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Turbulent swirling combustion of premixed natural gas and air Zhang, Dehong 1995

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TURBULENT SWIRLING COMBUSTION OF PREMIXED NATURAL GAS AND AIR By DeHong Zhang B. M.  Sc., Sc.,  Zhejiang University, Zhejiang University,  China, China,  1982 1984  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineering  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA February,  1995  © DeHong Zhang, 1995  _____  In presenting this thesis in partial fulfilment of the requirements for degree at the University of British Columbia, I agree that the Library freely available for reference and study. I further agree that permission copying of this thesis for scholarly purposes may be granted by the department  or  by  his  or  her  representatives.  It  is  understood  that  an advanced shall make it for extensive head of my copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  Department of The University of British Columbia Vancouver, Canada  Date Ap4L c7. ‘f?  DE-6 (2)88)  11  ABSTRACT  Constant-volume combustion of a stoichiometric homogenous mixture of natural gas and air with global rotational motion (swirl) in a short cylindrical chamber has been studied experimentally and simulated numerically. Swirl was generated by a rotating disc in the combustion chamber with variable intensity. Turbulence intensity was varied by changing the swirl level as well as changing the size of roughness on the rotating disc. Combustion was initiated at the centre of the cylindrical combustion chamber. Combustion pressure signals were used to determine the combustion rate at different swirl levels. High-speed laser schlieren photography was used to obtain schlieren images of flame kernel development at different swirling levels.  Combustion pressure measurements showed that: (i) at given turbulence intensity, there is a swirl level limit, below which swirl enhances the burning rate; above which swirl reduces the burning rate; (ii) the turbulence intensity has greater effect on combustion duration at high swirl than at low swirl; (iii) increased swirl leads to increased heat transfer rate; at the intermediate swirl, the total heat loss during combustion was the minimum. High-speed laser schlieren pictures showed some evidence of small flame kernel elongation along the rotating axis of swirl.  Multi-dimensional numerical modeling, which was based on the KIVA II code, was applied to simulate combustion. A combustion model with a two-step chemical reaction scheme, in which the fuel was treated as a mixture of a number of simple chemical components, was developed  111  to evaluate the burning rate with, and without, swirl. The numerical results show that (i) at the zero, low, and intermediate swirl levels, the predicted combustion rates were closely consistent with the measured combustion rates; at the high swirl level, the combustion rates were over predicted; (ii) the numerical simulation is consistent with the observed effect of swirl on the flame kernel development.  iv TABLE OF CONTENTS  ABSTRACT TABLE OF CONTENTS  iv  LIST OF TABLES  viii  LIST OF FIGURES  ix  ACKNOWLEDGEMENT  xii  CHAPTER 1. INTRODUCTION  1  1.1 Natural gas and its potential for pollutant reduction  1  1.2 Combustion enhancement in burning natural gas  1  1.3 Combustion enhancement in SI engines  2  1.4 Effects of swirling flow on combustion  3  1.5 Numerical modelling of combustion in SI engines  4  1.6 Summary of prior knowledge  6  1.7 Objectives  7  1.8 Methodology  8  CHAPTER 2. SWIRLING COMBUSTION  10  2.1 Introduction  10  2.2 Swirling flow in short cylindrical chambers  10  2.3 Turbulence generation in swirling flow  11  2.4 Definition of combustion duration  13  2.5 Effect of turbulence on combustion rate  15  2.6 Effect of swirl on combustion in SI engines  18  2.7 Effect of swirl-induced buoyancy on burning zone development  21  2.8 Previous research in constant-volume combustion chambers (CVCC)  22  V  2.9 Summary of prior experimental knowledge  CHAPTER 3. EXPERIMENTAL APPARATUS AND MEASUREMENTS  26  34  3.1 Introduction  34  3.2 Constant-volume combustion chamber  34  3.2.1 Test section  34  3.2.2 Driving section  35  3.2.3 Ignition section  37  3.3 Computer data acquisition and control  37  3.3.1 Hardware  37  3.3.2 Software  38  3.4 Experimental conditions  39  3.5 Velocity measurements  40  3.6 Pressure measurements  41  3.7 High-speed schlieren photography  44  3.8 Summary  46  CHAPTER 4. EXPERIMENTAL RESULTS  55  4.1 Introduction  55  4.2 Combustion duration  55  4.3 Heat transfer  59  4.4 Flame kernel configuration  61  4.5 Classification of swirling combustion  62  4.6 Summary  69  CHAPTERS. COMBUSTION MODELS  5.1 Introduction  85  85  vi 5.2 Time-averaged values  86  5.3 Conservation equations  87  5.4 k-e turbulence model  88  5.5 Thermodynamic equations  94  5.6 Chemical kinetics  95  5.6.1 One-step reaction  96  5.6.2 Multi-step reaction  97  5.6.3 Detailed reaction  98  5.7 Multi-component treatment of fuels  99  5.8 Turbulent combustion rate  102  5.8.1 Introduction  102  5.8.2 Eddy dissipation model  104  5.8.3 Flame sheet model  110  5.8.4 Comparison of two models  115  5.8.5 Modification in this thesis  117  CHAPTER 6 SPECIFICATIONS OF CALCULATION AND GRID SIZE EFFECT  119  6.1 KIVA II code  119  6.2 Mesh arrangement  l  6.3 Initial conditions and boundary conditions  121  6.4 Reaction rate evaluation  125  6.5 Effect of grid size  127  CHAPTER 7. RESULTS OF NUMERICAL SIMULATION  138  7.1 Combustion duration  138  7.2 Flame kernel growth  139  7.3 Burning zone development over whole combustion process  140  7.4 Velocity fields  140  7.5 Grid size independence  142  7.6 Summary  142  CHAPTER 8. DISCUSSION AND CONCLUSIONS  157  vii NOMENCLATURE  163  REFERENCES  167  APPENDIX I COMPOSITION OF NATURAL GAS  177  APPENDIX II SHEAR STRAIN INDUCED BY BURNING ZONE EXPANSION  178  APPENDIX III MASS FRACTION BURNED AND COMBUSTION PRESSURE  180  APPENDIX IV CONSTANTS IN CHEMICAL REACTION SCHEMES  182  APPENDIX VI WALL FUNCTIONS  185  viii LIST OF THE TABLES  Table 6-1 Values of the constants in k-e equations  138  Table 6-2 Numerical values of the constants in the combustion model  139  ix LIST OF FIGURES  Fig. 2-1 Swirl in a cylindrical chamber  30  Fig. 2-2 Swirl generated by an inlet port in an engine cylinder  31  Fig. 2-3 Determination of combustion duration from a pressure-time curve  32  Fig. 2-4 Regime of turbulence combustion in IC engines  33  Fig. 2-5 Correlation between turbulence intensity and turbulent burning rate  34  Fig. 2-6 Flame “pencilling” in a cylindrical chamber with swirl  35  FIg. 3-1 Experiment system  49  Fig. 3-2 Test section configuration  50  Fig. 3-3 Constant-volume combustion chamber  51  Fig. 3-4 Front view of the test section  52  Fig. 3-5 Rotating discs  53  Fig. 3-6 Speed increaser assembly  54  Fig. 3-7 Radial distributions of the mean tangential velocity and turbulence intensity  55  Fig. 3-8 Mean tangential velocity and turbulence intensity, hot wire measurements (present study) and LDV measurements (Riahi, 1990)  56  Fig. 4-1 Total combustion duration and maximum pressure with disc I, II, and III  73  Fig. 4-3 Initial and main combustion duration with disc I, II, and III  74  Fig. 4-3 Effect of swirl and turbulence on the main combustion duration  75  Fig. 4-4 Variation of total heat loss during combustion with swirl  76  Fig. 4-5 Variation of total heat transfer rate during combustion with swirl  77  Fig. 4-6 Relative position of the side view schlieren pictures  78  x Fig. 4-7 Schlieren images of flame propagation, Re  =  72,100  79  Fig. 4-8 Schlieren images of flame propagation, Re  =  108,000  80  Fig. 4-9 Schlieren images of flame propagation, Re  =  172,000  81  Fig. 4-10 Flame kernel radius vs. mass burned fraction at different swirl levels  82  Fig. 4-11 Flame kernel axial dimension vs. mass burned fraction at different swirl levels  83  Fig. 4-12 An axisymmetric burning vortex  84  Fig. 4-13 Regimes of SBV  85  Fig. 4-14 Normalized stable radius of a burning vortex at different swirl levels  86  Fig. 5-1 Distribution of flame surfaces  121  Fig. 6-1 Computational domain for grid size test  132  Fig. 6-2 Definition of flame thickness  133  Fig. 6-3 Computational domain near boundary  134  Fig. 6-4 Calculated combustion duration at different grid sizes  135  Fig. 6-5 Mesh arrangement of the computational domain  136  Fig. 6-6 Coordinator system of the computational domain  137  Fig. 7-1 Comparison of predicted and measured combustion duration at different Re  146  Fig. 7-2a Flame kernel growth, predicted and measured, Re  =  0  147  Fig. 7-2b Flame kernel growth, predicted and measured, Re  =  0  148  Fig. 7-3a Flame kernel growth, predicted and measured, Re  =  108,000  149  Fig. 7-3b Flame kernel growth, predicted and measured, Re  =  108,000  150  Fig. 7-4a Flame kernel growth, predicted and measured, Re  =  172,000  151  Fig. 7-4b Flame kernel growth, predicted and measured, Re  =  172,000  152  xi Fig. 7-5 Flame front propagation at Re  =  0  153  Fig. 7-6 Flame front propagation at Re  =  108,000  154  Fig. 7-7 Flame front propagation at Re  =  172,000  155  Fig. 7-8 Velocity field at Re  =  0  156  Fig. 7-9 Velocity field at Re  =  108,000  157  Fig. 7-10 Velocity field at Re  172,000  158  xii ACKNOWLEDGEMENTS  The author wishes to express his gratitude towards his supervisor, Professor P.G. Hill, for all his invaluable help, encouragement, and expert advice throughout the course of this research and the writing of this thesis.  The author wishes also to express appreciation to Bruce Hodgins, research engineer, for his assistance in preparing the data acquisition hardware, to Yinchu Tao, research engineer for his advice and suggestions for the thesis work, to Patric Quellette, my colleague, for his assistance in experimental and computer techniques, and discussions in numerical modelling, to Peter Mtui, my colleague, for discussions in numerical modelling.  The author is also indebted to Tom Nicol, Program analyst in computer science department, for his effort in conversion of KIVA II, and his assistance in solving the problems in using this computer program.  The special thanks go to Tony Besic, and Len Drakes, mechanical technician, for assistance in manufacturing the mechanical parts of the experiment apparatus, and to Don Bysouth, electrical technician, for assistance in building the electrical part of the experimental apparatus.  The author is grateful to the National Science and Engineering Research Council for the financial support.  1 CHAPTER 1. INTRODUCTION  1.1 Natural gas and its potential for pollutant reduction  Natural gas is a mixture of gaseous hydrocarbons with major components methane, ethane, and propane. There are three reasons why burning natural gas can be superior to burning gasoline in spark ignition (SI) engines. First, because natural gas has higher octane number than gasoline, the compression ratio of a natural-gas-fuelled engine can be made higher than with a gasolinefuelled engine and thus provide higher thermal efficiency. Second, because of lower adiabatic flame temperature than with burning gasoline, natural gas combustion results in lower emission of NOx than gasoline combustion. Third, due to its lower carbon-to-hydrogen ratio than that of 2 is usually not considered . CO 2 gasoline, burning natural gas could reduce the emission of CO as a pollutant, but is generally believed to be the major cause of global temperature rise, due to its green house effect. Given the advantages of burning natural gas, we have to be aware that these benefits can only be gained when the natural gas is properly burned.  1.2 Importance of combustion enhancement for burning natural gas  Previous research work showed that under engine-like conditions, natural gas tends to have a lower laminar burning rate than conventional engine fuels, such as gasoline (Andrew and Bradley, [1972]; Sharma et al, [1981]; Metghalchi and Keck, [1982]; Jones and Evans, [1985]).  In  engines, the burning zone propagates at turbulent flame speed, which can be empirically related  2 to the laminar flame speed by St  =  1 is the S f(u’), where S is the turbulent flame speed, S  laminar flame speed, u’ is the turbulence intensity, and f(u’) is a function of u’. With this relation, the turbulent burning rate of natural gas is proportional to the laminar burning speed which, under engine condition, is significantly lower than that of gasoline. The burning rate of natural gas has to be enhanced for obtaining thermal efficiency compatible with burning gasoline, and for reducing the pollutant emission.  Thermodynamic analysis of the SI (Spark Ignition) engine cycle indicates that the highest thermal efficiency will be achieved if the combustion takes place at top dead centre (TDC), ie. as in the ideal Otto cycle; this means infinite combustion rate. Combustion takes time; the shorter this time the higher the thermal efficiency. In conventional SI engines which burn stoichiometric gasoline-air mixtures, the combustion rate is sufficiently high. When conventional fuels are replaced by natural gas, the burning rate will tend to be too low, and needs to be increased. The effect of combustion rate on pollutant emission is more complicated. First, faster burning leads to higher thermal efficiency. Second, increased burning rate leads to more complete conversion 4 is another green house gas) and intermediate products from reactants (the major component CH , HC and CO emission. Burning 4 to final products; fast burning, therefore, leads to reduced CH natural gas, due to lower flame temperature than that of burning gasoline, can also reduce NOx emission.  1.3 Combustion enhancement in SI engines  3 There are different approaches to increase the burning rate in SI engines, such as using two or more spark plugs in one combustion chamber, reducing the surface-to-volume ratio of the chamber, increasing reactant temperature, and introducing squish and swirl.  Using more than one spark plug, which reduces the average flame travel distance from the ignition source to the end gas, is an effective method of combustion enhancement. But it tends to increase cost and also to be limited by the space available in the cylinder head. Using a compact combustion chamber (with the surface-area-to-volume ratio as low as possible) reduces the flame travel distance and thus combustion duration; it also reduces heat loss to the wall of the combustion chamber. Increasing reactant temperature, which increases the reaction rate, can be easily realized by preheating the intake air and fuel or by increasing the compression ratio. But preheating the intake air and fuel reduces the maximum power output; increasing the compression ratio is limited by knock. Squish (the production of a fluid jet by reducing the clearance between piston crown and the cylinder head at the end of compression stroke), which can substantially increase the turbulence level around top dead centre (TDC) and subsequently increase the burning rate, is effective in a short time period during the main combustion, and usually has the best effect when combined with swirl. Swirl, to which this thesis is addressed, defined as global rotational fluid motion in a short cylindrical chamber, is one of the most effective ways of combustion enhancement due to its long lasting effect on turbulence generation.  1.4 Effects of swirl on combustion  4 Previous research work has showed that swirl can affect combustion processes in different ways, e.g. in turbulence generation, in heat transfer, in flame propagation, and in burning rate. Previous measurements show that the TDC (Top Dead Centre) turbulence intensity with swirl can be twice as much as without swirl. This increased turbulence intensity can substantially increase the burning rate. On the other hand, introduction of swirl also leads to increased heat loss through the wall, and may lead to decreased burning rate. Correlations between swirl intensity and heat transfer coefficient have been suggested by previous research work; but the relation between turbulence intensity and the heat transfer coefficient remains to be made explicit. Schlieren pictures from a few experiments have shown that swirl can change the configuration of a burning zone so as to change the rate of burning zone expansion; but the mechanism of how swirlinduced buoyancy affects flame propagation is still not quite clear.  Experimental results from engines have shown that swirl can increase the combustion rate (or reduce the combustion duration). But there appears to be an optimum level of swirl above which its effects are disadvantageous. Most experiments in constant-volume combustion chambers have also indicate that swirl leads to faster burning; but a few results (Zawadzki and Jarosinski, [19831; Beer at al, (1971]) indicated that intensifying the swirl may reduce the combustion rate.  1.5 Numerical modelling of combustion in SI engines  Numerical modeling of combustion is becoming more and more attractive because: i/ modem computer technology has made it possible to solve the equations governing combustion processes  5 in a reasonable time period;  ui development in turbulence  modeling and chemical kinetics has  made possible the calculation of complicated combustion processes with acceptable accuracy; iii! computer modeling can possibly generate information provided by experimental measurements; iv! experiments in combustion are usually difficult, sometimes dangerous, and may be both expensive and time-consuming, and also generate pollutants; computer modeling, in contrast, is not only clean and safe but also potentially cheap and time efficient. The challenge we are facing is to develop numerical models to predict combustion processes accurately.  Previous numerical simulation of cold flow has showed that the in-cylinder flow, independent of the initial in-cylinder flow pattern by the end of induction stroke, will approach solid-bodyrotating swirl as the piston compresses the in-cylinder charge toward the TDC. In recent years, increasing numerical work has been reported in multi-dimensional in-cylinder combustion process simulation. Predicted combustion pressures can match measurements reasonably well. The early and the main combustion typically require different treatments to bring the numerical results in accordance with the measurements.  In widely-used turbulent combustion models for IC engines, the effect of turbulence on combustion rate is accounted for by introducing empirical relations between the turbulence intensity and the reactant consumption rate, or between the turbulence intensity and augmentation of the flame surface area, with which the turbulence combustion rate was evaluated by the product of the flame surface area and the laminar flame speed. The advantage of such is that little or no attention needs to be paid to the mechanism of chemical reactions. The drawbacks  6 are: i/they can not predict laminar or low-turbulence combustion, which is always the case near solid walls;  ui  they do not properly account for the dependence of combustion rate on  temperature; iii/ some of them can not handle incomplete combustion, ie. they can not predict pollutant formation. It is therefore very important to develop a combustion model which will be able at low and high turbulence levels to predict combustion rate, burning zone configuration, and pollutant emissions.  1.6 Summary of prior knowledge  i/ Most experimental results showed that increased swirl leads to increased combustion rate; but the reverse has been observed in few cases; it is therefore important to examine the effect of swirl on combustion rate in a broad range of swirl levels to see if an optimum swirl level exists in the use of swirl to minimize combustion rate.  ii! Swirl-induced buoyancy can affect the flame propagation and change the configuration of the burning zone, which could in turn affect the global combustion rate and heat transfer rate;  iiil Increased swirl leads to increased heat transfer coefficient; but extent to which the turbulence intensity can affect the total heat loss has not been made clear; it is important to understand how swirl and turbulence affect the heat loss so that one can avoid the effect of excessive heat loss on thermal efficiency.  7 iv! Multi-dimensional numerical modeling of turbulent combustion in IC engines is still premature; it can neither predict flame propagation accurately, nor predict heat transfer and pollutant formation accurately; it is important to develop a effective combustion model to produce detailed and reliable information about the turbulent combustion.  1.7 Objectives  The objectives of this thesis include:  • to examine how swirl affects the initial combustion duration (defined as the time period for 0  -  10% mass burned) and main combustion duration (10  -  90% mass burned);  • to determine if there is a optimum range of the swirl level in terms of minimizing the total combustion duration, and where it is; • to examine how swirl-induced turbulence affects the combustion duration; • to examine how the swirl-induced buoyancy affects the burning zone configuration and flame propagation; • to examine whether swirl increases or reduces the total heat loss during combustion, and to what extent; • to develop a method to classify the swirling combustion (combustion with swirl); • to predict the combustion pressure and flame propagation of transient swirling combustion processes over a broad swirl range (from zero-swirl laminar combustion to high-swirl turbulent combustion), and to validate the numerical model by comparing the numerical  8 results with measurements.  1.8 Methodology  A constant-volume combustion chamber (CVCC) was used in the experimental work needed to fulfil these objectives. In SI engines, combustion takes place near top dead centre (TDC), when the volume change of the combustion chamber is very slow. It is therefore common to use a CVCC to simulate the combustion process in engines because of the ease with which the experimental conditions may be controlled, and the ease of observation and measurements. Despite its limitation, a CVCC can be very useful in understanding the effect of swirl on combustion in SI engines.  In a CVCC, the swirling flow can be generated by tangential inlet injection or by a rotating disc. Tangential injection can only change the swirl intensity in a limited range and can hardly vary the swirl level and the turbulence intensity smoothly. The rotating disc can smoothly change the swirl intensity from zero to very high level, say 15,000 rpm. Besides, the turbulence intensity in the swirling flow can also be easily changed by changing the roughness size on the disc. Rotating discs were used in the experimental CVCC for swirl generation due to these advantages.  For simplicity of description it is common to define the equivalent angular speed of a swirling flow  ü,  as the angular speed of a solid-body having the same total angular momentum, the same  volume, and the same average density. The relative swirl intensity, called swirl ratio (or swirl  9 number), defined as the ratio of o to the rotational speed o of the engine crankshaft, is commonly used to evaluate the intensity of the swirl in IC engines.  The swirl intensity in  CVCCs has to be evaluated in the way other than in engines because there is no crankshaft. In this thesis, a non-dimensional number, the rotating disc Reynolds number Re, defined as Re=WR/v, was used to evaluate the swirl intensity, W being the tip speed of the rotating disc [mIs], R the s]. [m I radius of the combustion chamber [ml, and v the kinematic viscosity of the fluid 2  The CVCC was so designed that the combustion process can be viewed through three quartz windows. Flame propagation was recorded by high speed schlieren photography. Combustion pressure was measured by a piezometric pressure transducer.  