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Quantification of cooling channel heat transfer in low pressure die casting Moayedinia, Sara 2014

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  QUANTIFICATION OF COOLING CHANNEL HEAT TRANSFER IN LOW PRESSURE DIE CASTING   by   Sara Moayedinia  B.A.Sc. The University of British Columbia (Vancouver)   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE DEGREE OF MASTER OF APPLIED SCIENCE in The Faculty of Graduate and Postdoctoral Studies  (Materials Engineering) THE UNIVERSITY OF BRITISH COLOMBIA (Vancouver) July 2014 © Sara Moayedinia, 2014 ii Abstract The focus of this project is to develop a methodology to quantitatively describe the heat transfer in the cooling channels of the low-pressure die casting process, which is the dominant commercial technology for the production of aluminum automotive wheels, and to successfully implement the methodology in a numerical model of the casting process. Towards this goal, an algorithm capable of calculating heat transfer coefficient (HTC) based on process parameters and surface temperature within the cooling channel is developed. The algorithm was implemented in the form of a user-defined subroutine in a 3-D thermal model of the Low Pressure Die Casting (LPDC) process developed in the commercial finite element analysis package in ABAQUS.  The cooling channel HTC’s are often input into thermal models as an average constant value derived based on trial-and-error. The trial-and-error process to obtain the HTCs in the cooling channel involves, prescribing a trial set of HTC values and comparing the results of the casting simulation with thermocouple measurements. The trial cooling channel HTCs are then adjusted until a reasonable fit to the temperature measurements are achieved. The trial-and-error process is generally time consuming and does not accurately describe the physical phenomenon occurring in the cooling channel during casting. The constant cooling channel HTCs obtained through the trial-and-error process are tuned to a given set of operating conditions, compromising the utility and generality of the model.  To provide data necessary for model validation, casting plant trials were performed at Canadian Autoparts Toyota Inc. in Delta, British Columbia. The trials included temperature measurements at pre-determined locations within the top, side and bottom dies. The validity of HTC calculations have been assessed by comparing the predicted temperature history of the subroutine-based model with the measured thermocouple data collected during the casting cycle  iii and also comparing the model predictions with the base-case model with constant cooling channel HTC.                 iv Preface Dr. Carl Reilly, a Research Associate at the University of British Columbia, performed the temperature measurements detailed in Chapter 4. Dr. Carl Reilly as part of a larger APC program also developed the base case thermal model in Chapter 5. The development of the cooling channel subroutine, implementing the subroutine in a thermal model and comparisons to the temperature measurements are my work.   v Table of Contents Abstract ........................................................................................................................................... ii Preface ............................................................................................................................................ iv Table of Contents ............................................................................................................................ v List of Tables ................................................................................................................................ vii List of Figures .............................................................................................................................. viii List of Symbols .............................................................................................................................. xi Acknowledgements ...................................................................................................................... xiii  Introduction ............................................................................................................................... 1 1. 1.1 Low pressures die casting .................................................................................................. 2 1.2 Casting defects ................................................................................................................... 7 1.3 Thermal modeling of LPDC .............................................................................................. 9  Literature review ..................................................................................................................... 12 2. 2.1 Heat transfer in die cooling channels ............................................................................... 12 2.2 Forced convection heat transfer ....................................................................................... 13 2.3 Boiling heat transfer ......................................................................................................... 17 2.3.1 Pool boiling heat transfer .......................................................................................... 18 2.3.2 Flow boiling .............................................................................................................. 21 2.4 Application of heat transfer coefficients in LPDC ........................................................... 32 2.4.1 Effect of process parameters on the boiling curve .................................................... 35 2.4.2 Quantification of heat transfer coefficient in casting modeling ................................ 39  Scope and objectives ............................................................................................................... 43 3. 3.1 Objectives of the research programme ............................................................................. 43 3.2 Scope of the research program ......................................................................................... 43  Experimental measurements ................................................................................................... 46 4. 4.1 Temperature measurements ............................................................................................. 47 4.2 Flow measurements .......................................................................................................... 52 4.2.1 Flow rate ................................................................................................................... 53  vi 4.2.2 Cooling timing measurements (flow sensor) ............................................................ 53  Computational process modeling ........................................................................................... 57 5. 5.1 Thermal model development ........................................................................................... 57 5.2 Model geometry and mesh ............................................................................................... 58 5.3 Material properties ........................................................................................................... 61 5.3.1 Thermo physical properties ....................................................................................... 62 5.4 Initial conditions .............................................................................................................. 64 5.5 Thermal boundary conditions .......................................................................................... 65 5.5.1 Thermal boundary conditions-base model ................................................................ 66 5.5.2 Thermal boundary conditions-correlation-based approach via subroutine ............... 74 5.6 Convergence criteria ........................................................................................................ 86  Results and discussion ............................................................................................................ 87 6. 6.1 Cooling channel HTC ...................................................................................................... 87 6.1.1 Base-case thermal model with constant HTC ........................................................... 88 6.1.2 Thermal model with user-defined subroutine ........................................................... 89 6.2 Temperature comparison .................................................................................................. 96 6.3 Discussion ...................................................................................................................... 106  Summary and conclusions .................................................................................................... 110 7. 7.1 Recommendations for future work ................................................................................ 112 References ................................................................................................................................... 114 Appendices .................................................................................................................................. 120 Appendix A ............................................................................................................................. 120 Appendix B ............................................................................................................................. 121 Appendix C ............................................................................................................................. 122 Appendix D ............................................................................................................................. 124     vii List of Tables Table 5.1: The nominal composition of A356 and H13 ............................................................... 62 Table 5.2: Thermophysical properties of A356 and H13 used in the Thermal model .................. 63 Table 5.3: Heat transfer coefficient for wheel/die interfaces (*Height dependant boundary conditions to replicate filling at the wheel/die-components interfaces) ....................................... 68 Table 5.4: Heat transfer coefficient for die components and sprues interfaces ............................ 69 Table 5.5: Heat Transfer between the die and the environment (radiation boundary conditions) 71 Table 5.6: Cooling channel boundary conditions, trimming and constant heat transfer coefficient used in the base model .................................................................................................................. 73 Table 5.7: Water and Air flow rate in the cooling channels ......................................................... 75 Table 5.8: Cross sectional area and perimeter of cooling channels .............................................. 77 Table 5.9: Constants for use in Equation 5.12 .............................................................................. 80 Table 5.10: User-defined convergence control parameters .......................................................... 86 Table 6.1: Average HTCs calculated by the subroutine and constant HTC used in base-case thermal model ............................................................................................................................. 109   viii List of Figures   Figure 1.1: Schematic illustration of LPDC process 6 .................................................................... 4 Figure 1.2: Outboard face of wheel-427 model .............................................................................. 6 Figure 1.3: Side view wheel-427 model ......................................................................................... 6 Figure 2.1: Boiling curve of water at 1 atm 18 .............................................................................. 19 Figure 2.2: Flow boiling in circular tube  20 .................................................................................. 22 Figure 2.3: Flow pattern and temparture variation in subcooled flow boiling 19 .......................... 25 Figure 2.4: Boiling curve for secondry cooling regime for D.C.casting of aluminium 38 and contonius casting of steel 39 .......................................................................................................... 34 Figure 2.5:  Effect of water flow rate on the boiling curve of AA5182- free falling zone 38 ....... 36 Figure 2.6: Effect of initial surface temperature on the boiling curve of AA5182- free streaming zone 44 ........................................................................................................................................... 38 Figure 4.1: Thermocouple locations in the top die ....................................................................... 48 Figure 4.2: Thermocouple locations in the bottom die ................................................................. 48 Figure 4.3: Thermocouple locations in the side die ...................................................................... 49 Figure 4.4: Variation of temperature within cycles 26-32 for  TC1 ............................................. 50 Figure 4.5: Variation of temperature within cycles 26-32 for  TC2 ............................................. 50 Figure 4.6: Cast-in wheel thermocouples. From left: cycle 27, 29 and 30 ................................... 52 Figure 4.7: Schematic representation of cooling line showing the extend of piping from solenoid valve to the die. Note that there are 3 cooling lines in the top die, 1 in the side die and 2 in the bottom die. .................................................................................................................................... 54 Figure 4.8: Schematic  representation of flow sensor ................................................................... 55  ix Figure 4.9: Flow sensor and thermocouple sensors ...................................................................... 56 Figure 5.1. a: Inboard Face of wheel-427 model with five spokes,  b: Side view of heel-427 model ............................................................................................................................................. 58 Figure 5.2: 36˚ section of the wheel and the die ........................................................................... 59 Figure 5.3: Cooling channels in the 3-D thermal model ............................................................... 60 Figure 5.4: 36° mesh of wheel and the die ................................................................................... 61 Figure 5.5: Generic boiling curve indicating different heat transfer regimes- Linear interpolation in the nucleate boiling region 60 .................................................................................................... 83 Figure 6.1:  Contour plot of temperatures in the wheel and die prior to die open ........................ 89 Figure 6.2: Temperature history (a) and boiling curve (b) for side die cooling channel (SDC-CC)....................................................................................................................................................... 92 Figure 6.3: Temperature history (a) and boiling curve (b) for top die drum core cooling channel (TDDC-CC) .................................................................................................................................. 93 Figure 6.4: Temperature history (a) and boiling curve (b) for bottom die cooling channel 2(BD-CC2) .............................................................................................................................................. 94 Figure 6.5: Temperature history and calculated HTC for bottom die cooling channel 1(BD-CC1)....................................................................................................................................................... 95 Figure 6.6: Comparison of predicted and measured temperatures at three locations within bottom die spoke TC-21, 23, 25 and 24 .................................................................................................... 98 Figure 6.7: Comparison of predicted and measured temperatures at three locations within bottom die window TC-27 and TC-28 ...................................................................................................... 99 Figure 6.8: Comparison of predicted and measured temperatures at two locations within side die spoke TC-5 and TC-4 .................................................................................................................. 100  x Figure 6.9: Comparison of predicted and measured temperatures at two locations within side die window TC-14 and TC-15 .......................................................................................................... 101 Figure 6.10: Comparison of predicted and measured temperatures at a location within top die TC43 ........................................................................................................................................... 102 Figure 6.11: Comparison of predicted and measured temperatures at three locations within top die spoke TC-49, 46 and 50 ........................................................................................................ 103 Figure 6.12: Comparison of predicted and measured temperatures at two locations within top die window TC-47, TC-48 ................................................................................................................ 104 Figure 6.13: Comparison of predicted and measured temperatures at two locations in top die center pin TC-60 and top die drum core TC-61,TC-62 .............................................................. 105              xi List of Symbols Latin Symbols Description Units Cp Specific heat J/kg/K L Latent heat kJ/kg k Thermal conductivity W/m/K h Heat transfer coefficient W/m2/K P Pressure Pa q Heat flux W/m2 T Temperature °C 𝐷? Hydraulic diameter m 𝐴? Area m2 𝑅𝑒 Reynolds number  𝑢? Mean fluid velocity m/s 𝑁𝑢 Nusselt number  𝐺𝑟 Grashof number  𝑃𝑟 Prandtl number  ℎ™  Latent heat of vaporization kJ/kg Greek Symbols   ρ density kg/m3 α Thermal expansion coefficient  α Thermal diffusivity m2 /s σ Stefan-Boltzmann constant  𝜖 Emissivity of a surface  𝜇 Dynamic viscosity Pa/s 𝑣 Kinematic viscosity m2 /s  xii 𝜎 Surface tension N/m subscripts   sat Saturation temperature °C NC Nucleate boiling  FC Forced convection  wall Cooling channel surface  L liquid  g Gas/vapor  CHF Critical heat flux  ONB Onset of nucleate boiling           xiii Acknowledgements I would like to express my sincere gratitude to my supervisor, Professor Steve Cockcroft for the continuous support and guidance throughout the course of this work. I would also like to give thanks to Professor Daan Maijer for his advice and great involvement during my studies. I am grateful to Dr. Carl Reilly for his valuable contributions ranging from casting trials and model development to revising and editing this thesis. I would like to thank Dr. Matt Roy, Jianglan Duan, Xiaodan Wei, Farzaneh Farhang Mehr and Jun Ou for their help and support thorough the course of this research project. Finally I would like to thank my family for their unconditional love and support, and Filip for always being there with me.               1   Introduction 1.In today’s world accessibility plays an important role in prosperity and the well-being of societies. With countries’ urban populations booming and increases in economic and social networks, transportation is becoming increasingly important as the backbone of economic growth and social interactions. Unfortunately, many forms of transportation have an adverse effect on air quality and the environment. According to the United Nations Environment Programme, 90% of the air pollution in developing countries is attributed to vehicle emissions1. The drive for increased fuel efficiency is led by both consumer demands, as the price of fuel continues to increase, and governments, pushing for more stringent fuel efficiency standards. Due to these demands, the automotive industry has been forced to develop new technologies for more environmentally friendly vehicles.  The increased demand for more fuel-efficient vehicles has had a significant effect on the choice of materials used for cars driven by the need to reduce vehicle weight and thus reduce energy consumption. According to a study in The Institute for Energy and Environmental Research (IFEU), a 100-kilogram mass reduction of a standard vehicle results in fuel savings of 300 to 800 liters over the lifetime of a vehicle. This reduction can decrease greenhouse gas emissions by the equivalent of 9g of 𝐶𝑂?  per kilometer 2. Another study suggests that a 10% vehicle weight reduction results in 8-10% in fuel economy improvement 3. In response to the demand for a reduction in weight, there have been increased efforts to replace steel and cast iron with aluminum and magnesium in vehicles.  Aluminum has good formability, high strength and stiffness to weight ratio and superior corrosion resistance properties, making it an ideal substitute for heavier metals such as steel and cast iron. Today, aluminum is widely used for vehicle  2  components such as engine blocks, wheels, suspension components, brake calipers, bumpers, hoods and radiators. In the case of wheels, there is a considerable “knock-on-effect” associated with weight reduction. In a car, components above the suspension are defined as the sprung mass, such as the body and engine. Non-suspended, unsprung mass, parts include suspension components, brake calipers and wheels. The ratio between the sprung and unsprung mass influences the vibration transmitted to the vehicle occupant caused by unevenness in the road4. When a vehicle is on a poor or mediocre road, dynamic (vibratory) behavior affects the road-holding and comfort level. For example, for a vehicle on poor roads a 20% reduction in unsprung mass results in 10% increase in the level of occupant comfort (according to ISO standard 2632)5. The need to improve fuel consumption, along with the added benefit of better ride quality, - are incentives for automotive companies to manufacture lighter automotive wheels. Modern aluminum alloy wheels must also meet strict mechanical specifications including impact and fatigue performances to ensure safety standards are achieved. Additionally wheels are one of the prominent cosmetic features on cars and, consequently, have stringent aesthetic requirements. The drive for lighter aluminum wheels calls for a better wheel design, aiming to reduce mass (thinner rim, hub and spoke) without sacrificing the required mechanical and aesthetic specifications. 1.1 Low pressures die casting The low-pressure die casting (LPDC) process is widely used to manufacture automotive wheels owing to its ability to produce high quality, high metal yield and cost effective wheels. The LPDC process is currently used at Canadian Autoparts Toyota Inc. (CAPTIN). In the LPDC process heat is transferred from the cast metal to the die and ultimately to the environment. To facilitate heat removal the dies are constructed with cooling channels strategically placed in  3  different areas. Cooling channels contain fluids such as air, water or oil to extract heat from the surface of the channel. The LPDC process is categorized into two types: the convectional air-cooled version in which the die is cooled down by forcing compressed air through the cooling channels and the water-cooled version with water circulating through the cooling channels. Water-cooling is used to increase the cooling rate, resulting in a finer solidified microstructure, superior mechanical properties and reduced cycle time in comparison to air-cooling version.   