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The Modelling and Optimisation of High Performance Internal Combustion Engines

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The Modelling and Optimisation of High Performance Internal Combustion Engines The Modelling and Optimisation of High Performance Internal Combustion Engines by Julian Ross Panting A thesis submitted for the degree of Doctor of Philosophy of the Faculty of Engineering, University of London, and the Diploma of Imperial College July 1993 Department of Mechanical Engineering Imperial College of Science, Technology and Medicine University of London 1 Abstract The project described addresses the numerical modelling of two types of small, novel internal combustion engines of unusually high power/weight ratio in order to obtain data upon their suitability for automotive application. The particular data sought are reliable estimates of the part and full load thermal efficiencies and the maximum specific power output level. The engine types studied are an unusual form of two shaft gas turbine with and without a heat exchanger, and a compound highly turbocharged, spark ignition, high speed, four stroke piston engine. The latter may be considered a hybrid of gas turbine and spark ignition piston engines. Maximum specific power output projections are based upon the assumption of high turbine entry temperatures of the order of 1600K. This in turn would require future use of ceramics technology if an uncooled turbine were to be used. It is assumed the engine is coupled with a continuously variable transmission, which permits greater flexibility in engine operation and hence enhanced performance levels. The numerical models used are of well known types - iterative matching calculations based on turbomachinery maps for the gas turbine simulations and the filling and emptying model type for the compound turbocharged engine calculations. A feature of the studies as applied to the latter engine type is the use of a sophisticated multi - dimensional optimisation algorithm to maximise simulated engine performance. The particular algorithm used is of the well known conjugate - gradient type. With this algorithm, the value of a number of independent input parameters can each be chosen to obtain the best engine performance, with this being defined, for the purposes of this work, as the specific power output. 2 Acknowledgements My thanks go to the following people. To my supervisor, Dr. N.Baines for providing support and encouragement and for arranging a special grant which enabled my third year studies to continue. To my parents and sister for also providing support and encouragement and to my parents for providing considerable financial assistance. To Rev. W.Raines for arranging my student accommodation. To Dr. S.Etemad for permitting me to use his section's computing facilities. Finally to the Imperial College Computer Centre help desk for providing much helpful advice. 3 CONTENTS Chapter (1) Considerations for the Optimum Design of a High Specific Output, High Thermal Efficiency Powertrain (1.1) Overview 23 (1.2) Continuously Variable Transmission Design 27 (1.3) Hybrid Vehicles- 31 (1.4) Compact, High Efficiency Engines - the Gas Turbine verses the Compound Highly Turbocharged Engine 34 (1.5) Simultaneously Optimising Many Design Parameters and the use of Continuously Variable Mechanisms 36 (1.6) Emissions Considerations 39 (1.7) Turbine Entry Temperature Limits 40 (1.8) The Structure of this Thesis 41 (1.9) References 43 4 Chapter (2) The Determination of Fluid Properties (2.1) Overview 57 (2.2) The Calculation of Fluid Properties for 'Low' Temperatures 59 (2.3) The Calculation of Fluid Properties for 'High' Temperatures 62 (2.3.1) Burnt Fuel/Air Mixture Properties 62 (2.3.2) Concerning the Calculation of the Specific Gas Constant 66 (2.3.3) Unburnt Fuel Vapour Properties 67 (2.3.4) Combining Burnt and Unburnt Gas Mixture Properties 68 (2.3.5) The Fuel Heat Content Value 69 (2.4) Summary 70 (2.5) References 71 5 Chapter (3) Automotive Gas Turbine Studies (3.1) Overview 90 (3.2) Basic Gas Turbine Performance Analysis 92 (3.3) The use of Turbomachinery Characteristics 97 (3.4) The General Calculation Procedure Invoking the use of Turbomachinery Characteristics and Variable Properties 99 (3.5) Modelling a Single Shaft, Constant Speed Gas Turbine without Variable Geometry 102 (3.6) Modelling the Twin Shaft Differential Gas Turbine without Variable Geometry 105 (3.7) A Note Concerning the Differential Gas Turbine Operating Schedule 107 (3.8) Alternative Gas Turbine Concepts which were not Modelled 107 (3.9) Summary 109 (3.10)References 110 6 Chapter (4) The Compound Highly Turbocharged Engine (4.1) Overview 129 (4.2) The Theoretical Advantages of the Compound Turbocharged Engine 131 (4.2.1) The Efficiency of the Compound Turbocharged Engine in a Limiting Case 131 (4.2.2) Consideration of the Optimum Pressure