McGraw,:"Hill Series in Mechanical Engineering Jack P Holman, Southern Methodist University Consulting Editor Anderson: Modern Compressible Flow: With Historical Perspective Dieter: Engineering Design: A Materials and Processing Approach Eckert and Drake: Analysis of Heat and Mass Transfer Heywood: Internal Combustion Engine Fundamentals Hinze: Turbulence,2le Hutton: Applied Mechanical Vibrations JuvinaU: Engineering Considerations ofStress, Strain, and Strength Kane and Levinson: Dynamics: Theory and Applications Kays and Crawford: Convective Heat and Mass Transfer Martin: Kinematics and Dynamics ofMachines Phelan: Dynamics of Machinery Phelan: Fundamentals of Mechanical Design, 31e Pierce: Acoustics: An Introduction to Its Physical Principles and Applications Raven: Automatic Control Engineering, 41e Rosenberg and Karnopp: Introduction to Physics Schlichting: Boundary-Layer Theory, 71e Shames: Mechanics ofFluids, 21e Shigley: Kinematic Analysis of Mechanisms, 21e Shigley and Mitchell: Mechanical Engineering Design.4le Shigley and Uicker: Theory of Machines and Mechanisms Stoecker and Jones: Refrigeration and Air Conditioning, 21e Vanderplaats: Numerical Optimization Techniquesfor Engineering Design: INTERNAL COMBUSTION ENGINE FUNDAMENTALS John B.t!Ieywood Professor of Mechanical Engineering Director, Sloan Automotive Laboratory Massachusetts Institute of Technology With Applica(ions uauerle,neen; +VjSLt=lf [£) Xnderung nur Ober Fechbibliothek BFV21 rSfil McGraw-Hili, Inc New York St Louis San Francisco Aucklan~ Bo~ota Caracas Lisbon London -Madrid Mexico CJt~ MJlan Montreal New Delhi San Juan Smgapore Sydney Tokyo Toronto INTERNAL COMBUSTION ENGINE FUNDAMENTALS This book was set in Times Roman The editors were Anne Duffy and John M Morriss; the designer was Joan E O'Connor; the production supervisor was Denise L Puryear New drawings were done by ANCO Project Supervision was done by Santype International Ltd R R DonnelJey & Sons Company was printer and binder ABOUT THE AUTHOR See acknowledgements on page xxi Copyright © 1988 by McGraw-Hill, Inc AlJ rights reserved Printed in the United States of America Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher 14 15 16 17 DOCIDOC 9 ISBN 0-07-028637-X Library of Congress Cataloging-in-Publication Data Heywood, John B Internal combustion engine fundamentals (McGraw-Hill series in mechanical engineering) ~ibliography: p Includes index I Internal combustion engines I Title II Series TJ755.H45 1988 621.43 87·15251 This book is printed on acid-free paper Dr John B Heywood received the Ph.p degree in mechanical engineering from the Massachusetts Institute of Technology in 1965 Following an additional postdoctoral year of research at MIT, he worked as a research officer at the Central Electricity Generating Board's Research Laboratory in England on magnetohydrodynamic power generation In 1968 he joined the faculty at MIT where he is Professor of Mechanical Engineering At MIT he is Director of the Sloan Automotive Laboratory He is currently Head of the Fluid and Thermal Science Division of the Mechanical Engineering Department, and the Transportation Energy Program Director in the MIT Energy Laboratory He is faculty advisor to the MIT Sports Car Club Professor Heywood's teaching and research interests lie in the areas of thermodynamics, combustion, energy, power, and propulsion During the past two decades, his research activities have centered on the operating characteristics and fuels requirements of automotive and aircraft engines A major emphasis has been on computer models which predict the performance, efficiency, and emissions of spark-ignition, diesel; and gas turbine engines; and in carrying out experiments to develop and validate these models He is also actively involved in technology assessments and policy studies related to automotive engines, automobile fuel utilization, and the control of air pollution He consults frequently in -the automotive and petroleum industries, and for the U.S Government His extensive research in the field of engines has been supported by the U.S Army, Department of Energy, Environmental Protection Agency, NASA, National Science Foundation, automobile and diesel engine manufacturers, and petroleum companies He has pre-sented or published over a hundred papers on v vi ABOUT THE AUTHOR his research in technical conferences and journals He has co-authored two pre~ vious books: Open-Cycle MHD Power Generation published by Pergamon Press in 1969 and The Automobile and the Regulation of Its Impact on the Environment published by University of Oklahoma Press in 1975 He is a member of the American Society of Mechanical Engineers, an associate fellow of the American Institute of Aeronautics and Astronautics, a fellow of the British Institution of Mechanical Engineers, and in 1982 was elected a Fellow of the U.S Society of Automotive Engineers for his technical contributions to automotive engineering He is a member of the editorial boards of the journals Progress in Energy and Combustion Science and the International Journal of Vehicle Design His research publications on internal combustion engines, power generation, and gas turbine combustion have won numerous awards He was awarded the Ayreton Premium in 1969 by the British Institution of Electrical Engineers Professor Heywood received a Ralph R Teetor Award as an outstanding young engineering educator from the Society of Automotive Engineers in 1971 He has twice been the recipient of an SAE Arch T Colwell Merit Award for an outstanding technical publication (1973 and 1981) He received SAE's Homing Memorial Award for the best paper on engines and fuels in 1984 In 1984 he received the Sc.D degree from Cambridge University for his published contributions to engineering research He was selected as the 1986 American Society of Mechanical Engineers Freeman Scholar for a major review of "Fluid Motion within the Cylinder of Internal Combustion Engines." THIS BOOK IS DEDICATED TO MY FATHER, Harold Heywood: I have followed many ofthe paths he took vii CONTENTS Chapter 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Chapter 2.1 2.2 23 2.4 2.5 2.6 2.7 2.8 2.9 Preface xvii Commonly Used Symbols, Subscripts, and Abbreviations xxiii Engine Types and Their Operation Introduction and Historical Perspective Engine Classifications Engine Operating Cycles Engine Components Spark-Ignition Engine Operation Examples of Spark-Ignition Engines Compression-Ignition Engine Operation Examples of Diesel Engines Stratified-Charge Engines Engine Design and Operating Parameters Important Engine Characteristics Geometrical Properties of Reciprocating Engines Brake Torque and Power Indicated Work Per Cycle Mechanical Efficiency Road-Load Power Mean Effective Pressure Specific Fuel Consumption and Efficiency Air/Fuel and Fuel/Air Ratios 12 15 19 25 31 37 42 42 43 45 46 48 49 50 51 53 ix X CONTENTS 2.10 2.11 2.12 2.13 2.14 2.15 Chapter 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Chapter 4.1 4.2 4.3 4;4 4.5 4.6 4.7 4.8 4.9 CONTENTS Volumetric Efficiency Engine Specific Weight and Specific Volume Correction Factors for Power and Volumetric Efficiency Specific Emissions and Emissions Index Relationships between Performance Parameters Engine Design and Performance Data Thermochemistry of Fuel-Air Mixtures Characterization of Flames Ideal Gas Model Composition of Air and Fuels Combustion Stoichiometry The First Law of Thermodynamics and Combustion 3.5.1 Energy and Enthalpy Balances 3.5.2 Enthalpies of Formation 3.5.3 Heating Values 3.5.4 Adiabatic Combustion Processes 3.5.5 Combustion Efficiency of an Internal Combustion Engine The Second Law of Thermodynamics Applied to Combustion 3.6.1 Entropy 3.6.2 Maximum Work from an Internal Combustion Engine and Efficiency Chemically Reacting Gas Mixtures 3.7.1 Chemical Equilibrium 3.7.2 Chemical Reaction Rates Properties of Working Fluids Introduction Unburned Mixture Composition Gas Property Relationships A Simple Analytic Ideal Gas Model Thermodynamic Charts 4.5.1 Unburned Mixture Charts 4.5.2 Burned Mixture Charts 4.5.3 Relation between Unburned and Burned Mixture Charts Tables of Properties and Composition Computer Routines for Property and Composition Calculations 4.7.1 Unburned Mixtures 4.7.2 Burned Mixtures Transport Properties Exhaust Gas Composition 4.9.1 Species Concentration Data 4.9.2 Equivalence Ratio Determination from Exhaust Gas Constituents 4.9.3 Effects of FueljAir Ratio Nonuniformity 4.9.4 Combustion Inefficiency 53 54 54 56 56 57 Chapter Ideal Models of Engine Cycles 5.1 5.2 5.3 5.4 62 62 64 64 68 72 72 76 78 80 81 83 83 83 85 86 92 5.5 5.6 5.7 5.8 Chapter Gas Exchange Processes 6.1 6.2 100 6.3 100 102 107 109 112 112 116 6.4 6.5 6.6 123 127 130 130 135 141 145 145 148 152 154 Introduction Ideal Models of Engine Processes Thermodynamic Relations for Engine Processes Cycle Analysis with Ideal Gas Working Fluid with c.and c, Constant 5.4.1 Constant-Volume Cycle 5.4.2 Limited- and Constant-Pressure Cycles 5.4.3 Cycle Comparison Fuel-Air Cycle Analysis 5.5.1 SI Engine Cycle Simulation 5.5.2 CI Engine Cycle Simulation 5.5.3 Results of Cycle Calculations Overexpanded Engine Cycles Availability Analysis of Engine Processes 5.7.1 Availability Relationships 5.7.2 Entropy Changes in Ideal Cycles 5.7.3 Availability Analysis of Ideal Cycles 5.7.4 Effect of Equivalence Ratio Comparison with Real Engine Cycles 6.7 6.8 Chapter 7.1 7.2 Inlet and Exhaust Processes in the Four-Stroke Cycle Volumetric Efficiency 6.2.1 Quasi-Static Effects 6.2.2 Combined Quasi-Static and Dynamic Effects 6.2.3 Variation with Speed, and Valve Area, Lift, and Timing Flow Through Valves 6.3.1 Poppet Valve Geometry and Timing 6.3.2 Flow Rate and Discharge Coefficients Residual Gas Fraction Exhaust Gas Flow Rate and Temperature Variation Scavenging in Two-Stroke Cycle Engines 6.6.1 Two-Stroke Engine Configurations 6.6.2 Scavenging Parameters and Models 6.6.3 Actual Scavenging Processes Flow Through Ports Supercharging and Turbocharging 6.8.1 Methods of Power Boosting 6.8.2 Basic Relationships 6.8.3 Compressors 6.8.4 Turbines 6.8.5 Wave-Compression Devices 51 Engine Fuel Metering and Manifold Phenomena Spark-Ignition Engine Mixture Requirements Carburetors xi 161 161 162 164 169 169 172 173 177 178 180 181 183 186 186 188 189 192 193 205 206 209 209 212 216 220 220 225 230 231 235 235 237 240 245 248 248 249 255 263 270 279 279 282 xii CONTENTS 7.3 7.4 7.5 7.6 Chapter 8.1 8.2 8.3 8.4 8.5 8.6 8.7 CONTENTS 7.2.1 Carburetor Fundamentals 7.2.2 Modern Carburetor Design Fuel-Injection Systems 7.3.1 Multipoint Port Injection 7.3.2 Single-Point Throttle-Body Injection Feedback Systems Flow Past Throttle Plate Flow in Intake Manifolds 7.6.1 Design Requirements 7.6.2 Air-Flow Phenomena 7.6.3 Fuel-Flow Phenomena Charge Motion within the Cylinder Intake Jet Flow Mean Velocity and Turbulence Characteristics 8.2.1 Definitions 8.2.2 Application to Engine Velocity Data Swirl 8.3.1 Swirl Measurement 8.3.2 Swirl Generation during Induction 8.3.3 Swirl Modification within the Cylinder Squish Prechamber Engine Flows Creyice Flows and Blowby Flows Generated by Piston-Cylinder Wall Interaction 282 285 294 294 299 301 304 308 308 309 314 9.6.2 9.6.3 491 Essential Features of Process Types of Diesel Combustion Systems 10.2.1 Direct-Injection Systems 10.2.2 Indirect-Injection Systems 10.2.3 Comparison of Different Combustion Systems Phenomenological Model of Compression-Ignition Engine Combustion 10.3.1 Photographic Studies of Engine Combustion 10.3.2 Combustion in Direct-Injection, Multispray Systems 10.3.3 Application of Model to Other Combustion Systems Analysis of Cylinder Pressure Data 10.4.1 Combustion Efficiency 10.4.2 Direct-Injection Engines 10.4.3 Indirect-Injection Engines Fuel Spray Behavior 10.5.1 Fuel