UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Mechanistic jet impingement model for cooling of hot steel plates Nobari, Amir Hossein 2014

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2014_september_nobari_amirhossein.pdf [ 3.44MB ]
Metadata
JSON: 24-1.0167525.json
JSON-LD: 24-1.0167525-ld.json
RDF/XML (Pretty): 24-1.0167525-rdf.xml
RDF/JSON: 24-1.0167525-rdf.json
Turtle: 24-1.0167525-turtle.txt
N-Triples: 24-1.0167525-rdf-ntriples.txt
Original Record: 24-1.0167525-source.json
Full Text
24-1.0167525-fulltext.txt
Citation
24-1.0167525.ris

Full Text

MECHANISTIC JET IMPINGEMENT MODEL FOR COOLING OF HOT STEEL PLATES by  Amir Hossein Nobari  B.Sc., Sharif University of Technology, 2005 M.Sc., Sharif University of Technology, 2008  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Materials Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   June 2014  © Amir Hossein Nobari, 2014 ii  Abstract Accelerated cooling on the run-out table of a hot rolling mill is a key technology to tailor microstructure and properties of advanced steels. Thus, it is crucial to develop accurate heat transfer models in order to predict the temperature history of the steel plates on run-out tables. The present study describes a strategy to develop a mechanistic cooling model to simulate the temperature of the plate cooled by top water nozzles on a run-out table. Systematic experiments have been carried out on a pilot scale run-out table facility using two types of top nozzles: planar (curtain) and circular (axisymmetric) nozzles. Experimental results for cooling of stationary plates showed that the heat transfer rate depends strongly on the distance from the jet especially in the temperature range where the transition boiling regime occurs. Based on experimental results, a boiling curve model has been proposed that takes into account boiling heat transfer mechanisms and maps local boiling curves for cooling of stationary steel plates. The effects of water flow rate and water temperature on the heat extraction from the plate have been included in the model. Then, systematic experimental heat transfer studies were conducted to investigate the effect of plate speed on the heat transfer rate. It was found that the plate motion influences the heat transfer rate in the film boiling and transition boiling regimes; however, it does not have an effect on the heat flux in the nucleate boiling regime. Moreover, for the circular nozzle system, it was found that the nucleate boiling heat flux does not change with lateral distance. However, heat flux in the film boiling and transition boiling regimes decreases with increasing distance from the longitudinal centerline of the plate. In the next step, a cooling model was proposed by accounting for the boiling curves of single nozzle cooling for moving plates. Transient heat conduction within the plate was analyzed and surface heat flux and temperature histories were iii  predicted. The validity of the cooling model was examined with multiple nozzles experimental data from the literature. Very good agreement with experimental results has been obtained.     iv  Preface This thesis is based on original work conducted at the Materials Engineering Department, The University of British Columbia. I was the lead investigator, responsible for designing experiments, data collection, analysis and interpretation, modeling and writing the Thesis. My supervisors, Dr. Matthias Militzer and Dr. Vladan Prodanovic, were involved in all stages of the project, identified and designed the research program, provided guidance and assisted with the Thesis outline. v  Table of Contents  Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iv Table of Contents ...........................................................................................................................v List of Tables ................................................................................................................................ ix List of Figures .................................................................................................................................x List of Symbols .......................................................................................................................... xvii List of Abbreviations ................................................................................................................. xix Acknowledgements ......................................................................................................................xx Dedication ................................................................................................................................... xxi Chapter 1: Introduction ................................................................................................................1 1.1 TMCP (Thermo-Mechanical Controlled Process) steels ................................................ 1 1.2 Controlled accelerated cooling on the run-out table ....................................................... 2 1.3 Heat transfer mechanism on the run-out table ................................................................ 5 1.4 Background of UBC ROT research work ....................................................................... 7 Chapter 2: Literature review ........................................................................................................9 2.1 Jet impingement hydrodynamics .................................................................................... 9 2.2 Jet impingement boiling heat transfer ........................................................................... 13 2.2.1 Jet impingement boiling of stationary plates ............................................................ 13 2.2.1.1 Film boiling ....................................................................................................... 16 2.2.1.2 Wetting and minimum heat flux ....................................................................... 17 2.2.1.3 Transition boiling .............................................................................................. 21 vi  2.2.1.4 Critical heat flux ............................................................................................... 24 2.2.1.5 Nucleate boiling ................................................................................................ 26 2.2.1.6 Effect of multiple jets on jet impingement boiling ........................................... 27 2.2.2 Effect of surface motion on jet impingement boiling ............................................... 28 2.3 Heat transfer modeling of run-out table cooling ........................................................... 33 Chapter 3: Objectives ..................................................................................................................38 Chapter 4: Experimental methodology ......................................................................................39 4.1 Pilot-scale run-out table facility .................................................................................... 39 4.2 Test plates ..................................................................................................................... 42 4.3 Test procedure ............................................................................................................... 46 4.4 Data analysis ................................................................................................................. 47 4.4.1 Surface temperatures and heat fluxes ....................................................................... 47 4.4.2 Velocity and pressure distribution in liquid jet ......................................................... 51 Chapter 5: Experimental results: stationary plates ..................................................................54 5.1 Experimental matrix...................................................................................................... 54 5.2 Surface temperature and heat flux curves ..................................................................... 55 5.3 Boiling curves ............................................................................................................... 57 5.4 Comparison between steady-state and transient conditions .......................................... 62 Chapter 6: Boiling curve model for cooling of stationary plates .............................................65 6.1 Overview ....................................................................................................................... 65 6.2 Nucleate boiling ............................................................................................................ 65 6.3 Transition boiling: shoulder heat flux ........................................................................... 66 6.4 Minimum heat flux (MHF) and film boiling ................................................................ 75 vii  6.5 Model application to transient cooling (construction of boiling curves) ...................... 77 Chapter 7: Experimental results: moving plates ......................................................................84 7.1 Surface temperature and heat flux histories .................................................................. 84 7.2 Boiling curves ............................................................................................................... 89 7.2.1 Heat flux evolution with surface temperature ........................................................... 89 7.2.2 Effect of plate speed on boiling curves ..................................................................... 91 7.2.3 Effect of lateral distance on boiling curves ............................................................... 93 7.3 Integrated heat flux ....................................................................................................... 96 Chapter 8: Cooling model for moving plates ..........................................................................104 8.1 Single nozzle ............................................................................................................... 104 8.1.1 Overview ................................................................................................................. 104 8.1.2 Calculation of boiling curves: effect of plate speed ................................................ 106 8.1.3 Calculation of boiling curves: effect of lateral distance in circular nozzle system 109 8.1.4 Construction of boiling curves for moving plates................................................... 113 8.1.5 Water front .............................................................................................................. 116 8.1.6 Heat conduction within the plate ............................................................................ 118 8.1.7 Verification ............................................................................................................. 123 8.1.7.1 Planar jet ......................................................................................................... 123 8.1.7.2 Circular jet ...................................................................................................... 127 8.2 Double jet-line arrays .................................................................................................. 133 8.2.1 Jet-line arrangement ................................................................................................ 133 8.2.2 Validation ................................................................................................................ 136 8.2.2.1 Heat flux and surface temperature histories at y=0 ........................................ 136 viii  8.2.2.2 Surface contour plots ...................................................................................... 137 8.2.2.3 Exit temperature .............................................................................................. 141 Chapter 9: Conclusions and future work ................................................................................144 9.1 Summary and conclusions .......................................................................................... 144 9.2 Suggestions for future work ........................................................................................ 147 Bibliography ...............................................................................................................................150 Appendix A: Inverse heat conduction analysis .......................................................................156 Appendix B: Reproducibility of experiments ..........................................................................158 Appendix C: Experimental and calculated boiling curves for stationary plate tests ..........159  ix  List of Tables  Table 2.1 Experimental condition for citied works in section 2.2.1 (values that have not been reported are shown by “-“) ............................................................................................................ 15 Table 2.2 Experimental condition for citied works in section 2.2.2 (values that have not been reported are shown by “-“) ............................................................................................................ 29 Table 4.1 Experimental errors....................................................................................................... 41 Table 4.2 Chemical composition of HSLA steel .......................................................................... 42 Table 4.3 Mesh size for IHC analysis ........................................................................................... 47 Table 4.4 Streamwise water velocity; wji is jet impingement width at the surface; dji is jet impingement diameter at the surface ............................................................................................ 52 Table 5.1 Experimental matrix (SP: Stationary plate/Planar nozzle) ........................................... 54 Table 5.2 Experimental matrix (SC: Stationary plate/Circular nozzle) ........................................ 55 Table 7.1 Test matrix for MP series; process parameters: moving plate, single planar nozzle, Hn=0.1m ........................................................................................................................................ 84 Table 7.2 Test matrix for MC series; process parameters: moving plate, single circular nozzle, Hn=1.5m ........................................................................................................................................ 85 Table 8.1 Available experimental database for cooling of moving plates with single circular nozzle (Chan 2007) ..................................................................................................................... 110 Table 8.2 Available experimental database for double jet-line cooling (Franco 2008) .............. 136  x  List of Figures  Figure 1.1 Schematic of hot rolling mill of steel plates and strips. The schematic plot shows the variation of temperature vs. time and its effect on the phase transformation of austenite decomposition. A: austenite, F: ferrite, P: pearlite, B: bainite, M: martensite. .............................. 4 Figure 1.2 (a) curtain cooling system (planar jet); (b) laminar cooling system (circular jet); (c) spray cooling system (spray jet). .................................................................................................... 4 Figure 1.3 Typical pool boiling curve, showing qualitatively the dependence of the surface heat flux (q) on the surface temperature (Tsurface). .................................................................................. 7 Figure 2.1 Schematic of water impinging as a jet onto a surface (a) the free-surface and (b) plunging jets. ................................................................................................................................... 9 Figure 2.2 Schematic of free surface jet impingement and profile of liquid velocity parallel to the surface: (a) planar jets, (b) circular jets. ....................................................................................... 11 Figure 2.3 Schematic of downstream and upstream regions on the surface of a moving plate. ... 13 Figure 2.4 Schematic of the positions of different flow boiling regimes on the hot surface (modified from Filipovic et al. 1995a). ......................................................................................... 22 Figure 2.5 Local boiling curves; experimental condition: steady-state, ∆Tsub=16 ˚C, Vn=0.8 m/s, Hn=6mm (Robidou et al. 2002). .................................................................................................... 23 Figure 2.6 heat extracted for different nozzle stagger configurations as a function of entry temperature (the surface temperature of the plate, when the water jets first hit the plate during that pass) (Franco 2008)................................................................................................................ 33 Figure 4.1 (a) Schematic of pilot scale run-out table facility, and (b) Schematic of cooling tower (side view). .................................................................................................................................... 40 Figure 4.2 Schematic of (a) planar nozzle and (b) circular nozzle. .............................................. 41 Figure 4.3 Schematic of one spot welded thermocouple to the plate. .......................................... 43 Figure 4.4 Schematic of thermocouple locations with respect of the water jet for stationary plate experiments (a) for tests with the planar nozzle and (b) for tests with the circular nozzle. ......... 44 Figure 4.5 Schematic of thermocouple locations for moving plate experiments: (a) planar nozzle cooling and (b) circular nozzle cooling. ....................................................................................... 45 Figure 4.6 The domain used for inverse heat conduction (IHC) analysis. ................................... 48 xi  Figure 4.7 Effect of filtering approach on temperature data, (a) raw and filtered temperature data. Magnifications of temperature vs. time data are shown for (b) a not-wetted period and (c) a wetted period. The filter smoothens out short term fluctuations before wetting (figure b); however, the actual cooling slope during wetting (figure c) has been retained in the smoothed curve. ............................................................................................................................................. 49 Figure 5.1 (a) Surface temperature vs time curves, (b) schematic of thermocouple locations, (c) internal and surface temperatures at x=0mm, and (d) heat flux vs time curves; test SP01: FR=100 L/min, Twater=25°C. ....................................................................................................................... 56 Figure 5.2 Family of boiling curves; test SP01: FR=100 L/min, Twater=25°C. ............................. 58 Figure 5.3 Experimental maximum heat flux for the planar jet: (a) different water flow rates (b) different water temperatures; and for the circular jet: (c) different water flow rates (d) different water temperatures. ....................................................................................................................... 60 Figure 5.4 Schematic showing (a) the steady-state and (b) the transient boiling curves for jet impingement cooling when high subcooling condition is applied................................................ 62 Figure 5.5 The slope of the first stage in the transition boiling regime. Experimental errors are ±16% for the stagnation point and ±8% for positions away from the stagnation point. For clarity of presentation error bars are not shown. ...................................................................................... 63 Figure 6.1 Nucleate boiling heat flux at the stagnation point. Experimental errors are ±16%. For clarity of presentation error bars are not shown............................................................................ 66 Figure 6.2 Schematic of vapor patches on the surface in the transition bling regime and the liquid/vapor interface. The plot shows the critical size of diamater along the surface. ................ 69 Figure 6.3 Calculated critical diameter of vapor patches and shoulder heat flux profiles: planar nozzle, FR=100 L/min, Twater=25C, Hn=100 mm, wn=3mm. Here, the water temperature is assumed constant along the plate surface. .................................................................................... 71 Figure 6.4 Calculated shoulder heat flux vs. distance, experimental data from test SP01: planar jet, FR=100 L/min, Twater=25°C, (a) different ψ and (b) different β. ............................................ 74 Figure 6.5 Experimental data in Robidou et al. (2002) and the model prediction for the shoulder heat flux: planar jet, Vn=0.8m/s, Twater=84°C, Hn=6 mm. Bars show the scattering range in the shoulder heat flux measurements. ................................................................................................. 75 xii  Figure 6.6 Comparison between calculated MHF using equation (6.12) and the experiment of Robidou et al. (2002). ................................................................................................................... 76 Figure 6.7 Schematic plots showing the procedure of combining boiling regimes for three positions; (1) under the jet, (2) midway, and (3) far from the jet: (a) ideal boiling curves (b) boiling curves with the initial cooling stage. ................................................................................ 79 Figure 6.8 Calculated and experimental boiling curves: (a) test SP01: planar jet, FR=100 L/min, Twater=25°C; (b) test SC01: circular jet, FR=15 L/min, Twater=25°C. Experimental errors are ±16% for the stagnation point and ±8% for positions away from the stagnation point. For clarity of presentation error bars are not shown. ...................................................................................... 80 Figure 6.9 Calculated and experimental maximum heat flux profiles for the planar jet: (a) different water flow rates (b) different water temperatures; and the circular jet: (c) different water flow rates (d) different water temperatures. .................................................................................. 81 Figure 6.10 Calculated and experimental maximum heat flux profiles for (a) the planar jet and (b) the circular jet. ......................................................................................................................... 82 Figure 7.1 Surface temperature vs. time, (a) 15 cooling passes and (b) cooling pass 6; process parameters: planar nozzle, FR=100 L/min, Twater=25°C, Hn=0.1 m. ............................................ 86 Figure 7.2 Heat flux vs. time, (a) 15 cooling passes and (b) cooling pass 6; processes parameters: planar jet FR=100 L/min, Twater=25°C, Hn=0.1 m. ....................................................................... 87 Figure 7.3 Heat flux vs. time for different entry temperatures, process parameters: single circular nozzle, FR=30 L/min, Twater=25˚C, Vp=1.0m/s, position: longitudinal center line (y=0). ........... 88 Figure 7.4 Heat flux evolution vs. surface temperature during cooling pass 6; process parameters: planar jet, FR=100 L/min, Twater=25°C, Hn=0.1 m, cooling pass 6. The arrows show the path of heat flux evolution. ....................................................................................................................... 89 Figure 7.5 Peak heat flux vs. surface temperature, Process parameters: planar jet, FR=100 L/min, Twater=25°C, Hn=0.1 m. Experimental errors for PHF are ±16%. ................................................. 91 Figure 7.6 Effect of plate speed on peak heat flux, parameters: planar jet, FR=100 L/min, Twater=25°C, Hn=0.1m. Experimental errors for PHF are ±16%. .................................................. 92 Figure 7.7 Peak heat flux vs. surface temperature, parameters: circular jet, FR=15 L/min, Twater=25°C, Vp=1 m/s, Hn=1.5 m. P# shows the cooling pass number in the test. Experimental errors for PHF are ±16%. .............................................................................................................. 94 xiii  Figure 7.8 Contour plot showing the surface heat flux (MW/m2) for the test parameters: circular jet, FR=15 L/min, Twater=25°C, Vp=1 m/s, Hn=1.5 m. .................................................................. 95 Figure 7.9 Effect of time interval on the integrated heat flux; process parameters: circular jet, FR=15 L/min, Twater=25°C, Vp=1 m/s, Hn=1.5 m, y=0. Experimental errors for the integrated heat flux are ~±8%. For clarity of presentation error bars are not shown. ........................................... 98 Figure 7.10 Integrated heat flux (a) at y=0mm, (b) at y=38mm; Process parameters: circular jet, Twater=25°C, Vp=1 m/s, Hn=1.5 m. .............................................................................................. 100 Figure 7.11 Integrated heat flux (a) at y=0mm, (b) at y=38mm; Process parameters: circular jet, FR=15 L/min, Vp=1 m/s, Hn=1.5 m. ........................................................................................... 101 Figure 7.12 Integrated heat flux; process parameters: planar jet, FR=100 L/min, Twater=25°C, Hn= 0.1 m. (here, the integration time interval is equal to the time that the plate needs to travel 2m)...................................................................................................................................................... 102 Figure 8.1 Schematic of plate and nozzle, (a) planar nozzle system, (b) circular nozzle system...................................................................................................................................................... 105 Figure 8.2 Procedure for scaling boiling curve. .......................................................................... 108 Figure 8.3 Variation of PHFmax and PHFmin with plate speed. The experimental errors are ±16%...................................................................................................................................................... 108 Figure 8.4 Variation of TPHF,min with plate speed. ...................................................................... 109 Figure 8.5 Normalized PHFmax profile in lateral direction. ........................................................ 111 Figure 8.6 Normalized PHFMIN profile in lateral direction. ........................................................ 112 Figure 8.7 Normalized TPHF,MIN profile in lateral direction. ....................................................... 112 Figure 8.8 Procedure for scaling the idealized boiling curve for a moving plate. ...................... 113 Figure 8.9 Effect of speed on the calculated boiling curves, (a) at x=0 mm and (b) at x=120mm. Process parameters: planar nozzle, FR=100 L/min, Twater=25°C, Hn=0.1 m. The boiling curves have been calculated using the model procedures presented in section 6.5 in combination with the scaling factors. ...................................................................................................................... 114 Figure 8.10 Scaled boiling curves in lateral direction, (a) at x=0 mm and (b) at x=60mm. Process parameters: circular nozzle, FR=30 L/min, Twater=25°C, Vp=1.0m/s, Hn=1.5 m........................ 115 Figure 8.11 Water front in the upstream region of the jet impingement cooling. ...................... 116 Figure 8.12 Flow chart of the cooling model for temperature simulation of a moving plate. .... 121 xiv  Figure 8.13 Calculated temperature of the plate for one cooling pass, Vp=1 m/s, FR=15 L/min, Twater=25°C, y=0. ........................................................................................................................ 122 Figure 8.14 Comparison with experimental results, planar jet, FR=100 L/min, Twater=25°C, Vp=1 m/s, entry temperature: 470°C: (a) heat flux vs. time, (b) heat flux vs. distance, (c) heat flux vs. surface temperature, and (d) surface temperature vs. time. Thin dashed lines in figure c show the boiling curves at different longitudinal distances from the impinging point of the jet. These lines are used as the boundary condition to analyze the heat conduction within the plate. ................ 124 Figure 8.15 Heat flux and surface temperature histories, FR=100 L/min, Twater=25°C, Vp=1 m/s (a) entry temperature: 720°C and (b) entry temperature: 330°C. ............................................... 127 Figure 8.16 Comparison with experimental results, circular jet, FR=30 L/min, Twater=25°C, Vp= 1.3 m/s, entry temperature: 375°C, y=0: (a) heat flux vs. time, (b) heat flux vs. distance, (c) heat flux vs. surface temperature, and (d) surface temperature vs. time. Thin dashed lines in figure c show the boiling curves at different longitudinal distances from the impinging point of the jet. These lines are used as the boundary condition to analyze the heat conduction within the plate...................................................................................................................................................... 128 Figure 8.17 Heat flux and surface temperature histories, FR=30 L/min, Twater=25°C, Vp=1.3 m/s (a) entry temperature: 600°C and (b) entry temperature: 285°C. ............................................... 130 Figure 8.18 Heat flux and surface temperature histories at (a) y=0 mm, (b) y=12.7 mm, (c) y=25.4 mm, (d) y=38.1 mm; process parameters: FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature: 410°C. .................................................................................................................... 131 Figure 8.19 Simulated heat flux and surface temperature histories; process parameters: FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature=410°C. ...................................................... 132 Figure 8.20 Experimental heat flux and surface temperature histories; process parameters: FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature=410°C. ...................................................... 132 Figure 8.21 Schematic of different cooling regions during multiple jet-line cooling. Location of the lateral centerline of the plate is shown by a red rectangular. The water coverage is shown by a blue layer on the plate surface. ................................................................................................. 134 Figure 8.22 (a) non-stagger nozzles in double jet-line cooling, (b) nozzle configuration with respect to the thermocouple positions. ........................................................................................ 135 xv  Figure 8.23 Heat flux and surface temperature histories, Test F08: Sj=508 mm, Vp= 1.0 m/s, y=0, (a) entry temperature: 500°C and (b) entry temperature: 400°C. ............................................... 