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Effects of propane or ethane additives on laminar burning velocity of methane-air mixtures Hung, Jocelyn 1986

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EFFECTS OF PROPANE OR ETHANE ADDITIVES ON LAMINAR BURNING VELOCITY OF METHANE-AIR MIXTURES by JOCELYN HUNG A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineering We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1986 © JOCELYN HUNG, 1986 In presenting t h i s thesis i n p a r t i a l f u l f i l l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his or her rep-resentatives. It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Mechanical Engineering The University of B r i t i s h Columbia 1956 Main Ma l l Vancouver, Canada V6T 1Y3 Date June, 1986 ABSTRACT Laminar burning velocities of stoichiometric methane-air, ethane-air, propane-air as well as methane with propane and ethane additives have been determined from pressure-time records during combustion i n a constant-volume spherical combustion bomb with central ignition. Additives up to 20 volume percent were used. I n i t i a l pressure ranged from 1 to 8 atm. Results show that these additives increase the burning velocity of methane-air by an amount depending on the concentration and i n i t i a l pressure. Ethane appeared to be more effective than propane for the same volume percent. Two analytical methods were used to deduce the laminar burning velocity: Metghalchi and Keck (M and K) model and linear model. The M and K model i s a procedure to satisfy the conservation of mass and energy for a mixture consisting of two homogeneous regions, burnt and unburnt, separated by a flame of negligible thickness. The linear model, from the assumption that the fractional pressure rise i s linearly proportional to the fractional mass burnt, calculates the burning velocity based on the mass conservation equation. Results from these two methods agree to within 5%. Dissociation reactions, when neglected, were found to give values of burning velocities that are 10% too low. Ionization probes were used to detect flame a r r i v a l times at specific radial locations. Experimental and calculated results agree to within 2%. - i i TABLE OF CONTENTS Page Abstract i i L i s t of Tables v L i s t of Figures v i Nomenclature i x Acknowledgements x 1. Introduction 1 2. L i t e r a t u r e Review 3 2.1 Introduction 3 2.2 Techniques f o r Measuring Burning V e l o c i t i e s 4 2.3 Determination of Burning V e l o c i t y with Constant-Volume Spherical Bomb Method 5 2.3.1 Determination of Burning V e l o c i t y from Expansion Ratio 5 2.3.2 Determination of Burning V e l o c i t y from Direct Measurement of Unburnt Gas V e l o c i t y 9 2.3.3 Determination of Burning V e l o c i t y from Pressure-Time Records 10 2.4 P r e d i c t i o n of S u From T h e o r e t i c a l Models 13 2.5 Summary 13 3. Experimental Design 15 3.1 Apparatus 15 3.2 Procedures 16 3.3 Test Conditions 17 4. Data Reduction Model 18 4.1 Metghalchi and Keck Method 18 4.2 Linear Method 22 5. Discussion 24 5.1 Experimental Results 24 5.2 Comparisons of Methods of Analysis 29 - i i i -TABLE OF CONTENTS (Continued) Page 5.3 Io n i z a t i o n Probe Results 30 5.4 Error Analysis 31 5.4.1 Uncertainties i n Measurements 31 5.4.2 Uncertainties i n Pressure Data 32 6. Conclusions 34 7. Recommendations 35 Tables 36 Figures 45 References • 89 Appendices I. Gas Chromatography C a l i b r a t i o n s 94 I I . I n i t i a l Temperature C a l i b r a t i o n 99 I I I . C a l c u l a t i o n of Stoichiometric C o e f f i c i e n t s 100 IV. Program V e r i f i c a t i o n 107 V. Burnt Gas Properties 113 VI. Linear Model Equation Derivation 115 VII. C a l c u l a t i o n of Error i n Equivalence Ratio 119 - i v -LIST OF TABLES Page Table 1 Composition (mol %) of n a t u r a l gases from d i f f e r e n t regions ... 36 2 Comparisons of r e s u l t s obtained by previous and present investigators on the burning v e l o c i t y of methane-air mixture .. 37 3 Comparisons of r e s u l t s obtained by previous and present i n v e s t i g a t o r s on the burning v e l o c i t y of propane-air mixture .. 38 4 Test mixtures matrix 39 5 I n i t i a l conditions for text mixtures 40 6 Table of c o e f f i c i e n t s of S and 0 for s i n g l e and s p l i t uo , c o r r e l a t i o n 41 7 Comparisons of c o e f f i c i e n t s of S , a and $ with previous work 42 uo 8 Ionization probe test r e s u l t s 43 9 C i r c u i t independence t e s t r e s u l t s 44 - v -LIST OF FIGURES Figure 1 The dependence of laminar burning v e l o c i t y on i n i t i a l pressure f o r mixtures of a i r and methane, ethane, propane (present work) and octane [55]. 2 Laminar burning v e l o c i t y of methane-air mixtures published during 1916 to 1972, as compiled by Andrew and Bradley [8]. 3 Comparisons of burning v e l o c i t y of stoichiometric propane-air mixtures obtained by Metghalchi and Keck, Kuehl and present work. This f i g u r e i s adapted from Ref. 23. 4 Comparisons of predicted and experimental temperature dependence of stoichiometric methane-air mixtures at atmospheric pressure. This fig u r e i s adapted from Ref. 8. 5 Comparisons of predicted and experimental pressure dependence of stoichiometric methane-air mixtures at 298 K. This f i g u r e i s adapted from Ref. 8. 6 Schematic of the experimental apparatus. 7 View of the experimental apparatus. 8 Gas chromatograph c a l i b r a t i o n apparatus. 9 Ionization probe construction. 10 A t y p i c a l i o n i z a t i o n probe s i g n a l . 11 Schematic of combustion bomb showing positions of spark plug, i o n i z a t i o n probes, and pressure transducer. 12 Photograph of the s p h e r i c a l combustion bomb. 13 A t y p i c a l pressure-time record during combustion. 14 Laminar burning v e l o c i t i e s for stoichiometric methane-air mixtures at i n i t i a l pressures of 1,2,4,6 and 8 atm. 15 Laminar burning v e l o c i t i e s f o r stoichiometric ethane-air mixtures at i n i t i a l pressures of 1,2,4,6 and 8 atm. 16 Laminar burning v e l o c i t i e s for stoichiometric propane-air mixtures at i n i t i a l pressures of 1,2,4,6 and 7 atm. 17 Comparisons of laminar burning v e l o c i t i e s for stoichiometric mixtures of methane-air, ethane-air and propane-air at i n i t i a l pressure of 2 atm. - v i -LIST OF FIGURES (Continued) 18 Comparisons of laminar burning v e l o c i t i e s f o r stoichiometric mixtures of methane-air, ethane-air and propane-air at i n i t i a l pressure of 4 atm. 19 Comparisons of laminar burning v e l o c i t i e s for stoichiometric mixtures of methane-air, ethane-air and propane-air at i n i t i a l pressure of 6 atm. 20 E f f e c t s of ethane at various r e l a t i v e percent (%C2H6/CH1+) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 2 atm. A l l mixtures are of stoichiometric proportions. 21 E f f e c t s of ethane at various r e l a t i v e percent (%C2Hg/CH^) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 4 atm. A l l mixtures are of stoichiometric proportions. 22 E f f e c t s of ethane at various r e l a t i v e percent (%C2H6/CHlt) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 6 atm. A l l mixtures are of stoichiometric proportions. 23 E f f e c t s of ethane at various r e l a t i v e percent (%C2Hg/CH,t) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 8 atm. A l l mixtures are of stoichiometric proportions. 24 E f f e c t s of propane at various r e l a t i v e percent (%C2Hg/CH^) on the laminar burning v e l o c i t i e s of methane-air mixtures at an I n i t i a l pressure of 2 atm. A l l mixtures are of stoichiometric proportions. 25 E f f e c t s of propane at various r e l a t i v e percent (%C2H6/CH1+) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 4 atm. A l l mixtures are of stoichiometric proportions. 26 E f f e c t s of propane at various r e l a t i v e percent (%C2H6/CHI+) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 6 atm. A l l mixtures are of stoichiometric proportions. 27 E f f e c t s of propane at various r e l a t i v e percent (%C2Hg/CH^) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 8 atm. A l l mixtures are of stoichiometric proportions. 28 Percent change i n the burning v e l o c i t y of stoichiometric methane-air mixture due to various r e l a t i v e percent of ethane. 29 Percent change i n the burning v e l o c i t y of stoichiometric methane-air mixture due to various r e l a t i v e percent of propane. 30 Comparisons of laminar burning v e l o c i t i e s obtained from M and K model, M and K model without d i s s o c i a t i o n , and l i n e a r model f o r stoichiometric methane-air mixtures. - v i i -LIST OF FIGURES (Continued) 31 Comparisons of laminar burning v e l o c i t i e s obtained from M and K model, M and K model without d i s s o c i a t i o n , and l i n e a r model f o r stoichiometric ethane-air mixtures. 32 Comparisons of laminar burning v e l o c i t i e s obtained from M and K model, M and K model without d i s s o c i a t i o n , and l i n e a r model f o r stoichiometric propane-air mixtures. 33 Comparisons of i o n i z a t i o n probe r e s u l t s with that of the radius-time curves c a l c u l a t e d from M and K and l i n e a r model. The i o n i z a t i o n probes are located at the same radius. (Mixture composition: CH^+0.22 C 3H 8.) 34 Comparisons of i o n i z a t i o n probe r e s u l t s with that of the radius-time curves c a l c u l a t e d from M and K and l i n e a r model. The i o n i z a t i o n probes are located at d i f f e r e n t r a d i i . (Mixture composition: CH^+0.22 C 3H g.) 35 S e n s i t i v i t y of the laminar burning v e l o c i t i e s calculated from M and K model to i n i t i a l temperature and stoichiometry. Actual c o n d i t i o n was: P ± = 1 atm, = 1.00, T ± = 298 K. 36 S e n s i t i v i t y of the laminar burning v e l o c i t i e s calculated from M and K model to i n i t i a l temperature and stoichiometry. Actual c o n d i t i o n was: P ± = 8 atm, = 1.00, T ± = 292 K. 37 Repeatability tests of pressure-time records for stoichiometric methane-air mixtures taken from the same mixing tank (1 tank). 38 Repeatability tests of pressure-time records for stoichiometric methane-air mixtures taken from the two separately prepared mixing tanks (2 tanks). 39 Laminar burning v e l o c i t i e s corresponding to the pressure-time records i n Figure 37. 40 Laminar burning v e l o c i t i e s corresponding to the pressure-time records i n Figure 38. 41 Ty p i c a l d i g i t a l s i g n a l i n micro-scale. 42 Comparison of raw and smoothed pressure data and th e i r slopes. 43 Laminar burning v e l o c i t y plotted against unburnt gas temperature at various N, number of points f o r smoothing. 44 Maximum error introduced from the smoothing technique on the laminar burning v e l o c i t i e s of stoic h i o m e t r i c methane-air mixtures at i n i t i a l pressures of 1 and 8 atm. - v i i i -NOMENCLATURE A Area [m2] E Energy content of mixture [kg/kmol] E^ Expansion r a t i o M Mass of mixture [kg] P Pressure [kPa] R Radius of bomb [cm] S u Burning v e l o c i t y [cm/s] Flame speed [cm/s] T Temperature [K] V Bomb volume [m3] W Molecular Weight e S p e c i f i c energy [kJ/kg] m mass [kg] n f r a c t i o n burnt r radius [cm] t time [msec] x mass f r a c t i o n a temperature dependence c o e f f i c i e n t 8 pressure dependence c o e f f i c i e n t y r a t i o s of s p e c i f i c heats p density <f> equivalence r a t i o Subscript b burnt e end f flame i i n i t i a l u unburnt - i x -ACKNOWLEDGEMENTS I would l i k e to thank Professor P.G. H i l l for h i s supervision of the the s i s and a l s o Professors R.L. Evans, E.G. Hauptmann and Ahlborn f o r the guidance given during my graduate studies. I wish to thank the Environ-mental Engineering Laboratory of the C i v i l Engineering Department f o r allowing me to use the Gas Chromotograph, and i n p a r t i c u l a r , Ms. Paula Parkinson f o r her assistance i n the operation of the instrument. I wish to thank Dr. Teo for advice on the techniques of c a l i b r a t i o n and sampling. This work was supported through a contract from Energy Mines and Resources Canada. - x -1. INTRODUCTION As a f u e l for Internal combustion engines natural gas (consisting p r i m a r i l y of methane) o f f e r s the f o l l o w i n g advantages. It i s r e a d i l y a v a i l a b l e i n North America and r e l a t i v e l y inexpensive. Methane has a higher octane number (130) than gasoline (92); t h i s makes i t possible f o r a methane-fuelled engine to operate at r e l a t i v e l y high compression r a t i o . However, methane has the disadvantage of low c r i t i c a l temperature. Even with high storage pressures, energy density i s low and t h i s tends to l i m i t v e h i c l e range. A more s i g n i f i c a n t disadvantage i s the slow burning v e l o c i t y of methane at engine pressures. The pressure dependence of s t o i c h i o m e t r i c methane-air, ethane-air, propane-air and octane-air mixtures i s shown i n Figure 1. Although the burning v e l o c i t y i n engines Is t y p i c a l l y very dependent on turbulence, the