The swirling combustion was simulated with KIVA II, a computer program developed by Los Alamos Laboratory specifically for combustion modelling in IC engines.  The combustion  submodel in KIVA II has been replaced a multi-component two-step chemical reaction scheme and an improved eddy dissipation model for modelling turbulent combustion of stoichiometric mixtures of natural gas and air.  The content of this thesis consists of two parts, the experimental part and the numerical part. The experimental part, starting with the concept of swirling combustion and experimental work in swirling combustion in IC engines and in CVCCs, is to be discussed in the next chapter.  10 CHAPTER 2. SWIRLING COMBUSTION  2.1 Introduction  Swirling combustion is defined here as the rapid exothermic chemical reaction in a global swirling flow in a short cylindrical chamber. The burning rates of some fuels, e.g. natural gas, and lean or diluted mixtures are usually slower than those of chemically correct mixtures of conventional fuels (e.g. gasoline). Slow burning could result in decreased thermal efficiency and increased pollutant emission for reasons discussed in Chapter 1. It is therefore desirable to enhance the combustion rate when burning natural gas, or lean mixtures. Swirling combustion is one of the most effective ways to enhance the combustion process in engines. Swirl can generate turbulence in different ways. The generated turbulence, in turn, can effectively increase the burning rate.  The purpose of this chapter is to review what is known about swirling  combustion in SI engines and CVCCs.  2.2 Swirling flow in short cylindrical chambers  Swirling flow, or simply swirl, is herein defined as the global rotational fluid motion in a closed cylindrical chamber around an axis parallel to the cylinder axis. A swirling flow with near-solid body rotation is shown in Fig. 2-1, where R is the radius of the chamber, o is the rotating speed 8 is the tangential velocity of the fluid. and u a inlet port in an engine cylinder.  Figure 2-2 shows a swirling flow generated by  11 In engines, swirl can be generated by specially designed inlet ports (e.g. Catania [1982], Kajiyama [1984], Mikulec et al [1988], Arcoumanis [1989]) and/or by blocking part of the inlet pathway around the inlet valve (or valves) (e.g. Willis [1966], Hirotomi [1981], Kent et a! [1989], Khaligi [1990]) to cause asymmetric inlet flow with net angular momentum about the cylinder axis. In constant-volume combustion chambers, swirl can be generated by blocking part of the inlet pathway around the inlet valve (e.g. Dyer [1979]), by tangentially-directed jets (e.g. Inoue et al [1980], Wakisaka [1982], Herweg et al [1988]), or by rotating discs (e.g. Bolt and Harrington [1967], and Riahi [1990]). Intensity of swirl generated by an engine cylinder head may be evaluated on a steady flow test rig by impulse swirl-torque meters or rotating vane meters, or calculated from measured tangential velocity profiles of the swirl.  In the experiments, swirl was generated by a rotating disc.  The intensity of swirl was  characterized by the rotating disc Reynolds number Re, defined as Re=WRJv  (2-1)  where W is the tip speed of the rotating disc [m/s], R is the radius of the combustion chamber sl. [m / [m}, and v is the kinematics viscosity of the fluid 2  2.3 Turbulence generation in swirling flow  Swirl can generate turbulence, which, in turn, can effectively increase the burning rate. The subject of this section is how swirl generates turbulence.  12 (i) Wall boundary layer shear strain  The rate of turbulence generation due to tangential shear caused by swirl may be written  (2-2)  Gturb =r(__!—_) r ãr 0 is the mean tangential velocity and in which u  1 t  is the turbulent shear stress. The term in  parentheses approaches zero in the bulk of the flow as the swirl approaches solid-body rotation. However this does not mean that the turbulence production due to swirl vanishes; it tends to be concentrated near the solid surfaces where  Ir. 6 ar is much large than u /au 0  The LDV measurement  data of Hall and Bracco [1986] showed that turbulence intensity increased sharply near the wall, indicating a significant turbulence generation near the wall. Turbulent diffusion and possible secondary flow can transport this turbulence through the bulk of the flow.  (ii) Vortex shedding down stream of a blunt body  When a blunt object, such as a spark plug or a valve head, protrudes into the flow, vortex shedding will take place down stream of the object. degenerate to turbulence.  The shed vortices will subsequently  In the in-cylinder swirling flow, turbulence could be generated  downstream of the protruding objects, such as spark plug electrodes and valve heads. Due to high local turbulence intensity, increased flame propagation rate could be expected in these zones and this may contribute to the phenomenon of flame holding by the spark plug electrodes, as shown by Witze [19821 and Herweg et al [1988].  13 (iii) Shear Strain Induced by Burning Zone Expansion  With LDV measurement data, Hall and Bracco [1986] have shown a remarkable increase of turbulence intensity due to combustion by comparing radial distributions of turbulence intensity in non-firing cycles and in firing cycles at TDC, when the flame front was at about 0.8 cylinder radius in firing cycles. From their measured mean velocity profiles we noticed that the global in-cylinder flow was a solid-body rotation before and right after ignition (5° CA) and this solidbody rotation was distorted when the flame propagated through the disc-shaped combustion chamber. Kent, Haghgooie, Mikulec, Davis and Tabaczynski [1987] have suggested that flame propagation could induce shearing strain in a fluid which has solid-body rotation before ignition.  Using a simple two-zone axisymmetric model with central spark ignition in a cylindrical chamber, Hill and Zhang [1994] showed that in an initially strain-free swirl flow turbulence intensity could be enhanced by combustion-induced shear strain (see details in Appendix II).  Before further discussion on how swirl-generated turbulence affects combustion in SI engines and CVCCs, it would be helpful to have a brief description of the combustion duration.  2.4 Definition of combustion duration  The combustion processes in SI engines and CVCCs are unsteady chemical reactions from unburned reactants to burned products.  As flame propagates, the mass of burned products  14 increases, and the mass of unburned reactants decreases. Total combustion duration is the time interval between initiation of combustion (when the mass burned fraction x is equal to zero) to the end of combustion (when x is equal to one). The time history of combustion pressure, which is directly related to the heat release from the combustion, is usually used to determine the time history of the mass fraction burned x, ie. x  =  (P  -  Po)/(Pm  -  Po) in which P is the combustion  pressure, Po is the initial pressure before combustion, Pm is the maximum combustion pressure (Appendix III provides the deviation of this equation), from which combustion duration can be determined. By the end of combustion the change of heat release rate and the corresponding change of combustion pressure become very slow. It is therefore very difficult to determine the moment when the combustion pressure change is zero.  In practice, the time interval from  ignition to the 90% mass fraction burned is usually used for the measure of the total combustion duration (denoted herein as DTO-90%).  The total combustion duration DTO-90% is divided into the early combustion duration DTO- 10%, the time interval from ignition to 10% mass fraction burned, and main combustion duration DT1O-90%, the time interval from 10% to 90% mass fraction burned, shown in Fig. 2-3.  The reason to choose 10% mass burned fraction as the end of early combustion duration is similar to that to choose 90% for total combustion duration. The early combustion duration is usually considered as the chemical preparation time period after ignition. In this period, the mass conversion rate is strongly affected by the chemical properties of the reactants, and the combustion pressure change is very slow. The end of this period is usually considered as the  15 moment when the combustion pressure starts to increase significantly. From a typical combustion pressure curve, shown in Fig. 2-3, pressure starts to deviate from the base line (the initial pressure) at about 9 ms after ignition, when the mass fraction burned is about 1%. The moment of 1% mass burned could therefore be a reasonable end point of early combustion duration, or ignition lag. This is the reason why in the literature, the early combustion duration is sometimes defined as from ignition to 1% mass burned, and the main combustion duration defined as from 1% to 90% mass burned. A severe disadvantage of using 1% mass fraction burned to separate the early combustion duration and the main combustion duration is the difficulty of determining this point from the combustion pressure curves. From combustion pressure curves, in practice, the moment when 10% mass fraction burned can be more accurately determined than that when 1% mass fraction burned. This could be the reason why most experimental combustion durations are presented in the form of 0-10% and 10-90% mass fraction burned.  2.5 Effect of turbulence on combustion rate  In this section, starting with discussion about the classification of turbulence combustion regimes, a brief description about definition of combustion duration is followed. Experimental evidences that turbulence can effectively increase the burning rate are then reviewed. An empirical relation between the turbulent flame speed and turbulence intensity, derived from fractal analysis, is cited at the end of this section.  Turbulence can significantly affect the combustion process by wrinkling the flame front  16 (effectively increasing the global burning rate by increased the flame front area) when the turbulence length scale is larger than flame thickness, or by enhancing the mass and thermal diffusivities (effectively affecting the local chemical reaction rate) when the turbulence length scale is smaller than flame thickness. To classify the regime of turbulence combustion, a nondimensional number, Damkoehler number the characteristic turnover time  t  is usually used, which is defined as the ratio of  DaA  of a eddy of size A (‘ce  =  A/u’) to the characteristic travel time  ‘r of a laminar flame over a distance of the laminar flame thickness 8  =  Da  Al zi,U  1 = (t  , ie. /S 1 )  /  (2-3)  ii  1 is the laminar flame speed, A is the turbulence integral length where u’ is turbulence intensity, S scale, and 8 is laminar flame thickness, evaluated from  =  , 1 TIS  where  r’  is the thermal  diffusivity. The regime of turbulent combustion in engines has been identified by Abraham et al [1985], as shown by a small box enclosed by the dotted lines in Fig. 2-4. The regime in the present study was also estimated, as shown by a big box enclosed by the solid lines in the same Figure. Values used for the estimation are: A  =  0.01 (0.2L) [ml (Launder and Spaulding, [1972];  Borgnakke et al, [1980], Fraser et al, [1986]), u’ et al [1981], Johns and Evans [1985]), P  =  =  0.02  (0.15  -  -  5.0 (0.005W  -  0.05W) [mIs] (Sharma  4 [m /s], and 8 2 0.5) x i0  =  1 [m/s] P/S  (Abraham et al [1985]), where L is the length of the chamber, W is the tip speed of the rotating disc. It can been seen from Fig. 2-4 that most of the regime of engine combustion is included within the boundaries of the present study.  When  DaA <<  1, the size of turbulent eddies is much smaller than laminar flame thickness, a  17 laminar flame sheet can not exist in the turbulent flow; this is called the distributed reaction regime in Fig. 2-4. When DaA > 1, ie. the flame travel time is less than the turbulence eddy turnover time, chemical reactions occur in a thin sheet, ie. a laminar flame sheet. Turbulence affects combustion by wrinlding the flame sheet (reaction sheet regime in Fig. 2-4), which is the case for most of turbulence combustion in SI engines, and also in the present study. Based on this wrinkled flame model, the turbulent flame speed could be determined by  1 u/u  =  (2-4)  A/AI  1 is the smoothed surface area. The problem where A is the wrinkled flame surface area, and A encountered in application of Equation 2-4 is the difficulty in determining the turbulence flame surface area A. Much research work has been done, trying to determine the A, from which the turbulence flame speed can be derived. More often, turbulence intensity u’ is directly related to the turbulent flame speed by some empirical correlation, without relating it to the turbulence flame surface area A.  Measurements in engines (see e.g. the papers of Hoult and Nguyen [19851, Hamamoto et al [1984], Abdel-Gayed and Bradley [1981], and Kozachenko and Kuznetsov [1965]) have shown the strong effect of the root-mean-square turbulence velocity u’ on the flame speed. Baritaud [1989] has shown that burning rate in engines can be directly related to intensity of the turbulence generated by swirl. Kyriakides et al [1988] shown with his experimental results that the ignition delay (defined as time period for 0  -  10% mass burned) tended to decrease linearly  with measured turbulence intensity at the time of ignition.  Turbulence intensity also has  18 substantial effect on the main burning period (defined as time period for 10%  -  90% mass  burned) though increasing the turbulence may have diminishing returns.  In recent years considerable work has been done on fractal analysis of turbulent flame propagation, (see e.g. Gouldin [1987], Kerstein  { 1988], Mantzaras [1989], Santavicca et al  [1990], North and Santavicca [1990], Guelder [1990]). In good agreement with experimental data, Guelder [1990] has shown that the ratio of turbulent flame speed u to the laminar flame speed u 1 can be related to turbulence intensity u’ by  U  U’  =  U,  in which ReL  1! 4  1 +O.62(—) ReL 2  (2-5)  1 U  u’L/v and L is the integral length scale. Under engine conditions this can mean  ; it shows the great importance 1 that the turbulent flame speed may be over 5 times as large as u of increasingu’ in promoting burning rate in engines. Figure 2-5 shows the plot of Eq. 2-5 and the experimental data.  2.6 Effect of swirl on combustion in engines  In this section a review is provided of the evidence that swirl can have remarkable effects on combustion processes in various aspects, e.g. on ignition, flame propagation, and combustion duration.  Swirl can have substantial effect on early flame kernel growth by a number of effects. One of  19 these could be reduced heat transfer to the electrodes, because with off-centre spark plug location, swirling flow passing a spark plug can elongate the spark arc and reduce the contact area between the flame kernel and electrodes (Hattori, Goto, and Ohigashi, [1979]; Anderson and Asik [19831; Ziegler, Schoudt and Herweg [1986]).  The effect of mixture motion on heat  transfer to spark electrodes is apparent in the detailed observations of Pischinger and Heywood (1990) of individual flame kernels. They found that large flow velocity convected the flame kernel (initial burning zone with small size) away from the electrodes, reduced the contact area between the flame kernel and electrodes and therefore reduced the heat loss to the electrodes. The flow velocity was thus found to have a dominant effect on flame kernel growth in cases where ignition was limited by heat loss or by ignition energy. With central ignition, however, whether heat transfer from flame kernel to electrodes has important effect on early flame kernel growth is not clear.  In the present study, a natural gas and air mixture was ignited at the centre of the chamber, which is also the centre of swirl, where the mean flow velocity is negligible. Swirl would not reduce the contact area and heat loss from the flame kernel to the electrodes. In contrast, burning zone elongation due to swirl (which will be discussed in next paragraph) will increase the contact area and increase the heat loss. Swirl can also generate turbulence, which in turn increases the global burning rate and the heat release rate from the chemical reaction.  Increased swirl,  therefore, depresses flame kernel growth due to increased heat loss, and enhances flame kernel growth due to the increased turbulence burning rate. The net effect of swirl on flame kernel growth could be that (i) the increased swirl level leads to the increased flame kernel growth rate,  20 or (ii) the increased swirl level leads to the decreased flame kernel growth rate, or (iii) swirl does not change the flame kernel growth rate.  In the results of a number of engine experiments (such as those of Kent et a! [19891, Hamamoto et a! [1984], and Kido et a! [1980]) there is a strong positive correlation between increased swirl and decreased combustion duration. In the experiment of Mikulec et al [19881, changing the average swirl speed from 0 to 2.8 times engine crankshaft speed reduced the ignition lag (time period for 0-10% mass fraction burned) by about 25%, reduced main combustion duration (time period for 10- 90%), by about 10%, and significantly improved the combustion stability. In some tests (e.g., Witze and Vilchis [1981]), swirl reduced combustion duration more in lean burning (burning mixture with greater air/fuel ratio than stoichiometric mixture) than in rich burning (burning mixture with smaller air/fuel ratio than stoichiometric mixture). Tanaka et al [19801 used various methods to increase the swirl and found that all of these methods increased combustion rate, particularly when operating with lean mixtures. In contrast to the foregoing results, Zawadzki and Jarosinski [1983] concluded from their studies of combustion in a combustion chamber that intensifying the swirl reduces the combustion rate. They concluded that under some circumstances swirl can cause the flame to become more laminar-like, and hence to propagate at a lower speed, especially with lean mixtures. They state that their conclusion is compatible with the results of Beer and colleagues [1971]. In the present experiment, the effect of swirl on combustion duration will be examined with a wide range of swirl level.  21 2.7 Effect of swirl-induced buoyancy on burning zone development  Besides swirl-generated turbulence, swirl-induced buoyancy, which has a strong effect on the burning zone configuration and mixing process of burned and unburned gas, can also affect burning rate. In engines the average rotational speed of the swirl can be as high as 20,000 rpm or more. This means that at a mean radius of 25 mm the centripetal acceleration can be as high as 10,000 g. It is therefore not surprising that, with big density difference between burned and unburned mixture, substantial buoyancy effects should be observed in swirling combustion.  Demonstrating the effect of buoyancy on burning rate, Lewis [1970] conducted combustion experiments in a closed rotating tube with central ignition at one end; the tube L/D ratio was 24. At high rotational rates Lewis found that though ignition was difficult at 1 atm it was reliable at 2 atm. With centripetal acceleration up to 900 g the pressure rise rate in the cylinder was more than three times as great as with no rotation. Hanson and Thomas [19841 investigated flame development in a rotating disc-shaped chamber (LID  =  0.15) with central and off-central  ignition. A lean mixture (equivalence ratio 0.7) and a stoichiometric mixture were used in their experiment. The results showed that the buoyancy effect due to centripetal acceleration depresses the outward flame propagation in the radial direction with central ignition and increases the flame propagation rate toward the centre of the swirl. Photographs with central ignition showed a strong tendency for the flame zone to elongate along the axis, shown in Fig. 2-5.  In lean  mixtures this tendency for the burned gas to “pencil” along the axis of rotation led in some cases to quenching on the sidewalls. Inoue et al [1980] observed the tendency of the burned gases to  22 be driven toward the center of the chamber with off-centre ignition. Wakuri et al [19811 also observed a strong tendency in a swirl field of inflow of hot gases toward the centre, owing to buoyant forces. Laser shadowgraph photographs of Witze [1982] show a strong tendency for the combustion gases to be convected toward the centre under high swirl conditions.  The  experimental results of Herweg [1988] also show the effect of buoyancy on flame propagation. At high swirl level and with peripheral ignition, the flame tends to move toward the center of the combustion chamber.  Groff and Sinnamon [19821 report that with peripheral ignition,  buoyancy effects on the burned gases were noticeable at very high swirl conditions. With central ignition, no such effect can be seen. In the present study, swirl level has been changed in a wide range to examine the effect of swirl on combustion.  2.8 Previous research in constant-volume combustion chambers  The combustion processes in engines are very complicated. Investigation of combustion in the constant-volume combustion chambers can provide valuable information with which we can interpret the combustion processes in engines, based on two main reasons.  Firstly, in real engines the combustion processes take place near the TDC (top dead center) when the rate of volume change of the combustion chamber is very slow. Thus the combustion in real engines, especially in SI engines, is at nearly constant volume.  Secondly, many research investigations have shown that the swirl patterns near TDC of the  23 engines with pancake combustion chamber approach solid body rotation, virtually independent of the flow patterns during the intake stroke. Swirl in short cylindrical chambers shows a strong tendency for the bulk of the motion to become two-dimensional. It is because the tangential velocity component in short cylinders is so much larger than the axial component (and the radial gradient of pressure so much larger than the axial gradient) that the tangential velocity in the bulk of the flow tends to be independent of the axial coordinate. This is well demonstrated by the data of Dyer [1979] on swirl generated by tangential jet injection into a short cylinder. After a short period of adjustment the axial gradient of the tangential velocity approaches zero except in the wall boundary layer. In engines with disc combustion chambers a common observation is that between inlet valve closure and top dead center the tangential velocity distribution approaches that of solid-body rotation (see e.g. Inoue [1980], Witze and Vilchis [1981], Bopp, Vafidis and Whitelaw [1986], Haghgooie and Kent [1987]). Thus by studying nearly-solid-body rotating swirl and the associated combustion process in a constant volume chamber, we can obtain valuable knowledge of swirling combustion processes applicable to the engines.  Because of easy access to measurements and convenience of controlling experimental conditions, constant-volume combustion chambers have been used to simulate swirling combustion in engines.  Inoue et al [19801 studied combustion with swirl in a disc-shaped constant-volume combustion chamber of diameter 120 mm and length 27 mm. They generated fluid motion by jet injection (after evacuation of the cylinder), either in the radial direction (no swirl) or at 30° to the radial  24 direction, and measured mean swirl velocities and turbulence distributions during a decay period of 200 ms.  After an initial transient period, they found a strong tendency toward spatial  uniformity of the turbulence even though sharing strains are concentrated near the walls.  