The LPDC process is schematically shown in Figure 1.1. A typical LPDC casting machine consists of a die assembly with one or two die cavities, which sits on top of a sealed furnace containing the molten aluminum alloy. The die assembly is made of cast iron, or tool steel, and has four main sections: two side dies, a bottom die and a top die which all come together to create a cavity for the wheel (casting). The die cavity is usually coated with a thin layer of ceramic to protect and lessen the rate of heat transfer between the liquid metal and the die since the die cavity fills at a relatively slow velocity. The LPDC casting process is cyclic and starts with pressurizing the furnace. The molten aluminum is forced up into the cavity through a transition pipe and into the die cavity. The air in the die cavity escapes through venting channels in the die. The die filling takes 10-30 seconds depending on the wheel model and pressures used. Once the molten metal fills the cavity it starts to solidify. When the solidification front reaches the top of the riser pipe the furnace is de-pressurized and the unsolidified metal in the transfer tube and sprue fall back to the furnace. After the solidification is completed, the two side-dies open and the top die moves up vertically with the cast wheel attached to it. The wheel is attached to the top die due to the thermal contraction of aluminum alloy. The wheel is then ejected from the top die to a transfer tray. Before the next cycle starts, the operator may remove any solidified extra material from the die faces and touch up the ceramic coating on the die (happens ~every  4  100 wheels). The die then closes and the cycle starts again. The wheel is then visually inspected for surface defects before, heat-treating to the T6 condition, machining and painting to achieve the desired finish.    Figure 1.1: Schematic illustration of LPDC process 6    On average the cycle time for the air-cooled variant is around 5-6 minutes, compared to 3-4 minutes for the water-cooled variant. The cooling channels typically vary in size, location and shape depending on the die design (wheel model) and the wheel geometry. Cooling duration (on-off time) and cooling intensity (flow rate of the fluid) affect the die temperature and the solidification behavior of the wheel, and are usually optimized for a given wheel and die geometry using a trial-and-error methodology. The optimization is targeted at reducing the solidification defects including shrinkage porosity, cold-shuts and surface defects.   5  Automotive wheels have a complex geometry with different parts such as the rim, spokes and the hub containing the bolt holes. Figure 1.2 shows the outboard face of a wheel with five spokes (in the un-machined state), which is visible when the wheel is bolted to the car. Figure 1.3 shows the side view of the wheel. The rim forms part of a pressure vessel with the tire. The hub connects the wheel to the car and the loads are transferred between the rim and the hub via the spokes. Consequently, the spokes are subjected to both normal (weight of the car) and bending loads (during vehicle concerning).  Referring to Figure 1.2 and 1.3, solidification generally proceeds from the inboard rim flange, down the rim toward the outboard rim flange and across the spoke. A loss in directional control of the process of the solidification front in the wheel can result in liquid entrapment –i.e liquid material surrounded by solid. The subsequent solidification of the encapsulated liquid results in shrinkage porosity, which may constitute a defect if it falls outside of the specification for a given wheel (the specification generally relate to the size and location of the void).   6       Figure 1.2: Outboard face of wheel-427 model      Figure 1.3: Side view wheel-427 model    7  1.2 Casting defects Manufactured wheels must meet certain specifications which include: air tightness, structural requirements since wheels are a critical safety components, high quality surface finish, due to their importance in the overall cosmetic appearance of the car and rotational tolerance. In terms of the structural requirements, fatigue performance and impact resistance of the wheel are key. Casting defects related to porosity, entrained oxide film and hot cracks, the three most important casting defects in cast wheels, affect both the mechanical performance and the surface finish of casting wheel 7. Focusing first on porosity, depending on the size of the pore, porosity can be categorized as microporosity or macroporosity. Macroporosity or shrinkage porosity occurs during the liquid to solid transformation when liquid metal gets encapsulated by the solidified metal during the solidification of a component. As the liquid within this region solidifies the pressure in it drops due to a lack of feeding and leads to the cavitation of a liquid metal vapor bubble(s) resulting in macroporosity. In A356, a common alloy used for wheel casting, the shrinkage is around 5.4% by volume 8.  Liquid encapsulation often occurs in areas of casting where the thickness changes abruptly, since the thinner section solidifies rapidly, blocking the supply of liquid metal to thicker sections. Macroporosity defects can also occur due to gas entrainment when the die is filling with molten metal. In aluminum alloy macro or shrinkage-based porosity defects are usually present at the junction between the spoke and rim of the wheel due to a loss in directional solidification. The resulting defects dramatically affect fatigue and impact performance as well as the load bearing capability of the wheel 8. Microprosity (< ~300 µm in diameter) or hydrogen based porosity is described as small, dispersed voids 9. Microporosity is due to the creation of hydrogen gas bubbles due to the  8  reduced hydrogen solubility in the solid in comparison to the liquid. Inadequate feeding at a high fraction of the solid can also exacerbate the problem due to the accompanying reduction is pressure. Fast cooling of the metal decreases the size distribution of hydrogen related porosity, resulting in better mechanical performance of the wheel. Microporosity defects also affect the surface appearance and the fatigue performance of the wheel. Microporosity defects can be controlled through the hydrogen content of the molten metal and cooling rate 10,11. Oxide film related defects are due to the entrainment of oxidized aluminum during filling of the die. Oxide films can be entrained into the bulk liquid metal during charging of the melting furnace, turbulence induced by pouring of metal or die filling 10. Entrained oxide film, may act as stress concentration sites and cause fatigue cracking or act as nucleation sites for hot tearing and porosity 9. Hot tearing defects occur at elevated temperatures, often above solidus temperature. At high solid fractions, thermal tensile stress in the solid-liquid regime causes deformation of the solid, which pulls apart the dendrite arms in the liquid regions. In the absence of liquid for feeding, the deformation draws air, if at the surface, or result in cavitation of voids, which coalesce to form a crack or hot-tear defects 11. In conclusion, to achieve a structurally sound cast wheel, with minimal defects, the solidification should be closely controlled. In addition to alloy chemistry, dissolved gas and nonmetallic inclusions should be controlled in order to limit porosity and eliminate stress raising oxide films. Eliminating turbulence during the die filling and metal pouring and furnace charging can reduce the risks of entrained defects. Also directional solidification should be maintained within the wheel through proper die design and cooling optimization. Mathematical modeling of the LPDC  9  process allows the dies to be designed and cooling to be optimized, ensuring that directional solidification is achieved. 1.3 Thermal modeling of LPDC The drive to manufacture superior quality, less expensive and lighter wheels has led to the widespread use of computer-based process modeling and optimization. Computer modeling of the filling, feeding and solidification plays an important role in developing a better understanding and improving the casting process. These mathematical models describe the evolution of temperature and fluid flow throughout the casting process and can be used to predict defect formation. Consequently, better die geometry and cooling systems can be designed in order to achieve premium quality wheels. Casting simulation can be used as a predictive tool, enabling the wheel manufacturers to better understand the effect of key process parameters. Unnecessary casting trials, design errors and startup delays can be avoided once the key casting parameters and their effect on the final wheel product are identified. Casting solidification simulations of LPDC can be undertaken using a finite element method. The basic requirement of such a model requires that the geometry, material properties, initial conditions and boundary conditions be defined. The latter are defined in terms of the boundary needed to solve the governing Partial Differential Equation.  It is, however, a challenge to accurately quantify some of the boundary conditions; specifically at the casting/die and cooling channel/die interface 9,12. The majority of the heat removal during LPDC is achieved through the cooling channels with air and/or water flowing at specific rates and temperatures for a defined period of time. The heat transfer between the cooling fluid and the hot surface of the cooling channel can be categorized  10  as single phase or two-phase fluid flow-heat transfer. For example, in the case of water flowing in the channel, depending on the surface temperature of the channel, flow rate and pressure of water, boiling may occur. Single-phase heat transfer (air or water) can be quantified through forced convection heat transfer coefficient (HTC) correlations. However, describing two-phase flow heat transfer is a challenge due to the complex nature of boiling. The correct description of the HTC’s in the cooling channel is critical to achieving an accurate computational model, without which the accuracy and therefore the benefits of computational modeling are significantly degraded.   Currently, cooling channel HTC’s are often input into thermal models as an average constant value 7,13,14. Generally, the heat transfer coefficient is estimated using experimental data, inverse modeling techniques or using trial-and-error techniques. The use of a trial-and-error method to obtain the HTC in a cooling channel involves, estimating the HTC values used in the model and then comparing the final results of the casting simulation to thermocouple measurements. The boundary conditions are then adjusted for each model until a reasonable fit is produced 12. This process is extremely time consuming and does not accurately describe the physical phenomenon occurring during casting. Moreover, as the boundary condition is tuned to a given set of operating conditions and die geometry, the generality and utility of the model is greatly compromised.   The intensity of cooling varies depending on the dominant heat transfer phenomena (forced convection or boiling), which is dependent on parameters including flow rate, pressure and surface temperature 15. Boiling can also further be categorized into either saturated or subcooled boiling based on the bulk fluid temperature of water in channels. Within the boiling region, depending on the surface temperature, heat transfer can be dominated by nucleate, transition or  11  film boiling with each resulting in a different HTC 16. Quantifying the boundary condition at the cooling channel-coolant interface is challenging owing to the complexity and transient nature of each phenomena. Hence, efforts are needed to quantify realistic HTC values based on process parameters and geometry of the cooling channel. Quantifying the cooling channel boundary condition, as a local instantaneous HTC value, sensitive to process parameters and surface temperature, will reduce the inaccuracies currently associated with the definition of cooling channel boundary conditions in casting modeling greatly improving their utility as die design tools and process control optimization tools.              12   Literature review 2.2.1 Heat transfer in die cooling channels In the Low Pressure Die Casting (LPDC) process, heat is transferred from the casting to the die and then to the environment. To facilitate heat removal, dies are constructed with cooling channels strategically placed in different locations. Air or water is used to cool the surface of the cooling channels. The duration of the cooling within a cycle (the length of time a coolant is flowing in a channel) as well as fluid temperature, pressure and flow rate can be adjusted to control the die temperature and therefore the solidification occurring within the wheel. It is therefore crucial to be able to predict the heat transfer coefficient associated with cooling channels in LPDC dies under operational conditions. The aim of this literature review is: 1. To identify different cooling phenomena in the cooling channel associated with both water and air cooling, including forced convection and boiling heat transfer, in the case of water.  2. To understand the effect of various parameters such as flow rate, pressure, surface temperature, and coolant temperature on the rate of heat transfer. 3. To review and critically assess the existing research relevant to the cooling channel heat transfer coefficient quantification and casting modeling. Depending on the surface temperature of the cooling channel and cooling media the heat transfer phenomena can be categorized as forced convection heat transfer or boiling heat transfer. Forced convection is defined as the transfer of heat from the bounding surface (cooling channel) to a moving fluid experiencing bulk motion.  Boiling heat transfer is defined as the addition of heat to  13  a liquid in such a way that the generation of vapor occurs.  Davey and Hinduja were pioneers in recognizing the importance of boiling heat transfer in pressure die casting 17. Boiling heat transfer however has been a subject of interested for many researchers in the past century. In 1941 McAdams found that the local heat transfer coefficient, due to local boiling of the fluid passing through a horizontal tube, was four times that of single phase heat transfer 15. The substantial increase in the heat transfer coefficient associated with boiling dramatically affects the rate of heat extraction during casting. It is therefore important to understand both single phase and two-phase heat transfer modes that may occur in the cooling channel.  2.2 Forced convection heat transfer  Forced convection is the transfer of heat between a surface and a fluid moving over the surface. If the fluid flow is confined by a surface, for example flow in a pipe, the heat transfer process is categorized as internal forced convection. When fluid enters a pipe with a uniform velocity, the velocity profile quickly evolves under the influence of viscous forces subject to the constraint that the fluid immediately adjacent to the surface is at rest (zero velocity) relative to the fluid in the center of the pipe. The velocity profile from the center of the pipe to the surface changes along the pipe in the hydrodynamic entrance region (region near where fluid first enters the pipe). In the fully developed flow region of the pipe, the velocity profile does not change with distance along the pipe. The existence of fully developed flow in internal flow is important in developing the forced convection heat transfer coefficient correlations.   Fluid flow can be classified as compressible or incompressible depending on the density variation of the fluid during flow. Liquids are usually classified as incompressible since their densities are essentially constant. Mach number, a dimensionless quantity representing the ratio of a fluid’s velocity to the speed of sound is used to assess the compressibility of the fluid flow.  14  Gas flows can be assumed incompressible if the flow velocity is less than 20 percent of the velocity of sound in that gas 18. Hence, airflow could be considered incompressible at speeds less than 100 m/s. (a sample calculation of the Mach number can be found in the appendix A). In order to estimate the local forced convective heat transfer it is necessary to determine whether the flow is laminar or turbulent. For a given flow, the dimensionless Reynolds number, which is the ratio of the inertial forces to viscous forces, is used to characterize different flow regimes. The Reynolds number for flow in a circular tube is defined as:     𝑅𝑒 = 𝜌𝑢?𝐷𝜇 = 𝑢?𝐷𝑣    2.1.      𝑣 = 𝜇𝜌   2.2.   where:  𝜌 is the density of the working fluid ™??   𝑢? is the mean fluid velocity over the cross section ??   𝐷 is the diameter 𝑚   𝑣 = 𝜇 𝜌   is the kinematic viscosity ???   𝜇 is the dynamic viscosity ™ ?   𝑜𝑟   ?∙???   𝑜𝑟   ™?∙?  In the case of fully developed flow, the onset of turbulent flow is Re ≈ 2300 16. In laminar flow, viscous forces are dominant hence, fluid particles move in a highly ordered motion in smooth streamlines. In turbulent flow, due to strong inertial forces, fluid particles have chaotic motions promoting random velocity fluctuations and mixing. In turbulent flow, heat and momentum  15  transfer is enhanced; hence the convective heat transfer is increased substantially compared to laminar flow.  Defining the mean fluid velocity 𝑢? is important since the velocity varies over the cross-section. The rate of mass flow through the channel then can be defined as:    𝑚 = 𝜌𝑢?𝐴?    2.3.   Where42DAcπ=  is the cross sectional area of a channel. To provide a measure of the convective heat transfer, another dimensionless quantity, the Nusselt number is defined. The Nusselt number is the ratio of the heat transfer through a fluid layer as a result of convection relative to heat transfer due to conduction across the same fluid layer.    𝑁𝑢 = 𝐶𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛  𝐻𝑒𝑎𝑡  𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛  𝐻𝑒𝑎𝑡  𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 = ℎ™ ∆𝑇𝑘 ∆𝑇𝐷 =ℎ™ 𝐷𝑘    2.4.   In the above equation, 𝑘 is the thermal conductivity of the fluid 𝑊 ∙ 𝑚?? ∙ 𝐾??  and ℎ is the convective heat transfer coefficient   𝑊 ∙ 𝑚?? ∙ 𝐾?? . The larger the Nusselt number the more effective convection heat transfer is 18. For a given fluid, the Nusselt number depends primarily on the flow conditions, which can be categorized by the Reynolds number. In laminar flow, fluid flow is ordered and there is no mixing of warmer and colder fluid particles hence the heat transfer takes place solely by conduction. The Nusselt number for fully developed laminar flow under constant heat flux condition is constant, independent of Reynolds number and can be described as 18:  16      𝑁𝑢 = ℎ™ 𝐷𝑘 = 4.36      𝐿𝑎𝑚𝑖𝑛𝑎𝑟  𝑓𝑙𝑜𝑤   2.5.   Since all fluids with the exception of liquid metals have relatively low thermal conductivities the forced convection heat transfer coefficient for the laminar flow is relatively small. In turbulent flow, random movements of fluid particles result in mixing, and an increase in the rate of heat transfer. Most correlations developed for the heat transfer coefficient in turbulent flow are based on experimental studies due to the complex and chaotic nature of turbulent flow. Dittues and Boelter introduced the flowing correlation for fully developed flow in a smooth circular channel subjected to a constant heat flux18.    𝑁𝑢 = 0.023𝑅𝑒?.?𝑃𝑟?.?          𝑇𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡  𝑓𝑙𝑜𝑤(𝐷𝑖𝑡𝑡𝑢𝑠− 𝐵𝑜𝑒𝑙𝑡𝑒𝑟  𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛)   2.6.   where    𝑃𝑟 = 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦  𝑜𝑓  𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦  𝑜𝑓  ℎ𝑒𝑎𝑡 = 𝑣𝛼 = 𝐶?𝜇𝑘    2.7.    𝛼 = ??∙??  is thermal diffusivity ???  and Cp is specific heat   ?™ ∙?   The Prandtl number, Pr, is a dimensionless number, calculated as the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity, which signifies the relative thickness of the velocity and the thermal boundary layer.  17  In most applications, the flow of the liquid through a pipe or a channel can be approximated as one dimensional thus all the properties are uniform at any cross section normal to the flow direction 18. Hence, fluid properties in the above correlations are evaluated at the bulk mean fluid temperature 𝑇™? = ?? 𝑇™    + 𝑇™? . For flow through a noncircular channel, the Reynolds number and the Nusselt number are based on hydrodynamic diameter, defined as    𝐷? = 4𝐴?𝑝    2.8.   Where Ac is the cross section are and p is the perimeter. 2.3  Boiling heat transfer When liquid is in contact with a surface maintained at a temperature (Twall) above the saturation temperature of the liquid (Tsat) a liquid-vapour phase transformation occurs. The heat transfer from the solid surface to the liquid is presented in the following form according to Newton’s law of cooling.	     𝑞 = ℎ™????? 𝑇™?? − 𝑇™? = ℎ™????? ∆𝑇? = ℎ™????? Δ𝑇™?    2.9.   Where ∆𝑇? = Δ𝑇™?  is excess temperature or wall superheat which describes the excess of the surface temperature above the saturation temperature of the liquid.  The phase change in boiling is characterized by the rapid formation of vapour bubbles at the surface interface, which detach from the surface when they reach a certain size. The boiling heat transfer rate and coefficient are generally much larger than that of convection heat transfer due to latent heat and buoyancy-driven effects 16.  18  Many engineering applications with high heat flux involve boiling due to the high cooling capacity induced by the boiling phenomena. Boiling can be categorized as either pool or flow boiling depending on the type of fluid motion. In pool boiling, fluid is quiescent and its motion near the surface is induced by natural convection due to buoyancy, bubble growth and detachment form the surface. Flow boiling or forced convection boiling is when fluid motion is induced by an external means (for example a pump) as well as natural convection. Boiling is also classified based on the liquid bulk temperature.  If the temperature of the liquid is equal to or slightly higher than the saturation temperature, saturated boiling occurs. However, if the bulk temperature is lower than the saturation temperature, subcooled boiling is present where bubbles form at the surface and then later condense in the liquid.  To acquire physical understanding of the characteristic phenomena of boiling heat transfer, first pool boiling and then flow or force convection boiling is described. Flow boiling is significantly more complicated than pool boiling owing to the coupling between boiling heat transfer and thermodynamics of the flow. However, both pool boiling and flow boiling posses common phenomena. The following sections covers basic theory of pool boiling and the resulting boiling, curve followed by an in-depth description of flow boiling and parameters affecting the boiling heat transfer.  