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Jet impingement boiling heat transfer at low coiling temperatures Chan, Phillip 2007

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JET IMPINGEMENT BOILING HEAT TRANSFER AT LOW COILING TEMPERATURES By Phillip Chan B.A.Sc. (Metals and Materials Engineering), University of British Columbia, 2005  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Materials Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA December 2007 © Phillip Chan, 2007  Abstract The production of advanced high strength steels (AHSS) for use in the automotive and construction industries requires complex control of runout table (ROT) cooling. Advanced high strength steels require coiling at temperatures below 500 °C in order to produce a complex multi-phase microstructure. The research described here will investigate the boiling conditions that occur for moving plate experiments when steel is cooled towards low coiling temperatures. Experiments were performed on a pilot-scale ROT located at the University of British Columbia using industrially supplied steel plates. Tests were performed for four different speeds (0.3, 0.6, 1.0 and 1.3 m/s) and three different initial plate temperatures (350, 500 and 600 °C). Each plate was instrumented with thermocouples in order to record the thermal history of the plate. The results show that cooling is more effective at slower speeds within the stagnation zone for surface temperatures over 200 °C. Outside the stagnation zone regardless of speed cooling is primarily governed by air convection and radiation with minor effects from latent heat caused by splashing water. The maximum peak heat flux value increases with decreasing speed and occurs at a surface temperature of approximately 200 °C, regardless of speed. Below a surface temperature of 200 °C, speed has a negligible effect on peak heat flux. The maximum integrated heat flux seems to vary with speed according to a second order polynomial.  ii  Table of Contents Abstract ^ Table of Contents ^  ii iii  List of Tables ^  v  List of Figures ^  vi  Acknowledgements ^  x  1 Introduction ^  1  2 Literature Review ^  4  2.1 General Overview ^  4  2.2 Jet Impingement and Hydrodynamics ^  7  2.3 Boiling Heat Transfer ^  10  2.3.1 Boiling Curves ^  10  2.3.2 Single Phase Convection ^  13  2.3.3 Nucleate Boiling ^  14  2.3.4 Critical Heat Flux ^  16  2.3.5 Transition Boiling ^  17  2.3.6 Minimum Heat Flux ^  20  2.3.7 Film Boiling ^  20  2.4 Effect of Motion on Jet Impingement Heat Transfer ^  22  3 Research Objectives ^  27  4 Test Facility and Procedures ^  29  4.1 Pilot-Scale Runout Table ^  29  iii  4.2 Material and Sample Preparation ^  31  4.3 Test Procedure ^  33  4.4 Inverse Heat Conduction Model ^  37  5 Results and Discussion ^  43  5.1 Cooling Curves ^  43  5.2 Heat Flux ^  48  5.3 Energy Extraction ^  53  5.4 Visual Observations and Contour Maps ^  63  5.5 Effect of Plate Speed ^  72  6 Conclusion ^  78  References ^  82  Appendix A — Validation of 2-D Axisymmetric Assumptions ^ 87 Appendix B — Validation of Symmetric Cooling ^  90  iv  List of Tables Table 2.1: Test conditions from tests performed by Zumbrunnen [27] ^ 23 Table 4.1: HSLA steel chemistry, wt % ^  31  Table 4.2: Test matrix ^  34  Table 4.3: Thermal gradients in various directions for test #3, first pass ^ 39 Table 4.4: Thermophysical properties for 1008 steel [31] ^  40  Table B-1: Measured temperature values from thermocouples, equidistant from the centreline ^  92  v  List of Figures Figure 2.1: Runout table schematic (reproduced by Chester [7] from [8]) ^ 5 Figure 2.2: Different types of jet impingement (reproduced by Chester [7] from [4]) ^ 6 Figure 2.3: Various jet configurations (reproduced by Chester [7] modified from [4]) ^ 7 Figure 2.4: Pressure and velocity distributions of free surface jet configuration (reproduced by Chester [7] modified from [4]) 9 Figure 2.5: Jet impingement surface (reproduced by Chester [7] modified from [11]) ... 10 Figure 2.6: Schematic of pool boiling curve (reproduced by Chester [7] modified from [4])  11  Figure 2.7: Boiling curve for free surface jet [13] (reproduced with permission from Elsevier)  13  Figure 2.8: Transition boiling region expansion in jet impingement modified from [21] 19 Figure 2.9: Changing Nusselt number with increasing plate speed (modified from [27]) 23 Figure 2.10: Peak heat flux on plate surface as a function of initial temperature (modified from [28]) ^  25  Figure 2.11: Effect of plate speed on peak heat flux values modified from [29] ^ 26 Figure 4.1: Runout table schematic ^  30  Figure 4.2: Runout table facility located in AMPEL ^  31  Figure 4.3: Thermocouple configuration and location on HSLA plate ^ 32 Figure 4.4: Detailed thermocouple configuration ^  33  Figure 4.5: Installation of thermocouple wire ^  35  Figure 4.6: Fully instrumented plate, bottom surface ^  35  vi  Figure 4.7: Domain used for meshing (dimension in mm) ^  39  Figure 5.1: Measured thermal history for test #9 (plate speed = 1.0 m/s) ^ 45 Figure 5.2: Measured thermal history during the 1 St pass of test #9 ^ 46 Figure 5.3: Measured thermal history during the later cooling stages of test #9 ^ 47 Figure 5.4: Comparison of cooling curves for two different speeds ^ 48 Figure 5.5: Calculated heat flux history for test #9 — (plate speed: 1.0 m/s, start temperature: 600 °C) ^  49  Figure 5.6: Heat flux in first pass of test #9 ^  50  Figure 5.7: Heat flux in test #9 at a later pass with an entry temperature of —215 °C ^ 51 Figure 5.8: Peak heat flux vs. entry temperature for test #9 - plate speed: 1.0 m/s ^ 52 Figure 5.9: Schematic for integration ^  54  Figure 5.10: Evolution of the heat flux curves under the jet for test #3 ^ 55 Figure 5.11: Evolution of the heat flux curve under the jet for test #9 ^ 56 Figure 5.12: Quantification of peak width at half maximum and tail width for 0.3 m/s ^ 57 Figure 5.13: Quantification of peak width at half maximum and tail width for 1.0 m/s ^ 57 Figure 5.14: Integrated heat flux vs. entry temperature for test #9 - 1.0 m/s ^ 60 Figure 5.15a: Schematic of thermocouple locations under the jet used for the analysis in Figure  5.15b.  61  Figure 5.15b: Integrated heat flux versus entry temperature for four different thermocouple locations under the jet. - test #9 ^  61  Figure 5.16a: Schematic of thermocouples locations, 63.5 mm from stagnation ^ 62 Figure 5.16b: Integrated heat flux vs. entry temperature, thermocouples 63.5 mm from stagnation — test #9 ^  63  vii  Figure 5.17: Calculated surface temperature (left) and heat flux contour (right) plot for pass 1 of test #3 (speed: 0.3 m/s, entry temperature: 565 °C) ^  65  ^  65  Figure 5.18: Video image of pass 1, test #3 — 0.3 m/s, entry temperature: 565 °C ^ 65 ^  67  Figure 5.19: Calculated surface temperature (left) and heat flux contour (right) plots for pass 2 of test #9 (speed: 1.0 m/s, entry temperature: 550 °C) ^  67  Figure 5.20 Video image of Pass 2 Test #9 — 1.0 m/s. Entry Temperature: 550 °C ^ 67 Figure 5.21: Calculated surface temperature (left) and heat flux contour (right) plots for pass 4 of test #3 (speed: 0.3 m/s, entry temperature: 309 °C) ^  69  Figure 5.22: Video image of pass 4, test #3 — 0.3 m/s. entry temperature: 309 °C ^ 69 Figure 5.23: Calculated surface temperature (left) and heat flux contour (right) plots for pass 7 of test #9 (speed: 1.0 m/s, entry temperature: 350 °C) ^  71  ^  71  Figure 5.24: Video image of pass 7, test #9 — 1.0 m/s. entry temperature: 350 °C ^ 71 Figure 5.25: Peak heat flux vs. entry temperature for all speeds ^ 72 Figure 5.26: Peak heat flux vs. surface temperature - all speeds for comparison ^ 74 Figure 5.27 Integrated Heat Flux vs. Surface Temperature ^  75  Figure 5.28: Maximum integrated heat flux plotted as a function of plate speed ^ 77 Figure A-1: Thermal history of two thermocouples along the centreline of the plate ^ 87 Figure A-2: Thermal history of thermocouples in the lateral direction ^ 88 ^  90  viii  Figure B-1: Thermal history for two thermocouples equidistant from centreline on opposite sides of the plate — pass 1  ^  90  Figure B-2: Thermal history for two thermocouples equidistant from centreline on opposite sides of the plate — pass 14 ^  91  ix  Acknowledgements I would like to express my heartfelt gratitude to my supervisors Dr. Matthias Militzer and Dr. Mary Wells for the opportunity to perform research on the pilot-scale runout table. In addition, I would also like to thank them for their guidance and support in my research work. I am also grateful for the assistance that I received from Geoffrey Franco and Gary Lockhart for helping me with my experiments. An extended special thanks to Ross Mcleod, Carl Ng, and David Torok for machining the steel plates for my experiments. I would like to thank my family and friends including my girlfriend Diana Lee for their invaluable support during my studies.  Finally, I would like to dedicate this research in loving memory of my late father Shing Chan.  1 Introduction The global challenges in establishing sustainable economic growth and the competition with new low weight materials has prompted the steel industry to develop advanced high strength steels (AHSS) for the automotive and construction industries. The use of AHSS in automotive applications reduces weight in the vehicles structure because less material or thinner gauge sheet steels can be used to obtain the same specifications. Reducing the weight of the vehicle improves the efficiency as now it requires less fuel to operate. AHSS are also employed in pipelines, where oil and gas can now be transported at higher pressures enabling larger distances to be covered between pump stations. Dual phase (DP) steels are a typical example of AHSS with microstructures consisting of martensite islands surrounded by a ferrite matrix. New grades for pipelines are also characterized by complex multi-phase microstructures. The production of hot-rolled AHSS requires sophisticated control of runout table (ROT) cooling in order to obtain the desired microstructures and mechanical properties. Steel enters the ROT at an approximate temperature of 850 °C. Cooling on the ROT is accomplished through a series of top and bottom water jets which impart water on the surface of the steel so that a predefined coiling temperature and hence microstructure is obtained. Since the steel temperature is significantly higher than the boiling point of water the heat transfer is governed by boiling water heat transfer. Conventional steels with a predominately ferrite matrix are usually coiled at temperatures around 600 °C. However, advanced high strength steels require coiling at temperatures below 500 °C in order to form complex multi-phase microstructures.  1  In the steel industry, there are several types of nozzles available for jet impingement during ROT cooling. The most common are circular jet nozzles, water curtains and water sprays. Circular jet nozzles confine water within the nozzle; this generates momentum in the water which aids in heat transfer. Water curtains impart water on the steel with minimal momentum; however the advantage of water curtains is they can impart water over a greater width that is not confined to the nozzle diameter. Water sprays are a particular type of nozzle configuration which produces fine water droplets mixed in air. The advantage of this method is that it requires less water because of the addition of air. It is important to understand the effects of various ROT configurations on boiling heat transfer. However it would not be economically feasible to perform experiments on an industrial ROT. Many researchers have resorted to laboratory bench scale testing apparatus in an attempt to determine the heat transfer conditions present during ROT cooling. For laboratory tests to be representative for industrial applications it is critical to conduct investigations on the pilot scale. Therefore, the runout table research group at the University of British Columbia (UBC) has developed a pilot scale runout table. The pilot scale ROT is located in the Advanced Materials and Process Engineering Laboratory (AMPEL). The pilot scale ROT is equipped with industrial sized headers and nozzles. The ROT facility also has the capacity to heat steel plates up to 1000 °C and to accelerate the plates to speeds of up to 3.0 m/s. The versatile design of the pilot scale runout tables allows for close simulation of industrial conditions. The pilot scale facility at UBC offers a unique opportunity to make measurements that approximate the runout table cooling conditions experienced in industry. Initial investigations on the facility  2  emphasized conventional cooling practices (i.e. with coiling temperatures at approximately 600 °C). However, there is a lack of experimental data in the lower temperature range of the jet impingement boiling curve where there are very rapid increases and decreases in the heat flux or heat transfer conditiohs close to the critical heat flux From an industrial perspective, the pilot-scale ROT provides specific knowledge into factors governing jet impingement boiling heat transfer that cannot easily be observed during processing. On the pilot-scale ROT, the thermal history of steel can be continuously measured and subsequently analyzed to obtain valuable knowledge regarding the heat flux distribution on the surface. Of particular importance is the surface temperature corresponding to the critical heat flux. Coiling at temperatures near or below temperatures corresponding to the critical heat flux produces challenges because heat transfer modes are changing which could cause dramatic changes in heat transfer. Visual observations of the impingement zone on the surface of the steel, during cooling, presents information into specific boiling regimes that occur during jet impingement cooling. All of the knowledge and data acquired during pilot-scale experiments can be used to guide decisions regarding how the ROT should be setup and run to produce phases such as bainite or martensite which are essential to AHSS. The primary purpose of this research is to quantify the boiling heat transfer conditions that occur when cooling to temperatures below 500 °C. A secondary objective was to evaluate the effect of speed on boiling water heat transfer. To do this research, industrially supplied steel plates instrumented with thermocouples were cooled on the pilot scale ROT with impinging water from a single top jet.  3  2 Literature Review 2.1 General Overview In a hot strip mill, the runout table plays a vital role in the production of various steel products. Steel leaving the finishing mill at temperatures in the range of 800 - 900 °C is cooled on the ROT in a controlled manner in order to obtain specific microstructures and mechanical properties [1-3]. The use of water sprays, curtains and jet impingement nozzles arranged in various configurations extract heat from the steel. Each method of water impingement produces different cooling conditions. There is no formally established configuration for cooling. Industrial runout tables are designed based on specific needs such as: space requirements, types of steel produced and gauge thickness. Water is used for cooling because it is readily available, easy to handle and its ability to extract high amounts of heat from a hot object. Since the steel surface during runout table cooling is significantly higher than the boiling point of water, there is a phase change of the water from liquid to gas. This is known as boiling heat transfer or more specifically jet impingement boiling heat transfer when describing the heat transfer occurring on the runout table. The topic of jet impingement boiling heat transfer has been studied for many years and is well documented in the literature for steady state conditions [4-6], whereas boiling conditions on the runout table are highly transient. Despite little research for transient jet impingement boiling heat transfer, research in steady state boiling heat transfer provides a foundation of concepts, which can be applied to transient conditions.  