Injection 10.5.2 Overall Spray Structure 10.5.3 Atomization 10.5.4 Spray Penetration 10.5.5 Droplet Size Distribution 10.5.6 Spray Evaporation Ignition Delay 10.6.1 Definition and Discussion 10.6.2 Fuel Ignition Quality 10.6.3 Autoignition Fundamentals 10.6.4 Physical Factors Affecting Delay 10.6.5 Effect of Fuel Properties 10.6.6 Correlations for Ignition Delay in Engines Mixing-Controlled Combustion 10.7.1 Background 10.7.2 Spray and Flame Structure 10.7.3 Fuel-Air Mixing and Burning Rates 491 493 493 494 495 10.1 10.2 10.3 10.4 10.5 10.6 Chapter Combustion in Spark-Ignition Engines 9.1 9.2 9.3 9.4 9.5 9.6 Essential Features of Process Thermodynamic Analysis of SI Engine Combustion 9.2.1 Burned and Unburned Mixture States 9.2.2 Analysis of Cylinder Pressure Data 9.2.3 Combustion Process Characterization Flame Structure and Speed 9.3.1 Experimental Observations 9.3.2 Flame Structure 9.3.3 Laminar Burning Speeds 9.3.4 Flame Propagation Relations Cyclic Variations in Combustion, P~ial Burning, and Misfire 9.4.1 Observations and Definitions 9.4.2 Causes of Cycle-by-Cycle and Cylinder-to-Cylinder Variations 9.4.3 Partial Burning, Misfire, and Engine Stability Spark Ignition 9.5.1 Ignition Fundamentals 9.5.2 Conventional Ignition Systems 9.5.3 Alternative Ignition Approaches Abnormal Combustion: Knock and Surface Ignition 9.6.1 Description of Phenomena 371 371 376 376 383 389 390 390 395 402 406 413 413 419 424 427 427 437 443 450 450 457 470 Chapter 10 Combustion in Compression-Ignition Engines 326 326 330 330 336 342 343 345 349 353 357 360 365 Knock Fundamentals Fuel Factors xiii 10.7 Chapter 11 11.1 11.2 11.3 11.4 Pollutant Formation and Control Nature and Extent of Problem Nitrogen Oxides 11.2.1 Kinetics of NO Formation 11.2.2 Formation ofN0 11.2.3 NO Formation in Spark-Ignition Engines 11.2.4 NOz Formation in Compression-Ignition Engines Carbon Monoxide Unburned Hydrocarbon Emissions 11.4.1 Background 11.4.2 Flame Quenching and Oxidation Fundamentals 497 497 503 506 508 509 509 514 517 517 522 525 529 532 535 539 539 541 542 546 550 553 555 555 555 558 567 567 572 572 577 578 586 592 596 596 599 xiv CONTENTS CONTENTS 11.5 11.6 11.4.3 HC Emissions from Spark-Ignition Engines 11.4.4 Hydrocarbon Emission Mechanisms in Diesel Engines Particulate Emissions 11.5.1 Spark-Ignition Engine Particulates 11.5.2 Characteristics ofDiesel Particulates 11.5.3 Particulate Distribution within the Cylinder 11.5.4 Soot Formation Fundamentals 11.5.5 Soot Oxidation 11.5.6 Adsorption and Condensation Exhaust Gas Treatment 11.6.1 Available Options 11.6.2 Catalytic Converters 11.6.3 Thermal Reactors 11.6.4 Particulate Traps Chapter 12 Engine Heat Transfer 12.1 12.2 12.3 12.4 12.5 12.6 12.7 Importance of Heat Transfer Modes of Heat Transfer 12.2.1 Conduction 12.2.2 Convection 12.2.3 Radiation 12.2.4 Overall Heat-Transfer Process Heat Transfer and Engine Energy Balance Convective Heat Transfer 12.4.1 Dimensional Analysis 12.4.2 Correlations for Time-Averaged Heat Flux 12.4.3 Correlations for Instantaneous Spatial Average Coefficients 12.4.4 Correlations for Instantaneous Local Coefficients 12.4.5 Intake and Exhaust System Heat Transfer Radiative Heat Transfer 12.5.1 Radiation from Gases 12.5.2 Flame Radiation 12.5.3 Prediction Formulas Measurements of Instantaneous Heat-Transfer Rates 12.6.1 Measurement Methods 12.6.2 Spark-Ignition Engine Measurements 12.6.3 Diesel Engine Measurements 12.6.4 Evaluation of Heat-Transfer Correlations 12.6.5 Boundary-Layer Behavior Thermal Loading and Component Temperatures 12.7.1 Component Temperature Distributions 12.7.2 Effect of Engine Variables Chapter 13 Engine Friction and Lubrication 13.1 13.2 13.3 Background Definitions Friction Fundamentals 13.3.1 Lubricated Friction 13.3.2 Turbulent Dissipation 13.3.3 Total Friction Measurement Methods Engine Friction Data 13.5.1 SI Engines 13.5.2 Diesel Engines Engine Friction Components 13.6.1 Motored Engine Breakdown Tests 13.6.2 Pumping Friction 13.6.3 Piston Assembly Friction 13.6.4 Crankshaft Bearing Friction 13.6.5 Valve Train Friction Accessory Power Requirements Lubrication 13.8.1 Lubrication System 13.8.2 Lubricant Requirements 715 719 719 719 722 722 724 725 725 726 729 734 737 739 740 740 741 Chapter 14 Modeling Real Engine Flow and Combustion Processes 748 601 620 626 626 626 631 63.5 642 646 13.4 13.5 13.6 648 648 649 657 659 13.7 13.8 668 668 670 670 670 671 671 673 676 676 677 678 681 682 683 683 684 688 689 689 690 692 694 697 698 698 701 712 712 714 715 xv 14.1 14.2 14.3 14.4 14.5 Purpose and Classification of Models Governing Equations for Open Thermodynamic System 14.2.1 Conservation of Mass 14.2.2 Conservation of Energy Intake and Exhaust Flow Models 14.3.1 Background 14.3.2 Quasi-Steady Flow Models 14.3.3 Filling and Emptying Methods 14.3.4 Gas Dynamic Models Thermodynamic-Based In-Cylinder Models 14.4.1 Background and Overall Model Structure 14.4.2 Spark-Ignition Engine Models 14.4.3 Direct-Injection Engine Models 14.4.4 Prechamber Engine Models 14.4.5 Muiticylinder and Complex Engine System Models 14.4.6 Second Law Analysis of Engine Processes Fluid-Mechanic-Based Multidimensional Models /' 14.5.1 Basic Approach and Governing Equations 14.5.2 Turbulence Models 14.5.3 Numerical Methodology 14.5.4 Flow Field Predictions 14.5.5 Fuel Spray Modeling 14.5.6 Combustion Modeling Chapter 15 Engine Operating Characteristics 15.1 15.2 Engine Performance Parameters Indicated and Brake Power and MEP 748 750 750 751 753 753 753 754 756 762 762 766 778 784 789 792 797 797 800 803 807 813 816 823 823 824 xvi CONTENTS 15.3 Operating Variables That Affect SI Engine Performance, Efficiency, and Emissions 15.3.1 Spark Timing 15.3.2 Mixture Composition 15.3.3 Load and Speed 15.3.4 Compression Ratio SI Engine Combustion Chamber Design 15.4.1 Design Objectives and Options 15.4.2 Factors That Control Combustion 15.4.3 Factors That Control Performance 