Ratio for Efficiency for the Gas Turbine 133 (4.2.3) The Compound Turbocharged Engine Considered as a High Pressure Ratio Unit 135 (4.2.4) The Specific Power Outputs of Various Engine Types Compared 139 (4.2.5) Further Considerations 141 (4.3) A Brief Review of Past Compound Turbocharged Engine Designs 142 (4.4) Justifying Further Research into the Compound Turbocharged Engine 143 (4.5) The Proposed Design Layout 144 (4.5.1) Four Cylinder Layout 145 (4.5.2) Four Stroke, Spark Ignition, High Speed Cycle 145 (4.5.3) Hybrid Sleeve/Aspin Valves 145 (4.5.4) Swash Plate Crank Mechanism 147 (4.5.5) Variable Cylinder Compression Ratio 148 (4.5.6) Throttleless Concept 149 (4.5.7) High TET Operation 150 (4.5.8) The Overall Concept 150 (4.6) The Turbine Entry Temperature Limit 152 (4.7) Transient Response 154 (4.8) A Simple Quasi-Steady Compound Turbocharged Engine Model 154 (4.9) Summary 157 (4.10)References 158 7 Chapter (5) Time - Marching Numerical Models of Naturally Aspirated and Compound Turbocharged Spark Ignition Piston Engines (5.1) Overview 175 (5.2) A Comparison of Modelling Strategies 176 (5.3) The Filling and Emptying Model 178 (5.3.1) The Governing Ordinary Differential Equations 178 (5.3.2) The Mass Flow Differential Equation 180 (5.3.2.1) The Basic Mass Flow Rate Equation 180 (5.3.2.2) Determination of the Flow Coefficient and Port Area 182 (5.3.3) The Energy Flow Rate Differential Equation 184 (5.3.3.1) Combustion Simulation 184 (5.3.3.2) The Heat Transfer Rate 187 (5.3.3.3) Modelling Direct Fuel Injection 188 (5.3.3.4) Cylinder Volume Calculation 189 (5.3.3.5) Frictional Loss Calculations 190 (5.3.4) Convergence of the Solution 191 (5.3.5) The Order of Integration 192 (5.4) Modifications to Produce a Compound Turbocharged Filling and Emptying Model 192 (5.4.1) The use of Turbomachinery Characteristics 192 (5.4.2) Modelling an Aftercooler 197 (5.4.3) The use of a Variable Cylinder Volumetric Compression Ratio 198 (5.4.4) Estimating the Turbine Entry Temperature 199 (5.5) Determining the Power Output and Brake Thermal Efficiency 199 (5.6) Summary 200 (5.7) References 201 8 Chapter (6) Ensuring the Stability of the Integration of the Mass Balance O.D.E. (6.1) Overview 215 (6.2) An Example of the Mass Flow Rate Calculation Instability Problem 216 (6.3) Analytic Stability of Integration of an O.D.E. 217 (6.4) The Numerical Stability of the First Order Euler Scheme 221 (6.5) Applying the Stability Condition 222 (6.6) Numerical Integration and Ill - Conditioned Problems 223 (6.7) Controlling the Ill - Conditioned Problem 226 (6.8) The Complete Algorithm 229 (6.9) Summary 229 (6.10)References 231 9 Chapter (7) Minimisation of a Function of a Vector - and the Application of this Technique to Powertrain Design Optimisation (7.1) Overview 236 (7.2) Multi - Dimensional Optimisation Methods Employing Line Minimisations 239 (7.2.1) The Orthogonal Directions Method 240 (7.2.2) The Method of Steepest Descent 241 (7.2.3) The use of Conjugate Directions 241 (7.2.3.1) The Conjugate Directions Method 244 (7.2.3.2) The Conjugate Gradient Method 245 (7.2.4) Quasi - Newton or Variable Metric Methods 246 (7.3) Multi - Dimensional Optimisation Employing the 'Monte-Carlo' Technique 247 (7.4) The Choice of Multi - Dimensional Optimisation Method 248 (7.5) Bracketing the Minimum and Employing a Line Minimisation Technique 249 (7.6) Calculating the Distances to the Input Vector Boundaries 253 (7.7) Evaluating the Gradient Vector 256 (7.8) Convergence of the Solution 257 (7.9) Applying the Multi - Dimensional Minimisation Technique to Powertrain Design Optimisation 257 (7.10)Summary 259 (7.11)References 260 10 Chapter (8) Numerical Results (8.1) The Gas Turbine Models 262 (8.2) Validation of the Piston Engine Models 265 (8.3) Optimisation Results 267 (8.3.1) Employing Test Mathematical Functions 267 (8.3.2) Employing the Quasi-Steady Piston Engine Models 267 (8.3.3) Employing the Filling and Emptying Piston Engine Models 269 (8.3.4) Part Validation of the Optimisation Results 272 (8.4) Further Aspects of the Filling and Emptying Piston Engine Modelling 274 (8.4.1) Increasing the Bore/Stroke Ratio of the Naturally Aspirated Engine 274 (8.4.2) Some Adjustments to the Compound Turbocharged Engine Model Input Parameters 274 (8.4.3) Part Load Efficiency Contours 276 (8.4.4) Further Data from the Compound Turbocharged Engine Model 278 (8.5) Comparing the Gas Turbine and Piston Engines' Specific Power Output Figures 278 (8.6) References 280 11 Chapter (9) Conclusions and Suggestions for Further Work (9.1) Conclusions 320 (9.1.1) The Gas Turbine Simulations 320 (9.1.2) The Compound Turbocharged Engine Simulations 321 (9.1.3) Comparisons Between the Gas Turbine and Compound Turbocharged Engine Simulations 323 (9.1.4) The Optimisation Procedure 325 (9.2) Suggestions for Further Work 326 (9.2.1) Modifications to the Filling and Emptying Method 326
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