4  The runout table is one of the final stages in a hot strip mill. The purpose of the runout table is to cool steel to a predetermined coiling temperature (see Figure 2.1). Finishing Mill Exit Temperature  Finishing Mill  Coiling Temperature  Top Jet Bank^Header  11.11.1^URN, .n.^:11:^:w 1,0^ini^1 11 1^1 11 1^1111^1 11 1^1 11 1^1 11 1 .^.^.^.^.^.  1 11 1^1 11 1^1 11 1^1 11 1  (...)UULJULJUUUMULJUUU  dddddd  Down Coiler  ^URN, .H:  ddddd  Bottom Jets  41110  Figure 2.1: Runout table schematic (reproduced by Chester [7] from 181)  Conventional runout tables consist of motorized rollers which carry the rolled steel product down through a specific length. A typical runout table can be between 100 m to 200 m in length. In the span of this length banks of headers are located above and below the rollers. Water flows into the headers first to ensure even flow. Once water is collected in the header, it is then evenly deposited onto the steel through nozzles, curtains or introduced with air in sprays (see Figure 2.2). Water deposition by top jet impingement is usually gravity fed; however, bottom jet nozzles must be pumped in order to produce enough flow to overcome the effects of gravity. One common practice is to angle the bottom jet nozzle. It is believed that this will prevent falling water from disturbing the flow and to change the shape of the impingement zone [7].  5  Water curtain Bottom Jet Cooling  1P r°11P °I.A0  -  °  Spray cooling  .•• •  0%0 . ^‘ S  Figure 2.2: Different types of jet impingement (reproduced by Chester [7] from [4])  Tacke et al. and Kohring [9, 10] performed studies independently to determine the best method for water impingement. Their studies show that laminar and water curtains have higher heat transfer than spray cooling. In both laminar and water curtains, more liquid is deposited onto the surface and thus more water is available to extract heat from the surface. Further studies performed by Zumbrunnen et al. and Chen et al. [11, 12] show that the advantage of using a water curtain is its ability to cool steel across the width uniformly. Laminar flow jets are also of use to industry; water exits the jet with higher momentum than in a water curtain. Increase in water momentum increases the efficiency  6  of heat transfer. Momentum of the water penetrates the vapour layer more readily allowing for an increase in liquid contact to the steel.  2.2 Jet Impingement and Hydrodynamics The most common types of jet configurations are: free surface, plunging, submerged, confined and wall (see Figure 2.3) [4, 7]. For runout tables using circular nozzles, only the free surface and plunging jet configurations apply. Nozzle Centreline of Jet  Free Surface Stagnation Point  z V  Gas  Gas HI  Liquid  Liquid \\\\\\\\\\\\\\T\\\\\\\\\\\\\\ A. Free-surface  B. Plunging  Gas  Nc)zzLi P ate  L  Liquid  Liquid  \\\\\\\\\\\\\\\\\\\\\\\\\\\\\  \\\\\\\\\\\\\\\\\\\\\\\\\\\\\  C. Submerged  D. Confined  Nozzle Plate Gas Liquid \\\\\\\\\\\\\\\\\\\\\\\\\\\\\ E. Wall (free-surface)  Figure 2.3: Various jet configurations (reproduced by Chester 171 modified from [41)  7  A free surface jet condition occurs when liquid leaving the nozzle penetrates through a phase (i.e. gas) which has minimal restriction on the motion of the liquid. This situation occurs in the beginning of each cooling bank in a ROT where there is no water accumulated on the steel. When pooling occurs and the steel progresses through the cooling bank, the jet configuration changes to that of a plunging jet situation. For this configuration, at the point of impingement, the liquid exiting the nozzle must penetrate and displace liquid already on the surface. This condition differs from that of a free surface because now the liquid does not traverse in a radial direction away from the impingement zone with a given velocity. Instead, the height of the liquid increases on the surface, the effect of the impinging jet decreases because a portion of the liquid's momentum is used to displace the pool of water on the surface. Many industrial runout tables employ various techniques to remove liquid and minimize pooling. Figure 2.4 illustrates the pressure and velocity distribution as a function of distance, x, for a free surface jet situation. The region denoted by "A" is considered to be the stagnation or impingement region. In this region, the pressure is at its maximum, produced by the impinging liquid leaving the nozzle. Once the liquid expands beyond the diameter, dj, of the nozzle the liquid enters an acceleration region denoted by "B" (0.5 < X/dj < 2). In this region, the liquid will accelerate until it approaches the velocity of the liquid leaving the jet. For values of X/d j greater than 2, the fluid is in a parallel flow region, denoted by "C". In this region the fluid will traverse parallel to the surface at a velocity equal to that of the jet.  8  ^ ^  Nozzle  Free Surface _  \ I—^— Centreline of Jet 4,,,^ ,^/ 7 Stagnation Point •`. j Ac ^U(x) V, ,  -  x A. Stagnation Region  A B  ^  C  B. Acceleration Region C. Parallel Flow Region 1.0 —  1.1\(ix)  0.6  P(x)-Ps  P(0)-Ps 0.0  T 1.6^3.0 X  d;  Figure 2.4: Pressure and velocity distributions of free surface jet configuration (reproduced by Chester [7] modified from [4])  For jet impingement boiling, the four defined boiling regimes correspond to a distinct location on the plate surface (see Figure 2.5). Figure 2.5 shows that directly under the nozzle there could be a condition where the plate is cool enough that heat transfer is through single phase convection. In region "II", nucleate boiling begins due to high heat transfer causing bubble nucleation. In region "III and IV", the plate temperature is sufficient to produce a stable vapour film. For region "V", this section of the steel plate is far from the impingement zone such that it does not come in contact with any water. This region experiences only radiation and convection heat transfer.  9  Liquid Jet  v  Regions I - Single Phase Forced Convection II - Nucleate / Transition Boiling Ill - Forced Convection Film Boiling IV - Agglomerated Pools V - Radiation and Convection to Surroundings  Steel Plate  Figure 2.5: Jet impingement surface (reproduced by Chester [7] modified from 1111)  2.3 Boiling Heat Transfer 2.3.1 Boiling Curves On an industrial runout table, boiling heat transfer governs the amount of heat extracted out of the steel. There are four distinct boiling regimes associated with boiling heat transfer: single phase forced convection, nucleate boiling, transition boiling and film boiling [41. Figure 2.6 shows a schematic of a typical pool boiling curve which specifies where each boiling regime occurs in relation to heat flux and saturation temperature.  10  Single-Phase Forced Convection Regime  N ucleate Transition Boiling Boiling Regime Regime  Film Boiling Regime  LL  Max'mum Heat Flux  ^ Onset of ^ Minimum Nucleate Boiling Heat Flux Wall Superheat logAT.,  Figure 2.6: Schematic of pool boiling curve (reproduced by Chester [7] modified from [4])  Considering a situation where water is at room temperature, heat transfer to the water is through conduction and convection of the water. As more heat is transferred and the temperature of the water increases, the first point it will reach is denoted by "A", the onset of nucleate boiling. At this point the first bubbles will begin to form, as the heat in the system is sufficient to cause a change from liquid to vapour. Once bubbles begin to grow, there is a transition from single phase convection boiling regime to the nucleate boiling regime. In this regime, bubbles will continue to grow and coalesce to form vapour columns, as wall superheat increases. Because water is continuously changing from liquid to vapour, the heat flux in the system increases also because of increased momentum/turbulence of the water against the surface. The heat flux will continue to  11  increase up until the point of "B". This point denotes the maximum heat flux, at this point, the vapour is being produced at such a high rate that the vapour columns begin to coalesce to form vapour patches along the surface. Once vapour patches begin to form the heat flux will begin to decrease. This boiling regime is known as transition boiling. The reason for this is due to the mixture of liquid and vapour in contact with the surface. Because heat transfer through vapour is less than through liquid, as the amount of vapour contact increases, the capacity for the system to transfer heat decreases. This will continue until the final remaining droplets of water are in contact with the surface, at that moment, the system has reached point "C" on the pool boiling curve. At point "C" essentially all of the liquid has been converted to vapour, and heat transfer occurs through vapour only. This regime is known as the film boiling regime. The heat flux increases gradually as the wall superheat increases. While pool boiling offers the fundamental groundwork for boiling heat transfer, jet impingement heat transfer is a highly transient problem. Figure 2.7 is a boiling curve for jet impingement boiling developed by Robidou et al. [13]. It shows that there are differences in cooling behaviour from the stagnation region and away from the stagnation region. While the trend is quite different from a pool boiling curve, the individual boiling regimes are still present. At high temperatures (above 350 °C wall superheat) the plate experiences film boiling at all locations. Once the wall superheat drops to below 350 °C, the different locations on the plate experience different types of cooling. Inside the stagnation zone, the heat flux dramatically increases because of vapour layer breakdown, Robidou et al. consider this to be transition boiling. For the locations away from the stagnation zone, they continue to experience film boiling conditions because there is no  12  direct contact from the impinging water jet. At temperatures below 100 °C wall superheat, within the stagnation zone there is a slight decrease in heat flux. Robidou et al. mention that this point corresponds to the first minimum heat flux value. With continued cooling down to below 50 °C wall superheat causes, locations within the stagnation zone and away from the stagnation zone experiences critical heat flux values. While the critical heat flux values occur at the same wall superheat, the magnitudes are quite different. Below the temperature of the critical heat flux the system enters the nucleate boiling regime.  Transrbon boiling Licleate..1 •^  ^ding  •  E x  3  •  • •• • • . 4144.^•^•  • • •• • •■• •• •^• •• •^  •  •  Shoulder  4•? • •^••••••••• 4•• • •• +4, •  Leidertiost poilt  •^• •^♦^•^•^ • • • •^  ir.... ••• ••;•^•  • •^•  • le • •  2^• Transdb boiling  •  First minimum Film boiling  Forced^1 convection regime  Film boiling • • 1^•  ukti40 Atmet4mtm''  exc 4-#4,  0  50  100  6.  150  200  250  300  350  400  AT.,„ K  • Stagnation point • x=19 mm • x=44 mm  Figure 2.7: Boiling curve for free surface jet 1131 (reproduced with permission from Elsevier)  2.3.2 Single Phase Convection Single phase convection occurs when wall superheat is less than the saturation temperature of the liquid. Because the temperature of the liquid is less than the saturation temperature, boiling does not occur. In jet impingement heat transfer, the single phase convective heat transfer coefficient is a function of the boundary layer and hydrodynamics of the system. Wolf et al. [14] discovered that the convection heat  13  transfer coefficient is constant away from the stagnation region such that the effect of flow is negligent. Their studies show that the length downstream was approximately three jet diameters from the stagnation region.  2.3.3 Nucleate Boiling  The nucleate boiling regime is bound on the pool boiling curve (Figure 2.6), by point "A", the onset of nucleate boiling and point "B", the critical heat flux. Nucleate boiling occurs when the liquid is just above its saturation temperature. Point "A", the onset of nucleate boiling (see Figure 2.6), denotes the first incipience of bubble nucleation. A phase change due to latent heat effects causes liquid to convert to vapour thus producing bubbles. Point "A'" in Figure 2.6 denotes the point where constant production of bubbles occur, this is known as fully developed nucleate boiling. Bubbles generated, enhance heat transfer because the motion of the bubbles creates additional convection currents [14]. This is represented by a sudden increase in heat flux on the pool boiling curve (see Figure 2.6). As the wall superheat increases, bubbles will continue to grow up to the point of "B", which denotes the critical heat flux point and the transition into the transition boiling regime. In jet impingement, Wolf et al. [14] determined that the nucleate boiling region can be determined by the sudden increase in convection coefficient just beyond the single phase convection zone. Wolf et al. also considered the effect of jet velocity in their experiments and found a profound effect in the single phase convection region, however in the nucleate boiling regime; they found that velocity had little effect on heat transfer.  