Performance, Emissions and Combustion Characteristics of Natural Gas Fueling of Diesel Engines

PERFORMANCE, EMISSIONS AND COMBUSTION CHARACTERISTICS OF NATURAL GAS FUELING OF DIESEL ENGINES

BRAD DOUVILLE

B.Sc. in Mechanical Engineering, University of Alberta, 1992

A THESIS SUBMITI’ED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

THE FACULTY OF GRADUATE STUDIES

Mechanical Engineering Department

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April 1994

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The performance, emissions and combustion characteristics of natural gas fueling of diesel engines have been investigated. The natural gas fueling system employs electronically-controlled late-cycle direct injection of high pressure natural gas with a small amount of diesel fuel (diesel pilot). Since the temperature in the combustion chamber at the end of compression is below the autoignition temperature of natural gas, the diesel pilot is required for ignition. Diesel engine performance and emissions have been measured using both natural-gas and conventional diesel fueling, over a wide range of operating conditions. The combustion process in diesel engines has been modeled based on measured cylinder pressure to learn about the formation rates of oxides of nitrogen and fuel burning rates. This combustion model has been developed to deal specifically with the non-uniformities and pollutant formation associated with stratified-charge combustion in diesel engines. The test results demonstrate that the thermal efficiencies for both natural gas and conventional diesel fueling at low and medium engine loads, are almost identical. The thermal efficiencies at high loads for natural gas fueling are greater than for conventional diesel fueling.

Upon optimization of the natural gas and diesel pilot injection, lower pollutant exhaust emissions will be produced over the entire engine load range, while obtaining higher peak engine load

capabilities than with conventional diesel fueling.

Ii TABLE OF CONTENTS

ABSTRACT ii

LIST OF TABLES vu

LIST OF FIGURES viii

ACKNOWLEDGMENT xi

1 INTRODUCTION

1.1 Vehicle Exhaust Emissions and Alternative Fuels 1

1.2 Natural Gas Fueling of Diesel Engines 4

1.3 Intensifier-Injector for Natural Gas Fueling of Diesel Engines 9

1.4 Objectives of This Research 10

2 ENGINE TESTING APPARATUS

2.1 Introduction 12

2.2 Engine and Engine Control 13

2.3 Dynamometer and Dynamometer Control 14

2.4 Fuel Injection System 15

2.5 Engine Instrumentation 17

2.5.1 Output Torque 18

2.5.2 Engine Speed 18

2.5.3 Diesel Fuel Flow 18

2.5.4 Natural Gas and Air Flows 20

2.5.5 Cylinder Pressure 21

hi 2.5.6 Mean Engine Temperatures and Pressures 23

2.5.7 Exhaust Gas Analyzers 24

2.6 Data Acquisition System 26

3 DATA ACQUISITION AND CALCULATED PERFORMANCE PARAMETERS

3.1 Thermal Efficiency 29

3.2 Mean Effective Pressure 31

3.3 Cyclic Variation 32

3.4 Wet-Basis and Brake Specific Emissions 33

3.5 Unburned Mass Fraction of Fuel 36

4 PREVIOUS COMBUSTION ANALYSIS MODELS

4.1 The Stratified Charge Combustion Process 37

4.2 Thermodynamic Combustion Analysis 38

4.3 Estimating Instantaneous Heat-Transfer to Cylinder Walls 40

4.4 Simple-HeaLingCombustion Analysis 42

4.5 Chemical Reaction Combustion Analysis 45

4.6 Limitations of Pervious Combustion Analysis Models 49

5 PROPOSED THERMODYNAMIC COMBUSTION ANALYSIS MODEL

5.1 Formulation of Combustion Model 53

5.2 Calculation of Mass Fraction of Fuel Burned 58

5.3 Combustion Stoichiometry 61

5.4 Trapped Air and Residuals 63

5.4.1 Scavenging Process 64

5.4.2 Mass of Trapped Air 65

5.4.3 Mass of Trapped Residuals 66

5.4.4 Residual Gas Composition 68

iv 5.4.5 Residual Gas Temperature 68

5.5 Thermodynamic Properties of the Unburned Gas Zone 70

5.6 Thermodynamic Properties of the Diesel Fuel and Natural Gas Zone 72

5.7 Thermodynamic Properties of the Burned Gas Zones 76

5.8 Thermodynamic Properties of the Mixed Gas Zone 79

5.9 Calculation of NOx Formation 81

5.10 Calculation Procedure 84

6 PERFORMANCE, EMISSIONS AND COMBUSTION CHARACTERISTICS

6.1 Discussion of Combustion Analysis Results 87

6.1.1 Effect of Computation Method 88

6.1.2 Effect of Unburned Fuel in the Combustion Chamber 92

6.1.3 Computed Temperatures 92

6.2 Variables that Effect Diesel Engine Performance, Emissions, and Combustion 93

6.3 Effect of Fuel Injection Timing 95

6.4 Effect of Engine Load and Fuel Injection Rate 106

7 CONCLUSIONS AND RECOMMENDATIONS

7.1 Conclusions 120

7.2 Recommendations 122

8 REFERENCES 123

V APPENDICES

Appendix I - Hydraulic Wheatstone Bridge Diesel Fuel Measuring Device 126

Appendix II - Pressure Transducer Mounting ftr DDC 1-71 128

Appendix III - Pressure Transducer Mounhing for DDC 6V-92TA 129

Appendix IV - Software for Processing Cylinder Pressure Data 130

Appendix V - Brake Power Correction (SAE Standard J1349 JUN85) 132

Appendix VI - Calculation of Specific Humidity 134

Appendix VII - Calculation of Engine Cylinder Volume 136

Appendix VIII - Combustion Analysis Program XMF.BAS (QuickBASIC) 139

vi LIST OF TABLES

Table 1-1 Urban Bus Heavy-Duty Engine Emission Standards 1

Table 2-1 General Engine Specifications 13

Table 2-2 Measured Engine Parameters 27

Table 4-1 Szekely and Alkidas Combustion Analysis Model 48

Table 5-1 Rate Constants for the Extended Zeldovich Mechanism 82

Table 6-1 Local Equivalence Ratio as a Function of Injection Timing

for Diesel Fueling 87

Table 6-2 Normalizing Constants for Figures 6-7 through 6-10 96

Table 6-3 Normalizing Constants for Figures 6-11 and 6-12 99 Table 6-4 Measured and Estimated NO (DDC 1-71) 119

vii LIST OF FIGURES

Figure 1-1 Effect of Fuel Injection Timing (Normalized) 2

Figure 1-2 Methods of Using Natural Gas in Diesel Engines 5

Figure 2-1 Schematic of Engine Test Set-up and Instrumentation 12

Figure 2-2 Schematic of Engine Fuel Supply System 16

Figure 2-3 Natural Gas Electronic Unit Injector 17

Figure 2-4 Diesel Mass Flow Rate Measuring Device Schematic

(DDC 6V-92TA) 19

Figure 2-5 Effects of Charge Amplifier Time Constant on Cylinder

Pressure Data 22

Figure 2-6 Emissions Analysis System Schematic (heated instruments) 25

Figure 2-7 Emissions Analysis System Schematic (cool instruments) 26

Figure 3-1 Typical P-V diagram for a Two-Stroke Diesel Engine 32

Figure 4-1 Schematic of Combustion Chamber Thermodynamic System 39

Figure 5-1 Co11LpLualDiagram of Proposed Combustion Model 53

Figure 5-2 Engine Mass Flow Schematic 65

Figure 5-3 Scavenging Correlation 66

Figure 5-4 Initial NO Formation Rate as a Function of Temperature 84

Figure 5-5 Combustion Analysis Calculation Procedure 86

Figure 6-1 Effect of Computation Method on Mass Fraction of Burned Fuel 89

Figure 6-2 Effect of Computation Method on Heat Transfer Estimates 90

Figure 6-3 Effect of Computation Method on Initial Burned Gas Temperature 90 Figure 6-4 Effect of Computation Method on Estimated Exhaust NO 91

Figure 6-5 Computed Temperatures 92

VII’ Figure 6-6 Engine Performance Map (DDC 6V-92TA) 94

Figure 6-7 Effect of Fuel Injection Timing at 3 bar bmep, 1800 rpm

DDC 6V-92TA - Diesel Fueling (normalized) 97

Figure 6-8 Effect of Fuel Injection Timing at 3 bar bmep, 1200 rpm

DDC 6V-92TA - Diesel Fueling (normalized) 97

Figure 6-9 Effect of Fuel Injection Timing at 3 bar bmep, 1250 rpm

DDC 1-71 - Diesel Fueling (normalized) 98

Figure 6-10 Effect of Fuel Injection Timing at 1 bar bmep, 1250 rpm

DDC 1-71 - Diesel Fueling (normalized) 98

Figure 6-11 Effect of Fuel Injection Timing at 1 bar bmep, 1250 rpm

DDC 1-71 - Natural Gas Fueling (normalized) 100

Figure 6-12 Effect of Fuel Injection Timing at 3 bar hmep, 1250 rpm

DDC 1-71 - Natural Gas Fueling (normalized) 100

Figure 6-13 Effect of Fuel Injection Timing on Mass Fraction of Burned

Fuel (DDC 1-71 - Diesel Fueling at 3 bar bmep) 102

Figure 6-14 Effect of Fuel Injection Timing on Mass Fraction of Burned

Fuel (DDC 1-71 - Natural Gas Fueling at 3 bar bmep) 102

Figure 6-15 Effect of Fuel Injection Timing on Initial Burned Gas

Temperature (DDC 1-71 - Diesel Fueling at 3 bar bmep) 103

Figure 6-16 Effect of Fuel Injection Timing on Initial Burned Gas

Temperature (DDC 1-71 - Natural Gas Fueling at 3 bar hmep) 103 Figure 6-17 Effect of Fuel Injection Timing on Estimated Exhaust NO

(DDC 1-71 - Diesel Fueling at 3 bar bmep) 104 Figure 6-18 Measured and Estimated NO Emissions 105

Figure 6-19 DDC 1-71 Thermal Efficiency - 0.016’ dia. Gas Holes 107

Figure 6-20 DDC 1-71 Thermal Efficiency - 0.020” dia. Gas Holes 107

Figure 6-21 DDC 1-71 Carbon Monoxide - 0.016” dia. Gas Holes 108

Figure 6-22 DDC 1-71 Carbon Monoxide - 0.020” dia. Gas Holes 108

ix Figure 6-23 DDC 1-71 Oxides of Nitrogen - 0.016” dia. Gas Holes 109

Figure 6-24 DDC 1-71 Oxides of Nitrogen - 0.020” dia. Gas Holes 109

Figure 6-25 DDC 1-71 Methane - 0.016” dia. Gas Holes 110

Figure 6-26 DDC 1-71 Methane - 0.020” dia. Gas Holes 110

Figure 6-27 DDC 1-71 Non-Methane Hydrocarbons

0.016” dia. Gas Holes 111

Figure 6-28 DDC 1-71 Non-Methane Hydrocarbons

0.020” dia. Gas Holes 111

Figure 6-29 DDC 1-71 Diesel-to-Gas Energy Ratio

0.016” dia. Gas Holes 115

Figure 6-30 DDC 1-71 Diesel-to-Gas Energy Ratio

0)20” dia. Gas Holes 115

Figure 6-31 Effect of Load on Mass Fraction of Burned Fuel

Diesel Fueling of the DDC 1-71 116

Figure 6-32 Mass Fraction of Burned Fuel for Both Natural Gas and

Diesel Fueling of the DDC 1-71 (3 bar bmep) 117

Figure 6-33 Effect of Fuel and Load on Initial Burned Gas Temperature 118

Figure A-i Pressure Transducer Mounting in Cylinder of DDC 1-71 128

Figure A-2 Pressure Transducer Mounting in Cylinder of DDC 6V-92 129

Figure A-3 Engine Cylinder Geometry 138

x ACKNOWLEDGMENTS

Special thanks are in order to those who helped make this thesis a reality. I wish to express my deepest gratitude to my supervisor, Dr. P. G. Hill, for the opportunity to work with him and more importantly to learn from him. His enthusiasm for research and discovery is inspirational.

I would like thank Bruce Hodgins, research and project engineer, for driving the overall project, designing and developing the natural gas injector, and his technical guidance and support in the engine test cell set-up and instrumentation. His assistance in collecting and interpreting the measured data is also appreciated.

Thanks are due to Hardi Gunawan and Yinchu Tao for doing much of the preliminary work to give this thesis a starting point. Thanks are also due to my fellow graduate students in the combustion lab; Alain (Jack) Touchette, Patric Ouellette, Christoph Aichinger, Dehong Zang, and Alexander Chepakovich for being good friends.

Thanks are also in order for NSERC for financial support during this work.

xi 1. INTRODUCTION

1.1 Vehicle Exhaust Emissions and Alternative Fuels

Vehicle exhaust emissions have been identified as a substantial source of air pollution in urban centres world wide. Significant contributors to exhaust emissions in particular are diesel- powered urban buses. Diesel engines are the engine of choice in buses because of their greater durability and higher thermal efficiencies compared with gasoline engines. However, diesel engine manufacturers are facing increasingly stringent emissions regulations which will be difficult to meet using existing technology.

Table 1-1 Urban Bus Heavy-Duty Engine Emission Standards United States EPA Clean Air Act Amendments (1991) (g/bhp-hr measured during EPA heavy-duty engine test) Model year li 1990 6.0 1.3 15.5 0.60

1991 5.0 1.3 15.5 0.25

1993 5.0 1.3 15.5 0.10

1994 5.0 1.3 15.5 0.05

1998 4.0 1.3 15.5 0.05

The Environmental Protection Agency (EPA) in the United States was given the mandate

to establish the Clean Air Act, which places a high priority on the reduction of air pollution and

smog levels in urban America. As part of the Clean Air Act, regulations are placed on vehicle

exhaust emissions. The most recently proposed EPA emissions regulations for urban buses are

given in Table 1-1. While no reduction in HC or CO emissions are required between the years

1990 and 1998, 33% reduction of NON, and 92% reduction in PM are required. While diesel engine manufacturers are presently meeting regulations, considerable improvements will be required to meet the proposed 1998 emissions regulations. Diesel exhaust generally has the same concentrations of nitrogen oxides (NOr) as gasoline engines and slightly lower concentrations of hydrocarbons (HC), ,2C0 and CO. Diesel engines are however a major source of particulate matter (PM), which is the emission that is facing the toughest regulation. Particulate matter consists primarily of combustion generated carbonaceous material (soot) on which some organic compounds absorb.

0.9

0.8 0.7

0.6

0.5 0.4

0.3 0.2

0.1

0 159 161 163 165 167 169 171 173 175 177 BOl [°ABDC]

Figure 1-1 : Effects of Fuel Injection Timing (Normalized)

While the oxidation rate of PM generally increases with cylinder temperature, the

formation rate of NO does as well. At a given engine speed and load, changes in the fuel injection timing have a significant effect on exhaust emission levels of both NO and PM with

little effect on thermal efficiency. Figure 1-1 illustrates the effects of fuel injection timing on

emissions and thermal efficiency of a typical diesel engine. It demonstrates the traditional trade off between the reduction of either PM or NO in conventional diesel engines. Changing injection timing to decrease PM emissions will increase NO emissions and vise versa.

Strategies that can be employed to reduce diesel engine pollutant emissions include:

2 • Improvement of diesel engine design and electronic control

• Use of particulate traps or other exhaust after-treatments

• Use of alternative fuels Because of the trade-off between particulate matter and NO emissions tinder conventional diesel operation, the amount by which pollutant emissions can he reduced by improvements of diesel engine design or electronic control is limited. Particulate traps’ could be used to reduce PM emissions which would allow the engine designer to employ NO reduction strategies. Heywood

[112 points out that particulate traps are difficult to implement with heavy-duty diesel engines due to high particulate loading and relatively low exhaust temperatures. The reliability and cost of particulate traps are also concerns. Other exhaust after-treatment equipment such as catalytic converters and steady-flow thermal reactors are not effective with heavy-duty diesel engines.

Catalysts in catalytic converters are fouled by particulate matter and exhaust temperatures are not high enough for thermal reactors to be effective [1].

Diesel engine emissions can be improved by using a cleaner burning fuel. Preliminary testing of alternative fuels in engines has shown promise in reducing emissions sufficiently to meet the new regulations without concessions on thermal efficiency [2, 3, 4, 5, 6, and 7]. Natural gas is one alternative fuel in particular that seems to be attractive since it is relatively inexpensive and readily available. Since the carbon content of natural gas is less than that of diesel fuel, 2CO and PM emissions can be lower which allows the flexibility of using NO reduction techniques. This effectively decreases the prominence of the traditional trade-off between PM and NO emissions.

One drawback of using natural gas as an alternative fuel for vehicles is its low volumetric energy content. This requires large storage tanks to obtain reasonable vehicle range. Another drawback is the high autoignition temperature of natural gas compared with diesel fuel. In order for natural gas to ignite in a conventional diesel engine, either a supplementary ignition source, or a higher compression ratio is required. With no supplementary ignition source, a compression

1A temperature-tolerant filter or trap that removes particulate material from exhaust gases; the filter is “cleaned off”by oxidizing the accumulated particulates. [1] 2Numbers in square brackets designate references listed at the end of this thesis. 3 ratio on the order of 60 would be required for autoignition of natural gas. This is about three times conventional diesel engine compression ratios.

Compared to other pollutant reduction strategies, alternative fuels have the added benefit of offsetting the increasing dependency and demand for conventional fuels. Development of viable alternative fueling schemes for vehicles will have a significant impact on extending the world’s usable energy resources. Hence considerable motivation exists for investigating the use of alternative fuels in vehicle power plants.

1.2 Natural Gas Fueling of Diesel Engines

Three principal methods for natural gas fueling of diesel engines are:

• Manifold Injection

• Timed Port Injection

• Direct Injection

Figure 1-2 illustrates each method schematically. In the first method, natural gas is injected into the engine inlet manifold where it mixes with the inducted air to form a fully pre mixed fuel-air mixture before the initiation of combustion. The mixture is compressed and then ignited near top dead center by either a spark plug or a small pilot amount of diesel fuel directly injected into the cylinder. While this method is relatively easy to implement, it has sonic serious shortcomings when applied to vehicle engines.

Manifold injection is not suitable for two-stroke engines as a considerable amount of natural gas would find its way through the engine cylinder, into the exhaust, during the scavenging process. Furthermore, part-load efficiency is much lower than with its diesel counterpart since throttling of the intake air is required to maintain the pre-mixed air and fuel mixture ratio to within combustible limits. Knock can be encountered as a consequence of subjecting pre-mixed air and fuel mixtures to high compression ratios. Manifold injection of natural gas is best applied to engines that operate only at full load and constant speed conditions, such as engines for driving generators, compressors, or pumps.

4 NATURALGAS DIESEL FUEL AIR PREMIXED

GAS MIXER (A) NATURALFUMIGATION

GAS INJECTION DIESEL FUEL AIR

(B) TIMEDPORT INJECTION

HIGH—PRESSURE DIESEL FUEL NATURALGAS AIR

Figure 1-2 : Methods of Using Natural Gas in Diesel Engines (courtesy of H. Gunawan (SI)

5 The second method of natural gas fueling (timed port injection) is an improvement on the first but still has some of the same drawbacks. In this design, natural gas is injected near the intake port of each cylinder at timed intervals. With proper injection timing and little mixing during the compression stroke, charge stratification can occur to some extent which reduces the problems of fuel loss during scavenging and knock. Engines utilizing this method of natural gas fueling still require throttling of intake air and either a spark or diesel pilot to initiate combustion.

The final method of natural gas fueling of diesel engines uses direct injection of high- pressure natural gas into the engine cylinder near the end of the compression stroke. Since the temperature in the combustion chamber of a conventional diesel engine at the end of the compression stroke is below the autoignition point of natural gas, a supplementary ignition source is required. If a small amount of diesel is also directly injected into combustion chamber near the end of the compression stroke, then the autoignition of the diesel will initiate combustion of the natural gas. By directly injecting the natural gas, no throttling of the intake air is required for mixture control as the charge is fully stratified. This suggests that part and full-load efficiencies can be comparable to those of a conventional diesel engine.

In 1989 Beck et al. [3] reviewed the different concepts of natural gas fueling of compression ignition engines. They concluded that the high-pressure direct injection method described above has the following advantages:

• Uses the basic diesel cycle with compression ignition.

• Avoids engine knock.

• Experiences no throttling losses.

• Requires no mixture ratio control.

• Obtains diesel cycle efficiency.

• Produces negligible unburned fuel emissions.

Miyake et al. [4] in 1983 presented the results of research carried Out at the Mitsui

Engineering and Ship Building Company in Japan studying high-pressure gas injection in engines.

They investigated two ignition methods in a large bore (420 mm) single cylinder 4-stroke engine.

The first involved direct injection of compressed natural gas (CNG) and pilot diesel separately

6 with diesel injection preceding CNG. The second method involved direct injection of CNG and diesel pilot simultaneously as a mixture. Better performance and lower amounts of diesel needed for stable operation were achieved with the first method. With CNG injected at about 250 bar, thermal efficiency comparable to that obtained with diesel-only operation was obtained using 5% (of the total calorific value at full load) of diesel pilot at 85% and 100% of full load. No results were presented at low loads or at varying injection timings. A heat release analysis was performed, however no details of the analysis were given. The only emissions measurements presented were CO and smoke.

Similar work was presented by Einang, Koren, Kvamsdal, Hansen, and Sarsten [5] also in

1983. Their project involved high-pressure, direct injection natural gas fueling with diesel pilot of a single cylinder, two-stroke, loop-scavenged, 300 mm bore engine which produces 196 kW at

375 rpm. Since their main objective was to have the capability of running with up to 100% diesel, the diesel injector and its location were unaltered as gas was injected through a separate injector displaced off-center in the cylinder head. In preliminary tests without gas injection optimization, it was demonstrated that with 73% (by energy) natural gas, injected at pressures below 200 bar, thermal efficiencies were slightly better, smoke readings were slightly higher, and NO emissions were 24% lower than 100% diesel operation.

Later Einang, Engja, and Vestergren [6] were able to achieve reliable and stable ignition down to 2% diesel pilot in a medium speed, four-stroke diesel engine. The same thermal efficiency as the 100% diesel operation was obtained with 5% pilot. A single injector was used to inject both natural gas and the diesel pilot. The pilot fuel nozzle and spray pattern were identical to that of the standard diesel engine with the gas jets directed so as to avoid collisions with the diesel jets. In this work, details are presented for preliminary tests of their prototype injector in one cylinder of a multi-cylinder engine. They did not present results from full range performance or emissions tests, and a detailed combustion analysis was not undertaken.

In 1987 Wakenell, O’Neal and Baker [7] presented the results of testing of high-pressure, late cycle, direct injection of natural gas in a medium speed diesel engine. They injected natural

7 gas at 5000 psig (345 bar) into a two-cylinder, two-stroke, blower scavenged locomotive research engine (216 mm bore and 835 rpm maximum speed). Separate injectors were used for natural gas

and diesel. With the engine running on natural gas, rated speed and power were achieved with slightly lower thermal efficiency than with standard diesel operation.

The effects of diesel pilot quantity were investigated. Full power was achieved with a ratio of 99% natural gas and 1% diesel fuel, however audible knock was detected. It was found

that engine knock was unacceptable unless the pilot ratio was increased to approximately 10% of

the total fuel input which gave a thermal efficiency 21% less than the diesel baseline efficiency of

28.7% at full load. Part load was unobtainable at these natural gas injection pressures because of

unstable engine operation. While this work included a brief mention of fuel injection timing and

heat release analysis, results from a thorough investigation of either were not presented. This

work did however include some emissions measurements of smoke, NO, CO and hydrocarbons at

different engine operating conditions.

While much work has been done by other researchers on natural gas fueling of diesel

engines, there is presently no commercially available direct injection natural gas fueling system for

urban bus diesel engines that meet proposed EPA emissions regulations. An important factor in

applying natural gas fueling technology to urban buses, as compared with other applications, is

the requirement of good performance over the entire operating range of the engine. Performance,

emissions and combustion characteristics of a viable direct-injection natural-gas fueling system for

urban-bus diesel engines has not been comprehensively investigated over the entire engine

operating range.

Combustion analysis based on measured cylinder pressure time histories are important

engine diagnostic tools which also provide insight into in-cylinder processes, such as fuel burning

rates, fuel injection phenomena, heat transfer and pollutant formation. An accurate combustion

model is of primary importance in gaining a thorough understanding of the advantages and

limitations of natural gas fueling of diesel engines. As will be shown, previous combustion

analysis techniques have shortcomings when applied to stratified charge engines (i.e. diesel

8 engines). The need exists for a combustion analysis technique which can give a more accurate indication of the combustion phenomena occurring inside of a diesel engine.

1.3 Intensifier-Injector for Natural Gas Fueling of Diesel Engines

An intensifier-injector system for natural gas fueling of diesel engines is presently in the development stages at UBC. The intensifier-injector concept employs electronically-controlled, late-cycle, direct injection of high pressure natural gas with diesel pilot. It is proposed that natural gas be compressed from storage tank pressure up to injection pressure by an engine-driven intensifier compressor. Both natural gas and diesel fuel are directly injected into the combustion chamber at high pressure through a single injector of roughly the same outer dimensions as the standard diesel injector it is intended to replace.

Fuel injection is initiated toward the end of the compression stroke with diesel injection preceding CNG. Since the temperature in the combustion chamber at the beginning of injection is above the diesel fuel’s ignition point, diesel and air that have mixed to within combustible limits will spontaneously ignite after a delay period of a few crank angle degrees. Since the ignition point of the natural gas can not be achieved by compression alone, combustion of the diesel fuel is required to raise the temperature such that the natural gas will ignite.

The goal of the intensifier-injector project is to develop a retro-fit system for natural gas fueling of urban buses capable of meeting the stringent EPA emissions standards while

maintaining high efficiency. In obtaining this goal, it is important to have a minimum of changes

to engine components and systems such that this retro-filting is commercially viable. The work in

this thesis is part of the ongoing effort at UBC to achieve this goal.

Preliminary work at UBC concentrated on the evaluation of an electronically controlled

poppet type injector from which high-pressure natural gas along with a small pilot amount of

diesel fuel are injected [8, 9, 10, 11]. Just before leaving the injector tip through the poppet

valve, the diesel pilot is gas-blast atomized by the flow of high-pressure natural gas. Hence the

natural gas and diesel fuel are injected simultaneously as a mixture. Along with being tested in a

9 naturally aspirated, two-stroke, single-cylinder diesel engine, this prototype injector has been analyzed using flow visualization techniques.

The main findings of this preliminary work with the poppet type injector are that: • NO and 2CO 3emissions are lower than with conventional diesel operation over the entire operating range of the engine, while CO and hydrocarbon (both methane and non-methane)

emissions are greater.

• at high loads, thermal efficiencies exceeded those for conventional diesel operation; however lower part load thermal efficiencies were 4found • a minimum of 25% liquid diesel fuel (by energy). was required for stable engine operation over the entire load range.

Suggestions for improvements based on these findings are to:

• redesign the injector nozzle geometry to obtain better penetration and distribution of fuel in

the combustion chamber.

• separate injection of diesel and natural gas, with diesel injection preceding that of natural gas,

to improve ignition.

• improve diesel spray and atomization to reduce ignition delay periods and CO and

hydrocarbon emissions.

Implementation of these suggestions forms the basis for the objectives of the present research.

1.4 Objectives of This Research

This research is concerned with the investigation of diesel engine perfonnance, emissions

and combustion using natural gas fueling. The objectives of this work are as follows:

1) To measure diesel engine performance and emissions, using both natural-gas and conventional

diesel fueling, over a wide range of operating conditions.

2) To model the stratified-charge combustion process in diesel engines, based on measured

cylinder pressure.

3WhiIe 2CO is not a regulated emission, it is thought to be a contributor to global warming. 4High cycle-to-cycle variations were found at low loads. 10 3) To learn about the formation rates of oxides of nitrogen in diesel engines to gain a better understanding of how to reduce NO emissions.