Dyer [1979] measured the radial distribution of tangential velocity in a constant-volume cylindrical combustion chamber after sudden inlet air injection. The peak velocity is much closer to the axis in this case than in the measurements of Inoue et al [1980]. The dimensions of Dyer’s chamber are 80 mm in diameter and 29 mm between the windows on each side. The measured axial distribution of tangential velocity indicated the very strong tendency in a short cylinder for the swirl to be two-dimensional.  With increased swirl, substantial reduction of combustion duration has been observed in constantvolume chambers. Inoue et al [1980] measured the total combustion durations, which depend upon swirl intensity at the time of ignition. They are two-thirds as long for ignition at 50 percent radius as they are for central ignition. The tests of Dyer [1979] in a constant-volume chamber also showed the strong effect of swirl intensity on combustion duration.  Fluid motion appears to have greater effect on the combustion duration of lean mixtures than it does on stoichiometric mixtures. In their measurements of combustion duration in a bomb in which turbulence and swirl were created by a rotor in the combustion chamber Bolt and Harrington [1967] found that the combustion duration could be substantially reduced by high swirl velocity, especially for lean mixtures.  25 Constant-volume combustion chambers are also be used to study the buoyancy effect of swirling combustion. Inoue [19801, and Hanson and Thomas [1984] studied the effect of buoyancy on flame propagation in their constant-volume chambers.  Despite the similarity, the difference between the operating conditions in constant-volume chambers and in engines is not negligible. It is important to develop some methods to extend results from constant-volume combustion chambers for understanding the processes in engines. Numerical simulation appears to be a powerful tool, by which experiment results in constantvolume combustion chambers can be relatively easily extended to engine conditions by developing a combustion model which can cover the temperature and pressure ranges in both constant-volume combustion chambers and engines. The advantages of numerical simulation are that it is highly flexible and highly infonnative, and cheap relative to the experiment method. The disadvantages of the numerical method are limited understanding of turbulence mechanism, limited understanding of chemical reaction mechanism for most reactants, and limited computer memory and speed. But the numerical method can be so developed as not to be limited by any specific conditions and can provide extensive details which could be very helpful in understanding the in-cylinder processes not readily measured by the experiment method. Because the chemical reaction mechanisms of some hydrocarbon fuels with simple molecular structures, for example methane, ethane and propane, have been relatively well understood and because a number of turbulent models perform well for swirling flow in a cylindrical chamber,  it is  realistic to attempt to develop a reliable numerical model to predict the swirling combustion process of natural gas.  It should also be possible to extend the model to the real engine  26 conditions without substantial modification.  2.9 Summary of prior experimental knowledge  As a summary of this chapter, we conclude:  i/ heat transfer from the flame kernel to the surrounding plays a important role in early burning zone development; with off-centre electrode ignition, swirl can promote early flame kernel development; with central electrode ignition, the effect of swirl on early flame kernel development has not been fully examined;  ii! most experiments showed that, at a given swirl level, there is a positive correlation between increased swirl and decreased combustion duration, similar to those experiment results discussed in the beginning of this paragraph; but, as shown by few experimental results, when swirl intensity exceeds a certain level, the correlation between increased swirl intensity and combustion duration could be reversed. It is therefore important to know: (a) at which swirl level a significant combustion rate increase (for example over 10%) can be realized; (b) what is the limit beyond which increased swirl will have a negative effect on combustion;  iii! swirl-induced buoyancy has substantial effect on the burning zone development; in the “pencilling effect” the flame kernel propagates faster in the direction along the axis of the swirl than in the radial direction;  no classification of buoyancy effect on combustion in a short  27 cylindrical chamber appears to have been reported; no attempt appears to have been made to relate buoyancy effect to the optimum swirl level;  iv! constant-volume combustion chambers are widely used to provide valuable information about combustion processes in engines; easy control of experimental condition and easy access for measurement are two advantages of studying SI engine combustion in CVCC.  28  z axis  L  C)  wall  Fig. 2-1 Swirl in a cylindrical chamber  29  I? In let port  Enging  Inlet valve  cylinder  Piston  Fig. 2-2 Swirl generated by an inlet port in an engine cylinder  30  0.8  (‘5  a  G) C) D (‘5 C)  0.6  0.4  a) 1 D Cl) U)  ci)  0.2  a0.0  -0.2 0  25  50  time [ms]  Fig. 2-3 Determination of combustion duration from a pressure curve  31  -  AK TURBULENC  77  -  -r  7  REACTION SHEETS.  DaA  7  1O_2__ V?1 REGIMES  .—  DISTRIB AFIONS  OF VENGINE COMBUSTEON [ REGIMF OF [i-J PRESENT STUDY  4 i0  108  RA  Fig. 2-4 Regimes of turbulence combustion in IC engines, RA =Au’/v  32  10  8  6  4  2  0  0  2  4  6  8  10  12  14  Fig. 2-5 Correlation between turbulence intensity and turbulent burning rate (experimental data shown by the scatted symbols, Eq. 2-5 shown by the solid line; , Ru = u’l/v and ReL = u’L/v, where 1 is the Kolmogorov length scale 4 Ri ReL and L is the integral length scale), (Guelder, 1990)  33  Fig. 2-6 Flame “pencilling” in a cylindrical chamber with swirl (Hansen and Thomas,1984)  34 CHAPTER 3. EXPERIMENTAL APPARATUS AND MEASUREMENTS  3.1 INTRODUCTION  In Chapter 2, the reason why constant-volume combustion chambers (CVCC) are often used to study the combustion process in IC engines has been discussed. In this chapter, details about experimental equipments and test conditions will be given. An experimental apparatus has been set up by the author of this thesis for the experimental study of constant-volume combustion. The apparatus, shown in Fig. 3-1, consists of an assembly of the constant-volume combustion chamber, instruments for pressure signal collection and high-speed laser schlieren photography, and computer hardware and software for data acquisition and programming control.  3.2 CONSTANT-VOLUME COMBUSTION CHAMBER  The combustion chamber assembly consists of three major sections: the test section, the driving section, and the ignition section.  3.2.1 Test section  The test section shown in Fig. 3-2, which was designed and set up by the author of this thesis, is a cylindrical chamber with a rotating disk to generate swirl. The cross-sectional view of the test section is shown in Figure 3-3 (noted by number 1, 2, 3, 4, and 5); and the front view of the  35 test section is shown in Fig. 3-4.  The diameter of the chamber D is 50.8 mm, and the chamber length (L) to diameter (D) ratio (LID) is 1:2. There are two major reasons to use this LID ratio. First, previous work (Riahi, [1990], [1991]) has been done in cold flow velocity LDV measurement and numerical simulation in a CVCC with same L/D ratio, which can be used to confirm the velocity distribution before combustion from the measurements of this thesis. Second, with this L/D ratio, it is possible to set side windows with enough size to observe the early flame kernel development, which is essential to examine the effect of swirl on combustion.  The chamber, whose body is made from stainless steel, is gas sealed and can stand high temperature and pressure when combustion takes place inside the chamber. One front quartz window of diameter of 101.6 mm and two side quartz windows of diameter of 28.6 mm were used for optical access.  Swirl intensity can be changed by changing the rotating speed of the disc as well as the roughness size on the disc. Three discs with different roughness sizes, shown in Fig. 3-5, were used in the experiment.  3.2.2 Driving section  The driving section includes a submersible motor, a speed increaser, a power supplier with  36 variable frequency and a sealed cylindrical chamber.  The rotating disc is driven by the  submersible motor in a closed chamber filled with water, shown in Fig.3-3.  For successful operation at high rotating disc speed, sealing along the driving shaft is one of the key parts of the design. Using a submersible motor makes it possible to seal the shaft securely, because the water is virtually incompressible and has much higher density and viscosity than the gases in test section. At very high rotating speed, a substantial amount of heat will be generated by the friction between the rotating shaft and the sealing materials, and will cause excessive high temperature, which could burn out the sealing materials and even the shaft itself. To ensure successful operation at high rotating disc speed, measures have to be taken to prevent the burning of the mechanical parts. To do this there are two ways, ie. to reduce the friction, and to remove the generated heat efficiently. Filling water on the driving side not only has the benefit of secure sealing, but also has the benefit of effective cooling. To reduce the friction and to make the sealing section more compact, a combination of Teflon parts sealing in water side and graphite fibre glass packing sealing on gas side was developed to ensure secure sealing.  The rotational speed of the motor can be changed by changing the frequency of the power supply. The speed range of the disc can be varied from 470 to 9,500 rpm. A speed increaser with input/output speed ratio of 4, shown in Fig. 3-6, has been designed by the author for extending the speed range of the rotating disc. By placing the speed increaser between the driving shaft (No 6) and the submersible motor (No 8), shown in Fig. 3-3, the speed range of the disc can be extended to over 15,000 rev/mm. Plastic gears were used in the speed increaser so  37 that water can be used either as a coolant and a lubricant.  3.2.3 Ignition section  The ignition section includes a Heathkit capacitive discharge ignition assembly (Model CP- 1060), a conventional ignition coil, two electrodes located along the centre line of the cylindrical chamber (one is steady, mounted at the centre of the front quartz window; another is rotating with the disc, mounted at the tip of the driving shaft), shown in Fig. 3-2, and a transistor switch system with which ignition timing can be easily controlled by computer.  3.3 COMPUTER DATA ACQUISITION AND CONTROL  The computer data acquisition and control system includes two sections: hardware and software.  3.3.1 Hardware  A PCL-8 1 2PG enhanced multi-lab card of Advantech Co. Ltd. was used in the experiment of the thesis for data acquisition and process control. The maximum single channel AID sampling rate is 30 KHZ in DMA mode. The data acquisition rate used in this experiment was 20,000 Hz. A maximum of 2000 data can be picked up in one operation and cover a time period of 100 ms so that the rate was 20,000 Hz. Experimental tests have shown that data acquisition frequency is high enough to provide a detailed pressure history of the combustion process. The A/D input  38 range was set at +1- 5V. The accuracy of data conversion is 0.0 15%. The memory segment can save up to 32,767 bytes of conversion data. An INTEL 8253-5 Programmable Timer/Counter provides pacer output at the rate of 0.5 MHz to 35 minutes/pulse to the A/D, which cover a broad range of time period.  3.3.2 Software  A computer program in QUICK BASIC has been developed by the author of this thesis for data acquisition and control. The functions of the software mainly include:  (i) specifying the data acquisition mode and frequency. The data acquisition frequency was set to 20 KHz, and data were read in via direct memory access (DMA). The total data acquisition time period with above setting is 100 ms, which can cover the combustion duration with different swirl intensity (the combustion duration without swirl is about 50 ms).  (ii) programming the logical sequence for the events of high-speed camera initiation, data acquisition and ignition. Because the data acquisition process lasts only 100 ms, the ignition time has to be programming controlled and adjustable so that the whole combustion process (from ignition to the end of combustion) can be captured. The high-speed camera with 34 metre film runs only 2 seconds for maximum speed of 5000 frame per second. The first second is the camera acceleration period. The film reaches designated speed of 5000 frames per second about one second after the start of the camera. To ensure that the flame propagation images can be  39 captured during the last one second of the camera running period, the timings of the spark ignition and the start of the high speed camera have to be accurately controlled by the computer program.  (iii) monitoring the experiment by displaying the data right after combustion. By checking the experimental data right after collection of pressure signals with this function, data in error due to system malfunction can be rejected immediately.  3.4 EXPERIMENTAL CONDITIONS  Stoichiometric natural gas and air mixtures were used in the experiment. Dry air was supplied from an air cylinder. Natural gas from BC gas was used as fuel. The composition of BC natural gas is shown in Appendix II.  The amount of the natural gas was measured by a 50 cubic  centimetre (cc) medical syringe connected close to the fuel inlet port, shown in Fig. 3-3. The uncertainty of fuel measurement is under 0.2 cc, corresponding to a relative error less than 0.5%. Without swirl, ignition was triggered more than 60 seconds after injection of fuel into the chamber. Different waiting time periods had been used to check the reliability of the ignition. It was found that after 30 seconds waiting period, there were no changes in ignition reliability, and the pressure curves were repeatable.  The mixture was considered well mixed after 60  seconds waiting period for the no swirl case, because only after the fuel and air are well mixed, can ignition be reliable and pressure curves be repeatable. With swirl, from disc Reynolds number Re  =  36,000 to 252,000, the waiting period was set to 30 seconds (It was found that the  40 fuel and air were well mixed within five seconds by checking the ignition reliability and pressure curves). The initial pressure of the mixture was 0.1 MPa, and the initial temperature was 298 K. The gap of the electrodes is 2 mm, located at the centre of the cylindrical chamber.  3.5 VELOCITY MEASUREMENTS  The mean tangential velocity and turbulence intensity without combustion were measured by a DISA Type 55 DOl constant-temperature hot-wire anemometer.  The hot wire probe is a  DANTEC Probe 55-P 11. The wire is made of tungsten coated by platinum with diameter 5 micron and length 1.5 mm. The hot wire was calibrated in a wind tunnel before and after the measurements.  Air was used as working fluid. Three rotating discs with different roughness sizes (roughness height 1.5 mm of disc I, 3.0 mm of disc II, and 5.0 mm of disc III) were used in both cold flow measurements and combustion experiments, shown in Fig. 3-5. The tip speeds W of the rotating discs were used as the reference velocities. With the same disc roughness size, the dimensionless mean tangential velocity and turbulence intensity distributions appear to be independent of the rotating disc speed. As Fig. 3-7 shows, the profiles of mean tangential velocity (normalized by the tip speed of the rotating disc) are approximately the same within experimental uncertainties at rotating disc speeds of 4000 rev/mm and 6000 rev/mm, and as are the profiles of turbulence intensity. This similarity in velocity distribution indicates that for a given disc roughness the normalized velocities do not vary with Reynolds number WRJv. With different roughness sizes  41 the mean velocity profiles and turbulence intensity distributions are similar in shape but different in magnitude. Figure. 3-8 shows the measured radial distributions of mean tangential velocities and turbulence intensities on the middle plane between two side walls. The LDV measurements and the numerical modeling of Riahi ([1990], [1991]) have shown that the swirling flow generated by a rotating disc in a cylindrical chamber with same size as that used in present study is nearly two-dimensional except in the small regions close to the side walls.  The velocities from hot wire measurements were determined by the calibration curves, which were obtained by calibrating the hot wire probe in a wind tunnel before and after the velocity measurements.  The accuracy of velocity measurements is thus mainly determined by the  accuracy of the calibration curves. The errors in the calibration involve the uncertainty of the pilot tube readings and the truncation errors of the A/D conversion. Compared with the pitot tube measurement error, the truncation error of the A/D conversion is negligible. By proper setting of the pitot tube velocimeter, the relative error of the pitot tube reading can be as low as 3%.  3.6 PRESSURE MEASUREMENTS  A PCB 11 2A piezometric hi-sensitive pressure transducer was used to convert the pressure signals to electrical signals. The electrical signals were amplified by a PCB 462A charge amplifier before feeding to the A/D card in a 486 PC computer.  42 The combustion duration was determined by measured pressure data. The end of the combustion process was considered as the moment when the measured pressure P reaches its maximum value or when the pressure change rate DPJDt change the sign from positive to negative. From the measured pressure data we can directly derive the mass fraction burned. It has been shown (refer to appendix III) that a linear relation between combustion pressure and mass fraction burned provides a good approximation, ie. x  =(PPo)I(PmaxPo)  (Lewis [1987]; Hill [1988]), where x is  0 is the initial pressure, and the mass fraction burned, P is the pressure, P  max  is the maximum  combustion pressure.  The initial burning period was defined as the time period from ignition to 10% Pmax, noted as DTO-10%; similarly the main combustion duration, i.e. 10-90% mass burned, was defined as the time period of 10% Pmax to 90% Pmax, noted as DT1O-90%, for the reasons discussed in Chapter 2.  Errors in pressure measurement come from different sources. They are: i/the pressure transducer; ii/ the charge amplifier; iii/ the A/D conversion. Errors from the pressure transducer consist of two parts, the resolution error and the linearity error. The linearity of the pressure transducer PCB 1 12A is less than 1.0 percent with 14 Pa (0.002 PSI) resolution. Errors from the charge amplifier include the electronic noise and the linearity error. The linearity of the charge amplifier PCB 462A is 0.1 percent with electronic  43 noise (peak to peak) of 0.3 my. The A/D conversion resolution of the PCL 812-PG card is 0.02 percent of the full scale digital output.  Errors in experiments can usually be evaluated by standard deviations of measured quantities:  AY=  (3-1)  IE(.AX.)2 £ ax  44  1 1 is the independent variables, and Ax where Y is the measured quantity, AY is the error in Y, x . 1 is the error in x  Using Eq.3-1, we can evaluate the uncertainty of pressure measurement, ie. AP when P equals 0.6 MPa (about 90% mass burned):  =  J  (EfrP)2+(.Aq)2+(EP)2  +(.f Au) +( 2  aI’  2 AiiM,)  (3-2)  where P is pressure, E) is the linearity of the pressure transducer, q is the electrical charge, E)C is the linearity of the charge amplifier, u is the voltage, and  AI  is the digital output unit from  A/D conversion.  Using the data given in the manuals of the instruments, we can calculate the derivatives in Eq.3-2:  44  )P/3u  0.8427 [PSlfPicocoulomb]  =  300/356  =  ap/aq x aq/an  =  < fl/aU =  0.8427 x 0.1726 x 200 =29.09 [PSI/Volt]  29.09 x 10/4095  0.071 [PSI/unit].  aP/aflAD =  aP/au x  where  is the conversion unit of the charge amplifier.  cA  aU/aflAD =  =  Substituting all these values into Eq. 3-2, one obtains that zS.P equals 0.00604 [MPa], i.e. about one percent of the measured value.  3.7 HIGH SPEED SCHLIEREN PHOTOGRAPHY  A laser beam with two wave lengths 488.0 nanometres and 514.5 nanometres from the TSI 91007 LDV system was used as light source for schlieren photography. A laser beam (about 1 mm in diameter) from the LDV system is expanded to about 50 mm in diameter and then passes the test section through two parallel side windows of the same diameter-28.6 mm (direct schlieren). The side windows were so designed that, for best observation and photography, the electrode gap is at the middle of the illuminated area. A laser beam from the test section is reflected 90° by a plane mirror to the front of the test section and then converged by a lens. A thin metal sheet with a round hole of diameter 1 mm, serving as a circular knife, was placed at the focal point of the laser beam to cut  part  of the deflected lights to form schlieren image.  A Red Lake  HYCAM 16 mm high speed camera is located in the front of the test section and also right after the knife. With such an optical arrangement it is possible to obtain a three dimensional view of the combustion process in the test section by recording both the front normal image from front  45 window and the schlieren image from side view in the same picture.  Errors in high speed photography are mainly due to image distortion and errors in determining the film running speed.  The image distortion is caused by the imperfect optical system and the film developing process, and is very difficult to evaluate. Usually the quality of the image is ensured by the camera manufacturer and the standard film developing process. Only in the case that there are curved surfaces on the observation windows of the test section, is it necessary to correct the substantial image distortion due to the curved surfaces. In this experiment flat optical quartz windows were used. As a result, there is no visible distortion of the images.  The running speed of the film is determined by recording a optical signal with preset frequency on the film. The errors in determination of running speed Consist of the error in frequency of the optical signals and the uncertainty of determining the location of the optical signals on the film.  The optical signal frequency is 975 Hz.  With maximum deviation of ±1 Hz, the  uncertainty of the time interval between two neighbour optical marks is 0.00 105 milliseconds. Because there are five frames of pictures between two marks, the timing uncertainty for each picture due to frequency error is 0.00021 milliseconds. The uncertainty in optical mark location is 0.2 mm. From this, we find that the timing uncertainty due to location uncertainty of the optical marks is 0.00 105 milliseconds. The total timing uncertainty, by Eq. 3-2, is thus 0.00 107 milliseconds. For film speed of 5000 frames per second, this error corresponds to 0.5 percent  46 of the time interval between two succeeding pictures.  3.8 SUMMARY  From the proceeding discussion of this chapter, we can summarize that:  i/the test rig developed for this thesis work can generate swirl over a broad range from 0 rev/mm to 15,000 rev/mm, which makes it possible to examine the different effects of swirl on combustion;  ii/ the computer control system is reliable and flexible, which makes it possible to coordinate the transient events, e.g. ignition, pressure data acquisition, and high speed photography, and to make combustion pressure signal collection and schlieren photography simultaneously;  iii? the errors in fuel-air ratio are under 1%;  iv/ the errors in velocity measurements are within 5% of the measured values;  v/the errors in pressure measurements are within 1% of the measured values;  vi! the errors in timing of high-speed photography are within 0.5% of the time interval of two succeeding pictures.  