14  They speculated that the reason for this is because the creation of bubbles by latent heat effects is far more dominant than the hydrodynamics of the fluid. Mitsutake and Monde [15] characterized the region of nucleate boiling in jet impingement as an annulus that encircles the single phase force convection region. Beyond the annulus is a region that is essentially all film boiling. They varied liquid subcooling and jet velocity in their experiments. Mitsutake and Monde discovered that increasing the liquid subcooling in general decreased the size of the annulus. For a fixed liquid subcooling, they varied the jet velocity and found that the annulus traversed to a predetermined location faster. Based on these two variables, Mitsutake and Monde developed a relationship for the location of the trailing edge of the nucleate boiling regime in the form of a power function with respect to time i.e.  rwe,  =  a  x  r  (2.1)  Where a and n are experimentally determined constants, Net represents the radius of the wetting zone, and t is the time. Robidou et al. [13], also considered the boiling conditions outside the stagnation region for nucleate boiling. They performed stationary plate experiments using a free surface jet. The jet that was used was rectangular with a cross sectional area of 1 x 9 mm and the impinging plate material was copper. The jet velocity was fixed at 0.8 m/s, the water subcooling was 16 K, and the nozzle to plate distance was 6 mm. Figure 2.7 are boiling curves produced by Robidou et al., for different locations away from the stagnation region. Within the nucleate boiling regime, at wall superheat below 40 K, the boiling curves for each of the locations away from the stagnation region had a tendency to merge onto the boiling curve at the stagnation line.  15  2.3.4 Critical Heat Flux Critical heat flux is denoted by the point "B" on Figure 2.6. It represents the point where violent production of bubbles and vapour columns coupled with constant mixing of the two phases produces ideal conditions for maximum heat extraction. The critical heat flux is also the point of transition between two boiling regimes: nucleate boiling and transition boiling. In the event that heat flux was fixed at the value of the critical heat flux, any increase in wall superheat will cause a sudden transition from nucleate boiling to film boiling as denoted by the point "E". This phenomenon is known as burnout. If the wall superheat increased without keeping the heat flux constant, then the boiling mode becomes transition boiling, which will be discussed in a different section. Critical heat flux is a highly publicized topic in jet impingement boiling heat transfer. Several researchers have performed experiments varying jet impingement velocity and water subcooling [16-19] for the stagnation zone. Increasing the jet velocity caused an increase in critical heat flux. Similarly, increasing the water subcooling also caused an increase in critical heat flux. Despite differences in testing apparatus, they all came to similar conclusions. Robidou et al. [13] considered regions outside the stagnation zone (i.e. parallel flow region). Their tests showed that the critical heat flux value in the stagnation zone was greater by a factor of three, than the critical heat flux in the parallel flow zone (see Figure 2.7). However, despite the difference in magnitude of the critical heat flux, they also discovered that regardless of location, the critical heat flux occurs at similar wall superheat.  16  2.3.5 Transition Boiling  Transition boiling is represented on Figure 2.6 by the region bounded by the critical heat flux at point "B" and the minimum heat flux at point "C". As mentioned in the previous section the critical heat flux point "B" represents the stage that the heat extraction is at its optimum, with mixed liquid and vapour production. Once the wall superheat increases beyond point "B", vapour columns and bubbles begin to coalesce to form vapour patches on the surface. Now there is a mixture of liquid conduction and convection heat transfer, coupled by conduction heat transfer through vapour patches. Because heat transfer through vapour is considerably less than through liquid, the corresponding heat flux decreases. This trend will continue, as vapour patches grow larger and reduce liquid contact with the surface. Once the wall superheat reaches a point corresponding to point "C" on the graph, the contact of liquid to the surface is at its minimal stage. Any further increase in wall superheat beyond the point of "C" will transition into another boiling regime, film boiling. The transition boiling regime is considered to be essentially a mixture of nucleate boiling and film boiling regimes. Therefore some of the concepts of nucleate boiling will also hold true in transition boiling. Pan et al. [20] discovered that liquid turbulence and bubble agitation had a significant effect on values in the transition boiling regime. Robidou et al. [13] observed high heat flux values in the transition boiling regime, comparable to the critical heat flux (see Figure 2.7). They also draw a correlation to liquid turbulence by mentioning the effect of microbubble emission boiling. Microbubble emission boiling is the phenomenon where bubbles break apart and form  17  smaller bubbles. The constant creation of microbubbles increases the turbulent nature of the liquid and therefore enhances heat extraction. Mitsutake and Monde [15] defined a region of nucleate boiling as an annulus around the single phase region in jet impingement. Hammad et al. [21] speculate that within the annulus resides a region that is transition boiling. In their studies, they noticed that the heat flux in the annulus was not uniform. In the region of lower heat flux, they believe that the plate was not entirely wetted. Therefore they concluded that within the annulus, nucleate boiling and film boiling coexist and thus determined that it was transition boiling. In order to make such a claim, Hammad et al. were able to analyze images taken of the impingement surface and identify specific occurrences that happened within the impingement region. They believed that the transition boiling regime was bounded by the location where boiling ceases to occur and labelled it as rs and r,, for the impingement zone and the edge of the wetting front, respectively. Figure 2.8 shows the occurrence of rs and r,„ for the following test conditions: jet velocity was 5 m/s, water subcooling was 50 °C, the initial test temperature was 300 °C and the impingement surface was made from brass. Figure 2.8 shows that the transition boiling regime is not noticeable until after the first second of the test. For the given test conditions the transition boiling regime occurs approximately 15 mm away from the stagnation zone and progresses further away from the stagnation zone as the test progresses to completion. Another interesting observation that was made by Hammad was that the transition boiling region does not only move away from the stagnation region but it also expands in size. In Figure 2.8 rq is defined as the radial position where the maximum heat flux is experienced. Based on this figure, the maximum heat flux is experienced  18  inside an area where boiling does not occur, until after 4 seconds has elapsed where the maximum heat flux occurs at the boundary of where boiling occurs. In addition, Figure 2.8 also draws reference to rh which denotes the location at which the maximum heat transfer coefficient occurs, and has no effect on the transition boiling region.  0  ^  2  ^ ^ ^ 6 8 4  time (s) Figure 2.8: Transition boiling region expansion in jet impingement modified from [21]  19  2.3.6 Minimum Heat Flux  Minimum heat flux is the point denoted on Figure 2.6 by "C", it is also referred to as the Leidenfrost point. The corresponding temperature for which the minimum heat flux occurs is commonly known as the rewetting temperature. At this point on the graph, the final portion of liquid is in contact with the surface. Increasing the wall superheat will vaporize the remaining liquid and produce a stable uniform vapour layer. Ishigai et al. [22] performed tests in jet impingement varying jet velocity and subcooling. Based on their results they formulated a correlation to determine the minimum heat flux as a function of jet velocity and liquid subcooling and is given by. qmin  = 5.4 x (1+ 0.527AT., )x v°,7 x10 ^(2.2) 7  4  Liu [23] performed experiments in an attempt to develop a new correlation for minimum heat flux which included the diameter of the nozzle and is given by.  t  q m . = 0.200isub vje1 /d)0.5 x 10 4^(2.5) Liu found that his correlation generated values that were 20% less than that of Ishigai for the same conditions. Both correlations developed by Ishigai et al. and Liu, suggests that subcooling has a strong effect on the minimum heat flux. In addition Liu also observed that the temperature at which minimum heat flux occurs is linearly dependent on liquid subcooling. 2.3.7 Film Boiling  Film boiling is the boiling condition where heat transfer is through a stable vapour film. This occurs at high wall superheat beyond the minimum heat flux temperature. In 20  this boiling regime, heat is transferred into the liquid from the surface so quickly that it vaporizes instantly. The generation of the vapour film grows so quickly that all of the liquid does not have a chance to vaporize and thus is suspended by the vapour film. In all of the previous boiling regimes mentioned, heat transfer occurred between liquid and the surface or a mixture of liquid and vapour. In this regime, heat transfer occurs solely by conduction of heat through the vapour generated. In jet impingement, this region can be represented by a zone where wetting does not occur. Liu and Wang [2] observed in their study that in the film boiling regime, liquid subcooling had a stronger influence on heat transfer than jet velocity. They attribute this to the fact that subcooling causes the boiling curve to shift to higher superheat and heat flux. Zumbrunnen et al. [11] also noticed that heat transfer increases with increasing liquid subcooling. Robidou et al. [24] compared the effect of film boiling in both the stagnation zone and the parallel flow zone. They found that the heat flux within the film boiling regime in the stagnation zone is approximately 25% higher than in the parallel flow zone when the system is in film boiling. They believe that the increase in heat flux in the stagnation zone is attributed to the vapour layer being thinner in the stagnation zone. Another observation that was made was that Robidou et al. did not experience any temperature fluctuations while the experiment was in the film boiling regime This led them to believe that in film boiling, the film generated is stable and that there are no regions where liquid can penetrate and come in contact with the surface.  21  2.4 Effect of Motion on Jet Impingement Heat Transfer Incorporating plate motion into jet impingement heat transfer analysis has been challenging for many researchers. However, the need for such a study is quite evident in the steel industry, in particular to gain a better understanding of the heat transfer that occurs during ROT cooling of steel plate and strip. By introducing surface motion the hydrodynamics and heat transfer of the system change. In stationary tests, the jet impingement produced a uniform circular shape for circular nozzles. With the addition of surface motion, the shape of the impingement zone changes [25, 26]. Zumbrunnen et al. [11, 27] developed an apparatus where a test block sits on a track of rollers. Their initial tests were run with the surface moving at half the velocity of the jet. Figure 2.9 shows the effect of plate motion on Nusselt number. Larger Nusselt number indicated that the effect of heat transfer was greater. They speculate that the reason for larger Nusselt number was because the surface motion caused higher turbulence in the boundary layer thus increasing heat transfer. Further they argue a stationary surface had lower Nusselt numbers because a stagnant boundary layer will grow thicker and reduce heat transfer. In these tests, Zumbrunnen et al. used a pump to re-circulate water; however, the pump did not generate any positive pressure, which meant that the jet velocity was limited to acceleration due to gravity. Table 2.1 shows the test conditions corresponding to the results shown in Figure 2.9.  22  Table 2.1: Test conditions from tests performed by Zumbrunnen 127  Jet  1.02  Initial Plate Temperature (°C) 95  Water Temperature (°C) 21.2  2.60  1.02  106  22.9  2.60  1.02  92  21.3  Test S peed  Reynold's number  0 m/s  24000  Velocity (m/s) 2.60  0.15 m/s  24000  0.31 m/s  24000  Jet Width mm (^)  -10^ 8^-6^-4^-2^0^2 -  4  6  8  10  Position (mm) Figure 2.9: Changing Nusselt number with increasing plate speed (modified from 1271)  Han et al. [25] developed a test apparatus where the moving surface is driven by a chain conveyor with a suspended carriage. Because the carriage is suspended, the nozzle points upwards. This design only allows for bottom jet type experiments. Han et al. observed that motion of the surface caused the shape of the water film to stretch into an elliptical shape. They also found that surface motion does not affect the local heat transfer coefficient and that cooling inside the stagnation zone is similar in both stationary and moving plate experiments. In addition, because the tests were performed with bottom jet configuration, the effect of pooling on the surface is eliminated. Chen et al. [26] performed similar tests as Han et al. and noticed similar effects on the shape of  23  the water film. While Han et al. and Chen et al. show promising work on evaluating the shape of the impingement zone, their data is limited to low temperature tests. Because the maximum initial start temperature was only 240 °C, their tests were limited to the nucleate boiling and single phase forced convection regimes. Prodanovic et al. [1] performed tests for moving plate experiments using the pilot scale runout table at the University of British Columbia. The details of the test apparatus will be mentioned in the following chapter. They performed single nozzle tests using steel plates moving at two speeds: 0.3 and 1.0 m/s. They also varied the flow rate and subcooling of the water. Initial observations showed that cooling rate increased with decreasing plate speed. Prodanovic and Militzer [28] continued with similar experiments and concluded that the maximum cooling rates occurred between 300 and 350 °C and that the shape of the cooling zone increases in size with decreasing surface temperature. In addition preliminary calculations for surface heat flux as a function of initial temperature were performed and presented in Figure 2.10. Their tests show that peak heat flux values for slow speeds are generally higher than peak heat flux values for high speed tests  24  100^200^300^400^500  ^  600  ^  700  Entry Temperature (°C)  Figure 2.10: Peak heat flux on plate surface as a function of initial temperature (modified from 1281)  Most recently, Jondhale [29] performed multiple nozzle experiments on the runout pilot scale runout table. In his experiments, he investigated water flow rate, plate speed and nozzle spacing. In his investigation of plate speed, tests were performed at two speeds 0.22 m/s and 0.75 m/s. Figure 2.11 shows the peak heat flux data from the stagnation region of the centre nozzle plotted for both speeds. The data was generated for a test that had a nozzle to nozzle distance of 76 2 mm and the flow rate was 15 1/min per nozzle. The conditions for tests performed by Prodanovic et al. and Jondhale varied but the trend that they both observed were quite similar. Jondhale concluded that the point of maximum peak heat flux shifts to lower entry temperatures with increasing speed. Also he mentioned that in general heat fluxes were higher at slower speeds. Another observation that Jondhale makes is that the effect of strip speed on peak heat flux values is negligible in the nucleate boiling regime, but he fails to mention anything about the other boiling conditions that may be present.  