4) To learn about fuel burning rates to gain insight into the differences between combustion of diesel fuel and natural gas in diesel engines.

11 2. TESTING APPARATUS

2.1 Introduction

Two different engines have been used to test the natural gas fueling concept. Each engine was instrumented in order to measure key parameters such that a full analysis of engine performance and combustion could be carried out. Measured engine parameters include output torque, engine speed, fuel flow, air flow, intake air pressure and temperature, exhaust pressure and temperature, cylinder pressure, crank angle position, and exhaust emission levels. Measured exhaust gas constituents include ,2C0 CO, N0, 02, ,4CH and THC (total hydrocarbons). - Engine and I1Amb:ntAirempI I Dynamometer I Airbox I Control Panel T&P I L A lAir

I Flow i DseL V Flow \ Signal - Conditioning Gas Flow Exhaust Gas and Terminal Board [cL— — — ngneSpd_ V Exhaust Gas I & P Dynamometer Torque

TC = turbocharger Cylinder BDC & B = blower Pressure ICrank Angle Optical Incoder AC = after cooler

_IISAACI

Figure 2-1 : Schematic of Engine Test Set-up and Instrumentation (DDC 6V-92TA)

A computer controlled data acquisition system is used to tie the whole system together.

Engine sensor signals are sent to an IBM 286 PC after signal modification (i.e. AID conversion,

12 filtering, amplification, etc.). Software, developed in-house at UBC , is used to coordinate the acquisition of performance, emissions and high speed cylinder pressure data. Figure 2-1 is a schematic of the engine test set-up and instrumentation.

2.2 Engine and Engine Control

The engines used for testing are a single-cylinder, naturally aspirated Detroit Diesel 1-71 and a six-cylinder, turbo-charged and after-cooled Detroit Diesel 6V-92. These engines were chosen because six-cylinder versions of the 71 and 92 Series Detroit Diesel engines power more than 90% of the urban buses in North America. Both engines operate on a two-stroke cycle and use blower-forced uniflow scavenging. Table 2-1 lists the general specifications of these engines.

Table 2-1 : General Engine Specifications

DDC 1-71 DDC 6V-92TA

Basic Engine 2 cycle 2-cycle-Vee

Number of Cylinders 1 6

Control DDEC I DDEC II

Bore and Stroke 4.25 x 5.0 in (108 x 127 mm) 4.84 x 5.0 in (123 x 127 mm)

Displacement 70.93 cu in. (1.162 litres) 552 cu in (9.05 litres)

Compression Ratio 16.0 to 1 17.0 to 1

Gross Rated Power Output 15 BHP (11.2 kW) @ 1200 RPM 300 BHP (224 kW) @2100 RPM

Gross Rated BMEP 4.8 bar @ 1200 RPM 9.2 bar @ 1200 RPM

Rated Peak Torque 56lbft (76Nm) @ 1200 RPM 975lb1t (1322Nm) @ 1200 RPM

0 550 Inlet Port Closure 60 ABDC ABDC

The DDC 1-71 had originally been equipped with a mechanically controlled unit injector.

Its injection system was upgraded to a Detroit Diesel Electronic Control (DDEC) system similar

to the one used by the DDC 6V-92TA. The DDC 1-71 uses the first generation DDEC I system,

13 while the DDC 6V-92TA uses the improved DDEC II system. The electronic fuel injection system consists of electronic unit injectors, sensors and an electronic control module (ECM). The

ECM contains a microprocessor which control fuel injection timing and quantity by sending actuation signals to the injector solenoid. The ECM monitors the current in the injector solenoids to sense when the injector valve closes and uses this information as feedback to compute timing for subsequent injection events.

By interfacing with the ECM, the beginning and duration of fuel injection fuel can be freely selected manually. This creates the opportunity to fully explore engine performance, emissions, and combustion characteristics under a variety of fueling strategies. The DDC 6V-

92TA uses two separate ECMs; one to control the diesel injectors, the other to control the natural-gas injector independently.

2.3 Dynamometer and Dynainorneter Control

A dynamometer is used to dissipate mechanical energy developed by the engine and to measure engine output torque. The DDC 6V-92TA is coupled to an eddy current or inductor dynamometer, while the 1-71 is coupled to a water-brake dynamometer. In an eddy current dynamometer, the output shaft of the engine is connected to a rotor which rotates in a magnetic field provided by a DC current flowing through coils in a stator. Voltages induced in the rotor causes local currents to flow in short circuit paths or eddies. The energy of these eddy currents is dissipated in the form of heat which is carried away by the flow of water through a jacket on the

stator.

In a water-brake dynamometer, mechanical energy dissipation is created by a volume of

water within the dynamometer acting upon straight vanes on the stator and rotor. [121 The

volume of water within the dynamometer is determined by the water flow rate passing through the

unit. This flow rate is controlled by both a water inlet control valve and onfices in the outlet

water line. At the same time, the power developed by the engine is absorbed within the

dynamometer, converted into heat, and carried away by the outlet water.

The eddy current dynamometer has a rated absorption capacity of 200 hp, which is only

14 two thirds of the maximum rated power output of the six-cylinder engine. While testing however, instead of the dynamometer being power limited, it was found to be torque limited (independent of engine speed) at about 630 lbft. Looking at 1200 and 2100 RPM, for example, only 65% and

84% of maximum power could be achieved respectively. The water-brake dynamometer has a rated absorption capacity of 550 hp, which is more than sufficient for full load operation of the single cylinder engine.

In an eddy current dynamometer, torque is controlled by manipulating the DC field current since field current is proportional to torque. In the eddy current dynamometer controller used, both rpm and torque are measured and fed back to a PID controller. The proportional gain, integral time and derivative time can be tuned via pots on the control module to achieve optimum transient control. The manufacturer specifies that the precision is +1- 1 RPM for speed control and +1-0.1% (0.02% typ) for load control. Accept at high speed low load operation, these claims were found to be true. PID control is also integrated into the water-brake dynamometer controller, but is by-passed because the response times associated with changes in water flow rate are slow and lead to unstable dynamometer operation. Hence the water flow rate (which regulates torque) is controlled manually using an electro-pneumatically operated valve.

2.4 Fuel Injection System

Both natural gas and a small amount of diesel (pilot) are directly injected into the engine

cylinder at high pressure through a single injector. The natural gas and diesel fuel supply systems

are independent of one another, each with its own mass flowmeter. Figure 2-2 is a schematic of

the natural gas and diesel fuel supply systems. The diesel fuel, from a storage tank, flows into a

flow measuring device. The diesel fuel returning from the engine (not shown on the figure) also

flows into this measuring device such that the flow meter measures the net diesel fuel

consumption of the engine. Natural gas, from the main supply at a pressure of 14 kPa, is

compressed to 19 MPa by a commercially available compressor and stored in pressure bottles.

Natural gas drawn from these bottles flows first through a regulator and then through the flow

measuring device before reaching the injector.

15 O1PRESSOR

t34PRESSED NATURAL GAS

SUT-DFF

DUALrti.. UNIT IN.ECTOR

Figure 2-2 : Schematic of Engine Fuel Supply System (courtesy of H. Gunawan [8])

In conventional mechanical fuel injeclors, injection timing and injection rate are mechanically controlled by ports and helices machined in the hushing and plunger assembly. In an eiectromcally controlled fuel injector, liexibility and control are enhanced because timing and duration of the fuel injection is performed electronically. Figure 2-3 shows the schematic of the electronically controlled natural-gas unit injector. A cam is used to depress the plunger for pressurization of the liquid diesel fuel. A solenoid-operated spool valve performs the fuel

injection and metering functions.

When the solenoid coil is energized, the spool valve closes the diesel fuel flow passage.

Closure of the spool valve initiates pressurization of the liquid diesel fuel. Once the pressure has

reached a preset value, the diesel needle lifts to begin injection of diesel fuel. Pressure continues

to build until the opening pressure of the natural-gas needle has been reached to begin injection of

to natural gas. Opening of the spool valve causes pressure decay and end of injection. The duration of spool-valve closure, referred to as the pulse width (PW), determines the quantity of natural gas injected. The amount of diesel fuel injected is constant with changing pulse width. The engine controller sends actuation signals to the solenoids according to fuel timing and quantity requirements.

ACCESSORY SHAFT DRIVEN ACTUATOR

DDEC SOLENOID

DIESEL SUPPLY /RET URN

VALVE CHECK VALVE

CHECK PILOT NEEDLE VALVE

GAS NEEDLE

CNG StorcAge (20—200 bar)

CNQ Dleset PI(ot

Figure 2-3 : Natural-Gas Electronic Unit Injector (courtesy of K.B. Hodgins)

2.5 Engine Instrumentation

The principal measured parameters are output torque, engine speed, fuel and air flows,

cylinder pressure, intake and exhaust temperatures and pressures, and emissions levels. The

following sub-sections outline the measuring techniques used in each case.

17 2.5.1 Output Torque

The torque developed by the engine is measured with the use of the dynamometer and a strain gage load cell. The dynamometer is trunnion mounted such that the stator housing is free to rotate. A load cell, attached a to support, is used to restrict the rotation of the stator. As the rotor rotates within the stator, a torque is developed which as an applied force is measured by the load cell. The load cell can be calibrated by placing weights at the end of an extended moment arm bolted to the dynamometer casing. Maximun error in this instrument is ±0.1%.

2.5.2 Engine Speed

The engine speed measurement is acquired with a magnetic induction probe shaft encoder.

The magnetic induction probe is placed over a 60-tooth gear rotating with the crank shaft. This sensor provides a signal frequency proportional to engine speed (1RPM = 1 Hz). A hand-held digital tachometer was used to calibrate this sensor. With a piece of reflective tape attached to the engine output shaft and the hand-held tachometer pointed toward it, the unit sends out a continuous beam of light and counts the light pulses reflected by the tape. Maximun error in this instrument is ±0.1%.

2.5.3 Diesel Fuel Flow

The diesel mass flow rate measuring device used on the DDC 6V-92TA operates on the hydraulic “Wheatstone Bridge” principle. The system consists of three primary pieces of equipment: a fuel boost pump, a recirculating tank and the mass flow meter itself. Figure 2-4 is a schematic of this system. As illustrated, the diesel fuel, drawn from the fuel tank, passes through

a filter and is then pressurized by the boost pump to a specified level set with a relief valve.

Excess diesel fuel not used downstream is returned to the pump inlet through this relief valve.

This provides a clean smooth supply of fuel to the mass flow measuring device.

Diesel fuel pumped from the storage tank flows through the mass flow measuring device

into the recirculating tank. From the recirculating tank, the diesel fuel passes through a heat

exchanger which maintains its temperature at 40°C ± 3°C to conform with SAE standard J1995

18 JUN90 [16] and then flows to the engine. Since diesel fuel returning from the engine also flow into the recirculating tank, the mass flow measuring device measures the net fuel consumption of the engine. A vertical tube with small cross-sectional area, referred to as the stand pipe, sits atop the recirculating tank. By regulating the pressure of the supply fuel entering the recirculation tank, the mass flow meter measures the make up diesel flow required to maintain a constant level in the standpipe. Although sudden changes in the engine’s diesel fuel demands will cause the fuel level in the stand pipe to deviate, this set-up is designed to minimize the time for the level to return to its preset position.

ReliefValve Regulator

Engine Engine

C Shell-in-Tube I Heat P4 Regulator Exchanger Tank

Figure 2-4: Diesel Mass Flow Rate Measuring Device Schematic (DDC 6V-92TA)

The mass flow rate of the make up diesel fuel is measured directly using an arrangement of

four orifices and a constant volume pump in a “Wheatstone Bridge network [13]. When the

supply flow (Q) is greater than the recirculating flow (q) through the constant volume pump, the

mass flow rate can be directly related to the pressure difference P., — 3P if the products of the flow

19 coefficient and area of orifices ‘a’ and ‘d” are equal. When Q is less than q, the mass flow rate is directly related to the pressure difference 1P — 4P assuming the products of the flow coefficient and area of orifices “b’ and ‘c” are equal. The “Wheatstone Bridge” network allows the mass flow rate of diesel fuel to he determined by measuring only differential pressures without having

to uniquely determine the fuel density. The derivation of the proportionality between mass flow rate and differential pressure is given in Appendix I.

While the layout of the diesel mass flow rate measuring device used on the DDC 1-71 is similar to one used on the DDC 6V-92TA, it operates on a different principle than that described above. Here the weight of the recirculation tank is measured directly to give an estimate of the

mass flow rate. Fuel from the recirculation tank flows to the engine while fuel returning from the

engine flows into the recirculation tank. Hence the diesel fuel consumption rate of the engine can be determined by measuring the change in weight of the recirculation tank. When the

recirculation tank is nearly empty, it is re-filled from the diesel storage tank. A solenoid operated

valve is used to control the re-filling process, during which diesel flow measurements can not be

made. For accurate diesel fuel flow measurements, it is important to bleed each system to remove

any trapped air. The maximum diesel flow measurement error is ±2%.

2.5.4 Natural Gas and Air flows

The compressed natural gas mass flow is measured using an instrument which operates on

the Coriolis acceleration principle. The natural gas flows through a U-shaped tube which vibrates

at a frequency directly proportional to the product of the density and velocity of the gas. The

frequency of the signal produced is converted to a 4-20 mA signal and sent to the data acquisition

system via a remote flow transmitter. The manufacturer’s calibration, which was used for this

meter, demonstrated an average measurement error of ±0.4%.

The air volume flow rate is measured using a turbine meter located immediately

downstream of the air filter in the air intake. The maximum error, quoted by the manufacturer, is

±0.5% of full scale (DDC ÔV-92TA). The mass flow rate of the air is calculated from the air

density based on ambient temperature and pressure measurements.

20 2.5.5 Cylinder Pressure

Engine cylinder pressure is a key variable required in fundamental engine performance and combustion analysis. Engine cylinder pressures are used to determine the rate of combustion, indicated work, cyclic variation and engine friction. However to achieve adequate results in any analysis based on pressure data, the importance of its accuracy is paramount. Therefore some time has been spent on determining the most satisfactory way of collecting quality cylinder pressure data.

To measure cylinder pressure a piezoelectric pressure transducer and a charge amplifier are required. Piezoelectric pressure transducers generate an electrical charge proportional to the pressure they are sensing. A charge amplifier (charge amp) is required to produce an output voltage (generally -1OV to +1OV) proportional to this charge. When dealing with electrical charges, high insulation resistance in the transducer and all connections and cables between the transducer and charge amplifier are required. If this resistance is lowered in anyway, charge leakage will occur which will be seen as signal drift. Hence, care must be taken to clean all connections thoroughly using a cleaning spray which leaves no residue. Bending or stretching of cables can also lead to resistance degradation.

Proper setup of the charge amplifier is important for obtaining accurate pressure data.

The piezoelectric transducer has a high output impedance (on the order of a thousand megaohms)

[14] and a low output signal. Thus it is critical that the charge amplifier has a high input

impedance to match that of the transducer. If the impedances are mismatched, loading of the

transducer will occur. The loading effect is when the measured signal is distorted by the

measurement equipment. The longer the time constant of the charge amplifier, the higher the

input impedance. However, with time constants that are too long, signal drift can be encountered

[15].

To investigate the effect that charge amp time constant has on measured cylinder pressure,

pressure data at short, medium and long time constants were collected from a cylinder in the DDC

6V-92TA when running at 1200 rpm and a medium-high load condition (6 bar bmep). The data

collected at the medium and long time constants settings are almost identical throughout the entire

21 cycle. On the other hand, while the data collected at the short time constant setting matches the other two data sets near top-dead-centre, the pressures during compression are significantly higher and during expansion are significantly lower. The result is a narrower compression and expansion loop on the log-log plot of pressure versus volume with an exaggerated scavenging loop.

These effects can be seen in Figure 2-5. Figure 2-5 is a cylinder pressure versus volume log-log plot of the superposition of an average of 20 consecutive cycles of pressure data collected at both short and medium time constant setting on the charge amp at the same engine operating condition. A time constant of medium was found to give the most accurate results.

3.8

3.6

3.4

3.2

3 LO9(PC4) 2.8

2.6

2.4

2.2

2 I I 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 Iog(VcyI)

Figure 2-5 : Effects of Charge Amplifier Time Constant on Cylinder Pressure Data

The type of transducer and its mounting are equally important in obtaining accurate

pressure data. The hostile thermal environment of the diesel engine combustion chamber can

induce thermal strains on the piezoelectric material to give erroneous pressure readings. Hence,

the type of transducer and the manner in which it is mounted should be chosen in such a way that

the thermal effects are minimized while still measuring true cylinder pressures. Both water

cooling and recess mounting can be used to reduce thermal effects. Recessing the transducer

away from the fire deck can avoid the flame coming in direct contact with the transducer since the

22 flame will quench on the passage walls. With a passage mounting there can be the danger of acoustic delay and/or passage resonance. As an example of acoustic delay, assuming a cylinder composition of air at a temperature of 1000K, the speed of sound is approximately 620 rn/s. This means that for a transducer recessed 6mm, the pressure wave reaching the transducer’s sensing surface will be delayed by 0.7 °CA at 1200 rpm.

To investigate transducer thermal effects, a number of different types and mountings of

transducers were tested. Thermal effects on pressure data are similar to the effects of charge amp time constants shown above in Figure 2-5. As thermal effects become more apparent, the compression and expansion ioop becomes narrower and the scavenging loop becomes more exaggerated on the log-log plot of cylinder pressure versus volume. An immediate indication of

erroneous pressure data is seen when the resulting calculation of frictional work is unrealistically

low or negative.

Pressure transducers tested included a water cooled AVL 8QP 500c and several non-

water cooled PCB transducers with model numbers 112A05, 112A10, and 114M297. The PCB

112A05 is a high temperature model. The PCB 112A10 is the same as the 112A05, however it

includes an extended slotted head which is intended to further reduce thermal effects by

quenching combustion flames before they contact the transducer’s sensing surface. The 114M297

is a larger high temperature model. Several different recess lengths were experimented with when

mounting each of the transducers. The most satisfactory pressure data was collected using the

PCB 112A10. The pressure transducer mounting details for both the DDC 1-71 and the DDC

6V-92TA are given in Appendices II and Ill respectively

2.5.6 Mean Engine Temperatures and Pressures

Mean temperatures and pressures of fluids flowing through the engine are required to

operate, monitor and analyze the engine. Thermocouples are used to measure temperatures for

the following...

• ambient air

• air in the airhox

23 • exhaust products

i) directly outside each exhaust port in the exhaust manifold

ii) downstream of the turbocharger (DDC 6V-92TA)

• supply diesel fuel

• engine cooling water both entering and leaving

• engine oil temperature

• water leaving the dynamometer

Pressures were measured for the following...

• ambient air

• air in the airbox

• exhaust products upstream of the turbocharger (DDC 6V-92TA)

2.5.7 Exhaust Gas Analyzers

The concentration of exhaust gas constituents in the engine tail-pipe are measured on a volumetric basis. The measured constituents include NOR, C02, CO. THC (total hydrocarbons), ,4Cl 02, and smoke. The emissions instrumentation is shared between three engines used by the Alternate Fuels Research Group at UBC. The system has been given full treatment in other publications such as the M.A.Sc. thesis written by Y. Tao [9]. For completeness however, a brief description of the system will be given here.

The emissions analysis system consists of six distinct analyzers. Each of the exhaust gas constituents are measured using separate analyzers except for NO and 4H which are combined into a single analyzer. The Non-dispersive Infrared (NDIR) absorption detection method is used to measure the concentrations of CO, ,2CU NON, and .4CH The Flame Ionization Detection (FID) method is used to measure the concentration of total hydrocarbons. The paramagnetic

properties of oxygen are exploited to measure its concentration. Exhaust smoke levels are

measured independently of the rest of the system using a Bosch “Spot” Smokemeter.

So that hydrocarbons and nitrogen dioxides do not condense out of the sample gas before

reaching the measuring instruments, the exhaust gas analyzers are fed via a heated sampling

24 system which includes heated sampling lines, filters, pump, and valves. The FID instrument and

N07 to NO converter are also heated for the same reason. The NDIR instruments, on the other

hand, require a water free exhaust sample. Therefore a chiller is located upstream of these instruments to condense all of the water Out of the sample.

SAMPLE IN I I

*2 ICABINET 1 *3 z I — ci EXHAUST f

Figure 2-6 : Emissions Analysis System Schematic (heated instruments) (courtesy of Y. Tao f9j)

To conform with the SAE recommended practice J 177 APR82 [16], the sampling probe is

located in the exhaust line at a distance of 1-to 3m from the exhaust manifold outlet flange or the

outlet of the turbocharger. From the sampling probe exhaust gases flow through the heated

sampling lines to the heated instruments enclosure (Figure 2-6). After passing through particulate

filters, the flow is separated into two paths. One path leads to the FID to measure hydrocarbons,

the other leads to the heated pump. After passing through the pump, the flow is again separated

into two paths. One line goes through the heated NO7 to NO converter and then through the

25 chiller to the 4CHJNO instrument in the cool instruments enclosure. The other line flows through the chiller and is then separated into three paths in the cool instruments enclosure, each leading to the remaining instruments ,7(C0 CO, and 02). A schematic of the cool emissions instruments is given in Figure 2-7.

CABINET 2 #1 #2 NOx SAMPLE’

Figure 2-7 : Emissions Analysis System Schematic (cool instruments) (courtesy of Y. Tao [9])

2.6 Data Acquisition System

Output signals from all of the engine sensors (except for cylinder pressure) are sent to an interconnect board. The signals are then conditioned and converted from differential signals to single-ended signals with a common ground before being sent to a 12 bit AiD board (PCL 818) installed in an IBM PC. The PCL-818 AID board can accept up to 16 single-ended signals. Table

2-2 lists the 16 measured engine parameters along with their corresponding AID board channel numbers for both the DDC 1-71 and DDC 6V-Q2TA data acquisition systems.

26 The cylinder pressure output signal from the charge amp is sent to a self-contained high speed data acquisition unit (ISSAC) along with bottom dead centre (BDC) and crank angle signals from a crank shaft mounted optical encoder. The BDC signal is used to trigger data acquisition while the crank angle signal is used as an external clock to determine the intervals at which the cylinder pressure signal is to be sampled. Up to 100 consecutive cycles of pressure data can be taken and stored by the ISSAC. This data, in binary format, can be downloaded to the PC through a general purpose interface board.

Table 2-2: Measured Engine Parameters

CHANNEL DDC 1-71 DDC 6V-92TA

0 CNG Mass Flow CO emission

1 Beginning of Injection 2CO emission 2 Ambient Temperature NO emission

3 Pulse Width THC emission

4 Torque CNG Pressure

5 RPM RPM

6 Intake Air Pressure Torque

7 Diesel Mass Flow CNG Mass Flow

8 Intake Air Flow Diesel Mass Flow

9 CNG Pressure Airbox Temperature 10 4CH emission Ambient Temperature U 02 emission Airbox Pressure 12 2CO emission Exhaust Pressure 13 CO emission Intake Air Flow 14 THC emission 4CH emission 15 NO emission 02 emission

27 Software, written in-house at UBC, is used to coordinate the data acquisition, convert the signals to selected engineering units, perform calculations and display selected parameters. Each of the 16 channels on the AID board is sampled 1D()times and then averaged. Averaged data is used to calculate engine performance and emission parameters such as thermal efficiency, power output, and wet basis emissions. The averaged raw data and calculated data can be saved to disk when commanded to do so. The software is also used to interface with the ISSAC to acquire cylinder pressure data. A description of the software used for processing cylinder pressure is given in Appendix IV.

28 3. CALCULATED ENGINE PERFORMANCE AND EMISSIONS PARAMETERS

The parameters which are useful in comparing the performance and emissions characteristics of different engines, or the same engine at different operating conditions are thermal efficiency, mean effective pressure, coefficient of variation, wet basis and brake specific emissions, and unburned fuel fractions.

3.1 Thermal Efficiency Thermal efficiency (lth) is defined as the ratio of the engine output work to a measure of the chemical energy of the consumed fuel. Thermal efficiency can be written as

P hlthjjilj.IV (3-1)

where th and LHV are the mass flow rate and lower heating value of the fuel, respectively, and b is the engine brake power. When more than one fuel is involved in the combustion, the expression for thermal efficiency can be written more generally as

1th = (3-2)

The engine brake power is calculated from measurements made at the engine output shaft.

It is given by Pb=NWb (3-3)

29 where N is the engine speed and Wb is the engine output work. For a two-stroke engine the output work per crank shaft revolution is given by

Wb=2JtTb (3-4)

where Tb is the measured engine torque. In order to have a common basis for comparison under varying atmospheric conditions, the brake power is corrected to standard conditions (i.e. 100 kPa inlet air pressure, 99 kPa dry inlet air pressure, 25°C inlet air temperature). The correction procedure is in accordance with SAE Standard J1349 JUN85 [16] and is given in Appendix V.

The calculated engine brake power and thermal efficiency have an associated error due to the error in the measured parameters. The error in each calculated parameters is found by taking the differential of the expression representing that parameter. The relative error can then be found by dividing by the original expression. The relative error in brake power is given by

b Tb N

From chapter 2, the relative error in engine torque and speed measurements were both ±0.1. This gives a relative error in brake power of ±0.2%. Similarly, the relative error in thermal efficiency is given by

TI P diLHVi+Ihg•LHVg

which can be rewritten as

30 am m am gss — g = 8P rh thgs LHV + LHV rngas 1

Also from Chapter 2, the relative error in natural gas and diesel flow measurements were ±0.4% and ±2%, respectively. Using lower heating values of 49680 kJ/kg and 43200 kJ/kg for natural gas and diesel, respectively, and using a typical mass ratio of diesel fuel to natural gas of 30%, then the maximum relative error in thermal efficiency is ±0.9%.

3.2 Mean Effective Pressure

A parameter that scales out the effect of engine size on engine output work is the mean

effective pressure (mep). It is defined as follows

mep=-- (3-5)

where Vd is the engine displacement volume. As the name implies, the units of mep are pressure

units. The brake mean effective pressure (bmep) is the output work, as defined in equation (3-4),

divided by the engine displacement volume. The bmep can therefore be written as

bmep= — b (3-6) Vd

The indicated mean effective pressure (imep) is the sum of the bmep and the total friction

mean effective pressure (tfmep). The tfmep includes the work required to pump mixture into and

out of the cylinder, to overcome resistance to relative motion of all moving parts, and to drive

31 engine where by imep is

3.3 cycle-to-cycle

pressure efficiency desirable standard

the

Cyclic

area Wfld

accessories

Observation calculated

deviation

data

contained can

Variation

quantify

the

and

variability occur

Figure

directly

indicated

such

within

this

with

imep

called

3-1

successive

as P Cylinder

combustion in res (kPa)

from

high

divided

the

the work sure

Typical

the

blower,

pressure-volume

measured levels pressure 5000 4000 6000 7000 2000 3000

coefficient 1000

Wmd=fPdV

and

cycles

by 0

P-V 0

imep

variability. •

the

of VdC,,l

water

rise

diagram

cyclic

mean

cylinder =

engine Cylinder 0.5

due

pump, Wd

the

variation

imep

variation. 32

curve

One

for

pressures displacement

cylinder Volume

oil

combustion.

a 1

measure

Two-Stroke

pump,

follows

shown (litres)

From

imep

since

pressure 1.5

alternator,

volume

(COVjmp)•

cyclic the

Significant

Figure

diagnostic

Diesel

indicated

on 2

variability of

etc..

3-1.

Engine

oscilloscope

single

losses

point

work,

The

(3-7)

(3-8)

defined

cylinder.

imep

derived

defined

power

view,

indicates

given

from

The

and

the

is = lmep 0 xlOO (3-9) COVmep imep

Heywood [1] points out that vehicle driveability problems usually result when COV exceeds about 10 percent.

3.4 Wet-Basis and Brake-Specific Emissions

A volumetric analysis of the engine tail-pipe exhaust emissions gives a great deal of insight into the combustion phenomena and overall engine performance. It is informative to look at both the concentration of exhaust gas constituents measured in parts per million (ppm) or percent by volume and the brake specific emissions levels. Brake specific emissions are simply the mass flow

rate of each exhaust gas constituent divided by the engine brake power.