15.4.4 Chamber Octane Requirement 15.4.5 Chamber Optimization Strategy Variables That Affect CI Engine Performance, Efficiency, and Emissions 15.5.1 Load and Speed 15.5.2 Fuel-Injection Parameters 15.5.3 Air Swirl and Bowl-in-Piston Design Supercharged and Turbocharged Engine Performance 15.6.1 Four-Stroke Cycle SI Engines 15.6.2 Four-Stroke Cycle CI Engines 15.6.3 Two-Stroke Cycle SI Engines 15.6.4 Two-Stroke Cycle CI Engines Engine Performance Summary 15.4 15.5 15.6 15.7 827 827 829 839 841 844 844 846 850 852 857 858 858 863 866 869 869 874 881 883 886 Appendixes A B C D Unit Conversion Factors Ideal Gas Relationships B.1 Ideal Gas Law B.2 The Mole B.3 Thermodynamic Properties B.4 Mixtures of Ideal Gases Equations for Fluid Flow through a Restriction C.l Liquid Flow C.2 Gas Flow Data on Working Fluids Index PREFACE 899 902 902 903 903 905 906 907 907 911 917 Internal combustion engines date back to 1876 when Otto first developed the spark-ignition engine and 1892 when Diesel invented the compression-ignition engine Since that time these engines have continued to develop as our knowledge of engine processes has increased, as new technologies became available, as demand for new types of engine arose, and as environmental constraints on engine use changed Internal combustion engines, and the industries that develop and manufacture them and support their use, now play a dominant role in the fields of power, propulsion, and energy The last twenty-five years or so have seen an explosive growth in engine research and development as the issues of air pollution, fuel cost, and market competitiveness have become increasingly important An enormous technical literature on engines now exists which has yet to be adequately organized and summarized This book has been written as a text and a professional reference in response to that need It contains a broadly based and extensive review of the fundamental principles which govern internal combustion engine design and operation It attempts to provide a simplifying framework for the vast and complex mass of technical material that now exists on spark-ignition and compression-ignition engines, and at the same time to include sufficient detail to convey the real world dimensions of this pragmatic engineering field It is the author's conviction that a sound knowledge of the relevant fundamentals in the many disciplines that contribute to this field, as well as an awareness of the extensive practical knowledge base which has been built up over many decades, are essential tools for engine research, development, and design Of course, no one text can include everything about engines The emphasis here is on the thermodynamics, combustion physics and chemistry, fluid flow, heat transfer, friction, and lubrication processes relevant to internal combustion engine design, performance, efficiency, emissions, and fuels requirements xviii PREfACE From a fundamental point of view, how the fuel-air mixture within an internal combustion engine cylinder is ignited appropriately organizes the field From the method of ignition-spark-ignition or compression-ignition-follows each type of engine's important features: fuel requirements, method of mixture preparation, combustion chamber design, details of the combustion process, method of load control, emission formation mechanisms, and performance and efficiency characteristics While many engine processes (such as intake and exhaust flows, convective heat transfer, and friction) are similar in both types of engines, this distinction is fundamental and lies behind the overall organization of the book The book is arranged in four major sections The ·first (Chapters to 5) provides an introduction to, and overview of, the major characteristics of sparkignition and compression-ignition engines, defines the parameters used to describe engine operation, and develops the necessary thermodynamics and combustion theory required for a quantitative analysis of engine behavior It concludes with an integrated treatment of the various methods of analyzing idealized models of internal combustion engine cycles The second section (Chapters to 8) focuses on engine flow phenomena The details of the gas exchange processintake and exhaust processes in four-stroke and scavenging in two-stroke cycles-and the various methods of supercharging engines-are reviewed Fuel metering methods for spark-ignition engines and air- and fuel-flow phenomena in intake manifol(js are described The essential features of the various types of fluid motion within the engine cylinder are then developed These flow processes control the amount of air an engine will induct (and therefore its power), and largely govern the rate at which the fuel-air mixture will burn during combustion The third section of the book focuses on engine combustion phenomena These chapters (9, 10, and 11) are especially important The combustion process releases the fuel's energy within the engine cylinder for eventual conversion to useful work What fraction of the fuel's energy is converted depends strongly on how combustion takes place The spark-ignition and compression-ignition engine combustion processes (Chapters and 10, respectively) therefore influence essentially all aspects of engine behavior Air pollutants are undesirable byproducts of combustion Our extensive knowledge of how the major pollutants form during these combustion processes and how such emissions can be controlled is reviewed in Chapter 11 The last section of the book focuses on engine operating characteristics First, the fundamentals of engine heat transfer and friction, both of which detract from engine performance, are developed in Chapters 12 and 13 Chapter 14 then focuses on the methods available for predicting important aspects of engine behavior based on realistic models of engine flow and combustion processes Since the various