laminar burning v e l o c i t y i s thought to a f f e c t the randomness of i g n i t i o n delay and the combustion dura-t i o n . I t must be recognized that "natural gas" i s not s o l e l y methane and that the other constituents may have s u b s t a n t i a l e f f e c t s on combustion properties and storage density. Knock, f o r example, can be strongly dependent on propane content. The main constituents of natural gas are methane, ethane, and propane. The n a t u r a l gas found i n B r i t i s h Columbia, Canada, consists of 94% (by volume) methane, 3.3% ethane, 1.0% propane, 0.41% other hydrocarbons, and 1.3% other gases. However, the composition varies s i g n i f i c a n t l y over geographic l o c a t i o n s , as shown i n Table 1, and the e f f e c t s of such v a r i a t i o n on the combustion properties of n a t u r a l gas as an engine f u e l have not been f u l l y documented. It i s common practice to 2. extract propane and ethane from n a t u r a l gas before d i s t r i b u t i o n . The question then might be asked; what constitutes the optimum composition f o r engine use? L i t t l e data i s a v a i l a b l e f o r study of combustion properties of relevant mixtures. The laminar burning v e l o c i t y of methane-air mixtures has been deter-mined by many previous investigators using various techniques. However, as shown by Figure 2, the r e s u l t s s c a t t e r over a wide range (± 20%) even f o r standard temperature and pressure. The laminar burning v e l o c i t y corres-ponding to engine pressures and temperatures i s s t i l l more uncertain. In recent years several measurements have been made of the laminar burning v e l o c i t y of propane-air mixtures but no data have been found f o r ethane-air or for methane with propane or ethane a d d i t i v e s . The e f f e c t of pressure and temperature on burning v e l o c i t y of methane and propane have been correlated by various kinds of re l a t i o n s h i p s including power law, but the data was l i m i t e d to the low pressure range (-0.5 < P^ < 4 atm). The objective of the present work was to obtain data on laminar burning v e l o c i t y of methane-air mixtures with propane or ethane additives over a wide range of pressures and temperatures. Measurements were made i n a high pressure s p h e r i c a l combustion chamber with c e n t r a l i g n i t i o n . The burning v e l o c i t i e s were determined by analysis of the rate of pressure r i s e i n the chamber during combustion; i o n i z a t i o n probes were used to confirm the v a l i d i t y of the method of a n a l y s i s . The experimental mixtures were approximately stoichiometric combina-tions with a i r of methane plus up to 20 percent of eit h e r propane or ethane a d d i t i v e . Laminar burning v e l o c i t i e s were measured f o r i n i t i a l pressures of 1 to 8 atm and room temperature. In the case of constant-volume combustion the unburned gas pressures range from 1 to 80 atm, and the temperatures range from 300 to 500K. 3 . 2. LITERATURE REVIEW 2.1 Introduction The laminar burning v e l o c i t y i s property of a premixed gaseous combustible mixture. I t i s defined as the rate at which a plane flame f r o n t propagates, normal to i t s surface, i n t o the unburnt gas. A flame i s the r e s u l t of release of energy associated with a chemical reaction and i s usually made v i s i b l e by the luminosity of the burning gases. A flame front i s the surface separating the luminous zone and the unburnt gases. As the burnt gas expands, v e l o c i t y i s induced i n the unburnt gas. The burning v e l o c i t y i s defined as the difference between the observed flame speed S f and the unburnt gas v e l o c i t y S given by S = S - S . (2-1) u f g The burning v e l o c i t y can also be expressed, based on the mass co n t i n u i t y across a flame f r o n t of n e g l i g i b l e thickness, as , dm . dm, u A^p dt Acp dt * U Z ; f u f u The p r i n c i p a l parameters for the determination of burning v e l o c i t y are mixture composition, mixture strength, pressure, and unburnt gas temperature. This review i s primarily concerned with the determination of burning v e l o c i t i e s of methane-air and propane-air mixtures from pressure-time records f o l l o w i n g c e n t r a l i g n i t i o n of these mixtures i n a s p h e r i c a l bomb. 4. However, other methods and t h e i r t y p i c a l r e s u l t s are a l s o reviewed. No published data on mixtures of ethane-air, or methane-air with propane and ethane a d d i t i v e s were found. 2.2 Techniques f o r Measuring Burning V e l o c i t i e s Methods of measurement f a l l b a s i c a l l y i n t o two categories: those inv o l v i n g stationary flames and those Involving propagating flames. In the stationary flame method the v e l o c i t y of the premixed gas entering a f l a t stationary flame i s the burning v e l o c i t y . Some examples are various types of burners such as c i r c u l a r tube, rectangular slot-type, nozzle and o r i f i c e . Most of the e a r l i e r burning v e l o c i t y data a v a i l a b l e have been obtained by these methods. The methods of measurement and t h e i r d i f f i c u l -t i e s are discussed i n d e t a i l by Andrews and Bradley [1], Garforth and R a l l i s [2], and Gaydon and Wolfhard [3]. In the propagating flame method, the flame tr a v e l s through an i n i t i -a l l y quiescent mixture. One of the e a r l i e s t methods i n v o l v i n g propagating flames i s the tube method. Other methods are the soap bubble or constant-pressure method, which i s possibly the simplest, and the constant-volume sp h e r i c a l bomb method. The.latter i s the technique employed In the present work and w i l l be discussed i n greater d e t a i l i n the fol l o w i n g sections. Andrews and Bradley [1] and Garforth and R a l l i s [2] evaluated various techniques used by previous i n v e s t i g a t o r s . They concluded that the constant-volume s p h e r i c a l bomb method Is the most v e r s a t i l e and accurate. A comparison by Andrews and Bradley [1] of the maximum burning v e l o c i t y data of methane-air mixtures (reported since 1916) revealed a wide sc a t t e r of data (28 < S u < 50 cm/sec, see Figure 2). Measurements of burning v e l o c i t y of stoic h i o m e t r i c mixtures of methane and a i r at standard 5. temperature and pressure, made using the bomb method, range from 31 to 49 cm/s. Of p a r t i c u l a r i n t e r e s t to t h i s work are data obtained at conditions comparable to those of engine operation. Halstead et a l [4] obtained, from a r a p i d compression machine, a burning v e l o c i t y f o r stoi c h i o m e t r i c methane-a i r mixture at 19.4 atm and 710 K of 66 ± 10 cm/sec. Kuehl [5] measured the burning v e l o c i t y of propane-air mixtures over a range of temperatures and equivalent r a t i o s from a modified s l o t burner. At stoichiometry, 1 atm and 311 K, he reported a burning v e l o c i t y of 48 cm/sec. 2.3 Determination of Laminar Burning V e l o c i t y From Constant-Volume  Spherical Bomb The constant-volume s p h e r i c a l bomb method has the advantage of provid-ing burning v e l o c i t i e s over a f a i r l y wide range of pressure and temperature i n a s i n g l e experiment. In t h i s method, the mixture i n a s p h e r i c a l chamber i s i g n i t e d c e n t r a l l y . From the rate of pressure r i s e during explosion, the burning v e l o c i t y can be deduced. Three approaches have been used to measure t h i s property: 1. Determination of density r a t i o or expansion r a t i o during the pre-pressure period, 2. D i r e c t measurement of unburnt gas v e l o c i t i e s and flame speeds, 3. Evaluation of burning v e l o c i t y from pressure-time records. Each method i s now discussed i n turn. 2.3.1 Determination of Burning V e l o c i t y from Expansion Ratio The f i r s t method i s based on the e s s e n t i a l l y i s o b a r i c combustion process during the early stages of flame propagation. The assumptions made are: 1. The combustion process i s adiabatic and at constant pressure, 2. Both burnt and unburnt gases behave as perfect gases, 3. The burnt gas i s at chemical equilibrium, 4. The flame front i s s p h e r i c a l , 5. The pressure i s uniform throughout the combustion bomb. The burning v e l o c i t y S u can be determined from the r e l a t i o n s s - f t . . U P f O and S u = S f / E i i n which p^, p u are the densities of the burnt and unburnt gases, P Q i s the mixture density before combustion, i s the flame speed, i s the expansion r a t i o c a l c u l a t e d from the r e l a t i o n W T, E i - wTF- • <2'3> b u where u , T^ u are the molecular weights and temperatures of the burnt and unburnt gases. The d e r i v a t i o n i s shown i n Appendix V. T y p i c a l l y , the only experimental data i s the flame p o s i t i o n versus time curve which i s recorded by a high speed camera or s c h l i e r e n . The density of the unburnt gas Is assumed to be equal to the mixture density before combustion, since n e g l i g i b l e pressure r i s e (and therefore tempera-ture r i s e ) has occurred. The temperature of the burnt gas i s assumed to be the a d i a b a t i c flame temperature and i s c a l c u l a t e d from thermodynamic r e l a -7. t i o n s . However, the e f f e c t of flame f r o n t thickness and curvature on burn-ing v e l o c i t i e s were shown to be important i n the prepressure period [2,6]. Babkin et a l [6] showed that these e f f e c t s were s i g n i f i c a n t f o r a flame radius less than 3 mm i n stoichiometric methane-air mixtures. Consequently, some inv e s t i g a t o r s corrected f o r t h i s e f f e c t by computing an average burnt gas temperature based on an assumed temperature p r o f i l e across the flame f r o n t . Agnew and G r a i f f [7] determined the burning v e l o c i t i e s of methane-air, propane-air and other mixtures at pressures of 0.5 to 20 atm. They measured flame speed with i o n i z a t i o n probes. The presence of these probes did not appear to have disturbed the flame. They varied the i g n i t i o n energy and concluded that i t d i d not a f f e c t the flame speed. No c o r r e l a -t i o n of the pressure dependence of the burning v e l o c i t i e s of propane-air mixtures was given, but f o r stoichiometric methane-air mixture they reported that t h e i r data were represented by the r e l a t i o n s h i p S u = -6.78 £nP 1 + 32.9 cm/sec Andrews and Bradley [8] measured the flame speed with three o p t i c a l methods - v e r t i c a l k n i f e edge sc h l i e r e n , r e f l e c t i o n p l a t e s c h l i e r e n i n t e r -ferometry and Gayhart-Prescott fine-wire s c h l i e r e n interferometry. A l l three methods were found to give the same value of flame speed. They determined the burning v e l o c i t i e s of methane-air mixtures over a wide range of equivalence r a t i o s . They measured the flame thickness with a Gayhart-Prescott s c h l i e r e n interferometry and showed that the neglect of flame thickness i n the pre-pressure period would lead to values of burning v e l o c i t y that are too low. They expressed the density r a t i o i n the form: 8. nT I u where n i s the number of moles of burnt gas at adiabatic temperature per mole of unburnt gas and i s assumed to be constant across the flame, I i s the c o r r e c t i o n f a c t o r , i s the adiabatic flame temperature and i s the average burnt gas density calculated based on temperature p r o f i l e s previously measured. They showed a c o r r e c t i o n f a c t o r of 1.22 at the flame radius of 25 mm with P = 1 atmosphere, T u = 300 K and a flame thickness of 1.1 mm and 0.75 mm, measured by Dixon-Lewis and Wilson [9] and Janisch [10], r e s p e c t i v e l y . They a l s o found that I was a function of <j>. They correlated the pressure and temperature dependence separately by the r e l a t i o n s h i p i n which P i s i n atm. and T i s i n K. Agrawal [11] photographed flame growth with a r o t a t i n g drum camera. By assuming that the heat released for one mole of f u e l - a i r mixture burnt at constant pressure i s equal to that burnt at constant volume, he expressed the expansion c o e f f i c i e n t as a function of the pressure r a t i o , P e/P^, where P g i s the end pressure. He p l o t t e d with the experimental pressure r a t i o and found that there ex i s t e d a l i n e a r r e l a t i o n s h i p between E. and P /P. represented by the approximation S = 43 P ,-0.5 u S = 10 + 0.000371 T 2 cm/sec u u E., = 0.848 P /P., i e l This approximation enabled him to obtain s o l e l y from experimental radius-time records and pressure r a t i o . He compared the approximate expan-si o n r a t i o s with those computed using Eq. (2-3) and reported a maximum deviation of 1.8%. His r e s u l t s d i f f e r e d by a maximum of 4.5% from those of Agnew et a l and 4.15% from those of Babkin et a l [6]. Gttlder used the density r a t i o method to obtain S U data for a number of f u e l - a i r mixtures including methane and propane-air. He did not present the method of measurement or a n a l y s i s but compared and evaluated c o r r e l a -tions adopted by previous investigators [12]. He proposed the following empirical expression to c o r r e l a t e the burning v e l o c i t y data given by b u uo 4 ; {P } ' o o where S u q = W<j>n exp[-£(<j> - 1.075) 2] . The values of W, n, £, a and 8 are constants f o r a given f u e l . The constants f o r methane-air and propane-air mixtures are given i n Tables 2 and 3 r e s p e c t i v e l y . 