082.856  24455.446  7.903589288  Average  7.860408719  88  Table 4.7 Coefficient C of the Outer Radius Correlation Q (m3/s) 1.667e-4  2.5 e-4  5 e-4  7.5 e-4  Vp (m/s)  Rj / d  Q/ v.d  Vp. d / v  C = (Rj /d) / [ (Q/ d.v) α  (Vp.d/ v)β) ]  0.6  6.891  8685.079  11287.129  6.191131242  1.0  5.897  8685.079  18811.881  6.378331229  1.5  4.705  8685.079  28217.822  5.896145285  0.3  10.366  13027.619  5643.5644  6.192931205  0.6  8.442  13027.619  11287.129  6.487409598  1  7.246  13027.619  18811.881  6.702933322  1.3  6.583  13027.619  24455.446  6.698743357  1.5  5.729  13027.619  28217.822  6.140088292  0.6  11.643  26055.237  11287.129  6.848874232  1  9.061  26055.237  18811.881  6.416844627  1.3  8.1259  26055.237  24455.446  6.329917974  0.6  13.43  39082.856  11287.129  6.757005047  1  11.324  39082.856  18811.881  6.859107579  1.3  9.826  39082.856  24455.446  6.546584094  Ave  6.460431934     Figure 4.19 Correlated and Experimental Radii of the Hydraulic Jumps  89  4.8 Wetting Front (HJ) The variable radius of the noncircular HJ on the moving impingement surface depends on the polar angle  or the azimuthal location as well. The surface motion deformed the profile of the circular jump as seen in the above figures. Recently, Kate et al [89] investigated the noncircular HJ on a continuous moving surface based on the modelling of a noncircular HJ due to an oblique jet impingement on a stationary flat surface (Figure 4.20). They explored the striking of oblique laminar liquid jet on an infinitely flat horizontal continuous moving surface and derived the radius of noncircular HJ based on Bohr correlation [46] for CHJ (Table 1.2) in terms of jet angle inclination, jet velocity, plate speed and fluid viscosity. For normal impingement on moving plate ( = 90) the jump radius is [89]     2 d R j  c 8     5/8        1         V3      V 2  V p2       3 / 8 g 1 / 8 2    Vp  cos      V 2  V p2     4.11  where V is jet velocity as it falls on the surface (the nozzle is close to the target plate), Vp is velocity of the moving surface, and d is the jet diameter. Constant c is a constant determined by the chosen velocity profile of the flow [88]. Figure 4.21 illustrates the suggested profiles of the non-circular HJ from Equation 4.11 in polar coordinates on a moving surface of velocities in the range of the present experiments due to normal impinging 10 and 30 L/min water jets. It displays how the circular HJ on a stationary plate is deformed into a non-circular profile because of surface motion. The jump is stretched in the direction of motion and is transversely contracted more on plate surfaces with higher velocities. The effect of the moving surface is stronger on jumps from 10 L/min jets as expected.  90     Figure 4.20 A Hydraulic Jump due to an Oblique Circular Liquid Jet Impinging on Moving Plate  Figure 4.21 Theoretical Profiles of the Noncircular HJ on a Moving Surface from Equation 4.16 (a) 10 L/min Jet (b) 30 L/min Jet  91     The radii of HJ along the longitudinal axis Rj due to the water jets in the present experiments are computed from Equation 4.11 and are compared, in Table 4.6, with corresponding experimental data of outer wetting fronts (Table 4.4). The constant c is chosen to give closer results from Equation 4.11. The calculated Rj highly depart from experimental ones in lower flow rate jet tests (10 and 15 L/min) and Kate’s model anticipates greatly smaller jumps. However, as the effect of plate motion decreases, as in higher flow rates (30 and 45 L/min), close results are obtained from Equation 4.11 especially if the comparison is made with outer wetting fronts. Figures 4.22 to 4.25 show the comparison of HJ profiles predicted by Kate et al. (Equation 4.11) and the fitted curves for the inner and outer fronts in each series of the present experiments. The origin is at the stagnation point. The fitted curves are obtained by a least-squares method from accumulated experimental data in every experiment series. For lower jet flow rates (Figures 4.22 and 4.23), the Kate et al. jump profiles occurred far before the inner fronts of experimental jumps, and they are close to the outer fronts in the experiments of higher jet flow rates as expected (Table 4.8). The Table 4.8 Radius Rj of HJ from Kate’s Modeling and Present Experiments Flow rate (L/min) 10  15  30  45  Jet velocity Vj (m/s) 0.5878  0.8817  1.7635  2.6452  Plate velocity Vp (m/s)  Eq 4.11 (mm)  Exp (mm)  0.6  50.96  108.45  1.0  30.7  85.83  1.5  19.45  66.95  0.3  132.55  142  0.6  90.8  136.15  1.0  59.62  113.66  1.3  46.01  102.12  1.5  39.55  88.1  0.6  204.42  191.65  1.0  157.94  143.67  1.3  132.17  125.24  0.6  269.88  230.05  1.0  225.24  185.94  1.3  197.79  154.49  92  Rj  Inner Rj  Kate’s et al. jump profiles are in the range of jump radius unsteadiness for higher jet flow rates of 30 and 45 L/min (Table 4.4), but they are very much smaller in lower jet flow rate cases. Kate et al. [89] compared their jumps with Gradeck et al.’s jumps [87] and concluded that the experimental results are close to their jump profile. Actually, he assumed the moving surface to be infinitely large and the jump profiles are formed entirely over the target surface while the test plate in Gradeck et al.’s experiments has finite dimensions and only a segment the HJ profile is formed over the moving plate surface. In Gradeck et al.’s experiments [87], the flow does not radially expand over the entire impingement surface and it drains from the plate sides and then the drainage in longitudinal and transverse directions is not equal [89]. In the present experimental setup, the test surface size is large enough for the whole jump profile in lower flow rate experiments, especially for higher plate velocities. However, as shown in Figures 4.22 and 4.23, Kate et al.’s jump contours are considerably smaller than the experimental ones in these tests but their estimates are good in the higher flow rate tests where water drained from the plate sides (Figures 4.24, 4.25). Indeed, the formation of a closed noncircular configuration of the jump at the moving surface did not detect during these experiments although the test plate is 99d long. The wetted region is extended after the impingement point as an open contour which is not only likely due to the finite dimensions of the impingement surface. This is also owing to the different physics of impingement flow over moving target surface with respect to the impingement flow due to oblique jet on a stationary surface. Although plate motion changes the circular HJ to a noncircular one, it does not necessary mean that close contours will be obtained downstream as seen in the oblique jet impingement. For example, the observations in tests with 10 L/min jets where the effect of surface motion is highly promoted demonstrates that the wetted front tailing downstream never approached the middle of the plate to form a closed loop even far from the impingement point. Moreover, the existence of the fluid flow beyond the jump front on a stationary surface is an important factor in characterizing the HJ configuration and sizing. However, on a moving surface, there is no water after of the jump to control it. Therefore, Kate et al.’s solution for a non-circular HJ due to oblique impingement can be applied partially to wetting front when the effect of a moving surface is not enhanced. The open configuration for the non-circular HJ is expected to be detected over the  93  moving impingement surface, which is different than the closed profile suggested by Kate et al.’s solution.  Figure 4.22 HJ Profiles due to 10 L/min Jets        Figure 4.23 HJ Profiles due to 15 L/min Jets 94     Figure 4.24 HJ Profiles due to 30 L/min Jets     Figure 4.25 HJ Profiles due to 45 L/min Jets  95  Chapter 5 Experiments on Moving plate: Multiple Jets  In this chapter, the experiments on moving plate with two and three round nozzles are explained and the results for the measurements of interaction zones and wetting fronts and hydraulic jumps (HJ) are presented in detail.  5.1 Introduction A typical multiple-jet configuration encompasses of nozzles, impinging jets, target surface and outlet boundaries. Following the studies of Ishigai et al [75] and Kate [90] on twin water free-surface circular jets on stationary surface, the main regions of a multi-jet system can be delineated as shown in Figure 5.1 (this includes the free jet, the impingement region, the inner and outer wall regions, and the interaction region). The opposing liquid inner wall jets, outside of the impingement zones, collide along the interjet distance, come to be stagnant, and then turn upward. Depending on the strength of inner wall jets (the jet’s momentum), the thick interaction film with no splashing or a thin sheet of upwash fountain with splattering could be formed at the interaction zone (Int-Z). The entrainment of ambient air may also occur. The location of the fountain is strongly dependant upon the momentum ratio of opposing wall jets and it is quite sensitive to the jets’ conditions. The jets are called “equal jets” if they have equal strength or momentum (issued from same nozzle diameter with same exit velocity). The free jets are similarly called parent jets in the literature.  96  Figure 5.1 Twin Liquid Free-surface Impinging Jets (1. Free Jet, 2. Impingement Zone, 3. Inner Wall Region, 4. Outer Wall Region, and 5. Interaction Region)  5.2 Experimental Setup and Procedure The experiments with multi nozzles were run at same apparatus discussed in Section 2.1. The experiments conducted by using 2 and 3 nozzles (as shown in Figure 4.3a). Here, in the case of having 2 nozzles (N = 2), they were separated by a distance of 203.2 mm/ 8 inches (s/d  10.7). For the 3 nozzle experiments (N = 3), the nozzles were separated by a distance of 101.6 mm/4 inches (s/d  5.35). Both the multiple nozzle configurations had the nozzles lined up on the same horizon as a jet-line array. In typical industrial setups, the height of the nozzle ranges typically from 1 to 2 m or more, the strip speed is up to 15 m/s which greatly exceeds the impingement water velocity, and the velocity ratio of plate to jet exit is typically between 2.5 to more than 15 [33]. However, the attainable velocity at the UBC ROT pilot scale facility (where the present experiments were conducted) can go up to 1.5 m/s and is very smaller than the impingement velocities for 10 to 45 L/min jets (Vimp  5.5 – 6 m/s). To achieve a better velocity ratio, two nozzle heights (H) were considered: 0.5 m and 1.5 m. While keeping the same amount of water (same Q), the impingement velocities decreased more than 40% (Vimp  3.2 – 4 m/s). Therefore, a  97  higher velocity ratio was attained for this apparatus while the plate speed did not increase. The experimental parameters are summarized in Tables 5.1 and 5.2. The Re numbers is based on the nozzle outlet but Reimp is defined based on the impingement velocity and diameter. In total, 18 series of experiments with two nozzles were performed with various flow rates ranging from 10 to 30 L/min on a plate moving with velocities of 0.6, 1.0, and 1.5 m/s. Also, 15 test series with three nozzles were conducted with same range of jet flow rates and plate velocities as a test with two nozzles (except with a flow rate of 30 L/min). The splattering filled the space above the plate surface, making filming and measurements very difficult. Therefore, no test with a flow rate 45 L/min was carried out. Each series of experiments was repeated approximately 10 times or more. The experiments were conducted in the same manner as described in the Sections 2.3 and 4.1 for single nozzle tests except with the activation of 2 or 3 nozzles at the present series of multi jet experiments.  Table 5.1 Experimental Parameters for Two Nozzle Tests Flow rate Q (L/min)  10  15  22 30  Re  Plate velocity Vp (m/s)  H  Vimp  (m)  (m/s)  1.5  5.457  33,890  0.0  0.6  1.0  1.5  0.5  3.187  25,958  0.0  ----  1.0  1.5  1.5  5.496  41,666  0.0  0.6  1.0  1.5  0.5  3.254  32,125  0.0  ----  1.0  1.5  1.5  5.577  50,832  0.0  0.6  1.0  1.5  0.5  3.389  39,702  0.0  ----  1.0  1.5  1.5  5.704  60,032  0.0  0.6  1.0  1.5  Reimp  11,126  16,690  24,478 50,068  98  Table 5.2 Experimental Parameters for Three Nozzle Tests Flow rate  Re  Q (L/min)  10  15  22  Plate velocity Vp (m/s)  H  Vimp  (m)  (m/s)  1.5  5.457  33,890  0.0  0.6  1.0  1.5  0.5  3.187  25,958  0.0  ----  1.0  1.5  1.5  5.496  41,666  0.0  0.6  1.0  1.5  0.5  3.254  32,125  0.0  ----  1.0  1.5  1.5  5.577  50,832  0.0  0.6  1.0  1.5  0.5  3.389  39,702  0.0  ----  1.0  1.5  Reimp  11,126  16,690  24,478  Tables 5.3 and 5.4 show the time average nozzle flow rate (Q) and the time average plate velocity (Vp) during the all repeated tests for each set of experiments. The data is presented for each nozzle separately (N1 denotes the nozzle number 1 and so on). Moreover, for each series of experiments, the variations of Q and Vp during each repetitions as Q and Vp were found. Then the average of these variations were compared with the nominal magnitudes of Q and Vp, respectively, and are shown as Q% and Vp % within the tables. Instantaneous differences among the jet flow rates are not reflected from these tables and the average values resulting from each series are reported in Tables 5.3 and 5.4.  Again, a slower moving plate makes it harder to establish a steady motion for the plate and speed fluctuations, in general, are higher for 0.6 m/s tests. For higher jet flow rates, lesser differences (Q %) were obtained amongst the nozzles. According to these tables, the highest flow rate inequality and plate speed unsteadiness occurred in the series of 10 L/min and 0.6 m/s experiments. Variable plate speed and jet flow rates and the inequality between nozzle deliveries have influenced the interaction zone and increased the unsteadiness. Detailed information for every repetition is available in Appendix C.  99  Table 5.3 Average Nozzles Flow Rates and Plate Speeds with Variations in Twin Jets Tests Q (L/min)  H (m)  1.5 10 0.5  1.5 15 0.5  22  1.5  0.5 30  1.5  Vp (m/s)  Ave Vp (m/s)  Vp %  0.6  0.596  1.0  N1  N2  Ave Q (L/min)  Q %  Ave Q (L/min)  Q %  19.33  10.643  10.54  10.498  6  1.04  9.2  10.628  9.53  10.514  5.76  1.5  1.541  8.1  10.106  8.325  10.516  5.714  1.0  1.037  21.11  10.596  9.636  10.602  6.108  1.5  1.516  4.0  10.567  9.267  10.598  5.517  0.6  0.585  14.1  15.211  3  15.082  4.32  1.0  1.032  11.87  15.716  6.671  15.295  3.333  1.5  1.469  4.711  15.785  5.853  15.435  3.262  1.0  1.004  10.182  15.482  4.176  15.328  4.836  1.5  1.55  7.611  15.414  4.222  15.2  5.856  0.6  0.642  22.06  22.598  2.613  22.323  4.392  1.0  1.042  10.637  22.562  2.8  22.391  2.944  1.5  1.501  4.167  22.823  1.856  22.537  3.723  1.5  1.504  5.619  22.532  2.214  22.323  2.013  0.6  0.574  21.191  30.223  1.829  30.734  2.171  1.0  1.007  9.4  30.432  1.69  30.736  1.766  1.5  1.504  6.205  30.228  1.577  30.286  1.838  100  Table 5.4 Average Nozzles Flow Rates and Plate Speeds with Variations in Tests in Three Jets Q (L/min)  H (m)  Vp (m/s)  Ave Vp (m/s)  N1 Vp %  Ave Q  Q %  (L/min)  1.5 10  N3  N2 Ave Q  Q %  (L/min)  Ave Q  Q %  (L/min)  0.6  0.575  23.61  10.534  10.12  10.788  7.70  10.284  6.53  1.0  1.044  11.56  10.925  7.51  10.062  7.244  10.31  2.394  1.5  1.482  4.93  10.311  9.28  9.9401  11.91  10.393  5.39  1.0  1.5169  11.56  10.693  8.08  10.518  6.6  10.627  6.53  1.5  1.019  10.42  10.804  9.16  10.37  5.63  10.537  5.8  0.6  0.617  24.33  15.499  3.89  15.278  3.72  15.611  4.16  1.0  0.988  18.17  15.47  3.98  15.217  3.5  15.527  3.41  1.5  1.554  22.98  15.334  2.76  15.075  5.77  15.565  3.96  1.0  1.029  16.08  15.187  2.42  15.7  4.32  15.562  6.82  1.5  1.525  7.52  15.348  4.26  15.389  5.98  15.465  4.96  0.6  0.61  14.52  22.402  3.77  22.499  4.4  23.429  2.27  1.0  1.006  11.83  22.83  3.77  23.735  3.99  22.496  3.74  1.5  1.504  6.06  22.505  3.45  22.586  3.69  22.424  2.6  1.0  1.013  10.43  22.532  2.62  22.61  2.66  22.7  3.51  1.5  1.481  6.06  22.526  2.68  22.441  2.2  22.653  3.82  0.5  1.5 15  0.5  1.5 22  0.5  5.3 Data Processing The films taken from the experiments were processed frame-by-frame in a manner similar to the single nozzle experiments. Given the high degree of unsteadiness of the upwash flow in Int-Z, the inspection of a considerable number of frames from every film is required to measure the Int-Z value and to precisely gauge the effect of plate motion. Considering the scope of this research to study the overall effects of plate motion on impingement flow and jets interaction, 4 frames per each film were usually selected at the most different situations for up wash interactive flow (e.g., shape, place, etc.). It is  101  believed that the collected data from those frames represent, in general, the boundaries for the size and place of the Int-Z over the moving impingement surface during each test. However, these results do not reflect the instantaneous behaviour of the interfering wall jets. The steps in data processing are illustrated, for example, in Figure 5.2 for a sample experiment of two 10 L/min jets on a 1.0 m/s moving plate and in Figure 5.3 for a sample experiment of three 15 L/min jets on a 0.6 m/s moving plate. For each experiment, the selected frames were shown in parts (a) of the figures; the measurements for each frame are plotted in parts (b), and the accumulated data in parts (c). These steps were taken for all repeated tests from every series and then the accumulated data from all repetitions were combined to determine the final representative for each series. All multi jets experiments were processed according to these steps. As shown in the figures, the interaction of circular HJs due to multiple jets is highly unsteady. The resulting interaction flow (fountain), in general, was oscillatory and the location of stagnation line shifted randomly. In fact, the observations revealed that the upwash flow in interference zone was quite sensitive to small variations in jets conditions such as jet flow rate or a slight inequality between flow rates among the nozzles; this will be shown later. Moreover, the interaction is governed instantaneously by the parameters at that instant such as: the flow rates of the parent jets, the distance and position of the impingement points, turbulence in the impingement wall jets, plate velocity, etc. Such parameters were not constant during each experiment. The assessment of recorded flow rates during every experiment demonstrates (as summarized in the Tables 5.3 and 5.4) that the nozzles never delivered the same flow rate although the flow meters were carefully and frequently checked. Also, the impingement point was not usually coincident with the geometric center point beneath the jet and it instead oscillated over the plate surface. The oscillation amplitude reached up to 13 mm. However, great care was taken throughout each repeated test to assure that nearly identical conditions were maintained for jets in every series. For example, the nozzles were kept in the same position, each experiment started after steady and disturb-free inflow conditions were obtained with the least variation in flow rate, plate motion was managed for the least variable velocity  102  during the test, and the nozzles’ vertical alignment and the nozzle-to-nozzle spaces were checked repeatedly. But, some variations were unavoidable and beyond control as  Figure 5.2 Experiment N = 2, H = 1.5 m, 10 L/min, Vp = 1.0 m/s (a) Sample Images Selected Frames (b) Measurements of Interaction Film from the Frames (c) Accumulated Data  103  Figure 5.3 Data Processing at a Experiments N = 3, H= 1.5 m, 15 L/min, Vp = 0.6 m/s (a) Sample Images - Selected Frames (b) Measurements of the Interaction Film (c) Accumulated Data reflected in Tables 5.3 and 5.4 for the average magnitudes of Q and Vp during these transient experiments. Despite all the care taken during the experiments to ensure symmetry in the flow (and due to the above inevitable imperfections), the interference region and up-wash flow sometimes displayed a tendency to incline toward one of the weaker jet at that moment and the stagnation line was not a straight line. This verifies the high sensitivity of the fountain to asymmetries in jets conditions such as slightly unequal  104  flow rates among the jets in the jet array which are uncontrollable. This was also reported by other researchers [e.g., 72- 73]. Moreover, the experiments with single nozzles demonstrate that the impingement flow in the parallel region was turbulent (33,000 < Reimp < 61,000) with a wavy surface due to the transferred jet surface disturbances. The disturbed wall jet flow before collision in experiments with multiple nozzles is an indication of the interaction asymmetry and unsteadiness. Accordingly, the collected data as shown in parts (c) of Figures 5.2-5.3 do not display the Int-Z exclusively at every instant during the experiment. To ensure reproducible results from each series of experiments, some tests were ignored because of large fluctuations in plate velocity or deviations in the jet flow rate with respect to nominal magnitudes. The remaining tests have the least differences possible in experimental conditions among all repetitions in each series of tests.  