2.3.1 Pool boiling heat transfer  In 1934, S. Nukiyama performed a series of experiments where an electrically heated wire was immersed in saturated water and the heat flux from the wire to the liquid was measured. The results of his experiments concluded that, depending on the value of excess temperature or wall superheat, boiling could take different forms. The results of his work are illustrated on the boiling curve (Figure 2.1) where heat flux is plotted as a function of excess temperature or wall  19  superheat. This boiling curve is for pool boiling of water at 1 atm. It is important to know that the general form of the boiling curve or the increase or decrease in the heat flux with wall superheat, is the same for different kinds of fluid. However, the specific shape of the boiling curve (magnitude of defined points and gradients of the curve) is dependent on parameters including fluid pressure, surface-fluid interface conditions as well as whether or not fluid is quiescent or moving (flow boiling). The various heat transfer regions in the boiling curve lead to significantly different heat transfer coefficients; thus, each region must be described in detail.    Figure 2.1: Boiling curve of water at 1 atm 18   20  Forced convection (start to point A) This region signifies single phase natural convective heat transfer (forced convective heat transfer for flow boiling). No vapour bubbles form and wall superheat (excess temperature) Δ𝑇™?   ≤  5 °𝐶. Analytical solutions and experimental correlations have been derived which allow for the prediction of the heat transfer coefficient in this region – see for example the previous section. Nucleate boiling (Point A to C) When Δ𝑇™ ?   ≈30 °𝐶 nucleate boiling is the dominant phenomena and two regions can be observed: region A-B, where isolated bubbles are formed, and region B-C, where vapour emerges as jets or continuous columns of bubbles. In region A-B isolated bubbles form and dissipate into the liquid shortly after they form at the nucleation sites on the surface. The detachment of the bubbles agitates the liquid, which is the main cause of the increased heat flux and heat transfer coefficient in the nucleate boiling region. As the wall superheat increases, moving towards region B-C, more nucleation sites become active and vapour escapes in the form of continuous columns of bubbles. The large heat fluxes and heat transfer coefficients in this region are the result of both the increased rate of vapour formation (latent heat of vaporizations) and the increased mixing induced by the bubbles in the vicinity of the wall. Point C represents the critical heat flux point, or the end of nucleate boiling. The critical heat flux for pool boiling of water at atmospheric pressure exceeds 1  𝑀𝑊 ∙ 𝑚??. Because of high heat transfer rates and consequently high heat transfer coefficients associated with relatively small values of wall superheat, nucleate boiling is considered to be the most desirable boiling regime when heat extraction rates are required.   21   Transition boiling (point C-D) As the wall superheat increases beyond point C, the heat flux decreases since a vapour layer, affecting the extent to which the water can contact the surface, covers a large fraction of the heated surface. The thermal conductivity of vapour is lower than that of a liquid, therefore it act as an insulator, causing a decrease in heat flux 𝑞  and heat transfer coefficient h as the wall superheat increases. This region is called transition boiling or partial (unstable) film boiling. For the pool boiling of water at atmospheric pressure, transition boiling occurs over the excess temperature range from around 120 to 300 ˚C.  Film boiling (point D-E) Point D on the boiling curve in the film boiling regime is called the Leidenfrost point, this is the point where the heated surface is entirely covered by a vapour film and the heat flux reaches a minimum local value. As the surface temperature increases, heat flux increases due to radiation and conduction through the vapour film. 2.3.2 Flow boiling  In the case of LPDC process, water is pumped into the cooling channels during the casting cycle under conditions where the wall temperature is significantly above the saturation temperature of water resulting in flow boiling conditions. In addition to die-casting, flow boiling of a liquid in a channel is commonly encountered in other engineering applications including steam generators (boilers), distillation, refrigeration and high heat flux cooling systems. If boiling occurs in a cooling channel, the heat transfer is categorized as internal flow boiling. Internal flow boiling is  22  more complicated than pool boiling due to a lack of a free surface for bubbles to escape, and the coupling effect of boiling heat transfer and the hydrodynamics of flow. Historically, most empirical internal flow boiling correlations were developed for vertical flow configurations in boiler applications. The vertical orientation of the heat exchanger in boilers takes advantage of the buoyancy force enhancing the slip velocity between the two phases and the heat transfer 19. It should be noted that all of the cooling channels within the LPDC die structure are oriented horizontally hence; extra care should be employed in reviewing the flow boiling literature and correlations.  Figure 2.2 shows flow boiling regimes in a uniformly heated circular tube. Starting from the left, subcooled liquid enters the tube and is heated as it flows through the single-phase region by forced convection. The heat transfer coefficient in this region is almost constant unless there is significant variation in the properties of the fluid with temperature as it moves along the channel.    Figure 2.2: Flow boiling in circular tube  20    As the wall temperature reaches the saturation temperature (𝑇™??   =𝑇™?   ), the subcooled flow boiling region is reached. Nucleation does not occur immediately since a certain amount of wall  23  superheat is needed for the cavities existing on the wall to nucleate.  Bubbles start forming on the surface at the onset of nucleate boiling (ONB). The bubbles generated immediately downstream of the ONB will not grow because they condense as they are exposed to the subcooled fluid flow. Further downstream, more nucleation sites are activated and the contribution of nucleate boiling increases as the single phase forced convection contribution decreases.  This region is called partial nucleate boiling. As the wall temperature increases, fully developed boiling (FDB) is established where the effect of forced convection is minimal and nucleate boiling is predominant.  As the liquid’s bulk temperature is increasing in the flow direction, more bubbles form and at the point of net vapour generation (NVG), they start detaching from the surface and flowing towards the liquid core. Following NVG, heat transfer is in the two-phase region. Further downstream, significant void flow starts, where the effect of forced convection becomes important again due to the nature of two-phase flow. The vapour present after the NVG is at the saturation temperature 𝑇™?   , This implies the end of subcooled boiling. As the heat addition continues beyond 𝑥 = 0 flow falls into the saturated flow boiling regime. The state of the subcooled liquid can be defined using equilibrium “quality” 𝑥 which is based on the enthalpy of liquid relative to the saturation state    𝑥 = ℎ? − ℎ?, ™?ℎ™ = −𝐶?  ∆𝑇™?ℎ™        2.10.   Where ∆𝑇™? = 𝑙𝑖𝑞𝑢𝑖𝑑  𝑠𝑢𝑏𝑐𝑜𝑜𝑙𝑖𝑛𝑔 = 𝑇™? − 𝑇?   Equation 2.10 results in a negative quality for the subcooled flow-boiling region.  The first stage of saturated flow boiling region is described as bubbly flow. As the temperature increases, individual bubbles combine to form slugs of vapour, referred to as Slug Flow. Annular  24  flow then follows, where a liquid film covers the surface. Ultimately, dry patches appear on the surface and grow until the whole surface dries up (dry out). The very last region, Single Phase vapour, is described as mist flow where all the droplets are vaporized and superheated vapour is travelling along the channel. Once again single phase (gas rather than liquid) forced convection becomes dominant due to the increased vapour fraction and mean velocity. The local heat transfer coefficient varies significantly along the channel as 𝑥 increases. Compared to single phase forced convection, subcooled flow boiling improves the heat transfer rate substantially. Therefore, subcooled flow boiling has received significant attention in industries where high heat flux cooling is needed such as: fusion reactors, pressurized water reactors, high-power electronic devices and casting 20. The heat transfer coefficient is substantially lower in the fluid-deficient section of the channel (post slug flow, dry wall region) since sustained contact between the heated surface and the liquid does not occur. As a result, occurrence of dry out causes a significant temperature increase for the heated surface similar to the critical heat flux previously discussed for pool boiling (Point C and onwards on Figure 2.1). Figure 2.3 displays the distribution of vapour phases and the temperature variation in the fluid and on the pipe wall for flow boiling focusing on the initial three regions of behaviour. Point B, or onset of nucleate boiling (ONB), is considered as the start of boiling with a substantial increase in heat transfer coefficient due the bubble nucleation. The surface temperature drops at the ONB because of the sudden increase in the heat transfer coefficient. Studies show that the location of ONB (required heat flux and wall superheat) is a function of flow rate, liquid subcooling and contact angle 21. Bubbles are mainly attached to the surface from point B to E (partial nucleate boiling) but start detaching after point B. In region ΙΙ  the bulk temperature is  25  still below the saturation temperature, hence the name subcooled boiling. After point F, region ΙΙΙ  the liquid temperature reaches the saturation temperature and bulk boiling occurs. At this point the contribution of convection heat transfer is insignificant.  The flow pattern or the liquid-vapour morphology strongly affect the heat transfer coefficient in flow boiling 19. However, correlation based models are often used in modelling work to compute the local heat transfer coefficient in engineering design applications. It is therefore necessary to describe different boiling regions using physically sound correlations.    Figure 2.3: Flow pattern and temparture variation in subcooled flow boiling 19     26  As was noted earlier, ONB represents the start of boiling where boiling heat transfer along with forced convection contributes to heat transfer. Hsu 22(1962), Sato and Matsumura 23(1964) presented the following correlations for ONB subcooling and heat flux:   𝑤𝑎𝑙𝑙  𝑠𝑢𝑝𝑒𝑟  ℎ𝑒𝑎𝑡 = ∆𝑇™? , ™? =   𝑇™?? − 𝑇™? ™?           = 4. 𝜎. 𝑇™?   . ℎ?𝐾? . ℎ™        . 𝜌?        . 1+ 1+ 𝐾? . ℎ™        . 𝜌? . ∆𝑇™?2. 𝜎. 𝑇™?   . ℎ?                                2.11.      𝐻𝑒𝑎𝑡  𝑓𝑙𝑢𝑥  𝑞™? =   𝐾? . ℎ™        . 𝜌? ∆𝑇™? ?8. 𝜎. 𝑇™?    2.12.   where ∆𝑇™? = 𝑤𝑎𝑙𝑙  𝑠𝑢𝑝𝑒𝑟  ℎ𝑒𝑎𝑡 = 𝑇™?? − 𝑇™? , °𝐶 ∆𝑇™? = 𝑙𝑖𝑞𝑢𝑖𝑑  𝑠𝑢𝑏𝑐𝑜𝑜𝑙𝑖𝑛𝑔 = 𝑇™? − 𝑇? , °𝐶 𝜎 = 𝑠𝑢𝑟𝑓𝑎𝑐𝑒  𝑡𝑒𝑛𝑠𝑖𝑜𝑛,𝑁 𝑚 ℎ™ = 𝑙𝑖𝑞𝑢𝑖𝑑 𝑠𝑖𝑛𝑔𝑙𝑒  𝑝ℎ𝑎𝑠𝑒 ℎ𝑒𝑎𝑡  𝑡𝑟𝑎𝑛𝑓𝑒𝑟  𝑐𝑜𝑒𝑓𝑖𝑐𝑖𝑒𝑛𝑡, 𝑊 °𝐶.𝑚?   𝐾? = 𝑡ℎ𝑒𝑟𝑚𝑎𝑙  𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦,𝑊 𝑚. °𝐶 ℎ™        = 𝑙𝑎𝑡𝑒𝑛𝑡  ℎ𝑒𝑎𝑡  𝑜𝑓  𝑣𝑎𝑝𝑜𝑟𝑎𝑧𝑎𝑡𝑖𝑜𝑛, 𝐽 𝑘𝑔 𝜌? = 𝑑𝑒𝑛𝑠𝑖𝑡𝑦, 𝑘𝑔 𝑚? ℎ?(or ℎ™ ) is the single phase forced convection heat transfer coefficient discussed in the previous section(2.2). As discussed earlier the region between the ONB and the fully developed boiling (FDB) is identified as partial nucleate boiling. To calculate the heat flux for partial  27  nucleate boiling, Kandlikar suggested an interpolation method between ONB and FDB (equation 2.12, 2.13) 20.  The interpolation procedure assures a smooth transition from single phase forced convection to partial boiling and then to the FDB region.  There are various models describing fully developed subcooled boiling. In 1949 McAdams studied the water flow boiling heat transfer in vertical stainless steel annuli under a high heat flux 24. He proposed the first correlation for fully developed boiling in subcooled flow boiling:    𝑞 = 𝐶(∆𝑇™? )?. ™    2.13.   The dependence of wall heat flux to the wall superheat ∆𝑇™?  is expressed through a constant exponent of 3.86. The constant C is dependent on the dissolved air content in the air. One of the most widely accepted models, especially in the engineering and specifically automotive industry, is Chen’s model 25. Chen’s correlation is based on the superposition of forced convection heat transfer ℎ™   ,  and nucleate boiling heat transfer  ℎ™ .  The contribution of single phase heat transfer and two phase boiling heat transfer are additive to give an overall forced flow boiling heat transfer coefficient:    ℎ = ℎ™ + ℎ™    2.14.      𝑞 = ℎ™ 𝑇™?? − 𝑇™?? + ℎ™ 𝑇™?? − 𝑇™?    2.15.   The forced convection contribution is based on the 𝐷𝑖𝑡𝑡𝑢𝑠 − 𝐵𝑜𝑒𝑙𝑡𝑒𝑟  equation covered in the previous section (equation 2.6)    ℎ™ 𝐷𝑘 =   0.023𝑅𝑒?.?𝑃𝑟?.?  𝐹   2.16.    28     𝐹 = 1+ 𝑃𝑟 𝜌?𝜌? − 1 ?. ™    2.17.   The nucleate boiling contribution is based on Forster and Zuber’s correlations (1955)    ℎ™ = 0.00122 𝐾??. ™ 𝐶™ ?. ™ 𝜌??. ™𝜎??.?𝜇??. ™ ℎ™ ?. ™ 𝜌??. ™ ∆𝑇™? ?. ™ . ∆𝑃™? ?. ™ 𝑆   2.18.   where ∆𝑇™? = 𝑇™?? − 𝑇™?  and ∆𝑃™? = 𝑃™? ? − 𝑃™?  the difference in vapour pressure at the wall and at the saturation pressure. Details of the vapour pressure calculation are explained in appendix B.     𝑆 = 11+ 2.53. 10??𝑅𝑒??. ™    2.19.   All the variables with subscript L are liquid properties. F is the single-phase enhancement factor since the liquid velocity is increased during two-phase flow. S is the boiling heat transfer suppression factor since the effective wall superheat is suppressed in flow boiling when compared to pool boiling 26. Values of F > 1 imply high velocity and therefore increased the contribution of forced convective heat transfer in two-phase flow. Values of S < 1 indicates a lower effective wall superheat due to a thinner boundary layer where vapor bubbles grow in flow boiling compared to pool boiling 27. It is reported that for subcooled flow boiling, F can be set to unity since the vapor mass fractions are typically very small 27,28.  Thus far, two important sections of the boiling curve, forced convection and nucleate boiling for flow boiling have been discussed. It is important to mention that for steady state flow boiling in a  29  pipe, it is unlikely that the entire boiling curve occurs due to the transient nature of boiling 19. In other words, to produce a complete boiling curve with all four distinct heat transfer regions (forced convection, nucleate, transient and film boiling), the mass flux of the fluid and the local temperature of the wall and the fluid must remain constant. It is essential to cover the remaining regions of the (flow) boiling curve: Critical heat flux, transition and film boiling because the presence of these regions can lead to a significantly lower heat transfer coefficient compare to forced convection and nucleate boiling.  The critical (maximum) heat flux marks the end of nucleate boiling and is a significant threshold in flow boiling. Post critical heat flux regions consist of transition boiling and film boiling at higher wall superheats, where heat transfer coefficients decrease, making the cooling mechanism very inefficient. The critical heat flux and significant increases in surface temperature also signify the upper limit of safe operation and potential burnout for many cooling systems 19. The critical heat flux in flow boiling has received considerable attention due to an inordinate decrease in the rate of heat transfer associated with heat transfer post CHF. Most of the flow boiling critical heat flux studies were performed on upward vertical flows in boiling channels and pressurized nuclear reactors. Look up tables compiled by Groenveld provide an estimate for the CHF for upward flow of water in 8 mm tube as a function of pressure, mass flux and the quality of flow 29,30. Kandlikar reviewed the existing subcooled flow boiling CHF correlations and models and concluded that the CHF mechanism in flow boiling is still not completely understood. Carbajo (1985) reviewed the CHF correlations and suggested the following correlation for predicting the CHF temperature based on the saturation temperature, fluid temperature and surface material 31:  30     𝑇™? = 𝑇™? + 𝑏? + 𝑎? 𝑇™? − 𝑇?    2.20.      𝑎? = 0.096 𝐾?𝜌?𝐶™ ?𝐾?𝜌?𝐶™ ?   2.21.   where 𝑏? = 29  for stainless steel and thermal properties with subscript S and L are for solid surface and liquid (water) respectively. This correlation can only be used as an estimate since it was developed based on experimental studies on steel rods under atmospheric pressure.  McAdams performed a series of experiments on upward water flow in vertical annuli to study the effect of pressure, velocity and degree of subcooling on the critical heat flux 24. Based on his findings, for water flowing with velocity of 4 ft/s at a pressure of 60 psi and subcooling of 50 ℉ in annuli with hydrodynamic diameters of 0.52 inches, (half of that of a typical die cooling channel), the maximum heat flux is around 1.03E+06 (BTU/hr∙ft2), which is equivalent to 3.2E+06 W/𝑚?. McAdams also concluded that maximum heat flux increases with increasing the water velocity and degree of subcooling and was insensitive to pressure. Yu also reported that CHF is strongly affected by heat flux, mass flux and degree of subcooling, making it difficult to accurately predict the CHF temperature 32. After reaching the critical heat flux, as the wall superheat increases, transition boiling and (possibly) film boiling may occur depending on the flow parameters. Transition and film boiling are mainly studied in applications involving quenching of hot surfaces and in emergency rewetting of nuclear fuel rods. Forced flow transition and film boiling are not well understood due to their complex transient nature of heat transfer. Due to a scarcity of relevant data, transition-boiling correlations have limited applicability and should be used with extra caution.  31  Barnea 33 proposed the following correlation based on his experiments on quenching of heated vertical channels:    ℎ ™ ⌤? = ℎ™? . 𝑒𝑥𝑝 𝑇™? − 𝑇™??𝑇™? − 𝑇™?    2.22.   Heat transfer is exponentially decreased past the critical heat flux point.  The Leidenfrost point (in pool boiling) and the minimum film boiling in flow boiling (MFB) marks the end of transition boiling and the start of film boiling. Carbajo developed the following empirical correlation for minimum film boiling temperature 𝑇™?  based on rewetting temperature experiments in an emergency cooling system in a light water reactor 31:    𝑇™? = 𝑇™? + 𝑏 + 𝑎 𝑇™? − 𝑇?    2.23.   where for water on stainless steel 𝑎 = 1.94 and 𝑏 = 225 In film boiling, the heated surface is separated from the liquid by a vapour blanket and the dominant heat transfer mechanisms are radiation and conduction. To estimate the film boiling heat transfer coefficients, ℎ™ , Bromley’s correlation 34 can be used. Bromley’s correlation was developed based on experimental results of flowing subcooled liquid on the outside of a heated tube and is only an estimation of heat transfer coefficient values.     ℎ™ = 0.62 𝑘?? 𝜌? − 𝜌? 𝜌?ℎ™𝜇?𝑑° 𝑇™?? − 𝑇™?? ?   2.24.   In Eq 2.24 the subscript 𝑣 refers to vapour phase and 𝑑° is the outer diameter of tube.   32  2.4  Application of heat transfer coefficients in LPDC Thus far, forced convection correlations, flow boiling correlations and the applicable heat transfer phenomena have been introduced in preparation to predict the heat transfer coefficients associated with cooling channels in LPDC dies under operational conditions. Heat transfer to water flowing inside the cooling channel is by single phase forced convection as long as the liquid and wall are both below the saturation temperature at the local pressure. As the wall temperature exceeds the local saturation temperature, boiling can occur depending on the surface characteristics and the operating conditions. In the forced convection region, the heat transfer coefficient can be calculated using the Dittus-Boelter equation after calculating dimensionless parameters such as Reynols, Nusselt and Prandtl number. However, the boiling heat transfer coefficient varies significantly in different regions of the boiling curve.  Flow boiling in the cooling channel is subcooled if the fluid bulk temperature is below the saturation temperature. Determining the exact shape of the boiling curve and the corresponding heat transfer coefficient for a given cooling system is challenging due to the complex and non-steady nature of the boiling mechanism. Furthermore, process parameters such as the fluid’s pressure, temperature, flow rate, degree of subcooling as well as surface properties and temperature affect the boiling curve and heat transfer coefficients. In the case of water flow in the cooling channel, characterizing the boiling heat transfer coefficient is extremely difficult due to lack of information regarding the fluid temperature and the quality of flow along the cooling channel. In this section, the effect of process parameters such as fluid temperature, flow rate and surface temperature on the boiling curve and heat transfer coefficient is presented. Previous work on quantifying the heat transfer coefficient in casting and quenching modelling is reviewed.  33  Due to the scarcity of data on horizontal flow boiling, specifically the use of boiling heat transfer in LPDC modelling, it is suggested to extend the literature review to water cooling in continuous casting of steel and aluminum. The aim of this section is to review the previous work on DC casting of aluminum and steel and to understand the role water cooling plays in these processes to better predict the heat transfer coefficient in the cooling channels of LPDC.  When using the literature to predict the heat transfer coefficient in the cooling channel a few points should be kept in mind:  1. In LPDC process, water flows in the cooling channel made of tool steel H13. In some of the calculations it was assumed that the properties of H13 are very close to stainless steel. 2. Thermal conductivity of aluminum alloys is an order of magnitude higher than that of steel so the rate of heat extraction for the two metals under the same cooling conditions and temperature is different. Hence, comparing the aluminum DC casting boiling curve to H13 steel should be done cautiously. 3. In D.C casting of aluminum, secondary cooling in the sub mold area is due to a free-falling film of water at the 1 atm pressure, whereas for steel, water is sprayed on the surface through nozzles. In LPDC process cooling is internal and the fluid is pumped into the cooling channel with the required pressure (5-7 atm).  4. Thermal diffusivity of liquid aluminum is around 6 times higher than that of steel. Therefore, it takes substantially longer for heat to diffuse in steel.   