137 Figure 8.24 Predicted surface contour plots; (a) heat flux and (b) temperature; Sj=508 mm, FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature: 600°C. .......................................... 139 Figure 8.25 Experimental surface contour plots; (a) heat flux and (b) temperature; test F04: Sj=508 mm, FR=15 L/min, Twater=25°C, Vp= 1.0 m/s, entry temperature: 600°C. .................... 139 Figure 8.26 Predicted surface contour plots; (a) heat flux and (b) temperature; Sj=508 mm, FR=15 L/min, Twater=25°C, Vp= 1.0 m/s, entry temperature: 360°C. ......................................... 140 Figure 8.27 Experimental surface contour plots; (a) heat flux and (b) temperature; test F04: Sj=508 mm, FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature: 360°C. ..................... 140 Figure 8.28 Predicted and measured exit temperatures (1mm below the surface) in lateral positions in double jet-line tests:  (a) Vp=0.35 m/s, Sj=25.4 cm; (b) Vp=0.35 m/s, Sj=50.8 cm; (c) Vp=1.0m/s, Sj=25.4 cm; (d) Vp=1.0 m/s, Sj=50.8 cm. ................................................................ 142 Figure 8.29 Predicted and measured mean exit temperatures (1mm below the surface) in double jet-line tests. ................................................................................................................................ 143 Figure B.1 Maximum heat flux along the surface for a test with a planar nozzle, a water flow rate of 100 L/min and a water temperature of 25°C. ......................................................................... 158 Figure C.1 Family of boiling curves, test SP01, planar nozzle, FR=100 L/min, Twater=25°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, (f) 80 mm, and (g) 120 mm. ................. 159 Figure C.2 Family of boiling curves, test SP02, planar nozzle, FR=150 L/min, Twater=25°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, and (e) 120 mm. ...................................................... 160 Figure C.3 Family of boiling curves, test SP03, planar nozzle, FR=250 L/min, Twater=25°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, (f) 80 mm, and (g) 120 mm. ................. 161 Figure C.4 Family of boiling curves, test SP04, planar nozzle, FR=100 L/min, Twater=10°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, and (f) 120 mm. .................................... 162 Figure C.5 Family of boiling curves, test SP05, planar nozzle, FR=100 L/min, Twater=40°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, and (f) 80 mm. ...................................... 163 Figure C.6 Family of boiling curves, test SC01, circular nozzle, FR=15 L/min, Twater=25°C, r: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, (f) 80 mm, and (g) 120 mm. ................. 164 xvi  Figure C.7 Family of boiling curves, test SC02, circular nozzle, FR=30 L/min, Twater=25°C, r: (a) 0 mm, (b) 20 mm, (c) 40 mm, (d) 60 mm, (e) 80 mm, and (f) 120 mm. .................................... 165 Figure C.8 Family of boiling curves, test SC03, circular nozzle, FR=45 L/min, Twater=25°C, r: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, and (f) 80 mm. ...................................... 166 Figure C.9 Family of boiling curves, test SC04, circular nozzle, FR=15 L/min, Twater=10°C, r: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, (f) 80 mm, and (g) 120 mm. ................. 167 Figure C.10 Family of boiling curves, test SC05, circular nozzle, FR=15 L/min, Twater=40°C, r: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 60 mm, (e) 80 mm, (f) 120 mm....................................... 168  xvii  List of Symbols cp Specific heat (J/kg°C) d Jet diameter (m) D Diameter of test cell, m DH Jet hydraulic diameter (m) F Liquid-solid contact area fraction  FR  Water flow rate (L/min) hfg Latent heat of evaporation (J/kg)   Hn Nozzle to surface spacing (m) k Thermal conductivity (W/m°C)  K’  a constant g Gravitational acceleration (m/s2) h Convection heat transfer coefficient (W/m2°C)   Nu Nusselt number  P Pressure on the surface (Pa) P0 Ambient pressure (Pa) Pr Prandtl number  q Heat flux (W/m2 or MW/m2) Re  Reynolds number S Scaling factor Sj Jet-line spacing (m) Sn nozzle spacing (m) t time (s) T Temperature (°C) u Streamwise velocity (m/s) u' Modified streamwise velocity (m/s) V Velocity (m/s) w Jet width (m) x Distance (m or mm)  xviii  Greek letters α Thermal diffusivity (m2/s) β Fraction of heat released which is responsible for increase of water temperature ε  Emissivity factor λ Wavelength of the liquid/vapor interface (m) μ Dynamic viscosity (Pa.s) ν Kinematic viscosity (m2/s) ρ Density (kg/m3) σ Surface tension (N/m) or Stefan–Boltzmann constant (W/m2°C 4) γ Jet deceleration (m/s2) ψ Adjustable parameter in water stream profile  Subscripts crit. Critical j Jet or jet-line ji Jet impingement HZ High heat flux zone l Liquid lat Lateral  LZ Low heat flux zone n Nozzle  p Plate pool Pool boiling stag.  Stagnation point of the jet sat Saturated sub Subcooling sh Shoulder tot Total  v Vapor WF Water front  xix  List of Abbreviations ACC Accelerated cooling CHF Critical heat flux CR Cooling rate CT Coiling temperature DNB Deviation from nucleate boiling DQ Direct quenching to room temperature DQST Direct quenching and self tempering FS First stage in transition boiling regime IC Initial cooling MHF Minimum heat flux (Leidenfrost point) MC Moving plate/Circular nozzle MP Moving plate/Planar nozzle  NB Nucleate boiling ONB Onset of nucleate boiling PHF Peak heat flux PNB Partial nucleate boiling ROT Run-out table SC Stationary plate/Circular nozzle SP Stationary plate/planar nozzle ST Stop temperature TB Transition boiling TC Thermocouple TMCP Thermo-mechanical controlled processing UBC University of British Columbia   xx  Acknowledgements First of all, I would like to express my sincere gratitude to my supervisors, Dr. Matthias Militzer and Dr. Vladan Prodanovic, for providing continuous support, encouragement, and help. Participating in discussions of ROT group meetings was a great experience which I learned so much. Many thanks are extended to Dr. Daan Maijer for his valuable advice and suggestions.  I would also like to thank Mr. Gary Lockhart for providing valuable technical support for the experimental work of this project. Without his help, I could not even conduct one experiment. Moreover, I would appreciate the cooperation of the machine shop team, Mr. Ross McLeod, Mr. David Torok, and Mr. Carl Ng for preparation of samples.  I would also like to extend my appreciation to all my friends and colleagues at UBC. I would like to express my deepest gratitude to my mother, my father and my brother for their encouragement and support during my PhD study. Last but not least, I would like to thank my wife Marjan for standing beside me throughout my study and writing this dissertation.  xxi  Dedication       I would like to dedicate this dissertation to my wife Marjan for all of her love and support.   1  Chapter 1: Introduction   1.1 TMCP (Thermo-Mechanical Controlled Process) steels Steel continues to be an important engineering material for the energy, manufacturing, and transportation sectors because of its attractive mechanical properties, versatility and low cost. In the production of conventionally hot-rolled steels, achieving the nominal dimension, i.e. thickness, width, and length, of the steel product (plate and strip) is the main goal of the hot rolling process. The desired final microstructure and properties are obtained using as a post heat treatment such as normalizing or tempering. However, the recent increase in the demand for hot rolled steel products to be used in more severe service conditions has led to the development of new advanced steel grades with fine grained ferritic and bainitic microstructures. The production of these complex microstructures in steels has promoted the development of technologies to control the phase transformations of steels in the hot rolling process. Thermo-mechanical controlled processing (TMCP) enables the control of microstructural evolution of steel by two main sub-processes. First, in the controlled rolling process, the evolution of austenite microstructure is controlled and the proper austenite microstructure is achieved. Next, in the accelerated cooling process, the phase transformation of austenite decomposition is controlled to achieve the desired final microstructure. The main cooling parameters affecting the microstructure are the cooling rate (CR) and the cooling stop temperature (ST) for plates or the coiling temperature (CT) for strips. The balanced combination of CR and ST/CT controls and engineers the microstructure for different TMCP steel grades 2  (Schwinn et al. 2011). The application of TMCP steels are in different industries such as pipelines, ship hulls, bridges, offshore structures, building construction, and cryogenic tanks (Nishioka and Ichikawa 2012). In production of steel plates, the main goal in terms of mechanical properties is to meet the requirements of higher strength and toughness. In conventionally hot-rolled plates, these mechanical properties are most often obtained by alloying. Despite the fact that proper alloying improves strength and toughness, it can decrease the weldability of the plate and increase the production cost. One of the main advantages of using TMCP is that steel producers can manufacture steel with the same strength as conventional steels with lower alloying additions. Therefore, weldability of steel plates can be improved by using TMCP (Nishioka and Ichikawa 2012).  1.2 Controlled accelerated cooling on the run-out table The microstructural evolution processes such as austenite decomposition and precipitation, are thermally driven and are consequently directly affected by the intensity of cooling employed in TMCP. Different cooling paths of the steel on the run-out table lead to different phase transformation products such as ferrite, pearlite, bainite, and/or martensite (figure 1.1). Cooling conditions also have significant effects on the residual stress distribution and, hence, the flatness of the plate. For the end-user of the plate, the flatness of the plate is an important factor. A non-flat plate or a plate with residual stresses has a negative effect on the post-processes like bending, laser cutting, and welding operations (Carlestam 2011). In order to efficiently apply novel cooling technologies to achieve the desired microstructures as well as proper flatness, it is crucial 3  to develop accurate heat transfer models to predict the temperature profiles during cooling of steel. In plate mills, controlled cooling is classified as: ACC (Accelerated cooling), Heavy ACC (ACC with increased cooling rate), DQST (direct quenching and self tempering) and DQ (direct quenching to room temperature) (Schwinn et al. 2011). During accelerated cooling, water jets impinge on the surface of the steel while the steel is moving on the run-out table (ROT). There are three conventional types of cooling systems used on the run-out table: curtain cooling system, laminar cooling system, and spray cooling system (figure 1.2). In curtain cooling systems, water exits from a long planar nozzle. The water sheet coming from this type of nozzle provides a uniform cooling across the width of the plate. In laminar cooling systems, the steel is cooled with water jets impinging from circular nozzles. To provide sufficient cooling capacity as well as uniform cooling conditions, several circular nozzles are placed in one jet-line (a row of nozzles). In spray cooling systems, water is sprayed on the steel surface, typically covering a large area. Generally, curtain and laminar cooling systems provide higher heat extraction rates than the spray system. Besides the conventional cooling systems, recently some new cooling systems have been developed in order to provide a larger range of possible thermal treatments in hot rolling mills.  For example, the MULPIC (Multi-Purpose Interrupted Cooling) process was developed based on utilizing circular jets of water under high pressure (called Water Pillow Cooling) (Schutz et al. 2001). The aim of this system is to cool the hot rolled steel quickly to the desired stop temperature (for plates) or coiling temperature (for strips).  4   Figure 1.1 Schematic of hot rolling mill of steel plates and strips. The schematic plot shows the variation of temperature vs. time and its effect on the phase transformation of austenite decomposition. A: austenite, F: ferrite, P: pearlite, B: bainite, M: martensite.     Figure 1.2 (a) curtain cooling system (planar jet); (b) laminar cooling system (circular jet); (c) spray cooling system (spray jet). Temperature, °CTime, s (Distance, m)Run-out tableFBMPRolling millsA(a) (b) (c)5   1.3 Heat transfer mechanism on the run-out table Since the temperature of the steel on the run-out table is higher than the boiling temperature of the water impinging on the surface, the dominant mode of heat transfer is jet impingement boiling. The latent heat of evaporation and high specific heat capacity of water allow high rates of heat extraction from the hot steel during cooling.  The boiling curve is the most descriptive representation of surface heat transfer changes during cooling of a hot solid by a liquid. The boiling curve presents heat flux changes with respect to the surface temperature of the solid. This curve is shown qualitatively in figure 1.3 for pool boiling. Pool boiling occurs when a hot surface is submerged in a pool of liquid, whereas forced flow boiling refers to the condition in which liquid flows over the surface (Dhir 1998, Tong and Tang 1997). Although the boiling heat transfer observed during run-out table cooling is categorized as forced flow boiling (Wolf et al. 1993), a pool boiling curve offers the fundamental groundwork for understanding boiling heat transfer in general. Four main regimes occur during pool boiling: single-phase convection (natural convection), nucleate boiling, transition boiling, and film boiling (Dhir 1998, Wolf et al. 1993, Tong and Tang 1997). At low temperatures (below saturation temperature), the water is heated by natural convection. This regime is single-phase convection since no vapor forms and no boiling occurs. At a temperature slightly above the saturation temperature, isolated vapor bubbles begin to form on the surface. This temperature is shown as ONB (onset of nucleate boiling) in figure 1.3 and this boiling regime is called partial nucleate boiling. Partial nucleate boiling is characterized by a dynamic formation, growth and collapse of isolated vapor bubbles on the surface. The latent heat of evaporation and also the induced agitation due to the dynamics of bubbles increase the surface 6  heat flux. With a further increase in temperature the bubble population increases leading to the transition from partial nucleate boiling to fully developed nucleate boiling. It has been observed that in this mode, isolated bubbles begin to merge in the vertical direction and the vapor leaves the surface in the form of jets. Bubbles also merge in the horizontal direction forming occasional vapor patches. However, as the population of the bubbles further increases, the more frequent vapor patches obstruct the path of incoming liquid to the surface thereby decreasing the heat transfer rate. Due to this fact, a maximum in the heat flux curve appears, termed the critical heat flux (CHF). The maximum or CHF represents the upper limit of nucleate boiling heat flux and the termination of efficient cooling conditions on the surface (Dhir 1998). After the CHF point, the surface is covered alternately either by a vapor blanket or a liquid layer. In this regime, called transition boiling, vapor begins to cover larger portions of the surface due to the high evaporation rate. Since the thermal conductivity of the vapor is much lower than that of the water, the vapor acts as an insulating layer and decreases the heat transfer rate from the surface. Hence, in this regime the heat flux decreases with increasing surface temperature until the entire affected surface is covered by a blanket of vapor. At this point, liquid no longer wets the surface of the solid and a minimum heat flux (MHF) is reached in transition boiling region, which is the “Leidenfrost” point. The condition after the stable vapor blanket has formed is referred to as film boiling. In film boiling, heat must be conducted mainly through the vapor blanket before it reaches the liquid, until radiation becomes the dominant mechanism at higher surface temperatures. Despite significant effort to simulate accelerated cooling, it is challenging to accurately incorporate fundamental boiling mechanisms into the transient heat transfer models for the run-out table. This is due to the fact that different boiling regimes are simultaneously occurring at 7  different locations on the surface of the steel during jet impingement cooling. The cooling process is further complicated by the dependency of heat transfer regimes on process parameters such as nozzle geometry, water flow rate and water temperature. Moreover, on the run-out table, jet impingement cooling involves surface motion and interaction between neighboring water jets (Zumbrunnen et al. 1989, Filipovic et al. 1994b, Timm et al. 2002).   Figure 1.3 Typical pool boiling curve, showing qualitatively the dependence of the surface heat flux (q) on the surface temperature (Tsurface).  1.4 Background of UBC ROT research work The production of more conventional steels requires controlled cooling from a high temperature in the range of 800 - 1000°C to a temperature around 600°C. However, to obtain complex multi-phase microstructures in some advanced high strength steels knowledge on controlled cooling to q,W/m2Tsurface,˚CFilmboiling TransitionboilingNucleateboilingFilm boilingTransition boilingNucleate boilingLiquid waterWater vaporHot surfaceCHFLeidenfrost(MHF)ONBSinglephase8  lower temperatures ranges is essential. In order to study the thermal behavior of steel plates at the low temperature range, extensive experimental research work has been done recently using a pilot scale run-out table facility at the University of British Columbia (UBC) (Zhang 2004, Chester 2006, Chan 2007, Jondhale 2007, Franco 2008). The effect of various parameters, including nozzle configuration, plate speed, and water flow rate, on the subsequent heat transfer rate has been investigated. The versatile design of the facility allows for simulating the cooling process of the steel plates in a condition close to the industrial scale. Results of these experiments form a database for modeling the heat transfer during run-out table cooling. The present research work attempts to develop a cooling model for top water cooling by conducting systematic experimental studies on the pilot scale run-out table and considering the boiling heat transfer mechanisms. In order to achieve this goal, first, a boiling curve model needs to be developed to map the local boiling curves for different positions on the stationary plate surface. Then, the effect of plate motion is required to be incorporated into the boiling curves. Finally, a cooling model is developed for simulating the temperature of a moving steel plate. The research work aims to provide a predictive tool in order to control more accurately the temperature on the run-out able and thus improving the metallurgical properties of the steel product.   9  Chapter 2:  Literature review   2.1  Jet impingement hydrodynamics Water impinging as a jet onto a solid surface occurs in five different configurations, i.e. free-surface, plunging, submerged, confined, and wall jets (Wolf et al. 1993). However, on a run-out table in a hot rolling mill, only free-surface and plunging jets are observed (figure 2.1).  In free-surface impingement, the liquid jet impinges on a surface on which there is not a pool of liquid covering the surface. However, in the plunging jet, the water impinges on pre-existing water that has accumulated on the surface of the steel. The water depth on the surface is less than the nozzle to surface spacing. Plunging jets are commonly encountered in strip and plate mills (Cho et al. 2008). Intuitively, an existing water layer may decrease forced-convective effects of jet impingement and consequently, cooling efficiency of jets. The current study concentrates on free-surface jet impingement cooling.    Figure 2.1 Schematic of water impinging as a jet onto a surface (a) the free-surface and (b) plunging jets. 10   In a free-surface impingement type cooling, upon impinging, the liquid changes direction to traverse along the surface. Nozzle to surface spacing (Hn) can influence the velocity and the size of the water jet just before impinging on the surface. The Bernoulli equation is used to calculate the jet impingement velocity Vji (Jeffrey 2001):                             (2.1)  where Vj is the jet velocity at the nozzle exit and g is the gravitational acceleration. The flow of the liquid can be arbitrarily divided into two zones, the impingement zone characterized by a sharp increase in the streamwise velocity, and a parallel flow zone with a more gradual change of streamwise velocity. Figure 2.2 depicts the streamwise velocity (ul) for both planar and circular configurations. In both types of water jets, the streamwise velocity is zero at the stagnation point and increases to the jet impingement velocity Vji. The hydrodynamics of planar and circular jets differ in the parallel flow region. This is because the water velocity in the parallel flow zone of circular jets decreases, whereas the water velocity for the planar jet does not decrease (Webb and Ma 1995). 11    (a) (b) Figure 2.2 Schematic of free surface jet impingement and profile of liquid velocity parallel to the surface: (a) planar jets, (b) circular jets.    For the single-phase heat transfer, the local Nusselt number (kdhNu ) at stagnation point has been found as a function of Prandtl number (kc pPr) and Reynolds number ( dVRe) (Lienhard 2006):    nmstag cNu RePr.            (2.2) 12  where c, m, and n are constants. h is convective heat transfer coefficient, k is the conductivity of the liquid, cp is specific heat capacity of liquid, µ is dynamic viscosity of the liquid, and ρ is density of the liquid. V is the water jet velocity and d is nozzle diameter. In experiments conducted by Ochi et al. (1984) the impingement zone extends to approximately 1.28 times the circular jet diameter. However, for planar jets, Zumbrunnen et al. (1992) found the jet impingement zone extends to 1.75 times the jet width. The hydrodynamics of circular water jet impingement on moving cold plates was studied by Seraj (2011). The effect of water flow rate (10-45 L/min) and plate speed (0.3-1.5 m/s) were studied experimentally and numerically. It has been shown that an increase in water flow rate increases the size of the upstream region. Figure 2.3 shows the upstream and downstream regions for a jet impinging from a circular nozzle on a moving plate. A higher plate speed results in a smaller upstream region. The effect of moving surfaces on water flow interactions between two neighboring jets in one jet line was also investigated. Experimental results showed that decreasing water flow rate or increasing plate speed would decrease the severity of interaction and therefore decrease the splashing at the mid distance between the two jets. Fujimoto et al. (2011) studied the flow characteristics of a single circular water jet on a moving surface. They also investigated the influence of a preexisting water layer which flows toward the impinging jet on the moving surface. They presented a correlation showing that if the velocity of the preexisting water film exceeds a critical value the upstream zone of the impinging jet vanishes. In this case, the flow was observed to become turbulent (unsteady) in both upstream and downstream regions. Gradeck et al. (2006) studied an impinging jet on a moving surface for various jet and surface velocities as well as for various nozzle diameters and height. They also investigated the effect of process parameters on the position of hydraulic jump. At the hydraulic 13  jump, the rapidly flowing water is abruptly slowed and increases in height. The position of the jump has been experimentally measured. Then, a power relation was derived for calculating the position of the jump with respect to the impinging point of the jet.  Figure 2.3 Schematic of downstream and upstream regions on the surface of a moving plate.  2.2 Jet impingement boiling heat transfer 2.2.1 Jet impingement boiling of stationary plates Table 2.1 gives an overview of the processing parameters such as jet type, nozzle size, nozzle to plate spacing, plate thickness, water temperature, and water jet velocity for the experimental studies that will be discussed in this section. Jet impingement boiling has been studied in two conditions: steady-state and transient (quenching) state. In steady-state conditions either of the surface heat flux or the surface temperature is controlled during jet impingement cooling, whereas in transient conditions, the plate is first heated to a desired temperature and then exposed to the water jet. zyxnozzle14  According to table 2.1, most researchers have used carbon steel, stainless steel, copper or nickel for their experimental heat transfer studies. These experimental studies form the basis for the development of heat flux correlations of different boiling regimes which are discussed in more detail in the subsequent sections.    15  Table 2.1 Experimental condition for citied works in section 2.2.1 (values that have not been reported are shown by “-“) Authors Steady state /Transient Jet type Nozzle width or diameter Nozzle-to-surface spacing Plate material Thickness of plate Water temperature Jet velocity or flow rate Measurement positions Hall et al. (2001) Transient Circular, top jet 5.1mm 56.1mm Copper Cylindrical block 25°C 2-4m/s Radial Hammad et al. (2004)  Transient  Circular, bottom jet  - - Copper, brass, steel Cylindrical block (59mm height)  20-95°C 3-15 m/s Radial Ishigai et al. (1978) Steady-state/ transient Planar, top jet 6.2mm 15 mm Stainless steel  - 45-95°C 1-3.2 m/s Stagnation Islam et al. (2008) Transient Circular, bottom jet 2mm 45mm Steel, brass 5.9mm 20-95°C 3-15 m/s Radial Kokado et al. (1984) Transient Circular 10mm 200mm Stainless steel  10mm 20°C 1-7 L/min Radial Liu and Wang (2001) Transient Circular, top jet 10mm 10mm Stainless steel 2mm 20-95°C 1, 2, 3 m/s Stagnation Miyasaka et al. 1980 Steady-state Planar, bottom jet 10mm  - Platinum 15mm 15°C 1.1-15.3 m/s Stagnation Monde and Katto (1978) Transient Circular, top and bottom jets 2, 2.5 mm  - Copper  - 70-97°C 3.9-26 m/s Stagnation Monde et. al (1980) and Monde and Inoue (1991)  Steady-state Circular, top (2-4 jets) 2,2.1mm  - Copper  - ~100°C 2.5-15.1m/s Stagnation Monde and Mitsutake (1996) Steady-state Two and four circular jets 2mm  - Stainless steel 0.3mm 20-100°C  5-25m/s Stagnation Mozumder et al. (2005) Transient  Circular, bottom jet  2mm  44 mm Copper, brass, steel Cylindrical block  20-95°C 3 - 15 m/s Radial Mozumder et al. (2007) Transient Circular, bottom jet 2mm  44 mm Copper, brass, steel Cylindrical block 20-95°C 3 - 15 m/s Radial Pan and Webb (1995) Steady-state Circular, multiple bottom jets 1,2,3mm nozzle-to-plate / nozzle diameter: 2, 5 Stainless steel 0.025mm  - Re: 5000-20000 Radial Prodanovic and Wells (2006) Transient Circular, top jet 19mm 150cm Carbon steel 7 mm 30-95°C 15-45 L/min Radial Robidou et al. 2002 Steady-state Planar, top jet 1mm 3 - 10 mm Copper with a layer of nickel Copper: 5mm, Nickel: 0.5mm 83-93°C 0.6-0.8 m/s Longitudinal Slayzak et al. (1994a)   Steady-state (single phase)  Two planar jets  5.1mm  -  Ni-Cr-W-Mo  0.66mm  30°C  2.1-4.5m/s  Longitudinal Slayzak et al. (1994b)   Steady-state (single phase)  Two circular jets  4.9mm  89.7mm  Ni-Cr-W-Mo  0.66mm  30°C  2.1-4.5m/s  Longitudinal 16  2.2.1.1 Film boiling Although heat is more effectively removed by mechanisms of nucleate and transition boiling, at high temperatures film boiling may dominate a large area of the steel surface. Hence, a reliable model for this boiling mechanism is needed to predict the strip or plate temperature accurately on the run-out table.   For the film boiling regime in the stagnation zone, Liu and Wang (2001) argued that surface heat flux supplies the evaporation heat flux of liquid, the convection heat flux of subcooled liquid, and the radiative heat flux in the vapor layer. In the case of low water temperature, the convective heat transfer term is much larger than the other terms; therefore, by ignoring the evaporation and radiation terms, a theoretical value of the film boiling heat flux (qFB) has been estimated as: 212161212/satsub/lv/l/llsatFBl,d TTkkPrRekTdqNu      (2.3) where kv and kl are thermal conductivities of vapor and liquid (W/m°C), respectively. ∆Tsat is the surface superheat which is the difference between the surface temperature and saturation temperature (boiling temperature of water). In the above equation ∆Tsub, which is called subcooling, is the difference between liquid temperature and saturation temperature. Liu and Wang reported that the discrepancy between the predicted film boiling heat flux and the experimental results increases with increasing the water subcooling. They suggested to adjust the constant (using 2 instead of   ) for the above theoretical equation. Previously, Ma et al. (1993) found correlations for stagnation and parallel flow zones to predict film boiling heat flux in the case of high liquid subcooling: 17   satsubvlllvsatFBvd TTkkkTdqNu 2/12/12/1, PrRe2  (in stagnation zone) (2.4)  rdTTkkkTdqNusatsubvlllvsatFBd2/12/12/1PrRe3  (in parallel flow zone) (2.5) In order to obtain a good agreement with experimental data, they proposed to use a correction factor of 2.3 for the above theoretical equations. Ishigai et al. (1978) found that in film boiling, the heat removed from the surface increases by increasing the velocity of the water jet. Filipovic et al. (1995b) measured the effect of jet velocity and subcooling on the local convection coefficient for forced, subcooled film boiling with a preheated specimen exposed to a wall jet on its top surface. It was determined that the decrease in local heat transfer coefficient in the film boiling region with increasing distance from the wetted zone is due to the combined effect of two-phase (vapor and liquid) boundary layer development and also the decrease in local subcooling associated with increase in the bulk water temperature (Filipovic et al. 1995a). Moreover, it was found that increases in subcooling and flow velocity cause a reduction in the thickness of the vapor layer and consequently an increase in the convection coefficient (Filipovic et al. 1995b).   