25  •  2.0E+07 1.8E+07 1.6E+07 1 4E+07  E  -  1.2E+07 u- 1.0E+07 ; 8.0E+06 % CI' 6.0E+06 4.0E+06 2 0E+06 0.0E+00 ^ 0  ^  100  ^  200^300^400^500  ^  600  ^  700^800  Entry Temperature ( ° C)  Figure 2.11: Effect of plate speed on peak heat flux values modified from [29]  26  3 Research Objectives Although there has been considerable research performed related to jet impingement heat transfer most of it is not directly relevant to the conditions seen on the ROT. The reasons for this include speed of tests and non-industrial type nozzles. In particular there is a need to more accurately quantify the heat transfer close to the maximum heat flux region, as this heat transfer regime is of importance in the production of steels such as AHSS which are coiled at much lower temperatures relative to more conventional steels. Several researchers [11, 25-27] have performed bench scale experiments to investigate heat transfer on a moving surface. Because of limitations in scale there were several problematic issues that arose. Zumbrunnen et al. had limitations on jet velocity because they used gravity fed nozzles. Chen et al. and Han et al. also performed moving plate experiments; in their tests they considered heat transfer in nucleate boiling and forced convection regimes only. Research performed on the pilot scale runout table at UBC had a tendency to simulate industrial conditions more closely. Prodanovic et al. [1, 28] and Jondhale [29] both performed experiments to investigate the effect of speed and water flow rate, however their limitations were minimal data and knowledge of what is occurring at maximum peak heat flux values. The objective of this research is to address several deficiencies that were not considered in previous experiments and are as follows: • Quantify heat flux in the region of the critical heat flux (i.e. at temperatures below 500 °C).  27  •  Determine the effect of plate speed on peak heat flux.  •  Generate fundamental knowledge on the boiling mechanisms in the temperature range of 100 — 500 °C.  28  4 Test Facility and Procedures 4.1 Pilot-Scale Runout Table All experiments for the current study were performed using the pilot-scale runout table facility located in the Advanced Materials and Process Engineering Laboratory (AMPEL) at the University of British Columbia. The pilot-scale ROT facility is unique in the world and approaches the conditions seen during cooling of steel on an industrial ROT. The facility was originally designed for stationary experiments but has since been modified to accommodate moving plate experiments [1]. Either top jet cooling using two jetlines with up to three nozzles per jetline or single nozzle bottom jet impingement can be conducted. The pilot-scale ROT facility consists of several different components which are required to heat the sample to a prescribed initial temperature and move it along a conveyor such that it can be cooled via circular nozzles at the top or bottom of the plate. Figure 4.1 shows a schematic of the pilot-scale runout table. The facility consists of a Denver fireclay electric furnace at one end of the runout table (1). The furnace is capable of heating test samples to 1000°C and is fitted with a gas line to supply inert gas (nitrogen was used) during heating of the sample to minimize the formation of scale. Next to the furnace is the chain conveyor system (2) that drives the test sample to the cooling section (3). The distance between the furnace and the cooling section is 10 m; this allows the test sample to be accelerated to a maximum speed of approximately 3.0 m/s. Once the plate has cleared the cooling section, there is a 5 m section of the conveyor which allows for the deceleration of the plate. The total length of the chain conveyor is  29  15 m. A high torque motor (4) is located at one end of the chain conveyor drives the chains. The speed of the chains is controlled by an output voltage signals InstruNet data acquisition unit (Inet-100). The output voltage was controlled using DasyLab 6.0 data acquisition software. The cooling section (3) consists of the headers, nozzles, a recirculation pump and an upper and lower tank.  Figure 4.1: Runout table schematic  The height of the cooling tower is 6.5 m. A 30 kW heating element is located within the upper tank. The heating element in the upper tank is used primarily for the purpose of heating the water to a desired temperature. The lower tank acts as a vessel to contain water after it exits the nozzle. At the base of the lower tank is an 11 kW recirculation pump to recycle the water. Through a series of valves, water can be pumped to the upper tank for tempering, or routed to the header when running experiments. The cooling tower consists of two separate headers, each header can contain up to three nozzles. An electronic solenoid valve located above the header controls the flow of water to the header. Water collects in the header and then passes through a series of flexible hoses to stainless steel "U" shaped nozzles. Each nozzle has a diameter of 19 mm. The nozzles are attached to a set of rails, which are connected to an adjustable 30  frame. The flow of water to the nozzle is controlled using a valve and the flow rate is monitored with an Omega FTB-905 turbine flow meter. The flow meter's output voltage is converted to the flow rate and displayed in DasyLab. Experiments for this study were done using a single nozzle set with respect to the plate such that it impinged along the mid-width location of the plate. The stand off distance between the plate and the edge of the nozzle was set to 1.5m.  Figure 4.2: Runout table facility located in AMPEL  4.2 Material and Sample Preparation The test samples used for this research were made from High Strength Low Alloy (HSLA) steel plates that were supplied by Dofasco in the hot rolled condition. The chemical composition of the steel is given in Table 4.1 C  Mn  P  S  0.0512  1.289  0.012  0.0041  Table 4.1: HSLA steel chemistry, wt % Si Mo Al Cr Ni 0.1015  0.0434  0.0127  0.0106  0.0395  N  Ti  V  Nb  0.0045  0.0032  0.0061  0.0689  31  The plates received were 6.65 mm thick and sheared to approximate dimension of 1200 mm x 430 mm. Twenty 1.59 mm (1/16") diameter holes were drilled from the bottom face of the plate to a depth of approximately 1 mm below the top surface, based on the thermocouple configuration shown in Figures 4.3 and 4.4. The spatial distribution of the thermocouples was chosen so that a number of thermocouples were located in the impingement zone as well as various positions in the lateral direction away from the impingement zone.  9  -  Figure 4.3: Thermocouple configuration and location on HSLA plate  32  Centreline  Diameter of the nozzle and impingement zone  MM  63 5 mm  Figure 4.4: Detailed thermocouple configuration  4.3 Test Procedure A test matrix for this research was devised to study the effect of speed (0.3 — 1.3 m/s) on low coiling practices (<600 °C). A range of start temperatures was selected for the same cooling conditions so that the discrete data points will provide sufficient data in the areas of rapid increase and decrease in the heat flux near the maximum or critical heat flux. Table 4.2 shows the test matrix used for this research. The initial plate temperature reported in Table 4.2 denotes the temperature of the plate as it enters the cooling section for the first time  33  Table 4.2: Test matrix  Test  Speed (m/s)  1 2  0.30  Initial Plate Temperature (°C) 350  0.30  500  3  0.30  600  4  0.60  350  5  0.60  500  6 7  0.60 1.00  600 350  8 9  1.00 1.00  500 600  10 11  1.30 1.30  350 500  12  1.30  600  Prior to instrumentation, the plate was attached to a carrier. The carrier provides a vessel for the plate to sit on the chain conveyor and allows for the plate to be inserted and removed from the furnace. The carrier consists of two pieces of angle iron of length slightly longer than the plate, four reinforcement bars, and handles on the front end of the carrier. With the plate firmly attached to the carrier, each plate was instrumented with twenty Type K thermocouples (Omega INC-K-Mo — 1.6mm). Type K thermocouples were used because their operating range was within the designated testing temperature range. Instrumentation of the plate involved stripping the thermocouple sheath to reveal the thermocouple wires, placing the wires through an insulating ceramic tube, placing the ceramic tube and wire assembly into the hole, and spot welding the wires to the base of the hole. To prevent the spot welded wires from becoming detached during a test, screws were installed in the bottom surface to anchor the thermocouple wires. A diagram of the  34  installation of the thermocouple is shown in Figure 4.5. Figure 4.6 shows a fully instrumented plate, where all of the thermocouple wires have been anchored. Impingement Surface  Intrinsic Junction  Ceramic Insulator  A— Thermocouple Wire  Figure 4.5: Installation of thermocouple wire  Figure 4.6: Fully instrumented plate, bottom surface  After instrumentation, the location of the thermocouple holes was marked on the top side with a water resistant ink pen. The entire plate and carrier assembly was placed directly underneath the center nozzle. The recirculation pump was turned on and with the water running; the nozzle alignment was adjusted such that impingement occurred along the mid-width location of the plate directly above the thermocouples. After adjusting the nozzle, DasyLab software was started. The flow rate was set to 30 I/min by adjusting the  35  valve on the nozzle. The speed of the plate was displayed in the DasyLab program designed for the experiments. The speed was determined by and adjusting the input voltage of the hydraulic motor and running trial passes using the plate until the desired speed was obtained. Once the specific voltage was determined, the plate was placed into a pocket within the electric furnace. The opening of the pocket was then sealed using refractory bricks and insulating ceramic wool. Within the pocket, a nitrogen atmosphere was maintained to minimize scale formation during heating of the plate. The plate was heated to a temperature 100-120 °C above the specified start temperature in Table 4.2. The increase in temperature was chosen to compensate for the loss in heat between the moment the plate leaves the furnace and enters the cooling section. With the plate securely in the furnace, the water was pumped to the upper tank and was heated to 25 °C. Thermocouple wires were connected to a Daqbook data acquisition module. An acquisition rate of 30 Hz was used for all the tests. Once the water was at the correct temperature (i.e. 25 °C) and the plate reached its desired temperature, the water was gravity fed through a clear vinyl tube back into the lower tank. A Panasonic video camera was strategically placed to capture the impingement of the water onto the plate. When removing the plate from the furnace, the ceramic insulation and refractory bricks are removed opening the pocket. The plate and carrier assembly is slid out of the pocket and onto a set of rails which sits on the chain conveyor. Once secured on the rails, the entire assembly is driven through the cooling section. After the plate passes through the cooling section, the plate is stopped, the nozzle is turned off, and the plate is then driven back to set up for the next pass. The test  36  continues in this manor until the plate temperature reaches approximately 100 °C, and the test was then terminated. The digital video recorded was uploaded to a computer using Adobe Premier in *.avi files after the completion of each experiment. Specific images of the impingement zone of each pass for each test were extracted by using screen capture. The images were then cropped and sized appropriately in Adobe Photoshop Elements.  4.4 Inverse Heat Conduction Model All temperature and time data were processed using an inverse heat conduction model (IHC) developed by Zhang [30]. The model was developed to calculate surface temperature and heat flux based on a comparison between the model predictions and measurements made by the thermocouples using a finite element method (FEM). This is done essentially in two steps. The first step involves solving the direct solution of the heat conduction differential equation by making an assumption to heat flux and calculating the corresponding temperature. In the second step, the IHC code compares the measured temperature with the calculated temperature. The difference between the two temperature values is used to recalculate the heat flux. This process continues until the difference in measured and calculated temperatures reaches a pre-determined convergence criterion. Previous work [29] had shown that under high surface heat flux conditions the presence of the thermocouple hole can create errors in the calculation of the heat flux at the surface. This is because the thermal conductivity within the hole is lower than the surrounding material and the measured temperature at the tip of the thermocouple is not  37  representative of a similar depth from the surface without a thermocouple. In order to correct for this the thermocouple hole, its thermo-physical properties and geometry must be included in the analysis. As a result a 2-D axisymmetric domain was used for the analysis as shown in Figure 4.7. The assumption of a 2-D axisymmetric analysis is an approximation as there will be some thermal gradients in the material in the theta (0) direction. The domain can be simplified to the domain shown in Figure 4.7 because in the experiments, heat transfer through the thickness of the plate (z-direction) is an order of magnitude greater than the heat transfer through the radial direction (r-direction) of the domain as well as the circumferential (0—direction). One way to verify that this assumption is reasonable is to compare the thermal gradients in these three different directions. Table 4.3 shows the measured thermal gradients for the first pass of test #3 at 0.3 m/s, it is believed that the thermal gradients for this test condition will be the largest. The procedure for determining thermal gradients in the different directions for the justification that a 2-D axisymmetric domain is a reasonable approximation of the heat transfer occurring in the experiments is given in Appendix A.  38  Impinging Surface (S4)  z  1^  L^ r r^140 . 