11  .AOMN  UOD9  \  saj  48  W4ll  Rotating shaft  •‘  • .  side windows  : •  .  ;  .•/  —L  Z e1ectgd —-i.  . •  Frontwindow  Roughness  Rotating disC  r  \  Rotating shaft  side windows  -  /  Front window L  Roughness  IL r  Fig. 3-2 Test section configuration  49  o  0  o tA  .4  -  5  p .4 T (ON Cl  0  a  0  0  aD 0  TTT r  OOLn  (O  çd-3  ‘0 0  -  D<O  oc  0 f)  z ‘0  n  P1 0 cf  n  3-  C  w  C-)  Fig. 3-3 Constant-volume combustion chamber  C  Compressed Air Naturo.l gas  -  o ‘9  _____________________________________  FiieI lnlet valve  Exo.ust valve  0  Side windows  Fr’ont windows  Presur’e transdlAser  Air inlet valve  Charge  0  Ignition  Amplifier  O)O  Circuit  0  C.) I)  • -4  41)  0  ‘I  41.)  0  Cl)  0  Cl)  C  cM  0 95.2-  2 n  —  ,,  L Z3  -  Z4  Z3  ‘‘  Lf\’\  80 mm  //  -  N’_\  /  1’  1’  --  ><  ‘Ji  -Z2  Z2  z1  __rs_  //  ri__-u,:JL // // Ny/ //  power out  fli  Z1/Z2  n  Z3/Z4  power  4fl 1 = 2 fl  =2  =2  SPEED INCREASER  53  0.30 ——A—— -  ‘0.50 -K’  mean tangential velocity, Re=72,100 (disc II) velocity fluctuation, Re=72,100 (disc II) mean tangential velocity, Re=108,000 (disc II) velocity fluctuation, Re=1 08,000 (disc II) C  >s  0.20  5 0.40 0  4-  C.)  >  0.30  -  4-  C.) 0  C  -  Cu  >  4-.  -D  0.20  0.10  -  N =  S o  S 0  z  zolo -  0.00 0.00  I  I  I I  I  0.25  0.50 Radial position [r/R]  I  1  0.75  Fig. 3-7 Radial distributions of mean tangential velocity and turbulence intensity at different Re (disc II)  0.00  54  0.80  0.70  I  mean tangential velocity [Riahi, 1990]  • LI  -  —-—-  -  0.60 >  •1-  -•-  0.50  0.40  I  p  I  I  ——Q—-  velocity fluctuation [Riahi, 1990] mean tangential velocity (disc I) velocity fluctuation (disc I) mean tangential velocity (disc II) velocity fluctuation (disc II) mean tangential velocity (disc Ill) velocity fluctuation (disc Ill)  0.30 0 4-.  U  -  4-.  0 D  0.40  0.20  -  >.. 4-  0 0  C Cu  a) 0.30  >  -  ci)  N  N  0.20  0.10  0.10  -  -  •0  (2  0.00 0.00  --  -..-.  Th----...-.- a--c EVV  v--.L  —  0.25  0.50  --e  --  I  0.00  0.75  Radial position [rIR]  Fig. 3-8 Mean tangential velocity and turbulence intensity, hot wire measurements (present study) and LDV measurements (Riahi, 1990)  55 CHAPTER 4. EXPERIMENTAL RESULTS  4.1 INTRODUCTION  The experimental results in this chapter include the combustion pressures measured by a pressure transducer, and the flame propagation pictures taken by the high speed schlieren photography. Combustion duration at different swirl levels has been evaluated from the combustion pressure curves. Swirl intensity can be classified into three levels, ie. low, intermediate, and high levels, depending on the different effects of swirl on combustion duration. At low and high swirl levels the combustion durations were longer than that at intermediate swirl level. The high speed schlieren photography pictures showed that swirl-induced buoyancy suppressed the burning zone growth in the radial direction, causing spheroidal flame kernels.  At high swirl level it was  observed that, while the flame kernel kept expanding in the axial direction, its radial growth was supressed at a radius, which can be defined as the stable radius, depending on the swirl level and the physical and chemical properties of the mixture. The swirl intensity has been classified in terms of the ratio of the stable radius of the burning zone to the dimension of the combustion chamber.  4.2 COMBUSTION DURATION  Combustion duration at different swirl levels were obtained from measured combustion pressure signals. Three rotating discs (disc I, II, and III, with roughness height 1.5 mm, 3 mm and 5 mm  56 respectively) have been used in the experiment to produce different turbulence intensities (low turbulence, u’ 0.5% W, intermediate turbulence, u’ 1.5% W, and high turbulence u’ 3.5% W, where W is the tip speed of the rotating discs) at same Reynolds number.  They can be  considered as bulk average intensities, because within the uncertainty of measurements the turbulence intensity appears to be approximate uniform throughout the combustion chamber. Figure 4-2 shows the variation of the total combustion durations and maximum combustion pressures with Reynolds number at different turbulence intensities. From Re  =  0 to Re  the maximum combustion pressure increased with increased Reynolds number. increased from Re  =  =  36,000,  As swirl  36,000 to a Reynolds number, depending on turbulence intensity, the  maximum combustion pressures remained almost unchanged. This Reynolds number is about 120,000 at low turbulence intensity, 170,000 at intermediate turbulence intensity, and 230,000 at high turbulence intensity. The cause of this variation in the maximum combustion pressure should be the combined effect of turbulence and combustion duration on heat loss from the mixture to the walls of the combustion chamber.  The variations of early combustion duration (DTO-l0%) and main combustion duration (DT1O90%) with the swirl intensity is plotted in Fig. 4-2. It should be noticed from the plot that the initial combustion duration was less affected by the swirl level than the main combustion duration. At low turbulence, the initial combustion duration remains almost constant from Re  =  0 to 108,000, and then increases when the swirl intensity increases further. At intermediate and high turbulence, the initial combustion duration remains almost constant over a broader ranger than that at low turbulence intensity.  57 A number of experimental results (such as those discussed in Chapter 2) showed that the burning rate increases with increased turbulence intensity. On the other hand, the heat loss from the burning zone to the surrounding unburned gas and the solid surfaces (e.g. those of electrodes and the chamber wall) will significantly reduce the temperature of reaction zones close to boundaries so as to reduce the burning rate and even quench the flame in those regions. The rate of heat loss per unit volume of burning zone to the surrounding determines the rate of burning zone growth, and is affected by many factors. The surface-to-volume ratio of a burning zone is an important factor, especially in the early stage of flame kernel growth.  In the experiment of this thesis, electrodes are located on the axis of the cylindrical chamber; and the mixture is ignited at the centre of the chamber. Swirl induced buoyancy (which will be further discussed in section 4-3) can have significant effect on early flame kernel growth (e.g. 0-10% mass burned) by its effect on the surface-to- volume ratio. When there is no swirl, the flame kernel grows nearly spherically, and the surface-to-volume ratio is the minimum. With swirl, the growth of the flame kernel will be uneven due to the buoyancy effect, ie. the radial growth will be slower than axial growth. The result is flame kernel elongation which leads to greater surface-to-volume ratio, greater heat loss from the flame kernel to the electrodes, and slower flame kernel growth rate than without swirl. After the burning zone grows large (e.g. 10% mass burned), heat transfer to the electrodes is less significant because the surface area of the electrodes becomes negligible comparing to the total contact area between the burning zone and the chamber walls.  58 Increased swirl changes burning rate by increasing turbulence intensity, heat transfer, and buoyancy. The first factor could be expected to increase the burning rate; the second one could reduce the burning rate; and the third one could change the shape of the burning zone. The net effect may be the combination of these three factors.  The appearent insensitivity of early  combustion duration to swirl intensity at low and intermediate swirl could mean that the gain in burning rate due to turbulence is cancelled by the loss in burning rate due to heat transfer. However there are no direct experimental measurements which show that heat transfer can reduce burning rate.  The situation is different with the main combustion duration, which, with disc I for example, decreased continuously from no swirl to Reynolds number of 72,000, changed slowly from Reynolds number of 72,000 to 126,000, and then increased rapidly as the Reynolds number increased further. The maximum pressure experienced a reverse variation with swirl intensity. This indicates that shorter combustion duration results in higher maximum combustion pressure due to less heat loss in a shorter time period.  With discs II and III, the main combustion  duration varies with swirl intensity in a similar way.  From Fig. 4-2, we can also see that the shortest total combustion duration (0-90% mass burned) is less affected by the turbulence intensity, and occurred around Re  =  125,000. The significant  effect of turbulence on the burning rate is that higher turbulence leads to a broader range of swirl intensity over which the main combustion duration remains lower than that at lower turbulence. At low turbulence (disc I), the combustion duration started to increase rapidly after the Reynolds  59 number exceeded 120,000. But at higher turbulence the combustion duration did not increase substantially until the Reynolds number exceeded 170,000 for intermediate turbulence level (disc II) and 220,000 for high turbulence level (disc III).  To separate the effects of turbulence and swirl on the main combustion duration, curves with constant turbulence intensity were plotted, shown in Fig. 4-3. From this plot, we can conclude:  i/ at same turbulence intensity, increased swirl leads to increased combustion duration, except at very low turbulence intensity; uI at same swirl, increased turbulence intensity always leads to decreased combustion duration.  4.3 HEAT TRANSFER  Swirling flow and associated turbulence not only affect combustion duration, but also affect heat transfer from the burned and unburned mixture to the walls. Complete heat transfer analysis needs details about boundary layer structure, temperature distribution, species concentration distribution, and geometry of the combustion chamber, and is not the objective of this thesis. In this section, the focus is on global heat loss from the mixture to the surrounding during combustion.  The total heat loss during combustion was derived from the pressure difference between the adiabatic combustion pressure and the measured pressure. The adiabatic combustion temperature was calculated by KIVA II. With the calculated adiabatic combustion temperature, the adiabatic  60 pressure and internal energy of the burned mixtures were calculated by STANJAN, a FORTRAN program developed in Stanford University for thermal equilibrium state calculation.  With  measured maximum combustion pressures, the internal energy of burned mixtures at different swirl levels can be calculated in the same way by STANJAN. The total heat loss at different swirl levels can then be obtained by subtracting the corespondent internal energy from the adiabatic internal energy.  0 during combustion with swirl levels, Figure 4-4 shows variation of relative total heat loss QIQ where  0 is the total heat loss without swirl. Three curves Q is the total heat loss with swirl, Q  are corresponding to disc I, II, and III.  Similar to the combustion duration, total heat loss during combustion can be reduced in a certain range of swirl level. At low swirl, the relative heat loss decreased to about 80% of that without swirl, while Reynolds number increased from 0 to about 40,000. At intermediate swirl, heat loss kept low (about 20% lower that without swirl), and was relatively insensitive to the change of Re. At high swirl, the total heat loss increased with the increased Re, and exceeded the total heat loss without swirl at very high swirl level.  The average heat transfer rate, defined as the relative heat loss divided by DTO-90% (the time period from ignition to 90% mass burned), can also be affected by swirl, but in different pattern from the total heat loss. Figure 4-5 shows the mean heat transfer rate at different swirl levels, normalized by the mean heat transfer rate at zero swirl. The heat transfer rate increased almost  61 monotonically while the swirl intensity increased. The disc with biggest roughness is associated with highest heat transfer rate.  4.4 FLAME KERNEL CONFIGURATION  Images of flame kernel development at different swirl levels were recorded by high speed laser schlieren photography. The coverage and the view direction of schlieren pictures relative to the test section are shown in Fig. 4-6.  The pictures show that flames propagate in different shapes at low swirl, intermediate swirl and high swirl (corresponding to disc Reynolds numbers of 72,100, 108,000 and 172,000). quiescent (Re  =  0) and low swirl (Re  =  At  72,100 and lower), the observed flame shapes are nearly  spherical. Figure 4-7 shows the flame growth at Re  =  72,100 from ignition at centre up to  diameter 30 mm (the size of the side windows). It is seen that the initial flame shape is almost not affected by the buoyancy at low swirl.  At intermediate swirl (Re between 72,100 and  144,000), the flame shapes appear to be spheroidal with the long axis in the axial direction and the short axis in the radial direction of the cylindrical combustion chamber, as shown in Fig. 4-8. This indicates that at intermediate swirl the centripetal acceleration has suppressed the flame propagation in the radial direction. When swirl intensity increases further with Reynolds number of 172,00, as shown in Fig. 4-9, this suppression becomes large enough so apparently to stop radial expansion until the flame kernel approches the side walls. This happened at a radius of 10 mm and within the period of 2 milliseconds, as shown by Fig. 4-9(d) to 4-9(e).  62 This radial dimension freezing can also be seen in Fig. 4-10, a plot of radial dimension change versus mass burned fraction at different swirl levels.  At the same mass-fraction-burned, a  spherical burning zone has a larger radial dimension than a elliptical burning zone with the long axis along the swirl axis because the volume of these burning zones is the same. In Fig.4-l0, the curve with circular symbols represents the radial growth of the flame kernel at no swirl, a nearly spherical growth. As the swirl intensity increased, the radial dimension of the burning zones became smaller. When the swirl intensity increased further, to Re= 172,000 for example, the radial dimension increase stopped (at about 20% of the radius of the combustion chamber in this experiment) for a period from 0.3% to 0.4% mass fraction burned, shown as the lowest curve (Re= 172,000) in the Fig.4-10. The development of the axial size of the flame kernel has a reverse trend, shown in Fig. 4-11. The radial dimension freezing indicates that swirl-induced buoyancy not only reduced the radial dimension growth rate, but also froze the radial dimension growth at a swirl level. From the same curve (Re=172,000) one can also notice that the radius of the burning zone increased again after 0.4% mass burned fraction. This is due to the axial limitation of the burning zone development by the end walls of the combustion chamber.  4.5 CLASSIFICATION OF SWIRUNG COMBUSTION  In this section a method to classify the strength of swirling combustion is introduced. A nondimensional number SBV (Strength of the Burning Vortex) is proposed to classify the swirl level and characterize the behaviour of a rotating burning zone.  63 The mixture, in which combustion takes place, is considered as a continuous medium; in other words, no discontinuous changes in mixture properties, for example, density and temperature, are involved, though the results from this discussion could be applied to more general cases.  Considering an axisymmetric burning zone with flame front at a radius r (r is close to the stable radius r, which will be defined in succeeding paragraphs), rotating with a swirling flow at angular speed  Co.  shown as in Fig. 4-12, we denote this rotating burning zone as the ‘burning  vortex’, and define a non-dimensional number SBV (Strength of the Burning Vortex) to characterize the behaviour of the burning vortex.  Two time scales, which involve five independent variables (density ratio of unburned and burned gases Pu/Pb’ angular speed and radius of a burning vortex and  Co  and r, flame speed and thickness Sf  ), can be considered here.  The first is the buoyancy acceleration time scale ta  —  (3/a)”  ta,  given by (4-1)  where 6 is the flame thickness, a is the buoyancy acceleration due to density difference between burned and unburned gases.  Considering a parcel of burned gas immersed in a cold gas right ahead of the flame front at a radial location r, and rotating with the cold gas at the same angular speed  (0,  we can write the  force on the unit volume hot gas as F’=prCo . To keep rotating with the cold gas, the unit 2  64 volume of hot gas needs the force F”=  The difference of these two forces is usually  . 2 pbrco  called the buoyancy force (per unit volume), ie. F  =  F’- F”  =  (p  -  Pb)  r  0)2  (4-2)  Under this force, the hot gas parcel moves radially inward with the acceleration rate a. From Newton’s second law F  =  ma, ie.  (P  -  Pb) r  02  =  Pb a  we obtain the buoyancy acceleration of a unit volume of burned gas: a  =  (P  -  Pb)’Pb r  0)2  (43)  where p, and Pb are the densities of unburned and burned mixtures, r is the radius from the centre of the vortex to the location considered (the radius of the burning zone here), and Co is angular speed of the vortex. The effect of this buoyancy acceleration is to push the hot gas back to the burned side (to the rotating centre of the swirl). In the case of combustion, this acceleration suppresses the flame propagation against the acceleration and enhances the flame propagation along the acceleration. In other words, if the combustion initiates at the rotating centre of a swirling flow, the buoyancy force tends to keep the burning zone at the swirl centre. From Eq. 4-1, 4-3, we can see that the stronger buoyancy effect on combustion means shorter buoyancy acceleration time scale, and vice versa. Similarly, we can also consider a parcel of cold gas immersed in a burned gas, and will obtain the same relation between the acceleration and the density difference except in different proportion, which will not change the final result.  The second is the flame propagation time scale t,: öIS  (4-4)  65 where Sf is the flame speed.  To characterize the property of a burning vortex, we can define a non-dimensional number, say the strength of the burning vortex SBV, as the ratio of these two time scales, ie.  SBV  t =  -  (4-5)  ta  Substituting Eqs. (4-1) and (4-4) into Eq.(4-5), we have  Ôa  SBV  (4-6)  -  Using Eqn.(4-3) and considering —  F/Sf  (4-7)  we obtain  SBV  =  A  2 PPb  (4-8)  Pb where A is a constant and can be set to unit tentatively, F is the thermal diffusivity of the mixture. From Eqn.(4-8) we can see that the greater buoyancy acceleration (faster vortex rotating speed and larger density difference across the flame front) leads to larger value of SBV, while faster flame speed causes a smaller value of SBV, ie. reduces the buoyancy effect.  Consider a burning vortex rotating at  Co  and with radial expansion frozen at a radius r due to the  66 buoyancy effect, the burning zone being allowed to expand freely along the vortex axis, we can define the value of SBV at this case as critical value SBVC, and define the radius of this burning vortex as the stable radius r, which can be obtained from Eq. 4-8 by setting SBV equal to SBVC, ie.  =  SBT’C  (49) PrPb rt2  From the schlieren pictures shown in Fig. 4-9(d) and 4-9(e), we find that the burning zone was frozen at a radial location 11 mm away from the swirl rotating centre before reaching the side walls. By definition the stable radius is 11 mm. Leting Sf equal 0.6 [mIs], Pu/Pb equal 7, F equal Is], and o equal 50% of the rotating disc speed (9500 rpm), we find with Eqn. 4-8 2 0.15E-4 [m that the critical value of SBV is 1.1. If the SBV was properly defined, the critical value of it should be an invariant, i.e. independent of mixture properties, swirl intensity, and turbulence intensity.  The generality of Eqs. 4-8 and 4-9 could be checked by a specifically designed  experiments; but this has not yet been done.  The SBV values (normalized by the value of SBVC) of a burning vortex, with same radius (ie. 11 mm) at the different rotating disc Reynolds number Re, are plotted in Fig. 4-13, from which we can define three regimes of SBV, ie. subcritical, critical and supercritical. When the SBV is subcritical, the flame can still propagate radially against the centripetal acceleration; in other words, the burning vortex can still expand in radial direction; when the SBV is critical, the flame front will stop moving in radial direction, ie. the diameter of the burning vortex will be frozen; when the SBV is supercritical, the flame front will be pushed back towards the rotating centre  67 of the vortex and stabilized at the stable radius r with which the SBV is critical.  Fig.4-14 shows the stable radius of a burning vortex (defined by Eqn. 4-9, and normalized by the radius of the combustion chamber) at different swirl levels. This stable radius gives an upper limit of the radial dimension of a burning vortex if its expansion is not limited by the dimension of the combustion chamber. A burning vortex with a radius larger or smaller than this stable radius is radially unstable and tends to adjust its radius to the stable radius r.  It should be mentioned that the SBV value and the stable radius not only depend on the swirl intensity but also depend on the physical and chemical properties of the reactants and products, especially on the flame speed. From Eq. 4-8 we can see that 30% increase in the flame speed leads to about 50% increase in the stable radius; in other words, at same swirl level, in the mixture with faster flame speed, a burning vortex tends to grow thicker than that in the mixture with slower flame speed.  With the stable radius and referring to Fig. 4-1, we can classify the swirl levels into three categories, shown in Fig. 4-14: (i) low swirl (rJR> 1.5), at which the burning rate increases with increased swirl; (ii) intermediate swirl (1.5  rJR  0.5), at which the burning rate reaches its  maximum, and relatively insensitive to the change of the swirl level; (iii) high swirl (rJR < 0.5), at which the burning rate decreases with increased swirl.  From this classification, we can increase the burning rate by conducting the combustion process  68 at a proper swirl level, for example the intermediate swirl level, which can be considered as the optimum swirl level in term of maximizing the total combustion rate. Low swirl level is also acceptable if the requirement of combustion rate enhancement is not overwhelming; but high swirl level should be avoided to prevent unnecessary increase in combustion duration and heat loss.  From this classification, we find that the swirl level is not only dependent on the rotating speed of the swirl, but also dependent on the flame speed, density ratio, and even the size of the combustion chamber. At given rotating speed of a swirl, combustion could take place at high swirl if the flame speed is low, or at intermediate or low swirl if the flame speed is high enough. Furthermore, at given swirl speed and given flame speed, combustion could take place at high swirl if the combustion chamber is big, or at intermediate or low swirl if the combustion chamber is small.  In the above discussion, it is assumed that an axisymmetric burning zone is surrounded by unburned reactants, that expansion of burning zone along the rotating axis is unlimited, and that small perturbation parcels gain the local velocity instantaneously. The assumption of solid body rotation is also introduced in evaluation of centripetal acceleration.  