2.2.1.2 Wetting and minimum heat flux Wetting is the ability of a liquid to contact a large portion of the hot surface. Knowledge of the wetting temperature and heat flux is important to characterize boiling regimes in jet impingement cooling processes (Nelson 1986). Ueda et al. (1983) defined the wetting point as the point where the heat flux begins rising sharply with decreasing surface superheat. Before wetting occurs, film boiling is the dominant boiling mechanism, and the heat flux value is comparatively low. 18  However, after the liquid wets the surface, nucleate boiling is the dominant heat transfer mechanism and consequently, heat flux increases rapidly. Ishigai et al. (1978) compared the boiling curve for transient planar water jet cooling with visual observations in order to study the liquid-solid contact. Close to the minimum heat flux point in the boiling curve, the stable vapor film is broken and the jet touches the surface. In the case of high subcooling, the vapor interface looks white, probably due to the frequent and instantaneous liquid-solid contact. As the surface temperature decreases the heat flux increases and the wetted zone expands across the entire surface. Moreover, Ishigai et al. (1978) studied the effect of impinging jet velocity on the minimum heat flux (MHF) point. The following correlations have been proposed for planar and circular water jets, respectively:   607.04 527.01104.5 jisubMHF VTq       (planar jets)  (2.6)    828.05 /383.011018.3 jjisubMHF dVTq      (circular jets)  (2.7) where qMHF is in W/m2, Vji is in m/s and ∆Tsub is in °C. The jet impingement velocity has a more significant effect on minimum heat flux for circular jets than for planar jets. According to these equations, for both types of jets, the minimum heat flux has a linear relationship with the degree of subcooling. Also, it was found that if subcooling and jet velocity are high enough, the minimum heat flux point is not observed at the stagnation point, despite surface temperatures as large as 1000˚C.  Kokado et al. (1984) studied the influence of subcooling on the occurrence of film boiling for circular jets. Their results show that wetting temperature of the surface decreases linearly, as the water temperature approaches to saturation, i.e. 100˚C. However, they reported that for water 19  temperatures below 68˚C the linear relation is no longer valid since the wetting phenomena occur as soon as the water impinges on the plate. Liu (2003) proposed a correlation for calculating the Leidenfrost temperature in the stagnation zone of a circular jet. He assumed that the shear stress at the vapor-liquid interface in the whole stagnation zone is zero at the MHF condition. The superheat of the MHF point was then found to be linearly dependent on the water subcooling: vlvllsubsatMHF kkTT 3/1, Pr14         (2.8) where k is thermal conductivity and µ is viscosity of liquid (l) and vapor (v), respectively. Filipovic et al. (1995a) showed that the minimum heat flux temperature decreases monotonically with increasing distance from stagnation point. However, Hall et al. (2001) demonstrated that initially the temperature increases with increasing streamwise location while the liquid is being deflected from the surface at the boiling front. Then, at a sufficient distance downstream from the stagnation point, the liquid will no longer be deflected and will flow across a vapor blanket in a film boiling region that extends over the remaining non-wetted portion of the surface. From this distance, the minimum film boiling temperature will then decrease with increasing radius due to the increase in water temperature and decrease in fluid momentum.  A research group in Saga University, Japan, conducted several experimental studies on wetting propagation during transient cooling of an upward circular water jet which hits a bottom surface (Mozumder et al. 2005, 2006, 2007, Hammad et al. 2004, and Islam et al. 2008). Mozumder et al. (2005) investigated the delay of wetting propagation by defining a resident time as the time from when the jet first strikes the surface until the wetting front starts moving. They observed that when the wetting zone starts to expand, a sharp drop in surface temperature happens. There 20  is not any limitation for the resident time as it can be from fractions of a second to over 15 minutes depending on the experimental condition (Mozumder et al. 2007). It has been reported that the size of the initially wetted zone is different for different materials; for instance it is close to the size of the nozzle for steels. According to the observation of Hammad et al. (2004), in the resident time period a vapor layer prevents water from contacting the surface and the mechanism of heat transfer is film boiling. Islam et al. (2008) studied the flow behavior on a hot bottom surface preheated to 500-600˚C. They came up with different types of flow patterns such as splashed droplets, conical liquid, etc. Predicting flow patterns is still limited as two complex phenomenons have to be combined, i.e. jet impingement fluid flow and boiling heat transfer.     Prodanovic and Wells (2006) studied the size of the wetted region and propagation of the wetting front for transient cooling of a steel plate with initial temperature of 860˚C. According to their observations, first an initial circular wetted region of nearly constant diameter is formed. The propagation of this zone is triggered by penetration of the jet through an apparent vapor layer covering the initial wetting zone. They suggested that outside of the wetted zone, a stable vapor layer is formed which deflects the stream of the water. A simplified analytical model for the prediction of the Leidenfrost point at the stagnation zone was proposed by Karwa et al. (2011). Similar to Liu (2003), they assumed that the shear stress at the vapor-liquid interface in the whole stagnation zone is zero at the Leidenfrost condition. They compared the model prediction with the available literature data for planar jet cooling and subcooling in the range of 7 to 35°C. The comparison showed that the model underpredicts the heat flux of Leidenfrost by 5-47% and the Leidenfrost temperature by 40-70%.  21  2.2.1.3 Transition boiling The transition boiling regime represents a condition where a stable vapor layer cannot be maintained and collapses intermittently. The regime is considered to be essentially a mixture of nucleate boiling and film boiling regimes (Rohsenow 1952, Berenson 1962). This boiling regime is demarcated by the maximum and the minimum heat flux points in the heat flux vs. superheat curve. In pool boiling, it is characterized by a reduction in surface heat flux with an increase in surface superheat. Based on the transition boiling mechanism proposed by Berenson (1962), many researchers (Kao and Weisman 1985, Kalinin et al. 1987, Pan et al. 1989, Pan and Ma 1992) assume a dual-phase boiling combination model to describe the entire transition heat transfer regime mathematically: )1( FqFqq svslTB               (2.9) Here F is the fraction of the area in contact with the liquid, and ql-s and qv-s are the heat fluxes for the liquid-solid and vapor-solid contacts, respectively. Ragheb and Cheng (1979) and Nishio and Auracher (1999) replaced the liquid-solid and vapor-solid heat flux terms in the above equation with the maximum heat flux (CHF) and minimum heat flux (MHF), respectively. An approximation for F is to assume a linear relationship between the two points of CHF and MHF in a log/log-plot of the pool boiling curve.  In order to model heat transfer rate in the transition boiling regime, some researchers (Pan and Ma 1992, Shoji 1992, Hernandez et al. 1995) used the concept of macrolayer evaporation mechanism which was extended to the transition boiling regime. Filipovic et al. (1995a) reported that in the transition boiling region a very thin superheated liquid layer, which is termed macrolayer, exists between the stable vapor layer and solid. It has been observed that the region is bounded by positions of critical heat flux and wetting front (figure 2.4). In case of flow 22  boiling, where the fluid is not stagnant, F has been related to the length of macrolayer in the flow direction.  In this case the liquid-solid heat flux term in equation 2.11 can be replaced with the value of the heat flux due to macrolayer evaporation (Pan et al. 1989).   Figure 2.4 Schematic of the positions of different flow boiling regimes on the hot surface (modified from Filipovic et al. 1995a).  Some experiments have shown a specific trend of the jet impingement boiling curve in the transition boiling region which is called shoulder of heat flux (Ishigai et al. 1978, Ochi et al. 1984, Robidou et al. 2002, 2003). This region is characterized by a constant heat flux over a wide range of surface temperature in the transition boiling regime. Ishigai et al. (1978) investigated the effect of water subcooling on heat flux for transient planar water jet cooling. The shoulder of heat flux appears in the transition region of the boiling curve when the subcooling is higher than 25˚C. However, Robidou et al. (2002) reported the existence of the shoulder even for subcooling as low as 7˚C in the steady-state boiling curve. Moreover, Ishigai et al. (1978) found that the width of the shoulder increases by decreasing water temperature and increasing jet velocity.  According to the observation of Robidou et al. (2002, 2003) for steady-state conditions, the heat flux sharply increases at the minimum heat flux (MHF) point but then it remains almost constant 23  in the shoulder region with a relatively high heat flux value (figure 2.5). This phenomenon can be related to a better wetting in the transition regime due to the breakup of vapor patches into many smaller patches, which causes high heat transfer. In some studies, a minimum in the heat flux curve which is called “first minimum” has been observed (Robidou et al. 2002, 2003) with further decrease in temperature. The existence of this point, however, has not been reported by Ishigai et al. (1978), Miyasaka et al. (1980), and Ochi et al. (1984). Then, with a further decrease in surface temperature the heat flux level rises again and reaches the critical heat flux point.   Figure 2.5 Local boiling curves; experimental condition: steady-state, ∆Tsub=16 ˚C, Vn=0.8 m/s, Hn=6mm (Robidou et al. 2002).  The work of Seiler-Marie et al. (2004) remains the only attempt in the literature to develop a physically based model for the shoulder heat flux. Considering the experimental data of Robidou et al. (2002), the shoulder heat flux was related to the presence of periodic bubble oscillation at the surface due to the instability at the vapor/liquid layer interface. Two sources for creating the instability at the vapor/liquid interface were considered: pressure due to the presence of the 24  heavier phase (liquid) on the lighter phase (vapor) and pressure due the jet impingement on the surface. The Rayleigh-Taylor instability was used to determine the critical wavelength of the liquid/vapor interface. It has been assumed that the vapor patch diameter cannot be greater than the Rayleigh-Taylor critical wavelength. Thus, at each oscillation when the vapor patch diameter exceeds the critical diameter, the vapor patch breaks up into smaller patches. As a result, water spreads on the hot surface and its temperature increases rapidly to the boiling temperature. Finally, it is displaced into the bulk flow by the growth of bubbles.  The shoulder heat flux model of Seiler-Marie et al. (2004) is applicable to the stagnation point of jet impingement:    4/12/1,4/14/115.0 dVTcq jisublpvllshoulder         (2.10) where ρl and ρv are density (kg/m3) of liquid and vapor, respectively. σ, cp,l, and d are surface tension (N/m), liquid specific heat (J/kg°C), and nozzle diameter (m), respectively. The constant of the above equation was found to be 0.15 after adjusting the model prediction with the experimental data of Robidou et al. (2002).  2.2.1.4 Critical heat flux The critical heat flux is the point of transition between nucleate boiling and transition boiling regimes. Due to the importance of controlled cooling operations and also the high efficiency of cooling at this point, several researchers have performed experiments in order to find a correlation to predict the critical heat flux with respect to different parameters such as jet velocity, subcooling, etc.  25  Miyasaka et al. (1980) found a relationship between the critical heat flux in jet impingement boiling at the stagnation point and jet velocity. They defined the critical heat flux as the point in which the heat flux data deviates from nucleate boiling correlation (DNB):  38.0,, 86.01 jpoolsubDNBDNB Vqq          (2.11) where Vj is in m/s. Here qDNB,sub,pool is the critical heat flux for subcooled pool boiling in which the body of the liquid water as a whole is essentially at rest. Monde and Inoue (1991) proposed a generalized correlation using existing experimental data for saturated liquid cooling in the literature: 364.0343.02645.01)(2221.0 DddDVVhqjlvljfgvCHF     (2.12) where hfg, d and D are latent heat of evaporation (J/kg), jet diameter (m), and hot surface diameter (m), respectively. According to the review of Wolf et al. (1993), most of the literature demonstrates the critical heat flux to vary approximately with Vj1/3 at the stagnation point. For an upward circular jet, Hammad et al. (2004) found that with the movement of the wetting front, the position of the maximum surface heat flux also moves in the radial direction while the value of the maximum heat flux decreases during propagation of the wetting front. Hall et al. (2001) reported the same trend for downward circular jets. Mozumder et al. (2007) found that the maximum heat flux propagation velocity begins at a high value near the stagnation point, which decreases slowly and then increases again.  26  2.2.1.5 Nucleate boiling Among the different boiling mechanisms, the most quantitative analysis has been done for the nucleate boiling regime. The typical form of the correlation in the fully developed nucleate boiling (NB) regime steady-state cooling can be expressed as a function of surface superheat (Wolf et al. 1993):  nsatNB TCq            (2.13) Where C and n are processing-related constants and depend strongly on the type of fluid employed. According to Monde and Katto (1978), heat released from the surface in nucleate boiling provides the latent heat of evaporation of liquid.  For transient cooling with a circular free-surface jet at stagnation, Hall et al. (2001) reported that the heat flux depends on jet velocity. This behavior is inconsistent with results of most steady-state cooling studies (Wolf et al. 1993 and Robidou et al. 2002) where it was found that nucleate boiling heat flux is independent of impingement velocity but only dependent upon the surface superheat. In fact, motion of fluid during nucleate boiling on the surface is so active, that the state of fluid motion near the hot surface hardly changes even when forced convection is applied. Further, no influence of subcooling on the heat flux has been reported by Robidou et al. (2002, 2003). However, Monde and Katto (1978) reported that subcooling affects nucleate boiling at low surface superheat but not at higher surface superheats. Interestingly, in the fully developed nucleate boiling regime, Robidou et al. (2002) showed that the local boiling curves for different positions merge and the corresponding heat flux seems to be independent of distance from the stagnation point (figure 2.4). However, under transient cooling condition, this conclusion was not supported by the data of Hall et al. (2001). Omar et al. (2009) developed an analytical/empirical model to predict the nucleate boiling heat flux in the 27  stagnation region. The model is based on the hypothesis that bubble formation at the surface leads to increase of the value of the diffusivity term in conservation equations. Experimental data were used to determine the diffusivity term for different jet velocities and surface temperatures.   2.2.1.6 Effect of multiple jets on jet impingement boiling Pan and Webb (1995) investigated local single-phase heat transfer under different arrays of upward circular jets during cooling of a stationary surface. They found that the central jet stagnation Nusselt number is independent of jet spacing, but exhibited dependence on the nozzle-to-surface spacing. Away from the impingement zone, a secondary stagnation heat transfer zone was observed midway between adjacent jets as a result of the interjet flow interaction. However, Slayzak et al. (1994a,b) reported that although convection coefficients in interaction zone between planar jets are characterized by pronounced high heat flux value, the circular jets do not necessarily produce high heat flux values midway between adjacent jets.  Monde et al. (1980) performed some experiments with two and four circular saturated water jets to study the effect of nozzle configuration on nucleate boiling heat transfer mechanism. They reported that the number and placement of jets have little or no effect on the heat flux value in nucleate boiling. Also, characteristics of the critical heat flux in forced convective boiling with both single jet and multiple jets have been found similar, in spite of a difference in the flow condition on the surface between a single jet and multiple jets (Monde and Inoue 1991, Monde and Mitsutake 1996).  28  2.2.2 Effect of surface motion on jet impingement boiling Table 2.2 gives an overview of the processing parameters for the experimental studies which will be discussed in this section for cooling of moving surfaces. Although there has been significant research on jet impingement boiling heat transfer on stationary plates, the effect of surface motion on heat transfer has not received much attention. In fact, very limited experimental work has addressed the combined phenomena of jet impingement, moving surface, and also transient boiling heat transfer mechanism.  The effect of surface motion on heat transfer for circular water jets impinging on the steel plates with initial temperatures below 240˚C was experimentally studied by Chen and Kothari (1988), Chen et al. (1991a,b) and Han et al. (1991). The water flow pattern showed that the moving strip/plate causes the water film to stretch in the moving direction resulting in an enhancement of heat transfer downstream of the jet (Chen and Kothari 1988). As the surface passes in the cooling zone, the temperature reaches a minimum before it recovers and conductive heat transfer within the plate overcomes the convective cooling. They also reported that the location of the minimum temperature occurs slightly after the stagnation point (Chen et al. 1991b). It was also found that a higher plate speed results in a higher surface temperature at the stagnation region under jet impingement due to the lower residence time in the cooling zone (Hatta and Osakabe 1989, Han et al. 1991).     29   Table 2.2 Experimental condition for citied works in section 2.2.2 (values that have not been reported are shown by “-“) Authors Surface speed Steady state /Transient Jet type Nozzle width or diameter Nozzle-to-surface spacing Plate material Thickness of plate Water temperature Jet velocity or flow rate Measurement positions  Initial temperature  Chan (2007) 0.3-1.3m/s Transient Circular, top jet 19mm 150cm Steel (HSLA) 6.6mm 25°C 30 L/min Lateral 350-600°C Chen and Kothari (1988)  0.35m/s Transient  Circular, bottom jet  4.76mm  - Carbon steel 6.35mm  -  1.77m/s Lateral 85,122°C Chen et al. (1991a)  0.5m/s Transient  Circular, bottom jet  4.76mm  - Carbon steel 6.35mm  - -  Lateral 88,240°C Franco (2008) 0.35, 1.0 m/s Transient Circular, multiple top jets (two jetlines) 19mm 150cm Steel (HSLA) 6.6mm 25°C 15 L/min Lateral ~700°C Gradeck et al. (2009, 2011) Vj/Vp: 0.5-1.25m/s Transient Planar, top jet 4mm  - Nickel Rotating cylinder 17-90°C 0.8-1.2m/s Radial ~500°C Han et al. (1991) 0.15-1.44m/s Transient Circular, bottom jet 4.76mm  55mm Carbon steel 6.35mm 22-27°C 3.88m/s Lateral 38-240°C Jondhale (2007) 0.22-1.0m/s Transient Circular, three top jets (one jet-line) 19mm 150cm Steel (HSLA) 6.6mm 30°C 15,30 L/min Lateral ~700°C Pohanka et al. (2011) up to 12m/s Transient Spray, multiple top jets  - 300mm Steel Rotating cylinder - 15,5,1 L/s.m Lateral 1200°C Prodanovic et al. (2004) 0.3, 1.0 m/s Transient Circular, top jet 19mm 120cm Steel (low carbon) 6.38mm 30°C 15, 30 L/min Lateral ~700°C Prodanovic and Militzer (2005) 0.3-1.4m/s Transient Circular, top jet 19mm 120cm Steel (low carbon) 6.38mm 30°C 23 L/min Lateral ~700°C     30  Zumbrunnen et al. (1989) and Zumbrunnen (1991) analytically studied the effect of plate motion on boundary layer development in the vapor and liquid layers by solving the conservation equations for mass, momentum, and energy. They reported that the thickness of the vapor layer in the film boiling regime in the downstream zone decreases in comparison with stationary plate conditions since vapor flow is promoted by the plate motion. In contrast, in the upstream zone, the vapor thickness may increase since vapor can be drawn toward the jet. Further, for very high plate velocities (higher than water jet velocity) the estimation of film boiling heat transfer becomes more complicated since the plate motion can reverse the flow of vapor in the upstream region (Zumbrunnen et al. 1989). However, these analytical results have not been validated by any experiments. Filipovic et al. (1992a,1994b) analyzed the process of subcooled, forced convection film boiling under turbulent flow condition in the parallel flow region. For this purpose, they applied a two-phase (vapor and liquid) boundary layer model and assumed that the liquid/vapor interface is smooth.  Prodanovic et al. (2004) conducted some experiments in order to observe parametric trends in jet impingement heat transfer for hot moving steel plates using the pilot scale run-out table at the University of British Columbia (UBC). They performed single circular nozzle tests using plates moving at two speeds of 0.3 and 1.0 m/s and compared the heat flux results to data from stationary experiments. They reported that the cooling rate under the jet increases with decreasing the speed of the test plate and with increasing flow rate of the water jet. Prodanovic and Militzer (2005) found that maximum cooling rates were obtained in the temperature range of approximately 300-350˚C. It has also been observed that the size of the cooling zone for a single jet, and therefore the cooling efficiency increases with decreasing the surface temperature. 31  Chan (2007) performed single nozzle experiments on the pilot scale run-out table at UBC. He investigated the effect of plate speed (0.3, 0.6, 1.0, and 1.3 m/s) on peak heat flux and heat extraction. The peak heat flux is the maximum heat flux recorded as a result of the plate passing through the jet. The heat extraction is obtained from the integration of the heat flux vs. time in each cooling pass. It has been reported that both values decrease with increasing plate speed. Recently, Gradeck et al. (2009, 2011) conducted quenching experiments of a hot nickel cylinder by using a subcooled planar water jet and compared heat flux curves for stationary and rotating cylinders. The rotating cylinder allowed them to have a sufficiently long time of experimentation to be able to describe the entire boiling curve. A potential drawback of these tests though is that the existence of surface curvature may significantly affect the heat fluxes obtained. For the stationary cylinder, the boiling curve presents a heat flux shoulder at the stagnation point. However, in the parallel flow zone, they did not observe the shoulder. Moreover, the heat flux shoulder decreases as the rotating speed increases. For sufficient high rotating speed, the shoulder heat flux did not exist beneath the jet and local boiling curves have the same shape upstream, downstream, and beneath the jet axis. Moreover, a decrease of the heat flux has been observed as the surface velocity (i.e. rotation speed) increases.   Pohanka et al. (2009) investigated the effect of fast moving surfaces using spray cooling of a hot rotating cylindrical body. The main reason for using the cylindrical surface was to achieve high surface velocities up to 12 m/s. Although they reported a decrease in heat transfer intensity with the speed of rotation, the related data was not included in their paper. In addition to all of the complexities of boiling jet impingement heat transfer for moving plates, jet impingement cooling in strip and plate mills also involves interactions between adjoining jets. Filipovic et al. (1990,1994a) identified three cooling regions at the top surface of a strip on an 32  industrial cooling line: first is the impingement cooling zone where high heat flux is released. This zone is also called “effective cooling zone”. The second and third cooling zones are the interaction zones between two neighboring jets in the same jet line and between jets from consecutive jet lines. Jondhale (2007) studied local heat transfer of hot moving plate on the pilot scale run-out table at UBC by using three circular nozzles in one jet line. Three different nozzle configurations were employed with nozzle spacings of 38.1, 76.2 and 114.3 mm, respectively. For all nozzle spacings, locations below nozzles experience very high heat fluxes. The results also show that nozzle spacing has little effect on the peak heat flux value in impingement zone. However, reducing the nozzle spacing improves the uniformity of cooling across the width of the plate. In a subsequent study, Franco (2008) introduced a second line of three nozzles to advance the understanding of the effect of jet interactions. The stagger between nozzles and jet-line spacing were systematically varied to investigate their effects on cooling efficiency. The results showed that the cooling efficiency is unaffected by nozzle stagger as long as plate speed, jet-line spacing and flow rate are the same (figure 2.6). However, uniformity of cooling is strongly dependent on nozzle configuration especially in the range of 300 to 450˚C in which the highest heat fluxes and largest thermal gradients were observed. Moreover, it has been reported that although longer distances between jet-lines produce higher heat extracted values per pass, shorter distances between jet lines are found to extract more heat per unit length of jet-line spacing and are deemed more effective.  33   Figure 2.6 heat extracted for different nozzle stagger configurations as a function of entry temperature (the surface temperature of the plate, when the water jets first hit the plate during that pass) (Franco 2008).  2.3 Heat transfer modeling of run-out table cooling Many researchers use initial and final temperatures of the strip/plate and apply a fitting procedure to find heat transfer coefficients (Colas and Sellars 1987, Timm et al. 2002, Pyykkonen et al. 2010). However, these results are mill dependent, as they do not accurately predict the temperature of steel strips on another run-out table with different operating parameters. To develop a fundamental heat transfer model for the steel strip cooled by planar jets and coiled above 550°C, Colas and Sellars (1987) attempted to define constant heat transfer coefficients for impingement and parallel flow zones. Various combinations of coefficients and impingement width were evaluated. However, they were unable to define a set of values which give good agreement with observations. This discrepancy was believed to be related to the existence of an oxide layer on the surface of the strip/plate. 34  Guo (1992) applied a statistical approach to define a triangular shaped distribution of heat transfer coefficient at effective cooling zone by using data collected from several coils. A simple power-law equation was used to relate the maximum heat transfer coefficient to some operating parameters such as strip speed, strip thickness, surface temperature, and flow rate. Coiling temperatures were in the range of 594 to 743°C.  Filipovic et al. (1992a) developed a temperature model for the strip temperature distribution during cooling by an array of planar jets. To apply convective boundary conditions, two main zones were considered on the hot surface. For impingement cooling zone, they used a nucleate boiling correlation which had been found for the stagnation point. However, the correlation was extended to the impingement zone by defining the pressure gradient in the impingement zone. In their model the shape of the impingement zone is symmetrical with respect to the nozzle position and the width is a function of jet-to-strip spacing, jet velocity and jet width. Outside the impingement zone forced convection film boiling was considered. For the bottom surface, the same correlation was used for the impingement zone; however, due to the gravitational force the water stream separates from the strip and no film boiling region was considered. Their parametric study showed that the nozzle width has the largest influence on the thermal behavior of the strip among other control parameters such as jet velocity, strip speed, water flow rate, and water temperature (Filipovic et al. 1992b). This result was related to the large heat fluxes in the impingement region, where even a small change in the nozzle width and subsequent change in size of impingement region, can significantly alter strip thermal response. Filipovic et al. (1994a) extended their model to predict the 2-D behavior of the strip during cooling with circular water jets using the same basic assumptions. The correlation which was developed from stationary surface experiments by Ochi et al. (1984) was incorporated for the 35  impingement region. Based on the model, they found that heat extraction in film boiling region for a specific mill accounts for approximately 50% of the total heat extraction. Hernandez (1999) developed a heat transfer model for planar and circular water jet cooling on the run-out table. Similar to previous studies, the size of two cooling zones were held constant, i.e., independent of surface temperature. To find heat flux in either the impingement or the parallel flow zone, the macrolayer evaporation mechanism was adopted for contribution of nucleate boiling in the transition boiling regime. In contrast to most literature in which the film boiling mechanism is applied as the main mechanism of heat removal in the parallel flow zone, the definition of the transition boiling mechanism in the parallel flow region was used. The model was validated by comparing predicted temperatures with measurements in five different run-out table operations with coiling temperatures in the range of 540 to 740°C. It has been claimed that the model predicts the coiling temperatures within ±20°C. However, there are some weak points in the proposed heat transfer model that are apparent at coiling/stop temperatures below 500°C (Prodanovic, private communication). The transition boiling heat transfer rate has not been addressed properly in the model. As an example, the model which was proposed for the F parameter (the solid-liquid contact area in equation 2.9), is not reliable at lower plate speeds. Moreover, the proposed nucleate boiling correlations based on the macrolayer evaporation fails to predict the heat transfer rates at temperatures lower than 500°C. These weaknesses restrict the application of the heat transfer model for some advanced steels for which the controlled cooling process is required from high temperatures to temperatures below 500°C. Park (2011a, 2011b, 2012, 2013) developed a Computational Fluid Dynamics (CFD) model for plate cooling by multiple circular jets. To simulate the temperature evolution during cooling, film boiling was considered as the dominant heat transfer mechanism. Therefore, the model is 36  only applicable for plate cooling with high initial temperatures. To simulate the cooling process an iterative procedure was proposed to estimate the thickness of the vapor layer on the surface during film boiling (Park 2011a). Due to the limited information about this procedure in the paper as well as other details of the CFD model, it is not possible to justify the validity of the procedure. The model predicts that the overall cooling effectiveness of multiple jet cooling system increases with reducing nozzle diameter while maintaining the mass flow rate of water (Park 2012). It has also been predicted that a staggered jet arrangement has a greater cooling capacity than the in-line (non-staggered) arrangement (Kwon and Park 2013). This is in contrast to the experimental data of Franco (2008) where nozzle configuration does not have an effect on the cooling capacity. Unfortunately no comparison with experimental results has been provided in Park (2011a, 2011b, 2012, 2013) to support the predictions.  