As described in section 2.5.7, all but the total hydrocarbon (THC) analyzer require the

sample to be free from water vapour. Since water vapor constitutes a significant portion of the

engine tail-pipe exhaust, these “dry-basis” concentration measurements will overestimate the true

constituent concentrations. Therefore a conversion to “wet-basis” is required to account for the

water vapor present in the engine exhaust. The wet-basis values are the ones used in the brake

specific emissions calculations.

Heywood [1] derives the following relationship between wet and dry mole fractions using

the notation y. and y’ to denote respectively the wet and dry mole fraction of species i for a fuel

composition CnHm• y1 2o)Yi=(lYH (3-10)

where

* * + m y Yco (311) YH * / * i * * or . 2 [1+ y01/K Yco)+(m/2Yco + 2)jYco

2 33 Since two fuels are present (natural gas and diesel), the fuel composition CmHn represents an averaged composition based on the fuel flow rates of both fuels. The constant 1K relates the wet based basis concentrations of ,2C0 CO, 2H0, and 2 on available exhaust gas composition data in the following way:

1K = 2oYcoYH (3-12) 2Yco 2YH

1K is an empirical constant determined from published exhaust gas composition data. It is required since the concentration of 2H is not measured directly. Values of 3.8 and 3.5 are commonly used for .1K The difference between these values has little effect on the computed magnitude of the mole fraction of water. The relationship given in equation (3-10) is used with

the equations (3-11) and (3-12) to convert all of the mole fractions of the measured exhaust gas

constituents from a dry to a wet basis with the exception of THC, as it is the only one measured on a wet basis. In addition to the measured constituents ,2(C0 CO, NO, 02, ,4CH and THC), the use of the above equations enables the wet mole fractions of ,2N 112 and 20H to be calculated as well. An additional correction must be made to the mole fraction of N0 since the humidity of

the inlet air has an effect on the amount of NO chemically formed in combustion. The correction, from the SAE Recommended Practice J177 APR82 [16], is applied to the wet basis NO mole

fraction as follows:

YNOrr (3-13) =

where

2K =1+ 7A(H — 10.714)÷ 1.8B(T — 29.444) A = 0.044(F/A)_0.0038

B = _0.116(F/A)÷ 0.0053

34 T is the intake air temperature (in °C), F/A is the fuel-air mass ratio (dry basis), and H is the specific humidity in grams of water per kilogram of dry air. The calculation of specific humidity is given in Appendix VI. At 25°C, 20% relative humidity, and equivalence ratios of 0.2 and 0.8, 2K equals 1.12 and 1.07, respectively. At the same temperature and respective equivalence ratios, but at 80% relative humidity, 2K equals 0.85 and 0.96 respectively.

To calculate the brake specific emissions, the molecular weight of the exhaust must first be determined. The molecular weight of the exhaust is given by:

MWe . )1MW (3-14) where the species included in this summation are ,2C0 CO, ,2N NO, 02, 2H0, ,2H and THC. Since NO consists mostly of NO, the mole fraction and molecular weight of NO are used in the calculation of the exhaust molecular weight. However, the SAE recommendation is to express NO as 2NO for the brake specific calculations. Also, THC are analyzed on a carbon atom basis. Assuming the THC have the same hydrogen to carbon ratio as that of the average of the two fuels

(i.e. CnHm), then the molecular weight of THC per carbon atom is expressed as

MW =12.01+(-.1.01) (3-15)

The brake specific emission of a component )1(bs is equal to the mass flow rate of that emission )1(m divided by the engine brake power (b)

bs=-’- (3-16)

The mass flow rate of a component is given by

35 m MW. (3-17) 1VlW/

where the exhaust mass flow rate (me) is given by

mCXh mair + rnG + rnDSL (3-18)

where thr and rnDSL are the measured flow rates of air, compressed natural gas and diesel respectively.

3.5 Unburned Mass Fraction of Fuel

The unburned mass fraction of fuel is required for the mass fraction of fuel burned calculation, which is described in chapter 5. The unburned mass fraction of natural gas is given by

XUG = (3-19) mcG + mDSL

and the unburned mass fraction of diesel fuel is given by

m -th = THC 4CH xUDSL (3-O m(G +

36 4. PREVIOUS COMBUSTION ANALYSIS MODELS

This chapter begins with a description of the combustion phenomena occurring in the cylinder of a diesel engine. A description of basic combustion analysis techniques is then given, followed by an examination of previously developed combustion analysis models intended to identify their strong points and shortcomings.

4.1 The Stratified Charge Combustion Process

The stratified charge combustion phenomenon occurring in the cylinder of a diesel engine involves complex interactions of physical and chemical processes. A qualitative description of the complexities associated with the stratified charge combustion process is given by Edwards,

Siebers, and Hoskins as an introduction to their study of the autoignition process of a diesel spray via high speed visualization [17]. The stratified charge combustion process can briefly be described as follows.

The process begins when fuel is injected with high velocity into the combustion chamber shortly before the piston reaches top-dead-center (TDC). The high momentum fuel mixes and begins to chemically react with the relatively quiescent, but high temperature (9OOK) mixture of compressed air and residual combustion products. This mixing process is dependent on both time and location; hence a competition exists between parcels of fuel and air to see which, if any, will autoignite. Autoignition can be described as the point where the preferred chemical pathways of the fuel/air mixture are no longer endothermic or leading to non-participative intermediate species, but lead to the release of chemical energy. Sufficient chemical energy must be released to remain exothermic during subsequent mass and energy exchanges resulting from the mixing process.

37 Parcels of fuel and air adjacent to parcels which are autoignition sites exchange mass and energy, and may become favorable reaction sites themselves. Other sites which are chemically less mature, but are suddenly exposed to a flux of heat or species, may be consumed by a wave of chemical reaction or flame. The rate of combustion for the remainder of the process is dependent upon mixing. Volumetric expansion of the burning parcels generates convective motions which, along with residual motions from the fuel injection and compression-generated swirl, continue to mix reactants and products.

In short, the compression-ignition combustion process involves mixing with heat and mass transfer between parcels of varying compositions of species while complex chemical kinetics lead to the release of chemical energy and the production of pollutants. ‘Whilethe combustion process is exceedingly complex on a microscopic scale, the application of simplifying yet realistic assumptions and standard thermodynamics enable the progress of combustion to be investigated quantitatively using measured engine cylinder pressure data

A thermodynamic combustion model based on measured cylinder pressure data can potentially be a valuable diagnostic tool used to investigate the performance and emission characteristics of an engine under various operating conditions. If the model can provide insight into the processes occurring inside the combustion chamber (such as heat transfer, fuel injection, and pollutant formation), then steps can be taken to improve performance and reduce pollutant emissions of an engine.

4.2 Thermodynamic Combustion Analysis

A thermodynamic combustion analysis based on measured cylinder pressure typically begins with an energy balance on the engine cylinder contents. A schematic of the thermodynamic system as applied to the combustion chamber is illustrated in Figure 4-1. The first law of thermodynamics for this open system for a small crank change interval can be written as 1hoQ—oW=dE+2dm (4-1) 38 dmhm

I Control Volume boundary

Figure 4-1: Schematic of Combustion Chamber Thermodynamic System

Ignoring potential and kinetic energy changes in the cylinder gas, the change in total energy dE is equal to the change in total internal energy dU. The flow of mass and energy into and out of the system is accounted for in the summation of the differential mass (dm) multiplied by its corresponding enthalpy (h). The flow of enthalpy into the cylinder is associated with the injected fuel, while the flow out of the cylinder is due to the leakage past the piston rings or through the valves. The work transfer from the system, oW, is given by

OW = PdV

where P is the average pressure over a small time increment.

To estimate the instantaneous heat-transfer, OQ, to the cylinder walls, an estimate of a heat-transfer coefficient is required. A discussion of estimates of heat transfer to cylinder walls is given in the following section. Implementation details of the combustion analysis model hinge upon the thermodynamic description of the cylinder contents and the complexity of sub-models of certain in-cylinder processes (such as fuel injection, heat-transfer, pollutant formation, etc.).

While the implementation details vary with the application, there are two broad categories of methods. The first method treats combustion as simple heating. The second method accounts for chemical reaction. Discussions of these two methods are given in sections 4.4 and 4.5.

39 4.3 Estimating Instantaneous Heat-Transfer to Cylinder Walls

Annand [18] in 1963 reviewed existing formulae for internal combustion engine instantaneous heat-transfer rates and concluded that the dimensionless experimental convective heat-transfer coefficient (i.e. the Nusselt number) could be represented by 7Nu=a(Re)° (4-2) with 0.35 a0.8

Here the characteristic length used in both the Nusselt and Reynolds numbers is the cylinder bore, and the characteristic velocity used in the Reynolds number is the mean piston speed. The kinematic viscosity is evaluated at the mass-averaged gas temperature.

Woschni [19] in 1967 introduced a new method for determining the heat-transfer coefficient for internal combustion engines based on an overall energy balance of a four-stroke, open-chamber diesel engine. He suggested that the characteristic gas velocity used in the

Reynolds number should account for the convection resulting from both piston motion and combustion. Woschni determined that the Nusselt number could be expressed as

Nu = 80.035(Re)° (4-3) the exponent of 0.8 being the same as for turbulent fluid flow in pipes.

Woschni also used the cylinder bore as the characteristic length in both the Nusselt and

Reynolds numbers, but expressed the characteristic velocity as 2cbw=Clcm+C 4-4) Here 1C and 2C are constants, cm is the mean piston speed and Cb is a gas velocity which can be attributed to the burning process. This gas velocity is estimated by

40 VT cb r r

where V, P, and T are the volume, pressure and temperature, respectively. The subscript r refers to a convenient reference point such as inlet closure or beginning of combustion, and (P - )0P is the pressure difference between fired and non-fired cycles. The constants 1C and 2C depend on cylinder geometry and are selected such that approximately 85% of the total gas velocity results from piston motion, with the remaining 15% resulting from combustion intensity. Due to complexities associated with temperature gradients and fluid motion in the combustion chamber, this heat transfer estimate is expected to have a relatively high degree of uncertainty.

Radiation heat transfer inside the combustion chamber should also be considered.

Radiation in diesel engines consists of luminous (soot) and non-luminous (gaseous) radiation [20].

Soot particles formed during combustion assume almost the same temperature as the gases in the flame. If the soot concentration is high enough, this cloud of particles radiates like a solid body.

Soot emissivity is dependent on the soot concentration and the thickness of the soot cloud [19].

The non-luminous radiation from the combustion gases is primarily due to emission contributions from the tri-atomic molecules of carbon dioxide, and water vapor.

As reported by Szekely and Alkidas [20], the contribution of radiation to the total heat transfer in conventional diesel engines is significant. Their analysis shows that in the case of an open-chamber diesel engine, the ratio of radiation to total heat transfer could be 24% at full load.

They also reported findings from other researchers; Ebersole et al. found that the radiation contribution in a two-cycle open-chamber diesel to increase from 5 to 40% as load increased;

Oguri and Inaba found that the maximum contribution of radiation to be about 30%; and Dent and

Sulaiman indicated that radiation was under 20% of the total. Szekely and Alkidas also reported the non-luminous radiation to be negligible compared with the soot radiation which was confirmed by other researchers.

Since radiation heat transfer is only significant with high soot concentrations, no error should be incurred by ignoring radiation heat transfer calculations when no smoke is present in the

41 engine exhaust. Smoke levels at part loads in diesel engines are low. Smoke levels in natural gas

fueled diesel engines are also low.

4.4 Simple-Heating Combustion Analysis

Rassweiler and Withrow developed a simple-heating model in the 1930s [21]. It is easy

to implement and requires only cylinder pressure measurements and corresponding cylinder

volume details as inputs. Their analysis is based on observations from combustion of

homogeneous mixtures in constant-volume bomb experiments.

In constant-volume bomb experiments with combustion of homogeneous mixtures, there is

no work done and no flow of enthalpy into or out of the bomb during the combustion event.

Hence the first law of thermodynamics (equation 4-i) applied to a constant volume bomb reduces

to Q=AU (4-5)

The release of chemical energy during combustion is thought of as a simple heat addition process.

Assuming that the heat transfer to the walls of the bomb during combustion are negligible, then

the heat transfer, Q, is a fictitious heat addition.

Using the ideal gas law, the change in internal energy, AU, can be written as

AU = mCAT

= .y-i

(4-6) y -1

where V is the volume of the combustion bomb, ‘ is the ratio of specific heats, and AP is the

change in pressure in the bomb. Combining equations (4-5) and (4-6) gives

42 (4-7) ‘ -1

Assuming that the equivalent heat addition, Q, is proportional to the mass of fuel burned, that the ratio of specific heats is constant, and that there is no change in the molecular weight of the mixture during combustion, then it follows from equation (4-7) that for a constant volume bomb,

the mass fraction of burned fuel at some point in time can be written as

X=’ (4-8)

In this expression, P is the measured pressure, 1P is the initial pressure, and P is the maximum pressure achieved during combustion. For a given amount of heat addition, 0, it also follows

from equation (4-7) that pressure rise due to combustion is inversely proportional to volume.

(4-9)

In the combustion chamber of an engine however, the pressure change is a result of the

reciprocating piston motion as well as combustion. Assuming these two effects on pressure can

be considered independent then the following expression can be written.

combustion = APmeasured - 1Apiston (4-10)

Assuming that the compression and expansion processes are polytropic, then the pressure change due to piston motion 0AP between states 1 and 2 can be expressed by:

n = - 1P (4-11)

43 where n is the polytropic exponent obtained from the pressure data. Since APmeed = 2P - .1P then equations (4-10) and (4-11) can be combined to give:

n = 2P (4-12) -

If states 1 and 2 are considered respectively to be the beginning and end of successive small crank angle intervals, then the change in pressure due to combustion can be calculated at every crank angle between the beginning and end of combustion. However, since each crank angle corresponds to a different volume, to apply the analogy of equation (4-9) for the constant pressure bomb these pressures need to be referenced to a common volume (for example

Hence the mass fraction of burned fuel in the engine cylinder at some crank angle will be the sum of the pressure changes due to combustion (referenced to a common volume) divided by the total sum from beginning to end of combustion of these pressure changes as follows:

8 (AP ) / 0 o \\VTDC = BOC 1 Xmf (4-13). / 0V VTDC °BOC

The subscripts BOC and EOC refer to the beginning and end of combustion, respectively.

While this method is widely used, it suffers from the following drawbacks:

1. Although heat-transfer effects are accounted for to the extent that the polytropic exponent n

differs from the isentropic exponent, the polytropic exponent is difficult to estimate because it

is not constant during combustion.

2. The calculation of the mass fraction of burned fuel depends strongly on a measure of the

EOC. Since the EOC is difficult to obtain accurately from pressure data, the calculation of

mass fraction of burned fuel at a given crank angle can be quite uncertain.

44 3. The ratio of specific heats does not remain constant during combustion, which is inconsistent

with equation (4-13).

4. The energy changes of the cylinder charge represented by the pressure-time history of the

engine are not explicitly determined; hence spatially non-uniform properties (i.e. burned gas

temperatures) and pollutant-formation rates can not be computed.

Gatowski et al. [22] in 1984 developed, tested, and applied a one-zone combustion rate analysis procedure with the aim to maintain simplicity while including “all phenomena of significance”. A one-zone model describes all of the cylinder contents in terms of average properties. The cylinder contents are treated as uniform and homogeneous, with no distinction made between burned and unburned gases. The heat transfer term in the first law energy balance

(equation 4-1) is treated as the difference between the simple heat addition from combustion and the heat transfer from the cylinder gases to the combustion chamber walls. Using a heat transfer model and a representation of the sensible internal energy change of the cylinder contents, the heat release rate can be calculated. Spatially non-uniform properties (i.e. burned gas temperatures) can not be computed since only a single zone is used.

The ratio of specific heats (y) is the primary thermodynamic property representing the cylinder contents. The variance of ‘ with temperature was approximated by a linear fit which is evaluated at the bulk cylinder temperature. The correlation used for calculating cylinder heat transfer is based on the form proposed by Woschni. Details of the fuel injection event were not included in this analysis. For simplicity, the fuel mass was considered to be vaporized and premixed with the combustion chamber air at the beginning of the analysis. Finally, crevice effects were accounted for by using a simple modeling assumption. Crevice effects are the flow of gas into and Out of crevices in the combustion chamber which constitute a couple of percent of the clearance volume.

4.5 Chemical Reaction Combustion Analysis

Instead of treating combustion as a simple heat addition process, it would be more accurate to describe the release of chemical energy resulting from a change in composition from

45 unburned reactants to burned products. This can be represented thermodynamically by considering the differences in energy between the unburned and burned gases. The heat transfer term in the first law energy balance (equation 4-1) then strictly accounts for heat transfer from the cylinder gases to the combustion chamber walls.

Krieger and Borman [23] presented a one-zone thermodynamic combustion rate model in

1966. Their treatment assumes that the entire cylinder contents are made up of a homogeneous

mixture of air and combustion products which are in thermodynamic equilibrium at each instant. The products of combustion are assumed to be the result of the oxidation of 2CH in air. Data from the JANAF tables of thermodynamic properties are used to obtain mathematical expressions

for the internal energy and gas constant as functions of temperature, pressure, and equivalence

ratio. Dissociation of the combustion products is ignored. The release of chemical energy is

represented by changes in the internal energy and composition of the cylinder contents with

pressure and temperature.

Phenomena such as temperature gradients, pressure waves, nonequilibrium compositions,

fuel vaporization, mixing and so on are ignored in this model. The instantaneous heat-transfer

from the gas is computed from the Annand correlation. Five metal-surface areas representing the

head, piston, sleeve, and valves are each assigned a different constant temperature. These surface

temperatures must be either estimated from experimental data, or computed by the use of a cycle

analysis program.

Burning is assumed to take place incrementally. Fuel is assumed to be introduced into the

combustion chamber at the same rate that it is consumed. Thus unreacted fuel in either liquid or

vapor phase is never present. The equations of energy and mass continuity together with the

equations of state and the mathematical expressions for internal energy and the gas constant are

integrated to obtain the mass of fuel burned during each crankangle increment.

In 1985 Bedran and Beretta [24] discuss the elements of a generalized multi-zone

thermodynamic analysis method that can be applied to any level of modeling (zero-dimensional,

quasi-dimensional, or multi-dimensional) and any type of internal combustion engine

(homogeneous-charge, direct injection, indirect injection, etc.). The model uses a mass and

46 energy balance to determine the instantaneous mass fraction of burned gas mixture in differential equation form. The only assumptions made are as follows:

1. The mass of gas which is instantaneously burning is negligible.

2. The pressure is uniform throughout the control volume.

3. The burned and unburned gases behave as Gibbs-Dalton mixtures of ideal semi-perfect gases

(i.e. with temperature dependent specific heats).

4. The liquid fuel in the combustion chamber behaves as an incompressible fluid so that specific

volume and internal energy depend on temperature only.

Before any useful information can be attained from this analysis, it must be complemented by a set of modeling assumptions to account for such effects as fuel distribution after injection and vaporization, wall heat transfer, mass exchange with crevice volumes, mixing between unburned and burned gases, non-uniform distributions in temperature and composition and so on. While an application of the analysis was not developed and tested, Bedran and Beretta described how one might set up the problem of estimating, from cylinder pressure measurements, the mass fraction of burned gases as a function of time in a diesel combustion chamber with no residual burned fraction.

In this application the control volume coincides with the walls of the combustion chamber and a number of zones are defined. There are two burned gas zones; one corresponding to combustion at the cylinder core temperature and the other at the crevice temperature. There are

N+2 unburned zones which include a liquid fuel zone, unburned fresh charge at crevice temperature, and N gaseous zones with increasing fuel concentrations. Assuming enough independent models (i.e. vaporization, heat transfer to the walls, etc.) are available, a step by step solution scheme starting from an instant in time at which all the variables are known can be used to calculate the mass burned fraction. Each stepwise estimate of the mass fraction burned must be iteratively refined. Szekely and Alkidas [20] in 1986 presented a two-stage two-zone combustion analysis model for diesel engines. The two stages refer to two distinct modes of burning. In the first stage, combustion occurs at a stoichiometric equivalence ratio. In the second stage, combustion occurs at an equivalence ratio below the cylinder-averaged equivalence ratio

47 (i.e. fuel lean). These distinct burning modes are arbitrarily chosen such that the calculated exhaust NO corresponds to the measured value.

Table 4-1 Szekely and Alkidas Combustion Analysis Model (burning stages and zones)

unburned zone ( = 1) Stage I unburned zone ( < p) burned zone (( = 1)

unburned zone (q:< py) Stage II burned zone ( = 1) burned zone (( < 4avu)

Each burning stage has a corresponding burned and unburned zone, for a maximum of four zones. However, only three of the four zones are actually active at any one time. The zone which begins to react first is completely consumed prior to reaction of the second zone, and no mixing occurs between unburned zones or between the burned and unburned zones. Table 4-1 lists the corresponding zones for each burning stage. Each zone contains a homogeneous mixture of air, fuel and residual combustion products in thermodynamic equilibrium. Temperature gradients within the zones are ignored as is flow leakage through the valves and past the piston rings. Uniform pressure within the cylinder is assumed and the ideal gas law is assumed to be valid for each zone.

The equivalence ratio of the second stage is empirically derived by comparing calculated

NO emission levels to those directly measured in the exhaust. Szekely and Alkidas deduced that

67% to 75% of the fuel is burned in the second stage at an equivalence ratio of about 0.1 below the cylinder averaged value. The NO formation is described by the extended Zeldovich mechanism (described in chapter 5). Convective and radiative heat transfer are also accounted for as is the injection of liquid fuel. The convective heat transfer is described by Woschm’s empirical equation.

48 When comparing the results of this model to a single stage model, Szekely and Alkidas found that in the initial stages of combustion, the calculated rate of heat release was higher than the corresponding rate calculated by the single stage model.’ They also found the computed combustion temperatures for the stoichiometric burning stage to he consistently higher (7 to 22% on an absolute scale) than published flame temperature measurements. Model calculations also suggest that NO-decomposition reactions are insignificant which is contrary to some experimental findings.

Gunawan [81 in 1992 presented results from a two-zone combustion rate model to analyze diesel engine combustion when fueled with direct-injection natural-gas with diesel pilot. The two zones he considered were an unburned and burned zone. In this model the key assumptions are as follows:

1. The cylinder pressure is uniform.

2. Both the unburned and burned zones behave as ideal gases.

3. The combustion occurs at the cylinder averaged equivalence ratio.

4. The combustion products are in thermodynamic equilibrium.

5. All of the fuel is present in the cylinder at the beginning of injection.

6. The mass burned fraction of diesel fuel and natural gas are the same at any instant during the combustion process (i.e. proportional burning of natural gas and diesel).

7. The vaporization of the liquid diesel fuel occurs instantaneously with allowance made for heat of vaporization.

Heat transfer to the cylinder walls is ignored in this model which requires the calculated mass burned fraction curve to be normalized so that the final calculated mass burned fraction agrees with the measured exhaust composition.

4.6 Limitations of Previous Combustion Analysis Models

The combustion analysis techniques presented in this chapter have been classified into two broad categories: a) simple-heating models and b) models that account for chemical reaction.

Details of the single stage model were not given. t 49 While the latter are more tedious to implement than the former, they represent the thermodynamic properties of the cylinder contents more accurately.

A key feature of a combustion rate model is how the contents of the cylinder are described. One-zone models describe all of the cylinder contents in terms of average properties.

The cylinder contents are treated as uniform and homogeneous and there is no distinction made between burned and unburned gases. The advantages of a one-zone model are that the effects of heat-transfer and gas flow phenomena are simple to describe and the combustion can be considered either as a separate heat addition process or a chemical reaction process. Average cylinder temperatures, however, can not be used for modeling pollutant-formation processes (i.e. )1NO due to the high sensitivity of these processes to gas temperature. To permit more accurate treatment of thermodynamic properties of the cylinder gases, different zones can be considered. This approach is referred to as multi-zone modeling. Any number of zones can be specified. Each zone has uniform and homogeneous properties and is effectively treated as a separate thermodynamic system. While the implementation of a multi-zone model is more difficult than its one-zone counterpart, realistic gas temperatures can be computed.

The number and complexity of modeling assumptions used in a combustion model will have an effect on its accuracy. Modeling assumptions describing radiation and convection heat transfer, fuel injection, crevice flows, pollutant formation, etc. can be incorporated. The accuracy of the results from these modeling assumptions depend not only on their own level of complexity and accuracy, but also on the accuracy of the representation of the thermodynamic properties of the cylinder gases.

The accuracy with which the model represents stratified-charged, compression ignition combustion versus homogeneous-charge, spark-ignition combustion will also affect the results.

Most of the models presented in this chapter are based on models describing homogeneous charge combustion. While homogeneous-charge combustion can be accurately described using only an unburned and burned zone, the high degree of non-uniformity in composition and properties in stratified-charge combustion require a greater number of specified zones for proper

50 treatment. The basic models needed to simulate the stratified-charge diesel combustion process and the homogeneous-charge spark-ignition combustion process are quite different.

While the model developed by Szekely and Alkidas distinguishes homogeneous-charge from stratified-charge combustion, it does not deal with temperature gradients in the burned gases, or mixing between burned and unburned gas zones. Both of these factors have a significant influence on the accuracy of the predicted burned gas temperature. Since diesel engines operate with 50% to 400% excess air with turbulent flow inside the combustion chamber, it seems reasonable that the burned gases will not remain independent of unburned gases for the entire duration of combustion. Some mixing between burned and unburned gases must take place.

A problem immediately comes to mind when specifying a single zone to describe all of the burned gases. As the combustion process involves mixing, non-uniformities in the properties of the burned gases formed at different times and locations in the cylinder would have to be expected. Temperature gradients, for example, exist in the burned gases because products of combustion formed early in the combustion process are compressed to a higher temperature as combustion proceeds and cylinder pressure increases, while the last of the reactants to burn are compressed prior to combustion with no compression afterward.

An approximation to more effectively deal with the non-uniformities in the burned gases is to use many distinct burned gas zones, each with unique and independent properties. Instead of the size of a single burned gas zone growing as combustion proceeds, a new burned gas zone can be created during each calculation step (generally one crank angle). The size of each zone therefore depends on the instantaneous combustion rate. Once formed, the properties of each burned gas zone are updated with changing cylinder pressure for subsequent calculation steps.

The question which now arises is: should each of these burned gas zones be independent of each other and the other zones in the cylinder throughout the remainder of the combustion process’? The answer is no. Since the combustion in a diesel engine involves mixing of fuel with excess air, one would expect that burned gases formed at the flame front either diffuse away or are swept away by turbulence and then forced to mix with either unburned gases or other burned gases.

51 There is an important need for a combustion model that deals with the non-uniformities in the cylinder of a stratified-charge internal-combustion engine. A more accurate treatment of the stratified-charge combustion process will give more accurate pollutant-formation, burned gas temperature, and fuel burning rate predictions. A model which addresses non-uniformities in the combustion chamber has been developed and tested as part of this thesis. A detailed description of this model is given in the following chapter.

52 5. PROPOSED THERMODYNAMIC COMBUSTION ANALYSIS

5.1 Formulation of Combustion Model

The combustion analysis model developed here uses a mutli-zone description of the cylinder contents. As the intended application of this model is to investigate fuel burning rates, non-uniformities of cylinder gas properties, heat transfer, nitrogen oxide formation, and fuel injection for both diesel and natural gas fueling regimes, appropriate modeling assumptions are used. A conceptual diagram of the combustion analysis model is given in Figure 5-1. The figure illustrates the different zones and their interaction with one another

Figure 5-1 : Conceptual Diagram of Proposed Combustion Model

53 By definition zones have homogeneous and uniform thermodynamic properties, thus the key to the model formulation is how the zones are defined. The diesel fuel zone consists of the injected liquid diesel fuel. The natural gas zone consists of the injected compressed natural gas.

