A Numerical Investigation of a Two-Stroke Poppet-Valved Diesel Engine Concept

A NUMERICAL INVESTIGATION OF A TWO-STROKE POPPET-VALVED DIESEL ENGINE CONCEPT

Philip Robert Teakle BE MEngSc

Tribology and Materials Technology Group Mechanical, Manufacturing and Medical Engineering Queensland University of Technology

Submitted for the degree of Doctor of Philosophy 2004

Keywords Two-stroke, poppet valves, KIVA, thermodynamic modelling, zero-dimensional modelling, multidimensional modelling, engine modelling, scavenging models, scavenging simulations.

Executive Summary Two-stroke poppet-valved engines may combine the high power density of two - stroke engines and the low emissions of poppet-valved engines. A two-stroke diesel engine can generate the same power as a four-stroke engine of the same size, but at higher (leaner) air/fuel ratios. Diesel combustion at high air/fuel ratios generally means hydrocarbons, soot and carbon monoxide are oxidised more completely to water and carbon dioxide in the cylinder, and the opportunity to increase the rate of exhaust gas recirculation should reduce the formation of nitrogen oxides (NOx). The concept is being explored as a means of economically modifying diesel engines to make them cleaner and/or more powerful.

This study details the application of two computational models to this problem. The first model is a relatively simple thermodynamic model created by the author capable of rapidly estimating the behaviour of entire engine systems. It was used to estimate near-optimum engine system parameters at single engine operating points and over a six-mode engine cycle. The second model is a detailed CFD model called KIVA- ERC. It is a hybrid of the KIVA engine modelling package developed at the Los Alamos National Laboratory and combustion and emissions subroutines developed at the University of Wisconsin-Madison Engine Research Center. It was used for detailed scavenging and combustion simulations and to provide estimates of emissions levels. Both models were calibrated and validated for four-stroke cycle operation using experimental data. The thermodynamic model was used to provide initial and boundary conditions to the KIVA-ERC model. Conversely, the combustion simulations were used to adjust zero-dimensional combustion correlations when experimental data was not available. vi

Scavenging simulations were performed with shrouded and unshrouded intake valves. A new two-zone scavenging model was proposed and validated using multidimensional scavenging simulations.

A method for predicting the behaviour of the two-stroke engine system based on four-stroke data has been proposed. The results using this method indicate that a four-stroke diesel engine with minor modifications can be converted to a two-stroke cycle and achieve substantially the same fuel efficiency as the original engine. However, emissions levels can not be predicted accurately without experimental data from a physical prototype. It is therefore recommended that such a prototype be constructed, based on design parameters obtained from the numerical models used in this study. vii

Table of Contents

Keywords ...... v

Executive Summary ...... v

Table of Contents ...... vii

List of Figures...... x

List of Tables ...... xvi

Nomenclature ...... xix

Statement of Original Authorship ...... xx

Acknowledgements...... xxi

Chapter 1 - Introduction...... 1

1.1 BACKGROUND...... 1 1.1.1 Two-stroke poppet-valved engines...... 1 1.1.2 Outline of previous investigations ...... 3 1.2 ROTEC ENGINE CONCEPT...... 4 1.3 OBJECTIVES ...... 7 1.4 OUTLINE OF STUDY ...... 9 1.5 ORIGINAL CONTRIBUTIONS...... 10

Chapter 2 - Literature Review ...... 11

2.1 INTRODUCTION ...... 11 2.2 OVERVIEW OF TWO-STROKE POPPET-VALVED ENGINE STUDIES ...... 11 2.2.1 Motives for study ...... 11 2.2.2 Description of prototypes/models ...... 14 2.2.3 Simulation techniques...... 27 2.2.4 U-loop scavenging...... 29 2.2.5 Prototype performance ...... 36 2.2.6 Two-Stroke Poppet-Valved Diesel Emissions...... 41 2.2.7 Summary...... 41 2.3 OVERVIEW OF DIESEL ENGINE EMISSIONS ...... 42 2.3.1 Diesel emissions formation...... 42 2.3.2 Emissions regulations...... 44 2.3.3 Emissions control strategies ...... 46 2.4 SCAVENGING ...... 49 2.4.1 Fundamentals ...... 49 2.4.2 Scavenge pumps...... 50 2.5 ENGINE MODELLING...... 56 2.5.1 Thermodynamic modelling ...... 56 viii

2.5.2 One-dimensional modelling...... 57 2.5.3 Multidimensional modelling ...... 57 2.6 DISCUSSION ...... 58

Chapter 3 - Thermodynamic model development...... 60

3.1 REQUIREMENTS ...... 60 3.2 DESCRIPTION ...... 62 3.2.1 Basic assumptions ...... 62 3.2.2 Numerical solver ...... 66 3.2.3 Gas properties ...... 68 3.2.4 Heat transfer...... 74 3.2.5 Gas flow through valves and orifices ...... 75 3.2.6 Scavenging...... 77 3.2.7 Combustion...... 79 3.2.8 Turbocharging...... 101 3.2.9 Charge air cooling ...... 104 3.2.10 Mechanical friction...... 107 3.2.11 Automated parametric investigation...... 108 3.3 VALIDATION ...... 110 3.3.1 Caterpillar SCOTE data...... 110 3.3.2 Caterpillar 3406E data...... 117 3.4 DISCUSSION ...... 120

Chapter 4 - KIVA-ERC multidimensional model adaptation...... 123

4.1.1 KIVA package overview...... 123 4.2 ERC SPRAY AND COMBUSTION MODEL LIBRARY ...... 124 4.2.1 Turbulence...... 125 4.2.2 Heat transfer...... 125 4.2.3 Atomisation and drop drag...... 126 4.2.4 Fuel/wall impingement ...... 129 4.2.5 Ignition ...... 130 4.2.6 Combustion...... 130

4.2.7 NOx formation...... 132 4.2.8 Soot...... 132 4.2.9 Computational meshes...... 134 4.3 VALIDATION ...... 136 4.4 DISCUSSION ...... 142

Chapter 5 - Results...... 144

5.1 SCAVENGING SIMULATIONS ...... 144 5.1.1 Shroud geometry...... 144 ix

5.1.2 Initial and boundary conditions...... 147 5.1.3 Scavenging flow...... 149 5.1.4 Valve flow ...... 156 5.2 O-D SCAVENGING MODEL ...... 160 5.2.1 Description ...... 160 5.2.2 Comparison with KIVA-ERC calculations...... 164 5.3 SYSTEM SIMULATIONS ...... 177 5.3.1 Revision of combustion correlation constants ...... 177 5.3.2 Two-stroke adaptation of Caterpillar SCOTE...... 181 5.3.3 Addition of Reciprocating Air Pump...... 187 5.3.4 Addition of turbocharger ...... 193

Chapter 6 - Discussion ...... 199

6.1 THERMODYNAMIC MODEL PERFORMANCE ...... 199 6.1.1 Speed...... 199 6.1.2 Flexibility...... 201 6.1.3 Accuracy ...... 201 6.2 SCAVENGING OF TWO-STROKE POPPET-VALVED ENGINES...... 204 6.3 PERFORMANCE OF TWO-STROKE POPPET-VALVED ENGINES ...... 206 6.3.1 Numerical modelling procedure ...... 206 6.3.2 System simulation results...... 209

Chapter 7 - Conclusions and Further Work...... 212

7.1 SUMMARY...... 212 7.2 CONCLUSIONS...... 212 7.3 FURTHER WORK ...... 214 7.3.1 Improvements to the thermodynamic model ...... 214 7.3.2 Improvements to multidimensional modelling ...... 215 7.3.3 Two-zone scavenging model ...... 215 7.3.4 Further system studies ...... 215

References...... 217 x

List of Figures Figure 1-1: Two-stroke poppet-valved engine cycle...... 2 Figure 1-2: Common scavenging arrangements...... 3 Figure 1-3: Schematic of Rotec engine prototype. Cylinders may not be in this order in a practical engine block due to balancing considerations...... 5 Figure 1-4: Intake valve shroud...... 5 Figure 2-1: Toyota S-2 petrol-fuelled prototype (left) and cylinder detail (right) (Nomura and Nakamura, 1993)...... 15 Figure 2-2: Toyota S-2D diesel-fuelled prototype (left) and details of the cylinder head (right) (Nomura and Nakamura, 1993)...... 15 Figure 2-3: Ricardo "Flagship" engine prototype (Hundleby, 1990)...... 17 Figure 2-4: Shibaura/Honda water scavenging rig (Nakano et al., 1990)...... 19 Figure 2-5: Shibaura/Honda petrol engine prototype (left) with intake port section showing mask detail (right) (Nakano et al., 1990)...... 19 Figure 2-6: Computational mesh of Huh et al. (1993)...... 21 Figure 2-7: Water flow visualisation rig (left) and port layout (right) (Kang et al., 1996)...... 22 Figure 2-8: Cylinder cross-sections and injector location and orientation in the Loughborough study (Das and Dent, 1993)...... 24 Figure 2-9: Suzuki prototype cylinder head (Morita and Inoue, 1996)...... 25 Figure 2-10: Some valve arrangements investigated by Yang et al. (1999)...... 26 Figure 2-11: Toyota S-2 Petrol-Fuelled Engine Scavenging (Nomura and Nakamura, 1993)...... 31 Figure 2-12: Reported S-2 scavenging performance (Nomura and Nakamura, 1993)...... 31 Figure 2-13: Scavenging measurements of Sato et al. (1992)...... 32 Figure 2-14: Cylinder geometry and symbol definitions (Yang et al., 1999)...... 33 Figure 2-15: Calculated scavenging parameters for the cases in Table 2-9 (Yang et al., 1999). Note that symbols appear to be missing or ambiguous for cases 34 and 35...... 35 Figure 2-16: Power density vs speed for two-stroke poppet-valved engine prototypes...... 37 xi

Figure 2-17: Torque density vs speed for two-stroke poppet-valved engine prototypes...... 37 Figure 2-18: Bsfc vs engine speed for two-stroke poppet-valved engine prototypes.38 Figure 2-19: Estimated losses vs speed for the Suzuki prototype and original engine (Morita and Inoue, 1996)...... 40 Figure 2-20: Average composition of PM from analysis of 16 heavy-duty turbocharged diesel engines (Needham et al., 1991)...... 43 Figure 2-21: Representation of 6-mode FTP simulation for a Caterpillar 3406E 500 hp engine (Montgomery, 2000, p. 48). Circle size indicates the weighting of each mode...... 45 Figure 2-22: Typical injection strategy for a modern diesel fuel injector and problems addressed (Caterpillar, 1998)...... 46 Figure 2-23: Increases in injection pressure with engine model year (Tschoeke, 1999)...... 47 Figure 2-24: Roots-type blower (Heywood, 1988)...... 51 Figure 2-25: Vane compressor (Heywood, 1988)...... 52 Figure 2-26: Screw compressor (Bosch, 1986)...... 53 Figure 2-27: Spiral (scroll) supercharger (Bosch, 1986)...... 54 Figure 2-28: Elements of a centrifugal compressor (Bosch, 1986)...... 55 Figure 2-29: Reciprocating piston supercharger...... 55 Figure 2-30: Schematic of a thermodynamic model of a turbocharged , intercooled four-cylinder engine with EGR...... 56 Figure 3-1: Generalised compressibility chart (Van Wylen and Sonntag, 1985, p. 682)...... 64 Figure 3-2: Simplified flowchart for using VODE to solve an IVP...... 68 Figure 3-3: Calculated specific internal energy vs temperature for Fuel B-air mixtures at thermochemical equilibrium at various pressures...... 70 Figure 3-4: Calculated specific ideal gas constant vs temperature for Fuel B-air mixtures at thermochemical equilibrium at various pressures...... 71 Figure 3-5: Calculated specific internal energy vs temperature at 30 bar (‘Data”) and equation 3-16 (“Function”)...... 73 Figure 3-6: Calculated specific gas constant vs temperature at 30 bar (“Data”) and equation 3-17 (“Function”)...... 73 Figure 3-7: Caterpillar SCOTE intake and exhaust valve lift profiles...... 76 xii

Figure 3-8: Assumed poppet valve discharge coefficient vs valve lift/diameter ratio, based on Heywood and Sher (1999, pp. 187-8)...... 76 Figure 3-9: Estimated variation of effective area for intake and exhaust valves...... 77 Figure 3-10: Caterpillar SCOTE apparatus (Montgomery, 2000, p. 23)...... 85 Figure 3-11: Outline of the process for digitising graphs...... 88

Figure 3-12: Definitions of tID and β. CA = Crank Angle...... 89 Figure 3-13: Comparison of measured ignition delay and the ignition delay correlation vs mean pressure...... 92 Figure 3-14: Comparison of measured ignition delay and the ignition delay correlation vs mean temperature...... 93 Figure 3-15: Comparison of measurement and the β correlation vs δ...... 97

Figure 3-16: Comparison of measurement and the β correlation vs tID...... 97 Figure 3-17: Typical heat release rate diagram reported by Watson et al. (1980). Note the difference between this and Figure 3-12...... 98 Figure 3-18: Example of measured heat release rate and best fits for Equation 3-36 (Watson et al., 1980) and Equation 3-41 (labelled “Modified”)...... 99 Figure 3-19: Shape factor correlations - data points and linear regression are shown...... 100 Figure 3-20: Example of a compressor map...... 101 Figure 3-21: Example of a turbine map (values on axes omitted to protect manufacturer’s proprietary information)...... 103 Figure 3-22: Estimated fmep and correlation...... 108 Figure 3-23: Sample file specifying parameter values to be investigated. The first column is the initial values, the second column is the final values, the third column specifies the number of steps, and the fourth column describes the parameters...... 109 Figure 3-24: Mode 3 (high load, mid speed). Case numbers refer to Table 3-8...... 112 Figure 3-25: Mode 5 (mid load, high speed) . Case numbers refer to Table 3-8.....113 Figure 3-26: Mode 6 (low load, high speed). Case numbers refer to Table 3-8...... 114 Figure 3-27: Other comparisons using different engine hardware. Case numbers refer to Table 3-8...... 115 Figure 3-28: Cases 18-22 (75% load, 1600 rpm) (Kong, 2002). Case numbers refer to Table 3-8...... 116 xiii

Figure 3-29: Cases 23-27 (25% load, 1690 rpm) (Kong, 2002). Case numbers refer to Table 3-8...... 117 Figure 3-30: Schematic representations of models for Caterpillar 3406E simulations...... 118 Figure 4-1: Fuel injection and atomisation within the break-up length (Reitz and Diwakar, 1987)...... 127 Figure 4-2: 60º sector mesh of Caterpillar SCOTE cylinder. The mesh was supplied by the Engine Research Center at the University of Wisconsin-Madison...... 135 Figure 4-3: Computational mesh of Caterpillar SCOTE engine at BDC. The four valves and the “mexican hat” bowl-in-piston geometry can be discerned. The mesh was supplied by the Engine Research Center at the University of Wisconsin-Madison...... 136 Figure 4-4: KIVA-ERC model results and experimental data for Mode 3 (75% load, 993 rpm) . Case numbers refer to Table 3-8...... 139 Figure 4-5: KIVA-ERC model results and experimental data for Mode 5 (57% load, 1737 rpm) . Case numbers refer to Table 3-8...... 140 Figure 4-6: KIVA-ERC model results and experimental data for Mode 6 (20% load, 1789 rpm) . Case numbers refer to Table 3-8...... 141 Figure 5-1: Cross-section through cylinder mesh showing a shroud on the intake (left) valve...... 145 Figure 5-2: Cross-section of cylinder showing shroud geometries used in KIVA-ERC simulations. The intake poppet valves are in the lower half of the cylinder. The valve stems and shrouds appear white...... 146 Figure 5-3: Definitions of shroud parameters...... 147 Figure 5-4: Intake pressure vs crank angle for Cases 11 and 12...... 149 Figure 5-5: Scavenging efficiency versus delivery ratio for all cases with each shroud...... 150 Figure 5-6: Caterpillar SCOTE cylinder sections...... 151 Figure 5-7: Gas velocity vectors in section A-A for Case 6, Shroud 1. The intake valves are to the left. A small vortex is visible above the piston bowl...... 152

Figure 5-8: CO2 mass fraction contours in section A-A for Case 6, Shroud 1. Dark shading indicates low mass fraction. Intake valves are to the left...... 153 xiv

Figure 5-9: CO2 mass fraction contours in sections B-B to E-E for Case 6, Shroud 1. Dark shading indicates low mass fraction. The intake valves are to the left rear...... 154 Figure 5-10: Comparison of gas composition through sections B-B to E-E during scavenging for Cases 1 (left column) and 9 (right column) with Shroud 4. Adjacent images have approximately equal scavenging gas volumes in the cylinder...... 155 Figure 5-11: Calculated intake valve effective areas for shroud 1 based on KIVA- ERC results. Case numbers are indicated. The effective area estimated in Figure 3-9, reduced by the shroud area, is shown for comparison...... 156 Figure 5-12: Calculated exhaust valve effective areas for shroud 1 based on KIVA- ERC results. Case numbers are indicated. The effective area estimated in Figure 3-9, reduced by the shroud area, is shown for comparison...... 157 Figure 5-13: Pressure contours in the intake port for Shroud 1, Case 5 at 202 deg ATDC, showing the pressure gradient between the port boundary and the intake valves due to flow deceleration (the “ram effect”). Zero-dimensional modelling assumes constant pressure throughout the port...... 158 Figure 5-14: Pressure contours in the exhaust port for Shroud 1, Case 5 at 175 deg ATDC. Here, the pressure difference between the region above the valve and the port boundary appears to be due to the port geometry...... 159 Figure 5-15: α vs scavenging volume fraction for all cases with shroud 4...... 161 Figure 5-16: Representation of two-stage scavenging process...... 162 Figure 5-17: KIVA-ERC-calculated cylinder quantities for Case 4, Shroud 1 from EVO to IVC...... 169 Figure 5-18: Zone 1 quantities calculated from Figure 5-17 and matched calibration constants x = 0.1 and k = 8 × 10-4...... 170 Figure 5-19: Calculated exhaust gas purities and scavenging efficiencies for Case 4, Shroud 1...... 170 Figure 5-20: Comparison of KIVA and two-zone scavenging model results for no shroud on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.34 and k =1.0...... 171 xv

Figure 5-21: Comparison of KIVA and two-zone scavenging model results for shroud 1 on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.12 and k = 7 × 10-4...... 172 Figure 5-22: Comparison of KIVA and two-zone scavenging model results for shroud 2 on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.10 and k = 8 × 10-4...... 173 Figure 5-23: Comparison of KIVA and two-zone scavenging model results for shroud 3 on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.09 and k = 8.5 × 10-4...... 174 Figure 5-24: Comparison of KIVA and two-zone scavenging model results for shroud 4 on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.07 and k = 9.0 × 10-4...... 175 Figure 5-25: Ignition delay vs mean temperature...... 179 Figure 5-26: Ignition delay vs mean pressure...... 179 Figure 5-27: Comparison of KIVA-ERC results and the β correlation vs δ...... 180 Figure 5-28: Comparison of KIVA-ERC results and the β correlation vs ignition delay...... 180 Figure 5-29: Engine sub-unit comprising one reciprocating pump cylinder and two engine cylinders...... 188 Figure 5-30: Turbocharged and intercooled engine subunit...... 194 Figure 5-31: Comparison of KIVA-ERC and thermodynamic models for the cases in Table 5-11...... 198 Figure 6-1: Flowchart of two-stroke poppet-valved engine modelling process. The boxes represent tasks and the arrows represent the flow of information from one task to the next...... 208 xvi

List of Tables Table 2-1: Citations and author affiliations...... 12 Table 2-2: Motives for investigation of two-stroke poppet-valved engines...... 13 Table 2-3: Toyota S-2 Engine Specifications (Nomura and Nakamura, 1993)...... 16 Table 2-4: Ricardo “Flagship” Engine Specifications (Stokes et al., 1992)...... 18 Table 2-5: Shibaura/Honda flow visualisation rig and engine specifications (Nakano et al., 1990)...... 20 Table 2-6: KIVA-II engine model (Huh et al., 1993) and water flow visualisation rig (Kang et al., 1996) specifications...... 23 Table 2-7: Loughborough University of Technology engine model specifications (Das and Dent, 1993)...... 24 Table 2-8: Supercharger types selected for two-stroke poppet-valved engines...... 29 Table 2-9: Cases shown in Figure 2-15 (Yang et al., 1999)...... 34 Table 2-10: A comparison of scavenging methods (Abthoff et al., 1998; Knoll, 1998)...... 36 Table 2-11: Comparison of small engine performance (motorcycle and passenger engine data from Heywood and Sher, 1999)...... 39 Table 2-12: EU emissions standards for heavy-duty diesel engines...... 45 Table 2-13: Summary of compressor characteristics...... 56 Table 3-1: "Fuel B" analysis results (Montgomery, 2000, p. 27) ...... 69 Table 3-2: Calculated heat of combustion of Fuel B at 298.15 K using various fuel

models. O2 data from Van Wylen and Sonntag (1985) p. 658, products internal energy from thermochemical calculation using CEA (Gordon and McBride, 1994; McBride and Gordon, 1996)...... 81 Table 3-3: Summary of experimental apparatus (Montgomery, 2000)...... 86 Table 3-4: Measured and estimated data for determining calibration constants for the ignition delay correlation (Equation 3-32)...... 91 Table 3-5: Data used for calibration of β correlation (Equation 3-40)...... 96 Table 3-6: Charge air cooler data for Caterpillar 3406E-475hp engine (Wright, 2001)...... 105 Table 3-7: Estimated charge air cooler quantities and parameters...... 106 Table 3-8: Cases for calibration/validation of the O-D model...... 110 xvii

Table 3-9: Experimental and calculated results...... 111 Table 3-10: CAT3406E-500hp engine operating conditions. The first five rows are from Wright (2001, p. 62). The remainder are assumed or estimated as described in Section 3.2.9...... 119 Table 3-11: Comparison of measured and calculated data for CAT3406E engine model without turbcharger or charge air cooler...... 119 Table 3-12: Comparison of measured and calculated data for CAT3406E engine model with turbcharger and charge air cooler...... 120 Table 4-1: Adjustable parameters in KIVA-ERC model, adapted from Hessel (2003) and Kong (2002)...... 138 Table 5-1: Shroud parameters (see Figure 5-3 for definitions of symbols)...... 147 Table 5-2: Scavenging simulation cases...... 148 Table 5-3: Predicted air consumption for cases using KIVA-ERC and 0-D modelling...... 160 Table 5-4: Comparison of scavenging efficiencies calculated using the 0-D model and KIVA-ERC...... 176 Table 5-5: Turbulence and swirl values at IVC for the Shroud 1 cases listed in Table 5-2...... 178 Table 5-6: Predicted near-optimum valve timings, engine performance and combustion parameters for Modes 1-6 with the Caterpillar SCOTE engine running on a two-stroke cycle with Shroud 1 on the intake valves. Four-stroke results (italicised) are shown for comparison...... 185 Table 5-7: Modal BSFCs for valve timings optimised for a 6-mode FTP cycle approximation. (IVO=145, IVC=280, EVO=140, EVC=270ºATDC). Four- stroke baseline results are italicised...... 187 Table 5-8: Predicted near-optimum valve timings, engine performance and combustion parameters for Modes 1-6 for the arrangement in Figure 5-29 based on the Cat SCOTE engine with Shroud 1 on the intake valves. Four-stroke baseline results are italicised...... 190 Table 5-9: Modal BSFCs for parameters optimised for a 6-mode FTP cycle approximation. Four-stroke baseline results are italicised...... 192 Table 5-10: Predicted near-optimum valve timings, engine performance and combustion parameters for Modes 1-6 for the arrangement in Figure 5-30 based on the Cat SCOTE engine with Shroud 1 on the intake valves...... 195 xviii

Table 5-11: Optimised parameters for a 6-mode FTP cycle approximation. Four- stroke cycle baseline results are italicised...... 197 Table 6-1: Variation of x with average shroud angle...... 205

xix

Nomenclature ABDC After Bottom Dead Centre AHRR Apparent Heat Release Rate ATDC After Top Dead Centre BBDC Before Bottom Dead Centre BMEP Brake Mean Effective Pressure BTDC Before Top Dead Centre CA Crank Angle CFD Computational Fluid Dynamics EGR Exhaust Gas Recirculation EVC Exhaust Valve Close EVO Exhaust Valve Open HC Unburned hydrocarbons IMEP Indicated Mean Effective Pressure IVC Inlet Valve Close IVO Inlet Valve Open

NOx Oxides of nitrogen ODE Ordinary Differential Equation PM Particulate Matter RMS Root Mean Square ROI Rate of fuel injection RSSV Rotatable Shrouded Scavenging Valve SOI Start of injection TDC Top Dead Centre xx

Statement of Original Authorship The work contained in this thesis has not been previously submitted for a degree or diploma at any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written by another person except where due reference is made.

