Applied Science, Faculty of
Mechanical Engineering, Department of
DSpace
UBCV
Alakbari, Abdullah Al
Master of Applied Science - MASc
University of British Columbia
cooling process on a run-out table is a critical step that governs the final microstructure and the mechanical properties of the produced steels. In this research, we use a more recent method for obtaining the thermal history on the plate surface, which is the infrared thermal imaging technique. This technique has the advantage of capturing the surface temperature history remotely and with no contact with the plate. In this work, controlled cooling experiments under transient conditions were conducted on a hot stationary plate using an impinging top circular nozzle and a thermal camera to capture the temperature history. The measurements from the thermal camera (conducted in Abu Dhabi University) are compared with the conventional thermocouple measurements (University of British Columbia). The comparisons showed that the infrared camera gives more complete picture of the thermal history and more accurate results than thermocouple measurements. Reasons for the inaccuracy of the thermocouple (T/C) measurements include T/C response time, and distortion of the thermal field by the method of installation. These reasons are discussed in detail in the thesis. Additionally, we introduce a transient multiphase CFD numerical simulation to obtain the temperature profile on the plate surface and compare it with the experiments conducted. The numerical simulation was done using the Ansys-Fluent CFD software. A two-dimensional model was used with a highly intensive mesh near the wall region based on the wall y+ number. The surface temperature graphs for both measurements and simulation are compared at different radial locations (stagnation zone and parallel zone). Additionally, the obtained CFD results were verified and compared with the surface temperature of the experimental data.
Water Jet Impingement in Run-Out Table Cooling by Abdullah Al Akbari B.Sc., Abu Dhabi University, UAE, 2016 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2023 © Abdullah Al Akbari, 2023 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Water Jet Impingement in Run-Out Table Cooling submitted by Abdullah Al Akbari in partial fulfilment of the requirements for the degree of Master of Applied Science in Mechanical Engineering Examining Committee: Dr. Mohamed Gadala, Professor, Mechanical Engineering, UBC Co-supervisor Dr. Dana Grecov, Professor, Mechanical Engineering, UBC Co-supervisor Dr. Xiaoliang Jin, Associate Professor, Mechanical Engineering, UBC Supervisory Committee Member Dr. Nima Atabaki, Associate Professor of Teaching, Mechanical Engineering, UBC Additional Examiner iii Abstract The cooling process on a run-out table is a critical step that governs the final microstructure and the mechanical properties of the produced steels. In this research, we use a more recent method for obtaining the thermal history on the plate surface, which is the infrared thermal imaging technique. This technique has the advantage of capturing the surface temperature history remotely and with no contact with the plate. In this work, controlled cooling experiments under transient conditions were conducted on a hot stationary plate using an impinging top circular nozzle and a thermal camera to capture the temperature history. The measurements from the thermal camera (conducted in Abu Dhabi University) are compared with the conventional thermocouple measurements (University of British Columbia). The comparisons showed that the infrared camera gives more complete picture of the thermal history and more accurate results than thermocouple measurements. Reasons for the inaccuracy of the thermocouple (T/C) measurements include T/C response time, and distortion of the thermal field by the method of installation. These reasons are discussed in detail in the thesis. Additionally, we introduce a transient multiphase CFD numerical simulation to obtain the temperature profile on the plate surface and compare it with the experiments conducted. The numerical simulation was done using the Ansys-Fluent CFD software. A two-dimensional model was used with a highly intensive mesh near the wall region based on the wall y+ number. The surface temperature graphs for both measurements and simulation are compared at different radial locations (stagnation zone and parallel zone). Additionally, the obtained CFD results were verified and compared with the surface temperature of the experimental data. iv Lay Summary The steel is manufactured into thin sheets using a process known as run-out table (ROT) cooling. In ROT cooling, water jets are used to control the temperature of the steel sheets. Tracking the temperature of the steel is very important in ensuring that the final product has the desired properties. In this research, we are exploring a new method of measuring the surface temperature using an infrared thermal camera and comparing it with conventional methods. We observed that the infrared managed to capture the change in temperature more accurately because of the high sensitivity and low response time. Additionally, we performed a numerical simulation and compared it with a thermal camera. The results showed a good agreement, demonstrating the accuracy of the infrared methods. Based on our results, the infrared method has the ability to allow proper temperature measurement in industrial processes. v Preface This thesis is an original, unpublished, independent work by the author, Abdullah Al Akbari. vi Table of Contents Abstract .......................................................................................................................................... iii Lay Summary ................................................................................................................................. iv Preface............................................................................................................................................. v Table of Contents ........................................................................................................................... vi List of Tables ............................................................................................................................... viii List of Figures ................................................................................................................................ ix List of Symbols ............................................................................................................................... x List of Abbreviations ..................................................................................................................... xi Acknowledgments......................................................................................................................... xii Dedication .................................................................................................................................... xiii Chapter 1: Literature Review and Research Objective ................................................................... 1 1.1 Introduction ...................................................................................................................... 1 1.2 Background and Literature Review:................................................................................. 3 1.2.1 General Overview ..................................................................................................... 3 1.2.2 Jet Impingement Hydrodynamics ............................................................................. 5 1.2.3 Pool Boiling Heat Transfer ....................................................................................... 9 1.3 Review of Temperature Measurement Methods ............................................................ 17 1.3.1 Using Thermocouples ............................................................................................. 17 1.3.2 Infrared Thermal Cameras ...................................................................................... 20 1.4 Research objectives ........................................................................................................ 23 Chapter 2: Experimental setup ...................................................................................................... 25 2.1 UBC Industrial Scale Run-Out Table Facility ............................................................... 25 2.2 ADU Pilot Scale ROT Facility ....................................................................................... 27 Chapter 3: Formulation of the Computational Fluid Dynamics (CFD) Problem ......................... 31 3.1 Various Formulation Methods........................................................................................ 31 3.2 Law of the Wall .............................................................................................................. 36 3.3 Governing Equation for Multiphase Modeling .............................................................. 38 i) Continuity Equation. ............................................................................................... 39 ii) Momentum Equation............................................................................................... 39 iii) Energy Equation...................................................................................................... 40 vii 3.4 Turbulence Model .......................................................................................................... 42 Chapter 4: CFD Model, Results and Discussion........................................................................... 46 4.1 Model Description .......................................................................................................... 46 4.2 Model Parameters and Boundary Condition .................................................................. 48 4.3 Model verification .......................................................................................................... 50 4.4 Cooling Curve Results.................................................................................................... 52 Chapter 5: Conclusion................................................................................................................... 58 5.1 Recommendation and future work: ................................................................................ 59 6. References ............................................................................................................................. 60 viii List of Tables Table 4-1 Properties of the materials used in the model. .............................................................. 49 Table 4-2 Model Parameters and Boundary Conditions ............................................................... 49 ix List of Figures Figure 1-1 Run-out Table Cooling Systems (a) laminar cooling (b) curtain cooling (c) spray cooling [4]. ...................................................................................................................................... 2 Figure 1-2 Schematic of hot rolling mill of steel plate. The schematic shows the variation of temperature vs time and its effect on the phase transformation of austenite decomposition. A: austenite, F: ferrite, P: pearlite, B: bainite, M: martensite [4]. ....................................................... 4 Figure 1-3 Different configurations of jet impingement; modified from [8].................................. 6 Figure 1-4 Pressure, velocity profile, and flow regions for a circular jet with a uniform velocity profile [8] ........................................................................................................................................ 7 Figure 1-5 Schematic of free surface jet impingement and profile of liquid velocity parallel to the surface: (a) planar jets, (b) circular jets [4]. .................................................................................... 8 Figure 1-6 Boiling regimes at jet impingement surface; modified from [11]................................ 9 Figure 1-7 Schematic of pool boiling [8] ...................................................................................... 10 Figure 1-8 Boiling curve for a free surface jet at stagnation point, 19mm, and 44mm away from stagnation [14]............................................................................................................................... 