The unburned zone consists of a mixture of fresh intake air and residual combustion products from the previous cycle. The burned gas zones consist of the products of combustion between the fuel and the unburned zones. The ‘mixed” zone consists of a mixture of burned and unburned gases.

A new burned gas zone is formed during every calculation step. It remains independent with its properties changing with cylinder pressure for only a specified “mixing delay” period.

At the end of the mixing delay period the burned gas zone mixes out with a proportional amount of unburned zone in the mixed zone. This formulation is somewhat empirical in that the mixing delay period and the proportion of unburned gas that mix with the burned gas zone must be selected.

Application of conservation of mass and energy to the engine cylinder serves as the starting point in the combustion analysis. If m,, mg, m, m, and mm are the instantaneous masses of the diesel, natural gas, unburned gas, burned gas and “mixed” gas zones respectively, then the total mass in the cylinder at a given time is

0m = md +mg +m -f-mb +rnm (5-1)

Since the burned gases are represented by a number of zones, the total mass of the burned gases (mb) is written as mbI. If there is no leakage past the piston rings, then the only change in the

total cylinder mass once the intake and exhaust ports are closed is due to injection of fuel. The

total mass in the cylinder prior to fuel injection is the mass of air and residuals trapped at intake

and exhaust port closure (i.e. entirely unburned gas zone).

Using the same subscripts as above, the total cylinder volume at any given time in the

combustion process is

54 = V + Vg + + + Vm or

1V = mdvd + mgvg + mv + mmvm + (mbvb)1 (5-2)

where v is specific volume and k is the number of burned gas zones present at any time. The total cylinder volume can be determined as a function of crank angle from cylinder geometry (as calculated in Appendix VII). The specific volumes of each zone are functions of temperature and pressure. In a similar manner, the total energy of the cylinder contents can be written as

EcyI=Ed+Eg+Eu+Ebi+Em or

= mu + mgug + muuu + mmum + (mbub) (5-3)

where u is the specific internal energy.

Applying equations (5-1), (5-2) and (5-3) at every crank angle forms the basis of the combustion analysis. To proceed at this point, the following assumptions are made:

• Pressure is uniform throughout the cylinder.

• The combustion chamber gases exhibit ideal gas behavior.

• All of the diesel fuel burns before any of the natural gas (referred to as the sequential burning assumption).

• The composition of the unburned zone does not change during combustion.

• Natural gas and diesel fuel are assumed to be fuels composed of only one chemical species; pure methane )4(cH represents natural gas and 18CH represents diesel fuel. • Burned gas zones result from stoichiometric combustion.

55 • The composition of the residuals consists only of oxygen, nitrogen, carbon dioxide and water vapour.

• The composition of air is 21% oxygen and 79% nitrogen.

• NO is the predominant oxide of nitrogen inside the combustion chamber and is formed in the post flame gases by the extended Zeldovich mechanism.

The computation begins at the beginning of injection (BOI). At BOI, equations (5-1), (5-

2) and (5-3) are greatly simplified since only one zone, the unburned gas zone, is present. As the cycle proceeds, the changes in properties of each zone can be calculated independently.

Then by using a combination of equations (5-1), (5-2) and (5-3), the properties of the most recently formed burned gas zone can be found in one of two ways.

The first method for determining the properties of the most recently formed burned gas zone requires an estimate of the heat transfer to the cylinder walls. Based on this heat transfer estimate, the change in total energy from one crank angle to the next can be calculated from a first law energy balance as described in the previous chapter (section 4.2). Woshni’s convective heat transfer correlation is used to calculate the total heat transfer to the cylinder walls.

Radiation and convection are not treated separately, because the total heat transfer prediction is uncertain. Rearranging equations (5-2) and (5-3) with m from (5-1) gives

1V—mg(vg vU)md(vd vU)+vUmb 2(mbvb) fflm(Vm —vs) mtot 0m 0m

— mg(ug — un)—md(ud — u)+ uUmbI — (mbub)I — — u) k mk i=1 mtot 0m 0m

56 The superscript k denotes the most recently formed burned gas zone. For convenience, letting the left hand sides of the above equations equal the variables v and u, respectively, further rearrangement gives

=-L(v_v) ye—vu 0m (5-4)

(5-5) from which

mbvCvU UU (5-6) VbVU UbUU

Since the specific volumes and internal energies are functions of temperature and pressure, an iterative approach must be used to calculate the mass of the most recently formed burned gas zone, mt, from equation (5-6) as follows. Letting

= v0 — = — A v v uc—uu u—uu then

v — v = A(u — u) or

= Au — Au + If

B = —Aug+ v then v=Au-i-B (5-7)

57 A and B can be directly determined at the end of each time step since they are functions only of the unburned gas properties and the variables v and u which are determined independently. With A, B and the pressure known, a guess for the burned gas temperature is made. From tabulated burned gas properties, Vb and u, can be found. Each temperature guess is refined until equation (5-7) is satisfied; this signifies convergence. With the burned gas properties and the total mass of cylinder contents known, equation (5-6) is used to calculate the mass of the most recently formed burned gas zone.

The second method to determine the properties of the most recently formed burned gas zone requires an estimate of the burned gas temperature. The temperature of a small burned gas zone burned in a short time interval can be approximated by the adiabatic constant-pressure flame temperature. Once the burned gas temperature is known then the other burned zone properties can be found from tabulated values since the pressure is also known. By combining equations (5-1) and (5-2), the mass of the most recently formed burned gas zone can be calculated as follows:

Vc—mg(vg—vu)—md(vd—vu)+vumbj—(mbvb)j—mm(vm—vu) m=

In this case, since equation (5-3) is not required for determining the mass or properties of the most recently formed burned gas zone, it can be used to calculate the total energy of the cylinder contents. A first law energy balance can then be used to determine the total heat transfer to the cylinder walls.

5.2 Calculation of Mass Fraction of Fuel Burned

Once the mass of the most recently formed burned gas zone is known, the cumulative mass fraction of fuel burned (Xmf) can be determined. First a formal definition of X is required. Let 1m and m be defined respectively as the total mass of diesel and natural gas

58 injected into the cylinder for one complete cycle. Further, let mlbm, mgm and mthm be defined respectively as the cumulative mass of diesel, natural gas and air burned at some point in time during the combustion process. Then X is defined as follows,

— + mgm mf + m

By expressing the cumulative mass of burned gas m in terms of its constituents, an expression for X can be found as follows:

m = mlbm + mgbm + fllj

= 1(m + mg(Xmf + mi+mg)

f ‘bm 1m + = kmdSl + m X,,, + g mIbffl + 8bm 1m + mg

Rearranging and solving for X gives

cum Xmf= (5-8)

mdslbm + where AF and AF are the respective air/fuel mass ratios for diesel and natural gas combustion as determined from stoichiornetry. Since the mass of diesel and natural gas burned can not be found explicitly, to arrive at a solution for equation (5-8) a key assumption about the combustion process must be made. It is assumed that all the diesel fuel burns before any natural

59 gas burns. This assumption, referred to as the sequential burning assumption, is valid for two reasons. First, only a small amount of diesel fuel is injected and it is injected prior to the natural gas. Second, the autoignition point of natural gas is not achieved in the combustion chamber by compression alone at typical diesel engine compression ratios. Since the autoignition point of diesel fuel is reached under these conditions, it would be the first the bum.

For the initial diesel-only burning phase of the combustion process

1m 0 Xmf< 1m + m

Here mm = 0 thus equation (5-8) reduces to

mm X=f b (59) jmI + mg A’+ AF)

For the subsequent natural gas-only burning phase

1m Xmtl 1m + m

For X,11 in this range, mlbffl = 1m since all the diesel has combusted. The mass of natural gas burned can be expressed by

mm =Xmf(mi+mg)—ml (5-10)

Substituting equation (5-10) into equation (5-8) gives

60 m,cum x mf = mlAl+[Xmf(rnthJ +mg)_mdsI] +mgl+ / 1m m +Xmfkml +m)—mthI m, x mf — 1m + mg + _-(miMi +[Xmf(mthl + m)_ mi]A1)

x m,, — m + m + — A1)+ 1(m + mg)A1

Xfflf(mJSI+ m)(1+ = m — 1m(M — Ai)

m” — mI(AFdSI — AFS) 1 (5-li) Xmf= (m +m)(1÷M)

To proceed with the results of equations (5-9) and (5-11) it is necessary to specify methods for determining the properties of each zone as well as the mass of air and residuals trapped in the cylinder. Before the properties can be determined however, the composition of the burned gases must be established by the combustion stoichiometry. Hence the following sections give detailed descriptions of the combustion stoichiometry, calculation of trapped air and residual mass, and the determination of the zone properties.

5.3 Combustion Stoichioanetry

Near top dead center (TDC) before injection of fuel, the combustion chamber is filled with a mixture of fresh intake air and residual combustion products from the previous cycle.

This is identified as the unburned zone and is assumed to have an unchanging composition throughout the combustion process. At the beginning of injection (BOl), jets of fuel issue into the cylinder from a series of orifices in the injector tip. With propagation of the jet, entrainment and mixing with the air and residuals occur. The jet has the structure of a fuel-rich core

61 surrounded by a progressively leaner mixture of fuel and air. Experiments where the autoignition sites were recorded showed that autoignition occurred in a concentration band between the equivalence ratios of 1 and 1.5. Subsequent flame development was seen to occur along contours close to stoichiometric [1]. Consequently, it is reasonable to assume that burned gas zones result from stoichiometric combustion.

It is important to note that the fuel reacts with a mixture of air and residual combustion products. The composition of the residuals is assumed to consist only of oxygen, nitrogen, carbon dioxide and water vapour since the concentrations of other species such as carbon monoxide and oxides of nitrogen are comparatively small. At the flame front, as chemical energy is released from oxidization of the fuel; nitrogen, carbon dioxide and water vapor diffuse through the flame, acting as diluents to lower the flame temperature. If natural gas and diesel fuel can be assumed to be fuels composed of only one chemical species, then one simple combustion reaction can be written. Using ‘y” to denote the mole fraction of the constituents of the air-residual mixture, for complete combustion the reaction can be written as .C0+yN+yHO.110+yCOCHfl+A.(y .0.N02 )CO+(+A(1+Ayc 2yHo).110+A.yN . 2N Balancing oxygen 2atoms2 for stoichiometric combustion gives

1+ A = ) y02

Thus the combustion reaction can be written as

62 2OYH y02 y02 - y02 2(i+(i+).i).co +(+(i+). ° 2)Ho+(1+). 2N Since this reaction assumes a single species fuel, the single species representing natural gas and diesel must be identified. While the composition of natural gas varies with geographic location, it is not uncommon for it to consists of upwards of 95% methane 4).(CH Thus to assume that natural gas is pure methane is reasonable. Diesel fuel, on the other hand, can consist of up to 100 hydrocarbons and 100 to 200 trace species, and can show significant variations in properties with time, geographic location, and intended service [25j. Thus representing diesel by a single chemical species may lead to some inaccuracies. The best estimate of a single chemical species for diesel is obtained by looking at a typical chemical analysis that reveals its hydrogen-to-carbon atom ratio. The hydrogen-to-carbon ratio typical of the diesel fuel use for these experiments was found to be around 1.8; thus 18CH is used to represent diesel fuel.

Furthermore, to use the above reaction to determine the composition of the burned gases, the composition of the unburned mixture with which the fuel reacts must be known. This must be determined iteratively along with the moles of residuals trapped in the cylinder. This iteration procedure is described in the following section.

5.4 Trapped Air and Residuals

To determine the mass of air and residual combustion products trapped in the cylinder, the cylinder gas exchange process during scavenging and the in-cylinder mixing after inlet and exhaust port closure must be investigated. The temperature and composition of the trapped gases must also be determined since they are important for heat transfer calculations and determination of gas properties. A look at the fluid mechanics and thermodynamics of the

63 cylinder contents will give insight to the physics of this problem, and with a few assumptions a calculation procedure can be developed.

5.4J Scavenging Process

Uniflow scavenging is the configuration used in both the DDC 1-71 and 6V-92TA. In this configuration inlet ports, evenly spaced around the circumference of the lower part of the cylinder, are used to direct the incoming air such that swirling flow is created in the cylinder.

Exhaust valves located in the cylinder head allow the exhaust flow to exit. During scavenging, air delivered from the blower or compressor of the turbocharger is used to displace the combustion products from the cylinder. It is the question of how well the air displaces the combustion products that must be answered. Short-circuiting of fresh air and dead volumes of combustion products were found to occur in flow visualization experiments in liquid analogs of cylinder flow [1]. Using these observations, the following simplified model was used to describe the scavenging process.

With inlet and exhaust ports open, incoming fresh air forces all the combustion products out of the cylinder except for those found in the dead volumes. The flow into the exhaust manifold therefore consists of the discharged combustion products and the excess air that either short circuits through the cylinder or follows the combustion products Out. Adiabatic mixing of the air and combustion products is assumed to occur downstream of the exhaust port at constant pressure such that the exhaust manifold mounted thermocouple measures the mixed out temperature. Upon closure of the inlet and exhaust ports, it is assumed that the fresh air and residual combustion products contained in the cylinder mix adiabatically at constant volume. Figure 5-2 schematically describes the mass flows of the entire process. Here m is the delivered air (mass flow as measured in the engine intake), m is the mass of air trapped in the cylinder, 0m is the initial mass of the unburned gas zone, f is the fraction of unburned gas which participates in the combustion, mre, is the mass of residuals in the cylinder, rn is the mass of diesel injected, m is the mass of natural gas injected, rnbumed is the final total mass of the burned gas zones, and is the mass of the exhaust leaving the engine.

64 m11 m

mrn m burned

ma m (1-f) ÷ m m .1 atrap m00 0m atrap 1m ex11

m 4

maff - m atrap

Figure 5-2: Engine Mass Flow Schematic

5.4.2 Mass of Trapped Air

The mass of air trapped in the cylinder after intake and exhaust ports are closed is calculated using the following correlation [26] from Detroit Diesel based on their measured scavenging results. The values calculated with this correlation match values typical of uniflow scavenged engines published by Heywood [1].

e1h11] matmp = 1m [0.9—(i.o—0.34 (5-12)

for 80.5

The density of the air in the air box (p) is calculated using the ideal gas law with air box temperature and pressure. V is the displacement volume of one cylinder. All masses have units kg/cycle/cylinder.

The relationship between the mass of air trapped and the mass of delivered air provided by equation (5-12) is illustrated in Figure 5-3 using the ideal mass )1(m as defined above to 65 non-dimensionalize both variables. Once the mass of air trapped in the cylinder is known, an iterative approach is required to determine the mass, composition and temperature of the residuals.

0.9 0.85 0.8 0.75 matrap 0.7 m. 0.65 ideal equation (5-12) 0.6 0.55 0.5 0.45 0.4 0.5 0.7 0.9 1.1 1.3 1,5 1.7 rn/rnair ideal

Figure 5-3: Scavenging Correlation

5.4.3 Mass of Trapped Residuals

Trapped air and residuals are assumed to mix adiabatically at constant volume at intake and exhaust port closure (ipc). Since ipc represents the beginning of compression, the cylinder pressure (P) and trapped air temperature (Tar) at ipc can be approximated as the measured airbox pressure and temperature. The cylinder volume at ipc (V) can be calculated from cylinder geometry knowing when ipc occurs. Hence, the first law of thermodynamics for this instantaneous mixing process on a molar basis can be written as

Umix= n Uatrap +flres Ures (5-13)

but u = C T for an ideal gas; thus (5-13) becomes

66 (iap + ires)• vmix = t1atlap Cajr Tatp + n Cvres (5-14) where n and n are the number of moles of fresh air and residual combustion products, respectively, trapped in the cylinder. The ideal gas law written for the mixture is

(5-15)

Solving (5-14) and (5-15) for T and equating gives

= Cvres T PV n v +n (5-16) R C where

= + n+n (5-17)

Combining equations (5-16) and (5-17) and rearranging produces

. + CVr • n +[nap (vres T n j p.\\ )— — I — +nap CvaiHflatiapTa )=O (5-18)

Note that equation (5-18) is a quadratic in the moles of residuals. Since the moles,

temperature and specific heat of the trapped air are known, equation (5-18) can be used to

calculate the moles of trapped residuals once the specific heat and temperature of the residuals

are determined. Due to the dependence of the specific heat of the residuals on composition and temperature, equation (5-18) must be solved iteratively. The following sections describe the

calculations used to estimate the residual gas composition and temperature in this iteration.

67 5.4.4 Residual Gas Composition

In a diesel engine the amount of air trapped in the cylinder exceeds the amount required to react with all of the injected fuel. In other words, not all of the air trapped in the cylinder participates in the combustion. The residuals are therefore composed of a mixture of the products of stoichiometric combustion and the unburned gas zone that did not participate in the combustion from the previous cycle. Since the air trapped in the cylinder and the amounts of diesel and natural gas injected in one cycle are known, the moles of each of the constituents of the residuals can be found. From the combustion stoichiometry worked out in section 5.3, for every mole of fuel burned (1+n/4) moles of 02 are consumed and one mole of 2CO and n/2 moles of 1120 are 1produced. Assuming the composition of air is 21% oxygen and 79% nitrogen, the total moles of each species in the cylinder after complete combustion (ignoring dissociation) are given by

n0 =0.21n 0+y . 1—L45n —2n 2N =0.79n +YNflS

= + + +0.9n ÷2n 2HO = 2O,Y11 1 where ,y02 2r’YN 02r’ and 2O,YH are the mole fractions of the residual constituents iteratively calculated. The iteration begins by setting the composition of the residuals equal to that of pure air (i.e. y0 = 0.21, 2YN = 0.79, y = 0, and 2OYH = 0) and then proceeds using the above expressions to calculate new mole fraction estimates until convergence is achieved. Generally

five or six iterations are required for convergence.

5.4.5 Residual Gas Temperature

The residual gas temperature can be calculated by considering the flow out of the

cylinder. The flow into the exhaust manifold during scavenging is made up of the discharged

1n=1.8 for diesel and 4 for natural gas 68 combustion products and the excess air that either short circuits through the cylinder or follows the combustion products out. It is assumed that the scavenging air and the products of combustion mix adiabatically downstream of the exhaust port at constant pressure in the exhaust manifold. The thermocouple mounted in the exhaust manifold measures the mixed temperature, while the scavenging air is assumed to be at airhox temperature.

From Figure 5-2 during scavenging a mass balance in a control volume in the exhaust manifold just downstream of the exhaust valve is

me)th = (m — m) ÷ (m + 1m + m) or

mexh = mr + m + 1m( (5-19)

Considering the same control volume in the exhaust manifold, an energy balance of the constant pressure mixing process would be

(map + mg + mdSI) +(majr — map) hair= mexh (5-20)

but h = C, T for an ideal gas; thus (5-20) becomes

+ + C + (ma — map) T = mexh (5- 21) (map m )1m Cpair 0C xh where

Cpexh [(ma + m + mdSL) C ÷(m — map) CJ (5- 22) = exh

Combining (5-21) and (5-22) gives

69 = xh (X - (5-23) +

The specific heat of the residuals is a function of the temperature and composition of the residuals. Thus equation (5-23) is used to improve the estimate of the temperature of the residuals using the best estimate of the specific heat for that iteration.

5.5 Thermodynamic Properties of the Unburned Gas Zone

In the previous section the mass of trapped air and the mass and composition of residuals were calculated. Using this information the total moles of unburned zone prior to combustion can be written as

n0 = 2O.lna + ,2YO ares 2N 79_°.nauap +YNrflIeS n 02r 2 n0 = 2OrYH ares where ,2Yo ’2YN ‘2r’ and 2OrYH are the mole fractions of the residual constituents. While the total number of moles of unburned gas zone decrease as combustion proceeds, the unburned gas composition is assumed to remains the same. The assumption of an unchanging composition along with the assumption that the unburned gases exhibit ideal gas behavior are used to determine’ the zone properties. If y1 represents the mole fractions of the unburned gas constituents, then the molecular

weight and gas constant are calculated as follows

M 1M=y

70 R=—UM

The temperature of the unburned gas changes as a result of compression or expansion and heat transfer to the walls only in the absence of mixing with other zones. The first law written for the unburned gas zone as a control mass is

ôq =dh —vdP

= 11RT = Ry using v,, , dh, = CPdTUand leads to P 1-1

óq = y dT dP RET,, y—1T P or

dT—1dP KÔQW (5-24) T ‘ P mCT where K is some fraction of the total heat transfer to the cylinder walls (oQ) and ‘ is the ratio

of specific heats for the unburned gas. Since unburned gases are consumed during combustion,

K should vary over the combustion duration period. It would therefore seem reasonable to set K

as the ratio of the mass of the unburned zone to the total cylinder mass. Making this substitution

in equation (5-24) yields

di’,, —ldP÷ ( 1ôQ (5-25) T,, y P

With a known temperature at the beginning of the time step, equation (5-25) can be used

to calculate the temperature at the end of the time step. To begin the computation, the

71 temperature at the beginning of the first time step must be known. By beginning the

computation at the beginning of injection (BOl), only unburned gas is in the cylinder. This means that the total mass of the cylinder contents is equal to the trapped air and residuals as calculated in the previous section. Since the volume and pressure are known at this point, the

ideal gas law can be used to calculate the BOl temperature.

In order to calculate a value for y, an estimate of the specific heat is required. The

specific heat at constant volume can be determined using the following expression.

y[(T)]. -k = M (5-26)

As indicated in section 5.1, an estimate of the internal energy of unburned zone is required. The

enthalpy of the unburned gas can be determined using

Ic(T)dTj = i-i 29.15K h (5- 27) U N’I

then the internal energy is found using

where M is the molecular weight of the unburned gas and the overbar denotes a molar basis.

5.6 Thermodynamic Properties of the Diesel and Natural Gas Zones

The injection of fuel can be handled in a couple of different ways. The simplest

approach would be to assume that at any time there is no unburned fuel in the combustion

72 chamber. The fuel would be introduced at the same rate that it is consumed. This approach is

based on the assumption that the presence of unburned fuel has little effect on the mass and

energy balance in the cylinder since the amount of unburned fuel in the cylinder at any time is small compared to other cylinder constituents.

A more involved approach to deal with injected fuel would be to assume a rate of fuel

injection independent of the fuel burning rate. The properties and mass of unburned fuel in the

cylinder would then have to be accounted for. Assuming a constant rate of fuel injection over

the injection period, the changes in unburned diesel and natural gas properties can be determined

in the following way.

Diesel fuel is injected into the combustion chamber as a liquid. The temperature of the

diesel fuel entering the combustion chamber is roughly the same as the working temperature of

the injector. In a liquid state, the diesel fuel volume is negligible compared to that of the

cylinder gas and its internal energy and enthalpy are approximately equal. The temperature rise

in the liquid diesel due to compression in the cylinder is negligible. Hence by assuming that the

diesel does not evaporate or mix with other zones until the moment it combusts, the temperature

of the diesel zone does not change.

Natural gas injected into the combustion chamber is assumed to exhibit ideal gas

behavior. The temperature of the natural gas entering the combustion chamber is also roughly

the same as the working temperature of the injector. Ignoring heat transfer to the fuel from the

hot cylinder gases, the temperature of the injected natural gas will increase due to compression.

As stated earlier, each zone identified in the model has a uniform temperature. Therefore in

order for the natural gas zone to have a uniform temperature, it is necessary to assume that there

is a continuous mixing between the natural gas being injected and the accumulated unburned

natural gas already in the cylinder from prior injection.

By assuming that the natural gas undergoes a two-stage process during each time

interval, the temperature of the natural gas zone can be calculated. First, there is adiabatic,

constant pressure mixing between the incremental mass of natural gas injected and the

accumulated mass of unburned natural gas in the cylinder from prior injection. This change in

73 the temperature is referred to as .1dTg Second, there is a change in temperature 2dTg from isentropic compression (or expansion) of the gas. The total change in temperature of the natural gas is then the sum of 1dTg and .2dTg For the first stage the first law of thermodynamics as a control mass with is written as

ÔQ—ÔW=dE (528)

The heat transfer (öQ) is assumed to be negligible. The work (oW) is equal to PdVg. The

change in energy of the natural gas (dE) in the cylinder is equal to the change in internal energy if kinetic and potential energy changes are ignored. The internal energy at the initial state is

given by 1U = mgug + 0dmgu

where mg and u are the initial mass and internal energy per unit mass of the natural gas zone, and dmg is the mass of injected natural gas for the time step with its corresponding internal energy per unit mass .u0 The internal energy at the final state is given by

= (dmg + mg)ug2

where ug2 is the internal energy per unit mass of the natural gas zone after mixing. Combining

the expressions for internal energy and work into equation (5-28) gives

_PdVg = (dmg + 2mg)ug — 1mgug — 0dmgu (5-29)

Expanding equation (5-29) further leads to

_P{(dmg + 2mg)vg — 1mgvg — dmgvo] = (dmg + 2mg)ug — 1mgug — 0dmgu

74 but h = u + Pv thus

o = (dmg + 2mg)hg — 1mghg — drngho 0= 2_ho)mgdhg+dmg(hg 0 = 1mCd1 + drngCp 2(Tg —c) (5-30) where C, is the constant-pressure specific heat of the natural gas evaluated at the initial

temperature, and Cpavgis the average constant-pressure specific heat of the natural gas and is given by +c — c c 2PTg Pin Pavg 2

Finally solving equation (5-30) for 1dTg gives

dmCg (T-T) 1=dT (5-31)

For the isentropic compression of the second stage of the process, the following can be

written:

Tds=dh—vdP=0 0 = 2CpdTg — vdP vdP RT2p dTg2 =—= c c (5-32)

75 Now by adding equations (5-31) and (5-32) the total change in temperature of the natural gas zone dTg is accounted for. By applying this expression for temperature over every time step, the specific volume and internal energy for the zone at the end of each time step can be calculated.

The specific volume is calculated using the ideal gas law as follows:

RTg2 g p 2

To calculate the internal energy the enthalpy is determined first using

hgh+ fc(T)dT 2. 15K

then the internal energy is found using

hg u =——Pv & g

where Mg is the molecular weight of methane and the overbar denotes a molar basis.

5.7 Thermodynamic Properties of the Burned Gas Zones

The burned gases form as a result of the combustion of the fuel with the unburned gas

zone. Mixture which burns early in the combustion process is subsequently compressed as

combustion proceeds and cylinder pressure rises. If no mixing occurs, then this compression can

be thought of as isentropic. Further, dissociation, which occurs in the engine due to the high

temperature of the combustion products, can not be ignored. Its effects must be accounted for

such that the composition and properties of the burned gas are representative.

76 The properties and composition of the burned gases can be found using a chemical equilibrium solver. The products of combustion are assumed to be in equilibrium, except for oxides of nitrogen. The formation of oxides of nitrogen is discussed in a following section.

STANJAN [27] is an equilibrium solver that uses the method of element potentials to find the

minimum Gibb’s function for a chemical system subject to atom population constraints. Each

species is treated as an ideal gases using thermodynamic properties from the JANAF tables. To find the burned gas properties, STANJAN requires as inputs the atom populations of carbon,

hydrogen, oxygen, and nitrogen (CHON) in the reactants.

The CHON atom ratios relative to carbon can be found by looking at the combustion reaction from section 5.2 which is rewritten here.

CH ÷(1+).(o2 2N O+CO y02 )2H y02 _*(i+(i+ CO 1120+(i+ 2N y02 2 +(+(i+).) )--.

The CHON ratios relative to carbon are therefore

( nyu n+12+—2o I H \ 02Jy

77 \( Yco (1÷— 2+—+2-———2oY 2 0 ,y0024,y

flYN 1+J’ 2 h N 024jy 3= where ,2Y0 2Y y, and y110 are the mole fractions of the constiLuents of the unburned gas zone. Since the mole fraction ratios y 0/y and in the unburned gas are small, the above CHON ratios are closely approximated by

—=nH C 0/n

C \ ,41Y02

The ratios of hydrogen and oxygen to carbon are now simple expressions of n (the ratio of unburned is nearly the same hydrogen to carbon for the fuel). By noting that YN, 0/y in the gas as that for air (i.e. 3.76) and nearly constant, then the ratio of nitrogen to carbon is also a simple

expression in terms of n. Thus two tables of burned gas properties (one for diesel and one for

natural gas) can be created using the above CHON ratios as inputs to STANJAN. The matrix of

78 burned gas properties for both diesel and natural gas was generated for temperatures and pressures ranging from 1300 to 3100 K and 1 to 95 atmospheres respectively.