Signed:

Date:

xxi

Acknowledgements I would not have been able to undertake this project without the love, encouragement and patience of my family, Margot, Alex, Matthew and Felicity. Many thanks for allowing me to pursue this goal. Thanks also to my parents for their tremendous help during this project, and for encouraging my curiosity long before I started.

I am grateful to my supervisor Associate Professor Doug Hargreaves for the opportunity to undertake doctoral work with him, and for his support, encouragement and advice.

Rotec Design Ltd provided not only an interesting problem to explore, but also financial support and complete freedom to explore it. I trust that the knowledge and computational tools and techniques that have been generated will be of value now and in the future. My thanks go especially to Robert Rutherford, Paul Dunn and Mark Stefl for assistance, ideas, information and criticism. Glenn O’Brien not only contributed an important suggestion, but made the whole experience much more enjoyable.

The highlight of my study was the opportunity to visit in February 2002 the Engine Research Center (ERC) at the University of Wisconsin-Madison. I am grateful to Professor Patrick Farrell for hosting me and to students Mark Beckman, William Church and Toshiyuki Hasegawa for their help and hospitality. Dr Song-Charng Kong and Professor Rolf Reitz kindly allowed me to use the ERC’s version of KIVA, the ERCLIB emissions subroutines library and computational meshes of their research engine: arguably the best multidimensional model available at the time of writing to investigate the problem. Dr Kong and Dr Randy Hessel also gave much advice on engine modelling, both while I was there and by email correspondence when I returned to Australia. Dr David Montgomery kindly discussed with me the experimental data he collected while a student at the ERC. I look forward to returning to the ERC to present and discuss the results I obtained with its help.

The QUT Tribology and Materials Technology Research Concentration and the QUT Grants-in-Aid Scheme provided financial assistance with my overseas study visit. xxii

I was fortunate to have access to the QUT High Performance Computing Centre’s Silicon Graphics Origin 3000 supercomputer and to the support of Bernadette Savage, Dr Anthony Rasmussen, Dr Neil Kelson and Dr Mark Barry, who were always there when I needed computing assistance.

Thanks to Chris Middlemass of Garrett Turbo, Honeywell International Inc., for the proprietary turbocharger data I required to complete my model.

Finally, this project originated while I was working at Gilmore Engineers. I am grateful to Dr Duncan Gilmore for the opportunity to work on a wide variety of engineering problems that eventually led to this study.

Chapter 1 - Introduction

1.1 Background 1.1.1 Two-stroke poppet-valved engines The combination of two-stroke cycle and poppet intake and exhaust valves is unusual. Two-stroke engines typically have either intake and exhaust ports in the cylinder wall or an intake port and exhaust poppet valve. Four-stroke engines usually have poppet intake and exhaust valves.

One advantage of two-stroke engines is they can have a much greater maximum power density (rated power output per unit displacement) than four-stroke engines. This is due largely to the two-stroke cycle having one power stroke every engine revolution, whereas the four-stroke cycle has one every two revolutions. A higher power density is generally desirable because it generally allows smaller, lighter engines for a given application. The greater number of firing strokes results in smoother engine operation, an attractive feature in passenger vehicle applications.

Poppet valves have many advantages over cylinder ports. Port opening and closing is governed by piston motion and is necessarily symmetrical about bottom dead centre (BDC), whereas poppet valves can have asymmetric timing, which usually gives better engine performance and allows supercharging. Ports cause bore distortion (and therefore increased wear) through asymmetric liner temperatures. Oil tends to be swept into ports by the piston rings, where it accumulates and contributes to increased lubricant consumption and emission of unburned hydrocarbons. Ports require an increase in cylinder spacing to accommodate them.

The main advantage that ports have over poppet valves is their simplicity and low cost. However the disadvantages have meant that ported engines have not competed successfully with the cleaner and more efficient poppet-valved engines, except in those applications and markets where emissions and fuel efficiency are not strictly controlled.

The two-stroke poppet-valved engine cycle is illustrated in Figure 1-1. Compression, combustion and expansion all occur in a similar fashion to most two-stroke and four- stroke engines. At the end of the expansion phase the exhaust valves open, starting the blowdown period. The intake valves open shortly afterwards, starting the scavenging period. Because of the close proximity of the intake and exhaust valves, this arrangement is prone to short-circuiting of the fresh charge to the exhaust, indicated by the dotted line in Figure 1-1(e). Various means of reducing the short- circuiting of air from the intake to the exhaust and otherwise improving scavenging have been tested; these will be discussed further in Chapter 2. The U-shaped scavenge loop is sometimes called a “reverse tumble”, but is referred to as a “U- loop” herein. The exhaust valves close, trapping the charge while fresh charge is still being forced into the cylinder or is being blown back into the intake port. This is the supercharging phase. Finally the intake valves close and the cycle begins again.

Inlet Exhaust poppet poppet valve valve

Piston

(a) Compression (b) Combustion (c) Expansion

(d) Blowdown (e) Scavenging (f) Supercharging

Figure 1-1: Two-stroke poppet-valved engine cycle.

Note that the valve train must operate at twice the speed and the valve open periods are reduced relative to a four-stroke engine. The consequences can be: • Increased valve train requirements • Increased valve train noise, wear and friction • Reduced maximum engine speed • Valve open times that are longer-than-optimum • Reduced maximum valve lift

Similarly, fuel injection also occurs twice as often.

1.1.2 Outline of previous investigations A number of leading engine manufacturers, including Toyota, Honda, Ricardo Consultants and Suzuki built and tested two-stroke poppet-valved engine prototypes. Toyota constructed both diesel-fuelled and petrol-fuelled versions, whereas the remainder were exclusively petrol-fuelled. Reports on these tests appeared from 1989 to 1996.

Some studies concentrating on the scavenging behaviour of two-stroke poppet- valved engines were published from 1993 to 1999, although one appeared in 1981. Flow visualisation experiments and computational fluid dynamics (CFD) modelling indicated the U-loop scavenging could achieve scavenging efficiencies generally better than cross scavenging, similar to loop scavenging, but not quite as high as with uniflow scavenging. These alternative scavenge loops are illustrated in Figure 1-2.

(a) Cross scavenging (b) Loop scavenging (c) Uniflow scavenging

Figure 1-2: Common scavenging arrangements 4

1.2 Rotec engine concept

This study was inspired by investigations undertaken by Rotec Design Ltd, a company based in Brisbane, Queensland, Australia. They have developed a reciprocating blower-scavenged two-stroke poppet-valved diesel engine concept. A standard implementation using a four-cylinder engine block is represented diagrammatically in Figure 1-3. Intake air is compressed by a turbocharger and cooled by an intercooler, then fed to an intake manifold. This manifold distributes the air to the reciprocating air pump cylinders. Each pump cylinder has an intake reed valve. The air pump is external to the engine block and driven at twice the engine speed by a toothed belt connected to the engine crankshaft. Outlet reed valves are optionally placed at the pump cylinder exhausts to prevent back flow into the cylinder. Each pump cylinder supplies air to a transfer manifold, which distributes it to two engine cylinders that are 180° out of phase. In this way, one pump cylinder alternately scavenges two engine cylinders. Each engine cylinder operates on the cycle outlined in Figure 1-1. It is essentially identical to a four-cylinder engine, except that the valve train operates at twice the speed, the valve timing and open period is significantly altered and the fuel injector must inject fuel every engine revolution rather than every second revolution. A shroud is usually placed on each intake valve to reduce short-circuiting of air from the intake to the exhaust during scavenging (Figure 1-4). The engine exhaust is then delivered to a turbocharger turbine and exhausted. The air pump could conceivably be driven at three times the engine speed so that a two-cylinder air pump could scavenge a six-cylinder engine block. 5

Compressor Turbine

Intake Exhaust

Intercooler

Air pump Engine (2 x engine speed)

Reed valve Poppet valve Intake manifold Transfer manifold Exhaust manifold Figure 1-3: Schematic of Rotec engine prototype. Cylinders may not be in this order in a practical engine block due to balancing considerations.

Intake Exhaust

Shroud

Figure 1-4: Intake valve shroud. 6

Rotec Design has suggested that emissions might be reduced relative to equivalent four-stroke engines because of the increased air consumption of two-stroke engines. Two-stroke engines induct air into each cylinder once every revolution, whereas four-stroke engines induct air once every two revolutions. Thus a two-stroke engine will consume air at nearly twice the rate as a four-stroke engine with the same displacement, running at the same speed and having the same boost pressure. At the same load, the two-stroke engine will therefore burn its fuel at nearly double the air/fuel ratio as the four-stroke engine. An increase in air/fuel ratio generally results in a reduction of partially oxidised emissions, such as unburned hydrocarbons, carbon monoxide and particulate matter. However, this is often not true at high air/fuel ratios where a significant portion of the fuel forms a very lean mixture with the air and does not burn completely.

Additionally, exhaust gases could be cooled and mixed with the intake air, a technique called exhaust gas recirculation (EGR) that is known to be very effective in suppressing NOx formation at medium to high air/fuel ratios (discussed further in Section 2.3.1.1). EGR reduces air consumption because it displaces intake air, and excessive EGR causes unacceptable increases in other emissions.

Incomplete scavenging also reduces air consumption and increase the presence of residual exhaust gases during combustion. This “internal EGR” might suppress the formation of oxides of nitrogen (NOx). It is expected to be less effective than cooled external EGR, but would avoid the relatively high capital and maintenance cost of external EGR systems.

Finally, the charge should have greater turbulent kinetic energy in two-stroke engines because of: • the reduced time for dissipation of this energy between intake valve closure and fuel injection; • the greater rate at which the charge must be forced into the cylinder; • the presence of a turbulence-generating obstacle to short-circuit flow like a shroud.

This higher turbulent kinetic energy has been linked to improved combustion and emissions.

Rotec Design have built and tested prototypes based on three different engines. Two of these engines were small (1.6 litre and 2.0 litre) four-cylinder indirect injection automotive diesel engines. Exhaust measurements showed reductions in all emissions except particulate matter. Optimisation of the prototypes has proved difficult because of the problems of measuring in-cylinder processes, the expense of making and modifying hardware, and the large number of parameters that have to be optimised. These limitations suggest that a computational approach should be introduced if possible into the prototype development and optimisation process. Experiments would then be confined to validation and calibration of the computational model and fine-tuning of prototypes. This would result in faster and cheaper engine development. Because of the unusual cycle and unusual requirements (such as the ability to model shrouded intake valves), commercial engine modelling packages are not suitable. Computational models must be developed or adapted for this purpose.

The prospect of a cleaner diesel engine cycle is of great interest, possibly more so than that of an increase in power density. There is widespread opinion that current engine technology will not be able to meet the stringent emissions targets due to be phased in over the next few years. Should two-stroke operation allow considerable reductions in some or all of the emissions formed within the cylinder, the development and unit costs of future engines may be significantly reduced. Additionally, the capital cost of producing these engines could be reduced because of their similarity to current four-stroke engines. Finally, existing engines may be able to be economically adapted to two-stroke poppet-valved operation. If this concept were viable, this latter application would be the quickest and easiest to realise.

1.3 Objectives

As mentioned above, the potential advantages of two-stroke poppet-valved engines are numerous. However, investigations to date have been limited to the construction of a small number of prototypes adapted from research or production engines, and very basic analytical and numerical investigations of parts of the system. Detailed 8

CFD simulations incorporating moving valves, which are a cheaper, faster way of estimating in-cylinder processes than experimentation, were not readily available until 1997 with the release of the KIVA 3V engine simulation program, after most of these investigations were reported. An opportunity exists to apply this new simulation tool and the increase in computing power to more systematically investigate the two-stroke poppet-valved diesel engine concept.

The objectives of this study are to: a) develop and validate flexible and inexpensive numerical tools for rapidly simulating two-stroke poppet-valved engine systems; b) use the tools to investigate scavenging and combustion processes in a two-stroke poppet-valved engine cylinder; c) undertake a parametric investigation of the fuel consumption and emissions potentials for prototypes that might be constructed to continue this investigation. Chapter 2 - Literature Review

2.1 Introduction

Since 1990, several studies of two-stroke poppet-valved engine prototypes have been reported in the technical literature. This chapter begins with a summary of the motives for these investigations. The investigations are then briefly described and the outcomes are grouped under various sub-headings. Subsequent sections on diesel emissions, scavenging and computational engine modelling establish some background for the following chapters.

2.2 Overview of two-stroke poppet-valved engine studies 2.2.1 Motives for study Previous studies of two-stroke poppet-valved engines have generally been stimulated by the shortcomings of conventional two-stroke and four-stroke engines. Often there is a desire to combine the advantages of each type of engine. The relatively few experimental studies can be grouped by author affiliation as in Table 2-1, while the stated motives for the studies are shown in Table 2-2.

Table 2-1: Citations and author affiliations. Citation Author affiliations (abbreviation) (Nomura and Nakamura, Toyota Motor Company (Toyota) 1993) (Hundleby, 1990), (Stokes et Ricardo Consulting Engineers (Ricardo) al., 1992) (Sato et al., 1981), (Nakano et Shibaura Institute of Technology, Honda R&D Co. al., 1990), (Sato et al., 1992) (Shibaura/Honda) (Das and Dent, 1993) Loughborough University of Technology (Huh et al., 1993), (Kang et al., Pohang Institute of Science and Technology, 1996) Daewoo Motor Co., Korea Institute of Machinery and Metals (Korean Studies) (Morita and Inoue, 1996) Suzuki Motor Corporation (Suzuki) (Yang et al., 1997), (Yang et Kanazawa University, Gunma University al., 1999) (Kanazawa/Gunma) (Rutherford and Dunn, 2001) Rotec Design Ltd (Rotec)

Table 2-2: Motives for investigation of two-stroke poppet-valved engines.

Toyota Ricardo Shibaura/Honda Korean Suzuki Kanazawa/Gunma Rotec Higher torque and power density compared to 3 3 3 3 3 four-stroke engines Reduction of emissions from lubricant 3 3 3 3 3 3 consumption relative to ported two-stroke engines Asymmetric valve timing, unavailable in ported 3 3 3 3 engines The ability to be supercharged, difficult in ported 3 3 3 3 engines Smoother operation due to the increased number 3 3 3 3 3 of firing strokes Reduction of bore distortion due to asymmetric 3 3 3 3 3 cylinder heating, giving better piston ring and liner durability The possibility of combining manufacture with 3 3 3 3 3 four-stroke engines Closer cylinder spacing (smaller engine size) 3 relative to uniflow engines due to the absence of ports Lower mechanical friction losses relative to four- 3 stoke engines due to lower peak pressures and lower speed operation for the same torque output Reduction in emissions and fuel consumption due 3 to higher turbulent kinetic energy in the trapped cylinder gas at the point of fuel injection and more available air and/or EGR

Nakano et al. (1990) of Shibaura/Honda, claimed that ported two-stroke engines would never succeed in automotive applications due to the excessive consumption of lubricant inherent in piston-ported engines. Investigation of this alternative to non- ported two-stroke concepts was therefore warranted. Nomura (1993) from the Toyota Motor Company started from the premise that ported two-stroke lubrication in general was unsatisfactory and saw the use of poppet valves as a method of employing superior four-stroke lubrication techniques.

Hundleby (1990) of Ricardo Consulting Engineers claimed that a major barrier to adoption of two-stroke engines was their dissimilarity to current production engines, and that two-stroke poppet-valved engines may lead the way because of the reduced investment required to test and produce the engines. While the performance of these engines was potentially greater, it was at the expense of increased cost and complexity, so it was suited to high-performance prestige cars. Interest in two-stroke engines in general in the 1980s and 1990s was also sparked by the advent of direct petrol fuel injection. Electronic fuel injection (EFI) means that the gas entering the cylinder can be air, rather than a mixture of fuel and air. Thus should any inlet gas be exhausted during scavenging, no unburned fuel will be taken with it. Additionally, EFI allows a stratified charge to be formed in the cylinder. Thus lean overall air-fuel ratios can be achieved, as long as the mixture in the vicinity of the spark is readily ignitable. Lean burning helps reduce emissions and fuel consumption. The former is largely through more complete oxidation of fuel, and the latter is largely through a reduction in pumping work at part load.

More recent studies have tended to concentrate on the scavenging of cylinders with poppet intake and exhaust valves.

2.2.2 Description of prototypes/models 2.2.2.1 Toyota Motor Corporation Toyota created two engine prototypes called S-2 and S-2D for “supercharged two- stroke” and “supercharged two-stroke diesel”, respectively. These engine are discussed in Nomura and Nakamura (1993). The authors presented scavenging flow patterns generated by a simulation that appears to use a 3-dimensional mesh and 15 moving valves. The specifications of the engines are shown in Table 2-3. The engines are illustrated diagrammatically in Figure 2-1 and Figure 2-2.

Figure 2-1: Toyota S-2 petrol-fuelled prototype (left) and cylinder detail (right) (Nomura and Nakamura, 1993).

Figure 2-2: Toyota S-2D diesel-fuelled prototype (left) and details of the cylinder head (right) (Nomura and Nakamura, 1993).

Table 2-3: Toyota S-2 Engine Specifications (Nomura and Nakamura, 1993).

A later article by Freudenberger (1995) discussed another prototype of the S-2 petrol-fuelled engine, stating that it displaced three litres, had double overhead cams and four (rather than five) valves per cylinder.

According to the Toyota Australia public relations department1, the S-2 engine had emissions problems and a four-stroke S-4 engine is under development.

2.2.2.2 Ricardo Consulting Engineers Hundleby (1990) and Stokes et al. (1992) described the development of a single- cylinder two-stroke poppet-valved petrol-fuelled research engine. This engine first ran in May 1989. The basic specifications reported in Stokes et al. (1992) are given in Table 2-4. During experimentation, many of these specifications were varied. This engine is illustrated in Figure 2-3.

Figure 2-3: Ricardo "Flagship" engine prototype (Hundleby, 1990).

1 From a telephone conversation with Mr Greg Storok of Toyota Australia Public Relations on 10th July 2000. 18

Table 2-4: Ricardo “Flagship” Engine Specifications (Stokes et al., 1992).

2.2.2.3 Shibaura Institute of Technology and Honda R&D Co. Nakano et al. (1990) first conducted scavenging flow visualisation experiments with a single-stroke dynamic simulator adapted from a diesel engine (illustrated in Figure 2-4). Tracer gas was illuminated and filmed through a Pyrex window. This system was also used for measurements of scavenging efficiency. In this case, this cylinder was filled with CO2 and scavenged with compressed air. The density of the remaining CO2 was analysed to obtain a volumetric scavenging efficiency.

Figure 2-4: Shibaura/Honda water scavenging rig (Nakano et al., 1990).

A four-stroke petrol-fuelled motorcycle engine was then modified to two-stroke poppet-valved operation. The modifications included reduction of the exhaust valve lift to prevent contact between the intake and exhaust valves, and reduction of the geometric compression ratio to 7.84 due to knocking (autoignition) phenomena at a geometric compression ratio of 11. The engine and test equipment are illustrated in Figure 2-5.

Figure 2-5: Shibaura/Honda petrol engine prototype (left) with intake port section showing mask detail (right) (Nakano et al., 1990).

The flow visualisation and engine specifications are shown in Table 2-5.

Table 2-5: Shibaura/Honda flow visualisation rig and engine specifications (Nakano et al., 1990).

A follow-on study (Sato et al., 1992) replaced the intake port deflector with shrouds on the inlet valves. The inlet valves were prevented from rotating so that the shrouds were always oriented in the most favourable direction.

They found that the shroud reduced the delivery ratio because it reduced the effective intake area. However, the charging efficiency, trapping efficiency and overall engine performance were improved. The prototypes were carburetted, however the authors recommend using a direct injection system to reduce the loss of unburned fuel to the exhaust ports.

They also conducted flow visualisation experiments using water/dye systems to qualitatively observe the scavenging flow pattern.

2.2.2.4 Korean studies Huh et al. (1993) used a modified KIVA-II CFD code to simulate the scavenging of a two-stroke poppet-valved engine cylinder. The computational mesh is shown in Figure 2-6. The authors modified the KIVA-II code so that moving valves could be approximated. The simulation is discussed in more detail in Section 2.2.3.

Figure 2-6: Computational mesh of Huh et al. (1993).