12 Figure 1-9 Installation of thermocouples [23] .............................................................................. 18 Figure 1-10 Different measuring junctions for thermocouples [24]. ............................................ 19 Figure 1-11 Schematic of spot welded embedded thermocouple [4]............................................ 19 Figure 1-12 Various spectral bands of electromagnetic waves [26] ............................................. 21 Figure 2-1 Schematic of thermocouple locations with respect of the water jet for stationary plate experiments[4]. ............................................................................................................................. 26 Figure 2-2 Schematic of pilot scale run-out table facility [4]. ...................................................... 26 Figure 2-3 Schematic diagram for the Run-out Table Facility. .................................................... 29 Figure 2-4 Photograph of the furnace and ROT facility of ADU. ................................................ 29 Figure 2-5 Moving mechanism: (a) Hydraulic Unit. (b) Conveyor-chain system. (c) Test bed... 30 Figure 3-1 Sublayers for Turbulent boundary layer [65] .............................................................. 37 Figure 4-1 The modeled mesh with the applied boundary conditions. ......................................... 47 Figure 4-2 Comparison between experimental and simulation temperature history for different zones at the top plate surface using 0.5 m/s jet velocity ( 𝑇 = 25 𝑜𝐶). (a) stagnation region 0mm, and 15mm, and (b) parallel flow region 50mm, and 85mm. .............................................. 51 Figure 4-3 The free stream radial velocity along the plate for different elapsed times ................ 52 Figure 4-4 Temperature history comparison between Thermocouple (Nobari et al. [4]) and Infrared camera at stagnation. ....................................................................................................... 56 Figure 4-5 Temperature history comparison between Thermocouple (Nobari et al. [4]) and Infrared camera for 60mm away from stagnation point. .............................................................. 57 Figure 4-6 Temperature history comparison between Thermocouple (Nobari et al. [4]) and Infrared camera for 120mm away from stagnation point. ............................................................ 57 x List of Symbols 𝑐𝑝 Specific heat at constant pressure (J/kg. K) 𝐶𝑓 Friction coefficient d Nozzle diameter (m) 𝐸 Energy (J) ℎ Heat transfer coefficient (W/𝑚2.K) 𝑔 Gravity acceleration (m/𝑠2) 𝑘 Thermal conductivity (W/m.K) K Thermal conductivity vector (W/m.K) 𝐿 Length of the plate (m) 𝑃 Pressure vector (Pa) 𝑟 Radial location from the stagnation point(m) 𝑅𝑒 Reynolds number 𝑡 Time (s) 𝑇𝑤 Temperature of the water (℃) 𝑇𝑙 Temperature of the liquid (℃) 𝑇𝑣 Temperature of the vapor (℃) 𝑇𝑠𝑎𝑡 Saturation Temperature 𝑢 Local radial velocity along the plate (m/s) 𝑢𝜏 Friction velocity or shear velocity (m/s) 𝑢+ Non-dimensional radial velocity 𝑈 Velocity vector or free stream radial velocity (m/s) 𝑦 Height from the wall (m) 𝑦+ Non-dimensional height from the wall 𝜌 Density (kg/m3) 𝜐 Kinematic viscosity (m2/s) 𝜇 Dynamic viscosity (N.s/m2) α𝑖 Volume fraction of each phase 𝜏𝑤 Wall shear stress (Pa) κ Von-Karman’s constant ɸ Viscus Dissipation 𝑞 Heat flux (𝑊/𝑚2) ?⃗? Velocity vector (m/s) ?̇? Mass Flow rate (Kg/s) ?̅? Mean Velocity (m/s) ?̀? Fluctuation Velocity (m/s) xj Coordinate direction (m) δij Kronecker delta xi List of Abbreviations ADU Abu Dhabi University AHSS Advanced High Strength Steel AMPEL Advanced Materials and Process Engineering Laboratory CFD Computational Fluid Dynamics CHF Critical heat flux DNS Direct numerical simulation FSP Field Synergy Principle HSLA High Strength Low Alloy LES Large Eddy Simulation RANS Reynold-Averaged Navier-Stokes RHS Right Hand Side RNG Re-Normalisation Group ROT Run Out Table RTD Resistance Temperature Detectors SST Shear-Stress Transport UBC University of British Columbia VOF Volume of Fluid Method xii Acknowledgments I would like to express my deepest gratitude to all those who have helped and supported me throughout the journey of completing this thesis. First and foremost, I am immensely grateful to my advisors, Dr. Mohamed S. Gadala and Dr. Dana Grecov for providing me with valuable guidance and mentorship throughout the research process. Your patience, knowledge, and encouragement have been instrumental in shaping the direction and quality of this work. I would also like to thank my family and friends for their unwavering support and encouragement. Your belief in me and my abilities has been a constant source of inspiration, and I could not have made it this far without your love and support. xiii Dedication I would like to dedicate this thesis to my parents and my wife. Thank you very much for everything. Words cannot express my gratitude and appreciation for you. 1 Chapter 1: Literature Review and Research Objective 1.1 Introduction In the past few years there have been a rapid development in the industry of Advanced High Strength Steel (AHSS). The production of steel worldwide increased to 174.4 million metric tons in May 2021, which is a 16.5% increase compared to 2020 [1]. The most commonly methods of manufacturing steel plated is hot rolling, and then cooling on runout tables. The steel strips are widely used in many industries including automotive, construction, and manufacturing industries. Thus, the quality of these hot rolled steel strips are of a top priority in several industries and the progress of AHSS plays a major role in the field of sustainable engineering solutions. For instance, novel steel can efficiently contribute to improving the fuel consumption efficiency by decreasing the overall weight of the vehicle. In many industries, there is a pressing demand for producing steel with desirable mechanical properties such as strength, toughness, formability, and metallurgical properties such as microstructure and hardness. Hence, less material, or thinner gauge sheets are being used while maintaining the desired requirements in the specific industry. Energy industry is one of the most beneficial of the development of AHSS; pipelines in oil and gas industry require such specification that allow higher pressure with larger diameter by utilizing hot rolled AHSS steel. This will help reducing the number of pumping station used and the operation cost. Another example of AHSS is Dual phase (DP) steel with microstructures consisting of martensite islands coupled by ferrite matrix. Hot rolling process in Run Out Table (ROT) commences with a continuous casting facility followed by cooling process and coiler at the final step. First, the hot strips pass through a rolling machine that feeds the strip, which is then immediately carried to the ROT to be cooled. Conventionally, the finishing hot rolling temperature before cooling is between 800ºC to 950ºC 2 and giving the strip thickness and steel grade the coiling temperature is typically between 500ºC to 750ºC [2]. Two factors play a vital role in managing the steel properties are the coiling temperature and the cooling rate. Consequently, the accurate control of strip temperature and the cooling path is experienced by the efficient cooling technique on ROT to acquire desirable properties of AHSS. There are three mainly cooling methods used on ROT which are laminar cooling, curtain cooling, and spray cooling as seen in Figure 1-1. In laminar cooling, the water poured from a circular nozzle creates a round area of locally high cooling rate because of the high contact time between the hot surface and the water. Then, the water jet penetrates the layer of vapor over the surface due to impact pressure, resulting in nonuniform heat transfer over the plate. In the water curtain, the water is flowing from a large nozzle as a sheet of fluid and a line of cooling is obtained through the entire width which enhances the uniformity of cooling [3]. In spray cooling, the water issue as rain like behavior which covers relatively large area because of the addition of air. The drawback of this method is the low heat removal ability and the high maintenance cost. Commonly, the upper surface is mainly cooled via the impingement of water sheets, whereas the bottom surface is cooled by water sprays or jets. Figure 1-1, shows the three cooling methods described above. Figure 1-1 Run-out Table Cooling Systems (a) laminar cooling (b) curtain cooling (c) spray cooling [4]. 3 It is significant to understand the influence of several ROT parameters on boiling heat transfer. Since experimenting on industrial ROT is expensive and not always feasible, many researchers have resorted to perform tests on a bench scale apparatus to evaluate the heat transfer condition. In order for experiments to be a realistic representative for industrial application, it is important to carry out a thorough investigation on a setup that is close to the industrial runout tables. Thus, the research group at the University of British Columbia has developed a pilot scale apparatus of ROT with parameters similar to those used in industry. The apparatus is located in the Advanced Materials and Process Engineering Laboratory (AMPEL). The ROT facility is equipped with a furnace that can heat up the steel plates up to 1000 ºC, and then the plate will be accelerated to speeds up to 3.0 m/s through a conveyer. Due to the versatile design of the ROT, it can accommodate close simulation of industrial conditions. In addition, Abu Dhabi University (ADU) researchers have built a pilot scale ROT apparatus that is very similar to the UBC equipment with the main difference in introducing infrared thermal camera for temperature measurement. 1.2 Background and Literature Review: 1.2.1 General Overview During the quenching process of steel, the cooling process on the runout table plays a crucial role in defining the mechanical properties of steel. The temperature of steel ranges from 800 – 900 °C after leaving the finishing mills. Then, steel enters the ROT for controlled cooling process in which it will acquire desirable microstructure and mechanical properties [5][6]. There are several ways of extracting heat from the steel which are laminar cooling, curtain cooling, and spray cooling. Each technique provides different cooling condition, and, in general, there is no established setup for the cooling process. Based on industrial needs, each ROT is designed 4 according to specific requirement such as space requirements, types of steel produced and gauge thickness. The most used fluid in cooling is water since it is readily available, easy to handle, has an ability to extract high amount of heat from hot objects. In the ROT cooling, the surface of the plate is extremely hot comparing to the boiling temperature of water indicating the occurrence of phase change for water from liquid to gas. The subject of boiling heat transfer in ROT has been extensively covered in the literature for steady state condition [7][8], however, the boiling conditions in ROT are extremely transient. Based on the research conducted in steady state boiling heat transfer, a foundation layer of concepts may be applied to the transient condition. Figure 1-2 Schematic of hot rolling mill of steel plate. The schematic shows the variation of temperature vs time and its effect on the phase transformation of austenite decomposition. A: austenite, F: ferrite, P: pearlite, B: bainite, M: martensite [4]. 5 The ROT length ranges between 100 m to 200 m and a height of nine meter. Typical ROT comprises of motorized rollers that carry the steel product along its length, in the range of the table there will be banks of headers that are placed above and below the table. The water is collected through the headers to provide an even flow distribution. After that, the water will be deposited on the steel via either nozzle, curtain, or spray. The difference between top and bottom deposition is that the moving force of the above is gravity, whereas at the bottom, the water must be pumped to overcome the effects of gravity. Numerous studies have been conducted to determine the best method to extract heat from the steel. In the studies of Tacke et al. [9] and Kohring et al. [10] they determined that the best methods for heat extraction are laminar and curtain. They based their observation according to the amount of liquid deposited onto the surface; the more water impinges at the surface the more heat extracted. Additional studies conducted by Zumbrunnen et al. [11] and Chen et al. [12] argue that curtain method is able to cool steel across the width uniformly. In industry, laminar flow jets have higher momentum than curtain. The increase in water momentum, translates to a more efficient heat transfer. The high momentum of water in the laminar method penetrates the vapor film, resulting in an increase contact between the liquid and steel. 