69 4.6 SUMMARY  The experimental results and the following analysis in this chapter can be summarized as:  (i) the combustion pressure data showed that swirl has significant effect on burning rate; at low swirl, combustion duration increased with increased swirl; the shortest combustion duration can be reached at intermediate swirl, which can be considered as the optimum swirl level in term of combustion rate enhancement; the combustion duration increased when the swirl intensity increased from intermediate to high; swirl has stronger effect on main combustion duration (1090% mass burned) than on the initial combustion duration (0-10% mass burned) with central ignition;  (ii) the total heat loss is also affected by swirl; at intermediate swirl level, the total heat loss was the minimum; the total heat loss rate increased when the swirl intensity increased; increased turbulence intensity led to increased total heat loss and increased total heat loss rate;  (iii) the high speed schlieren photograph pictures showed that swirl-induced buoyancy has a substantial effect on the burning zone configuration, leading to elongation of the burning zone in the direction along the axis of the swirl; it was observed that, at high swirl, the radius of the burning zone froze at a size, which was defined as the stable radius of a burning vortex, while its axial expansion was not limited by the end walls of the combustion chamber;  70 (iv) with the ratio of the stable radius r to the radius of the combustion chamber R, ie. r/R, the swirl can be classified into three categories: a/low swirl (rJR> 1.5), at which the burning rate increases with increased swirl; b/intermediate swirl (1.5  rJR  0.5), at which the burning rate  reaches its maximum, and relatively insensitive to the change of swirl intensity; c/ high swirl (rJR <0.5), at which the burning rate decreases with increased swirl; from this classification, intermediate swirl (some times low swirl if combustion rate enhancement is not a overwhelming issue) is recommended, and high swirl should be avoided for effective combustion.  71  0  0 DT U I U C 0  1.4  x  combustion duration (0-90% mass burnt) at Re=0  --  0 Pmax  --  E IA  maximum combustion pressure at Re=0  E  0  combustion pressure  1.2  ci) (4) Co  a)  I-.  D  1.0  I.  0  0  Co  .4-.  0.8  1))  :3  .  E  S  I  0 C.)  0.6  combustion duration  0.6  0  .4-.  S  —0---- maximum pressure, disc I  0.4  -—•-----  N  -0  0.4  DTO-90%, disc I maximum pressure, disc II  S  DTO-90%, disc II —---0------ maximum pressure, disc III DTO-90%, disc HI  ——-  0  C)  C :3  .1-•  G)  0  0.2  z  0.2  CII  -—-•—•  0.0  0.0 0  50,000  100,000  150,000  ci) •  200,000  250,000  0  z  Re [WR/vJ  Fig. 4-1 Total combustion duration (0-90% mass burned) and maximum pressure ’ 3.5% W) 9 with disc I (us’ 0.5% W), disc II (u’ 1.5% W), and disc III (u O-90% = 37±1 [msj 0 at different swirl levels (Re = WRJv), DT  72  01.8 I—  U  I— 1.6 ED 21.4 D -  1.2  C 0  j1.0 gO.8  a) .  0.6  Q0.4  z  0.2  0.0 0  50,000  100,000  150,000  200,000  250,000  Re [WR/v]  Fig. 4-2 Initial combustion duration (0-10% mass burned) and main combustion duration ’ 0.5% W), disc II (u’ 1.5% W), and 9 (10-90% mass burned) with disc I (u ’ 3.5% W) at different swirl levels (Re = WR/v), 0 disc III (u -10%/DT = 0.95±0.02 OO-90% DT 1 O-1O% = 18±1 [ms], 0 0 DT  73  0  1U  1.2  i  i  i  p  -  -  I  I  I  I  I  I  I  I  I  I  I  turbulence intensity [mis]  -  0 0)  I— U  1 .0  _u’  0.4  0 [mIs] 0.03  0.21  A  0 0.05  4-.  I  0.6  A  0.8  -  V C 0  0.16  0.19  A  11  A A  Cl)  D  0.13 A  0.16  0.8 1.0 1.2  A  S 0.6  0 C) V 0) N  S I  1.4 A  1.74 1.46  0.4  0  z  0 DT 0  =  18 [ms], main combustion duration at Re 50,000  100,000  =  0  150,000  Re [WR/]  Fig. 4-3 Effect of swirl and turbulence on the main combustion duration  74  1.2 0  0 1.0 C 0 4-  Co  .0  0.8  2  0 C) C  0.6  V 0 Co 0  0.4  4-  a) 0.2  0.0 0  50,000  100,000  150,000  200,000  Re [WR/v]  Fig. 4-4 Variation of total heat loss during combustion with swirl, 0 30% of the total heat release from combustion Q  250,000  75  I  0 C) 0  I—  1.8  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  —0—discl ——-discII —A——disclll  I.’J  0  0.8  0.6 0.4  -  Q total heat loss during combustion with swirl Qo total heat loss during combustion without swirl DTO-90% total combustion duration with swirl 0 0-90% total combustion duration without swirl DT -  -  a)  0.2  -  -  -  0.0 0.000  I  I  I  50,000  150,000  ioo,ooo  I  200,000  Re [WR/v]  a  Fig. 4-5 Variation of total heat transfer rate during combustion with swirl, 0 30% of the total heat release from combustion Q  250,000  76  L  kernel  rotating disc  III  wall  Fig. 4-6 Relative position of the side view schlieren picture  77  (a) 1 ms after ignition  (b) 2 ms after ignition  3 ms after ignition  (d) 4 ms after ignition  (e) 5 ms after ignition  () 6 ms after ignition  (C)  Fig. 4-7 Schlieren images of flame propagation, Re  =  0  78  (a) 1 ms after ignition  (c) 3 ms after ignition  (e) 5 ms after ignition  (b) 2 ms after ignition  (d) 4 ms after ignition  (f) 6 ms after i  Fig. 4-8 Schlieren images of flame propagation, Re  =  108,000  79  (a) 1 ms after ignition  (b) 3 ms after ignition  (c) 5 ms after ignition  (d) 7 ms after ignition  (c)9 rns after ignition  (1) 11 ms after ignition  Fig. 4-9 Schlieren images of flame propagation, Re  =  172,000  80  0.4  0.3 0 Cl)  C G)  E E -D  0.2 as ci) C  U)  [.i  0.0 0.0  0.1  0.2  0.3  Mass burned fraction [%]  Fig. 4-10 Flame kernel radius vs. mass burned fraction at different swirl levels (Re = WRJv)  0.4  0.5  81  0.4  C”  a  0.3  C 0 4-.  ci) E E 0.2  x c’ ci) C 0)  [.1  0.0 0.5  Mass burned fraction [%]  Fig. 4-11 Flame kernel axial dimension vs. mass burned fraction at different swirl levels (Re = WR/v)  82  Fig. 4-12 An axisymmetric burning vortex  83  1.8 1.6 1.4  >  1.2  Cl)  1.o Cl)  0.8 0.6 0.4 0.2 0.0 0.OEO  4.0E4  8.0E4  1.2E5 Re  1.6E5  2.0E5  2.4E5  Fig. 4-13 Regimes of SBV (Strength of Burning Vortex)  84  5.0 4.5 4.0 3.5 3.0 U)  2.5 2.0 1 .5 1.0 0.5 0.0 0  50  150  100  200  250 x10 3  Re  Fig. 4-14 Normalized stable radius of a burning vortex at different swirl levels (Re = WRJv, r is the critical radius, R is the radius of the combustion chamber)  85 CHAPTER 5. COMBUSTION MODEL  5.1 Introduction  A combustion model is an approximate mathematical expression of the physical and chemical processes in combustion. The discussion in this chapter focuses on multi-dimensional numerical modelling of IC engine combustion, though general knowledge in combustion will also be mentioned.  The multi-dimensional simulation of engine combustion processes started with modelling of incylinder cold flow, i.e. fluid flow without chemical reaction (Gosman and Johns [1978]; Griffin et al [19781; Borgnakke et al [1981]). Multi-dimensional numerical modelling of cold flow has been shown to be an effective way of representing the important features of fluid flow in IC engines. Trends can be quite well predicted, though considerable approximations are involved in numerical simulations. There is need for more accurate turbulence models to evaluate the momentum, thermal and mass diffusivities, and more measurement data to evaluate the effectiveness of these numerical simulations.  Multi-dimensional combustion modelling appears to be more complicated and less mature than the multi-dimensional cold flow modelling. In numerical simulation of combustion processes, two extra problems over the cold flow modelling have to be addressed. evaluation of chemical reaction rate, or burning rate.  The first one is the  The second is the evaluation of the  86 interaction between the turbulence intensity, lengthscale and chemical reaction rate. In the text following, starting with the basic governing equations, different approaches to these two problems will be discussed.  5.2 Time-averaged values  In turbulent flow, all quantities, such as velocity, temperature, density and pressure fluctuate randomly. In describing turbulence, the instantaneous value of a quantity, usually decomposed into a mean value cL and a fluctuating value  0’,  0  for example, is  such that (5-I)  There are two methods, ie. time average and spatial average, to obtain the mean value. The time average method has been used here because the turbulent flow is inhomogeneous. The time average ‘1 in Eq. 5-1 is defined by  4-lim  ft  —  (5-2)  T-.r In practice, only limited average time T is used, depending on the accuracy desired.  By  decomposing instantaneous values in the Navier-Stokes equations in the way given by Eq. 5-1, and taking the average of all terms, we can obtain the equations for mean values.  The governing equations used in the computer program are for time-averaged mean values. The turbulence correlation terms in those equations have been modelled so that they can be evaluated by the mean values. In the following sections, the conservation equations, the k-e equations, and  87 the thermodynamic equations are given in the form presented in the KIVA II manual (Amsden et al, [19891); the chemical kinetics equations and the equations for turbulent combustion rate evaluation used in this study for turbulent combustion modeling are presented in the following pages.  5.3 Conservation equations  The mass conservation equation for chemical component m is in the form:  !!f+V.(pjj)  =  V•(PDVXm)+Sm  where p is the mass density of component m, u is the velocity of the mixture, p is the mass density of the mixture, D is the mass diffusivity,  Xm  is the mass fraction of component m, and  Sm is the source term of the component m, which is evaluated by the combustion sub-model. The total mass conservation equation can be obtained by summing Eqn. 5-1 over all components.  The momentum conservation equation is  +V(puu)=-Vp+Vo-V(2/3pk)  (5-4)  where p is the pressure, k is the turbulent kinetic energy defined later, and a is the stress tensor.  The energy conservation equation is where i is the specific internal energy of the mixture, the term pc is the heat release due to the  88  +V(pisi) = —pVi4 VJ+pe +Sq —  (5-5)  dissipation of the turbulent kinetic energy, Sq is the source term of heat release by chemical reaction, and J is the heat flux due to heat conduction and enthalpy transfer by mass diffusion:  J  =  -KWpDE(hmVxm)  (5-6)  where K is the thermal diffusivity, T is the temperature, D is the mass diffusivity, hm the specific enthalpy of component m.  5.4 k-e model  There are a number of turbulence models for evaluating the turbulence diffusivities, among these models the k-e turbulence model has been most widely used.  This model was originally  proposed to model nearly isotropic grid-generated wind tunnel turbulent flow (Launder and Spalding, 1972), but later was also used to predict different kinds of turbulent flows. In this model, the turbulent kinetic energy k defined by  k  =  (57)  ’ are the velocity fluctuation components in radial, tangential and axial 2 where ui.’, u’ and u directions, and its dissipation rate e are used to characterize the turbulent flow. The e is defined  89 by 3  (5-8)  2 k  —i1 =cI  where c is a constant, and 1 is the turbulence length scale.  The k-E equations for the turbulent kinetic energy k and its dissipation rate e are  (5-9)  =  &  Prk  and  (510)  p €VU+ClPk—CZ-3 +V•(pue)=V•(.—-Ve)+C  where C , C 1 , C 2 3 are constants, Pr is the Prandtl number for turbulence kinetic energy k, Pc is the Prandtl number for e, and  k  is the production term. The modelled form of  k  in Cartesian  tensor notation is  =  1 2.iS  -  .pkS  where S 1 is the strain rate tensor given by  auau 1  S  =  ‘‘  11 and S is the velocity divergence, ie. S  =  2ax,  ax  Vu. With the solution of k and e from the equations  given above, the effective turbulence momentum diffusivity  jt  can be evaluated by  90  =  Cp-  (5-11)  where C is a constant. In KIVA II these constants have the values shown in Table 5-1. These values were used in the present work.  In IC engine turbulent flow modelling, the k-c turbulence model has been widely used, though modifications to the model have been deemed to be necessary.  Ramos and Sirignano [19801 applied the k-c turbulence model to calculate the mean velocity, turbulence kinetic energy and heat transfer rate with axisymmetric cold flow in a piston-cylinder configuration.  Using their axisymmetric two-dimensional model incorporating the k-c turbulence equations, Grasso and Bracco [1983] obtained results which indicate small decay in total angular momentum, substantial generation of turbulence by swirl, and the tendency of the turbulence to become uniform even in the presence of swirl. In good agreement with experimental data, their numerical results show that TDC turbulence intensity is proportional to engine speed, insensitive to compression ratio, and linearly dependent on load in the absence of the swirl, and insensitive to load in the presence of swirl. Following up on this work Hayder, Varma and Bracco [1985] used a k-c model to show the importance of diffusion of turbulence generated near the cylinder wall. They also demonstrated the possible importance of swirl, and of piston motion on TDC turbulence intensity. Comparison with the measurements of Liou and Santavicca [1983] served  91 to establish the conditions under which their turbulence representation is realistic.  Gosman, Tsui and Watkins [1984] presented comparisons of predictions with measurements of three-dimensional flows and turbulence intensities in a model engine operating at 200 rpm and 6.7 compression ratio. The ensemble-averaged equations of motion and energy conservation were solved with a compressible flow version of the k-e model. The numerical results show moderate agreement with the experimental data.  Kondoh, Fukumoto, Ohsawa and Ohkubo [19851 applied a two-dimensional computer program with the k-e turbulence model to predict the swirling flows in the compression and expansion strokes for various combustion chamber geometries. Their numerical results agreed reasonably well with measurements and provided a more complete description of the time history of mean velocity than could be obtained by experiments.  Henriot, Le Coz and Pinchon [1989] simulated the in-cylinder flow with a k-e turbulence model in a 4-valve single-cylinder engine with pent roof combustion chamber. In the case of one inlet valve opening, the measured flow is a combination of tumble and swirl and the computational results agree well with the measured ones. But with two inlet valves open, the measured in cylinder flow was a complex tumbling motion which appeared to break up near TDC though not in close agreement with measurements. After similar work Le Coz et al [1990] reported that “the general trends of the fluid motion seem to have been correctly predicted although a detailed agreement with the measurements is not reached”.  92 Naitoh et al [1 990b1 reported both numerical simulation results and comparisons with the LDV measurement. Their computations started at the beginning of the induction stroke and continued to the end of the compression stroke. Computations were performed for both two-valve and fourvalve engines with pentroof combustion chambers, running at 1400 rpm. Their computational results showed that the turbulence intensity with high swirl levels is higher than that with low swirl levels. Their computed flow patterns in the intake process show good agreement with the LDV measurements.  For in-cylinder flow it has been shown by a number of research workers that the k-c equations need to be modified to take into account of the effects of compression on the turbulence generation and streamline curvature on the turbulence diffusivity.  Following the work of Reynolds [1980], who pointed out the important effect of the compressive term on the turbulence generation in highly compressive flow, Elkotb, Abou-Ellail and Salem [1982] have used the k-c model to estimate turbulence behaviour and swirling velocity distributions in a cylindrical swirl chamber of a diesel engine. They confirmed that without modifications to take account of the effect of compression the standard k-c turbulence model does not predict correctly the development of turbulence under the engine conditions. Davis, Mikulec, Kent, and Tabaczynski [1986] performed numerical estimates of the behaviour of rotating turbulent flow in the cylinder for spark ignition engines.  However they found it  necessary to make substantial change to the estimates of the production of turbulent kinetic energy used in standard models in order to bring experimental and numerical values into  93 agreement. In particular they found that the TDC turbulence tends to be strongly affected by turbulent diffusion from the cylinder wall. Ahmadi-Befrui and Gosman [1989] applied the three modified k-e models, due to Watkins [1977], Morel and Mansour [19821 and El Tahry [19831, in their multi-dimensional numerical model to take account of the compressibility effects on incylinder flow. The effectiveness of these modifications was examined by comparing numerical results with measurements from an Imperial College model engine. They concluded that the proportional constants in the introduced compressive terms have to be carefully selected so that the compression effect on both turbulence kinetic energy generation and dissipation is compatible.  Bradshaw [1969, 1973] reviewed extensive evidence that the wall shear stress increases in flow over concave surfaces and decreases in flow over convex surfaces. To account for the effect of streamline curvature on shear stress, it is necessary to modify the widely used standard k-e model (proposed by Jones and Launder [1972]), which usually works well in predicting the incompressible isotropic turbulent flow without or with minor curvature effect, to accommodate the specific case for in-cylinder, compressible turbulent swirling flow. It has been shown (see Wilcox and Chambers [19771) that the effect of streamline curvature is mainly to increase or decrease the normal component of turbulent fluctuation, and thus the shear stress without substantially changing the total turbulence energy. A full account of the effects of curvature on turbulent shear stress requires separate treatment of three turbulent fluctuation components, u’, v’ and w’. However, even in the cold flow case, solution of the nine differential equations for separate treatment would require extensive computation time and storage capacity. To avoid this complexity a number of approximations have been tested. In their numerical simulation Riahi,  94 Salcudean and Hill [1990] compared three turbulence models, designated as k-i, k-e and e-2 (or Wilcox and Chamber model).  The effects of streamline curvature were accounted for by  introducing a modification term in the standard k-l and k-e models. The e-2 model due to Wilcox and Chamber model [1977] is concerned only with the contribution of the normal component of turbulent fluctuation v’ to the Reynolds stress. This implies that the effect of curvature is manifested primarily by its effect on v’, which in turn affects the shear stress and the dissipation. The computational results showed that with suitable adjustment of empirical constants the modified k-i model and k-e model can represent curvature effect within the investigated range. The Wilcox and Chamber model, which requires no additional empirical constants, can accurately represent the streamline effect on shear stress in two-dimensional axisymmetric flows.  The effect of rapid compression on the turbulence generation and dissipation are taken account Vii in Eqn. 5-9, 5-10. The effect of streamline curvature 2/3C 1 3 (C by terms -2/3pkVii and ) on turbulence diffusivity has not been fully accounted for in the k-e equations above. And no wall damping effect on turbulence decay rate is included in this model. Improvement of the present k-e turbulence model used in the KIVA II code will be left for further research work. The main purposes of the numerical part of this thesis are to examine the effect of swirl on combustion process and to develop a turbulence combustion model with a multi-reaction-step and multi-fuel-component scheme.  5.5 Thermodynamic equations  95 The working fluid is assume to be an ideal gas mixture. The total thermal state quantity is equal to the summation of the quantities of each species from which the mixture is consist of, i.e.  p = RT  S (p/W)  p i(T) =  S p Im(T)  p Cp(T) =  S p CPm(T)  hm(T) = Im(T)  +  RTIWm  where R is the universal gas constant, Wm is the molecular weight of component m, i(T) is the specific internal energy of component m, the specific enthalpy and specific heat at constant pressure for component m are denoted by hm(T) and Cpm(T), which are read from a input data subroutine constructed from different data sources.  5.6 Chemical kinetics  Evaluation of chemical reaction rate is the topic of chemical kinetics, which defines relations between species concentration, temperature, activation energy and conversion rate from reactants to products for element reactions. In engineering problems, for example combustion of most hydrocarbon fuels in which the mechanism of chemical reaction is too complicated to be  96 interpreted, a simplified chemical reaction scheme, which empirically assumes that the conversion of reactants to products completes in one or a small number of chemical reactions, is usually used to evaluate the chemical reaction.  A chemical reaction scheme consists of two parts: a chemical reaction formula (one-step reaction scheme) or a set of chemical reaction formulae (multi-step reaction scheme), and a mathematical expression or a set of mathematical expressions with which the rates of disappearance or appearance of chemical species are evaluated. In this section different chemical reaction schemes are discussed.  5.6.1 One-step reaction  An one-step chemical reaction scheme assumes that the combustion is a one-step chemical process. For a chemical reaction with reactants F and 0 to form product P, for example, the chemical reaction formula of the one step scheme is in the form:  F÷OP kb  (5-9)  where kf is the forward reaction constant, and kb is the backward reaction rate constant. The generalized Arrhenius form is usually used to evaluate the reaction constants.  For forward  97 reaction constant, for example,  k =ATYexp(---) RT  (510)  where T is temperature in Kelvins, y is a constant, Ef is the activation energy for forward reaction, R is the universal gas constant. For combustion of a fuel, the reaction with the one-step scheme is usually treated as irreversible, i.e. the reaction going only in one direction from reactants to products. With kb being equal to zero, the rate of disappearance of the fuel F and oxidant 0 is then given by  =  k[Fr[O]’  (5-11)  where [F] is the concentration of the fuel, [0] is the concentration of oxidant, a and b are two constants.  5.6.2 Multi-step reaction  In the one-step scheme discussed in the last section, the combustion process is considered as a one-step conversion from fuel to combustion products. The real chemical reaction process is much more complicated.  The one-step schemes can not provide any information about the  intermediate products, and usually are valid only in a narrow temperature range (some times also in a restricted pressure range). Multi-step chemical reaction schemes provide more information about the intermediate products and are more flexible to adjust for covering wider temperature range than one-step scheme. Generally speaking, the more reaction steps are chosen, the more accurate the evaluated reaction rate can be, and also the more numerical calculation is required.  98 As the simplest example of the multi-step scheme, a two step chemical reaction scheme with intermediate reaction product carbon monoxide CO can be in the form: 1 via at the first step, fuel reacts with oxidant 0 to form intermediate product P  p  F ÷0  (5-12)  I  2 via 1 is further oxidized to form final product P and at second step, the intermediate product P  2 P  1 +0 P  (5-13)  H  where k is the reaction constant, and subscripts f and b stand for forward and backward reaction, subscripts I and II stand for first step reaction and second step reaction.  