5.8 Thermodynamic Properties of the Mixed Gas Zone

As mentioned in the opening section of this chapter, the mixed zone is a mixture of burned and unburned gases. Burned gases only remain at the high temperatures of the flame front for a specified mixing delay period until they are forced to mix with a portion of unburned gas and previously mixed out burned gases. By assuming a two-stage process, the properties of the mixed zone can be determined. The first stage of the process is an instantaneous mixing at constant-pressure between the burned gas zone which has reached the end of the mixing delay period with a proportional amount of unburned zone and the contents of the previously formed mixed zone. The second stage of the process deals with the change in properties resulting from isentropic compression (or expansion).

The first law of thermodynamics applied to the mixed zone as a control mass for the constant-pressure instantaneous mixing process is

ÔQ—ÔW=dE (5-33)

where the work is equal to

— 34) = PdV = P[(mm + dmb + 2dmu)vm — mmv,i,i — dmbvb dmv] (5-

and the change in energy is equal to

(5-35) dE= (mm + dmb + 2dm)u — mmumi—dmbub —dmu

The subscripts b and u refer to the burned and unburned zones respectively and dm is the mass

of burned or unburned zone that mixes. The subscripts I and 2 refer to the respective states

79 before and after mixing, and m is the mass of the mixed zone before mixing. Assuming heat transfer during the instantaneous mixing is negligible, then using equations (5-34) and (5-35) in equation (5-33) gives

—P[(mm+ dmb + 2dmu)vm — mmvmi — dmbvb — dmv] = (m + dmb + 2dmu)um — mmumj —dmbub —dmu (5-36) using u + Pv = h and Pv = RT and solving (5-36) for 2urn yields

h h +dm h — m m ml ÷dm b b u — m2 mm ÷dmb ÷dm

If the temperature at state 2 2Tm is approximated by the mass-averaged value, then equation (5- 37) gives the internal energy of the mixed zone after mixing.

For the isentropic compression of the second stage of the process, the first law of thermodynamics as a control mass is

óq—ôw=du (5-38) where the work is 2Vmi)ôW=Pavg(Vm (5-39) Here the subscripts 1 and 2 refer respectively to the states before and after compression. The average pressure avg is an average of the pressures at these states. If as a first approximation the heat transfer is neglected, then the change in internal energy of the mixed zone due to expansion is given by substituting equation (5-39) into equation (5-38) as follows:

-vmi)du=—Pavg(vm (5-40) 2 80 The specific volumes can be estimated using the ideal gas law. To use the ideal gas law however, the temperature change due to expansion is required. The change in temperature of the mixed zone can be calculated assuming isentropic expansion as follows:

ldPdTmIfl (5-41) 3 y P where ‘ is the ratio of specific heats for the mixed zone.

5.9 Calculation of NOx Formation Oxides of nitrogen (NOr) are composed of nitric oxide (NO) and nitrogen dioxide 2).(NO Chemical equilibrium considerations indicate that for burned gases at typical flame temperatures, 2N0/NO ratios should be negligibly small. Mole fractions of NO are typically more than 1000 times that of 2N0.[27] Thus by assuming that inside the combustion chamber of an engine nitric oxide is the predominant oxide of nitrogen produced, an estimate of the formation rate of NO is obtained by determining the formation rate of NO.

The mechanism of NO formation in the combustion of near-stoichiometric fuel-air mixtures is widely accepted to be described by the following reactions which are referred to as the extended Zeldovich mechanism. [1]

O÷N—*NO+N (1) N+0—*NO÷O (2) 2N÷OH—NO+H (3) The forward and reverse rate constants (k7 and k respectively) of these reactions have been

measured experimentally. Heywood [1] has made a critical review of this published data and

recommends using the values given in Table 5-1.

81 Table 5-1 : Rate Constants for the Extended Zeldovich Mechanism

Reaction Rate Constant 3(cm / mol s) (1) 0+ 2N —*NO+N 7.6x10’exp[-38000/TJ (-1) N + NO — 2N + 0 1.6 x 1013 (2) N+ —*NO+O 3 02 6.4xlOTexp[-3150!T] (-2) 0 + NO —* 02 + N 1.59 x Texp[-19500/T1 (3) N+OH—*NO+H 134.1x10

(-3) H + NO —* OH + N 2.0 x iO’ exp[—23650/T]

Using the law of mass action, the rate of formation of NO can be written as:

—k[NO][N]—k [N0][0]—k[N0][H] (5-42) where []denotes species concentration in mole / .3cm Similarly, the rate of formation of N can be written as:

— k1 [NO] [N] + k [NO] [0] + k [NO] [H] (5- 43)

Since [N] is much less than the concentrations of other species of interest ( 10 mole fraction) d[N] [1], the steady-state approximation, = 0, is used to eliminate [N].

The NO formation rate then becomes

82 [NOj d[NO] =2k[0][N 2K[O,][N (544) 1+ ]2 k[0.,]] + k[0H] where K = 1(ç/k-)(k;/k) = 20.267exp(_21650/T) If it is assumed that all of the NO forms in the postflame gases, then the concentrations of 0, 02, OH, H, and 2N can be approximated by their equilibrium values at the pressure and temperature of the burned gas zone. By using [ le to denote equilibrium concentration and substituting the reaction rates from Table 5-1 into equation (5-44), then the NO formation rate becomes (in units mol / 3cm . s)

- [NOr 1 d[N0] 20.267exp(-21650/T)[0 L[N ] =t52x1O’exp(-38OOO/T)[0]e[N 2 2 dt [NO] 1+ ]e 4 x 1OTexp(_315O/T)[O + 2i625[0H]

To eliminate from the above expression, use2can be made of the equilibrium oxygen atom 2 [Ole

by: ] concentration given K()[O I ]e 02 = ] 2(T)” where )0K( is the equilibrium constant for the reaction -402 = 0 and is given by )0K( = 3.6x exp(—31090/T) atm112

The final form of the expression used to calculate the NO formation rate becomes

83 [NO] 1— 2 d[NOJ 166x10 exp(69o9o/T)[O 20.267exp(-21650/T)[O,]e[N,]e dt — T112 12[N [NO] 1+ 1O4Texp(—315O/T)[O 2L 4x 2 + 2.5625[OHL which is also in units mol / 3cm s. The strong temperature dependence of NO formation rate can be demonstrated by considering the initial value of d[NO]/dt when [NO] = 0. Figure 5-4 illustrates the initial formation rate of NO at 35 atm.

10000

1000

d[NOJ 100

cit [nI/cm3 SI 10

0.1 2200 2300 2400 2500 2600 2700 2800

T enperciture [KI

Figure 5-4 : Initial NO Formation Rate as a Function of Temperature

5.10 Calculation Procedure

The input data required in this computation are cylinder pressure versus crank angle,

engine speed, air manifold temperature and pressure, exhaust temperature, air and fuel mass flow

rates, and the unburned fuel fractions. After the mass of air and residuals trapped in the cylinder

are determined, the combustion analysis begins at the beginning of injection (BOl). At BOl only

unburned gas is present in the cylinder, thus the total cylinder energy can be determined at the

84 beginning of the first time step as it is equal to the internal energy of the unburned gas at BOl conditions. The calculation of BOl conditions are based on the measured air manifold temperature and pressure and the exhaust temperature.

As the process proceeds, the changes in properties of each zone can he calculated independently. As mentioned in the opening section of this chapter, the properties and mass of the most recently formed burned gas zone can be found in one of two ways. Either the heat transfer to the cylinder walls must be estimated or the burned gas temperature must be estimated by the adiabatic flame temperature. When the second method is used, the actual heat transfer to the cylinder walls can be calculated directly.

Once combustion begins, a new burned gas zone is created every calculation step

(generally one crank angle). As the combustion process continues, the properties of the previously formed burned gas zones that have not yet mixed out must be updated with the changing cylinder pressure. The changes in these properties are assumed to be the result of isentropic compression (or expansion). Therefore at every calculation step, the tables of burned gas properties are interpolated at the cylinder pressure and constant value of entropy of each previously formed burned gas zone.

Figure 5-5 illustrates the entire combustion analysis calculation procedure in the form of a flow chart. The source code (in QuickBASIC) of the analysis has also been included

(Appendix VIII).

85 ______CYLINDER CALCULATE Figure ITERATE GAS-ZONE TO COMPUTE CYUNDER CALCULATE COMPUTE CALCULATE iiEPARE TO ENERGY SPECIFY 5-5 CALCULATE HEAT FIND PROPERTIES (X)RRESPNDING AMOUNT CALCULATE CALCULATE SPECIFY ITERATE DErERMINE WAIlS TRANSFER Combustion TEMPERATURE BURNED- WHICH BALANCE BULKTEMPERATURE VARIABLES UPDATE STEP WORIC DUE MASS OF PROPERTIES PROPERTIES TO TO ONE AN(YI’HERRANKANGIE NO MASS FUEL EITHER MASS DONE OF PIUNTOUTPUTDATA FIND COMPRESSLONIIIXPANSION PROPERTIES READINPUTDATA FORMED STOICHIOMETRIC FNFHALPY CRANK NEWLY () fOR IS OFAIR NO INTERVAL? ANAL PRACI’ION DURING OF MASS, BURNING OF NEXT TRAPPED Analysis 1 1 1 OF ANGLE DURING FORMED MIXED TRAPPED 86 IN COMPOSITION OF EACH OF CRANK CRANKANGLE COMBUSTION INJECTED OF AND OR EACH TO I INtERVAL CALCULATE CYLINDER ITERATE ZONE RESIDUALS ZONE BURNED AIR-FUEL CRANK BURNED IN CALCIJLATE FLAME ANGLE ZONE Calculation CYLINDER AFtER AT CYUNDER ANGLE TO AND BOl FUEL TEMPERATURE GAS ENERGY INTERVAL RATIO INTERVAL CHAMBER7 HEAT FIND MIXING I I ZONE THE INTERVAL ADIABATIC WAIlS TRANSFER Procedure YES 6 PERFORMANCE, EMISSIONS AND COMBUSTION CHARACTERISTICS

6.1 Discussion of Combustion Analysis Results

The analysis described in Chapter 5 and the computer code given in Appendix VIII are consistent with the nominal requirement that in the diffusive burning zone the equivalence ratio is unity. During testing of the combustion analysis, it was found that the calculated mass fraction of burned fuel would not reach the value deduced from an exhaust composition analysis. In the results which follow, the local equivalence ratio was adjusted to differ somewhat from unity to cause the calculated mass fraction of burned fuel to reach the measured final value.

Table 6-1 : Local Average Equivalence Ratio as a Function of Injection Timing for Diesel Fueling

. Local Equivalence Local Equivalence Injection Timing Ratio Ratio (°ABDC) (1 bar brnep) (3 bar bmep)

173 0.97 1.07

171 1.03 1.09

169 1.03 1.10

167 1.05 1.11

165 1.05 1.15

163 1.10 1.17

The departures from an equivalence ratio of one are shown in Table 6-1 for different fuel injection timings with diesel fueling of the DDC 1-71. These results indicate that the average local equivalence ratios are generally slightly rich of stoichiometric. As fuel injection timing is advanced and load is increased, the combustion becomes more fuel rich. The overall cylinder

87 averaged equivalence ratios at 1 bar and 3 bar bmep are 0.17 and 0.28, respectively. The calculation of burned gas temperature is affected by changes in the local equivalence ratio, hut this has not been taken into account in the computation. Thus the results which follow reveal the general effects of wall heat transfer, mixing delay, and method of estimating the burned gas temperatures, but they do not account for the full thermodynamic effect of equivalence ratio.

6.1.1 Effect of Computation Method

As described in Chapter 5, two different methods can be used to calculate the properties of the burned gases. The output from the combustion model is dependent on which method is used. The first method for determining the temperature of the most recently formed burned gas zone requires an estimate of the heat transfer to the cylinder walls. Based on this heat transfer estimate, the change in total energy from one crank angle to the next can be calculated from a first law energy balance. Woshni’s convective heat transfer correlation is used to calculate the total heat transfer to the cylinder walls. This method is referred to as the “Qwl” method. The second method for determining the temperature of the most recently formed burned gas zone is to use the constant-pressure adiabatic flame temperature. In this method, while the combustion process is assumed to take place adiabatically, the heat transfer to the cylinder walls is taken into account. This method is referred to as the “Tad” method. While the follow results show in general the effects of the different methods for computing the burned gas temperatures, they do not allow for the full thermodynamic consequences of the changing equivalence ratio.

The equivalence ratio used in the computation in generating the following results was held constant at 1.05.

Figures 6-1 through 6-4 illustrate the differences in output from the combustion model using these two different methods. For the Qwl method, results have been generated using three different constants (Cl) in Woshni’s heat transfer correlation. Values for Cl of 0, 0.02, and 0.04

have been used. When Cl = 0, there is no heat transfer to the cylinder walls. As Cl increases, so does the heat transfer.

8$ The effect of computation method on the calculation of mass fraction of burned fuel is illustrated in Figure 6-1. The results from the two methods agree when Cl = 0. For the 0wl method, as the heat transfer to the cylinder walls is increased, the calculated mass fraction of burned fuel increases at a given crank angle in the later stages of combustion.

1 0.9 0.8

0.7 Tad 0.6 x + (Ci=0) mf Qwl 0.5 Qwl (Ci=0.02) 0.4 Qwl (Ci=0.04) 0.3 0.2 0.1 0 190 210 230 crank angle (°ABDC)

Figure 6-1 Effect of Computation Method on Mass Fraction of Burned Fuel

The calculated values of heat transfer to the cylinder walls and the initial burned gas temperature are shown in Figures 6-2 and 6-3, respectively. For the Tad method, uncertainty is apparent in the calculation of heat transfer. For the Qwl method, uncertainty is apparent in the calculation of the initial burned gas temperature. This indicates that the inherent uncertainty can be associated with the energy equation in each case. With this incremental burning model, the mass of the newly formed burned gas zone is small compared to the masses of the other zones.

Hence the uncertainty in the results can be attributed to small differences between large numbers

(i.e. subtractive cancellation results in a large loss of significant digits). In each computation method, the uncertainty shows up in the dependent variable.

89 0.009 0.008 0.007 0.006 0.005 Qi 0.004 0.003 (kJ) 0.002 0.00 1 0 -0.001 -0.002 -0.003 -0.004 170 190 210 230 crank angle (°ABDC)

Figure 6-2 : Effect of Computation Method on Heat Transfer Estimates (kJ)

2700 -

2500

2300 T.bi (K) 2100 Tad

+ Qwl (C1=0) 1900 ° Qwl (C1=0.02) QwI (Cl =0.04) 1700

1500 I I 180 200 220 240 crank angle (°ABDC)

Figure 6-3 Effect of Computation Method on Initial Burned Gas Temperature (K)

90 As with the calculation of mass fraction of burned fuel, the best agreement in the heat

transfer and burned gas temperature calculation between the two methods is found when Cl is set to zero in the Qi method. This same result, however, does not occur in the calculation of NO. Figure 6-4 illustrates the estimates of exhaust NO. As shown in chapter 5, NO formation is highly sensitive to burned gas temperature. As a result of the fluctuations in the calculated burned gas temperature with the Qwl method, different characteristics in the NO formation are seen. The calculated NO formation rate for the Qi method is higher in the initial stages of combustion as a result of the fluctuating burned gas temperatures. Due to the high sensitivity of NO to burned gas temperature, the computation method based on the constant-pressure adiabatic flame temperature has been used for analysis in the remainder of this thesis since it provides better burned gas temperature estimates.

400

350

300

250

NO 200 (ppm) 150

100

0 170 190 210 230 crank angle (°ABDC)

Figure 6-4 : Effect of Computation Method on Estimated Exhaust NOx (ppm)

91 6.1.2 Effect of Unburned Fuel in the Combustion Chamber

In Chapter 5, it was stated that two methods could be used to describe the injected fuel.

The simplest method assumes that at any time there is no unburned fuel in the combustion

chamber, because fuel is introduced into the combustion chamber at the same rate that it is

consumed. In this case, there is no fuel zone present. The more involved method assumes a rate of fuel injection independent of the fuel burning rate. The properties and mass of unburned fuel in

the cylinder are then accounted for in the fuel zone. Computations for both diesel and natural gas fueling showed no differences in combustion rate, burned gas temperature or NO formation with or without fuel zones. While these results show in general the effects of unburned fuel in the combustion chamber, they do not allow for the full thennodynamic consequences of the changing equivalence ratio.

6.1.3 Computed Temperatures

Typical computed temperatures for each of the zones specified in the combustion analysis are illustrated in Figure 6-5. This particular analysis is based on pressure data collected from the DDC 1-71 operating on diesel fuel at 1250 rpm and 3 bar bmep. The initial burned gas temperature is denoted as Tb,, the temperature of the “mixed” zone is Tm the cylinder mass

averaged bulk temperature is TbUIk, the temperature of the unburned zone is T, and the temperature of the natural gas zone is Tg• The initial burned gas temperature is the temperature

at which each new burned gas zone forms.

Since at BOl, the cylinder contains only unburned gases, the bulk temperature is the same

as the unburned gas zone temperature. Upon initiation of combustion, the bulk temperature

begins to depart from the unburned gas zone temperature and approach the mixed zone

temperature as combustion proceeds. This indicates that the unburned zone is being depleted and

the mixed zone is growing. It also demonstrates that the mass of burned gases, at high flame

temperatures, is considerably less than the mass of either the unburned zone or the mixed zone.

performance

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It is thermal efficiency on a plot of brake mean effective pressure versus engine speed. These plots are referred to as performance maps and are used to illustrate the performance characteristics of a particular engine. In generating a performance map, the fuel injection rate will generally he held constant, hut the fuel injection timing will vary. The injection timing is selected at different engine loads and speeds to provide the best possible thermal efficiency with emission levels low enough to satisfy constraints imposed by emission regulations.

The performance map for the DDC 6V-92TA using diesel fueling with factory selected fuel injection timing values and a set fuel injection rate has been generated based on engine test cell measurements. This map, shown in Figure 6-6, does not show the entire engine load range since the dynamometer, to which this engine is coupled, is only capable of absorbing a brnep of just over 6 bar. The rated peak bmep of this engine is 9.2 bar at 1200 rpm. Ultimately, a similar performance map of this engine when fueled with directly injected natural gas would be the best tool for fully evaluating this newly developed fueling concept.

6.0

5.0

4.0 BMEP (bar) 3.0

2.0

1.0

1000 1250 1500 1750 2000 Engine Speed (rpm)

Figure 6-6 : Engine Performance Map (DDC 6V-92TA)

94 Presented in this chapter are results from tests performed using the newly developed prototype natural gas injector described in Chapter 2. These results illustrate the effects of fuel injection timing, fuel injection rate, engine load and engine speed with the prototype injector operating in both the naturally-aspirated single-cylinder diesel engine and in one cylinder of the turbo-charged and after-cooled six-cylinder diesel engine. The performance and emissions characteristics of the natural gas fueling system are compared with those of conventional diesel fueling. Results of combustion analysis of both diesel and natural gas fueling using the combustion analysis model developed in the previous chapter are presented.

6.3 Effect of Fuel Injection Timing

The effect of fuel injection timing on performance and emissions near optimum are shown in Figures 6-7 and 6-8 for the DDC 6V-92TA and Figures 6-9 and 6-10 for the DDC 1-71. The results presented for the DDC 6V-92TA are at the same load (3 bar bmep), but at different speeds

(1200 and 1800 rpm). The results presented for the DDC 1-71, on the other hand, are at the same speed (1250 rpm), but at different loads (1 and 3 bar bmep). The behavior of thennal efficiency (11th), Bosch Smoke, carbon monoxide (CO), oxides of nitrogen (NOr), and total hydrocarbons (THC) with fuel injection timing are illustrated. At the DDC 1-71 low load case, and the DDC 6V-92 low speed case, smoke was not present in the exhaust.

The presented measurements have been normalized by dividing by the maximum value of each parameter. These normalizing constants are given in Table 6-2. The much improved emissions with the DDC 6V-92 compared with the DDC 1-71 can be attributed to better fuel injection characteristics. The figures illustrate that while thermal efficiency is quite insensitive to changes in injection timing, NO, smoke and carbon monoxide (CO) emissions are strongly effected. Retarding injection timing decreases 1NO emissions at the expense of increasing CO and smoke emissions. This makes it impossible to achieve optimum thermal efficiency with low levels of all emissions with conventional diesel fueling at any engine load and speed.

95 Table 6-2 : Normalizing Constants for Figures 6-7 through 6-1()

Engine DDC 6V-92TA DDC 6V-92TA DDC 1-71 DDC 1-71 rpm 1800 1200 1250 1250

brnep (bar) 3 3 3 1 11hmax (%) 29.6 33.7 25.5 16.3 NOxm (ppm) 484 677 794 436

Bosch 0.6 - 2.7 - Smokemax COm 92 102 459 538 (ppm) THCm 10 11 322 413 (ppmc)

96 1

0.9

0.8

0.7 0.6

0.5 0.4

0.3 0.2

0.1

0 161 163 165 167 169 171 173 175 177 179 BOl [°ABDC]

Figure 6.-7 : Effect of Fuel Injection Timing at 3 bar bmep, 1800 rpm DDC 6V-92TA - Diesel Fueling (normalized)

0.9 0.8

0.7 0.6

0.5 0.4

0.3

0.2

0.1

0 161 163 165 167 169 171 173 175 177 179 BOl [°ABDC]

Figure 6-8 Effect of Fuel Injection Timing at 3 bar bmep, 1200 rpm DDC 6V-92TA - Diesel Fueling (normalized)

97 1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 159 161 163 165 167 169 171 173 175 177

BOl [°ABDC1

Figure 6-9 : Effect of Fuel Injection Timing at 3 bar bmep, 1250 rpm DDC 1-71 - Diesel Fueling (normalized)

0.9

0.8

0.7

0.6

0.5 0.4

0.3

0.2

0.1

0 163 165 167 169 171 173 175 177 BOl [°ABDCI

Figure 6-10 Effect of Fuel Injection Timing at 1 bar bmep, 1250 rpm DDC 1-71 - Diesel Fueling (normalized)

98 The effect of fuel injection timing on performance and emissions near optimum for natural gas fueling of the DDC 1-71 are shown in Figures 6-11 and 6-12. The results presented are at the same speed (1250 rpm), but at different loads (1 and 3 bar bmep). The normalizing constants for these figures are given in Table 6-3.

Table 6-3 : Normalizing Constants for Figures 6-11 and 6-12

Engine DDC 1-71 DDC 1-71 rpm 1250 1250

bmep (bar) 3 1 lthmax (%) 25.1 14.8 NOxm (ppm) 790 395 CO 246 608 (ppm) THCm 932 1584 (ppmc) CH4max 118 920 (ppm)

As with diesel fueling, these results demonstrate thaI thermal efficiency is quite insensitive to changes in fuel injection timing, while NO is strongly effected. With natural gas fueling, however, carbon monoxide (CO) emissions are much less sensitive to changes in fuel injection timing, and no particulate matter emissions are produced at any fuel injection timing at these loads. At the low load case (1 bar bmep) shown in Figure 6-1 1, the tradeoff between NO and

CO is much less prominent than with diesel fueling. At the medium-high load case (3 bar bmep) shown in Figure 6-12, there are no tradeoffs between any of the emissions. Therefore, in this case the fuel injection timing can be selected such that all emission levels are low without seriously sacrificing thermal efficiency.

99 1 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 159 161 163 165 167 169 171 173 BOl [°ABDC]

Figure 6-11 Effect of Fuel Injection Timing at 1 bar bmep, 1250 rpm DDC 1-71 (normalized) 0.020” dia. Gas holes, 140 bar Gas pressure

0.9 0.8

0.7

0.6

0.5

0.4

0.3 0.2

0.1

0 159 161 163 165 167 169 171 173 BOl [°ABDCJ

Figure 6-12 Effect of Fuel Injection Timing at 3 bar bmep, 1250 rpm DDC 1-71 (normalized) 0.020” dia. Gas holes, 140 bar Gas pressure

100 The effect of fuel injection timing on combustion characteristics near optimum are shown in Figures 6-13 through 6-18. Results using six different fuel injection timings at two crank angle degree increments are presented. The equivalence ratios listed in Table 6-1 have been used in this analysis. While the following results show in general the effects of fuel injection liming on combustion characteristics, they do not allow for the full thermodynamic consequences of the changing equivalence ratio. The effects of fuel injection timing on mass fraction of burned fuel for both diesel and natural gas fueling are illustrated in Figures 6-13 and 6-14, respectively. As shown in both cases, the characteristic shape of each curve does not change with injection timing.

The ignition delay time is also unaffected. Hence combustion rate is unaffected by injection timing near optimum for diesel and natural gas fueling.

101 1

0.9

0.8

0.7

0.6

Xmf 0.5

0.4

0.3

0.2

0.1

0 160 180 200 220 240 crank angle (°ABDC)

Figure 6-13 : Effect of Fuel Injection Timing on Mass Fraction of Burned Fuel (DDC 1-71 Diesel Fueling at 3 bar bmep)

0.9

0.8

0.7

0.6 X mf 0.5

0.4

0.3

0.2

0.1

0 160 180 200 220 240 crank angle (°ABDC)

Figure 6-14: Effect of Fuel Injection Timing on Mass Fraction of Burned Fuel (DDC 1-71 Natural Gas Fueling at 3 bar bmep)

102 2600

T. 163 bi °ABDC °ABDC (K)

2500

2400

160 180 200 220 240 crank angle (°ABDC)

Figure 6-15 : Effect of Fuel Injection Timing on Initial Burned Gas Temperature (K) (DDC 1-71 Diesel Fueling at 3 bar bmep)

2600

T. hi (K)

2500

2400

160 180 200 220 240 crank angle (°ABDC) 2600

Figure 6-16 : Effect of Fuel Injection Timing on Initial Burned Gas Temperature (K) (DDC 1-71 Natural Gas Fueling at 3 bar bmep)

103 The effects of fuel injection timing on the initial burned gas temperature for both diesel and natural gas fueling are shown in Figures 6-15 and 6-16, respectively. The effect of advancing injection timing is seen clearly in Figure 6-15 to increase the initial burned gas temperature during the early stages of combustion. This same effect can not be seen as clearly in Figure 6-16 as a result of the diesel pilot combustion phase. In the natural gas fueling case, it is assumed that all of the diesel pilot bums prior to the combustion of the natural gas. Due to the lower combustion temperature associated with natural gas, the burned gas temperatures shown in Figure 6-16 are lower than in Figure 6-15.

An increase in burned gas temperature, with more advanced injection timings, has a significant effect on the amount of NO that forms. For the diesel fueling case, these effects are seen in Figure 6-17, which illustrates the effect of injection timing on NO formation. It can also be seen that NO formation occurs early in the combustion process, when burned gas temperatures are highest.

800

700

600

500 NO (ppm) 400

300

200

100

0 160 180 200 220 240 crank angle (°ABDC)

Figure 6-17 : Effect of Fuel Injection Timing on Estimated Exhaust NOx (ppm) (DDC 1-71 Diesel Fueling at 3 bar bmep)

104 The estimates of exhaust NO depend on the number of burned gas zones present at any time during combustion. The more burned gas zones present, the longer the burned gases remain at high temperatures before mixing out. Hence more NO is formed. The presence of two, three and four burned gas zones correspond to mixing delay 1periods of 0.27 ms, 0.40 ms, and 0.52 ms respectively. The measured and estimated NO values at different injection timings are plotted in Figure 6-18 for the diesel fueling case. Estimates of exhaust NO are shown using either two, three, or four burned gas zones present at any time during combustion. At less advanced injection timings, the measured NO values are bracketed by NOestimates using two and three burned gas zones. At the highly advanced injection timings, the measured values fall in-between the estimates using three and four burned gas zones. Assuming that the burned gas temperature predictions are accurate for each injection timing case, this suggests that at highly advanced injection timings, mixing delay periods are longer.

