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Heat Transfer During the Piston-Cylinder Expansion of a Gas

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Heat Transfer During the Piston-Cylinder Expansion of a Gas AN ABSTRACT OF THE THESIS OF Matthew Jose Rodrigues for the degree of Master of Science in Mechanical Engineering presented on June 5, 2014. Title: Heat Transfer During the Piston-Cylinder Expansion of a Gas Abstract approved: ______________________________________________________ James A. Liburdy The expansion of a gas within a piston-cylinder arrangement is studied in order to obtain a better understanding of the heat transfer which occurs during this process. While the situation of heat transfer during the expansion of a gas has received considerable attention, the process is still not very well understood. In particular, the time dependence of heat transfer has not been well studied, with many researchers instead focused on average heat transfer rates. Additionally, many of the proposed models are not in agreement with each other and are usually dependent on experimentally determined coefficients which have been found to vary widely between test geometries and operating conditions. Therefore, the expansion process is analyzed in order to determine a model for the time dependence of heat transfer during the expansion. A model is developed for the transient heat transfer by assuming that the expansion behaves in a polytropic manner. This leads to a heat transfer model written in terms of an unknown polytropic exponent, n. By examining the physical significance of this parameter, it is proposed that the polytropic exponent can be related to a ratio of the time scales associated with the expansion process, such as a characteristic Peclet number. Experiments are conducted to test the proposed heat transfer model and to establish a relationship for the polytropic exponent. The tests are performed using an apparatus that consists of a single piston-cylinder, which allows for pressure-volume data to be collected during the expansion of a hot gas. These experiments justify the polytropic expansion assumption, and from these results models are developed for the polytropic exponent. Heat transfer data are also collected from these experiments through applying an energy balance on the gas during expansion. These heat transfer data are used to compare the Nusselt number predicted by the proposed model with the experimentally determined Nusselt number. It is found that the proposed model agrees very well with the experimental data, and accurately captures the time dependence of the heat transfer characteristics. The proposed model also accurately handles variations in the heat transfer characteristics due to the different test conditions studied. By capturing the transient effects of heat transfer during the expansion process, the proposed model should be a more accurate tool in determining heat loss during the expansion of a gas than previously developed models. ©Copyright by Matthew Jose Rodrigues June 5, 2014 All Rights Reserved Heat Transfer During the Piston-Cylinder Expansion of a Gas by Matthew Jose Rodrigues A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Presented June 5, 2014 Commencement June 2014 Master of Science thesis of Matthew Jose Rodrigues presented on June 5, 2014 APPROVED: Major Professor, representing Mechanical Engineering Head of the School of Mechanical, Industrial, and Manufacturing Engineering Dean of the Graduate School I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request. Matthew Jose Rodrigues, Author ACKNOWLEDGEMENTS There have been many people involved in the preparation of this thesis, both directly and indirectly, to whom I am extremely grateful. Dr. Liburdy, thank you for your guidance; allowing me to explore, get confused, and ultimately learn, while keeping me on track and teaching me both in and out of the classroom. Without your investment of patience, knowledge, time, and energy none of this research would have been completed. Bill Snell, I am extremely grateful for the time and energy you have invested into me, both personally and professionally, and for providing the opportunity for me to combine the worlds of academia and industry. Sean Kirkpatrick, you have been a continual resource and source of advice in the preparation of this thesis, and I am thankful to have you as a lab-mate and friend. Dr. Evans, Dr. Kanury, and Dr. Skyllingstad, thank you for being willing to serve as members of my committee, and for your valuable input to this work. I am also thankful to Long Haul Power, LLC, for their financial support and for use of the test equipment in this research. Finally, I would like to thank my parents, Northon and Doris, for giving me such a strong educational foundation; my siblings, Nathaniel and Jennifer, for their constant encouragement; and my wife Natalie, who is my greatest encourager, supporter, adviser, and friend. TABLE OF CONTENTS Page 1 Introduction ................................................................................................................... 1 1.1 General Problem Statement ................................................................................... 2 1.2 Literature Review .................................................................................................. 5 1.2.1 Pseudo-Steady State Models ......................................................................... 7 1.2.2 Transient Models ........................................................................................ 12 1.3 Specific Problem Statement ................................................................................. 16 2 Analysis....................................................................................................................... 18 2.1 Model Development ............................................................................................ 18 2.2 Alternate Expressions .......................................................................................... 24 2.3 Model Discussion ................................................................................................ 26 2.4 Flow Considerations ............................................................................................ 30 2.5 Polytropic Exponent ............................................................................................ 32 3 Experimental Methodology ........................................................................................ 37 3.1 Experimental Setup.............................................................................................. 38 3.2 Data Reduction .................................................................................................... 41 3.3 Test Conditions .................................................................................................... 47 3.4 Uncertainty Analysis ........................................................................................... 50 TABLE OF CONTENTS (Continued) Page 4 Results & Discussion .................................................................................................. 56 4.1 Experimental Results ........................................................................................... 57 4.2 Expansion Characteristics.................................................................................... 63 4.3 Heat Transfer Characteristics .............................................................................. 72 4.4 Alternative Length Scales .................................................................................... 76 4.5 Model for the Polytropic Exponent ..................................................................... 82 4.5.1 Model Based on the Characteristic Peclet Number .................................... 83 4.5.2 Model Based on the Mean Piston Speed..................................................... 89 4.6 Heat Transfer Model Validation .......................................................................... 93 4.7 Model Comparison .............................................................................................. 99 5 Conclusions ............................................................................................................... 107 5.1 Transient Predictive Capability ......................................................................... 108 5.2 Universality ....................................................................................................... 110 5.3 Recommendations ............................................................................................. 112 BIBLIOGRAPHY ........................................................................................................... 115 APPENDIX ..................................................................................................................... 118 LIST OF FIGURES Figure Page 1.1 Schematic of heat transfer during a piston-cylinder expansion process as currently studied . 2 2.1 Schematic showing control volume used for the analysis of the expansion process. 19 3.1 Schematic of experimental apparatus used to conduct tests. 39 4.1 Bomb data for Test Case D, used to determine combustion time. 58 4.2 Pressure and volume versus time for a combustion and expansion event, showing that combustion is complete by the time expansion begins. Data shown is from Test Case D . 59 4.3 Measured cylinder volume versus time during expansion for Test Case D. 60 4.4 Measured cylinder pressure versus time during expansion
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