A follow-on study (Kang et al., 1996) used the same simulation code as discussed in Huh et al. (1993) and a water flow visualisation rig (Figure 2-7). The simulation code was used to model the water flow visualisation rig experiments. The rig had stationary valves and a stationary piston, which compromised the realism of the experiment. The authors’ aims were to obtain qualitative insights into U-loop scavenging with and without intake valve shrouds.

The specifications of the modelled engine used in the study by Huh et al. (1993) and the flow visualisation rig used by Kang et al. (1996) are presented in Table 2-6.

Figure 2-7: Water flow visualisation rig (left) and port layout (right) (Kang et al., 1996).

Table 2-6: KIVA-II engine model (Huh et al., 1993) and water flow visualisation rig (Kang et al., 1996) specifications.

2.2.2.5 Loughborough University of Technology Das and Dent (1993) also used KIVA-II with some modifications to study scavenging, fuel spray development and combustion in a four-poppet-valved fuel- injected spark ignition engine. The modifications to KIVA-II included new subroutines to account for fuel spray/wall interaction and mixing-controlled combustion. A one-dimensional model was used to estimate the pressure at the outlet port. They used a relatively coarse 3-D cylinder mesh with 4000 cells. The specifications of the engine they modelled are shown in Table 2-7.

Table 2-7: Loughborough University of Technology engine model specifications (Das and Dent, 1993).

Figure 2-8: Cylinder cross-sections and injector location and orientation in the Loughborough study (Das and Dent, 1993). 25

2.2.2.6 Suzuki Motor Corporation Morita and Inoue (1996) adapted a 1.3 litre petrol-fuelled four cylinder four-stroke engine to two-stroke poppet-valved operation. They reduced the compression ratio from 11 to 8.7. The engine had a supercharger, intercooler and high-pressure fuel injection. The engine is illustrated in Figure 2-9.

They also did a numerical scavenging simulation and experimentally measured the tumble induced by the intake port.

Figure 2-9: Suzuki prototype cylinder head (Morita and Inoue, 1996).

2.2.2.7 Kanazawa and Gunma Universities Yang et al. (1997) and Yang et al. (1999) concentrated on scavenging simulations using fog-marked gas and CFD. The CFD simulations were based on the Flagship engine geometry (Figure 2-3 and Table 2-4), but investigated the effects of changes to the cylinder head and valves (Figure 2-10), port spacing, piston bore/stroke ratio, valve timing and boost pressure.

Figure 2-10: Some valve arrangements investigated by Yang et al. (1999).

The basic engine specifications and the parameters investigated by Yang are presented in Section 2.2.4.

2.2.2.8 Rotec Design Ltd Rotec Design Ltd (Rotec) has been experimenting with two-stroke poppet-valved engines since the early 1990s. Their basic concept is illustrated in Figure1-3. Their latest prototypes have been retrofitted indirect injection (IDI) diesel engines from passenger vehicles.

The company claims reduced development cost and time compared with other emissions reduction technologies such as NOx catalysts for diesels, low sulphur fuels and regenerating particulate filters. In addition, the concept can be combined with other emissions reducing technologies if and when they become available. Given that the engine block and valve gear is largely the same as conventional four-stroke 27 engines, engine manufacturers would have smaller capital costs in retooling for this sort of engine than for more radical concepts (Rutherford and Dunn, 2001).

2.2.3 Simulation techniques Nomura and Nakamura (1993) presented scavenging flow patterns generated by a simulation that appeared to use a 3-dimensional mesh and moving valves. These features would have made it a sophisticated simulation for its time, however the authors did not present any details apart from the images. No other simulation techniques are mentioned, although they may have been used.

Hundleby (1990) reported that overall engine performance predictions were made using a one-dimensional engine model. This type of model is discussed in more detail in Section 2.5.2. One-dimensional models estimate gas parameters throughout the engine, and can account for wave effects in pipes. The model was initially used to optimise valve timing and overlap. The technique used is worth noting briefly as optimising valve timing is a task to be performed in this study. The rated condition was chosen for analysis, in this case 95 kW/litre at 5000 rpm. Valve timings were varied until an optimum condition was found. Once valve timings were chosen, the engine performance over the entire speed and load range was calculated. In the present study, it is desired to optimise engine parameters for a standard engine cycle comprising several load/speed conditions.

Hundleby modelled the scavenging flow using a two-dimensional CFD simulation. No details were given of the results of the modelling. No indication was found as to whether the CFD model was a transient or steady-state model.

Sato et al. (1981) and Nakano et al. (1990) employed a transparent cylinder to observe scavenging flow. The same apparatus was used with gas sampling techniques to measure scavenging efficiencies. The prototype engine had a number of significant differences to the scavenging simulator, especially cylinder dimensions, piston displacement, cylinder head and valve geometry, and the use of valve shrouds on the simulator and deflectors on the prototype. The follow-up study reported in Sato et al. (1992) employed a dye-marked water flow visualisation rig for 28 qualitative observations of scavenging.

Huh et al. (1993) and Kang et al. (1996) simulated cylinder scavenging using a modified version of the KIVA-II CFD code. KIVA is described in more detail in Section 2.5.3. The model used a three-dimensional mesh. Valves were simulated by making valve-shaped blocks of cells into “obstacle cells” with zero fluid velocity on the nodes. To represent valve movement, cells in the direction of the valve movement were progressively converted from fluid cells to obstacle cells, while those on the opposite surface were converted from obstacle cells back to fluid cells. Air at a constant temperature and pressure was specified at the intake port boundary, and a constant pressure exhaust boundary was specified.

Morita and Inoue (1996) used CFD to simulate the scavenging flow. The figures they reproduced in their report showed simplified valve geometry without valve motion. Piston motion was simulated, indicating that it was a transient simulation.

Yang et al. (1997) employed a flow visualisation rig to view scavenging flow in a cylinder. Later, a numerical study was undertaken using KIVA 3V Release 2 (Yang et al., 1999). The CFD model used constant pressure boundary conditions, a three- dimensional mesh, realistic valve geometry, simulated moving valves and piston, and had a total of 25,578 grid nodes. This model employed all of the features available to CFD modellers for this type of problem and therefore represents the most realistic numerical simulation of the problem prior to this present study.

Scavenge pumps Section 2.4 discusses scavenge pumps more generally. This section briefly describes the scavenge pumps used in the studies discussed above.

Toyota elected to use a helical-rotor Roots-type blower (Nomura and Nakamura, 1993). Hundleby (1990) compared the engine air requirement for full load and the characteristics of centrifugal and positive displacement blowers. He concluded that neither type of blower matched the engine air requirement satisfactorily when driven directly by the engine. At high speeds, positive displacement pumps would barely generate the desired boost pressure and would probably do so at low efficiency, 29 whereas centrifugal pumps would generate excessive boost at high speed and insufficient boost at low speed. He concluded that a variable ratio drive was necessary, probably coupled to a centrifugal compressor. It was noted that the variable ratio drive could be used to regulate the air supply according to the engine load over much of its load range, without throttling or bypassing air. The studies by Hundleby and Stokes et al. did not actually use a blower, but used compressed air to simulate a blower.

Nakano et al. (1990) employed a centrifugal blower with a variable-speed electric drive to provide scavenging for their prototype. This was not intended to be the system employed for future production engines.

Morita and Inoue (1996) used what they termed a “Reshorm” (assumed herein to be mis-translated “Lysholm”, i.e. Roots-type) supercharger.

Rotec used a reciprocating piston air pump directly driven by the engine, as described in Section 1.2.. Rotec intends the reciprocating pump to provide pulses of air that are timed to maximise scavenging efficiency and reduce pump work.

The scavenge pump types are summarised in Table 2-8.

Table 2-8: Supercharger types selected for two-stroke poppet-valved engines. Organisation Scavenge pump type Reference Toyota Roots-type positive displacement Nomura and Nakamura (1993) Ricardo Centrifugal with variable ratio Hundleby (1990) drive Suzuki Roots-type positive displacement Morita and Inoue (1996) Rotec Reciprocating piston positive Rutherford and Dunn (2001) displacement

2.2.4 U-loop scavenging The close proximity of the intake and exhaust poppet valves, coupled with the largely radial velocity distribution over the valve heads, means that a significant fraction of the scavenge flow gets “short-circuited” from the intake to the exhaust, without scavenging any residual gases in the cylinder. This reduces scavenging and trapping efficiency, wasting pump work and decreasing charge purity. Various methods were employed by researchers to reduce the scavenge flow.

Toyota elected to use a “mask” between the intake and exhaust valves for their S-2 prototype as shown in Figure 2-11 (Nomura and Nakamura, 1993). The bulk of the intake flow was directed away from the exhaust valve, along the cylinder wall, forming an effective scavenge flow. The reported scavenging efficiency (Figure 2-12) was very high, approximately the same as for uniflow scavenging. The performance is compared with perfect displacement and perfect diffusion scavenging models. Perfect displacement, in which the residual gas is displaced by the incoming gas without mixing, is obviously preferable to perfect diffusion, in which the incoming gas mixes thoroughly with the residual gas, because the amount of gas required to achieve a given charge purity is minimised. In practical engine systems, scavenging can be considered a mixture of displacement, diffusion and short-circuit flow.

The diesel-fuelled S-2D had a flat cylinder head with vertical valves and no apparent means of reducing the short-circuit flow. The intake port was quite vertical, which may have improved scavenging by imparting a downwards momentum to the intake flow. The scavenging performance of the S-2D was not discussed.

Figure 2-11: Toyota S-2 Petrol-Fuelled Engine Scavenging (Nomura and Nakamura, 1993).

Figure 2-12: Reported S-2 scavenging performance (Nomura and Nakamura, 1993).

Hundleby (1990) also used downward-directed inlet ports (Figure 2-3). The use of shrouds on the valves or flow deflectors was avoided, as the authors felt that the engine would be limited by its ability to “breathe”, and they did not wish to reduce the valve effective area. This could have been offset by increasing the valve lift, but the combination of high lift and high speed could have caused problems with valve spring surge, valve bounce, noise, wear and vibration. A minimum of four valves per cylinder was considered necessary for adequate gas exchange.

Nakano et al. (1990) sketched the scavenging flow with and without inlet valve shrouds based on high-speed photography of flow visualisation experiments. They 32 noted that short-circuit flow was apparent without the shrouds, and that the remainder of the scavenging flow took time to reach the bottom of the cylinder. When a 90° shroud was added, short-circuit flow was almost absent and a U-shaped scavenge loop was formed. Some residual fluid was trapped near the centre of a vortex near the middle of the cylinder. Sato et al. (1992) measured scavenging efficiency using gas sampling experiments (Figure 2-13). The results indicated that a 90° shroud was best, giving a scavenging efficiency better than that of perfect diffusion.

Figure 2-13: Scavenging measurements of Sato et al. (1992).

Kang et al. (1996) used flow visualisation experiments and numerical simulations to qualitatively investigate scavenging flow with shrouded intake valves. The authors concluded that too large a shroud (>>90º) caused a large vortex to form near the middle of the cylinder. This was considered undesirable, as residual gases would be trapped within it. Too small a shroud (<<90º) allowed a significant fraction of the intake flow to “short-circuit” straight to the exhaust valve.

Morita and Inoue (1996) used a fixed mask (Figure 2-9) very similar to that used in Toyota’s prototype. The scavenging performance was not reported.

Yang et al. (1999) used CFD to investigate many combinations of vertical and canted valves, masks, intake valve shrouds, bore-stroke ratio, port spacing, valve timing and boost pressure. The results are summarised in Table 2-9, Figure 2-14 and Figure 2-15. 33

Figure 2-14: Cylinder geometry and symbol definitions (Yang et al., 1999).

Figure 2-15 shows that scavenging efficiencies exceeding those calculated using the perfect diffusion model were predicted for many configurations. The engine speed being modelled was 5,000 pm. The delivery ratio and scavenging efficiency would presumably have been increased at lower speeds if the boost pressure remained constant, because of the greater scavenging time.

Table 2-9: Cases shown in Figure 2-15 (Yang et al., 1999).

Figure 2-15: Calculated scavenging parameters for the cases in Table 2-9 (Yang et al., 1999). Note that symbols appear to be missing or ambiguous for cases 34 and 35.

Yang et al. concluded: a) The optimum stroke/bore ratio was in the range 0.4 to 0.6. Most engines have a ratio of approximately 0.8 to 1.1. The scavenging efficiency (the ratio of the delivered mass retained to the total trapped mass) increased from 72% to 77% when the stroke/bore ratio was decreased from 0.89 to 0.5. b) The optimum shroud angle was in the range 69º to 108º. This is consistent with previous studies that suggested a shroud angle of approximately 90º was optimal. c) A shroud turn angle of approximately 18º was better than 0º. d) Separating the valves improves performance without a shroud, because of the lengthening of the “short circuit”; however it reduced performance with a shroud because of interference between the inlet valve and cylinder wall. e) Canted valves have better scavenging because the angled flow against the cylinder wall is better converted to a smooth scavenging loop, whereas with vertical valves the scavenging flow is normal to the cylinder walls and more of it is converted to turbulent flow.

Abthoff et al. (1998) and Knoll (1998) briefly discussed the relative merits of port loop scavenging, poppet-valve loop scavenging and uniflow scavenging. Their conclusions are combined in Table 2-10. 36

Table 2-10: A comparison of scavenging methods (Abthoff et al., 1998; Knoll, 1998).

The claimed limited swirl capability is debatable, as adequate swirl is generated in four-stroke poppet-valved engines and the orientation of intake shrouds can generate significant swirl. Additionally, uniflow scavenging is still struck by problems with lubricating oil consumption (and therefore the associated high emissions discussed later in Section 2.2.6) because of the intake ports.

2.2.5 Prototype performance One of the main reasons cited for the interest in two-stroke engines is their high power and torque density (see Table 2-2). In this section, the demonstrated performance (power/torque output, fuel consumption and emissions) of two-stroke poppet-valved engine prototypes is briefly reviewed.

The power density of the prototypes was calculated from data published in the references listed in Table 2-2 and shown in Figure 2-16. This figure shows a wide variation, from a maximum of over 60 kW/litre for the Suzuki prototype at high speed to approximately 20 kW/litre for the Shibaura/Honda prototype. Interestingly, the Ricardo Flagship engine showed a general decline in power density with speed, indicating progressively deteriorating performance with speed.

70 Suzuki 60 Toyota S-2 50

40 Toyota S-2D

30 Ricardo

20 Shibaura/Honda Power density (kW/litre) Power density 10

0 0 1000 2000 3000 4000 5000 6000 Engine speed (rpm)

Figure 2-16: Power density vs speed for two-stroke poppet-valved engine prototypes.

Torque density (proportional to brake mean effective pressure, bmep) for the prototypes was calculated and is shown in Figure 2-17. The torque curves generally show maxima at 2000-3000 rpm, except for Ricardo’s Flagship prototype, which again showed a steady decline with speed.

200

160 Suzuki Toyota S-2 120 Toyota S-2D

Ricardo Torque density (kW/litre) density Torque 40 Shibaura/Honda

0 0 1000 2000 3000 4000 5000 6000 Engine speed (rpm)

Figure 2-17: Torque density vs speed for two-stroke poppet-valved engine prototypes. 38

The fuel efficiency of the prototypes is shown in Figure 2-18. They demonstrate a marked sensitivity to operating speed. Generally, at high speeds the blower losses become significant.

500

Suzuki 450 Toyota S-2 Shibaura/Honda Ricardo 400

350 Toyota S-2D bsfc (g/kWh)

300

250 0 1000 2000 3000 4000 5000 6000 Engine speed (rpm)

Figure 2-18: Bsfc vs engine speed for two-stroke poppet-valved engine prototypes.

To put these figures in context, Table 2-11 compares the two-stroke poppet-valved engine performance with “typical” values for medium-sized two-stroke and four- stroke engines.

Table 2-11: Comparison of small engine performance (motorcycle and passenger engine data from Heywood and Sher, 1999).

Stokes et al. (1992) reported that very high BMEP (greater than 13 bar indicated) was achieved at low speeds, however operation at high speed was prevented by the onset of knock, even at low loads. The maximum speed was increased by the use of high octane fuels, delaying the onset of knocking. One hypothesis for the early onset of knock was elevated charge temperatures caused by the retention of residual gas. The reverse tumble scavenge loop was thought to trap residuals in the core of the induced vortex. It was thought that improvements in scavenging would reduce the amount of trapped residuals and hence the onset of knock. Blower losses were expected to increase rapidly with boost pressure, so that net output actually reduced with increasing boost pressure above 1.3 bar. To achieve the target operating conditions, trapping efficiency had to be increased, minimising pumping losses. Successive improvements to test engines included increasing the ratio of areas of exhaust ports to inlet ports, redesign of the inlet system to reduce short-circuiting and 40 increase the tumble speed, increasing the valve overlap and delaying exhaust valve opening to reduce the temperature of the trapped charge.

Nakano et al. (1990) noted insufficient cylinder charging at high speeds. The exhaust valve lift was reduced to avoid clashing with the intake valve, and the intake valve deflector (Figure 2-5) reduced the port flow area. Consequently, their external blower could not supply enough air. The authors noted that improvements could be made if boost pressure could be adjusted appropriately with speed (Ricardo addressed this problem with a variable ratio centrifugal blower).

Morita and Inoue (1996) analysed the friction losses of the Suzuki four-stroke engine and its two-stroke adaptation. Their results are reproduced in Figure 2-19. Note the dominant effect of the scavenging blower. Obviously, a design challenge is to reduce the contribution of the scavenge pump to the engine losses. The basic two-stroke losses (neglecting the blower) are presumably slightly higher than the four-stroke losses because of the higher mean effective pressure in the cylinder. This causes greater rubbing friction between the piston and cylinder.

Figure 2-19: Estimated losses vs speed for the Suzuki prototype and original engine (Morita and Inoue, 1996).

A two-stroke poppet-valved engine prototype demonstrated a 71% increase in continuous torque and power over the original Peugeot XUD11 engine at approximately 1600 rpm (Gilmore, 1998).

2.2.6 Two-Stroke Poppet-Valved Diesel Emissions

Toyota claimed a reduction in both NOx and PM emissions with the S-2D prototype (Nomura and Nakamura, 1993). These reductions were not quantified. Rotec has not published the results of their testing.

2.2.7 Summary Some broad conclusions can be drawn from the studies discussed in this section: a) Two-stroke poppet-valved prototypes demonstrated significant torque and power increases over the parent four-stroke engine at low to medium speeds (Hundleby, 1990; Nakano et al., 1990; Sato et al., 1992; Stokes et al., 1992; Freudenberger, 1995; Morita and Inoue, 1996; Gilmore, 1998). b) Combustion problems occurred at higher speeds, possibly due to insufficient charge flow into the engine and combustion gases trapped in the vortex caused by the tumbling motion of the gas in the cylinder (Hundleby, 1990; Nakano et al., 1990; Sato et al., 1992; Stokes et al., 1992; Morita and Inoue, 1996). c) Losses using centrifugal blowers were unacceptably high at high speeds (Hundleby, 1990; Nakano et al., 1990; Sato et al., 1992; Stokes et al., 1992; Morita and Inoue, 1996). More efficient supercharging is required for satisfactory fuel consumption. d) Matching of the engine air demand and blower supply characteristics required special techniques (Hundleby, 1990). e) Acceptable scavenging, approaching that of Uniflow scavenging, could be achieved at high speeds through the use of valve shrouds and canted valves (Sato et al., 1992; Yang et al., 1999).

2.3 Overview of diesel engine emissions 2.3.1 Diesel emissions formation Any diesel engine concept must be able to comply with stringent emissions regulations. Therefore, an understanding of the fundamentals of diesel emissions, regulations and control strategies is required.

Diesel exhaust is mostly a mixture of nitrogen, water, carbon dioxide and unburned oxygen. Carbon dioxide is a “greenhouse gas”. The term “pollutants” or “emissions” usually refers to the fraction of exhaust gas (less than 1%) made up mostly of (in approximately decreasing order): a) Nitrogen oxides (NOx – mostly NO and NO2) b) Carbon monoxide (CO) c) Unburned hydrocarbons (HC – sometimes further broken down to methane (CH4) and non-methane hydrocarbons (NMHC)) d) Particulate matter (PM)

There are numerous other potentially harmful compounds emitted in much smaller quantities, but these are not regulated presently. They include: e) Nitrous oxide (N2O) f) Sulphur dioxide (SO2) g) Aldehydes h) Polycyclic aromatic hydrocarbons (PAH) i) Soluble organic fractions (SOF) j) Dioxins k) Metal oxides

The regulated emissions are discussed in greater detail in the following sections.

2.3.1.1 Nitrogen oxides (NOx)

NOx represents NO and NO2. NO is formed by the combination of atmospheric nitrogen and oxygen at high pressures and temperatures, conditions found in diesel engines during combustion. Once emitted into the air, NO readily oxidises to form

NO2, which is an irritant and an important component in smog formation. 43

2.3.1.2 Particulate matter (PM) PM is also sometimes called soot. It is a complex product, defined as whatever is caught in filters in diluted exhaust. Thus it is a mixture of solid particles, liquid droplets and condensed vapours. It consists mainly of (Kittelson, 1998): a) tiny carbon particles, either single or agglomerated, with heavy hydrocarbons from the fuel and lubricant adsorbed onto the surface b) Metal ash, from engine wear and corrosion and lubricant additives c) hydrated sulphuric acid droplets, formed from sulphur in the fuel and lubricant d) unburned heavy hydrocarbons, from the fuel or lubricant.

Figure 2-20: Average composition of PM from analysis of 16 heavy-duty turbocharged diesel engines (Needham et al., 1991).

The carbon particles are thought to be formed in fuel-rich regions around the injected fuel droplets and in cooler regions near the walls of the combustion chamber (Horrocks, 1994). Part of the fuel spray usually forms a film on the cylinder wall or the piston bowl, which also gives rise to a cool, fuel-rich region conducive to soot formation.

2.3.1.3 Unburned hydrocarbons (HC) HC denotes unburned fuel or lubricant hydrocarbons in the gas phase. Those in the liquid phase are counted as PM. These are formed in the same regions as PM. As HC levels decrease, the contribution of fuel retained in the injector nozzle is becoming significant, which has forced injector redesign in recent years.

2.3.1.4 Carbon monoxide (CO) CO is present in very small amounts when fuel/air mixtures are at chemical equilibrium; however, chemical kinetics is the dominant mechanism of formation of CO in diesel engines. CO emissions from diesel engines are relatively low. Bowman (1975) states that CO formation is one of the principal paths in hydrocarbon combustion. It is thought to oxidise readily in the presence of hydroxyl radicals to

CO2. However, hydroxyl is thought to react preferentially with hydrocarbons, so CO oxidation only occurs late in the diesel combustion cycle when the concentration of HC is low.