In the past few years, various studies were performed to predict the heat transfer coefficient and boiling curve in casting processes. The majority of these studies were quench test experiments,  34  where a hot surface was cooled with a water film (external flow) and the boiling curve was predicted using inverse heat transfer analysis 35,36. Weckman and Niessen used the nucleate boiling and forced convection theories and developed empirical correlations to predict the heat transfer coefficient in the secondary cooling region in direct chill casting of A6063 37. As stated earlier, in D.C casting of aluminum, secondary cooling in the sub mold area is due to a free-falling film of water, whereas for steel, water is sprayed on the surface through nozzles.  A typical boiling curve for secondary cooling regimes of continuous casting of steel and D.C. casting of aluminum is shown in Figure 2.4. The basic features or the general shape of the boiling curve for both steel and aluminum is the same. However, the magnitude of CHF and Leidenfrost point is different due to the differences in the thermophysical properties of metals. It can be suggested that the free-falling film of water in D.C. casting of aluminum is similar in nature to the internal flow in the LPDC cooling channels.  However the boiling curve in Figure 2.4 cannot be directly extended to LPDC due to the differences in thermophysical properties of aluminum and tool steel and the effect of pressure on the saturation temperature of water.     Figure 2.4: Boiling curve for secondry cooling regime for D.C.casting of aluminium 38 and contonius casting of steel 39    35   2.4.1 Effect of process parameters on the boiling curve In this section the effects of different process parameters on the boiling curve for water film flow in DC casting, pool boiling and internal flow boiling are discussed. It is important to note that the effects of parameters on the boiling curve are reported in the qualitative way in the literature. In other words, a certain parameter increases or decreases the surface heat flux or the transition temperature between various boiling regions. Hence, the influence of such parameters cannot be easily used in characterizing the cooling channel heat transfer in LPDC.   The effect of  water flow rate (mass flux) and subcooling: Wells and Cockcroft studied the effect of water flow rate, initial surface temperature and surface morphology on the water boiling curve of aluminum alloys under conditions similar to direct-chill (DC) casting. Based on their study, increasing the water flow rate increases the critical heat flux temperature and the rate of heat transfer in the transition-boiling region. Yu studied the effect of flow rate on flow boiling in a horizontal stainless steel tube and concluded that increasing the water flow rate significantly increased the critical heat flux. The degree of subcooling or the amount that the fluid bulk temperature is below the saturation temperature affects the boiling curve and heat transfer coefficient. It has been shown that the flow rate and subcooling does not affect the nucleate boiling region but will affect the critical heat flux point and transition boiling curve 32,40,41.  Cheng studied the effect of mass flux and subcooling on boiling curves of water at 1 atm with cylindrical copper blocks. Based on his findings, increasing the mass flux and degree of subcooling does not have a significant effect on the nucleate boiling HTC. However, increasing the subcooling and mass flux increases the transition boiling and the film boiling heat flux 42,43.  McAdams stated that increasing mass flux and the  degree of subcooling increases the critical  36  heat flux value 24. In general, higher flow rates increase the heat transfer coefficient in the single phase forced convection region but does not have a significant effect on nucleate boiling region. This is possibly due to bubble formation and agitation in the liquid. The effect of flow rate on the boiling curve for free-falling zone flow in DC casting AA5182 is shown in Figure 2.5 The range of flow rates used (0.25-0.47 l/s) is very close to that of the flow rate of water in the cooling channel in LPDC. This is generally around 0.33 l/s. Increasing the water flow rate increased the critical heat flux but did not have a substantial effect the forced convection or nucleate boiling regions.     Figure 2.5:  Effect of water flow rate on the boiling curve of AA5182- free falling zone 38    Effect of initial surface temperature: Boiling heat flux is strongly dependent on the initial surface temperature when water first comes in contact with the hot surface. Figure 2.6 shows the effect of the initial surface temperature on the boiling curve of AA5182. At high initial surface temperature, heat flux is enhanced mainly for the transition and nucleate boiling region 38. Li and  37  colleagues studied the effect of initial surface temperature on the boiling curve during quenching of the AISI 316 stainless steel (transient cooling). They concluded that higher initial surface temperatures increased the critical and transition boiling heat flux but did not have any significant effect on convection and nucleate boiling HTCs. Another important result from their work is the lack of film boiling in the boiling curve for the water spray zone and the water flow zone (flow rate=1.27 l/s and water temperature=15°𝐶) when the initial surface temperature of steel is below 500 ˚C 61. This signifies the importance of estimating the initial conditions of the die temperature and the cooling channel surface temperature in LPDC modeling. Collecting temperature history using thermocouples strategically placed within the die will help one make a fair assumption.  38  Effect of pressure: The primary contribution of pressure on a cooling process is its effect on the saturation temperature of the liquid. Pressure was found to have a very weak influence on the CHF in flow and pool boiling 45.  Effect of surface morphology and thermo physical properties: Micro geometry or surface roughness also affects the boiling curve since it influences the bubble growth, detachment enhancing fluid flow, turbulence and rate of heat transfer. Due to lack of information regarding the surface morphology of the cooling channel, it was assumed that the surface was machined and relatively smooth. Thermal conductivity of the material also affects the boiling curve. In general, the higher the thermal conductivity, the higher the rate of heat transfer and the higher the     Figure 2.6: Effect of initial surface temperature on the boiling curve of AA5182- free streaming zone 44        39  critical heat flux. Thermal conductivity of aluminum alloys is much higher than that of steel (carbon and stainless steel), an important point to take into consideration in heat transfer coefficient prediction.  2.4.2 Quantification of heat transfer coefficient in casting modeling  The ability to use process models to design water-cooled LPDC process dies hinges critically on the application of physically realistic heat transfer coefficients to describe the heat transfer in the various cooling channels, based on the process parameters and die cooling channel surface temperatures. Historically, in most of the casting modeling work, the heat transfer coefficient is prescribed as an average constant value to the cooling channel’s surface 7,13,14,46,47. The constant values are generally calculated based on the forced convection correlations while considering the flow rate and geometry of the cooling elements. The heat transfer coefficient can also be estimated through inverse engineering techniques and trial and error methods. In the trial and error approach, the heat transfer coefficient is approximated and used in a numerical model. Model output is then compared to the experimental data and necessary adjustments are made until a reasonable fit to the experimental temperature history data is achieved 12. This process is rather time consuming, since often numerous adjustments to the boundary conditions in the model are needed to obtain a close fit to the experimental data. Zhang et al developed a 3-D thermal model of an air-cooled LPDC die, considering a 30° slice of the wheel and the die and used values between 75 to 175 𝑊 ∙ 𝑚?? ∙ 𝐾??   to quantify the forced convection air cooling of the bottom die cooling channel. They also incorporated an angular dependence in the bulk coolant temperature to account for temperature increase as air travels  40  through the channel. It is well documented that water cooling is a much more effective cooling media compared to air cooling due to the high cooling capacity of water 7. Shepel and Paolucci used forced convection heat transfer correlations to calculate the heat transfer coefficient for water-cooling channels in solidification modeling of a permanent mold casting.  Shepel stated that water evaporation occurs initially when water-cooling was turned on but after a short transitional regime, water flow in the channel became turbulent and steady hence, fully developed flow can be assumed. In their work the average temperature of water circulating through the cooling channels was assumed constant 40 °C with flow rate of 6.3×10?? ???  and a constant convection coefficient of 1.2×10? 𝑊 ∙ 𝑚?? ∙ 𝐾??   was calculated and implemented in the model 14.  Bounds et al designed a test-casting with two die assemblies, two cooling channels and a die cavity to estimate the heat transfer coefficient at the cooling channel and die-casting interface. They measured the temperature throughout the casting cycle at various locations in the die and the cast. The thermocouple data was compared with a 3-D thermal model.They predicted a maximum heat transfer coefficient of 97   𝑘𝑊 ∙ 𝑚?? ∙ 𝐾??   for water running through the channel. While presenting a forced convection heat transfer coefficient value of 9.8 𝑘𝑊 ∙ 𝑚?? ∙𝐾?? , Bounds emphasized the presence of boiling and the increase in the rate of heat extraction in the pressure die casting process 46. It can be concluded that simply assuming a single forced convection value for the cooling channel is a significant oversight, and boiling along with forced convection should be implemented at the cooling channel boundary condition.  Clark argued that in cooling and solidification of aluminum and zinc melts, the release of latent heat of fusion and the liquid metal superheat is sufficient enough to induce boiling at the surface  41  of a cooling channel 48. He developed a temperature based boiling model using existing empirical correlations, which estimates the cooling channel heat flux. The cooling channel boiling model was then implemented in a Boundary element (BE) model for a time-averaged thermal analysis of pressure die casting. In Clark’s boiling model, a series of interpolations between different parts of the boiling curve were performed to achieve a continuous first derivative.    Twohig developed a temperature dependent heat transfer coefficient subroutine for flood cooling modeling of a mechanical component with water. In her work, single phase and two-phase heat transfer correlations were implemented in a subroutine to describe the transient heat transfer coefficient on the wetted surface of the component in a finite element model. To confirm the validity of the boiling correlations, Twohig compared the calculated transient temperature history with experimental data from quenching of a vertical hot copper block in water 40,49.   Achieving a realistic, physically sound model of forced convection and boiling in the cooling channel is still a challenge. For example, for flow boiling in a cooling channel, it is highly impractical to deterministically describe the sub process of bubble nucleation in a mathematical model. The complex contact physics at the interface of the fluid, solid and gas phases makes it incredibly challenging to create an applicable and accurate model. In the existing casting simulations an average constant heat transfer is estimated based on the temperature measurements. However, more accurate simulation results can be obtained using the instantaneous, local heat transfer coefficient values. The local heat transfer coefficient might vary significantly based on the surface temperature and operational parameters such as flow rate and pressure.   42  An easy to implement temperature dependent heat transfer coefficient code that is sensitive to process parameters such as flow rate, pressure and size and shape of the cooling channels would be a step forward in casting modeling. Through this approach, inconvenient manual modifications and trial and error as well as numerous repetitive calculations would be avoided and significant amounts of simulation time saved. An analytical heat transfer coefficient algorithm that is sensitive to surface temperature and casting cooling operational parameters can greatly reduce the inaccuracies associated with casting modeling.            43   Scope and objectives 3.3.1 Objectives of the research programme  The core objectives of the present study are: 1.  To formulate a methodology for calculating the continuous variation in heat transfer coefficient for a given cooling channel based on process parameters and channel surface temperatures in the LPDC of automotive wheels, and in so doing, gain a fundamental understanding of the cooling mechanisms active in the process.  2.  To develop a mathematical model of the LPDC process and implement the improved HTC formulation, and ultimately validate the model, using temperature data collected from a casting trial.  3.  To compare the HTC’s calculated by achieving objectives 1 and 2 with those previously used, which were obtained through trial-and-error process.  3.2 Scope of the research program As described the goal of this project is to develop a methodology to quantitatively describe the heat transfer in the cooling channels of the low-pressure die casting process used to produce aluminum automotive wheels and to successfully implement the methodology in a numerical model of the casting process. To achieve this goal, an algorithm capable of calculating the heat transfer coefficients based on process parameters and surface temperature within the cooling channel will be developed. The algorithm is used in a mathematical model of the LPDC process and the results compared to temperature measurements from a casting plant trial to investigate the validity of the HTC calculation methodology.   44  The mathematical model is based on the commercial finite element software ABAQUS and quantifies heat extraction through the cooling channels via heat transfer coefficients prescribed as boundary conditions. The heat transfer coefficient in a given cooling channel is defined, or quantified, within a user-subroutine implemented within the ABAQUS model. The user-subroutine is a FORTRAN program that calculates the heat transfer coefficients as a function of temperature for both stagnant and flowing water or air in the cooling channels. Cooling timing (the on/off timing of water and/or air) and cooling intensity (flow rate of the fluid) vary from one channel to another depending on the cooling program selected by the operator for a given die design. Additionally, for each cooling channel, the area, perimeter and shape of the channel are input to the program. The fluid flow rate, pressure and bulk temperature are also defined for each cooling channel. Thermo-physical properties of water and air are formulated in a temperature dependent format in the program. In the case of air-cooling, forced convection and natural convection heat transfer correlations are used. For water-cooling, correlations describing single phase and two-phase heat transfer are used for both force convection and boiling heat transfer in the cooling channels. Depending on the surface temperature of the cooling channel and saturation temperature of the water (pressure dependent), the dominant heat transfer mode is either single phase forced convection or two-phase boiling. For forced convection heat transfer, the Dittus-Boelter equation is implemented in the code. In the boiling regime, depending on the surface temperature and process parameters, such as flow rate and bulk temperature of water, various modes of boiling might be present. Nukiyama’s boiling curve describes forced convection, nucleate boiling, transition boiling and film boiling. The subroutine describes all regimes of Nukiyama’s boiling curve with the exception of film boiling. Various correlations such Forster and Zuber’s empirical correlations and Chen’s superposition model are used to calculate the heat transfer coefficient in the nucleate boiling region. The subroutine was designed  45  in a modular fashion for ease of use and to facilitate variation in the process parameters such as flow rate, pressure, fluid bulk temperature and cooling channel geometry.  To evaluate the validity of the model and the associated HTC calculations, casting plant trials were performed. The trials included temperature measurements at pre-determined locations of the die and the wheel. The validity of the HTC calculations have been assessed by comparing the predicted temperature history of the model with measured thermocouple data collected during the casting cycle and also comparing the model predictions with a base-case model, developed in previous work using trial-and-error approach to evaluate the HTC’s. To accurately determine the correct cooling sequence and timing in the channel in a cycle, water sensors were designed and built. Unfortunately, due to time limitations, water sensor measurements were not performed for this study. This water sensor design and experiment is described in the experimental work for future work.            46   Experimental measurements 4.Experimental data was used to develop, verify and validate the computational thermal model of the LPDC process.  In the early stages of model formulation, assumptions were made for the initial and boundary conditions. Experimental measurements were then carried out to verify these assumptions and were used for directing further modifications and tuning of the model.  By comparing the experimental data to the model data, the predictive capability of the model is examined. In other words, the degree to which the model can represent a real physical system is determined. In the present study, a general user-defined subroutine describing heat transfer in a water/air cooling channel under conditions typical of those existing in the LPDC of aluminum automotive wheel has been developed. Experimental data was used to assess the subroutine’s ability to predict the heat transfer and the temperature history in locations close to the cooling channels in the thermal model. Ideally, both temperature measurements at discreet locations within the die and the wheel, and water/air flow measurements in the cooling channel in a production die during operation would be made to support model development and validation. Originally, measurements were to be performed on advanced prototype die under development in collaboration with Canadian Autoparts Toyota Inc. (CAPTIN) at their wheel manufacturing facility in Delta, British Columbia, as a part of broader Automotive Partnership Canada(APC) program to develop an advanced water-cooled die. However, due to delays in the prototype die fabrication and the time constraints of the present project, temperature data was only been collected on a production die. The production die is referred to as the 427 wheel model die within CAPTIN production system. The 427 is a five-spoke wheel that is one of the optional wheels available for Toyota RAV4SUV.  47  It is important to note that the measurements undertaken at CAPTIN may not be accurate due to issues relating to conducting measurements in an industrial setting. Issues to contend with include: 1) limitations in the sensitivity and accuracy, stemming from the type of thermocouple sheathing and method of installation used; and 2) errors in the location of thermocouple within the die structure. In addition to collecting thermocouple data from a 427 die, work was undertaken to develop and demonstrate a technique to measure the timing and duration of water-cooling in a production die. Phase detecting flow sensors were designed, fabricated and successfully tested at UBC. The design and development of the flow sensors is described in this chapter. The flow sensors have recently been employed in trials with the prototype die at CAPTIN 4.1 Temperature measurements To record temperature history during casting cycles, thermocouples were placed in a production 427 die at predetermined locations. In addition, several thermocouples were cast into the wheel. Temperature data throughout a number of cycles, including under steady-state cyclic conditions, were recorded to validate the heat transfer model. The thermocouple measurements were carried out by Dr. Carl Reilly, a Research Associate on the APC project team.  The details of the thermocouple instrumentation are as follows. Stainless steel sheathed, 3.17 mm diameter, Type-K thermocouples were placed in 40 predrilled holes at various locations within the die components and held in-place using compression fittings. The thermocouples located at the die/wheel interface were welded in place; the weld was ground flush with the die surface leaving the thermocouple ~2 mm below the surface. Figures 4.1, 4.2 and 4.3 shows the location of thermocouples in top die, bottom die and side die, respectively. Data from the 40  48  thermocouples was recorded throughout 32 casting cycles using LabVIEW software and a National Instruments CompactRIO-9022 DAQ system at a sample rate of 5 Hz.     Figure 4.1: Thermocouple locations in the top die      Figure 4.2: Thermocouple locations in the bottom die    49     Figure 4.3: Thermocouple locations in the side die   The cyclic steady state condition is defined as when the temperature at all locations of the die at the start of a casting cycle have the same values as the temperatures at the end of the previous cycle to within a small error, generally less than 10 to 15 °C. The steady state condition is typically achieved after approximately 25 casting cycles. The variation in temperature at two locations in the side die are shown in figures 4.4 and 4.5, for cycle 26 through 32.    50     Figure 4.4: Variation of temperature within cycles 26-32 for  TC1      Figure 4.5: Variation of temperature within cycles 26-32 for  TC2      51  Figure 4.4 shows the results recorded for thermocouple 1 (TC 1), and Figure 4.5 shows the results recorded for thermocouple 2 (TC 2). Both are located in the side die (see Figure 4.3 for approximate location). The temperature histories for TC1 and 2 are approximately consistent from cycle-to-cycle to within 15 °C, indicating steady state is reached (except the small deviation in cycle 29). The thermocouple results corresponding to cycle 30 were used for model validation.  The variation of temperature within a given casting cycle reflects the various operational stages within the cycle. When die filling starts at the beginning of a cycle, it takes approximately 30 seconds for the liquid metal to fill up the die and reach the location (height) of TC 1. A sharp temperature increase at both thermocouples indicates approximately when the liquid metal arrives at the height of the thermocouple. The temperature continues to increase with time until approximately 60s then decreases as the rate of heat removal from the die (cooling channels and environmental) exceeds the rate of heat input from the wheel.  