Tesla Turbine Torque Modeling for Construction of a Dynamometer And
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TESLA TURBINE TORQUE MODELING FOR CONSTRUCTION OF A DYNAMOMETER AND TURBINE Tamir Ali Emran, B.S. Thesis Prepared for the Degree of MASTER OF SCIENCE UNIVERSITY OF NORTH TEXAS May 2011 APPROVED: Matthew J. Traum, Major Professor Kuruvilla John, Committee Member Mitty Plummer, Committee Member Costas Tsatsoulis, Dean of College of Engineering James D. Meernik, Acting Dean of the Toulouse Graduate School Emran, Tamir Ali. Tesla turbine torque modeling for construction of a dynamometer and turbine. Master of Arts (Mechanical Engineering), May 2011, 80 pp., 10 tables, 23 illustrations, bibliography, 53 titles. While conventional turbines have been extensively researched and tested, Tesla and boundary layer type turbines have not. In order to construct a dynamometer, thermodynamic flow apparatus and future turbines, we modeled the Tesla turbine using theoretical calculations and preliminary experiments. Thus a series of experiments were run to determine stall torque and maximum run speed for a known pressure range. This data was then applied to modeling formulas to estimate stall torque over an extended range of variables. The data were then used to design an appropriate dynamometer and airflow experiment. The model data also served to estimate various specifications and power output of the future turbine. An Obi Laser SSTG‐001 Tesla turbine was used in the experiments described. Experimental stall torque measurements were conducted in two stages. Shaft speed measurements were taken with an optical laser tachometer and Tesla turbine stall torque was measured using a spring force gauge. Two methods were chosen to model Tesla turbine stall torque: 1) flow over flat plate and 2) free vortex with a sink. A functional dynamometer and thermodynamic apparatus were constructed once the model was confirmed to be within the experimental uncertainty. Results of the experiments show that the experimental turbine at 65 PSI has a speed of approximately 27,000 RPM and a measured stall torque of 0.1279 N‐m. 65 PSI is an important data point because that data set is the cut‐off from laminar to turbulent flow. Thus at 65 PSI, a rejection of the null hypothesis for research question one with respect to the flow over flat plate method can be seen from the data, while the vortex model results in a failure to reject the null hypothesis. In conclusion, the experimental turbine was seen to have a laminar and a turbulent flow regime at different air pressures, rather than the assumed laminar flow regime. As a result of this model work, a new Tesla turbine of different dimensions was designed to adjust for flaws in the experimental turbine. The theoretical stall torque models were then applied to the new Tesla turbine design. Results of the models show that the vortex model sets the upper bound for theoretical stall torque for the new and the flat plate flow model sets the lower bound. Copyright 2011 by Tamir Emran ii ACKNOWLEDGMENTS I would like to thank my thesis advisor, Dr. Matthew J. Traum, who I am greatly indebted to for spending many hours revising, providing valuable advice and encouraging me throughout my thesis research. I should not forget to thank Dr. Traum for providing me with funding through my course of study, without which would have made this research a very difficult undertaking. I would also like to thank Mr. Doug Burns, our technician in the Mechanical and Energy Engineering Department, and Mr. Bobby Grimes, laboratory manager of the Engineering Technology Department, for providing me with technical support and hardware assistance throughout my thesis research. I would like to acknowledge that this research was funded in part by the National Science Foundation Research Experiences for Undergraduates (REU) program (NSF Grant Number EEC‐100485) and by the Center for the Study of Interdisciplinarity at the University Of North Texas http://www.csid.unt.edu/. Additional UNT support was provided to Dr. Traum through the Junior Faculty Summer Research Fellowship, the Research Initiation Grant Program and by the Department of Mechanical and Energy Engineering. I gratefully acknowledge Solar Logic, Inc. of Muenster, TX, which provided a Tesla‐turbine‐focused summer co‐op experience that, in part, motivated this research. I also acknowledge and thank Mr. William Tahil for providing a useful insight into the modeling and operation of a Tesla Turbine, and to Paul Stoffregen, whose Teensy Microcontroller greatly simplified and miniaturized the Hall Effect Tachometer that I constructed. iii Finally, I would like to thank my parents and my brothers who have been a continuous source of inspiration for me. iv TABLE OF CONTENTS ACKNOWLEDGMENTS ..................................................................................................................... iii LIST OF TABLES ................................................................................................................................ ix LIST OF ILLUSTRATIONS................................................................................................................... ix CHAPTER 1 BACKGROUND .............................................................................................................. 1 1.1 Introduction ...................................................................................................................... 1 1.2 Statement of Problem ...................................................................................................... 4 1.4 Research Question ........................................................................................................... 5 1.5 Literature Review ............................................................................................................. 6 1.6 Theory of Operation ......................................................................................................... 9 1.7 Assumptions ................................................................................................................... 12 1.8 Limitations ...................................................................................................................... 13 CHAPTER 2 EXPERIMENTAL METHOD ........................................................................................... 14 2.1 Test Apparatus and Measurement Techniques ............................................................. 14 2.1.1 Force and Speed Experiments ................................................................................ 14 2.1.2 Air Leakage Experiment .......................................................................................... 19 2.2 Stall Torque Analytical Calculation ................................................................................. 20 2.2.1 Flow over Flat Plate ................................................................................................. 20 2.2.2 Vortex Method ........................................................................................................ 24 v 2.2.3 Moment of Momentum Method for a Centrifugal Pump ...................................... 26 2.2.4 Frictional Torque, Accelerating Torque and Angular Deceleration ........................ 27 2.3 Construction of the Dynamometer ................................................................................ 28 2.4 Design of Protective Shield ............................................................................................ 33 2.5 Construction of Thermodynamic Flow Apparatus ......................................................... 34 2.6 Experiments with Dynamometer and Flow Apparatus .................................................. 37 CHAPTER 3 RESULTS AND DISCUSSION ........................................................................................ 39 3.1 Preliminary Experimental Results .................................................................................. 39 3.2 Air Leakage Experimental Results .................................................................................. 42 3.3 Flow Over Flat Plate Theoretical Model Results ............................................................ 42 3.4 Vortex Method Results................................................................................................... 44 3.5 Observations .................................................................................................................. 47 CHAPTER 4 CONCLUSIONS ............................................................................................................ 49 CHAPTER 5 FUTURE TURBINE DESIGN .......................................................................................... 50 APPENDIX A EXPERIMENTAL RESULTS .......................................................................................... 56 APPENDIX B EXPERIMENTAL APPARATAE..................................................................................... 61 B1 Preliminary Experimental Apparatus ......................................................................... 62 B2 Dynamometer Apparatus ........................................................................................... 62 APPENDIX C PRO‐E WILDFIRE DRAWINGS .................................................................................... 63 vi C1 Educational Turbine .................................................................................................... 64 C2 Electric Dynamometer ................................................................................................ 65 C3 Air Flow Apparatus ....................................................................................................