8 14  5.20  Figure 4.7: Domain used for meshing (dimension in mm)  Table 4.3: Thermal gradients in various directions for test #3, first pass  Thermal Gradient (°C/mm)  Direction Through thickness (z-direction) Lateral Longitudinal  84.6 4.1 2.7  The heat flow in the plate can thus be represented by the following differential equation, in cylindrical coordinates.  1a(  kr  ar + a ( k ar^aT  rarr ar i az,z  a z ,^at  (4.1)  Where k is the conductivity of the material, p is the density, Cp is the specific heat capacity, T is the temperature, t is the time, r denotes the radial distance and z is the  39  height. Measured temperature and time data constitute the input to the model. The domain used for the FEM is shown in Figure 4.7. The domain in Figure 4.7 was meshed into discrete linear elements each containing four nodes. 614 nodes were used to generate 559 elements. A denser mesh was used at the impingement surface because it was determined that large temperature gradients through the thickness of the material can occur during cooling. In region A of Figure 4.7, the mesh consisted of elements that were 0.08 mm in width and 0.123 mm in height. This mesh density was used in order to accurately capture the temperature profile for the region just above the thermocouple. In region B, the elements were 0.306 mm in width and the 0.123 mm in height. Mesh density in region B was less than that of region A because it is assumed that most of the heat transfer occurs through the thickness of the sample and therefore the width was increased. In region C the elements were 0.316 mm in width and 0.330 mm in height. This mesh density was chosen because the bulk of the remaining material is quite large and the highest temperature gradients were experienced closer to the surface. The model also incorporates thermo-physical properties of steel taken from the literature for 1008 steel [31]. These properties are shown in Table 4.4. Table 4.4: Thermo h sical properties for 1008 steel f311.  Property  Value  Conductivity: k  60.571-0.03849*T [W/m°C]  Density: p  7800 [kg / m 3 ]  Specific heat: c p  470 [J / kg °C]  40  Boundary conditions were assigned to each of the free surfaces of the domain (see Figure 4.7). For surface S1, located at r = 6 mm and for all values of z from 0 mm to 6.65 mm the boundary equation is given by:  k  aT ar  _  qII  (4.2)  r=6 mm  Because Si is not a true boundary between steel and air, but instead part of a cylindrical domain that was extracted from the plate, the heat transfer through surface Si is purely heat conduction from the thermal mass of the plate and the heat flux is calculated based on Fourier's Law. For surface S2, located at z = 0 mm and for all values of r from 0.8 mm to 6 mm air cooling occurs. Then, the boundary condition involves radiation and convection and is given in by:  k  aT az  = h(T —T.)  (4.3)  z=0 mm  Where T is the ambient temperature (25 °C) and h is the heat transfer coefficient which is comprised of contributions from radiation, h r , and convection, h c i.e. (h=h r +h c). ,  However, because heat transfer through air is much less than radiation at high temperatures, therefore it is assumed that II, is negligible and thus h=hr  .  The radiation heat transfer coefficient is governed by:  hr = o-e(T 2 + T.2 XT +T.)^(4.4) Where a is the Stefan-Boltzman constant and c is the emissivity that is given by the following equation [32].  41  T (^T e =^0.125 ^ 0.38 +1.1^(4.5) 1000^1000^i  For surface S3 (top of hole and along the edge of the hole), a ceramic insulator was inserted into the hole and the conductivity of heat through the ceramic insulator is much smaller than the conductivity of heat within the steel and therefore relative to the steel, heat transfer through this surface is considered negligible and the surface is considered to be adiabatic. Thus no heat transfer occurs when z values are between 5.65 mm and 6.65 mm. Centreline surface is also considered adiabatic for all z values at r = 0.  k  aT ar  = 0^ (4.6) r-=0 mm  The initial condition used for the model is based on the assumption that the entire domain at the start of a test begins at uniform temperature. Prior to running the model, the initial temperature as measured by the thermocouples was assumed as initial temperature for all of the nodes.  Tfr, 4  =0  (4.7)  For surface S4 (impingement surface), at z = 6.65 mm and for values of r from 0 to 6 mm, the heat flux is unknown. The inverse heat conduction model uses the boundary conditions outlined in equations 4.2 — 4.6 and the initial condition given by equation 4.7 to calculate surface heat fluxes and surface temperature.  42  5 Results and Discussion 5.1 Cooling Curves In the present study, twelve single nozzle jet impingement experiments were performed to investigate the effects of heat transfer during cooling of steel in particular at temperatures close the critical heat flux for a range of plate speeds passing under the jet. Typical measured internal temperature and time data acquired from the tests are presented in this chapter. In addition, all acquired temperature and time data, were further processed using an IHC program to calculate surface heat fluxes and temperatures. Representative cooling curves of measured internal temperature versus time are presented in Figure 5.1. The data shown in Figure 5.1 are from a test performed with an initial plate temperature of approximately 600 °C and the speed of the plate was 1.0 m/s. Temperature readings reported in this section are approximately 1.0 mm from the top surface. Two thermocouple locations are displayed in Figure 5.1, 0.0 mm location representing a thermocouple located directly in the stagnation zone under the jet and a thermocouple located 63.5 mm away from the centre of the jet in the width or lateral direction. Figure 5.1 shows a clear trend of the thermal history that one thermocouple exhibits during a test. When the plate passes through the cooling section, an immediate decrease in temperature is experienced in the stagnation zone. After the plate leaves the cooling section, the temperature of the steel at that location begins to rebound due to the thermal mass of the plate. This behaviour represents a "pass" typical to that experienced in industry. Cooling and rebounding continues to occur under the jet until pass 14. After  43  this pass the temperature in the plate has been lowered sufficiently that there is no longer enough thermal mass in the plate to cause a rebound as it leaves the jet. For regions far away from the jet, there is only a slight decrease in temperature during each pass. As shown in Figure 5.1, during the 14 th pass, the thermocouple 63.5 mm away from the stagnation region exhibits similar cooling effects to that under the jet. This is an indication that at this point the wetting front has reached this thermocouple position. Figure 5.1 also shows a gradual build up of a gradient between the two thermocouples. This is shown as a deviation between the two lines as the test goes to completion. This gradient is caused when the plate does not have the chance to come to uniform temperature before the next pass through the cooling section. A gradient will not affect the actual boiling conditions as they are surface temperature dependent. However, it is believed that a gradient will produce a narrower wetted zone and that the progression of the wetting front will be delayed until the region outside the wetted zone cools to lower temperatures.  44  ^ ^  800 ^ 750 700 650 600 550 500 450 -  -  0.0 mm 63.5 mm  P1  P2 • = 115 400 P3 350 -a) P4 • 300 P5 - 250 P6 14 P7 P15 200 P8 P9 P16 P10 150 P17 P11 P2 100 P13 50 0^ ^ 0^100^200^300^400^500^600^700 800  Time (s) Figure 5.1: Measured thermal history for test #9 (plate speed = 1.0 m/s)  Figure 5.2 shows a blow-up for pass 1 of test #9 shown in Figure 5.1. The thermocouple directly under the jet shows a large decrease in temperature relative to the thermocouple located 63.5 mm away. The difference in cooling can be attributed to the differences in the hydrodynamics of the water with the surface of the plate experienced at these two locations. Directly underneath the nozzle in the stagnation zone water is available for cooling, whereas, 63.5 mm away the plate only experiences convection and radiation effects coupled with water splashing from the stagnation zone. These differences in cooling are seen until pass 14 when the water is able to move out radially and wet the 63.5 mm location. During this pass the heat transfer between the stagnation zone and the 63.5 mm position are very similar.  45  — -  640 -  0.0 mm 63.5 mm  620 U N `5 600 Vs  N Q  a) 580 1– 560 -  540 ^ ^ 138.5 139.0^139.5^140.0 140.5  Time (s) Figure 5.2: Measured thermal history during the 1 st pass of test #9  The boiling mode and heat transfer occurring on the surface of the plate is dictated predominately by the surface temperature. Therefore comparisons between thermocouples at similar entry temperatures should be made. Figure 5.3 displays data for the 12 th pass in the stagnation zone under the jet and the 14 th pass for the 63.5 mm position at similar entry temperatures. Entry temperature from herein will refer to the temperature reading provided by the thermocouple just prior to entering the cooling section. For an entry temperature of approximately 215 °C, the water is able to wet both surfaces as it moves out radially from the 0.0 mm location. Figure 5.3 suggests that at an entry temperature of 215 °C, the boiling conditions at the stagnation point and a point 63.5 mm in the lateral direction are similar. The situation presented in Figure 5.3 is associated with nucleate boiling.  46  -  00  0.5  1.0  1.5  0 mm - Pass 12 63.5 mm - Pass 14  2.0  2.5  30  Time (s) Figure 5.3: Measured thermal history during the later cooling stages of test #9  Figure 5.4 shows a comparison of the cooling curves for two different speeds at a location directly under the jet. As expected, cooling of the plate occurs over a shorter period of time and requires less passes for the test conducted at a slower speed (0.3 m/s). Figure 5.4 also shows that the amount of cooling in the early passes (as evidenced by the temperature drop) is much larger for the sample that was run at a slower speed. Cooling at a slower speed is more pronounced during each pass due to the increased time spent underneath the water jet.  47  ^ ^  650 ^ 600 550  2  — —  'ss•  mm - 0.3 m/s 0 mm - 1.0 m/s  500 450  -  E 400 N  •  350  •  300 -  E a)  250  111 sz_  -  -  200 150 H 100 50 0^ 0^100^200^300^400^500^600^700  Time (s) Figure 5.4: Comparison of cooling curves for two different speeds  5.2 Heat Flux Temperature and time data measured during each test was input to an IHC model so that calculations of surface heat flux and surface temperature could be made. Figure 5.5 displays the calculated heat flux histories for test #9, i.e. for the cooling curves shown in Figure 5.1. For the position under the jet, initially the peak in the heat flux is approximately 2.0 MW/m 2 for the first two passes. After the first two passes, the peak heat flux continually increases for the next few passes and reaches a maximum value at the 6 th pass. This is consistent with the heat transfer associated with the different boiling modes moving from film boiling, to transition boiling and reaching the maximum or critical heat flux. Prior to pass 14, the low heat flux values for the 63.5 mm thermocouple location, represents that occurring via natural air convection, radiation and latent heat effects  48  caused by splashing water. During pass 14, a sudden increase in heat flux indicates that the water is finally able to wet this area and as a result there is a significant increase in the heat flux. In fact during this pass the heat flux at the 63 5 mm location is slightly higher than that at the 0.0 mm location. 5.0 ^ -  4.5 4.0  P6  -  P5 N  E  z ▪ (6 U)  3.5  -  P7 P8 P9  P4  3.0  P0 P11  P3  -  P12  2.5 2.0 -  0.0 mm 63.5 mm  P4  P  P13  P2  P15  1.5 P16  1.0 -  P17  0.5 a  0.0 0  100^200^300  400^500  rk.  600^700  800  T ime (s) Figure 5.5: Calculated heat flux history for test #9 — (plate speed: 1.0 m/s, start temperature: 600 °C)  Figure 5.6 illustrates the heat flux curve for the first pass of test #9. This figure shows not only the magnitude of the heat fluxes experienced during this pass but also the distribution of the heat flux from entry to exit at a discrete location. The shape of the curve presented implies that as the water impinges on the surface, cooling begins and the heat flux increases to a maximum value. After the thermocouple leaves the jet, cooling stops and the water evaporates. At a speed of 1.0 m/s, the thermocouple experiences this cooling in a span of less than one second. The shape of the heat flux curves is similar for  49  the position under the jet and that away from the jet. However, the magnitude of the extracted heat is much lower away from the jet. 3.0 ^ -  2.5 -  E  =  0.0 mm 63.5 mm  2.0 -  1.5 -  co a) 1.0 -  0.5 -  0 .0 ^ ^ ^ ^ 1.4 1.6 00^02^0.4^0.6^0.8^1.0^12 1.8^2.0  Time (s) Figure 5.6: Heat flux in first pass of test #9  Figure 5.7 shows the heat flux history experienced during later passes with similar entry temperature where at both locations the water is able to wet the surface of the steel plate. Unlike Figure 5.6, the heat flux history in Figure 5.7 does not have a symmetric shape. After the curves reach a maximum value, there is a slow decrease in heat flux and it is extended out to longer times by displaying a distinct shoulder. This appears to be consistent with pooling of water on the surface of the plate at lower plate temperatures. At these temperatures, there is insufficient heat to cause immediate evaporation. The two locations also show similar maximum heat fluxes which is an indication that water has been able to progress laterally to the 63.5 mm location thermocouple.  