According to the literature survey presented above, the major problem for modeling the heat transfer on the run-out table is defining the local heat transfer condition on the strip/plate surface based on surface temperature and process parameters such as strip/plate speed, nozzle configuration, jet velocity, and water temperature. In fact, without properly considering the boiling mechanisms (i.e. film boiling, transition boiling, and nucleate boiling) the developed heat transfer models may not be applicable to predict thermal behavior of the steel on different run-out tables with different process parameters. Furthermore, some of the models that have been developed have not been validated with experimental data. Moreover, the emphasis of almost all heat transfer models is for jet impingement cooling for temperatures higher than 600°C. However, for the production of advanced TMCP steels controlled accelerated cooling needs to be extended to lower temperatures. At temperatures lower than 600°C, transition and nucleate boiling become the dominant heat transfer 37  mechanisms. Therefore, these mechanisms need to be addressed more accurately in the developed heat transfer models for the run-out table. It is worth mentioning that, even for run-out tables with conventional stop/coiling temperatures (>600°C), the surface temperature of the plate is much lower than the average temperature of the plate. Therefore, heat transfer models which are not able to accurately predict the heat extraction rate at surface temperatures lower than 600°C, may have significant limitation. The main attempt in the present study is to develop a heat transfer model for jet impingement cooling of steel plates with surface temperatures in the range of 250 to 600°C.      38  Chapter 3: Objectives   The overall objective of this work is to develop a mechanistic heat transfer model for jet impingement cooling of the top surface of moving hot steel plates. A particular emphasis will be placed on cooling to below conventional coiling or cooling stop temperatures, e.g. 600˚C, where nucleate and transition boiling are the dominant boiling mechanisms. In order to achieve the overall objective, the following tasks must be completed: (1) Quantify heat extraction during cooling of stationary plates with systematic experimental heat transfer studies on the pilot scale run-out table facility available at UBC. Here, the role of nozzle geometry, water flow rate and water temperature will be investigated. (2) Develop a boiling curve model for single jet cooling of stationary plates considering the underlying boiling mechanisms, i.e. film boiling, transition boiling, and nucleate boiling. (3) Quantify heat extraction during cooling of moving plates with systematic experimental heat transfer studies on the pilot scale run-out table facility. Here, the role of plate speed will be investigated in addition to nozzle geometry, water flow rate and water temperature.  (4) Develop a mechanistic cooling model for moving plates using boiling curves. Here, the model for stationary plates will be extended by incorporating the effect of plate speed on heat extraction for both single and multi-jet cooling.  39  Chapter 4: Experimental methodology   4.1 Pilot-scale run-out table facility In the present study a pilot scale run-out table facility was used. A schematic of the run-out table facility is shown in figure 4.1. The facility has been designed to simulate industrial cooling conditions for run-out table cooling in hot strip and plate mills (Prodanovic et al. 2004). It enables heat transfer to be studied during cooling of stationary plates as well as moving plates. Heating is provided by an electric furnace where a steel plate can be heated up to a temperature of 900°C. The furnace is fitted with a gas line to supply nitrogen gas during heating of the plate to minimize the formation of scale. Using a hydraulic motor and a chain drive system, the steel plate is transported from the furnace to the cooling tower for stationary experiments. For moving plate experiments, after the steel plate is transported close to the cooling tower the plate is moved back and forth with pre-scribed speeds of 0.2-2 m/s, i.e. cooling is conducted in multiple passes. The cooling tower features a closed water loop where 1.5 m3 of water is circulated through the cooling nozzles. Water temperature and flow rate are controlled. The water pump can provide total water flow rates of as high as 500 L/min. An electric heater is situated in the upper tank and is primarily used to adjust the temperature of the water (10-90°C). In this work two types of nozzles were used: planar (curtain) and circular (axisymmetric) nozzles. The cross section of the planar nozzle outlet is 3 x 300 mm and the inner diameter of the circular nozzle is 19 mm (figures 4.2a and 4.2b). 40   (a)  (b) Figure 4.1 (a) Schematic of pilot scale run-out table facility, and (b) Schematic of cooling tower (side view). FurnaceTest platePlate moving directionHydraulic motorWater pumpCooling towerHeaders and nozzlesCooling towerHeaderNozzleTest plateUpper watertankWater containmenttankElectricheater41    (a) (b) Figure 4.2 Schematic of (a) planar nozzle and (b) circular nozzle.  Two different commercial hardware packages are used. Iotech DaqBook 2005 is used to measure temperature of the test plate. A GW Instruments instruNet (INet100) is used to measure signals from the flow meters and to control speed and direction of the steel plate. DASYLab 8.0 data acquisition software is used to transfer measurement data to a computer. According to the equipment specifications, the experimental errors were estimated as summarized in table 4.1.  Table 4.1 Experimental errors Quantity Measurement error Temperature  ±2°C (T<277°C) ±0.75% (T>277°C)  Flow rate (Zhang 2004) ±0.5%  Water temperature  ±0.5°C Plate speed ±0.05m/s  42  4.2 Test plates Plates used were as-received hot rolled High Strength Low Alloy (HSLA) steel and the thickness of all samples was 6.6 mm. The chemical composition of the steel is given in table 4.2. For each test, a new plate was used in order to have the same surface quality and plate flatness for all experiments. The surface roughness (ISO 1997) was measured using Mitutoyo Surface Roughness Measurement Surftest (SJ-310). The roughness profile determined from deviations about the mean line within an evaluation length of 1cm was measured. The arithmetic average of roughness (Ra) was 1.36 µm. Prior to instrumentation of the plate with thermocouples, the steel plate was first mounted on a steel frame (carrier), which permitted the easy transport of the plate to and from the furnace, and enabled precise positioning of the plate on the chain drive system.   Table 4.2 Chemical composition of HSLA steel Element C Mn P S Si Cu Cr Ni wt. % 0.0614 1.1203 0.0111 0.0027 0.2383 0.1567 0.0746 0.0509 Element Mo Al N Ti V Sn Nb Fe wt. % 0.0167 0.0286 0.0058 0.0148 0.0045 0.0098 0.0399 Balance  In order to measure the transient temperature response, 1.59 mm (1/16”) type K thermocouples were employed. Flat bottom holes, 1.59 mm in diameter, were drilled from the bottom face of the plate to a depth of approximately 1 mm below the top surface. The depth of the pre-drilled holes for the thermocouples was measured with an accuracy of ±0.01 mm using a sheet metal micrometer. The thermocouple wires entering the holes were separated by a ceramic tube insulator and each thermocouple wire was spot welded to the top of the flat bottom hole as shown in figure 4.3. 43    Figure 4.3 Schematic of one spot welded thermocouple to the plate.   The steel plates used for stationary tests were 60 x 43 cm for planar nozzle cooling tests and 40 x 43 cm for circular nozzle cooling tests. Figure 4.4 shows the location of thermocouples for both sets of stationary experiments, i.e. with planar and circular nozzles. More thermocouples were positioned close to the jet where a sharp gradient in heat extraction rates was expected. The steel plates used for moving tests were 60 x 43 cm for planar nozzle cooling tests and 120 x 43 cm for circular nozzle cooling tests. Figures 4.5a and 4.5b show the location of thermocouples for the moving plates for planar nozzle cooling and circular nozzle cooling, respectively. The thermocouple spatial distribution for the circular nozzle cooling tests was chosen such that the thermal history of different cooling scenarios along the lateral direction (y) on the surface could be captured. Moreover, a number of thermocouples were located to serve as back-ups.  44   (a)  (b) Figure 4.4 Schematic of thermocouple locations with respect of the water jet for stationary plate experiments (a) for tests with the planar nozzle and (b) for tests with the circular nozzle.     45   (a)  (b) Figure 4.5 Schematic of thermocouple locations for moving plate experiments: (a) planar nozzle cooling and (b) circular nozzle cooling.  46  4.3 Test procedure After the desired temperature (900°C) was reached in the furnace, the plate was transported toward the cooling section. For stationary tests, the center of the plate was positioned under the nozzle, and the water flow was started. In order to secure the desired water flow rate at the beginning of the tests with a planar nozzle, prior to running the experiment, the header was completely filled up with water. After the plate was positioned under the nozzle, using a solenoid value the water flow was started. However, prior to running the tests with a circular nozzle, a diverter pipe was used to divert the water jet and bypass the water to the water containment tank. After the plate was positioned under the nozzle axis, the diverting pipe was removed quickly to permit the water jet impinges on the plate surface.    For the tests with stationary plates, the initial temperature of the plate (Tinitial) at the onset of water cooling was about 720°C. Temperature data were collected until the temperature of the plate at all thermocouple locations dropped below 100°C. For the test with moving plates, after the plate passed through the cooling section of the first cooling pass, the plate was stopped for a sufficient time such that the maximum temperature difference at all thermocouple positions was less than 20°C. Then, the plate was moved back through the cooling section for the next pass at a lower temperature. This process was repeated until the plate temperature in all locations dropped below 100°C.  47  4.4 Data analysis 4.4.1 Surface temperatures and heat fluxes In order to study jet impingement boiling heat transfer, surface heat flux and surface temperature need to be determined. In the present study, the inverse heat conduction (IHC) analysis developed by Zhang (2004) was used to determine the top surface temperature and heat flux from the measured temperature for each thermocouple separately. The analysis is based on a 2D axisymmetric finite element method (FEM). More details about the IHC program can be found in appendix A. The domain used and boundary conditions applied for the IHC analysis are shown in figure 4.6. The domain is meshed using 175 linear elements. A dense mesh is applied in the areas adjacent to the top surface since large thermal gradients are expected in this region. Details of the mesh density are presented in table 4.3 (Franco 2008). It was found that the calculated surface heat flux changes less than 1% when the number of elements increases from 175 to 559.  Table 4.3 Mesh size for IHC analysis Section Number of elements Arrangement (r×z) A 25 5×5 B 50 10×5 C 100 10×10  Boundary conditions for the domain in the IHC analysis are shown in figure 4.6 and are defined as follows: Boundary a: The boundary condition at the top surface (quench surface) is the heat flux to be calculated. Boundary b: Due to the symmetry at the centerline, an adiabatic condition is assumed. 48  Boundary c: An adiabatic condition is assumed between the thermocouple insulator and the steel.  Boundary d: As with boundary (c), an adiabatic condition is assumed between the thermocouple insulator and the steel. Boundary e: Air cooling (free convection and radiation) is assumed at the bottom surface of the steel plate. Boundary f: It is assumed that temperature gradient away from the thermocouple position is not significant; therefore, an adiabatic condition is assumed.  Figure 4.6 The domain used for inverse heat conduction (IHC) analysis.  The measured temperature data for stationary plate tests was smoothed and filtered before being input into the inverse heat conduction program. To do so, a filtering approach proposed by Caron (2008) was applied. The approach uses a moving median filter followed by a second filter which 49  is a moving average. The moving median was proposed to smooth out short term fluctuations and highlight the main trend of the temperature-time curves. The second filter was applied to remove the existence of arbitrary edges in the curves resulting from the moving median filter. More details can be found elsewhere (Caron 2008). The first filter was a 41-point moving median, in which each temperature point was replaced by the median of 41 consecutive measurements. The second filter was a 5-point moving average, in which each temperature point was replaced by the average of 5 consecutive measurements. Figure 4.7 shows the effect of filtering approach on temperature data. Careful checks and comparisons showed that all features of the actual temperature histories were retained in the smoothed curves.  Figure 4.7 Effect of filtering approach on temperature data, (a) raw and filtered temperature data. Magnifications of temperature vs. time data are shown for (b) a not-wetted period and (c) a wetted period. The filter smoothens out short term fluctuations before wetting (figure b); however, the actual cooling slope during wetting (figure c) has been retained in the smoothed curve. time, s4 5 6 7 8 9Temperature, oC200300400500600Raw data Filtered data time, s5.6 5.8 6.0 6.2 6.4Temperature, oC540550560570580590time, s8.5 8.6 8.7 8.8Temperature, oC200250300350400450500(a)(b)(c)50  The maximum data recording rate for temperature measurement that could be obtained was governed by the specification of the data acquisition system and also the number of the thermocouples used. In the present study, the measured data frequency was between 30 to 100 Hz depending on the number of thermocouples used in each series of experiments. Previously Franco (2008) showed that a low acquisition rate (<100 Hz) does not constitute sufficient density of measured data for the IHC analysis. He found that 100Hz is the proper value for the data frequency to be use in IHC analysis. Thus, he suggested the measured temperature vs. time data can be subjected to a spline interpolation to adjust data frequency. Since in the present study, the experimental frequency for data collection was lower than 100 Hz, a cubic Hermite spline interpolation (a spline where each piece is a third-degree polynomial specified in Hermite form) was used (Späth 1995). The Hermite spline was applied to each interval (ti,ti+1) separately. The resulting spline with a data frequency of 100 Hz is continuous and has a continuous first derivative.  After improving temperature-time data frequency, thermocouple data were analyzed by using the IHC program to calculate surface heat flux and surface temperature. The calculation procedure in the IHC analysis is as follows. First, the direct heat conduction differential equation is solved by using an initial guess for the surface heat flux. The IHC program uses a finite element approach to solve the nonlinear transient heat conduction problem and calculate the temperature within the plate. Then, the IHC program compares the measured temperature with the calculated temperature at the thermocouple tip location. The temperature difference between measured and calculated values is then used to estimate a new heat flux value for the top surface. Then the procedure is repeated using the new heat flux value until a set of predetermined convergence criteria have been met. More details about the convergence criteria can be found elsewhere 51  (Zhang 2004, Franco 2008). It should be noted that in this study the heat flux and surface temperature calculated by the IHC program will be referred to as experimental data. As it is described in table 4.1, there is some uncertainty for measured values of temperature and thermocouple depth. These values are input in the IHC program and these errors can cause uncertainty in the output of the IHC output which is surface temperature and heat flux. Vakili (2011) used a numerical procedure, called Computerized Uncertainty Analysis, to calculate the uncertainty in the values and reported that the uncertainty in the values of surface heat flux is between ±16% for the stagnation point and ±8% for the parallel flow zone. The cooling conditions used in this previous analysis are similar to those employed in the present study. Thus, the above uncertainty values are taken as the representative errors of the experimental heat fluxes reported in the present work.       4.4.2 Velocity and pressure distribution in liquid jet To study jet impingement cooling of steel plates, quantification of the fluid flow phenomena involved in jet cooling is required since the heat transfer processes are strongly dependent on how water flows on the steel surface. As discussed in section 2.1, two different cooling zones, i.e. impingement and parallel flow zones, are formed in a free-surface impingement type cooling where upon impinging, liquid traverses along the surface. The streamwise velocity of the water (ul) in both zones has significant influence on the convective heat transfer rate.  In this work the proposed streamwise velocity by Vader et al. (1991) was used for the planar jet (table 4.4). For the circular jet, numerical results for the streamwise velocity (Seraj et al. 2012) of a circular jet impinging on a cold surface were used. Curve fitting on the numerical results were applied to derive the equations for the streamwise velocity of the water (table 4.4).  52   Table 4.4 Streamwise water velocity; wji is jet impingement width at the surface; dji is jet impingement diameter at the surface  Impingement zone  Parallel flow zone  Planar jet (Vader et al. 1991)                           (4.1)                             (4.2) Circular jet                         (4.3)                                                        (4.4)  (4.5)  Using the streamwise velocity of the water, the jet pressure profile along the surface can be obtained. The local pressure on the surface in the impingement zone of the planar nozzle is given by the Bernoulli equation:                             (4.6) where Pstag is the sum of the ambient pressure (P0) and the jet pressure on the surface at the stagnation point:                              (4.7) The normalized pressure is calculated as                                    (4.8) For circular jets, the normalized water jet pressure distribution was obtained as:                                                (4.9) 53  by analyzing the data of Seraj et al. (2012). The equations for the water velocity and the pressure distribution (equations 4.1-9) will be used to develop a model for mapping boiling curves (see chapter 6).    54  Chapter 5: Experimental results: stationary plates   5.1 Experimental matrix A test matrix has been designed to study the effect of water jet velocity and water temperature on the cooling of stationary plates with planar or circular nozzles. In order to study the effect of the jet velocity, the water flow rate was varied between 100 and 250 L/min for the planar nozzle, and between 15 and 45 L/min for the circular nozzle. Water temperatures were varied between 10 and 40°C. The selected ranges for water flow rate and water temperature are relevant to industrial conditions. The standoff distance between the test plate and the nozzle was set to 0.1 m. Details of the selected experimental parameters for the individual tests are summarized in tables 5.1 and 5.2. Jet impingement velocities were calculated using equation 2.1. In order to ensure the reproducibility of experiments, a few repeats have been performed. An example has been provided in appendix B. Table 5.1 Experimental matrix (SP: Stationary plate/Planar nozzle) Test Nozzle FR,  L/min Jet impingement velocity (Vji), m/s Twater, °C SP01 Planar 100 2.3 25 SP02 Planar 150 3.1 25 SP03 Planar 250 4.8 25 SP04 Planar 100 2.3 10 SP05 Planar 100 2.3 40  55   Table 5.2 Experimental matrix (SC: Stationary plate/Circular nozzle) Test Nozzle FR,  L/min Jet impingement velocity (Vji), m/s Twater, °C SC01 Circular 15 1.7 25 SC02 Circular 30 2.3 25 SC03 Circular 45 3.0 25 SC04 Circular 15 1.7 10 SC05 Circular 15 1.7 40  5.2 Surface temperature and heat flux curves As an example, figure 5.1a shows temperature-time curves (cooling curves) for the planar nozzle test SP01 observed at 7 different locations (figure 5.1b) from the stagnation point. The temperature-time curves represent calculated surface temperatures based on the IHC analysis of the internal temperature measurements (as explained in section 4.4.1). Figure 5.1c shows the measured internal temperature and calculated surface temperature for one location (x=0mm). Figure 5.1d shows the corresponding surface heat flux. The time reference (t=0) in figure 5.1 has been chosen to be at 1 s prior to the heat flux at the stagnation point reaching 0.1 MW/m2. When the jet impinges on the surface (t≈1 s), the heat flux at the stagnation point (x=0 mm) increases rapidly to ~13.5 MW/m2 and the surface temperature quickly falls below 200°C. Following this rapid cooling, the heat flux gradually drops, lowering the cooling rate accordingly. The surface temperatures at positions far from the jet (x ≥ 40 mm) first drop about 100°C in approximately 1 s before starting to continuously decrease at a much slower rate until a sudden drop in temperature to about 200°C occurs. The time to reach this sudden drop increases 56  with distance and coincides with the progression of the wetting front. The sudden drop in temperature is related to a sudden increase of heat flux which can be observed in figure 5.1c. The peak value of the heat flux in general decreases with distance, and attains ~4 MW/m2 for x=120 mm which is the TC location farthest away from the stagnation point. As for the stagnation point (x=0 mm), the surface temperature decreases further after the sudden temperature drop but at a reduced rate.               (a) (b)             (c)    (d) Figure 5.1 (a) Surface temperature vs time curves, (b) schematic of thermocouple locations, (c) internal and surface temperatures at x=0mm, and (d) heat flux vs time curves; test SP01: FR=100 L/min, Twater=25°C. time, s0 5 10 15 20Tsurface, oC0200400600800SP01, x=0mmtime, s0 1 2 3 4 5 6Temperature, oC02004006008001mm below the surface(TC measurement)Surface temperaturetime, s0 5 10 15 20q, MW/m202468101214x = 0 mm x = 10 mmx = 20 mmx = 40 mmx = 60 mmx = 80 mmx = 120 mm57   5.3 Boiling curves Figure 5.2 shows the family of boiling curves for the experimental data presented in figure 5.1. The boiling curves show the variation in heat flux with surface temperature, which can be plotted for the measurement locations (here shown for selected positions). Boiling curves for all experiments are shown in appendix C.  In the early stage of cooling, an initial cooling stage (IC) is observed in all boiling curves. This can be explained as the transition from air cooling to water cooling. Figure 5.2 shows that the film boiling region is not observed at the stagnation point of the jet (i.e. x=0 mm). It is believed that this is due to high pressure of the water jet and high subcooling preventing the formation of a stable vapor layer. The heat flux increases with a decrease of the surface temperature to approximately 320°C and, after passing the maximum heat flux, it starts decreasing. The heat flux approaching the maximum point (qmax) shows a relatively sharp incline and no shoulder regime is observed. This is in contrast to the experimental data of Robidou et al. (2002) for steady-state cooling where a shoulder heat flux was observed at the stagnation point. For the boiling curve far from the impinging jet (i.e. x=120 mm), i.e. in the parallel flow zone, the film boiling regime can be clearly observed in the early cooling stage (430°C<Tsurface<650°C). The heat flux in the film boiling regime is almost constant and decreases slightly before reaching the Leidenfrost temperature (TMHF) where the vapor layer is not stable anymore and breaks down. The Leidenfrost point marks the onset of transition boiling where the heat flux increases initially as surface temperature decreases (first stage in transition boiling) until the heat flux shoulder is reached (second stage in transition boiling). At a 58  temperature at around 210°C, the transition boiling regime terminates and the heat transfer mechanism changes to nucleate boiling.   Figure 5.2 Family of boiling curves; test SP01: FR=100 L/min, Twater=25°C.  The boiling curve at x=10 mm shows an intermediate case between those described above. Here, the film boiling regime is observed. As the surface temperature decreases below ~520°C, the heat flux increases in the transition boiling regime. However, similar to the boiling curve at x=0mm, the shoulder region is not observed and heat transfer starts to decrease at 300°C.  One important feature of the results in figure 5.2 is that the maximum heat flux strongly depends on the distance from the jet and varies in this experiment between 13.5 and 4.5 MW/m2. Moreover, the boiling curves of the parallel flow zone show a broad heat flux maximum that is associated with the shoulder heat flux zone. Finally, at lower temperatures, the nucleate boiling Tsurface, oC0 200 400 600 800q, MW/m20481216x = 0 mm x = 10 mmx = 120 mmFilm boilingNucleate boilingShoulder qmaxFirst stage in transition boilingInitial cooling59  curves for different positions essentially merge into one curve as the temperature decreases.  Therefore, the results clearly indicate that the distance from the jet affects the value of heat flux as well as the trend and shape of the boiling curves. Thus, it is essential to develop a model that takes into account the influence of distance from the jet and predict the local heat flux for different locations. To further evaluate the effect of distance as well as the processing parameters, i.e. water flow rate and water temperature on the heat transfer rate, the maximum heat fluxes are plotted for all experiments against the distance from the jet (figure 5.3). In order to identify qmax, two cases are considered. In the first case, the heat flux approaching the maximum point (qmax) shows a sharp incline and after passing the maximum heat flux, it starts decreasing. In this case qmax is equal to the maximum point. In the second case, after an incline in the heat flux as the surface temperature decreases below the Leidenfrost point, the heat flux remains relatively constant with some fluctuations (shoulder heat flux). These fluctuations in the shoulder region have been previously observed by Robidou et al. (2002). For thermocouple positions where the shoulder heat flux is observed, the experimental maximum heat flux (qmax) is represented by the average of the heat flux values in the shoulder region. The maximum heat flux in the experiments with the planar nozzle is shown in figure 5.3a and 5.3b. In most experiments, for a position close to the nozzle (less than about 40mm), the maximum heat flux decreases sharply with increasing distance from the jet. For a position farther than 40mm, the maximum heat flux also decreases but with a reduced slope. It is believed that closer to the jet the variation of heat flux is influenced by the local jet velocity as well as subcooling, whereas farther from the jet it is predominantly subcooling.  60    (a) (b)   (c) (d) Figure 5.3 Experimental maximum heat flux for the planar jet: (a) different water flow rates (b) different water temperatures; and for the circular jet: (c) different water flow rates (d) different water temperatures.   Figure 5.3a represents the variation of the maximum heat flux with the distance from the planar jet for different water flow rates. Generally the maximum heat flux increases with increasing water flow rate. The increase in the water flow rate from 100 L/min to 250 L/min increases the x (distance from the water jet), mm0 20 40 60 80 100 120 140qmax, MW/m205101520FR = 100 L/minFR = 150 L/minFR = 250 L/minPlanar nozzleTwater = 25oCx (distanc  from the water jet), mm0 20 40 60 80 100 120 140qmax, MW/m205101520Twater= 10oCTwater= 25oCTwater= 40oCPlanar nozzleFR = 100 L/minr (distance from the water jet), mm0 20 40 60 80 100 120 140qmax, MW/m20246810121416FR = 15 L/minFR = 30 L/minFR = 45 L/minCircular nozzleTwater = 25oCr (distanc from the water jet), mm0 20 40 60 80 100 120 140qmax, MW/m20246810121416Twater= 10oCTwater= 25oCTwater= 40oCCircular nozzleFR = 15 L/min61  jet impingement velocity at the plate surface from 2.3 to 4.8m/s. This increase in jet impingement velocity increases the maximum heat flux from ~13.5 to ~17 MW/m2. The variation of the maximum heat flux with the water temperature is presented in figure 5.3b for the experiments with a planar nozzle. With the increase of water temperature the maximum heat flux decreases significantly. At the stagnation point of the jet, the increase of the water temperature from 10 to 40°C leads to a decrease in the maximum heat flux from ~15 to ~11.5 MW/m2.  