At around 150 s in the casting cycle the wheel is fully solidified and the top die moves up with wheel attached to it. The side die is then exposed to the environment and hence, the temperature at TC1 decreases from 150 s to the end of the cycle. Although the side die is exposed to the environment, it is being heated by a side heater explaining the temperature increase at TC2 even after the die opens. To capture the cooling behavior at several locations within the wheel, three thermocouples were cast into each wheel during steady state cycles 27 to 30. During the warm up stage, when the die is open, thermocouples were placed in the die cavity. When the top die descends (die closes), it entraps the thermocouples in the die cavity. X-Ray imaging and sectioning were used on the wheel to determine the final location of the cast-in thermocouples. Figure 4.6 shows the location of cast-in thermocouples for cycle 27, 29 and 30. The location of the in-cast thermocouples for cycle 28 was not determined since the wheel was accidently discarded by CAPTIN. In cycle 29,  52  thermocouple B is outside of the wheel because it was trapped in the window section when the die closed.    Figure 4.6: Cast-in wheel thermocouples. From left: cycle 27, 29 and 30   4.2 Flow measurements To control the cooling during a casting cycle, water and/or air is circulated through the cooling channel with a predetermined sequence and intensity.  Generally, the water or air is switched on at a specified time in a casting cycle and remains on for a prescribed time. In the case where water is the primary coolant, air may be forced through the channel, for a period of time, after the prescribed cooling time has elapsed to displace the water. Once the water has been displaced the flow of air is suspended and only stagnant air remains in the channel. The water/air flow is turned on or off using solenoid valves. Flow rate controls are used to govern the water/air flow rate. To successfully describe the heat transfer in the thermal model, the flow parameters for the water and air such as fluid flow rate, temperature, and on-off timing in each cooling channel needs to be measured. In the current 427 die deigns, water is used as the primary coolant for all the cooling channels expect for bottom die cooling channel 1 which is only air-cooled.   53  4.2.1 Flow rate To monitor and control the fluid flow in the 427 die, flow switches are used in the CAPTIN cooling system. The fluid flow rate is programmed for each cooling channel and is displayed on the corresponding flow switches. SMC digital flow switch PF2W was used to set and monitor the water flow rate 50. The output signal of the flow switches was not suitable for flow rate measurements using a DAQ system. Therefore, it was assumed that the flow rate was accurate as indicated on the switch and was consistent from when the flow control valve is open to when the valve is closed (no overshoot or fluctuation). The flow rate was read and manually recorded during each casting cycle.   4.2.2 Cooling timing measurements (flow sensor) Unfortunately, in a typical casting machine there are significant variable lengths of piping length between the control solenoid used to switch the water/air on and the point of entry of the line into the die cavity. Thus, it is not possible to obtain accurate die cooling timing from logging the on/off time of the solenoids on the machine. At CAPTIN, water is forced through the cooling pipes by a water pump running at a pressure between 0.5-0.7 MPa. Figure 4.7 is a schematic representation of the cooling system delivering water or air to the die components. Based on the physical lengths shown for the piping in figure 4.7 the lag time is estimated to be in the range of 5-10 s.    54     Figure 4.7: Schematic representation of cooling line showing the extend of piping from solenoid valve to the die. Note that there are 3 cooling lines in the top die, 1 in the side die and 2 in the bottom die.   To address this issue, it was initially proposed to install flow meters close to the die for each cooling line to capture accurate timing and flow rates during each casting cycle. The voltage output signal from each flow meter would be collected using a DAQ system to be used for model validation. However, due to the fact that both water and air would at times be flowing through a given channel, it was not possible to source a single meter. Instead, flow sensors were designed and fabricated by Dr. Carl Reilly to be installed on the flexible hosing, which connects the cooling pipes to the die. The flow sensor is essentially a resistivity/conductivity probe, which is designed based on the difference in electrical conductivity of water and air. The flow sensor consists of two electrically conductive probes inserted into a pipe facing each other with a small  55  distance between their tips. A small voltage is then applied across the two probes. Figure 4.8 shows a schematic representation of a flow sensor. The sensor is made of a stainless steel 3/4" cross fitting, housing two electrically conductive screws that are used as probes. The probes were assembled from stainless steel screws, screwed into two 3/4" diameter Nylon Rods (1" Length), exposing the ends of the screws. The nylon-screw probes were then inserted using compression fittings into the two vertical (and opposite side) openings of the cross fitting. A voltage source and a resistor were used to create an electrical circuit and a small voltage (~9  𝑉) is supplied through the head of each screw.    Figure 4.8: Schematic  representation of flow sensor   When the tips of the probes are in contact with continuous water (water flow), electrical circuit is closed and an output voltage is recorded. In contrast when air, exists between the probes the circuit is open and the voltage drops to zero. Additionally, to generate more accurate data on how long it takes for the fluid to travel through the cooling channels in the die, sensors were also  56  installed at the outlet pipes leaving the die. Hence, for each cooling channel two sets of flow sensors are used at inlet and outlet piping entering and exiting the die. The voltage fluctuation is logged and used to determine the exact time of water entering and exiting a channel during each cycle.  In addition, a tee pipe fitting, housing a thermocouple was connected to the flow sensor to measure the inlet and outlet fluid temperature. This was comprised of a 1/8" Type-K thermocouple press fitted in the vertical opening of the tee pipe. Figure 4.9 exhibits the final assembly of the flow sensor and the flow thermocouple. The cross fitting on the left houses the nylon-screw probes and the tee fitting on the right contains a thermocouple.     Figure 4.9: Flow sensor and thermocouple sensors     57   Computational process modeling 5.As noted in the introduction section, defects such as macroporosity, microporosity and entrained oxide films affect the final quality and performance of aluminum wheels. Wheel manufacturers are constantly trying to develop strategies to eliminate or reduce the occurrence of such defects. For example, macroporosity defects caused by liquid encapsulation can be eliminated through directional solidification, which can be maintained through controlled cooling of the die. Traditionally, such process parameters are optimized via trial-and-error methods which is inherently time consuming and costly. As a result, both foundry engineers and academic researchers are turning to the use of computational models to better understand, design and optimize the casting process. Computational modelling is used to describe and study complex systems, such as casting, in which analytical solutions are not available. In this study a computational model was developed to predict the heat transfer within a die cast aluminum wheel in LPDC process. The model was validated against plant trial temperature measurements using embedded thermocouples within the die and the wheel. This chapter will focus on the model formulation including; model geometry and initial conditions, material properties and boundary conditions. 5.1 Thermal model development  A 3D mathematical model of the low-pressure die casting process for the production of A356 aluminum alloy wheels was developed to predict the evolution of temperature in the die and the wheel. The heat transfer model was developed using the finite element package ABAQUS. ABAQUS was chosen for developing the thermal model because of its ability to include user-defined subroutines as well as its ability to handle geometrically complex and nonlinear problems 7. As previously described, the objective of present program is to develop a user- 58  defined subroutine to describe the complex heat transfer behavior occurring in the cooling channels, formulated in an algorithm using correlations based on the cooling channel geometry, water/fluid type and flow rate, and interface temperature. Time consuming trial-and-error methods used to describe the heat transfer at the cooling channel interface can now be replaced by a modular subroutine that is sensitive to process parameters such as flow rate, pressure of coolant, and surface temperature without the need for tuning.  5.2 Model geometry and mesh The model geometry is based on a five-spoke wheel, known as 427 wheel model within CAPTIN’s production system. Figure 5.1 shows the inboard and side view of the 427-wheel.    a) b)   Figure 5.1. a: Inboard Face of wheel-427 model with five spokes,  b: Side view of heel-427 model   Dr. Carl Reilly created the 3D CAD model in CATIA and the geometry was then transferred to ABAQUS. Given the 427 wheel geometry, the analysis domain was reduced by assuming circumferential symmetry, to a 36˚ section of the wheel in order to reduce computation size of  59  the problem. A 36° section of the wheel and the die are used in the present study. A 36˚ section of the wheel and the die sections are shown in Figure 5.2.     Figure 5.2: 36˚ section of the wheel and the die   The geometry includes the cooling channels at various locations. These cooling channels are referred to as : the top die cooling channel (TD-CC), the side die cooling channel (SDC-CC), the top die drum core cooling channel (TDDC-CC) and two bottom die cooling channels (BD-CC-1, BD-CC-2) shown in Figure 5.3.    60     Figure 5.3: Cooling channels in the 3-D thermal model   The geometry was meshed using the ANSYS ICEM CFD meshing software and then converted to ABAQUS input file format using a mesh conversion script. In general, an increased number of elements improve the accuracy of the model while increasing the calculation time. In the present study a mix of “fully integrated” heat transfer continuum elements are used. 3-D four-noded linear tetrahedron (DC3D4) elements were used for 191420 elements along at the interfaces, or surfaces, where a refined mesh is desirable for modeling accuracy. To decrease the element count and computation time 3-D eight-noded linear brick-hexahedral (DC3D8) is used for 2504 elements in the bulk area of the wheel and the die. In areas where the temperature gradient was expected to be high, such as the wheel, top die drum core and drum core, a finer mesh is generated. In total, the model contains 193924 elements and 45772 nodes. Figure 5.4 shows the 36° mesh of wheel and the die. To define the surfaces of each component, elements were  61  grouped together creating element sets. Heat transfer between surfaces of the die sections or between the die and wheel are modeled using contact or surface-to-surface boundary conditions.     Figure 5.4: 36° mesh of wheel and the die   5.3 Material properties The cast wheels are made of strontium-modified aluminum alloy A356 (Al-7Si-0.3Mg). The majority of the die is fabricated from H13 tool steel, excluding the upper sprue, which is made of tungsten carbide, and the lower sprue which is made of cast iron. The chemical composition of A356 and H13 is listed in Table 5-151,52.    62    Composition Si Cu Mg Mn Fe Zn Al A356 6.5-7.5 0.20 0.25-0.45 0.10 0.20 0.10 Balance         Composition C Mn Si Cr Mo V Fe H13 0.32-0.45 0.20-0.50 0.80-1.20 4.75-5.50 1.10-1.75 0.80-1.20 Balance          5.3.1 Thermo physical properties The thermo physical properties used in the model include: density, thermal conductivity, specific heat and latent heat which were extracted from various references 7,53,54 and are listed in Table 5-2. During the liquid to solid phase transformation of A356, the latent heat of solidification released is 397.5 kJ/kg 55,56. This is released in proportion to the evolution of fraction solid as outlined in Table 5-2.         Table 5.1: The nominal composition of A356 and H13  63   Table 5.2: Thermophysical properties of A356 and H13 used in the Thermal model   Material Thermal Conductivity Specific Heat             Latent Heat Density T  (°C) k  (W/m/K) T  (°C) Cp (J/kg/K) Temperature Range (°C) L (kJ/kg) ρ  (kg/m3) A356   25 163 25 880  613.2 > T ≥ 610.7 51.02 2380  100 165 100 921 610.7 > T ≥ 588.2 91.20   200 162 200 967 588.2 > T ≥ 567.2 48.74   300 155 300 1011 567.2 > T ≥ 563.6 170.36   380 153 380 1046 563.6 > T ≥533.0 36.18   400 153 400 1055     500 145 500 1098     567 134 567 1127     614 400 614 1190     700 400 700 1190    H13   20 24.60 23 458.8  N/A 7850  200 26.25 200 518.5     500 27.30 400 587.8     600 27.76 600 726.2     800 28.07 700 905.4     850 28.39 760 1151.10    Cast iron   20 49 25 490  N/A 7200   100 48 100 510     200 46 200 555     300 43 300 600     400 42 400 640     500 41 500 700     600 38 600 785     700 35 700 1000    Tungsten Carbide   20 84.2 25 166  N/A 15600    100 183       200 196       300 205       400 211       500 217       600 221       700 224     64  5.4 Initial conditions As explained in the introduction, the LPDC process is cyclic. At the beginning of the first cycle the dies are heated to a hot-face temperature of approximately 500 ℃. During a cycle, as the wheel cools, the die temperature changes. After approximately 15-25 cycles, the temperatures at all locations of the die at the start of a casting cycle have approximately the same values as the temperatures at the end of a previous cycle. In other words, die temperature at the end of each cycle no longer changes significantly and steady state is reached.  In the model the initial condition used at the beginning of the first cycle was considered as uniform 500 ℃ for the dies. To simulate steady state operation the model is run repetitively using a computer program developed by APC Research Associate, Dr. Carl Reilly at UBC. After each cycle was finished the steady state criteria was checked. If steady state was not obtained the model was run again using the last temperatures in the die as the initial condition of the die temperature. This was repeated until steady state was achieved. The steady state condition was defined as a maximum 5 ℃ difference between the start and the end of a cycle temperature for all locations within the die. Due to difficulties in including fluid flow and filling in the ABAQUS model, die filling was not modeled.  However, based on the excepted filling sequence (variation of metal height within the die with time), the interfacial cooling between the wheel and die was activated as a function of time. Additionally, the initial condition of the cast (wheel) was set to 700 ℃ in the sprue area and is linearly decreased from 700 ℃ at the hub area, to 620 ℃ at the in-board flange. The model typically took 6-8 cycles to reach steady state.   65  5.5 Thermal boundary conditions There are various boundary conditions (BCs) that need to be defined in the thermal model in order to simulate the flow of heat from the wheel to the die and environment. The boundary conditions implemented in the model were based on literature, previous plant trials and experimental measurements characterizing the process 7. Typically, the necessary adjustments were implemented after comparing the experimental measurements (thermocouple data) to the model until a reasonable fit was achieved.     The total time for one casting cycle is 210 seconds. To describe the conditions active during a LPDC casting cycle, thermal boundary conditions were defined in accordance with the following five steps:  Step 1: with a total time span of 154.9 s, this step is the longest step of the model and describes the die components coming together, filling of the die cavity and cooling channels being turned on through to solidification of the wheel. For the first 7 s, the top die is raised and side dies and bottom die are in contact. Heat transfer is through conduction at the side die-bottom die interface and to the environment through convection and radiation heat transfer. At 7 second, the top die descends creating the die cavity (die closes) filling starts and cooling is turned on. Filling starts with pressurizing the furnace at 10.4 s and liquid metal starts to go up the riser pipe and cast sprue. At 20 and 30 s the sprue and spoke are filled, respectively. As mentioned earlier the effect of metal filing is incorporated into the model through time/height dependant conductance between wheel and die components and initial wheel temperature. Based on thermocouple data, it was concluded that it takes 32 s for the molten metal to fill the die cavity and reach the in-board flange area. During the remainder of step 1, the wheel solidifies as heat is removed from the wheel to the die and to the cooling channel and ultimately to the environment. The cooling  66  channel user subroutine is active in step 1 and passes the calculated corresponding heat transfer coefficient values for water or air in the cooling channel to the ABAQUS model.  Step 2: This step has a total duration of 0.1 s. Pressure is released and the left over liquid metal falls back to the furnace. The side dies open and the top die moves up while the wheel is attached to the top die owing to the thermal contraction of the wheel during solidification. Casting sprue and interfaces are removed in the model. Step 2 occurs at 154 s of the casting cycle. Steps 3: With a total time span of 8.9 s, the wheel is still attached to the top die and heat is removed from the wheel to the top die through conduction and to environment through natural convection and radiation.  Step 4: During this step the wheel is ejected from the top die. This operation takes 0.1 s. The top die-wheel interface is removed from the model. Top die is now exposed to the environment and cools down through natural convection and radiation.  Step 5: Die components are cooled down for 46 seconds at this step. During this time the casting operator performs die maintenance such as touching up the ceramic coating of the die or cleaning the flashing pieces. The end of step 5 marks the end of one casting cycle. The results of the model are used for the next casting cycle as initial conditions and the simulation is run repeatedly until steady state is achieved.  5.5.1 Thermal boundary conditions-base model Interfacial (contact) Boundary Conditions-An interface type boundary condition is used to simulate the heat transfer for two surfaces in contact or in proximity to each other, such as  67  wheel/die, wheel/sprue, and interfaces between various die components. The governing equation of interface type boundary condition is in the following form:    𝑞 = ℎ 𝑇? − 𝑇?    5.1   where q is the heat flux (𝑊 ∙ 𝑚??) occurring across the interface and h is the interfacial heat transfer coefficient (𝑊 ∙ 𝑚?? ∙ 𝐾??) describing the resistance to heat flow across the interface. 𝑇? and 𝑇? are the local surface temperatures.  Table 5-3 shows the wheel/die interface heat transfer coefficients employed in the model. The dependence on temperature is used to reflect the effect of the geometric contraction of the wheel during solidifications and the resulting formation of a gap between the die and the wheel, which acts as resistance to heat flow. As previously described, a time/height-dependence is also used in some of the heat transfer coefficients to simulate the filling process. For example, the wheel/die heat transfer coefficient is set to zero at locations higher than the estimated liquid metal height at a given time during die filling. At locations lower than the estimated liquid metal height, heat transfer is activated using the temperature-dependence shown in Table 5-3.       68  Interface Boundary Time(cycle step) Temperature Range  Heat Transfer Coefficient    (s)  (°C) (W/m2/K) Top die/wheel 0 < t < 10.4(step 1) - 0  10.4 ≤ t ≤ 163.9(step 1,2,3) T ≥ 614 3700   614 > T ≥ 567 55T – 30135   T < 567 1110 Top die/wheel, thermal break 0 < t < 10.4(step 1) - 0      10.4 ≤ t ≤ 163.9(step 1,2,3)* T ≥ 614 500   614 > T ≥ 567 7.4T – 4072   T < 567 150 Bottom die/wheel 0 < t < 10.4(step 1) - 0  10.4 ≤ t ≤ 154.9(step 1)* T ≥ 614 3500   614 > T ≥ 567 52T -28506   T < 567 1050 Upper sprue/wheel 0 < t < 10.4(step 1) - 0  10.4 ≤ t ≤ 154.9(step 1)* T ≥ 614 3500   614 > T ≥ 567 52T -28506   T < 567 1050 Side die, Side die core/wheel 0 < t < 10.4(step 1) - 0  10.4 ≤ t ≤ 154.9(step 1)* T ≥ 614 3250   614 > T ≥ 567 55 T -30716   T < 567 650 Side die core/wheel 0 < t < 10.4(step 1) - 0  10.4 ≤ t ≤ 154.9(step 1)* T ≥ 614 2000   614 > T ≥ 567 34T -18902   T < 567 400 Lower sprue/cast metal 0 < t < 10.4(step 1) - 0  10.4≤ t ≤ 154.9(step 1)* T ≥ 614 4000   614 > T ≥ 567 59T-32579   T < 567 1200 Table 5-4 shows the heat transfer coefficients for the die components in contact with each other. As mentioned earlier, contact boundary conditions are time-dependent reflecting different steps of the process. For example, for the first 7 seconds of step 1, the heat transfer coefficient between the top die and side die is zero since the side die is open and the top die is elevated (not in contact). Table 5.3: Heat transfer coefficient for wheel/die interfaces (*Height dependant boundary conditions to replicate filling at the wheel/die-components interfaces)  69  Interface Boundary Time(cycle step) Heat transfer Coefficient    (s) (W/m2/K) Side die/top die 0 < t ≤ 7(step 1) 0  7<  t ≤ 154.9(step 1) 800 Side die/top die-thermal break 0 < t ≤ 7(step 1) 0  7<  t ≤ 154.9(step 1) 250    Side die core/bottom die 0  ≤ t ≤ 210(step 1-5) 750 Side die core/bottom die-thermal break 0  ≤ t ≤ 210(step 1-5) 250    Side die/ Side die core-internal 0  ≤ t ≤ 210(step 1-5) 750 Side die/ Side die core-external 0  ≤ t ≤ 210(step 1-5) 250 Side die/ Side die core-thermal break 0  ≤ t ≤ 210(step 1-5) 200 Bottom die/upper sprue  0  ≤ t ≤ 210(step 1-5) 500 upper sprue/lower sprue  0  ≤ t ≤ 210(step 1-5) 500 Top die/ bottom die 0 < t ≤ 7(step 1) 0 Top die/ Top die drum core  0  ≤ t ≤ 210(step 1-5) 2500 Top die/ Top die drum core-thermal break 0  ≤ t ≤ 210(step 1-5) 1000 Top die/ Top die center pin 0  ≤ t ≤ 210(step 1-5) 1000 Top die/ Top die center pin-thermal break 0  ≤ t ≤ 210(step 1-5) 250 Top die drum core/ Top die center pin 0  ≤ t ≤ 210(step 1-5) 750 Top die drum core/ Top die center pin-thermal break 0  ≤ t ≤ 210(step 1-5) 250  Environment Radiation Boundary Conditions- At different times transport of heat from the die/wheel to the environment is occurring by radiation. The mathematical form of the radiation heat transfer has the form: Table 5.4: Heat transfer coefficient for die components and sprues interfaces  70     ℎ™? = σϵ(𝑇™??? + 𝑇™?? )(𝑇™?? + 𝑇™? )   5.2   where, ℎ™?  is the radiation heat transfer coefficient, σ is Stefan-Boltzman constant, ϵ is the emissivity of the surface. 𝑇™??  and 𝑇™?  are the surface and environment or sink temperatures.  Table 5-5 shows the radiation heat transfer conditions.               