50  00  ^  0.2^0.4^0.6^0.8^1.0^1.2  ^  1.4  ^  1.6  ^  1.8  ^  20  Time (s) Figure 5.7: Heat flux in test #9 at a later pass with an entry temperature of —215 °C  One way to analyze and compare heat flux data is to extract the peaks from each pass. This is consistent with the analysis done in previous work [1, 28, 29]. The peak heat flux is the maximum heat flux experienced in a specific pass. Pseudo boiling curves were generated using the peak heat flux in a pass and plotting it against measured entry temperature (see Figure 5.8). Figure 5.8 shows how different the heat extraction is between a location under the jet and one in the lateral direction 63 5 mm away from the jet. The peak heat flux versus entry temperature graph for the thermocouple position under the jet has a similar shape to that of the pool boiling curve (see Figure 2.5). This test shows that the initial peak heat flux for the first pass is approximately 2.0 MW/m 2 at an initial entry temperature of 600 °C. For decreasing temperature, there is a corresponding decrease in peak heat flux towards a minimum value. This is analogous to the film boiling regime in the pool boiling curve. In the film boiling regime, for  51  decreasing temperatures there is a corresponding decrease in heat flux until the minimum heat flux. From the minimum point on Figure 5.8, a decrease in temperature causes an increase in heat flux. This resembles the transition boiling regime where the liquid penetrates through the vapour layer and causes heat flux to increases to a maximum heat flux. From the maximum value of peak heat flux, decrease in temperature causes the peak heat flux values to also decrease. This is analogous to the nucleate boiling regime in the pool boiling curve.  0^100^200^300^400^500  ^  600  ^  700  Entry Temperature (CC) Figure 5.8: Peak heat flux vs. entry temperature for test #9 - plate speed: 1.0 m/s  At the 63.5 mm location the peak heat fluxes are significantly lower than at the 0.0mm location until an entry temperature of —215°C. This is consistent with lower heat extraction via convection, radiation and latent heat effects from water splashes until the water is able to wet this location. A similar trend to this was observed by Jondhale [29].  52  5.3 Energy Extraction While peak heat flux values show interesting trends, variability in test results is quite large as only one data point is being used. Another technique to analyze the data is to integrate the heat flux history for a given pass. Integration of the curve should reduce variability because rather than relying on one data point, integration captures the entire range of data for the thermal history that the thermocouple experiences. In order to perform the integration specific conditions for start and end of the integration were identified. For each pass the integration was initiated when the heat flux reached a value of 0.1 MW/m2 . The value 0.1 MW/m 2 was used because heat extraction by jet impingement will most certainly exceed this value, whereas values less than 0.1 MW/m2 could be noise generated by the inverse heat condition model. The end condition was determined to be the time that is required to move the entire plate through the cooling section. The use of the plate length offers a standard condition for the determination of the time interval for integration. The plate length can be converted to time based on the plate speed. For test #9, the plate length is 1200 mm and the plate speed was 1.0 m/s, therefore the range of time to integrate was 1.2 seconds. Figure 5.9, shows schematically how the integration was performed for a given pass.  53  2.5 — — 2.0 -  Starting Condition: 0.1 MW/m 2  Ending Condition: Plate Length (1200 mm), @ 1.0 m/s — 1.2 sec.  <NE -§  1.5  LL  1.0 -  its a)  0.0 mm 63.5 mm  0.5 -  0. 1 mw/m 2 0.0 138.5^139.0  ^  139.5  ^  140.0^140.5  Time (s) Figure 5.9: Schematic for integration  The integration was performed on for each pass for two different speeds: 0.3 and 1.0 m/s. Figure 5.10 and 5.11 shows the change in the shape of the heat flux curve as the test proceeds to lower entry temperatures for 0.3 and 1.0 m/s respectively. Early in the tests at high entry temperatures, the distribution of the peak is symmetric. The peaks start to deviate from symmetry at lower entry temperature. The peak begins to widen first, followed by the development of a tail in the heat flux curve. It is believed that during this moment, pooling begins to occur on the surface and because the temperature of the steel is low, the water pool does not evaporate instantly but instead stays on the steel plate for extended periods of time.  54  Entry Temperature: 565.3 °C Pass Number: 1  7-  =  2 0  ),  00  1.0^1.5^2.0^2.5^3.0  3.5^4.0^4.5^5 0  Time (s)  8 N  0.5  Entry Temperature: 379.4 'C Pass Number: 3  76 5-  2 -  = 0 00  0.5^1.0^1.5^2.0^2.5^3.0^3.5^4.0^4.5  50  Time (s)  8^  Entry Temperature: 302.7 °C Pass Number: 4  7 6  -  5  -  ti 21 1-  0 00  ^  0.5^1.0^1.5^2.0^2.5^3.0  3.5  4.0  4.5  50  Time (s) Entry Temperature: 214.9 "C Pass Number: 5  7N  E  6 5  4 LI 3 t 2 I  0 0 0^0.5^1.0^1.5^2.0^2.5^3.0^3.5^4.0^4.5^5 0  Time (s)  Figure 5.10: Evolution of the heat flux curves under the jet for test #3  55  3.5 Entry Temperature: 501.5 °C Pass Number: 3  3.0 2.5 2 2.0 x 1.5U1.0'2) 0.5 -  0.0 ^ 00^02^0.4^0.6^0.8^1.0^1.2^1.4^1.6  1.8  20  Time (s) 3.5 Entry Temperature: 215.1 'C Pass Number: 12  3.0 2.5 -  0.5 0.0 00^02^0.4^0.6^0.8^1.0^12^1.4^1.6^1.8^20  Time (s) 3.5 Entry Temperature: 173.5 'C Pass Number: 13  3.0  E  2.5  2 2.0 1.5 LL io 1.0 0.5 0.0 00^02^0.4^0.6^0.8^1.0^1.2^1.4^1.6^1.8^20  Time (s) 3.5 ^ Entry Temperature: 100.4 °C Pass Number: 15  3.0 2.5-  2 2.0 x  1.5 -  LL  16' 1.0 -  0.5 1 0.0 ^ 0 0^0.2^0.4^0.6^0.8^1.0^1.2^1.4  1.6  1.8^20  Time (s)  Figure 5.11: Evolution of the heat flux curve under the jet for test #9  56  1.0  4.4 4.0  0.9 -  3.6 0.8 3.2 0.7 -  2.8 _c 2.4 -2.0^al I- 1.6  0.4 - 1.2 0.3 -  - 0.8  0.2 ^ 0^100  0.4 200^300^400  500  600  Entry Temperature (°C)  Figure 5.12: Quantification of peak width at half maximum and tail width for 0.3 m/s  0  ^  100  ^  200^300^400^500  ^  600  ^  700  Entry Temperature (°C)  Figure 5.13: Quantification of peak width at half maximum and tail width for 1.0 m/s.  57  Figure 5.12 shows the peak width and tail width for the curves from test #3 (0.3 m/s). The width of the peak is determined at half maximum and starts to grow at approximately 450 °C. At this temperature it is believed that with a plate speed of 0.3 m/s, the water jet cools the steel well into the nucleate boiling regime and because the magnitude of cooling is high, the remainder of the bulk material cannot supply heat fast enough to re-heat the region that was cooled. Therefore the effect of cooling seems to extend to longer times as shown Figure 5.10. The tail length is essentially a measure as to how long the water continues to cool the steel plate effectively. This is done in a similar manner to peak width at half maximum, except in measuring tail length; the start of the integration criterion (0.1 MW/m2 ) was used, i.e. the tail time indicates the time elapsed during cooling when the heat flux returns to a value of 0.1 MW/m 2 . For the 0.3 m/s test the tail width is constant at high temperatures up until just under 400 °C entry temperature. Then a rapid increase of tail width is observed. Figure 5.13 is a quantification of the size and shape of all of the heat flux curves for each pass including those shown Figure 5.11 for a test performed at 1.0 m/s. The width of the individual heat flux curves is essentially constant at 0.25 s. until an entry temperature of approximately 250 °C. At 250 °C the width drastically increases, which corresponds to pass 12 in Figure 5.10. Below 200 °C, the widths of the curves again showed a similar tendency to be even except now the curves are wider than at the start of the test, i.e. the width is approximately 0.35 s. This trend is somewhat different than that for 0.3 m/s. Figure 5.12 shows that once the width starts to increase, it does not return to lower values but instead continues to increase.  58  Similar to the evolution of the width for 1.0 m/s, the tail width remains constant until the entry temperature has dropped below 250 °C. Then a rapid increase of the tail width is observed. The largest tail for 1.0 m/s occurred at an entry temperature of 173 °C (pass 13). For lower temperatures, the tail width returns rapidly to its initial value as observed for higher temperatures. While the peak width data between the two speeds shows quite different trends, the tail width has the same trend, except that for 0.3 m/s the magnitude of the tail width is almost double of that for 1.0 mIs Figure 5.14 shows the integrated heat flux as a function of entry temperature for the two locations. Similar trends can be seen to those shown in Figure 5.8 for the two thermocouple locations. In Figure 5.8, the curve for the data underneath the nozzle shows a gradual decrease from the maximum peak heat flux value towards zero peak heat flux. In Figure 5.14, there is a similar maximum integrated heat flux value which occurs at approximately 400 °C, but in this figure, the curve does not gradually decrease to zero integrated heat flux. At an entry temperature of approximately 200 °C, there is a sudden increase in the integrated heat flux. This drastic increase can be attributed to water beginning to pool on the surface. Figures 5.10 to 5.13 clearly show that despite the peak heat flux values are decreasing, it is evident that the width of the peak and the length of the tail section are increasing. Because integration essentially is a measure of the area underneath the heat flux versus time curve, passes that have extended cooling to longer times will have a larger area and hence larger integrated heat flux values. Figure 5.14 also shows that the largest amount of energy extracted does not occur at the same instance as the maximum peak heat flux value.  59  0^100^200^300^400^500  ^  600  ^  700  Entry Temperature ('C) Figure 5.14: Integrated heat flux vs. entry temperature for test 1#9 1.0 m/s -  The data presented up to this point have been for one thermocouple location under the jet as well as one thermocouple position away from the jet. In order to assess heat flux variability across the length of the plate, a comparison was made between the integrated heat flux versus entry temperature for several thermocouples under the jet as well as several thermocouples at a constant position away from the jet. Figure 5.15a, is a schematic showing the thermocouples used for this analysis labelled A, B, C, and D and Figure 5.15b shows the results. Despite the difference in location along the length of the plate, the measured data are very similar in terms of the integrated heat flux indicating that the data is very consistent and that the plate was properly aligned under the nozzle and did not move in the lateral direction.  60  A ^  •  • •  Figure 5.15a: Schematic of thermocouple locations under the jet used for the analysis in Figure 5.15b.  1.50  1.25 N  C  E  2 1.00 x 1.1  a)  0.75 -  a)  V, 0.50 rf a) 0.25 -  0.00 0  ^  100  ^  200^300^400^500  ^  600  ^  700  Entry Temperature (CC) Figure 5.15b: Integrated heat flux versus entry temperature for four different thermocouple locations under the jet. - test #9  61  A similar analysis was conducted for thermocouples 63.5 mm away from the jet in the lateral direction. The thermocouple locations considered are shown in Figure 5.16a and Figure 5.16b shows the integrated heat fluxes for these locations.  Cl  •  ^  •  B C2^ D •  Figure 5.16a: Schematic of thermocouples locations, 63.5 mm from stagnation  62  0^100^200^300^400^500  ^  600  ^  700  Entry Temperature CC)  Figure 5.16b: Integrated heat flux vs. entry temperature, thermocouples 63.5 mm from stagnation — test #9  Figure 5.16b confirms that the thermal history experienced by each thermocouple along the length of the plate is similar. In addition, thermocouple locations C 1 and C2 are equidistance away from the stagnation line on both sides of the plate. Both thermocouples experience the same cooling history highlighting the symmetry in these tests. 5.4 Visual Observations and Contour Maps Calculated surface temperature and heat flux contour maps were also generated based on the IHC analysis developed in the previous section. Using the thermocouple in the centre of the plate (i.e. 0 mm), the minimum surface temperature was first identified for each pass and assigned the coordinates for the centre of the contour map (i.e. 0, 0). 63  All the temperatures for thermocouples lateral from the centre (0 mm — 63.5 mm) were given the corresponding lateral coordinates. Because it was proven in the previous section that the cooling is symmetrical, the same data was applied to the opposite side of centre (i.e. 0 mm — -63.5mm). Data along the length of the plate was determined based on the fact that thermocouples experience the same cooling along the length of the plate. This allows for measurements made on a time scale to be converted to a spatial coordinate on the plate since the plate speed is known. All of the discrete temperature values with corresponding spatial coordinates are then plotted. In generating the contour map, the program performs a linear interpolation between the discrete temperature values. Heat flux contour maps were developed using the same approach as for surface temperature contour maps. Each cooling test that was performed was video taped using a Panasonic miniDV camcorder. Representative images were extracted from the video using Adobe Photoshop. The extracted images provide a visual representation of the water distribution during a pass underneath the cooling section. Figure 5.17 show the calculated surface temperature contour plot and corresponding heat flux contour for test #3 — 0.3 m/s and an approximate plate entry temperature of 600 °C. The corresponding video image of the pass is shown in Figure 5.18.  