thermodynamic-based and fluid-mechanic-based models which have been developed over the past fifteen years or so are increasingly used in engine research and development, a knowledge of their basic structure and capabilities is most important Then, Chapter 15 presents a summary of how the operating ·characteristics-power, efficiency, and emissions of spark-ignition and compression-ignition engines depend on the major engine design and oper- PREfACE xix ating variables These final two chapters effectively integrate the analytical understanding and practical knowledge of individual engine processes together to describe overall spark-ignition and compression-ignition engine behavior Material on internal combustion engine fuels is distributed appropriately throughout the book Each chapter is extensively illustrated and referenced, and includes problems for both undergraduate and graduate level courses While this book contains much advanced material on engine design and operation intended for the practitioner, each major topic is developed from its beginnings and the more sophisticated chapters have introductory sections to facilitate their use in undergraduate courses The chapters are extensively crossreferenced and indexed Thus several arrangements of the material for a course on engines can be followed For example, an introductory course on internal combustion engines could begin with Chapters and 2, which review the different types of engines and how their performance is characterized, and continue with the parts of Chapters and 5, which introduce the key combustion concepts necessary to understand the effects of fuel/air ratio, and ideal cycle analysis Selections from the introductory sections of Chapters 6, 9, 10, 11, and 15 could then be used to explain several of the practical and design aspects of spark-ignition and diesel engine intake and exhaust processes, combustion, emissions,· and performance A more advanced course would review this introductory material more rapidly, and then move on to those sections of Chapters and 5, which cover fuel-air cycle analysis, a more extensive discussion of engine breathing using additional sections of Chapter 6, and more in-depth treatment of engine combustion and emissions processes based on the appropriate sections of Chapters 9, 10, and 11 Material on engine heat transfer and friction selected from Chapters 12 and 13 could be included next While Chapter 14 on modeling the thermodynamics and fluid dynamics of real engine processes is primarily intended for the professional scientist and engineer, material from this chapter along with selections from Chapter 15 could be used to illustrate the performance, efficiency, and emissions characteristics of the different types of internal combustion engines I have also used much of the more sophisticated material in Chapters through 15 for review seminars on individual engine topics and more extensive courses for professional engineers, an additional important educational and reference opportunity Many individuals and organizations have assisted me in various ways as I have worked on this book over the past ten or so years I am especially indebted to my colleagues in the Sloan Automotive Laboratory at M.I.T., Professors Wai K Cheng, Ahmed F Ghoniem, and James C Keck, and Drs Jack A Ekchian, David P Hoult, Joe M Rife, and Victor W Wong, for providing a stimulating environment in which to carry out engine research and for assuming additional burdens as a result of my writing Many of the Sloan Automotive Laboratory's students have made significant c.ontributions to this text through their research; their names appear in the reference lists The U.S Departmentof Energy provided support during the early stages of the text development and funded the work on engine cycle simulation used extensively in Chapters 14 and 15 I am grateful XX PREFACE to Churchill College, Cambridge University, for a year spent as a Richard C Mellon Visiting Fellow, 1977-78, and the Engineering Department, Cambridge University, for acting as my host while I developed the outline and earlier chapters of the book The M.LT sabbatical leave fund supported my full-time writing for eight months in 1983, and the Mechanical Engineering Department at Imperial College graciously acted as host I also want to acknowledge several individuals and organizations who have provided major inputs to this book beyond those cited in the references ~embers of General M~tors Research Laboratories have interacted extensively wIth the Sloan AutomotIve Laboratory over many years and provided valuable advice on engine research developments Engineers from the Engine Research and Fluid Mechanics Departments at General Motors Research Laboratories reviewed and critiqued the final draft manuscript for me Charles A Amann, He~d of the Engine Research Department, made especially helpful inputs on engme performance John J Brogan of the U.S Department of Energy provided valuable assistance with the initial organization of this effort My regular interactions over the years with the Advanced Powertrain Engineering Office and Scientific Research Laboratories of the Ford Motor Company have given me a broad exposure to the practical side of engine design and operation A long-term relationship with Mobil Research and Development Corporation has provided comparable experiences in the area of engine-fuels interactions Many organizations and individuals supplied specific material and illustrations for the text I am especially grateful to those who made available the high-quality photographs and line drawings which I have used and acknowledged McGraw-Hill and the author would like to express their thanks to the following reviewers for their useful comments and ·suggestions: Jay A Bolt, University of Michigan; Gary L Borman and William L Brown, University of Wisconsin at Madison; Dwight Bushnell, Oregon State