2.3.2 Determination of Burning V e l o c i t y From Direct Measurement of Unburnt  Gas V e l o c i t y In the second approach, the unburnt gas v e l o c i t y i s measured with a hot-wire anemometer and the flame growth by o p t i c a l means such as Schlieren or high-speed camera. The burning v e l o c i t y i s obtained from the d e f i n i t i o n (Eq. 2-1) 10. Bradley and Hundy [13] used a hot-wire anemometer to measure the unburnt gas v e l o c i t y i n a c y l i n d r i c a l vessel, 12" i n diameter and 12" i n length, with c e n t r a l i g n i t i o n . Values of S y were obtained for s t o i c h i o -metric methane-air mixture at pressures of 0.25 to 1.5 atm and equivalent r a t i o s of 0.7 to 1.2. Their r e u s l t s were higher than those of previous investigators (see Figure 2). They used a r e f l e c t i o n - p l a t e interferometer f o r flame v i s u a l i z a t i o n and showed "undistorted s p h e r i c a l flame development" i n methane-air mixtures. The assumption of s p h e r i c a l flame propagation has been inve s t i g a t e d by numerous researchers. E l l i s [14], i n 1934, obtained photographs showing s p h e r i c a l propagation from a c e n t r a l i g n i t i o n point i n a s p h e r i c a l glass v e s s e l . For slow-burning mixtures such as carbon monoxide, convective r i s e was observed. Flame fr o n t i r r e g u l a r i t i e s have been observed at high v e l o c i t i e s and pressures i n constant pressure experiments [15,16]. Andrews and Bradley [8] used a hot-wire anemometer to measure the unburnt gas v e l o c i t y i n a sph e r i c a l bomb. They recorded the flame front p o s i t i o n with three d i f f e r e n t o p t i c a l methods as discussed i n 2.3.1. Burning v e l o c i t i e s calculated from density r a t i o method using an average burnt gas temperature (see 2.3.1) and those measured d i r e c t l y compared to within 5%. 2.3.3 Determination of Burning V e l o c i t y From Pressure-Time Records In the t h i r d approach, the pressure h i s t o r y , together with the flame growth records are used to determine burning v e l o c i t i e s from derived equations. These equations are discussed by Lewis and Von Elbe [17] , Fiock 1 1 . et a l [18] , R a l l i s and Tremeer [19] , R a l l i s and Garforth [8], and Metghalchi and Keck [12]. The basic assumptions made were 1. The flame f r o n t i s smooth, th i n , and sp h e r i c a l , 2. The pressure i s uniform throughout the bomb, 3. The unburnt gas i s compressed i s e n t r o p i c a l l y , 4. The burnt gas i s at chemical equilibrium. Garforth [20] used a modified Michelson interferometer system to measure density i n the unburnt gas. He showed the error introduced by assuming a d i a b a t i c compression of the unburnt gas was on the average 1.5%, and did not exceed 3%. Garforth and R a l l i s [21] determined the burning v e l o c i t y f o r stoichiometric methane-air mixtures for pressures of 0.59 to 2.26 atm and temperatures of 29 to 525 K. The e f f e c t of flame thickness was taken i n t o account by using the thick flame equation and they concluded that corrections were important at pressures near the region of the i n i t i a l pressure. For an i n i t i a l pressure of 1 atm, they showed that corrections to burning v e l o c i t i e s were s i g n i f i c a n t only f o r pressures of l e s s than 0.15 MPa. They used the temperature d i s t r i b u t i o n through the flame from burner tes t s given by Dixon-Lewis and Wilson's [9,10] plane flame data to ca l c u l a t e an average burnt gas density. They showed that the neglect of both the temperature and density d i s t r i b u t i o n r e s u l t s i n erro r as large as 12% i n burning v e l o c i t y . No co r r e l a t i o n s for the pressure and temperature dependence were given. Sharma et a l [22] used a r o t a t i n g drum to measure flame growth during combustion. They obtained laminar burning v e l o c i t y of methane-air f o r pressures of 0.5 to 8 atm, temperatures of 300 to 600 K and equivalence r a t i o s of 0.8 to 1.2. They calculated the burning v e l o c i t i e s with s i x 1 2 . d i f f e r e n t equations derived by previous i n v e s t i g a t o r s ( r e f e r to Ref. 21 for d e t a i l s ) . They correlated the pressure, temperature and mixture strength dependence i n t o r e l a t i o n s given by S = C4 (T / 3 0 0 ) 1 , 6 8 / / < l > f o r <b < 1.0 u u r and S u - C4 (T / 3 0 0 ) 1 , 6 8 ^ * f o r <b > 1.0 , where 04 i s a function of <b (see Table 2). Values obtained by t h i s equation compare with r e s u l t s of other i n v e s t i g a t o r s to w i t h i n 4.5 to 34%. However, the natural gas they used contained 94.52% methane, 4.765% ethane, 0.596% propane, and 0.119% other gases but they computed the burning v e l o c i t y assuming the gas to be methane. Metghalchi and Keck [23] determined, from the pressure-time record alone, the burning v e l o c i t y of propane-air for pressures of 0.4 to 40 atm, temperatures 298 to 750 K, and equivalence r a t i o s of 0.8 to 1.5. Their analysis i s based on the conservation of energy and volume. This method of an a l y s i s i s used i n the present work and w i l l be discussed i n greater d e t a i l i n Chapter 5. A curve f i t over the experimental data gave the following pressure and temperature dependence S = 31.9 i ) 2 ' 2 7 ( I - ) " 0 ' 1 7 u VT P o o where T q = 298 K, P = 1 atm. Three ion probes placed at the perimeter of the combustion bomb measured the flame a r r i v a l time and they concluded that the flame i s symmetrical. Comparison of the r e s u l t s with those measured by Kuehl and present work i s shown i n Figure 3. 13. 2.4 Pre d i c t i o n of Burning V e l o c i t y From Theoretical Models In t h e o r e t i c a l studies of laminar flame propagation, a set of d i f f e r e n t i a l equations are obtained from a prescribed r e a c t i o n mechanism. The governing equations are conservation of mass and energy, and species c o n t i n u i t y . These equations are discussed by Spalding [24] and Tsatsaronis [25]. The basic assumptions are n e g l i g i b l e heat loss and i d e a l gas behaviour. However, s o l u t i o n to these equations requires a knowledge of the mechanisms involved and data on chemical k i n e t i c constants such as re a c t i o n rates and transport c o e f f i c i e n t s . In p r a c t i c e i t i s often too expensive to solve the system of relevant equations. Spalding et a l [24] have su c c e s s f u l l y applied a computational procedure o r i g i n a l l y developed for the s o l u t i o n of steady two-dimensional boundary layers equation to solve equations of one-dimensional unsteady flame propagation model. D e t a i l s of the procedure are given i n Ref. 33. Bradley and Hundy [13] attempted to obtain a t h e o r e t i c a l value of S u for methane-air flames from Spalding's expression. Their r e s u l t s suggested that rate-determining r e a c t i o n i s i n the breakdown of the hydrocarbon molecule. Smoot et a l [26] and Tsatsaronis [25] used Spalding's computation procedure to determine the laminar burning v e l o c i t y of methane-air mixtures. They predicted the pressure and temperature dependence and found good agreement with experimental data. However, Tsatsaronis modified the k i n e t i c data to obtain better agreement. The predicted and experimental r e s u l t s are compared i n Figures 4 and 5. 2.5 Summary Experimental r e s u l t s and empirical c o r r e l a t i o n s obtained by various methods and inv e s t i g a t o r s are compared i n Tables 2 and 3. The values of S 14. at 1 atm and 298 K f a l l s i n the range 32 to 46 cm/sec f o r stoichiometric methane-air mixtures. The predicted and experimental pressure and tempera-ture dependence of laminar burning v e l o c i t y f o r methane-air i s shown i n Figures 4 and 5. Only l i m i t e d data i s a v a i l a b l e f o r propane-air mixtures. No data on methane with propane and ethane a d d i t i v e s were found. 15. 3. EXPERIMENTAL DESIGN 3.1 Apparatus A schematic of the experimental set-up and d e t a i l s of the s p h e r i c a l bomb are shown i n Figures 6 and 11. The apparatus consists of a constant-volume s p h e r i c a l bomb, f u e l system, i g n i t i o n system, i o n i z a t i o n probes, and the data a c q u i s i t i o n system. Figure 7 shows a view of the set up. The combustion bomb consisted of two flanged hemispherical sections which when bolted together, form a s p h e r i c a l chamber of 15.24 cm (6.0 i n . ) i n t e r n a l diameter. These sections were cast from a heat-resistant s t a i n l e s s s t e e l (ACI type HK), then machined to the desired dimensions. The design pressure i s 50 atm, with a safety f a c t o r of 4. The design stress of the material i s calculated from supplier's s p e c i f i c a t i o n . A capacitance absolute pressure transducer (MKS type 222BHS) with an accuracy of ±0.3% of reading was used to measure pressures greater than 1 atm. For pressures l e s s than 1 atm, a bourdon gauge accurate to ±0.5 mmHg was used. The mixture strength was determined from the gas chromatograph located i n the Environmental Engineering Laboratory. Mixtures of methane-a i r , ethane-air and propane-air with known compositions over the range of equivalence r a t i o s , 0.0 < A < 1.05, were obtained to c a l i b r a t e the i n s t r u -ment. Each c a l i b r a t i o n mixture was prepared by i n j e c t i n g the predetermined volume of f u e l with a gas-tight syringe i n t o a f l a s k of known volume f i l l e d with test a i r i n i t i a l l y at atmospheric pressure. The apparatus i s shown i n Figure 8. D e t a i l s of the gas chromatograph c a l i b r a t i o n are given i n Appendix I. A standard cap a c i t i v e discharge i g n i t i o n system s i m i l a r to those used i n automobiles was employed. The spark plug, modified from an Auburn 16. i g n l t o r (type 163), together with a s t a i n l e s s s t e e l ground electrode, form a spark gap of 00.13 cm (0.05 in) at the center of the bomb. The t i p s of the electrodes were tapered to a point to ensure c e n t r a l i g n i t i o n . The electrode of the spark plug was covered with a ceramic sheath to prevent sparks from forming across to the bomb wal l . The i o n i z a t i o n probes employed a rod-within-a-tube construction as shown i n Figure 9. The brass electrodes were in s u l a t e d from each other and a p o t e n t i a l of 75 v o l t s was applied across them during operation. The signals were ampl i f i e d and recorded on the os c i l l o s c o p e . The flame a r r i v a l time was assumed to be the time at which a sharp r i s e i n voltage occurred. A t y p i c a l i o n i z a t i o n probe s i g n a l i s given i n Figure 10. The locatio n s of the probes r e l a t i v e to the center of the bomb were measured with a depth gauge placed on f i x e d supports as i l l u s t r a t e d i n Figures 11 and 12. The pressure-time record was measured by an air- c o o l e d AVL piezo-e l e c t r i c pressure transducer, c a l i b r a t e d to give a reading of 0.05 V / p s i . The pressure transducer was located at approximately one diameter from the in s i d e bomb wal l . The pressure s i g n a l was transmitted by a low noise cable to an AVL charge amplifier (model 3059) and then displayed on a Nicole t d i g i t a l storage o s c i l l o s c o p e . The t e s t data were then transferred to an IBM PC and stored on floppy diskettes, which were l a t e r transferred to the host computer (VAX/VMS) f o r processing. A t y p i c a l pressure trace Is shown i n Figure 13. 3.2 Procedures The mixing tank and the f u e l system were f i r s t evacuated with a vacuum pump and then flushed a few times with the a i r used i n the t e s t s . The f u e l and a i r were mixed i n i t i a l l y by p a r t i a l pressures c a l c u l a t e d from the 17. i d e a l gas law. The components, s t a r t i n g with the smallest quantity, were admitted to the mixing tank u n t i l the desired pressures were reached. At le a s t 24 hours were allowed f o r thorough mixing to take place before a sample was drawn for composition a n a l y s i s . From the stoichiometry measured by the gas chromatograph, appropriate corrections were ap p l i e d to the mix-ture. Another sample was taken for analysis a f t e r 24 hours. Corrections continued u n t i l stoichiometry was attained. When the mixture was ready, the combustion bomb was evacuated and flushed a few times with the t e s t mixture. I t was then f i l l e d to the desired i n i t i a l pressure. A waiting time of 10 minutes was allowed for the mixture to become quiescent. To check that t h i s i s s u f f i c i e n t , t e s t s i n v o l v i n g waiting times of 5 to 60 minutes were conducted. No e f f e c t was observed and ten minutes was considered a reasonable i n t e r v a l . A thermo-couple placed on the outside bomb wall was used to Infer the i n i t i a l temperature of the gas i n s i d e . A temperature r i s e as high as 6°C was registered a f t e r an explosion at high i n i t i a l pressure. To determine the gas temperature, a c o r r e l a t i o n with the outside w a l l temperature was estab-l i s h e d as a function of time immediately a f t e r explosion. I t was found that a f t e r 10 minutes, the gas temperature came with i n 1°C of the outside wall temperature which was uniform over the en t i r e surface (see Appendix I I ) . Therefore, a minimum of 15 minutes was allowed between t e s t s . 