71  Surface Time(cycle step) Heat Transfer Coefficient Ambient temperature Surface emissivity  (s) (W/m2/K) (°C)  Side die( and side die core)     Heater surface 0  ≤ t ≤ 210(step 1-5) 1500 475 - External surfaces 0  ≤ t ≤ 210(step 1-5) 20 100 0.7 Mating surface with top/bottom die 154.9  ≤ t ≤ 210 (step 2-5) 20 100 0.7  Contact with wheel  154.9  ≤ t ≤ 210 (step 2-5) 20 100 0.7 Bottom die     External surfaces 0  ≤ t ≤ 210(step 1-5) 20 100 0.7 Mating surface with side die  154.9  ≤ t ≤ 210 (step 2-5) 20 100 0.7 Contact with wheel 154.9  ≤ t ≤ 210 (step 2-5) 20 100 0.7 Top die     External surfaces 0  ≤ t ≤ 210(step 1-5) 20 100 0.7 Mating surface with side die 154.9  ≤ t ≤ 210 (step 2-5) 20 100 0.7 Contact with wheel  164 ≤ t ≤ 210 (step 4-5) 20 100 0.7 Lower sprue     Top of stalk 0  ≤ t ≤ 210(step 1-5) 2000 710 - External surfaces  0  ≤ t ≤ 210(step 1-5) 20 100 0.7 Contact with cast sprue 154.9  ≤ t ≤ 210 (step 2-5) 20 500 0.7 Upper sprue     Contact with cast sprue 154.9  ≤ t ≤ 210 (step 2-5) 20 500 0.7 Contact with wheel 154.9  ≤ t ≤ 210 (step 2-5) 20 100 0.7 Cast sprue 0≤ t ≤ 154.9  Step 1 2000 710 - Wheel surfaces  163.9≤ t ≤ 210 (step 3-5) 20 100 0.7      Environment Convection Boundary Conditions – At different times transport of heat from the die/wheel to the environment is also occurring by convection. This includes heat transfer occurring at the internal cooling channels within the die and the external surfaces of the die component and the wheel. The heat flux on the surface due to convection heat transfer is described as:    𝑞 = ℎ 𝑇™?? − 𝑇?    5.3   Table 5.5: Heat Transfer between the die and the environment (radiation boundary conditions)  72  where q is the heat flux  (𝑊 ∙ 𝑚??) and h is the convective heat transfer coefficient  (𝑊 ∙ 𝑚?? ∙𝐾??). 𝑇™??  is the surface temperature and 𝑇? is the environment or fluid(air or water) temperature. For example, in the case of external surfaces of the die, 𝑇? is the ambient temperature and in the case of water flowing in a cooling channel, 𝑇? is the bulk or sink temperature of the water or air. The surface convective heat transfer coefficients for surfaces excluding the cooling channels are listed in Table 5-5.  There are five cooling channels within the die, each having specific geometry and locations (shown in Figure 5.3). Air and water flow in the cooling channel in predetermined sequence that are summarized in Table 5-6. Based on the information provided by CAPTIN at early phases of this project, water is purged out of some the cooling channels (TDDC_CC, SDC_CC and BD_CC2) midway or close to the end of a casting cycle. However, further communication with CAPTIN made it clear that no purging was performed and water was left in the cooling channel to evaporate for 10 s, marked as “Stagnant Water” in Table 5-6. For example, in SDC_CC for the first 7 seconds of a cycle, the cooling channel is empty (Stagnant Air). Then, water flow is turned on from 7 to 157 s. Water flow was tuned off next and the remaining stagnant water evaporated (10 s) followed by stagnant air in the channel until the end of the casting cycle.      73  Cooling Channel Time Type Heat Transfer Coefficient Sink temperature  (s)  (W/m2/K) (°C) TD_CC (pond) 0 < t < 7 Stagnant Air  200 50  7 ≤ t ≤ 210 Water Flow  2500 30    4  TDDC_CC 0 < t < 67 Stagnant Air  4 25  67 ≤ t ≤ 107 Water Flow  4000 30  107 < t ≤ 117 Stagnant Water  50 30  117 ≤ t ≤ 210 Stagnant Air  4 25      SDC_CC 0 < t < 7 Stagnant Air  4 25  7 ≤ t ≤ 157 Water Flow  20,000 30  157 < t ≤ 167 Stagnant Water  50 30  167 ≤ t ≤ 210 Stagnant Air  4 25      BD_CC1 0 < t < 47 Stagnant Air  4 25  47 ≤ t ≤ 187 Air Flow  200 25  187 ≤ t ≤ 197 Air Flow  50 25  197 ≤ t ≤ 210 Stagnant Air  4 25      BD_CC2 0 < t < 77 Stagnant Air  4 25  77 ≤ t ≤ 127 Water Flow  8000 30  127 < t ≤ 137 Stagnant Water  50 30  137 ≤ t ≤ 210 Stagnant Air  4 25       Generally, the convective heat transfer coefficients for a given cooling channel are determined by estimation and the results of the casting simulation are then compared to the thermocouple measurements. The cooling channel boundary conditions are then adjusted until a reasonable fit to the thermocouple data is achieved. The values appearing in Table 5-6 have been estimated using this trial-and-error approach in the previous studies and were used in the base thermal model. Table 5.6: Cooling channel boundary conditions, trimming and constant heat transfer coefficient used in the base model  74  5.5.2 Thermal boundary conditions-correlation-based approach via subroutine The trial-and-error methodology described above is time consuming and does not accurately depict the physical phenomena occurring during casting. Furthermore, the use of constant boundary condition corresponds to only one specific set of operating conditions, severely limiting the flexibility and generality of the model. To predict a physically sound and dynamic heat transfer coefficient boundary conditions a user subroutine, FILM, was developed in Fortran and used in a second thermal model.  The only difference between the second model (with the user subroutine) and the first- base model (with constant HTCs listed in Table 5-6) is the cooling channel heat transfer coefficients, all other boundary conditions were identical in both models. The user subroutine was developed based on there being the possibility of single phase forced (water or air flow) cooling; natural convection (stagnant air) or boiling heat transfer (water flow) correlations. The subroutine calculates the local HTC based on fluid type, surface temperature of the channel, flow rate, temperature and pressure of the fluid in the channel and passes the computed values to the ABAQUS thermal model. The subroutine was activated for four of the cooling channels. The top die cooling channel, a.k.a. pond HTC was assumed constant due to the fact that it is large and constantly filled with circulating water. It is important to note that to calculate Stagnant Water HTC, linear interpolation from Flow Water to Stagnant Air HTC was performed. The interpolation approach was used to avoid the complications associated with water fully evaporating in the cooling channel and is justified because of the relatively short duration of this stage (10 s) compared to the rest of the casting cycle.  The remainder of this chapter presents a detailed description of the subroutine formulation, correlations and operational parameters used to calculate the local instantaneous heat transfer coefficient for a given cooling channel at a given time. First, the basic fluid flow and heat  75  transfer dimensionless numbers used in the subroutine (such as Reynolds and Nusselt numbers) are described. Then, the formulation for the natural and forced convection HTCs for air presented followed by the Forced convection and boiling HTC formulation for water. The subroutine has a modular programming structure in order to facilitate the future modification of process parameters such as water/air flow rate, pressure, temperature and cooling channel shape. The following variables were defined for each cooling channel: flow rate, temperature (bulk or sink), pressure, shape, cross sectional area and perimeter. Fluid flow rates for each of the cooling channels are shown in Table 5-7 Cooling Channel Water flow rate Air flow rate  (𝐿 min  ) (𝐿 min  ) TD_CC (pond) 20 400    TDDC_CC 12 400    SDC_CC 12 400    BD_CC1 - 400    BD_CC2 14 400     It was assumed that the air temperature (sink) remains constant at 50 °C in the top die cooling channel and 25 °C in the four remaining cooling channels. Water temperature (bulk or sink) was evaluated at an average temperature defined as:    𝑇™?? = 12 𝑇™    + 𝑇™?    5.4   Table 5.7: Water and air flow rate in the cooling channels  76  where 𝑇™    is the inlet water temperature going into the die, set to 20 °C, and 𝑇™?  is the outlet water temperature coming out of the die, 40 °C(based on the information provided by CAPTIN). Air and water temperatures for each cooling channel are also listed in Table 5-6 in the sink temperature column.  Based on the data provided by CAPTIN, the water line pressure during operation is between 0.5-0.7 MPa. Water pressure was introduced as an operational variable in the user subroutine, and 0.6 MPa was used for the present study.  Fluid temperature and pressure was assumed to be constant along the 36° section of the cooling channels in the thermal model. To calculate the local HTC value in the cooling channels, dimensionless numbers such as Reynolds and Nusselt number must be computed based on the diameter of the channel. Due to the non-circular shape of the cooling channels hydrodynamic diameter was defined in following form:     𝐷? = 4𝐴?𝑝    5.5   where 𝐴? is the cross section area of the cooling channels and 𝑝 is the perimeter. The cross sectional area and perimeter of cooling channels are listed in Table 5-8. To simplify the forced convection heat transfer calculations it was assumed that the surface of the cooling channels is smooth.     77  Cooling Channel Cross sectional area Perimeter  𝑚? m TD_CC (pond) 5×10?? 3.5×10??    TDDC_CC 5.1×10?? 2.5×10??     SDC_CC 9.5×10?? 3.5×10??    BD_CC1 7.7×10?? 3.6×10??    BD_CC2 1.4×10?? 4.7×10??     The velocity of the fluid in the cooling channel varies over the cross section from zero at the wall due to the no-slip condition to maximum at the center. Therefore, an average or mean velocity 𝑢? ??   which remains constant in incompressible flow is defined and calculated in the following form:    𝑢? = 𝐹𝑙𝑜𝑤  𝑅𝑎𝑡𝑒𝐴?    5.6   Temperature-dependent thermophysical properties of the fluid such as density, thermal conductivity, viscosity, and specific heat and Prandtl number are evaluated at the film temperature defined in the following form:    𝑇™?? = 12 𝑇™??   + 𝑇™??    5.7   where 𝑇™??  is the estimated instantaneous surface temperature of the cooling channel passed on to the user subroutine for heat transfer analysis.  Table 5.8: Cross sectional area and perimeter of cooling channels  78  To characterize different flow regimes, the Reynolds number was calculated in the following form:    𝑅𝑒 = 𝜌𝑢?𝐷?𝜇    5.8    where  𝜌 is the density of the working fluid ™?? , 𝑢? is the mean fluid velocity over the cross section ?? , 𝐷? is the hydrodynamic diameter 𝑚  and 𝜇 is the dynamic viscosity ™ ?   𝑜𝑟   ?.???   𝑜𝑟   ™?.? . The flow is laminar for 𝑅𝑒 ≤ 2300, transitional for 2300 < 𝑅𝑒 <4000 and turbulent for 𝑅𝑒 > 4000. In the subroutine 𝑅𝑒 > 4000 was chosen as the criterion for turbulent flow. It was assumed that the flow is hydrodynamically fully developed and its velocity profile is not changing along the cooling channel. The Nusselt number is defined as the ratio of convection to conduction heat transfer and is constant for fully developed laminar flow. For fully developed turbulent flow in smooth tubes, the Nusselt number is a function of Reynolds number and Prandtl number as described by the 𝐷𝑖𝑡𝑡𝑢𝑠 − 𝐵𝑜𝑒𝑙𝑡𝑒𝑟  𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛.     𝑁𝑢 = ℎ™ 𝐷?𝑘 = 4.36      𝐿𝑎𝑚𝑖𝑛𝑎𝑟  𝑓𝑙𝑜𝑤   5.9      𝑁𝑢 = ℎ™ 𝐷?𝑘 = 0.023𝑅𝑒?.?𝑃𝑟?.?          𝑇𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡  𝑓𝑙𝑜𝑤  (𝐷𝑖𝑡𝑡𝑢𝑠− 𝐵𝑜𝑒𝑙𝑡𝑒𝑟  𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛)   5.10   where K is the conductivity of fluid ??∙?  and Prandtl number 𝑃𝑟 = ????  in which 𝐶? is specific heat ?™? .    79  Subroutine Formulation-Air  Heat transfer at the cooling channel-air interface is in the form of forced convection when air is flowing in the channel and in the form of natural convection for stagnant air as shown in Table 5-6.  Properties of air are evaluated at the film temperature according to Equation 5.7. Temperature-dependent properties such as density, specific heat, viscosity and thermal conductivity were computed using the correlations extracted from literature. These correlations are listed in Appendix C.  Natural convection To calculate the natural convection heat transfer coefficient, a dimensionless number called the Grashof number is calculated first. The Grashof number represents the ratio of the buoyancy forces to the viscous forces and has the following form:     𝐺𝑟 = 𝑔𝛽 𝑇™?? − 𝑇?     𝐷??    𝑣    5.11   where 𝑣 = 𝜇 𝜌   is the kinematic viscosity ???  and g is acceleration due to gravity, 𝑇™??  is the cooling channel surface temperature and 𝑇? is the sink or bulk temperature of air. The volume coefficient of expansion for ideal gases can be defined as  𝛽 = ?? ™??  and 𝑇™??  is absolute average film temperature 1816. Free convection heat transfer is represented in the following functional form:    𝑁𝑢 = 𝐶(𝐺𝑟. 𝑃𝑟)?   5.12    80  The product of Grashof and Prandtl number is called Rayleigh number. C and m are constant dependant on the geometry, orientation of the surface and Rayleigh number. Table 5-9 shows the constant values for horizontal cylinder geometry 57.   Geometry 𝐺𝑟. 𝑃𝑟 C m Horizontal Cylinder 10? − 10? 0.85 0.18  10? − 10™  0.48 0.25  10? − 10™  0.12 0.33     After calculating the Nusslet number, the local heat transfer coefficient for stagnant air is calculated in the following form:    ℎ™ = 𝑁𝑢 ∙ 𝑘𝐷?    5.13   Forced convection Air flow through the cooling channel was considered incompressible since the density changes are less than 30 percent of the velocity of sound in that gas (detailed description in Appendix A). To calculate a forced convection HTC, first the Reynolds number was calculated using Equation 5.8 based on the mean velocity, hydraulic diameter and temperature dependent properties of air. Depending on whether the air flow is laminar or turbulent, the local HTC value was then computed using the correlation 5.9 or 5.10.  Subroutine Formulation -Water  Water is present in all of the channels, with the exception of BD_CC1, throughout the majority of step 1, high heat extraction rates from the die for solidification of the wheel are needed. Heat Table 5.9: Constants for use in Equation 5.12  81  transfer to water flowing inside the cooling channel is governed by single phase forced convection as long as the liquid and the surface temperature are below the saturation temperature of the water at the local pressure. As the surface temperature increases, depending on the surface characteristics and operating conditions, boiling may occur 58. The bulk water temperature may still stay below the saturation temperature; this condition is called subcooled flow boiling. Based on the thermocouple data at the cooling channel outlet, subcooled flow boiling is considered the dominant boiling mode since bulk outlet temperature is below the saturation temperature. Due to the complexity of the fluid mechanics and phase-change thermodynamics, the majority of the flows boiling heat transfer correlations have been derived empirically. The transient nature of boiling and the scarcity of flow boiling correlations have required that a number of approximations be made to develop the HTC algorithm. This section discusses the heat transfer correlations used in the user subroutine to compute heat transfer coefficient for water flow in the cooling channel. Temperature-dependent thermophysical property correlations for water were extracted from the literature and implemented in the subroutine (detailed in Appendix D). Flow boiling is a complicated phenomenon due to the coupling effect between hydrodynamics and boiling heat transfer processes. Heat transfer can be controlled by forced convection, nucleate boiling, transition boiling and film boiling, which are different regions of the boiling curve. Not all of the regions may be present in the cooling channel depending on the surface temperature and process parameters. Correlations were selected for their generality and relative accuracy to predict the principle features of the boiling curve. Interpolation techniques were used between these limits to form the boiling curve. To predict the defining features of the boiling curve (shown in Figure 5.5) two critical points, the onset of nucleate boiling (ONB) and the critical heat flux (CHF), were defined in the subroutine.  82  The onset of nucleate boiling (ONB) marks the start of boiling where bubble nucleation induces a sudden increase in the heat transfer coefficient. It was assumed that boiling starts as soon as the surface temperature reaches the saturation temperature (𝑇™?? = 𝑇™? = 𝑇™? ). When the surface temperature of the cooling channel is below the saturation temperature of water, single phase forced convection is in effect. The saturation (boiling) temperature 𝑇™?  of water as a function of pressure was computed in the following form:     𝑇™? = (A+ CX)/(1+ BX+ D𝑋?)   5.14   where X=Ln (P), A=179.96, B=-0.106, C=24.22, D=2.951×10?? and P is pressure in MPa 59. The second defining point of the boiling curve, the critical heat flux (CHF), is the threshold in boiling heat transfer signifying the end of nucleate boiling and a sudden reduction in the heat transfer coefficient. Lookup tables are widely used to predict the critical heat flux. However, various process parameters such as liquid subcooling, flow rate and flow quality affect the critical heat flux. In the present study, the critical heat flux is formulated based on the pool boiling data and is roughly estimated as 𝑇™? (°𝐶) = 𝑇™? + 35 16. Heat transfer falls in the nucleate boiling regime when the cooling channels surface temperature is below the 𝑇™?  and in the transition, or film boiling regime when above the critical heat flux.   83     Figure 5.5: Generic boiling curve indicating different heat transfer regimes- Linear interpolation in the nucleate boiling region 60    Forced convection (𝑇™?? < 𝑇™? )- Heat is transferred from the surface of the cooling channel to the water through single phase forced convection, since the surface temperature is below saturation temperature or onset of boiling 𝑇™? . First, the Reynolds number is calculated using Equation 5.8. The forced convection HTC is then calculated using Equation 5.9 for laminar flow or 5.10 for turbulent flow. Nucleate boiling (𝑇™? ≤ 𝑇™?? < 𝑇™? )- Nucleate boiling (in flow boiling) is complex and may consist of sub-regions such as partial and fully developed nucleate boiling. To ensure a smooth transition between the forced convection and nucleate boiling and to reduce the complexity of the sub-processes associated with the nucleate boiling, an interpolation approach was used in calculating the nucleate boiling heat transfer coefficient. Throughout this approach the HTC in the nucleate boiling region is linearly interpolated from the Onset of nucleate boiling (ONB) to the critical heat flux (CHF). Although bubbles form on the surface at ONB, they do not grow  84  since they are exposed to the subcooled fluid. Hence, forced convection correlations were used to calculate the heat transfer coefficient at the onset of nucleate boiling ℎ™? . To calculate the HTC at the critical heat flux, Chen’s superposition model was used in which the contribution of nucleate boiling and forced convection are considered additive. The forced convection HTC, ℎ™  is calculated using the Dittus-Boelter Equation (5.10).    ℎ™? = 𝐹. ℎ™ + 𝑆. ℎ™         Chen  correlation     5.15   where F signifies the contribution of convection to heat transfer in the nucleate boiling region and is dependent on the heat flux, flow rate and liquid subcooling. It is, however, very challenging to quantify F for the water flow in the cooling channel without knowing the local heat flux and degree of subcooling. In the present study F was set to 0.5, meaning that the contribution of forced convection drops to half from the start of the boiling to the critical heat flux. The nucleate boiling contribution  ℎ™  is calculated using the Forster and Zuber’s correlations:    ℎ™ = 0.00122 𝐾??. ™ 𝐶™ ?. ™ 𝜌??. ™𝜎??.?𝜇??. ™ ℎ™ ?. ™ 𝜌??. ™ ∆𝑇™? ?. ™ . ∆𝑃™? ?. ™    5.16   where ∆𝑇™? = 𝑇? ™? − 𝑇™?  and ∆𝑃™? = 𝑃™?? − 𝑃™?  the difference in vapour pressure at the wall and at the saturation pressure. The thermophysical properties of liquid water used in the Forster and Zuber’s equation were evaluated at the saturation temperature  𝑇™? . The boiling heat transfer suppression factor S was computed using an empirical correlation suggested by Chen:    𝑆 = 11+ 2.53. 10??𝑅𝑒??. ™    5.17    85  The heat transfer coefficient in the nucleate boiling region was then calculated by linear interpolation for Onset of nucleate boiling ℎ™?  to the critical heat flux  ℎ™?  as shown in the Figure 5.5.  Transition and film boiling (𝑇™?? ≥ 𝑇™? )- Heat transfer in the post critical heat flux region can occur via transition or film boiling. Film boiling occurs if the cooling channel surface temperature is above the Leidenfrost or minimum film boiling temperature (𝑇™?? > 𝑇™? ). Due to the challenges in quantifying the minimum film boiling temperature in the cooling channel, steel-quenching literature was reviewed and used to make assumptions 60,61. Based on the collected die temperature data and the review of quenching literature, it was assumed that the cooling channel surface temperature does not exceed the minimum film boiling temperature and film boiling does not occur in the cooling channel. To calculate HTC in the transition boiling region, the heat transfer coefficient was exponentially decreased from the value at critical heat flux ℎ™?   as proposed by Barnea.    ℎ ™ ⌤? = ℎ™? . 𝑒𝑥𝑝 𝑇™? − 𝑇™??𝑇™? − 𝑇™?    5.18   It is important to note that the majority of the flows boiling heat transfer correlations have been derived empirically from experimental databases that are either measured by the author of the correlation, compiled from the literature or both. In either case, a specific correlation is valid for the specific flow configuration and operating conditions that the database is built upon. Therefore, caution must be exercised in applying the empirical correlations that are specifically tailored to the unique features of flow boiling.  Flow boiling heat transfer coefficient correlations were mainly developed as a function of heat flux. Such correlations cannot be used in developing a flow boiling heat transfer coefficient code for LPDC since the local heat flux at the cooling  86  channel/die interface is not known. Therefore, developing a subroutine capable of predicting boiling heat transfer coefficient involves significant approximations. 5.6 Convergence criteria  Complex boundary conditions, specifically at the cooling channels, due to boiling and convection as well as temperature-dependent material properties used in the thermal model makes this analysis highly non-linear. In such cases, a numerically converged solution may be difficult to achieve with the default ABAQUS convergence criteria parameters. The default provide efficient and accurate solutions for a broad range of non-linear problems. However, the default convergence criteria parameters are strict by engineering standards and can be tuned to provide flexibility 62. The user-defined convergence criteria used in the thermal model and the default values are listed in Table 5-10.   