64  300 250  300  Plate Movement  250  200  200  150  150  100  100  50  50  Plate Movement  E et,  0  -50  I  0 -50  -100  -100  -150  -150  -200  -200  -250  -250  -300  -300 20^40^60^-60 -40 -20^0^20 -60^-40^-20^0 wed-, (mm) Width (mm)  40^60  Figure 5.17: Calculated surface temperature (left) and heat flux contour (right) plot for pass 1 of test #3 (speed: 0.3 m/s, entry temperature: 565 °C)  Figure 5.18: Video image of pass 1, test #3 — 0.3 m/s, entry temperature: 565 °C  The surface temperature plot in Figure 5A7 shows a characteristic shape for moving surface jet impingement where the shape is slightly elongated in the moving direction. There is a distinct region in the middle (blue) where the plate experiences high  65  cooling. This is essentially the single phase forced convection zone describe in Figure 2.6. Mitsutake and Monde mentioned in their research [15] that the region of nucleate boiling in jet impingement was represented by an annulus around the single phase forced convection zone. The surface temperature plot in Figure 5.17 clearly shows a distinct annulus (green) stretched in the direction of plate motion which is assumed to be the nucleate boiling region. Han et al. [25], mentioned that the impinging zone was stretched for their moving experiments. The surface temperature plot in Figure 5.17 also shows that the shape is indeed elongated in the moving direction. The heat flux contour plot in Figure 5.17 shows that in the early passes the maximum heat flux occurs directly in the centre under the jet consistent with the lower temperatures found there. The corresponding image extracted from test #3 also confirms what is shown in Figure 5.17. Figure 5.18 shows that in the stagnation zone under the jet there is a clear wetted region (represented in the image as a dark zone). This occurs because the plate is travelling at slow speed. Slow plate movement through the cooling zone translates to increased time in the cooling section. This causes a larger degree of cooling and with the wetting zone present in Figure 5.18; it is believed that the steel is cooled from originally being in the film boiling regime into the nucleate boiling regime. Figure 5.19 show the calculated surface temperature and heat flux contours for test #9 — 1.0 m/s and an entry temperature of 550 °C. Figure 5.20 shows the corresponding video image for the same pass shown in Figure 5.19.  66  300  300 ^  Plate 250 I Movement  • E  g  250  200  200  150  150  100  100 ▪ E  50 0  50 0  -50  -50  -100  -100  -150  -150  -200  -200  -250  -250  -300 -60^-40^-20^0^20^40^60  -300  Width  (rn)^  Plate Movement  -60 -40 -20^0^20^40^60 Width  (rrrn)  Figure 5.19: Calculated surface temperature (left) and heat flux contour (right) plots for pass 2 of test #9 (speed: 1.0 m/s, entry temperature: 550 °C)  Figure 5.20 Video image of Pass 2 Test #9 — 1.0 m/s. Entry Temperature: 550 °C  67  The surface temperature plot in Figure 5.19 unlike Figure 5.17 does not have a distinct shape outlined by the impinging jet. Also there is no distinct cooled region visible in Figure 5.19. It is believed that the test conditions of test #9 (i.e. 1.0 m/s and 600 °C start temperature) did not cool the steel to temperatures below the film boiling regime inside the stagnation zone. Therefore no distinct wetted zone was visible in Figure 5.20. Because the test was performed at higher speeds, the plate spends less time in the cooling section. There is a slight decrease in temperature, and this can be attributed to latent heat effect at the instant the water impinges onto the surface. For lateral distances away from the stagnation zone the plate is essentially cooled by air convection and radiation. A slight temperature decrease was experienced and it is believed that this is caused by latent heat effects from water that splashed away from the stagnation zone. Figure 5.21 are contour plots for test #3 when the entry plate temperature is approximately 400 °C. The surface temperature contour plot in Figure 5.21 is quite different from what is shown in Figure 5.17 for an earlier pass with an entry temperature of 565 °C. The surface temperature contour plot in Figure 5.17 shows a distinct cooled area in the centre. Now, the boiling conditions have changed and the wetted zone has expanded in the lateral direction. The corresponding heat flux contour shows two distinct maximum spots at the region where the edge of the wetting front is located. The maxima are caused because the wetting front is growing, as it grows, it encompasses steel at higher temperatures. Therefore, it is expected that at the edge of the wetting front higher heat fluxes are observed.  68  300  300 — 250 200  Plate Movement  ▪ ▪ 11111  150  'c 'c  250  433 "C  200  8JC 'C 0)  150  44  o  8 tiv  100  100 E  Plate Movement  50  E  0  0,  50 0  -50  -50  -100  -100  -150  -150  -200  -200  -250  -250  -300 --60  -300 -40 -20  0 Width ( mm)  20  40^60  -60 -40 -20^0^20^40^60 w■cith (mm)  Figure 5.21: Calculated surface temperature (left) and heat flux contour (right) plots for pass 4 of test #3 (speed: 0.3 m/s, entry temperature: 309 °C)  Figure 5.22: Video image of pass 4, test #3 — 0.3 m/s. entry temperature: 309 °C  The video image displayed in figure 5.22 shows a similar trend to that seen in the calculated surface temperature contour maps. Despite a large amount of steam it is clear  69  that there is a wetted zone and the shape is representative of the surface temperature contour plot shown in Figure 5.21 Figure 5.23 are contour plots generated for pass 7 with a plate speed of 1.0 m/s. Figure 5.24 shows the corresponding video image of the same pass. The surface temperature contour plot in Figure 5.23 shows that there is a distinct cooled section in the stagnation zone, unlike for the earlier pass shown in Figure 5.19. At an entry temperature of 350 °C, for this current test condition, the water jet is able to cool the plate to temperatures within the nucleate boiling regime. Figure 5.24 now clearly shows a wetted region, whereas at higher temperatures (Figure 5.20) for the same speed, there was no wetted region on the surface of the plate.  70  300 250  300  Plate Movement  200  E  50  250  11.11 300'C 400 "C  200  MI^C C r5  150 100  am 100 ‘c In 200 :C  150 100  Yr  50  E  E 0  S  g  -50  0 -50  -100  -100  -150  -150  -200  -200 -250  -250 -300  _MEM  -60^-40^-20^0^20^40^60 Mth (mm)  -300 -60 -40 -20^0^20^40^60 width (nrn)  Figure 5.23: Calculated surface temperature (left) and heat flux contour (right) plots for pass 7 of test #9 (speed: 1.0 m/s, entry temperature: 350 °C)  Figure 5.24: Video image of pass 7, test #9 —1.0 m/s. entry temperature: 350 °C  71  5.5 Effect of Plate Speed When considering the effect of speed, only thermocouples located directly under the jet were considered. Peak heat flux values were extracted from each test for one specific test speed and plotted in scatter plots with respect to entry temperature as shown in Figure 5.25 for the location under the jet.  100^200^300^400^500  ^  600  ^  700  Entry Temperature (°C)  Figure 5.25: Peak heat flux vs. entry temperature for all speeds  In Figure 5.25, for 0.3 m/s, it would seem that the trend of peak heat flux is to decrease linearly with decreasing temperature. For 0.3 m/s it is believed that this occurs because the steel experiences such high cooling, that peak heat flux values in all passes are representative of those in nucleate boiling. If the experiments were to begin at a higher entry temperature, the 0.3 m/s trend would be similar to the curves seen for the other speeds.  72  For 0.6 m/s, the tests performed show a similar trend to 0.3 m/s with a linear region between 100 and 400 °C. Above 400 °C the trend for the data points seem to level off. It is believed that at 0.6 m/s the initial passes through the cooling section cools the plate down to a point near the maximum heat flux portion of the boiling curve. For speeds of 1.0 m/s and 1.3 m/s it is clear that the scatter plot generated has similar trends of a typical boiling curve. The first passes of the test cools the plate down to values representative of minimum heat flux values. Between approximately 450 °C and 550 °C, the trend shows increasing peak heat flux values, similar to transition boiling. Between 300 °C and 450 °C the maximum peak heat flux values occur. For temperatures below 300 °C a linear trend of decreasing heat fluxes is observed, which is considered to be representative of nucleate boiling. Figure 5.25 also shows that the maximum peak heat flux values shift to lower entry temperatures with increasing speed. Jondhale [29] made similar observations in his research. For slower speed, more time is spent in the cooling section and therefore more cooling occurs. Because the magnitude of cooling is larger for slow speeds, the ability to cool to the maximum peak heat flux occurs at higher entry temperatures. Whereas tests performed at higher speeds experience less cooling, because the plate spends less time in the cooling section. Therefore, the cooling to the maximum peak heat flux region can only occur at lower entry temperatures.  73  (\i  —  E •  15 ^ 14 13 12 -  0.3 m/s 0.6 m/s 1.0 m/s 1.3 m/s 0 m/s [31] 0.22 m/s [29] 1.0 m/s [29]  to aD,  u -  z 8 EC 7 X  co 6 a) 5  as 4a) o_^3-1 2I0 0  100 200 300 400 500 600 700  800  900  1000  Surface Temperature (°C)  Figure 5.26: Peak heat flux vs. surface temperature - all speeds for comparison  Figure 5.26 shows the peak heat flux as a function of surface temperature for the different speeds. In this representation it appears that regardless of the speed, the maximum value for peak heat flux will occur at a surface temperature of approximately 200 °C. For comparison, Figure 5.26 also provides literature data from previous experiments. Hauksson [31] performed tests with similar flow rate and material for stationary plates. It is quite noticeable now that increasing the speed from stationary plate conditions reduces the value of the peak heat flux. The data from multiple nozzle experiments by Jondhale [29] was taken from thermocouple readings in the stagnation zone of the centre nozzle for tests with the largest investigated nozzle spacing of 114.3 mm. His data followed similar trends to those obtained in this study. The slight differences may be due to secondary effects caused by multiple nozzles. Figure 5.27 shows a plot of integrated heat flux versus surface temperature. This figure is representative of the effective energy extraction. While Figure 5.26 shows the  74  relative occurrence of the boiling conditions, during actual tests, pooling occurs and contributes to the heat extracted. Figure 5.26 showed that the maximum peak heat flux values had a tendency to occur at 200 °C surface temperature. Figure 5.27 shows that the greatest heat extraction occurs at a surface temperature of less than 200 °C.  0  ^  100^200^300^400  ^  500  ^  600  Surface Temperature (°C)  Figure 5.27 Integrated Heat Flux vs. Surface Temperature  As shown in the quantitative analysis of the peak width in section 5.3, the width and shape of the curve for each pass under the cooling section plays a large role in the energy extracted. Early passes for each test show a symmetrically distributed curve. As the speed changes from slow speeds to high speeds, the shape of the curve changes. The heat flux curves for each pass in tests with slow speed have larger peak heat flux values and longer residence times in the cooling section. This translates to taller and wider peaks than those of a higher speed test (see Figure 5.10). Once integrated, the energy extraction is quite large for slow speeds. For higher speeds, the opposite effect occurs. The heat flux curves for each individual pass are narrower and shorter because the plate  75  spends very little time under the cooling section. Integration of this shape of curve shows that there is substantially less cooling for high speeds (see Figure 5.11). For tests performed at slow speeds the deviation in symmetry occurs early in the test (see Figure 5.12). After the second pass the width begins to grow dramatically. For tests performed at higher speeds, the symmetric shape of the heat flux curves will occur until approximately 200 °C entry temperature (see Figure 5.13). This is the region where a significant pooling effect begins and the corresponding heat flux curves now begin to deviate from symmetry. The heat flux curves now show a significant tailing effect that contributes to further heat extraction. Integration will account for the additional energy extraction that occurs when pooling occurs. The additional energy extraction is shown in the curve as a sudden increase towards maximum integrated heat flux values at surface temperatures just below 200 °C. In order to determine the effect of speed on the maximum energy extraction, the maximum integrated heat flux values were plotted as a function of speed in Figure 5.28. This figure shows that the maximum integrated heat flux values decrease with increasing speed. Several attempts were made to determine a numerical correlation between maximum integrated heat flux versus speed, with little success. Based on the data, it seems that it is quite possible that the maximum integrated heat flux varies based on a power function relationship.  