3.3 Test Conditions Stoichiometric mixtures of methane-air, ethane-air, propane-air, and selected mole f r a c t i o n s of ethane or propane i n methane were tested at i n i t i a l pressures of 1, 2, 4, 6, 8 atm. Table 4 l i s t s the mixture matrix and Table 5 l i s t s the test conditions f or each run. 4. DATA REDUCTION 18. 4.1 Metghalchi and Keck (M and K) Method The p r i n c i p a l method of analysis i s based on that presented by Metghalchi and Keck [12]. The analysis assumes: i ) The flame propagates s p h e r i c a l l y . i i ) The flame front i s smooth and t h i n . i i i ) Pressure i s uniform throughout the bomb. i v ) Both burnt and unburnt gases behave as i d e a l gases. v) The unburnt gas i s i s e n t r o p i c a l l y compressed as the burnt gas i s expanded. v i ) The burnt gas i s at thermodynamic equilibrium. v i i ) There i s no heat transfer u n t i l the end of combustion which i s ind i c a t e d by peak pressure. v i i i ) Combustion i s complete. At any instant during combustion, the mixture i s considered to c o n s i s t of two homogeneous regions - a burnt region at PtT^, and an unburnt region at P»T u « The equations to s a t i s f y are conservation of energy and volume: x 1 E/M = J e f edx + / e bdx o x X 1 V/M = / v f edx + / v bdx O X where M = mass of mixture i n bomb E = energy of mixture i n bomb 19. eb > e u = s p e c i f i c energy of the burnt, unburnt gas v b » v u = s p e c i f i c volume of the burnt, unburnt gas x = mass f r a c t i o n of burnt gas For the unburnt gas: v = v (P,T ) u u u e = e (P,T ) u u u where the pressure P i s obtained experimentally and the unburnt gas temper-ature T u i s c a l c u l a t e d from r e l a t i o n s on i s e n t r o p i c compresion (assumption v ) , u, P, (y -1/Y ) 2_ _ 2 v "u 'u T " C P / u l 1 For the burnt gas: vb = vp>v eb = e b ( p ' V However, the burnt gas i s not a l l at the same state because the gases burnt at d i f f e r e n t times are compressed along d i f f e r e n t isentropes. The burnt gas s p e c i f i c energy and s p e c i f i c volume can be expressed as: % = eb(p>V + 4r> 1 3 2 e h (T-T ) + j ( -) T, 9T2 P b _ ( T - T b ) 2 + T b % = VP«V + <ir> i 3 2 u h (T-T, ) + ± ( -) T 8T2 P b _ ( T - T b ) 2 + T b where T, i s the mass average temperature of the burnt gas: 20. 1 T = - f T, dx b x b o Neglecting terms of order (T-T^) and higher, the conservation equations become: Metghalchi and Keck estimated the error i n x for a temperature spread of 500 K i s l e s s than 0.002 which i s n e g l i g i b l e . The two unknowns, x and T^, are solved by an i t e r a t i v e procedure. Properties of the burnt gas are f i r s t computed from an assumed average burnt gas temperature, T^. The mass f r a c t i o n burnt, x, i s then determined from Eq. (4-1). The volume computed from Eq. (4-2) based on t h i s x was then compared to the actual bomb volume, V. A proportional chopping tech-nique i s then used to reduce the d i f f e r e n c e between the ca l c u l a t e d and actual volume, to 0.1%. When evaluating T^, s i x d i s s o c i a t i o n s reactions are considered: A. CO = CO + 1/2 0 2 E/M = x e b(P,T b) + (1-x) e u(P) (4-1) V/M = x v b ( P , T b ) + (1-x) v u ( P ) (4-2) B. D. C. H 20 = 1/2 H 2 + OH H 20 = H 2 + 1/2 0 2 1/2 N 2 + 1/2 0 2 = NO E. F. = 2 H = 2 0 21. The burning v e l o c i t y , S^t i s obtained from mass c o n t i n u i t y , (Eq. 2-2), S - Mx(t )/p A., u u f and the flamea speed, S^, from the d e f i n i t i o n , S f = dR f/dt From assumption i , the flame area, A^, and the flame radius, R^, can be expressed as: A f = 4rrR f 2 R f = {(3/4) Mxv b}!/ 3 . The advantage of t h i s analysis i s that the pressure-time record and the i n i t i a l c o n d i t i o n are the only experimental data required. A computer program was developed to c a l c u l a t e the laminar burning v e l o c i t y from the pressure h i s t o r y . A progressive burning procedure was used to model the combustion process. The smoothed pressure h i s t o r y was divided i n t o equal time i n t e r v a l s except f o r the f i r s t 8 ms i n t e r v a l which has i n s i g n i f i c a n t pressure r i s e . Procedure for smoothing and i t s errors are discussed i n Chapter 5.4.2. The state of the mixture p r i o r to i g n i t i o n was the i n i t i a l conditions used to obtain the properties of the f i r s t time step. The properties of each subsequent time step were c a l c u l a t e d based on properties of the previous time step. This process continued u n t i l the end of combustion which was assumed to occur at peak pressure. Det a i l s of the c a l c u l a t i o n procedure i s given i n Appendix I I I . 22. The program i s v e r i f i e d by comparing c a l c u l a t e d with known adiabatic temperatures and dissociated species concentrations (see Appendix IV)• A l i s t i n g of the program i s given i n Appendix V I I I . To determine the import-ance of d i s s o c i a t i o n , the d i s s o c i a t i o n reactions were neglected i n the c a l c u l a t i o n of burnt gas temperature and r e s u l t s were compared. 4.2 Linear Method The M and K method involves an elaborate computer model to evaluate the properties of the burnt gas. To obtain an approximate check value of S u > the l i n e a r model i s introduced. In t h i s model, an expression for the burning v e l o c i t y i s derived from the mass co n t i n u i t y f o r the unburnt gas (Eq. 2-2), dm /dt = -S A , / p u u f u to be dependent on pressures only: S = u 1/Y. P - P _ 1/y [ i - c r i p - v c f - ) u ] u 2/3 e o o The d e r i v a t i o n i s shown i n Appendix VI. The major assumption i s that the mass f r a c t i o n burnt i s c a l c u l a t e d from the approximation derived by Lewis and Von Elbe [16] (see Appendix VI for d e r i v a t i o n ) : 23. where P i s the pressure at the end of combustion, and P i s the i n i t i a l e r o pressure. This approximation greatly s i m p l i f i e s the determination of S u, since i t i s independent of the burnt gas properties. 5. RESULTS AND DISCUSSION 2 4 . This chapter presents the r e s u l t s of c a l c u l a t i o n s of the burning v e l o c i t y of methane, ethane, propane, and methane with ethane or propane a d d i t i v e s . In the c a l u l a t i o n s the M and K method of analysis was used except where otherwise noted. Comparisons with previous r e s u l t s as w e l l as the uncertainty of the present r e s u l t s are discussed. The burning v e l o c i t y data are p l o t t e d as functions of unburnt gas temperature T^; the i n i t i a l value of T u i s approximately 300 K i n each case; the test conditions are l i s t e d i n Table 5. Each curve i s the r e s u l t of one i g n i t i o n and the value of T u was determined (as shown i n Section 4.1) from the instantaneous pressure using the i s e n t r o p i c r e l a t i o n s h i p s . 5.1 Experimental Results The burning v e l o c i t i e s of stoichiometric methane, ethane and propane-a i r mixtures of various i n i t i a l pressures are shown i n Figures 14, 15 and 16. For any p a r t i c u l a r run, the burning v e l o c i t i e s were found to increase with increase i n unburnt gas temperature T u except possibly near the end of the run. Comparing d i f f e r e n t runs of the same mixture at a given T u i t may be seen that the burning v e l o c i t y decreases as pressure increases. The r e l a t i v e decrease i n burning v e l o c i t y pressure was greatest f o r methane, lea s t f o r ethane. For an i n i t i a l pressure of 2 atm i t was observed (Figures 14-16, 17-20 and 24) that the form of the S -T curve i s c h a r a c t e r i s t i c a l l y d i f f e r e n t u u from those at other i n i t i a l pressures. This c h a r a c t e r i s t i c was observed for a l l mixtures tested. One possible explanation could be that at a c e r t a i n combination of pressure and temperature some chain-branching r a d i c a l s become active and therefore a l t e r the rate of combustion. At the i n i t i a l stage of combustion when the burnt volume was small, the pressure r i s e was i n s i g i f l e a n t . Therefore, the determination of the pressure-time d e r i v a t i v e (and thus the c a l c u l a t e d value of S u) during that period was uncertain. Consequently, the values of S u shown were not expected to be very accurate for T^ < 350 K. Figures 17 to 19 show comparisons of burning v e l o c i t i e s of methane, ethane and propane at various i n i t i a l pressures. For methane-air combus-t i o n (Figure 14) i t was observed that f o r T y > 450 K the c a l c u l a t e d values of S u began to decline well before the maximum T u ( i . e . maximum pressure) was reached. This tendency was not observed for propane or ethane (Figures 15 and 16). Since the burning v e l o c i t y of methane was found to be the slowest (ethane the f a s t e s t ) , t h i s e f f e c t may be due to buoyancy which could be expected to influence the flame geometry. Above an unburnt gas temperature of approximately 470 K, for methane and methane with propane or ethane additive mixtures (Figures 14, 20 to 27), the burning v e l o c i t y was found to decrease. The flame front of a s p h e r i c a l l y propagating flame would have reached a radius equal to approximately 93% of the bomb radius at 470 K. Therefore, even i f buoyancy e f f e c t s were small, the upper part of the flame could have entered the thermal d i f f u s i o n layer near the chamber wall and became p a r t i a l l y extinguished. The e f f e c t of buoyancy could e xplain why the c a l c u l a t e d values of S^ (which were dependent on the rate of pressure r i s e ) decline r a p i d l y near the end of the combustion period. Consequently, f o r methane-air mixtures, the values of S^ at high T^ (> 450 K) were not considered r e l i a b l e and the best r e s u l t s may be found i n the range 350 < T < 450 K. u Figures 20 to 23 show the e f f e c t s of various ethane concentrations on the burning v e l o c i t i e s of methane-air mixtures for i n i t i a l pressures of 2,4,6 and 8 atm. Figures 24 to 27 show the e f f e c t s of various propane concentrations on the burning v e l o c i t i e s of methane-air mixtures for i n i t i a l pressures of 2,4,6 and 8 atm. For both ethane and propane, the e f f e c t s of trace quantities (< 1% by volume) and quantities up to 20% are presented. Except f o r P = 4 atm (Figures 21, 25) trace q u a n t i t i e s of ethane or propane appeared to have no s i g n i f i c a n t e f f e c t . Even f o r P^ = 4 atm, the differences i n S due to e i t h e r a d d i t i v e were found to be within u experimental uncertainty ( s e c t i o n 5.4) f o r the range 350 < T y < 450 K. In general, there was a smooth progression i n burning v e l o c i t y as the f u e l was v a r i e d from 100% methane to 100% ethane or 100% propane. The mixtures were approximately stoichiometric i n a l l cases. A few burning v e l o c i t y curves (Figures 14, 22, 26) were p a r t i c u l a r l y ragged i n appearance. This occurrence was found to be independent of i n i t i a l conditions or mixture type. Excess noise i n the d i t i a l s i g n a l was believed to be the cause. The author was uncertain of the source of the noise. Figures 28 and 29 show the r e l a t i v e effectiveness of ethane and propane i n increasing the burning v e l o c i t y of stoichiometric mixtures. These curves were approximate f i t s to the experimental data of Figures 20-27 at an unburnt gas temperature of 400 K. I t was observed that: 1) The percent change i n S u increases as the a d d i t i v e concentration was increased. 2) S u b s t a n t i a l increases i n a d d i t i v e concentrations were required to induce s u b s t a n t i a l increases i n S . u 3) The percent changes i n increases as the i n i t i a l pressures was increased. 