Convergence Criteria  Default User-defined  Convergence tolerance parameters for heat flux    Criterion for residual heat flux for a nonlinear problem 0.005 0.05 Criterion for temperature correction in nonlinear problem 0.01 0.1    Time incrimination control parameters   Maximum equilibrium iterations allowed 16 32 Cut-back factor after divergence  0.25 0.1      Table 5.10: User-defined convergence control parameters  87    Results and discussion 6.The objective of this research was to develop a methodology to quantitatively describe the heat transfer in the cooling channels of the low-pressure die casting process and to successfully implement the methodology in a 3D thermal model. Towards this goal, a user-defined subroutine describing heat transfer in water/air cooling channels under conditions typical of those existing in the LPDC of aluminum automotive wheel has been developed. To begin, as a base-case, a 3D thermal model of LPDC was run using constant HTC values in the cooling channels that were obtained by trial-and-error. It took approximately 7 cycles for the model to reach steady state and each cycle took around 9 hours. Then, a second model was run using the user-defined subroutine to quantify the heat transfer in the cooling channel, was run - refer to Chapter 5 for the detailed description. In Chapter 6, the results of the base-case model (constant HTC) and the subroutine-implemented model are presented. The results of both models are compared to the plant trial temperature measurements to assess the subroutine’s ability to predict the heat transfer and the temperature history in locations close to the cooling channels. 6.1 Cooling channel HTC The majority of the heat removed during LPDC is achieved through the cooling channels with air and/or water flowing through at a specific rate for a defined period of time. There are five cooling channels in total and each is controlled separately as shown in Table 5-6 and Figure 6.1. The heat transfer between the cooling fluid and hot surface of the cooling channel can be categorized as single-phase or two-phase fluid flow-heat transfer. Single-phase heat transfer occur as forced convection (air or water flow) or natural convection (stagnant air). When the  88  cooling channel surface temperature is above the saturation temperature of water, boiling occurs and two-phase flow heat transfer is dominant.   6.1.1 Base-case thermal model with constant HTC  In the base-case thermal model constant HTC values for each cooling channel were used-refer to Table 5-6. As previously described, the trial-and-error process to obtain HTC values is extremely time consuming and does not accurately describe the physical phenomenon occurring during casting. Moreover, the constant HTCs correspond to a given set of operation conditions and die geometry, compromising the generality and utility of the model.  It took 6 cycles for the base-case model to reach steady state.  Figure 6.1 is a contour plot showing the temperature distribution in the wheel and the die at 154 s, just before the die opens. The baseline thermal model was able to predict the temperature field and the progress of solidification front during the casting process. Looking at the temperature distribution around the cooling channels, TD-CC and SDC-CC have the lowest temperatures just before die open, since water flows in these two channels for the majority of the casting cycle (192 s TD-CC and 150 s for SDC-CC). Water flows in TDC-CC and BD-CC2 for 50 seconds. BD-CC1 has the highest temperature since it is air-cooled, providing an indication of the substantial lower cooling capacity of air compared to water. It can be seen in Figure 6.1, that the temperature around the surface of cooling channels is not uniform-see TDC-CC and BD-CC2. Clearly, the surface areas facing the wheel experience higher temperature compared to the opposite side, which will have implications in terms of heat extraction.    89     Figure 6.1:  Contour plot of temperatures in the wheel and die prior to die open    6.1.2 Thermal model with user-defined subroutine To increase the generality of the model, its accuracy and to avoid the time consuming trial-and-error process, a user-defined subroutine, capable of calculating a local instantaneous HTC based on cooling channel geometry and surface temperature as well as process parameters, was developed. The subroutine was implemented in the thermal model for all cooling channels excluding TD-CC (cooling pond). The constant HTC value for TD-CC used in the base-case model was also employed. It should be noted that the only difference between the base-case  90  model and the model with subroutine is the cooling channel HTCs (excluding the TD-CC). All other boundary conditions are identical in both models. The subroutine calculates the local HTC based on surface temperature of the channel, flow rate, temperature and pressure of the water/air and passes the computed values to the ABAQUS thermal model. The overall thermal model is run normally-i.e. repeatedly - until steady state is reached. In this section, the cooling channels’ HTC values calculated by the subroutine and the resulting cooling curve are presented. As mentioned earlier, the temperature at the surface of the cooling channel is not uniform, and exhibits the highest temperature on areas of the surface nearest the cast wheel. To extract the calculated HTC and the temperature history of the cooling channels from the model, one element on the hot (wheel-facing) side of each cooling channel was selected. Temperature history and the calculated HTC and the resulting boiling curve for the selected element were output from the model and graphed.  Figure 6.2(a) shows the variation of HTC, surface temperature and sink temperature with time and Figure 6.2(b) shows the calculated boiling curve for SDC-CC. Referring to Figure 6.2(a), for the first 7 seconds, the cooling channel is empty of water and heat transfer happens through natural convection to the air in the channel. The calculated natural convection HTC is  ~  13  (W ∙m?? ∙ K??). Then, water flow is turned on from 7 s to 157 s of the casting cycle. When water first comes in contact with the surface of the cooling channel, the temperature is around 170 (°C), causing boiling to occur and the HTC increases up to ~  22,000(W ∙ m?? ∙ K??). The high heat transfer coefficient due to nucleate boiling decreases the surface temperature substantially, to below the saturation temperature of water causing the heat transfer to occur via the forced convective region- see Figure 6.2(b). The forced convective HTC decreases, as the surface temperature drops. However, it remains stable around 12,000(W ∙ m?? ∙ K??) during the majority  91  of the water flow cooling. From 167s to the end of the casting cycle, the cooling channel is empty and heat is transferred to stagnant air through natural convection. As explained in Chapter 5, based on the information provided by CAPTIN from 157-167s, for the side die cooling channel, water is not circulated in the cooling channel and is left to evaporate. Therefore, during this time period, HTC is linearly interpolated from the water flow mode to the stagnant air. As shown in Figure 6.2(b), out of four regions of a typical boiling curve, only two regions, namely forced convection and nucleate boiling, are present. This is because the side die cooling channel surface temperature is not high enough for transition or film boiling to occur. The main feature of this curve is the greatly increased heat transfer when boiling occurs (doubled HTC). The transition between single phase forced convection and nucleate boiling (T™? ) occurs at surface temperature of 159 (°C).             92      Figure 6.2: Temperature history (a) and boiling curve (b) for side die cooling channel (SDC-CC)      Figures 6.3 (a) and (b) show the temperature history and the boiling curve for TDDC-CC respectively. Before water starts flowing in the cooling channel, heat transfer happens through natural convection to air with a calculated HTC of ~  16  (W ∙ m?? ∙ K??). From 67 to 107 s of the casting cycle water flows through the channels producing the boiling curve shown in Figure 6.3 (b). When water first starts to flow, the cooling channel surface temperature is around 280 (°C), well above the critical heat flux temperature T™?  and in the transition-boiling region. The transition boiling heat transfer lasts a very short time (less than 1 s) as the surface temperature drops rapidly due to high heat flux. The peak heat transfer coefficient~  33,000(W ∙ m?? ∙ K??) corresponds to the critical heat flux threshold from which the cooling process enters the nucleate  93  boiling region. As the surface temperature decreases, forced convection heat transfer occurs and remains the dominant mode of heat transfer for the rest of the water cooling duration. From 107 s to 117s water fully evaporates in the cooling channel and heat is then transferred to the air in the channel through natural convection until the end of the casting cycle.      Figure 6.3: Temperature history (a) and boiling curve (b) for top die drum core cooling channel (TDDC-CC)   In BD-CC2, water flow starts at 77 s and ends at 127 s of the casting cycle as shown in Figure 6.4 (a). The cooling process in BD-CC2 follows the previous cases in the form of stagnant air followed by water flow, water evaporation (interpolation) and stagnant air. As shown in the boiling curve in Figure 6.4 (b) the three regions of a typical boiling curve: transition and nucleate  94  boiling as well as forced convection are present. It is important to note that the critical heat flux temperature  T™?  and temperature at which boiling starts T™?  are kept constant for all the cooling channels. However, the HTCs corresponding to the two threshold temperatures are unique for each cooling channel due to the effect of cooling channel geometry and water flow rate. For example, when comparing the boiling curves of TDC-CC to BD-CC2 (bottom plots in Figure 6.3. and 6.4) the HTCs in the forced convection and nucleate boiling regions for TDC-CC are significantly higher (double) compared to that of BD-CC2. This is because the cross-sectional surface area of TDC-CC is significantly smaller than that of BD-CC2, resulting in a higher fluid mean velocity (for the same fluid flow rate) which itself increases the Reynolds number and the heat transfer coefficient.      Figure 6.4: Temperature history (a) and boiling curve (b) for bottom die cooling channel 2(BD-CC2)    95  Comparing the variation of HTC and surface temperature of SDC-CC, TDC-CC and BD-CC2 with time during a steady state casting cycle shows that during water cooling, boiling occurs for a short period of time, resulting in a high heat transfer coefficient, which drops the surface temperature in the forced convective region. Forced convection remains the dominant and stable mode of heat transfer during water-cooling of the die.  Figure 6.5 shows the variation of HTC and surface temperature with time for BD-CC1. This cooling channel is only air-cooled, resulting in a substantially lower overall heat transfer coefficient compared to the rest of the cooling channels. From 47 s to 187 s air is flowing in the cooling channel resulting in a forced convection HTC of~  250(W ∙ m?? ∙ K??). Heat transfer happens through natural convection from the cooling channel to air for the remaining time of the casting cycle.     Figure 6.5: Temperature history and calculated HTC for bottom die cooling channel 1(BD-CC1)   In summary, the user-defined subroutine is capable of calculating instantaneous local temperature-dependent HTCs based on the process parameters and geometry of the cooling channels. The natural and forced convection as well as boiling heat transfer coefficients were  96  calculated and passed to the thermal model. The subroutine can produce a continuous relationship between the heat transfer coefficient and the surface temperature for different regions of the boiling curve.  6.2 Temperature comparison  Sub-surface thermocouples are often used in quenching experiments to collect the temperature history of the surface 61. The cooling curves measured in very close proximity to the surface capture the changes in the surface heat flux and therefore can serve as a means of verifying the heat transfer conditions applied in the numerical model. However, due to the complex geometry of the die and the casting machine, and the complicated orientation of the cooling channels within the die, it is challenging to drill holes through the die and install thermocouples in close proximity to the channel/die interface. From the thermocouple positions available, those closest to the cooling channels have been chosen for comparison. The locations of the thermocouples are detailed in Chapter 4.  Bottom Die Figure 6.6 shows the measured and predicted temperature histories for three locations in the bottom die spoke area, TC-21, TC-23,TC-25 and TC-24. The blue line corresponds to the measured temperature history from the casting trial, the red line is the output from the constant HTC model and the black line is the output from the subroutine-based HTC model. Some of the features on the plot may be related back to steps within a casting cycle. For example, at location TC-21 from 0 to approximately 25 s, the temperature starts to increase rapidly since the liquid metal has reached the location in the spoke adjacent to TC-21. Following this sharp temperature increase, heat is removed from the wheel to the die and to the cooling channel and ultimately to  97  the environment. Similar behavior is visible in TC-24. The effect of die filling in the form of a rapid temperature increase around 23 s is less visible in TC-23, 25 since the two thermocouples are not in close proximity of the die-wheel interface. In general, temperature measurements in locations close to the die-wheel interface (TC-21 and TC-24) show a rapid increase in temperature after filling, followed by a stable period before beginning to drop towards the end of the cycle. In case of the thermocouples close to the exterior faces of the die (TC-23, 25) temperature variations within a cycle are dampened due to the intervening thermal mass of the die. At location TC-21 the predicted temperature from both of the thermal models is higher than the measured value for a short period of time (~24-40s) and then remains 20~80 °C lower than the measured value. For TC-23, 25 the predicted temperatures are higher than the measured values throughout the casting cycle with a maximum difference of 40 °C. At TC-24, the predicted temperatures from both models are always lower than the measured temperature. In all locations, temperature predictions from the subroutine-implemented model are slightly lower than that of the base-case model with maximum difference of approximately ~20 °C.   98     Figure 6.6: Comparison of predicted and measured temperatures at three locations within bottom die spoke TC-21, 23, 25 and 24    Figure 6.7 shows the measured and predicted temperature histories for two locations in the bottom die window area, TC-27 and TC-28. For both TC-27 andTC-28, the measured temperature is higher (~50 °C) than the predicted temperature from the two thermal models (base-case and subroutine).   99     Figure 6.7: Comparison of predicted and measured temperatures at three locations within bottom die window TC-27 and TC-28     In summary, within the bottom die window and spoke, temperature predictions from the model with the subroutine are slightly lower (~10− 20  °C) than that of the base-case model with constant HTC. This may be attributed to higher HTCs calculated by the subroutine for BD-CC1 and BD-CC2 compared to the constant values used in the base-case model (listed in Table 5-6).  Side Die  In the side die, thermocouple comparison was limited to locations in the lower part of the rim since the upper rim thermocouples were in close proximity to TD-CC (identical HTCs for both thermal models). Temperature comparison for the two locations in the side die spoke TC-4 and  100  TC-5 is shown in Figure 6.8. The variations of temperature with time reflect the various operational stages such as die cavity filling and die opening within a cycle. Approximately, the same behaviour is observed at the location of these thermocouples as previously described with the exception that once the wheel is fully solidified, at ~155s, the top die moves up and side die opens, causing a temperature drop shown in Figure 6.8, specifically visible for TC-5. In both locations the temperature history predicted by the base-case model with constant HTC is similar to temperature variation predicted by the user-subroutine based thermal model. For TC-5 the temperature predicted by the two models is higher than the measured temperature (maximum difference ~50 °C) for a majority of the casting cycle except from 48 to 80 s of the casting cycle. At location TC-4 the predicted temperature by the thermal models surpasses the measured temperature at around 40 s for a short period of time, and then remains 10~75°C lower than the measured value.    Figure 6.8: Comparison of predicted and measured temperatures at two locations within side die spoke TC-5 and TC-4    101   Figure 6.9 compares the measured and predicted temperature at locations in the side die, window section. At locations TC-14 and TC-15 similar trends to those of TC-4 and TC-5 are observed.    Figure 6.9: Comparison of predicted and measured temperatures at two locations within side die window TC-14 and TC-15    Top Die The measured and predicted temperatures in the top die in proximity to external surface, TC-43, is shown in Figure 6.10. The measured temperature stays almost constant throughout the casting cycle. Temperature history predicted from the base-case model is approximately 25 °C higher than the measured temperature. However, temperature predicted by the model with the cooling channel subroutine is very close to the measured temperatures. The nearest cooling channel (except the TD-CC) to this location is the top die drum core cooling channel TDDC-CC with  102  water cooling on for 40 s. The average HTC calculated by the subroutine for water-cooling in TDDC-CC is ~18,000 W/m2/K, substantially higher than the constant value of 4,000 used in the base-case model. The immediate effect of such a high heat transfer coefficient is suppressed by the thermal breaks located between the top die and top die drum core making the temperature variations of TC-43 with time insignificant. However considering cyclic behavior of the LPDC process, the effect of such high HTC in the thermal model with the cooling subroutine accumulates over time, resulting in the lower temperature at TC-43 location compared to the base-case model. This could serve as a possible explanation of why the temperature history in the subroutine model is lower than that of the base-case model considering that all other boundary conditions are identical for both models.      Figure 6.10: Comparison of predicted and measured temperatures at a location within top die TC43    Figure 6.11 shows the comparisons between the predicted and the measured temperature at the top die spoke locations close to the wheel interface. Temperature variations at TC-49, TC-46 and TC-50 show similar trends to those observed in TC-21 in bottom die (Figure 6.6). The  103  temperature predicted by the two thermal models is lower than measured except for a small time where at the location of TC-49 the model predict a higher temperature than was measured. The maximum difference between the measured temperature and the predicted temperature is ~25˚C in TC-46.     Figure 6.11: Comparison of predicted and measured temperatures at three locations within top die spoke TC-49, 46 and 50   The measured and predicted variation of temperature with time for two location in the top die window TC-47 and TC-48 are shown in Figure 6.12. For TC-47 the characteristic shape of the temperature curve is similar to temperature variations in top die spoke locations, especially TC-46. For TC-48 the general shape of the temperature curve is very similar to the temperature variation in bottom die window locations TC-27 and TC 28 shown in Figure 6.7. The temperatures predicted by both thermal models are lower than the measured temperatures with the highest difference ~60 ˚C.  104     Figure 6.12: Comparison of predicted and measured temperatures at two locations within top die window TC-47, TC-48   Temperature comparison in top die center pin TC-60 and top die drum core TC-61, TC-62 are shown in Figure 6.13. For TC-60 the predicted temperatures from both models are lower than the measured temperature except for a duration of 10 s after the liquid metal reaches the location of thermocouple in which the temperature in the base-case model slightly exceeds the measured temperature. At locations TC-61, TC-62 in the top die drum core, temperature measurement shows a sharp increase around 30 s due to filling. The temperature continues to increase as heat is drawn from the wheel to the die (center pin) and to TDDC-CC and the environment. The effect of water-cooling in TDDC-CC is visible as the temperatures predicted by both of the thermal models drop from 70 to 100 s of the casting cycle. The temperature difference between the base-case model with constant HTC and the model with subroutine is  ~40˚C due to the substantially  105  higher HTCs calculated by the subroutine compared to the constant values used in the base-case model.     Figure 6.13: Comparison of predicted and measured temperatures at two locations in top die center pin TC-60 and top die drum core TC-61,TC-62    To summarize, the measurements in locations of the die in proximity to the wheel-die interface show a rapid temperature increase within 20-30 s of the casting cycle start as a result of the die cavity filling. The temperature is then stable for a short period of time, followed by a gradual decrease. The temperature plateau right after the filling peak (specifically visible in wheel-top and bottom die interface locations) is likely linked to the evolution of latent heat during solidification. Once latent heat has evolved, the temperature starts to gradually decrease as the rate of heat output from the die exceeds the heat input from the wheel. Towards the end of the  106  cycle ~155s, there is a sharper temperature drop due to the die opening and exposure to the environment. For thermocouple locations close to the exterior surface of the die (except TC-43), these regimes are present however, delayed and dampened due to the effect of the die thermal mass.  It is evident that both of the thermal models (base-case and subroutine-implemented) reproduce the trends in the measured data qualitatively, reflecting the various operational stages of the casting process such as filling, cooling, solidification and die opening. Hence, the basic formulation of the models in terms of describing each casting cycle in the form of various steps (described in chapter 5) is correctly implemented. The difference between the temperature histories predicted by the two models and the measured data could be due to a variety of factors such as the definition of materials properties, mesh size or various boundary conditions in the thermal models.  The predicted temperatures from the model with subroutine are in general very close to the temperature predictions by the base-case model with constant HTCs in a majority of the locations examined. In a few locations, such as center pin TC-61, TC-62 and external surface of top die TC-43 and bottom die spoke TC-23 and TC-25 the subroutine-implemented model shows a closer fit to the thermocouple data compared to the base-case case. However, overall it appears that the subroutine did not enhance the accuracy of the thermal model in predicting the evolution of temperature in the die and the wheel.  