The greatest problems for diesel engine manufacturers are NOx and PM. Emissions of HC and CO are usually small compared with spark ignition engines and the emissions regulations (Schindler, 1997). A well-known problem in diesel engine design is the “NOx–PM tradeoff”, in which most measures that reduce one tend to increase the other (Han et al., 1996). Measures that reduce both are eagerly sought.

2.3.2 Emissions regulations Two most widely adopted emissions standards are those of the European Union (EU) and the USA. Compliance to standards from either place is acceptable for heavy vehicles in Australia. EU standards for heavy duty diesel engines since 2000, for example, use a combination of a 13-mode steady-state (ESC) test and 4-mode transient (ELR) test. The EU Emissions Standards are summarised in Table 2-12 to show the dramatic rate of improvement required in diesel engine emissions in the recent past and near future.

Table 2-12: EU emissions standards for heavy-duty diesel engines. Date & Test CO HC NOx PM Smoke* Tier Category Cycle (g/kWh) (g/kWh) (g/kWh) (g/kWh) (m-1) 1992 4.5 1.1 8.0 0.612 <85 kW Euro I 1992 ECE 4.5 1.1 8.0 0.36 >85 kW R-49 1996.10 4.0 1.1 7.0 0.25 Euro II 1998.10 4.0 1.1 7.0 0.15

Euro III 2000.10 2.1 0.66 5.0 0.10 0.8 ESC & Euro IV 2005.10 ELR 1.5 0.46 3.5 0.02 0.5 Euro V 2008.10 1.5 0.46 2.0 0.02 0.5 *Measured as the extinction coefficient, which is the inverse of the path length over which light intensity decreases by the factor of e (2.718).

Researchers often use simplified procedures that approximate the standard tests. One such test is a 6-mode Federal Transient Procedure (FTP) simulation. An example of test conditions corresponding to the 6-mode cycle for a Caterpillar 3046E 500 hp heavy-duty diesel engine is shown in Figure 2-21.

Figure 2-21: Representation of 6-mode FTP simulation for a Caterpillar 3406E 500 hp engine (Montgomery, 2000, p. 48). Circle size indicates the weighting of each mode. 46

2.3.3 Emissions control strategies

Diesel engines generally produce less NOx, HC and CO but more PM than petrol engines. Petrol engine exhausts have a very low oxygen and PM content, which allows effective catalytic conversion of NOx, HC and CO relatively easily. The same technologies can not be used for diesel engines because of the high oxygen content of the exhaust gas and the relatively high emissions of PM. In order to meet the strict emissions requirements, a system approach has proved necessary, as no one method has been found to be sufficient. Those diesel engine emission control options relevant to the present study are discussed briefly below.

2.3.3.1 Electronic engine control Electronic engine control presently allows control of coolant and lubricant temperatures. Fuel injection timing is important, with earlier timing improving efficiency and PM emissions but increasing NOx emissions, all due to the higher average combustion temperature. The opposite is true for injection retardation. Recently, fuel injection rate shaping has been made possible. The benefits of rate shaping on emissions are discussed in Han et al. (1996). One scheme described by an engine manufacture is illustrated in Figure 2-22.

Figure 2-22: Typical injection strategy for a modern diesel fuel injector and problems addressed (Caterpillar, 1998). 47

2.3.3.2 Fuel Injection System Modifications One of the striking trends in modern diesel engine fuel injection systems is the increase in fuel injection pressures (Figure 2-23). Higher pressures have been found to reduce PM and HC emissions, however this is at the expense of increased NOx emissions. In combination with other techniques such as injection rate shaping, split injection and injection retardation, NOx can be reduced as well. Examples of new fuel injection technologies allowing higher pressures over the entire engine speed range and electronic control include Electronic Unit Injectors and Common Rail injection systems.

Figure 2-23: Increases in injection pressure with engine model year (Tschoeke, 1999).

2.3.3.3 Exhaust Gas Recirculation (EGR) The addition of cooled exhaust gases to the intake charge has been found to significantly reduce NOx emissions at the expense of a small increase in PM and HC. The reasons for this are the depression of the combustion temperature through the increase of the specific heat of the charge and the dilution of the available oxygen (Stokes et al., 1992; Ladommatos et al., 1996; Ladommatos et al., 1996; Ladommatos et al., 1997; Ladommatos et al., 1997). If the recirculated exhaust gases are cooled, more charge can be fitted into the cylinder and the initial charge temperature is reduced (which reduces NOx emissions) (Ladommatos et al., 1998). Cool EGR is therefore more effective than hot EGR or “internal EGR” caused by incomplete scavenging. However, EGR equipment adds cost and complexity to 48 engines, and there are durability problems associated with handling corrosive exhaust streams that have condensed water and reactive compounds.

2.3.3.4 Combustion Air Intake Improvements

Charge air cooling reduces NOx formation by reducing combustion temperatures (the rate of NOx formation is sensitive to temperature). Charge air cooling has been investigated by Dickey et al. (1998) and others. Charge air cooling can cause poor starting and increased PM and HC in cold climates.

An increase in intake turbulence has been shown to reduce NOx emissions (Timoney et al., 1997). The turbulence was generated by a shroud on the intake valve. Since a shroud may be necessary to prevent short-circuiting of the charge in two-stroke poppet-valved engines, it may have a beneficial side-effect in reducing emissions.

2.3.3.5 Exhaust aftertreatment Aftertreatment refers to modification of the exhaust gas composition after it has left the cylinder.

Diesel Oxidation Catalysts are effective in reducing CO and HC, however these are already at low levels. They remove some of the HC adsorbed to PM, but do not reduce the carbonaceous material, sulphates or ash.

Lean NOx Catalysts aim to reduce NOx despite the oxidising (lean) exhaust stream. Sulphur in the fuel poisons some of the proposed catalysts, and none have been shown to be both durable and effective.

Selective Catalytic Reduction (SCR) catalysts use urea or ammonia to reduce NOx. They are used in stationary engines but are difficult to apply to automotive engines where the exhaust gas composition and temperatures change very rapidly.

Diesel Particulate Traps collect PM. One type of system uses catalytic material on the filter that causes regeneration (decomposition of the PM and removal of the residue), in a continuous or periodic manner, during the regular operation of the 49 system. Another approach uses an electric heater or fuel burner to heat the filter and regenerate the trap.

Despite the large amount of activity on diesel exhaust aftertreatment, especially in the last ten years, only the Diesel Oxidation Catalyst has been commercially available for use with commonly available fuels.

2.4 Scavenging 2.4.1 Fundamentals Scavenging in two-stroke engines is analogous to the combined exhaust and induction processes in a four-stroke engine. Since exhaust and induction are fairly separate and simple processes in a four-stroke engine, they are relatively easy to model accurately. This is obviously not the case in two-stroke engines.

Two-stroke engines require some means of creating a pressure drop between the intake and exhaust ports to generate scavenge flow. Ported two-strokes often use crankcase compression, which is simple but does not allow wet sump lubrication. Multicylinder engines generally do not have a changing crankcase volume (downward pistons are balanced by upward pistons) so external compression is necessary. This does allow wet sump lubrication, which is generally superior in terms of friction, probability of engine seizure, lubricant consumption and emissions (Nomura and Nakamura, 1993).

After the blowdown phase the inlet valve opens and the fresh charge is forced in under pressure. External compression is usually from a turbocharger and/or crank- driven supercharger. When both are used, they may be in parallel or series (Heywood and Sher, 1999). The residual gases are a combination of unburned air and combustion products, mostly carbon dioxide and water vapour.

The incoming air partly displaces, partly mixes with and partly bypasses (by “short- circuiting”) the residual gases. The upper limit of scavenging efficiency is bounded by perfect displacement. Some mixing will occur. Although this dilutes the residual gases, it also means some of the fresh charge is exhausted with the residual gases 50 and, conversely, some of the residual gases are retained when the exhaust valves close. Short-circuiting merely absorbs pumping work.

The scavenging air supply may not be purely fresh air. Often, the charge contains cooled exhaust gases in a process commonly referred to as exhaust gas recirculation

(EGR). EGR has been found to significantly reduce NOx emissions without significantly increasing PM and unburned hydrocarbon emissions (see Section 2.3.3.3).

There are many quantitative measures of scavenging performance. Some of them are defined below:

delivered mass Equation 2-1 Delivery ratio rd = swept volume× pump inlet density

delivered mass retained Equation 2-2 Scavenging efficiency ηs = trapped mass

delivered mass retained Equation 2-3 Trapping efficiency ηt = delivered mass

delivered mass retained Equation 2-4 Charging efficiency ηc = swept volume× pump inlet density

trapped mass Equation 2-5 Volumetric efficiency ηv = swept volume× pump inlet density

2.4.2 Scavenge pumps A number of compressor and blower types have been used as superchargers, including roots blowers, sliding vane compressors, screw compressors, rotary piston pumps, spiral-type superchargers, variable displacement piston superchargers, and centrifugal compressors. With the exception of the centrifugal compressor, all are positive displacement pumps that deliver a specific volume of air per revolution. 51

Since the volumetric efficiency is almost constant, the flow is proportional to the supercharger or engine speed. Positive displacement devices can provide high boost pressures without the need for high speed. This is an advantage in two-stroke engines, where reasonable pressure is required for scavenging at all speeds. A turbocharger alone would be unlikely to provide sufficient pressure at low speeds, because little exhaust power would be available to drive the turbine. Positive displacement superchargers are well suited for a mechanical connection with the engine, such as through a gearbox or a belt/pulley drive. Centrifugal compressors boost the pressure roughly proportionally to the square of the supercharger speed, so they are better suited for coupling with high speed electric motors or to the engine via a variable ratio gearbox (as in Ricardo’s Flagship prototype described in Hundleby, 1990). Much of the following discussion is taken from Heywood (1988) and Bosch (1986).

In a Roots-type or Lysholm supercharger (Figure 2-24), leakage between the rotors as well as backflow from the receiver to the inlet side of the blower take place, thus reducing its overall compression process. Roots blowers are used in applications where the pressure ratio is rather low, typically in the range of 1.0-1.3. More losses would be experienced at higher pressure ratios, where the use of Roots-type blowers would be questionable.

Figure 2-24: Roots-type blower (Heywood, 1988).

Roots blowers have good volumetric efficiency (about 90%) as well as reasonable mechanical efficiency (85%). However, their isentropic efficiency is usually less than 65% and strongly contributes to the modest overall efficiency of about 55%

In the vane compressor, thin vanes are housed in slots (Figure 2-25). They are flung outwards by centrifugal force, trapping the charge in the cavity formed by the vanes, the rotor and the housing. At low speeds the contact pressure is low and leakage can be high. The rotor itself is mounted eccentrically in the housing. This causes compression of the charge near the outlet.

Figure 2-25: Vane compressor (Heywood, 1988).

Heating results from the friction of the rotors against the housing. Unless this heat is dissipated through cooling, it is transferred to the air thus decreasing its density and increasing its volume. This reduces the compressor efficiency and adds to the engine cooling system load.

The overall efficiency of the sliding vane compressor is only 40%. This is due to a combination of low volumetric efficiency (85%), mechanical efficiency (about 65%), and an isentropic efficiency of just 60%.

As the screw compressor (Figure 2-26) rotor turns, air is inducted through ports arranged around the cylindrical housing and occupies the volume between two consecutive screws and the housing. This air is delivered through a discharge port, as shown in Figure 2-26. The delivery pressure is a function of the rotor speed and the discharge port flow area. Screw compressors rotate at 3,000 to 30,000 rpm, and generate substantial heat from friction between the rotor and the housing. Measures are usually required to dissipate the heat to maintain the compressor’s mechanical 53 integrity. Screw compressors have high volumetric efficiencies as long as their clearances are kept extremely small.

Figure 2-26: Screw compressor (Bosch, 1986).

The spirals in a Spiral (or Scroll) supercharger are arranged in a flat-sided casing having a shaft that rotates eccentrically. Sandwiched in between the fixed spirals are moving displacer walls attached to a disc that is connected to an eccentric pin roller bearing (Figure 2-27). As the drive shaft rotates, the displacer performs an oscillating circular motion of double eccentricity. Air entering the blower moves from one working chamber to the next. The rotation of the eccentric and the rotor is through a toothed belt.

Figure 2-27: Spiral (scroll) supercharger (Bosch, 1986).

The overall efficiency of this supercharger is about 55%. Its isentropic efficiency is 68% and its volumetric efficiency is close to 90%. The speed range for this type of supercharger is 0-13,000 rpm, and it can deliver up to 80 kPa boost pressure. The spiral-type supercharger is also often referred to as a scroll-type supercharger.

The centrifugal compressor is normally used with an exhaust-driven turbine. However, it can also be coupled to the engine crankshaft or driven independently by a high speed electric or hydraulic motor. It usually consists of a single stage radial compressor. The air is accelerated to a high speed and flows radially outward via a stationary diffuser stage toward a volute as shown in Figure 2-28. The volute converts the kinetic energy of the air to pressure. The centrifugal compressor is ideal for providing high mass flow rates at a pressure ratio of less than 3.5, which is desirable in internal combustion engine applications.

Figure 2-28: Elements of a centrifugal compressor (Bosch, 1986).

Reciprocating piston compressors (Figure 2-29) are commonly used outside of automotive applications. They are characterised by high efficiencies, low mass flow rates and high pressure ratios.

One-way valve

Figure 2-29: Reciprocating piston supercharger.

The various types of compressors are summarised in Table 2-13.

Table 2-13: Summary of compressor characteristics. Roots Vane Screw Rotary Spiral Centrif- Recip. piston ugal piston Overall efficiency 55 40 ~55 ~55 ~55 ~60 ~65 (%) Max pressure 1.3 N/A* 1.5 1.8 1.8 3.5 >10 ratio Positive Yes Yes Yes Yes Yes No Yes displacement * No data available

2.5 Engine modelling 2.5.1 Thermodynamic modelling Thermodynamic engine models of the type also known as "zero-dimensional", "lumped parameter" or "filling and emptying" models represent engine systems as a number of control volumes that may be linked by elements such as pipes, orifices, valves, compressors, turbines and heat exchangers. An example of a system representing a turbocharged, intercooled four cylinder engine is illustrated in Figure 2-30.

Intake Exhaust poppet poppet Plenum Cylinders Plenum valves valves Turbine Plenum

Compressor Throttle valve Waste gate valve

EGR valve Figure 2-30: Schematic of a thermodynamic model of a turbocharged , intercooled four-cylinder engine with EGR.

The physical engine system can be reduced to a system of ordinary differential equations using conservation of mass, the First Law of Thermodynamics 57

(conservation of energy) and the perfect gas law (or other suitable relationship between gas properties). Several sub-models regarding heat transfer, combustion, gas flow etc. are required to complete the model. Given initial values of parameters in each control volume, such as temperature, pressure and composition, the problem is then an initial value problem, which can be solved numerically. The solution can then be used to estimate the performance (power output, fuel consumption etc.) of the engine. For steady-state calculations, the solution may be calculated over many engine cycles to allow the effects of the initial conditions to diminish, as the solution usually converges towards a periodic solution.

The advantages of this type of model are simplicity, minimum computational effort and the ability (that it shares with one-dimensional modelling, discussed below) is that it is suited to modelling entire engine systems.

2.5.2 One-dimensional modelling In real engine systems there are spatial variations of gas properties within pipes and manifolds. One-dimensional modelling use one-dimensional unsteady conservation equations for mass, momentum and energy for gas flow in a duct. These equations are solved by either the method of characteristics or finite difference procedures (Heywood and Sher, 1999).

One-dimensional modelling can resolve ram effects (pressure gradients due to flow acceleration) and pressure wave effects. It can also resolve gas concentration gradients.

Drawbacks of models with one-dimensional elements include greatly increased computational effort relative to thermodynamic models, and difficulties in representing some wave behaviour such as shocks.

2.5.3 Multidimensional modelling Neither thermodynamic nor one-dimensional models describe detailed behaviour within control volumes such as engine cylinders. For many purposes, such as obtaining overall performance estimates of conventional engine systems, this is not a 58 problem. However, where the gas flow, fuel spray formation, combustion or emissions formation details need to be simulated, a multidimensional model is required. Initially, thermodynamic models were adapted to this task by breaking up control volumes into many zones (e.g. Hiroyasu and Nishida, 1989; Bazari, 1992). Through the use of many semi-empirical correlations the number of zones could be kept to a minimum and calculations could be done with only modest computing power. As the computing power available to researchers increased, computational fluid dynamics (CFD) models based on more fundamental principles became popular. These models still require some semi-empirical correlations, as the computational effort required to capture the very wide range of length scales and time scales involved in engine processes is prohibitive. For example, fuel droplets may have diameters of the order of microns, while the engine bore might be on the scale of 100 mm – a difference of five orders of magnitude. Presently a large grid has of the order of 105 elements, which is far too coarse to resolve details at the droplet scale.

A survey of emissions modelling literature shows that KIVA is the most widely used CFD package for engine research. Commercial packages that have been used to model internal combustion engines include FIRE, STAR CD and VECTIS. The latest release of KIVA has the ability to model moving canted valves, spray formation and evaporation, combustion and moving pistons (Amsden, 1999). Additional subroutines have been developed at the Engine Research Center at the University of

Wisconsin-Madison which estimate wall heat transfer and the formation of NOx and PM (Hampson and Reitz, 1995; Hampson et al., 1996). These have been used with

KIVA to explain such phenomena as the reduction in PM and NOx with split injection schemes (Han et al., 1996). Other institutions have developed their own subroutines for emissions formation (Beatrice et al., 1996).

2.6 Discussion

A review of engine modelling suggests that at least two-types of model are necessary: thermodynamic models (possibly including one-dimensional elements) to represent the behaviour of the overall engine system, and a CFD model to represent details of the cyinder, valves and ports. The thermodynamic model would provide 59 boundary conditions for the CFD model, and the CFD model would be used to tune submodels within the thermodynamic model.

Commercial thermodynamic engine models are unlikely to be able to model scavenging through poppet valves satisfactorily since this is such an unusual case. A purpose-built model would allow complete control over the simulation tasks.

Some consideration has been given to the validity or otherwise of a purely zero- dimensional thermodynamic model in this study, since sufficient time is not available to include a one-dimensional modelling capability. Wave and ram effects should least affect low-speed engines with relatively short pipe lengths, especially turbocharged heavy-duty diesel engines. For example, a pressure wave travels more than ten metres in the time it takes for a heavy duty diesel engine at a high speed of 2000 rpm to complete one revolution. If the engine is turbocharged, pipe lengths on a heavy-duty diesel engine are typically of the order of 1 metre, and the spatial variation of gas properties should be small. Turbines and compressors also tend not to transmit poppet valve-induced waves, although the turbocharger speed does vary slightly in response to pulsations in the exhaust flow.

Comparisons of filling and emptying models and models with one-dimensional elements indicate that for most engine simulations, especially those concerning turbocharged engines, the filling and emptying models are sufficiently accurate (Chen et al., 1992). However, during the course of this study the validity of the zero- dimensional modelling will be assessed. Chapter 3 - Thermodynamic model development

3.1 Requirements

After reviewing the literature on engine modelling for Section 2.5, it was apparent that there were many ways that thermodynamic engine models had been implemented. In order to assist in choosing between alternatives, it was helpful to have a set of model requirements. Each alternative had pros and cons, the most common trade-off being accuracy versus speed, another being generality versus speed. Reference to the model requirements often clarified the decision.

Briefly, the model requirements were: a) Speed. When evaluating relatively novel systems that are not yet well understood, it is advantageous to be able to run many simulations in a short period. For example, if the effects of nine interacting parameters are to be investigated, and six values of each parameter are chosen, the number of runs is 96 or about 530,000. Clearly, the investigation must be carefully designed to minimise the number of cases investigated; however, a fast model will allow the investigation of more cases and reduction of the chance of missing a feature. b) Flexibility. It was envisaged that not only the parameters of engine systems would be varied, but the systems themselves. For example, model validation would largely have to be done with a well-studied four-stroke engine, while a two-stroke adaptation would be the main object of study. Various turbocharger and/or supercharger characteristics (or no turbo- or supercharger) might be examined. A major goal was not having to rewrite any of the model when such a change was made. Another goal was the ability for automatic optimisation. Equally important was knowing what was not required to be changed. For example, it was envisaged that the model would be used only for heavy-duty direct injection diesel engine simulations and not indirect injection or spark ignition engines. Moreover, it was likely that most of the study would be based on one particular engine block and fuel system, so a completely generalised internal combustion engine model was not necessary. In many cases, this allowed great simplifications to be made. 61

so a completely generalised internal combustion engine model was not necessary. In many cases, this allowed great simplifications to be made. c) Accuracy. The model should account for all of the major thermodynamic processes occurring in the engine, using well-known submodels and semi- empirical correlations. The method of solution should not introduce significant errors.

There were many instances in which techniques had to be invented or adapted. For example, there was not found in the literature any attempt to develop a zero- dimensional two-stroke poppet-valved scavenging model. Also, the most common heat release rate model could not be made to satisfactorily match experimental data on the engine and had to be adapted.

To achieve the best accuracy, it was decided to validate the model using a well- studied research engine. In reviewing the literature, the University of Wisconsin Engine Research Center was one source notable for its many contributions to the literature on engine modelling and engine analysis. During a study visit to the Engine Research Center published data from their Caterpillar Single Cylinder Oil Test Engine was obtained, much of it from a single source: a PhD thesis by David Montgomery (Montgomery, 2000). The Engine Research Center also kindly supplied a detailed KIVA mesh and some sample input files of the Caterpillar SCOTE engine. This engine is a single-cylinder version of the Caterpillar 3406E 6-cylinder 14.6 litre heavy-duty engine. Given the relative wealth of data on this engine that was suitable for modelling and validating, and the interest in adapting four-stroke heavy duty engines to two-stroke cycles, the logical choice of basic engines for this study were the Caterpillar SCOTE and Caterpillar 3406E engines.

If the thermodynamic and KIVA models could be validated, they could then be used to simulate the adaptation of the Caterpillar 3406E engine to two-stroke operation and fulfil the goals of the study.

3.2 Description 3.2.1 Basic assumptions The thermodynamic model was based on three fundamental principles: • Conservation of mass • Conservation of energy • Ideal gas equation of state

They can be expressed mathematically as follows: dm dm Equation 3-1 = ∑ i dt i dt

Equation 3-2 d dmi dV dQ ()mu = ∑ hoi − P − dt i dt dt dt

PV = mRT Equation 3-3

where: m = mass of gas within the control volume mi = mass flow entering from a separate control volume i u = specific internal energy hoi = stagnation enthalpy of flow to or from control volume i P = absolute pressure V = volume of the control volume Q = heat transfer out of the control volume R = specific ideal gas constant T = gas temperature (absolute) t = time

Note that implicit in Equation 3-2 is the assumption that gas properties are constant throughout the control volume. This is sometimes far from the case, for example when a control volume represents a diesel engine cylinder during the early stages of combustion. One consequence is that this type of model is not suitable for 63 simulations of detailed in-cylinder processes. Provided that correlations are available that make knowledge of these detailed processes unnecessary, the model should yield a good approximation of the overall behaviour of the engine system. The advantage of this assumption is once again simplicity and rapidity of calculation.