750 ° Measured NO 700 + Estimated NO 650 (2 burned gas zones) ° Estimated NO 600 (3 burned gas zones) NO 550 Estimated NO (4 burned gas zones) (ppm) 500 450

400

350

300

250 I I I I 163 165 167 169 171 173 Injection Timing (crank angle °ABDC)

Figure 6-18: Measured and Estimated NO Emissions (ppm exhaust)

1 At 1250 rpm and using a one crank angle degree calculation step. 105 6.4 Effects of Engine Load and Fuel Injection Rate

The effect of engine load on the performance and emissions of the DDC 1-71, using various natural gas fueling rates and operating at a constant speed of 1250 rpm, are illustrated in

Figures 6-19 through 6-28. The emissions are given on a wet basis, which accounts for water vapour in the exhaust. The natural gas fueling results are compared with diesel fueling results.

For diesel fueling, the fuel injection rate is held constant. Natural gas injection pressures of 100,

120 and 140 bar are used along with two different natural gas fuel-injector nozzle areas. Injector tips with gas hole diameters of either 0.016” or 0.020” are used. The injection timing is selected for both diesel and natural gas fueling such that the beginning of combustion occurs at TDC.

106 30

22 th 18 (%) 14

BMEP (bar)

Figure 6-19 : DDC 1-71 Thermal Efficiency (%)- 0.016” dia. Gas holes

22 Baseline th 18 (%) 0 100 bar 14 + 120 bar 10 140 bar

0 1 2 3 4 BMEP (bar)

Figure 6-20 : DDC 1-71 Thermal Efficiency (%)- 0.020” dia. Gas holes

107 2000

1500 Co (ppm) 1000

500

0 1 2 3 4 BMEP (bar)

Figure 6-21 DDC 1-71 Carbon Monoxide [wet] (ppm) 0.016” dia. Gas holes

2000

1500 Co (ppm) 1000

500

0 1 2 3 4 BMEP (bar)

Figure 6-22 : DDC 1-71 Carbon Monoxide [wet] (ppm) 0.020” dia. Gas holes

108 500 100 bar 450 + 120 bar 140 bar 400

NO 350 (ppm) 300

250

200

I I 150 I I I —— 0 1 2 3 4 BMEP (bar)

Figure 6-23 : DDC 1-71 Oxides of Nitrogen [wet] (ppm) 0.016” dia. Gas holes

500

450

400

NO 350 (ppm) 300

250

200

150 0 1 2 3 4 BMEP (bar)

Figure 6-24 : DDC 1-71 Oxides of Nitrogen [wet] (ppm) 0.020” dia. Gas holes

109 800

700 D 100 bar + 120 bar 600 140 bar 4CH 500 (ppm) 400

300

200

100 Diesel Baseline 0 I I I I I I I I 0 1 2 3 4 BMEP (bar)

Figure 6-25 : DDC 1-71 Methane [wet] (ppm) 0.016” dia. Gas holes

800

700 100 bar

600 + 120 bar ° 140 bar 4CH 500 (ppm) 400

300

200

100 Diesel Baseline 0 I I 0 1 3 4 BMEP (bar)

Figure 6-26: DDC 1-71 Methane [wet] (ppm) 0.020” dia. Gas holes

110 900

800 100 bar 700 120 bar 140 bar 600 NMHC 500 (ppm) 400

300

200

100

0 I I I I I I 0 1 2 3 4 BMEP (bar)

Figure 6-27 DDC 1-71 Non-Methane Hydrocarbons [wet] (ppmc) 0.016” dia. Gas holes

900 100 bar 800 + 120 bar 700 ° 140 bar 600 NMHC (ppm) 500 400

300 Diesel Baseline 200

100

0 0 1 2 3 4 BMEP (bar)

Figure 6-28 : DDC 1-71 Non-Methane Hydrocarbons [wet] (ppmc) 0.020” dia. Gas holes

111 For a given gas pressure engine operation becomes unstable below a certain load, which may be designated the low load limit. For example, at a gas pressure of 140 bar, engine operation below 1 bar bmep experiences misfiring or high cycle-to-cycle variations. The high load limit at a given gas pressure is set by an upper limit on fuel injection duration. An injection duration of about 15 crank angle degrees is used as the upper limit to avoid over-pressurization of the diesel pilot which can damage the injector. Larger gas hole diameters (0.004h1larger) and higher gas injection pressures allow greater load capability for a given injection duration, because of increased gas mass flow.

Figures 6-19 and 6-20 illustrate the effects of gas injection pressure and gas-fuel-injector nozzle area on the thermal efficiency. At low and medium loads, the thermal efficiencies for both natural gas and conventional diesel fueling are almost identical. At high loads, the thermal efficiencies for natural gas fueling are greater than those for conventional diesel fueling.

Furthermore, while the diesel thermal efficiency begins to decrease with increasing load before maximum load is reached, natural gas thermal efficiencies have not yet begun to decrease.

Carbon monoxide emissions, illustrated in Figures 6-21 and 6-22, dramatically increase at high load for the diesel fueling case. A similar increase in CO emissions does not occur for the natural gas fueling case. Large amounts of CO in the exhaust generally correspond to rich combustion and high levels of smoke, since too much fuel has been injected for proper air utilization. These high smoke levels at high loads usually determine the maximum engine load.

The fact that the natural gas fueling regime is not smoke limited, and because the thermal efficiencies do not drop off at high loads, a higher load capability than with conventional diesel fueling is implied.

Figures 6-23 and 6-24 illustrate the effects of gas injection pressure and fuel-injector nozzle area on emissions of oxides of nitrogen. These figures show that at injection pressures of 120 and 140 bar, emissions of NO are greater than for diesel fueling. However, as shown in the previous section, the injection timing can be retarded to produce lower NO emissions without penalties in thermal efficiency or CO and smoke emissions.

112 Figures 6-25 and 6-26 illustrate the effects of gas injection pressure and fuel -injector nozzle area on emissions of methane. As natural gas is about 95% methane, an increase in methane emissions over diesel fueling is expected. There can be a number of reasons why the methane and non-methane hydrocarbon emissions from natural gas fueling are higher than for diesel fueling. Some of the fuel-air mixture may become too lean or too rich to support a propagating flame. The trends depicted in Figure 6-25 and 6-26 show that methane emissions generally increase with increasing gas injection rate at a given load. Assuming that mixing between natural gas and air increases with increasing gas injection rate, then this suggests that as the injection rate increases, the gas-air mixture becomes increasingly overlean due to overmixing.

Methane emissions are particularly high at low loads. Ignition delay periods are longer at low loads due to lower gas temperatures. Hence more time is available at low loads for the injected gas to mix with the air to become too lean to support a propagating flame. It also seems reasonable that overlean mixtures would tend to occur when the overall cylinder averaged equivalence ratio is lower, which is the case at low loads.

Figures 6-27 and 6-28 illustrate the effects of gas injection pressure and fuel-injector nozzle area on emissions of non-methane hydrocarbons (NMHC). While only about 5% of natural gas consists of NMHC, some NMHC compounds are formed as intermediate species in the oxidation reaction of natural gas. Figures 6-27 and 6-28 indicate that NMHC emissions increase with increasing load. Assuming that the majority of NMHC emissions can be attributed to unreacted diesel pilot, since the amount of diesel fuel injected remains more or less constant with increasing load, the increase in NMHC emissions may be the result of a competition for air between the diesel fuel and the natural gas. The implication is that the natural gas injection interferes with the diesel pilot injection such that sufficient air for complete combustion of the diesel fuel is not available.

Figures 6-27 and 6-28 also indicate that for natural gas fueling NMHC emissions are generally higher than for diesel at all loads. CO emissions, shown in Figures 6-21 and 6-22, are also higher for natural gas fueling (at low and medium loads). CO emissions are associated with rich combustion, but are also formed as intermediate species during oxidation. The higher CO

113 emissions could be the result of poor atomization of the diesel pilot resulting in an over-rich diesel-air mixture. This is assuming that the natural gas combustion is lean and that CO emissions primarily result from the combustion of the diesel pilot.

Methane, NMHC, and CO emissions and ignition delay periods are greater for the injector tip with 0.020” gas holes. While the diesel pilot holes in the two different injector tips were intended to be identical, small differences have resulted in slightly different diesel pilot injection characteristics. Greater diesel pilot ignition delay periods allow the natural gas to mix longer and become leaner before it begins to combust. This may be another reason why methane emissions are greater with the injector tip with 0.020” gas holes. It appears that the diesel pilot injection characteristics in the injector tip with the 0.020” gas holes are not as good as with the tip with the

0.016” gas holes.

The prototype natural-gas injector has been designed to inject a constant amount of diesel for all injection durations. Thus the diesel-to-natural gas ratio varies with engine load. Figures 6-

29 and 6-30 show the diesel-to-natural gas ratios (by energy) for each gas nozzle diameter. The diesel-to-natural gas energy ratio varies from about 50% at no-load to 20% at full-load, and has similar characteristics for all gas injection rates.

The effect of engine load on the mass fraction of burned fuel (for diesel fueling of the

DDC 1-71) is shown in Figure 6-31. The combustion analysis is performed on an average of 20 consecutive engine cycles of pressure data. The figure shows that slightly slower burning occurs in the higher load case. Slower burning can be associated with mixing controlled combustion versus premixed combustion. This suggests that at lower loads a greater fraction of the injected fuel premixes with air during the ignition delay period. The more prernixing that occurs prior to ignition, the leaner the fuel-air mixture becomes. Hence, the local equivalence ratio is expected to be smaller at lower loads to indicate leaner combustion. The local equivalence ratios determined from the combustion analysis were 1.03 at 1 bar bmep and 1.09 at 3 bar bmep.

I 14 55

50 IJ 100 bar

45 + 120 bar 140 bar Diesel 40 Ratio (%) 35

15 0 1 2 3 4 BMEP (bar)

Figure 6-29 : DDC 1-71 Diesel-to-Gas Energy Ratio (%),0.016” dia. Gas holes

50 u 100 bar

45 + 120 bar 140 bar 40 Diesel Ratio 35 (%) 30

15 0 3 4 BMEP (bar)

Figure 6-30 : DDC 1-71 Diesel-to-Gas Energy Ratio (%),0.020” dia. Gas holes

115 1

0.9 0.8 0.7 0.6 x mf 0.5 0.4 0.3 0.2

0.1

crank angle (°ABDC)

Figure 6-31 : Effect of Load on Mass Fraction of Burned Fuel Diesel Fueling of the DDC 1-71

The mass fractions of burned fuel for both natural gas and diesel fueling of the DDC 1-71 at 3 bar bmep are shown in Figure 6-32. The shapes of the burning curves are quite similar, which is also the case at 1 bar bmep (not shown). In the natural gas fueling case, a distinction between combustion of the diesel pilot and the natural gas can not be made. It was thought that because these curves were generated using 20 cycles of averaged cylinder pressure data, details of distinct burning phases would be masked through averaging. However, single cycles of pressure data were also analyzed, and again no distinction could be made between the combustion of each fuel. This suggests that some of the natural gas begins to burn before combustion of the diesel fuel is complete.

Low cycle-to-cycle variability indicates that the 20 cycles of averaged pressure data is representative of each cycle. For the diesel fueling cases the calculated coefficient of variation in indicated mean effective pressure (COVimep)was about 0.7%. For the natural gas fueling cases, the calculated COVimePwas about 1.0%. A COVimePgreater than about 10% indicates excessive

116 cycle-to-cycle variability. The local equivalence ratios for the natural gas burning phase determined from the combustion analysis are 0.78 at 1 bar bmep and 0.95 at 3 bar bmep. The lower equivalence ratio at low load suggests (in accordance with the earlier argument) that the natural gas combustion is leaner at lower loads.

0.9 0.8 0.7 X mf 0.6 0.5 0.4

0.3 0.2

0.1

0 160 180 200 220 240 crank angle (GABDC)

Figure 6-32: Mass Fraction of Burned Fuel for both Natural Gas and Diesel Fueling of the DDC 1-71 (3 bar bmep)

Figure 6-33 illustrates the initial burned gas temperatures for both diesel and natural gas fueling at 1 and 3 bar bmep. The burned gas temperatures for natural gas fueling are lower due to the lower combustion temperatures associated with natural gas. In the early stages of combustion, the burned gas temperatures for natural gas fueling are the same order of magnitude as for diesel fueling because of combustion of the diesel pilot.

117 2600

2500 ibar dsl T. bi + lbar gas (K) 3bar dsl 3bar gas 2400

I I I I I I I I 160 180 200 220 240 crank angle (°ABDC)

Figure 6-33 : Effect of Fuel and Load on Initial Burned Gas Temperature (K) DDC 1-71

While the above results show in general the effects of fuel and load on combustion rate and burned gas temperature, they do not allow for the full thermodynamic consequences of the changing equivalence ratio. Table 6-4 gives, for each case, the measured and estimated NO values along with the number of burned gas zones used in the combustion analysis. Accurate estimates of NO for natural gas fueling require more burned gas zones than for diesel fueling. Assuming that the predicted burned gas temperatures are correct for both diesel and natural gas combustion, this implies that the burned gas mixing delay period is longer for natural gas fueling.

118 Table 6-4 : Measured and Estimated NO (DDC 1-71)

Engine Fueling bmep Measured NO Estimated NO Number of (bar) (ppm) (ppm) Burned Gas Zones Diesel 1. 265 265 3

Natural Gas 1 240 240 4 Diesel 3 345 395 3 Natural Gas 3 440 420 5

119 7. CONCLUSIONS AND RECOMMENDATIONS

7.1 Conclusions

Based on the investigation of performance, emissions and combustion characteristics of natural gas fueling of diesel engines, the following conclusions can be made:

1. In a conventional diesel engine, retarding fuel injection timing reduces NO emissions at the expense of increasing CO and smoke emissions. With natural gas fueling of diesel engines, NO emissions can also be reduced by retarding fuel injection timing, however there is no penalty in

CO or smoke emissions.

2. The thennal efficiencies for both natural gas and conventional diesel fueling at low and medium engine loads, are almost identical. The thermal efficiencies at high loads for natural gas fueling are greater than for conventional diesel fueling.

3. A sharp increase in carbon monoxide and smoke emissions occurs when approaching peak engine load with conventional diesel fueling but not with natural gas fueling. This along with higher thermal efficiencies at high loads implies higher peak engine load capability with natural gas fueling.

4. The high methane emissions at low loads with natural gas fueling are consistent with overleaning of the natural gas due to overmixing prior to ignition.

120 5. Accurate predictions of engine exhaust NO emissions can be made using the presented combustion analysis model. The accuracy of NO predictions strongly depend on the accuracy of the burned gas temperature results, due to the high sensitivity of NO formation to burned gas temperature. From combustion analysis results, it is evident that NO forms early in the combustion process when burned gas temperatures are highest. Hence, reduction of peak burned gas temperatures results in a reduction of NO emissions.

6. Accurate estimates of both heat transfer from the combustion gases to the cylinder walls and burned gas temperatures can not be made simultaneously using the presented combustion analysis model. This is attributed to numerical error associated subtractive 1cancellation and summation errors, and measurement error of engine parameters (such as air and fuel flow rates).

7. Before the presented combustion analysis model can be used to give conclusive information about the local equivalence ratio at which combustion takes place inside the engine, it needs modification to account for the effect of lean or rich burning on the computed burned gas temperatures.

8. For natural gas fueling, the rate of combustion is greater than for conventional diesel fueling as a result of more predominate pre-mixed combustion versus mixing-controlled combustion. The combustion rates for both fueling regimes decrease with increasing load as mixing-controlled combustion predominates over pre-mixed combustion.

Subtractive cancellation is the subtraction of two nearly equal numbers that cause a large loss in the number of significant1 digits. 121

properties

analysis.

allowable

efficiencies.

loads

emissions.

made:

characteristics

7.2

Investigate

Account

Minimize

Delay

Improve

Recommendations

complete

Based

reduce

the

amount

for

diesel

Stable

the

injection

the

comparison

non-stoichiometric

methane

amount

burned

what

effects

natural

pilot

engine

diesel

was

spray

and

emissions

natural

gas

operation

pilot.

between

diesel

engine

learned

unburned

characteristics

fueling

gas

pilot

equivalence

speed

conventional

and

after

low

the

gases

low

minimize

loads.

the

diesel

investigation

performance,

cycle-to-cycle

injection

122

obtain

ratios

reduce

engines,

diesel

exhaust

greater

hydrocarbon

and

the

diesel

the

performance,

emissions

variability

calculation

natural

accuracy

following

pilot

gas

and

will

greater

from

fueling.

carbon

emissions

recommendations

combustion

composition

maximize

indicate

the

amount

monoxide

combustion

and

the

thermal

combustion

minimum

and

obtain

lower

are

a be 8. REFERENCES

1. Heywood, J. B., “Internal Combustion Engine Fundamentals”, McGraw-Hill Inc., New York,

1988.

2. Communication, “Information Update”, Detroit Diesel Corporation, Sept. 1993

3. Beck, N. J., Johnson, W.P., George, A. F., Peterson, P. W., van der Lee, B., and Klopp, G.,

“Electronic Fuel Injection for Dual Fuel Diesel Methane”, SAE Technical paper 891652,

Aug., 1989.

4. Miyake, M., Biwa, T., Endoh, Y., Shimotsu, M., Murakami, S., and Kornoda, T., “The

Development of High Output, Highly Efficient Gas Burning Diesel Engines”, CJMAC Paper

D11.2, Conference Proceedings, Paris, France, June 1983.

5. Einang, P., Koren, S., Kvamsdal, R., Hansen, T., and Sarsten, A., “High-Pressure,

Digitally Controlled Injection of Gaseous Fuel in a Diesel Engine, With Special Reference to

Boil-Off from LNG Tankers”, Proceedings CIMAC Conference, Paris, France, June 1983.

6. Einang, P., Engja, H., and Vestergren, R., “Medium Speed 4-Stroke Diesel Engine Using High

Pressure Gas Injection Technology”

7. Wakenell, J. F., O’Neal, G. B., and Baker, 0. A., “High-Pressure Late Cylce Direct

Injection of Natural Gas in a Rail Medium Speed Diesel Engine”, SAE Technical paper

872041, Nov., 1987.

8. Gunawan, H., “Performance and Comb ustion Characteristics of a Diesel-Pilot Gas

Injection Engine”, Unpublished M.A.Sc. Thesis, Department of Mechanical Engineering,

University of British Columbia, June, 1992.

9. Tao, Y., “Performance and Emission Characteristics of a Gas-Diesel Engine”, Unpublished

M.A.Sc. Thesis, Department of Mechanical Engineering, University of British Columbia,

August, 1993.

123 10. Ouellette, P., “High Pressure Injection of Natural Gas for Diesel Engine Fueling”,

Unpublished M.A.Sc. Thesis, Department of Mechanical Engineering, University of British

Columbia, January, 1992.

11. Chepakovich, A., “Visualization of Transient Single- and Two-Phase Jets Created by Diesel

Engine Injectors”, Unpublished M.A.Sc. Thesis, Department of Mechanical Engineering,

University of British Columbia, April, 1993.

12. Go-Power Corporation Publication “Operation, Installation, Service and Repair of Models D

and DA-316 -516 Dynarnomters”, May, 1984.

13. Pierburg Instruments Inc. “Instruction Manual - Model FT1OE Electrical Mass Flow Transmitter”

14. deSilva, C. W.,”Control Sensors and Actuators”, Prentice-Hall inc., New Jersey, 1989, p. 37 15. Lancaster, D. R., Krieger, and R. B., Lienesch, J. H., “Measurement and Analysis of Engine

Pressure Data”, SAE Technical paper 750026, 1975.

16. “1992 SAE Handbook Volume 3”, Society of Automotive Engineers, 1992

17. Edwards, C. F., Siehers, D. L., and Hoskins, D. H., “A Study of the Autoignition

Process of a Diesel Spray via High Speed Visualization”, £4E Technical paper 920108, 1992.

18. Annand, W. J. D., “Heat Transfer in the Cylinder of Reciprocating Internal Combustion

Engines”, Proc Insin Mech Engrs, Vol.177 No. 36, 1963.

19. Woschni, G., “A Universally Applicable Equation for the Instantaneous Heat Transfer

Coefficient in the Internal Combustion Engine”, SAE Technical paper 670931, 1967.

20. Szekely, G. A. and Alkidas, A. C., “A Two-Stage Heat-Release Model for Diesel

Engines”, SAE Technical paper 861272, 1986.

21. Shayler, P. J. and Wiseman, M. W., “Improving the Determination of Mass Fraction Burnt”,

SAE Technical paper 900351, 1990.

22. Gatowski, J. A., Balles, E. N., Chun, K. M., Nelson, F. E., Ekchian, and I. A., Heywood, J.

B., “Heat Release Analysis of Engine Pressure Data”, SAE Technical paper 841359,1984.

23. Krieger, R. B. and Borman, 6. L., “The Computation of Apparent Heat Release for

Internal Combustion Engines”, ASME paper 66-WA/DGP-4, Nov, 1966.

124 24. Bedran, E. C. and Beretta, G. P., “General Thermodynamic Analysis for Engine

Combustion Modeling”, SAE Technical paper 850205, 1985.

25. Ferguson, C. R., “Internal Combustion Engines - Applied Thermosciences”, John Wiley& Sons, Inc., 1986

26. Personal Communication from Detriot Diesel Corporation.

27. Reynolds, Wm. C., “STANJAN chemical equilibrium solver v 3.93 IBM-PC”, Mech. Eng.

Dept., Stanford University, 1987

28. Van Wylen, G. J. and Sonntag, R.E, “Fundamentals of Classical Thermodynamics”, third

edition, John Wiley& Sons, inc., 1985

125

Rearranging and

“d”

“a” HYDRAULIC

then

squaring

and

the

With

same

assuming

“c’

the

will

flow

gives

the

reference

relationship

WHEATSTONE

above

through

K 2 CA

half

expressions

of to

for

orifices

Figure =

—

K 2 CA orifice

°=

0±q

2-4,

The

‘b”

BRIDGE

and

“a”

Qq=k 1

and

flow

if then

=KCdAdP1P3

k 1

the

APPENDIX

“d”

versus

subtracting

recirculating

DIESEL

constant) will

126

/P 1 p 2

pressure

half

FUEL

the

flow,

result

drop

expression

MEASURING q,

relationship

and

less

for

the

than

orifice

flow

for

the

DEVICE

orifice

through

“a”

measured

from

“d”

orifices

orifice flow, determining can Bridge’ Hence Q, diesel Since the be q mass final once By calculated. is network a a expression flow the the preset similar diesel flow rate will constant development, characteristics (Qp) Then density. for give the is measuring a directly flow diesel measure rate if of mass the proportional Qp=h(P 1 Qp=-(P 2 —P 3 ) the the and of recirculating flow orifices the proper k 1 q q rate 127 is diesel also —P 4 ) to are is differential the flow, determined, mass a differential constant, q, flow is pressures greater rate this the pressure constant expression directly than from (P, the of without the — measured P 3 ). shows proportionality 11 Wheatstone uniquely that flow, the APPENDIX II

PRESSURE TRANSDUCER MOUNTING IN CYLINDER OF DDC 1-71

PRESSURE SIGNAL CHARC AMPLIFIER EXHAUSTVALVE ID CYL

I A , \/i ‘\ _(_

DTME

PRESSLR TRANSDUcER CPtB M, 11EA SECTV A—A

Figure A-I : Pressure Transducer Mounting in Cylinder of DDC 1-71 (courtesy of I-i.Gunawan [8])

128 -9 C ri I-

ri x / I C V

- (j

E ri C/I V

—--,-‘ 3 3 C C—)- 213 n I -< F — V z — — m I- ;tJ nU I

ri 0 - — niX CD fl F C 0 z x w rn in

(_) I

-U V z APPENDIX IV

SOFTWARE FOR PROCESSING CYLINDER PRESSURE DATA

Pressure data acquired using the ISAAC are stored in Basic binary format. The ISAAC samples the pressure transducer at a specified rate (i.e. every crank angle), digitizes the sampled value and stores it as an integer. Each engine cycle of pressure data collected is stored in a separate file with a numerical file extension. Pressure data from the first cycle will be stored in a file with the extension .001. Similarly, the twentieth consecutive cycle of pressure data will be stored in a file with the extension .020. This binary data must be converted to ASCII format, scaled, and then averaged for use in the combustion analysis.

PDC (Pressure Data Conversion Utility)

The program PDC is used to convert binary ISAAC pressure data files to ASCII text.

Since the ISAAC pressure data is a digitized value stored as an integer, when the data is converted to ASCII it must also be scaled. The system gain and the transducer-charge amplifier calibration factor are used to convert the integer data to relative pressures. The relative pressures are shifted by a constant value to obtain absolute cylinder pressure (in kPa). There are several techniques for determining the magnitude of the shift required. In PDC the assumption made is that the cylinder pressure at BDC is equal to the mean intake air manifold pressure.

In PDC there are two methods in which the conversion is done; 1) Convert each binary file to its ASCII equivalent directly, and 2) Extract pressure data from a set of files and merge into a single file, in preparation for mass of fuel burned analysis.

PDC is also used to attach other pertinent engine data (such engine speed, exhaust temperature, etc.) to the ASCII file in the form of a header. PDC is menu-driven. Menu options are given in

130 Figures AX-i and AX-2. If the file PDC.INI exist in the directory that you started PDC from, then PDC uses it to establish initial settings for the various menu options. The current session’s settings are saved in PDC.INI upon exiting the program (changes are not saved if Ctrl-C is pressed to exit). The .INI file is in ASCII format and can be modified using a text editor.

XPDATA (Pressure Data Averaging and Indicated Work Calculation Utility)

The program XPDATA uses the output data file from PDC directly if the ‘prepare for mass burn analysis” option in PDC was selected (no modifications to this file are necessary).

XPDATA averages any number of engine cycles of pressure data, calculates the indicated work for each cycle, then calculates the average indicated work and coefficient of variation in imep.

The reason why combustion analysis uses averaged pressure data is because the engine is itself an averaging device which responds to mean values of air and fuel flows by generating a mean power output. It is therefore appropriate to use the mean pressure data of many cycles for combustion analysis as the other quantities (e.g. fuel and air flow, exhaust and inlet temperature, etc.) used in the analysis are mean engine measurements.

Different pressure data averaging techniques can be used. The technique used in

XPDATA is to calculate the mean pressure at each crank angle.

XPDATA requires some user input. It first prompts the user to select the engine type

(DDC 6V-92 or DDC i-71), then to enter the input file name (and directory). The output file of

XPDATA is used directly as the input file for the combustion analysis program (XMF). Hence the user is prompted to enter the unburned fractions of diesel and natural gas, even though they are not directly used for computation in this program.

As the computation proceeds, XPDATA graphically displays each cycle of pressure data on a log-log plane of cylinder pressure and volume. The indicated work for each cycle is also displayed. After the averaging is complete, the average pressure data and the average indicated work and coefficient of variation in imep are displayed. The user is then asked if more data from files are to be averaged.

131 AP1ENDIX V

BRAKE POWER CORRECTION (SAE STANDARD J1349 JUN85)

The correction is made against standard inlet air conditions:

Inlet Air Pressure (Absolute) : 100 kPa

Inlet Air Temperature : 25°C

Dry Inlet Air Pressure (Absolute) : 99 kPa

The correction factor f applied to the observed brake power is a function of the atmosphere factor a and the engine factor m The following empirical relationship is used:

)fm = (fa

The atmosphere factor is calculated based on the measured dry inlet air pressure BdO(in kPa) and the measured inlet air temperature t0 (in °C) as follows:

a LBdO]L 298 J

For the DDC 1-71 a=1.0 and for the DDC 6V-92TA a=0.7. The engine factor is a function of the fuel flow F (in g/s), the engine displacement D (in litres), the engine speed N (in rpm), the fuel delivery q, and the pressure ratio r of measured inlet manifold pressure to measured inlet air pressure. The value of m is given as:

132 = 0.3 for (q/r) <40

= (0.036)_ H4 for 40 < q/r < 65

f=1.2 for (q/r)>65

where q = 60000 —f- DN

The correction factor applied to the observed brake power is within the range of 0.90 to 1.10.