5.6.3 Detailed reaction  The detailed chemical reaction scheme consists of a relatively complete set of fundamental chemical reactions, represents the chemical reaction mechanism of a combustion process. The chemical reaction mechanisms of most of the hydrocarbon fuels are too complicated to be interpreted. The research work in the reaction mechanism of few simple hydrocarbon fuels is relatively complete. The reaction mechanisms of the methane and propane have been reported, e.g. by Westbrook [1981, 19841, Paczko et al [1986], Hennessy et al [19861. Even burning the simplest hydrocarbon fuel, methane, more than a hundred fundamental reactions can be involved.  99 By involving all (or most of all) fundamental chemical reactions, the reaction rates and the species concentration could be well predicted. Progress has been made in simulation of methane combustion with detailed reaction scheme, e.g. Smoot et al [1976], Tsatsaronis [1978], Gardiner et al [19871, Karim and Hanafi [1992], Zhou and Karim [1994]. But no application of detailed fundamental reaction scheme to the multi-dimensional combustion models has been reported. Two major problems have to be solved before reaching this goal. The first one is limitation of computer capacity (speed and memory).  Increase of the computer capacity relies on the  development of computer technology. The second one is the limited knowledge of the interaction between turbulence and chemical reaction. It is the second problem that challenges the research workers in the field of combustion science.  In the next section, we will discuss turbulent  combustion models, in which the effects of turbulence on burning rate are addressed.  5.7 Multi-component treatment of fuels  Most of the fuels, such as gasoline, diesel and natural gas, have more than one chemical component. They can be treated either as a single chemical component or a mixture of different species. The one-step reaction scheme can be applied to both cases. If treating natural gas, for example, as a single component fuel, we can directly apply Eqn. 5-10 and 5-11 (where F stands for concentration of the natural gas) to evaluate the burning rate. The reaction constant kf and exponents a and b in the Eqn. 5-10 and 5-11 have to be determined empirically. Almost all of the previous work in multi-dimensional IC engine combustion modelling has used single component treatment of a fuel. The advantage of this treatment is its simplicity. But this single  100 component treatment has the drawback of composition dependence. The composition of natural gas (as shown in appendix I), for example, tends to vary from region to region and from time to time. This variation makes it inappropriate to use a single component treatment to evaluate the combustion rate of the natural gases from different origins. To overcome this disadvantage, a multi-component treatment can be considered. Natural gas, for example, can be treated as a mixture of three single chemical species, i.e. methane, ethane and propane.  The one-step  chemical reaction scheme can then be applied to each component.  For methane, the one-step irreversible chemical reaction formula is  4 +202 CH  -,  2 ÷2H CO 0 2  (5-14)  and the rate of CH 4 consumption SCH 4 is ScH =k[CH,r[o]b  (5-15)  where reaction constant k is given by  k=Aexp(-—,) The one-step chemical reaction formulae for ethane and propane are  -  101  CH 26  +  22  2C02 +3H0 2  -.  (5-17)  and 8 ÷ 502 H 3 C  -  2 3C0  +  0 2 4H  (5-18)  The constants a, b, A and £ in Eqn. 5-15 and 5-16 can be determined by experiments and usually need to be adjusted depending on the temperature range, pressure range, and stoichiometric ratio. The advantage of the multi-component treatment is its composition independence.  In other  words, the change in fuel composition does not affect the validity of the chemical reaction schemes with multi-component treatment.  Instead of the one-step oxidation, defined by Eqn. 5-14, 5-17 and 5-18, a two-step scheme with multi-component treatment of natural gas was used in this work. In the first step, methane, ethane and propane are oxidized to form carbon monoxide and water via reactions: k CH  +  CO  22  +  2H0 2  11 Ic H C26  and  +  O 22  2C0  +  3H2o  (5-19)  (5-20)  102  CH 38  +  7 —0  22  3C0  +  0 2 4H  (5-1)  In the second step, the carbon monoxide is further oxidized to form carbon dioxide and water via the reaction:  Co  +  1 —o 22  k .  co2  (5-22)  The CmHn consumption rate SCmHfl is given by (Westbrook, 1981) SCmHn  = k. [CmHnJa[O,]b  (5-23)  . The CO consumption 8 H 3 ,C 4 , and C 6 H 2 111 and CmHn stands for CH k ,, 1 11 , k where K, stands for k 0 is given by (Yetter et al, 1986) rate S  V1H,or 2 1 [co]a[0 0 = k S  (5-24)  In this two-step scheme, four reactions are involved. With only one more equation than the one step scheme we can make the combustion model more flexible and possibly more accurate.  5.8 Turbulent combustion rate  5.8.1 Introduction  In section 5.3, we discussed the approaches to evaluate the species conversion rate in chemical reactions. No flow properties, such as turbulence intensity and turbulence lengthscale, have been  103 involved in the above discussion. In the real case, the burning rates of most of the fuels are strongly affected by the turbulence. In this section, different approaches to evaluate the effect of turbulence on burning rate are discussed.  In a turbulent combustion process, the reactants are converted to the products in a reaction zone, or more than one reaction zone, at a rate dependent on the chemical properties of the reactants, the concentrations of the chemical species, the temperature, and generally the pressure. The chemical reaction schemes are those for evaluating the local chemical reaction rate, which is usually in moles per unit volume and unit time or mass fractions per unit volume and unit time, at given local temperature, pressure and species concentration. The total combustion rate depends both on local reaction rate and on the geometry and size of the reaction zones. In modelling of laminar combustion, the reaction zones are usually treated as single sheets with simple shapes, such as a flat plane, cylindrical shell or spherical shell, with reference to which the total burning rate can be calculated. For turbulent combustion the situation becomes more complicated, due to the irregular shape of the reaction zones and the local fluctuations of species concentration, temperature. and pressure.  Evaluation of the interaction between chemical reaction rate and turbulence is usually called turbulence coupling. Turbulence coupling answers two questions: (i) how turbulence affects combustion, and (ii) how combustion affects turbulence. Much research work has focused on the first question, which is also the focus of this section. In the next two sections, the two most often used turbulence coupling methods will be discussed.  104 5.8.2 Eddy dissipation model  Before we start discussion of this method, it is necessary to introduce the concepts of mixingcontrolled combustion and chemical-controlled combustion, which will be frequently used in the following discussion. If combustion rate or the conversion rate from reactants to products is only determined by turbulence mixing rate, the combustion is said to be mixing controlled; and if the combustion rate is only determined by chemical kinetics, the combustion is said to be chemically controlled.  Spalding [1970, 1976] proposed an eddy-break-up model to take account of the turbulence effect on burning rate. In this model the premixed turbulent reaction flow is considered as a mixture of unburned and burned gas eddies; and the reaction is supposed to take place on the interfaces between burned and unburned eddies. Based on the concept of mixing-controlled combustion, the chemical reaction rate per unit volume was considered dependent on the rate of the breakup of those eddies; and this rate, as further suggested by Spalding,  could be assumed to be  proportional to the decay rate of turbulence energy.  i/ Magnussen’s proposal  The concept of eddy-break-up was applied by Magnussen and Hjertager (1976) in their ‘eddy dissipation combustion model”. In diffusion flames, fuel and oxidant occur in separate eddies. It can be assumed that the chemical reactions are very fast so that the rate of combustion will  105 be determined by the rate of mixing of fuel and oxidant eddies, in other words, by the rate of dissipation of the eddies, and also by the concentration of the reaction species. Thus the reaction rate can be expressed by: (a)  R=Ac,(eIk)  where A is an empirical constant,  [_4t.]  (5-25)  ms  ,k (kg/rn ) is the local time-mean fuel concentration 3  and e are the turbulent kinetic energy and dissipation rate, and elk is used as a measure of turbulent eddy dissipation rate;  or (b)  =A(çIr?(e/k) 1 R  (5-26)  is the local time-mean oxygen concentration, and r is the stoichiometric oxygen  where 02  requirement;  or (c) in premixed turbulent flames (fuel and oxygen will be in same eddies which will be  106 separated and heated by eddies of hot combustion products),  Rf=ACBC(cP/(1+r)) (elk)  where B is another empirical constant, and  (527)  is the local time-mean concentration of  products.  The three equations are assumed to be applicable to diffusion and premixed combustion. The equation that gives the lowest reaction rate is the one that determines the local rate of turbulent combustion.  ii! Gosman and Harvey’s modification  Ahmadi-Befrui and Gosman (1981) applied Magnussen’ s formulation as a combustion submodel for their multi-dimensional simulation of combustion in a homogeneous charged engine in a compact form of:  —  Rf  .  =  A p = k  mm  _m —i, Bm C P) (m , 1 rf 1+rf  (5-28)  where m is the mass fraction, the subscripts f, o and p refer to fuel, oxygen and product respectively, rf is the stoichiometric oxygen requirement per unit mass of fuel, and min(...) is a ‘minimum value of’ operator.  107 Afterwards Gosman and Harvey( 1982) introduced one more model of the Arrhenius form for the chemical-kinetically controlled combustion in the form of (5-29)  2 mfmØ Exp(—E/R7) —A15  =  1 and E are empirical coefficients which normally need to be tuned for each application, where A and R is the universal gas constant. Then they evaluated Rf from either Eqn. 5-28 or Eqn. 5-29 according to whether the combustion process is chemical-kinetically controlled or turbulent 1 , defined as ‘u 1 mixing-controlled by comparing the turbulent time scale t kinetics time scale  t,  defined as ;  =  t t / 1  kk, with the chemical  Ap Exp[-E/(RT)j, i.e.  =  If the ratio  =  A pExp(—E/R1) e/k  (5-30)  is greater than unity the combustion is considered turbulent-mixing-controlled;  otherwise it is chernical-kinetically controlled. This usually implies an abrupt transition from kinetics to mixing control.  iii! Abraham and Bracco’s extension  Abraham and Bracco (1985) further extended Magnussen’s model for their computation on premixed engine combustion.  In their model the species conversion rate is given by  108 1 p where superscript  *  ‘5-31  *  =  p -/t 1 (p )  denotes the local and instantaneous thermodynamic equilibrium value, and  ‘r is the characteristic time for the achieveñent of such equilibrium which is assumed to be the longer of laminar conversion time  1 t  and turbulent mixing time  t,  i.e. (5-32)  =  The laminar conversion time was evaluated with a empirical equation obtained by matching the measurement data for propane-air mixtures in the form of  =  ° exp[(1÷O.0814—1.151) E/RTJ T/(pfp 75 [ 2 1.54x10’ ) 0 ]  0 where D is fuel-air equivalence ratio (from 0.5 to 2.5), and p  =  (533)  1 atm.  The turbulent time scale is given by a modified Magnussen model,  =  or  2 cm  -  ” [1—e’ ’ t  1  (534)  109  =  -  (1+s)(?1) [1—e tt  (535)  ]  depending on whether C “‘ (Y-Y  or <1  (5-36)  *  1 +S)(YFY;) Cm ( 2  (  *  02 1 with Eqn.5-34 and <1 with Eqn.5-35), where s = (Y  concentration,  is  t  time of  ignition,  td  -  Y02*)/(YF  14 Cmi 12 k, C 3 , l = k 1 = C1Is  -  F),  Y is the ’ 75 ) 0 (T[F  2.75, and 1s =  T = 293k, 0 l. p = 10 is the laminar flame speed at 0 25 where s (plp(,)°’  iv, Applications by others  Kuo and Reitz (1989) applied the same model to evaluate the species conversion rate in simulating premixed-charge combustion in engines with pancake and pent roof combustion chambers. Some modifications were introduced to evaluate the characteristic time method a delay coefficient f was used, i.e.  +  t =  f  t,  where f = 1  -  ‘t.  exp(-(t-tS)/td),  In their similar to  Bracco’s formulation. And the laminar time scale has the same form as that of Bracco’s, except  that the laminar flame speed was evaluated by the correlation of Metghaichi and Keck (1982), i.e.,  Si  where a = 2.18  -  0.8 (c1 -1),  =  4_4m)27:p(1_2.1r) Bm_B ( 2  13 = -0.16  +  0.22(4  -  (537)  0 and P 0 are the temperature and pressure 1), T  at the reference point o in the unburned gas normalized by 298 K and one atm. r is the residual  110 mass fraction.  Be,,  m  2 are constants with the values of 0.341, 1.08 and 0.847 for and B  isooctane.  The same combustion model was applied by Reitz and Rutland (1991) to calculate diffusive combustion in diesel engines. The numerical results showed that the model is able to reproduce the measured pressure data.  5.8.3 Flame sheet model  (i) Marble and Broadwell’s proposal  Marble and Broadwell (Marble, 1977) proposed a coherent flame model (also named flamelet model or flame sheet model by others) to relate turbulence to burning rate. They treated the turbulent flame structure as a distribution of laminar flame elements with small thickness in comparison with the large turbulence eddies. A scalar quantity, flame surface density D (ie. flame surface area per unit volume), was defined in this model. An extra differential equation was introduced to govern the evolution of  .  The consumption rate of reactants is given by the  product of the local flame surface density D and the reactant consumption rate per unit area of the laminar flame surface.  (ii) Others’ extension  111 Based on Marble and Broadwell’s concept, Cheng et a! [1991] developed a flame sheet burning rate model in their numerical modelling of SI engine combustion.  The laminar flame is assumed to be thin compared to the length scale of turbulence.  The  combustion is in the wrinkled laminar flame regime. The reaction rate is considered proportional to the laminar flame sheet area. To evaluate the chemical reaction rate a flame surface density is defined as the flame sheet area per unit volume, which has the dimension of [1/mi. The flame sheet model is a description of evolution of Z, which is initiated by the spark ignition, transported by convection and diffusion, generated by fluid straining and dissipated by local laminar flame propagation or by over-straining.  A differential equation in the form of quantity conservation can be applied to Z, ie.  .-‘-V(pDVE)÷GT+DT  (5-38)  1 is generation term and DT is dissipation term. where GT  The flame surface generation rate is modeled proportional to the product of local density of E and local average strain rate e, ie.  GTE  =  cceE  (5-39)  where x is proportional constant of the order of 1 to 10.  The mean strain rate e may be connected to the turbulence properties. For the k- model the  112 authors suggested by dimensional analysis:  (5-40)  where Ce is a proportional constant (with a value of 5 for engine application).  The dissipation term consists of destruction of  by excessive strain rate, DTS, and the burned  out of the flame sheet, DTb.  The rate of destruction of the flame surface would be proportional to the amount of over-strain [Veynanta, 1989]:  DTS  {  —y(e—e)E 0  for e>e 3 3 fore<e  where y is a proportional constant, and e is the critical strain rate defined later.  (541)  And this  destruction is also related to the laminar burning consumption of the flame sheet. The flame surface density decrease may be formulated in a manner shown in Fig. 5-1. Let Y be the mass fraction of unburned mixture, p the density of unburned mixture and p the mean density of the 1 the laminar flame speed. In the Fig.5-1 there are N flame charge in the computation cell and S sheets of unit area evenly distributed in the computation cube of unit volume. The flame density E is then N; the volume of unburned mixture in this cube is pY/p. The thickness I of the  113 unburned mixture slab is given by  (5-42)  1= This slab would burn through in a time 1 SI  (543)  Therefore the destruction of the flame sheet density by burning is  DT  =  =  -  2 E 1 PP5  t  where  (544)  pYu  is another proportional constant.  The turbulent diffusivity of the flame sheet density is modeled as  DE  2 k  =  (545)  cs—  where C is set so that the diffusivity D is the same as the mass diffusivity of the species.  If we use p as a variable the conservation equation could be written as a(pE)  ÷V(puE) -V[pDV(pE)]  )pE— 3 =ciepE—y(e—e  (pE) 1 S f3p U 2  (5-46) —(Vu)pE  Y 2 p The extra term, (V. u) p Z, in Eqn.5-46 is the result of the change of variable.  114 Ignition  When the flame is initiated by ignition, the flame kernel is small; the flame does not see the turbulence and grows as a sphere with a radius R within the computation cell:  R  =  T 0 Sj(t_tjgn) +R  (5-47)  where burned temperature Tb and unburned temperature T can be determined from the 0 is a result of the gas expansion thermodynamics of the combustion; the initial flame radius R due to input ignition energy, typically with a value of 0.5 mm.  The flame sheet density for a  spherical flame is then  4icR 2 (cell volume)  (5-48)  This laminar growth of the flame kernel is continued until the flame radius either reaches the size of the computational cell or the typical eddy size  given by 3  -  c  (5-49)  where C is a constant, usually with a value of i/V 15 for isotropic turbulence [Tennekes, 1972], but the Cheng used a value of 0.1 for engine application.  The laminar flame speed  1 can be evaluated empirically, for example in the form given by Eq. The Laminar flame speed S  115 1 on temperature, pressure, fuel type, equivalent 5-37, which takes account of the dependence of S ratio and residual gas fraction.  Critical strain rate  For flame quenching by strain, the critical strain rate e could be given by  e  =  K8  (5-50)  where 8 is the laminar flame thickness, and K is the critical Karlovitz number of the order of 10 (Jarosinski, 1986). For typical engine conditions with fuel-air equivalent ratio of 0.8 to 1.2, e 5 1/s. Typical value of e for a engine at 5000 rpm is less than io 1/s. Thus is of the order of i0 flame quenching by turbulence should not be important for the engines operated near stoichiometric fuel-air ratio.  5.8.4 Comparison of two models  The advantage of the eddy dissipation model is its simplicity. It can be easily implemented in any multi-dimensional computer program without substantial modification and additional differential equations. The disadvantage is its limited application, it can only be applied to mixing controlled combustion. But when it is applied to transient combustion processes, e.g. combustion in CVCC or in IC engines, problems arise. Generally, combustion in conventional gasoline engines and diesel engines is a combination of chemically-controlled and mixing-  116 controlled processes. In the early combustion period or during ignition delay, the combustion is chemically-controlled; in the main combustion period, the combustion could be mixingcontrolled, chemically-controlled, or mixing plus chemically-controlled (ie. the effects of mixing and chemical properties of the mixture on combustion being in same order). The conclusion is that it is inappropriate to apply the eddy dissipation model alone to calculate the combustion rate in transient combustion in IC engines. In this work, the combustion model was based on a modified eddy dissipation model, which combines the chemically controlled reaction and the mixing-controlled reaction, and will be discussed further in section 5.8.5.  The flamelet model is more informative than the eddy dissipation model. The combustion rate is not only affected by turbulence (by its effect on flame sheet density  ), but also by the laminar  flame speed, which could be a function of temperature, pressure, fuel/air equivalent ratio. The effects of turbulence and chemical kinetics on the global combustion rate can be incorporated in this model without any arbitrary shifting from one reaction regime to another as modified eddy dissipation model does. The disadvantages of this model are its complexity to cope with multi step or detailed chemical reaction schemes. The need for additional differential equations not only makes it more difficult to implement, but also leads to increased computational time and increased computer memory requirement.  The difficulty in accommodating the multi-step  chemical reaction schemes or detailed schemes, which are essential for predicting pollutant formation, limits its application to predicting the global combustion rate, or heat release rate. In calculating the combustion rate, ie. the product of flame sheet density  with the laminar flame  speed and the local density of the reactants, this model implies complete conversion from  117 reactants to products. This assumption neglects the important facts that all combustion is incomplete and most pollutants, such as hydrocarbon (HC), carbon monoxide (CO), particulate, come from incomplete combustion.  5.8.5 Modification in this work  The combustion model used in this work is based on the eddy dissipation model. The chemical kinetics time scale is evaluated from  t =  01 n, cv. are E E)/(RT)] A T 1 +n xp[-(E }, where A , , 1 1/{ 01  constants determined by fitting experimental results without swirl, and the turbulent time scale is evaluated from  t =  B’k/e, where B’ is a constant determined by fitting the experimental  results with low and intermediate swirl, listed in Table 6-2. Instead of dividing combustion into two regimes, ie. chemically-controlled and mixing-controlled as suggested by Gosman and Harvey [1982], a buffer regime was inserted between the two regimes. The combustion process was divided into three regimes: (1) chemically-controlled combustion, when  t/t >  10, or there  is no turbulence or the turbulence is very low; the reaction rate was calculated from RR (2) chemically and mixing-controlled combustion, when 10 calculated from RR 1 ‘cit  , where D 1/(Dt+(1-D)t ) 1  =  0.1, the reaction rate was calculated from RR  ‘rI(t =  + ti);  çI’c(  =  0.1; the reaction rate was  and (3) mixing-controlled, when  . The advantages of this treatment are: 1 lit  aJ more smooth transition from chemically-controlled to mixing-controlled combustion than Gosman and Harvey’s treatment; b/ easy application and reduced computation compared to Abraham and Bracco’s modification; c/ being able to simulate laminar combustion or combustion with very weak turbulence.  118  121  bubu  / I  ii  -  Unburned mixture  b burned mixture -  Fig. 5-1 Distribution of flame surfaces  119 6. SPECIFICATIONS OF NUMERICAL SIMULATION AND GRID SIZE EFFECT  6.1 KIVA II code  KIVA-Il, a computer program specifically developed for IC engine modelling in Los Alamos Laboratory (Amsden et al, [1989]), has been used as a solver of partial differential equations for numerical simulation of the combustion processes.  In KIVA-Il, a time step in the temporal  differencing is also noted as a cycle, which is performed in three stages or phases (phases A, B and C). Phase A and B constitute a Lagrangian calculation in which computational cells move with the fluid, so that no calculation of convection terms are needed. Phase A is a calculation of fuel spray.  