The conservation laws are incontrovertible, but the ideal gas assumption is an approximation rather than a “law”. It is a very convenient approximation because of its simplicity, and is very accurate when the intermolecular forces between gas molecules are negligible (Van Wylen and Sonntag, 1985, p. 379). The compressibility factor is a measure of how well a particular gas at a particular state approximates ideal gas behaviour and is defined as follows:

PV Equation 3-4 Z = mRT

A compressibility factor of unity indicates ideal gas behaviour. At 1 bar and 300 K the specific volume of nitrogen (R = 296.80 J/(kg·K)) is 0.890205 m3/kg (Van Wylen and Sonntag, 1985, p. 644), giving a compressibility factor of 0.9998. This indicates that air, which is mostly nitrogen, at ambient conditions behaves very much like an ideal gas. The worst case in terms of deviation from ideal gas behaviour occurs at the maximum temperature and pressure. In a turbocharged diesel engine the maximum pressure seldom exceeds 15 MPa and the maximum bulk gas temperature seldom exceeds 2000 K. The compressibility factor at this state can be estimated using a “generalised compressibility chart”, such as that shown in Figure 3-1. Once again approximating air using the properties of nitrogen, the critical temperature and pressure is 126.2 K and 3.39 MPa, respectively (Van Wylen and Sonntag, 1985, p. 650). The “reduced” temperature and pressure is defined as the ratio of the absolute values and the critical values. Thus, the maximum reduced temperatures and pressures are up to 15.8 and 4.4, respectively. Figure 3-1 indicates this gives a worst- case compressibility factor of approximately 1.03. It can be concluded that the ideal gas assumption is sufficiently accurate throughout the entire internal combustion engine system, and that the gain in accuracy to be made in using a more complicated equation of state would be very small.

Figure 3-1: Generalised compressibility chart (Van Wylen and Sonntag, 1985, p. 682).

The equivalence ratio of a fuel-air mixture is used here to describe the burnt gas fraction. It can be written:

m f φ = Equation 3-5 ma ⋅ FAS 65 where: φ = equivalence ratio mf = mass of burnt fuel in the mixture ma = mass of air originally in the mixture FAS = stoichiometric fuel-air ratio

If φ is zero, there is no burned fuel in the mixture. If φ is unity, the mixture is comprised of the combustion products of a stoichiometric mixture of fuel and air. It is possible to have φ greater than unity in which the mixture is comprised of the combustion products of a richer-than-stoichiometric mixture of fuel and air.

For diesel engine modelling purposes, it is argued in Section 3.2.3 that the internal energy of gases within the control volumes can be considered a function of temperature and equivalence ratio, and that the gas constant can be considered a function only of the equivalence ratio. Note that pressure is omitted. The effect of unburned fuel vapour is also neglected. If u = u(T,φ) and P is replaced with (mRT/V) (Perfect Gas Law), the First Law equation (Equation 3-2) can be rewritten:

Equation 3-6 ∂u dT ∂u dφ dm dmi mRT dV dQ m ⋅ + m ⋅ + u = ∑ hoi − − ∂t dt ∂φ dt dt i dt V dt dt

which may be rearranged to form a first order differential equation:

dm mRT dV dQ ∂u dφ dm Equation 3-7 h i − − − m ⋅ + u dT ∑ oi dt V dt dt ∂φ dt dt = i dt ∂u m ∂T

The rate of change of the equivalence ratio in the control volume can be obtained by differentiating Equation 3-5:

dφ 1  dm dm  Equation 3-8 = m f − m  2  f  dt FAS ⋅ m  dt dt  66

mf changes due to fuel burning within the control volume and due to burnt fuel-air mixture being carried across the control volume boundaries. These can be expressed as:

Equation 3-9 dm f d()mfb dmi = fuel + FAS∑φi dt dt i dt

where: mfb = mass fraction of the fuel charge that has been burnt fuel = total mass of fuel injected into the control volume

φi = equivalence ratio of mass flow i entering or leaving the control volume

Combining Equation 3-8 and Equation 3-9 we get a first order ODE for the equivalence ratio in each control volume:

Equation 3-10 dφ 1  fuel d()mfb dmi dm  =  + ∑φi −φ  dt m  FAS dt i dt dt 

There is now a system of three first order ordinary differential equations (Equation 3-1, Equation 3-7 and Equation 3-10) for each control volume.

In order to be able to solve the equations, the internal energy must be expressed as a function of the gas composition and state, and functions for mass and heat flow across the control volume boundaries must be supplied. These are discussed in the following sections.

3.2.2 Numerical solver The system of first order ordinary differential equations (ODEs), when combined with initial conditions, form an initial value problem (IVP). Most forms of this problem are not able to be solved analytically. The best alternative is to obtain an accurate approximation to the solution using numerical methods.

The program went through stages of using solvers created by the author based on Euler and implicit improved Euler methods (Equation 3-11 and Equation 3-12) to using packaged Runge-Kutta solvers in Mathcad and Fortran numerical libraries.

yn+1 = yn + hf(tn,yn) Equation 3-11

f (t , y ) + f (t , y ) Equation 3-12 y = y + n n n+1 n+1 h n+1 n 2 where: dy f (t, y) = dt h = step size

It was recognised that the system of ODEs might be stiff for some problems and non- stiff for others (especially when combustion and valve flow was not being modelled). “Stiffness” in systems of ODEs appears from the mathematical literature to be difficult to define precisely. Byrne and Hindmarsh (1975) noted that stiff systems of ∂f ODEs have a Jacobian matrix (matrix of partial derivatives ) has one or more ∂y eigenvalues whose real parts are negative and large in modulus. Another suggestion due to Shampine (1994) was that stiff ODEs are those that are best solved with backward difference or implicit methods. Equation 3-12 is an example of an implicit formulation. The unknown yn+1 appears on both sides of the equation and is not defined explicitly on the right hand side. The equation must be solved iteratively, which takes more time than explicit formulations, but for some problems this is more than offset by the increased step size allowed for the same accuracy.

Finally, it was decided to use a public domain IVP solver called VODE (Byrne and Hindmarsh, 1975; Brown et al., 1988). It has been regularly upgraded and tested for nearly 30 years. The latest revision at the time of writing was in April 2002. It has the option of efficient stiff and non-stiff solvers (the type of solver is selected by setting a variable to the appropriate value). The program dynamically adjusts the solution step interval and the “order” of the method used to keep the estimated error 68 within the user-defined bounds. Since stiff and non-stiff solvers are available, it is possible to do a few test runs with each type and see which method works best, based on the CPU time used.

To use VODE in solving an IVP, all that is required is to have a subroutine that calculates f(t,y(t)), set the method variable to stiff or non-stiff, and call VODE for every point at which the solution is desired.

Initial conditions, method flag (stiff or non-stiff solver), local and global error tolerances

dy Calculate derivatives dt

Set time for first solution point

Call VODE

Write solution point to file

Set time for next End of solution interval? solution point No Yes Calculate and write solution summary

End

Figure 3-2: Simplified flowchart for using VODE to solve an IVP. Error handling options are not shown.

3.2.3 Gas properties In order to solve Equation 3-1, Equation 3-7 and Equation 3-10, it is necessary to be able to express the internal energy and specific ideal gas constant as functions of the gas state. Initially, a simple correlation from (Krieger and Borman, 1966) for fuel with the general formula CnH2n (i.e. alkenes) was used. However, the experimental 69 data used to validate the model used a commercial diesel fuel denoted “Fuel B” with the characteristics shown in Table 3-1. The C/H mass ratio of 7.25 means the average formula was CnH1.643n, which would be expected to have a lower heat of combustion than CnH2n.

Incidentally, the other commercial diesel fuel (“Fuel A”) analysed by Montgomery had a slightly lower C/H ratio (6.869 versus 7.253). Fuel A was used on experiments with multiple injection that were not used for model validation.

Table 3-1: "Fuel B" analysis results (Montgomery, 2000, p. 27)

Since the fuel properties were known, a simple correlation like Krieger and Borman’s could be generated to get the internal energy and specific gas constant as functions of temperature, pressure and equivalence ratio. In this form, the ideal gas equation has the form:

PV = m R(T,P,φ) T Equation 3-13

Since P appears on both sides, it is an implicit equation that must be solved for P. It would be far more convenient if the pressure variable could be neglected. To see whether (or under what conditions) the pressure can indeed be neglected, the following analysis investigates the effect of pressure on the internal energy and specific ideal gas constant.

Thermochemical equilibrium calculations were performed using the NASA “Chemical Equilibrium with Applications” (CEA) program (Gordon and McBride, 70

1994; McBride and Gordon, 1996), . The Fuel B composition was assumed to be

CnH1.6430nN0.00038nO0.00033nS0.00027n, based on Table 3-1. The C, H and S weight percentages do not quite sum to 100%, so the balance was assumed to be equal weight percentages of nitrogen and oxygen, the two elements in addition to carbon, hydrogen and sulphur that are found in appreciable quantities in assays of some crude oils and fuel oils (Avallone and Baumeister, 1996, p. 7-11). The molar composition of air was assumed to be (Gordon, 1982):

N2 = 78.084%, O2 = 20.9476%, Ar = 0.9365%, CO2 = 0.0319% This gives a stoichiometric air/fuel ratio of 14.253.

The results of the calculations are summarised in Figure 3-3 and Figure 3-4.

2000

phi = 0 1000

1 bar 3 bar 0 10 bar 30 bar 100 bar -1000

phi = 1 -2000

-3000 Specific internal energy (kJ/kg original original air) (kJ/kg energy internal Specific

-4000 0 500 1000 1500 2000 2500 3000 Temperature (K)

Figure 3-3: Calculated specific internal energy vs temperature for Fuel B-air mixtures at thermochemical equilibrium at various pressures. 71

315

310 1 bar phi = 0 3 bar 305 10 bar 30 bar 100 bar 300

295

phi = 1 290 Specific ideal gas constant (J/kg*K original air) original (J/kg*K constant gas ideal Specific

285 0 500 1000 1500 2000 2500 3000 Temperature (K)

Figure 3-4: Calculated specific ideal gas constant vs temperature for Fuel B-air mixtures at thermochemical equilibrium at various pressures.

A number of observations can be made: • Pressure becomes a significant factor above approximately 1600 K. • The difference between the internal energy and gas constant at pressures between 10 bar and 100 bar up to 2200 K are very small. • The effect of pressure increases with equivalence ratio. • The variation in specific internal gas constant with temperature and pressure is small (less than 1%) below 2200 K.

For diesel engine applications, the bulk gas temperature seldom exceeds 2200 K. Bulk gas temperatures between 1600 K and 2200 K generally occur in diesel engine cylinders early in the expansion stroke, when the gas is generally between 10 bar and 100 bar. As the gas is further expanded it cools and the composition is “frozen”.

The decision was made therefore to fit polynomial functions to the 30 bar pressure lines. At low temperatures the 30 bar curve converges to all the other pressure curves, while at high temperature the pressure is likely to be in the vicinity of 30 bar. The gas constant was assumed to be a function of equivalence ratio only. These simplifications obviously introduce small errors and limit the applicability of the 72 correlation to internal combustion engine applications. However, this does not compromise the requirements, and enables a high-speed model.

Krieger and Borman (1966) used a function of the form:

u(T,φ) = π1(T) - φ·π2 (T) Equation 3-14 where:

π1(T), π2(T) = polynomial functions of temperature that are chosen to fit the thermochemical calculations.

A 5th-order polynomial was fitted to the u(T,P=30 bar,φ=0) calculations in Figure 3-3, and a 4th-order function was fitted to ∆u(T) = u(T,P=30 bar,φ=0) - u(T,P=30 bar,φ=1), using the least-squares method. The resultant expression for internal energy per kilogram of air (not fuel-air mixture) was: u(T,φ) = -2.8981×105 + 6.4230×102T + 8.8373×10-2T 2 + Equation 3-15 3.3536×10-5T 3 – 2.1769×10-8T 4 + 4.1123×10-12T 5 - φ (3.029×106 + 1.3741×102T - 4.1489×10-1T 2 + 2.3227×10-4T 3 - 4.8360×10-8T 4) (J/kg air)

and the expression for the specific gas constant with respect to kilograms of original air was:

R(φ) = 287.05 + 17.52φ (J/(kg air)·K) Equation 3-16

These functions are compared with thermochemical calculations in Figure 3-5 and Figure 3-6

2000

1000

0 Data, phi=0 Curve fit, phi=0 (kJ/kg original air) Data, phi=0.5 -1000 Curve fit, phi=0.5 Data, phi=1 -2000 Curve fit, phi=1

-3000 Specific internal energy -4000 0 500 1000 1500 2000 2500 3000 Temperature (K)

Figure 3-5: Calculated specific internal energy vs temperature at 30 bar (‘Data”) and equation 3-16 (“Function”).

310

305 Data, phi=0

300 Function, phi=0

Data, phi=0.5 295 Function, phi=0.5

290 Data, phi=1

Function, phi=1

Specific ideal gas constant (J/kg*Kconstant originalSpecific ideal gas air) 285 0 500 1000 1500 2000 2500 3000 Temperature (K)

Figure 3-6: Calculated specific gas constant vs temperature at 30 bar (“Data”) and equation 3- 17 (“Function”).

The agreement is obviously very good.for specific internal energy, and good for the specific gas constant at low equivalence ratios or temperatures below about 2200 K.

3.2.4 Heat transfer The simple heat transfer correlation due to Hohenberg (1979) is well-known and matches experimental results reasonably well. The heat transfer to the walls, cylinder head and piston is obviously difficult to measure accurately, so accurate calibration is not possible. Fortunately, errors in the estimated heat transfer result in only relatively small errors in the estimated engine performance (Assanis and Heywood, 1986).

Hohenberg’s relationship takes the form:

C P 0.8 Equation 3-17 h = 1 v + C 0.8 0.06 0.4 ()p 2 Volcyl T

where: h = heat transfer coefficient (W/m2·K) P = cylinder pressure (bar) 3 Volcyl = instantaneous cylinder volume (m ) T = instantaneous bulk gas temperature (K) v p = mean piston speed (m/s)

C1,C2 = calibration constants

Equation 3-18 Q& = h A()T − Tw

where: Q& = total heat transfer rate (W) A = heat transfer area (m2)

Tw = wall temperature (K)

Hohenberg suggested values of 130 for C1 and 1.4 for C2. The model was modified slightly to allow the piston face to have a different temperature to the walls.

3.2.5 Gas flow through valves and orifices Gas flow through poppet valves is estimated using compressible flow equations for choked and unchoked flow as appropriate (Streeter and Wylie, 1983). For unchoked flow, the equation is:

Equation 3-19 2  k−1  dm k  P  k  P  k = A 2P ρ   1−    eff o o       dt k −1 Po   Po   

whereas for choked flow:

k +1 Equation 3-20 dm k  2  k −1 = Aeff Po   dt RTo  k +1

Flow is choked if:

k Equation 3-21 P  2  k −1 ≥   Po  k +1

where: R k = ratio of specific heats = 1+ (from the ideal gas equation) ()∂u ∂T

Aeff = effective flow area = discharge coefficient × flow area ρ = density u = specific internal energy subscript o indicates upstream conditions

The poppet valve lift profile of the Caterpillar Single Cylinder Oil Test Engine (SCOTE) was used in the model. This is shown in Figure 3-7. No adjustment was made to the maximum lift to compensate for changes in the poppet valve acceleration as discussed in Hundleby (1990) as it was not known whether valve train speed was a limiting factor. 76

8 Intake Exhaust Valve lift (mm) 4

0 OPEN0 CLOSE1

Figure 3-7: Caterpillar SCOTE intake and exhaust valve lift profiles.

The valve lift and valve diameter (Table 3-3) was used to calculate the valve curtain area. In the absence of flow data for the Caterpillar SCOTE poppet valves, the discharge coefficient was assumed to follow a relationship similar to that reported in Heywood and Sher (1999, pp. 187-8). The relationships used are reproduced in Figure 3-8.

0.8

0.7

D Intake 0.6 C Exhaust

0.5

0.4 00.10.20.30.4 Valve lift/diameter

Figure 3-8: Assumed poppet valve discharge coefficient vs valve lift/diameter ratio, based on Heywood and Sher (1999, pp. 187-8).

The valve curtain areas were multiplied by the discharge coefficient to obtain functions of valve effective area, shown in Figure 3-9.

0.0025

0.002 ) 2

0.0015 Intake Exhaust 0.001 Effective area (m area Effective 0.0005

0 OPEN01CLOSE

Figure 3-9: Estimated variation of effective area for intake and exhaust valves.

Reed valves were simply treated as one-way orifices. The effective area of the reed valve block was assumed constant. More complex models were available (e.g. Fleck et al., 1997) but the effect of reed valve design on engine performance was not intended to be a variable in this study. Instead, the model can be thought of as idealised reed valves, permitting flow through the maximum effective area of the reed block in one direction only.

3.2.6 Scavenging The simplest models are perfect displacement and perfect diffusion, respectively. The former assumes that the incoming gas volume displaces an equal volume of residual gases. There is no mixing. Perfect displacement assumes that the incoming gas instantaneously and completely mixes with the residual cylinder gases. Each model represents an extreme case, whereas the actual scavenging behaviour is expected to involve some displacement, some mixing and some short-circuit flow (not accounted for in either model).

In four-stroke engines the perfect diffusion model is acceptable because there is relatively little valve overlap, therefore displacement and short-circuiting are minimal. Instead, residual gases are well-mixed with the fresh charge during the induction stroke, so the perfect diffusion model is most appropriate.

As it happens, perfect diffusion is the default behaviour of the thermodynamic model, as all quantities including species concentration are always averaged (“mixed”) over the cylinder volume. During scavenging, combustion is neglected, and the change of gas composition can be expressed as (from Equation 3-10):

Equation 3-22 dφ 1  dmi dm  = ∑φi −φ  dt m  i dt dt  where: φ = burnt gas fraction in the engine cylinder m = total mass of cylinder gas

φi = burnt fraction of gas entering from control volume i mi = mass entering from control volume i

Until a more accurate model was developed for scavenging through poppet valves, inspection of scavenging simulations for poppet-valved engines (e.g. Figure 2-12, Figure 2-13 and Figure 2-15) showed that the behaviour was reasonably approximated by perfect diffusion. No single-zone models were found in the literature that specifically addressed the scavenging of two-stroke poppet-valved engines. This is perhaps not surprising given the relatively small amount of work on the subject. The best scavenging data is from Yang et al. (1999), but that was for one particular engine at one particular speed. Other scavenging models were examined.

The development of a scavenging model for this project is described in Section 5.2.

To investigate scavenging through the poppet valves, a KIVA 3V model of a Caterpillar SCOTE cylinder, including valves and intake and exhaust ports was used. The KIVA program and the model is described more fully in Chapter 4. Obtaining a 79 correlation for scavenging through the poppet valves became a major part of this project, and is discussed in Section 5.1.

3.2.7 Combustion 3.2.7.1 Calculation of heat release The heat of combustion of fuel is measured by reacting a mixture of fuel and oxygen at a certain temperature in a sealed constant volume “bomb”. Heat is transferred from the bomb to the surroundings until the products reach the temperature of the original mixture. The process may be expressed in terms of the First Law of Thermodynamics as:

Q + muR = muP Equation 3-23

where: Q = the quantity of heat transferred from the bomb calorimeter m = mass of reactants and products uR = the specific internal energy of the reactants uP = the specific internal energy of the products

The internal energy of the products can be calculated using the CEA thermochemical equilibrium program (see Section 3.2.3), and the internal energy of the oxygen can be calculated from thermodynamic tables. If the fuel is liquid, its internal energy is calculated using the following relationship:

 o P  U = mh f + ∆h −  Equation 3-24  ρ  where: U = internal energy m = mass h°f = enthalpy of formation at reference conditions ∆h = difference in enthalpy between the current state and the reference conditions P = pressure ρ = fuel density 80

so that Equation 3-23 may be rewritten as:

m + m m Q air fuel  o P  O2 = u − h f + ∆h − − []h − RT P   O2 Equation 3-25 m fuel m fuel  ρ  fuel m fuel

where the subscripts denote the properties of the fuel, oxygen or products.

The internal energy of the reaction products can be calculated using the CEA program (the correlation developed in Section 3.2.3 is for fuel-air mixtures and not applicable to fuel-oxygen mixtures). Those for oxygen can be found the same way or using thermodynamic tables such as Van Wylen and Sonntag (1985, p. 658). Diesel fuel, being a complex mixture of hydrocarbons with carbon numbers ranging on average from about C13 to about C21 (Avallone and Baumeister, 1996, p. 7-12), is sometimes approximated by another compound or by a fictitious compound with properties similar to that of diesel fuel. Some approximations that have been used are n-dodecane C12H26 (e.g. Borman and Johnson, 1962), n-tetradecane C14H30 (e.g. Fuchs and Rutland, 1998), and fictitious compounds “df2” and “di” (Amsden, 1993, p. 36). “df2” is a fictitious compound with the heat of formation of diesel, the latent heat of vaporisation of n-hexadecane and the enthalpy of n-dodecane. “di” uses diesel properties compiled from a number of sources and has the chemical formula

C13H23.