4) For the same volume percent, ethane appeared to be more e f f e c t i v e than propane i n r a i s i n g burning v e l o c i t y . A p l o t , using logarithmic coordinates, of the burning v e l o c i t y S y against the instantaneous pressure P, at constant T u provides a s t r a i g h t l i n e with slope -B so that S a P " P u S i m i l a r l y , a logarithmic plot of S y versus T u at constant P resulted i n a st r a i g h t l i n e with slope a so that S a T a u u The e n t i r e set of experimentally derived values f o r each f u e l - a i r mixture were f i t t e d to the formula u uo  KT * VP ' o o where P = 101.3 kPa and T = 298 K. The r e s u l t i n g values of S , a and 3 o o uo are given i n Table 6. The standard deviations of the f i t f o r a l l mixtures were 7% at most. S p l i t t i n g the data set into two pressure ranges, 1 < P^ < 4 atm and 4 < P < atm, gave somewhat d i f f e r e n t values of S , ct and 3 as uo shown i n Table 6. Taking experimental uncertainty into account, however, the d i f f e r e n c e s appeared to be i n s i g n i f i c a n t . The standard deviations f o r the split-range f i t s were less than 5%. Comparisons of the present work and previously reported r e s u l t s f o r the pressure and temperature dependence of S y for stoichiometric methane-a i r mixtures are given i n Figures 4 and 5. In previous work, various experimental techiques and methods of data analysis were used to determine S . The pressure and temperature 28. dependence obtained here were c a l c u l a t e d using the power law with a = 1.8 and 8 = -0.3 (Table 6). In both f i g u r e s , even at 1 atm and 298 K, there was at l e a s t 20% spread i n the values of as determined by various i n v e s t i g a t o r s . In view of t h i s , i t was not unexpected that there was a large s c a t t e r i n the high pressure data. The differences are associated with differences i n e x p e r i -mental techniques and methods of data a n a l y s i s . For the bomb technique, Gttlder [12] and Andrew and Bradley [8] a l l reported a pressure c o e f f i c i e n t of -0.5 as compared to -0.3 from the present work. Although the pressure c o e f f i c i e n t s were quite d i f f e r e n t , the values of for the range 1 < P < 10 atm were found to agree to within experimental uncertainty. I t should be noted that these i n v e s t i g a t o r s c a l c u l a t e d the burning v e l o c i t i e s using the density r a t i o method. As discussed i n 2.3, this method was based on the e s s e n t i a l l y constant-pressure combustion process during the i n i t i a l stages of flame propagation. Flame thickness and curvature may have been sources of error i n t h e i r c a l c u l a t i o n s of S^t though the work of Andrews and Bradley [8] may be taken as an i n d i c a t i o n that t h i s i s not so. Comparisons of present r e s u l t s f o r propane-air mixtures with those obtained by Metghalchi and Keck [23], who used b a s i c a l l y the same technique and method of a n a l s y i s , are shown i n Figure 3. It may be seen that the present data agree quite c l o s e l y with the c o r r e l a t i o n of Metghalchi and Keck f o r sto i c h i o m e t r i c propane-air mixtures. These authors have analyzed possible errors due to heat transfer to the outer wall from the unburnt gases, r a d i a t i o n from the burnt gases to the unburnt, heat l o s s to the electrodes, temperature gradients i n the burnt gases, and flame thickness. They found that the possible e r r o r i n S due to each of these e f f e c t s would u be of the order of 1%. Therefore, i t appears that the present method of 29. analysis i s quite accurate. The i o n i z a t i o n probe data (to be discussed l a t e r ) further supports t h i s conclusion. Ryan and Letz [56] have a l s o determined the burning v e l o c i t i e s of propane and methane-air mixtures. Their r e s u l t s , however, were considered questionable because the method of a n a l y s i s they adopted appeared to be i n c o r r e c t . Metghalchi and Keck [23] have concluded that the assumption made by Ryan and Letz of constant volume combustion f o r each time step "leads to an inc o r r e c t value of the entropy for the burnt gas which could i n turn a f f e c t the c a l c u l a t e d flame speeds". 5.2 Comparisons of Method of Analysis Comparisons of the burning v e l o c i t i e s computed from the M and K and l i n e a r models, discussed i n Chapter 4.1 are shown i n Figures 30 to 32. Th absence of d i s s o c i a t i o n reactions f o r the M and K model l e d to a higher computed burnt gas temperature and therefore higher burned gas s p e c i f i c volume at a given pressure. Thus, the mass burned f r a c t i o n required to account f o r a given pressure r i s e would be lower. This i n turn would r e s u l t i n a lower value of S u (which i s proportional to mass burning rate) The e f f e c t due to d i s s o c i a t i o n was found to be quite important. I t s neglect was found to produce a 10% d i f f e r e n c e i n S u, depending on the f u e l and the pressure. Figures 30 to 32 show that the simple l i n e a r model i n which the assumption 30. was made. The value f o r P used i n the c a l c u l a t i o n was the experimental e maximum pressure which was l e s s than the adiabatic pressure due to w a l l heat t r a n s f e r . Agreement between the l i n e a r model and the M and K model was found to be the best at higher pressures because t h i s was the region i n which dP/dt was most accurately estimated. At lower pressures, the agree-ment between these two models was worse because t h i s was the region i n which the estimation of dP/dt was most uncertain. 5.3 Ionization Probes Results The i o n i z a t i o n probes were used to check the flame symmetry. More importantly, they provided a d i r e c t measurement of the flame a r r i v a l times against which the computed values can be compared. Therefore, they are a means to assess the accuracy of the method of a n a l y s i s . By p l a c i n g two i o n i z a t i o n probes at the same radius, one can compare the flame a r r i v a l times - which would be equal i f the flame i s s p h e r i c a l . Two d i f f e r e n t r a d i i were tested and the r e s u l t s are shown i n Figure 33. The signals d i f f e r by approximately 1.2 ms i n both cases. One possible explanation f o r t h i s error i s that there e x i s t s a d i f f e r e n c e i n response c h a r a c t e r i s t i c of the probes. To evaluate the accuracies of the models, experimental flame a r r i v a l times at known r a d i i are compared with those computed using the l i n e a r and M and K models. There i s generally good agreement between the measured and calculated values of e i t h e r model. The r e s u l t s , shown i n Figure 34, appeared to favour the M and K model. However, within experimental error, no conclusion can be drawn as to which model i s better. Since the l i n e a r model i s much simpler to use, i t appeared to provide a good approximation i n the determination of burning v e l o c i t y . 3 1 . 5.4 Error Analysis The maximum erro r from a l l sources on the burning v e l o c i t y i s estimated to be 10%. The contributing factors are discussed i n the fol l o w i n g sections. 5.4.1 Uncertainties i n Measurements The p o t e n t i a l sources of un c e r t a i n t i e s are i n the measurement of equivalence r a t i o s , pressures - time d e r i v a t i v e and i n i t i a l temperature. The maximum error i n equivalent r a t i o s i s estimated to be 1.2%, with 0.9% due to impurities of the gases and 0.3% to errors i n the c a l i b r a t i o n of the gas chromatograph. D e t a i l s of the c a l c u l a t i o n s i s given i n Appendix VII. For small quantities of ad d i t i v e , the error i n the mole f r a c t i o n can be as large as 2%. However, t h i s has i n s i g n i f i c a n t e f f e c t on the value of the equivalence r a t i o . The i n i t i a l pressures are accurate to 0.3% accord-i n g to manufacturer s p e c i f i c a t i o n . The s e n s i t i v i t y of cal c u l a t e d values of S u t o equivalence r a t i o i s shown i n Figure 35. A 1% change i n equivalence r a t i o has v i r t u a l l y no e f f e c t on the burning v e l o c i t y . Because the i n i t i a l temperature was measured by a thermocouple placed on the combustion chamber wall, and because the chamber wa l l temperature rose somewhat with repeated f i r i n g s the thermocouple may not have accurately i n d i c a t e d the temperature of the f r e s h charge entering the chamber. The estimated uncertainty i n the i n i t i a l temperature, allowing f o r t h i s d i f f e r e n c e plus inaccuracy of c a l i b r a t i o n i s estimated to be 2 K. Figure 36 shows the s e n s i t i v i t y of the calculated burning v e l o c i t y to large changes i n the i n i t i a l temperature. Changes i n i n i t i a l temperature s h i f t the e n t i r e curve to one side or the other depending on the sign of the error. The maximum erro r due to a 2 K deviation from the input i n i t i a l temperature i s 1-2%. 3 2 . The r e p e a t a b i l i t y of the pressure h i s t o r y f o r the same prepared mixture (1 tank) and separately prepared mixtures (2 tanks) of the same composition i s shown i n Figures 37 and 38. The corresponding e f f e c t s on burning v e l o c i t i e s are shown i n Figures 39 and 40. The var i a t i o n s i n pressure-time records introduced a maximum uncertainty of 3% on the values of S except at the extremes where the values are most uncertain. The u values at the s t a r t of combustion are subject to errors due to flame thickness and curvature e f f e c t s and those at the end, wall e f f e c t s . Therefore, values at the extreme are not presented and were excluded from the determination of pressure and temperature dependence. 5.4.2 Uncertainties i n Pressure - Time Derivative Smoothing was used to f i l t e r out f l u c t u a t i o n s i n the d i g i t a l s i g n a l s . The pressure s i g n a l i n micro-scale i s shown i n Figure 41. Smoothing was applied to the voltage before conversion to pressure took place. The pressure trace was recorded as 4000 points over the selected time span on the o s c i l l o s c o p e . It was found that no s i g n i f i c a n t pressure r i s e occurred during the f i r s t 8 ms. Therefore, a s t r a i g h t l i n e was f i t t e d over the f i r s t N points corresponding to 8 ms. Subsequent data were a l s o f i t t e d with s t r a i g h t l i n e s , but over every 25 points. Linear regression was performed over each of these i n t e r v a l s . Pressures were computed at the mid-points of each of these regression l i n e s . The smoothed curve was then constructed from these smoothed pressures and the corresponding times. The slopes were computed using the smoothed curve. Comparisons between the raw data and that smoothed by s t r a i g h t l i n e and t h e i r corresponding slopes are shown i n Figure 42. Every 25 points was chosen because i t gave a reason-able mean of the observed f l u c t u a t i o n s not only i n the pressure s i g n a l s , 33. but a l s o i n the r e s u l t i n g burning v e l o c i t i e s . For a large value of N, the burning v e l o c i t y was found to deviate s i g n i f i c a n t l y from the mean values. The e f f e c t of N was i l l u s t r a t e d i n Figure 4 3 . The errors due to the smoothing technique are shown i n Figure 4 4 . They were computed based on a pressure r i s e to the observed values rather than the smoothed values. They were found to d i f f e r by a maximum of 5%. 6. CONCLUSIONS 34. Laminar burning v e l o c i t i e s of stoichiometric mixtures of methane-air, ethane-air, propane-air and methane with ethane or propane ad d i t i v e s were measured i n a constant volume chamber, for pressures of 1 to 80 atm and with unburnt gas temperatures i n the range 300 to 500 K, with an experimental uncertainty of about 10 percent. The pressure and temperature dependence of the burning v e l o c i t i e s were c o r r e l a t e d f o r the whole range of experimental conditions for each f u e l - a i r mixture by the r e l a t i o n s h i p b u uo4 J ^P ; o o with a standard deviation of not more than 7 percent. The v a l i d i t y of the method of c a l c u l a t i o n of burning v e l o c i t i e s from pressure-time data was confirmed by ion-probe measurements of flame a r r i v a l time, by agreement with an independent method of analysis (the l i n e a r model) and by comparison with the determinations of other workers of the burning v e l o c i t y of methane and propane. At a given pressure and temperature and with stoichiometric mixtures, propane and methane add i t i v e s increased the burning v e l o c i t y of methane-air mixtures s u b s t a n t i a l l y . The greatest r e l a t i v e increase i n burning v e l o c i t y was at highest pressure, f o r a given temperature. Trace amounts of propane or ethane do not appear to have s i g n i f i c a n t e f f e c t s on the burning v e l o c i t y . For the same volume f r a c t i o n of a d d i t i v e s , ethane r a i s e s the burning v e l o c i t y of methane-air mixtures more than propane does. 7. RECOMMENDATIONS 35. This work was primarily concerned with pressure e f f e c t s i n a f a i r l y low temperature range. It would be desi r a b l e to extend the experiments to higher temperatures. Because of i n t e r e s t i n the combustion of lean mixtures i n engines, the e f f e c t s of additives should be investigated over a range of equivalence r a t i o s . The possible e f f e c t of buoyancy was not investigated i n the present work. It i s recommended that t h i s be studied, e s p e c i a l l y with slow burning mixtures, with the a i d of a d d i t i o n a l i o n probe measurements. Since error i n i n i t i a l temperature contributed to a s i g n i f i c a n t uncertainty i n the burning v e l o c i t y , d i r e c t measurement of the i n i t i a l mixture temperature should be made. The accuracy of pressure d e r i v a t i v e determination could be improved by using other smoothing techniques such as spline f i t s . 