Citation: Sowale, Ayodeji (2015) Modelling and Optimisation of a Free Piston Stirling Engine for Micro-CHP Applications. Doctoral thesis, Northumbria University. This version was downloaded from Northumbria Research Link: http://nrl.northumbria.ac.uk/29625/ Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University’s research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html Modelling and Optimisation of a Free Piston Stirling Engine for Micro-CHP Applications Ayodeji Olubayo Sowale A thesis submitted in partial fulfilment of the requirements of the University of Northumbria at Newcastle for the award of Doctor of Philosophy Research undertaken in the Mechanical and Construction Engineering Department of the Faculty of Engineering and Environment November 2015 Abstract This study is carried out to investigate the solar thermal energy conversion for generating power. This form of renewable energy can be utilised for power production deploying the free piston Stirling engines, which convert thermal energy into mechanical energy. Such systems have an advantage of production of work using low and high temperature differences in the cycle which could be created by different sources of heat including solar energy, combustion of a fuel, geothermal energy, nuclear energy or waste heat. The thermodynamic analysis of the free piston Stirling engine have been carried out and implemented in past studies with different methods of approach with various difficulties exhibited. In the present study isothermal, ideal adiabatic and Quasi steady flow models have been produced and used for investigation of the engine performance. The approach in this study deals with simultaneous mathematical modelling of thermodynamic processes and pistons dynamics. The steady state operation of the engine depends on the values of damping coefficients, spring stiffness and pressure drop within the heat exchangers during engine’s operation, which is also a result of the energy transfer in each engine’s component. In order to design effective high performance engines it is necessary to develop such advanced mathematical models to perform the analysis of the engine’s operation and to predict its performance satisfactorily. The aim of this study was to develop several levels of mathematical models of free piston Stirling engines and to evaluate their accuracy using experimental and theoretical results available in published sources. The validation of the developed free piston Stirling engine models demonstrates a good agreement between the numerical results and experimental data. The validated model then was used for optimisation of the engine, deploying Genetic Algorithm approach with the purpose to determine its optimal design parameters. The ii developed optimisation procedure provides a noticeable improvement in the engine’s performance in terms of power output and efficiency. iii Table of Contents Chapter 1 Introduction ..................................................................................................................... 1 1.1 The ideal Stirling cycle ............................................................................................................ 3 1.2 Objectives ................................................................................................................................. 6 1.3 Methodology of research .......................................................................................................... 6 1.4 Thesis structure ......................................................................................................................... 8 1.5 Original contribution to knowledge ........................................................................................ 10 Chapter 2 Literature Review ......................................................................................................... 11 2.1 Introduction ............................................................................................................................. 11 2.2 Stirling engine modelling ........................................................................................................ 11 2.2.1 Zero order modelling ....................................................................................................... 11 2.2.2 First order modelling ........................................................................................................ 12 2.2.3 Second order modelling ................................................................................................... 15 2.2.4 Third order modelling ...................................................................................................... 21 2.2.5 Optimisation of Stirling engines ...................................................................................... 22 2.3 Free piston Stirling engine modelling ..................................................................................... 24 2.3.1 First order model .............................................................................................................. 26 2.3.2 Second order model ......................................................................................................... 26 2.3.3 Third order model ............................................................................................................ 28 2.4 Optimization of free piston Stirling engines ........................................................................... 29 2.5 Optimization using the Genetic Algorithm procedure ............................................................ 31 2.6 Designs of free piston Stirling engine prototypes ................................................................... 32 2.7 Conclusions ............................................................................................................................. 33 Chapter 3 Theory and Applications of Stirling engines .............................................................. 35 3.1.1 Configurations of Stirling engines ................................................................................... 35 3.1.2 Free piston Stirling engine operational principles ........................................................... 39 3.1.3 Types of free piston Stirling engines. .............................................................................. 40 3.1.4 Advantages of Stirling engines ........................................................................................ 42 3.1.5 Disadvantages of Stirling engines .................................................................................... 42 3.1.6 The specific characteristics of Stirling engines ................................................................ 43 3.1.7 Critical parameters of Stirling engines ............................................................................ 43 3.1.8 Stirling engine heat exchangers ....................................................................................... 44 iv 3.1.11 Factors which determine performance of Stirling engines............................................. 47 3.1.12 Losses in Stirling engines .............................................................................................. 52 3.1.14 Calculation scheme of the free piston Stirling engine................................................... 57 3.1.15 Applications of Stirling engines ..................................................................................... 60 3.2 Conclusions ............................................................................................................................. 67 Chapter 4 Isothermal Mathematical Modelling of the Free Piston Stirling Engine ................. 68 4.1 Introduction ............................................................................................................................. 68 4.2 Isothermal model .................................................................................................................... 68 4.2.1 General analysis ............................................................................................................... 70 4.2.2 Methodology for preliminary design of FPSE ................................................................. 73 4.2.3 Procedure for numerical simulation ................................................................................. 82 4.2.4 Numerical Simulation results ........................................................................................... 84 4.3 Conclusions ............................................................................................................................. 86 Chapter 5 Mathematical Modelling of the Free Piston Stirling Engine using the Adiabatic Model ...............................................................................................................................................