University; Jerald A Caton, Texas A & M University; David E Cole, University of Michigan; Lawrence W Evers, Michigan Technological University; SamuelS Lestz, Pennsylvania State University; Willard Pulkrabek, University of Wisconsin; Robert F Sawyer, University of California at Berkeley; Joseph E Shepherd, Rensselaer Polytechnic Institute; and Spencer C Sorenson, The Technical University of Denmark Special thanks are due to my secretaries for their faithful and thoughtful assistance with the manuscript over these many years, beyond the" call of duty"; Linda Pope typed an earlier draft of the book, and Karla Stryker was responsible for producing and coordinating subsequent drafts and the final manuscript My wife Peggy, and sons James, Stephen, and Ben have encouraged me throughout this long and time-consuming project which took many hours away from them Without their continuing support it would never have been finished' for their patience, and faith that it would ultimately come-to fruition, I will ~lways be grateful John B Heywood ACKNOWLEDGMENTS The auth.or wishes to acknowledge the following organizations and publishers for permIssIon to reproduce figures and tables from their publications in this text: The American Chemical Society; American Institute of Aeronautics & Astronautics; American Society of Mechanical Engineers; Robert Bosch GmbH CIMAC, Cambridge University Press; The Combustion Institute' Elsevie; Sci~nce Publishing Company;? T Foulis & Co Ltd.; General Mot~rs CorporatIon; Gordon & Breach SCIence Publishers; The Institution of Mechanical Engineers; The Japan Society of Mechanical Engineers; M.LT Press; Macmillan Press Ltd.; McGraw-Hill Book Company; Mir Publishers; Mobil Oil CorporatIOn; Morgan-Grampian Publishers; Pergamon Journals, Inc.; Plenum Press Corporation; The Royal Society of London; Scientific Publications Limited' Society ~f Autom?tive ~ngineers; Society of Automotive Engineers of Japan: I~c.; SocI.ety ~f TnbologIsts and Lubrications Engineers; Department of Mechameal EngIneenng, Stanford University xxi APPENDIX B IDEAL GAS RELATIONSHIPS 903 B.2 THE MOLE APPENDIX B It is convenient to introduce a mass unit based on the molecular structure of matter, the mole: The mole is the amount of substance which contains as many molecules as there are carbon atoms in 12 grams of carbon-12.t Thus, the number of moles n of gas is given by IDEAL GAS RELATIONSHIPS m n=M (B.4) pV = nRT (B.5) and Eq (B.3) becomes Values for the universal gas constant in different units are given in Table B.1 In the SI system, the value is 8314.3 Ifkmol· K TABLE 8.1 Values of UDiversai gas constant R 8314.3 JJkmol' K 8.3143 J/mol' K 1.9859 Btu/lb-mole· OR 1543.3 ft ·Ibf/lb-mole· OR B.l IDEAL GAS LAW The gas species which make up the working fluids in internal combustion engines (e.g., oxygen, nitrogen, carbon dioxide, etc.) can usually be treated as ideal gases This Appendix reviews the relationships between the thermodynamic properties of ideal gases The pressure p, specific volume v, and absolute temperature T of an ideal gas are related by the ideal gas law pv = RT R=M 902 u=u(T) Since the enthalpy h is given by u (B.6) + pv, it follows also that h=h(T) (B.7) (B.2) where R is the universal gas constant (for all ideal gases) and M is the molecular weight of the gas Since v is given by Vim, where V is the volume of a mass of gas m, Eq (B.l) can be rewritten as mRT pV=mRT=-M It follows from Eq (B.1) that the internal energy u:j: of an ideal gas is a function of temperature only: (B.l) For each gas species, R is a constant (the gas constant) It is different for each gas and is given by R B.3 THERMODYNAMIC PROPERTIES (B.3) t This is the SI system definition of the mole; it was formerly called the gram-mole The kilogrammole (kInol) is also used; it is 1000 times as large as the mole t The symbol &I will be used for internal energy per unit mass, jj for internal energy per mole, and U for internal energy of a previously defined system of mass m Similar notation will be used for enthalpy, entropy, and specific heats, per unit mass and per mole 904 Cu INTERNAL COMBUSTION ENGINE FUNDAMENTALS APPENDIX B IDEAL GAS RELATIONSHIPS The specific heats at constant volume and constant pressure of an ideal gas, and cp , respectively, are defined by u= (:;)u = :; (B.8) C = (:~) p - cp :~ (B.9) From Eq (B.1) it follows that (B,10) (B.11) An additional restrictive assumption is often made that the specific heats are constants This is not a necessary part of the ideal gas relationships In general, the internal energy and enthalpy of an ideal gas at a temperature T relative to its internal energy and enthalpy at some reference temperature To are given by r cu(T) dT h = ho + r cp(T) dT JTo T u = Uo + B.4 MIXTURES OF IDEAL GASES The working fluids in engines are mixtures of gases The composition of a mixture of ideal gases can be expressed in terms of the following properties of each component: Partial pressure PI' The pressure each component would exert if it alone occupied the volume of the mixture at the temperature of the mixture Parts by volume VJV The fraction of the total mixture volume each component would occupy if separated from the mixture, at the mixture temperature and pressure Mass fraction mass of mixture m The ratio of specific heats, y, is a useful quantity: XI' The mass of each component m l , divided by the total Mole fraction XI' The number of moles of each component nl, divided by the total number of moles of mixture n From Eq (B.5) it follows that PI J'l M_ p=-y=x I M I =XI (B.12) JTo Molecular weight (B.13) M =-" n""' nlM ="""' x.M I Internal energy, enthalpy, and entropy On a mass basis: dv v u= C T c T + R - = :I! dT - dp RP (B.14) I I XIU I (B.17) I I The entropy at T, v, and P, relative to the entropy at some reference state To, vo , Po' can be obtained from the relationships ds = - u dT (B.16) The thermodynamic