COMBUSTION CALCULATIONS

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1 COMBUSTION CALCULATIONS

2 COMBUSTION CALCULATIONS Theory, worked examples and problems E. M. Goodger School of Mechanical Engineering. Cranfreld Institute of Technology M

3 ~ E. M. Goodger 1977 All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, without permission. First published 1977 by THE MACMILLAN PRESS LTD London and Basingstoke Associated companies in New York Dublin Melbourne Johannesburg and Madras ISBN DOI / ISBN (ebook) This book is sold subject to the standard conditions of the Net Book Agreement. The paperback edition of this book is sold subject to the conditions that it shall not, by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. iv

4 CONTENTS Preface units Notation vii ix xi 1. INTRODUCTION 1 2. COMBUSTION REACTANTS 3 3. COMBUSTION PRODUCTS 8 4. PROPORTIONS OF REACTANTS AND COOLED PRODUCTS Individual Hydrocarbons Volumetric Fuel Blends Gravimetric Fuel Blends Gas Absorption Analysis Fuel and Mixture Calculation from Product Analysis Physical Characteristics of Mixtures and Products Examples PROPORTIONS OF HOT PRODUCTS Kinetic Equilibrium Equilibrium Product Composition in Hydrocarbon/Air 35 Combustion 5.3 Examples COMBUSTION ENERGIES Standard Energy of Formation Standard Energy of Reaction Calorific Value Maximum Useful Work Examples 55 v

5 7. COMBUSTION TEMPERATURES Sensible Energy Determination of Maximum Temperature in Steady Flow Influence of Fuel Type and Operating Parameters Examples COMBUSTION EFFICIENCIES 8.1 Work Transfer Applications 8.2 Heat Transfer Applications 8.3 Work Transfer Applications 8.4 Examples in Non-flow in Steady Flow in Steady Flow OXIDATION IN THE FUEL CELL 9.1 Reactions at Electrodes 9.2 Examples SlMfARY 11. PROBLEMS References and Bibliography Index

6 PREFACE Examination syllabuses concerned with combustion reactions and their products tend to draw on material appearing in texts on chemistry, physics, thermodynamics, fuel science and the few publications devoted to combustion itself. Furthermore, some aspects of the subject tend to be handled in a 'case law' manner by depending solely on worked examples to illustrate the techniques of solution, whereas a prior general statement of the relevant theory permits much wider application. The objectives of this present book, therefore, are threefold. (1) To assemble in one small volume the key relationships of stoichiometry, thermochemistry and kinetics that apply to the calculation of combustion quantities. (2) To unify these relationships by starting with a general combustion equation, in simple terms of molecular products only, and adapting this systematically to each aspect in turn. (3) To provide solutions in general terms before illustrating their use in examples typical of examination questions met in combustion and allied fields. The motivation for a work of this kind stemmed from experience with examination marking at H.N.C., H.N.D. and first- and higherdegree levels in various branches of engineering and fuel technology, where it has become apparent that questions of this type present difficulties to some candidates. This approach can also serve in professional practice as a reminder of the basic principles involved before turning to the more sophisticated instrumentation and computational techniques available in industry and research. The book opens with a brief review of the main features of atmospheric air and conventional fuels, together with those of the most common combustion products and their methods of measurement. The following chapter deals with the determination of the proportions of reactants, and of the cooled, stable products of combustion. Chapter 5 is concerned with the determination of proportions of hot products that are still reacting but have reached some condition of dynamic equilibrium. Chapter 6 deals with the quantities of energy involved in combustion reactions, and chapter 7 with the temperatures reached under adiabatic, or some other specified, conditions. The efficiency of combustion is covered in chapter 8, whereas chapter 9 indicates the enhanced efficiency realised by electrochemical oxidation in the absence of substantial heat release. All key equations are numbered in sequence, and listed in a final summary. As a general rule, decimal fractions are used, but it has occasionally proved more convenient to include such a term as (~ + y/4) rather than (x + O.2Sy). Worked examples are included at the vii

7 ends of chapters, and a number of problems provided, with answers. SI units are used throughout, and extracts from the wealth of thermochemical data published in kcal/mol have been converted by the relationship (X) kcal/mol = 4.l84(X) kj/mol Acknowledgement is made gratefully to colleagues and students of the University of Newcastle, N.S.W., and the Cranfield Institute of Technology, Bedfordshire, for much valued assistance in discussion and feedback, to the National Bureau of Standards for helpful comments, and particularly to Professor R. S. Fletcher of the Cranfield School of Mechanical Engineering, for the facilities that made this work possible. Cranfield, 1976 E. M. GOODGER

