TURBINE-COMPOUND FREE-PISTON LINEAR ALTERNATOR ENGINE by Chang-ping Lee A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical Engineering) in the University of Michigan 2014 Doctoral Committee: Associate Professor Claus Borgnakke, Co-Chair Professor Dionissios N. Assanis, Co-Chair, Stony Brook University Professor Andre Boehman Professor Jin Sun Russell Durrett, General Motor Co. © Chang-ping Lee 2014 Table of Contents LIST OF TABLES vi LIST OF FIGURES viii ABSTRACT xii CHAPTER 1 1 Introduction 1 1.1 Free-Piston Engine 1 1.1.1 Pescara Free-Piston Compressor 3 1.1.2 Pescara Gas Turbine & SIGMA GS-34 4 1.1.3 Free-Piston Engine for Automotive Use 4 1.2 Free-Piston Linear Alternator (FPLA) 5 1.3 Motivation: Turbine-Compound Free Piston Linear Alternator (TCFPLA) Engine 10 1.4 Fundamentals of TCFPLA Engine 12 Bibliography 16 CHAPTER 2 18 Modeling Approach 18 2.1 Model Overview 18 2.2 Thermodynamic Model 19 2.3 Flow Model 20 2.4 Combustion and Ignition Model 22 2.5 Heat Transfer Model 23 2.5.1 Heat Transfer for Compressing Volumes 23 2.5.2 Heat Transfer for Air Box 24 2.6 Piston Dynamics and Friction 25 2.7 Linear Alternator Model 26 ii 2.8 Turbine Model 28 2.9 Free-Piston Engine System 28 Bibliography 36 CHAPTER 3 37 TCFPLA Engine Model Demonstration 37 3.1 Configuration of SIGMA GS-34 37 3.2 GS-34 Experimental Results 39 3.3 Numerical Analysis of the GS-34 Engine 40 3.4 Demonstration of New Matlab/Simulink Model 45 3.5 Discussion on the Model Demonstration 49 3.5.1 Sensitivity to Burn Rate 52 3.5.2 Sensitivity to Heat Transfer 56 3.5.2 Sensitivity to Friction 58 Bibliography 62 CHAPTER 4 63 TCFPLA Engine Configuration and Operation 63 4.1 Parametric Study on Dimensions of Hyprex 63 4.1.1 Bounce Chamber Offset 64 4.1.2 Piston Mass 66 4.1.3 Compressor Offset 68 4.1.4 Exhaust Port Opening Position 70 4.1.5 Compressor-to-Combustion Area Ratio 72 4.2 Resizing for 100-kW TCFPLA 73 4.3 Detailed Linear Alternator Model and Validation 76 4.4 Parametric Study for Detailed Alternator and Comparison with Simplified Model 81 4.4.1 Parametric Study for Number of Coils and Magnets in Alternator 82 4.4.2 Comparison of Detailed Alternator Model and Simplified Alternator Model 85 4.5 Low Load Strategy 88 iii 4.6 100-kW TCFPLA Operation 91 4.6.1 Bounce Chamber Mass Effects 92 4.6.2 Injection Position Effects 93 4.6.3 Engine Map 95 Bibliography 101 CHAPTER 5 102 TCFPLA Analysis by First Law of Thermodynamics 102 5.1 Introduction 102 5.2 Air Box Heat Recovery 104 5.3 Energy Transformation for Alternator 106 5.4 Energy Distribution 109 5.5 Useful Work 114 CHAPTER 6 118 TCFPLA Analysis by Second Law of Thermodynamics 118 6.1 Introduction 118 6.2 Availability in Volumes 123 6.3 Irreversibility of Flow 129 6.3.1 Flow Through Restricted Area 129 6.3.2 Flow throughout Turbine 130 6.4 Irreversibility of Heat Recovery 131 6.5 Potential Improvement Based on Second Law 134 6.6 Exergy Flow Through TCFPLA 137 Bibliography 141 CHAPTER 7 142 Crank-Driven Opposed-Piston Gas Turbine 142 7.1 Configuration of Crank-Driven Opposed-Piston Gas Turbine 142 7.2 Comparison of Operation 144 7.2 Comparison of Heat Transfer 145 7.3 Applying Heat recovery 148 iv CHAPTER 8 151 Conclusion on TCFPLA Engine 151 8.1 Summary 151 8.2 Future Work 156 Bibliography 158 APPEXDIX A 159 Reed Valve 159 v LIST OF TABLES Table 3-1 Geometric information of GS-34 38 Table 3-2 Experimental results of GS-34 reported by Eichelberg 39 Table 3-3 Summary of SIGMA GS-34 Design and Performance 41 Table 3-4 Results comparison for London’s and UM model 45 Table 3-5 Sensitivity study of burn rate/peak pressure effect 54 Table 3-6 Sensitivity study of heat transfer effect 56 Table 3-7 Sensitivity study of total friction amount effect 58 Table 3-8 Sensitivity study of friction force models 60 Table 4-1 Fuel sweep for Bounce Offset/Bore = 2.0 64 Table 4-2 Fuel sweep for Bounce Offset/Bore = 2.2 65 Table 4-3 Piston dimensions of GS-34 and Hyprex 67 Table 4-4 The effects of piston mass with same fueling rate 110 mg/cycle 67 Table 4-5 The effects of compressor offset at the same fueling rate 69 Table 4-6 The effects of EPO at the same fueling rate 71 Table 4-7 Effects of the area ratio at the same fueling rate = 160 mg/cycle 73 Table 4-8 Further downsized TCFPLA for target of 100 kW 75 Table 4-9 Comparison of performance numbers for the addition of alternator 80 Table 4-10 Coil number sweep for the study of alternator 82 Table 4-11 Magnet number sweep for the study of alternator 83 Table 4-12 Alternator comparison with different combinations of coil/magnet number 84 Table 4-13 Comparison between detailed and simplified alternator model 86 Table 4-14 Throttled turbine inlet effect 88 Table 4-15 Sample results for low load condition with recirculation 91 Table 4-16 