5.4 Experiments on Stationary Plate (H = 1.5 m) In the present experiments with twin water free round jets (d = 19 mm), the jet flow rate was varied, Q = 10 - 30 L/min. At the beginning, the experiments took place at a stationary surface and then later on a moving plate. In liquid wall jet collision, the HJ due to each parent jet interferes in the Int-Z. Then the study of HJs interaction is necessary in this regard. Kate [90] was the first to notice the HJ interaction in a wide range of interjet distances. He classified the upwash flow in Int-Z according to the jet-to-jet distance (indicated as s in Figure 5.1): “Fardistant” jets, “Distant” jets, and “Adjacent” jets. If the neighbouring jets are very far from each other then no interaction occurs and the each HJ will be circular with an unaffected radial symmetry (Far-distant). However, if the jets are moved inward together, the HJ contact is initiated and the HJ profile will be converted to non-circular shapes (Distant). With a greater decrease in the distance s, the water upwash sheet will be more stands up and, eventually, the fountain upwash sheet occurs if the jets are very close (Adjacent). Therefore, the flow structure in interaction region is dependent on jet-to-jet space (pitch) for a given jet flow rate. On other hand, a higher jet flow rate excites the HJ interaction for a given s/d.  105  The demarcations between the three classes were found experimentally for a range of Q < 10-4 m3/s and 7 < s/d < 50 [90]. For a higher jet flow rate an earlier HJ interaction is expected at the same s/d. Accordingly, jet interactions should occur in the present experimental setup and the jets are distant or adjacent. Figures 5.4a and b illustrate the sample images from the top and front views of HJ interference for different jet flow rates on a stationary plate. The full size for each HJ was not taken place over the plate surface due to the plate size. Indeed, different interaction films were created. The inner opposite wall jets were spreading radially and touched each other creating a typical interference for each case: a thick film with almost straight stagnation line due to weak interaction for 10 and 15 L/min jets (distant jets) but a thin upwash fountain because of a strong interaction for 22 and 30 L/min jets (adjacent jet). For distant jets in the case of lower Q (10 and 15 L/min), the thick interaction film with a small stand up is the consequence of direct HJs interference. Actually, the radial symmetry of the HJs was affected only in the collision region and noncircular jumps were resulted. The HJ was untouched in the outer wall regions similar to single jet impingement with a circular shape of same jump radius (Rjmax). The film thickness in the contact region is elevated at the interjet space along the stagnation line due to the association of opposing radial streams from the inner wall jets. Therefore, a dome-shape thick film is formed in the twin jet configuration on a stationary surface in these Qs experiments. But the thickness is not constant along the stagnation line. Kate et al [90] demonstrated that the thickness layer is the highest at the center of the stagnation line where the jump radius is the smallest (Rjmin) and is decreased gradually along the line outward by draining the water in both directions. The thickness in the center increases with an increase in Q (keeping s fixed); the thicker interference film is obtained from 15 L/min jets compared to a 10 L/min jet as shown in Figure 5.4b. The interference film thickness has a controlling effect on the location of noncircular interactive HJs similar to what the fluid thickness downstream of single circular HJ has [38, 46]. The change in  106  (a)  (b) Figure 5.4 (a) Hydraulic Jump Interaction on a Stationary Surface - Top view (H =1.5 m) (1. Free Jet, 2. Inner Wall Jet, 3. Outer Wall Jet, 4. Hydraulic Jump, and 5. Int-Z) (b) Hydraulic Jump Interaction on a Stationary Surface - Front view (H =1.5 m)  jump radius in the azimuthal direction (angle) or noncircularity of the jump (e.g. radius ratio Rjmin / Rjmax) also depends on s and Q. As shown in Figure 5.4a for 10 and 15  107  L/min jets, the larger noncircularity or a smaller Rjmin / Rjmax value should be obtained for higher flow rate jet interactions. Interesting features were also detected. The liquid streams from each inner wall jet do not mix completely and keep their identity at interference region (Figure 5.5) which is more clear at experiments with Q = 10 L/min at H = 0.5 m. The wall jets separation is also observed for twin 15 L/min jets but harder because the wall streams collided at higher velocities and eventually merged. This feature was also reported by Kate [90] using different colours for the twin jets. Another feature is observed along the Int-Z far from the center of interjet distance where the two radial wall flows are affected by the interaction stream flowing along the stagnation line at above and below the center (outflows from Int-Z). The jumps segments at these areas are displaced showing an oblique intersection as a butterfly (see Figure 5.6a). However the jumps retain their shapes because the interaction flow is not strong at that region. Figure 5.6b schematically illustrates the two HJs’ interaction with two circles. The filled gray region is the Int-Z and the dashed lines show the radial wall streamlines from each impingement point in addition to the returning flow from above and below of the Int-Z (“x” and “y” in Figure 5.6b). The two neighbouring HJs are affected but their shapes are preserved because they are not colliding directly. Therefore, the interference of HJ of inner wall jets depends to angular direction of radial stream as well. Decaying thickness outward along line “xy” in Figure 5.6b is a consequence of dependency to angular direction [90] and signifies the complexity involve in liquid jets interaction.  Figure 5.5 Wall Jets Separation at Int-Z of 10 L/min Jets  108  (a)  (b) Figure 5.6 (a) Sample Images of HJs Interaction and Returning Flow on Stationary Surface (H = 1.5 m) (b) HJs Interaction for Two Adjacent Jets, 1. HJ and 2. Int-Z The circular HJs from a single jet at Q = 22 and 30 L/min have larger radii and the space s at the present experiments is less than (Rj1 + Rj2) / 2 where Rj1 and Rj2 are HJ radii due to the individual impinging jets 1 and 2. For twin adjacent jets in the case of the above higher Qs, an upward spring is observed (Figure 5.4) between the jets because of strong jet interaction. Higher liquid jet flow rates create higher velocity opposing wall jets (higher strength parent jets) which collide and produce upward vertical flows emerging as a thin high velocity liquid sheet called an upwash fountain. This is a different phenomenon from the thick interaction film with a short height in the case of lower flow rate jet interference (10 and 15 L/min). Figure 5.7a illustrates the side view of  109  the high stand up vertical upwash flow for a 22 L/min jet, for example. Considerable splashing had erupted which presented spatial spreading of the water stream into ambient (also observed from front view in Figure 5.4b). For the upwash water fountain, the uprightness, outer rim, and thinness of the fountain was not captured from the front view (Figure 5.4b) but was clearly visible from the side view (Figure 5.7). The upwash sheet fluctuated over the impingement surface between the two jets in an unsteady manner and was very sensitive to the instantaneous position of the impingement points and relative jet flow rates. The oscillating impingement point, for example, originated a wavy stagnation line whose fountain was displaced and inclined toward the weaker jet; one jet instantaneously had a lesser jet flow rate or a more distant impingement point from the center of interjet line. The fountain was more unstable with a more intensified splashing for the case of the 30 L/min impinging jet as shown in Figure 5.4. For a higher nozzle height (H =1.5 m) more upwash unsteadiness was observed. Kate [90] demonstrated the upwash flow goes back to the surface from both ends the fountain far from the center of stagnation line. Subsequently, it interferes with the jumps similar to what was seen in the lower jet flow rate cases. Actually, in this case the strong and high speed wall streams due to high flow rate parents produced the peripheral returning stream from Int-Z greatly influenced the jumps (Figure 5.7b). It could wash the parts of the jumps at that region in the case of very close jets or high strength jets. Furthermore, the two HJs are now as two intersecting circles which deformed at the interjet space. This is not the case shown in Figure 5.6b and a narrow Int-Z is created instead of a thick interference region (the gray zone in Figure 5.6b).  Figure 5.7 Upwash Liquid Fountain in Adjacent Jets (N = 2, 22 L, H = 0.5 m) (a) Side View (b) The Interaction of Upwash Stream and HJs 110  Similar to what was seen in experiments so far with nozzles at H = 1.5 m, the distant jets are obtained by 10 and 15 L/min with H = 0.5 m and adjacent jets for 22 L/min jets experiments (Figures 5.5, 5.7). However in general, less unsteadiness and splashing were detected due to weaker interactions respect to the H = 1.5 m case. With a lowered nozzle, the inner wall jets collided with smaller velocities (weaker jets). Moreover, the jet column surface before impingement is smooth and disturbance-free for the 10 and 15 L/min jets. However, the surface of the 22 L/min free jet was not smooth but had fewer disturbances with respect to the jet issued from 1.5 m high nozzle.  5.5 Experiments of Twin Jets on a Moving Plate (H = 1.5 m) The twin jets experiments were done with 10, 15, 22, and 30 L/min jets on a plate moving at 0.6, 1.0, and 1.5 m/s velocities.  5.5.1 Flow Observation Figures 5.8-5.9 illustrate sample images from impingement flow development and the jets’ interactions. These images were extracted from the films of twin jet experiments for different jet flow rates and plate velocities. Parts (a) of the figures show images taken from above by the top camera and parts (b) show the images taken from the front camera for the same experiments. It was difficult and unsafe to mount the second camera at the side of the lower tank where the plate moving over it and hence the camera was posed on a tripod at the end of the tracks where the plate was going back and forth. However as shown in the previous part for stationary plate tests (see Figures 5.4b and 5.7a), some features such as fountain thinness, etc were not detectable from the front view. In general, the flow from each jet started spreading individually over the plate surface early after impingement. But soon, the inner wall jets met and the interference started. For higher Qs, earlier interactions were observed. Then, the splattering gradually faded when the impingement flow progressed and maintained at the middle part of the plate and afterward. For the 30 L/min jet (not shown), however, the splashing was intensified and persistent during the test. The Int-Z, in general, was fluctuating and the wavy stagnation line was playing around the longitudinal axis of the plate. For a lower jet flow rate, a calmer and less unstable interference was detected.  111  On a moving impingement surface, the thin radial wall jets were not allowed to flow freely forward and confined by the plate motion and the thick wetting front (HJ) results. As shown in Figures 5.8 for 10 and similarly for 15 L/min jets at 1.5 m/s velocity, whenever the effect of plate motion was promoted for lower jet flow rates, the double curved front of wetted area appeared above each impingement point similar to what was observed for single jet tests on a moving plate with a regular curved wetting front. Moreover, the HJs interfered in a similar manner to twin jets tests on a stationary plate at these flow rates and the thick interaction film took place over the surface as seen in Figure 5.4. On other hand, as shown in Figure 5.9 in the case of higher Q and lower Vp, if the wall jets are strong enough then the high speed radial streams from each jet linked together and the upwash fountain occurred as seen in Figures 5.4 and 5.7a on a stationary plate. Moreover for a lower Vp, the returning flow from the Int-Z combined with the accumulated water ahead of the Int-Z and pushed forward the wetting front. Then the impingement water sheet covered a large area over the impingement surface. This also happened at experiments with a single nozzle at a higher jet flow rate (30 and 45 L/min) on a slower plate motion. However for twin jet experiments, the wetted front grew locally around the center line of the plate (swelling) as seen in Figure 5.9a. The round waves, which originated from the surface disturbances along the jet column, also agitated the fountain unsteadiness. This effect was similarly observed for HJ (wetting front) unsteadiness as well for single jet experiments. The plate motion could change what occurs at the interaction region between the jets (Figure 5.9b). This is explained more when the effect of plate velocity is investigated.  112  (a)  (b) Figure 5.8 Sample Images for Impingement Flow Development and Jet Interaction (N = 2, H = 1.5 m, 10 L/min, 1.5 m/s) (a) Top View (b) Front View  113  (a)  (b) Figure 5.9 Sample Images for Impingement Flow Development and Jet Interaction (N = 2, H = 1.5 m, 22 L/min, 1.0 m/s) (a) Top View (b) Front View  114  5.5.2 10 and 15 L/min Jets Experiments Every film taken in the series of 10 and 15 L/min experiments was checked and one film for each Q and Vp which illustrates clearly the impingement flow was chosen. This procedure was followed for all the next figures of every series. Figures 5.10 and 5.11 show the sample images for 10 and 15 L/min tests, respectively, at various plate speeds. Parts (a) and (b) show the images from top and front views of the same tests, respectively. A thick low stand up interaction film was created which oscillated at the interjet distance with a wavy stagnation line but the two jumps kept their identities similar to what seen before at a stationary plate (parts a). As shown in parts b for each Q, higher stand up and thinner the interaction film was detected on faster plate moving and for each Vp, wider and higher stand up the interaction film was resulted from stronger jet (15 L/min). After the interaction film formed and developed (in general at the middle part of the plate and after), the returning flow from the Int-Z interfered with the radial inner wall streams. On a stationary plate, the displacing of the HJ front results from this interference (Figure 5.7) and the interaction film freely flows outward along the stagnation line in both directions. However, the motion of the impingement surface restricts the wetting front ahead of the interaction region and increases complexity there. Whenever the effect of moving plate is not promoted such as Vp = 0.6 m/s tests and/or higher jet flow rate (15 L/min) tests as shown at parts a, the wetting front was not close to the Int-Z and the joining radial streams from two wall jets made a pool of water ahead of the Int-Z and then the returning interaction flow successfully pushed the wetting front outward. Consequently, the swelling of the wetting front was observed above the Int-Z; a large projection over the wetted area was obtained centrally over the moving surface. Indeed, the wetting front detached from the individual HJ fronts at the region above the Int-Z because of a returning interaction flow. At the same Vp, the wetting zone was expanded further far from the jet centerline and a bigger local central enlargement was obtained at 15 L/min jet tests. Faster moving plates (Vp = 1.0 m/s) present a smaller bump ahead of the interaction region. No local enlargement along the wetting front had appeared at for Q = 10 L/min, Vp = 1.5 m/s tests and two complete noncircular colliding HJs had taken place above the impingement point as a wetting front at the moving surface (Figure 115  5.10a). But, the small swelling eventually occurred ahead of Int-Z which 10 L/min, Vp = 1.5 m/s tests. The plate motion, on other hand, facilitates the flow drainage from the Int-Z after the jets’ centerline; it spreads while diverting from the centerline of the Int-Z. The delivery flow after the Int-Z spanned a larger area over the impingement surface at a lower plate velocity (parts b). In the experiments Q = 10 L/min, Vp = 0.6 m/s, the inner wall jets were distinguishable from each other and did not merge at the Int-Z as seen before on a stationary plate. However, this separation disappeared for the tests at Vp =1 and 1.5 m/s which is an indication of the effect of confinement ahead of the Int-Z due to plate motion. For 15 L/min jets, the wall jet separation at the interference region was hardly detected in the Vp = 0.6 m/s tests. Generally, no splashing was detected during all experiments.  116  (a)  (b) Figure 5.10 The Interaction of 10 L/min Jets on the Moving Surface at Different Velocities (N = 2, H = 1.5 m) (a) Top View (b)  117  (a)  (b) Figure 5.11 The Interaction of 15 L/min Jets on a Moving Surface at Different Velocities (N = 2, H = 1.5 m) (a) Top View (b) Front View  5.5.3 Data Measurements (H = 1.5 m) As mentioned in the section 5.3, the Int-Z was measured at each repetition test and the collected data was obtained for each series. The general aspect of the effect of plate motion on multijet impingement can be drawn from the resulting plots. Figure 5.12 depicts the accumulated data from all repetitions in the series of experiments of 10 and 15 L/min jets on a moving plate. Interestingly, some features which were explained before  118  are reflected in the data measurement. For lower Q (10 and 15 L/min), the interaction film was thinning as the plate moved faster. The fronts of HJs were measured partly up to  Figure 5.12 Data Measurements of Int-Z (N = 2, H = 1.5 m, 10, 15 L/min) (a) Vp= 0.6 m/s (b) Vp = 1.0 m/s (c) Vp = 1.5 m/s  119  above the impingement points. The moving plate pushes back the wetting front (HJs) when Vp increased. For 10 L/min jets, the HJs are approximately at around Y/d  5.5 for Vp = 0.6 m/s and above Y/d  3.5 for Vp = 1.5 m/s. But for a 15 L/min jet, the HJs are roughly at Y/d  6 for Vp = 0.6 m/s and above Y/d  4 for Vp = 1.5 m/s. The jets of 15 L/min jet, keeps the HJs at a larger distance above the impingement points with respect to Q = 10 L/min jet at the same plate speed but thicker interaction film is obtained at 15 L/min. These results are in accordance with what found before for 10 and 15 L/min jets. The approximate measured magnitudes of the radius of HJ (Y/d) for each of the 10 and 15 L/min jets are comparable to Rj values which were found from single impinging jets on a moving plate (Table 4.4) for same jet flow rate. The wetting front from single (N = 1) and twin jets (N = 2) experiments of Q = 10 L/min and Vp = 1.5 m/s is shown at Figure 5.13, double curved wetting front due to twin jet test but single curve wetting front due to single jet test. The impingement point of single HJ was originally at the centerline of the plate but it was shifted along the jets centerline at two sides as –s/2 and +s/2 for sake of comparison and coinciding it with the two impingement points for twin jets test. Therefore, two offset interaction single HJ are created similar to double curve wetting front. Both inner and outer fronts in twin jets (N = 2) show that the HJ interaction starts near the intersection point of two offset single HJs (N = 1) along the stagnation line. The outer wall jets spread individually untouched similar to single nozzle experiments. It has to be noted that the Q variation for jets were not identical during these two tests and the impingement points of twin jets were not coincident with the shifted impingement points of the curves from single nozzle test. However, the wetting front from twin jet is reproduced well by two intersecting wetting fronts for single jet and the double curved wetting front due to twin jet can be assembled approximately from two individual interacting HJs. The wetting fronts of interaction HJ were obtained from one test in the series of experiments but the overall checking of other repetitions support this result. Therefore, the interference of HJ of inner wall jets on moving plate depends to angular direction of radial stream as well.  120  Figure 5.13 Wetting Front for Single and Twin 10 L/min Jets Experiments (H = 1.5 m, Vp = 1.5 m/s) (a) Inner Fronts (b) Outer Fronts  5.5.4 22 and 30 L/min Jets Experiments Figures 5.14 and 5.15 illustrate the 22 and 30 L/min experiments on various plate velocities at the top (part a) and front (part b) views from the same test, respectively. The larger pool of water ahead of Int-Z was formed and the wetting front was forced further far respect to the lower Q tests. The returning flow from the Int-Z launched larger bump long the stagnation line outward with a higher growth rate due to strong jets interaction. The upwash fountain was obtained with a noticeable splashing particularly at the beginning. But, it gradually decreased progressively after the development of wetting front over the moving surface. For 22 L/min test, a high raised upwash fountain started the transition to a liquid sheet from the upside of the Int-Z. Finally, the splashing was reduced tremendously and a low stand up oscillating liquid layer was established entirely at the Int-Z (Figures 5.9, 5.14b) similar to Int-Z at lower Q test. Faster converting was detected at higher Vp where the wetting front is closer to above the Int-Z. For Vp = 0.6 m/s tests, the wetted front was most distant from Int-Z and then the splashing erupted with more intensity. Therefore, the transfer in the interaction flow started later and did not extend fully through the Int-Z. For 30 L/min test, a stronger upwash fountain resulted with a bigger pool of water ahead. Intensified splashing had occurred because of the collision of high strength wall  121  (a)  (b) Figure 5.14 The Interaction of 22 L/min Jets on Moving Surface at Different Velocities (N = 2, H = 1.5 m) (a) Top View (b) Front View 122  (a)  (b) Figure 5.15 The Interaction of 30 L/min Jets on a Moving Surface at Different Velocities (N = 2, H = 1.5 m) (a) Top View (b) Front View streams. The water eruption decreased but did not diminish as seen in the 22 L/min test. For a faster plate motion, a less intensified splashing was detected. Careful assessment of the films revealed that the shift at upside of the Int-Z over the moving surface started with reduced splashing and thicker sheet but is more detectable over a faster moving surface (e.g. Vp = 1.5 m/s at Figure 5.15a) where the wetting front was the closest to the Int-Z end. This was not observed at Vp = 0.6 m/s tests. However, the transfer performed partly and did not settle down as observed for the 22 L/min jets. Indeed, the effect of moving 123  plates is least comparable to other jet flow rate tests and the fountain features are mostly controlled by parent jet conditions. Therefore, the splashing was persistent and the upwash thin fountain flow structure was not changed to a non-splattering liquid layer (figure 5.15b) although the transition was started somehow (Figure 5.15a). Wetting front detaching from HJs was established fully almost at all Vp tests. The HJ was not visible on a stationary plate for the 22 and 30 L/min tests. Actually in these cases, the HJ may happen at a large radius which not captured by the camera. However, HJs appeared at the moving plate (Figures 5.14a and 5.15a). Actually, the wetting front after the HJ influenced the jumps location and made it smaller. This is similar to the controlling effect of the rim around the plate border on the HJ. It is a method used in experimental studies to position and configure the CHJ by changing the height of the rim [38, 46]. Therefore, the plate motion influences both the HJs and interaction region simultaneously by controlling the wetting front.  