1.2.2 Jet Impingement Hydrodynamics The most popular jet configuration are: free surface, plunging, submerged, confined, and wall as shown schematically in Figure 1-3. For Run-out table with circular nozzle, the configurations of free surface and plunging jet are applied. 6 Figure 1-3 Different configurations of jet impingement; modified from [8]. In a free surface jet, the liquid exits the nozzle and penetrate the gas phase which has minimal restriction on the motion of the liquid. After that water impinges on the surface, and the liquid moves radially away from the impingement zone. Such a situation in run-out tables occur at the beginning of each nozzle when no water has accumulated on the surface of the steel. The plunging condition occur when there is an excessive water accumulation on the surface during the impingement. In this case, the water liquid should penetrate and displace the already existing liquid prior to impinging the surface. This scenario is different than that of free surface due to the liquid not moving freely away from the impingement point with a given velocity. As time progresses the 7 height of liquid increases on the surface, meaning that the effect of impinging decreases. Many industries use several configurations to remove the excess liquid to minimize pooling. Figure 1-4 demonstrates the pressure and velocity as a function of distance for free surface. In the figure, the region ‘A’ is known as the stagnation region. During this region, the pressure reaches its maximum value which is produced from the liquid leaving the nozzle. Region ‘B’ is known as acceleration region (0.5 ≤ 𝑋/𝑑𝑗 ≤ 2) in which the water tries to escape from the high-pressured area to lower pressure. During this region, the liquid reaches a velocity that is similar to that when the liquid leaving the nozzle. Region ‘C’ is known as parallel flow region when 𝑋/𝑑 is greater than 2 in which the flow is parallel to the surface. Figure 1-4 Pressure, velocity profile, and flow regions for a circular jet with a uniform velocity profile [8]. 8 Figure 1-5 Schematic of free surface jet impingement and profile of liquid velocity parallel to the surface: (a) planar jets, (b) circular jets [4]. Boiling heat transfer in jet impingement has four distinguish regimes which corresponds to four distinct locations on the plate surface. Region I, refer to Single Phase Forced Convection which is located directly beneath the nozzle, and it coincides with a rapid drop in the local surface temperature. Region II is known as nucleate boiling regime which occur when the high heat transfer causes bubbles formation. Region ‘III and IV’ occur when the temperature of the plate is sufficient to yield a stable film. Region V occurs far away from the impingement zone, and the heat transfer is conducted by radiation and convection only. 9 Figure 1-6 Boiling regimes at jet impingement surface; modified from [11]. 1.2.3 Pool Boiling Heat Transfer Initial boiling heat transfer studies were carried out by observing pool boiling experiments in which a coolant is held adjacent to a heated surface. The observed boiling phenomena in run-out table cooling is undoubtedly different in that it is extremely transient. Pool boiling, however, provides the fundamental basis for the boiling heat transfer. Various studies show that the pool boiling heat transfer consists of different heat transfer mechanisms that vary with the surface temperature. Nukiyama et al. [13] were first to identify these different boiling regimes, and then verified by Wolf et al. [8] Boiling heat transfer can be categorized into four main schemes which are single phase forced convection, nucleate boiling, transition boiling, and film boiling. Figure 1-7 illustrates a conventional pool boiling curve which demonstrates the four distinct regimes with respect to heat flux and saturation temperature. 10 Figure 1-7 Schematic of pool boiling [8]. Initially, as the heat transfer increases between the hot plate and the impinged water, this is translated into an increase of water temperature which is done mainly by convection; this is due to the temperature being below saturation point. This can be denoted by single phase convection regime at point (𝐴). Because of sufficient heat, at the onset of nucleate boiling bubbles will begin to form causing an increase of heat transfer, and this will catalyze the water to change its state from liquid to vapor. The bubbles will constantly form till reaching the point denoted by (𝐴′), hence the transition from single phase convection boiling regime to the nucleate boiling regime. After point (𝐴′) the bubbles will keep growing and the chaotic interaction between the bubbles will keep increasing the heat transfer until a vapor layer starts to form. Due to the phase change of water, the heat flux in the system experiences an increase because of the turbulent interaction between water and plate’s surface until it reaches the maximum heat flux point known as the 11 critical heat flux (CHF) that is denoted by point (𝐵). After this stage the vapor will be produced at a much higher rate than before leading the vapor columns to unite into vapor patches located along the surface, which will act as s separator between the impinging water and the plate surface and will decrease the heat flux. This stage is known as transition boiling regime. During this stage the change in the contact area between the hot surface and the water will result in changing the heat flux. Since the heat transfer rate of liquid is much higher than that of vapor, the overall heat flux will decrease because of the increase of vapor contact with the hot surface. The process will continue until there is minimal droplets of liquid in contact with the hot surface which is the end of transition boiling and denoted by (𝐶). The final regime is called film boiling, and it occurs when there is a stable vapor layer separating the impingement water and the plate surface. Even though, pool boiling provides the fundamental basis for boiling heat transfer, the heat transfer in jet impingement is transient problem. Robidou et al. [14] developed a boiling curve for jet impingement boiling shown in Figure 1-8 . It shows that there are differences between the pool boiling curve and the boiling curve developed by Robidou et al. [14] ,yet both curves shows the four distinct boiling regimes. Figure 1-8 shows that there are noticeable differences in the cooling behavior in the stagnation region and away from the stagnation region. Film boiling regime observed at high superheat surface temperature above 350 ᵒC. When the surface temperature of the plate drops to below 350 ᵒC, various locations away from the stagnation point begin to experience different types of cooling. The heat flux increases dramatically inside the stagnation region because the jet begins to break down the vapor layer causing transition boiling region. However, away from the stagnation zone, the vapor layers remain stable and film boiling continues. Since the heat flux decreases at temperature below 100 ᵒC within the stagnation zone, Robidou et al. [14] denoted this point to be the first minimum heat flux. Further cooling down to 12 below 50 ᵒC, wall super heat experiences critical heat flux values for the stagnation zone and locations away from the impingement zone. The values of the critical flux vary for different locations. Nucleate boiling regime occurs at wall temperature below critical heat flux. Figure 1-8 Boiling curve for a free surface jet at stagnation point, 19mm, and 44mm away from stagnation [14]. In the following, I will briefly discuss the various boiling regimes and the critical heat flux points mentioned above. i) Single phase convection At this region, the temperature of the wall superheat is less or equal to the saturation temperature of the cooling liquid. Therefore, boiling heat transfer will not occur, and the heat will be transferred by only single phase forced convection. Investigations carried by Wolf et al. [8] showed that the heat flux is affected by the radial distance from the stagnation point during the single-phase convection regime. It was observed that the heat transfer coefficient is dependent on 13 the characteristic of the boundary layer developed at the surface and the hydrodynamic of the cooling liquid. At certain radial distance away from the stagnation the heat transfer coefficient is constant, and the effect of flow characteristic is negligible. ii) Nucleate boiling Nucleate boiling regime occurs when the wall temperature exceeds the saturation temperature of the cooling liquid. This region exists between the temperature range of point (𝐴) and (𝐵). Point (𝐴) denotes the onset of nucleate boiling, where the wall superheat becomes high enough to cause vapor nucleation at the hot surface. At the onset of nucleate boiling, bubbles begin to form and detach from the hot surface, consequently enhancing the circulation of fluid and increasing the heat transfer. As shown in Figure 1-7, the region between points (𝐴′) and (𝐵) represents fully developed nucleate boiling. The generation of bubbles improve the heat transfer; this can be attributed to the additional convection currents formed from the motion of bubbles [8] and it is indicated by the steady increase in the heat flux as shown in Figure 1-7. Nucleate boiling has been studied by several researchers due to its high efficiency in heat transfer. Wolf et al. [8] were able to determine nucleate boiling regime by the increase in convection coefficient which is beyond the single-phase convection. They also noticed a change in the single-phase convection region once the jet velocity is varied; whereas, in the nucleate boiling zone they noticed that the jet velocity has almost no effect on the heat transfer. They attributed this to the creation of bubbles via the latent heat effects, which is far more dominant than the hydrodynamic of the fluid. Therefore, they observed that the heat flux in the nucleate boiling region depends only on the surface temperature. Robidou et al. [14] and Nobari et al. [4] observed the same trend. However, Hall et al. [15] reported that the heat flux depends on the jet velocity. 14 Mitsutake et al. [16] speculate the region of nucleate boiling as annulus that encircles the single-phase forced convection region, and the film region is denoted by the area beyond the annulus. They have varied two parameters in their experiment which are jet velocity and subcooling. They found that by increasing the liquid subcooling, the size of the annulus decreases. In the case of fixed liquid subcooling, they varied the jet velocity and determined that the annulus has traversed to a predetermined location much faster. According to their findings, they developed a formula for the location of the trailing edge. 