6.3 Discussion  It is important to reiterate that the constant HTCs used in the base-case model were obtained through a time-consuming trial-and-error process and hence correspond to a given set of  107  operational parameters and geometry. Hence, the generality and utility of the model is limited. The subroutine used for the present study, however, calculates local instantaneous HTCs using a physical model based upon natural and forced convection as well as flow boiling correlations as a function of cooling channel surface temperature. The subroutine was also designed to have a modular structure in order to facilitate adding new heat transfer correlations and tuning process parameters such as water/air flow rate, temperature and the cooling channel geometry. Initially, it was thought that using the subroutine would increase the accuracy of the model since the subroutine calculates local temperature dependent HTCs. For example, during water-cooling, the intensity of cooling is dramatically increased if boiling occurs, resulting in a large non-liner variations in HTC with temperature (boiling curve) at water/cooling channel interfaces. Variations in HTC due to boiling and the surface temperature were discussed earlier in section 6.1.2. As an example, for water flow in BD-CC2 (77 to 127 s of the casting cycle), a constant HTC value of 8,000 W/𝑚?/K was used in the base-case model while the subroutine calculates HTC values of ~100− 35,000 W/𝑚?/K as a result of water boiling in the channel. Boiling occurs for a very short period of time when water first comes in contact with the surface of cooling channel, resulting in a high HTC. The temperature then quickly drops transitioning the heat transfer into the forced convective region of the boiling curve. Forced convection then remains the dominant heat transfer mechanism for the majority of water-cooling duration and the associated HTC remains approximately constant also. Thus, it would appear that an average HTC is sufficient to describe the heat transport between water and the surface of cooling channel for the majority of the time. To better understand this, mean HTC values were calculated during each mode of cooling channel operation over a casting cycle- i.e. the HTCs calculated by the subroutine are time averaged for water and for air. The results are shown in Table 6-1. For  108  example, in BD-CC2 the averaged HTC values calculated by the subroutine are two orders of magnitude higher than the constant values used in the base-case model during water cooling. Comparing the temperature predictions for locations around this cooling channel in the two models, TC-23, TC-25(Figure 6.6), it can be seen that the temperatures predicted from the user-defined subroutine model are only slightly lower than the temperature predictions from the base-case model, despite the much larger HTC. This indicates that the model is very insensitive to the magnitude of the cooling in this channel, which is consistent with the fact that it is a small channel located in thick (massive) section of the die far from the wheel/die interface. In another example, TDDC-CC, the average calculated HTC for water flow is 18,000 W/𝑚?/K, compared to constant 4,000 W/𝑚?/K used in the base-case model. The results for TC-43 located above the TDDC-CC are shown in Figure 6.10. These results show that at this location higher HTC predicted by subroutine brings the model into closer agreement with the measurements. In summary, the user-defined subroutine is an important step forward, eliminating the need for repetitive trial-and-error fitting to describe the heat transfer coefficients predicted by the subroutine-based formulation in higher average values (some that are significantly higher). These in turn under predict temperatures in the die relative to measured TC data even more so than the trial-and-error fit model. The lack of sensitivity to the cooling channel HTC’s reflects that the cooling channels examined the 427 die are relatively small and located in section of the die that are thick (massive). To fully test and validate the subroutine implementation a die with larger cooling channels would be needed.     109  Cooling Channel Time Cooling Mode Average HTC (subroutine) Constant HTC (base-case model)   (s)  (W/𝑚?/K) (W/𝑚?/K) TDDC_CC 0 < t < 67 Stagnant Air  16 4  67 ≤ t ≤ 107 Water Flow  18,000 4,000  107 < t ≤ 117 Stagnant Water  7,000 50  117 ≤ t ≤ 210 Stagnant Air  15 4      SDC_CC 0 < t < 7 Stagnant Air  13 4  7 ≤ t ≤ 157 Water Flow  11,000 20,000  157 < t ≤ 167 Stagnant Water  5,000 50  167 ≤ t ≤ 210 Stagnant Air  12 4      BD_CC1 0 < t < 47 Stagnant Air  17 4  47 ≤ t ≤ 187 Air Flow  261 200  187 ≤ t ≤ 197 Air Flow  264 50  197 ≤ t ≤ 210 Stagnant Air  17 4      BD_CC2 0 < t < 77 Stagnant Air  14 4  77 ≤ t ≤ 127 Water Flow 9,000 8,000  127 < t ≤ 137 Stagnant Water  4,000 50  137 ≤ t ≤ 210 Stagnant Air  13 4        Table 6.1: Average HTCs calculated by the subroutine and constant HTC used in base-case thermal model  110   Summary and conclusions  7.The objective of this project was to develop a methodology to quantitatively describe the heat transfer in the cooling channels of the low-pressure die casting process used to produce aluminum automotive wheels, and to successfully implement the methodology in a numerical model of the casting process. Towards this goal, the work has focused on the development of a user-defined subroutine capable of calculating local instantaneous heat transfer coefficients (HTCs) based on the process parameters and the surface temperature of a given cooling channel. The subroutine was implemented in a 3-D thermal model of the Low Pressure Die Casting (LPDC) process developed in the commercial finite element analysis package in ABAQUS. This model was referred to as the subroutine-based model thorough the thesis.   As part of a broader program focused on die design, funded under the Canadian Automotive Partnerships Program (APC), temperature data was collected from an instrumented die, CAPTIN model 427, to provide data suitable for model validation. This data, obtained from thermocouples placed at locations within the top, side and bottom die sections was compared directly with the subroutine-based model predictions. The positions selected for comparison where chosen to be as close to the water cooling channels described by the subroutine as possible. Dr. Carl Reilly, the Research Associated supported by the APC program, oversaw the collection of the data. To further assess the validity of the subroutine-base model, output from it was also compared with output from a base-case model that utilized constant HTCs derived based trial-and-error approach. The trial-and-error process to obtain the HTCs in the cooling channel involves, prescribing a trial set of HTC values and comparing the results of the casting simulation with thermocouple measurements. The trial-cooling HTCs are then adjusted until a reasonable fit to the temperature measurements is achieved. The trial-and-error approach is generally time  111  consuming does not accurately describe the physical phenomenon occurring in the cooling channel during casting. Furthermore, the cooling channel boundary conditions obtained through this approach are tuned to a given set of operating conditions, compromising the utility and generality of the model.  For water flow in the cooling channels, depending on the surface temperature and the saturation temperature of the water (pressure), the dominant heat transfer mode might be single phase forced convection or two-phase boiling. Within the boiling region, various modes of boiling such as nucleate or transition boiling exist dependent on the temperature. The subroutine uses various correlations such as Dittus-Boelter equation; Forster and Zuber’s empirical correlations and Chen’s superposition model to calculate the heat transfer coefficients corresponding to different regions of the boiling (Nukiyama) curve.  Analysis of the results obtained from applying the subroutine-based model to the 427 die revealed that the cooling channel user-subroutine was able to calculate local temperature dependent heat transfer and produce a continuous relationship between HTC and surface temperature for three regions of the boiling curve: 1) forced convection; 2) nucleate boiling; and 3) transition boiling. In three of the cooling channels with water-cooling, boiling occurred for a short period of time after water was introduced into the channel resulting in high heat transfer coefficient. The surface temperature was then observed to drop quickly transitioning heat transfer into the forced convection region, which remained the dominant mode of heat transfer for the remaining duration of water flow-based cooling.   Temperature predictions from the base-case model with constant HTC and the thermal model with user-subroutine were compared to the measured temperatures obtained from the 427 die. Both models were able to qualitatively reproduce the trends in the measured data, reflecting the  112  various operational stages of the casting process such as filling, cooling and solidification, and, die opening. In majority of locations within the top die and bottom die, the predicted temperatures from the model with subroutine are marginally lower than the predicted temperature from the baseline model with constant HTC due to higher heat transfer coefficients calculated by subroutine for TDDC-CC, BD-CC1 and BD-CC2. In side die locations; the predicted temperatures from both models were almost identical. Both models suffer from errors in the range of 3-20%, suggesting other issues limiting the predictive capabilities of the model or alternatively limitations in the ability of the thermocouple used to accurately measure temperatures in the die. In general, measurement errors can be divided into two categorizes systematic errors and random errors. An example of systemic errors could be the insulation used at the tip of the thermocouples. An example of random error is the cycle to cycle variation of temperature in order to reach steady state operation. The steady state condition was defined as a maximum 5 ℃ difference between the start and the end of a cycle temperature for all locations within the die.  One notable observation is that the subroutine-based model was able to achieve a similar accuracy to the trial-and-error fit model, after only one application. With some additional validation, the user-subroutine with modular programming structure, will serve as a tool for future casting modeling, greatly improving model’s utility as die design tools and process control optimization tools. 7.1 Recommendations for future work In order to correctly describe the transport processes involved in aluminum alloy wheel casting process, coupled modeling of heat transfer, fluid flow, phase and deformation is required. However the model adopted for the present study is thermal only, meaning the effect of various  113  phenomena such as cavity filling and die/wheel behavior are approximated. A major shortcoming in the thermal model is correctly implementing the thermal boundary conditions, more specifically the interfacial heat transfer at the wheel/die interface. The formation and evolution of a gap and/or pressure during solidification of the wheel will significantly alter the wheel/die interfacial heat transfer coefficient, which in turn will affect the wheel cooling, and solidification. A coupled thermo-mechanical model with the implemented cooling channel subroutine, which predicts the wheel deformation and evolution of air gap and pressure would offer a more accurate and realistic model of the casting process. Finally, in terms of experiential measurements, the inlet and outlet temperature and pressure of air and water going through each cooling channel should be accurately measured. Such information can be used in better formulating the subroutine and better predicting the fluid’s bulk temperature for HTC calculations. Ideally, cooling channel sub-surface thermocouples, capturing surface temperature would provide a better measure for the physical phenomenon occurring at the water/cooling channel interface during the casting process.          114   References 1. United Nations Environment Programme. Urban air pollution. http://www.unep.org/urban_environment/issues/urban_air.asp. Updated 2005. 18 May 2014. 2. Helms H, Lambrecht U. The potential contribution of lightweighting to reduce transport energy consumption. The International Journal of Life Cycle Assessment. 2006.  3. Morita A. Aluminum alloys for automobile applications. . 1998:25-32.  4. Hrovat D. Influence of unsprung weight on vehicle ride quality. J Sound Vibrat. 1988;124(3):497-516.  5. Caglioti G. The technical and economic advantages of lightweight aluminium alloy wheels. 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McAdams W, Kennel W, Minden C, Carl R, Picornell P, Dew J. Heat transfer at high rates to water with surface boiling. Industrial & Engineering Chemistry. 1949;41(9):1945-1953.  25. Chen JC. Correlation for boiling heat transfer to saturated fluids in convective flow. Industrial & Engineering Chemistry Process Design and Development. 1966;5(3):322-329.  26. Warrier GR, Dhir VK. Heat transfer and wall heat flux partitioning during subcooled flow nucleate boiling-A review. TRANSACTIONS-AMERICAN SOCIETY OF MECHANICAL ENGINEERS JOURNAL OF HEAT TRANSFER. 2006;128(12):1243.  27. Gungor K, Winterton R. A general correlation for flow boiling in tubes and annuli. Int J Heat Mass Transfer. 1986;29(3):351-358.  28. Steiner H, Kobor A, Gebhard L. A wall heat transfer model for subcooled boiling flow. Int J Heat Mass Transfer. 2005;48(19):4161-4173.  29. Groeneveld D, Leung L, Kirillov P, et al. The 1995 look-up table for critical heat flux in tubes. Nucl Eng Des. 1996;163(1):1-23.  30. Groeneveld D, Shan J, Vasić A, et al. The 2006 CHF look-up table. Nucl Eng Des. 2007;237(15):1909-1922.  31. Carbajo JJ. A study on the rewetting temperature. Nucl Eng Des. 1985;84(1):21-52.  32. Yu, W., France, D. M., Wambsganss, M. W., & Hull, J. R. Two-phase pressure drop, boiling heat transfer, and critical heat flux to water in a small-diameter horizontal tube. International Journal of Multiphase Flow. 2002;28(6):927-941.  33. Barnea Y, Elias E, Shai I. Flow and heat transfer regimes during quenching of hot surfaces. Int J Heat Mass Transfer. 1994;37(10):1441-1453.   117  34. Bromley LA, LeRoy NR, Robbers JA. Heat transfer in forced convection film boiling. Industrial & Engineering Chemistry. 1953;45(12):2639-2646.  35. Langlais, J., Bourgeois, T., Caron, Y., Beland, G., & Bernard, D. Measuring the heat extraction capacity of DC casting cooling water. Light Metals. 1995:979-986.  36. Larouche A, Langlais J, Bourgeois T, Gendron A. An integrated approach to measuring dc casting water quenching ability. Light Metals. 1999;1101:235-245.  37. Weckman D, Niessen P. A numerical simulation of the DC continuous casting process including nucleate boiling heat transfer. Metallurgical Transactions B. 1982;13(4):593-602.  38. Wells M, Li D, Cockcroft S. Influence of surface morphology, water flow rate, and sample thermal history on the boiling-water heat transfer during direct-chill casting of commercial aluminum alloys. Metallurgical and Materials Transactions B. 2001;32(5):929-939.  39. Brimacombe JK, Samarasekera I, Lait J. Continuous casting: Heat flow, solidification and crack formation. In: Vol 2. Iron & Steel Society; 1984:109-123.  40. Twohig AA. Flood-cooling of mechanical components. .  41. Baburajan P, Bisht G, Gupta S, Prabhu S. Measurement of subcooled boiling pressure drop and local heat transfer coefficient in horizontal tube under LPLF conditions. Nucl Eng Des. 2013;255:169-179.  42. Cheng S, Ng W, Heng K. Measurements of boiling curves of subcooled water under forced convective conditions. Int J Heat Mass Transfer. 1978;21(11):1385-1392.  43. eng, X. F., B. X. Wang, and G. P. Peterson. Film and transition boiling characteristics of subcooled liquid flowing through a horizontal flat duct. International journal of heat and mass transfer. 1991;35(11):3077-3083.  44. Sengupta J, homas BG, Wells MA. The use of water cooling during the continuous casting of steel and aluminum alloys. Metallurgical and Materials Transactions. 2005;A 36(1):187-204.   118  45. Kandlikar SG. Critical heat flux in subcooled flow boiling-an assessment of current understanding and future directions for research. Multiphase Science and Technology. 2001;13(3&4).  46. Bounds S, Davey K, Hinduja S. An experimental and numerical investigation into the thermal behavior of the pressure die casting process. Journal of manufacturing science and engineering. 2000;122(1):90-99.  47. Shoumei X, Lau F, Lee W. An efficient thermal analysis system for the die-casting process. J Mater Process Technol. 2002;128(1):19-24.  48. Clark L, Rosindale I, Davey K, Hinduja S, Dooling P. Predicting heat extraction due to boiling in the cooling channels during the pressure die casting process. Proc Inst Mech Eng Part C. 2000;214(3):465-482.  49. Mitsutake Y, Monde M, Kawabe R. Transient heat transfer during quenching of a vertical hot surface with bottom flooding. . 2003:257-266.  50. SMC European Marekring Centre. Digital flow switches. http://www.smc.eu/portal/NEW_EBP/16)Detection_Switch/16.3)Elec_Flow_Switch/a)PF2A/PF2A_EU.pdf. 10 May 2014. 51. Volume AH. 1: Properties and selection: Irons, steels, and high-performance alloys. ASM International. 1990:430.  52. Volume AH. 9, metallography and microstructures. ASM International, Materials Park, OH. 2004:644.  53. Mills KC. Recommended values of thermophysical properties for selected commercial alloys. In: Woodhead Publishing; 2002:119-126.  54. Shackelford JF, Alexander W. CRC materials science and engineering handbook. CRC press; 2000.  55. Thevoz P, Desbiolles J, Rappaz M. Modeling of equiaxed microstructure formation in casting. Metallurgical Transactions A. 1989;20(2):311-322.   119  56. Thompson S, Cockcroft S, Wells M. Advanced light metals casting development: Solidification of aluminium alloy A356. Materials science and technology. 2004;20(2):194-200.  57. Holman JP. Heat transfer. In: 10th ed. McGraw-Hill; 2010:327-335.  58. Crowe CT. Multiphase flow handbook. In: CRC Press; 2005:3-1-3-37.  59. Crabtree A, Siman-Tov M. Thermophysical properties of saturated light and heavy water for advanced neutron source applications. . 1993.  60. Sengupta J, Thomas B, Wells M. Understanding the role water-cooling plays during continuous casting of steel and aluminum alloys. Materials Science & Technology. 2004:179-193.  61. Li D. Boiling water heat transfer during quenching of steel plates and tubes. 2003.  62. Simulia D. Analysis convergence controls . In: ABAQUS 6.11 analysis user's manual. ; 2011:7.2.  63. Antoine C. Tensions des vapeurs; nouvelle relation entre les tensions et les températures. Comptes Rendus des Séances de l’Académie des Sciences. 1888;107:681-684.  64. Syeilendra Pramuditya. Water thermodynamics properties. http://syeilendrapramuditya.wordpress.com/2011/08/20/water-thermodynamic-properties/. Updated 2011.  18 May 2014. 65. Dixon J. The shock absorber handbook. appendix A. properties of air. In: John Wiley & Sons; 2007:365-378.        120  Appendices Appendix A Compressible versus incompressible flow: Air flow through the cooling channel was considered incompressible since the density changes are less than 30 percent of the velocity of sound in that gas1. In other words, if the Mach number of flow is less than 0.3, incompressible flow can be assumed. The Mach number is defined as     𝑀𝑎 ≡ 𝑉𝑎   2.11.   where 𝑉 and 𝑎 are the gas velocity and speed of sound respectively. The velocity of sound in air at room temperature is 346   𝑚 𝑠 .  For example, during purging with the flow rate of  𝑄 =600  ( ?™? ) in a circular cooling channel diameter 𝐷 = 0.02(𝑚):    𝑉 =𝑄𝐴 = 𝑄2𝜋(𝐷2)? =600  𝐿𝑚𝑖𝑛 × 10.00031𝑚?× 1000𝑐𝑚?1𝐿 × 1𝑚?10?𝑐𝑚?× 1𝑚𝑖𝑛60𝑠= 32.25  (𝑚 𝑠)  2.12.      𝑀𝑎 ≡ 𝑉𝑎 = 32.25346 = 0.09   2.13.        121  Appendix B Pressure Estimation Method  In order to calculate the vapour pressure in the Zuber correlation for nucleate boiling, ∆𝑃™? =𝑃™?? − 𝑃™?  the difference in vapour pressure at the wall and at the saturation pressure need to be calculated. To calculate the vapour pressure based on temperature, the Antoine equation, which is derived from the Clausius-Clapeyron relation, is used63.     𝐿𝑜𝑔™ 𝑃 = 𝐴 − 𝐵𝐶 + 𝑇   2.14.   where for water A=16.3872, B=3885.70, C=230.170 for temperature range of 0-200.            122  Appendix C Properties of Air  Various correlations describing the temperature-dependent properties of air were extracted from the literature and reviewed in the process of formulating the subroutine. The correlations listed below were the ones that fitted the best to the tabulated data and were chosen due to their general ease of use. It was assumed that the air pressure in the cooling channel remains constant during the LPDC process. Density ™??  Air is treated as an ideal gas; at absolute pressure  𝑃  (𝑁 𝑚? = 𝑃𝑎 𝑝𝑎𝑠𝑐𝑎𝑙 ) density is calculated in the following form with pacific gas constant 𝑅 = 287.05 ?™ ∙?  57.    𝜌 = 𝑃𝑅 ∙ 𝑇     Specific heat ?™ ∙?  Specific heat follows the quadratic relationship with temperature in the following form 66.    𝐶? = 1030.5− 0.19975𝑇 + 3.9734×10??𝑇?     Dynamic viscosity ™ ?   𝑜𝑟   ?.???   𝑜𝑟   ™?.?  Sutherland’s equation is used to calculate viscosity as a function of temperature 67.    𝜇 = 1.458×10??𝑇?.?𝑇 + 110.4       123  Thermal conductivity ??∙?  Temperature dependant thermal conductivity can be calculated using following expression68.    𝑘 = 0.02624 𝑇300 ?. ™ ⌢         124  Appendix D Properties of water Density ™??  Density is approximated using the following for pressure of 1 bar and temperature range of 5-95 64.    𝜌 = 1001.1− 0.0867𝑇 − 0.0035𝑇?      Specific heat ?™ ∙?   Specific heat is approximated with 0.2% accuracy for temperature range of 2-200℃ using the following correlation 65.    𝐶? = 4209− 1.31𝑇 + 0.014𝑇?     Thermal conductivity ??∙?  Thermal conductivity is calculated with 0.3% accuracy from 1-200 65.    𝑘 = 0.5706+ 1.756×10??×𝑇 − 6.46×10??𝑇?     Properties of saturated water can be estimated using steam tables.  Crabtree developed correlations describing the thermo physical properties of light and heavy water for temperature of 20-300  ℃ and corresponding saturation pressure 0.0025-8.5 MPa 59. Deviation between Crabtree’s correlations and steam table does not exceed 1.0% except in the case of vapour density (1.76%). Light water correlations where used in the subroutine due to their ease of use  125  and their relative accuracy in predicting the material properties of water when compared to the tabulated data in literature.   𝑘? 𝑊𝑚 ∙ 𝐾 = 𝐴 + 𝐵𝑇 + 𝐶𝑇? + 𝐷𝑇? A=0.567	  B=1.877×10??	  C=−8.179×10??	  D=5.662×10??      𝐶™ 𝑘𝐽𝑘𝑔 ∙ 𝐾   = 𝐴 + 𝐶𝑇 1+ 𝐵𝑇 + 𝐷𝑇? ?.? A=17.489	  B=  −1.675×10??	  C=  −0.031	  D=  −2.874×10?     𝜌? 𝑘𝑔𝑚? = (𝐴 + 𝐵𝑇? + 𝐶𝑇??)  𝑇? = 1.8𝑇 + 32  𝐴 = 1004.789  𝐵 = −0.046  𝐶 = −7.973×10??     126    𝜌? 𝑘𝑔𝑚?= 𝐴 + 𝐶𝑇 + 𝐸𝑇? + 𝐺𝑇? 1+ 𝐵𝑇 + 𝐷𝑇? + 𝐹𝑇? + 𝐻𝑇?   𝐴 = −4.375×10??  𝐵 = −6.947×10??  𝐶 = 7.662×10?? 𝐷 = 2.418×10?? 𝐸 = −5.963×10?? 𝐹 = −4.227×10?? 𝐺 = 2.867×10?? 𝐻 = 2.594×10? ℡       𝜎? 𝑁𝑚 = 𝐴𝑋?(1+ 𝐶𝑋)  𝑋 = (373.99− 𝑇) 647.15  𝐴 = 235.8×10??  𝐵 = 1.256  𝐷 = −0.625      𝜇?(𝑁. 𝑠𝑚? ) = 𝑒𝑥𝑝 (𝐴 + 𝐶𝑇) (1+ 𝐵𝑇 + 𝐷𝑇?)   𝐴 = −6.325  𝐵 = 8.705×10??     127  𝐶 = −0.088  𝐷 = −9.657×10??    ℎ™ 𝑘𝐽𝑘𝑔   = 𝐴 𝐴 + 𝐵𝑇 + 𝐶𝑇? + 𝐷𝑇? ?.?  𝐴 = 6254828.56  𝐵 = −11742.33  𝐶 = 6.336  𝐷 = −0.049           

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