5.5.5 Data Measurements (22 and 30 L/min) The data measurements for 22 and 30 L/min tests are shown in Figure 5.16. For 22 L/min jets, the measured Int-Zs were thinner for Vp = 0.6 and 1.0 m/s tests but thicker for Vp = 1.5 m/s tests. Actually for Vp = 1.5 m/s tests, the measurements were carried out when the transition completed at Int-Z. However, the thinness of liquid fountain sheet is not apparent from measurements on the lower plate velocities (Figure 5.16). Due to splashing, it is not possible to capture the upwash fountain adequately by top and front cameras and then the thick Int-Z was obtained especially at 30 L/min due to high strength splattering. Therefore, the measurement was not finished for 30 L/min tests. These measurements reveal that the impingement point is not fixed below the nozzle and its position was changing around the geometrical center of the jet over the plate surface. For higher jet flow rates, larger variations were obtained; the oscillation was up to 3/4d (d is nozzle diameter) in the case of the 30 L/min jet. Variable instantaneous position of the impingement point was from jet unsteadiness. Therefore, opposing wall inner jets had variable velocity which promoted instability of the flow field at Int-Z.  124  Figure 5.16 Data Measurements of Int-Z (N = 2, 22, H = 1.5 m, 30 L/min) (a) Vp = 0.6 m/s (b) Vp = 1.0 m/s (c) Vp = 1.5 m/s  125  5.5.6 Interaction Zone Transition The change in the flow field character at the Int-Z from the upwash high rise fountain to a low stand up liquid layer with no splashing is a direct effect of a moving plate which not seen before at lower jet flow rates or at stationary plate tests. The complex flow results at the regions below and above the Int-Z over the plate surface due to the interfering the exiting flows from the Int-Z outlets with the radial inner wall streams and the HJs. At the stationary surface, the conditions at both upside and downside the Int-Z are the same. However, the plate motion presents different boundary conditions at two outlets of the Int-Z. Above the Int-Z over the moving surface, the outflow delivery constrains by the attached wetting front directly at 1.5 m/s tests or by the pool of accumulated water bounded with a wetting front at Vp = 0.6 m/s test. On the other side, the returning interaction flow is freely drained below over the plate surface and is also accelerated by the plate motion. Therefore, different outflow conditions occur at ends of the Int-Z over the moving plate surface and the drainages from both ends are not the same. If consider the Int-Z as a control volume (see Fig. 27) then the change in the outlets condition is necessary to maintain comparable drainages and accommodate the balance between outflows and inflows although some water erupts outside by splashing. Moreover, the effect of plate motion can be considered as superposing a Couette flow to beneath the Int-Z which increases the flow flux in direction of motion. Indeed, the transition from thin upwash to thick film started from upside of the Int-Z where the exiting flow push the wetting front forward to lift its limiting effect on drainage ahead of Int-Z such as seen in the present 22 and 30 L/min experiments. Therefore, the moving surface could change essentially the characteristic and flow structure of Int-Z. This has been not reported in the literature yet. Figure 5.17 illustrates the sequence of the Int-Z alteration occurring in a test of Q = 22 L/min, Vp = 1.5 m/s. The upwash thin fountain formed after the jet interactions initiated (images 1 and 2 Figure 5.17) but gradually the thick interaction layer was visible at upper end of the Int-Z near the wetted front as it was swelling. The splashing fountain disappeared gradually and was replaced by the thick non-splashing interaction layer (images 3 and 4). Ultimately, the alteration encompassed the Int-Z entirely (images 5 and 6). But compared to the Int-Z observed for lower jet flow rates of 10 and 15 L/min  126  (Figures 5.10 and 5.11) the new Int-Z is highly raised and greatly oscillating (as shown for Vp = 1, 1.5 m/s in Figure 5.14b). The oscillation of a new thick and tall interaction dome-shape is related directly to the higher level of unsteadiness in jets of 22 L/min and stronger interactions at these conditions.  Figure 5.17 Simple Schematic of Int-Z as a Control Volume  Figure 5.18 Int-Z Alteration (N = 2, H = 1.5 m, 22 L/min, 1.5 m/s)  127  5.6 Experiments with Three Nozzles on Stationary Plate (H = 1.5 m) The experiments were conducted with three in-line circular water jets (d = 19 mm) at jet spacing s = 101.6 mm or 4 in (s/d  5.35) and the jet flow rate of Q = 10 – 22 L/min. Figure 5.19 illustrates the three jet interactions on a non-moving plate for 10, 15, and 22 L/min flow rates at top and front views. An interaction had occurred between each of the two neighbouring jets and the two interference regions were obtained. The strong upwash high-rise liquid fountains were created due to strong interactions; the jets space became half at the same flow rates and then the inner wall jets met the others at a higher velocity and stronger interaction resulted. Therefore, the jets are adjacent. For higher Q jets, higher rise fountains are created. For a lower Q jet, a thinner upwash liquid sheet was expected (Figure 5.19). The splashing is more intensified and higher stand up with respect to twin jets at the same Q (Figures 5.4b, 5.19). The fountains are more unsteady as well; three impingement points were oscillating and the three flow rates were not identical. The central jet influenced both fountains and then its Q variation and its impingement point oscillation are important. However, each fountain oscillation at the interjet distance is the result of central and one side jet conditions.  5.7 Experiments of Three jets on Moving Plate (H = 1.5 m) The three 10, 15, and 22 L/min jets impinging on the plate moving at 0.6, 1.0 and 1.5 m/s velocities were tested.  5.7.1 Flow Observation Figures 5.20a and b show sample images from a 10 L/min test on 1.0 m/s moving plate from top and front views of the same tests, respectively. Inner wall jets collided soon after the starting of impingement even for low flow rate jet of 10 L/min and two upwash fountains formed. Noticeable water blow up were obtained from the two Int-Zs because the inner wall jets met at a smaller distance (higher velocity) with respect to the twin jet case. Afterward, a pool of water covered a large area ahead of the Int-Zs because of larger amount of water pouring over the impingement surface by the three jets. Then the splattering of upwash fountains water dropped during the test. For the twin 10 L/min impinging jets, however, a thick interaction film occurred with no splashing.  128     Figure 5.19 Three jets Interaction on Stationary Surface - Top and Front views (H = 1.5 m) Q = 10 L/min (b) Q = 15 L/min (c) Q = 22 L/min (1. Free Jet, 2. Inner Wall Jet, 3. Outer Wall Jet, and 4. Upwash Fountain)  The wetting zone took place at the plate surface further away at these tests with respect to the twin jets or a single jet at the same jet flow rate and plate velocity. This also affects the interaction flow transition because the wetting front does not remain close to the Int-Z  as the twin impinging jets. An incomplete transition may be observed at higher plate speeds. The impingement flow evolution and jet interaction for other jet flow rates and plate speeds are similar. Next, these experiments are presented.  129  (a)  (b)   Figure 5.20 Sample Images for Impingement Flows Development and Jets Interaction (N = 3, H = 1.5 m, 10 L/min, 1.0 m/s) (a) Top View (b) Front View  130  5.7.2  10, 15 and 22 L/min Jets Experiments  Figures 5.21-5.23 illustrate the sample images from impingement flows development and the jets interactions of 10, 15, and 22 L/min three water jets (parts (a) for top view and parts (b) for front view). Generally, the upwash high rise fountains at the two Int-Zs with powerful splashing and the flood of impingement water are the pertinent features in the three impinging jet tests. The size of wetted zone over the plate surface depends on both Q and Vp. For a given Q, a smaller water pool was formed on the faster moving plate (see Vp = 1.5 m/s tests in the figures). The returning flow from Int-Zs made two bumps along the wetting front ahead of the fountains. The double swelling is clearly seen at Vp = 1.5 m/s tests for each flow rate (Figures 5.21a-5.23a) because the wetting front is closer to the fountain outlets. The front views demonstrate that the higher strength eruption of water results from a higher jet flow rate at the same Vp although this view does not show clearly what happened at the wetting front nearby. For higher plate speed (Vp = 1.5 m/s) experiments at every Q, the moving plate influenced more portion of the mainstream impingement flow and smaller wetting zone occurred over the faster moving plate; the wetting front was displaced to the Int-Zs nearby. More closely approaching the wetting front results a greater restriction on the drainage above the interference region. Consequently, the beginning of transition at the Int-Zs may be occurred. The film assessments of the three jets tests revealed that the splashing from upside of the upwash interaction flow is decreased greatly near the end of the Vp = 1.5 m/s test. Actually, the white bright regions appeared connected to the upper end of the fountains and developed more during the test at the rear white part of the plate. This is also observed for the 30 L/min twin impinging tests. The start of the transition is more visible for the 10 L/min tests because the effect of plate is more pronounced. However, the two upwash fountain sheets were strong and then longer plate is needed to demonstrate better the start of the transition. Generally, the transition in the Int-Z occurred whenever the wetting front stays too close in the case of faster plate motion.  131  (a)  (b)   Figure 5.21 The Interaction of 10 L/min Jets on a Moving Surface at Different Velocities (N = 3, H = 1.5 m) (a) Top View (b) Front View  132  (a)  (b)   Figure 5.22 The Interaction of 15 L/min Jets on a Moving Surface at Different Velocities (N = 3, H = 1.5 m) (a) Top View (b) Front View  133  (a)  (b)   Figure 5.23 The Interaction of 22 L/min Jets on a Moving Surface at Different Velocities (N = 3, H = 1.5 m) (a) Top View (b) Front View  5.8 Experiments on Moving Plate with Lower Nozzle (H = 0.5 m) The nozzles were lowered to H = 0.5 m to gain a higher velocity ratio. For a given jet flow rate, the same amount of impingement water spread at a smaller velocity while the plate speed was kept the same as before. For H = 1.5 m experiments, the velocity ratio was 0.11 < Vp / Vimp < 0.28 at Q = 10-30 L/min and Vp = 0.6-1.5 m/s. But for H = 0.5 m tests, 0.18 < Vp / Vimp < 0.47 at Q = 10-22 L/min and Vp = 1.0, 1.5 m/s; 10 L/min 134  experiments had a higher velocity ratio. Higher plate velocities were chosen to elevate the velocity ratio. Although at a mill operation scale the velocity ratio is about 0.5 < Vp / Vimp < 2.5 but improving the velocity ratio at a lower height is noticeable. The nozzle distance did not change (s/d = 5.35).  5.8.1 Experiments of Twin Jets on Moving Plate (H = 0.5 m) Figures 5.24-5.26 show the sample images taken from 10, 15, and 22 L/min experiments at various plate speeds. Thick dome-shape interaction films were obtained for Q = 10 and 15 L/min experiments without splashing (Figures 5.24 and 5.25). The front views were similar to the series of experiments with the same parameters (Q and Vp) at H = 1.5 m (see Figures 5.10b and 5.11b) and were thus not repeated here. Similar to H = 1.5 m experiments for 10 and 15 L/min jets, a bump ahead of Int-Z was induced for during Vp = 1.0 m/s tests. The bump enlargement depends to Q and Vp. Lager central swelling at wetting front occurred at higher Q for same Vp = 1.0 m/s tests but no swelling or small one detected at Vp = 1.5 m/s test (Figure 5.24, 5.25). In general, wider Int-Z occurred on slower plate moving. A narrow Int-Z was detected at the beginning of jet interaction but then thickened and widened particularly during the experiments; the effect of moving plate developed and influenced larger part of two inner wall jets during the tests. The two inner wall jets remained separated at 10 L/min, 1.0 m/s experiments but joined at the 1.5 m/s moving plate. These experiments again demonstrated the effect of a moving impingement surface on flow hydrodynamics features at the Int-Z.  135  Figure 5.24 The Interaction of 10 L/min Jets on a Moving Surface at Different Velocities – Top View (N = 2, H = 0.5 m)  Figure 5.25 The Interaction of 15 L/min Jets on a Moving Surface at Different Velocities – Top View (N = 2, H = 0.5 m)  136  Figure 5.26 The Interaction of 22 L/min Jets on a Moving Surface at Different Velocities (N = 2, H = 0.5 m, Vp = 1.5 m/s)  For 22 L/min (Figure 5.26), the jet interactions initiated an upwash fountain with splashing which was weaker with respect to its counterpart in the H = 1.5 m experiments. However, similar to those tests, the transition to a thick high stand up wide interaction with a nonsplashing dome-shape occurred but earlier than in the H = 1.5 m case. The plate motion more efficiently influenced the weaker interaction of the two 22 L/min lower speed inner wall jets over the plate surface. The sample images front view from this transition at the same experiment are shown in Figure 5.26 as well. Plate motion successfully changed the mode of jet interactions and splattering reduced tremendously or was diminished at the end of the plate. Therefore, the conversion of whole interaction zone almost happened completely over the plate surface.  5.8.2 Data Measurements for Twin Jets (H =0.5 m) Figures 5.27-5.29 plot the accumulated data from all repetitions in the series of experiments of 10, and 15, and 22 L/min jets on a moving plate for two heights of the nozzles, respectively. The measurements for 22 L/min were accomplished after upwash fountains transformation. Similar features for two nozzle heights can be seen. For each flow rate, a wider interaction zone is obtained on slower plate moving. For a higher Vp, a smaller HJ and closer wetting front resulted. Generally, the HJ fronts for shorter and longer jets were comparable which demonstrates that the jet height is not significant for HJ for a given flow rate. This is reported in literature for CHJ due to single jet as well  137  [47, 53]. The jet velocities moderated 40% at the H = 0.5 m case but was insignificant of the HJ front. Therefore, the jet velocity was of secondary importance and jet flow rate and Vp are the most important parameter in shaping the HJ (wetting front) for twin water impinging jets.  Figure 5.27 Data Measurements of Int-Z (N = 2, 10 L/min)  138  Figure 5.28 Data Measurements of Int-Z (N = 2, 15 L/min)  Figure 5.29 Data Measurements of Int-Z (N = 2, 22 L/min, Vp = 1.5 m/s)  139  5.8.3 Experiments of Three Jets on Moving Plate (H = 0.5 m) Every jet flow rate of 10, 15 and 22 L/min was tested for 1.0 and 1.5 m/s moving plates. Figures 5.30 to 5.32 show the sample images from the interactions of the jets. Parts (a) of the figures show the top view and parts (b) the front view the same experiments. Both the top and front views are shown in Figure 5.32. Generally, two upwash fountains were obtained due to three adjacent jet interactions but with less splashing and unsteadiness at a given Q respect to higher nozzles tests. The highest water eruption was detected at 22 L/min experiments. The faster moving the plate, the lower the stand up splattering had detected for a given Q. The upwash sheets were weaker and thinner with respect to the previous tests at H = 1.5 m. Therefore, the thinness and outer uneven arc rim of the upwash sheet are more evident from the top view images in 10 L/min tests (see Figure 5.30a) but was difficult to capture in 15 L/min experiments. These were not clearly seen before at the H = 1.5 m case. At three nozzles tests at H = 1.5 m, the transition was not effectively started and spread into the Int-Zs even at Vp = 1.5 m/s. However in the lower nozzle case (H = 0.5 m), the moving plate crushed the fountains due to three 10 L/min jets and successfully converted them to nonsplashing thick and wide dome-shape Int-Z zones. Figure 5.30 illustrates that the upwash splashing fountains at Vp = 1.5 m/s tests were transformed to thick high raised buckets of water and the splashing disappeared. This has not occurred previously because the stronger parent jets created higher strength upwash interaction flows. Therefore, moving plate can conquer the splashing fountain due to close spaced jets depends on the velocity ratio; it converted the fountain at the distant jets previously but not at the adjacent jets setup. However, the transition had not taken place over the surface for the 10 L/min, 1.0 m/s experiments; the water front is further far from the heading end of Int-Z. The velocity ratio at Q = 15 L/min, Vp = 1.5 m/s tests is higher than the Q = 10 L/min, Vp = 1.0 m/s test. Then, white and bright regions were built up above the Int-Zs and the splashing faded more there (Figures 5.31a, b). However, the 1.0 m/s plate cannot agitate the conversion for 15 L/min jet interactions. The 22 L/min jet interaction is strong enough to preserve the upwash fountain identity even for a Vp = 1.50 m/s moving plate (Figure 5.32) and then the images for the Vp = 1.0 m/s tests were not shown to avoid 140  repetition. Splattering was kept during all the 22 L/min tests. A higher velocity ratio or longer plate is needed for transition at this Q.  (a)  (b)  Figure 5.30 Interaction of 10 L/min Jets on a Moving Surface at Different Velocities - (N = 3, H = 0.5 m) (a) Top View (b) Front View  141  (a)  (b)  Figure 5. 