8 UNITS In any system of units, certain quantities are defined as basic to the system, and all further quantities derived from them. If the system is coherent, the products and quotients of any two or more unit quantities themselves become the units of the derived quantities. Thus, in the case of Newton's second law, F = ma, 1 derived unit of force is equal to (1 unit of mass) x (1 unit of length)/(l unit of time)2 One of the most significant developments in this area is the adoption of a rationalised system of metric units known as SI (Syst~me International d'unit~s), which is coherent, with a derived unit of energy common to the mechanical, electrical and most other forms. SI includes the following base units length mass time electric current thermodynamic temperature amount of substance metre (m) kilogram (kg) second (s) ampere (A) kelvin (K) mole (mol) It should be noted that the kelvin is also used for temperature intervals, and that the mole relates to what was formerly cailed the 'gram-mole' and not the 'kilogram-mole' (kmol). SI includes the following derived units force pressure energy power newton (N) = kg m/s2 pascal (Pa) = N/m2 = k~/m s2 joule (J) = N m = kg m /s2 watt (W) = J/s = kg m2/s3 No change is made to any symbol to indicate the plural. SI has been adopted by various industries (for example, Recommended SI units, Institute of Petroleum, London, 1970), some of which also use earlier metric units such as the litre and the bar, which are not part of SI but are considered acceptable. Since the adoption of SI is not yet worldwide, the following conversion factors and other metric relationships are given. length volume mass density 1 ft = m 1 ft 3 = m3 1 U.K. gal = U.S. gal 1 lb = kg 1 tonne = 1000 kg 1 lb/ft3 = kg/m3 ix litre

9 force pressure energy specific energy specific energy capacity volumetric energy power 1 1bf = N 1 1bf/in. 2 = kpa 1 mm Hg = Pa 1 atm = kpa = bar 1 bar = 100 kpa = 105 Pa 1 Btu = kj 1 Chu = kj 1 kca1 (international table) = kj 1 kca1 (thermochemical) = kj 1 kwh = 3.6 MJ 1 hp h = MJ 1 therm = 105 Btu = MJ 1 Btu/1b = kj/kg 1 Btu/1b or = 1 Chu/1b K = kj/kg K 1 Btu/ft 3 = kj/litre (or MJ/m 3) 1 Btu/U.K. gal = kj/litre (or MJ/m 3) 1 hp = W

10 NOTATION When two symbols are given for one item, upper case represents an extensive property (dependent on mass) and lower case a specific property (per unit mass). When one symbol is used for more than one item, the particular meaning in any instance will be apparent from the context. A air mass A, a non-flow availability function A A/F air mass flow rate air/fuel ratio by mass or by volume B, b steady-flow availability function C c C/H CV E e F molar heat capacity specific heat capacity carbon/hydrogen mass ratio calorific value electrical potential charge/electron fuel mass F fuel mass flow rate G, g Gibbs free-energy function (g) GCV (gr) gas gross calorific value graphite H, h enthalpy i ip K k electrical current indicated power equilibrium constant rate constant xi

11 (1) M m iii NCV n n-f p Q, q Ro RAM RMM r S, s (s) s-f T t U, u V, v W, w X x y z ex y t:, liquid number of moles of oxygen/gram of fuel number of moles of oxygen/mole of fuel mass consumption rate net calorific value number of moles of a combustion product/mole of fuel non-flow pressure heat transfer (note: not a property) universal gas constant relative atomic mass (formerly atomic weight) relative molecular mass (formerly molecular weight) ratio entropy solid steady-flow absolute thermodynamic temperature (K) empirical temperature (oc); time internal energy volume work transfer (note: not a property) any oxygen-consuming component of a fuel number of atoms of carbon/molecule fuel number of atoms of hydrogen/molecule fuel number of atoms of oxygen/molecule fuel cut-off ratio in diesel cycle ratio of specific heat capacities finite change xii

12 efficiency equivalence ratio Superscripts o * Subscripts A a ad C standard state of 25 c ( K) and 1 atm concentration basis; theoretical; molar basis algebraic sum of sensible and standard formation air atomisation adiabatic change c combustion; corrected cc F f fg I i j max max useful min 0 0 p P R r combustion chamber fuel formation saturated vapour - saturated liquid initial any arbitrary reactant component any arbitrary product component maximum maximum useful minimum absolute zero temperature; environment observed products pressure (constant) reactants; reverse reaction xiii

13 s T t v, v v WG stoichiometric temperature (either constant, or equal initial and final); total total head volume (constant) volumetric water gas

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