Calculations assumed a temperature of 298.15 K. At this temperature the fuel is nearly all liquid. The vapour fraction can be neglected. The properties of n- tetradecane, and a “modified” n-tetradecane with the enthalpy of formation adjusted to give good agreement with the measured heat of combustion were assumed. For comparison, results using no fuel model were also calculated. Tetradecane data were obtained from the National Institute of Standards and Technology’s Chemistry WebBook (NIST, 2003). The fuel composition for the CEA calculations was assumed to be CnH1.6430nN0.00038nO0.00033nS0.00027n, and the oxygen/fuel ratio was assumed to be stoichiometric. The results of the calculations are summarised in Table 3-2. 81

Table 3-2: Calculated heat of combustion of Fuel B at 298.15 K using various fuel models. O2 data from Van Wylen and Sonntag (1985) p. 658, products internal energy from thermochemical calculation using CEA (Gordon and McBride, 1994; McBride and Gordon, 1996). Products uP with H2O(l) (MJ/kg) -10.6969 uP with H2O(g) (MJ/kg) -10.1436 Reactants hO2 (J/kg) 0.0

RO2 (J/kg·K) 259.84

Fuel model C14H30 Mod. C14H30 No model -2.033 -0.728 0 h°f (MJ/kg) Fuel ∆h (MJ/kg) 0 0 0 Heat of combustion Q with H2O(l) (MJ/kg) 43.69 44.94 45.73 m fuel Discrepancy with measured -3.0% -0.2% 1.6% gross heat of combustion Q with H2O(g) (MJ/kg) 41.32 42.56 43.35 m fuel Discrepancy with measured -2.7% +0.2% 2.1% net heat of combustion (%)

Note: O2/Fuel mass ratio = 3.29867

The “modified” tetradecane has a calculated enthalpy of formation higher than that of n-tetradecane, which is consistent with Fuel B being an unsaturated hydrocarbon. Saturated hydrocarbons generally have lower enthalpies of formation than unsaturated hydrocarbons.

In the thermodynamic model, the internal energy of the products is for fuel-air mixtures, not fuel-oxygen, and it is estimated using a polynomial. However, the net heat of combustion should still be very close to the measured value of 42.47 MJ/kg. This can be easily verified. If the reference temperature is 298.15 K, the pressure is 82 low and the reactant and product temperatures are also 298.15 K, then Equation 3-23 can be expressed as:

Q = mair u()T,φ P − (mair u ()T,φ R + m fuel h° f ) Equation 3-26 where:

φR, φP = the fuel-air equivalence ratios of the reactants and products, respectively

Dividing both sides by mfuel:

Q mair ∂u = δφ + h° f Equation 3-27 m fuel m fuel ∂φ

Using Equation 3-5: Q 1 ∂u = + h° f Equation 3-28 m fuel FAS ∂φ

Evaluation of Equation 3-28 for all values of φ between 0 and 1 and using the enthalpy of formation of “modified” tetradecane gives a net heat of combustion of 42.53 MJ/kg fuel, which is 0.14% from the measured value.

The actual energy balance used in the thermodynamic model during combustion is as follows (from Equation 3-6):

 2  Equation 3-29 ∂u dT ∂u dφ P vfuel mRTdV dQ m ⋅ +m ⋅ = ROIh° +c ()T −T + + − −  f p inj ref  ∂t dt ∂φ dt  ρ 2  V dt dt where: ROI = rate of injection of fuel cp = specific heat at constant pressure of liquid fuel vfuel = the injection velocity of the fuel

Tinj = the temperature of the injected fuel

Tref = the reference temperature on which the enthalpy of formation of the fuel is based

Note that the heat of formation, if it is for the liquid state, accounts for the heat of vaporisation.

In the model, the specific heat of liquid tetradecane was used, being 2200 J/(kg·K) (NIST, 2003).

The injection velocity was calculated from the rate of injection, which for the Caterpillar SCOTE engine was found to agree generally with:

-4 ROI = 0.051 + 6.8*10 ω (θ-θinj) Equation 3-30 where: ROI = rate of injection (kg/s) ω = engine speed (rad/s) θ = engine crank angle (radians)

θinj = start of injection angle (radians)

This expression forms a ramped injection pulse, which is consistent with the standard Caterpillar electronic unit injector. This has a rocker arm which follows a constant ramp rate cam (Montgomery, 2000, p. 27).

The injection velocity is calculated from:

2 vfuel ROI/(ρfuel.Nnoz.π/4dnoz ) Equation 3-31 where:

ρfuel = fuel density

Nnoz = the number of injector nozzle holes dnoz = the injector hole diameter

Note that Nnoz = 6 and dnoz = 0.214 mm for the Caterpillar SCOTE engine (Montgomery, 2000, p. 28).

3.2.7.2 Heat release rate correlation A commonly used and very simple combustion correlation is that of Watson et al. (1980). The ignition delay (interval between start of fuel injection and start of 84 combustion) is calculated from the average bulk cylinder temperature and pressure during the ignition delay period. Two burning modes are assumed: premixed (causing an initial spike in the heat release rate data) and diffusion-controlled (see Figure 3-12 for definitions). The proportion of premixed fuel combustion and diffusion-controlled combustion was correlated to the equivalence ratio and the ignition delay. Finally, the fuel combustion rate was modelled as a linear combination of two functions that fitted the shapes of their heat release rate data. The relationships proposed by Watson et al. were:

 A   2  A1 exp   Tm  Equation 3-32 t ID (Tm , Pm ) = A3 Pm

A5 A6 β (Ftr ,t ID ) = 1.0 − A4 Ftr t ID Equation 3-33

C C p1 p 2 M p (τ ) = 1− [1−τ ] Equation 3-34

Cd 2 M d (τ ) = 1− exp[− Cd1 ⋅τ ] Equation 3-35

M t (τ ) = β M p (τ ) + (1− β )M d (τ ) Equation 3-36 where: tID = ignition delay period

Tm, Pm = mean bulk temperature and pressure during ignition delay period β = proportion of fuel mass in premixed combustion

Ftr = trapped equivalence ratio τ = proportion of total combustion duration

Mp = Cumulative mass of fuel burnt in premixed combustion

Md = Cumulative mass of fuel burnt in diffusion combustion

Mt = Cumulative total mass of fuel burnt

A1… A6, Cp1, Cp2, Cd1, Cd2 = constants selected to fit experimental data for a particular engine 85

3.2.7.3 Experimental data The engine selected for calibration of the correlations was the University of Wisconsin-Madison’s Caterpillar Single Cylinder Oil Test Engine (Caterpillar SCOTE), a single-cylinder version of Caterpillar’s production six-cylinder 3406E 14.6 litre heavy duty direct injection diesel engine. This engine has various ratings from 355 hp and 1800 rpm to 550 hp and 2100 rpm (Caterpillar, 2002). The data from the Caterpillar SCOTE engine used to find constants for equations 3-21 to 3-25 were reported in Montgomery (2000). The experimental apparatus is summarised in Figure 3-10 and Table 3-3.

Figure 3-10: Caterpillar SCOTE apparatus (Montgomery, 2000, p. 23).

Table 3-3: Summary of experimental apparatus (Montgomery, 2000).

The engine operating conditions for which the calibration data was gathered is summarised in Table 3-8. The cases shown in the table represent three modes of the six-mode FTP simulation: mode 3 (high load, mid speed), mode 5 (medium load, high speed) and mode 6 (low load, high speed). They are all of the runs reported by Montgomery for which the engine apparatus was consistent. In other runs, the fuel 87 injection equipment was altered, and this was shown to adversely affect the calibrations.

The fuel injection rate and cylinder pressure were measured. From the pressure trace, the heat release rate was inferred. All three quantities were plotted versus crank angle. Rather than try to locate the original electronic data, the plots were digitised using a scanner at 150 dpi and saved in bitmap format. The bitmap was converted to a matrix using a built-in Mathcad function. Each value in the matrix represents the shade of grey of a particular pixel. Since the traces were usually between three and five pixels wide, a program was written to convert the trace to an average trace just one pixel wide. The scale of the bitmap was then used to convert the pixel position to a value on the x- and y-axes. In summary, the graphical information was digitised and converted to vectors of x values and corresponding y values. The process is illustrated in Figure 3-11. The digitised information was then in a form that was amenable to automated analysis.

Step 1: The plotted data (from Montgomery, 2000) is scanned.

Step 2: The required data is isolated (in this case it’s the apparent heat release rate).

01 0 -30 -2.607·10 -4 1 -29.869 -2.607·10 -4 2 -29.739 -2.607·10 -4 3 -29.608 -2.607·10 -4 4 -29.477 -2.607·10 -4 XY = 5 -29.346 -2.607·10 -4 6 -29.216 -2.607·10 -4 7 -29.085 -2.607·10 -4 8 -28.954 -2.607·10 -4 9 -28.824 -2.607·10 -4 10 -28.693 -2.607·10 -4

Step 3: The bitmap is analysed to determine the middle of the trace. The axis scales are measured and the position of the trace pixels (non-white) are converted to x- and y-values (the first eleven pixels are shown above)

0.05

0.04

0.03

〈〉1 XY 0.02

0.01

0.01 30 20 100 1020304050 〈〉0 XY Step 4: The result is graphed and checked against the original plot for accuracy.

Figure 3-11: Outline of the process for digitising graphs. 89

The apparent heat release rate (AHRR) plots were used to measure the ignition delay and premixed burn fraction. The ignition delay was measured from the elbow in the injection rate plot, i.e. where the injection rate starts levelling off after its initial rapid rise, to the bottom of the initial dip in the AHRR plot. After this point the AHRR trace starts rising due to combustion of the fuel. The dip may be partly due to the AHRR algorithm not accounting correctly for the heat transfer of the compressed charge through the walls, and it may be partly due to the absorption of heat from the charge in the evaporation of the fuel spray. The premixed burn fraction β was estimated by measuring the area under the first peak in the AHRR plot. Since the AHRR data was normalised, the total area under the AHRR curve by definition equals unity. The area under the first peak is therefore the fraction of heat released in premixed burning. If the heat of combustion is assumed roughly constant, that area is also the proportion of fuel consumed in premixed burning. These definitions of the ignition delay period and premixed burn fraction are illustrated in Figure 3-12.

CA1 CA2

CA2 β = ∫ AHRR dCA tID CA1

Figure 3-12: Definitions of tID and β. CA = Crank Angle.

3.2.7.4 Ignition delay correlation In order to estimate the mean temperature and pressure during the ignition delay period, a Mathcad worksheet was used that simulated induction and compression in the Caterpillar SCOTE engine. Equations 3-1, 3-2 and 3-3 were integrated using a built-in adaptive Runge-Kutta scheme. Gas flow through the poppet valves was modelled as described in Section 3.2.5, and heat transfer to the cylinder walls was modelled as described in Section 3.2.4. The boundary conditions were obtained from Table 3-8. In this way, the temperature and pressure history of the cylinder during induction and compression was estimated. The mean temperature and pressure during the ignition delay period was found using:

SOI +tID 1 Tm = T (t)dt tID ∫ Equation 3-37 SOI

SOI +tID 1 Pm = P(t)dt tID ∫ Equation 3-38 SOI

where: SOI = the time at the start of injection

The data obtained from the digitised graphs, and the estimated mean temperatures and pressures during the ignition delay are shown in Table 3-4.

Table 3-4: Measured and estimated data for determining calibration constants for the ignition delay correlation (Equation 3-32).

Case Tm (K) Pm (bar) tID (ms) 1 892 6.82 0.44 2 895 6.97 0.42 3 886 6.57 0.42 4 892 6.82 0.42 5 877 6.26 0.46 6 899 7.73 0.45 7 912 8.00 0.38 8 893 7.57 0.48 9 908 7.96 0.40 10 885 7.34 0.54 11 899 7.73 0.45 12 905 5.22 0.64 13 897 4.97 0.70 14 904 5.24 0.67 15 898 5.17 0.69 16 902 5.10 0.60 17 905 5.22 0.60 18 941 8.08 0.6 19 944 8.28 0.4 20 940 8.26 0.5 21 927 7.95 0.5 22 903 7.29 0.6 23 884 5.67 0.8 24 890 5.87 0.7 25 888 5.91 0.7 26 876 5.68 0.8 27 854 5.24 0.9

Calibration constants for Equation 3-32 were fitted to the data using the least-squares method. Owing to the complicated nature of the data, the result was dependent on the initial guesses of the constants. A short program was written to vary all of the initial guesses by small steps as follows:

A3 = 0.5, 0.7…2.5

A2 = 1000, 1100…11000 92

A1 was estimated assuming that the ignition delay period was 0.5 ms, the mean pressure was 65 bar and the mean temperature was 900 K. A1 was then varied from half this value to 1.5 times the value in ten steps. This reduced the number of iterations and focussed the search on that part of the parameter space where the solution was known to lie.

The results were:

A1 = 2.33

A2 = 2230

A3 = 0.94

This is reasonably similar to the values calculated by Watson et al (1980), who derived A1 = 3.45, A2 = 2100 and A3 = 1.02.

The results are plotted against the original data in Figure 3-13 and Figure 3-14.

0.8

0.6 Measured Correlation 0.4 Ignition delay (ms)

0.2

0 40 50 60 70 80 90 Mean pressure P (bar) m Figure 3-13: Comparison of measured ignition delay and the ignition delay correlation vs mean pressure. 93

0.8

0.6 Measured Correlation 0.4 Ignition delay (ms)

0.2

0 840 860 880 900 920 940 960 Mean temperature T (K) m Figure 3-14: Comparison of measured ignition delay and the ignition delay correlation vs mean temperature.

The agreement can be seen to be reasonably good and the trends are predicted correctly. The Hardenberg and Hase (1979) correlation for ignition delay was examined, but generally overpredicted the ignition delay and did not match the experimental data as well as Watson’s correlation.

The use of the mean temperatures and pressures complicated the implementation of this model. Equation 3-37 and Equation 3-38 require pressure and temperature be known as functions of time. The subroutine kept an array with the temperature and pressure history. The numerical solver was known to jump forwards or backwards in time to satisfy the user-supplied error tolerance, so the history array had to be carefully maintained so that only those values prior to the current time were in the array. If the correlation was an explicit function of temperature and pressure, the task would have been much easier.

In the subroutine, ignition was assumed to have started when the following condition was satisfied: 94

δti ∑ ≥ 1 Equation 3-39 i t ID ()Ti , Pi where: i = time steps between SOI and the present time δt = length of time step i

Ti,Pi = average temperature and pressure in time step i

3.2.7.5 Premixed combustion fraction correlation The correlation for β suggested by Watson et al. (Equation 3-33) could not be made to fit the measured data well, or predict the measured trends. A new correlation was therefore proposed. It seemed reasonable that the proportion of fuel in premixed combustion should depend mostly strongly on the proportion of fuel that had been injected up until ignition. Otherwise, there was the absurd possibility of more fuel undergoing premixed combustion than had been injected to that point. The other factor that was thought to influence the amount of premixed combustion was the ignition delay period. A short ignition delay should not allow much time for premixing. The correlation proposed was of the form:

A5 A6 β (δ ,t ID ) = δ − A4δ t ID Equation 3-40 where: δ = (amount of fuel injected up to ignition)/(total amount of fuel to be injected)

When comparing Equation 3-40 with Equation 3-33, note that the “1” has been replaced with δ, which sets the upper bound for β. The trapped equivalence ratio has also been replaced by δ.

Values for δ were calculated from Montgomery’s data (Montgomery, 2000) and Kong’s data (Kong, 2002), which included the rate of injection. This data is summarised in Table 3-5. The calibration constants were determined using a least squares method. The results were: 95

A4 = 0.41

A5 = 1.50

A6 = 1.17

A comparison of the data and the correlation is shown in Figure 3-15 and Figure 3-16. Again, the agreement with the data and the trends are good.

Table 3-5: Data used for calibration of β correlation (Equation 3-40). Case Measured proportion of fuel Measured proportion of fuel injection prior to ignition, δ in premixed combustion, β 1 0.101 8.0 2 0.108 8.1 3 0.103 8.5 4 0.104 8.0 5 0.113 8.5 6 0.171 9.1 7 0.152 7.2 8 0.202 10.2 9 0.161 8.1 10 0.246 11.5 11 0.194 9.4 12 0.571 28.4 13 0.590 31.3 14 0.549 29.2 15 0.626 31.5 16 0.512 28.1 17 0.508 28.0 18 0.288 8.8 19 0.176 9.5 20 0.176 9.7 21 0.233 11.1 22 0.288 13.5 23 0.986 27.2 24 0.907 40.1 25 0.907 40.4 26 0.986 45.5 27 1.0 66.9

80 β

Measured 40 (%) Correlation

20 Proportion of fuel in premixed combustion 0 0 20406080100 Proportion of fuel injected before ignition δ (%)

Figure 3-15: Comparison of measurement and the β correlation vs δ.

80 β

Measured 40 (%) Correlation

20 Proportion of fuel in premixed combustion 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Ignition delay t (ms) ID

Figure 3-16: Comparison of measurement and the β correlation vs tID.

3.2.7.6 Combustion rate shape parameter correlation The heat release rate correlation proposed by Watson et al. (1980) did not match the shapes of the heat release rates measured from the Caterpillar SCOTE engine. When attempts were made to fit the shape parameters to the data, large residual errors 98 resulted. Often the resultant shapes bore little qualitative resemblance to the data. The resemblance could be greatly improved if the start of diffusion burning occurred near the conclusion of premixed combustion. It is as though the fuel-air mixture ignites and consumes all of the mixed fuel and air, and then all that remains is diffusion-controlled combustion. In most of the heat release data from the Caterpillar SCOTE engine the heat release almost returns to zero after the initial peak, which is quite different to the heat release profiles reported by Watson et al. (compare Figure 3-12 and Figure 3-17. The differences could be due to the presumably much higher injection pressures in the Caterpillar SCOTE engine. Watson’s correlation assumes that both premixed and diffusion combustion commence at approximately the same time.

Figure 3-17: Typical heat release rate diagram reported by Watson et al. (1980). Note the difference between this and Figure 3-12.

Equation 3-36 was modified to reflect a delayed start of diffusion combustion as follows:

M t (τ ) = β M p (τ ) if τ < τd Equation 3-41 M t (τ ) = β M p (τ ) + (1− β )M d (τ −τ d ) if τ ≥ τd where:

τd = start of diffusion burning

This introduces another parameter into the correlation, but after investigation it was decided that this drawback was much more than offset by the improvement in the predicted heat release rate.

Again, a least squares method was used to fit the parameters to the data in cases 1-17 (referring to Table 3-8). Cases 1-17 were used because they were from the same source (Montgomery, 2000) and using the same equipment. The data was therefore likely to be most consistent. Data from other sources had differences in engine hardware which made correlating the data difficult. A comparison of the data and fitted correlation is shown in Figure 3-18.

Measurement

Watson et al.

Modified

Figure 3-18: Example of measured heat release rate and best fits for Equation 3-36 (Watson et al., 1980) and Equation 3-41 (labelled “Modified”).

The shape parameters were then examined to see whether they could be correlated to engine operating conditions. The best correlations that could be found are shown in

Figure 3-19. Note that Cp2 was assumed to be 5000.

100

3 40

2.5 30

2 20

1.5 10 0 0.2 0.4 0.6 0.8 1 10 14 18 22 26 (a) Cp1 vs β -1.07 -0.90 (b) Cd1 vs φ β

0.06 1.8

0.04

1.4 0.02

0 1 2 2.2 2.4 2.2 2.6 3 3.4 3.8 -0.33 -0.40 (d) τd vs Cp1 (c) Cd2 vs φ β Figure 3-19: Shape factor correlations - data points and linear regression are shown.

It can be seen that the diffusion burning shape parameters Cd1 and Cd2 are reasonably well correlated. The other parameters are more weakly correlated. Fortunately, they vary over narrow range and have only small influence over the overall shape.

The expressions for the rate shape constants used in the model were:

Cp1 = 2.15 + 0.10β

Cp2 = 5000 -1.07 -0.90 Cd1 = 0.079 + 1.47φ β -0.33 -0.40 Cd2 = -0.061 + 0.53φ β

τd = -0.14 + 0.081 Cp1

How well all of these correlations agree with the measurements is shown in Section 3.3.

101

3.2.8 Turbocharging 3.2.8.1 Compressor The turbocharger subroutine assumes a compressor map is available. The turbo speed and the stagnation pressure ratio across the compressor are known, and a double interpolation is done to obtain the mass flow rate and the isentropic efficiency. A typical compressor map is shown in Figure 3-20.

Figure 3-20: Example of a compressor map.

The isentropic efficiency is used to calculate the compressor outlet temperature according to (Joyce, 1999):  γ −1  γ   P2      −1   P  T = T   1  +1 2 1  η  Equation 3-42       102 where: T = temperature P = pressure γ = ratio of specific heats η = isentropic efficiency subscript 1 indicates inlet conditions, subscript 2 indicates outlet conditions.

The rate of work done by the compressor is calculated using:

W& = m& ()h2 − h1 Equation 3-43 where: W& = rate of work done by the compressor m& = mass flow rate h = enthalpy

3.2.8.2 Turbine The turbine mass flow parameter and isentropic efficiency were assumed functions of the turbine pressure ratio:

m T T & ref  P1  = f   Equation 3-44 P Pref  P2  and

 P1  η = f   Equation 3-45  P2  where:

Tref, Pref = reference temperature and pressure specified by the turbine manufacturer.

A turbine map which is amenable to this treatment is shown in Figure 3-21. 103

Mass flow parameter Efficiency

Pressure ratio

Figure 3-21: Example of a turbine map (values on axes omitted to protect manufacturer’s proprietary information).

Fifth-order polynomials were fitted to the turbine mass flow parameter and efficiency data. Using polynomial functions obviously simplifies and speeds up the procedure greatly, relative to interpolating map data. Additionally, it is a more robust method, less susceptible to failure due to excursions outside mapped regions. These are common especially in the initial conditions before the modelled engine behaviour settles down to a periodic function.

The turbine efficiency is used to calculate the turbine outlet temperature as follows (Joyce, 1999):

  1−γ   P  γ  T = T 1+η  1  −1  2 1     Equation 3-46  P2     

The rate of work done on the turbine is calculated similarly to Equation 3-43.

3.2.8.3 Turbocharger speed The turbocharger acceleration is given by:

ηmW&t +W&c α = Equation 3-47 ω()I t + I c

104 where: α = angular acceleration of turbocharger

ηm = mechanical efficiency of turbine-compressor connection ω = angular speed of turbocharger I = moment of inertia subscripts t and c indicate the turbine and compressor, respectively.

The turbocharger speed at time step i is simply:

ω i = ω i−1 +αδti Equation 3-48 where: δt = the duration of the time step

In implementing this procedure in a subroutine, a history of the turbocharger speed at recent time steps had to be stored. The numerical solver sometimes stepped forwards and backwards several steps, so the history array had to be large enough to accommodate the largest steps backwards. An array size of ten steps has always proved to be sufficient.

A compressor and turbine map for a 475 hp Caterpillar 3406E engine was kindly supplied by Mr Chris Middlemass of Garrett Turbo, Honeywell International Inc. (Middlemass, 2002).