Figures 5.3c and 5.3d show the local maximum heat flux variations in the experiments with the circular nozzle. In most experiments three parts in the variation of the maximum heat flux with radial position can be distinguished. For a position close to the jet (0≤r<~10mm), the maximum heat flux remains constant or falls slightly. For a position between 10 and 80mm (~10≤r<~80mm), the maximum heat flux falls more rapidly. In the last part (r≥~80mm), the maximum heat flux does not change significantly with the distance from the jet or falls slightly.   The effect of the water flow rate on the local maximum heat flux variations is shown in figure 5.3c. The increase of the water flow rate from 15 to 30 L/min increases the maximum heat flux from 11.5 to 12.5 MW/m2 at the stagnation point of the jet. However, a further increase in water flow rate from 30 to 45 L/min does not increase the maximum heat flux significantly.  Figure 5.3d shows the effect of the water temperature on the maximum heat flux. An increase of water temperature from 10 to 40°C decreases the maximum heat flux from 12 to 8.5 MW/m2. However, the figure shows that changes in the maximum heat fluxes are not significant for water temperatures of 10 and 25°C.  62  5.4 Comparison between steady-state and transient conditions Comparing the boiling curves of the steady-state (temperature controlled) condition (Robidou et al. 2002) and the transient (quenching) condition reveals some differences in the trend of the boiling curves. As shown schematically in figure 5.4, the first difference is the existence of the initial cooling (IC) stage in the transient cooling tests (the transition stage from air cooling to water cooling). The existence of this stage in the transient cooling condition has been previously reported by Li et al. (2007) as well.   (a) (b) Figure 5.4 Schematic showing (a) the steady-state and (b) the transient boiling curves for jet impingement cooling when high subcooling condition is applied.  Another difference observed between steady-state and transient cooling is after the transition from the film to the transient boiling regime the heat flux does not immediately jump to its shoulder value. During transient cooling conditions this change is gradual and has been identified as the first stage in the transition boiling regime. The slope of the boiling curves at this stage was ShoulderFilm boilingCHFFirst MHFFilm boilingInitialcoolingFirst stage intransition boilingShoulderTsurface,oCq,MW/m2Tsurface,oCq,MW/m2TinitialqmaxStagnation pointParallel flow zone63  calculated for all experiments and presented as a function of distance from the stagnation point in figure 5.5.   Figure 5.5 The slope of the first stage in the transition boiling regime. Experimental errors are ±16% for the stagnation point and ±8% for positions away from the stagnation point. For clarity of presentation error bars are not shown.  Although there is some scattering in the data, it was found that the slope value does not depend significantly on processing parameters, i.e. water temperature and water flow rate, or on the distance from the water jet. As Li et al. (2007) discussed, when film boiling is not observed in the area close to the jet, the initial cooling stage changes very quickly to the first stage of transient boiling (figure 5.4b). Therefore, for these cases it is not easy to demarcate the boundary between these two stages.  x (planar jet); r (circular jet), mm0 20 40 60 80 100 120 140dq/dTsurface, MW/m2oC -0.10-0.08-0.06-0.04-0.020.00Planar, 100,  25oCPlanar, 150,  25oCPlanar, 250,  25oCPlanar, 100,  10oCPlanar, 100,  40oCCircular, 15,  25oCCircular, 30,  25oCCircular, 45,  25oCCircular, 15.  10oCCircular, 15,  40oCMeanNozzle, F.R.      Twater(L/min)   (oC)+25%-25%64  The absolute mean value for the slope of the first stage in transition boiling has been found to be 0.044 MW/m2°C. Previously, Caron (2008) has shown that the thermal conductivity of the plate strongly affects the slope of this stage in the transition boiling regime. Higher thermal conductivity facilitates higher heat transfer within the plate and decreases the time required to switch from one level of heat flux to a higher level. In the steady-state condition without the time constraint the first stage in the transition boiling regime vanishes and the film boiling heat flux jumps to the shoulder heat flux in a very narrow temperature range (e.g. boiling curves in figure 2.5).   Additionally, the steady-state boiling curves of Robidou et al. (2002) showed the existence of the critical heat flux (CHF) and first minimum heat flux (First MHF) points which were not observed in the current experiments. Highly transient and severe quenching conditions are likely the reason that these phenomena were not observed.      65  Chapter 6: Boiling curve model for cooling of stationary plates   6.1 Overview As discussed in chapter 5, during transient jet impingement cooling, different heat transfer rates are observed at different distances from the nozzle. To date, the majority of boiling heat transfer studies have dealt only with the area directly under the jet (Seiler-Marie et al. 2004, Ishigai et al. 1978, Ochi et al. 1984, Miyasaka et al. 1980, Liu and Wang 2001).  A key distinction between the present study and previous studies is the attempt to map the heat flux along the surface of a stationary plate. Following the analysis of experimental results in chapter 5, a model for calculating heat fluxes on stationary plates during jet impingement boiling is proposed in this chapter. The proposed model, which is called a boiling curve model in this study, provides a foundation towards the development of a cooling model to simulate the temperature histories of moving steel plates during jet impingement cooling. 6.2 Nucleate boiling As illustrated in figure 6.1, experimental results show that the nucleate boiling heat flux at the stagnation point depends only on the surface temperature of the plate. It is independent of nozzle geometry, water flow rate and water temperature. Therefore, the following correlation of the nucleate boiling is proposed for both types of water jets based on the stagnation point experimental data:                                                     (6.1) where 66                                          (6.2) Here q and Tsurface have the units of W/m2 and °C, respectively. As illustrated in figure 5.2, the nucleate boiling curves for other positions show that distance from the nozzle has a negligible effect on the nucleate boiling heat flux. Therefore, the proposed correlation can be used for all positions.  Figure 6.1 Nucleate boiling heat flux at the stagnation point. Experimental errors are ±16%. For clarity of presentation error bars are not shown.  6.3 Transition boiling: shoulder heat flux In order to develop a model for the transition boiling regime, two different phenomena have to be addressed, i.e. (i) the shoulder heat flux that is the maximum heat flux in the transition regime Tsurface, oC100 1000q, MW/m2110Circular: 15 L/min, 25oCCircular: 30 L/min, 25oCCircular: 45 L/min, 25oCCircular: 15 L/min, 10oCCircular: 15L/min , 40oCPlanar: 100 L/min, 25oCPlanar: 150 L/min, 25oCPlanar: 250 L/min, 25oCPlanar: 100 L/min, 10oCPlanar: 100 L/min, 40oCNB equation67  and (ii) the gradual increase from the MHF to the shoulder heat flux. The gradual increase of heat flux can be described with the slope of 0.044 MW/m2°C independent of process parameters, as illustrated in figure 5.5. The shoulder heat flux was analyzed in this work by starting with the approach of Seiler-Marie et al. (2004) who proposed that the heating of a subcooled liquid, which wets the hot surface at each periodic bubble oscillation, is the main mechanism of the heat transfer in the heat flux shoulder region. Seiler-Marie et al. derived equation 2.10 by assuming that the vapor patches cannot be greater than the Rayleigh-Taylor critical wavelength. However, in a more general format, the following heat flux equation was proposed:          (6.3) Here K' is a constant, ρl is the density of water, and cp,l is the specific heat of water. tot is the total deceleration which is the sum of the gravitational and jet decelerations and Dcrit is the critical size of vapor patches. ΔTsub is subcooling which is the difference between the water temperature and the saturation temperature of the water. In the surface area close to the water jet, the jet pressure can increase the saturation temperature to higher temperatures than 100°C. However, the maximum increase in the highest local pressure for conditions related to cooling on the run-out table has been found to be less than 5°C (Seraj 2011). Therefore, in this research the effect of jet pressure on the saturation temperature of the water is neglected and the saturation temperature is assumed to be 100°C. As discussed in section 2.2.1.3, the model of Seiler-Marie et al. (2004) is based on the Rayleigh-Taylor instability and describes the shoulder heat flux at the stagnation point. In order to apply the model for the prediction of heat fluxes outside the stagnation point several factors need to be taken into account. First, the water velocity changes with distance which results in a component   subtotvlcrittotlplTBsh TuuDcKq   ,2 ' 2/12/1,,68  of the velocity vector parallel to the surface. The stability of the vapor/liquid interface depends strongly on the local velocity of the liquid at the liquid/vapor interface, particularly on its parallel velocity component. Also, the subcooling will vary with distances from the stagnation point as heat released from the hot surface increases the temperature of the water.   Therefore, in order to expand the model to different positions on the surface, the local values for γtot, Dcrit, and ΔTsub need to be found and incorporated into equation 6.3. The value of K' previously obtained by Seiler-Marie et al. (2004) for the stagnation point (K'=0.15) from the experimental data of Robidou et al. (2002) for steady-state cooling is kept the same.    The total deceleration is calculated as:                       (6.4) where g is the gravitational deceleration and γjet is the effective jet deceleration along the plate surface that can be calculated from:                                (6.5) Here, the jet deceleration at the stagnation point (γjet,stag.) is given by (Seiler-Marie et al. 2004):      (6.6)   where DH,ji is the jet hydraulic diameter which is equal to twice the jet width for a planar jet and is equal to the jet diameter for a circular jet.  As discussed earlier, the concept of shoulder heat flux is based on the assumption that the instabilities at the vapor-liquid interface during jet impingement promote oscillations and jiHjistagjet Dv,2., 69  breaking of the vapor layer, subsequently resulting in increased heat transfer. The modeling of this phenomenon relies on the ability to determine the size of vapor patches.  The liquid/vapor interface is stable if it can withstand a disturbance and still return to its original state. The aim of instability analysis is to determine the range of conditions for which the interface is unstable with respect to an arbitrary disturbance of the interface. Figure 6.2 shows the schematic of the two phase structure in the transition boiling regime during jet impingement cooling. Disturbances of all wavelengths may be present at the interface. However, only the amplitude of disturbances with long wavelengths will grow with time and cause the interface to become unstable (Carey 2007).   Figure 6.2 Schematic of vapor patches on the surface in the transition bling regime and the liquid/vapor interface. The plot shows the critical size of diamater along the surface. 70  Although the Rayleigh-Taylor instability criterion can be applied for calculating the critical wavelength (λcrit) at the stagnation point, the instability criterion needs to be modified for other positions on the surface. Here, the relative velocity of liquid and vapor outside the stagnation point needs to be incorporated into the criterion to determine the stability of the vapor/liquid interface. The Kelvin-Helmholtz instability analysis predicts the critical wavelength of the vapor/liquid interface (λcrit):     (6.7) where σl/v is the surface tension of the vapor/liquid interface.  In the current analysis, the velocity of the vapor along the plate surface (uv) inside the vapor patches is assumed negligible compared to the streamwise (parallel) velocity component of the liquid (ul). The equation contains three terms. The first term which includes surface tension of the vapor/liquid interface (σl/v) is a stabilizer term. The other terms, however, related to total deceleration and relative velocity, respectively, tend to destabilize the interface.  In the current study, similar to the work of Seiler-Marie et al. (2004), the critical diameter of the vapor patches (Dcrit) is assumed to be equal to the critical wavelength of the liquid/vapor interface. As long as the size of a vapor patch remains smaller than λcrit, it is assumed that there is no chance for the formation of a disturbance with a long wavelength (λ>λcrit) at its interface. Therefore, the vapor patch is stable. However, due to evaporation and growth of the vapor patch, the size of the vapor patch may become larger than λcrit after some time. In this condition, a disturbance with long wavelength (λ>λcrit) can form and cause the vapor patch to breakdown. It is assumed that vapor patches break down into smaller vapor patches with the size of the critical       022 22/  vlvlvlvlvlcrittotvlcritvl uu71  diameter. Figure 6.3 shows an example of calculated critical diameter and shoulder heat flux profiles as a function of distance from the stagnation point. The critical diameter of vapor patches increases as the distance from the stagnation point increases. Then, as the pressure of the jet on the surface vanishes for positions far from the jet it remains constant. The shoulder heat flux decreases sharply close to jet impingement. However, for positions far from the jet (x>10mm), the shoulder heat flux remains constant.  Figure 6.3 Calculated critical diameter of vapor patches and shoulder heat flux profiles: planar nozzle, FR=100 L/min, Twater=25C, Hn=100 mm, wn=3mm. Here, the water temperature is assumed constant along the plate surface.  Water subcooling plays a key role in controlling the heat removal from the surface. In the area directly under the jet, the temperature of the water is the same as the one at the nozzle exit. However, as water flows away from this area, the heat extracted from the surface gradually x, mm0 5 10 15 20 25qsh,TB , MW/m2 051015202530Dcrit, mm05101520Planar jetF.R. = 100 L/minHn = 100 mmWn = 3 mm72  increases the temperature of the water stream. The rise in the water temperature can be obtained by performing a steady-state heat balance, i.e. increment of increase in water temperature is given by       (6.8)    Here, Ai is the surface area increment for the ith position, and qi is the local heat flux at the surface. cp,l is the specific heat capacity for the liquid, and   l is the mass flux of the water at the nozzle exit. The distance step size for the area close to the jet (planar jet: x≤5cm, circular jet: r≤5cm) has been chosen 0.1mm. For the farther positions (planar jet: x>5cm, circular jet: r>5cm) a step size of 1mm has been chosen. The surface area increment for the planar jet cooling has a rectangular-shape, however for the circular jet has a ring-shape. Heat released from the surface may increase the water temperature, vaporize the water, and dissipate as radiation. In the above equation, β is the fraction of heat released which leads to an increase in the water temperature. In this study, β is considered as an adjustable parameter which is determined by comparison between calculated shoulder heat flux and experimental data. The comparison between model calculations and our available experimental database suggests that a second adjustable parameters (ψ), which is related to the size of the high heat flux area close to the jet, is necessary. Observations indicate that the size of the high heat flux area close to the jet is larger than the size of the impingement zone defined by the hydrodynamic equations (equations 4.1-9). Therefore, as a first approximation to calculate the total deceleration, the streamwise water velocity profile for the planar nozzle has been modified as follow:                         (6.9) lpliiil cMAqT,, 73  The normalized pressure profile for the planar nozzle (equation 4.8) has been calculated using the modified velocity profile. For the circular jet, the following modifications have been applied:                         (6.10)                                (6.11) As seen in figure 6.4a, the change in ψ affects the size of high heat flux area. The ψ has been chosen to be 3 for both planar and circular nozzles based on our comparison between the predicted heat flux profile and our experimental results. It should be noted that close to the stagnation point of the jet (x<~20mm), the shoulder heat flux has a very high heat flux value. Therefore, as shown in figure 5.4, the shoulder heat flux is not observed in the transient boiling curves close to the jet. After adjusting ψ in the model, β is adjusted as shown in figure 6.4b. For the case where the heat extracted from the surface does not increase the temperature of the parallel water flow (β=0), the shoulder heat flux decreases as the distance to the impinging point increases, up to a distance of 30mm. After that point the heat flux remains constant and the model significantly overpredicts the heat flux in the parallel flow zone. Increasing the value of β leads to a gradual decrease of the heat flux in the parallel flow zone and β=0.5 was selected in the model proposed here. In order to verify the approach proposed in this study to describe the shoulder heat flux, the calculated heat flux can be compared with an independent experiment in the literature. The comparison between the prediction of proposed heat flux model and the steady-state experimental data of Robidou et al. (2002) is shown in figure 6.5. The figure shows the validity of the approach for calculating the shoulder heat flux along the surface of the plate.  74   (a)  (b) Figure 6.4 Calculated shoulder heat flux vs. distance, experimental data from test SP01: planar jet, FR=100 L/min, Twater=25°C, (a) different ψ and (b) different β.  x, mm0 20 40 60 80 100 120 140qsh,TB, MW/m20510152025Model:=1, =0Model:=3, =0Model:=5, =0qmax, test SP01x, mm0 20 40 60 80 100 120 140qsh,TB, MW/m20510152025Model:=3, =0Model:=3, =0.5Model:=3, =1qmax, test SP0175   Figure 6.5 Experimental data in Robidou et al. (2002) and the model prediction for the shoulder heat flux: planar jet, Vn=0.8m/s, Twater=84°C, Hn=6 mm. Bars show the scattering range in the shoulder heat flux measurements.   6.4 Minimum heat flux (MHF) and film boiling A model for the heat flux at the Leidenfrost temperature has been proposed by Seiler-Marie et al. (2004) for the stagnation point. The model assumes that the total heat flux is a combination of two phenomena, i.e. liquid evaporation and liquid heating:                                                                                                               (6.12) In order to extend the application of the model for positions beyond the stagnation point, two parameters, i.e. γtot, and ΔTsub, which depend on the distance from the jet need to be replaced by their local values using the procedures described above for transition boiling (equations 6.4 and x, mm0 10 20 30 40 50 60qsh,TB, MW/m2012345ModelExperiment (Robidou et al. 2002)76  6.8). Figure 6.6 compares the calculated minimum heat flux with the experimental data of Robidou et al. (2002) to verify the proposed approach.   Figure 6.6 Comparison between calculated MHF using equation (6.12) and the experiment of Robidou et al. (2002).   Most literature shows that the film boiling heat flux for the case of jet impingement cooling condition weakly depends on surface temperature (Robidou et al. 2002). This also has been shown in the experimental results of the present research. Therefore, in this study film boiling heat flux is assumed independent of surface temperature and has been set equal to qMHF, as calculated by equation 6.12.   x, mm0 10 20 30 40 50 60qMHF, MW/m20.00.40.81.2 ModelExperiment  (Robidou et al. 2002)77  6.5 Model application to transient cooling (construction of boiling curves) The different boiling regimes need to be combined to construct a boiling curve which represents the variation of the surface heat flux with surface temperature of steel over the range of temperatures applicable in the hot strip/plate mills. To do so, the following procedure is proposed: 1. For surface temperatures higher than the Leidenfrost temperatures, the effective heat transfer mode is film boiling and the heat flux can be calculated using equation (6.12). The Leidenfrost temperature, as the lower temperature limit for the application of this equation, must be determined separately. As such, in the present study, the following empirical correlations were used to calculate the Leidenfrost temperature (in °C) for planar and circular jets, respectively:                                                     (6.13)                                                      (6.14) where x (m) is distance from the planar jet and r (m) is distance from the circular jet. ∆Tsub,stag. is the water subcooling at the stagnation point (∆Tsub,stag.=100°C-Twater,stag.). 2. For surface temperatures immediately below the Leidenfrost temperature, the values of the heat flux increases linearly with a slope of 0.044 MW/m2°C from the Leidenfrost temperature. This straight line represents the first stage of the transition boiling regime as discussed in section 5.4 and illustrated in figure 5.4b. The line will intersect either the transition boiling curve (shoulder heat flux) or the nucleate boiling curve depending on the distance from the jet, as shown in figure 6.7. From this point, the heat flux is calculated either using the correlations for the transition boiling shoulder heat flux, equation (6.3), or nucleate boiling, equation (6.1). In other words, for temperatures lower than the Leidenfrost temperature, the heat fluxes of nucleate 78  boiling and the transition boiling shoulder are determined at each surface temperature to identify the temperature range where the shoulder heat flux is below that of nucleate boiling. For low temperatures (100°C<Tsurface<~165°C), the heat transfer mechanism is partial nucleate boiling. As such, the following empirical correlation is used to calculate the heat flux at low temperatures:     42 1040.3202.1/  surfacePNB TmWq       (6.15) The procedure described in steps 1 and 2 leads to the construction of ideal boiling curves for cooling of a stationary plate. The schematic in figure 6.7a shows the construction of ideal boiling curves for three positions on the surface: (1) under the jet, (2) midway, and (3) far from the jet.  3. Starting from the initial temperature of the plate, a straight line denoting the initial cooling stage is drawn with the slope of 0.044 MW/m2°C, as discussed in section 5.4. This method, which has also been applied by Li et al. (2007), helps determine the surface heat fluxes during the initial quenching stage of a stationary plate. The schematic in figure 6.7b shows the modified ideal boiling curved by adding the initial cooling stage. For the position under the jet (1), the film boiling region may exist or not depending on the initial surface temperature. Uncertainty at this position is because the stable vapor layer forms only if the initial temperature is high enough. Also, the heat flux level of the shoulder regime at a location under the jet may be too high to be reached in the transient cooling condition. However, the shoulder heat flux is present for positions (2) and (3). 5. The transition at the intersections of the different boiling modes is made smoother by using a 19-point moving average technique where the temperature spacing between two data points is 5°C. 79       (a)           (b) Figure 6.7 Schematic plots showing the procedure of combining boiling regimes for three positions; (1) under the jet, (2) midway, and (3) far from the jet: (a) ideal boiling curves (b) boiling curves with the initial cooling stage.   As an example, figure 6.8 illustrates the verification of our model development for a family of boiling curves for two different conditions. Figure 6.8a shows the calculated and measured boiling curves for the experiment with a planar nozzle, a water flow rate of 100 L/min and a water temperature of 25°C. The calculated curves match the experimental data with reasonable accuracy. Figure 6.8b compares boiling curves for the test with a circular nozzle, a water flow rate of 15 L/min and a water temperature of 10°C. Although some discrepancies are observed in the mid temperature range (~300-500°C), in general the approach used to calculate boiling curves is acceptable.  A significant advantage of the model is that it uses identical algorithms for two different nozzle geometries to predict the heat flux at different positions on the surface. The Tsurface,oCq,MW/m2(1)(2)(3)TinitialTsurface,oCq,MW/m2Sh.1(1)(2)(3)Sh.2Sh.3NBFBPNBInitial cooling80  effects of the water flow rate and water temperature have been included in the model. Calculated and measured boiling curves for all experiments are shown in appendix C.              (a)            (b) Figure 6.8 Calculated and experimental boiling curves: (a) test SP01: planar jet, FR=100 L/min, Twater=25°C; (b) test SC01: circular jet, FR=15 L/min, Twater=25°C. Experimental errors are ±16% for the stagnation point and ±8% for positions away from the stagnation point. For clarity of presentation error bars are not shown.  To further evaluate the boiling curve model, the predicted maximum heat fluxes are compared with the experimental results in figures 6.9. Figures 6.9a and 6.9b show the variation of the maximum heat flux for planar jet cooling. The model predicts that the maximum heat flux decreases sharply close to the jet impingement region. However, for positions far from the jet (x>~40mm), the maximum heat flux decreases slightly with the distance. Figures 6.9a and 6.9b show good agreement between the experimental data and the model.  The maximum heat flux changes with distance from the circular jet are shown in figures 6.9c and 6.9d. The model predicts that the maximum heat flux decreases slightly in areas close to the jet (r<~20mm). For positions further away (r>~20mm) the heat flux first decreases more rapidly and Tsurface, oC0 200 400 600 800q, MW/m205101520Exp.: x= 0 mmExp.: x=10 mmExp.: x=120 mmModelTsurface, oC0 20 40 60 800q, MW/m202468101214Exp.: r=0mmExp.: r=40mmExp.: r=80mmModel81  then the slope of the reduction decreases. Although a few data points fall outside of the predicted curves, generally the model prediction is in a good agreement with the experimental data (figure 6.10).    (a) (b)   (c) (d) Figure 6.9 Calculated and experimental maximum heat flux profiles for the planar jet: (a) different water flow rates (b) different water temperatures; and the circular jet: (c) different water flow rates (d) different water temperatures.  x (distance from the water jet), mm0 20 40 60 80 100 120 140qmax, MW/m205101520FR = 100 L/minFR = 150 L/minFR = 250 L/minModel (100 L/min)Model (150 L/min)Model (250 L/min)Planar nozzleTwater = 25oCx (distance from the water jet), mm0 20 40 60 80 100 120 140qmax, MW/m205101520Twater= 10oCTwater= 25oCTwater= 40oCModel (10oC)Model (25oC)Model (40oC)Planar nozzleFR = 100 L/minr (distance from the water jet), mm0 20 40 60 80 100 120 140qmax, MW/m205101520FR = 15 L/minFR = 30 L/minFR = 45 L/minModel (15 L/min)Model (30 L/min)Model (45 L/min)Circular nozzleTwater = 25oCr (distance from the water jet), mm0 20 40 60 80 100 120 140qmax, MW/m205101520Twater= 10oCTwat r= 25oCTwater= 40oCModel (10oC)Model (25oC)Model (40oC)Circular nozzleFR = 15 L/min82   (a)  (b) Figure 6.10 Calculated and experimental maximum heat flux profiles for (a) the planar jet and (b) the circular jet. qmax, MW/m2Experiment0 2 4 6 8 10 12 14 16 18 20Model02468101214161820100 L/min, 25oC150 L/min, 25oC250 L/min, 25oC100 L/min, 10oC100 L/min, 40oC+20%-20%qmax, MW/m2Experiment0 2 4 6 8 10 12 14 16 18 20Model02468101214682015 L/min, 25oC30 L/min, 25oC45 L/min, 25oC15 L/min, 10oC15 L/min, 40oC+20%-20%83  Figure 6.9b and 6.9c show that the agreement between the model and the experiment is outside of the zone of ±20% for some data points in experiments with a water temperature of 40°C. These discrepancies are mainly observed for positions close to the jet. The discrepancies can primarily be related to the prediction of the nucleate boiling curves using equation 6.1 (figure 6.1, figure C.5 and C.10 in appendix C). The calculated heat flux is markedly larger than the measured one in the nucleate boiling regime at temperatures above 250°C for a water temperature of 40°C, and therefore, a higher maximum heat flux is predicted. 84  Chapter 7: Experimental results: moving plates   7.1 Surface temperature and heat flux histories Two series of experiments were carried out to study the heat transfer of a moving steel plate during jet impingement cooling. In the first series which are called MP (Moving plate/Planar nozzle) tests, four experiments were performed with a single top planar jet to quantify the effect of plate speed on heat extraction. The nozzle gap (wn) was 3mm. Details of the experiments are summarized in table 7.1. As shown in the table, the flow rate and water temperature were kept constant in all experiments. The nozzle to plate surface distance (Hn) was 0.1 m, which is the same as in the experiments with stationary plates of chapter 5. In the second series of experiments which is called MC (Moving plate/Circular nozzle) tests, five experiments were carried out using a single top circular nozzle (dn=19mm). Details of these experiments are shown in table 7.2. Plate speed was kept at 1.0 m/s in all experiments. The nozzle to plate surface distance was set to 1.5 m, which is the same as in the experiments of Chan (2007), Jondhale (2007) and Franco (2008). The effects of water temperature and water flow rate on the heat transfer of a moving plate were investigated in this test series.  Table 7.1 Test matrix for MP series; process parameters: moving plate, single planar nozzle, Hn=0.1m Test Vp, m/s FR, L/min Twater, °C MP01 0.2 100 25 MP02 0.5 100 25 MP03 1.0 100 25 MP04 1.6 100 25  85  Table 7.2 Test matrix for MC series; process parameters: moving plate, single circular nozzle, Hn=1.5m Test Vp, m/s FR, L/min Twater, °C MC01 1.0 15 25 MC02 1.0 30 25 MC03 1.0 45 25 MC04 1.0 15 10 MC05 1.0 15 40  A representative plate surface temperature history is shown in figure 7.1a for the test with a planar jet and a plate speed of 1 m/s. The surface temperature of the plate before the first cooling pass is about 680°C. Each drop represents one cooling pass. Figure 7.1b shows a closer look at cooling pass 6 of this experiment. Here, the surface entry temperature (Tentry) of the plate is ~470°C before a sharp temperature drop to ~300°C. The sharp drop occurs when the plate passes beneath the water jet. After the plate leaves the water jet the temperature rebounds. The rebound in the temperature occurs due to heat conduction from the bottom of the plate which is still hot compared to the top surface.  