𝑟𝑤𝑒𝑡 = 𝑎 ∗ 𝑡𝑛 1.1 Where 𝑎 and 𝑛 are experimental constants, 𝑟𝑤𝑒𝑡 demonstrates the radius of the wetting zone, and 𝑡 is the time. Robidou et al. [14] considered other boiling conditions outside the stagnation region. Their experiments were performed with stationary plate using a free surface jet. The feature of the jet used was rectangular with cross sectional area of 1 * 9 mm, and the plate material was copper. The jet velocity in the experiment was fixed at 0.8 m/s, the distance between the nozzle and the plate was 6 mm, and the water subcooling was 16 K. Figure 1-8 illustrates the boiling curves produced by Robidou et al. [14] in which different locations away from the stagnation region were considered. They observed that the nucleate boiling regime somewhere at wall superheat below 40 K, and the boiling curves for each of the several locations away from the stagnation region seemed to converge into the boiling curve at the stagnation line. iii) Critical Heal Flux Point (𝐵) is known as the critical heat flux (CHF) which represents the rapid formation of bubbles along with the vapor layer which produces the ideal conditions of maximum heat extraction. Critical heat flux is also known as the transition between two regimes which are 15 nucleate boiling and transition boiling. An important phenomenon called burnout occurs when any increase in wall superheat causes a sudden transition from nucleate boiling to film boiling which denoted by (𝐵′). Robidou et al. [14] performed an experiment to investigate the critical heat flux (CHF) outside the stagnation zone. They discovered that the critical heat flux in the stagnation zone was greater by magnitude of three than the critical heat flux outside the stagnation zone. In addition, they discovered that despite having different magnitude of critical heat flux at different location, the critical heat flux occurs at similar wall superheat. Many researchers, e.g. Liu and Zhu [17] and Mitsutake and Monde [18] conducted experiments to study the critical heat flux by varying the jet impingement velocity and water subcooling for the stagnation. They observed that, critical heat flux increased when increasing the jet velocity, and water subcooled. iv) Transition Boiling: Transition boiling occurs between point 𝐵 and 𝐶 as shown in Figure 1-7. As indicated above, the CHF (point B) signifies the maximum heat flux. Increasing the surface temperature beyond the CHF point will yield an unstable blanket that will form over the surface. At this stage there is a mixture of conduction and convection heat transfer through the liquid and vapor patches. Since the heat transfer through vapor is significantly less than the liquid, the heat flux will decrease. This phenomenal will remain as the vapor patches grow larger which reduces the contact area between the water and the surface. The contact area reaches it minimal between the water and the surface at point C. Further increase in the wall superheat will lead to the transition to film boiling. The transition boiling regime is characterized by a mixture of film and nucleate boiling. Chin et al. [19] indicated that bubble agitation and liquid turbulence had a determinantal effect on heat flux values during the transition boiling region. Robidou et al. [14] and Chin et al. [19] observed that the fluid hydrodynamic effects the heat flux. Figure 1-8 shows a considerable 16 difference in the transition boiling heat flux at different distances from the stagnation point. Robidou et al. [14] concluded that the increase of liquid turbulence is due to the bubbles breaking to microbubbles, and the continuous creation of microbubbles enhance the heat extraction. v) Minimum Heat Flux: The minimum heat flux is defined as the Leidenfrost point which is denoted by point 𝐶 as shown in Figure 1-7. The minimum heat flux occurs at temperature known as the rewetting temperature for which the final portion of liquid is in contact with the surface. As the wall superheat increases, remaining liquid will vaporize and eventually produce a stable uniform vapor layer. Based on experimental work performed by Ishigai et al . [20] by applying different jet velocities and subcooling, they were able to develop a formula to determine the minimum heat flux as a function of jet velocity and liquid subcooling. 𝑞𝑚𝑖𝑛 = 5.4 ∗ (1 + 0.527∆𝑇𝑠𝑢𝑏) ∗ 𝑣𝑗𝑒𝑡0.607 ∗ 104 1.2 In another experiment carried out by Liu [21] the correlation was done for the minimum heat flux and the diameter of the nozzle and the jet velocity. 𝑞𝑚𝑖𝑛 = 0.20(∆𝑇𝑠𝑢𝑏) (𝑣𝑗𝑒𝑡𝑑)0.5∗ 104 1.3 Both correlations developed indicate that the subcooling has a strong effect on the minimum heat flux. vi) Film Boiling Film boiling is the regime after the minimum heat flux point where the heat transfer occurs through a stable vapor film. This regime takes place beyond the minimum heat flux temperature at high wall superheat. Due to the rapid growth of vapor films, the liquid won’t have the chance to 17 vaporize; hence, it would be suspended by vapor film. The heat transfer in the above regimes was between the liquid and the surface or a mixture of liquid and vapor with surface. However, in this regime, the heat transfer occurs through convection only between the vapor and the hot surface. During this regime wetting does not occur. Liu and Wang [6] conducted an experiment and concluded that the effect of subcooling on heat transfer is much stronger than jet velocity. This is due to the fact that subcooling causes the boiling curve to shift to higher superheat and heat flux. Another study by Zumbrunnen et al. [11] indicated that the transfer increases as the liquid subcooling increases. Robidou et al. [22] conducted an experiment to compare the effect of film boiling in the stagnation zone and the parallel flow zone. They showed that there is 25% increase in the heat transfer in the stagnation zone than the parallel flow zone. They believed that the increase of heat flux in the stagnation zone is due to the thinner layer of vapor compared to the parallel flow zone. Robidue et al. [22] also observed that there is no temperature fluctuation in the film boiling which led them to the conclusion that the generated vapor film is stable and there is no contact between the liquid and the surface. 1.3 Review of Temperature Measurement Methods In the following section, we provide a brief review of two main methods for temperature measurement, namely: using thermocouples, and using infrared thermal cameras. 1.3.1 Using Thermocouples Thermocouples have been used extensively as temperature sensors in temperature measurement during water jet cooling. There are different connections of thermocouple junction, the typical one is by twisting the wires together and then bonding the joint on the specimen which forms a bead. Separate junction as seen in Figure 1-10 is the other type of thermocouple junction. In this type of junction, the individual thermocouple wires are separately installed on the specimen. 18 For instance, Hauksson et al. [23] employed a pair of thermocouples to measure temperature at each measuring location on the plate surface: one is fixed at the plate surface and the other one is embedded as shown in Figure 1-9 and Figure 1-11. Xu and Gadala [24] investigated the temperature measurement errors associated in measuring the plate temperature during water jet impingement by employing intrinsic thermocouples. They observed that the surface thermocouples generate higher error than the internal thermocouples measurements. Additionally, they investigated the connections of thermocouples wires at the measuring junction for the bead and separated type as showed in Figure 1-10. They concluded based on temperature measurement error that the separate junction should be avoided in the moving plate temperature measurement for water cooling. Figure 1-9 Installation of thermocouples [23] 19 Figure 1-10 Different measuring junctions for thermocouples [24]. Nobari et al. [4] has used imbedded thermocouples (1 mm below the plate surface) of the bead type K installed in a hole with diameter of 1.59 mm. The installation procedure of such thermocouples requires high technical skills. Firstly, flat bottom hole with 1.59 mm in diameter were drilled from the bottom to a depth of approximately 1 mm below the top surface of the plate. The accuracy of the pre-drilled holes was measured using sheet metal micrometer with accuracy of ±0.01 mm. The thermocouples wires that enter the holes were separated by a ceramic tube insulator, and the inserted thermocouples tip was spot welded to the flat end of the bottom hole as shown in Figure 1-11. Figure 1-11 Schematic of spot-welded embedded thermocouple [4]. 20 Even though the temperature measurement using the above method is considered to be accurate, the installation process is time consuming and requires high technical skills. Additionally, the thermocouple should be installed precisely in multiple locations inside the plate to be able to capture the temperature map. Furthermore, temperature measurements are only limited to the number of thermocouples installed. 1.3.2 Infrared Thermal Cameras Infrared thermal cameras provide a non-contact technique for measurement temperatures. The data processed by the thermal camera provide two-dimensional thermal image of an object. The infrared camera captures the portion of thermal radiation that exists in IR range and transform it into an electric signal that is processed to display the temperature distribution [25]. There are several advantages of thermal camera over standard thermocouple measurement techniques. In standard techniques, the temperature measurement of an object is employed by a contact type transducer such as thermocouples and resistance temperature detectors (RTDs). These techniques provide information at a single location. Generally, thermocouples are spot welded permanently on a target surface and installed at a certain depth from the surface. Afterward, the recorded temperature data is utilized to evaluate the surface heat flux. This technique entails the problem of changing the thermal and the flow fields, at least locally, during the experiment. i) Principle of infrared thermal imaging technique. All bodies emit electromagnetic radiation to the atmospheric when their temperature is above the absolute temperature (T > 0). The electromagnetic radiation is directly proportional to the intrinsic body temperature, and it consists of various spectral bands such as gamma rays, X-rays, ultraviolet, infrared light, microwave, and radio waves as shown in Figure 1-12. 21 Figure 1-12 Various spectral bands of electromagnetic waves [26] Generally, infrared radiation waves are not detectable by the human eyes and are categorized by four bands such as near infrared, middle infrared, long infrared, and extreme infrared (0.76—1.5 µm, 1.5-5.6 µm,5.6-14 µm, 14-1000 µm respectively). Lenses on the thermal camera help to capture the invisible waves and the electromagnetic radiations are focused on radiation sensor. The sensor comes with variety of pixel configuration and creates the electrical signal, which is proportional to incident radiation [27]. Subsequently, the electrical signal is amplified and transformed into an output signal. The output signal obtained is proportional to surface temperature of an object. There are three major components of an infrared thermal camera. These are the lens, the radiation detector, and the electronic panel. The lens element concentrates the infrared radiation emitted from the object into the detector. Then the signal obtained by the detector is amplified with the assistance of digital signal processing, and the amplified electrical signal is transformed into an output signal which is proportional to the surface temperature of the object. Several parameters should be given as an input parameter to the software such as emissivity, ambient temperature, ambient humidity, absorptivity, and transmissivity. 22 Several researchers utilized the thermal imaging technique to measure the surface temperature for jet impingement. Meola and Carlomagno [28] utilized the infrared technique to detect heat flux in heated thin foil. AbdulNour et al. [29] applied the infrared imaging to measure the wall temperature for the uniform heat flux boundary condition. The obtained results from infrared imagining showed good accuracy and the method provided quick technique to determine the distribution of the local convective heat transfer coefficient for the isoflux boundary condition. Feldheim et al. [30] investigated both experimentally and numerically the heat transfer characteristics for an array of stagged jets onto a flat plate. They used the infrared imaging techniques to measure the local heat transfer distribution. Kim and Giovannini [31] conducted an experimental study to characterize global and local flow field around squared cylinder by using particle image velocimetry and flow visualization, and infrared thermography method to measure the wall temperature field. Their results provided an overall understanding of the flow and heat transfer rate. Katti and Prabhu [32] investigated experimentally the heat transfer enhancement from a flat surface by using air jet impingement involving rib-rougheners. They employed thermal infrared camera to measure the local temperature distribution at the surface of the plate. Znamenskaya et al. [33] utilized high speed infrared radiation thermography to analyze the turbulent water boundary layer in two basic configuration of a submerged jet flow. The thermal camera recorded the radiation emitted from the water boundary layer in turbulent flow. Carlomagno and Cardone [34] found that infrared thermography can be used to measure convective heat fluxes for both steady and transient techniques. Additionally, they have stated that when comparing to the standard transducers, it shows valuable results because it has high sensitivity and low response time. Fujimoto et al. [35] investigated experimentally the flow structure and heat transfer of a circular water nozzle impinging on a moving plate, and the 23 temperature distribution of the plate was captured by infrared thermography. Modak et al. [36] carried out an experimental investigation to analyze the heat transfer characteristic on stainless steel foil by impinging circular jets. They have used pure water and 𝐴𝑙2𝑂3- water nanofluid as coolant fluid and employed infrared techniques to measure the temperature of hot foil during impingement. Michalski et al. [37] experimentally compared two temperature measurement techniques for measuring the surface temperature of the heated foil to analyze the flow boiling heat transfer. They found that the thermal camera measurement has advantages over the other techniques because it captures the full two-dimension image, produces the whole temperature history, and it has high sensitivity and low response rate. Zhang et al. [38] recently built an experimental apparatus and performed a numerical work to study the field synergy principle (FSP) based on minimum entropy generation method. They used Fluke thermal camera which produces fully radiometric thermal imagers to capture and store calibrated temperature data for thousands of points. The plate is painted with a spray paint to achieve a uniform emissivity all over the surface, and they vary emissivity value until thermal camera reads the temperature that is comparable to thermocouples. They conducted the experiment using plate temperature less than 100 ºC where no boiling phenomena occurs. The utilization of the thermal camera allows for capturing unlimited points of temperature measurements which makes it unique study for the water jet cooling. 