31 Interaction of 15 L/min Jets on a Moving Surface at Different Velocities - (N = 3, H = 0.5 m) (a) Top View (b) Front View  142  Figure 5.32 The Interaction of 22 L/min Jets on Moving Surface Top View (N = 3, H = 0.5 m, Vp = 1.5 m/s)  5.8.4 Fountain Asymmetry Figures 5.30 and 5.31 illustrate briefly the fountain unsteadiness and asymmetry. The upwash sheet formed along the wavy stagnation line did not stay unchanged at the interjet space. Sometimes, it was inclined toward one jet and was not vertical. Figure 5.33 shows the fountains due to three 10 L/min jets during a Vp = 1.0 m/s test. The low flow rate experiment was chosen to be able to capture fountain clearly by the front camera. The nozzles Q were fluctuating and the impingement points were oscillating. By checking frame-by-frame film and the recorded nozzles flow rates, it was discovered that the inclination of fountains was influenced by the relative Q amongst the nozzles at that instant and also by the relative distance between the impingement points. For example, if the impingement point of the side jet moved inward, then the fountain between this jet and center jet will tilt toward the center jet. Therefore, fountain symmetry and uprightness were disturbed by different variable Q and unequal neighbouring jet distances over the impingement surface. It was also noted from the films of the front camera that the plate was not always kept horizontally during motion through tracks at the acceleration zone before entering the test site; it went up and down but moved straight ahead during the test. This may have also induced vibrations from the long plate to the impingement flow. Indeed, the plate was secured to test bed at a 1.2 m length and has two free ends. However, it does not have major effect. Interestingly, more asymmetry was  143  detected, in general, for Vp = 0.6 m/s tests when the effect of plate motion is least to counteract the jets. On other hand, the best results were obtained over a Vp = 1.5 m/s moving surface. Therefore, the interaction zone is mainly impacted by jets conditions although some other minor factors are also influential such as unidentical nozzle spaces or alignment but these parameters have a secondary effect. Moreover, great care was devoted everyday to the nozzles and plate conditions before starting the experiments (as explained at the beginning of this chapter).  5.8.5 Data Measurements for Three Jets The measurement was also done for three jets (H = 0.5, 1.5 m) from the top view images. Although many efforts took on measurements, the top view images did not represent the thinness of upwash fountain. The plots are available in Appendix D.  5.9 Summary and Conclusion In this chapter, the liquid jet interactions were studied experimentally by two and three impinging jet configurations. Depending on the nozzle spacing, distant and adjacent jet  Figure 5.33 Fountain Unsteadiness and Inclination during a Test (N = 3, H = 0.5 m, 10 L/min, Vp = 1.0 m/s)  144  interactions produced thick interaction films and upwash splashing fountains, respectively, at the stationary plate. The jet Q and the plate Vp were systematically changed to inspect the influence of plate motion. On a moving plate, the same interaction types were obtained when the plate motion was slow or the jet interactions were strong due to the high jet Q. However, the plate motion can essentially change the Int-Z characteristics if the effect of plate motion is enhanced enough (lower Q or higher Vp). The wetting front vicinity to Int-Z plays is important. The interaction flow identity transforms from a splashing upwash fountain to a weak nonsplashing interaction domeshape region (e.g. Figures 5.14 and 5.18 for twin jets). The transition of the interaction region was successfully performed for the adjacent three jets (close nozzles) by lowering the nozzle (H = 0.5 m) which is not possible at H = 1.5 m tests due to higher strength interactions or stronger parent jets. In addition to Int-Z, the plate motion influences the individual HJ due to each jet and the wetting front controls HJ radius as well; HJ from 22 and 30 L/min was not captured on stationary plate because of large radius but it is evident on moving plate.  145  Chapter 6 Numerical Simulations  The flow field due to impinging water jets was simulated numerically with laminar and appropriate turbulent models. The numerical modeling and the results are presented in this chapter.  6.1 Turbulent Flow Modeling The mass and momentum conservation equations for incompressible laminar flow (Navier-Stokes equations or N-S Eqn.) with constant density and viscosity are given by [see for example: 52, 96]  U i 0 xi    U i U i p   U j   t x j xi x j  6.1   U U j    i  xi   x j     g i    6.2  where Ui are the components of the velocity vector U, p is pressure, ρ is density, μ is viscosity and g is body force (e.g., gravitational acceleration) and xi are the coordinate directions. If the flow is turbulent then the velocity and pressure are not constant and ___  have fluctuating parts (e.g. for velocity U i  U i  ui' where U i is the mean part and ui is  the fluctuating part). Then the governing flow equations will be  146  ___  U i 0 xi  6.3  ___ ___ ___ __   ___ ___  Ui Ui  p    Ui U j   U j     t x j xi x j   x j xi      _______    u' u'    g i i j      6.4  where U and p are mean magnitudes of the velocity and pressure, respectively, and u _______ ' i j  and p are their fluctuating parts, respectively. The  u u  term in the time-average  momentum equation 6.4 is the source of difficulty because it is not known a priori and turbulent modelling is needed for its calculation. This term is called turbulent Reynolds  stress tensor and the equation may be written as: ___  ___  __  ___  Ui Ui  p  ij   U j     gi t x j xi x j  6.5  ___  ___  _______  U  U j   i    u 'i u 'j  ij    x j xi       Turbulent  6.6  Laminar  Equation 6.6 is written by considering mathematically similar role of Newtonian viscous _______  stresses for the  u ' u ' term. Therefore, it is traditionally treated as molecular shear and i  j  normally called turbulent shear t but doesn’t have physical meaning. For example in 2-D turbulent flow it is defined as ____ ' '   t    u v  t  u y  6.7  where t is eddy viscosity with the same dimension of . Reynolds stresses, in general, is found based on Boussinesq hypothesis [96, 108] from mean velocity gradients and assuming t as isotropic scalar quantity; __  __  Ui U j   u u  t   xi  x j  _____ ' ' i j    2   3 k ij    6.8  147  ______ ' '  where k is turbulent kinetic energy k  1 / 2( u i u i ) and ij is Kronecker delta. Then one can solve equation 6.3 and mean momentum equation 6.4 for turbulent flow; these equations are called Reynolds-Average Navier-Stokes (RANS) thereafter. This method has the advantage of low computational cost but the fluctuating parts of velocity components and turbulent parameters are not obtained. Hence, many turbulent models have been developed afterwards by introducing mostly semi-empirical correlations for turbulent parameters. They were developed in different ways including kinetic energy k, turbulent dissipation ( ), turbulence length scale, vorticity fluctuations ( ) and various stress relations. They are classified according to the number of extra equations introduced to solve the governing equations such as two equations k- and k-. Another approach is to model each Reynolds stress term separately (Reynolds stress model RSM) which increases the extra equations for closure. The abovementioned models are commonly called RANS-based models. There are more turbulent models such as largeeddy simulation (LES), direct numerical simulation (DNS), etc. These sophisticated models are, in general, complicated and numerically expensive. Acceptable accuracy and reasonable computational cost makes two equations turbulent models as a best candidate for flow and heat transfer simulations of industrial applications [96, 117].  6.1.1 Two Equations k- Turbulent Model In the one equation turbulent models, an equation for kinetic energy k is utilized to find out the eddy viscosity. But in k- model proposed first by Launder and Spalding [118], one more equation for  is coupled with k equation. The transport equations for k and  _______________  (  (  /  ) (ui' / x j ) 2 ) as dissipation rate of k are [96, 119]    ___  k k   U j x j x j t   t    k    k     Pk    x j   6.9    ___      U j x j x j t   t           2    C1Pk  C2  k k  x j   6.10  148  _____ ' ' i j  ___  Ui Pk    u u x j  6.11  The constants are empirically found for attached boundary layer flow as k = 1,  = 1.3, C1 = 1.44 and C2 = 1.92 but they are not universal and have to be found for other  problems [119]. Once k and  are obtained from equations 6.9 and 6.10, the turbulent eddy viscosity is modelled as  t  C   k  2    with C = 0.09 and, then, mean momentum  equation 6.5 can be solved by implementing t in equation 6.8. The k- turbulent model is mainly developed for the simulation of engineering high Re number turbulent flows far from the wall [117]. The original version of this model did not consider the molecular viscosity and it was valid up to above the wall. Therefore, many improvements have been implemented to apply this model to wallbounded low Re flows by investigating different eddy viscosities and deriving new transport equations for dissipation rate (). Indeed for wall treatment [e.g. 120], some semi-empirical functions (wall function) are set to link velocity and turbulent parameters at the wall to the corresponding variables at the cells near the wall. The wall functions save the computational time because the grid does not resolve the region just above the wall and it is modelled with wall functions. In addition, special wall functions called nonstandard wall function have been developed to improve the accuracy for case of pressure  gradient and rapid gradient such as jet impingement (see for example [121]). The twolayer model [117] is another approach to account for the wall effect. The whole domain is split into a region of fully turbulent outer flow (solving by k- ε model) and a small region of wall viscosity affected (solving by one equation for k). The variables are then blended across the interface smoothly. This needs finer mesh above the wall leading to more computational cost. In this study, the non-equilibrium wall function method was selected in k- ε simulations because the boundary layer is not of particular interest here. The wall functions are available in different versions of k-ε turbulent model. In general, the standard and traditional k-ε models (SKE) are not recommended for impinging round jet where the pressure gradient and strong streamline curvature and vortices are prominent [117, 121]. The realizable k-ε model (RKE) [120] is a recent 149  improvement which predicts jet spreading rate more accurately than standard model specifically for round jets. Kim et al [122] compared wall functions (standard and nonequilibrium) with two-layer method for the variants of k-ε model (SKE, RKE, etc). The non-equilibrium wall functions with RKE and other advanced k- ε models presented best results in comparison to the measured data for 0 and 6 wall-angles. The two-layer model with any turbulent models gave better physical meaning to velocity field but predicted poorly the measured data even with finer mesh (almost doubled the cell number). RKE model was used in k-ε simulations.  6.1.2 Two Equations k- Turbulent Model The turbulent k-ω model, first introduced by Wilcox [123], is a popular model for low Reynolds near-wall flows because of resolving the turbulence up to the wall without using wall damping functions which required correcting the k- behaviour at wall vicinity. The k-ω model is based on k and specific dissipation rate ω [108] which present two extra equations to the mean momentum equation  k ___ k  U j x j x j t    * k *     t   Pk   k  x  j   6.12   ___   U j  t x j x j      2    t     Pk   k x j    6.13  t       k  6.14    The model constants are found as  = 5/9,  = 3/40, * = 0.09,  = 0.5, * = 0.6 by examining boundary layer in different cases for incompressible flow [120]. This is standard versions of k-ω model (SKW). Wilcox [124] improved the original model by variable s coefficients. Moreover, shear-stress transport k-ω model (SST) [e.g. 125] has been developed as a combination of a low Re k-ω model used at inner region of boundary layer and a transformed high Re k- model used at outer free stream region far from the wall. This model is used in our numerical simulation. At the domain above the plate surface, the realizable k- model is suitable for high Re turbulent jet pre-impinging. On 150  other hand, the k- ω model is a good choice for thin impingement water layer while propagating over the plate surface. The k- ω models is more computationally expensive with respect to k- model because of resolving the whole domain by the grid up the wall.  6.2 Volume of Fluid Method (VOF) The Volume-of-fluid (VOF) [126] is a well known multi-phase method to trace the interface of two immiscible fluids in a mixture. VOF method was utilized in these twophase (e.g., water and air) simulations to construct the surface of incoming free surface jet before impingement and the free-surface of water film and wetting front after impingement. By defining the scalar parameter f for each phase, the volume fraction of the fluid inside each cell is determined and the phase is located in the domain; for example, scalar f = 1 means a cell full of water and f = 0 stands for an empty cell, whereas cells with 0 < f < 1 indicate the interface between air and water. In each control volume (cell), the total volume fraction of the two phases is unity. Thus the variables and properties of each cell (, ) is of one phase (f = 0 or 1) or of a mixture of phases (0 < f < 1). If index w stands for water (fw) and a for air then     w f w   a (1  f w )  6.15     w f w  a (1  f w )  6.16  The continuity equation for volume-fraction of one phase can be used to track the interface   f      fU   0 t  6.17  Therefore, the region of each phase is demarcated inside the domain. The velocity vector U which is shared amongst phases will be found by solving one momentum equation for  the entire domain,       U     ( UU)  p     U  UT  g t  151  6.18  6.3 Numerical Simulations of Stationary Plate The three long water jets of 15, 30, and 45 L/min were modelled numerically on experimental conditions of fixed test plate (Table 6.1) by laminar and different turbulent models using CFD package FLUENT 6.3. The available turbulent models in FLUENT are Spalart-Allmaras model, k-ε models, k-ω models, the RSM models, and the large eddy simulation (LES) model. According to the discussion in the literature review (section 1.2.6), there is no RANS turbulent model to predict all aspects of flow hydrodynamics and heat transfer accurately over the entire area of impingement plate. Moreover, there is no general acceptance of one turbulent model for all classes of problems. RANS-based methods utilize the average flow variables with whole scale of turbulence which decreases significantly the computational cost and is accepted broadly in engineering applications [96]. However for higher classes of the turbulent models such as LES and DNS, the additional computational resource and efforts are not justified yet through an established practice in industrial CFD applications [114]. Therefore, versions of two-equation k-ε and k-ω models were considered for the present industrial numerical simulations, particularly the RKE and SST models. The main objective in these simulations is the overall assessment of industrial jet impingement at ROT scale using low cost turbulent models available in FLUENT. These include tracking the spreading of impingement layer and the CHJ on stationary plate and achieving the overall understanding of fluid flow over the moving plate while capturing wetting fronts (HJ) and tracing the velocity field. The two RKE and SST models seem sufficient to serve these aims.  dj (mm)  19  Table 6.1 Jet Parameters Vimp Q V Re (L/min) (m/s) (m/s) 15 0.88 16,690 5.49  Reimp  41,666  30  1.76  33,380  5.7  60,032  45  2.65  50,068  6.03  75,627  152  6.3.1 Numerical Procedure The circular water jets were solved through transient flow Navier-Stokes equations (equations 6.1 to 6.4) using finite volume method along with the VOF method. Laminar and the suitable turbulent models for liquid jets (RKE, SST) were examined in the present numerical simulations. The system of governing equations is integrated over finite volumes and a set of linear algebraic equations in terms of velocity and pressure are obtained. The computations used implicit first order discretization for time (available with VOF), second order upwind schemes for momentum and turbulence model parameters, combined with a geo-reconstruction scheme for the VOF discretization. The pressure and velocity were coupled by Pressure-Implicit with Splitting of Operators (PISO) scheme which recommended for transient simulations. The set of algebraic equation then solved sequentially using iterative method. In general, the normalized residuals were set at O (10-4) for continuity and O (10-6) for velocity and turbulent parameters for solution convergence. The details of the above formulations and schemes are available in the FLUENT user guide. The air and water were considered at atmospheric condition with constant properties; for water ρ = 998.2 kg/ m3 and μ = 1.003e-3 kg/ m.s and for air ρ = 1.225 kg/ m3 and μ = 1.7894e-5 kg/ m.s and σ = 0.0728 N/m for water/air.  The transient simulations were performed long times (e.g. 5,000 -10, 000 more time steps) after the water layer fully covered the plate surface and an almost unchanged condition was established. The time step was usually 1-2 10-5 sec or smaller and the Courant number was kept below 1 to avoid crashing the solution. Therefore, the computation for each case was run for hundreds of thousand time steps and the elapsed time was in terms of weeks. Generally, the computational for fixed plate cases was costly due to long time needed for covering the plate by impingement water and establishing steady condition; regular PC machine could not accommodate these simulations and FLUENT with parallel processing option on dual cores was used. The computations were preformed for 8 combinations of jet flow rate and laminar/turbulent modelling. 45 L/min jet was simulated by only turbulent models.  153  6.3.2 Domain, Boundary Conditions and Meshes The circular impinging water jet was modeled as an axisymmetric free-surface liquid jet with the nozzle axis as the symmetry axis. As a first attempt, the domain was split into two sections. The results revealed that the water jet has insignificant effect on the air far from the jet (r/d > 7) and thereafter this part was excluded and the remaining domain modeled as a whole (Figure 6.1a) [127]. Uniform normal velocity V and turbulent parameters at the inlet (nozzle exit) was specified based on the length scale of nozzle diameter d and 4% turbulent intensity (I = 0.04). The parameters used for turbulent models are given by k  3 VI 2 , 2    k 1/ 2 C1/ 4l    C3 / 4  k 3/ 2 l  and  (Cμ = 0.09) [114]. The pressure-outlet condition was employed at the open  borders as far-field boundaries and no backflow was allowed. Turbulent conditions at the pressure outlets were the same as the inlet conditions. It is noted that using default FLUENT values for the turbulence parameters resulted in an unrealistic retardation of the jet flow pre-impingement. A no-slip wall boundary condition was applied at the test plate surface (u = v = 0). Initially, the domain was considered full of stagnant air with turbulent parameters corresponding to inlet condition. The domain was built and meshed using ANSYS and Gambit programs and solved by FLUENT. Figure 6.1a shows schematically the geometry, the system of coordinates and the applied boundary conditions. The domain was meshed with a non-uniform structural grid using rectangular cells (Figure 6.1b) which was clustered toward jet axis and plate surface where the water flow encountered. The mesh density varied according to laminar/turbulent models requirement. The original meshes were refined regionally or based on an iso-value of VOF at regions where the jet travels downward pre-impingement and near the plate surface where the radial water layer propagates after impingement (shaded areas in Figure 6.1b). This ensured an accurate jet diameter and velocity at the impingement surface and a continuous development of the thin water sheet on the top of the plate. The water layer formed over impingement plate was very thin of O(0.1) mm and intermittencies were detected in cases of unsatisfactory meshes. Then the gird was highly concentrated above the plate. Indeed, in addition to the appropriate wall y+, a 154  discontinuous flow should be avoided by good mesh resolution; y+   w z /  where τw is the wall shear stress and z is the distance from the wall. The wall y+ was kept smaller than 3 for SST simulations but 5 < y+ < 10 for the RKE simulations using nonequilibrium wall functions. Therefore, smaller time step of O(1e-6) sec and more iterations were required. The mesh refinement was done at 1.5 mm above the plate surface; this near-wall region is adequate considering the thinness of water layer O(1e-1) mm.  