76  Speed (m/s) Figure 5.28: Maximum integrated heat flux plotted as a function of plate speed  77  6 Conclusion Single nozzle experiments designed to investigate heat transfer during low coiling temperatures were performed successfully on the pilot scale runout table apparatus located at the University of British Columbia. Twelve tests were performed at varying speeds and initial start temperature. The speeds chosen for this study were: 0.3, 0.6, 1.0 and 1.3 m/s. For each speed, three different initial start temperatures were chosen: 350, 500 and 600 °C. The primary purpose for using three different start temperatures for each speed condition was to obtain a vast amount of data near the maximum heat flux value. The four different speeds were chosen such that the effect of speed on heat transfer can be quantified. The results clearly show cooling is more effective at slower speeds within the stagnation region and for surface temperatures above 200 °C. The corresponding peak heat flux curves also confirm this by showing the higher values of peak heat flux. Visual observations for slow speed tests show a distinct wetted zone early in the test, whereas in higher speed tests, this wetted zone does not exist. It is believed that at low speeds, in the initial stages of the test the velocity of the jet has sufficient time to cool the steel into the nucleate boiling regime which is represented by a distinct wetted zone. At higher speeds there is insufficient time for the water jet to cool the steel below the film boiling regime into the nucleate boiling regime inside the stagnation zone. Therefore no clear wetted zone was seen in the early stages of high speed tests. However heat transfer is still greater than for distances away from the stagnation zone in the lateral direction. It is believed that at higher speeds, in the initial stages of the test, the water jet  78  cools the steel plate partially because the transformation of liquid to vapour and the latent heat vaporization accounts for the difference in heat extraction inside the impingement zone compared to regions away from the impingement zone. As the temperature of the steel reduces, and the water jet can cool the plate beyond the film boiling regime, a noticeable wetted zone appears. Heat transfer outside the stagnation zone above 200 °C surface temperature is believed to be a combination of air convection, radiation and the effect of latent heat of vaporization from liquid converting to vapour from water which splashes away from the impingement zone. As the region outside the stagnation cools and the surface temperature decreases, the wetting front begins to grow radially around the stagnation region. Surrounding regions outside the stagnation zone become encompassed by the wetting front and cause the heat transfer conditions to change from film boiling to nucleate boiling. The maximum peak heat flux values, for each speed, occur at surface temperatures near 200 °C in the stagnation zone. At this surface temperature, nucleate boiling commences. The magnitude of the maximum peak heat flux values changes with changing plate speed. In fact the maximum heat flux value increases with decreasing plate speed. Plate speed governs the time that the plate spends in the cooling section. At slower speeds, the plate incurs a larger decrease in temperature, which translates to higher peak heat flux values, whereas, for higher speeds the opposite occurs. The effective heat extracted can be determined by considering integrated heat fluxes. Despite the largest peak heat fluxes occurring at 200 °C, larger heat extraction takes place at surface temperatures under 200 °C. It is believed that more heat can be  79  extracted when pooling occurs. When pooling occurs, heat continues to be extracted out of the plate well after it leaves the cooling section, producing an asymmetric heat flux curve. A quantitative analysis of the evolution of the heat flux curve under the jet reinforces the fact that tail width of the curve contributes greatly to the increase in heat extraction. Therefore, the most effective heat extraction does not necessarily occur at the largest peak heat flux values. For surface temperatures below 200 °C, the effect of speed is negligible on peak heat flux values. The boiling condition inside the stagnation region is purely nucleate boiling and single phase forced convection. In terms of energy extraction at temperatures well below 200 °C, it seems that heat extraction increases with decreasing speed. In this boiling regime, it is believed that residence time under the cooling section accounts for the difference in energy extraction. The maximum integrated heat flux value was plotted as a function of speed. A quadratic regression was performed on the data. It was determined that the relationship between maximum integrated heat flux and speed can be represented by a simple quadratic equation. To further validate these observations for actual ROT cooling additional studies should be performed. In detail, based on this study following recommendations can be made for future work: 1. Using an additional jetlines in order to quantify the effect of neighbouring jets and to determine the optimal nozzle to nozzle spacing and jetline distance.  80  2. The use of different types of nozzles can enhance heat transfer and uniformity of cooling. 3. Quantify the effect of speed on heat flux values beyond 1.3 m/s.  81  References 1.  Prodanovic V., Fraser D., Militzer M., Simulation of Runout Table Cooling by Water Jet Impingement on Moving Plates - A Novel Experimental Method. in 2nd International Conference on Thermomechanical Processing of Steel., p. 25-32, ed. M. Lamberights, Belgium, July 2004.  2.  Liu Z.H., Wang J., Study on Film Boiling Heat Transfer for Water Jet Impinging on High Temperature Flat Plate. International Journal of Heat and Mass Transfer, 2001. 44: p. 2475-2481.  3.  Militzer M., Hawbolt E.B., Meadowcroft T.R., Microstructural Model for Hot Strip Rolling of High-Strength-Low-Alloy Steels. Metallurgical and Materials Transactions A, 2000. 31A: p. 1247-1259.  4.  Wolf D.H., Incropera F.P., Viskanta R., Jet Impingement Boiling. Advances in Heat Transfer, 1993. 23: p. 1-131.  5.  Kalinin E.K., Berlin LI., Kostyuk V.V., Transition Boiling Heat Transfer. Advances in Heat Transfer, 1987. 18: p. 241-323.  6.  Kalinin E.K., Berlin LI., Kostyuk V.V., Film-Boiling Heat Transfer. Advances in Heat Transfer, 1975. 11: p. 51-197.  7.^Chester, N., A Study of Boiling Heat Transfer on a Hot Steel Plate Cooled by an Inclined Circular Bottom Water Jet, MA.Sc. Thesis. 2006, University of British Columbia, Vancouver.  82  8.  Liu, Z.D., Experiments and Mathematical Modelling of Controlled Runout Table Cooling in a Hot Rolling Mill, Ph.D. Thesis. 2001, University of British  Columbia, Vancouver. 9.  Tacke G., Litzke H., Raquet E., Investigations into the Efficiency of Cooling Systems for Wide-Strip Hot Rolling Mills and Computer Aided Control of Strip Cooling. in Accelerated Cooling of Steel., p. 35-54, Pittsburgh, Pennsylvania.  10.  Kohring F.C., WATERWALL Water-Cooling Systems. Iron and Steel Engineer, 1985. 62(6): p. 30-36.  11.  Zumbrunnen D.A., Viskanta R., Incropera F.P., The Effect of Surface Motion on Forced Convection Film Boiling Heat Transfer. Journal of Heat Transfer, 1989.  111: p. 760-766. 12.  Chen S.J., Tseng A.A., Spray and Jet Cooling in Steel Rolling. International Journal of Heat and Fluid Flow, 1992. 13(4): p. 358-369.  13.  Robidou H., Auracher H., Gardin P. , Lebouche M., Controlled Cooling of a Hot Plate with a Water Jet. Experimental Thermal and Fluid Science, 2002. 26: p.  123-129. 14.  Wolf D.H., Incropera F.P., Viskanta R., Local Jet Impingement Boiling Heat Transfer. International Journal of Heat and Mass Transfer, 1996. 39(7): p. 1395-  1406. 15.  Mitsutake Y., Monde M., Heat Transfer During Transient Cooling of High Temperature Surface with an Impinging Jet. Heat and Mass Transfer, 2001. 37: p.  321-328.  83  16.  Liu Z.H., Zhu Q.Z., Prediction of Critical Heat Flux for Convective Boiling of Saturated Water Jet Impingement on the Stagnation Zone. Journal of Heat Transfer, 2002. 124: p. 1125-1130.  17.  Monde M., Mitsutake Y., Critical Heat Flux in Forced Convective Subcooled Boiling with Multiple Impinging Jets. Journal of Heat Transfer, 1996. 117: p. 241243.  18.  Mitsutake Y., Monde M., Ultra High Critical Hat Flux During Forced Flow Boiling Heat Transfer with an Impinging Jet. Journal of Heat Transfer, 2003. 125: p. 1038-1045.  19.  Liu Z.H., Tong T.F., Qiu Y.H., Critical Heat Flux of Steady Boiling for Subcooled Water Jet Impingement on the Flat Stagnation Zone. Journal of Heat Transfer, 2004. 126: p. 179-183.  20.  Pan C., Hwang J.Y., Lin T.L., The Mechanism of Heat Transfer in Transition Boiling International Journal of Heat and Mass Transfer, 1989. 32(7): p. 13371349.  21.  Hammad J., Mitsutake Y., Monde M., Movement of Maximum Heat Flux and Wetting Front During Quenching of Hot Cylindrical Blocks. International Journal of Thermal Science, 2004. 43: p. 743-752.  22.  Ishigai S., N.S., Ochi T. Boiling Heat Transfer for a Plane Water Jet Impinging on a Hot Surface. in Proceedings of the 6th International Heat Transfer Conference., p. 445-450, Hemisphere, Toronto, Canada, 1978.  23.  Liu Z.H., Prediction of Minimum Heat Flux for Water Jet Boiling on a Hot Plate. Journal of Thermophysics and Heat Transfer, 2003. 17(2): p. 159-165.  84  24.  Robidou H., Auracher H., Gardin P., Lebouche M., Bogdanic L., Local Heat Transfer from a Hot Plate to a Water Jet. Heat and Mass Transfer, 2003. 39: p. 861-867.  25.  Han F., Chen S.J., Chang C.C., The Effect of Surface Motion on Liquid Jet Impingement Heat Transfer. American Society of Mechanical Engineers - Heat Transfer Division, 1991. 180: p. 73-81.  26.  Chen S.J., Kothari J., Tseng A.A., Cooling of a Moving Plate with an Impinging Circular Water Jet. Experimental Thermal and Fluid Science, 1991(4): p. 343353.  27.  Zumbrunnen D.A., Incropera F.P., Viskanta R., Method and Apparatus for Measuring Heat Transfer Distributions on Moving and Stationary Plates Cooled by a Planar Liquid Jet. Experimental Thermal and Fluid Science, 1990. 3(2): p. 202-213.  28.  Prodanovic V., Militzer M., Runout Table Cooling Simulation for Advanced Linepipe Steels. in Pipeline for the 21st Century - The Metallurgical Society of CIM. 2005. p. 127-142, Montreal,Canada.  29.  Jondhale, K., Heat Transfer During Multiple Jet Impingement on the Top Surface of Hot Rolled Steel Strip, MA.Sc. Thesis. 2007, University of British Columbia, Vancouver.  30.^Zhang, P., Study of Boiling Heat Transfer on a Stationary Downward Facing Hot Steel Plate Cooled by a Circular Waterjet, MA.Sc Thesis. 2004, University of British Columbia, Vancouver.  85  31.  Hauksson A., Experimental Study of Boiling Heat Transfer During Water Jet Impingement on a Hot Steel Plate, MA.Sc. Thesis. 2001, University of British Columbia, Vancouver.  32.  Serendinski F., Prediction of Plate Cooling During Rolling-Mill Operation. Journal of Iron Steel Institute, 1973,211, p.197-203.  86  Appendix A — Validation of 2-D Axisvmmetric Assumptions In order to validate the assumption that heat transfer is primarily through the thickness of the steel plate, temperature measurements from specific thermocouple locations were compared for the first pass of test #3. Figure A-1 shows the thermal history of the first pass for thermocouples located on the centreline of the plate, used in the calculation of the thermal gradient in the longitudinal direction. The thermocouple labelled 'B' experiences cooling first, followed by 'C'. The two thermocouples are 31.8 mm apart.  600 -  550 -  0.0 mm - B 0.0 mm - C  500450 -40 350 300 250 200 56.0  1^f 56.5^57.0  57.5  58.0  Time (s) Figure A-3: Thermal history of two thermocouples along the centreline of the plate  87  650 600 550 -  0  500 -  a)  iv E a)  450 400 -  I350 300 250 56.0  56.5  57.0  57.5  58.0  Time (s) Figure A-4: Thermal history of thermocouples in the lateral direction  Figure A-2 shows the thermal history for thermocouples in the lateral direction for the first pass of test #3. Test #3 was chosen because at a speed of 0.3 m/s, it is believed that the thermal gradients would be the largest. The first step in justification was to determine when the minimum calculated surface temperature occurred for the 0.0 mm thermocouple. This value was subtracted from the measured temperature at thermocouple, 1 mm below the surface at the same instant. The resulting calculation shows that the temperature gradient through the thickness is 84.6 °C/mm.  (328.5 - 243.86) 1  = 84.6 "C \  (A-1)  For the validation of the lateral and longitudinal directions, measured temperature values for the nearest adjacent thermocouples, at the same instant that the minimum 88  surface temperature occurred under the jet, were considered. The closest thermocouples in the lateral and longitudinal direction were 31.8 mm away from the point of interest. Similar to the calculation for determining the temperature gradient in the thickness, the difference of the measured temperatures was divided by the distance. The temperature gradient is therefore calculated for the lateral and longitudinal directions to be 4.1 and 2.7 °C/mm, respectively.  (458.3 - 328.5) 31.8  = 4.1  (328.5 - 242.4) = 2.7 31.8  ( °C \ mmj i  °C  \mm)  (A-2)  (A-3)  89  Appendix B — Validation of Symmetric Cooling It is believed the shape of the nozzle and the wetted zone that is produced should provide symmetric cooling across the centreline of the plate. Great care was taken during the setup of the experiment to ensure that the nozzle was aligned such that the water impinged directly on the centreline of the plate. If the cooling was truly symmetric, then the degree of cooling experienced by the two thermocouples located equidistance away from the centreline on either side of the plate should be similar. The following figures show the thermal history for two thermocouple locations equidistant from the centreline of the plate. Figure B-1 shows the thermal history for the first pass of test #9. Figure B-2 shows the thermal history for the 14 th pass of the same test.  620 -  E ) 610 -.  63.5 mm 63.5 mm  -  2 CD  a)  E F- 600 -  590 138.5  ^  139.0^139.5^140.0^140.5  Time (s) Figure B-1: Thermal history for two thermocouples equidistant from centreline on opposite sides of the plate - pass 1  90  Appendix B — Validation of Symmetric Cooling It is believed the shape of the nozzle and the wetted zone that is produced should provide symmetric cooling across the centreline of the plate. Great care was taken during the setup of the experiment to ensure that the nozzle was aligned such that the water impinged directly on the centreline of the plate. If the cooling was truly symmetric, then the degree of cooling experienced by the two thermocouples located equidistance away from the centreline on either side of the plate should be similar. The following figures show the thermal history for two thermocouple locations equidistant from the centreline of the plate. Figure B-1 shows the thermal history for the first pass of test #9. Figure B-2 shows the thermal history for the 14 th pass of the same test.  620 — —  -63.5 mm 63.5 mm  '6` 610 L.  co a)  E H  1— 600 -  590 ■ ^ 139.0^139.5^140.0^140.5 138.5  Time (s) Figure B-1: Thermal history for two thermocouples equidistant from centreline on opposite sides of the plate — pass 1  90  606  ^  607  ^  608  ^  609  ^  610  Time (s) Figure B-2: Thermal history for two thermocouples equidistant from centreline on opposite sides of the plate — pass 14  Figure B-1 shows that despite the two thermocouples having different temperature, the effect of cooling from the nozzle is quite similar. Figure B-2 shows that after the experiment has progressed to the 14 th pass, the temperature reading of the thermocouple was similar and the amount of cooling between the two different thermocouples was still the same. Table B-1 is a summary of the minimum temperature values experienced by the same two thermocouples for each pass of the experiment. The largest variance between the two thermocouples was 16.7 °C during pass 13. Contour maps of the impingement surface were produced under the assumption that cooling was symmetric across the centreline of the plate. Table B-1 confirms the validity of that assumption.  91  Table B-2: Measured temperature values from thermocouples, equidistant from the centreline  Pass 1 2 3 4 5 6 7 8 9 10 11  12 13 14 15 16 17  -63.5 mm 598.1 546.8 504.6 466.5 434.7 406.5 381.4 357.4 334.1 314.1 288.4 263.8 223.8 148.2 126.2 99.7 84.1  63.5 mm 603.5 547.2 505.4 466.2 435.1 408.1 383.7 358.9 337.7 316.1 287.9 258.3 240.5 143.6 122.5 100.7 86.1  92  

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