1.4 Research objectives The main objective of this research may be summarized in the following points: ▪ Investigating the suitability of using thermal infrared cameras in temperature measurements in the jet impingement of hot steel plates. 24 ▪ Comparing thermal infrared camera measurements with conventional methods, e.g., thermocouples. ▪ Establishing a numerical CFD multi-phase model for studying the jet impingement quenching of steel plates. 25 Chapter 2: Experimental setup 2.1 UBC Industrial Scale Run-Out Table Facility The facility in UBC has been designed to simulate industrial cooling environments for run-out tale cooling in a hot plate. This experimental pilot scale facility enables the study the heat transfer cooling for stationary and moving plates. The pilot scale run-out table consists of several component to heat the sample plate to a desired initial temperature and move it via conveyer to be cooled by circular nozzle at the top and/or bottom of the plate Figure 2-2. The run-out table main components include electric furnace, test bed, hydraulic torque motor, water nozzles, water pipe system, and test plate. Initially, heating is provided by an electric furnace which can heat up the plate up to 900 ºC. By the use of hydraulic motor and chain drive system, the steel plate is transported from the heating zone to the cooling towers at a prescribed speed. The distance between the furnace and the cooling section is 10 m; this allow the plate to be accelerated to a maximum speed of 3.0 m/s. A series of water nozzle is installed above the spray zone and water pipe system (consist of pipes, flow meters, globe valves, hoses, and headers) to deliver the fluid from the upper tank to the nozzles. The upper tank is installed at the top of the 6.5 m rigid tower as fluid reservoir with internal heaters to control the water temperature. The cooling tower is a closed water loop where 1.5 𝑚3 is circulated through the cooling nozzle. The lower tank is an open tank which is placed below the heated plate and used to collect the wasted water from the experiment. A centrifugal pump used to deliver the water to the upper tank, and it can provide total water up to 500 L/min. Water is delivered to the nozzles through pipes and headers at the required flow rate. The cross section of the inner diameter of the circular nozzle is 19 mm. The test plate is a 40 x 43 cm high strength low alloy (HSLA) steel plate with embedded thermocouples of the bead type K inserted 1 mm below the plate surface in a hole with a diameter of 1.59 mm. Locations of thermocouples are shown in Figure 2-1. 26 Figure 2-1 Schematic of thermocouple locations with respect of the water jet for stationary plate experiments [4]. Figure 2-2 Schematic of pilot scale run-out table facility [4]. 27 2.2 ADU Pilot Scale ROT Facility The pilot scale run-out table at Abu Dhabi university is similar to the one described above and is constructed to simulate metal and non-metal cooling conditions for hot strips and mills with parameters similar to those used in industry. This facility can be used to conduct stationary and moving plate conditions to study the fluid and heat transfer of hot plate. The primary elements of the ROT setup in Abu Dhabi university are: a furnace, test bed, chain conveyor, hydraulic motor, water tanks, piping system, headers, nozzles, a hydraulic pump, mechanism to remove the plate from the oven, and mechanism to attach the thermal camera to the top and/or bottom of the plate as shown in Figure 2-3. Temperature measurements are performed using an infrared thermal camera (FLIR A615 type). The camera is connected to a data acquisition system using the commercial FLIR Tools software. The cooling system consists of several components including heater tanks, a water pump, an upper storage tank, a piping system with valves, as well as nozzles and a bottom tank. Firstly, the water heaters (Rheem E10-30-G 10-gallon capacity) are used to regulate the temperature of the cooling water up to 75°C. Then, the centrifugal pump can be used to transfer the water to the higher storage tank, which has a capacity of 2.25 cubic meters and is located at a height of 5 m above ground level. The centrifugal pump is rated to deliver a maximum water flow capacity of 135 L/min. The water is delivered from the upper tank to the nozzles through a water pipe system, with the header placed just before the nozzles. The nozzle height to the test plate can be adjusted as required. The heating mechanism used is a furnace (Nabertherm model N641) that can heat up the test plates up to 1200 °C. After the heating process, the test plate is placed on top of the test bed, utilizing the mechanism to move the plate from the furnace to the cooling zone. This moving mechanism consists of a hydraulic drive system, the conveyor-chain system, the test bed, and 28 motion-controlled system as seen Figure 2-5. Then the test plate is moved to the cooling chamber underneath the nozzle with the assistance of the chain conveyor and the hydraulic motor. When the plate is directly beneath the nozzles, a 19 mm nozzle impinges the water jet into the surface of the plate. The test plates used were rectangular shape low carbon stainless steel 316L type with the dimensions of 45 x 50 cm and the thickness is 6 mm. ROT setup in ADU and the furnace are shown in Figure 2-4. The thermal camera was initially positioned in a fixed manner above the steel plate, directed towards the upper surface of the plate. However, this approach exhibited a sharp drop in temperature upon the addition of water droplets between the plate and thermal camera. The presence of a water film resulted in the absorption of a portion of the radiation that was emitted by the steel plate. This, consequently, caused a reduction in the quantity of radiation that reached the camera, which led to an underestimation of the temperature values of the steel plate. In order to address this issue, a thermal camera was installed beneath the steel plate, measuring the temperature from the bottom. Afterwards, the inverse heat conduction program (INTEMP) was employed to determine the temperature of the upper surface. The INTEMP program utilizes the finite element technique to solve both linear and nonlinear inverse heat conduction problems, as proposed by Trujillo and Busby [39]. 29 Figure 2-3 Schematic diagram for the Run-out Table Facility. Figure 2-4 Photograph of the furnace and ROT facility of ADU. 30 Figure 2-5 Moving mechanism: (a) Hydraulic Unit. (b) Conveyor-chain system. (c) Test bed. (a) (b) (c) 31 Chapter 3: Formulation of the Computational Fluid Dynamics (CFD) Problem In the following chapter, we briefly review the formulation method and present the governing equations used in the formulation. 3.1 Various Formulation Methods For the jet impingement problem, various numerical simulation is available. Namely: Reynold-Averaged Navier-Stokes (RANS) analysis, Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). There are various studies in the literature on the numerical modeling of the water jet impingement boiling. Many of the studies are dealing with the challenges of the numerical modeling of the boiling phenomenon and correlating it with existing experiments. In this work, we use Reynold-Averaged Navier-Stokes (RANS) analysis for adiabatic two-phase flow. The Volume of Fraction (VOF) and the Eulerian-Eulerian approaches are the most widely used in multiphase flow. The Eulerian-Eulerian techniques gives more accurate results since it solves the balance equations of mass, momentum, and energy for each phase separately. The multiphase coupling is accomplished by introducing a source term such as interfacial forces. Despite the accuracy of this technique, it is computationally expensive [40]. On the other hand, we can use a mixture multiphase Eulerian formulation with VOF tracking model. This is a Eulerian formulation, i.e., the mesh is fixed and no mesh motion, that uses the VOF for tracking the interface surface between the phases using a volume fraction equation. The mixture model solves for the mixture momentum equation and prescribes relative velocities to describe the dispersed phases . Krepper and Rzehak [41] modeled the boiling heat transfer in a pipe flow using the Eulerian-Eulerian approaches. Most of their results exhibited a good agreement with experimental results, except for the bubble size radial distribution. A recent study by krepper et al . [42] modified 32 the model by implanting a population balance method. They considered the variations of bubble size due to bubble break, coalescence, and condensation/evaporation processes. Their model showed a huge improvement for the bubble size distribution. Kunkelmann and Stephan [43] used the Volume of Fluid (VOF) method to simulate the nucleate boiling heat transfer in Open FOAM solver. They captured the growth, departure, and the movement of the bubbles. Their results showed a good agreement with the experimental results, especially for the bubble size and the mean wall superheat. Narumanchi et al. [44] did a similar simulation using ANSYS fluent. They used the Eulerian multiphase model to predict the dispersed flow condition resulting from boiling on superheated surface. In order to simulate the interface interaction, various models were employed such as interfacial area concentration, turbulent dispersion force, life, and bubble departure diameter. Their results showed 20% deviation from experimental results at stagnation, which considered to be an appropriate error because of the complexity of the physics involved. Similar study was done by Abishek et al. [45] using the mixture Eulerian model. They showed that the RNG k-𝜀 model with enhanced wall treatment provides enhanced accuracy than the other RANS-based turbulence model. Shademan [46] numerically investigated the flow, heat transfer, and mass transfer of a circular nozzle by using Eulerian-Eulerian two-phase model to study the boiling phenomenon. They considered the effect of interfacial forces, bubble breakup/coalescence, and the interfacial area concentration. Esmailpour et al. [47] simulated the hydrodynamics and heat transfer phenomena regarding phase-change jet impingement of nucleate boiling regime. They used a Eulerian multiphase model with RNG k-𝜀 turbulence and considered an appropriate interfacial term to study the effect of Reynolds number and standoff distance. Their results showed a good agreement with the experimental work at stagnation with minimum error of 4% and maximum error of 15%. 