Different girds according to model requirements were used. The grids were tested at different flow rates, laminar/turbulent models, and before/after impingement. For example, the mesh was refined around the jet axis until the variations in the impingement velocity and impingement time were less than 3 and 2 percent, respectively, in laminar flows and less than 6 percent in all turbulent models (e.g. case 1 table 6.2 for 15 L/min simulations). Moreover, the impingement jet velocity and diameter and impingement time were obtained close to correspondences obtained from theory, equations 2.2 and 2.3 (Table 6.3). The cell number was then almost doubled by FLUENT in the region between  Figure 6.1 Modeling (a) Flow Domain (b) Grid (Not to Scale) 155  the inlet (nozzle exit) and the plate surface around the jet axis (Case 2, Table 6.2). Figure 6.2a illustrates the axial jet velocity near the plate for 15 L/min simulations. The vertical distance above the plate z is normalized with the nozzle diameter and the axial jet velocity was normalized with the impingement velocity. The jet decelerates before hitting the plate. The effect of mesh adaptation is restricted to a few percent except for the laminar model. Twice refinement of the laminar mesh did not much improve the results. In addition to continuity for impingement water layer, the effect of mesh on the wetting front advancement was also examined for RKE 15 L/min and the differences found to be less than 5 percent. Also after a continuous thin water layer covered the plate surface, the effect of mesh near wall on the velocity also checked. For example for SST 45 L/min simulation, the 1 mm region above the plate containing water layer was meshed with 26 and 36 cells. Figure 6.2b shows the velocity in this region at 0.3 and 0.7 mm distance from the plate. The free-surface of the water sheet was about 0.6-0.7 mm above the plate surface. The flow velocities over the plate surface at these two heights are very close. Therefore in general, the meshes which kept the liquid layer continuous over the plate surface with acceptable y+ were found reasonably refined and the computational results were not improved noticeably with more refinement. The cell number was, in general, 3,000 or more in r-direction and 10-27 in z-direction near the plate surface with finer mesh used in SST simulations. However, the laminar simulations required more iteration to converge than turbulent models and they needed more mesh adaptations for 15 L/min jets because the water layer was still intermittent. For laminar 30 L/min simulation, the convergence was not usually obtained even with highly refined mesh and very small time step of O (10-7). Therefore, the laminar model was not utilized for higher jet flow rate of 30 and 45 L/min cases. The velocity and pressure profiles presented in the following were taken after almost steady conditions were maintained. Table 6.2 Meshes before Impingement Simulations  Flow rate L/min  Laminar Turb k-ω Turb k-ε  15 30 45  Cell No Case 1 67415 62015 69015 156  Case 2 134930 124130 135230  Figure 6.2 Gird Dependency (a) Jet Speed Deceleration near the Surface (b) Radial Velocities at Two Distances above the Plate Surface for SST 45 L/min Simulation  6.3.3 Impinging Jet The numerical velocity and height of incoming jet for all flow rates are compared with analytical solution (equations 2.1, 2.2) in Figure 6.3. Numerical simulations obtained smaller results with respect to the analytical ones but turbulent heights and velocities are closer than laminar ones and the realizable k-ε (RKE) gave the best performance at preimpingement. Wavy surface of incoming jet was observed in the experiments and promoted as flow rate increased. However in the numerical simulations, smaller jet surface disturbances were formed but not established and eventually smooth jet surface was preserved; the turbulent simulations did not produce sufficient disturbances along the jet surface as what was seen in the experiments. More adequate inlet turbulence conditions are necessary for modeling of jet disturbances. The order of discretization for momentum and turbulent is influenced jet heights and velocities. No noticeable difference was found between standard and improved revisions of turbulent modelling for lower flow rates especially for 15 L/min (not shown in Figure 6.3). However in 45 L/min case, the jet was retarded more in standard k-ω respect to SST k-ω model which shows the low performance of standard k-ω (SKW) for the free high Re flow. The jet impacted the plate by speed of 5.5 m/s in SKW compared to 6.05 m/s in SST and the flow velocity was not recovered to the impingement velocity inside the impingement zone and downstream. Figures 3.3 and 6.3 show that the experimental data 157  Figure 6.3 Jet Computations before Impingement (a) Height (b) Axial Speed are closer than numerical results to the analytical ones for 15 L/min but not for the other two flow rates where larger disturbances developed along the jet surface in the tests. The axial velocity vectors of incoming water jet from two 30 L/min RKE and SST turbulent simulations are taken as an example and are sketched around the jet axis at 0 < r < d/2 in Figure 6.4a, b at different levels from the nozzle exit. The velocities profiles  are flattening while the jet approaching the plate. The jet accelerates and contracts simultaneously due to gravity significantly. The jet velocity increased from 1.76 m/s at the nozzle outlet to around 5.7 m/s at the plate surface. Although these velocity profiles are computed for uniform jet exit velocity, the effect of nozzle and inlet velocity is limited to close to nozzle. Tong [95] and Fujimoto [93] investigated numerically different inlet velocity profiles at water jet impingement such as uniform, parabolic and 1/7th power. Tong found the effect of velocity profile to be pronounced for H/d < 1.52 and similar velocity profile has resulted near the target plate for higher nozzle elevation (H/d > 2). Lienhard [18] also stated that the velocity nonuniformity inside the jet is diminished  by turbulence and viscosity if the H/d is large and the uniform velocity at the bulk of the turbulent jet is attained at the distance of (3-5)d. Therefore, the computed velocity profiles at impingement surface from our simulations where H/d is 78 is not sensitive to different inlet velocity profiles. Also the radial velocity gradient at the plate surface and hydrodynamics and heat transfer at impingement region should not change at this typical industrial H/d for various nozzle types and inlet velocity profiles.  158  Table 6.3 includes the impingement diameters and velocities of the jets from experiments and numerical simulations. The numerical impingement parameters were computed at different times during the period of simulation after impingement and then averaged.  Figure 6.4 Axial Velocity Profiles of 30 L/min at Different Level beneath the Nozzle in Turbulent Simulations (Not to Scale) (a) RKE (b) SST Table 6. 3 The Jet Impingement Parameters Vimp Flow rate dimp(mm) (L/min)  15  30  45  (m/s)  Analytical  7.6  5.496  Laminar  7.477  5.457  Turb RKE  7.857  5.427  Turb SST  7.857  5.455  Analytical  10.565  5.704  Turb RKE  10.844  5.642  Turb SST  10.801  5.66  Analytical  12.579  6.035  Turb RKE  12.955  5.982  Turb SST  13.174  5.818  159  6.3.4 Jet Axial Velocity In experimental research on short jets where the effect of gravity is negligible, Liu and Lienhard [18] and Steven and Web [20] found that the jet starts to slow down before hitting the plate at about half the nozzle diameter above the plate (z/d = 0.5) due to the presence of the wall. Tong [95] found that the velocity acceleration for laminar jet due to gravity was reversed at H/d  1.5 and the jet velocity decreased at this space above the plate; further above this distance the velocity increased due to gravity. The computed jet speeds along the jet centerline (r = 0) were assessed for our long jets to determine where the jets stop speeding up. The impingement diameter is used for normalization. Generally as shown in Figure 6.5a, the long jets were decelerated before impingement similar to short jets but at further distances above the plate, depending on the flow rates. For a 15 L/min flow rate, the jet acceleration stopped above z/dimp = 0.7 and the velocity was 0.99Vimp at z/dimp = 0.5. For 30 L/min jet, the increase of the jet speed was halted at z/dimp = 1 while the retardation was less then 5% with respect to the impingement  velocity at z/dimp = 0.5 in both the k-ε and k-ω turbulent simulations. The impedance of the turbulent 45 L/min jet was initiated at about z/dimp = 1.17 while the velocity was about 0.9Vimp at z/dimp = 0.5. Therefore, numerical results show that the long turbulent jets felt the wall earlier than the short jet but decrease in jet speed is not noticeable above z/dimp = 0.5 for higher jet flow rates and was negligible for 15 L/min jet. The jet speed  deceleration at a higher distance from the impinging surface according to the jet Reynolds number. These results (Figure 6.5a) are similar for laminar and turbulent modeling during the simulations. Figure 6.5b for example, illustrates the vertical velocity for a 15 L/min jet at the two times of t = 0.6 sec (early after impingement) and t = 4 sec (long after impingement). The velocity reductions are almost the same except just above the surface. Velocity disturbances were detected only above the impingement point in the k-ω simulations at t = 0.6 sec; this is 0.1 sec after the impacting occasion and could be attributed to flow recirculation or reflection due to initiation of impingement. These disturbances were pronounced according to the flow rate. The laminar and turbulent k-ε models did not capture this feature.  160  Figure 6.5 Axial Jet Velocity Reduction above Surface a) 15, 30 and 45 L/min Jets (b) 15 L/min Jet at t = 0.6 and 4 s  6.3.5 Frontal Propagation Numerical development of water flow could be traced by exploring the distribution of VOF and velocity along lines parallel to the plate surface at different heights above the surface [127]. As a typical example, the wetting front and free surface of the impingement water layer was tracked by VOF contours and it is shown in Figure 6.6 at various times during 45 L/min SST turbulent simulation. The wetting front spreads radially over the plate surface away from impingement point. The thin water layer forms with wavy free-surface and round end due to surface tension. The front of liquid sheet finally passes the open boundary of computational domain and the water film fully covers the plate surface. Very fine mesh was used in the simulation to keep this thin water sheet continuous. The computed velocities of wetting fronts (Uf) resulting from laminar and turbulent RKE and SST simulations are compared with experimental data for every flow rate in Figure 6.7. The bold line represents the fitting to all experimental data while the hollow squares illustrate the velocities at four directions 0, 90, 180, 360 over test plate (Figure 3.1). The agreement is good. Generally, numerical simulations produced larger velocities after the impingement zone but it decreased faster than experiments afterward. For 15 L/min case, the numerical velocity is higher up to r/d < 6 where 161  Figure 6.6 The Development of Thin 45 L/min Water Layer over Fixed Plate Surface at SST Turbulent Simulation demarcates approximately the place of hydraulic jump and then is lower after the jump noticeably. The 30 and 45 L/min wetting fronts in experiments were captured at around r/d < 4 and almost r/d ≈ 2, respectively. The effect of impingement was prominent on the  instant development of flow after impingement. Chaotic hitting of the plate and splashing were observed in the experiments while the jet impacted the plate smoothly in numerical simulations especially in SST simulations. It is noted that the wavy free-surface with splashing was observed in the experiments while less wavy free-surface with almost no splashing was produced in the simulations from the impingement water layer. The insufficient disturbances over the incoming jet surface at pre-impinging in the simulations also influenced the subsequent expansion of water sheet after impingement.  162  Figure 6.7 Experimental and Numerical Frontal Velocities Uf (a) 15 L/min (b) 30 L/min (c) 45 L/min Avoiding intermittent spreading of thin water layer became harder as the front further flowed in the parallel zone. Higher velocity for wetting front propagation was obtained by SST revision of k-ω model for 45 L/min because thinner water layer covered the plate. The turbulent conditions at nozzle outlet should be measured to be modeled adequately in numerical simulations. Moreover, the default surface condition was accepted at computations while it is not necessarily the same as surface condition of test plate.  6.3.6 Velocity at Impingement Zone Stevens et al [15, 21] experimentally and Liu et al [14] analytically investigated the structure of the impingement inviscid flow from free-surface liquid round jets and obtained nearly linear radial velocity in the stagnation zone. The experimental data on 163  fully-developed jets issued from pipe-type nozzles with 2.1 ≤ d ≤ 23 mm, H/d ≤ 4 (mostly H/d = 1) and 8000 ≤ Re ≤ 62,000 was correlated to give the distribution of mean radial  velocity in the stagnation zone (0 ≤ r/d ≤ 0.5) near the wall (0 ≤ z/d ≤ 0.5) by Stevens et al [20] as,  u   z  r   1.83  3.66   V   d  d   6.19  where, z is the vertical distance from the target surface, r is the radial distance from the stagnation point, u is the radial velocity and V and d are the jet velocity and diameter at nozzle exit, respectively. The nozzle was close to the target plate (mostly H/d ≤ 1) and the effect of gravity was neglected. However, gravity considerably accelerates and shrinks our long and fully developed jets where H/d = 78. In a 15 L/m jet for example, the jet diameter is reduced 60% and the jet is speeded up 6 times at impingement surface (Table 2.1). Therefore, the jet velocity and diameter have to be adapted with respect to the gravity acceleration. Therefore, the impingement diameter dimp and the impingement velocity Vimp are used instead of d and V in using the above correlation, respectively. The radial velocity in the stagnation zone near the plate from laminar and turbulent RKE and SST simulations of 15L/min jet is compared with Stevens’ measured velocities in Figure 6.8. The numerical velocities were taken exclusively above the boundary layer up to the distance where the effect of the plate on the incoming jet disappears (z/dimp > 0.5). The thickness of the hydrodynamic boundary layer is generally of    rimp / Vimp     1/2  for a laminar jet [44]. The turbulent jet, however, tends to break up the  boundary layer beneath the jet and a thinner boundary layer is expected. The very thin boundary layer is estimated to be tens of microns and all velocities were extracted from 0.1 mm or more above the plate. The comparison is made for same flow rate and same distance from wall (z/d) between Stevens’ and our numerical velocity profiles. As shown in Figure 6.8, computed velocities start from zero at the impingement point and are raised almost linearly as is predictable for inviscid flows and are in good agreement with Steven’s measurements. Laminar velocity is slightly closer to Stevens’ data because the jet in his experiments was laminar [20]. Far from the plate surface (z/ dimp > 0.5), the approaching flow is essentially axial. Moreover, the numerical results indicate that radial 164  velocity is not just a function of radius but also of distance from the plate (u = f(r, z)). The slope of the profile u/ Vimp versus r/ dimp with linear variation for a given Reynolds number and a vertical distance z represents the gradient of radial velocity B to which heat transfer is related [14]. Our numerical velocity profile showed that closer to the plate the velocity gradient is higher and hence higher cooling rates would be expected. Ochi et al [22] used a circular water jet where d = 10 mm, the nozzle-to-plate distance 25 mm (H/d = 2.5), and jet velocity is V = 3 m/s and measured the wall pressure and calculated the velocity along the plate surface and proposed linear variations for velocity and pressure,  Figure 6.8 Radial Velocity Profiles along Plate Surface in Stagnation Zone for 15L/min Jet Simulations (a) Laminar (b) Turbulent RKE (c) Turbulent SST 165  u 1 r    V 1.28  d   6.20  where, V and d are the jet velocity and diameter at the nozzle exit, respectively. The impingement zone was found as r / d = 1.28. Lienhard [23], using a stagnation flow solution, found linear variation for velocity and pressure just above the wall (z/d ≈0) and suggested that below velocity variation,  u Br r   0.916 V 2d d  r /d  0.5  6.21  where B is the velocity gradient (determined experimentally as 1.831). Liu et al [14] consider the surface tension in the solution of the stagnation zone and found that Vimp was achieved at r ≈ d. Stevens experimentally found B ≈ 1.83 while Ochi measured it as 1.5625. Figures 6.9 to 6.11 illustrate numerical radial velocity profiles of 15, 30, and 45 L/min long jets for different distances from the plate which are compared to Liu et al.’s [14] and Ochi et al.’s [22] suggestions. All numerical velocities are obtained above the boundary layer (z ≥ 0.1 mm) and stand for inviscid, free-surface impingement water jet flows. Considering the effect of gravity, dimp and Vimp were utilized in Liu et al.’s and Ochi et al.’s equations (6.20, 6.21). The velocity variations are depicted up to r/ dimp ≈ 1.28. Generally, the velocity increases almost linearly and matches Liu’s prediction better than Ochi’s correlation which underestimates the velocities. Close to the stagnation point (r/ dimp < 0.3), the numerical profiles change linearly in good agreement with the both predictions. At small values for z/d, the velocity is nearly linear up to around r/ dimp < 0.8. But at larger radii, before the maximum velocity is attained, the velocity rise is  slowed down and flattened. The peak of velocities is almost equal to the impingement velocity (0.95Vimp < u < 1.03 Vimp). At a higher distance above the plate, a higher maximum velocity is obtained which occurs at a larger radius from the impingement point. At larger values for z/d, the contracted jet surface is at r/ dimp < 1.28 and the maximum velocity occurs before the curved free-surface and it then decreases at the freesurface nearby which is the interface of water and air. Far from the plate, the velocity profiles are lowered and curved because of less effect of the wall on the incoming axial 166  jet flow. Similar results are obtained at the same distance from plate among different flow rates. However as the flow rate increased, the velocity deviates at a smaller radius from the linear variation which basically developed for a laminar and short jet. No significant distinction is detected at a given Re number and distance from the plate among numerical simulations for each flow rate jet and during time process but turbulent simulations usually gave better results than the laminar model and were more close to Liu’s linear variation.  Figure 6.9 Radial Velocity Profiles along Plate Surface in Impingement Zone for 15 L/min Long Jet Simulations (a) Laminar (b) Turbulent RKE (c) Turbulent SST  167  Figure 6.10 Radial Velocity Profiles along Plate Surface in Impingement Zone for 30 L/min Long Jets Simulations (a) Turbulent RKE (b) Turbulent SST  Figure 6.11 Radial Velocity Profiles along Plate Surface in Impingement Zone for 45 L/min Long Jets Simulations (a) Turbulent RKE (b) Turbulent SST The velocity gradient B value for our long jets in the vicinity of plate was found as B ≈ 2 which is larger than what found for short jets. Higher velocity gradient B besides the turbulence effect enhances the heat transfer inside the stagnation zone for long jets. Examining all the extracted velocity data for all flow rates and simulations of our industrial water jet close to the plate surface (z/d < 0.25) reveals that velocity is linear (near-linear) up to radius of (0.8-1) dimp and Ochi overpredicts the size of the impingement point which greatly influences the total heat removal from the hot metal plate.  