133 APPENDIX VI

CALCULATION OF SPECIFIC HUMIDITY

Specific humidity H (g of 20H per kg of dry air) of an air-water vapour mixture is defined as the ratio of the mass of water vapour m (kg) to the mass of dry air ma (kg) [28].

H=1000-- (1) ma

The equation of state for both water vapour and dry air can be written in terms of partial pressures as follows:

= mRT (2)

PaV = maRaT (3)

The gas constant R for water vapour is 461.62 i/kg-K. The gas constant Ra for air is 287.0 J/kg-K.

Dividing equation (2) by equation (3) gives:

mw(RaIPw (4 ma wIa

Substituting equation (4) into equation (1) and using Ra/Rw = 0.6219 gives:

H=621.9-- (5)

134 Relative humidity is defined as the ratio of the partial pressure of water vapour P to the saturated steam pressure P evaluated at the dry bulb temperature.

(6)

The barometric pressure Pb is the sum of the partial pressures of dry air and water vapour.

Pb=Pa+Pw (7)

Substituting equations (6) and (7) into (5) gives:

H=621.9 PS (8) —

To calculate the humidity ratio using equation (8), barometric pressure b (inHg), relative humidity (%),and dry bulb temperature T (°F) are measured directly. The saturated steam pressure (inHg) is expressed in terms of T (°F) by an equation from a curve fit on the Saturated

Steam Tables [28] from 40 to 140 °F.

5P = —0.46192 + 0. (i29439T —0.00045T + 0. 3000004T

135 APPENDIX VII

CALCULATION OF ENGINE CYLINDER VOLUME

The cylinder volume calculations for both the DDC 1-71 and the DDC 6V-92 were done in the same manner. An illustration of the engine cylinder geometry is given in Figure A-3.

The cylinder volume is given by

V 1B

where B is the cylinder bore, V is the clearance volume, and the distance y is as defined in

Figure A-3. The clearance volume is given by V dr — cr-i

where is the cylinder displacement volume and cr is the compression ratio. The length y can be expressed by

y = Li— L2 where

S Li = — + r + L3 and

136 L2 = sin(O— qr2 90)+ _[cosO_ 90)1+

= [sinOcos9o — cos0sin90]

+ 2 2_()[cosOcos9() + 2sinOsin9O] + L3

= —cosO+ r2 — sinO + L3 2 2 ) hence

_(sinü)2) y = r4(1+cosO)_(r2

137 fY

Li L2 r

0 /

Figure A-3 : Engine Cylinder Geometry

s = stroke

B = bore

c = clearance height

r = connecting rod length

138 APPENDIX VIII

COMBUSTION ANALYSIS PROGRAM - XMF.BAS (Qu1ckBASIC)

1= XMF.BAS

This program calculates the mass fraction of fuel burned in the cylinder of a DDC 6V92-TA or 1-71 diesel engine based on pressure vs. crank angle data. This analysis is valid for two fueling scenerios. It can handle fueling with natural gas and diesel pilot as well as fueling with straight diesel. It is assumed that burning occurs at stoichiometric air/fuel ratios, with all of the diesel fuel burning prior to the natural gas. Either the adiabatic flame temperature is used to estimate the burned gas temperature or it is calculated based on an estimate of heat transfer to the cylinder walls. Written by Brad Douville The arrays “PcyP’and ‘ca” contain the pressure and crank angle data

DIM ca(360), Pcyl(360), P(120), x(10), y(10) DIM mbz(10), vbz(10), ubz(10), sbz(10), Thz(10, 10), NOxz(10) DECLARE SUB unburned (Tu!, hu!, uu!, Cvu!, visc!, 1%) DECLARE SUB gas (Tg!, Cpg!, ug!, 1%) DECLARE SUB burned (P!, Th!, vu!, vm!, vb!, uu!, urn!, ub!, sb!, xmbi!, dNO!, NOe!, 1%) DEClARE SUB tad (P!, Th!, vu!, vb!, hu!, ub!, sb!, dNO!, NOe!, 1%) DECLARE SUB qwall (Tm!, P!, Po!, vol!, asurf!, dqwl!, 1%) DECLARE FUNCTION Vcyl! (ca!) DECLARE FUNCHON Cvair! (Tair!) DECLARE FUNCTION Cvres! (Tres!) DECLARE SUB table (Thx!, Pbx!, hbx!, sbx!, ubx!, vbx!, dNO!, NO!, NOe!, 1%) DECLARE SUB cubics (np%, x!O,y!, xset!, ycalc!) DECLARE FUNCTION Acyl! (ca!) DIM ShARED bore, stroke, rod, VcIr DIM SHARED mtot, nres, natrap, Ru, dt DIM SHARED yO2r, yN2r, yCO2r, yH2Or residual composition DIM SHARED y02, yN2, yCO2, yH2O, wtmol a mole fractions and molar mass of unburned mixture CLS PRINT INPUT” Enter pressure data file name (eg. octO2a): “, pdata$ PRINT PRINT” Output to File? (yin)” oputfile$ = INPUT$(1) IF oputfile$ = “y” OR oputfile$ = Y” THEN PRINT 139 PRINT” Data output filename?

INPUT ‘ (do not include file extension) “,out$ PRINT PRINT ‘ Output will be stored as c:\wk\brad\outV’; out$; “.out’ END IF ‘PRINT ‘INPUT” Enter a mass ratio of unburned gases that mix with burned gases: “, mixratio mixratio = I PRINT INPUT” Enter local equivalence ratio for diesel burning phase: “, phidsl PRINT INPUT” Enter local equivalence ratio for gas burning phase: “, phigas PRINT DO INPUT” Enter the number of existing burned gas zones at any instant (ito 6): “, brndzones% LOOP UNTIL brndzones% < 7 AND brndzones% > 0 DO PRINT

PRINT ‘ Select computation method:

PRINT ‘ 101Estimate the burned gas temp. using the adiabatic flame temp.” PRINT” [1] Calculate the burned gas temp. based on an estimate of” PRINT “ heat transfer to the combustion chamber walls.” PRINT INPUT” “, method LOOP UNTIL method = 0 OR method = 1

Read the engine fluid properties and operating parameters: rpm is the engine crank shaft rotational speed (rev/mm) Pabox is the engine air box pressure [kPaj Tabox is the engine air box temperture [KI Tres is the engine exhaust port temperature [Ki mair is the delivered air flow [kgJcycle/cylinderj mdsl is the diesel flow [kg/cycIe/cylinder mgas is the natural gas flow [kgJcycle/cylinderl note: if mdsl=0 then mgas must also equal zero capri is the crank angle of the first pressure record caboi is the crank angle of the beginning of injection of diesel fuel dca is the crank angle interval size capw is the total pulsewidth of fuel injection in crank angle degrees capwd is the pulsewidth of diesel pilot npr% is the # of pressure records. nca% is the # of ca intervals to be analyzed ncyc% is the # of engine cycles of averaged pressure data bore is cylinder bore (m) stroke is the cylinder stroke (m) rod is conn rod length(m) Cr IS compression ratio Vclr is clearance volume(m**3/cyl) Vdisp is displacement volume(m**3/cyl) caipc is a crank angle (ABDC) after all ports are closed xudsl is the unburned fraction of diesel in the exhaust xugas is the unburned fraction of natural gas in the exhaust MWexh is the molar mass of the engine exhaust

OPEN “c:\wk\brad\ascii\” + pdata$ + “.xpj” FOR INPUT AS #1 INPUT #1, rpm, Pabox, Tabox, Texh INPUT #1, mair, mdsl, mgas 140 INPUT #1, caprl, caboi, dca, capw INPUT #1, npr%, nca%, ncyc% INPUT #1, engine%, xudsl, xugas FOR i% = 1 TO npr% INPUT #1, ca(i%), Pcyl(i%) NEXT i% CLOSE #1 dt= dca/rpm/6 MWexh = 28.8

IF engine% = 1 THEN engine$ = “171” PRINT” Pressure data is from the DDC 1-71 engine ELSE engine$ = “6V92” PRINT” Pressure data is from the DDC 6V-92TA engine END IF PRINT PRINT” working...”

IF engine$ = “6V92” THEN bore = .12294 rod = .257175 cr=17 Vdisp = .0015075 caipc = 55 ELSEIF engine$ = “171” THEN bore = .10795 rod = .254 cr = 16 Vdisp = .001162 caipc = 60 END IF stroke = .127 VcIr = Vdisp / (Cr - 1)

‘set up graphics screen CLS SCREEN 12 LOCATE 1,60 PRINT pdata$ LOCATE 2,60 PRINT “mixratio = “; mixratio LOCATE 3,60 PRINT “brndzones = “; brndzones% LOCATE 4,60 PRINT “phidsi = “; phidsi LOCATE 5,60 PRINT “phigas = “; phigas LOCATE 6,60 PRINT USING “Xmfmax = #.##“; 1 - xudsl - xugas LOCATE 4,5 PRINT “cylinder” LOCATE 5,5 PRINT “pressure” LOCATE 6,5

141 PRINT ‘ (kPa)” LOCATE 2, 16 PRINT “7000” LOCATE 3, 16 PRINT “4000 LOCATE 5,16 PRINT “2000 LOCATE 8, 17 PRINT “500” LOCATE 12,17 PRINT “100” LOCATE 15,3 PRINT “ mass’ LOCATE 16,3 PRINT” burned” LOCATE 17,3 PRINT “fraction” LOCATE 22,16 PRINT “0” LOCATE 18,14 PRINT “0.5” LOCATE 14, 14 PRINT “1.0” VIEW PRINT 25 TO 30 VIEW (100, 0)-(500, 180) WINDOW (-10, 4.5)-(-6, 9.5) LINE (LOG(Vcyl(ca(1))), LOG(i00))-(LOG(Vcyl(ca(npr% / 2))), LOG(i00)), 14 LINE (LOG(Vcyl(ca(1))), LOG(500))-(LOG(Vcyl(ca(npr% I 2))), LOG(5(X))),14 LINE (LOG(VcyI(ca(1))), LOG(2000))-(LOG(Vcyl(ca(npr% / 2))), LOG(2000)), 14 LINE (LOG(Vcyl(ca(1))), LOG(4000))-(LOG(Vcyl(ca(npr% / 2))), LOG(4000)), 14 LINE (LOG(Vcyl(ca(1))), LOG(7000))-(LOG(Vcyl(ca(npr% / 2))), LOG(7000)), 14 LINE (LOG(Vcyl(ca(npr% / 2))), LOG(100))-(LOG(VcyI(ca(npr% / 2))), LOG(7000)), 14 LINE (LOG(Vcyl(ca(1))), LOG(100))-(LOG(VcyI(ca(1))), LOG(7000)), 14 PSET (LOG(Vcyl(ca(1))), LOG(Pcyl(1))), 11 FORi%=2TOnpr% LINE -(LOG(Vcyl(ca(i%))), LOG(PcyI(i%))), 11 NEXTi%

‘Estimate the residual gas mole fraction, fresnres/(nres+natrap) ‘and the mass of air trapped in the cylinder, matrap(Kg) ‘A correlation of scavenging data from DDC, the ideal gas law and ‘an energy balance at ipc are used to determine Fres. ‘Ra=[KJ/Kg-K] Rbar4KJ/KmoI-K1

Ra — .287 rhoabox Pabox I (Ra * Tabox) mideal = rhoabox * (Vdisp) rscav = mair / mideal matrap = mideal * (.9 - (1 - .34 * rscav) * ((2.71828) “(1.11 * rscav))) natrap = matrap / 28.97 flair = mair / 28.97 ndsl = mdsl / 13.8 ngas = mgas /16.04 ‘specify initial residual composition to begin iteration yO2r = .21 yN2r = .79 yCO2r=0 142 yH2Or = 0 Tres = Texh iter% = 0 DO iter% = iter% + 1 yO2old = yO2r ‘the equation for nres is a quadratic so use the quadratic formula a = Cvres(Tres) * Tres * * b = natrap (Cvres(Tres) Tres + Cvair(Tabox) * Tabox) - Pabox * VcyI(caipc) * Cvres(Tres) / 8.3144 * * c = natrap Cvair(Tabox) (natrap * Tabox - Pabox * Vcyl(caipc) / 8.3144) nresl =(b+SQR(b*b4*a*c))/(2*a) nres2=(bSQR(b*b4* a* c))/(2 *a) IF (nresl > 0) AND (nresl 0) AND (nres2 < natrap) THEN nres = nres2 ELSE PRU\IT nres is out of range nres = 0 END IF

calculate the composition of the residuals * n02 = .21 natrap + yO2r * nres - 1.45 * ndsl - 2 * ngas nN2 = .79 * natrap + yN2r * nres nCO2 = yCO2r * nres + ndsl + ngas nH2O = yH2Or * nres + .9 * ndsl + 2 * ngas totmols = n02 + nN2 + nCO2 + nFI2O yO2r = n02 / totmols yN2r = nN2 I totmols yCO2r = nCO2 / totmols yll2Or nH2O / totmols mwres = yO2r * 31.999 + yN2r * 28.013 + yCO2r * 44.01 ÷ yH2Or * 18.015 ‘calculate residual gas temperature Cpair = (Cvair(Tabox) + 8.3144) / 28.97 ‘U/kg K Cpres = (Cvres(Tabox) + 8.3144) / mwres ‘kJ!kg K Tres = Texh + (Texh - Tabox) * (mair - matrap) * Cpair / (matrap + mgas + mdsl) / Cpres LOOP UNTIL ABS(yO2old - yO2r) < .0001

Fres = nres / (nres + natrap) mres = mwres * nres rdeliv = mair / (mres + matrap) degp = matrap / (mres + matrap)

PRINT USING “## iterations were required to converge on the residual composition”; iter% PRINT USING “rdeliv = #.## degp = #.## fres = #.## mwres = ##.# “; rdeliv; degp; Fres; mwres PRINT USING “matrap = mres = #.## A; matrap; mres PRINT USING ‘Tres = ### K Texh = ### K Tabox = ### K”; Tres; Texh; Tabox PRINT USING “The mass of fuel burned should reach a maximum of #.##“; 1 - xudsl - xugas INPUT “Press any key to continue... “, cont$

OPEN “c:\wk\brad\chneq\dsl.dat” FOR INPUT AS #1 OPEN “c:\wk\brad\chneq\cng.dat” FOR INPUT AS #2

CALL unburned(ql, q2, q3, q4, q5, 1) CALL gas(ql, q2, q3, 1) IF method = I THEN CALL burned(ql, q2, q3, q4, q5, q6, q7, q8, q9, qlO, ql 1, q12, 1) 143 CALL qwall(ql, q2, q3, q4, q5, q6, 1) ELSE CALL tad(ql, q2, q3, q4, q5, q6, q7, q8, q9, 1) END IF

CLOSE #1 CLOSE #2

IF oputfile$ = “y” OR oputfile$ = “Y” THEN OPEN “c:\wk\brad\out\” + out$ + “.out” FOR OUTPUT AS #1 PRINT #1, CHR$(34); “Output from XMFBAS “+ DATE$ +“ file: “+ pdata$ + “.out”; CHR$(34) PRINT #1, CHR$(34); “Engine is DDC” + engine$; CHR$(34) PRINT #1, PRINT #1, CHR$(34); PRINT #1, USING “####rpm Tres = ### K Texh = ### K Tabox = ### K”; rpm; Tres; Texh; Tabox; PRINT #1, CHR$(34) PRINT #1, CHR$(34); PRINT #1, USING “Number of burned gas zones = # mixratio = #.##“; brndzones%; mixratio; PRINT #1, CHR$(34) PRINT #1, CHR$(34); PRINT #1, USING “Gas velocity/mean piston speed proportionality factor = #.#“; Cl; PRINT #1, Cl-iR$(34) PRINT #1, CHR$(34); PRINT #1, USING “rdeliv = #.## degp = #.## fres = #.## mwres = ##.# “; rdeliv; degp; Fres; mwres; PRINT #1, CHR$(34) PRINT #1, CHR$(34); PRINT #1, USING “diesel combustion is complete when xmf =#.### “; (mdsl/ (mdsl + mgas) - xudsl); PRINT #1, CHR$(34) PRINT #1, PRINT #1, CHR$(34);” CAØ P [kPa] Tu [K] Tbi [K] Tm [K] Tg [K] Tbulk[K1 NOx [ppm] xmf xmu xmm xmd xmg dqwl”; CHR$(34) END IF

Redefine pressure and crank angle arrays such that they span from (BOI÷1)-->359 deg. instead of from PR1-->359 deg. for mass burned fraction analysis. kboi% = (caboi - capri) \ dca + 1 Pboi = Pcyl(kboi%) ca(1) = caboi + dca Pcyl(1) = Pcyl(1 + kboi%) FORi%=2TOnpr%-kboi% ca(i%) = ca(i% 1) + dca Pcyl(i%) = Pcyl(i% + kboi%) NEXTi%

‘Draw mass fraction of burned fuel graph VIEW (100, 190)-(500, 370) PRINT PRINT PRINT PRINT PRINT WINDOW (caboi - 10, ..2)-(caboi + nca% + 10, 1.1) LINE (ca(1), 0)-(ca(nca%), 0), 4 LINE (ca(l), .25)-(ca(nca%), .25), 4 LINE (ca(1), .5)-(ca(nca%), .5), 4

144 LINE (ca(1), .75)-(ca(nca%), .75), 4 LINE (ca(1), 1)-(ca(nca%), 1), 4 LINE (ca(1), 0)-(ca(1), 1), 4 LINE (ca(nca%), 0)-(ca(nca%), 1), 4

‘initialize variables capwd = mdsl / (mdsL+ mgas) * capw ‘approximate dsl pulse width xmf = 0 ‘mass fraction of burned fuel mb = 0 ‘cummulative mass of burned gas mbi = 0 ‘mass of the ith burned gas zone mbilast = 0 ‘mass of the burned gas zone to be mixed in the mixed” zone mbiml = 0 ‘mass of the i-i burned gas zone mbim2 = 0 ‘mass of the i-2 burned gas zone mbim3 = 0 ‘mass of the i-3 burned gas zone mbim4 = 0 ‘mass of the i-4 burned gas zone mbim5 = 0 ‘mass of the i-S burned gas zone mbim6 = 0 ‘mass of the 1-6burned gas zone mm = 0 ‘mass of the mixed zone NOimi =0 NOim2 =0 NOim3 = 0 NOim4 =0 NOimS =0 NOim6 =0 Thimi = 0 Thim2 =0 Thim3 = 0 Tbim4 = 0 ThimS = 0 Tbimó = 0 sbiml =0 sbim2 =0 sbim3 =0 sbim4 = 0 sbim5 =0 sbim6 = 0 NOx =0 ‘AFdsl is the stoichiometric air-fuel ratio for diesel ‘AFgas is the stoichiometric air-fuel ratio for methane AFdsl = 1.45 * wtmol / yO2 / 13.8 / phidsi AFgas = 2 * wtmol / yO2 / 16 / phigas fuel$ = “diesel” fuel% = 0 ‘latch required for tracking previously formed burned gas zones fuelswitch% = 0 ‘stores the increment # when fuel switches from dsl to CNG Vi = Vcyl(ca(i)) asurfi = Acyl(ca(i)) mtot = matrap + mres + (dca / capwd) * mdsl mu = matrap + mres Tu = Pcyl(1) * Vi / Ru! mu CALL unburned(Tu, hu, uu, Cvu, visc, 2) etot = uu * mu etoti = uu * mu Thoi = Tu Vboi = VI Pboi = Pcyl(i) Po = Pcyl(l) P(1) = Pcyl(i)

145 Tfi = 325 ‘injected fuel temperature in K Tg = Tfi CALL gas(Tg, Cpgi, ug, 2) Rg = .51835 ‘gas constant for methane in units U/kg K mwgas = 16.04 ‘molar mass of methane mwdsl = 148.6 ‘molar mass of C10.8H 18.7 mwmixed = 28 ‘approximated molar mass of mixed zone ‘calculate enthalpy of gas and diesel at injection temp ‘enthaply equation for methane integrated from Cp from vW&S pg.652 ‘enthapy equation for diesel from Heywood pg.132 hgas = (-74873 -672.87 * Tfi + 111.246 * Tfi A 1.25 - .449496 * Tfi A 1.75 ÷ 6477.6 * SQR(Tfi)- 39442.3)! mwgas ‘[U/kg] * * A * A * A hdsl = (-3.81 Tfi + .51666 Tfi 2 - 2.0047E-04 Tfi 3 + 3.3816E-08 Tfi 4 - 2167300 / Tfi - 209736)! mwdsl ‘[kJ/kg ud = hdsl Thulk = Tu ‘bulk temperarure of all cylinder contents delmd = (dca! capwd) * mdsl ‘amount of diesel injected over dca md = delmd IF capwd <> capw THEN delmg = (dca / (capw - capwd)) * mgas ‘amount of CNG injected over dca ELSE delmg 0 END IF PSET (ca(1), 0), 11

FOR i% =2 TO nca% Determine the mass of fuel present and its enthalpy IF dca * i% <= capwd THEN md = (dca * i% / capwd) * mdsl - xmf * (mdsl + mgas) mg = 0 mtot = matrap + mres + (dca * i% / capwd) * mdsl Hd = hdsl * delmd Hg = 0 ELSEIF dca * i% > capwd AND dca * i% <= capw THEN IF xmf < (mdsl / (mdsl + mgas) - xudsl) THEN md mdsl - xmf * (mdsl + mgas) mg = ((dca * i% - capwd) / (capw - capwd)) * mgas ELSE md = xudsl * (mgas + mdsl) * * mg = ((dca i% - capwd) / (capw - capwd)) mgas - (xmf * (mdsl + mgas) - mdsL) END IF mtot = matrap + mres + mdsl + ((dca i% - capwd) / (capw - capwd)) * mgas Hd = 0 Hg = hgas * delmg ELSEIF dca * i% > capw THEN IF xmf < (mdsl / (mdsl + mgas) - xudsl) THEN md = mdsl - xmf * (mdsl + mgas) mg = mgas ELSE md = xudsl * (mgas + mdsl) mg = mgas - (xmf * (mdsl + mgas) - mdsl) END IF mtot = matrap + mres ÷ mdsl + mgas Md = 0 Hg = 0 END IF IF mg < xugas * (mgas + mdsl) THEN mg = xugas * (mgas + mdsl) 146 IF md capw AND mg> mgprev THEN mg = mgprev IF dca * (i% - 1) > capw AND md > rndprev THEN rnd = mdprev mgprev = mg ‘used to prevent formation of fuel after mdprev = md ‘xmf has reached its maximum value

mtot = matrap + mres + xmf * (mdsl ÷ rngas) md=O mg=O Hd=0 Hg=O

V2 = Vcyl(ca(i%)) vol=(V2+V1)/2 asurf2 = Acyl(ca(i%)) asurf = (asurf2 + asurfi) I 2 ‘smooth measured cylinder pressure IF xmf> 0 THEN P(i%) = (Pcyl(i% - 1) + Pcyl(i%) + Pcyl(i% + 1)) I 3 ELSE P(i%) = Pcyl(i%) END IF

find unburned zone properties CALL unburned(Tu, hu, uu, Cvu, visc, 3) gu = I + Ru / Cvu ‘isentropic exponent IF method = 1 THEN * * Tu = Tu (1 + (gu - 1) / gu (P(i%) - P(i% - 1)) / P(i% - 1)) + dqwl / (mtot * (Ru + Cvu)) ELSE * * Tu = Tu (1 + (gu - 1)! gu (P(i%) - P(i% - 1))/ P(i% - 1)) END IF IF Tu <300 ThEN Tu = 3(X) vu = Ru * Tu / P(i%) CALL unhurned(Tu, hu, uu, Cvu, visc, 2)

find mixed zone properties IFTm <>0 THEN gm 1.3 ‘approximated isentropic exponent vmprev = 8.3144 I mwmixed * Tm / P(i% - 1) * * Tm = Tm (1 + (gm - 1)/gm (P(i%) - P(i% - 1)) / P(i% - 1)) IF Tm <300 THEN Tm = 300 vm 8.3144 / mwmixed * Tm / P(i%) * urn urn - (P(i%) + P(i% - 1)) / 2 (vm - vrnprev) END IF

find natural gas zone properties IF mg > xugas * (mgas + mdsl) AND Tg> 3(X)THEN IF delrng I mg < I THEN CALL gas(Tg, Cpg, ug, 2) * * Tg = Tg + (delmg / mg (Cpgi + Cpg) / 2 (Tfi - Tg) + Rg * Tg * (P(i%) - P(i% - 1)) / P(i% - 1)) / Cpg vg = 8.3144 * Tg / 16.04 / P(i%) IF Tg> 300 ThEN CALL gas(Tg, Cpg, ug, 3) END IF END IF

update previously formed burned zone properties 147 IF mbiml <>0 THEN IF (i% - fuelswitch%) = 1 THEN fuel$ = ‘diesel CALL table(Thiml, P(i%), h, sbiml, ubimi, vbirnl, dNO, NOimi, q8, 5) NOx = NOx ÷ dNO * vbiml * mbiml * MWexh / (mair + mgas + mdsl) * 10 ‘ 9 END IF IF mbirn2 <> 0 AND brndzones% >= 2 ThEN IF (i% - fuelswitch%) = 2 THEN fuel$ = “diesel” CALL table(Thim2, P(i%), h, sbim2, ubim2, vbim2, dNO, NOim2, q8, 5) NOx = NOx + dNO * vbim2 * mbim2 * MWexh / (mair + mgas + mdsl) * 10 A 9 END IF

IF nibim3 <>0 AND brndzones% >= 3 THEN - IF (i% - fuelswitch%) = 3 THEN fuel$ = “diesel” CALL table(Thim3, P(i%), h, sbim3, ubim3, vbirn3, dNO, NOim3, q8, 5) NOx = NOx + dNO * vbim3 * mbim3 * MWexh / (mair + mgas + mdsl) * 10 A 9 END IF IF mbim4 <> 0 AND brndzones% >= 4 THEN IF (i% - fuelswitch%) = 4 THEN fuel$ = “diesel” CALL table(Thim4, P(i%), h, sbim4, ubim4, vbim4, dNO, NOim4, q8, 5) NOx = NOx + dNO * vbim4 * mbim4 * MWexh / (mair + mgas + mdsl) * 10 A 9 END IF IF mbim5 <>0 AND brndzones% >= 5 THEN IF (i% - fuelswitch%) = 5 THEN fuel$ = “diesel” CALL table(Thim5, P(i%), h, sbim5, ubim5, vbim5, dNO, NOimS, q8, 5) NOx = NOx + dNO * vbim4 * mbim5 * MWexh / (mair + mgas + mdsl) * 10 A 9 END IF IF mbitn6 <> 0 AND brndzones% >= 6 THEN IF (i% - fuelswitch%) = 6 THEN fuel$ = “diesel” CALL table(Tbim6, P(i%), h, sbimó, ubim6, vbim6, dNO, NOimô, q8, 5) NOx = NOx + dNO * vbim6 * mbim6 * MWexh / (mair + mgas + mdsl) * 10 A 9 END IF

calculate work dwrk = (V2 - Vi) * (P(i% - 1) + P(i%)) /2

‘identify the combusting fuel IF mgas = 0 OR xmf < (mdsl / (mdsl + mgas) - xudsl) THEN fuel$ = “diesel” ELSE fuel$ = “gas” END IF