Figure 7.2 displays the calculated top surface heat flux vs. time for the same experiment shown in figure 7.1. For the first 4 cooling passes the peak heat fluxes are relatively low; i.e. approximately 4 MW/m2. However, a significant increase in the peak heat flux to ~8.5 MW/m2 is observed in cooling pass 6. After cooling pass 7, the peak heat flux decreases gradually. The increase in the peak heat flux followed by the decrease is consistent with the changes of heat flux in a boiling curve from high to low temperature. Figure 7.2b shows the heat flux history experienced during cooling pass 6. It is expected that the peak heat flux occurs when the TC position is at or very close to the impinging point of the jet.   86   (a)  (b) Figure 7.1 Surface temperature vs. time, (a) 15 cooling passes and (b) cooling pass 6; process parameters: planar nozzle, FR=100 L/min, Twater=25°C, Hn=0.1 m.  87   (a)  (b) Figure 7.2 Heat flux vs. time, (a) 15 cooling passes and (b) cooling pass 6; processes parameters: planar jet FR=100 L/min, Twater=25°C, Hn=0.1 m.  88  Figure 7.3 shows a typical variation of calculated heat fluxes using the IHC program with respect to the time for selected cooling passes with different entry temperatures. Results shown are for a test with a single circular nozzle and a plate speed of 1 m/s. The water flow rate is 30 L/min and the water temperature is 25°C. The heat flux was calculated using temperature data measured at the thermocouple which passes beneath the nozzle (y=0). As a first approximation, the peak heat flux can be associated with the location of the thermocouple at the stagnation point of the jet, and the variation of the heat flux with distance from the stagnation point can be clearly observed. The peak heat flux varies with surface temperature, which is consistent with the trends of a classical boiling curve. Furthermore, the heat flux curve is not symmetric. It stretches in the downstream direction indicating a larger area of efficient cooling past the stagnation point of the jet. It also extends further out for lower entry temperatures. These general trends are commonly observed in most experiments with different processing parameters.  Figure 7.3 Heat flux vs. time for different entry temperatures, process parameters: single circular nozzle, FR=30 L/min, Twater=25˚C, Vp=1.0m/s, position: longitudinal center line (y=0). 0 0.2 0.4 0.6051015(a) Tentry(C): 621time, sq, MW/m20 0.2 0.4 0.6051015(b) Tentry(C): 569time, sq, MW/m20 0.2 0.4 0.6051015(c) Tentry(C): 411time, sq, MW/m20 0.2 0.4 0.6051015(d) Tentry(C): 364time, sq, MW/m20 0.2 0.4 0.6051015(e) Tentry(C): 322time, sq, MW/m20 0.2 0.4 0.6051015(f) Tentry(C): 280time, sq, MW/m289  7.2 Boiling curves 7.2.1 Heat flux evolution with surface temperature Figure 7.4 shows the heat flux evolution with surface temperature for one cooling pass (pass 6) in test MP03. The heat flux starts to increase from a very low value consistent with air cooling at the entry temperature (here, Tentry≈470°C). As the plate moves toward the jet the heat flux increases while the surface temperature decreases. This trend continues until the TC location on the plate reaches the impinging point of the jet. After this point, which corresponds to the peak heat flux (PHF) point in figure 7.2b, the heat flux decreases. The surface temperature rebounds shortly after the PHF point. Finally, an air cooling regime with a low heat flux is reached again at the exit temperature (here, ~430°C). The trend of heat flux change vs. temperature highlights the complexity of the boiling heat transfer for transient cooling of a moving plate.   Figure 7.4 Heat flux evolution vs. surface temperature during cooling pass 6; process parameters: planar jet, FR=100 L/min, Twater=25°C, Hn=0.1 m, cooling pass 6. The arrows show the path of heat flux evolution.  90  The peak heat fluxes for all cooling passes in test MP03 are shown in figure 7.5. The peak heat flux points are plotted against their corresponding surface temperatures. Since the nozzle is planar, the plate experiences the same temperature histories in all lateral positions. The peak heat flux follows a trend which is similar to a boiling curve for a stationary surface. The peak heat fluxes are almost constant at surface temperatures higher than ~480°C (TPHF,min) and the dominant boiling mechanism of heat transfer is expected to be film boiling. At temperatures lower than 480°C, the peak heat flux first increases with decreasing temperature indicating that the heat transfer mechanism has changed. It can be speculated that at temperatures below ~480°C the stable vapor layer cannot withstand the pressure of the jet; therefore, the water jet penetrates and wets the surface at the impinging point of the jet. The heat transfer mechanism changes from film to transition boiling. The maximum peak heat flux is observed in the range of 200 to 300°C. At even lower temperatures nucleate boiling is expected to be the boiling mechanism where the peak heat flux decreases sharply as the surface temperature decreases, as illustrated in figure 7.5. The change in the slope of the PHF plot at temperature around 150°C can be attributed to the boiling mechanism transition from fully developed nucleate boiling to partial nucleate boiling.  91   Figure 7.5 Peak heat flux vs. surface temperature, Process parameters: planar jet, FR=100 L/min, Twater=25°C, Hn=0.1 m. Experimental errors for PHF are ±16%.  7.2.2 Effect of plate speed on boiling curves The effect of plate speed on PHF is shown in figure 7.6. For comparison, the boiling curve at the stagnation point for cooling of a stationary plate has been plotted in figure 7.6 as well. Water flow rate, water temperature, and nozzle-to-surface height are the same for all tests. In general, the PHF values in moving plate tests are lower than the qmax in the stationary plate test.  For all plate speeds, the overall trends of PHF variation with surface temperature are identical. It can be observed that the plate speed has an effect on the peak heat fluxes in the regions of film boiling and transition boiling. However, the plate speed does not have an effect on the nucleate boiling region. This finding is consistent with the observation of Gradeck et al. (2009) for transient cooling of a rotating cylinder. Planar nozzleTsurface,oC0 100 200 300 400 500 600 700PHF, MW/m2024681012Vp = 1.0 m/sPHFminPHFmax92   Figure 7.6 Effect of plate speed on peak heat flux, parameters: planar jet, FR=100 L/min, Twater=25°C, Hn=0.1m. Experimental errors for PHF are ±16%.  For the very low plate speed of 0.2 m/s, the exposure time to the cooling water jet is comparatively high. Therefore, the amount of heat extraction from the plate in each cooling pass is such that the temperature of the plate is reduced to around 100°C after only three cooling passes. As seen in figure 7.5, the PHF of the first cooling pass is very high (~12.5 MW/m2). The temperature of the first PHF point is ~250°C and indicates that during the first cooling pass a substantial temperature drop happens. It is expected that if the initial temperature of the steel plate were higher, the same trend as the trends of PHF variation for higher plate speeds would be observed where nucleate boiling is attained in later cooling passes.  As the plate moves faster, the transition and film boiling regimes are initially observed with a shift to lower heat fluxes and lower surface temperatures as speed increases. For example the Planar nozzleTsurface,oC0 200 400 600 800q, MW/m20246810121416PHF: Vp=0.2 m/sPHF: Vp=0.5 m/sPHF: Vp=1.0 m/sPHF: Vp=1.6 m/sstationary plate (q vs. Tsurface)93  maximum heat flux, PHFmax, decreases from 12.5 to 8 MW/m2 as the plate speed increases from 0.2 to 1.6 m/s. The minimum peak heat flux, PHFmin, decreases from 4.5 to 2 MW/m2 as the plate speed increases from 0.5 to 1.6m/s whereas, the Leidenfrost temperature (temperature of PHFmin) decreases from 490 to 445°C. These experimental data will be used to incorporate the effect of plate speed in the construction of boiling curves for a moving plate (see chapter 8).   7.2.3 Effect of lateral distance on boiling curves Because of the geometry of the planar nozzle, the heat transfer rate is the same at each lateral distance (y) from the centerline of the plate. However, due to the radial distribution of water for circular jets, it is expected that in this case the heat transfer rates are strongly dependent on the distance from the longitudinal centerline of a moving plate. Figure 7.7 shows the variation of PHF for three lateral distances of 0, 19, and 38 mm from the centerline of the plate. In this experiment, the water flow rate is 15 L/min, water temperature is 25°C, and the nozzle to plate distance is 1.5 m. As the distance increases, the pressure of the jet on the surface decreases, and hence the heat flux in the film boiling and the transition boiling regions decreases. However, no significant dependency of nucleate boiling heat flux on the lateral distance is observed.  Figure 7.7 also shows that the Leidenfrost (PHFmin) temperature decreases as the distance from the jet in lateral direction increases. This verifies that at high temperature, the lateral width of the wetted zone is narrow. As the temperature decreases, the wetted zone propagates in the lateral direction. According to the figure, at temperatures above ~430°C, all measured locations, i.e. 0mm, 19 mm and 38 mm, are outside of the wetted zone while at temperatures below ~240°C, they are all inside the wetted zone. 94   Figure 7.7 Peak heat flux vs. surface temperature, parameters: circular jet, FR=15 L/min, Twater=25°C, Vp=1 m/s, Hn=1.5 m. P# shows the cooling pass number in the test. Experimental errors for PHF are ±16%.  Contour plots are a good representation of the overall cooling condition on the surface of a moving plate. The contours can be plotted by transforming the surface heat flux data points from time coordinates to distance coordinates based on the plate speed. The heat flux data points for all lateral positions are combined and contour plots are generated. Figure 7.8 shows the heat flux contour plots for cooling passes of 2, 5, and 10 in test MC01. The moving direction of the plate is from left to right. The corresponding cooling pass numbers i.e. P2, P5, and P10 are shown in figure 7.7 as well. As is seen in figure 7.7, film boiling is the dominant heat transfer mechanism during water cooling in all positions during cooling pass 2. In fact the entry temperature of the plate is high enough (Tentry=520°C) such that no wetted area is observed during this cooling pass.  Figure 7.8a Circular nozzleTsurface,oC0 100 200 300 400 500 600 700PHF, MW/m202468101214y = 0 mmy = 19 mmy = 38 mmP2P5P10P2P2P5P10P5P1095  shows the heat flux contour plot of this cooling pass. The contour plot shows that the heat extraction during this cooling pass is at all points below 3 MW/m2.   Figure 7.8 Contour plot showing the surface heat flux (MW/m2) for the test parameters: circular jet, FR=15 L/min, Twater=25°C, Vp=1 m/s, Hn=1.5 m. 96   As can be seen in figure 7.7, in cooling pass 5, the positions of 0 and 19 mm are in the wetted zone and the heat flux in the wetted zone is relatively high (~7-10 MW/m2). However, the lateral position of 38 mm is still in the non-wetted zone.  The contour plot in figure 7.8b clearly shows the size and the shape of the high heat flux area inside the wetted zone.  According to figure 7.7, in cooling pass 10 (with an entry temperature of 240°C) all three lateral positions are in the wetted zone and the heat transfer mechanism is nucleate boiling. The contour plot of pass 10 (figure 7.8c) shows that the high heat flux zone (~4-6 MW/m2) has grown to cover a wide surface area. This leads to more uniform cooling across the width of the plate.   7.3 Integrated heat flux Although plots of the peak heat flux vs. surface temperature (e.g. figures 7.5-7) represent the characteristic trend of boiling regimes during jet impingement cooling of moving plates, for each lateral position, these plots only show one data point in each cooling pass. The heat flux profile in upstream and downstream regions is not reflected in this type of plot. In order to present the amount of heat extracted from the plate during one cooling pass, the heat flux data can be integrated over time. Then, the integrated heat flux can be plotted with respect to the entry temperature of the plate in each cooling pass.  In order to perform the integration, the start and end points for the time domain need to be defined and the procedure must be kept consistent in all analyses. The start time is chosen as the time at which the heat flux at the centerline of the plate (y=0) rises to 0.1 MW/m2. The selection of this value takes into account the background noise in the experimental heat flux data, such that this value is close to air cooling conditions while reasonably capturing the entire heat flux 97  associated with a single jet. The start time for integration is found from the data at the centerline of the plate, and then is applied to the heat flux integration in all lateral TC positions. For multiple nozzle cooling systems, the time that the plate needs to travel between two neighboring jet-lines can be used as the integration time interval (the time difference between start point and end point). However, in the present study where a single nozzle is applied, the integration time interval value needs to be defined differently. Different distances (0.5, 1.0, 2.0 and 3.0 m) were chosen and corresponding times that the plate needs to travel these distances were calculated based on the plate speed. The calculated time values were applied as the integration time intervals. Figure 7.9 shows the calculated integrated heat flux vs. entry temperature for different integration time intervals (0.5, 1.0, 2.0, and 3.0 s). Significant variations in the data are observed for entry temperatures between ~120°C and ~250°C. The reason is that in cooling passes with a low entry temperature, the water evaporation rate is relatively low, and therefore, a layer of water still exists on the plate surface for a time period after the plate leaves the jet. This increases the amount of heat extracted from the plate in each cooling pass. However, at entry temperatures higher than ~250°C, as shown in figure 7.9, the integration time interval does not significantly affect the calculated integrated heat flux. In order to be consistent throughout the heat transfer study for single nozzle tests, the time interval of 2 s, which corresponds to a distance of 2 m, was chosen in all subsequent analyses. Calculation of the integrated heat flux using this value (2 m) captures the actual and more practical trend of heat extraction in the entire entry temperature range.  98   Figure 7.9 Effect of time interval on the integrated heat flux; process parameters: circular jet, FR=15 L/min, Twater=25°C, Vp=1 m/s, Hn=1.5 m, y=0. Experimental errors for the integrated heat flux are ~±8%. For clarity of presentation error bars are not shown.  Figure 7.10 shows the variation of the integrated heat flux with respect to the entry temperature for different water flow rates, a water temperature of 25°C and plate speed of 1 m/s. Figure 7.10a shows this variation at the plate’s centerline (y=0), which passes under the nozzle when the plate moves. As expected, the overall heat extraction from the surface increases at higher temperatures as the water flow rate increases. Further, at entry temperatures lower than ~200°C, the integrated heat flux does not depend on the water flow rate. In fact, it only depends on the entry temperature of the cooling pass. This dependency is very pronounced since small changes in the entry temperature of the plate can significantly change the amount of heat extraction. In cooling passes with entry temperatures in the range of ~250-450°C, the integrated heat flux remains almost constant. As the water flow rate increases from 15 to 30 L/min, the average Entry temperature, oC0 100 200 300 400 500 600 700 800Integrated heat flux, MJ/m20.02.0e-14.0e-16.0e-18.0e-11.0e+01.2e+00.5 s (0.5 m)1.0 s (1.0 m)2.0 s (2.0 m)3.0 s (3.0 m)Integration time interval99  integrated heat flux increases from 0.6 to 0.8 MJ/m2. However, a further increase in water flow rate from 30 to 45 L/min, only increases the integrated heat flux ~0.1 MJ/m2. Moreover, the entry temperature corresponding to the Leidenfrost point increases from 510 to 590°C as the water flow rate increases from 15 to 45 L/min. Figure 7.10b shows the variation of the integrated heat flux at a lateral position of 38mm (y=38mm). At low entry temperatures (<200°C), trends similar to those as seen at y=0mm are observed and the integrated heat flux does not depend on the water flow. Moreover, the amount of heat extraction is the same as at the centerline of the plate (y=0). In other words, the integrated heat flux in cooling passes with entry temperatures lower than 200°C is the same and uniform across the plate width for different water flow rates (15 to 45 L/min). At entry temperatures between 250 to 450°C, strong dependency of the integrated heat flux on the water flow rate can be seen. The integrated heat flux increases from 0.1 to 0.8 MJ/m2 by increasing the water flow rate from 15 to 45 L/min. At entry temperatures higher than 450°C no significant influence of the water flow is observed.  100    (a) (b) Figure 7.10 Integrated heat flux (a) at y=0mm, (b) at y=38mm; Process parameters: circular jet, Twater=25°C, Vp=1 m/s, Hn=1.5 m.  Figure 7.11 shows the variation of the integrated heat flux for different water temperatures for a water flow rate of 15 L/min and a plate speed of 1 m/s. At both lateral positions, i.e. y=0mm and y=38mm, the integrated heat flux decreases at higher plate temperatures as the temperature of water increases since the ability of water to absorb heat decreases. However, the integrated heat fluxes at both positions are independent of the water temperature in cooling passes with a low entry temperature (<200°C).  For the position of y=0mm, an increase of water temperature from 10 to 40°C decreases the average integrated heat flux from ~0.7 to ~0.5 MJ/m2 in the temperature range of ~250-450°C. For entry temperatures higher than 450°C, the decrease in the amount of heat extracted from the surface is not significant as the water temperature increases from 10 to 40°C. At the position of y=38mm, a clear decrease in the integrated heat flux is Position: 0 mmEntry temperature  (oC)0 200 400 600 800Integrated heat flux (MJ/m2)0.00.20.40.60.81.01.21.41.615 L/min30 L/min45 L/minPosition: 38 mmEntry emperature  (oC)2 4 6 800Integrated heat flux (MJ/m2)0.00.20.40.60.81.01.21.41.615 L/min30 L/min45 L/min101  observed as the water temperature increases from 10 to 25°C. However, no significant decrease in the integrated heat flux is observed as water temperature increases further from 25 to 40°C.     (a) (b) Figure 7.11 Integrated heat flux (a) at y=0mm, (b) at y=38mm; Process parameters: circular jet, FR=15 L/min, Vp=1 m/s, Hn=1.5 m.  The effect of plate speed on the integrated heat flux is presented in figure 7.12 for the tests with a planar jet, a water flow rate of 100 L/min and a water temperature of 25°C. As the plate moves slower, it experiences a longer exposure time in the cooling section. Therefore, higher heat extraction is attained at lower plate speeds. As shown in figure 7.12, for the plate speed of 0.2 m/s, in the first cooling pass with the entry temperature of 630°C, substantial heat energy (4.8 MJ/m2) is removed from the plate. According to the peak heat flux plot (figure 7.6), the exposure time to the cooling section is long enough that in the first cooling pass the surface temperature reaches 250°C at the impinging point of the jet. As such, the nucleate boiling regime becomes the dominant heat transfer mechanism in the area under the jet. In the second cooling pass with Position: 0 mmEntry temperature  (oC)0 200 400 600 800Integrated heat flux (MJ/m2)0.00.20.40.60.81.01.210oC25oC40oCPosition: 38 mmEntry temperature  (oC)2 0 4 0 6 0 800Integrated heat flux (MJ/m2)0.00.20.40.60.81.01.21.410oC25oC40oC102  an entry temperature of 410°C, higher integrated heat flux is observed (6.3 MJ/m2). Due to the high heat extraction in the second cooling pass, the plate temperature decrease is very pronounced such that the entry temperature of the third cooling pass is around 160°C.   Figure 7.12 Integrated heat flux; process parameters: planar jet, FR=100 L/min, Twater=25°C, Hn= 0.1 m. (here, the integration time interval is equal to the time that the plate needs to travel 2m).  For plate speeds of 0.5, 1.0, and 1.6 m/s more cooling passes are observed because the amount of heat extraction in each pass is much lower than for a plate speed of 0.2 m/s. Although the experimental data clearly show that the overall heat extraction decreases with increasing plate speed, plate speed has a marginal influence at low entry temperatures (<250°C). Beside the differences in the amount of heat removal for each plate speed, the maximum of the integrated heat flux plots shifts to lower entry temperatures as the plate moves faster. For the plate speed of Planar nozzleEntry temperature,oC0 100 200 300 400 500 600 700 800Integrated heat flux, MJ/m2012345678Vp=0.2 m/sVp=0.5 m/sVp=1.0 m/sVp=1.6 m/s103  0.2 m/s, the maximum of integrated heat flux is observed at 410°C, whereas for the plate speed of 1.6 m/s, the maximum occurs at 240°C.     104  Chapter 8: Cooling model for moving plates   8.1 Single nozzle  8.1.1 Overview The cooling model developed in this chapter is intended to simulate the temperature evolution of a moving steel plate cooled by water jets and to rationalize the results of chapter 7. A model is first developed for a single planar nozzle as well as a single circular nozzle. In section 8.2, the model is applied to predict temperature evolution of a moving plate cooled by a double jet-line array.    The schematic of the single nozzle systems that are modeled is given in figure 8.1. Figure 8.1a shows a single planar nozzle cooling system. Due to the geometry of the planar nozzle system, one position at the lateral direction of the plate can represent the thermal changes along the y direction. However, for the circular nozzle system due the radial distribution of the water flow (figure 8.1b), more than one position along the lateral direction of the plate must be chosen for the temperature analysis. Details on the assumptions made in the present model are discussed in the following sections.    105   (a)  (b) Figure 8.1 Schematic of plate and nozzle, (a) planar nozzle system, (b) circular nozzle system.   xzyPlanar nozzlePosition of 1D domainin the cooling modelxzyCircular nozzlePositions of 1D domainsin the cooling model106   8.1.2 Calculation of boiling curves: effect of plate speed The cooling model uses boiling heat transfer correlations (boiling curves) to impose the thermal boundary conditions on heat conduction within the plate. Therefore, the first step in the temperature prediction model is to map the family of boiling curves for a moving plate cooled by impinging jets on the top surface. The procedure discussed in chapter 6 can map the family of boiling curves for a stationary plate. However, plate motion influences the heat transfer rate of the plate on the run-out table. This influence has not received much attention in the literature. According to the experimental results in figure 7.6, the heat flux in high and mid temperature ranges, where the dominant heat transfer mechanisms are film and transition boiling, is highly affected by the speed of the plate such that increased plate speed leads to a decrease of heat flux. In contrast, the nucleate boiling heat flux does not show any dependency on plate speed.  In order to incorporate the effect of plate speed on the boiling curves, the transition and film boiling portions of the boiling curves are scaled with respect to plate speed (figure 8.2). To do so, the shoulder heat flux, the minimum heat flux (MHF), and the Leidenfrost temperature are scaled by introducing suitable scaling factors, i.e.:    xVqSxVq pshVppsh ,0., ,1          (8.1)    xVqSxVq pMHFVppMHF ,0., ,2          (8.2)    xVTSxVT pMHFVppMHF ,0., ,3          (8.3) where S1,Vp, S2,Vp, and S3,Vp are the scaling factors.  qsh(Vp=0,x), qMHF(Vp=0,x), and TMHF(Vp=0,x) are the shoulder heat flux, the minimum heat flux, and the Leidenfrost temperature in the boiling 107  curves of a stationary plate, respectively. To find the scaling factors, the normalized values of PHFmax, PHFmin, and TPHF,min are used. These three values are taken from the plots of peak heat flux vs. surface temperature (figure 7.6) for the impinging point of the water jet (x=0) and presented in figures 8.3 and 8.4 as a function of plate speed. The following linear correlations are found: pVp VS 257.01,1            (8.4) pVp VS 334.01,2            (8.5) pVp VS 084.01,3            (8.6) when the plate speed, Vp, is in m/s. The scaling factors are used to calculate qmax, qMHF, and TMHF for a moving plate. Then, the new values of qmax, qMHF, and TMHF are used to construct a boiling curve for a moving plate at the impinging point of the jet (dotted curve in figure 8.2). To construct the evolution of the heat flux curve with time for a cooling pass the longitudinal distance from the impinging point of the jet is considered that can be obtained by translating time into distance as described in chapter 7. Then, it is assumed that the heat flux for each different position can be obtained by scaling the stationary heat flux as a function of longitudinal distance (see e.g. figure 6.8a) using the same scaling factors as proposed in equations 8.4-6.  108   Figure 8.2 Procedure for scaling boiling curve.  Figure 8.3 Variation of PHFmax and PHFmin with plate speed. The experimental errors are ±16%. Tsurface,oCq,MW/m2 qshScaled qshMHFScaled MHFStationary boiling curveScaled boiling curvePlate speed, m/s0.0 0.5 1.0 1.5PHF, MW/m203691215PHFmaxPHFminqmax in cooling of a stationary plate 109     Figure 8.4 Variation of TPHF,min with plate speed.  8.1.3 Calculation of boiling curves: effect of lateral distance in circular nozzle system Due to the complexity of the hydrodynamics of water flow during cooling of a moving plate by a circular water jet, empirical characterization of the heat transfer rate is found to be the most appropriate approach. For cooling at the centerline of the plate, the same scaling factors developed in section 8.1.2 are used. For the lateral positions on the plate, the experimental data obtained in this research (MC test series in chapter 7) and also the experimental data of Chan (2007) (table 8.1) serve as the basis for characterizing the boiling heat transfer. In these sets of experiments, a single circular water nozzle was used and the heat transfer rates were measured not only at the longitudinal centerline of the plate (y=0) but also in other lateral positions.    Plate speed, m/s0.0 0.5 1.0 1.5TPHF,min , oC400420440460480500520540110  Table 8.1 Available experimental database for cooling of moving plates with single circular nozzle (Chan 2007) Test  Number of nozzles Vp, m/s FR, L/min Twater,˚C Hn, m C01 1 0.6 30 25 1.5 C02 1 1.0 30 25 1.5 C03 1 1.3 30 25 1.5  According to figure 7.7, the nucleate boiling heat flux does not change with lateral distance. The heat flux in the film boiling and transition boiling regimes is reduced as the distance from the longitudinal centerline of the plate increases. Based on the trend of the heat flux changes with surface temperature, the following scaling equations are proposed:    x,yq.Sx,yq shlat,sh 01                 (8.7)    xyqSxyq MHFlatMHF ,0., ,2          (8.8)    xyTSxyT MHFlatMHF ,0., ,3          (8.9) where S1,lat, S2,lat, and S3,lat are three scaling factors for qsh, qMHF, and TMHF, respectively. qsh(y=0,x), qMHF(y=0,x), and TMHF(y=0,x) are the shoulder heat flux, the minimum heat flux, and the temperature of the minimum heat flux in boiling curves of a moving plate at y=0, respectively. qsh (y,x), qMHF(y,x), and TMHF(y,x) are the shoulder heat flux, the minimum heat flux, and the temperature of the minimum heat flux, in boiling curves in lateral positions of a moving plate, respectively. Figures 8.5-7 show the lateral variations of PHFmax, PHFmin , and TPHF,min, when normalized to their respective values under the jet line for a range of different cooling conditions. The dependency of these normalized PHFmax, PHFmin, and TPHF,min does not markedly depend on 111  water flow rate and plate speed. Therefore, the scaling factors can be expressed as function of the lateral distance such that:    756000231625037501 ./.dyexp/..Sjilat.                (8.10)   590143941099109902 ./.dyexp/..Sjilat,     (8.11)   874007641515048503 ./.dyexp/..Sjilat.      (8.12) where y/dji is the normalized distance in lateral direction from the centerline of the plate (y=0) in the single nozzle cooling system. These scaling factors are indicated by the solid lines in figures 8.5-8.7.  Figure 8.5 Normalized PHFmax profile in lateral direction. 0 1 2 3 4 5 6 7 80.20.40.60.81.01.2 Fit FR=30L/min, Vp=0.6m/s FR=30L/min, Vp=1.0m/s FR=30L/min, Vp=1.3m/s FR=15L/min, Vp=1.0m/sPHFmax / PHFmax,y=0y / dji112   Figure 8.6 Normalized PHFMIN profile in lateral direction.  Figure 8.7 Normalized TPHF,MIN profile in lateral direction.  0 1 2 3 4 5 6 7 80.00.20.40.60.81.01.2 FR=30L/min, Vp=1.0m/s FR=30L/min, Vp=1.3m/s FR=15L/min, Vp=1.0m/s FitPHFMIN / PHFMIN,y=0y / dji0 1 2 3 4 5 6 7 80.40.60.81.0 FR=30L/min, Vp=1.0m/s FR=30L/min, Vp=1.3m/s FR=15L/min, Vp=1.0m/s FitTPHF,MIN / TPHF,MIN,y=0y / dji113  8.1.4 Construction of boiling curves for moving plates To find the complete boiling curve a similar procedure is used to the one proposed in section 6.5.  Figure 8.8 summarizes the procedure for mapping the scaled boiling curves for a moving plate. Here, the scaled values of qmax, qMHF, and TMHF are used to build the curves. Figure 8.9 shows some examples of the calculated boiling curves for planar jet cooling. Boiling curves at x=0 (impinging point of the jet) are plotted in figure 8.9a for plate speeds of 0, 0.5, and 1.5 m/s. It should be noted that in the cooling model idealized boiling curves are used. Hence, the initial cooling (IC) stage is not included in the calculated boiling curves. Figure 8.9b shows the calculated boiling curves for different plate speeds at a distance of 120mm from the nozzle. As explained in section 8.1.2, the same scaling factors are used as given in equations 8.4-6 for boiling curves for all positions at the longitudinal direction.    