6.3.7 Velocity in Wall (parallel) Zone The radial velocity along the plate surface is presented in Figures 6.12 and 6.13 at different vertical distances from the plate (z) for the 15 and 45 L/min jets, respectively. The velocity at first was increasing in the impingement zone and then decreasing in the 168  parallel zone. The water sheet in the radial zone is generally thin. For example for turbulent 15 L/min jets, the free-surface stands almost at z = 0.4 mm while the laminar layer thickness is as low as z = 0.1 mm in the middle of surface and the wavy free-surface at higher distance (z > 0.1 mm) but with intermittency. Therefore, different velocity variation resulted from the turbulent simulations which presented thicker films. Instability and intermittency were detected before hydraulic jump place which occurred in all 15 L/min jet simulations. Negative velocity at the location of hydraulic jump is a sign of flow recirculation at the jump place and is demonstrated well by SST k-ω simulation. The thickness of the water sheet increased according to flow rates. Smooth propagation of the water layer is obtained from turbulent simulations for all jets but smoother and thicker from the SST k-ω simulation, in general. Because the laminar flow is more vulnerable to intermittency as tested for 15 L/min and 30 L/min jets, then the laminar simulation was not employed for 30 and 45 L/min jets. Similar velocity patterns were achieved for 30 L/min and 45 L/min jets. At higher Reynolds numbers (i.e. 45 L/min jet), the RKE turbulent model presented a closer velocity profile and a film thickness to the SST k-ω model which was basically developed for near-wall flow (Figure 6.15). For a mean free-surface velocity uo in the parallel zone, Steven et al [17] suggested the below correlation for fully-developed turbulent liquid jets issued from pipe-type nozzle (17,000 < Re < 47,000 and 2.1 < d <9.3 mm)   0.125(r / d ) 2  0.625(r / d )  0.303 u0  Vimp  .0936(r / d )  1.33  0.5  r/d  2.86 2.86  r/d  14  6.22  and found the maximum in near r/d = 2.5, which surpassed the jet exit velocity by 20% in some cases. This correlation is depicted in Figures 6.12 and 6.13 which over-predicts the velocity for all of our long water jets.  169  Figure 6.12 Flow Velocity Parallel the Plate Surface for 15 L/min Jet Simulations (a) Laminar (b) Turbulent RKE (c) Turbulent SST  Figure 6.13 Velocity Parallel the Plate Surface for 45 L/min Jet Simulations (a) Turbulent RKE (b) Turbulent SST 170  6.3.8 Pressure at Impingement Region Ochi et al [22] measured pressure along the plate surface as  p  po r p(r )   1  0.61  pstgn  po d   2  6.23  where, po is the ambient pressure, pstgn is the stagnation pressure which can be found from Bernoulli’s equation,  pstgn  po   1 2 Vimp 2  6.24  Liu et al [14] also analyzed impingement flow field and drew analytically the pressure profiles considering the effect of surface tension in the impingement zone. Here, the pressure field near the wall (very small z/d but outside the boundary layer) is investigated and compared with Ochi et al [22] and Liu et al [14]. The effect of surface tension on pressure field is negligible as the Weber number is above 200 for our jets [14] and Liu’s pressure profile for We ≈ ∞ is used for comparison. Figure 6.16 shows the pressure profiles in the impingement zone. The numerical pressure profiles are similar for all flow rates which show that jet Re number is insignificant for the pressure inside the impingement zone. Close agreement with Liu’s pressure distribution is obtained but Ochi’s equation overestimates the pressure distribution which is consistent with what seen for velocity profiles in impingement zone. Better results are obtained from the SST simulations respect to RKE model.  6.3.9 Heat Transfer Correlation Correlations of heat flux in boiling heat transfer are based on: wall superheat temperature (∆Tsat = Tsurface – Tsat ) which is the difference between surface temperature and saturation temperature; on subcooling (∆Tsub=Tsat-Tw) which is the difference of the coolant temperature and the saturation temperature and on the jet parameters (type, velocity, nozzle, etc). Saturation temperature is usually assumed 100 ⁰C for ambient pressure in these equations. But the local pressure distribution along the plate surface influences the local Tsat of water at the vicinity of hot plate. The pressure, for example, is at least 80% higher than the ambient pressure for r/d < 0.5. The associate change in saturation temperature is up to 5 ⁰C at the highest local pressure for our jets. Table 6.5 171  Figure 6.14 Pressure Distribution along the Plate Surface for 15, 30, and 45 L/min Jets shows the corrected boiling temperature of water (T'sat). The variation of liquid Tsat produces variable local surface superheat (∆Tsat) and variable local subcooling (∆Tsub) along the hot surface which is neglected in most publications though it has an impact on the amount of surface heat flux and, specifically, on stagnation heat transfer. Table 6.4 Stagnation Pressure and Corrected Tsat' Flow rate (L/min)  Vimp  Experimental  15  5.5  103.9  Numerical  15  5.47  103.9  Experimental  30  5.7  104.3  Numerical  30  5.65  104.2  Experimental  45  6.04  104.7  Numerical  45  5.9  104.5  172  (m/s)  Tsat' (oC)  Table 6.5 Effect of Impingement Pressure on Heat Flux Correlation  Authors  0.5 0.608 q  C (Tsub )Vimp d Tsat0.14  Filiovisic et al [4] * Wolf et al [8]** Wolf et al [6]* Ochi et al [22]  q  450(Tsat ) 2.7 q  63.7(Tsat ) 2.95   3.18 105 (1  0.383Tsub )(Vimp / d )0.828 qmin  Average change (%)  Jet type  Boiling regime  0.5 0.608 =8-9 q / Vimp d  Circular  Nucleate   = 3-4 qave  Circular  Nucleate   = 3-4 qave  Planar  Nucleate   /(Vimp / d ) 0.828 )  6-7 (qmin  Circular  Transition  *derived from Monde and Katto experimental data [128] **derived from Ochi et al [22] experimental data  The effect of the corrected saturation temperature (T’sat) on heat flux at stagnation point is utilized using some boiling heat transfer correlations, for example, where the superheat temperature changing between 100 to 1000 oC relevant to the ROT cooling and  ∆Tsat = Tsurface – T'sat and ∆Tsub = T'sat-Tw (Table 6.5). In the ROT case where the heat flux is in range of 1-10 Mw/m2, small percentage increases in heat removal is noticeable and hence more accurate results expected from available correlations. As shown in Table 6.5, changes in heat flux due to local pressure variation along the plate surface is up to 9% and has to be taken into account when using the pertinent correlations in ROT modeling.  6.3.10 Hydraulic Jump The hydraulic jump was tracked numerically for 15 L/min simulations by evaluating the VOF magnitude along the parallel lines at different heights above the plate [127]. The numerical results shows smaller jump radius than the experiments (Table 6.6). Generally, the thickness of the water layer gradually increased over the jump site and the jump moved outward. The HJ was unstable and showed different profiles during its formation. As shown in Figure 6.15a, b, HJ configurations with and without rollers were obtained in the simulations before steady condition attained. The jumps in laminar and SST models are usually without rollers, but stretched over larger area than the jumps in the RKE model simulation, (Figure 6.15a). In the RKE model, however, the jump with sudden change in thickness was observed (Figure 6.15b). VOF contours spotted some air trapped inside the water layer at the jump place which showed the air entrainment into  173  Table 6.6 Numerical Hydraulic Jump Radius (15 L/min) Jump radius  Exp  Lam  Turb SKE  Turb SST  Rj / d  8.8-10.3  6.4-7.6  5.1-6.3  7.5-10  Figure 6.15 Circular Jump Configurations at Jump Site in 15 L/min Numerical Simulations Shown by VOF Contours (a) No Roller (Turbulent SST) (b) One Roller (Turbulent RKE) the water flow recirculation (see figure 6.16 for SST). Negative velocity at the place of the jump was obtained from SST modeling. Mesh refinement was also made around the interface place and at the hydraulic jump position in order to better capture the jump in layer thickness.  6.3.11 Jet Disturbances and Splattering Generally in the all numerical models, the splashing was not represented adequately as observed in the experiments for fixed plate. Few water drops migrated from the jet tip before impingement. Yet, the amount was well below the threshold of 5 percent suggested by Lienhard [56]. In the parallel zone, RKE model produced less splattering from the free-surface than laminar and SST models. Splashing was captured only by 2nd order momentum discretization. Intensive mesh refinement around the free-surface is needed to study the effect of mesh on the splashing before and after impingement and assess the capability of available turbulent models. Disturbances on the surface of incoming jet were seen in SST k- turbulent modeling but the jets had smooth surface in RKE and laminar simulations. Again, the jet surface disturbance was not obtained by 174  Figure 6.16 Circular Jump Configurations during RKE 15 L/min Numerical Simulation present simulations appropriately. The splattering and surface disturbances are a good test case for higher level turbulent models such as DNS.  6.4 Numerical Simulation of Moving Plate The moving plate simulation is a 3D problem and not a 2D axisymmetric one as the case for stationary plate. Low cost RKE k- turbulent model was employed in these simulations with non-equilibrium wall function because SST k- simulation is costly due to meshing requirements. Two phase water/air VOF transient 3D simulations were performed for different jet flow rates and plate speeds in 8 cases including Q = 15, 30 and 45 L/min at Vp = 1.3 m/s and Q = 30 L/min at Vp = 0.6, 1.0, 1.3, 5 and 10 m/s. Two 175  cases of very fast moving plate of Vp = 5 and 10 m/s ( 2Vimp) were also tested to examine the flow field at fast moving plate. The procedure setup is very similar to the fixed plate simulations and is not repeated here. The time step was usually 1-2 10-5 sec to maintain solution stability and 100,000-200,000 time steps are needed to establish unchanged wetting front over the moving surface.  6.4.1 Geometry, Boundary Condition and Mesh The size of the computational domain is a concern due to number of cells. Half of the plate was modeled due to symmetry. The appropriate size of the domain to minimize the number of cells was found by careful examining the place of wetting front over the moving plate surface in the experiments in this study. Also, the space above the plate for modeling was determined by checking the thickness of impingement water layer from numerical simulations of fixed plate. It turned out that 10 mm, in general, above the plate surface and 325 mm after the impingement point and 100 mm below it were best to model the impingement flow upstream and downstream and to track the wetting front (HJ) for all Q and Vp series of single nozzle simulations. The jet exit was considered high enough at 50 mm above the plate (Figure 6-17). The velocity, diameter for water jet and the turbulent parameters at inlet were obtained from the RKE fixed plate simulations at 50 mm height and implemented into the program. The no slip moving wall with prescribed speed in –Y direction was assigned to the bottom of the domain (Figure 6.17). The default surface condition (e.g. roughness, etc) was accepted. The left side plane (XZ plane) was considered as symmetry plane which is along the middle line of the plate surface. All other boundaries are considered as open pressure outlets. The top boundaries were open to atmosphere where the turbulent parameters were obtained from the fixed plate RKE simulations. The impingement water layer exits the domain from the lower end (parallel to X-axis). Low amount of turbulence was assigned to the right side boundary where water exits with no back flow allowed. Non-uniform structural grid was used. The mesh density is increased in Xdirection toward the symmetry plane and in Z-direction toward the moving surface. The  176  Figure 6.17 Computational Domain and Boundary Conditions of Moving Simulations (a and b are Given at Table 6.8) first attempts for meshing obtained about 2 millions cells. The original mesh resulted in discontinuous spreading of thin water layer over the plate surface far from impingement point. Mesh refinement increased the cell number to 3 millions nodes but the flow continuity was not resumed all over the moving impingement. Full refinement introduced 4-5 millions cells to resolve the problem but handling these huge meshes was not feasible within the existing computer resources. Therefore, the models were run at high performance computing facility by running Parallel FLUENT at a Westgrid cluster which is a consortium of grids of parallel computational cores. After primary tests, it was revealed that at least 16 cores or more are needed to run one case within 4 weeks. However, long waiting time for more than 16 cores due to limitations of accessible computational nodes and available memory made this approach very lengthy. Therefore, the computation of full domain was stopped and the domain size decreasing was noted as an economical way to run the model in reasonable time on a new 8 core high performance I7-PC machines. The downstream length was shortened to 50 mm after the impingement point and 95 mm (5d) of the plate width is modeled. In fact, the jet-space in a jet line at ROT is 3-5d. The space above the plate is stepped upward gradually by considering the flow thinness and the approximate place of the thick wetting front (Figure 6-16). The dimensions “a” and “b” of the optimized domain were determined for each 177  case separately according to the corresponding single nozzle experiment (Table 6.7). It was noted that mesh refinement preserved the continuous development of water flow over the plate surface even for very fast moving plate cases and obtained reasonable maximum y+ in the range of 5-14. In this way, the control volumes number was decreased to 0.7-1.35 million cells and each case consumed 6-8 weeks CPU time to reach steady conditions. Figure 6.18 show the comparison of wetting fronts found from the two meshes which are close together. The velocities at various distances above the plate are also found in good agreement. Therefore, the first gird was used for all numerical simulations presented below. Table 6.7 a and b Dimensions in Moving Simulations Case  a (mm)  b (mm)  15 L/min, 1.3 m/s  55  80  30 L/min, 0.6m/s  150  110  30 L/min, 1.0m/s  150  110  30 L/min, 1.3m/s  75  100  30 L/min, 5.0m/s  55  80  30 L/min, 10.0m/s  55  80  45 L/min, 1.3 m/s  100  120  Figure 6.18 Wetting Fronts for Two Grids (30 L/min, 1.3 m/s) 178  6.4.2 Impingement Flow Spreading The computed spreading of impingement film over the moving surface can be traced by VOF contours during simulation. As an example, figure 6.19a illustrates the wetting area propagation during the simulation of 15 L/min over 1.3 m/s moving plate. The impingement water flow was developed symmetrical around the impingement point early after the impact incident but gradually the plate speed influences the flow expansion and the flow is stretched along the impingement surface (up to t = 0.05 s in the figure). The water sheet quickly passed the downside outlet and the quick expansion of water layer decreased above the impingement point. The backward motion of wetting front also detected with accumulation of water at the front (not shown). Afterward, the front advancing took place at longer time and finally the impingement water approximately settled down over the plate (t = 1.15 sec for this case). The calculated wetting front (HJ) at symmetry plane is also shown at Figure 6.19b. The jump at water layer thickness occurred sharply or developed over large width as the wetted area expands over the surface during time; the thickness reaches to the maximum of 5 mm height. In general, the transient simulations were performed until the wetting front is established over the moving surface; the computation was then run for more 5,000-10,000 time steps to ensure the steady conditions.  179  (a)  (b) Figure 6.19 VOF Contours at Q = 15 L/min, Vp = 1.3 m/s (a) Impingement Flow over Moving Surface: Red Color Shows Water (b) Wetting Front (HJ) at Symmetry Plane 180  6.4.3 Wetting Front The wetting front is measured from the VOF contours on impingement surface (as shown at Figure 6.19) for every case using Matrox Inspector program. Figure 6.20a illustrates the measured wetting fronts for 30 L/min impinging jet on moving plate at 0.6, 1.0 and 1.3 m/s velocities similar to the experiments series of single nozzle. The computed wetting fronts for 15, 30 and 45 L/min impinging jets on moving surface of 1.3 m/s are also shown in Figure 20b. The curve-fitted wetting fronts are compared with the experimental data and with Kate’s relation [89] for each case (shown at Figures 4.234.25). The computed fronts of wetted areas are in good agreement with those observed in the experiments considering the unsteadiness of HJ at the experiments and the range of variation of wetting front detected over the moving plate (Table 4.4 and figures 4-10 and 11). The simulated wetting front is more stable during simulations when compared to the experiments and almost steady front was maintained over the moving plate. Generally the computed front is smaller than experimental correspondences but when the plate speed increased, the numerical simulation gave better correlation with experiments and Kate’s prediction. One reason is the surface condition of moving plate in these simulations. The default surface condition is defined for material such as aluminum which is accepted here because the surface condition of Plexiglas is not available. However, the Plexiglas test plate is smoother and probably exerted less friction on the fluid. Therefore, the impingement water flow develops easier over Plexiglas and then larger radius for HJ is attained with respect to spreading over metal surface. As in section 3.8, smaller wetted area was observed on steel plate with respect to the experiments on Plexiglas. This was also reported by Chen [76]. Kate’ relation (equation 4.11) is good for smaller velocity ratio of plate to jet as found in chapter 4.  181  (a)  (b) Figure 6.20 Wetting Front (a) 30 L/min Jets at Various Plate Speeds (b) Different Jet Flow Rates at 1.3 m/s Moving Plate 182  6.4.4 Impingement Zone on Moving Surface The Y-component of velocity along the longitudinal axis of the plate (Vy) is found around the impingement point at symmetry plane. The normalized Vy velocity profiles at impinging jets over 1.3 m/s moving plate, for example, are shown at Figure 6.21 for 0.1 mm interval distance above the surface. The smallest distance z = 0.1 mm is above the thin boundary layer as mentioned above. Nearly linear increasing velocity is obtained but the velocity variation is not the same before and after the impingement point due to surface motion. The velocity gradient is smaller before but velocity recovered faster after the impingement point. The smaller the distance above the plate (z), the more pronounced the plate effect and higher discrepancy in velocity recovery at the two sides of the impingement point is detected. This may result in unsymmetrical heat removal at the impingement region for cooling of moving surface with single nozzle. Figure 6.22 show the Vy velocity variation for 30 L/min impinging jet on fast moving plates (Vp =5, 10  m/s). The higher plate velocity impacts larger portion of impingement flow at higher z above the surface and the stagnation point is shifted considerably ahead. Actually if the velocity ratio of plate to jet exceeds certain limit then the plate motion entrains the impingement region and the velocity is not recovered (e.g. z = 0.1-0.2 mm distances). Also, backward flow occurred above the impingement point which is called backwash flow and then the jet may not be able to reach the surface even at impingement zone and consequently higher affect on the heat transfer would be expected. The velocities variation reveals that velocity is not zero at the geometrical center beneath the nozzle over the moving surface but is negative in motion direction. Indeed, the stagnation point is moved upward over the surface where the impingement flow balances the motion of surface and the velocity becomes zero; thereafter the velocity increases in opposite direction of plate motion as shown in Figure 6.21 until rising to about Vimp and exiting the impingement region. Kate [89] used the analogy of elliptical HJ due to oblique impinging jet on stationary surface and conjectured of an elliptic impingement zone and eccentric stagnation point as a result of normal impinging jet on moving surface which elongate in motion direction (Figure 4.20). The assessment of velocities along the X and Y axes verifies that the impingement region is not symmetric around the impingement point. Figure 6.23 illustrates the distances at two sides of 183  Figure 6.21 Velocity in Y Direction at Impingement Zone on 1.3 m/s Moving Plate (RKE Simulation)  Figure 6.22 Velocity in Y Direction at Impingement Zone for 30 L/min Jets  impingement point along Y-Axis and a distance along X-axis where the velocity recovers to about Vimp. The magnitudes of these distances are shown in Table 6.8 which demonstrates that the impingement region is noncircular around the impingement point at normal impinging jet on moving plate. Actually for very fast moving plate (Vp = 10 m/s), the velocity is not started from zero near the surface. There is no velocity recovery but it is accelerated in motion direction below the impingement point over the surface.  184  Figure 6.23 Moving Impingement Surface (Point O is Impingement Point)  Table 6.8 Distances of Velocity Recovery case  a /dimp  b1/dimp  b2/dimp  15 L/min, 1.3 m/s  1.046  1.176  0.986  30 L/min, 0.6 m/s  0.993  0.987d  0.986d  30 L/min, 1.0 m/s  0.993  1.176  0.956  30 L/min, 1.3 m/s  1.0  1.198  0.978  30 L/min, 5.0 m/s  0.999  1.356  0.96  30 L/min, 10.0 m/s  1.12  -----  0.922  45 L/min, 1.3 m/s  1.078  1.0143  0.984  The comparison of velocity in impingement zones over fixed and moving surfaces is shown in Figure 6.24 for 15 L/min and 1.3 m/s as an example case. Near the surface (z  = 0.1 mm), the velocity linearly increased equally at both sides of impingement zone on non-moving plate but the moving surface slows down the velocity ahead of impingement and accelerates the flow after impingement. The effect of moving surface is faded at higher distance (z = 0.4 mm). Linear variation predicted by equation 6.19 [23] is also added for comparison. 