36. Table 1 Composition (mol %) of n a t u r a l gases from d i f f e r e n t regions Region B.C. Canada N. Zealand Kapuni C a l i f o r n i a Netherlands Groningen North Sea Brunei Libya A l g e r i a N i g e r i a 94.0 82.80 87.0 81.3 94.8 88.0 71.4 86.5 88.1 C A 3.3 9.23 8.0 2.85 3.0 5.1 16.0 9.4 6.3 cK «c± 1.0 4.16 1.6 0.39 0.6 4.8 7.9 2,6 2.1 0.2 0.93 0.1 0.13 0.2 1.8 3.4 1.1 0.3 0.15 C CH -n 0.02 0.13 0.1 0.03 0.2 0.2 1.3 0.1 1.1 5 1 2 - i 0.02 C 6 H l < I i 0.01 0.01 CO 0.3 2.07 0.6 0.9 2.1 N 2 1.0 0.68 2.5 14.3 1.2 0.1 0.3 °2 0.1 Table 2 Comparisons of results obtained by previous and present Investigators on the burning velocity of methane-air mixtures Author Ref Approach* Experiment Range S u in cm/sec S u (4-1. P [atm] Equation Correlation „ ,„ „ (. in atm 1 atm, 298K) Agnew & Gralff 3 1 by ion probe 1 0.5-20 298-500 W E i Su»-6.78£nP1+32.9 32.9 cm/s Andrew & Badley 8 1 & 2 8g by optical means by hot wire 0.6-1.6 1-10 298-500 W ' o S f Su= Sf- Sg S =43 P - 0' 5 P > 5 atm Su-10+0.000371 T u 2 43 Garforth & Rallis 2 1 rb- f c P-t by photographs records 1 0.59-2.26 290-525 Thick Flame Eq. - 34 Agrawal 11 1 V * by photographs 0.8-1.2 1-40 298-500 Su=Sf/(0.848 Ji.) - 33.6 Bradley & Hundy 13 5 rb- c  B g by optical means by hot wire 0.7-1.2 0.25-1.5 298-500 V S f S g (S U a P-°'5) 46 Sharma et a l 21 3 Sf P-t by photographs records 0.8-1.2 0.5-8.0 300-600 6 Equations derived by previous Inves-tigators (refer to Ref. 3) Su" CM< Tu / 3 0 0 ) 1" 6 8 / /* +*1'0 S U " C M ( V 3 0 0 > 1 , 6 8 / * * > 1 - ° C^—418+1287/((r-1196/0)2+360/«>3-15o>(log J 0P) 33.3 GUlder Present Work 12 1 3 S f P-t by ion probes records Nc 1 t Avallab 1-80 Le 300-500 W P u S f E/M-xeb+(l-x)eu V/M=xvb+(l-x)vu V S u o < P > B (T u/298) a Suo-42.2o>0'5exp[-5.18(«>-1.075)2] •t,=l:Su-41(P)~0*5(Tu/298)2*0 S U=33(P)~ 0' 3 0 (Ty/298) 1' 8 0 41 33 *1 Density ratio or expansion ratio method 2 Direct measurement 3 From P-t records Table 3 Comparisons of re s u l t s obtained by previous and present Investigators on the burning v e l o c i t y of propane-air mixtures Approach* Experiment Range Author Ref P atm T u K Equation Correlation 1 atm, 298K) Metghalchi & Keck 23 3 P-t records 0.8-1.5 0.4-40 298-750 E/M=xe b+(l-x)e u V/M=xv b+(l-x)v u Suo< P> B< Tu / 2 9 8> a S u-31.9(P)-0.17(T u/298) 2' 1 3 32 Kuehl 5 Modified s l o t burner r b - t P n 0 t 0 8 r a P h u 0.7-1.7 0.25-1.0 311-870 Standard angle method S u-6.036-4.9381og[10'»/T f+900/T 1]p- 0. 02 P i n inHg 48 Gtllder 12 1 Sj by Ion probes N Dt Available W P u S f Su-Suo<P>B(V298>a S u 0 -0.446$ 0 , 1 2expl-4.95(4r-1.075) 2] ()>=l:S u-43(P)" 0- 2(T u/298) 1- 7 7 43 Present Work 3 P-t records 1 1-80 300-500 E/M-xe b+(l-x)e u V/M=xv b+(l-x)v u S U-35(P)"° , 1 3 ( T u / 2 9 8 ) 1 , 6 6 35 *1 Density r a t i o or expansion ratio method 3 From P-t records Table 4 Test mixtures matrix C 2 H 6 C„H 0 3 8 1 0 0 0 1 0 0 0 1 1 0.0070 0 1 0.110 0 1 0.215 0 1 0 0.0076 1 0 0.0090 1 0 0.110 1 0 0.220 Table 5 I n i t i a l conditions f o r t e s t mixtures Mixture P Q kPa T Q °C • 102.45 — _ 1 ^ 202.7 25 1.00 405.6 23 1.00 608.3 25 1.00 811.2 22 1.00 C o H C 118.8 26 1.00 2 6 202.5 22 1.00 405.3 27 1.00 607.7 25 1.00 810.4 21 1.00 C,HQ 101.6 _ 1.01 3 8 202.7 18 1.01 404.9 26 1.01 608.2 — 1.01 696.6 — 1.01 CH,+0.007 C 0H C 108.7 25 1.01 4 2 6 202.5 25 1.01 404.8 25 1.01 607.7 24 1.01 810.2 20 1.01 CH +0.11 C H 104.3 21 1.00 <• 2 6 202.5 18 1.00 405.2 22 1.00 607.7 22 1.00 810.0 19 1.00 CH +0.215 C„H r 104.7 24 1.00 2 6 202.9 23 1.00 405.6 24 1.00 607.7 26 1.00 809.6 22 1.00 CH +0.0076 C H n 169.2 23 1.00 h 3 8 203.1 25 1.00 405.1 22 1.00 607.7 25 1.00 810.2 21 1.00 CH +0.0090 C H „ 109.8 24 1.01 h 3 8 202.8 21 1.01 405.2 27 1.01 607.7 26 1.01 810.1 25 1.01 CH+0.11 C H 104.9 23 1.00 4 3 8 202.9 24 1.00 405.1 22 1.00 607.7 25 1.00 810.5 21 1.00 CH+0.22 C„H Q 102.5 24 1.00 3 8 202.5 25 1.00 405.2 24 1.00 607.6 20 1.00 810.9 18 1.00 41. Table 6 Table of c o e f f i c i e n t s S U Q , a and B for single and s p l i t c o r r e l a t i o n S u = S u o ( T / T 0 ) a (P/P 0)P Stoichiometric 1 < P., < 8 atm 1 < P, < 4 atm 4 < P ± < 8 atm C o e f f i c i e n t C 2 H 6 C,HD 3 8 Suo e a Suo e a Suo B a 1 0 0 32.9 -0.299 1.796 32.5 -0.266 1.796 33.7 -0.315 1.87 0 1 0 34.6 -0.121 1.545 34.6 -0.121 1.56 36.6 -0.183 1.90 0 0 1 34.2 -0.133 1.658 37.6 -0.243 1.94 35.2 -0.117 1.74 1 0.0070 0 32.0 -0.283 1.851 31.5 -0.268 1.82 34.7 -0.331 2.02 1 0.110 0 33.2 -0.259 1.849 32.8 -0.233 1.75 37.6 -0.331 2.14 1 0.215 0 33.5 -0.230 1.770 32.8 -0.215 1.78 35.9 -0.265 1.88 1 0 0.0076 32.3 -0.302 2.028 31.5 -0.294 1.06 32.9 -0.315 2.07 1 0 0.0090 33.3 -0.281 1.826 33.0 -0.268 1.801 36.0 -0.328 2.00 1 0 0.110 33.0 -0.266 1.887 32.3 -0.25 1.88 35.1 -0.299 2.00 1 0 0.220 33.1 -0.255 1.941 32.7 -0.221 1.77 38.2 -0.336 2.28 42. Table 7 Comparisons of c o e f f i c i e n t s of S , a and 8 with previous work Mixture Investigator Suo a 8 CH - A i r Andrew & Bradley [8] 43 — -0.5 GUlder [12] 41 2.0 -0.5 Present Work (1 < ? ± < 4 atm) 33 1.69 -0.27 C 3 H 8 - A i r Metghalchi & Keck [23] 31 2.13 -0.17 Gulder 43 1.77 -0.2 Present Work 1 < P ± < 4 atm 35 1.56 -0.12 Table 8 Ionization probe test r e s u l t s Mixture R l R 2 RUN* fc2 At CH+0.22C H Q *• 3 8 5.06 5.02 1 2 23.00 20.68 24.08 22.14 1.08 1.46 CH,+0.11C,Ho 3 8 2.87 5.09 1 2 12.4 11.9 22.6 22.4 10.2 10.5 CH,+0.11C„H C 4 2 6 2.87 5.09 1 2 13.22 11.58 26.16 24.20 12.94 12.62 Table 9 C i r c u i t independence test r e s u l t s Probe # C i r c u i t # t[ms] At 1 1 30.4 2.0 2 2 28.4 1 2 32.4 2.1 2 1 30.3 45. Figure 1. The dependence of laminar burning v e l o c i t y on i n i t i a l pressure f o r mixtures of a i r and methane, ethane, propane (present work) and octane [ 5 5 ] . 46. • • o n * S o a p t u b e * F B V T M Kernel m m • • Cylindrical Burner • T O T A L A R E A C O N E A N G U • • • I T 0 0 M o i z J * Burner * * A * 4 4 * [5] 4 • [3] • • W5 B20 s » £ o So So YEAR OF PUBLCATKM (A.CO Figure 2. Laminar burning v e l o c i t y of methane-air mixtures published during 1916 to 1972, as compiled by Andrew and Bradley [2]. 47. Figure 3. Comparisons of burning v e l o c i t y of stoichiometric propane-a i r mixtures obtained by Metghalchi and Keck, Kuehl and present work. 48. 150 200 3CO 400 500 6CO 7O0 BOO 900 KXX) UNBURNT GAS TEMPERATURE [K j Figure 4. Comparisons of predicted and experimental temperature dependence of stoichiometric methane-air mixtures at atmospheric pressure. This f i g u r e i s adapted from Ref. 8. 49. ExDerimsntal' o 7 Barb R e s u l t s : • 37 Bart A 6 'Barb I \ • i i • • • **i i i i i i 1 1 ii > I I I — 1 1 1 1 0.1 v 1.0 10 100 Pressure [atm] Figure 5. Comparisons of predicted and experimental pressure depend-ence of stoichiometric methane-air mixtures at 298 K. This f i g u r e i s adapted from Ref. 8. COMBUSTION BOMB CHARGE AMPLIFIER IGNITION SYSTEM IONIZATION PROBE SIGNAL AMPLIFIER OSCILLOSCOPE o CAPACITANCE PRESSURE TRANSDUCER X VACUUM AIR METHANE ADDITIVE Figure 6. Schematic of the experimental set-up. Figure 7 . General overview of the experimental set-up. Figure 8. Gas chromatograph c a l i b r a t i o n apparatus. HIGH VOLTAGE -I CERAMIC INSULATOR Figure 9. Ionization probe construction. Figure 10. A t y p i c a l i o n i z a t i o n probe s i g n a l . 55. Figure 11. Schematic of combustion bomb showing posi t i o n s of spark plug, i o n i z a t i o n probes, and pressure transducer. 5 6 . Figure 12. Photograph showing d e t a i l s of the s p h e r i c a l combustion bomb. 57. F i g u r e 1 3 . A t y p i c a l p r e s s u r e - t i m e r e c o r d d u r i n g c o m b u s t i o n . 58. 60-1 50-40-1 , 3 0 H D CO 20 10 CH4-Air Pl=102.4 KPo PI=202._7_KPa P l=405.6 KPo P l =608 .3 KPa m^mtmw • •> • www • • • •» Pl=811.2 KPa \ •<1 o T 1 1 1 1 i 1 1 1 1 i 1 1 1 1 i 1 1 1 1 i 300 350 400 450 500 Tu[K] Figure 14. Laminar burning v e l o c i t i e s f o r stoichiometric methane-a i r mixtures at i n i t i a l pressures of 1,2,4,6 and 8 atm. Figure 15. Laminar burning v e l o c i t i e s f o r stoichiometric ethane-a i r mixtures at i n i t i a l pressures of 1,2,A,6 and 8 atm. 60. Figure 16. Laminar burning v e l o c i t i e s f o r stoichiometric propane-a i r mixtures at i n i t i a l pressures of 1,2,4,6 and 8 atm. 61. 10-f 300 350 400 Tu[K] 450 500 Figure 17. Comparisons of laminar burning v e l o c i t i e s f o r stoichiometric mixtures of methane-air, ethane-air and propane-air at i n i t i a l pressure of 2 atm. 62. Figure 18. Comparisons of laminar burning v e l o c i t i e s f o r stoichiometric mixtures of methane-air, ethane-air and propane-air at i n i t i a l pressure of 4 atm. 63. Figure 19. Comparisons of laminar burning v e l o c i t i e s f o r s t o i c h i o metric mixtures of methane-air, ethane-air and propane a i r at i n i t i a l pressure of 6 atm. 64. 70 60 50-1 O 40 to 30 20 10 Pi=2atm 0 . 0 0 * C2H6 0.70X_C2H6 11.0* C2H6 21.5X C2H6 PURE C2H6 / 300 350 400 Tu [Kl 450 500 Figure 20. Effects of ethane at various relative percent (%C2Hg/CH^) on the laminar burning velocities of methane-air mixtures at an i n i t i a l pressure of 2 atm. A l l mixtures are of stoichiometric proportions. 65. 70 60 50 3 1 0 30 20 10 Pi=4atm 0 . 0 0 * C2H6 0.70X_C2H6 11.0% C2H6 21.5X C2H6 £PJS_C2H6_ / 300 350 400 Tu[K] 450 500 Figure 21. E f f e c t s of ethane at various r e l a t i v e percent (%C2H6/CH4) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 4 atm. A l l mixtures are of stoichiometric proportions. 66 Pi=6atm 10-300 350 400 Tu[K] 450 500 Figure 22. E f f e c t s of ethane at various r e l a t i v e percent (%C2H6/CH4) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 6 atm. A l l mixtures are of sto i c h i o m e t r i proportions. 67. 60 50 40-1 in 30 20 10-J Pi=8atm 0 . 0 0 * C2H6 0.70X_C2H6 11.0* C2H6 21.5% C2H6 £ U R E _ C 2 H 6 _ S / / S s 300 350 400 450 500 Figure 23. E f f e c t s of ethane at various r e l a t i v e percent (%C2H6/CH^) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 8 atm. A l l mixtures are of stoichiometric proportions. 68. 60-i 50-40-1 , o, 3 V) 30 20 Pi=2oim 0.00X C3H8 0 . 7 6 \ C S H 8 0 . 90% C3H8 11.OX C3H8 t a W B a m • • • «a^BBB» • • • W . O X M H S 10+-F 300 350 400 TuflO 450 500 Figure 24. E f f e c t s of propane at various r e l a t i v e percent (%C2H6/CH^) on the i n i t i a l laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 2 atm. A l l mixtures are of stoichiometric proportions. 69. 60-1 1 . o. 3 in Figure 25. E f f e c t s of propane at various r e l a t i v e percent U C H 6/CH 4) on the Figure ^ P v e l o c i t i e s o f m e t h a n e . a i r m i x t u r e s at an i n i t i a l pressure of A atm. A l l mixtures are of stoichiometric proportions 70. 60 50 40 f , o. 3 30 10 Pi=6atm 0 . 0 0 % C3H8 0 . 90% C3H8 11.0% C3H8 2 2 . 0 % £ 3 H8 PURE C3H8 300 350 400 Tu[K0 — i — 450 500 Figure 26. E f f e c t s of propane at various r e l a t i v e percent (J^Hg/CH^) on the laminar burning v e l o c i t i e s of methane-air mixtures at an i n i t i a l pressure of 6 atm. A l l mixtures are of stoichiometric proportions. 71. Pi=8atm 0.00% C3H8 0.76\C3HB 10 T 1 1 1 1 I 1 • 1 • I 1 1 1 1 I 1 1 1 1 I 1 300 350 400 450 500 TuN Figure 27. Effect of propane at various relative percent (%C2Hg/CH4) on the laminar burning velocities of methane-air mixtures at an i n i t i a l pressure of 8 atm. A l l mixtures are of stoichiometric proportions. Volume Percent of Ethane Figure 28. Percent change i n the burning v e l o c i t y of stoichiometric methane-air mixture due to various r e l a t i v e percent of ethane. 73. Figure 29. Percent change i n the burning v e l o c i t y of stoichiometric methane-air mixture due to various r e l a t i v e percent of propane. -74. Figure 30. Comparisons of laminar burning v e l o c i t i e s obtained from M and K model, M and K model without d i s s o c i a t i o n , and l i n e a r model f o r stoichiometric methane-air mixtures. 75. Figure 31. Comparisons of laminar burning v e l o c i t i e s obtained from M and K model, M and K model without d i s s o c i a t i o n , and l i n e a r model f o r stoichiometric ethane-air mixtures. 76. Figure 32. Comparisons of laminar burning v e l o c i t i e s obtained from M and K model, M and K model without d i s s o c i a t i o n , and l i n e a r model for stoichiometric propane-air mixtures. 77. Legend M a K Modol Llnaor Modal • Ion Prob* 8 2 0 10 20 30 40 50 t [ms] F i g u r e 33 . C o m p a r i s o n s o f i o n i z a t i o n p r o b e r e s u l t s w i t h t h a t o f t h e r a d i u s - t i m e c u r v e s c a l c u l a t e d f r o m M and K and l i n e a r m o d e l . The i o n i z a t i o n p r o b e s a r e l o c a t e d a t t h e same r a d i u s . ( M i x t u r e c o m p o s i t i o n : CH^+0.22 C3H3. ) 78. T " 1 10 20 1 i ' 30 40 50 t [ms] F i g u r e 34. C o m p a r i s o n s o f i o n i z a t i o n p r o b e r e s u l t s w i t h t h a t o f t h e r a d i u s -t i m e c u r v e s c a l c u l a t e d f r o m M and K and l i n e a r m o d e l . The i o n i z a t i o n p r o b e s a r e l o c a t e d a t d i f f e r e n t r a d i i . ( M i x t u r e c o m p o s i t i o n : CH^+0.22 C ^ H g . ) 79. 