33 Craft et al. [48] studied different turbulence models to analyze the heat transfer in the jet impingement region. They concluded that, the achieved results showed poor agreement with the experimental results due to the basic weakness of the eddy viscosity stress-strain relation. Cooper et al. [49] reported that k-𝜀 model over predicts the turbulence kinetic energy near the stagnation region. Therefore, different turbulence models were considered to reduce this effect by considering the non-isotropic nature of the turbulent viscosity. Several turbulent models have been used to study the impingement flow on stationary plate such as k-𝜀 and k-𝜔 models. The DNS turbulent model is the best to evaluate the jet impingement flow, however, it’s extremely expensive compared to the other turbulent models. The reason for that is because it can resolve all eddy scales. In order to simulate all scale of turbulent impingement flow, it requires to have the total numerical nodes to be in the order of (𝑅𝑒)9 4⁄ (Chattopadhyay and Saha [50]). Large eddy simulation falls between the DNS and RANS in terms of the fraction of the resolved scales. In order to resolve only the large eddies, LES model allows the use of relatively coarser mesh and larger time step size than DNS model. However, for high Reynolds number LES requires substantially finer mesh near wall region to resolve the small-scale element than the RANS model. Based on several studies, the standard low level methods such as k-𝜀 and k-𝜔 are not accurate to characterize the jet impingement cooling at the stagnation zone [51][52]. Nevertheless, an appropriate correction has been used to enhance the model’s performance such as wall treatment. Craft et al. [53] and Sagot et al. [54] developed a new version of the k-𝜔 model (the shear-stress transport (SST)). This version accurately predicts the flow structure near the wall when using fine mesh. Thus, the outcomes of any turbulent model are extremely depended of on the mesh size and refinement [55]. As a result, the enhanced version of k-𝜀 and then k-𝜔 models are the most widely used turbulent models to predict the hydrodynamics and the heat transfer of industrial flow 34 applications because of reasonable accuracy results and the less requirement of the computational cost. Stark and Fritsching [56] developed a numerical model to study the flow fields and the conjugate heat transfer of a flat plate with a single submerged water jet. They performed the model for unsteady cooling process with wall temperature above the boiling point. They used an Eulerian multiphase bubble-crowding model to predict the distribution of the heat transfer coefficient and the distribution of the vapor and liquid fractions during transient problem. They have used the k- 𝜔 -SST (shear stress transport) model with enhanced wall treatment and their results showed a good agreement with experiments for both free-surface and submerged jet impingement cooling. Their approach was able to capture all the boiling phases in the cooling process by using single model. Another study by Aghahani et al. [57] investigated the effect of the jet Reynolds number and the plate-to-jet velocity ratio (R) on the Nusselt number by employing 𝑣2 − 𝑓 turbulence model. Their results indicated that at a fixed plate-to-jet velocity ratio and an increase of Reynolds number lead to the enhancement of the average Nusselt number. However, the Nusselt number decreases as the plate-to-jet velocity ratio increased for each Reynold number. Waldeck et al. [58] numerically developed a model by employing a Eulerian multiphase flow to analyze the heat fluid flow process. They compared the progression of the wetting front and the temperature distribution on the back side of the plate with experimental approaches, and their result shows a good agreement. Moreover, they concluded that the heat transfer coefficient at the Leidenfrost point is only dependent on the Reynolds number. Ghasemian et al. [59] simulated the quenching jet impingement to analyze the effects of conjugation and mass transfer. They investigated the effects of jet to plate distance, jet to jet spacing, and velocity inlet function. They used the VOF method to capture the liquid–gas interface. Toghraie [60] numerically simulated the boiling heat transfer 35 and investigated the quenching phenomena via fluid jet on a horizontal plate. They used the volume of fluid (VOF) method to capture the liquid-gas interface and k-ɛ turbulence model. In this simulation, they showed by that the convective heat transfer coefficient increases by decreasing the fluid temperature. Heyerichs and Pollard [61] numerically investigated the performance of k-w and k-e turbulence models, especially near the wall region. the results showed the k-w model indicates greater performance than k-e for predicting convection heat transfer in turbulent flows. Dutta et al. [62] numerically compared the various RANS models to predict the heat transfer and flow rate for slot jet impingement. They observed that for small nozzle to plate distance (H/B < 5), the SST k-𝜔 with transitional model showed the best agreement with the experimental work. Nevertheless, the k-𝜀 model with enhanced wall treatment provide superior performance for high value of nozzle to plate ratio. Kalita et al. [63] predicted the flow patten numerically for turbulent plane jets by employing k-𝜀 turbulence model. The comparison between the predication and the experimental data showed a good agreement. Zhang et al. [38] studied the field synergy principle (FSP) based on minimum entropy generation method experimentally and numerically. They used different turbulence models to compare the experimental work with various models, namely: standard k− ε, renormalization group RNG k − ε, realizable k −ε, standard k− ω and shear stress transport SST k− ω models. They observed that the numerical average Nusselt number is considerably higher near the stagnation compared to the experimental data. They found that the realizable k −ε predicted a monotonic decrease of average Nusselt number and showed a similar trend as the experimental data yet failed to capture the secondary peak. The SS k− ω model showed a better overall agreement with the experimental data compared to the other turbulence models. 36 3.2 Law of the Wall Turbulence models are generally used in CFD simulations. However, some turbulence models such as k-𝜀 model is only valid in the fully developed region, and do not perform well in the area near to the wall. Therefore, in order to deal with the near wall region, a wall function is used to modify the response in the viscous layer near the wall. Wall functions are empirical equations used to satisfy the flow physics near the wall region and the first cell center must be placed in the log law region to ensure the accuracy of the model. Wall functions are used to bridge the inner region between the wall and the fully developed flow region. The flow region near the wall is characterized into three sub-regions. The first region is the laminar region where the viscosity effect is dominant. In contrast, the outer layer is called fully turbulent region which the mean velocity has logarithmic behavior. The third intermediate region is called buffer layer that lies between the inner and outer layers, in this region the effect of molecular viscosity and turbulence are equally important [40][64]. Based on von Karman law of the wall, the three sublayers are as follows: • Viscus sublayer (𝑦+ < 5). • Buffer layer ( 5 < 𝑦+ < 30). • Log-law or fully developed region (𝑦+ > 30). 37 Figure 3-1 Sublayers for Turbulent boundary layer [65] The law of the wall is represented in the dimensional graph shown in Figure 3-1 Sublayers for Turbulent boundary layer [66] and may be written as follows [64]. 𝑢+ =𝑈𝑢𝜏=1𝜅𝑙𝑛𝑢𝜏𝑦𝑣+ 𝐶 3.1 Where 𝑢+is the dimensionless velocity parallel to the wall. The dimensionless wall function 𝑦+ is the distance normal to the wall utilized to describe the mesh intensity for a particular flow in CFD and is defined as follows: 𝑦+ =𝑦 𝑢𝑇𝜈 3.2 Where 𝑦 is the height of the first cell, 𝜈 is the kinematic viscosity, and 𝑢𝜏 is the friction velocity which can be calculated by: 𝑢𝜏 = √𝜏𝑤𝜌 3.3 38 Where 𝜏w is the wall shear stress, and may be calculated as follows: 𝜏𝑤 =𝜌𝑈2𝐶𝑓2 3.4 Where 𝐶𝑓 is the skin friction coefficient. The value of 𝑦+and 𝑢+are affected by the location of the sublayers. In the viscus sublayer region, the value of 𝑦+is typically less than 5, and the 𝑢+is linearly proportional with respect to 𝑦+as indicated in the following equation: 𝑦+ = 𝑢+ 3.5 In the fully turbulent region, the values of 𝑦+is more than 30. The relationship between 𝑦+and 𝑢+ is best described with a logarithmic equation as: 𝑢+ =1𝜅𝑙𝑛𝑦+ + 𝐶 3.6 Where 𝜅 is the von Karman constant 𝜅 ≈ 0.41, and C ≈ 5. 3.3 Governing Equation for Multiphase Modeling The governing equation used in the CFD problem are continuity equation and momentum equation. In addition, energy equation is required since the problem includes temperature changes. One of the main formulations used in the literature is the multiphase Eulerian mixture formulation with VOF tracking model. This is a Eulerian formulation, i.e., the mesh is fixed and no mesh motion, that uses the VOF for tracking the interface surface between the phases using a volume fraction equation. The mixture model solves for the mixture momentum equation and prescribes relative velocities to describe the dispersed phases. The mixture model may be used without 39 relative velocities for the dispersed phases to model homogeneous multiphase flow. The mixture model differs from the Eulerian-VOF model in allowing the phases to move at different velocities, using the concept of slip velocities. Additionally, the mixture model allows the phases to be interpenetrating and the volume fractions 𝛼𝑙 (for a liquid phase) and 𝛼𝑔 (for a gas or vapor phase) for a control volume can therefore be equal to any value between 0 and 1. The mixture model solves the continuity equation for the mixture, the momentum equation for the mixture, and the volume fraction equation for the secondary phases, as well as algebraic expressions for the relative velocities (if the phases are moving at different velocities). i) Continuity Equation. The continuity equation is a mass balance equation utilized to calculate the mass flow in and out of a domain. Based on the current application, for incompressible flow with constant properties, the differential form of the continuity equation can be represented as follows [66]: 𝛻 . 𝑉 = 0 3.7 Where the symbol 𝛻 is a vector defined as 𝛻 = 𝜕𝜕𝑥+𝜕𝜕𝑦 and 𝑉 is the velocity vector. ii) Momentum Equation The momentum equation may be written as [66]: 𝜌𝜕𝑉𝜕𝑡+ 𝜌(𝑉.𝛻)𝑉 = − 𝛻𝑝 + 𝜇𝛻2𝑉 + 𝐵 3.8 Where the first term is a transient (change with time), and the second term is a convective term. The net pressure force, the net viscus force and the body force are presented on the RHS of the equation, and B is a source term. 40 iii) Energy Equation The energy equation is basically the conservation of energy utilized to balance the flow of energy in and out a domain and may be written as [66][67]: 𝜌𝐶𝑝𝜕𝑇𝜕𝑡+ 𝜌(𝑉. 𝛻)(𝐶𝑝𝑇) = 𝐾𝛻2𝑇 − 𝑃(𝛻 . 𝑉) + 𝜇ɸ 3.9 The first term is rate of accumulation of energy, followed by net rate of advection term caused by fluid motion. The first term on the RHS is the conduction term, followed by pressure work and the viscus dissipation term and ɸ is the dissipation term. The volume of fluid method is commonly used to track the phases in multiphase problem and to capture the interface between the two immiscible fluids by solving a single set of momentum equation and tracking the volume fraction of each fluid. This method is used in the multiphase problem of a jet impingement cooling, which can capture the phase difference at the interface of dissimilar fluids such as air, liquid water, and vapor. The Volume of Fluid method uses the concept of the volume fraction of the fluid in order to locate and shape the difference phases. The method defines a scaler parameter (volume fraction) which has a range from 0 to 1 as follows: 𝛼𝑙 = 0, the cell is empty cell of the 𝑙𝑡ℎ 𝑓𝑙𝑢𝑖𝑑 0 < 𝛼𝑙 < 0, the cell contains the interface between the 𝑙𝑡ℎ𝑓𝑙𝑢𝑖𝑑 𝑜𝑟 𝑚𝑜𝑟𝑒 𝑜𝑡ℎ𝑒𝑟 𝑓𝑙𝑢𝑖𝑑𝑠 𝛼𝑙 = 1, the cell is full of 𝑙𝑡ℎ fluid The tracking of the interfaces between the different phases is accomplished by the solution of conservation of mass (Continuity Equation) for the volume fraction of one or multiple phases. The volume fraction equation for multi-phase will be as the following [40]: 41 𝜕𝜕𝑡(𝛼𝑙𝜌𝑙) + ∇. (𝛼𝑙𝜌𝑙𝑉𝑙) = ∑(?̇?𝑣𝑙 − ?̇?𝑙𝑣𝑛𝑝=1) 3.10 The subscripts 𝑙 𝑎𝑛𝑑 𝑣 refer to the liquid and vapor phases, respectively. Where ?̇?𝑙𝑣 is the mass flow rate transfer between the two phases from 𝑙 phase to 𝑣 phase and ?̇?𝑣𝑙 is the mass transfer from phase 𝑣 to phase 𝑙,. The RHS of the equation accounts for any phase changes that occur. For instance, if the phase interaction is selected as evaporation-condensation mechanism, it means at a specified saturation temperature, the fluid will either evaporate or condensate. For this mechanism, ?̇?𝑙𝑣 will account for rate of evaporation and ?̇?