Figure 8.8 Procedure for scaling the idealized boiling curve for a moving plate.   Tsurface,oCq,MW/m2 qmaxScaled qmaxMHFScaled MHFStationary boiling curveScaled boiling curveqmax(Vp, y, x) = S1,Vp. S1,lat. qmax(Vp=0, y=0, x)qMHF(Vp, y, x) = S2,Vp. S2,lat. qMHF(Vp=0, y=0, x)TMHF(Vp, y, x) = S3,Vp. S3,lat. TMHF(Vp=0, y=0, x)qmax(Vp, x) = S1,Vp. qmax(Vp=0, x)qMHF(Vp, x) = S2,Vp. qMHF(Vp=0, x)TMHF(Vp, x) = S3,Vp. TMHF(Vp=0, x)Planar jet:Circular jet:114   (a)  (b) Figure 8.9 Effect of speed on the calculated boiling curves, (a) at x=0 mm and (b) at x=120mm. Process parameters: planar nozzle, FR=100 L/min, Twater=25°C, Hn=0.1 m. The boiling curves have been calculated using the model procedures presented in section 6.5 in combination with the scaling factors.   Tsurface, oC0 200 400 600 800q, MW/m2024681012141618Vp = 0 m/sVp = 0.5 m/sVp = 1.5 m/sPlanar nozzlex = 0mmTsurface, oC0 200 400 600 800q, MW/m202468102Vp = 0 m/sVp = 0.5 m/sVp = 1.5 m/sPlanar nozzlex = 120mm115  For mapping boiling curves in lateral positions of a circular nozzle, the proposed scaling factors in equations 8.10-12 are used. Figure 8.10 shows some examples of the calculated boiling heat fluxes for different lateral positions with respect to the longitudinal centerline of the moving plate.  (a)  (b) Figure 8.10 Scaled boiling curves in lateral direction, (a) at x=0 mm and (b) at x=60mm. Process parameters: circular nozzle, FR=30 L/min, Twater=25°C, Vp=1.0m/s, Hn=1.5 m. Tsurface, oC0 200 400 600 800q, MW/m202468101214y = 0 mmy = 25.4 mmy = 50.8 mmCircular nozzlex = 0mmTsurface, oC0 200 400 600 800q, MW/m20246810y = 0mmy = 25.4mmy = 50.8mmCircular nozzlex = 60mm116   8.1.5 Water front  When a water jet impinges on a moving surface, the deposited water flows toward the upstream and downstream regions. In the downstream region, the flow of water is facilitated by the motion of the surface because water flow and surface motion are in the same direction. However, in the upstream region, the surface motion is in the opposite direction of the water flow on the surface and this can restrict the water coverage area and leads to the formation of a water front in the upstream region (figure 8.11). In the area between the impinging point of the jet and the edge of the water front, the plate surface is covered and cooled with water. However, beyond the position of the water front, the plate is dry and the heat transfer mechanisms are convective and radiative air cooling. Hence, it is important to determine the position of the water front in order to apply the correct heat transfer mechanism in the upstream region.  Figure 8.11 Water front in the upstream region of the jet impingement cooling.  117  Experimental work by Seraj (2011) using a single top circular jet and a moving plate at room temperature reveals that when the plate speed increases, the water front distance from the nozzle decreases. It has also been reported that the jet impingement velocity or water flow rate has an important influence on the location of the water front with respect to the nozzle. The increase of the water flow rate can increase the water front radius and expand the water upstream region on a moving surface. The empirical correlation of Seraj (2011) is applied here to calculate the water front distance at the centerline of the plate in the cooling model: 360390466.lnp.lnncircular,WF dVdFR.dd             (8.13) where dWF,circular is the distance between the water front and the impinging point of the circular jet at the centerline of the plate (m),  FR is water flow rate (m3/s), dn is  the nozzle diameter (m), and νl is the kinematic viscosity of the water (m2/s). In the current study it is assumed that the location of the water front with respect to the impinging water jet is independent of temperature of the plate surface. The water front in the upstream region across the plate width is not flat and has a curvature due to the radial flow of water impinging from a circular jet (figure 8.2). However, close to the centerline of the plate (-3.5dn<y<3.5dn), the water front has a minimum curvature and has a fairly flat front. In order to have uniform cooling on industrial run-out tables, nozzle are placed relatively close to each other in one jet-line (Sn<7dn). Therefore, in the cooling model the water front is assumed to be flat and is located at the distance of dWF from the jet (or the jet-line). For the planar jet, no correlation has been found in the literature. Therefore, equation (8.13) has been modified for use with a planar jet. To do so, dn is replaced with the jet hydraulic diameter at 118  the nozzle exit (dH) and FR is replaced by Vn/4dH2. The distance between the water front and planar nozzle (dWF,planar) is given by: 36.039.02,, 4lHplHHnPlanarWFHPlanarWF dVddVCdd      (8.14)  The constant value, CWF,Planar, is determined later (see section 8.1.7.1) in order for the predicted heat flux curves to match the corresponding experimental curves.   In the current study, it is assumed that the water covers the entire downstream region. Therefore, the mechanism of heat transfer in the downstream region is only water cooling.   8.1.6 Heat conduction within the plate After determining the appropriate heat transfer mechanism at the top surface of a moving plate, the heat conduction within the plate needs to be analyzed. The general heat conduction equation inside a solid which is moving in x direction is xTVctTczTkzyTkyxTkx x       (8.15) However, due to the geometry of the plate and also the conditions on the run-out table, the following assumptions can be made for simplification: 1. Since the thickness of the plate is much smaller than the other dimensions, the heat conduction along x and y axes is negligible, i.e. 0xTkx          (8.16) 119  0yTky          (8.17)  2. During the cooling operation on the run-out table the temperature of the plate at any fixed position with respect to the ground does not change with time (Filipovic 1990). Therefore, the temperature field inside a long plate along the moving direction (x) can be assumed to be at steady-state: 0tTc            (8.18) 3. Time (t) can be transformed to the position in x direction using the plate speed, i.e.: tVx x             (8.19) By taking the derivative of the last equation with respect to the temperature and substituting the resulting term for Vx into equation 8.15, the following governing equation is derived which is applicable for cooling of a moving plate: tTczTkz           (8.20)  The 1D domain and the governing equation are discretized using a finite difference method with the Forward Euler scheme. To solve the differential heat conduction equation, the boundary conditions need to be applied. The boundary conditions are expressed as:    44   TTTThdzdTk air     (bottom surface: air cooling)         (8.21) surfacetopqdzdTk        (top surface: water cooling or air cooling)  (8.22) 120  Here σ is the Stefan–Boltzmann constant (5.67·10-8 W/m2 ˚C 4) and ε is the emissivity factor (0.8). hair is the free convective heat transfer coefficient which is taken to be 12 W/m2˚C (Nobari and Serajzadeh 2011). The ambient temperature (T∞) is assumed to be 25°C and the initial thermal condition is given by   entryTt,zT  0           (8.23) The thermal diffusivity of steel (α) as a function of temperature (in °C) is given by  (8.24)  A flow chart of the cooling model developed in this study is shown figure 8.12. At the beginning, the cooling model generates the family of boiling curves for a moving plate. The initial position of the plate is assumed at 1 m from the nozzle. At each time step, the plate position is calculated based on the plate speed. Thermal boundary conditions are applied based on the position of the plate (x) with respect to the nozzle and plate surface temperature. Then the transient heat conduction inside the plate is calculated and a new temperature profile inside the plate is recorded. At the next time step, the new surface temperature is used to determine the heat flux from the top and the bottom surfaces of the plate. Then, the transient heat conduction inside the plate is solved. This procedure is repeated until the final time is reached and the calculation of the temperature of the plate stops. The final time is considered as the time that the plate reaches a distance of 1 m from the nozzle. To run the model, time step and node spacing dependency were investigated. These parameters were refined until changes in the output of the model (i.e. top surface temperature) were less than 0.5% for different cooling conditions. In all analyses, a node spacing of 0.2 mm and a time step of 0.5 ms are applied.       smTckTp258 108603.1109273.1121   Figure 8.12 Flow chart of the cooling model for temperature simulation of a moving plate. StartInput: 1. Thermo-physical properties (steel, water, and vapor): density, conductivity, specific heat, emissivity, convective coefficient, …2. Process parameters: water flow rate, water temperature, nozzle geometry, nozzle height, plate’s entry temperature, plate’s speed, plate’s thicknesst = t +ΔtApplying boundary conditions: (heat flux from top and bottom surfaces) based on y, x and TplateCalculation of temperature field inside the plate using FDMRecording: Tplatet < tfinalEndYesNoCalculation of plate’s position (x)(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)Calculation of family of boiling curves for a moving platey = y + ΔSlateraly< ymaxNot = 0Yes122  In the case of a circular nozzle system, the family of boiling curves for different lateral positions needs to be generated as discussed in section 8.1.3. For each lateral position, the heat conduction equation is solved separately. The number of lateral positions in the model is considered equal to the number of thermocouples used in the lateral direction in the experiment. As an example, figure 8.13 shows the calculated temperature of the plate at four different depths from the top surface during a cooling pass with an entry temperature of 455°C. The temperature at top surface drops about 180°C. As the plate leaves the nozzle the surface temperature rebounds. At the bottom surface (6.6mm), the temperature decreases with a very slow cooling rate since the mechanism of heat transfer at this surface is natural air cooling.   Figure 8.13 Calculated temperature of the plate for one cooling pass, Vp=1 m/s, FR=15 L/min, Twater=25°C, y=0. Tentry = 455oCtime , s0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Temperature, oC2002503003504004505000mm (top surface)1 mm 3.3 mm (middle) 6.6 mm (bottom surface) 123   8.1.7 Verification 8.1.7.1 Planar jet The cooling model developed in this chapter is used to simulate the temperature history of the steel plate as it is moving while being cooled by a single top jet. The validity of the cooling model is examined by applying the actual process parameters used during experiments (MP tests) on the pilot scale run-out table facility and comparing the cooling model predictions with the measured heat fluxes and temperatures.   Figure 8.14 shows an example of the calculated and measured heat flux and surface temperature variations during one cooling pass. The experimental data shown here is from test MP03, i.e. a plate speed of 1.0 m/s, a flow rate of 100 L/min, and water temperature of 25°C. The nozzle height is 0.1m and plate length is 0.6m. The entry temperature which is the surface temperature of the plate just before the cooling pass was 470°C. These process parameters are first applied in the boiling curve model to map the family of boiling curves. Then the boiling curves are used to simulate the temperature history as the plate moves. In the cooling model, the distance between the initial position of the lateral centerline of the plate and the planar jet is set to 1 m for all simulations in this chapter. At the distance of 1 m from the nozzle, the entire plate is outside the cooling zone and is completely dry.  Figure 8.14a shows the calculated top surface heat flux histories for one cooling pass. The heat flux is initially very small since the plate is dry and the heat transfer mechanisms are convective and radiative air cooling. After the plate’s lateral centerline reaches the water front and enters the upstream region of water flow, the surface heat flux starts to increase. After reaching its peak value the heat flux decreases and when the whole plate leaves the water cooling zone (t=1.3 s), 124  the heat transfer mode switches from boiling heat transfer to air cooling heat transfer. The calculated heat flux history is in a good agreement with the experimental results. A constant value in equation 8.14, CWF,Planar, of 25.84 is applied such that the predicted heat flux curve matches with the corresponding experimental curves. This constant is applied in further analyses in this research for cooling with a planar jet.   Figure 8.14 Comparison with experimental results, planar jet, FR=100 L/min, Twater=25°C, Vp=1 m/s, entry temperature: 470°C: (a) heat flux vs. time, (b) heat flux vs. distance, (c) heat flux vs. surface temperature, and (d) surface temperature vs. time. Thin dashed lines in figure c show the boiling curves at different longitudinal distances from the impinging point of the jet. These lines are used as the boundary condition to analyze the heat conduction within the plate. (a)  (b)  (c)  (d)  125   Figure 8.14b shows the variation of heat flux in longitudinal direction (plate moving direction), i.e. transforming time to distance using the plate speed. The water front position in figure 8.14b is where the heat transfer mechanism at the top surface changes from air cooling to water cooling. The calculated distance between the nozzle and the water front (dWF) is ~15.0 cm. Also, the position is shown where the entire plate leaves the jet.  In contrast to a stationary plate, the residence time under the cooling section is limited for a moving plate. Therefore, using the cooling model, heat flux evolution along the plate moving direction is determined step by step. At each time step, heat flux from the top surface is calculated based on the position of the plate (x) with respect to the nozzle and plate surface temperature. The model prediction and experimental data for heat flux are shown in figure 8.14c. Also, the boiling curves, calculated based on the procedure described in section 8.1.4, are superimposed. These boiling curves are used as the boundary condition during water cooling period. In the current study, the same scaling factors are used for the upstream and downstream regions of the impinging jet. The asymmetry in the heat flux curve is related to the differences in surface temperature.  This plot gives valuable information about the boiling mechanisms which play a role in the cooling process. In the upstream region, the distance of a plate location from the stagnation point decreases as the plate approaches the impingement region. Accordingly, the heat flux increases until it reaches a maximum at the impinging point of the jet. Subsequently, in the downstream region, the heat flux decreases. Although the temperature first decreases in the short downstream region, after passing the stagnation point it starts to rebound significantly due to the thermal mass of the plate. This temperature rebound affects the heat flux evolution path.  126  For the plate approaching the jet impingement region (upstream region) in figure 8.14, heat flux is controlled first by film boiling and then by transition boiling. When the plate leaves the jet the boiling mechanism becomes film boiling again after some distance. In this cooling pass, the entry temperature is high enough, such that the temperature does not reach the temperature corresponding to nucleate boiling, even at the impinging point of the jet. Figure 8.14d shows the surface temperature as a function of time which is an important output of the model. The predicted surface temperature is in reasonable agreement with the experimental data. Since the plate surface temperature is a significant factor affecting the boiling heat transfer behavior, the cooling model is verified with different entry temperatures. Figures 8.15a and 8.15b show the heat flux and surface temperature histories for a high (720°C) and a low (330°C) entry temperature. As seen in figure 8.15, the cooling model is capable to predict the peak heat flux as well as the variation of heat flux in upstream and downstream zones very well. In the cooling pass with 720°C the surface maximum temperature drop is about 80°C while for the cooling pass with low entry temperature (330°C) the drop is about 180°C. The figures show that the cooling model can predict the surface temperature for both high and low entry temperatures.   127              (a)             (b) Figure 8.15 Heat flux and surface temperature histories, FR=100 L/min, Twater=25°C, Vp=1 m/s (a) entry temperature: 720°C and (b) entry temperature: 330°C.  8.1.7.2 Circular jet  Figure 8.16 compares the cooling model and the experimental results for circular jet cooling of a moving plate with a speed of 1.3 m/s at the longitudinal centerline of the plate (y=0). The length of the steel plate is 1.2 m, nozzle height is 1.5 m, water flow rate is 30 L/min, and water temperature is 25°C. The entry temperature of the plate is 375°C.   0 0.5 1 1.5 20246time, sq, MW/m2  Exp.Model0 0.5 1 1.5 2640660680700720740time, sSurface temperature, C  Exp.Model0 0.5 1 1.5 20246time, sq, MW/m2  Exp.Model0 0.5 1 1.5 2150200250300350time, sSurface temperature, C  Exp.Model128   Figure 8.16 Comparison with experimental results, circular jet, FR=30 L/min, Twater=25°C, Vp= 1.3 m/s, entry temperature: 375°C, y=0: (a) heat flux vs. time, (b) heat flux vs. distance, (c) heat flux vs. surface temperature, and (d) surface temperature vs. time. Thin dashed lines in figure c show the boiling curves at different longitudinal distances from the impinging point of the jet. These lines are used as the boundary condition to analyze the heat conduction within the plate.  Figure 8.16a shows the top surface heat flux history. The heat flux increases from air cooling heat flux to water cooling heat flux as the lateral centerline of the plate reaches the water front. Figure 8.16b shows the variation of heat flux in the longitudinal direction which is along the moving direction of the plate. Figure 8.16c shows the heat flux evolution with respect to the 129  surface temperature. The scaled family of boiling curves, which are used as the boundary condition in the cooling model, are also shown in figure 8.16c. As seen in the figure, the first dominant heat transfer mechanism after the water covers the plate’s center point is film boiling. As the plate gets closer to the nozzle, the heat transfer mechanism becomes transition boiling and eventually nucleate boiling. As the plate leaves the nozzle the surface heat flux decreases. First, the heat flux follows the nucleate boiling regime. However, as the plate moves further, the dominant heat transfer mechanism becomes transition boiling followed by film boiling. Figure 8.16d shows the surface temperature history which is the most important output of the model. The cooling model was verified with a high and a low entry temperature in figures 8.17a and 8.17b. As seen in figure 8.17, the cooling model is capable of calculating the peak heat flux as well as the variation of heat flux in upstream and downstream zones reasonably well. The model predicts the exit surface temperatures (surface temperature at 1 m distance from the jet) within ±30°C. In addition to the position under the jet, the model has to be evaluated at locations in the lateral direction for a circular nozzle. To do so, the transient heat conduction inside the plate at different lateral positions can be analyzed separately using the 1D cooling model. Figure 8.18 shows the surface heat flux and surface temperature at different distances from the nozzle in the lateral direction: 0, 12.7, 25.4, and 38.1 mm. As seen in the figure, the model clearly replicates the strong dependence of the heat transfer rate on distance from the nozzle.     130         (a)  (b) Figure 8.17 Heat flux and surface temperature histories, FR=30 L/min, Twater=25°C, Vp=1.3 m/s (a) entry temperature: 600°C and (b) entry temperature: 285°C. 0 0.5 1 1.5-20246time, sq, MW/m2  Exp.Model0 0.5 1 1.5450500550600time, sSurface temperature, C  Exp.Model0 0.5 1 1.5-20246time, sq, MW/m2  Exp.Model0 0.5 1 1.5150200250300time, sSurface temperature, C  Exp.Model131   Figure 8.18 Heat flux and surface temperature histories at (a) y=0 mm, (b) y=12.7 mm, (c) y=25.4 mm, (d) y=38.1 mm; process parameters: FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature: 410°C.  In order to gain a better appreciation of the cooling model, the results of the cooling model at different locations in the lateral direction are combined and contour plots are generated. Figure 8.19 shows the simulated contour plots of heat flux and surface temperature for the test with the same process parameters as shown in figure 8.18. The moving direction of the plate is from left to right. Comparison of the predicted heat flux and surface temperature contour plots with the experimental results, shown in figure 8.20, indicates that good agreement has been achieved. The model is able to describe the size and the shape of the high heat flux area (yellow, red, and orange) as seen in figures 8.19a and 8.20a. Moreover, the significant gradient of the heat flux in the lateral direction has been predicted by the model. This gradient leads to severe non-uniformity in surface temperature across the plate width. According to figures 8.20a and 8.20b, 0.5 1 1.5 2024681012time, sq, MW/m2(a) TC: 1  ModelExp.0.5 1 1.5 2150200250300350400time, sSurface temperature, C0.5 1 1.5 2024681012time, sq, MW/m2(b) TC: 3  ModelExp.0.5 1 1.5 2150200250300350400time, sSurface temperature, C0.5 1 1.5 2024681012time, sq, MW/m2(c) TC: 5  ModelExp.0.5 1 1.5 2150200250300350400time, sSurface temperature, C0.5 1 1.5 2024681012time, sq, MW/m2(d) TC: 7  ModelExp.0.5 1 1.5 2150200250300350400time, sSurface temperature, C132  the predicted size and the shape of the surface temperature rebound area are in good agreement with the experimental contour plot.     Figure 8.19 Simulated heat flux and surface temperature histories; process parameters: FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature=410°C.  Figure 8.20 Experimental heat flux and surface temperature histories; process parameters: FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature=410°C. 133  8.2 Double jet-line arrays 8.2.1 Jet-line arrangement The proposed cooling model has so far been employed to simulate the temperature history of plate cooling with a single jet. However, for the application of the proposed model on the run-out table of a hot mill it is important to test the model for multiple jet-lines.  Figure 8.21 shows schematically the simulation approach for two jet-line cooling regardless of the nozzle type. The initial position of the plate is in the dry zone (A). In the model, the plate is positioned 1 m upstream from the first jet-line. As the plate moves from left to right, the head of the plate is wetted with the water; while the lateral centerline of the plate is still in the dry zone (B). Eventually the lateral centerline of the plate enters the upstream region of the first jet-line (C). The position of water front is calculated using equations 8.13 and 8.14 for circular jets and planar jet, respectively. Further, it is assumed that the boundary between the downstream region of the first jet-line and the upstream region of the second jet-line is located at the water front location of the second jet-line. At (D) the lateral centerline of the plate has left the area affected by the first jet-line and is in the upstream region of the second jet-line. As the plate moves further, the lateral centerline of the plate reaches the downstream region of the second jet-line (E). As the entire plate leaves the second jet-line, the heat transfer mechanism becomes air cooling (F).   134    Figure 8.21 Schematic of different cooling regions during multiple jet-line cooling. Location of the lateral centerline of the plate is shown by a red rectangular. The water coverage is shown by a blue layer on the plate surface.  In the experiments (Franco 2008) used to validate the model, 6 circular nozzles were used in two jet-lines with 3 jets each (figure 8.22). The spacing between the two jet-lines (Sj) was either 25.4 cm or 50.8 cm and the spacing between two nozzles in one jet-line (Sn) was 10.16 cm. Two plate speeds of 0.35 and 1.0 m/s were studied. Temperature was measured at 9 different thermocouple positions. The thermocouples were positioned in a line in the lateral direction (y direction) of the plate and spaced 12.6 mm apart. In these experiments, nozzles were positioned in a non-x (moving direction)UpstreamDownstreamJet-line 1 Jet-line 2UpstreamDownstreamDry zoneDry zonedWF(A)(t=0)(B)(C)(D)(E)(F)1mdWFLateral centerline of the plate and position of the 1D domain135  staggered configuration (figure 8.22). Table 8.2 shows the process parameters of the double jet-line experiments.  (a)  (b) Figure 8.22 (a) non-stagger nozzles in double jet-line cooling, (b) nozzle configuration with respect to the thermocouple positions. SnSjCenter line (y=0)x (moving direction)y (lateraldirection)TC linenozzleJet-line 1Jet-line 2136   Table 8.2 Available experimental database for double jet-line cooling (Franco 2008) Test  Number of nozzles Vp, m/s FR, L/min Sn, cm Sj, cm Twater ,˚C Hn, m F01 6 0.35 15 10.16 25.4 25 1.5 F02 6 1.0 15 10.16 25.4 25 1.5 F03 6 0.35 15 10.16 50.8 25 1.5 F04 6 1.0 15 10.16 50.8 25 1.5  8.2.2 Validation 8.2.2.1 Heat flux and surface temperature histories at y=0 Figure 8.23 shows heat flux and surface temperature histories as predicted from the cooling model, and as measured in a double jet-line experiment with a plate speed of 1 m/s and a jet-line spacing of 50.8cm for two entry temperatures of 500°C and 400°C. When the plate passes through the double jet-line cooling section, two peak heat fluxes can be observed. In between the jet-lines the heat flux is very low and the temperature of the plate rebounds. The experimental results in figure 8.23 indicate that in the cooling pass with the higher entry temperature (500°C), the heat flux at the second jet-line is higher than the first peak. Consequently the drop in surface temperature at the second jet-line is larger than the drop at the first jet-line. In contrast, for the pass with an entry temperature of 400°C, the first peak heat flux is higher than the second peak heat flux and the temperature drop at the first jet-line is larger than the temperature drop at the second jet-line. Figure 8.23 shows that the cooling model can predict these experimental observations in heat flux and surface temperature histories very well.  137    (a) (b) Figure 8.23 Heat flux and surface temperature histories, Test F08: Sj=508 mm, Vp= 1.0 m/s, y=0, (a) entry temperature: 500°C and (b) entry temperature: 400°C.  8.2.2.2 Surface contour plots One of the interesting capabilities of the cooling model is the ability to predict the surface temperature and heat flux histories in different lateral positions on the surface. This provides valuable insight into the different heat transfer rates experienced in different areas of the plate. In order to plot the contours, the surface temperature and heat flux data are translated from varying in time to varying spatially based on the plate speed. Figures 8.24-27 show two examples of the contours plots. In these figures, the contours of experimental and predicted data for the middle jets are repeatedly shown for the upper and lower jets to illustrate the periodic cooling pattern expected for run-out table cooling with a multiplicity of jets across the width of a plate. In figure 8.24, the entry temperature of the plate was 600°C and the plate moves from left to right along its longitudinal direction. Since the nozzles are placed in a line (non-stagger), the temperature 0 0.5 1 1.5 2 2.5-5051015time, sq, MW/m2Pass: 4 , Plate speed: 1 P.lenght:(m) 1.2  Exp.Model0 0.5 1 1.5 2 2.5200300400500time, sSurface temperature, C  Exp.Model0.5 1 1.5 2 2.5-5051015time, sq, MW/m2Pass: 6 , late speed: 1 P.lenght:(m) 1.2  Exp.Model0.5 1 1.5 2 2.5100200300400500time, sSurface temperature, C  Exp.Model138  gradient in the lateral direction is significant. Figure 8.25 shows the experimental surface contours for entry temperatures of 600°C. Figure 8.26 depicts the surface contour plots for a lower entry temperature (360°C). In this plot, the high heat flux zone is expanded in the moving direction because the entry temperature of the plate is low. The effect of this expansion is very clear on the larger delay in temperature rebounding in downstream regions in figure 8.26b. Figure 8.27 shows the experimental surface contours for entry temperatures of 360°C. The comparison between the simulation results (figures 8.24 and 8.26) and experimental results (figures 8.25 and 8.27) indicates that the cooling model is able to predict size and shape of the high heat flux zone reasonably well. The model predicts that the heat fluxes of the high heat flux zones (green/yellow/orange color regions) at both jet-lines are fairly similar for the cooling pass with the higher entry temperature (600°C). However, in the cooling pass with the lower entry temperature (360°C), the heat flux of high heat flux zones at the second jet-line is significantly lower than the heat flux at the first jet-line. Also, the comparison between the simulation and experimental results shows that the cooling model is able to predict the size and shape of the areas where the surface temperature drops significantly (blue/purple regions). Moreover, the model is able to predict the development of a banded temperature profile at the top surface due to the staggered nozzle configuration. The model predicts that the delay in temperature rebounding after the second jet-line is larger than the delay after the first jet-line for both high and low entry temperatures. These predictions are in agreement with the experimental measurements which are shown in figures 8.25b and 8.27b. There are some discrepancies in the shape of high heat flux zones between model and experiment which can be related to the fact that in the developed model the interactions between the two jets in a jet-line as well as the interactions between two jet-lines have not be included. 139     Figure 8.24 Predicted surface contour plots; (a) heat flux and (b) temperature; Sj=508 mm, FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature: 600°C.  Figure 8.25 Experimental surface contour plots; (a) heat flux and (b) temperature; test F04: Sj=508 mm, FR=15 L/min, Twater=25°C, Vp= 1.0 m/s, entry temperature: 600°C. 140   Figure 8.26 Predicted surface contour plots; (a) heat flux and (b) temperature; Sj=508 mm, FR=15 L/min, Twater=25°C, Vp= 1.0 m/s, entry temperature: 360°C.  