185  Figure 6.24 Velocities at 15 L/min Impingement Zone on Fixed and 1.3 m/s Moving Plates The pressures at impingement region near the surface (z = 0.1 mm) for three jet flow rate on the 1.3 m/s moving plate are plotted in Figure 6.25. The pressure normalized with stagnation pressure Pstgn and Po is ambient pressure. The pressure profiles are similar to what seen before for fixed plate at Figure 6.16 for same jet flow rates. However, the peak of the pressure is moved slightly above the impingement point according to the stagnation point shift.  Figure 6.25 Pressure at Impingement Zone 186  6.4.5 Velocity in Symmetry Plane The velocity along plate axis (Vy) at symmetry plane was found at different distances (z) above the moving surface (Figure 6.26) to examine the effect of plate motion on the wetted area (impingement zone + wall zone). The wetting fronts of impingement flow due to 15, 30 and 45 L/min jets over 1.3 m/s moving plate are depicted at Figure 6.27. The flow velocity after exiting the impingement region is steadily decreasing similar to the stationary plate (Figures 6.12, 6.13) due to surface friction and the water film thickness is decreasing accordingly. But when the moving surface overcomes the flow momentum then the velocity becomes negative while water sheet thickness is elevated and the wetting front appeared as HJ. However the negative velocity was detected on fixed plate when HJ occurred for 15 L/min impinging jet but not for 30 and 45 L/min jets. Therefore, the moving plate agitates the occurrence of HJ and has a controlling role on HJ similar to the role of a rim around the outer edge of stationary plate. The sharp decrease of the velocity profiles marks the outer front of HJ over the plate surface and delineates the plate into wetted and non-wetted zones. The rate of velocity decreasing above the impingement point over surface is more than the velocity recovery after it due to different effect of moving plate on impingement flow. Indeed, the water layer thickness is decreased monotonically and free-surface downstream the impingement zone is at z = 0.3- 0.4 mm.  187  Figure 6.26 Velocity at Y Direction along the Middle of Moving Plate Vp = 1.3 m/s  Figure 6.27 Wetting Front over Moving Plate Vp = 1.3 m/s  188  The velocity of 30 L/min impingement flow over the surface of various velocities is shown at Figure 6.28 and the attributed wetting fronts at figure 6.29, respectively. As the plate velocity increased, the velocity reversed and smaller wetting front was established. For Vp = 10 m/s where the plate velocity is about twice the impingement velocity, the plate motion completely reverse the flow direction over the surface up to 0.2  mm; the velocity increased only at a part of impingement region for z = 0.2 mm but quickly was held backed by the plate motion. The mainstream flow could not recover fully at impingement point at z = 0.3 mm and higher; the velocity lifts up to 0.8Vimp while it reaches Vimp at other cases. Therefore, backward flow near the impingement surface occurs and penetrates more the bulk of mainstream over the surface (backwash flow). The free surface is lowered to 0.3-0.4 mm near the impingement region but the very thin water film (about 0.1 mm) takes place after impingement point. Splashing and ragged wetting front are detected for Vp = 5, 10 m/s simulations and the wetting front is not maintained over the moving surface especially for Vp = 10 m/s as seen for the lower plate velocity simulations. The flow separation is also detected over very fast moving surface of Vp = 10 m/s as partially shown in Figure 6.29.  189  Figure 6.28 Velocity at Y Direction of 30 L/min Jet along the Middle of Moving Plate  Figure 6.29 Wetting Fronts of 30 L/min Jets on Moving Surface at Different Velocities 190  6.5 Conclusion For stationary plate pre-impingement, RKE turbulent model better simulated the impinging long liquid jet, in general, and gave closer results to experimental data than analytical model. However, the spreading thin impingement layer and hydraulic jump better represented with SST turbulent model. The correlations and analytical relations for velocity and pressure distributions at impingement and parallel zones for short jet estimated well the variation of computed velocity and pressure only after being adapted to long jet by using jet impingement velocity and jet diameter, i.e., considering gravity effects. The computed wetting fronts from the RKE simulations of moving plate are comparable to the measured experimental data of single jet. If the plate velocity is high enough then the longitudinal negative velocity encompasses large portion of mainstream impingement flow and then washes back the impingement flow in direction of motion even beneath the nozzle.  191  Chapter 7 Summary, Conclusions and Recommendations  Heat transfer analysis of hot plate and hydrodynamics of jet impingement have been studied experimentally and numerically by many researchers and has been actively investigated by the UBC ROT group. In this work, the focus is placed on one aspect of this research area; the hydrodynamic of circular water jet impingement on stationary and moving plate. The experimental part of the work was conducted at an industrial pilotscale ROT facility with relevant parameters (Q, d, H, Vp) pertinent to industrial cooling in steel mills. To inspect the influence of plate motion, the jet flow rate Q and the plate speed Vp were systematically changed to simulate typical industrial setups (Q = 10-45 L/min and Vp = 0.3–1.5 m/s). Numerical simulation of long turbulent water jet was performed to examine the impingement flow field.  7.1 Summary of the Results 7.1.1 Fixed Plate Experiments The high Re number long jet was unsteady when impinging on stationary plate. Surface disturbances develop along jet and the impingement point is unsettled at the plate center. Jet unsteadiness increased with the jet flow rate. Bigger surface disturbances and larger impingement point oscillation observed for higher jet flow rate Q. The disturbances were transmitted into the impingement flow and originated the surface waves at impingement region. The waves developed and broke down at parallel zone, perturbed the thin liquid impingement film and agitated splashing. Noticeable splattering was detected at the 45 L/min jet tests. The Surface waves and splashing are pronounced features observed at impingement water layer over fixed plate due to long jet unsteadiness. The amount of  192  splashing is directly related to water consumption and should be controlled to reduce the wasted water in industrial applications. The circular hydraulic jump CHJ is spatially unsteady with variable geometrical configurations unsymmetrical around the center of the plate beneath the jet due to the disturbances and the oscillation of impingement point. The surface waves passed the jump and disturbed the slow moving flow after the jump. A simple correlation based on jet flow rate Q has been developed which predicts the radius of CHJ for these long water jet with ± 10% error.  7.1.2 Moving Plate Tests- Single Jet Major part of the experimental work focussed on moving plate with single and multiple impinging jets. Single impinging jet experiments on a moving plate were performed to assess the relation of size and shape of wetting region (or wetting front) with jet flow rate and plate speed. The demarcation of wetting zone over plate surface is important in modeling the associated heat transfer. Different boiling regimes are attributed to the wetting and non-wetting areas which influences the total predicted cooling rate by the model. For a given jet flow rate, a smaller jump occurs on faster moving surfaces. For a given plate velocity, a larger wetting zone results by the higher jet flow rate. The moving plate interferes with the spreading of radial flow in all direction and asymmetrical wetting zone take place over surface because the plate treat dividing impingement flow differently in parallel and opposite motion direction. The water film and the wetting front (HJ) are vulnerable to instability due to surface waves and variable impingement point. The wetting front unsteadiness and change in HJ radius ΔRj along the longitudinal axis, were found to be correlated with the jet flow rate Q and the HJ radius also change in accordance with Q and Vp variability during the test. A correlation for the radius of hydraulic jump Rj has been presented in terms of jet flow rate, Q and plate speed, Vp. The presented correlation matches all experimental data within ±7% error. The motion of impingement surface increases the complexity and consequently noncircular wetting front (HJ) would be normally formed. Kate et al.’s model of non-circular HJ on a moving surface [89] was found to be applicable when the effect of surface motion is not  193  pronounced. The plate motion has controlling effect on the jump front similar to the role of boundary condition at the fixed plate edges on CHJ.  7.1.3 Moving plate Tests-Multiple Jets Subsequently, the effect of plate motion on the interaction between liquid jets was studied experimentally using in-line arrays of two and three jets. Two different flow structures at the interaction zone (Int-Z) resulted depending on the nozzle space, s, jet flow rate, Q, nozzle height, H and plate speed, Vp. These are: non-splashing thick interaction film and thin upwash splashing fountain. If the effect of plate motion is not enhanced then the interaction flow characteristics is preserved similar to stationary plate. However, the moving plate can successfully alter the interaction flow type from strong splashing fountain to nonsplashing thick film if the velocity ratio Vp / Vimp passed certain magnitude for a given nozzle spacing distance s. Higher velocity ratio is provided by lowering the nozzles from H = 1.5 m to H = 0.5 m. It is noted that increasing the plate speed or lowering the jet flow rate would decrease splashing and the interaction fountain would more likely change to dome-shape interaction film. For example, the interaction flow conversion occurred at the series of experiments at 22 L/min twin jets (both H = 0.5 and 1.5 m) on 1.5 m/s plate and at 10 L/min three jets (H = 0.5 m) on 1.5 m/s plate. Partial transition at Int-Z was obtained if the plate speed decreased or the jet flow rate increased for a given nozzle separation H. For example, the thin sheet upwash fountain was not changed entirely at twin jets experiments of Q = 22 L/min, Vp = 1.0 m/s, H = 1.5 m or three jets experiments of Q = 15 L/min, Vp = 1.5 m/s, H = 0.5 m. The change in flow characteristics at Int-Z and the diminishing splattering fountain, even for closespaced nozzles, are direct results of plate motion which does not take place on nonmoving impingement surface. The wetting vicinity to Int-Z has influential role on the start of transition because it exerts unequal outflow conditions on drainages from upside and downside ends of the Int-Z over the plate surface in addition to splashing from top of the region. Strong splashing that was observed at the beginning of the test weakens by the development of impingement water. Indeed, the wetting front is created initially attached to the upside end of Int-Z which block the outflow and triggers huge splashing at the start of the test.  194  The above observations also depict the influence of surface wetness on splashing. The splashing was more agitated when the jet hits the front of moving plate partially because of impinging on a dry surface which presented non-wetted solid surface condition to the jet. However, the splattering from upwash fountain decreased gradually as the jet moved over the plate surface because it impinged into the pool of water instead of dry surface. This is similar to the difference of free surface and plunging jets impingement. Then one may infer that less water is wasted by a plunging jet due to reduced splashing with respect to a free-surface jet. Impinging circular water jets at ROT cooling are, in general, plunging jets. This helps to maintain strong pool of water over strip surface with reducing water waste. In addition to affecting the Int-Z, the plate motion also affected the HJ due to multiple parent jets. In twin jet experiments (22 and 30 L/min), the wetting front on moving surface contracted the interacting jumps and wall jets with respect to stationary plate. The large pool of water splits the wetting front from the HJ front which, in turn, is controlled by the wetting front. For 10 and 15 L/min jets the wetting front was unified with HJ similar to single jet experiments. The comparison of HJ at single, twin and three jets experiments reveals that similar HJ shape and HJ radii above the impingement point was represented for a given Q and Vp. Fountain asymmetry, unsteadiness and wavy stagnation line are rooted mainly from non-identical conditions of the parent jets (Q, etc) which are inevitable from practical considerations.  7.1.4 Numerical Simulations Stationary plate simulations with laminar and suitable turbulent models for jet impingement show that the experimental and analytical results for velocity and pressure fields obtained for short and laminar jets are valid for long turbulent liquid jet if the effect of gravity is included in the correlations by using Vimp and dimp. However, Ochi correlations (equations 6.21, 6.22) under/overestimate the velocity and pressure, respectively. This may lead to an elevated heat transfer coefficient at the stagnation zone for turbulent long jets. Generally, shear-stress transport k-ω model (SST) have better performance in modeling of thin impingement water layer in the parallel zone especially  195  for lower flow rates and in locating the hydraulic jump. However, realizable k-ε turbulent model (RKE) models better predicts the jet axial velocity before impingement. The moving plate simulations of single jet performed for different jet flow rates and plate speed up to Vp = 10 m/s. They demonstrate that impingement region deforms and becomes noncircular over surface. The shifted stagnation point introduces noncircular impingement region and unsymmetrical radial spreading of impingement flow. The negative flow velocity in longitudinal direction resulting from higher plate speed shows that the backward flow in parallel zone is pushed toward the impingement zone in direction of plate motion and it interferes with the outgoing flow from incoming jet which would influence the heat transfer at impingement region. If the plate velocity is high enough (e.g. Vp = 10 m/s) then the negative velocity covers a large portion of mainstream impingement flow and ultimately it washes the impingement flow beneath the nozzle in direction of motion. The water flow below the impingement point is forced to speed up in direction of moving plate and the water layer thins significantly downstream. This backwash flow was seen and reported in mill production [33] but now demonstrated numerically by these simulations. Therefore, the number of nozzles in a jet line and the distance between following jet-lines should be adjusted adequately to have enough amount of water covering the moving surface due to accelerated thinning of water layer below the impingement point. Otherwise, the hot surface quickly dries out in motion direction and nonuniform heat removal would result. This more complicates the CFD-ROT study especially when adding the mixing effect of boiling. In general, these industrial simulations were numerically expensive due to computational requirements and simulation time. The simulation of full scale domain has to run on parallel high capacity computers (or a cluster) for 2-3 months with at least 16 cores. Running the present experiments, extracting the data from films, assessment and processing the results needed to spend long time and put many efforts. For each series of experiments, conducting the tests took 1-2 days, inspecting films, data processing and measurement took 3 weeks, etc.  196  7.2 Conclusions The outcomes of this research are summarized below: a) The hydrodynamics of water jet impingement has been investigated experimentally for industrial scale parameters used in steel mills. In particular, the following cases have been investigated and the results are documented: -  Single jet impinging on cold stationary plate.  -  Single jet impinging on moving unheated plate.  -  Hydraulic jump on stationary and moving plate due to single impinging jet.  -  The wetting zone on moving surface.  -  Multiple jets impinging on stationary cold plate.  -  Multiple jets impinging on moving unheated plate.  -  Effect of moving impingement surface on liquid jets interaction.  b) Existing empirical relations in the literature governing flow characteristics (such as velocity and pressure distributions and HJ) have been checked and their validity for the industrial conditions has been discussed. c) A correlation for circular hydraulic jump on fixed plate has been proposed which predicts CHJ radius within ±10 errors while existing correlations in the literature over/underestimate the jump radius and they are suitable for short jets. d) A correlation for the radius of noncircular hydraulic jump on moving surface in terms of relevant industrial parameters has been developed which represents the present experimental data by ±7 errors. e) Numerical simulations of jet impingement on fixed and moving plate with industrial scale were performed with appropriate turbulent models. This involved modeling and simulation of both the free falling long jet as well as the impingement and parallel flow regimes. f) Demonstrating backwash flow by numerical simulation of moving plate at mill operating conditions (where plate velocity is much higher than jet velocity).  197  7.3 Recommendations and Future Works Experiments and numerical simulations were performed on unheated plate. However, the results can guide the modeling efforts of industrial heat transfer processes and for assessing the existing empirical correlations for short jets. The following points are identified for future work and for improvements that would hopefully lead to better understanding and accurate simulation of the hydrodynamics and heat transfer simulation of industrial impinging jets: a) Numerical simulations show good comparison of flow velocity and pressure at impingement and parallel zones on fixed plate. However, experimental measurements on long fully developed turbulent liquid jets (H/d > 50) and high Re number, typically above 30, 000, discharging from large diameter nozzle relevant to industries are needed to fully characterize the flow field along the plate experimentally and to study the common features with short jets where no unsteadiness and jet contraction are encountered. Appropriate measurements of the amount of splattering and the surface wave frequency (wavelength) on moving surface should be investigated to quantify the effect of these features on cooling liquid jet impingement particularly with multiple jets. b) So far, heat transfer and hydrodynamics of water jets have been studied separately at UBC ROT facility and in most of the literature. However, boiling add mixing and turbulence into the impingement flow over the surface. Hence, an important step is the study of impingement flow hydrodynamics over hot plate at this facility especially on hot stationary/moving plate by single/multiple impinging jets. Delineating the wetting region and investigating the wetting front on hot plate at different process parameters is quite valuable for ROT modeling. Excessive vapour covers the hot plate surface and blocks proper observation and filming necessary for studying the wetting area. Special fan knife or other techniques should be tested with careful setup to reduce the vapour. c) The flow structure at interaction zone is important for the overall heat extracted from the plate. Previous researchers [61-63] show secondary peak in heat transfer coefficient due to jet interactions t this region. The upwash high speed thin liquid  198  fountain has higher level of turbulence when compared with the calm interaction thick film and more likely higher rate of heat removal would occur. However, some water is wasted by splashing from thin fountain sheet leading to more water usage. Proper heat transfer experiments are needed to compare the effect of these two types of interaction liquid flow on heat extraction. Moreover, the experimental measurement of turbulence intensities at this region is also important to assess the effect of turbulence level on heat transfer. d) The experimental results for moving plate were obtained with speed limitation in the UBC-ROT (Vp not exceeded 0.5Vimp or 1.5 m/sec). Experiments with higher plate speeds similar to those encountered in industry (~ 5m/sec) are required to properly examine jet interaction, wetting front and splashing at velocity scale of mill production. Attaining such speeds requires major changes in the existing experimental setup. e) Other changes in the existing experimental setup are required to fully study the characteristics of the flow for multiple jet impingement on moving plate. For example, the cross flow between adjacent jets (for in-line array of nozzles) may be studied by mounting a camera below a clear test plate. This is not possible with the available and existing setup. f) Splashing was somewhat captured using second order discretization scheme in the numerical simulations but jet surface disturbance, surface wave and detailed splashing were not captured adequately. Investigating different numerical scheme, turbulent modeling and grid dependency, is important in the regards. g) High velocity simulations, i.e., Vp = 5, 10 m/s prove flow separation from fast moving plate. Sophisticated turbulent models for flow separation and adverse pressure gradient should be examined for proper simulation of impingement flow interaction with plate surface in mill scale velocity. Certainly, this increases the computational expense noticeably and should not start with full scale modeling. h) The capability of FLUENT on flow boiling simulation in simple cases such as nucleate boiling in the impingement zone should be examined by writing userdefined functions and exploiting different multi-phase models.  