Phase B calculates pressure gradients in the momentum equations, velocity  divergence terms in the mass and energy equations, the spray momentum source term, diffusion terms, and remaining source terms in mass, momentum, energy and turbulence equations. In phase C the convection terms are calculated by freezing the flow and rezoning the computational mesh.  The spatial computational domain is divided into many small cells, the corners of which are called vertices in the KIVA-Il. All cells constitute the mesh with which spatial finite differences are formed. Velocities are located at the vertices, and scalar quantities, such as p. p. T, I, k and e, are located at cell centres. Besides regular cells, momentum cells and momentum control volumes are introduced for convenience of finite difference formulation and performance of the computer programm.  120 The main time step size in the KIVA II code depends on accuracy conditions and stability conditions. The first one is the cell distortion time step  AtdIS,  which is so set as to limit the cell  distortion that can occur due to uneven mesh movement in the Lagrangian phase. The second one is the chemical reaction time step  AtCh,  which is based on the requirement that the total heat  release from all chemical reactions in a cell should not exceed a small fraction of the total internal energy in the cell. The third one is the spray time step  which is based on the  requirement that the total mass and heat exchange between the spray and the flow in a cell should not exceed a small fraction of the total mass and total internal energy in the cell. Two other time step limitations are the progressive time step At, which limits the amount by which the time step can grow at next cycle, and the input maximum time step  Atmax,  which is  predetermined in the input file. The main time step is then determined by At =  , AtCh, 1 min(Atd  Atsp, Atpro, Atmax)  The Courant stability condition is introduced to determine the convection time step At 0 in the subcycle in Phase C, where the convection terms are calculated by rezoning the computational domain. The expressions for calculating those time steps are lengthy, and can be found in the technical description of KIVA-Il by Amsden, O’Rourke, and Butler [19891.  6.2 Mesh arrangement  The test section is a closed cylindrical chamber with a rotating disc at one end, as shown in Fig. 3-2. Figure 6-1 shows the 3-D mesh of half of the computational domain. The cylindrical coordinate was used with 51 x50 (rxz) axisymmetric grid arrangement (corresponding regular cells  121 in KIVA II), as shown in Fig. 6-2. The cell size is 1.0 mm, uniformly distributed in both the axial direction and the radial direction.  The effect of grid size on the numerical results has been tested. A criterion has been set by this test, under which the effect of grid size on the numerical results is minimized. The grid system used in the numerical modeling meets the criterion, so that the combustion model developed for present study, which performs well in predicting the constant-volume combustion process in the condition of this experiment, can be applied to more general cases.  6.3 Initial conditions and boundary conditions  Initial conditions  Initial conditions were set to match the experimental conditions in the constant-volume combustion chamber. Initial temperature and pressure were 298 K and 0.1 MPa. Stoichiometric mixtures of natural gas and air were used.  The initial velocity distribution before combustion was obtained from experimental measurements of cold flow at different rotating disc speeds. In numerical modeling, the cold flow can be started without motion, and accelerated by the rotating disc, reaching a steady state when the driving force from the rotating disc was balanced by the friction on the walls. It takes about 1 second for the flow to reach steady state. At high rotating disc speed, e.g. over 4000 rev/mm,  122 the time step has to be very small (in the order of 1 06 to I O second) to ensure that the numerical iteration converges. It will, therefore, take more Cpu time to simulate the cold flow than to simulate the combustion process. The numerical results showed that tangential velocity was much higher than axial and radial velocities, and that the tangential velocity distribution is nearly two-dimensional, in other words, the tangential velocity variation with radius are almost the same along the axial direction, except in the small region near the driving disc and the end walls. This near-two-dimensional distribution makes it easy to preset the initial flow field. To model combustion processes with swirl generated by a rotating disc, the mixture was ignited at the beginning by presetting the initial steady-state mean velocity distribution and turbulence intensity based on experimental measurements, shown in Fig. 3-8.  Boundary conditions  The impermeable wall boundary condition was applied to the constant-volume combustion chamber, i.e. no mass transfer and only energy transfer by thermal conduction through the walls of the chamber. The wall-functions (defined in Appendix V  ) were applied to evaluate the  momentum and heat transfer, and the turbulent kinetic energy and its dissipation rate at the cells closest to the solid boundaries.  The normal velocity component u was set equal to zero at walls, ie u  0. The wall stress was  evaluated with the wall-functions, ie. uy  y 11.63  (6-1)  123 for the laminar sublayer or  for the logarithmic region, where  K  (6-2)  y> 11.63  u  is Karman constant (with the commonly accepted value of  0.4), and B is another constant with an experimentally determined value of 5.5 for smooth walls (Schlichting, [1968]). In these equations, the dimensionless variables were introduced:  UT  U  =  kf  U  +  UT Ut),  +  y  where  t  ILI p  is the wall shear stress, p is the fluid density, p is the viscosity, u is the tangential  velocity component, and y is the normal distance from the wall, shown as Fig. 6-3. The distance y has been assumed small enough to be in the logarithmic region or the laminar sublayer region of the turbulent boundary layer. For given distance y and tangential velocity u, the wall shear stress  t  can be determined from Eq. 6-1 or Eq 6-2. In a given cell, the tangential velocity  change in a time step At due to the wall shear stress (pVu)’’  -  (pVu)”  =  A  t  t  can then be evaluated from  At  (6-3)  where p is the fluid density, V is the volume of the cell, A is the cell surface area parallel to the wall, superscript n denotes the quantities at time after a time interval At from  t,  and superscript n+1 denotes the quantities  t.  Temperature boundary conditions on walls are introduced by specifying the wall temperature.  124 The wall heat flux J is evaluated by wall functions: (6-3) =  for the laminar sublayer, or T  =  (6-4)  .In(y ) + C  for the logarithmic region, where C is a constant, whose value has to be determined 1 (Kays and Crawford, [1993]), and the dimensionless experimentally, and could depend on P temperature T is defined by  =  pCu “ w  where Cp is the specific heat, and T is the wall temperature. In KIVA II, the constant C was determined by equating Eq. 6-3 and 6-4 at y C  =  11.63. With P  1 P  1, this treatment yields  5.5, same as B in Eq. 6-2.  In addition to the wall heat loss, there is a frictional heating source to the internal energy due to wall shear stress:  Q where  = t  u  Q is the heating rate per unit area of wall, u is the tangential velocity.  The boundary conditions for turbulent kinetic energy k and its dissipation rate  k and  =  C2u  are taken to be  125 3  KY  where c is a constant with a value given in Table 6-1.  A derivation of these boundary  conditions can be found in Appendix V.  6.4 Reaction rate evaluation  The two-step chemical reactions, shown in Eq. 5-19, 5-20, 5-21, and 5-22, were treated as irreversible reactions so that only those forward reaction rate constants need be evaluated. For convenience, we designate the reactions of methane, ethane and propane with oxygen to form carbon monoxide and water as reactions I, II, and III, and the reaction of monoxide with oxygen to form dioxide and water as reaction IV. The values of A, E and a, b, c in these reactions given in Appendix IV have been suggested by Westbrook [19811 and Yetter [19861.  The general form of the chemical reaction rate constant is given by Eq.5- 10. In this thesis, y is set to zero. The chemical reaction constant is thus in the form of  k  =  Aexp(_Em) RT  (6-1)  The activation energy E in Eq. 5-10 is usually treated as a constant in numerical modeling of chemical conversion rate from reactants to products. For elemental reactions, this treatment is in most cases satisfactory. But for those global reaction schemes which do not represent the  126 mechanism of the chemical reactions, treating activation energy as a constant may lead to some problems. For steady-state constant-pressure combustion, the treatment of constant activation energy could still produce reasonable agreement between the experimental data and numerical results because, in this case, the temperature difference across the flame front is relatively small (around 1500 K) and ignition does not need to be considered. But for the unsteady constantvolume combustion, which is the case of this work, the typical temperature difference across the flame front is much larger than that of steady constant-pressure combustion (usually exceeds 2200 K). The constant-volume combustion process starts at ignition (chemical reaction at low temperature around 1000 K), and proceeds with flame propagation (chemical reaction in a temperature range from 1000 K to 2500 K), and then completes with burning of the end gas (chemical reaction at much higher temperature than that of constant pressure combustion at 0.1 MPa).  Numerical tests showed that with constant activation energy, the predicted ignition delay was over ten times as long as the main combustion duration, and inconsistent with the measurements. Experimentally the ignition delay and the main combustion duration was almost the same. To solve this problem, a temperature-dependent activation energy has been formulated as E  =  0 E  +  nTa  (6-2)  where E 0 is the constant part of the activation energy, and n and o are two constants determined by fitting the experimental results without swirl, shown in Table 6-3. To save CPU time, only reactions (I) and (IV), which have major effect on the global reaction rate, used variable activation energy defined by Eq. 6-2. The activation energy in reactions (II) and (Ill) were still  127 treated as constant.  6.5 Grid size effect  Before we start to run the KIVA II code, it is very important to make sure that effect of grid size on the numerical results have been minimized, or at least understood.  In numerical simulation of fluid dynamics, errors arise from two major sources, i.e. incompleteness of physical and chemical models, and approximation in numerical discretization. The grid size, on which the numerical calculation is based, should be properly determined either to ensure reasonable computational time and memory requirement or to reduce or eliminate the dependence of numerical results on the grid size. In the combustion process, the gradients of the scalar fields, e.g. temperature, species concentrations, are very steep across the flame front; and the dependence of chemical reaction rate on temperature and species concentration is nonlinear. This could make the numerical results more sensitive to the grid size with combustion than with cold flow. For the KIVA code, the dependence of burning rate on grid size has been mentioned by Amsden et al [1989], and has been confirmed by our numerical modeling of natural gas combustion with this code. The purpose of following procedure is to examine the effect of spatial grid size on calculated burning rate with KIVA II, and to show how to reduce or to eliminate this effect.  A stoichiometric mixture of natural gas and air at 289 K and 1 atm in a axisymmetric disc  128 shaped constant-volume combustion chamber (with the diameter of 60 mm and the axial dimension of 3 mm) was ignited at the center of the chamber. The reason for testing the grid size effect in a smaller chamber than that used in the experiment is to save computational time and because of the limitation of computer memory. Once the grid size effect is eliminated, the behaviour of a combustion model will be independent of the mesh arrangement.  Figure. 6-3 shows the 3-D plot of one eighth of the computational domain. The computation was two-dimensional. The grids are uniformly distributed in the computational domain and with same size along both the radial and axial directions. Four different grid sizes, 1.5, 1.0, 0.5, 0.25 mm, were tested.  Flame thickness was used as the characteristic length scale in this test. The flame thickness is defined as the distance between calculated low and high temperature contour lines where temperature varies nearly linearly and temperature gradient has the maximum value, shown as in Fig. 6-4.  The time history of the volume-averaged combustion pressure was used for the combustion rate evaluation. The global mass burned fraction x was deduced from the pressure data by a good approximation, i.e. x  =  )/(P-P (refer to Appendix III), where P is the combustion pressure (P-P ) 0  0 is the initial pressure and at the time of evaluation, P  ‘m  is the maximum combustion pressure  (refer to appendix III). The initial combustion durations DTO- 10%, defined as time period of 010% mass burned, the intermediate combustion duration DT1O-50%, defined as the time period  129 of 10-50% mass burned, and the main combustion duration DT1O-90%, defined as the time period of 10-90% mass burned, were calculated with different grid sizes.  The calculated  combustion duration with 0.5 mm grid size are taken as reference. The numerical results are shown in Fig. 6-5.  It is clear, from Fig. 6-5, that the calculated combustion durations decrease with decreased grid size, and have a rapid transition when the grid size is close to the calculated flame thickness. When the grid sizes were smaller than the calculated flame thickness (about 1 mm in this test), the variation of reaction rate (reverse of the combustion duration) with the grid size was relatively small. But when the grid size became bigger than the flame thickness, a rapid slow down of reaction rate was predicted. Further tests for smaller grid sizes have not been performed because of the clear trend that further reduction of the grid size has only very limited effect on the predicted combustion rate.  From this numerical test, several conclusions can be drawn: (i) predicted burning rate decreases with increased grid size; (ii) there is a rapid change of the predicted burning rate when the grid size changes from smaller to bigger than the flame thickness; (iii) the predicted burning rate is insensitive to grid size when the grid size is smaller than the flame thickness.  130  Fig. 6-1 Mesh arrangem of the computational domain  131  I g n ti on  Z 20 0 p  CD O U,  n  --  -  --  --  -  -  --  -  --  --  -  -  --  -  --  --  -  -  --  -  -  --  -  --  -  -  -  -  -  -  -  -  --  --  --  -  -  •  •  I  I  I  -  •  •  -  I  I.—,—’  Fig. 6-2 Coordinator system of the computational domain  132  (I,J+1)  (I+1,J+1)  (U)  (I+1,J) 1  T (I, J —1)  WALL  Fig. 6-3 Computational domain near boundary  j  133  Fig. 6-4 Computational domain for grid size test  134  T Tb  products  Sf reactants  Pu T  r  Fig. 6-5 Definition of flame thickness  135  7.0 E E  L) 0  6.0  0  0  DtO.5mm  --  00.5 mm  --  Ar 5.0  calculated flame thickness with 0.5 mm grid size  grid size DtO-10% Dt1050% DtlO-90%  -  0 4-’ I-.  4.0  calculated combustion duration with 0.5 mm grid size  -  C  0 (1)  z  -D  3.0  -  2  0 C.) V ci) N  2.0  -  c’ 0  z  1.0  0.0 0.25  I  .  .  I  I  0.75  1.00  -  0.50  Normalized grid size A no 5 . 0  1.25 mm  Fig. 6-6 Calculated combustion duration at different grid sizes  1.50  136  TABLE 6-1 VALUES OF THE CONSTANTS IN K-e EQUATIONS 1 C  7 C  3 C  Prk  Pre  L44  1.92  -1.0  1.0  1.3  0.09  137  TABLE 6-2 NUMERICAL VALUES OF THE CONSTANTS IN THE COMBUSTION MODEL REACTION  I  II  III  A [(mole/rn ) “/sec] 3  5 2.0x10  1.OxlO”  7.8x1O°  Eo [J/rnole]  3 11.86x10  3 83.14x10  3 83.14x10  IV  628xK) 3 107.25x10 1.0  a  -0.3  0.1  0.1  b  1.3  1.65  1.65  c  0  0  0  0.5  n [J/(mole Ku)]  0.638  0  0  -0225  a  0.95  0  0  0.95  B’  0.5  0.5  0.5  0.65  0.5  138 CHAPTER 7. RESULTS OF NUMERICAL SIMULATION  The geometric dimension corresponding to the domain of numerical simulation is shown in Fig. 6-1.  At different swirl levels, the mixtures started burning at the centre of the cylindrical  chamber, and then propagated outward. In this chapter, predicted combustion duration, flame kernel growth, burning zone development and velocity field from ignition to the end of combustion for disc I are presented.  7.1 Combustion duration  Predicted combustion duration at different swirl levels (with u’ equal to 0.5% W) is shown in Fig. 7-1. Both predicted early combustion duration (0-10% mass burned; the curve with delta symbols) and main combustion duration (10-90% mass burned, the curve with circle symbols) were normalized by the measured ones (disc I).  It is clearly shown in Fig. 7-1 that the predicted combustion duration is close to the measured one at low and intermediate swirl (ie. Re  =  0 to 130,000, DTnUm/DTeXP  1). When the swirl  increases further from intermediate swirl to high swirl, both curves in the Fig. 7-1 start to deviate from the measuements (ie. Re  >  130,000,  DTnUm/DTeXP <  1).  This means that the predicted  combustion duration is shorter than measured one, or in other words, at high swirl the combustion model over predicted the combustion rate (the inverse of the combustion duration).  139 7.2 Flame kernel growth  The early-stage burning zone, due to its small size, is usually called the flame kernel. The effect of swirl on the flame kernel shape has been predicted. Numerical results showed that flame kernel grew nearly spherically at zero and low swirl levels. For comparison to the high speed schlieren pictures shown in Fig. 4-8, Fig. 7-2a and 7-2b show the half image of the predicted early flame kernel growth with zero swirl. At low swirl level (0  <  Re  70,000), the shape of  the flame kernel is also nearly spherical. The agreement between the measured flame kernel growth and numerical one is reasonably good in quiescent and low swirl combustion (Re  =  0  -  70,000).  At intermediate swirl level (70,000  Re  130,000), flame kernel elongation along the rotating  axis of the swirl has been well predicted. Figure 7-3a and 7-3b compare the predicted flame kernel configuration with the experimental one at Re  =  108,000, which represents the feature of  flame kernel shape at intermediate swirl, ie. spheroidal flame kernel shape with long axis along the rotating axis of the swirl.  At high swirl, flame kernel elongation became so strong that the shape of the flame kernel became nearly cylindrical. Figure 7-4a, 7-4b show the extensive elongation of the flame kernel at high swirl, though agreement between predicted flame kernel shape and measured one is not as good as at low and intermediate swirl.  140 6.3 Burning zone development over whole combustion process  In section 6.2, comparison has been made between predicted flame kernel growth and the measured one. From the comparison, a conclusion can be draw that the combustion model performed properly in predicting the effect of swirl on early flame kernel growth. In this section, only numerical results will be presented, because high speed schlieren pictures are not available for the whole combustion process due to the limitation of the side window dimension.  Figure 7-5 shows the flame propagation over the total combustion process from ignition to 30 ms after ignition at zero swirl. The flame propagated spherically before touching the flat sidewalls of the cylindrical chamber as expected (Fig. 7-5a, 7-5b, 7-5c); after reaching the walls, the flame front became less spherical and more cylindrical as it propagated outward in the radial direction (Fig. 7-5(d), 7-5(e)); at about 30 ms after ignition (corresponding to about 50% mass burned), the shape of the flame front was almost cylindrical (Fig. 7-5(f)).  With swirl, the burning zone developed faster in the axial direction than in the radial direction. The burning zone had an oval shape and touched the side walls earlier than without swirl. The burning zone became cylindrical at about 23 ms after ignition (about 10% mass burned) at Re =  108,000, and at about 20 ms after ignition (about 5% mass burned) at Re  higher the swirl level, the earlier the burning zone became cylindrical.  7.4 Velocity fields  =  172,000. The  141 The predicted combustion-induced velocity fields at zero swirl is shown in Fig. 7-8. At the early stage of the combustion (before 10 ms from ignition), there was substantial outward fluid motion perpendicular to the flame front in the unburned mixture due to spherical expansion of burned mixture; and the fluid motion in the burned region was negligible.  When the flame front  propagated outward, the velocities decreased in the unburned region and increased in the burned region. At the intermediate stage of the combustion (from 15 to 20 ms), the velocities at both unburned and burned regions were of the same order of magnitude. At the late stage of the combustion (from 25 ms to the end of the combustion), the situation was the opposite of the early stage, ie. fluid motion was stronger in the burned mixture than in the unburned mixture.  The predicted velocity fields with swirl are different from those without swirl mainly in two aspects: (i) in the early stage of combustion, there was recirculating flow near the corner of the steady cylindrical chamber, usually called swirl-induced secondary flow. The swirling flow in a cylindrical chamber will cause a radial pressure gradient, which provides the centripetal acceleration of the rotating fluid. This pressure gradient would not change substantially along the axial direction in a short cylindrical chamber because the axial velocity is negligible comparing to the tangential velocity. Near the stationary side wall, the rotating motion of the fluid is negligible due to fluid viscosity. The radial pressure gradient tends to push the fluid near the side wall toward rotating centre, causing secondary flow. In SI engines, the secondary flow was considered a possible mechanism in turbulence, mass and energy transportation (Hill and Zhang, [1994]). But in a constant-volume combustion chamber with DIL ratio 2, the calculated secondary flow was weak and limited to small regions near the corners of the cylindrical  142 chamber. From Fig. 7-9, and 7-10, no substantial effect of secondary flow on combustion can be seen. (ii) with swirl, the outward velocity from flame front to the unburned mixture became smaller than that without swirl; and at high swirl, the fluid velocity in front of the flame front can even become negative, ie. unburned mixture moving toward the burning zone.  7.5 Grid size independence  In each plot shown in the Fig. 7-2, 3, 4, 5, 6, 7, there are ten temperature contour lines. The inside contour line with the symbols ‘H’ represents the high temperature; and the outside contour line with the symbols ‘L’ represents the low temperature. The temperature difference between two neighbour contour lines is the same.  From these temperature contour line plots, flame thickness can estimated. The flame thickness, defined by Fig. 6-4, can be taken to be the distance between two contour lines, between which contour lines are evenly distributed, and the temperature gradient is the maximum. It can be seen that the flame thickness is in the range of 1 2  -  -  2 mm without swirl, shown in Fig. 7-2, and about  6 mm with swirl, shown in Fig. 7-3 and 7-4, ie. the flame thickness is greater than the grid  size. From the criterion set in chapter 6, ie. grid size should be smaller than the flame thickness to minimize the grid size effect, the numerical results presented in this chapter can be considered as grid-size independent.  