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Riser Feeding Evaluation Method for Metal Castings Using Riser Feeding Evaluation Method for Metal Castings Using Numerical Analysis DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Nadiah Ahmad Graduate Program in Industrial and Systems Engineering The Ohio State University 2015 Dissertation Committee: Dr. Jerald Brevick, Advisor Dr. Theodore Allen Dr. Jose Castro i Copyright by Nadiah Ahmad 2015 ii Abstract One of the design aspects that continues to create a challenge for casting designers is the optimum design of casting feeders (risers). As liquid metal solidifies, the metal shrinks and forms cavities inside the casting. In order to avoid shrinkage cavities, risers are added to the casting shape to supply additional molten metal when shrinkage occurs during solidification. The shrinkage cavities in the casting are compensated by controlling the cooling rate to promote directional solidification. This control can be achieved by designing the casting such that the cooling begins at the sections that are farthest away from the risers and ends at the risers. Therefore, the risers will solidify last and feed the casting with the molten metal. As a result, the shrinkage cavities formed during solidification are in the risers which are later removed from the casting. Since casting designers have to usually go through iterative processes of validating the casting designs which are very costly due to expensive simulation processes or manual trials and errors on actual casting processes, this study investigates more efficient methods that will help casting designers utilize their casting experiences systematically to develop good initial casting designs. The objective is to reduce the casting design method iterations; therefore, reducing the cost involved in that design ii processes. The aim of this research aims at finding a method that can help casting designers design effective risers used in sand casting process of aluminum-silicon alloys by utilizing the analysis of solidification simulation. The analysis focuses on studying the significance of pressure distribution of the liquid metal at the early stage of casting solidification, when heat transfer and convective fluid flow are taken into account in the solidification simulation. The mathematical model of casting solidification was solved using the finite volume method (FVM). This study focuses to improve our understanding of the feeding behavior in aluminum-silicon alloys and the effective feeding by considering the pressure gradient distribution of the molten metal at casting dendrite coherency point. For this study, we will identify the relationship between feeding efficiency, shrinkage behavior and how the change in riser size affects the pressure gradient in the casting. This understanding will be used to help in the design of effective risers. iii Acknowledgments All praises and thanks to Allah, the Almighty for His blessings that have allowed me to succeed in achieving my goal of obtaining a doctoral degree. Special gratitude and profound appreciation to my advisor, Dr. Jerald Brevick for his invaluable insights, advices, encouragements, supports and understanding throughout my research work. I would also like to express my gratitude and great appreciation to my dissertation committee members, Dr. Theodore Allen and Dr. Jose Castro for their advices, reviews and recommendations in helping me progressing well toward completing my dissertation. I would like to sincerely thank the Government of Malaysia, through Universiti Teknikal Malaysia Melaka and The Ministry of Education for providing scholarship opportunity to fund my graduate studies. Finally, I am deeply grateful to my spouse, Radin Zaid Radin Umar and my family for their continuous supports and encouragements during my study. Special thanks as well for everyone who had helped me in any ways during my reseach conduct. iv Vita 2002 – 2003 ...................................................American Degree Foundation Program, Universiti Teknologi MARA, Malaysia 2003 – 2007 ...................................................B.S. Industrial Engineering, University of Wisconsin – Madison, WI 2007 – 2009 ...................................................Tutor, Universiti Teknikal Malaysia Melaka 2009 – 2010 ...................................................M.S. Industrial Systems Engineering, The Ohio State University 2011 to 2015 .................................................Graduate Teaching Associate, Department of Integrated Systems Engineering, The Ohio State University Fields of Study Major Field: Industrial and Systems Engineering. Manufacturing Systems and Processes. Casting Solidification Analysis and Optimization. v Table of Content Abstract ................................................................................................................................ii Acknowledgments............................................................................................................... iv Vita ....................................................................................................................................... v List of Tables ....................................................................................................................... ix List of Figures ....................................................................................................................... x Chapter 1: Introduction ...................................................................................................... 1 1.1 Metal Casting Overview ........................................................................................ 1 1.2 Research Problem ................................................................................................. 5 1.3 Research Objective and Outline ............................................................................ 8 Chapter 2: Literature Review ............................................................................................ 11 2.1 Riser Design Approaches ..................................................................................... 12 2.1.1 Geometric Reasoning Method .................................................................... 12 2.1.2 Numerical Modeling Techniques ................................................................ 17 2.2 Solidification Modeling ....................................................................................... 21 2.3 Feeding Mechanisms ........................................................................................... 24 vi 2.4 Summary ............................................................................................................. 27 Chapter 3: Numerical Modeling of Solidification ............................................................. 31 3.1 Solidification Model ............................................................................................ 32 3.1.1 Governing Equations ................................................................................... 33 3.1.1.1 Momentum Source and Sink .............................................................. 35 3.1.1.2 Energy Source Term ............................................................................ 37 3.2 Boundary Conditions ........................................................................................... 38 3.2.1 Temperature ............................................................................................... 38 3.2.2 Velocity ....................................................................................................... 39 3.3 Finite Volume Method ........................................................................................ 40 3.3.1 Solution Algorithm for Pressure and Velocity Calculation ......................... 42 3.3.1.1 Predictor ............................................................................................. 44 3.3.1.2 Corrector Step ..................................................................................... 44 3.3.2 Numerical Schemes..................................................................................... 46 3.3.3 Pressure Gradient Calculation. ................................................................... 46 Chapter 4: The Analysis of the Casting Solidification Behavior Using Convective Fluid Flow ................................................................................................................................... 49 4.1 Casting Designs and Input Parameters ............................................................... 52 4.2 Thermal Analysis and Experimental Results ....................................................... 55 vii 4.3 Flow Analysis of the Casting Models ................................................................... 59 4.4 Pressure Analysis ................................................................................................. 74 4.5 Evaluation of Feeding Efficiency Using Convective Fluid Flow Analysis ............. 79 4.6 Sensitivity Analysis of the Constant C Value in the Solidification Simulation. .... 88 4.6 Evaluation of Feeding Effectiveness on Long Freezing Range Alloy: Application to AlSi7Mg Casting .............................................................................................. 93 Chapter 5: Summary ....................................................................................................... 105 5.1 Contributions ...................................................................................................
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