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Parameter Optimization of a Low Temperature Difference Gamma-Type Stirling Engine to Maximize Shaft Power by Calynn James Adam S

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Parameter Optimization of a Low Temperature Difference Gamma-Type Stirling Engine to Maximize Shaft Power by Calynn James Adam S Parameter Optimization of a Low Temperature Difference Gamma-Type Stirling Engine to Maximize Shaft Power by Calynn James Adam Stumpf A thesis submitted on partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical Engineering University of Alberta © Calynn James Adam Stumpf, 2019 Abstract An investigation was performed with three main objectives. Determine the configuration and operating parameter of a low temperature difference Stirling engine (LTDSE) that would result in the maximum shaft power. Calculate the mean West number for LTDSEs and compare it to the mean West number for high temperature difference Stirling engines (HTDSEs). Validate the methods used to estimate the compression ratio of a Stirling engine. Three different LTDSEs were developed: The Mark 1, Mark 2, used for initial development and the EP-1. The EP-1 used a bellows for its power piston and was the main engine investigated. A test rig was used that allowed for measurement of temperature, pressure, torque, engine speed, and crank shaft position. The LTDSEs were operated with a thermal source and sink temperature of 95 °C and 2 °C, respectfully, and were heated and cooled with two water flow loops. They used air as a working fluid and a constant buffer pressure of the atmosphere, which was equal to 92.5 kPa. The compression ratio, phase angle, position of the thermal source heat exchanger, and power piston connection to the workspace was varied on the EP-1 to determine its maximum shaft power. A compression ratio of 1.206 ± 0.017, phase angle of 90 ± 1°, and the thermal source heat exchanger residing on top with the power piston connected to the expansions space resulted in the configuration that produced the maximum local shaft power. This was a shaft power of 6.58 ± 0.09 watts that occurred at an operating speed of 67.7 ± 0.3 rpm. A global maximum shaft power was not found due to limitations of the power piston. The West number for the configuration that produced the maximum local shaft power when using a power piston swept volume of 1835 ± 50ml was 0.238 ± 0.001. ii The mean West number was calculated from 12 different LTDSEs that used air as the working fluid, the atmosphere as the buffer pressure, and a temperature difference less than 150 °C, and equaled 0.21. This was lower, but close to the mean West number for HTDSEs of 0.25. This suggests that the West number can be used for comparison of Stirling engine that operate at all temperature differences. Three methods that estimated the compression ratio for Stirling engines were investigated. The compression ratios produced by these methods were compared to the compression ratio that produced the local maximum shaft power for the EP-1 of 1.206 ± 0.017. The three methods used were Kolin’s compression ratio, Egas’ ideal compression ratio, and Senft’s optimum swept volume ratio. Using Kolin’s method, a compression ratio of 1.085 was calculated by. If the experimental average temperature of the working fluid in the compression and expansion space of the EP-1 was used for Egas’ method, a compression ratio of 1.156 was produced. If the thermal source and sink temperature was used for Egas’ method, a compression ratio of 1.338 was calculated. Senft’s method predicted the compression ratio closely when a mechanism effectiveness of 0.75 was used. Based on the compression ratios used by the 12 experimental LTDSEs, a model was proposed to estimate the compression ratio that could produce the maximum shaft power. This model is applicable to LTDSEs that using air as a working fluid and a buffer pressure of atmospheric. The shaft power compression ratio was calculated from the temperature ratio of the thermal source and sink temperature. To further validate the model, more compression ratio optimization tests should be performed for various temperature ratios and LTDSEs. iii Preface This thesis is an original work by Calynn Stumpf. Aspects of the research have been published in the following conference publications: Conference Papers: Speer, C.P., Michaud, J.P., Miller, D.A., Stumpf, C.J.A. and Nobes, D.S. (2017) Empirical Heat Transfer Correlations of Finned-Tube Heat Exchangers in Pulsatile Flow. World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 11(6), 1150-1155. Stumpf, C.J.A., Hunt, A.J. and Nobes, D.S. (2018) Effect of Scaling Up Low Temperature Differential Stirling Engines, 18th ISEC International Stirling Engine Conference, Tainan, Taiwan, Sept 19-21, 2018 Stumpf, C.J.A, Middleton, S. and Nobes, D.S. (2017) "Heat Transfer in Oscillating Fluid Flow Through Parallel Flat Plate Channel Heat Exchangers", Okanagan Fluid Dynamics Meeting, Kelowna, British Columbia, Canada, Aug 22-23, 2017 Speer, C.P., Michaud, J.P., Miller, D.A., Stumpf, C.J.A. and Nobes, D.S. (2017) ‘Empirical heat transfer correlations of finned-tube heat exchangers in oscillating flow for low temperature Stirling engines’, ICFMHTT 2017: 19th International Conference on Fluid Mechanics, Heat Transfer and Thermodynamics, Venice, Italy June, 21-22, 2017 Speer, C.P., Michaud, J.P., Miller, D.A., Stumpf, C.J.A. and Nobes, D.S. (2017) ‘Modification of an ST05G-CNC Stirling Engine to Use a Low Temperature Heat Source’, AIAA-2017-4793, 14th International Energy Conversion Engineering Conference, AIAA Propulsion and Energy Forum 2017, Atlanta, George, USA, July, 10-12. 2017 iv Acknowledgements The author gratefully acknowledges the support of his wife, • Ashli MacDonald Stumpf Supervisor, • Dr. David Nobes Lab mates (Team Stirling), • Alex Hunt • Jackson Kutzner • Jason Michaud • Steven Middleton • David Miller • Michael Nicol-Seto • Connor Speer Fellow academics, research groups, and co-op students. • Dr. Jonathan Banks • Nobes Research Group (ODL, RGL, DTECL) • Co-op Students And who all helped to make this project a success. Financial support for this research was provided by the following funding bodies: • Natural Sciences and Engineering Research Council (NSERC) of Canada • Canadian Foundation of Innovation (CFI) • Alberta Innovates Energy and Environment Solutions • Terrapin Geothermics • Future Energy Systems (FES) v Table of Contents Abstract ........................................................................................................................................... ii Preface............................................................................................................................................ iv Acknowledgements ......................................................................................................................... v Table of Contents ........................................................................................................................... vi List of Tables ................................................................................................................................ xii List of Figures .............................................................................................................................. xvi List of Symbols ........................................................................................................................... xxv Chapter 1 Introduction and Literature Review ............................................................................... 1 1.1 Motivation ........................................................................................................................ 2 1.2 The Ideal Stirling Cycle ................................................................................................... 4 1.2.1 Isochoric Heat Addition ............................................................................................ 5 1.2.2 Isothermal Expansion................................................................................................ 5 1.2.3 Isochoric Heat Rejection ........................................................................................... 5 1.2.4 Isothermal Compression ........................................................................................... 5 1.2.5 Indicator Diagram and Indicated Work .................................................................... 6 1.3 Application of the Ideal Stirling Cycle ............................................................................ 8 1.3.1 Displacer Piston and Cylinder .................................................................................. 8 1.3.2 Heat Exchangers ....................................................................................................... 9 1.3.3 Regenerator ............................................................................................................. 11 1.3.4 Power Piston ........................................................................................................... 12 1.4 Stirling Engine Types ..................................................................................................... 15 1.5 The Practical Stirling Cycle ........................................................................................... 16 1.5.1 Phase Angle ............................................................................................................ 16 vi 1.5.2 The Practical Indicator Diagram ............................................................................. 17 1.6 Stirling Engine Operating Parameters ............................................................................ 19 1.6.1 Compression
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