IF method = 1 THEN ‘Calculate heat transfer to cylinder walls IF ca(i%) < 180 THEN polyexp = 1.3 ‘polytropic exponent for motored comp/expansion ELSE polyexp = 1.4 END IF Po = Po * (Vi / V2) A polyexp ‘estimated motored engine P IF Po> P(i%) THEN Po = P(i%) CALL qwall(Thulk, P(i%), Po, vol, asurf, dqwl, 2)

cylinder energy balance etot etot - dwrk + dqwl + 1-Id+ Hg

prepare for burned gas properties iteration

148 * * * * vc = (V2 - mg (vg - vu) + md vu - mbiml (vbiml - vu) - mbim2 (vbim2 - vu) - rnbim3 * (vbim3 - * * * * vu) - mbim4 (vbim4 - vu) - mbim5 (vbim5 - vu) - mbim6 (vbim6 - vu) - mm (vm - vu)) / mtot * * * * uc = (etot - mg (ug - uu) - md (ud - uu) - mbiml (ubimi - uu) - mbim2 (ubim2 - uu) - mbim3 * * * * (ubim3 - uu) - mbim4 (ubim4 - uu) - mbim5 (ubim5 - uu) - mbim6 (ubirn6 - uu) - mm * (urn - uu)) / mtot CALL burned(P(i%), Thi, vu, vc, vbi, uu, uc, ubi, sbi, xmbi, dNO, NOe, 2) mbi = xmbi * mtot ‘mass of the ith burned gas zone IF mbi <0 AND xmf <= 0 ThEN mbi =0 ELSE

calculate the adiabatic flame temperature CALL tad(P(i%), Thi, vu, vbi, hu, ubi, sbi, dNO, NOe, 2)

cylinder energy balance * etot2 md ud + mg * ug + mu * uu + mm * urn + mbi * ubi + mbiml * ubimi + mbim2 * ubim2 + mbim3 * ubim3 + rnbim4 * ubim4 ÷ mbim5 * ubim5 + mbim6 * ubim6 dqwl = etot2 - etoti + dwrk - lid - Hg

‘mass of the ith burned gas zone * * * * mbi = (V2 - rntot vu - rng (vg - vu) + md vu - rnbiml (vbiml - vu) - mbim2 * (vbim2 - vu) - * * * * mbim3 (vbim3 - vu) - mbim4 (vbim4 - vu) - rnbim5 (vbim5 - vu) - rnbim6 (vbim6 - vu) - mm * (vm - vu)) / (vbi - vu)

END IF

mb mb + mbi ‘total cummulative mass of burned gas

‘Calculate the mass fraction of fuel burned IF mgas = 0 OR mb < (indsi - (mdsl + mgas) * xudsl) * (1 + AFdsl) THEN xmf = mb I (mdsl + mgas) / (1 + AFdsl) ELSE xmf = (mb + (mdsl - (mdsL + mgas) * xudsl) * (Afgas - AFdsl)) / (mdsl + mgas) / (1 + AFgas) EN]) IF

NOi = dNO NOx = NOx + dNO * vbi * mbi * MWexh /(mair + mgas + mdsl) * 10” 9

mu = mtot - md - mg - mbi - mbiml - mbim2 mbim3 - mbim4 - mbim5 - mbim6 - mm Thulk = (mbi * Thi + mbiml * Thiml + mbim2 * Thim2 + mhim3 * Thim3 + mbim4 * Thim4 + mbim5 * Thim5 + mbim6 * Thim6 + mg * Tg + md * Tfi + mu * Tu + mm * Tm) / rntot

PRINT USING “###ø P=####kPa Tu=####K Thi=####K Tg=####K NOx=###ppm xmm=#.## xmf=#.##”; ca(i%); Pcyl(i%); Tu; Tbi; Tg; NOx; mm / mtot; xmf PRINT USING “###ø P=####kPa Thi=####K Thinil=####K Thim2=##K NOx=I##hIppm xmf=#.##”; ca(i%); Pcyl(i%); Thi; Thimi; Thim2; NOx; xmf PRINT USING “xmu=#.### xmm=#.### xmb=#.### xmg=#.### xmd=#.### sum=#.##’; mu / mtot; mm / mtot; (mbi + mbiml + mbim2 ÷ mbim3 + rnbim4) / mtot; mg / mtot; md / rntot; (mu ÷ mm + mbi + mbiml + mbim2 + mbim3 + mbim4 + mg + md) / mtot IF oputfile$ = “y” OR oputfile$ = “1” THEN PRINT #1, USING” ### #### #### #### #### #### #### #### #.## #.## #.## #.## ### ##““; ca(i%); Pcyl(i%); Tu; Thi; Tm; Tg; Thulk; NOx; xmf; mu / mtot; mm / mtot; md I mtot; mg / — mtot; dqwl END IF IF dca * i% C1NT(capw) ThEN LINE -(ca(i%), xmt), 14 ELSEIF fuelS = “gas” THEN LINE -(ca(i%), xmf, 10 149 ELSE LINE -(ca(i%), xmf), 11 END IF

IF fuel$ = gas” AND fuel% = 0 THEN ‘set latch fuel% = 1 fuelswitch% = i% END IF

Calculate the properties of the mixed zone after mixing Adiabatic, constant pressure mixing in the mixed zone Aapproximate the mixed zone temperature using a mass averaged value IF brndzones% = 1 THEN mbilast = mbiml ubilast = ubimi vbilast = vbiml Tbilast = Thimi ELSEIF brndzones% = 2 THEN mbilast = mbim2 ubilast = ubini2 vbilast = vbim2 Thilast = Thim2 ELSEIF brndzones% = 3 THEN mbilast = mbim3 ubilast = ubirn3 vbilast = vbim3 Thilast = Thim3 ELSElF brndzones% =4 THEN mbilast = mbim4 ubilast ubim4 vbilast = vbim4 Thilast Thirn4 ELSEIF brndzones% = 5 ThEN mbilast = mbim5 ubilast = ubim5 vbilast = vbim5 Thilast = Thim5 ELSElF brndzones% =6 THEN mbilast = mbimó ubilast = ubim6 vbilast = vbim6 Thilast = Thim6 END IF mui = mixratio * mbilast ‘mui is the mass of unburned zone that mixes with last burned zone IF mu <= 0 THEN mui = 0 IFmui > mu THEN mui =mu IF rnbilast <>0 OR miii <> 0 OR mm <> 0 THEN hm = um + P(i%) * vm hb = ubilast + P(i%) * vbilast Tm = (Thilast * mbilast + Tu * mui + Tm * mm) / (mbilast + mui + mm) urn = (hb * mbilast + hu * mui + hm * mm) / (mbilast + mui + mm) - 8.3144 / mwmixed * Tm END IF mm = mm + mbilast + mui

prepare for next step Vi = V2 150 etoti = etot2 IF brndzones% = 6 THEN mbimô = mbim5 Thim6 = ThimS sbim6 sbim5 NOim6 = NOim5 END IF IF brndzones% >= 5 THEN mbim5 = mbim4 Thim5 = Thim4 sbim5 = sbim4 NOim5 = NOim4 END IF IF brndzones% >= 4 THEN mbim4 = mbim3 Thim4 = Thim3 sbim4 = sbim3 NOim4 = NOim3 END IF IF brndzones% >= 3 THEN mbim3 = mbim2 Thim3 = Thim2 sbim3 = sbim2 NOim3 = NOim2 END IF IF brndzones% >= 2 THEN mbim2 = mbiml Thim2 = Thimi sbim2 = sbiml NOirn2 = NOimi END IF mbiml mbi Thirni = Thi sbimL = sbi NOimi NOi NEXT i% PRINT “Cl = “; Cl. CLOSE #1 END

FUNCTION Acyl (Ca) Calculates the cylinder surface area for a given degree ca pi# = 3.14159265359# Apisten = (pi# / 4) * bore “2 car = ca * pi#/ 18() z = rod + (stroke / 2) * (1 + COS(car)) - SQR((rod) “2 - ((stroke / 2) * SIN(car)) “2) Acyl = z * pi# * bore + 2.5 * Apiston END FUNCTION

SUB burned (P, Th, vu, vc, vb, uu, uc, ub, sb, xmbi, dNO, NOe, 1%)STATIC SHARED fuel$ IF1%= 1 THEN CALL table(ql, q2, q3, q4, q5, q6, q7, q8, q9, 1) xmbi = 0 END IF IF 1% =2 THEN Find the linear relationship between ub and vh at the flame front

151 a = (vc vu) / (uc - uu) b = vu - a * uu ‘Iterate to find Tb, ub, and vb. TIow = 1500 Tint = 200 iter% = 0 found$ ‘false rangeS = “okay” DO iter% = iter% + I Tup = Tiow + Tint CALL table(Tlow, P, hhl, sbl, ubl, vbl, dNOl, 0, NOel, 3) CALL table(Tup, P. hbu, sbu, ubu, vbu, dNOu, 0, NOeu, 3) yl = vbl - (a * ubi + b) yu=vbu-(a * ubu+h) IFyl=OTHEN found$ = “true’ Tb = Tlow ELSEIFyu=OTHEN found$ = “true” Tb = Tup ELSEIF yl * yu < 0 THEN Tint = Tint / 10 IFTint <2 THEN found$ = “true” Tb = (Tiow + Tup) / 2 END IF ELSE Tow = Tup END IF IF Tiow = 2900 THEN range$ “exceeded” LOOP UNTIL found$ “true” OR range$ = “exceeded” IF vb <> vu AND range$ = “okay” THEN CALL table(Th, P, hb, sb, ub, vb, dNO, 0, NOe, 4) xmbi = (vc - vu) / (vb - vu) ELSE xrnbi = 0 dNO =0 END IF END IF EN]) SUB

SUBcubics(np%,xO,yO,xset,ycaic) np% is the number of x,y data pairs DIM d(10), e(10), f(10), g(I0) = np% - 1 mm% = np% - 2 CALCULATION OF SECOND DERIVATIVES g(i%) g(1) = 0 g(np%) = 0 FOR i% =2 TO m% d(i%) = x(i%) - x(i% - 1) * e(i%)= 2 (x(i% + 1) - x(i% - 1)) f(i%) = x(i% + 1) - x(i%) * g(i%) = 6 / f(i%) (y(i% + 1) - y(i%))+ 6 / d(i%) * (y(i%- 1) - y(i%)) NEXT i% FORi%=2TOmm% 152 fa d(i% + 1) / e(i%) e(i% + 1) = e(i% + 1) - Ia * f(i%) g(i% + 1) = g(i% + 1) - fa * g(i%) NEXT 1% FOR i% =2 TO rn% * g(np% + 1 - i%) = (g(np% + 1 - i%) - f(np% + 1 - i%) g(np% + 2 - i%)) / e(np% + 1 - i%) NEXT i% CALCULATION OF INTERPOLATED VALUE ycaic AT x=xset d(np%) = x(np%) - x(np% - 1) i% = 1 DO i% = i% + 1 LOOP WHILE (xset >= x(i%)) AND (i% < np%) deim = xset - x(i% - 1) deip = x(i%) - xset * ‘ * ycaic = g(i% - 1)! 6 / d(i%) deip 3 + g(i%) / 6/ d(i%) delrn” 3 + (y(i% - 1)! d(i%) - g(i% - 1) * d(i%) / 6) * deip + (y(i%) / d(i%) - g(i%) * d(i%) / 6) * deim EN]) SUB

FUNCTION Cvair (Tair) ‘Cvair has units kJ/kmol K Tdiin = Tair / 100 Tdim2 Tdim * Tdim Tdim3 = Tdim2 * Tdim Tdim32 = Tdim 1.5 Cp02 = 37.432 + .020102 * Tdim32 - 178.57 / Tdirn32 + 236.88 / Tdim2 CpN2 = 39.06 - 512.79 / Tdim32 + 1072.7 / Tdim2 - 820.4 / Tdirn3 Cvair = .21 * Cp02 + .79 * CpN2 - 8.3144 END FUNCTION

FUNCTION Cvres (Tres) STATIC ‘Cvres has units kJ/kmol K Tdim = Tres / 100 Tdimsq = SQR(Tdim) Tdim2 = Tdim * Tdim Tdirn3 =Tdim2*Tdim Tdiml4 = Tdim .25 Tdirn32 = Tdim” 1.5 Cp02 = 37.432 + .020102 * Tdim32 - 178.57 / Tdim32 + 236.88 / Tdim2 CpN2 = 39.06 - 512.79 / Tdim32 + 1072.7 / Tdim2 - 820.4 / Tdirn3 * * * CpH2O = 143.05 - 183.54 TcIirnl4 + 82.75 1 Tdimsq - 3.6989 Tdim CpCO2 = -3.7357 + 30.529 * Tdimsq - 4.1034 * Tdim + .024198 * Tdirn2 * * Cvres = yO2r Cp02 + yN2r CpN2 + yCO2r * CpCO2 + yH2Or * CpH2O - 8.3144 END FUNCTION

SUB gas (Tg, Cpg, ug, 1%) STATIC 1% = 1---> INITIALIZE SUBROUTINE 1% =2---> CALCULATE SPECIFIC HEAT U/kg K 1%=3---> CALCULATE INTERNAL ENERGY kJ/kg

IF 1% = I THEN mwCH4 = 16.04 hfCH4 = -74873 ELSE Tdim=Tg/100 Tdimsq = SQR(Tdim) Tdiml4 = Tdim” .25

153 Tdim54 = Tdim 125 Tdim74 = Tdim” 1.75 Tdim34 = Tdim ‘ .75 END IF IF 1% = 2 THEN Cpg = (-672.87 + 439.74 * Tdiml4 - 24.875 * Tdim34 + 323.88 / Tdimsq) / mwCH4 ELSEIF 1% = 3 THEN * * * dhCFI4 = -67287 Tdim + 35179.2 Tdim54 - 1421.43 Tdim74 + 64776 * Tdimsq - 39442.3 ug = (hfCH4 + dhCH4 - 8.3144 * Tg) / mwCH4 END IF END SUB

SUB qwall (Thulk, P. Po, vol, asurf, dqwl, 1%)STATIC Calculates the heat transfer from the gas to the cylinder wall SHARED a, dca, rpm, Thoi, Vboi, Pboi, Cl, C2 IF1%= 1THEN dqwl = 0 INPUT “Enter gas velocity/mean piston speed proportionality factor: ‘, Cl C2 = Cl / 700 ‘gas velocity/combustion intensity proportionality factor pi# = 3.14159265359# pisvel = rpm * stroke / 30 ‘mean piston speed ELSEIF 1%=2 THEN * gasvel = c pisvel + C2 * vol * Tboi / Pboi / Vboi * (P - Po) dens = mtot / vol CALL unburned(Tbulk, ho, uu, Cvu, visc, 4) Renum = dens * gasvel * bore / visc CALL unburned(Thulk, hu, uu, Cvu, visc, 3) Cpg = Cvu + Ru thcond Cpg * visc / .7 Tw = 450 ‘The wall temperature (K) is assumed to be constant * dqwl = asurf thcond / bore * Renum (.8) * (Tw - Thulk) Convert from kW to kJ dqwl = dqwl * 60 * dca / (rpm * 360) END IF END SUB

SUB table (Thx, Pbx, hbx, sbx, ubx, vbx, dNO, NO, NOe, 1%)STATIC 1% = 1 ---> INITIALIZATION 1%=2 ---> FIND BURNED GAS ENTHALPY GIVEN P AND Th 1% = 3 ---> FIND BURNED GAS PROPERTIES GIVEN P AND Th (excludes NO calculation for more efficient iterating) 1%=4 ---> FIND BURNED GAS PROPERTIES GIVEN P AND Th (includes NO calculation) 1%=5 ---> FIND BURNED GAS PROPERTIES GIVEN P AND sb (includes NO calculation)

SHARED fuel$ DIM Ptab(10), Tbtab(10), amdtab(10, 10), amgtab(i0, 10) DIM ubdtab(10, 10), sbdtab(10, 10), ubgtab(10, 10), sbgtab(10, 10) DIM cN2dtab(10, 10), cO2dtab(10, 10), cOHdtab(10, 10) DIM cN2gtab(10, 10), cO2gtab(10, 10), cOllgtab(10, 10) DIM cNOdtab(10, 10), cNOgtab(10, 10), hbdtab(10, 10), hbgtab(10, 10) DIM ya(10), yu(10), ys(10), ycN2(10), yCO2(10), ycOH(10), ycNO(10) DIM amp(l0), up(10), sp(10), N2p(10), O2p(lO), OHp(10), NOp(I0) IF 1% = I THEN Pstore = -10(X) Read tables of burned gas properties resulting from 154 stoichiometric combustion of diesel or natural gas with air. suffix “g” --> burned gas properties for NG combustion suffix “d” --> burned gas properties for dsl combustion FORj% = 1 TO 10 FOR i% = 1 TO 10 INPUT #1, Thtab(i%), P, amdtab(i%, j%),vbd, ubd, hbd, sbd, yOl-ldtab, yNOdtab, yN2dtab, yO2dtab INPUT #2, Thtab(i%), P, amgtab(i%, j%),vbg, ubg, hbg, sbg, yOHgtab, yNOgtab, yN2gtab, yO2gtab ‘convert from J/kg to KJ/kg for h and u ‘convert from J/kg K to KJ/kg K for s ubdtab(i%,j%) = ubd * .001 hbdtab(i%, j%)= hbd * sbdtab(i%, j%) sbd * ubgtab(i%, j%)= ubg * hbgtab(i%,j%) = hbg * .001 sbgtab(i%,j%) = sbg * ‘convert equilibrium mole fractions to equilibrium concentrations in units mole/cin”3 cN2dtab(i%, j%)= yN2dtab / vbd / amdtab(i%, j%)/ 1000 cO2dtab(i%, j%)= yO2dtab / vbd / amdtab(i%, j%)/ 1000 cOHdtab(i%, j%)= yOHdtab / vhd / amdtab(i%, j%)I 1000 cNOdtab(i%, j%)= yNOdtab / vbd / arndtab(i%, j%)I 1000 cN2gtab(i%, j%)= yN2gtab / vbg / amgtab(i%, j%)/ 100() cO2gtab(i%, j%)= yO2gtab I vbg / amgtab(i%, j%)/ 1000 cOHgtab(i%, j%)= yOHgtah / vbg / amgtab(i%, j%)/ 1000 cNOgtab(i%, j%)= yNOgiab / vbg / amgtab(i%, j%)/ 1000 NEXT i% Ptab(j%) = P * 101.325 ‘pressure converted from atm to kPa NEXTj% ELSE! F Pbx <> Pstore ThEN Pstore = Pbx FOR i% = 1 TO 10 IF fuel$ = “diesel” THEN FORj% = ITO 10 yu(j%) = ubdtab(i%, j%) yh(j%) = hbdtab(i%, j%) ys(j%) sbdtab(i%, j%) ya(j%) = amdtab(i%, j%) ycN2(j%) = cN2dtab(i%, j%) yCO2(j%) = cO2dtab(i%, j%) ycOH(j%) = cOHdtab(i%, j%) ycNO(j%) = cNOdtab(i%,j%) NEXT j% ELSE FORj% = 1 TO 10 yu(j%) = ubgtab(i%, j%) yh(,j%) = hbgtab(i%, j%) ys(j%) = sbgtab(i%, j%) ya(j%) = amgtab(i%, j%) ycN2(j%) = cN2gtab(i%, j%) yCO2(j%) = cO2gtab(i%,j%) ycOH(j%) = cOHgtab(i%, j%) ycNO(j%) = cNOgtab(i%, j%) NEXT j% END IF

155 CALL cubics(1O, PtabO, yuO, Pbx, up(i%)) CALL cubics(10, PtabO, yhO, Pbx, hp(i%)) CALL cubics(1O, PtabO, ysO, Pbx, sp(i%)) CALL cubics(10, PtabO, yaO, Pbx, amp(i%)) CALL cubics(10, PtabO, ycN2O, Pbx, N2p(i%)) CALL cubics(1O, PtabO, yCO2O, Pbx, 02p(i%)) CALL cubics(10, PtabO, ycOHO, Pbx, OHp(i%)) CALL cubics(1O, PtabO, ycNOO, Pbx, NOp(i%)) NEXT i% END IF IF 1%=2 THEN CALL cubics(10, ThtabO, hpO, Tbx, hbx) ELSEIF 1% = 3 THEN CALL cubics(10, ThtabO, upO, Thx, ubx) CALL cubics(10, ThtabO, spO, Thx, sbx) CALL cubics(10, ThtabO, ampO, Thx, amx) vbx=8.3144/amx *Thx/Pbx ELSEIF 1%=4 THEN CALL cubics(10, ThtabO, upO, Thx, ubx) CALL cubics(10, TbtabO, spO, Tbx, sbx) CALL cubics(10, ThtabO, ampO, Thx, amx) vbx= 8.3144/amx * Thx/Pbx ‘N2e, 02e, OHe, and NOe are equilibrium ‘concentrations in mol/cmA3 CALL cubics(10, ThtabO, N2p0, Tbx, N2e) CALL cubics(10, ThtabO, 2p0. Thx, 02e) CALL cubics(10, ThtabO, OHpO,° Thx, OHe) CALL cubics(10, ThtabO, NOpO, Thx, NOe) ‘calculate the change in NO concentration over one time step dNO = (6E+16) / SQR(Thx) * EXP(-69090 / Thx) * SQR(02e) * N2e * ((1 - NO “ 2 / 20.267 / EXP( 21650 / Thx) I 02e / N2e) / (1 + NO / (.0004 * Thx * EXP(-3150 / Thx) * 02e + 2.5625 * ORe))) * dt ‘dNO and NOe are in units mol/cm”3 ELSEIF 1%=5 THEN CALL cubics(10, spa, ThtabO, sbx, Thx) CALL cubics(10, spO, upO, sbx, ubx) CALL cubics(10, spO, ampO, sbx, amx) vbx=8.3144/amx *Thx/Pbx IFThx> 1200THEN ‘N2e, O2e, OHe, and NOe are equilibrium concentrations in mol/cm”3 CALL cubics(10, spO, N2p0, sbx, N2e) CALL cubics(10, spO, 2Op0, sbx, 02e) CALL cubics(10, spO, OHpO, sbx, OHe) ‘calculate the change in NO concentration over one time step dNO = (6E+16) I SQR(Tbx) * EXP(-69090 / Thx) * SQR(02e) * N2e * ((1 - NO “2! 20.267 / EXP(-21650 I Thx) / 02e/ N2e)/ (1 + NO /(.0004 * Thx * EXP(-3 150 / Thx) * 02e + 2.5625 * OHe))) * dt dNO is in units mol/cm”3 END IF END IF EN]) SUB

SUB tad (P. Tb, vu, vb, hu, ub, sb, dNO, NOe, 1%)STATIC SHARED fuel$, hdsl, hgas, phidsi, phigas IF1%= 1 THEN CALL table(ql, q2, q3, q4, q5, q6, q7, q8, q9, 1) END IF IF 1% = 2 THEN 156 IF fuel$ = ‘diesel’ THEN mwfuel = 14 hfuel = hdsl n=2 Hreact = (hfuel * mwfuel ÷ 1w * (1 + n / 4)! yO2 / phidsi * wtmol) / (mwfuel + wtmol * (1 + n / 4) /yO2) ‘[kJ/kgJ ELSE mwfuel = 16 hfuel = hgas n=4 Hreact = (hfuel * mwfuel + hu * (1 + n / 4)! yO2 / phigas * wtmol) / (mwfuel + wtmol * (1 + ii / 4) IyO2) ‘[kJ/kgj

END IF Tb = 2900 Tint = 200 iter% = 0 found$ = “false” range$ = “okay” DO iter% = iter% + 1 CALL table(Th, P, hb, sb, ub, vb, dNO, 0, NOe, 2) IF hb = Hreact THEN found$ = “true” ELSEIF hb < Hreact THEN IFTint> 1 THEN Th = Th + Tint Tint = Tint / 10 ELSE found$ = “true” END IF ELSE Th = Th - Tint END IF IF Th <= 1300 OR Tb> 3100 THEN range$ = “exceeded” LOOP UNTIL found$ = “true” OR range$ = “exceeded” IF range$ = “okay” THEN CALL table(Th, P, hb, sb, ub, vb, dNO, 0, NOe, 4) ELSE PRINT “*** RANGE EXCEEDED IN FLAME TEMP CALC “ END IF END IF END SUB

SUB unburned (Tu, hu, uu, Cvu, visc, 1%)STATIC 1%= 1 ---> IMTIALIZE SUBROUTINE 1%=2---> CALCULATE ENTHALPY AND INTERNAL ENERGY l%=3---> CALCULATE Cv 1%=4---> CALCULATE VISCOSITY

IF 1%= 1 THEN ‘molar mass mwO2 = 31.999 mwN2 = 28.013 mwH2O = 18.015 mwCO2 = 44.011 enthalpy of formation [kJ/kmol] 157 hfO2 = 0 hfN2 = 0 hfH2O = -241827 hfCO2 = -393522

n02 = yO2r * nres + .21 * natrap nN2 = yN2r * nres + .79 * natrap nCO2 = yCO2r * nres nH2O = yH2Or * nres denorn = n02 + nN2 + nCO2 + nH2O y02 = n02 / denom yN2 = nN2 / denom yCO2 nCO2 / denom yH2O = nH2O I denom * * * * wtmol = yO2 mwO2 + yN2 rnwN2 + yCO2 mwCO2 + y112() mwH2O Ru = 8.3144 I wtmol ELSE Tdim=Tu/100 Tdimsq = SQR(Tdim) Tdim2 = Tdim * Tdim Tdim3 = Tdim2 * Tdim Tdim4 = Tdim3 * Tdim Tdiml4 = Tdim A .25 Tdim54 = Tdim” 1.25 Tdim74 = Tdim A 1.75 Tdim32 = Tdim” 1.5 Tdim52 = Tdim 2.5 Tdim34 = Tdim A 75 END IF

IF 1% = 2 THEN ‘Calculate molar enthalpy differences between 298K and Tu, then calculate the internal energy uu jki/kgj dhO2 = 3743.2 * Tdim + .80408 * Tdim52 + 35714 / Tdimsq - 23688 / Tdim - 23911 dhN2 = 3906 * Tdim + 102558 / Tdirnsq - 107270 / Tdim + 41020 / Tdim2 - 39677 dhH2O = 14305 * Tdim - 14683.2 * Tdim54 + 5516.73 * Tdirn32 - 184.95 * Tdim2 - 11881.33 dhCO2 = -373.57 * Tdim + 2035.27 * Tdirn32 - 205.17 * Tdim2 + .8066 * Tdim3 - 7561.65 * * * * hu = (yO2(hfO2 + dhO2) + yN2 (hfN2 + dhN2) + yH2O (hfH2O + dhH2O) + yCO2 (hfCO2 + dhCO2)) / wtmol uu = hu - 8.3144 * Tu / wtmol ELSEIF 1%=3 ThEN ‘Calculate specific heat Cvu [U/kg KI Cp02 = 37.432 + .020102 * Tdim32 - 178.57 / Tdim32 + 236.88 / Tdim2 CpN2 = 39.06 - 512.79 / Tdim32 + 1072.7 / Tdim2 - 820.4 / Tdim3 CpH2O = 143.05 - 183.54 * Tdiml4 + 82.751 * Tdimsq - 3.6989 * Tdim CpCO2 = -3.7357 + 30.529 * Tdimsq - 4.1034 * Tdim + .024198 * Tdim2 * * * * Cvu = (yO2 Cp02 + yN2 CpN2 + yCO2 CpCO2 + yFl2O CpH2O - 8.3144) / wtrnol ELSEIF 1%=4 THEN ‘Estimate the mean viscosity of gas mixtures Tn = Tu A .645 * * * * * * * * visc = (yO2 mwO2 5.09 + yN2 mwN2 4.57 + yH2O mwH2O 3.26 + yCO2 mwCO2 3.71) / wtmol * 10 A (7) * Tn EN]) IF END SUB

FUNCTION Vcyl (ca) ‘ca is crank angle degrees ABDC. Vcyl(m**3). 158 pi# = 3.14159265359# car= ca* pi#/180 * * * Vcyl = pi# ((bore / 2) “ 2) (rod + (stroke / 2) (1 + COS(car)) - SQR(rod “ 2 - ((stroke / 2) * SIN(car)) 2)) + Vclr END FUNCTION

159