Figure 8.27 Experimental surface contour plots; (a) heat flux and (b) temperature; test F04: Sj=508 mm, FR=15 L/min, Twater=25°C, Vp=1.0 m/s, entry temperature: 360°C. 141   8.2.2.3 Exit temperature To further examine the validity of the cooling model, the exit temperatures predicted at 1 mm below the top surface can be compared with thermocouple measurements. Exit temperatures are the temperatures of the plate at positions in the lateral direction and at the time when the plate leaves the second jet-line zone and reaches a distance of Sj from the second jet-line. The exit temperatures at 1 mm below the surface are plotted against the measured values in figure 8.28. For the lower plate speed (Vp=0.35 m/s) as shown in figures 8.28a-b, some discrepancies in the predicted and the measured exit temperatures are observed. However, for the tests with the higher plate speed (Vp=1 m/s), very good agreement with experimental data is seen. The mean temperature across the plate width is more important in an industrial hot mill than the temperature at a specific location. Therefore, the mean exit temperature after each cooling pass with the double jet-line configuration was calculated. Figure 8.29 shows the predicted mean exit temperature plotted against the corresponding measured values. Results are from four tests with two different plate speeds and two different jet-line spacing. Very good agreement between the predicted and measured mean exit temperatures is seen for all tests with low and high plate speeds (most data points are within ±25°C).  In low plate speed experiments, as the plate leaves the second jet-line, large temperature gradients are observed in the case of non-staggered nozzle configuration. These temperature gradients lead to the formation of hot and cold regions and consequently conduct heat from hot regions toward cold regions. As a result, in cold regions, the measured temperature rebound is quicker than predicted. On the other hand, in hot regions the measured temperature rebound is slower than predicted. Therefore, although some deviations are observed in predicted local exit 142  temperature plots in the case of low speed plates (figure 8.28a-b), the predicted mean exit temperature is in good agreement with the corresponding measured data (figure 8.29).      (a) (b)   (c) (d) Figure 8.28 Predicted and measured exit temperatures (1mm below the surface) in lateral positions in double jet-line tests:  (a) Vp=0.35 m/s, Sj=25.4 cm; (b) Vp=0.35 m/s, Sj=50.8 cm; (c) Vp=1.0m/s, Sj=25.4 cm; (d) Vp=1.0 m/s, Sj=50.8 cm.  0 100 200 300 400 500 600 7000100200300400500600700ExperimentModel  Local exit temp. (C)100 200 300 4 0 5 0 600 7000100200300400500600700ExperimentModel  Local exit temp. (C)0 100 200 300 400 500 600 7000100200304567ExperimentModel  Local exit temp. (C)1 200 300 400 500 600 7000100200304567ExperimentModel  Local exit temp. (C)143   Figure 8.29 Predicted and measured mean exit temperatures (1mm below the surface) in double jet-line tests.   Mean exit temperature (oC) at 1mm below the top surfaceExperiment0 100 200 300 400 500 600 700Model0100200300400500600700Vp=0.35m/s, Sj=25.4cmVp=0.35m/s, Sj=50.8cmVp=1.0m/s,   Sj=25.4cmVp=1.0m/s,   Sj=50.8cm+25oC-25oC144  Chapter 9: Conclusions and future work    9.1 Summary and conclusions The main goal of this work was to develop a cooling model for the heat transfer in a steel plate during top water jet impingement cooling conditions that are typical for industrial run-out table cooling. The work was done in two major steps. First, a boiling curve model was proposed for cooling of a stationary steel plate. The proposed boiling curve model considers the boiling mechanisms (i.e. film boiling, transition boiling, and nucleate boiling) and is able to map the boiling curves at different positions on the plate surface. In the second step, a cooling model was developed for simulating the temperature of a moving steel plate. To simulate the temperature, the cooling model calculates the evolution of the surface heat fluxes based on the underlying boiling mechanisms.  In detail the findings and contributions of this research can be summarized as follows: a. Stationary plate experiments The experimental results show that both the value of the heat flux and the trend and shape of the boiling curves change with distance from the jet. The transition and film boiling portions of boiling curves strongly depend on distance. However, at lower temperatures, the nucleate boiling curves merge into one curve as the temperature decreases regardless of position.  Generally, as water flow rate increases, the maximum heat flux increases. This is due to the increase in jet impingement velocity at the plate. An increase in water temperature at the nozzle 145  exit decreases the potential of the water to absorb heat. Thus, it decreases the maximum heat flux of the boiling curves. This decrease is prominent in the area close to the nozzle.  It was also found that there are differences between the boiling curves generated through steady-state (temperature controlled) conditions and transient (quenching) conditions. The main differences are the existence of the initial cooling stage as well as the first stage of cooling in the transition boiling in the latter condition. It was found that the slope of the first stage in the transition boiling curve does not depend on the water flow rate, water temperature, or the distance from the jet.  b. Boiling curve model for stationary plates The nucleate boiling heat flux was found to strongly depend on the surface temperature, while it is independent of nozzle geometry, water flow rate, and water temperature. Moreover, the distance from the jet has a negligible effect on the nucleate boiling heat flux. In this work, two sub-regimes in the transition boiling mechanism were addressed: (1) the first stage in which heat flux increases gradually from the MHF point; (2) the shoulder region which has a constant heat flux. For the first stage in transition boiling, the gradual increase of heat flux was described with a universal slope independent of the process parameters. To calculate the shoulder heat flux, the size of the vapor patches on the plate surface was determined using the Kelvin-Helmholtz instability. Also, the local water subcooling was calculated by performing a heat balance. The minimum heat flux was calculated by a model available in literature. In order to extend the application of the minimum heat flux model for positions beyond the stagnation point, two parameters, which depend on the distance from the jet i.e. γtot and ΔTsub, were replaced by their local values.  146  Finally, a procedure was proposed to combine different boiling regimes and to construct a family of boiling curves for transient cooling of stationary plates.  c. Moving plate experiments Peak heat flux (PHF) curves for different plate speeds show the same trend. However, as the plate moves faster, the PHF curves in the transition and film boiling regimes tend to shift to lower heat fluxes and lower surface temperatures. The plate speed does not have any effect on the nucleate boiling region of the PHF curves. Thus, it can be concluded that speed of the plate plays different roles depending on the heat transfer mechanism. Besides, for single circular jets, it was found that due to the radial distribution of the water, the heat transfer rates strongly depend on the lateral distance from the impinging line of the jet. As the lateral distance increases, the PHF in the film boiling and the transition region decreases.    The effect of process parameters on the integrated heat flux, which represents the amount of energy per unit area, was studied. Generally, as the water flow rate and subcooling increase, the integrated heat flux increases in cooling passes with entry temperatures above ~200°C. However, for cooling passes with entry temperatures lower than ~200°C, the integrated heat flux is independent of the water flow rate and water subcooling.   d. Cooling model for moving plates  In order to incorporate the effect of plate speed on the boiling curves, transition and film boiling portions were scaled with respect to the plate speed. To do so, three scaling factors for the shoulder heat flux, the minimum heat flux and the Leidenfrost temperature were proposed. Moreover, for the single circular nozzle cooling system, the effect of the lateral distance from the jet was analyzed. Based on the trend of the heat flux changes with surface temperature at different lateral distances, three scaling factors for the shoulder heat flux, the minimum heat flux 147  and the Leidenfrost temperature were proposed. In the model, the location of the water front in the upstream region is calculated in order to apply the correct heat transfer mechanism (air cooling or water cooling) in that region. Then, thermal boundary conditions were applied based on the plate surface temperature and plate’s position with respect to the nozzle. Transient heat conduction within the plate was analyzed and predicted heat flux and temperature histories were plotted. Moreover, the plot of predicted heat flux evolution with surface temperature gives valuable information regarding boiling mechanisms which play a role in a cooling pass. The model is also capable of mapping the surface heat flux and surface temperature. These plots are a good representation of the overall cooling condition on the plate surface. An important output of the model is the exit temperature of the plate after each cooling pass. The validity of the developed cooling model has been examined by comparing the predicted temperatures with single independent multiple nozzle experiments. Very good agreement with experimental results has been obtained.  9.2 Suggestions for future work Based on the results obtained from the present experimental and modeling studies, the following points are suggested for future work:   a. Experimental study of higher plate speeds Conducting experiments with higher plate speeds (>2 m/s) will be of significance to generate data that will enable extension of the proposed models to the conditions of run-out table cooling in hot strip mills. Although the available pilot scale run-out table facility has been designed for accelerating the plate up to a speed of 5 m/s (Prodanovic et al. 2004), safety issues prevent us from running high speed tests in the laboratory. In fact, obtaining the required high plate speeds 148  (2 – 10 m/s) will require modifications to the facility (e.g. extending the length of the tracks to much longer than the current 15m length and changing the design of the plate carrier to prevent the carrier from detaching from the chain drive system at high speeds). b. Extending the application of the cooling model to bottom jet cooling  On a run-out table the steel plate or strip is cooled from both the top and bottom. Thus, it is critical to extend the cooling model developed here to bottom jet cooling. Some experimental studies have already been performed on bottom jet cooling using UBC’s pilot scale run-out table facility (Zhang 2004, Chester 2012). This previous work emphasized bottom cooling of a stationary plate with a single circular nozzle. Initial experiments were also conducted for bottom jet cooling of a moving plate. These tests, however, constitute more of a proof of concept rather than a systematic study which will be required to extend the model proposed for top jet cooling to bottom jet cooling.   c. Experimental study of the effect of plunging jet impingement As the plate moves on the run-out table of a hot mill, water accumulates on the top surface of the plate. The accumulated water on the top surface decreases the forced-convective effect of the jet impingement (Cho et al. 2008). This may lead to a significant drop in the efficiency of the top cooling system. Systematic experimental studies need to be conducted in order to quantify the effect of the thickness of the pre-existing water layer on jet impingement heat transfer using the procedures proposed by Prodanovic et al. (2011). Also, the effect of the jet impingement velocity on the heat transfer rate of a plunging jet needs to be investigated. The results of these experiments will be critical in order to incorporate the role of water accumulation into the run-out table cooling model.   149  d. Verifying the developed model with industrial run-out table data The overall goal of developing these cooling models is their application to industrial run-out tables. In the present work the proposed cooling model was validated with independent experimental data rather than industrial data. After extending the model to bottom jet cooling and incorporating the role of water accumulation on the top surface it will be paramount to evaluate its predictive capabilities for industrial cooling conditions. Typically, the industry records finish mill exit temperatures, (i.e. run-out table entry temperatures) and coiling or cooling stop temperatures (i.e. run-out table exit temperatures). Having such data will enable a first validation of the cooling model but for an in-depth validation it would be desirable to have temperature measurements at intermediate run-out table positions. Such measurements can be performed using an infrared video camera (e.g. as Honda et al. 2009). By comparing the model results with the temperature measurements, the range of applicability and the accuracy of the model can be examined for industrial conditions.   150  Bibliography Beck, J.V., Blackwell, B., St. Clair, C.R., 1985, Inverse Heat Conduction, John Wiley and Sons. Berenson, P.J., 1962, International Journal of Heat Mass Transfer, 5: 985-999. Carey, V.P., 2007, Liquid vapor phase change phenomena, Second edition, Taylor & Francis. Carlestam , A., 2011, International Symposium on the Recent Developments in Plate Steels, AIST,  June, Winter park, Colorado, 223:232. Caron, E.,2008 ,PhD Thesis, University of British Columbia, Vancouver. Chan, P., 2007, M.A.Sc. Thesis, University of British Columbia, Vancouver. Chen, S.J., Kothari, J., 1988, American Society of Mechanical Engineers, November-December, WA/NE4 8p.  Chen, S.J., Kothari, J., Tseng, A.A., 1991a, Experimental Thermal and Fluid Science, 4: 343-353. Chen, S.J., Tseng, A.A., Han, F., 1991b, Heat Transfer in Metals and Containerless Processing and Manufacturing, ASME, Vol. 162, July: 1-11. Chester, N.L., 2006, M.A.Sc. Thesis, University of British Columbia, Vancouver. Chester, N.L., Wells, M.A., Prodanovic, V., 2012, Journal of Heat Transfer, 134: 122201.1-122201.9. Cho, M.J., Thomas, B.G., Jong Lee, P., 2008, Metallurgical and Materials Transactions B, 39: 593-602.  Colas, R., Sellars, C.M., 1987, Proc. International Symposium on Accelerated Cooling of Rolled Steel, G.E. Ruddle, A.F. Crawley, Eds., Pergamon Press, Winnipeg, Canada, August: 121-130. Dhir, V.K., 1998, “Boiling heat transfer”, Annual Review of Fluid Mechanics, 30: 365-401. Filipovic, J., 1990, M.Sc. Thesis, Purdue University.  Filipovic, J., Viskanta, R., Incropera, F.P., Veslocki, T.A., 1992a, Steel Research, 63: 438-446. Filipovic, J., Viskanta, R., Veslocki, T.A., 1992b, Steel Research, 63: 496-499. Filipovic, J., Viskanta, R., Incropera, F. P., Veslocki, T. A., 1994a, Steel Research, 65: 541-547. Filipovic, J., 1994b, Ph.D. Thesis, Purdue University. 151  Filipovic, J., Incropera, F.P., Viskanta, R., 1995a, Experimental Heat Transfer, 8: 97-117.  Filipovic, J., Incropera, F.P., Viskanta, R., 1995b, Experimental Heat Transfer, 8: 119-130.  Franco, G., 2008, M.A.Sc. Thesis, University of British Columbia, Vancouver. Fujimoto, H., Suzuki, Y., Hama, T., Takuda, H., 2011, ISIJ International, 51: 1497-1505. Gradeck, M., Kouachi, A., Dani, A., Arnoult, D., Borean, J.L., 2006, Experimental Thermal Fluid Science, 30: 193-201.  Gradeck, M., Kouachi, A., Lebouche, M., Volle, F., Maillet, D., Borean, J.L., 2009, International Journal of Heat Mass Transfer, 52: 1094–1104. Gradeck, M., Kouachi, A., Borean, J.L., Gardin, P., Lebouche, 2011, International Journal of Heat Mass Transfer, 54: 5527–5539.  Guo, R. M., 1992, 10th Process Technology Conference Proceedings, Iron and Steel Society, April, Toronto, Canada: 49-59. Hall, D.E., Incropera, F.P., Viskanta, R., 2001, ASME Journal of Heat Transfer, 123: 901-910.  Hammad, J., Mitsutake, Y., Monde, M., 2004, International Journal of Heat Mass Transfer, 43: 743–752.  Han, F., Chen, S.J., Chang, C.C., 1991, Fundamentals of forced and mixed convection and transport phenomena, ASME, Vol.180: 73-81. Hatta, N., Osakabe, H., 1989, ISIJ International, 29: 919-925. Hernandez, V.H., Samarasekera, I.V., Brimacombe, J.K., 1995, 36th MWSP Conf. Proc., ISS-AIME, Vol. 32: 345-356. Hernandez, V.H., 1999, Ph.D. Thesis, University of British Columbia, Vancouver.  Honda, T, Nakagawa, S., Uematsu, C., Tavhibana, H., Buei, Y., Sakagami, K., 2009, ICROS-SICE International Joint Conference August, Japan: 2774-2777.  Ishigai, S., Nakanishi, S., Ochi, T., 1978, Proceedings of the 6th International Heat Transfer Conference, Vol.1, FB-30: 445-450.  Islam, M.A., Monde, M., Woodfield, P.L., Mitsutake, Y., 2008, International Journal of Heat Mass Transfer, 51: 1226–1237.  Jeffrey, A., 2001, Advanced Engineering Mathematics, Academic Press. 152  Jondhale, K., 2007, M.A.Sc. Thesis, University of British Columbia, Vancouver. Kalinin, E.K., Berlin, I.I., Kostiouk, V.V., 1987, Advanced in Heat Transfer, 11: 241-323. Kao, Y.K., Weisman, J., 1985, AIChE Journal, 31: 529-540. Karwa, N., Gambaryan-Roisman, T., Stephan, P., Tropea, C., 2011, International Journal of Thermal Sciences, 50: 993-1000. Kokado, J., Hatta, N., Takuda, H., Harada, J., Yasuhira, N., 1984, Arch. Eisenhuttenwes, 55: 113–118.  Kwon M.J., Park, I.S., 2013, ISIJ International, 53: 1042-1046. Li, D., Wells, M.A., Cockcroft, S.L., Caron, E., 2007, Metallurgical and Materials Transactions B, 38: 901-910. Lienhard, J.H., 2006, 18th National and 7th ISHMT-ASME Heat and Mass Transfer Conference, January, IIT Guwahati, India, 1:16.  Liu, Z.H., Wang, J., 2001, International Journal of Heat Mass Transfer, 44: 2475-2481.  Liu, Z.H., 2003, Journal of Thermophysics and Heat Transfer, 17: 159-165. Ma, C.F., Gan, Y.P., Tian, Y.C., Lei, D.H., 1993, Journal of Thermal Science, 2: 32-49.  Miyasaka, Y., Inada, S., Owase, Y., 1980, J. Chemical Engineering of Japan, 13: 29-35. Monde, M., 1991, Trends in Heat, Mass & Momentum Transfer, 1: 33-44. Monde, M., Katto, Y., 1978, International J. Heat Mass Transfer, 21: 295-305. Monde, M., Kusuda, H., and Uehara, H., 1980, Heat Transfer-Japanese Research, 9: 18-31. Monde, M., Inoue, T., 1991, Journal of Heat Transfer, 113: 722-727. Monde, M., Mitsutake, Y., 1996, Journal of Heat Transfer, 117: 241-243. Mozumder, A.K., Monde, M., Woodfield, P.L., 2005, International Journal of Heat and Mass Transfer, 48: 5395–5407.  Mozumder, A.K., Monde, M.,Woodfield, P.L., Islam, 2006, International Journal of Heat and Mass Transfer, 49: 2877–2888.  Mozumder, A.K., Woodfield, P.L., Islam, M.A., Monde, M., 2007, International Journal of Heat Mass Transfer, 50: 1559–1568.  153  Nelson, R.A., 1986, Mechanism of quenching surfaces, in N.P. Cheremisinoff, Ed., Handbook of heat and mass transfer, Vol. 1, Heat transfer operations, Gulf publishing, Houston, TX: 1103-1153.  Nishio, S., Auracher, H., 1999, Kandlikar, S.G., Shoji, M., Dhir, V.K., Eds, Taylor Francis, Philadelphia, PA. Nishioka, K., Ichikawa, K. 2012, Science and Technology of Advances Materials, 13, 23001-23021. Nobari, A.H., Serajzadeh, S., 2011, Applied Thermal Engineering, 31: 487-492. Ochi, T., Nakanishi, S., Kaji, M., Ishigai, S., 1984, Multi-Phase Flow and Heat Transfer III. Part A: Fundamentals, Amsterdam, 671-681. Omar, A.M.T, Hamed, M.S., Shoukri, M., 2009, International Journal of Heat and Mass Transfer, 52: 5557-5566. Pan, C., Hwang, J.Y., Lin, T.L., 1989, International Journal of Heat and Mass Transfer, 32: 1337-1349. Pan, C., Ma, K.T., 1992, Proc. Engineering Foundation Conference on Pool and External Flow Boiling, ASME, March, Santa Barbara, California: 263-270.  Pan, Y., Webb, B.W., 1995, Journal of Heat Transfer, 117: 878-883. Park, I.S., 2011a, ISIJ International, 51: 743-747. Park, I.S., 2011b, ISIJ International, 51: 1846-1869. Park, I.S., 2012, ISIJ International, 52: 1080-1085. Park, I.S., 2013, ISIJ International, 53: 71-75. Pohanka, M., Bellerova, H., Raudensky, M., 2009, Journal of ASTM International, 6: 1-9. Prodanovic, V., private communication. Prodanovic, V., Fraser, D., Militzer, M., 2004, 2nd International Conference on Thermomechanical Processing of Steel, July, Belgium: 25-32. Prodanovic, V., Militzer, M., 2005, Pipeline for the 21st Century - The Metallurgical Society of CIM, Montreal, Canada: 127-142. 154  Prodanovic, V., Wells, M., 2006, ECI, 6th International Conference on Boiling Heat Transfer, May, Spoleto, Italy: 1-6. Prodanovic V., Militzer, M., Schorr, R., Kirsch, H., Tacke, K., 2011, International Symposium on the Recent Developments in Plate Steels, AIST, June, Winter park, Colorado: 317-322. Pyykkonen, J.M., Martin, D.C., Somani, M.C., Mantyla, P.T., 2010, Materials Science Forum, 638-642: 2706-2711. Ragheb, H.S., Cheng, S.C., 1979, Journal of Heat Transfer, 101: 381-383. Robidou, H., Auracher, H., Gardin, P., Lebouche, M., 2002, Experimental Thermal and Fluid Science, 26: 123-129. Robidou, H., Auracher, H., Gardin, P., Lebouche, M., Bogdanic, L., 2003, Heat and Mass Transfer, 39: 861-867. Rohsenow, V.M., 1952, ASME Journal of Heat Transfer, 74: 969-976. Schutz, W., Kirsch, H.J., Fluss, P., Schwinn, V., 2001, Ironmaking and Steelmaking, 28: 180-184.   Schwinn, V., Bauer, J, Fluss, P., Kirsch, H., Amoris, E., 2011, International Symposium on the Recent Developments in Plate Steels, AIST,  June, Winter park, Colorado, 1-11. Seiler-Marie, N., Seiler, J., Simonin, O., 2004, International Journal Heat and Mass Transfer, 47: 5059-5070. Seraj, M.M., 2011, Ph.D. Thesis, University of British Columbia, Vancouver. Seraj, M.M., Mahdi, E., Gadala, M.S., 2012, Transaction on Control and Mechanical Systems, 1: 290-299. Shoji, M., 1992, Proc. Engineering Foundation Conference on Pool and External Flow Boiling, ASME, Santa Barbara, CA, March: 237-242. Slayzak, S. J., Viskanta R., Incropera, F. P., 1994a, International Journal of Heat and Mass Transfer, 37: 269-282. Slayzak, S. J., Viskanta, R., Incropera, F. P., 1994b, Journal of Heat Transfer, 116: 88-95. Timm, W., Weinzierl, K., Leipertz, A., Zieger, H., Zouhar, G., 2002, Steel Research, 73: 97-104. Späth, H., 1995, One dimensional spline interpolation algorithms, A K peters. 155  Tong, L.S., Tang, Y.S., 1997, Boiling heat transfer and two-phase flow, 2nd ed., Taylor & Francis, Washington, D.C: 1-10. Ueda, T., Tsunenari, S., Koyanagi, M., 1983, International Journal of Heat Mass Transfer, 26: 1189–1198.  Vader, D.T., Incropera, F.P., Viskanta, R., 1991, International Journal of Heat and Mass Transfer, 34: 611-623. Vakili, S., 2011, Ph.D. Thesis, University of British Columbia, Vancouver. Webb, B.W., Ma, C.F., 1995, Advances in Heat Transfer, 26: 105-217.  Wolf, D.H., Incropera, F.P., Viskanta, R., 1993, Advances in Heat Transfer, 23: 1-131.  Zhang, P., 2004, M.A.Sc. Thesis, University of British Columbia, Vancouver. Zumbrunnen, D.A., Viskanta, R., Incropera, F.P., 1989, ASME Journal of Heat Transfer, 111: 760-766. Zumbrunnen, D.A., 1991, ASME Journal of Heat Transfer, 113: 563-570. Zumbrunnen, D.A., Incropera F.P., Viskanta R., 1992, Warme- und Stoffubertragung, 27: 311-319.   156  Appendix A: Inverse heat conduction analysis  In the Inverse Heat Conduction (IHC) program proposed by Zhang (2004), the function specification method was used. This method assumes a pre-determined functional form for the heat flux within a future time interval (Beck et al. 1985) and solves the heat conduction problem in sequential manner. Moreover, the function specification method was combined with the zero-order Tikhonov regularization method to solve the inverse heat conduction problem with a sequential-in-time concept and improved computational efficiency. In order to consider the lag of time and hence enhance the accuracy of the calculation, the future information was included in the sequential-in-time method (Zhang 2004).  The developed IHC program can be used for analyzing single or multiple TC readings. In the current study, each thermocouple data were analyzed separately by using the IHC program to calculate the surface heat flux that is then considered to be independent of the exact position on the quench surface in the analyzing domain (see figure 4.6). Moreover, the program does not account for the latent heat generated during phase transformation. For the present study, this limitation is of minor significance as it can be expected that the austenite-ferrite transformation occurs for the investigated low-carbon steel during the air cooling period before executing the first cooling pass. In detail, the IHC program uses the following procedure to solve the heat conduction problem: a. Input initial data: measured temperature at different time steps and assumed heat flux at the top surface (q0). b. Call a direct FEM heat conduction problem solver to calculate temperature inside the plate 157  c. Solve sensitivity equation and calculate sensitivity matrix. The sensitivity matrix denotes the changes of temperature with respect to the change in q.  d. Update q using q = q0 + ∆q. To calculate ∆q, the sensitivity matrix is used to find a proper increment for the heat flux at the surface.  e. Repeat steps a to d until the sum of square error between the calculated and measured temperature at the position of the TC tip is smaller than a critical number. To improve the computational efficiency, the sum of squares function was modified by adding the zero-order regularization function.    158  Appendix B: Reproducibility of experiments  In order to ensure the reproducibility of experiments, a few repeats have been performed. As an example, figure B.1 shows the profile of the maximum heat flux along the surface for a test with a planar nozzle, a water flow rate of 100 L/min and a water temperature of 25°C. The curve for the repeated test matches the original experimental data with reasonable accuracy (most data points are within ±20%).  Figure B.1 Maximum heat flux along the surface for a test with a planar nozzle, a water flow rate of 100 L/min and a water temperature of 25°C.   x, mm0 20 40 60 80 100 120 140qmax, MW/m2024681012141618SP01SP01 (repeat)159  Appendix C: Experimental and calculated boiling curves for stationary plate tests  Figures C.1-10 show the experimental and calculated boiling curves for all stationary plate experiments.   Figure C.1 Family of boiling curves, test SP01, planar nozzle, FR=100 L/min, Twater=25°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, (f) 80 mm, and (g) 120 mm.   0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 10 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 40 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 60 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(f) x = 80 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(g) x = 120 mm  Exp.Model160     Figure C.2 Family of boiling curves, test SP02, planar nozzle, FR=150 L/min, Twater=25°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, and (e) 120 mm.    0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 10 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 40 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 120 mm  Exp.Model161   Figure C.3 Family of boiling curves, test SP03, planar nozzle, FR=250 L/min, Twater=25°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, (f) 80 mm, and (g) 120 mm.     0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 10 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 40 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 60 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(f) x = 80 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(g) x = 120 mm  Exp.Model162   Figure C.4 Family of boiling curves, test SP04, planar nozzle, FR=100 L/min, Twater=10°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, and (f) 120 mm.     0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 10 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 40 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 60 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(f) x = 120 mm  Exp.Model163   Figure C.5 Family of boiling curves, test SP05, planar nozzle, FR=100 L/min, Twater=40°C, x: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, and (f) 80 mm.      0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 10 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 40 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 60 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(f) x = 80 mm  Exp.Model164   Figure C.6 Family of boiling curves, test SC01, circular nozzle, FR=15 L/min, Twater=25°C, r: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, (f) 80 mm, and (g) 120 mm.      0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 10 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 40 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 60 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(f) x = 80 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(g) x = 120 mm  Exp.Model165   Figure C.7 Family of boiling curves, test SC02, circular nozzle, FR=30 L/min, Twater=25°C, r: (a) 0 mm, (b) 20 mm, (c) 40 mm, (d) 60 mm, (e) 80 mm, and (f) 120 mm.      0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 40 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 60 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 80 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(f) x = 120 mm  Exp.Model166   Figure C.8 Family of boiling curves, test SC03, circular nozzle, FR=45 L/min, Twater=25°C, r: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, and (f) 80 mm.      0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 10 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 40 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 60 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(f) x = 80 mm  Exp.Model167   Figure C.9 Family of boiling curves, test SC04, circular nozzle, FR=15 L/min, Twater=10°C, r: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 40 mm, (e) 60 mm, (f) 80 mm, and (g) 120 mm.      0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 10 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 40 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 60 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(f) x = 80 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(g) x = 120 mm  Exp.Model168   Figure C.10 Family of boiling curves, test SC05, circular nozzle, FR=15 L/min, Twater=40°C, r: (a) 0 mm, (b) 10 mm, (c) 20 mm, (d) 60 mm, (e) 80 mm, (f) 120 mm.    0 200 400 600 800051015Tsurface, Cq, MW/m2(a) x = 0 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(b) x = 10 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(c) x = 20 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(d) x = 60 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(e) x = 80 mm0 200 400 600 800051015Tsurface, Cq, MW/m2(f) x = 120 mm  Exp.Model

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0167525/manifest

Comment

Related Items