𝑣𝑙 will account for condensation. They are calculated based on the following equation [40]. If 𝑇𝑙 > 𝑇𝑠𝑎𝑡 (evaporation): ?̇?𝑙𝑣 = 𝑐𝑜𝑒𝑓𝑓 ∗ 𝑎𝑙𝜌𝑙(𝑇𝑙 − 𝑇𝑠𝑎𝑡)𝑇𝑠𝑎𝑡 3.11 If 𝑇𝑙 < 𝑇𝑠𝑎𝑡 (condensation): ?̇?𝑣𝑙 = 𝑐𝑜𝑒𝑓𝑓 ∗ 𝑎𝑣𝜌𝑣(𝑇𝑠𝑎𝑡 − 𝑇𝑙)𝑇𝑠𝑎𝑡 3.12 Where 𝑐𝑜𝑒𝑓𝑓 is the mass transfer intensity factor with the unit of 𝑠−1, 𝑇 is the fluid temperature and the subscript 𝑠𝑎𝑡 refers to the saturation temperature. The symbols 𝛼 and 𝜌 are the phase volume fraction and density, respectively. The properties in the transport equations are determined by the existence of the phase component in each control volume. The density in two phase flow in VOF model is found by the following: 42 𝜌 = 𝛼2𝜌2 + (1 − 𝛼2)𝜌1 3.13 All other properties such as (e.g., viscosity) are found in same way. The momentum equation in the multiphase mixture model is given by: 𝜕𝜕𝑡(𝜌𝑉) + 𝛻. (𝜌 𝑉𝑉) = − 𝛻𝑃 + 𝛻. (𝜇𝑒𝑓𝑓(𝑉𝑉)) + 𝜌 𝑔 3.14 Where: 𝜌 = 𝑎𝑣𝜌𝑣 + (1 − 𝑎𝑣)𝜌𝑙 3.15 𝜇𝑒𝑓𝑓 = 𝑎𝑣𝜇𝑣 + (1 − 𝑎𝑣)𝜇𝑙 3.16 Finally, the energy equation for the mixture multiphase model can be written as follows: 𝜕𝜕𝑡(𝜌𝐸) + 𝛻. (𝑉 (𝜌𝐸 + 𝑃)) = 𝛻. ((𝑘𝑒𝑓𝑓) 𝑉 𝑇) 3.17 And the effective conductivity is given by: 𝑘𝑒𝑓𝑓 = 𝛼2𝑘2 + (1 − 𝛼2)𝑘1 3.18 Where energy (E) and temperature (T) are averaged variables. The effective thermal conductivity (𝑘𝑒𝑓𝑓),and the effective viscosity (𝜇𝑒𝑓𝑓) are shared between the phases. For incompressible flow E = ℎ, where ℎ is the sensible enthalpy. 3.4 Turbulence Model Fluid can be characterized by its flow nature whether it is a laminar or turbulent and the Reynolds numbers (Re) is the key element to differentiate the nature of the flow. The higher the value of the Reynolds number mean the more turbulent the nature of the flow. In the current study, 43 the free surface water jet delivered from a single rounded nozzle located at a specific height will yield to increase the velocity of the fluid and Reynolds number. For the jet impingement problems, if the flow Reynold number is more than 50,000, the conditions are considered to be turbulent. The nature of the flow to be a turbulent depends on multiple parameters such as Nozzle to height distance and the flow rate. As a result, the abovementioned Navier-stokes equations are not adequate to solve the turbulent nature of the flow without considering the effect of turbulence. Therefore, a turbulent model should be selected to resolve the governing equations with the extra turbulent terms. In considering the turbulence, we express the velocity field as 𝑢 = ?̅? + ?̀?, where 𝑢 is the instantaneous velocity, ?̅? is the mean velocity, and ?̀? is the fluctuation velocity. Thus, the Navier-stokes equation and the energy equation will take the following form [40] [67]: 𝜌𝜕?̅?𝑖𝜕𝑡+ 𝜌?̅?𝑗𝜕?̅?𝑖𝜕𝑥𝑗= −𝜕𝑃𝜕𝑥𝑖+ 𝜕𝜕𝑥𝑗[ 𝜇 (𝜕?̅?𝑖𝜕𝑥𝑗+𝜕?̅?𝑗𝜕𝑥𝑖) − 𝜌𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ ] + 𝜌𝑔𝑖 3.19 𝜌𝐶𝑝𝜕?̅?𝜕𝑡+ 𝜌(𝑉. 𝛻)(𝐶𝑝?̅?) = 𝐾𝛻2 ?̅? − 𝑃(𝛻 . 𝑉) + 𝜇ɸ̅ + 𝑇𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡 𝑡𝑒𝑟𝑚 3.20 where 𝑢𝑖 is the components of the velocity vector u and 𝑥𝑗 is the coordinate directions, and the velocity, pressure, temperature, and density are averaged terms. The bar above the variables ( ̅ ) indicates the mean value, and the fluctuation part is denoted by (‘). The additional term called turbulent shear stress (Reynold stresses) which arises from the Reynold averaging process. Since, the Reynold stresses is unknown parameter, so it requires a turbulent modeling in order to resolve it. Boussinesq 1877 is perhaps the first to move towards modeling of the turbulence. He proposed the turbulent viscosity term ( 𝜌𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ = 𝜇𝑡𝜕?̅?𝜕𝑡 ), that Reynold stress is related to the mean velocity gradient by the dynamic eddy viscosity or turbulent viscosity (𝜇𝑡) while (𝜇𝑡 is a property of flow, 44 not fluid). In general, the Reynold stresses can be found by using Boussinesq theory as follows [40]: 𝜌𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ = 𝜇𝑡 (𝜕?̅?𝑖𝜕𝑥𝑗+𝜕?̅?𝑗𝜕𝑥𝑖) −23𝜌𝑘δij 3.21 Where k is the turbulent kinetic energy 𝑘 =12(𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ ), and δij is the Kronecker delta. The advantage of this approach is the moderately low computational cost associated with the computation of the turbulent viscosity. However, the disadvantage of the Boussinesq hypothesis is that it assumes the turbulent viscosity to be isotropic scalar quantity, which is not true. The assumption of an isotropic turbulent viscosity works well for shear flows dominated by only one of the turbulent shear stresses. Alternative turbulence models were developed to overcome lack of the previous model such as the k − ε and the k − ω models. The k − ε model introduces two additional equations to resolve the turbulent flow such as kinetic energy k and turbulent dissipation ε. The two additional equations are coupled with the original RANS equations. The k − ε model was first proposed by Launder and Spalding [68]. This model is based on transport equations for the turbulence kinetic energy (k) and the dissipation rate (ε). The assumptions used to derive this model is that the flow is fully turbulent, and the effects of the molecular viscosity are negligible. The transport equations for the kinetic energy and the dissipation rate as follows [40]: 𝜕𝜕𝑡(𝜌𝑘) +𝜕𝜕𝑥𝑖(𝜌𝑘𝑢𝑖) =𝜕𝜕𝑥𝑗[(𝜇 +𝜇𝑡𝜎𝑘)𝜕𝑘𝜕𝑥𝑗]+ 𝐺𝑘 − 𝜌𝜀 3.22 𝜕𝜕𝑡(𝜌𝜀) +𝜕𝜕𝑥𝑖(𝜌𝜀𝑢𝑖) =𝜕𝜕𝑥𝑗[(𝜇 +𝜇𝑡𝜎𝜀)𝜕𝜀𝜕𝑥𝑗]+ 𝐶1𝜀𝜀𝑘(𝐺𝑘 + 𝐶3𝜀𝐺𝑏) − 𝐶2𝜀𝜌𝜀2𝑘 3.23 45 Where 𝜇𝑡 is turbulent viscosity, computed by 𝜇𝑡 = 𝜌𝐶𝜇𝑘2𝜀, and 𝐺𝑘 = 𝜌𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ ̅𝜕𝑢𝑖𝜕𝑢𝑗 represents the generation of turbulence kinetic energy due to the mean velocity gradients. 𝐶1𝜀, 𝐶2𝜀, 𝐶𝜇, 𝜎𝑘, and 𝜎𝜀 are constants having values 1.44, 1.92, 0.09, 1.0, and 1.3 by default, respectively. Due to the fluctuation of the mean velocity and pressure gradient at the impingement region, the standard k- ε model is not recommended for jet impingement and the realizable k- ε model is shown to give better results [40][69]. There are several methods used to model the wall effects. The first approach is called the low-Reynolds number model where the damping functions are added to the transport equations of k and ε and to the definition of the eddy viscosity. The common approach to correct for the near wall effect is to use a wall function, where the first grid point is located in the fully turbulent method and empirical relations are utilized to prescribe the quantities at the first grid point. In another approach, called enhanced wall treatment (two-layer approach), the entire domain in this approach is subdivided into a viscosity effected region and the fully turbulent region. A wall distance based turbulent Reynold number is utilized to demarcate between the inner and outer region. 46 Chapter 4: CFD Model, Results and Discussion 4.1 Model Description The ANSYS-FLUENT software is widely used in the field of fluid dynamics and heat transfer for simulation purposes, because of the capability to simulate a wide range of parameters. The simulation model presented in this study is for the jet impingement cooling process of hot steels on Run-out Tables (ROT). The ANSYS-Fluent solver was employed for this simulation, and the aim was to investigate the heat transfer and fluid flow behavior in the near-wall region. To properly represent the behavior near the wall, it is necessary for the model to have a mesh with high intensity in the inner boundary layer region. In order to ensure this, it is essential to have a set of high-quality prism layers (also known as inflation layers) located in the near-wall region, with the initial layer having a 𝑦+ value of approximately one. However, the challenge here is to develop a model that has an optimal mesh intensity and efficiently captures the boundary layer effect with reasonable computational cost and CPU time. Since the plate is stationary and the jet is circular, a 2D axisymmetric model was implemented. The model consists of two main sections: the fluid environment and the solid plate with the impinging fluid interface. Generating the mesh for the impingement problem is a critical stage that affects the accuracy and stability of the results. The final model used in our analysis is shown in Figure 4-1. A highly refined mesh was applied by using the multi-zone technique with an unstructured grid with a mix of triangular and quadrilateral elements, and the refinement of the mesh increased towards the surface of the plate to capture the physics near the wall region. The 𝑦+ value for the first layer attached to the wall was kept around (1.0). The 𝑦+ value is calculated from: 47 𝑦𝑝 =𝑦+μ ρ uτ 4.1 Where the viscosity (μ) and the density (ρ) are the properties of the liquid water, and ( uτ) is the friction velocity given by: 𝑢𝜏 = √𝜏𝑤𝜌 4.2 Where 𝜏𝑤 is the wall shear stress, given by: τw = 0.5 𝐶𝑓 ρ 𝑉2 , 𝐶𝑓 is skin friction factor given by: 𝐶𝑓 = 0.074 (𝑅𝑒𝐿(1 5⁄ ))⁄ , and the Reynolds number is given by: 𝑅𝑒𝐿 = (𝜌𝑉𝐿 𝜇⁄ ). In the above equations, the free stream velocity 𝑉 is taken as the jet velocity and the characteristic length 𝐿 is the nozzle diameter. For our final model, the first cell height is 5.2𝑥10−5𝑚, and the total number of elements are 384,300. Figure 4-1 The modeled mesh with the applied boundary conditions. 48 4.2 Model Parameters and Boundary Condition The standard no-slip boundary conditions were implemented at the wall. A multiphase model was used, with three different fluids defined to coexist: liquid water, vapor, and air. The hot plate was defined to be steel with an initial temperature of 660𝑜𝐶. The selected material properties under atmospheric pressure were considered, as summarized in Table 4-1. The nozzle diameter was 19 mm and it was placed at a height of 25 cm. Inlet velocity boundary condition is located in the top left corner of the schematic of Figure 4-1, where the water is issued from a circular nozzle and falls down towards the impingement plate. The flow leaving the nozzle is assumed to be fully developed. The temperature of the impinged fluid is 𝑇𝑤 = 25°𝐶 and the velocity at the inlet is 𝑉 = 0.5 𝑚/𝑠. Pressure outlet is applied on the right and top right of the fluid domain. The pressure value is assigned as zero-gauge pressure. The interface between the fluid domain and solid domain is coupled by using the inbuilt command in ANSYS. For the initial condition, the temperature of the steel is patched with 𝑇𝑤 = 660 °𝐶, the initial volume fractions of water liquid and water vapor is 𝛼𝐿 = 1 and 𝛼𝑣 = 0, respectively. Table 4-2 summarize the boundary conditions used in the simulation model. 49 Table 4-1 Properties of the materials used in the model. Table 4-2 Model Parameters and Boundary Conditions Solver • Ansys Fluent: Pressure Based, Transient with gravity into account Model • Realizable k-ε turbulence model, Enhanced Wall Function with Energy enabled. • Multiphase Eulerian formulation with (VOF) tracking method Phases • Air • Liquid water • Vapor Phase-Interaction • Two mass transfer mechanism: Evaporation-Condensation model • Mass transfer from water to vapor & vapor to water. • Piece-wise Linear profile: Saturation temperature in terms pressure Boundary Conditions • Heated plate: 660C (Initial condition) • Water Jet Impingement: 𝑉 = 0.5 𝑚/𝑠 and 𝑇 = 25 °𝐶 • Fluid walls: Pressure Outlet Transient Cooling Cycle ~ 30 seconds (adaptive range1e-5 to 5e-3) Property Water (Liquid) Water (Vapor) Steel Saturation temperature (oC) 100 100 N/A Surface tension (N/m) 0.059 0.059 N/A Latent heat (J/kg) 2,257,000 2,257,000 N/A Density (kg/m3) 997.13 0.6 7,320 Specific heat (J/kg. K) 4,219 2,010 1,000 Dynamic viscosity (kg/m. s) 2.82E-04 1.23E-05 N/A Thermal conductivity (W/m. K) 0.68 0.025 31.8 50 4.3 Model verification In this section we present a comparison between the experimental results from the ROT facility and the simulation results. Several experiments were conducted in the ADU ROT facility utilizing a jet nozzle for the purpose of verification. A nozzle diameter of 19 mm was used, and the nozzle was positioned at a height of 25 cm from the steel surface. The simulation model was developed utilizing the precise parameters of experiments conducted at the ROT facility, and subsequently, the results were captured using a thermal camera. The problem in jet impingement cooling is the existence of complex boiling at the stagnation point on the cooling surface, which could potentially obstruct the visual observation of the surface, thereby resulting in inaccurate thermal camera measurements. To overcome this concern in the impingement zone, the thermal camera was placed at the bottom of the plate, and two-dimensional inverse heat conduction (IHC) analysis was used to calculate the temperature of the upper surface by using commercial software INTEMP [39]. In the parallel zone, the thermal camera was placed at the top surface and the results were directly obtained from the camera. The temperature history drop curves for different zones along the plate surface are shown in Figure 4-2. Two points located in the stagnation zone were examined, one at 0 mm (stagnation point) and the other at 15 mm from the axis. In addition, two points in the parallel zone were considered: at locations of 50 mm and 85 mm from the axis. The fluid temperature was 𝑇 = 25 °𝐶, and the jet velocity was 0.5 m/s. The curves show very good agreement between the simulation and experimental results in both the parallel flow zone and the stagnation zone. The findings verify that the developed simulation model accurately predicts the temperature history drop and that the calibration and readings of the thermal infrared camera are well achieved. 