properties of mixtures of ideal gases can be computed from the following relationships: T and 90S h =I I XI hi I , s= I XISI (B.18a, b, c) I On a mole basis: which integrate to give s = So r ~ dT + R In ~ JTo T + r S! dT - R In J! JTo T Po + (B.19a, b, c) T (B.15a) Vo and s = So T (B.15b) The properties u, h, and s can be evaluated on a per unit mass or per mole basis On a mass basis, cu , cp , and R would have the units J/kg' K (Btujlbm' OR); on a mole basis u, h, and s are replaced by il, ii, and So R is then the universal gas constant R., Cu and cp are replaced by Cu and cp, and cu, cp, and R would have the units J/kmol· K (Btu/lb-mol· OR) APPENDIX C EQUATIONS FOR FLUID FWW THROUGH A RESTRICTION APPENDIX C EQUATIONS FOR FLUID FLOW THROUGH A RESTRICTION : 907 _hir - -iL~ ~~-_- 1~_f-l! - FIGURE C.I Schematic of liquid flow through orifice C.l LIQUID FLOW Consider the flow of a liquid through an orifice as shown in Fig C-l For the ideal flow, Bernoulli's equation can be written PI Vi vi + P 2" = P2 + P For an incompressible flow, continuity gives VIAl = V2 A and the ideal mass flow rate through an orifice is given by mid •• J [ 2P(P1 - P2) I _ (A /A )2 l = A2 J l /2 (C.l) The real mass flow rate is obtained by introducing the discharge coefficient: • mr••• In many parts of the engine cycle, fluid flows through a restricti~n or re~uction in flow area Real flows of this nature are usually related to an eqwvalent Ideal flow The equivalent ideal flow is the steady adiabatic reversible (frictionless) flow of ~n ideal fluid through a duct of identical geometry and dimensions For a real ~uld flow, the departures from the ideal assumptions listed above are taken mto account by introducing a flow coefficient or discharge coefficient CD, where actual mass flow CD = -id-e-al-m-a-s-s :fl::-o-w- Alternatively, the flow or discharge coefficie.nt can be defined in terms of an effective cross-sectional area of the duct and a reference area The reference area A R is usually taken as the minimum cross-sectional area The effective a~ea of the flow restriction A E is then the cross-sectional area of the throat of a friCtionless nozzle which would pass the measured mass flow between a large upstrea~ reservoir at the upstream stagnation pressure and a large downstream reservOir at the downstream measured static pressure Thus AE CD = - AR 906 [ 2p(P1 - P2) I _ (A /A )2 l = CD A Jl /2 (C.2) The discharge coefficient is a function of orifice dimensions, shape and surface roughness, mass flow rate, and fluid properties (density, surface tension, and viscosity) The use of the orifice Reynolds number = pV2 D2 = J-2D Re o Jl v as a correlating parameter for the discharge coefficient accounts for the effects of m, p, v, and D2 to a good approximation Co2 GAS FLOW Consider the flow of an ideal gas with constant specific heats through the duct shown in Fig C-2 For the ideal flow, the stagnation temperature and pressure, 10 and Po' are related to the conditions at other locations in the duct by the steady flow energy equation and the isentropic relation 908 APPENDIX C EQUATIONS FOR FLUID FLOW THROUGH A RESTRlCfION INTERNAL COMBUSTION ENGINE FUNDAMENTALS 909 This ratio is called the critical pressure ratio For (PT/PO) less than or equal to the critical pressure ratio, m )(1+ 1)/2(Y-1) 5Rf Idcal~=y P -n-\ Poided L {-3L [1 _ m = CDATpo (PT)l/Y Po real P JRT real I I I Po 'I - For a choked flow, • mrcal FIGURE C-2 , Pressure distribution for gas flow throu~ a nozzle L -;:-x i By introducing the Mach number M = VIa, where a is the sound speed (= JyRT), the following equations are obtained: To T (e.7) The critical pressure ratio is 0.528 for 'I = 1.4 and 0.546 for 'I = 1.3 For a real gas flow, the discharge coefficient is introduced Then, for subcritical flow, the real mass flow rate is given in terms of conditions at the minimum area or throat by r-._._._., I '1+ ATpo I (2 = + 'I - M2 = JRT (e.4) The mass flow rate mis 'I (2 'I + - PT/PO (e.8) )(1+ 1)/2(y-1) Equation (e.8) can be rearranged in the form of Eq (C.2) (with A 2 mrcal = C DA R [2po(Po - PTW/ (1) where (1) is given by (1) = {[y/(y - 1)][(PT/PO)2/ Y- (PT/PO)(Y+ 1)/1]}1/2 (C.3) Po ( 'I - 2)Y/(Y-1) - = 1+ M P CAp D T 1/2 (PT)(1- )/1]}1/2 Po (e.9) ~ A l)as (e.l0) (e.ll) Figure C-3 shows the variation of (1) and (m/m*)ldcal with (Po - PT)/PO' m* is the mass flow rate through the restriction under choked flow conditions (when the Mach number at the throat is unity) For flow rates less than about 60 percent of the choked flow, the effects of compressibility on the mass flow rate are less than percent m=pAV With the ideal gas law and the above relations for P and T, this can be rearranged as ('I - )-(Y+1)/2(Y-1) m1dcal ~ = '1 M + - - M (e.5) Apo Y{ [ m.'dcalyyft-'-Jj CRT = 'I (p)l/ or - - - (p)(Y-1)/1]}1/2 (e.6) Apo Po 'I - Po 3f 1.00!""""~ == rl 0.80 0.60 l' For given values of Po and To, the maximum ma~s flow occurs ~hen t~e velocity at the minimum area or throat equals the velOClty of sound This condItion is called choked or critical flow When the flow is choked the pressure at the throat, PT' is related to the stagnation pressure Po as follows: PT = Po (_2_)1/(1- 1) 'I +1 = 1.4 0.472 I I I 1.0 0.9 I 0.7 0.6 0.528 FIGURE C-3 Relative mass flow rate rh/rh· and compressible flow function C1l [Eq (C.Il)] as function of nozzle or restriction pressure ratio for ideal gas with y = 1.4 (From Taylor ) 910 INTERNAL COMBUmON ENGINE FUNDAMENTALS - Flow coefficients are determined experimentally and are a function of the shape of the passage, the Reynolds number and Mach number of the flow, and the gas properties For a Mach number at the throat less than about 0.7 and for passages of similar shape, the flow coefficient is essentially a function of Reynolds number only Orifice plates are frequently used to measure gas flow rates Standard methods for determining flows through orifice plates