2 5 300 350 400 Tu[K] 450 500 Figure 35. S e n s i t i v i t y of the laminar burning v e l o c i i t e s calculated from M and K model to i n i t i a l temperature and s t o i c h i o -metry. Actual condition was: P. = 1 atm, = 1.00, 298 K. T . = l 80. 10-300 350 400 Tu[K] 450 500 Figure 36. S e n s i t i v i t y of the laminar burning v e l o c i t i e s calculated from M and K model to i n i t i a l temperature and s t o i c h i o -metry. Actual condition was: 292 K. P. = 8 atm, = 1.00, T. = l ' ' i 81. 10 20 i 30 'I 1 1 1 40 50 60 i 70 t [ms] Figure 37. Repeatability t e s t s of pressure-time records for stoichiometric methane-air mixtures taken from the same mixing tabk (1 tank). 82. 4000-3500-3000-2500-X 2000-1500 1000-500 2 Tanks R u n 1 t o n k 1 R u n _2_*ank J R u n 1 t o n k 2 R u n 2 t a n k 2 10 2 0 30 40 50 t [ms] 60 70 • • i Figure 38. Repeatability t e s t s of pressure-time records f o r stoichiometric methane-air mixtures taken from the two separately prepared mixing tanks (2 tanks). Figure 39. Laminar burning v e l o c i t i e s corresponding to the pres time records i n Figure 37. 10 H o f i i i i i • i • • i •' • • •—I 1 1 1 1 i 300 350 400 450 500 Tu[K] Figure 40. Laminar burning v e l o c i t i e s corresponding to the pressure-t records i n Figure 38. 85. Figure 41. T y p i c a l d i g i t a l s i g n a l i n micro-scale. 8 6 . Figure 42. Comparison of raw and smoothed pressure data and t h e i r slopes. 87. 300 250 400 450 500 55U Unburnt Gas lemperature T w [K] Figure 43. Laminar burning v e l o c i t y plotted against unburnt gas temperature at various N, number of points f o r smoothing. 88. 6 0 -5 0 -4 0 £ , U, 3 CO 3 0 2 0 -1 0 Legend Smoo1h*d , Pl = 1olm E r r o r , P_l = 1 o|_m _ S m o o l h « d , P1=8atm E r r o r ; P I=8atm 3 0 0 3 5 0 4 0 0 Tu[K] 4 5 0 5 0 0 Figure 44. Maximum error introduced from the smoothing technique on the laminar burning v e l o c i t i e s of stoichiometric methane-a i r mixtures at i n i t i a l pressures of 1 and 8 atm. 89. REFERENCES [I] Andrews, G.E., Bradley, D., "Determination of burning v e l o c i t i e s : A c r i t i c a l review", Combustion and Flame 18, 1972, 133-153. [2] Garforth, A.M., R a l l i s , C.J., "The determination of laminar burning v e l o c i t y " , Progress i n Energy and Combustion Science, V o l . 6, 1980, 303-329. Gaydon, A.G., Wolfaard, H.G., "Flames, t h e i r structure, r a d i a t i o n and temperature", Chapman and H a l l , London (1953). Halstead, M.P., Pye, D.B., Quinn, CP., "Laminar burning v e l o c i t i e s and weak flammability l i m i t s under engine-like conditions", Combustion and Flame 22, 1974, 89-97. Kuehl, D.K., "Laminar burning v e l o c i t i e s of propane-air mixtures", Eighth Symposium (Int.) on Combustion, I960, 510-521. Eschenbach, R.C., Agnew, J.T., "Use of the Constant Volume Bomb Technique f o r Measuring Burning V e l o c i t y " , Combustion and Flame 2, 1958, 273-285. Agnew, J.T., G r a i f f , L.B., "The pressure dependence of laminar burning v e l o c i t y by the s p h e r i c a l bomb method", Combustion and Flame 5, 1961, 209-219. [8] Andrews, G.E., Bradley, D., "The burning v e l o c i t y of methane-air mixtures", Combustion and Flame 19, 1972, 275-288. [9] Dixon-Lewis, G., Wilson, M.J.W., Trans. Faraday Soc. 1106, 1957, 47. Cited by Andrews and Bradley [2]. [10] Janisch, G., Cheme-Ing. Techn. 561, 1971, 43. Cited by Andrews and Bradley [2]. [II] Agrawal, D.D., "Experimental determination of burning v e l o c i t y of methane-air mixtures i n a constant volume ve s s e l " , Combustion and Flame 42, 1981, 243-252. [12] GUlder, O.L., "Correlations of laminar combustion data for a l t e r n a t i v e S.I. engine", unpublished. [13] Bradley, D., Hundy, G.F., "Burning v e l o c i t i e s of methane-air mixtures using hot wire anemometer i n closed-vessel explosions", Thirteenth Symposium (Int.) on combustion, the Combustion I n s t i t u t e , Pittsburgh, 1971, 575-583. [14] Spalding, D.E., Stephenson, P.L., Taylor, R.G, A C a l c u l a t i o n Procedure f o r the P r e d i c t i o n of Laminar Flame Speeds, Combustion and Flame 17, 1971, 55-64. [3] [4] [5] [6] [7] 9 0 . [15] Linnett, J.W., "Methods of measuring burning v e l o c i t i e s " , Fourth Symposium (Int.) on Combustion, Williams and Wilkins, Baltimore, 1953, 20-35. [16] E l l i s , O.E., Morgan, E., Trans. Faraday Soc. 30, 1934, 287. Cited by Lewis and Von Elbe [16]. [17] Lewis, B., von Elbe, G., "Combustion, Flames and Explosions of Gases, Academic Press: New York, 1951. [18] Flock, E.F., Marvin, C.F., "The measurement of flame speeds", Chem. Rev. 21, 1937, 367-387. [19] R a l l i s , C.J., Tremeer, G.E.B., "Equations for the determination of burning v e l o c i t y i n a s p h e r i c a l constant volume ve s s e l " , Combustion and Flame 7, 1963, 51-61. [20] Garforth, A.M., "Unburnt gas density measurement i n a s p h e r i c a l combustion bomb by i n f i n i t e - f r i n g e l a s e r Interferometry", Combustion and Flame 26, 1976, 343-352. [21] Garforth, A.M., R a l l i s , C.J., "Laminar burning v e l o c i t y of stoichiometric methane-air: Pressure and temperature dependence", Combustion and Flame 31, 1978, 53-68. [22] Sharma, S.P., Agrawal, D.D., Gupta, CP., "The pressure and temperature dependence of burning v e l o c i t y i n a s p h e r i c a l combustion bomb", Eighteenth Symposium (Int.) on Combustion, The Combustion I n s t i t u t e , 1981, 493-501. [23] Metghalchi, M., Keck, J.C., "Laminar burning v e l o c i t y of propane-air mixtures at high temperature and pressure", Combustion and Flame 38, 1980, 143-154. [24] Babkin, V.S., Kozachenko, L.S., Kuznetzov, J.L., P.M.T.F. 3, 1964, 145. Cited by Bradley, D., Hundy, G.F., Ci t e d by Lewis and Von Elbe [16]. [25] Tsatsaronic, G., "Prediction of propagating laminar flames i n methane, oxygen, nitrogen mixtures", Combustion and Flame 33, 1978, 217-239. [26] Smoot, L.D., Hecker, W.C., Williams, G.A., "Prediction of propagating methane-air flames", Combustion and Flame 26, 1976, 323-342. [27] Edmondson, H., Heap, M.P., "Ambient Atmosphere E f f e c t s i n Flat-Flame Measurements of Burning V e l o c i t y " , Combustion and Flame 14, 1970, 195, Cited by Garforth, R a l l i s , [8]. [28] Fristrom, R.M., Westenberg, A.A., "Flame structure", McGraw-Hill Book Co., New York, 1965. [29] Edmondson, H., Heap, M.P., "The burning v e l o c i t y of methane-air flames i n h i b i t e d by methyl bromide", Combustion and Flame 13, 1969 472-478. 91. [30] Flock, E.F., "A survey of combustion research i n the chemical back-ground f o r engine research", (Eds. Burk, R.E. and Grummit, 0.), Fr o n t i e r s i n Chemistry, Vol. I I . , Interscience Publishers, New York, 1943, 1-53. [31] Maxworthy, T., Phys. F l u i d s 5, 1962, 407. Cited by Andrew and Bradley [1]. [32] Gerstein, M., Levine, 0., and Wong, E.L., J . Am. Chem. Soc. 73, 1951, 418. Cit e d by Andrew and Bradley [1]. [33] Henderson, H.T., H i l l , G.R., J . Phys. Chem. 60, 1956, 874. Cited by Andrew and Bradley [1]. [34] Egerton, A.C., Lefebvre, A.H., Proc. Roy. Soc. (London), Ser. A 222, 1954, 206. Cite d by Andrew and Bradley [1]. [35] Stevens, F.W., NACA Rept. Nos. 208, 305, 337, 372, 1923-1930; J . Am. Chem. Soc. 50, 1928, 3244. C i t e d by Andrew and Bradley [1]. [36] Strauss, W.A., Edse, R., "Burning V e l o c i t y Measurements by the Constant Pressure Bomb Method", Seventh Symposium (Int.) on Combustion, Butterworth, London, 1959, 377. [37] Simon, D.M., Wong, E.L., "An Evaluation of the Soap Bubble Method f o r Burning V e l o c i t y Measurements Using Ethylene-Oxygen-Nitrogen and Methane-Oxygen-Nitrogen mixtures", NACA Tech. Note 3106, February, 1954. Cit e d by Garforth and R a l l i s [8]. [38] Babkin, V.S., and Kozanchenko, L.S., "Combustion Explosion and Shock Waves", 2, 1966, 46. [39] Babkin, V.S., Kuzoretsov, I.L, Kozanchenko, L.S., "Influence of Curvature on the Rate of Propagation of a Laminar Flame i n a Lean Propane/Air Mixture." Dokl. Akad. S c i . SSR 146(3), September 1962, 625-627; E n g l i s h Translation, Proc. Acad. S c i . USSR, Phys. Chem. Soc. 146, 1962, 677-679. Cited by Garforth and R a l l i s [8]. [40] Barrassin, A., L i s k e t , R., Combourieu, J . and L a f f i t t e , P., B u l l , de l a Societe Chimique de France, No. 7, 1967, 2521. Cited by Andrews and Bradley [2]. [41] Dugger, G.L., "Effe c t of I n i t i a l Temperature on Flame Speed of Methane-Air, Propane-Air and Ethylene-Alr Mixtures", NACA Rep. 1061, 1952. Cited by Andrews and Bradley [2]. [42] Halpern, C , J . Res. N a t l . Bur. Std. 60, 1958, 535. Cited by Andrews and Bradley [2]. [43] Johnston, W.C., Soc. Auto. Eng. J . 55, 1947, 62. Cited by Andrews and Bradley [2]. [44] Passauer, H., Gas und Wasserfach 73, 1930, 313. Cited by Andrews and Bradley [2]. 92. [45] Clingman, W.H., and Pease, R.N., J . Am. Chem. Soc. 78, 1956, 1775. Cited by Andrews and Bradley [2]. [46] Diederichsen, J., and Wolfhard, H.G., Trans. Faraday Soc. 52, 1956, 1102. C i t e d by Andrews and Bradley [ 2 ] . [47] G i l b e r t , M., Sixth Symposium (Int.) on Combustion, Reinhold. New York, 1957, 74. Cit e d by Andrews and Bradley [2]. [48] Egerton, A.C. and Lefebvre. A.H. Proc. Roy Soc. (London), 222A, 1954, 206. C i t e d by Andrews and Bradley [2]. [49] Manton, J. and M i l l i k e n , B.B., Proc. Gas Dynamics Symposium on Aerothermochemistry, Northwestern U n i v e r s i t y , Evanston, I l l i n o i s , 1956, 151. Cited by Andrews and Bradley [2]. [50] Singer, J.M., Grumer, J., and Cook, E.B., Proc. Gas Dynamics Symposium on Aerothermochemistry, Northwestern U n i v e r s i t y , Evanston, I l l i n o i s , 1956, 139. Cited by Andrews and Bradley [2]. [51] Unpublished. [52] Benson, R.S., "Advanced Engineering Thermodynamics", 2nd E d i t i o n , Pergamon Press, 270-271. [53] Benson, R.S., "Internal Combustion Engine", Pergamon Press, 40. [54] Van Wylen, G., Sonntag, R.E., "Fundamentals of C l a s s i c a l Thermodynamics", 2nd E d i t i o n , John Wiley and Sons, 683-684. [55] Evans, R.L., Report APL-83-04, Univ e r s i t y of B r i t i s h Columbia, 1983. [56] Ryan, Thomas, Lextz, X., "The Laminar Burning V e l o c i t y of Iso-octane, N-Heptane, Methanol, Methane, and Propane at Elevated Temperature and Pressures i n the Presence of a D i l u t e n t " , Combustion and Flame 31, 1978, 53-68. 93. APPENDIX: I Gas Chromatograph C a l i b r a t i o n II I n i t i a l Temperature C a l i b r a t i o n I I I Computer Program C a l c u l a t i o n Procedures IV Program V e r i f i c a t i o n V Expansion C o e f f i c i e n t Derivation VI Linear Model Equation Derivation VII C a l c u l a t i o n of E r r o r s i n Equivalence Ratio 94. APPENDIX I - GAS CHROMATOGRAPH CALIBRATION The gas chromatograph used a sing l e Parapak Q column to separate the hydrocarbons and a i r . Each component i s i d e n t i f i e d by the retention time, time for the component to go through the column, which i s a function of column temperature. The component then goes through a wheat-stone bridge detector. The change i n resistance due to the presence of the component produces a peak on the recorder. The area under t h i s peak i s proportional to the volume i n j e c t e d . Thus, the volume percent can be determined from the area percent. Three chromatograms of the same mixture i s shown i n Appendix IA. The r e p e a t a b i l i t y i n the area percents was found to be within 0.3%. The c a l i b r a t i o n curves are shown i n Appendix IB, IC and ID. APPENDIX IA T y p i c a l O u tput from Gas Chromatograph I N J I RT i . 27 3. 26 S T O P TVPE HP 33600 DL V OFF NV. 't l ! t » 1. 27 =— 3. 26 17. ~l - -4 - 9 ? RRER X AREA 326128 19667 STOP 2« H i IN LUU 94. 31 5. 687 L a R F J F C T OFF r l 14J / • 1. 28 3. 29 RT 1. 28 3. 29 HP 3388R DLV OFF MV/H . 39 'STOP TVPE RRER 7. RRER 326785 19683 STOP 15 RTTN LOG 94. 32 5. 681 REJECT OFF 1NJ J RT 1 28 3 30 STOP TVPE HP 3388R DLV OFF 1. 28 3. 30 RRER V. RRER 327992 19758 STOP 15 94. 32 5. 679 PEJECT OFF APPENDIX IB Calibration Curve for Methane-Air ea of Methane i n n o . Area of Air x 1 0 0 % APPENDIX IC Calibration Curve for Ethane-Air APPENDIX ID C a l i b r a t i o n Curve for Propane-Air E. © 1 2 3 4 5 £ 7 ea of Propane i n n i Area of A i r x w o % APPENDIX II - INITIAL TEMPERATURE CALIBRATION TIME TEMPERATURE °C TRAIL (min) BOMB GAS 1 0 24 32 5 22 24 7 22 23 10 21 23 13 21 23 2 0 33 38 5 30 33 10 30 31 15 29 30 3 0 30 31 5 29 30 11 27 28 23 26 26 100. APPENDIX I I I - COMPUTER PROGRAM CALCULATION PROCEDURES 1. C a l c u l a t i o n of Stoichiometric C o e f f i c i e n t s For complete combustion of NCH kmol of hydrocarbon f u e l , C ^ H ^ , with AC kmol of a d d i t i v e , C ^ L ^ at a r e l a t i v e a i r to f u e l r a t i o , the combustion equation i s : ( N C H ^ H ^ + (AC)C CH H + (02) ) 2 + (N2)N 2 (C)2)C0 2 + (H20)C0 2 + (N2)N 2 (E02)0 2 where () are stoichiometric c o e f f i c i e n t s for complete combustion. In program, Program Symbol 02 = number of kmols of 0 2 i f <j> =• 1 02T1 = t o t a l number of kmols of 0 2 • 0 2 N2 = number of kmols of N 2 i f $ = 1 N2T1 " t o t a l number of kmols of N 2 = N 2 E02 - number of kmols of unburnt 0 2 = 0 for <p > 1 Mass balance f o r each element gives: C02 = CN + C*AC H20 = (HM + H*AC) 12 02 - (2*C02 + H20)/2 N2 - 3.76*02 E02 = (2*LAM*02 - 2*C02 - H20)/2 The t o t a l number of kmols of reactants, SUMNS, i s : SUMNS = NCH + AC + 02T1 + N2T1 1 0 1 . 