199  i) Testing high level turbulent models such as Large-Eddy Simulation (LES) for multiple jets with 3-D simulation at interaction zone to assess details of complex flow structure particularly for thin upwash splashing fountain. Limited information on turbulence intensity, eddy scales, etc. at interaction zone is available in the literature due to liquid wall high speed jets. j) Combined heat transfer and hydrodynamics simulation of liquid jet interaction is very valuable and opens the window to numerical simulation of ROT cooling. Intensive parallel computational facilities are needed for such full scale simulation. 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Heat Mass Transfer, Vol.21, pp. 295-30, 1978.  209  Appendix A Flow Rate Measurement at Fixed Plate Tests This appendix includes the information of the repetition tests for the series of single jet experiments on stationary plate for 15 and 30 flow rates.  Table A.1 Experiments on Fixed Plate, Jet Flow Rate Q = 15 L/min Ave Q STDV Ave Q STDV Exp No. Exp No. (L/min) (L/min) (L/min) (L/min) 1  14.976  0.340616  24  14.760  0.344398  2  14.921  0.341458  25  14.738  0.366353  3  14.890  0.33744  26  14.691  0.342584  4  14.852  0.341332  27  14.642  0.342954  5  14.812  0.339827  28  14.646  0.348486  6  14.802  0.344281  29  14.638  0.345961  7  14.768  0.341952  30  14.944  0.386546  8  14.744  0.343572  31  14.878  0.33987  9  14.763  0.341838  32  14.898  0.338703  10  14.762  0.345172  33  14.845  0.340186  11  14.967  0.341913  34  14.789  0.340606  12  14.939  0.343335  35  15.676  0.381106  13  14.942  0.343554  36  15.783  0.351331  14  14.926  0.343062  37  15.785  0.331708  15  14.920  0.339392  38  15.791  0.33644  16  14.940  0.341791  39  15.775  0.350018  17  14.937  0.341452  40  15.669  0.357184  18  14.939  0.343253  41  15.621  0.339192  19  14.939  0.339469  42  15.541  0.343642  20  14.953  0.338767  43  15.512  0.341852  21  14.827  0.379395  44  15.436  0.346412  22  14.809  0.346692  45  15.357  0.341554  23  14.781  0.344774  Average  15.033  0.358112  210  Table A.2 Experiments on Fixed Plate, Jet Flow Rate Q = 30 L/min Ave Q STDV Ave Q STDV Exp No. Exp No. (L/min) (L/min) (L/min) (L/min) 1  29.215  0.306463  22  30.658  0.298242  2  29.322  0.30604  23  30.672  0.297448  3  29.412  0.304432  24  30.677  0.349695  4  29.490  0.2975  25  30.707  0.297047  5  29.560  0.296779  26  29.782  0.311076  6  29.652  0.305616  27  29.844  0.315636  7  29.592  0.298937  28  29.816  0.314481  8  29.694  0.298565  29  29.778  0.308479  9  29.707  0.302739  30  29.843  0.302415  10  29.850  0.300474  31  29.860  0.305582  11  29.956  0.299368  32  29.927  0.302415  12  30.062  0.298685  33  30.169  0.307926  13  30.150  0.302153  34  30.204  0.303074  14  30.357  0.301712  35  30.251  0.292847  15  30.415  0.296541  36  30.256  0.302687  16  30.496  0.300211  37  30.290  0.296176  17  30.512  0.30181  38  30.329  0.301097  18  30.498  0.298513  39  30.335  0.297011  19  30.576  0.302145  40  30.365  0.305692  20  30.587  0.300017  41  30.407  0.301753  21  30.624  0.297806  Average  30.095  0.418066  211  Appendix B Flow Rate and Plate Velocity Measurements at Moving Plate Tests: Single Jet This appendix includes the information of the repetition tests for a sample series of single jet experiments on moving plate for three flow rates. The information for all series of the experiments is available on a CD and in not presented here for sake of briefness.  The series of experiments for: 10 L/min Flow rate, 0.6 m/s plate speed Table B.1 Nozzle flow rates (L/min) Exp No  Ave Q L/min  STDV  Conf. 95%  Q L/min  1  10.289  0.0946  0.01239  0.53  2  9.993  0.1013  0.01241  0.54  3  10.096  0.1051  0.01287  0.55  4  10.145  0.1052  0.01289  0.99  5  10.183  0.0908  0.01113  0.48  Average  10.141  0.0994  0.0123  0.618  Ave Q (%)  6.18  Where: Q is the nominal jet flow rate issued from the nozzles at the test (= 10, 15, 22, 30 L/min), Ave Q is the average jet flow rate during the test (L/min), Q = Qmax – Qmin , Qmax and Qmin are the maximum and minimum flow rate recorded during the test, respectively.  212  Table B.2 Plate velocities (m/s) STDV  Conf. 95%  Vp  0.633  0.02109  0.00491  0.07  2  0.627  0.01696  0.00029  0.08  3  0.582  0.04809  0.00794  0.18  4  0.624  0.02842  0.00463  0.1  5  0.604  0.01997  0.00377  0.07  Average  0.614  0.02691  0.00430  0.1  Exp No  Ave Vp  1  m/s  Ave Vp (%)*  m/s  16.67  Where: Vp is the nominal plate speed of the test (= 0.6, 1.0, 1.5 m/s), Ave Vp is the average plate velocity during the test, Vp = Vpmax – Vpmin , Vpmax and Vpmin are the maximum and minimum velocity recorded during the test, respectively.  213  The series of experiments for: 15 L/min Flow rate, 0.3 m/s plate speed Table B.3 Nozzle flow rates (L/min) STDV  Conf. 95%  1  Ave Q L/min 15.237  0.10449  0.01004  Q L/min 0.62  2  15.157  0.11070  0.01064  0.62  3  15.121  0.10756  0.00996  0.56  4  15.168  0.10523  0.00941  0.64  5  14.995  0.10867  0.01006  0.58  6  15.041  0.11002  0.00984  0.57  7  15.026  0.10947  0.01014  0.57  8  14.993  0.11528  0.01068  0.66  9  14.988  0.11105  0.00993  0.59  10  15.043  0.11114  0.00994  0.62  11  15.056  0.11026  0.01060  0.61  Average  15.075  0.10944  0.01011  0.604  Ave Q (%)  4.02  Exp No  Table B.4 Plate velocities (m/s) STDV  Conf. 95%  Vp  0.313  0.00575  0.00072  0.03  2  0.311  0.02591  0.00303  0.09  3  0.310  0.02152  0.00268  0.08  4  0.298  0.00620  0.00082  0.03  5  0.306  0.00689  0.00085  0.03  6  0.299  0.00589  0.00063  0.03  7  0.301  0.00777  0.00083  0.06  8  0.307  0.00626  0.00068  0.03  9  0.298  0.00593  0.00062  0.03  10  0.289  0.00606  0.00065  0.03  11  0.322  0.00598  0.00105  0.03  Average  0.305  0.00947  0.00114  0.043  Ave Vp (%)  14.24  Exp No  Ave Vp  1  m/s  214  m/s  The series of experiments for: 30 L/min Flow rate, 1.0 m/s plate speed Table B.5 Nozzle flow rates (L/min) STDV  Conf. 95%  1  Ave Q L/min 30.208  0.30357  0.03719  Q L/min 1.36  2  29.895  0.28650  0.04052  1.11  3  30.620  0.50698  0.05071  1.96  4  30.488  0.29054  0.04110  1.52  5  30.531  0.29950  0.03922  1.29  6  30.568  0.29184  0.04128  1.39  7  30.613  0.28896  0.04087  1.32  8  30.869  0.23725  0.03107  1.16  9  30.561  0.30400  0.03981  1.4  10  30.457  0.32228  0.04220  1.63  Average  30.481  0.31314  0.04040  1.414  Ave Q (%)  4.714  Exp No  Table B.6 Plate velocities (m/s) STDV  Conf. 95%  Vp  1.026  0.01585  0.00453  0.09  2  1.023  0.01799  0.00499  0.06  3  1.034  0.01655  0.00459  0.09  4  1.036  0.01353  0.00395  0.04  5  1.038  0.01918  0.00537  0.06  6  1.039  0.01501  0.00454  0.04  7  1.046  0.01479  0.00447  0.04  8  1.058  0.01749  0.00343  0.05  9  0.944  0.01475  0.00288  0.05  10  0.930  0.01601  0.00311  0.06  Average  1.017  0.01611  0.00419  0.058  Ave Vp (%)  5.8  Exp No  Ave Vp  1  m/s  215  m/s  The series of experiments for: 45 L/min Flow rate, 1.3 m/s plate speed Table B.7 Nozzle flow rates (L/min) STDV  Conf. 95%  1  Ave Q L/min 45.777  0.17990  0.02545  Q L/min 0.79  2  45.795  0.17724  0.02746  0.79  3  45.792  0.17801  0.02758  0.78  4  45.760  0.17975  0.02785  0.71  5  45.716  0.17187  0.02663  0.74  6  45.768  0.17484  0.02473  0.75  7  45.693  0.17957  0.02782  0.8  8  45.719  0.16837  0.02382  0.81  9  45.696  0.16085  0.02275  0.73  10  45.695  0.17938  0.02537  0.78  Average  45.741  0.17498  0.02595  0.768  Ave Q (%)  1.71  Exp No  Table B.8 Plate velocities (m/s) STDV  Conf. 95%  Vp  1.260  0.00854  0.00258  0.03  2  1.278  0.00947  0.00252  0.03  3  1.288  0.01296  0.00371  0.04  4  1.270  0.01082  0.00276  0.03  5  1.324  0.01340  0.00354  0.06  6  1.314  0.11525  0.03227  0.27  7  1.339  0.02568  0.00759  0.12  8  1.288  0.01515  0.00469  0.08  9  1.237  0.01846  0.00579  0.08  10  1.305  0.01151  0.00270  0.05  Average  1.290  0.02412  0.00682  0.079  Ave Vp (%)  6.08  Exp No  Ave Vp  1  m/s  216  m/s  Appendix C Flow Rate and Plate Velocity Measurements at Moving Plate Tests: Multiple Jets This appendix includes the information of the repetition tests for a sample series of two and three jets experiments. The information for all series of the twin and triple jets experiments is available on a CD which appended to this thesis but included here for sake of briefness.  The series of experiments for: No. of nozzles: N=2, flow rate: 10 L/min, plate speed: 1.5 m/s and Height H=1.5 m Table C.1 Nozzle flow rates (L/min) Exp No 1 2 3 4 5 6 7 8  N  Ave Q  STDV  Conf. 95%  Q  1  10.59535  0.269848  0.033056  10  2  10.58383  0.105783  0.012958  5.2  1  10.13766  0.234285  0.033139  8.4  2  10.55698  0.112814  0.015957  5.8  1  10.11073  0.232875  0.03294  8.8  2  10.55802  0.099324  0.014049  5  1  10.1067  0.237534  0.031106  8.2  2  10.54455  0.113394  0.01485  5.6  1  10.09724  0.233254  0.032993  8.3  2  10.52755  0.108901  0.015404  5.5  1  10.06785  0.220647  0.027029  8  2  10.52016  0.114086  0.013975  7.7  1  10.06906  0.212692  0.030085  8.1  2  10.52594  0.112693  0.01594  5.2  1  10.06406  0.217003  0.026582  8.3  2  10.49523  0.11435  0.014008  5.6  217  Table C.1 Nozzle flow rates (L/min) - Cont. Exp No 8 9 10 11 12 13 14 Average  N  Ave Q  STDV  Conf. 95%  Q  1  10.06406  0.217003  0.026582  8.3  2  10.49523  0.11435  0.014008  5.6  1  10.05652  0.221476  0.02713  8.4  2  10.49121  0.114791  0.014062  5.4  1  10.04019  0.217407  0.033687  7.8  2  10.49256  0.114646  0.017764  5.6  1  10.03432  0.217105  0.030709  8.4  2  10.50318  0.111232  0.015734  7.1  1  10.03667  0.222389  0.031457  8.2  2  10.4774  0.113144  0.016004  5.6  1  10.0349  0.209587  0.029646  7.8  2  10.47031  0.113539  0.01606  5.3  1  10.02724  0.216612  0.030639  7.8  2  10.48229  0.115609  0.016353  5.4  1  10.1056  0.14486  0.07588283  8.325  2  10.5164  0.03478  0.01821842  5.714  Where: Q is the nominal jet flow rate issued from the nozzles at the test (= 10, 15, 22, 30 L/min), Ave Q is the average jet flow rate during the test (L/min), Q = Qmax – Qmin , Qmax and Qmin are the maximum and minimum flow rate recorded during the test, respectively.  218  Table C.2 Plate velocities (m/s) Exp No  Ave Vp  STDV  Conf. 95%  Vp (%)  1  1.595593  0.044422  0.011335  10  2  1.606552  0.060191  0.015491  12.667  3  1.536508  0.10018  0.024738  16  4  1.590317  0.047924  0.011834  11.333  5  1.544921  0.020936  0.00517  6  6  1.608525  0.049794  0.012496  12.667  7  1.520317  0.019425  0.004797  7.333  8  1.518095  0.01605  0.003963  5.333  9  1.525806  0.01325  0.003298  4  10  1.53697  0.017539  0.004231  6.667  11  1.54  0.013198  0.003259  5.333  12  1.540313  0.016994  0.004163  5.333  13  1.545254  0.016954  0.004326  5.333  14  1.555238  0.014904  0.00368  5.333  Average  1.5405  0.06193  0.0324405  8.0953  Where: Vp is the nominal plate speed of the test (= 0.6, 1.0, 1.5 m/s), Ave Vp is the average plate velocity during the test, Vp = Vpmax – Vpmin , Vpmax and Vpmin are the maximum and minimum velocity recorded during the test, respectively.  219  The series of experiments for: No. of nozzles: N=3, flow rate: 15 L/min, plate speed: 1.5 m/s and Height H=1.5 m  Table C. 3 Nozzle flow rates (L/min) Exp No 1  2  3  4  5  6  7  8  N  Ave Q  STDV  Conf. 95%  Q  1  15.40516  0.116794  0.01652  3.066667  2  15.21047  0.107758  0.015242  4.4  3  15.72536  0.104355  0.014761  3.733333  1  15.39831  0.121806  0.018874  3.666667  2  15.13119  0.156998  0.024327  8.333333  3  15.692  0.121307  0.018796  4.266667  1  15.35214  0.113286  0.016024  3.8  2  15.07625  0.15327  0.02168  5.4  3  15.55375  0.085348  0.012072  3.6  1  15.3216  0.10077  0.012344  2.733333  2  15.08352  0.139324  0.017067  5.733333  3  15.54031  0.085977  0.010532  3.533333  1  15.32365  0.098364  0.01136  3.066667  2  15.06569  0.151502  0.017497  5.8  3  15.59625  0.090333  0.010433  3.066667  1  15.31094  0.098439  0.013924  3.066667  2  15.07922  0.134253  0.01899  5.533333  3  15.56979  0.085706  0.012123  3.266667  1  15.31569  0.297576  0.046109  25  2  14.9485  0.162094  0.025116  5.066667  3  15.48206  0.072443  0.011225  2.6  1  15.29031  0.086768  0.012273  2.8  2  15.01854  0.160467  0.022698  6.666667  3  15.47995  0.085526  0.012097  2.866667  220  Table C.3 Nozzle Flow Rates (L/min) - Cont. Exp No 9  Average  N  Ave Q  STDV  Conf. 95%  Q  1  15.28799  0.087008  0.011394  2.666667  2  15.05866  0.132911  0.017406  5  3  15.44951  0.101492  0.013291  8.666667  1  15.334  0.04273  0.02791946  2.763  2  15.0748  0.07142  0.04666079  5.7704  3  15.5654  0.09407  0.06146007  3.956  Table C.4 Plate Velocities (m/s) Exp No  Ave Vp  STDV  Conf. 95%  Vp (%)  1  1.381408  0.040118  0.009332  10  2  1.628525  0.047323  0.011876  14.667  3  1.565753  0.169361  0.038851  46  4  1.619265  0.091036  0.021637  26  5  1.59875  0.097435  0.023871  25.333  6  1.555692  0.020537  0.004993  6.667  7  1.620896  0.09201  0.022032  28  8  1.483377  0.119754  0.026748  36.667  9  1.52913  0.040284  0.009505  12.667  Average  1.55364  0.08049  0.0525838  22.889  221  The series of experiments for: No. of nozzles: N=2, flow rate: 22 L/min, plate speed: 0.6 m/s and Height H=1.5 m Table C.5 Nozzle Flow Rates (L/min) Exp No 1  2  3  4  5  6  7  Average  N  Ave Q  STDV  Conf. 95%  Q  1  22.45141  0.144655  0.015849  3.5  2  22.55681  0.113014  0.012382  3.545455  3  23.47213  0.064676  0.007086  2  1  22.35045  0.137464  0.015876  3  2  22.48455  0.261585  0.030211  6.818182  3  23.43833  0.065922  0.007613  2  1  22.41278  0.178294  0.020592  5.409091  2  22.54344  0.128001  0.014783  4.590909  3  23.41719  0.074862  0.008646  2.136364  1  22.33691  0.145249  0.016775  3.409091  2  22.55132  0.114975  0.013279  3.954545  3  23.4092  0.069951  0.008079  2.318182  1  22.47236  0.141562  0.016349  3.590909  2  22.56156  0.123195  0.014228  3.136364  3  23.40951  0.06012  0.006943  1.909091  1  22.46635  0.150503  0.017382  3.090909  2  22.22587  0.328926  0.037988  5.545455  3  23.41229  0.067609  0.007808  2.363636  1  22.32578  0.155756  0.01908  4.363636  2  22.56742  0.118866  0.014561  3.181818  3  23.44629  0.071064  0.008705  3.181818  1  22.4021  0.06354  0.04706913  3.766  2  22.4987  0.12337  0.09139234  4.396  3  23.4291  0.02385  0.0176678  2.273  222  Table C.6 Plate Velocities (m/s) Exp No  Ave Vp  STDV  Conf. 95%  1  0.616477  0.012286  0.001815  2  0.612025  0.013154  0.002019  3  0.577742  0.043846  0.006301  4  0.604211  0.015506  0.002465  5  0.616684  0.016493  0.002345  6  0.607525  0.01626  0.002265  7  0.640979  0.031294  0.005129  Average  0.60959  0.02568  0.01902574  223  Vp (%) 11.667 11.667 23.333 8.3333 10 15 21.667 14.523  The series of experiments for: No. of nozzles: N=2, flow rate: 30 L/min, plate speed: 1.0 m/s and Height H=1.5 m Table C. 7 Nozzle flow rates (L/min) Exp No 1 2 3 4 5 6 7 8 9  Average  N  Ave Q  STDV  Conf. 95%  Q  1  30.20518  0.093655  0.012265  1.566667  2  30.79598  0.099631  0.013047  1.633333  1  30.44384  0.118581  0.015529  1.933333  2  30.7375  0.106779  0.013983  2.033333  1  30.45156  0.127743  0.015648  2.1  2  30.71414  0.109941  0.013468  1.9  1  30.42281  0.127486  0.016695  2.3  2  30.76299  0.111554  0.014609  1.9  1  30.45772  0.121684  0.015935  1.766667  2  30.73089  0.120224  0.015744  2.166667  1  30.46585  0.116566  0.015265  2  2  30.83353  0.105527  0.013819  1.733333  1  30.52214  0.111252  0.015736  1.766667  2  30.79698  0.112176  0.015867  2.333333  1  30.40938  0.116074  0.015201  1.833333  2  30.76696  0.104584  0.013696  1.7  1  30.50478  0.110104  0.014419  1.633333  2 1  30.73098  0.116388  0.015242  2.266667  30.4316  0.09216  0.06020766  1.69  2  30.7634  0.03933  0.02569454  1.766  224  Table C.8 Plate velocities (m/s) Exp No  Ave Vp  STDV  Conf. 95%  Vp (%)  1  1.011143  0.029817  0.005703  11  2  1.012115  0.019887  0.003822  9  3  0.929667  0.02981  0.006159  12  4  1.018812  0.024425  0.004763  10  5  0.99951  0.026788  0.005199  10  6  1.023366  0.030175  0.005885  12  7  1.019604  0.024038  0.004688  10  8  1.036296  0.024821  0.004681  10  9  1.017857  0.026134  0.005174  10  Average  1.00711  0.03104  0.02027875  9.4  225  The series of experiments for: No. of nozzles: N=3, flow rate: 15 L/min, plate speed: 1.0 m/s and Height H=0.5 m Table C.9 Nozzle flow rates (L/min) Exp No 1  2  3  4  5  6  7  8  N  Ave Q  STDV  Conf. 95%  Q  1  15.25763  0.079065  0.010354  2.6  2  15.60701  0.076266  0.009988  2.666667  3  15.6179  0.111643  0.01462  3.733333  1  15.22554  0.077914  0.010203  2.533333  2  15.68098  0.143817  0.018834  8.6  3  15.61665  0.1003  0.013135  3.466667  1  15.24153  0.084158  0.008792  2.866667  2  15.69668  0.109282  0.011416  4.866667  3  15.53991  0.093892  0.009809  4.466667  1  15.17875  0.069277  0.009072  2.333333  2  15.72125  0.102148  0.013377  4.866667  3  15.52201  0.12614  0.016519  7.466667  1  15.16  0.072162  0.010207  2.8  2  15.71839  0.094797  0.013409  3.466667  3  15.46594  0.079739  0.011279  2.666667  1  15.17558  0.065596  0.00859  2.133333  2  15.68982  0.105999  0.013881  3.733333  3  15.48433  0.092171  0.01207  3.066667  1  15.18951  0.068391  0.008956  2.6  2  15.72094  0.101028  0.01323  3.8  3  15.47728  0.374028  0.048981  37.66667  1  15.19891  0.072385  0.008867  2.733333  2  15.71547  0.125897  0.015422  4.733333  3  15.45348  0.092876  0.011377  3.666667  226  Table C.9 Nozzle flow rates (L/min) - Cont. Exp No 9  10  11  12  Average  N  Ave Q  STDV  Conf. 95%  Q  1  15.19005  0.074725  0.01057  2.666667  2  15.71875  0.126824  0.017939  4.066667  3  15.50552  0.098309  0.013906  3.6  1  15.1475  0.061949  0.008763  2.066667  2  15.73677  0.117215  0.01658  4.133333  3  15.54615  0.101004  0.014287  3.666667  1  15.13823  0.05881  0.008319  1.866667  2  15.69302  0.100497  0.014215  2.933333  3  15.63057  0.106595  0.015078  3.733333  1  15.14151  0.063091  0.008924  1.866667  2  15.6949  0.106624  0.015082  3.933333  3  15.88833  0.143159  0.02025  4.666667  1  15.1873  0.03886  0.0219851  2.422  2  15.6995  0.03351  0.01895886  4.317  3  15.5623  0.1195  0.06761137  6.822  227  Table C.10 Plate velocities (m/s) Exp No  Ave Vp  STDV  Conf. 95%  Vp (%)  1  0.983505  0.039818  0.007924  14  2  1.021856  0.021376  0.004254  9  3  1.063523  0.119597  0.024988  33  4  1.004242  0.034496  0.006795  15  5  1.073868  0.071121  0.013539  22  6  1.014667  0.030855  0.005902  13  7  1.024206  0.115375  0.021861  29  8  0.953737  0.020131  0.003966  8  9  1.097938  0.029893  0.005949  15  10  1.065213  0.025346  0.005124  13  11  1.020194  0.030996  0.005986  13  12  1.030194  0.022965  0.004435  9  Average  1.02943  0.04042  0.02286983  16.083  228  The series of experiments for: No. of nozzles: N=2, flow rate: 22 L/min, plate speed: 1.5 m/s and Height H=0.5 m Table C.11 Nozzle flow rates (L/min) Exp No 1 2 3 4 5 6 7 Average  N  Ave Q  STDV  Conf. 95%  Q  1  22.5375  0.136188  0.021102  2.545455  2  22.134  0.062376  0.009665  1.454545  1  22.51625  0.135247  0.01913  2.772727  2  22.17646  0.062671  0.008865  1.545455  1  22.53406  0.130742  0.020258  2.636364  2  22.17319  0.083781  0.012982  1.909091  1  22.52927  0.126758  0.01793  2.272727  2  22.1199  0.068407  0.009676  1.954545  1  22.53443  0.135969  0.019233  2.681818  2  22.55177  0.11438  0.016179  2.181818  1  22.53713  0.121859  0.018882  2.818182  2  22.56131  0.113786  0.017631  2.636364  1  22.53281  0.128871  0.019968  2.545455  2  22.54094  0.121235  0.018785  2.409091  1  22.5316  0.00733  0.00542654  2.214  2  22.3225  0.21506  0.15931757  2.013  229  Table C.12 Plate velocities (m/s) Exp No  Ave Vp  STDV  Conf. 95%  Vp (%)  1  1.46717  0.012462  0.003355  3.333  2  1.464068  0.011465  0.002925  2.667  3  1.468833  0.012226  0.003093  3.333  4  1.465179  0.009722  0.002546  2  5  1.469615  0.012828  0.003487  3.333  6  1.592586  0.047186  0.012144  14  7  1.5975  0.036494  0.009558  10.667  Average  1.50356  0.06254  0.04632748  5.619  230  Appendix D Interaction Zones Measurements This appendix includes the plots of sample measurements of interaction zones at three jets experiments. The information for all series of triple jets experiments are available on a CD which appended to this thesis but included here for sake of briefness.  Figure D. 1 Data Measurements of Int-Z (N = 3, 10 L/min, Vp = 1.0 m/s) (a) H = 1.5 m (b) H = 0.5 m  Figure D. 2 Data Measurements of Int-Z (N = 3, 10 L/min, Vp = 1.5 m/s) (a) H = 1.5 m (b) H = 0.5 m  231  

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