can be found in Ref REFERENCES Lichtarowicz, A., Duggins, R K., and Markland, E.: "Discharge Coefficients for Incompressible Non-Cavitating Flow through Long Orifices,~ J Mech Eng Sci., vol 7, no 2, pp 210-219,1965 Taylor, C F.: The Internal Combustion Engine in Theory and Practice, vol I, p 506, MIT Press, 1966 Marks' Standard Handbookfor Mechanical Engineers, 8th ed., McGraw-Hill, 1978 APPENDIX D DATA ON WORKING FLUIDS 011 912 INTERNAL COMBUSTION ENGINE FUNDAMENTALS APPENDIX D DATA ON WORKING FLUIDS TABLE D.I TABLE D.2 Thermodynamic properties of air at low densityt Standard enthalpy of formation and molecular weight of species , T, K 41 c c kJfkg 250 275 409.9 435.0 338.1 356.0 4.4505 4.5187 7.6603 7.7559 38.81 54·14 1849.0 1458.0 1.003 1.003 0.715 0.716 1.401 1.401 300 325 350 375 460.1 485.2 510.4 535.6 374.0 391.9 409.9 427.9 4.5811 4.6385 4.6919 4.7416 7.8432 7.9236 7.9982 8.0678 73.39 97.13 125.9 160.5 1173.0 960.6 797.8 670.8 1.004 1.006 1.007 1.010 0.717 0.718 0.720 0.723 1.400 1.400 1.399 1.397 400 425 450 475 560.8 586.2 611.6 637.2 446.0 464.2 482.5 500.8 4.7884 4.8324 4.8742 4.9139 8.1330 8.1945 8.2527 8.3079 201.4 249.6 305.6 370.4 570.0 488.9 422.7 368.1 1.013 1.016 1.020 1.024 0.725 0.729 0.733 0.737 1.396 1.394 1.392 1.390 500 525 550 575 662.8 688.6 714.5 740.5 519.3 537.9 556.6 575.5 4.9518 4.9881 5.0229 5.0565 8.3606 8.4109 8.4590 8.5053 445.0 530.2 627.1 736.8 322.6 284.3 251.8 224.0 1.028 1.033 1.039 1.044 0.741 0.746 0.752 0.757 1.387 1.385 1.382 1.379 600 625 650 675 766.7 793.0 819.5 846.1 594.5 613.6 632.9 652.3 5.0888 5.1201 5.1503 5.1796 8.5499 8.5929 8.6344 8.6745 860.6 999.5 1155.0 1329.0 200.1 179.5 161.5 145.9 1.050 1.056 1.061 1.067 0.763 0.768 0.774 0.780 1.376 1.374 1.371 1.368 700 725 750 775 872.9 899.8 926.8 954.0 671.9 691.7 711.5 731.6 5.2081 5.2358 5.2628 5.2891 8.7135 8.7512 8.7879 8.8236 1521.0 1735.0 1972.0 2233.0 132.1 119.9 109.2 99.63 1.073 1.079 1.085 1.091 0.786 0.792 0.798 0.804 1.365 1.362 1.360 1.357 800 825 850 875 981.4 1008.9 1036.5 1064.3 751.7 772.1 792.5 813.1 5.3147 5.3397 5.3641 5.3880 8.8584 8.8922 8.9252 8.9574 2520.0 2836.0 3181.0 3559.0 91.12 83.52 76.71 70.58 1.097 1.103 1.108 1.114 0.810 0.816 0.821 0.827 1.354 1.352 1.350 1.347 900 925 950 975 1092.2 1120.2 1148.4 1176.7 833.8 854.7 875.7 896.8 5.4114 5.4342 5.4566 5.4786 8.9889 9.0196 9.0496 9.0790 3971.0 4419.0 4907.0 5436.0 65.07 60.08 55.58 51.49 1.119 1.124 1.129 1.134 0.832 0.837 0.842 0.847 1.345 1.343 1.341 1.339 1000 1025 1050 1075 1205.1 1233.7 1262.3 1291.1 918.1 939.4 960.9 982.5 5.5001 5.5212 5.5419 5.5622 9.1078 9.1360 9.1636 9.1907 6009.0 6629.0 7299.0 8020.0 47.77 44.39 41.30 38.48 1.139 1.144 1.148 1.152 0.852 0.856 0.861 0.865 1.337 1.335 1.333 1.332 1100 1125 1150 1175 1319.9 1348.9 1378.0 1407.1 1004.1 1025.9 1047.8 1069.8 5.5821 5.6017 5.6209 5.6399 9.2172 9.2432 9.2688 9.2939 8797.0 9632.0 10529.0 11490.0 35.90 33.53 31.35 29.36 1.157 1.161 1.165 1.168 0.870 0.874 0.878 0.881 1.330 1.329 1.327 1.326 1200 1436.4 1091.9 5.6585 9.3185 12520.0 27.51 1.172 0.885 1.324 t Abstraclcd ", kJ/(kgoK) P ' .ur Molecular h, kJ/kg welgltt kJ/(kgoK) 'Y with permission from Thermodynamic Properties in SI (Graphs, Tables, and Computational Equations for Forty Substances), by W C Reynolds, Published by the Department of Mechanical Engineering, Stanford University, Stanford, CA 9430S, 1979 Species Oxygen Nitrogen Carbon Carbon monoxide Carbon dioxide Hydrogen Water Water Methane Propane Isooctane Isooctane Cetane Methyl alcohol Methyl alcohol Ethyl alcohol Ethyl alcohol Formula gfmole Statet MJ/kmol kcal/mol N2 C CO 32.00 28.01 12.011 28.01 gas gas solid gas 0 -110.5 0 -26.42 CO 44.01 gas -393.5 -94.05 °2 H2 H 2O H 2O CH4 C 3H s CaH l I CaH l I C l6 H 34 CH 0H 2.016 18.02 18.02 16.04 44.10 114.23 114.23 226.44 32.04 gas gas liquid gas gas gas liquid liquid gas -241.8 -285.8 -74.9 -103.8 -224.1 -259.28 -454.5 -201.2 CH 0H 32.04 liquid -238.6 -57.02 C H 5OH 46.07 gas -234.6 -56.08 C H 5OH 46.07 liquid -277.0 -66.20 t At 298.IS K (2S°C) and I atm.• -57.80 -68.32 -17.89 -24.82 -53.57 -61.97 -108.6 -48.08 913 914 INTERNAL COMBUSTION ENGINE FUNDAMENTALS ~oo I I I i'" I I I N'" "'00 TABLE D.3 Enthalpy of C, CO, CO z , Hz, HzO, N z , Oz N'( 7)- "(198.15) teal/mol 7lI') co c 298 0.000 0.000 0.000 0.000 0.000 0.000 0.000 300 0.004 400 500 0.250 0.569 0.013 0.711 1.417 0.016 0.958 1.987 0.013 0.707 1.406 0.015 0.825 1.654 0.013 0.710 1.413 0.013 0.724 1.455 600 700 800 900 1000 0.947 1.372 1.831 2.318 2.824 2.137 2.873 3.627 4.397 5.183 3.087 4.245 5.453 6.702 7.984 2.106 2.808 3.514 4.226 4.944 2.509 3.390 4.300 5.240 6.209 2.125 2.853 3.596 4.355 5.129 2.210 2.988 3.786 4.600 5.427 1100 1200 1300 3.347 3.883 4.432 4.988 5.552 5.983 6.794 7.616 8.446 9.285 9.296 10.632 11.988 13.362 14.750 5.670 5.917 6.718 7.529 8.350 9.179 6.266 7.114 7.971 8.835 9.706 jltf ~~t;rr;:;~ 7.148 7.902 8.668 7.210 8.240 9.298 10.384 11.495 9.446 10.233 11.030 11.836 12.651 12.630 13.787 14.964 16.160 17.373 10.015 10.858 11.707 12.560 13.418 10.583 11.465 12.354 13.249 14.149 j (',1 - 13.475 14.307 15.146 15.993 16.848 18.602 19.846 21.103 22.372 23.653 14.280 15.146 16.015 16.886 17.761 15.054 15.966 16.882 17.804 18.732 18.638 19.517 20.398 21.280 22.165 19.664 20.602 21.545 22.493 23.446 1400 1500 1600 1700 1800 1900 2000 6.122 6.696 7.275 7.857 8.442 10.130 10.980 11.836 12.697 13.561 16.152 17.565 18.987 20.418 21.857 2100 2200 2300 9.029 9.620 10.212 10.807 11.403 14.430 15.301 16.175 17.052 17.931 23.303 24.755 26.212 27.674 29.141 2400 2500 2600 2700 2800 2900 3000 12.002 12.602 13.203 13.807 14.412 18.813 19.696 20.582 21.469 22.357 30.613 32.088 33.567 35.049 36.535 6.404 17.708 18.575 19.448 20.326 21.210 24.945 26.246 27.556 28.875 30.201 Source: JANAF Thermochemical Tables, National Bureau of Standards Publication NSRDSNBS37,1971 ~1f~ ("\fV"l't"lOONO\ r r r t oor NNNNNN 00'" 1010 NN ili l j]::i "1'l1lf:~t