51 Figure 4-2 Comparison between experimental and simulation temperature history for different zones at the top plate surface using 0.5 m/s jet velocity ( 𝑇 = 25 𝑜𝐶). (a) stagnation region 0mm, and 15mm, and (b) parallel flow region 50mm, and 85mm. Another verification was performed using the free stream velocity as shown Figure 4-3. The figure shows the variations in the free stream radial velocity along the heated plate during four predetermined times of the jet impingement (𝑡 = 0.5, 1.0, 1.5, 2.0 𝑠𝑒𝑐). At the stagnation point (𝑟 = 0 𝑚𝑚), the free stream velocity is zero. The velocity then starts to increase in the acceleration zone until it reaches a maximum value of 1.7 𝑚/𝑠 which is equivalent to the jet impingement velocity. A radius approximately equal to the nozzle radius generally defines the impingement zone (𝑟 < 19 𝑚𝑚). In the parallel zone, the free steam velocity steadily drops until reaching virtually zero at 𝑟 = 140 𝑚𝑚. The frequent phase change between liquid to vapor caused the fluctuations in the parallel zone. The velocity profile described above is obtained from the simulation model, and it is quite similar to profiles reported in various literature. 52 Figure 4-3 The free stream radial velocity along the plate for different elapsed times 4.4 Cooling Curve Results Cooling curves are a graphical representation of the temperature change with respect to time at different locations. Cooling curves are a valuable tool for controlling the heat treatment and the final mechanical properties materials. In the literature, cooling curves are normally established experimentally with some numerical assessment. The wide variety of experiments conducted in the literature makes it difficult to compare different experimental results due to variations in experimental conditions and parameters, such as initial steel temperature or water flow rate, as well as differences in configuration, such as jet diameter or sample size. In this study, we compare infrared measurements conducted in the ADU facility with thermocouple temperature data from experiments done at the UBC ROT facility [4]. In the comparison of results, we mainly 00.20.40.60.811.21.41.61.80 0.02 0.04 0.06 0.08 0.1 0.12 0.14Velocity (m/s)Radial Location (m)Free stream Radial velocity vs Radial locationt = 0.5 st = 1.0 st = 1.5 st = 2.0 s 53 use three different locations on the plate surface: stagnation region, at 60 mm radius from the stagnation center, and at 120 mm away from stagnation. In the UBC experiment, the used plate was high strength low alloy (HSLA) steel, and embedded thermocouples (1 mm below the plate surface) of the bead type K installed in a hole with a diameter of 1.59 mm were used for temperature measurement. The plate was heated up to 720 °C, and its dimensions are 40 x 43 cm. In the ADU experiment, low carbon stainless steel 316L is used with a dimension of 45 x 50 cm and a thickness of 6 mm. The initial temperature of the wall was approximately 660 °C, and the plate temperature was almost uniform before the cooling process. The fluid temperature and jet impingement velocity were 𝑇 = 25 °𝐶 and 𝑉 =1.7 𝑚/𝑠, respectively. Figure 4-4 demonstrates the transient temperature profile on the plate surface at impingement for both ADU and UBC experiments. Since both experiments have different initial plate temperatures, we must locate the time when the cooling fluid is in contact with the heated plate, or, in other words, the time of impingement. To do that, we manually draw two tangential lines, one at the steady trend (before one second) and the other after the sharp drop (after one second). The intersection of the two tangent lines is the start of impingement. After that, we match the time of impingement for ADU results and compared them with Nobari et al. [4] experiment. As shown in Figure 4-4, the gray line is Nobari et al. [4] temperature measurements by utilizing thermocouples. The orange line is the thermal camera temperature measurement from underneath the plate without fluid disturbance while the red line is the top surface measurement after using INTEMP code [39]. Both methods predict similar behavior at the stagnation point. Nobari et al. [4] initial temperature was 720 °C and heat transfer before impingement is cooled by 54 air convection, at the time of impingement the temperature drops dramatically to almost 160 ºC in just two seconds. On the other hand, the measured temperature from thermal camera shows a sudden drop in less than one second. Then the gradient decreases slightly for all curves until reaching a plateau. Both temperature measurements demonstrate similar temperature drop behavior with a deviation; this deviation could result from various reasons. One reason is that when a thermocouple is inserted into the plate, there is change of geometry that causes change in thermal field, and an energy imbalance between the thermocouple's hot junction and the entire system. Additionally, the thermocouples primarily measure the temperature of their own hot junction rather than directly measuring the temperature of the sample. Hence, due to their own thermal inertia and the presence of thermal contact resistances when attaching the sensor to the plate. Another vital reason is that the installation of the thermocouples might disturb the thermal field inside the material due to the small holes drilled to embed the thermocouples and wiring. The removal of some materials may cause changes in the thermal field and the cooling curve. Xu and Gadala [25] and Attia et al. [70] found that a source of error could arise because of temperature field distortion due to thermocouple holes. Additionally, the thermocouple’s response time affects the temperature change. The aforementioned reasons can be found in the sudden drop in Figure 4-4. Since thermocouples have an inherent response time which exhibit a delay in temperature measurements, as seen in the first two seconds. This can be noted in the temperature difference between both techniques. Because of this delay, thermocouples overestimate temperature compared to the infrared. Oliveira et al. [71] stated that Nobari et al. [4] fast response time thermocouples give three times higher in heat flux. Also, they stated that a correction method is essential in fast transient experiments involving 55 thermocouple measurements in order to obtain precise estimations of heat flux when addressing inverse heat conduction problems. Therefore, the infrared technique gives a more accurate temperature measurement because it can instantaneously measure the temperature. Several cooling studies that involve a high-temperature plate have utilized the INTEMP program [72][73][74][75]. The INTEMP code have shown a track record of demonstrating an accurate result. The code as expected predicted lower temperature measurement which can be observed in the lagging results. This is mainly because of no fluid disturbance. From Figure 4-4, it can be observed in the infrared technique that the temperature drops from 660 °C to almost 110 °C in less than one second, while thermocouple drops to the same temperature in eight seconds. In a study conducted by Castanet et al. [76], it was demonstrated through the use of infrared thermography that the surface temperature can decrease by 140 °C (initially at 550 °C) during a single drop of water impact in less than one second, which would not be measured equally by a thermocouple. Figure 4-5 and Figure 4-6, show the temperature-time curves for the parallel zone at radial distances of 60 mm and 120 mm from the impingement point, respectively. In the cases of the 60 mm and 120 mm, the temperature reading was initially compared during the steep drop in temperature (time of impingement). For the case of the 60 mm, as seen in Figure 4-5, both techniques exhibited a general pattern of a sudden drop in temperature until reaching a steady state. The infrared camera demonstrates the sharpest drop in temperature from 660 ºC to 100 ºC in less than one second. However, thermocouples reach 100 ºC in more than 10 seconds which is quite a long period. Similarly, for the case 120 mm away from the zone, temperature readings from the infrared camera using the INTEMP code are more authentic since they give a lagging temperature reading than thermocouples (capturing the change in temperature quicker). 56 As stated above, the discrepancy in temperature readings is due to the fact that thermocouples have a response time effect, which requires a proper correction method to minimize errors. Also, thermocouples have thermal field distortion due to the drilled holes and measure their hot junction rather than surface temperature. Figure 4-4 Temperature history comparison between Thermocouple (Nobari et al. [4]) and Infrared camera at stagnation. 57 Figure 4-5 Temperature history comparison between Thermocouple (Nobari et al. [4]) and Infrared camera for 60mm away from stagnation point. Figure 4-6 Temperature history comparison between Thermocouple (Nobari et al. [4]) and Infrared camera for 120mm away from stagnation point. 58 Chapter 5: Conclusion The cooling procedure on a run-out table is a crucial step that determines the steel's final microstructure and mechanical properties. In this study, we acquire the thermal history on the plate surface using the more recent technique of infrared thermal imaging. This technique has the advantage of capturing the surface temperature history remotely and with no contact with the plate, and it can capture the temperature history for the entire plate. In this work, controlled cooling experiments under transient conditions were conducted on a hot stationary plate using an impinging top circular nozzle and a thermal camera to measure thermal information. The thermal camera measurements (conducted in Abu Dhabi University) have been compared to the thermocouple measurements (University of British Columbia). The infrared camera coupled with inverse heat transfer (for impingement zone) may provide more accurate results than thermocouples due to the response time effect of thermocouples, which needs a correction method to reduce errors. In addition, due to the drilled holes, thermocouples have a thermal field distortion and measure their hot junction rather than the surface temperature. Therefore, the thermal infrared technique allows suitable temperature measurement in the jet impingement of hot steel plate. Additionally, we present a transient multiphase numerical simulation to determine the temperature profile on the plate surface and compare it to thermal camera results. The numerical simulation was done using the Ansys-Fluent CFD simulation software. The simulation model findings for a jet impingement cooling case showed very good match with the experimental data available from ADU ROT facility (by using thermal camera). The results demonstrate that the developed simulation model can predict temperature history drops with good accuracy and assure that the calibration and readings of the experimental thermal infrared camera are accurate. The ability of being able to predict the thermal history with numerical simulation, rather than mostly 59 experimental, has great potential in studying multitude of practical parameters that are difficult to attain experimentally. 5.1 Recommendation and future work: Based on the findings of the experimental work and the simulation model, the following points are suggested for further study. • Consider a three-dimensional (3D) model instead of a 2D axisymmetric. 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Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Gadala, Mohamed
Grecov, Dana
Water jet impingement in run-out table cooling
Text