7.6 Summary  143 (i) Combustion duration has been well predicted at zero, low and intermediate swirl levels, and under predicted at high swirl level;  (ii) numerical results showed that flame front with swirl was about three times as thick as that without swirl due to swirl-induced turbulence;  (iii) the effect of the swirl on flame kernel growth has been qualitatively predicted at low, intermediate, and high swirl levels;  (iv) numerical results showed that without swirl the burning zone developed spherically before touching the side walls, and became cylindrical after 50% mass burned, but with swirl the burning zone developed spheroidally before touching the side walls, and became cylindrical much earlier than without swirl.  144  30DTO-10%, experimental DT1O-90%, experimental DTO-10%, numerical DT1 0-90, numerical  A •  E  2O  -  ElO 0 C.)  0  I  0  I  I  100,000  50,000  150,000  Re [WR/v]  Fig. 7-1 Comparison of predicted and measured combustion duration at different swirl levels  145  (a) 1 ms after ignition  (b) 2 ms after ignition  (c) 3 ms after ignition Fig. 7-2a Flame kernel growth, predicted (contour plot, left) and measured (photo, right), (relative to the side windows shown in Fig. 4-5), ReO  146  (d) 4 ms after ignition  (e) 5 ms after ignition  (f) 6 ms after ignition Fig. 7-2b Flame kernel growth, predicted (contour plot, left) and measured (photo, right), (relative to the side windows shown in Fig. 4-5), Re=O  147  (a) 1 ms after ignition  (b) 2 ms after ignition  (c) 3 ms after ignition Fig. 7-3a Flame kernel growth, predicted (contour plot, left) and measured (photo, right), (relative to the side windows shown in Fig. 4-5), Re= 108,000  148  (d) 4 ms after ignition  (e) 5 ms after ignition  (d) 6 ms after igntion Fig. 7-3b Flame kernel growth, predicted (contour plot, left) and measured (photo, right), (relative to the side windows shown in Fig. 4-5), Re= 108,000  149  (a) 1 ms after ignition  (b) 3 ms after ignition  (c) 5 ms after ignition Fig. 7-4a Flame kernel growth, predicted (contour plot, left) and measured (photo, right), (relative to the side windows shown in Fig. 4-5), Re=172,000  150  (d) 7 ms after ignition  -  (c) 9 ms after ignition  (d) 11 ms after igntion Fig. 7-4b Flame kernel growth, predicted (contour plot, left) and measured (photo, right), (relative to the side windows shown in Fig. 4-5), Re= 172,000  151  (a) 5 ms after ignition  (c) 15 ms after ignition  (e) 25 ms after ignition  (b) 10 ms after ignition  (d) 20 ms after ignition  (0 30 ms after ignition  Fig. 7-5 Flame front propagation at Re = 0 (temperature contour lines; lines with H mean high temperature, and with L mean low temperature)  .  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U  0  C  Ct ct  @4  0  0  I-  Co  C  a)  C..)  cC  E In  C.)  a  11 /  {  /  I  /i/ii  —  \/c;4-  -  Th—  .  / / I  I  ::: J::’  /  .‘\‘\/  U — 4 /-—_r:--  .-_1tZ::<?l  -  ?E— ittI  /1:/i’  r  ii  //>;/Z  ii l1t  I  ‘\  Il ijiiIh 1 .1IC/Ct  .2  Ct  In  Ct  o n  C’  C 0  :  It  @4  C  a)  C  eq  0 0 0  N  II  a)  t  a) 4-  C  .t  -  157 CHAPTER 8. CONCLUSIONS AND DISCUSSION  General findings  The combustion rate of premixed natural gas and air can be significantly affected by swirl. Under experimental conditions of this work, ie. with stoichiometric natural gas and air mixtures ignited at the centre of a cylindrical chamber with length-to-diameter ratio 0.5, Reynolds number from 0 to 252,000, swirl has both positive and negative effects on combustion rate enhancement depending on its intensity. Under certain intensity, swirl is advantageous; above this intensity, swirl is disadvantageous.  To maximize overall combustion rate there is an optimum swirl  intensity.  The negative effect of swirl on combustion rate in the regime investigated can not be due to turbulence because at a given swirl level, increasing turbulence always increased the combustion rate. Buoyancy affects the configuration of the flame kernel; but it is notable that the early combustion rate is not affected as much as main combustion duration. The adverse effect of high swirl on overall combustion rate can therefore not be explained only as the effect of buoyancy on the small flame kernel.  It appears that the stabilizing effect of the radial pressure gradient and the radial discontinuity in density acts to reduce the turbulent fluctuations at the intersection of burned and unburned mixture. This could reduce the turbulent flame speed, and thus reduce the overall combustion  158 rate. But the stabilizing effect can not make the combustion rate lower than without swirl due to reduced turbulent mixing. Heat transfer, on another hand, could cause lower combustion rate with swirl than without swirl. After ignition, the temperature of unburned mixture will increase due to compression, and become higher than the wall temperture. Swirl increases heat transfer rate, which in turn reduces temperature of unburned mixture, thus leads to lower chemical reaction rate than no swirl. With intensive swirl, the negative effects of stabilizing and heat transfer could overweight the positive effect of turbulence on the combustion rate enhancement, and result in even lower combustion rate than without swirl.  From the experimental results  (i) Swirl affects combustion duration in a complex way. Under the experimental conditions of this thesis, the swirl can be classified into three levels, i.e. low, intermediate, and high swirl, because of the effect of swirl on the total combustion duration (the time period from 0 to 90% mass burned). At low swirl, the total combustion duration decreases with increased swirl; at intermediate swirl, the total combustion duration is the lowest (70-80% of that without swirl), and is relatively insensitive to the variation of swirl intensity. At high swirl, the total combustion duration increases rapidly with increased swirl intensity.  (ii) Swirl can reduce the total heat loss during combustion period to the minimum (about 80% of the heat loss at no swirl) at intermediate swirl level because of reduced combustion duration, though increased swirl led to increased heat transfer rate.  159 (iii) At given Reynolds number, change of turbulence intensity in the range of 0.5% to 3.5% of the disc tip speed has substantial effect on the combustion duration. Doubling the turbulence intensity can lead to reduction of total combustion duration up to 35%.  (iv) At low swirl, swirl has negligible effect on the shape of flame kernels; the flame kernel grew nearly spherically while the kernel diameter was less than half the chamber length.  At  intermediate swirl, the flame propagated unevenly, i.e. faster in the axial direction than in the radial direction, resulting in an elliptical flame shape. At high swirl, the radial flame propagation was so strongly suppressed by the buoyancy that the burning zone became cylindrical before its radial dimension reached half of the radius of the combustion chamber.  (v) For a given mixture ignited at the centre of a swirl, it was observed that there was a stable radius, which sets the maximum radial size of a burning vortex if it is allowed to expand freely in the axial direction; From dimensional analysis and the experimental data, the stable radius r is shown to be dependent on swirl intensity o, flame speed Sf and thermal diffusivity f’, and density ratio of reactants and products Pu/Pb in the form of  r £  Pb  f  .  But this  2 PPbFø  relationship should be further tested experimentally.  From the numerical modeling  (vi) A two-step chemical reaction scheme with temperature-dependent activation energy and  160 multi-component treatment of a fuel was used for evaluation of chemical reaction rate; an eddydissipation model combining with the original k- turbulence model in the KIVA II was used to take account of the effect of turbulence on burning rate; the numerical results for disc I showed that the total combustion duration at zero, low and intermediate swirl was predicted with deviation within 15%, and was under-predicted at high swirl. Numerical results were not obtained for discs II and III.  (vii) The effect of swirl on flame kernel growth has been predicted qualitatively over a broad swirl range.  (viii) The predicted burning zone development over the total combustion process showed that: (a) at zero and low swirl, the shape of the burning zone was nearly spherical before touching the side walls of the cylindrical chamber; after touching the side walls, the burning zone became cylindrical at about 30  -  50% mass burned; (b) at intermediate swirl, the burning zone had a  spheroidal shape before touching the side walls; after touching the side walls, it became cylindrical at about 10 30% mass burned; (c) at high swirl, the burning zone became cylindrical -  at less than 10% mass burned.  (ix) With the KIVA II code, the calculated burning rate is sensitive to the grid size.  With  reaction rate constants in Arrhenius form, calculated burning rates slow down when the grid size increases. The dependence of the burning rate on the grid size is minimized when the grid size becomes smaller than the flame thickness.  161 Discussion and recommendations  In swirling combustion, turbulence, heat transfer, buoyancy, and the stabilizing can affect combustion in different ways.  Swirl generates turbulence which in turn leads to reduced  combustion duration. In spark-ignition engines, reduced combustion duration means increased thermal efficiency. Swirl also leads to increased heat transfer rate. At given time period, the increased heat transfer rate leads to increased heat loss and reduced temperature of unburned mixture, which in turn reduce overall burning rate and combustion pressure.  The reduced  combustion pressure could cause reduced thermal efficiency in spark-ignition engines. Swirlinduced buoyancy causes flame kernel elongation, ie. increases surface-to-volume ratio of the burning zone; this leads to increased heat transfer from the reaction zone to the electrodes, and reduces chemical reaction rate. The stabilizing effect could cause reduced turbulent mixing of hot combustion products with cold reactants, and therefore reduce turbulent flame speed. But the stabilizing effect has to be further verified. More detailed evaluation of the effect of heat transfer on combustion duration is necessary so that the heat transfer effect and the stabilizing effect on combustion duration can be examined separately. The net effect of swirl on the combustion duration should be the combination of these effects, ie. the effect of turbulence, the effect of heat transfer, the effect of buoyancy, and the effect of stabilizing.  The present  experimental results showed that, at intermediate swirl, the combustion duration was the shortest, and the combustion pressure was the highest. Intermediate swirl is therefore recommended to increase the burning rate of natural gas in spark-ignition engines. Intermediate swirl can also be applied to more general cases, e.g. to increase the burning rate of lean or diluted air fuel  162 mixtures. Further experimental studies recommended are i/ quantitative analysis of the stabilizing effect of swirl; ii! more detailed cold flow velocity field measurements; iii! combustion with different air-fuel ratios; iv! variation of spark plug location; v/three dimensional photography of combustion.  The two-step chemical reaction scheme with temperature-dependent activation energy and multicomponent treatment of a fuel developed in this thesis is superior to the commonly used one-step chemical reaction scheme with constant activation energy and single-component treatment of a fuel: (a) a two-step scheme represents a chemical reaction process more realistic and can generally simulate a combustion process more accurate than a one-step scheme. (b) with temperature-dependent activation energy, the chemical reaction rate can be well represented in a broader temperature range than with constant activation energy; (c) with multi-component treatment of a fuel, the combustion model still keeps valid when the component fraction of a fuel changes, such as the component fraction of natural gas, which changes from region to region; but with single-component treatment of a fuel, the combustion model has to be modified if the component fraction of a fuel changes. Further studies recommended for improving the accuracy of numerical simulation of turbulent swirling combustion include: i/introducing the curvature effect on turbulence diffusivities; ii/ introducing the stabilizing effect on turbulent mixing and on turbulent mixing controlled reaction rate evaluation; iii/ introducing more chemical reactions for chemically controlled reaction rate evaluation; iv! refining heat transfer modelling.  163 NOMENCLATURE  A  Constant in formulas for chemical reaction rate  a  Buoyancy acceleration  b  Axial dimension of flame kernel  B’  Constant in eddy dissipation model Specific heat at constant pressure  D  Diameter of combustion chamber  0 DT  Combustion duration at Re  DTO-10%  Early combustion duration (0  DTO-90%  Total combustion duration (0  DT1O-90%  Main combustion duration (10  E  Activation energy  0 E  Constant part of activation energy  hm  Specific enthalpy of chemical component m  =  0 10% mass fraction burned)  -  -  90% mass fraction burned) -  90% mass fraction burned)  Specific internal energy of chemical component m k  Turbulent kinetic energy  kb  Backward chemical reaction rate constant  kf  Forward chemical reaction rate constant  L  Axial length of combustion chamber  164 M  Total angular momentum of swirling flow  n  Constant in combustion model  P  Pressure  ax 1 m  Maximum combustion pressure  0 P  Initial pressure before combustion Production term in k and e equations Prandtle number  Q  Total heat loss during combustion  0 Q  Total heat loss during combustion at Re  r  Radial coordinate  rms  Root mean square Radial dimension of flame kernel  r  Stable radius of burning vortex  R  Radius of combustion chamber  R  Reynolds number  S  Shear strain rate  Sf  Flame speed  SI  Laminar flame speed  S,  Shear strain tensor  Su  Normal strain tensor  SBV  Strength of burning vortex  SR  Swirl ratio  0  165 Sf  Flame speed  1 S  Laminar flame speed  T  Temperature  TDC  Top dead centre  UI  Radial component of mean velocity  9 U  Tangential component of mean velocity  u  Axial component of mean velocity  Ur’  Radial component of velocity fluctuation  ’ 9 u  Tangential component of velocity fluctuation  u’  Axial component of velocity fluctuation  W  Tip speed of rotating disc  Wm  Molecular weight of component m  x  mass fraction burned  z  Axial coordinate  GREEK SYMBOLS  P  Thermal diffusivity Flame thickness  9  Tangential coordinate  p  Density of mixture  Pb  Density of unburned mixture  166 Density of burned mixture t  Time scale Turbulent shear stress Molecular viscosity (dynamic) Turbulent viscosity  v  Molecular viscosity (kinematic) Angular speed  167 REFERENCES  ABRAHAM, J., WiLLIAMS, F.A., AND BRACCO, “A Discussion of Turbulent Flame Structure in Premixed Charges”, SAE paper’850345, 1985. 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COMPOSITION OF NATURAL GAS  The natural gas used in this thesis work has the following composition.  TABLE I-i THE COMPOSITION OF NATURAL GAS  COMPOSITION  IN VOLUME [BC Hydro NG]  4 CR  9640 -‘1- 0.30  6 H 2 C  2.50 +1- 0.30  8 H 3 C  0.20 ÷1- 0.10  0 C 1 H 4  0.07 -I- 0.04  2 CO  0.20 +1- 0.10  2 N  0.53 I- 0.04  OTHERS  0.53 I- 0.04  TOTAL  100.00  178 APPENDIX II. SHEAR STRAIN INDUCED BY BURNING ZONE EXPANSION  Using a simple two-zone axisymmetric model with central spark ignition in a cylindrical chamber shear strain rate S can be related with the mass fraction burned x in a initially strain free swirl of solid body rotation by (Hill and Zhang, [19941)  (pjpb—l) s x 2  to  (11-1)  2 (r/R  where o is the angular speed of the swirling motion, R is the radius of the cylindrical chamber, p and Pb are the density of unburned and burned mixture. Equation 11-1 is plotted on Fig. Il-i for several values of mass burned fraction with the flame radius calculated for each value of x.  Thus it appears that, in an initially strain-free swirl flow, turbulence intensity could be enhanced by combustion-induced shear strain. The quantitative significance of this effect on turbulence and on burning rate appears yet to be evaluated.  179  Mass Burned Fraction =x  5  0  0.5  au 1 u S=—(--—---); r or (1)0 .  1.o p —=8 Pb  Fig.II- 1 Radial distribution of combustion induced strain rate at different mass burned fraction (Hill and Zhang, [1994])  180 MASS BURNED FRACTION AND COMBUSTION PRESSURE  APPENDIX III  In this Appendix, a relation between mass lumed fraction x and combustion pressure P in a constant volume V is derived using a simple heating model.  Assumptions: i/ combustion is represented as a heating process, ie. no chemical reaction and no mole number change; ii! the mixture is treated as a ideal gas, ie. PV  =  RT and C,,  =  constant; iii! the process is adiabatic, ie. no heat transfer between the mixture and the container.  After a mass fraction dx is burned, heat dQ is released and the temperature of the mixture increases by dT, ie. dQ  =  (111-1)  m C, dT  where m is the total mass of the mixture in the volume V, C,, is the specific heat at constant volume, and dQ can be determined by the heat of formation dQ  =  (111-2)  m dx  =  Combining Eqs. 111-1, 111-2 and assuming PV dx  ie.  =  RT, one obtains (111-3)  B dP  where B = Cv V/(RAH), is constant by assumption. Integrating Eq. 111-3, and setting P the beginning of the combustion, one obtains x Considering P  = m  when x  =  1, where  =  K (P  m  -  =  0 at P  (111-4)  ) 0 P  is the adiabatic pressure after all mass is burned, one  obtains from Eq. 111-4 X  = (P  -  o)I(Pm  -  ) 0 P  (111-5)  181 In the real case, there is always heat loss to the wall of the combustion chamber. At beginning . During and at the end of combustion, the combustion pressure 0 of combustion, the pressure is P and the maximum pressure should be (P DP),. and (PmDPm), where P and Pm are the adiabatic -  pressures, and DP and DPm are the pressure drops during and at the end of combustion due to heat loss. Note that DP = 0 at the beginning of combustion and DP = DPm at the end of combustion. If the adiabatic pressures in Eq. 111-5 are replaced by measured pressures, one obtains x’ = [(P  -  ) 0 P  -  DPI/[(Pm  -  ) 0 P  -  (111-6)  DPm].  Now we assume that both pressure curves (measured and adiabatic) are similar, then X’  = [(P  -  ) 0 P  -  DP]/[(Pm  -  ) 0 P  -  DPm] = (P  -  DP)/(Pm  -  DPm) =  X.  (111-7)  And therefore it follows that one can generally say x = (P  -  1o)’(Pm  ) 0 P  (1118)  where both P and 1 m are now taken to be measured values. In other words, heat loss has no effect on the mass fraction evaluation by Eq. 111-5.  182 APPENDIX IV CONSTANTS IN CHEMICAL REACTION SCHEMES  In this appendix, the values of constants are cited from different sources for one-step and two step chemical reaction schemes for combustion of some light hydrocarbon fuels.  i/ One-step reaction  For the reaction CmHn  +  2 (m+nJ4)O  —>  mCO  +  n12 H O, the CmHn conversion rate 2  mHn 5 C  is in  the form:  mHn = 5 C  -  Table IV  b [CmHnla[O 1 A exp(-EIRT) 2  -  (IV-1)  1 The constants for CmHn conversion in one-step scheme  (Units are cm, sec, mole, kcal, and Kelvins.)  Fuel  A  E  a  b  CH4  1 .3E9  48.4  -0.3  1.3  CH4  8 3E6  30 0  -0 3  1 3  C2H6  1 1E12  300  0 1  1 65  C3H8  8.6E1 1  30.0  0A  1.65  Temperature  Source Westbrook, 1981  “I,  183 ii? Two step reaction  For the first step reaction: CmHn SCmHn  +  (m12+n/4) 02  —*  n CO  +  , the fuel conversion rate H 0 m/2 2  is in the same form as Eq.(IV-1).  Table IV  -  2 The constants for CmHn conversion in two-step scheme  (Units are cm, sec, mole, kcal, and Kelvins.)  Fuel  A  E  a  b  Temperature  CH4  2.8E9  48.4  -0.3  1.3  1450  CH4  1 5E6  30 0  -O 3  1 3  C2H6  1 3E12  30 0  0 1  1 65  C3H8  1 .OE 11  30.0  0.1  1.65  For the second step reaction: CO  0= S  -  +  1/2 02  -4  -  2000  Source Westbrook, 1981  I’  , the CO conversion rate S is in the form: 2 C0  14 ]b[H 2 [COla[O A exp(-E/RT) O  (IV-!)  184 Table IV  -  3 The constants for CO oxidation  (Units are cm, sec, mole, kcal, and Kelvins.)  A  E  a  b  c  Temperature [ki  [kcallmole]  Pressure  Source  [MPa1  l.0E14.6  40.0  1.0  0.25  0.5  1030-1230  0.1  Dryer, 1972  1.3E14  30.0  1.0  0.5  0.5  840-2360  0.1  Howard, 1972  1.06E11  21.0  1.0  0.25  0.5  1600-2100  Yetter, 1986  7.2E20  69.0  1.0  0.25  0.5  900-1000  Yetter, 1986  5.8E14  56.0  1.0  0.25  0.5  650-750  Yetter, 1986  185 APPENDIX V  WALL FUNCTIONS  The mass and momentum equations for steady 2D turbulent flow are (V-i)  0  =  axay  and pu-+pv-  =  -f+  (V-2)  8x8y  ay  where x is the coordinate in the streamwise direction, y is the coordinate in the direction perpendicular to walls, u and v are mean velocities parallel and perpendicular to walls, and t is the shear stress given by  =  where  j.i  is the molecular viscosity and  (I.L+I.L)  -  (V—3)  is the effective turbulence viscosity.  Near a wall, the terms on the left hand side of Eq. V-2 are negligible; and Eq. V-2 becomes at ay  Integrating Eq. V-4, one obtains  (V-4)  -  8x  186  (V—5)  In absence of pressure gradient, =  =  constant  (V-6)  Combining Eq. V-3 and V-6, one obtains  (i’i.)  =  (V—7)  -  By introducing the difinition:  -  1.1./P  one can write Eq. V-7 in the form of  1  =  (l+.f.)L.  (v—8)  1.1.  Very near the wall the molecular viscosity dominates, ie  i>>p,  so that the solution of Eq. V-8  is u  =  y  (V-9)  Away from the wall, where turbulent viscosity dominates, ie. Rip>>l, Eq. V-8 becomes Introducing the relation by Townsend [1956]  187  1  (V—1O)  =  8y (V—li)  j=icpuy  where k is Karmann constant (with common accepted value 0.4), one can integrate the Eq.V-l0 to obtain (V—12)  u+ =-1n(y)÷B  where B is another constant with a experimentally determined value of 5.5 for smooth walls (Schlichting, [1968]). The transition from Eq. V-9 to Eq. V-12 can be made at y  y  =  11.63,  obtained by equating these two equations.  From Eq. V-9 and V.42, one can obtains the shear stress near the wall in the laminar region or in the logarithmic region, once the local streamwise velocity u and the distance from the wall y are determined.  Similarly, the energy conservation equation near a wall is  (v-13) ay  where  r  and P are lamina Prandtl number and turbulent Prandtl number.  By introducing dimensionless temperature  188  T  =  PCLU (T-T)  (V-14)  I.Lt  (V—15)  Eq. V-13 can be written as  1  (_L+  =  ay÷  r  Comparing Eq. V-15 with V-8, one can immediately obtain the solution of Eq. V-15 for laminar sublayer (V—16)  =  and for logarithmic region  =  p —f-1n(y) ÷C  (V17)  where C is a constant, which value has to be determined experimentally, and could depend on 1r (Kays and Crawford, [1993]). In KIVA II, C was determined by equating Eq. V-16 and V-17  at y  =  With P,  =  P  =  1, this treatment yields C  =  5.5, same as B.  From Eq. V-16 and V-17, heat flux through the wall can be obtained once the velocity, temperature near the wall and the distance from the wall are determined.  For steady turbulent flow near wall, the k-e equations become (_±) aY Prk 8;’  .—-.  +  =  (V—iS)  189 and  (---)  ÷c  ()2_Cp  =  0  (V-19)  Assuming generation and dissipation rates of k in the near wall region interested are balanced, ie.  =  PC  (V—20)  one can obtain by combining Eq. V-il and Eq.V-12:  (V—21)  =  The solution for k is  k  —  ci  2  u2  (V-22)  After u and y are determined, the value of k and e near walls can be calculated from Eq. V-2 I and V-22.  

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