3.2.9 Charge air cooling The intercooler subroutine in this model assumed constant heat exchanger effectiveness, pressure loss factor and ambient temperature. The effectiveness and pressure loss factor are defined as follows (Joyce, 1999):

Tin − Tout ε = Equation 3-49 Tin − Tamb

105 where: ε = effectiveness

Tin = temperature of the charge entering the charge air cooler

Tout = temperature of the charge leaving the charge air cooler

Tamb = ambient temperature

f 2ρ ∆P 2 = 2 Equation 3-50 A m& where: f = pressure loss factor A = flow area ρ = charge density ∆P = pressure drop across the charge air cooler m& = mass flow rate through the charge air cooler

The charge air cooler effectiveness and pressure loss factor for a Caterpillar 3406E engine were estimated as follows. Data for a Caterpillar 3406E–475hp charge air cooler at three operating conditions were found in Wright (2001). The data are replicated in Table 3-6.

Table 3-6: Charge air cooler data for Caterpillar 3406E-475hp engine (Wright, 2001). 106

If a compressor inlet temperature and pressure of 293.8 K and 96.8 kPa, respectively, and an ambient pressure of 101.3 kPa are assumed, the ambient temperature can be estimated from:

γ −1  P  γ  2  T2 = T1   Equation 3-51  P1 

This gives an ambient temperature of approximately 298 K.

The compressor outlet temperatures can be estimated from Equation 3-42, which then allows estimation of the density of the flow from the ideal gas equation (Equation 3-3).

From these calculations, the charge air cooler effectiveness and pressure loss factor can be estimated. The results are shown in Table 3-7.

Table 3-7: Estimated charge air cooler quantities and parameters. Condition 1 Condition 2 Condition 3 Compressor outlet 419.7 425.2 430.0 temperature (K) Compressor outlet 2.156 2.216 2.261 density (kg/m3) Charge air cooler 0.844 0.814 0.822 effectiveness Charge air cooler 1.232×105 1.270×105 1.378×105 pressure loss factor (m-4)

The mean effectiveness and pressure loss factor of the charge air cooler over the three conditions were 0.827 and 1.293×105, respectively. These values were used in the charge air cooler subroutine.

107

3.2.10 Mechanical friction Several simple correlations reported in Stone (1992) have been tried. The one used in this model has the form:

P fmep = a + max + cv b p Equation 3-52 where: fmep = friction mean effective pressure

Pmax = maximum cylinder pressure v p = mean piston speed a, b, c = calibration constants

Up to this point, the model is sufficiently well-developed to estimate the indicated mean effective pressure (imep) and Pmax for the Caterpillar SCOTE engine. The difference between the imep and the measured brake mean effective pressure (bmep) can be assumed to be the fmep.

The calibration constants from these data were determined to be: a = 1.23 b = 193.7 c = 0.063

The correlation is compared with the data inferred from Cases 1-17 (Table 3-8) in Figure 3-22. 108

2.4

2.3 Fmep (bar) Data 2.2 Correlation

2.1

1000 1400 1800 Speed (rpm)

Figure 3-22: Estimated fmep and correlation.

3.2.11 Automated parametric investigation The initial intention was to develop an automatic optimisation scheme. Optimisation generally involves maximising or minimising an objective function, subject to constraints. For example, if minimum fuel consumption was desired, the problem might be stated: f(X) = bsfc where:

X = {x1, x2 … xn} which is an array of parameters such as start of injection, boost pressure, inlet valve open timing etc. bsfc = brake specific fuel consumption Equation 3-53 Find X which minimises f(X) subject to p constraints: gi(X) = 0, i = 1, 2…m hj(X) < 0, j = m+1, m+2…p

109

Constraints could include maximum cylinder pressure and maximum exhaust, coolant and component temperatures.

It is helpful in optimisation to have some understanding of the behaviour of the objective function. The simplest way to achieve this is to evaluate the objective function over a range of all the input parameters. The parameter space can be limited if it is known in advance that there is little merit in searching outside certain boundaries. For parameters such injection timing, the range can be known reasonably well in advance.

The parameters to be searched are put in a table. The minimum and maximum values are entered, as well as the number of steps. An objective function and constraints must be built into the output subroutine. The program then automatically evaluates the objective function for every combination of the parameters. The minimum or maximum is noted, as well as violation of any constraints.

Figure 3-23: Sample file specifying parameter values to be investigated. The first column is the initial values, the second column is the final values, the third column specifies the number of steps, and the fourth column describes the parameters.

110

3.3 Validation 3.3.1 Caterpillar SCOTE data Table 3-8: Cases for calibration/validation of the O-D model. Case Engine Fuel rate Start of Intake Intake Exhaust EGR rate Ref. number speed (kg/hr) injection temp (K) pressure pressure (%) (rpm) (ºATDC) (kPa) (kPa) 1 993 6.276 -5.5 301 161 137 0 1 2 993 6.330 -3.5 301 161 137 0 1 3 993 6.288 -7.5 301 161 137 0 1 4 993 6.306 -5.5 301 161 137 0 1 5 993 6.312 -9.5 301 161 137 0 1 6 1737 6.930 1.5 305 184 181 0 1 7 1737 6.936 -3.5 305 184 181 0 1 8 1737 6.876 2.5 305 184 181 0 1 9 1737 6.972 -0.5 305 184 181 0 1 10 1737 6.876 3.5 305 184 181 0 1 11 1737 7.002 1.5 305 184 181 0 1 12 1789 3.846 -5.5 301 121 135 0 1 13 1789 3.732 -9.5 301 121 135 0 1 14 1789 3.810 -3.5 301 121 135 0 1 15 1789 3.786 -1.5 301 121 135 0 1 16 1789 3.816 -7.5 301 121 135 0 1 17 1789 3.828 -5.5 301 121 135 0 1 18 1600 8.064 -7.0 Conditions at 144º BTDC: 2 19 1600 8.064 -4.0 Pressure = 212.1 kPa 2 20 1600 8.064 -1.0 2 Temperature = 361.4 K 21 1600 8.064 2.0 2 22 1600 8.064 5.0 Burned gas fraction 0.007 2 23 1690 3.054 -9.0 Conditions at 144º BTDC: 2 24 1690 3.054 -6.0 Pressure = 148.4 kPa 2 25 1690 3.054 -3.0 2 Temperature = 334 K 26 1690 3.054 0.0 2 27 1690 3.054 3.0 Burned gas fraction 0.007 2 28 1737 6.804 -7.5 306 181 191 18.3 1 29 1737 6.798 -4.5 309 181 191 19.4 1 30 1737 6.786 -1.5 310 181 191 19.6 1 31 1737 6.810 -1.5 305 181 191 0 1 32 1737 6.834 -5.0 305 181 191 0 1 33 1737 6.870 -7.5 305 181 191 0 1 34 1789 3.84 -5.5 310 103 115 26.9 1 35 750 0.522 -8.0 299 100 100 0 3 36 953 2.022 -0.5 302 108 112 0 3 37 1657 10.140 7.5 313 239 220 0 3 Reference 1: Montgomery, D.T. (2000) University of Wisconsin-Madison PhD Thesis Reference 2: Kong, S-C (2002) Personal communication. Reference 3: Wright, C. C. (2001) University of Wisconsin-Madison MSc. Thesis 111

Table 3-9: Experimental and calculated results. Ignition Premixed Air flow Maximum Brake BSFC Ref. delay burn fract. rate pressure power (kW) (g/kWh) (ms) (%) (kg/min) (MPa)

Exp Cal Exp Cal Exp Cal Exp Cal Exp Cal Exp Cal 1* 0.44 0.52 8.0 8.8 1.77 2.16 10.3 10.6 29.6 29.5 212 212 1 2* 0.42 0.50 8.1 8.4 1.77 2.16 9.4 9.8 29.0 29.5 218 215 1 3* 0.42 0.54 8.5 9.4 1.76 2.15 11.0 11.5 30.0 29.8 209 211 1 4* 0.42 0.51 8.0 8.7 1.77 2.16 10.2 10.6 29.6 29.7 213 212 1 5* 0.46 0.58 8.5 10.2 1.75 2.16 11.7 12.4 30.3 30.1 208 210 1 6* 0.45 0.45 9.1 10.4 4.20 4.16 8.1 8.1 28.4 27.9 244 251 1 7* 0.38 0.42 7.2 9.4 4.16 4.16 8.4 8.7 30.3 29.6 229 234 1 8* 0.48 0.47 10.2 11.1 4.17 4.16 8.1 8.1 27.6 27.6 249 249 1 9* 0.40 0.43 8.1 9.6 4.20 4.16 8.1 8.1 29.1 29.0 240 241 1 10* 0.54 0.49 11.5 11.9 4.21 4.16 8.1 8.1 26.9 27.3 256 252 1 11* 0.45 0.45 9.4 10.4 4.17 4.16 8.1 8.1 28.4 28.5 247 246 1 12* 0.64 0.65 28.4 27.0 3.15 2.8 6.3 6.4 12.7 12.9 303 299 1 13* 0.70 0.70 31.3 30.9 3.15 2.8 7.0 7.3 12.7 12.4 294 302 1 14* 0.67 0.65 29.2 27.0 3.15 2.9 6.2 6.1 12.4 12.5 306 305 1 15* 0.69 0.67 31.5 28.3 3.15 2.8 5.8 5.8 11.9 12.2 317 311 1 16* 0.60 0.67 28.6 28.3 3.14 2.8 6.7 6.9 12.7 12.8 300 298 1 17* 0.60 0.65 28.1 27.0 3.13 2.8 6.5 6.4 12.7 12.8 301 300 1 18 0.6 0.41 8.8 7.5 - - 11.1 10.1 - - - - 2 19 0.4 0.39 9.5 7.0 - - 9.7 8.9 - - - - 2 20 0.4 0.39 9.7 7.1 - - 9.1 8.4 - - - - 2 21 0.5 0.42 11.1 7.8 - - 8.6 8.4 - - - - 2 22 0.6 0.48 13.5 9.4 - - 8.6 8.4 - - - - 2 23 0.8 0.67 27.2 30.2 - - 7.9 7.5 - - - - 2 24 0.7 0.63 40.1 27.3 - - 7.5 6.9 - - - - 2 25 0.7 0.62 40.4 26.9 - - 7.1 6.5 - - - - 2 26 0.8 0.66 45.5 29.4 - - 6.1 6.0 - - - - 2 27 0.9 0.74 66.9 36.0 - - 6.1 6.0 - - - - 2 28 0.05 0.47 - 11.1 3.32 3.30 9.3 9.6 31.1 29.1 219 233 1 29 0.10 0.44 - 10.1 3.26 3.23 8.7 8.6 29.6 28.4 230 239 1 30 0.15 0.44 - 10.1 3.22 3.21 8.4 8.1 27.9 27.5 244 246 1 31 0.09 0.43 - 9.8 4.07 4.07 8.6 8.2 28.8 28.0 236 243 1 32 0.14 0.43 - 9.9 4.08 4.07 8.9 8.8 29.6 29.0 231 235 1 33 0.06 0.46 - 10.6 4.08 4.07 9.4 9.6 30.3 29.7 227 231 1 34 0.57 0.80 28.0 38.2 1.74 1.73 6.1 6.0 13.0 12.5 297 306 1 35 1.24 0.88 77.0 65.0 ? 1.0 5.6 5.8 0.3 0.2 1700 2781 3 36 0.91 0.75 75.9 32.5 ? 1.3 6.8 5.8 7.6 7.4 266 274 3 37 0.50 0.44 13.1 7.6 ? 5.1 10.0 10.5 38.4 40.9 264 248 3 *These experiments were used for model calibration. Other experiments used different injectors, and in cases 25-34 there may have been additional differences.

112

The calculated and experimental pressure and heat release rate curves are shown.

Experimental Calculated

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure (MPa) 2 0.02 2 0.02 0 0 Heat release rate (normalised)

0 0 Heat release rate (normalised) -2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 60 -30 -20 -10 0 10 20 30 40 50 60 Crank angle (deg ATDC) Crank angle (deg ATDC) (a) Case 1 (b) Case 2

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure (MPa) 2 0.02 2 0.02

0 0 0 0 Heat release rate (normalised) Heat release rate (normalised) -2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 60 -30 -20 -10 0 10 20 30 40 50 60 Crank angle (deg ATDC) Crank angle (deg ATDC) (c) Case 3 (d) Case 4

14 0.14 12 0.12

10 0.1

8 0.08

6 0.06

4 0.04 Pressure (MPa) 2 0.02

0 0 Heat release rate (normalised)

-2 -0.02 -30 -20 -10 0 10 20 30 40 50 60 Crank angle (deg ATDC) (e) Case 5 Figure 3-24: Mode 3 (high load, mid speed). Case numbers refer to Table 3-8. 113

Experimental Calculated

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure (MPa) 2 0.02 2 0.02

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure (MPa) 2 0.02 2 0.02

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure (MPa) 2 0.02 2 0.02

. 114

Experimental Calculated

8 0.16 8 0.16 7 0.14 7 0.14 6 0.12 6 0.12 5 0.1 5 0.1 4 0.08 4 0.08 3 0.06 3 0.06 2 0.04 2 0.04 Pressure (MPa) Pressure (MPa) 1 0.02 1 0.02 0 0 0 0 Heat release rate (normalised) Heat release rate (normalised) -1 -0.02 -1 -0.02 -30 -20 -10 0 10 20 30 40 50 60 -30 -20 -10 0 10 20 30 40 50 60 Crank angle (deg ATDC) Crank angle (deg ATDC) (a) Case 12 (b) Case 13

8 0.16 8 0.16 7 0.14 7 0.14 6 0.12 6 0.12 5 0.1 5 0.1

4 0.08 4 0.08

3 0.06 3 0.06

2 0.04 2 0.04 Pressure (MPa) Pressure (MPa) 1 0.02 1 0.02 0 0 Heat release rate (normalised)

0 0 Heat release rate (normalised) -1 -0.02 -1 -0.02 -30 -20 -10 0 10 20 30 40 50 60 -30 -20 -10 0 10 20 30 40 50 60 Crank angle (deg ATDC) Crank angle (deg ATDC) (c) Case 14 (d) Case 15

Note: the experimental pressure trace in this table was scaled down to give approximately the same pressure at 30° BTDC as the calculation. It is believed that the original pressure data was incorrectly calibrated because the reported data was inconsistent with calculations based on the reported intake pressure, the reported air flow rate, and the reported pressure data for other runs with similar intake pressures. Scaling the reported pressure data by a factor of 0.77 brought the peak pressure and the air consumption into line with the reported intake pressure and other reported results. Pressure data in other tables were not scaled.

115

Experimental Calculated

14 0.14 8 0.32

12 0.12 7 0.28

10 0.1 6 0.24 5 0.2 8 0.08 4 0.16 6 0.06 3 0.12 4 0.04 2 0.08 Pressure (MPa) 2 0.02 Pressure (MPa) 1 0.04 0 0 Heat release rate (normalised) 0 0 Heat release rate (normalised) -2 -0.02 -1 -0.04 -30 -20 -10 0 10 20 30 40 50 60 -30 -20 -10 0 10 20 30 40 50 60 Crank angle (deg ATDC) Crank angle (deg ATDC) (a) Case 34, Mode 6 with high pressure injector (b) Case 35, Mode 1 (idle) and 26.9% EGR

8 0.32 14 0.14

7 0.28 12 0.12

6 0.24 10 0.1 5 0.2 8 0.08 4 0.16 6 0.06 3 0.12 4 0.04 2 0.08 Pressure (MPa) Pressure (MPa) 1 0.04 2 0.02 0 0 0 0 Heat release rate (normalised) Heat release rate (normalised) -1 -0.04 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 60 -30 -20 -10 0 10 20 30 40 50 60 Crank angle (deg ATDC) Crank angle (deg ATDC) (c) Case 36, Mode 2 (low load, low speed) (d) Case 37, Mode 4 (high load, mid speed) Notes: %CO2 − %CO2 1. %EGR = inlet ambient ×100 %CO2exhaust − %CO2ambient 2. For Fuel B composition, air consumption ≈ total intake × (1 – EGR fraction) Figure 3-27: Other comparisons using different engine hardware. Case numbers refer to Table 3-8.

116

Experimental Calculated

Figure 3-28: Cases 18-22 (75% load, 1600 rpm) (Kong, 2002). Case numbers refer to Table 3-8.

117

Experimental Calculated

Figure 3-29: Cases 23-27 (25% load, 1690 rpm) (Kong, 2002). Case numbers refer to Table 3-8.

3.3.2 Caterpillar 3406E data Wright (2001) published some data for a production CAT3406E-500hp engine. The data represents measurements at maximum load and high speed for the engine system including turbocharger and charge air cooler. The operating conditions are reported in Table 3-10 and the calculated and experimental results are compared in Table 3-11 and Table 3-12. The first table represents modelling of the six cylinder 118

engine block without the turbocharger and charge air cooler (Figure 3-30a). The boundary conditions were estimated from Wright’s reported data. The second table represents calculated results for the complete model, including turbocharger and charge air cooler (Figure 3-30b).

Note that the turbocharger data is for a CAT3406E-475hp engine that has a rated speed of 1800 rpm. This is the only turbocharger data that could be obtained for this study. It was expected to be similar to the CAT3406E-500hp turbocharger.

Intake Exhaust poppet poppet Plenum valves Cylinders valves Plenum

(a) Model for Table 3-11.

Intake Exhaust poppet poppet Plenum valves Cylinders valves Plenum Plenum

Turbine Plenum

Compressor Charge air cooler

(b) Model for Table 3-12.

Figure 3-30: Schematic representations of models for Caterpillar 3406E simulations. 119

Table 3-10: CAT3406E-500hp engine operating conditions. The first five rows are from Wright (2001, p. 62). The remainder are assumed or estimated as described in Section 3.2.9. Engine speed (rpm) 1700 1900 2100 Fuel rate (kg/min) 1.241 1.254 1.233 SOI (° ATDC) -7.1 -10.6 -15.7 Assumed compressor intake 96.8 96.8 96.8 pressure (kPa) Assumed compressor intake 293.8 293.8 293.8 temperature (K) Estimated intake manifold 268.5 258.7 246.6 pressure (kPa) Estimated intake manifold 320 322 317 temperature (K) Estimated exhaust manifold 225.3 234.6 241.9 pressure (kPa) Brake power (kW) 364 365 359

Table 3-11: Comparison of measured and calculated data for CAT3406E engine model without turbcharger or charge air cooler. Engine speed (rpm) 1700 1900 2100 Exp. Calc. Exp. Calc. Exp. Calc. Brake power (kW) 364 355 365 359 359 347 Air flow (kg/min) 35.2 34.7 37.2 36.8 38.4 38.9

120

Table 3-12: Comparison of measured and calculated data for CAT3406E engine model with turbcharger and charge air cooler. Engine speed (rpm) 1700 1900 2100 Exp. Calc. Exp. Calc. Exp. Calc. Brake power (kW) 364 346 365 349 359 336 Air flow (kg/min) 35.2 34.8 37.2 37.0 38.4 38.0 Turbo speed (1000 rpm) 85.5 87.2 85.8 87.1 85.4 85.9 Turbine pressure ratio 2.23 2.67 2.32 2.76 2.38 2.76 Compressor pressure ratio 2.88 2.96 2.79 2.86 2.68 2.70 Turbine efficiency % 72.6 69.7 69.8 69.2 67.8 69.3 Compressor efficiency % 76.2 74.7 76.3 74.5 76.0 73.7 Intercooler pressure loss (kPa) 10.4 9.6 11.0 11.1 11.7 12.2 Intercooler temp. drop (K) 112 114 107 109 106 101

3.4 Discussion

The thermodynamic model has been calibrated for the Caterpillar SCOTE and 3406E-500hp engines at the University of Wisconsin-Madison Engine Research Center, based on data published by Montgomery (2000) and Wright (2001).

The agreement with the Caterpillar SCOTE calibration cases (cases 1-17 in Table 3-9) is clearly very good, with most quantities being within 5% of experimental values. There is generally an underprediction of pressure dip due to fuel injection. This could be remedied by increasing the fuel enthalpy of formation. This would also bring the overall pressure rise due to combustion more into line with the experimental data. However, it would also reduce the net heat of combustion, and presently this agrees very well with the Fuel B analysis (Table 3-1).

As expected, the more that the engine hardware departs from that used in the calibration runs, the poorer the agreement. However, the trends are still reflected in the calculations. The difference between the experimental and calculated pressure traces in cases 34-37 are thought to be errors in the reported data rather than errors in the calculation. Wave effects are unlikely owing to the relatively short intake ports 121 and low speeds in cases 35 and 36. Also, there is generally excellent agreement between measurement and calculation during the compression strokes in the other cases that are at similar speeds.

Similarly, the discrepancies between the reported and calculated air flow rates in cases 1-5 and 12-17 are difficult to explain, because all of the other results are in such good agreement. The experimental results could be in error, because a small error in the charging efficiency should be magnified in the pressure trace. Sometimes the agreement is excellent, as in cases 6-11 and 28-34.

In Section 3.2.3 it was argued that the maximum cylinder temperatures seldom exceeded 2000 K and the pressure was also high, so that dissociation could be neglected. Reviewing all of the cases, the maximum temperatures were calculated for cases 1-5, in which the maximum bulk gas temperature was 2060 K at a pressure of 9 MPa (90 bar). Looking at Figure 3-3 and Figure 3-4, the errors in the specific internal energy and specific gas constant are very small, much less than 1%. In all of the other cases, including the Caterpillar 3406E simulations, the maximum bulk gas temperature was less than 1800 K. The decision to simplify the gas property calculations by neglecting the effects of pressure (i.e. dissociation) would appear to be justified, provided future simulations do not exceed these temperatures.

The model generally under-predicted the brake power output of the Caterpillar 3406E engine (Table 3-11 and Table 3-12). In the case of Table 3-11, in which the engine block only was modelled, the major source of error could be the friction correlation, which was unchanged from the Caterpillar SCOTE simulations. The parasitic losses in the Caterpillar SCOTE engine are expected to be greater per unit displacement than in the Caterpillar 3406E engine, because the single cylinder has to drive all of the ancillary equipment, such as the fuel system, valve train, oil and coolant pumps etc. Additionally, errors in the estimated boundary conditions would have an effect.

In the case of Table 3-12, in which the entire engine was modelled, including charge air cooler and turbocharger, the errors listed above would have been compounded by the differences between the correct turbocharger and the turbocharger for which data 122 was available. Nevertheless, the errors are relatively small, considering the model was calibrated solely on a single-cylinder version of the engine. (The charge air cooler model was calibrated on the Caterpillar 3406E data).