2. Calculation of Burning Velocity Pressure data are divided into equal time intervals. For each input pressure subroutine COMB i s called to calculate properties of the burnt and unburnt gas. Properties at the end of a time interval become properties at the beginning of the next time interval. Changes i n mass fraction burnt, and hence the mass fraction burnt rate (DXPR) can be calculated. The burning velocity, S u, and the flame speed, S^, can be obtained from: S = Mx(t)/p A, u u f S f = dRf/df where M • total mass of mixture i n Kg, • X ss mass fraction burnt rate i n s e c - 1 , p u = density of the unburnt gas in Kg/m3, A f flame front area in m2, R f flame front radius i n m. From the spherical flame front assumption, the flame radius can be expressed as: R f - [ 3 / 4 T r)v b]l / 3 where V^ • volume of the burnt gas = Mxv, [m3] 102. The flame area Is: A f - 4irR f 2 . The burning velocity can be rewritten as: S u(t) = [Mx(t ) p u ] / [ 4n ( 3Mxp b / 4 T r)l / 3 The unknowns, specific volumes, v u > v^, and mass fraction burnt as a function of time, x(t), are calculated in subroutines COMB, ENRCT, and ENERGY. 3. Calculation of Properties Subroutine ENRCT and ENERGY calculate the specific energy, specific volume, mole fraction of each component, gamma and specific heats of the unburnt and burnt gases at a given temperature and pressure. Assumptions A mixture of gases i s considered to be comprised of ideal gases which obey the following: i) The gas mixture as a whole obeys the equation of state, PV=Nm^xRT, where N ^ y i s the total number of kmols of components. i i ) The total pressure of the mixture equals the sum of the pressures each component would exert i f i t alone occupied the whole volume at the same temperature. i i i ) The internal energy and enthalpy of the mixture equals the sum of the internal energy and enthalpies each component would have i f It alone occupied the whole volume at the same temperature. 1 0 3 . 3.1 Calculation of Mixture Energy From assumptions ( i i ) and ( i i i ) , the energy equation i s : Energy of Mixture = I Energy of component " * n i ( * * T , P ~ * T ) i [ K J ] where n^ «* number of kmols of the i * " * 1 component h T • enthalpy at temperature and pressure T,P R • universal gas constant - 8.314 [KJ/KMOL K] The specific energy of the unburnt gas (SEU) and the burnt gas (SEB) are calculated as: e u " Z lni<Vp-*T)i/MlReactants [ K J / K G ] SEU « EU/MRCT in program e b ' 1 tVYp-* T )i / Mlproducts [KJ/KG] SEB « EB/MPROD in program where MRCT - mass of the reactants MPROD = mass of the products The enthalpies h_ are given by h T > p = hj + Ah 104. enthalpy of formation at 0.1 MPa, 298K difference of enthalpy from the reference state of .1 MPa, 298K The delta h values of each of the reactants (DHR) and products (DH) are found using equations given i n Ref. 50,51 and values from expressions given i n Ref. 52. The components of the unburnt gas are the reactants, C ^ r L ^ , c Q H ^ » 0 2 and N 2« The components of the burnt gas are the dissociated products, C0 2 H20, N 2, 0 2, CO, 0, H2, OH, H, NO. 3.2 Dissociation Calculations The dissociation reactions considered are: a) C0 2 <—> CO + 1/2 0 2 - A A 1/2 A b) H20 <—-> 1/2 H 2 + OH -B 1/2 B B c) H20 <—i> H 2 + 1/2 0 2 -C C 1/2 C d) 1/2 N 2 + 1/2 0 2 <—> NO -1/2 D -1/2 D D e) H 2 <—> 2H -E 2E f) 0 2 <—> 20 -F 2F where h f Ah 105. where A,B,C,D,E,F, are the change i n kmols of each component due to dissociation. For a dissociation reaction A . B X v C . D v + v. <—> v + v, a b c d a dissociation equation can be written in the form yC C * yD d K yA V f l ' y B V b P v c + Vd - va " vb P o where P° i s the standard pressure 0.1 MPa, K i s the equilibrium constant found by f i t t i n g curves of the form InK • A+B(lnT) C to the data given i n Ref. 52 and y^ is the mole fraction of the 1 component given by: y i " l x i If K,L,M,N represents the number of kmols of C0 2, H20, unburnt 0 2 > and N 2, respectively, before dissociation, the number of kmols of each component after dissociation are given by: Program Symbols x ( i ) = CO, = K-A X(2) S CO •= A X(3) B H,0 L-B-C X(4) = H* - C+B/2-E X(5) °2 B M-F+(A+C-] X(6) 8= N2 B N-D/2 X(7) s NO = D X(8) H = 2E X(9) = 0 B 2F X(10) OH = B S=ZX(i) = K+L+M+N+(A+B+C)/2+E+F 106. Therefore the s i x d i s s o c i a t i o n equations are: A+C-D.^ n Program Symbol KC0 2 a) C0„ — ^ = = KA v S ' P^ •^ -+C-E ( 2 _ ) l / 2 *H 0<0H) b) HO(OH) = — = KB rL-B-C,l P 1/2 I — — J p-( V - ) 1 C r 2 — ) V < 0 2 > c) H 2 0 ( 0 2 ) ^ - — - KC rL-B-C,l P 1/2 I S ' P75" d) N, ( N-D/2)l/2 M-F+( ^ ) 1 / 2 KD e) H„ = = KE .C-rB/2-E-, 2 s J f ) P~~ P*" KF APPENDIX IV - PROGRAM VERIFICATION Given: Fuel = 1 kmol of C^ 4> - 1.0 i n i t i a l pressure = 101.3 KPa i n i t i a l temperature • 298 K 1. Stoichiometry Given a reaction: CH^ + a 0 2 + bN £ • cC0 2 + dH 20 + eN £ + f 0 2 > the stoichiometric c o e f f i c i e n t s a,b,c,d,e, and f can be determined from mass balance for'each element: Since f = 0.0 f o r complete combustion C balance: c = 1 H balance: 4 = 2d or d - 2 0 balance: 2a - 2c + d or a • 2 N balance: b • 3.76a « d or b = d • 7.52 Reaction i s : CH^ + 20 2 + 7.52N2 •»• C0 2 + 2H 20 + 7.52N 2 2. Calculations of I n i t i a l Properties Number of kmols of mixture i n i t i a l l y , N . , i s : N . - 1 + 2 + 7.52 - 10.52 mix Mole f r a c t i o n s , n^'s: 108, r. •= 1/10.52 = 0.0951 n - 2/10.52 = 0.1901 °2 n^ = 7.52/10.52 - 0.7148 2.1 Mixture Molecular Weight (MWMIX) M T T M T V - Total Mass of Mixture rlWMlX Total Number of Moles of Mixture 16.04(1) + 31.999(2) + 28.013(7.52) 10.52 27.6327 kg/kmol 2.2 Mixture Specific Volume (v i x ) Assume mixture behaves as ideal gas: PV «= nRT or nRT P (10.52)(8.3143)(298) KJ 101.3 KN/m2 257.3055 m3/kmol of CH, mix MW . N , mix mix 257.3055 m3 (27.6327)(10.52) kg 0.885 m3/kg per kg of reactant mixture 109. 2.3 Gamma (y) T Cv Cv - Cp - R Cp - Z(nCp)i On a per kmol basis: Cp(CH^) - (2.2537 KJ/kg K)(16.04 kg/kmol) - 36.15 KJ/kmol K Cp(02) - (0.9216)(31.999) KJ/kg K = 29.49 KJ/kmol K Cp(N2) - (1.0416)(28.013) KJ/kg K = 29.18 KJ/kmol K C pmix e ( O - 0 9 5 1 ^ 3 6 - 1 ^ ) + (0.1901)(29.49) + (0.7148)(29.18) - 29.9018 KJ/kmol K Cv = 29.9018 - 8.31434 - 21.5874 KJ/kmol K Y - 21.*5874 " 1 , 3 8 5 1 C1.3853) 2.4 Specific Energy E t o t a l " * n i <EJ + A S " * T ) i But, at standard pressure and temperature, Ah = 0.0, also, h° = 0.0 for 0 2 and N 2, therefore, E t o t a l " [ n ^ ] c -iNRT = 0.0951(-74873) + 10.52(8.31434)(298) - -9594.7773 KJ/Kmol/CH^ E " M -9594.7773 KJ 27.6327 kg = -347.23 KJ/kg (-347.28) 1 1 0 . 3. Flame Temperature 3.1 With no Di s s o c i a t i o n s Reaction i s : CH^ '+ 20 2 + 7.52N2 + C0 2 + 2H 2) + 7.5N2 - -74873 KJ [-393522 + V + 2 l -241827 + h ^ ] + 7.52[h N ] 2 TEMP A HCO 2 A\o Hp [K] [KJ/kmol] [KJ/kmol] [KJ/kmol] [KJ] 2200 103575 83036 63371 -130979 2300 109671 88295 67007 -87022 2400 115788 93604 70651 -42884 By i n t e r p o l a t i o n , the adiabatic flame temperature i s found to be 2328 K (program value: 2323 K) . 3.2 With Diss o c i a t i o n s Reaction i s (from program): CH^ + 20 2 + 7.52N2 -• 0.9047CO2 + 0.0953CO + 1.9492H20 + 0.04980 2 + 0.0375H2 + 0.02580H + 0.0202NO + 0.00220 + 0.0042H + 7.5N 2 H R - -74873 KJ H p «= 0.9047[-393522 + AhQQ ] + 0.0953[-110529 + Ah"co] + 1.9492[-241827 + Ah„ A ] + 0.0498[Ah_ ] + 0.0375[Ah H ] H 2 ° °2 H2 + 0.0258[39463 + Ah Q H] + 0.0202[-90592 + Ah N Q] + 0.0022[249195 + Ah Q] + 0.0042[217986 + Lh^] + 7.5099[Ah"N ] 1 1 1 . TEMP Ah C ( ) 2 Ah c o A h ^ A h ^ A h ^ A h ^ Ah Q Ah H A h ^ A h ^ ^ 2200 103575 64019 83036 59860 66802 65216 39882 39535 60752 63371 -87246 2300 109671 67676 88295 63371 70634 68906 41961 41610 64283 67007 -43326 By interpolation, the flame temperature i s found to be 2223 K (program value: 2222 K). 4. Equilibium Constants For a dissociation reaction v A + v, B v C + v .D a b c d a dissociation equation can be written in the form v v. c d yC * yD m K V V, V +V.-V -v, a b c d a b yA * y B f -Given: P° -' 101.3 KPa P - 523 KPa From program: Tfe • 2505.2 K Mole Fractions: C0 2 « 0.07829 CO - 0.01553 H20 «* 0.1786 H 2 = 0.005787 0 2 - 0.007102 112, N 2 - 0.7034 NO - 0.007102 OH - 0.005613 0 - 0.0005551 H - 0.0008697 D i s s o c i a t i o n r e a c t i o n : K t a b l e K c a l c u l a t e d N ™ nn ^ W o n n n o t n o o o (0.01553) (0.007102) *'2 ,523.'2 a) C0 2 CO + l/20 2 0.037 0.038 =-i ofo7829 (l0T3) b) HO « 1/2H, + 0H 0.053 0.054 = (0.005787)1/2(0.005613) (523^0 2 2. U.l/oo 1 U 1.J c) H 2 0 ~ H 2 + l / 2 0 2 0 . 0 0 6 1 0 . 0 0 6 2 • ( 0 - 0 0 5 7 8 o ; ^ ° 0 5 6 1 3 ) t l g ^ ) " 2 « 1 / 2 N 2 + l / 2 0 2 «• NO 0 . 059 0 . 059 - (0.70i4) W ° ( " o 0 7 1 0 2 ) ( m ^ ) 0 e) H 2 « 2H 0 . 0 0 0 6 4 0 . 00067 - < ° f f g j g > ' f> 0 , ~ 2 0 0 . 0 0 0 2 2 0 . 0 0 0 2 2 - * 2 j " 0 » g i i (|g£,' 113. APPENDIX V ~ EXPANSION COEFFICIENT DERIVATION 1. Derivation of a General Burning Velocity Equation Assumptions: 1) Spherical flame propagation 2) Isentropic compression of the unburnt gas 3) Ideal gas behaviour for both burnt and unburnt gases 4) Thin flame. Mass continuity across a flame of negligible thickness: 1 d m b S u A ,p dt f u m b = T * V pb d t - = 3 , r r b 3 d t - + 4 , T PbV dT" Assumption (2): P » constant • c Yb pb d p b 1_ 1 dP dt = Y b pb P dt d mb 4 ,1 p b d P A . 2 d rb dt~~ " I ^ b 7 F d t ' pb r b F D 114. 2. Equation for Constant-Pressure Combustion For constant pressure combustion: ^ « 0 P = p K u Ko d m b , 2 dr dT " 4 i r r b 2 pb dT " A f pb s f Assumption ( 3 ) : P RT From equation of state: — = — where R = universal gas constant W • molecular weight P W p B R I b = b o P ° W T, Ko o b Let E W T, o b i W T b o u E S f 1 APPENDIX VI ~ LINEAR MODEL EQUATION DERIVATION 1. Burning V e l o c i t y Equation Mass c o n t i n u i t y across the flame gives: dm - r - ^ - - S A , p dt u f u But, m u = M(l-x) m -X o - 1 -dx = 1 ^ _ " S u A f P u dt " M dt M • c « M dx dP ** u A,p dt dt f u For sph e r i c a l flame propagation: A, = 4irr,2 For sph e r i c a l with radius R: M = p Q y TTR3 • S = 2^- fR-^R dx dP " S u ^ R dP dt P . f V = V, + V b u v b + ( 1 _ x ) f- = > v b = vC 1^ 1-^) u u f b u l / r . But f - ( f ) *o O 1/YU r dx dP 1 ,P v U R dP dt > U - 3 (—J ( 1 - ( 1 - x ) J>) u Using Lewis and Von Elbe's approximation: x = p- ?o p -p e o dx dP P -P e o can be expressed as f(P) only: R 1 dP S 3 P -P dt e o u (f-) I1 - {r=p)/(f) 1 P -P „ 1 / - r u r £ - » [1 - | V (f) ] e o o where P g « experimental peak pressure, P^ 2. Mass Fraction Approximation Adiabatic compresion gives: F = P 1 / Y v . - pd-Tf)^ RT mole for volume v , occupied by 1 mole of gas. mole Before combustion of mass: fraction dn (1-Y )Y ( 1 _Y )Y u u u u F - P RT - P. RT. u u i i 117. where subscripts u, i denotes unburnt gas and i n i t i a l state of mixture, respectively. This assumes that over the temperature range T^ to T u, the specific heats, and therefore Y u » remain constant. After combustion of mass fraction dn, i t s temperature r i s e from Tfe to some temperature T.p, corresponds to the subsequent pressure: where m — moles i n the vessel after complete combustion e m^  • moles i n the vessel before combustion. This assumes i s constant over the temperature range T^ to T^p* Since total volume of the vessel i s constant and equal to m.RT./P F. - RT, P D D (2) (3) Combine equations (1), (2) and (3), F (1-n) P 1/Yb-1/Y, u Differentiating: 1/Yb-1/Y, u ( l - n ) . l 1/Y b-1/Y u"l F P u u dn (A) 1 1 8 . Assume C ,, x and C , s are constant, energy equation becomes: v(b) v(u) ' 0 7 n m C /ux (T V-T V T.) = m. C , v(T -T.) (5) e v(b) v b bP' i v(u) v u i ' ' Combine (1), (2) and (5): 1 < Yb" 1 ) / Yb 1 < Y U - D / Y U " ° F. — ———s- P U F = K (6) v.-1 b Y -1 u 'b 'u where K i s a constant. Solve F f e from Eq. (6), substitute i n Eq. (4), integrate between limits of n, and apply the boundary condition P=Pe when n=l; one obtains: RT. P -P. . i e i 1 - n = — (7) yhTy Fi RT - 5 - ^ + (Y .-1)K u Y -1 x ' b u But: and P, , T * T. when n = 0 i ' u i An approxiate equation for n i s : P-P± 119. APPENDIX VII - CALCULATION OF ERROR IN EQUIVALENCE RATIO Gas Composition Gas Minimum Purity CH, 99% C 2H 6 99% C 3H g 99.5% Air 99.96% Calculation of error i n stoichiometry: Stoichiometric CH-air combustion: CH^ + 20 2 + 2(3.76)N2 + C0 2 + 2H20 + 7.52N2 Theoretical fuel to air ratio: ~2^~52 " °*1050 Error due to impurities: 0.99CH^ + 0.9996(202 + 2(3.76))N2 * 0.99C02 + 1.98H20 + 7.52N2 + 0.0402 n QQ F u e l / A i r = 0.9996^2+7.52) ' 0.1050-0.1040 E r r o r 3 0O05 A Fuel/Air = 0.009 Similarly: for C 2H 6, A Fuel/Air - 0.0005 C 3H 8, A Fuel/Air = 0.0008 A c t u a l * = §fl5T=1-01 A$ » 0.01 

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