Effects of different bounce chamber mass at given operating condition 92 Table 4-17 Comparison of injection position effects on system performance 93 vi Table 5-1 Useful work generated by turbine and alternator 107 Table 5-2 Energy distribution at different injection positions 109 Table 5-3 Energy distribution for different alternator power takeout 111 Table 5-4 Energy distribution for operation under different bounce chamber mass 112 Table 6-1 Availabilities as the percentages of fuel availability 136 Table 6-2 Irreversibility of volumes as the percentage of fuel availability 136 Table 6-3 Flow exergy at each state in the unit of [Joule/cycle] 138 vii LIST OF FIGURES Figure 1-1 Pescara Air Compressor, 1931 3 Figure 1-2 GS-34 concept and the actual device 4 Figure 1-3 Stirling free-piston linear alternator 6 Figure 1-4 Galileo and West Varginia University FPLA design 7 Figure 1-5 Sandia free-piston linear alternator 8 Figure 1-6 Architecture of the free-piston engine-alternator by Li et al. 9 Figure 1-7 Opposed-piston free-piston linear alternator with mechanical springs 9 Figure 1-8 Scheme of the DLR free-piston linear generator 10 Figure 1-9 Configuration of TCFPLA 12 Figure 1-10 Operating procedures of the TCFPLA engine 13 Figure 1-11 TCFPLA operation principles and relations between volumes 14 Figure 2-1 TCFPLA engine model structure 18 Figure 2-2 Reed valve structure and flow direction 22 Figure 2-3 Force balance on the piston 25 Figure 2-4 Free-piston position vs. velocity 32 Figure 2-5 Combustion chamber heat transfer coefficient in a cycle 33 Figure 2-6 Cumulative mass during one scavenging process 33 Figure 2-7 Pressure vs. piston position for all control volumes 34 Figure 3-1 Configuration of SIGMA GS-34 with transparent view on the left piston 38 Figure 3-2 P-V diagram of combustion chamber 43 Figure 3-3 P-V diagram of compressor chamber 43 Figure 3-4 P-V diagram of bounce chamber 44 Figure 3-5 Pressure-volume diagram of combustion chamber 47 Figure 3-6 Pressure-volume diagram of compression chamber 48 Figure 3-7 Pressure-volume diagram of bounce chamber 48 viii Figure 3-8 London’s modified expansion process 50 Figure 3-9 P-V diagram of combustion chamber from London’s result 51 Figure 3-10 Energy release rate for free-piston engine combustion 52 Figure 3-11 Mass fraction burn rate with different Weibe coefficient “a” 53 Figure 3-12 Pressure profiles with corresponding Wiebe functions in Figure 3-11 54 Figure 3-13 Different friction force models 60 Figure 4-1 TCFPLA symbols for dimensions 64 Figure 4-2 Cylinder and bounce chamber pressure with different Offset/Bore values 66 Figure 4-3 Piston velocity vs. position show the effects of piston mass 68 Figure 4-4 Piston velocity vs. position profile on different compressor offsets 70 Figure 4-5 Piston velocity vs. position profile on different EPO’s 72 Figure 4-6 BSFC as a function of total power for Hyprex TCFPLA engine 74 Figure 4-7 Coils and magnets in an alternator 76 Figure 4-8 Flux2D model and the geometry information of Sandia alternator 77 Figure 4-9 Magnetic flux for coil 1, 7 and 12 as examples 78 Figure 4-10 Simulink® model for alternator and rectifier, developed by SBU 79 Figure 4-11 Alternator voltage, sum of 14 coils in 100 kW TCFPLA device 79 Figure 4-12 Battery charging voltage (DC) after the rectifier and filters 80 Figure 4-13 Magnetic flux as a function of piston position for coil 1, 6, and 13 83 Figure 4-14 Alternator electromagnetic force acting on the traveling piston 86 Figure 4-15 LogP-LogX diagram showing the pressure profile affected by combustion 94 Figure 4-16 BSFC contour for TCFPLA operation at different power extraction ratio 96 Figure 4-17 Frequency contour for TCFPLA operation at different power extraction ratio 98 Figure 4-18 BSFC vs. total power at different fueling and alternator power takeout 99 Figure 4-19 Mass flow rate for turbine only operaion 100 Figure 5-1 Energy distribution for comparison of heat recovery 104 Figure 5-2 Thermal efficiency breakdown for comparison of alternators 106 ix Figure 5-3 Log-P Log-V diagram showing the combustion phasing 110 Figure 5-4 Bounce chamber pressure profile for different mass setup 113 Figure 5-5 Relation between compressor work input and turbine work output 115 Figure 5-6 Relation between indicated work and compressor work input 116 Figure 6-1 System standard enthalpy profile shown in one full cycle 121 Figure 6-2 System standard enthalpy profile shown in one full cycle 122 Figure 6-3 Cumulative availability of bounce chamber 123 Figure 6-4 Cumulative availability of compressor chamber 124 Figure 6-5 Cumulative availability of compressor chamber (zoom-in) 125 Figure 6-6 Cumulative availability of air box 126 Figure 6-7 Cumulative availability of