Comparison of the simulations and experimental data give good confidence that the model will give useful results for the predicted behaviour of engine systems based on the Caterpillar 3406E engine. The accuracy of the adaptation of the model to two- stroke operation is obviously contingent upon the development of a suitable model for two-stroke poppet-valved cylinder scavenging. Chapter 4 - KIVA-ERC multidimensional model adaptation

4.1.1 KIVA package overview KIVA was selected for the multidimensional modelling phase of this study for several reasons, including: a) It contains specialised engine modelling features such as moving pistons and valves and modelling of diesel spray formation, evaporation, ignition and combustion. b) The source code comes with the package, allowing the calculation methods to be known exactly, enabling troubleshooting of difficulties and modifications to suit requirements. c) Independently-developed subroutines, such as those developed at the University of Wisconsin-Madison Engine Research Center (ERC), are readily available. These provide alternatives to the original subroutines for the estimation wall heat transfer and the formation of NOx and PM. d) Low cost, no yearly maintenance fees.

Another advantage, not known at the time of selection, was the availability of meshes, experimental data and input files for the Caterpillar SCOTE engine, which was the engine used to validate many of the ERC subroutines.

KIVA is a package that numerically solves the unsteady equations of motion of a turbulent, two- or three-dimensional, chemically reactive mixture of ideal gases with a single-component vaporising fuel spray (Amsden et al., 1989). The computational domain is divided into hexahedral finite volumes. The vertices of the mesh may move with time. The gas flow is solved using an arbitrary Lagrangian-Eulerian (ALE) method. During the Lagrangian phase, the vertices are assumed to move with the fluid velocity (i.e. there is no convection across the fluid boundaries). In the Eulerian phase, the flow field is frozen, the vertices are moved to new user-specified positions, and the flow field is remapped to the new mesh by convecting material across the cell boundaries. 124

Extensive use of implicit formulations is used to enhance the overall stability of the solver, which generally allows the use of larger time steps based on the desired accuracy of the solution. The main time step size is calculated from several accuracy conditions related to mesh size, mesh distortion limits, rate of chemical heat release and rate of mass and energy exchange with the fuel spray. There are also time steps for convection subcycles, and their size is determined by the Courant stability condition which relates the mesh size and fluid velocity relative to the mesh.

KIVA is described in detail in Amsden et al. (1989); Amsden (1993); Amsden (1997) and Amsden (1999).

4.2 ERC Spray and Combustion Model Library

The finest practicable mesh for engine simulations cannot adequately resolve many important phenomena, such as gas turbulence, spray formation, combustion and emissions formation. Semi-empirical submodels are used to estimate these processes occurring within each small finite volume element. The relatively small scale of these elements allows far greater reliance on the fundamental physics than the single- zone thermodynamic model.

The University of Wisconsin-Madison Engine Research Center (ERC) has developed a library of submodels for use with KIVA called the ERC Spray and Combustion Model Library (ESC-lib). A license was granted for the use of the library in this project. The submodels are based largely on experimental work using the Caterpillar SCOTE and similar engines. ESC-lib should therefore be particularly suitable for this study.

The subroutines are compiled with KIVA and complement or replace the standard submodels that come with the KIVA package. “KIVA-ERC” is used to distinguish KIVA compiled with ESC-lib from the standard KIVA release. A brief description of each ESC-lib submodel is included in the following sections. 125

4.2.1 Turbulence A modified renormalised group (RNG) k-ε model is used. This was first developed for KIVA by Han and Reitz (1995) at the ERC. It has been incorporated as a standard option in KIVA since 1997, and is not actually a part of the ESC-lib. This model has been shown to predict large-scale flame structures, and therefore the in-cylinder temperature field and NOx formation, better than the original k-ε turbulence model. Features of this submodel include the accounting for the effects of compressibility and spray-turbulence interaction.

4.2.2 Heat transfer Han and Reitz (1997) developed a gas-wall convective heat transfer model through a temperature wall function. This allows reasonable accuracy with relatively coarse grids. It is based on the one-dimensional energy conservation equation. Variations in gas density and the turbulent Prandtl number in the boundary layer are accounted for. The expression for heat transfer is:

 T  ρc u′T ln  p  T  q =  w  Equation 4-1 w 2.1 ln()y′ + 2.513

u′y y′ = ν Equation 4-2

1 1 4 2 u′ = Cµ k Equation 4-3 where: qw = wall heat flux ρ = density cp = specific heat at constant pressure

T, Tw = flow temperature, wall temperature y = distance from the wall ν = molecular viscosity

Cµ = RNG k-ε turbulence model constant (value = 0.0845) k = turbulent kinetic energy 126

4.2.3 Atomisation and drop drag Except where noted, the rate of injection was calculated using Equation 3-30. The validation runs used the measured injection rate shapes. KIVA automatically scaled the user-specified rate shapes give the user-specified quantity of fuel injected per cycle. The injection velocity is calculated from the injection rate, the nozzle diameter and the nozzle discharge coefficient. The latter was set to a nominal value of 0.7. This is the default value, and is suggested in Han et al. (1996) based on experimental results.

The physical fuel is emitted from the nozzle as a continuous jet. The jet is discretised in KIVA as a series of fuel “parcels” or “blobs”. The initial diameter of the blobs is assumed to be the same as the effective diameter of the nozzle:

d eff = d noz CD Equation 4-4 where: deff = effective diameter dnoz = nozzle diameter

CD = nozzle discharge coefficient

Liquid fuel jets are observed to have a liquid core for a certain length, called the break-up length. Surrounding the core are liquid fuel droplets that have been stripped off the liquid jet. The droplet stripping occurs because of the high relative velocities at the liquid-gas interface.

127

Figure 4-1: Fuel injection and atomisation within the break-up length (Reitz and Diwakar, 1987).

This process is modelled using the concept of Kelvin-Helmholtz instability, in which initial perturbations in the liquid jet grow at a rate that is a function of the wavelength. The maximum growth rate and its corresponding wavelength are estimated. The radius of the droplets stripped off the blobs is assumed to be proportional to this wavelength. The diameter of the original blob is reduced as fuel droplets are stripped off. The rate of change of the parent blob is assumed to follow the rate equation: dr r − r 0 = − 0 ()r ≤ r dt τ 0 Equation 4-5

3.726B r τ = 1 0 ΛΩ Equation 4-6 r = B0 Λ ()B0 Λ ≤ r0 Equation 4-7 128 where: r0 = radius of parent blob r = droplet radius τ = break-up time Λ = maximum wave growth rate Ω = wavelength corresponding to Λ

B0, B1 = constants

This model is detailed by Reitz and Diwakar (1987).

Beyond the break-up length, the fuel is a spray consisting of many small droplets with fuel vapour and entrained gas. In this regime, Rayleigh-Taylor instability is assumed to occur as well as the Kelvin-Helmholtz instability described above. Rayleigh-Taylor instability is also a surface wave instability caused by an acceleration perpendicular to the interface between two fluids of different densities. If the growth time of the Rayleigh-Taylor waves exceeds a certain break-up time, the droplet disintegrates. The Rayleigh-Taylor break-up mechanism competes with the Kelvin-Helmholtz break-up mechanism beyond the break-up length.

Incidentally, KIVA models droplet collision and dispersion as described in Amsden et al. (1989). If two spray “particles”, which represent groups of droplets, are in the same computational cell, then they either collide or not according to a random process following a Poisson distribution. If they collide, they either coalesce or graze according to an impact parameter that is based on the droplet sizes and Weber number. The Weber number is a dimensionless parameter related to the ratio of the droplet inertia and surface tension forces. Droplet dispersion due to turbulence is estimated by imposing a randomly-fluctuating velocity following a Gaussian distribution with a mean square deviation proportional to the specific turbulent kinetic energy.

Droplet drag was initially modelled in KIVA by assuming the droplets were spherical. Liu and Reitz (1993) observed that droplets in air with a large relative velocity were flattened so that they had a higher drag coefficient than spheres. A 129 spring-mass analogy is used to estimate the distortion of a droplet (the Taylor Analogy Break-up model described in Amsden et al., (1989)). The drag coefficient is then approximated as a function of a droplet distortion parameter. This model is summarised in Kong et al. (1995).

4.2.4 Fuel/wall impingement Fuel droplets may impact on liner or piston surfaces, particularly where high- pressure injectors and bowl-in-piston geometries are used. When this happens, droplets may break up, suddenly vaporise, form a thin liquid film, rebound or slide along the surface (Kong et al., 1995).

The impingement submodel considers only rebounding or sliding phenomena. Droplets rebound if:

Wei < 80 2 ρV d Equation 4-8 We = n 0 i σ where:

Wei = incident Weber number ρ = droplet density

Vn = droplet velocity normal to the surface d0 = droplet diameter σ = surface tension

If this condition is not satisfied, droplets are assumed to slide.

After impingement, droplets have been observed to be highly distorted and tend to break-up sooner. This is modelled by reducing the break-up time constant B1. This also has the effect of bringing the post-impingement droplet sizes into line with experiment.

130

4.2.5 Ignition ESC-lib uses a multistep kinetics combustion model called the “Shell” combustion model. This model was proposed by Halstead et al. (1977) to account for cool flame and two-stage ignition phenomena that are observed during the autoignition of hydrocarbons. Eight reactions represent the transition from fuel through intermediate species to oxidised products. One reaction in particular appears to govern the transition from cool ignition to hot ignition. The pre-exponential constant of this reaction rate is adjusted to match experimental ignition delay periods (Kong et al., 1995).

4.2.6 Combustion The Shell ignition model is considered suitable for low temperature chemistry. Once the temperature reaches 1000-1100 K, a combustion model is activated. The combustion model uses a characteristic time formulation that has been used in spark ignition combustion modelling. Spark ignition engines often have a homogeneous premixed charge, in which the rate of combustion is governed by laminar and turbulent flame speeds. Diesel combustion is obviously very different, with fuel evaporating from many small droplets, resulting in a very heterogeneous mixture. However, combustion in both cases is assumed to be dominated by laminar phenomena initially, then increasingly governed by turbulence (Kong et al., 1995).

Seven species are considered: fuel, oxygen, nitrogen, carbon dioxide, carbon monoxide, hydrogen and water. Six species are considered reactive (all but nitrogen). The rate of change of mass fraction of species m is formulated as:

dYm Ym − Ym * = Equation 4-9 dt tc 131 where:

Ym = mass fraction of species m

Ym* = thermodynamic equilibrium mass fraction of species m tc = characteristic time to reach equilibrium

The characteristic time is assumed the same for all species, and is a combination of a laminar timescale and turbulent timescale: tc = tl + ftt Equation 4-10 where: tl = laminar timescale tt = turbulent timescale f = “delay coefficient”, controlling the significance of turbulence

The laminar timescale is derived from experiments, and the turbulent timescale is proportional to the eddy turnover time: k t = C t 2 ε Equation 4-11 where:

C2 = 0.1 if the RNG k-e model is used.

The coefficient f is calculated by: 1− e −r f = Equation 4-12 1− e−1 where: Y + Y + Y + Y r = CO2 H 2O CO H 2 1− Y Equation 4-13 N2 132

r indicates the completeness of the fuel-air reaction, varying from 0 (no combustion products) to 1 (all combustion products).

4.2.7 NOx formation The well-known extended Zel’dovich mechanism is used. This consists of the following series of reactions:

O + N2 ↔ NO + N Equation 4-14

N + O2 ↔ NO + O Equation 4-15

N + OH ↔ NO + H Equation 4-16

Heywood (1988) expressed the rate of formation of NO as a single equation:

2 d[]NO 1− [NO] (K[O2 ][N 2 ]) = 2k1 f [][]O N 2 dt 1+ k1b []NO ()k2 f []O2 + k3 f []OH Equation 4-17 k k K = 1 f 2 f k1b k2b where: k = reaction rate constant subscripts f and b indicate forward and reverse reaction directions square bracket indicate molar (or volumetric) concentrations.

The rate constants recommended by Bowman (1975) are used. The resultant NO is multiplied by 1.533 to account for the transformation of NO to NOx in the tailpipe and atmosphere.

4.2.8 Soot Soot production is modelled as two separate processes: soot formation from fuel and soot consumption through oxidation. Soot formation is modelled as an Arrhenius rate equation:

133

1  E  2  sf  M& sf = Asf P exp− M fv Equation 4-18  RT  where:

M& sf = rate of soot formation

Asf = pre-exponential constant P = pressure

Esf = the apparent activation energy R = the molar ideal gas constant T = temperature

Mfv = fuel vapour mass

The Nagle and Strickland-Constable (1962) model is used for soot oxidation. It is based on measurements of the oxidation of graphite. The soot surface is assumed to have reactive “A” sites and less reactive “B” sites. Some A sites are converted to B sites. The reaction rate is given by:

K P R = A O2 X + K P ()1− X tot 1+ K P B O2 Z O2

Where X is the proportion of A sites: Equation 4-19

P X = O2 P + K K O2 T B

PO2 = Oxygen partial pressure K = various experimentally-determined rate constants

The soot mass oxidation rate is:

6MWC M& so = Cso M s Rtot Equation 4-20 ρ s d s 134 where:

MWC = the molar weight of carbon

ρs = soot density ds = nominal soot particle diameter

Cso = constant

The parameter Asf is used to tune the model to experimental results.

4.2.9 Computational meshes Two computational meshes representing the Caterpillar SCOTE engine were kindly made available by the Engine Research Center at the University of Wisconsin- Madison. The smaller mesh was a 60º sector mesh. The Caterpillar SCOTE injectors have six equispaced nozzles, and when the valves are closed the combustion chamber therefore has six-fold symmetry. Modelling just one-sixth of the cylinder allows large reductions in computational memory and CPU time requirements, and/or a reduction in the mesh cell size and increase in accuracy. The mesh is shown in Figure 4-2. It has nearly 19,000 cells and 21,000 vertices.

135

Figure 4-2: 60º sector mesh of Caterpillar SCOTE cylinder. The mesh was supplied by the Engine Research Center at the University of Wisconsin-Madison.

For intake and scavenging simulations it was necessary to model the entire cylinder, the valves and a substantial portion of the intake and exhaust ports. Fortunately, such a mesh of the Caterpillar SCOTE engine existed. It is shown in Figure 4-3, and has approximately 150,000 cells and 160,000 vertices. KIVA by default allows up to 50,000 vertices, so modifications had to be made to the source code to allow arrays of sufficient size. Files containing the valve lift profiles were bundled with the model. These valve lift profiles were used in the zero-dimensional simulation described in the preceding chapter.

136

Figure 4-3: Computational mesh of Caterpillar SCOTE engine at BDC. The four valves and the “mexican hat” bowl-in-piston geometry can be discerned. The mesh was supplied by the Engine Research Center at the University of Wisconsin-Madison.

4.3 Validation

Validation of the KIVA-ERC multidimensional model was done using the same experimental data reported by Montgomery (2000) as was used to validate the zero- dimensional model. Specifically, the model results were compared to cases 1-17 described in Section 3.3.1. The procedure for validation was as follows: a) For each case, the zero-dimensional thermodyncamic model was run through ten cycles. The cylinder pressure, temperature and burnt gas fraction at IVO (25º BTDC) were noted. The burnt gas fraction was converted to mass fractions of oxygen, nitrogen, carbon dioxide and water.

137 b) A KIVA-ERC simulation using the full mesh, the initial conditions estimated by the zero-dimensional model and the boundary conditions reported by Montgomery was run until IVC (217º ATDC). c) A KIVA-ERC simulation using the sector mesh was run from IVC until just before SOI. The initial cylinder temperature, pressure, burnt gas fraction, swirl ratio and turbulence parameters at IVC were obtained from the previous KIVA-ERC full mesh simulation. The temperature and pressure were very close to those predicted by the 0-D simulation. KIVA-ERC predicted a slightly higher burnt gas fraction, perhaps because it could account for the piston geometry, which traps residual gases. d) KIVA-ERC simulations using the sector mesh were continued from the previous step, but with a finer time step. This was required to model the injection and combustion processes. This step was repeated several times, with small adjustments made to model parameters until satisfactory agreement between calculation and experiment was reached.

Despite the complexity of the KIVA-ERC model, only a few parameters are adjusted to account for variations in fuel properties and engine hardware. All but one are associated with ESC-lib submodels. They are summarised in Table 4-1. The parameters are adjusted in the same order as the combustion process; for example, the ignition delay parameter is adjusted before the combustion parameters, and the combustion parameters are adjusted before the emissions parameters. The parameters “distant” and “cnst22” are only adjusted if a satisfactory match cannot be achieved by adjusting the first three parameters alone.

138

Table 4-1: Adjustable parameters in KIVA-ERC model, adapted from Hessel (2003) and Kong (2002). Parameter Effect Typical value Model name or range value af04 A larger value speeds up ignition, 104 – 5.0×105 1.25×105 reducing the ignition delay period. denomc A larger value increases the proportion 0.768×1010 0.768×1010 of premixed combustion. cm2 Turbulent timescale constant. A larger 0.1 – 5.0 0.25 value slows diffusion burning. distant Initial break-up length 1.4 – 2.0 1.9 cnst22 Droplet break-up time constant before 10 - 60 40 impingement. Smaller value makes smaller droplets which vaporise faster. asf A larger value increases soot oxidation - 250 rate, reducing the total soot produced rsc Affects NOx formation 1.45 – 2.0 1.47

The model results are compared with Montgomery’s data in Figure 4-4, Figure 4-5 and Figure 4-6.

139

Experimental Calculated

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure Pressure (MPa) 2 0.02 2 0.02 Heat release rate (normalised) release Heat 0 0 0 0 Heat release rate (normalised)

-2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 40 50 Crank angle (deg ATDC) Crank angle (deg ATDC) (a) Case 1 (b) Case 2

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure Pressure (MPa) 2 0.02 2 0.02 Heat release rate (normalised) release Heat 0 0 0 0 Heat release rate (normalised)

-2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 40 50 Crank angle (deg ATDC) Crank angle (deg ATDC) (c) Case 3 (d) Case 4

14 0.14 12 0.12

10 0.1

8 0.08

6 0.06

4 0.04 Pressure (MPa) Pressure 2 0.02

0 0 rate (normalised) release Heat

-2 -0.02 -30 -20 -10 0 10 20 30 40 50 Crank angle (deg ATDC) (e) Case 5

0.8

0.6 Measured KIVA 0.4 2 Soot (g/kg fuel) 14 5 3 4 0.2 5 2 1 3

0 0 102030405060 NOx (g/kg fuel)

(f) Soot vs NOx emissions for Cases 1-5 Figure 4-4: KIVA-ERC model results and experimental data for Mode 3 (75% load, 993 rpm) . Case numbers refer to Table 3-8. 140

Experimental Calculated

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure Pressure (MPa) 2 0.02 2 0.02 Heat release rate (normalised) release Heat 0 0 0 0 Heat release rate (normalised)

-2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 40 50 Crank angle (deg ATDC) Crank angle (deg ATDC) (a) Case 6 (b) Case 7

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure Pressure (MPa) 2 0.02 2 0.02 Heat release rate (normalised) release Heat 0 0 0 0 Heat release rate (normalised)

-2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 40 50 Crank angle (deg ATDC) Crank angle (deg ATDC) (c) Case 8 (d) Case 9

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure Pressure (MPa) 2 0.02 2 0.02 Heat release rate (normalised) release Heat 0 0 0 0 Heat releaserate (normalised)

-2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 40 50 Crank angle (deg ATDC) Crank angle (deg ATDC) (e) Case 10 (f) Case 11 0.8

0.6 7 9 6 11 Measured 0.4 8 7 10 KIVA 6 8

Soot (g/kg fuel) 9 0.2 10 11

0 0 102030405060 NOx (g/kg fuel)

(g) Soot vs NOx emissions for cases 6-11 Figure 4-5: KIVA-ERC model results and experimental data for Mode 5 (57% load, 1737 rpm) . Case numbers refer to Table 3-8. 141

Experimental Calculated

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure Pressure (MPa) 2 0.02 2 0.02 Heat release rate (normalised) release Heat 0 0 0 0 Heat release rate (normalised)

-2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 40 50 Crank angle (deg ATDC) Crank angle (deg ATDC) (a) Case 12 (b) Case 13

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure Pressure (MPa) 2 0.02 2 0.02 Heat release rate (normalised) release Heat 0 0 0 0 Heat release rate (normalised)

-2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 40 50 Crank angle (deg ATDC) Crank angle (deg ATDC) (c) Case 14 (d) Case 15

14 0.14 14 0.14

12 0.12 12 0.12

10 0.1 10 0.1

8 0.08 8 0.08

6 0.06 6 0.06

4 0.04 4 0.04 Pressure (MPa) Pressure Pressure (MPa) 2 0.02 2 0.02 Heat release rate (normalised) release Heat 0 0 0 0 Heat releaserate (normalised)

-2 -0.02 -2 -0.02 -30 -20 -10 0 10 20 30 40 50 -30 -20 -10 0 10 20 30 40 50 Crank angle (deg ATDC) Crank angle (deg ATDC) (e) Case 16 (f) Case 17 1

0.8

1214 0.6 17 16 14 15 Measured 12 13 17 16 13 KIVA 0.4 15 Soot (g/kg fuel) 0.2

0 0 102030405060 NOx (g/kg fuel)

(g) Soot vs NOx emissions for cases 12-17 Figure 4-6: KIVA-ERC model results and experimental data for Mode 6 (20% load, 1789 rpm) . Case numbers refer to Table 3-8. 142

4.4 Discussion

The cases used in the validation of the KIVA-ERC model range from high load, low speed operating conditions to low load, high speed conditions. The essential combustion phenomena, such as ignition delay, premixed combustion (which causes the initial spike in the heat release rate curve), diffusion-controlled combustion are well-predicted over all operating conditions. This indicates that the KIVA-ERC turbulence, spray formation, ignition and combustion submodels, all of which affect these results, are reasonably accurate. The model constants were generally at their default values. Deviation from these values caused deterioration in the model predictions.

There is often a slight divergence of the pressure traces during combustion with the experimental pressure traces falling below the calculated pressure traces (see Figure 4-4, Figure 4-5 and Figure 4-6). The reason for this is not clear. The experimental heat release rate is calculated from the pressure trace, and since the heat release rate shapes are similar, the pressure traces should also be similar.

The emissions trends are generally well-predicted, although there are errors in the absolute values. The model constants were equal for all cases. If the model was matched for each mode, the emissions predictions would be much more accurate. There is also some uncertainty in the emissions measurements. The magnitude of this uncertainty can be estimated from by the difference in measured emissions for the pairs of cases 1 and 4, 6 and 11, and 12 and 17, in which the engine operating conditions are almost identical.

Since the model will be used in the following sections to predict the behaviour of a novel engine system for which there is no experimental data, the emissions models cannot be calibrated. Therefore, there cannot be much confidence in the predicted emissions levels. This means that the model can not reliably indicate whether the two-stroke cycle engine will emit higher or lower levels of pollutants than the four- stroke cycle engine. The only way to improve the predictions would be to improve the emissions models (Kong, 2003), which is outside the scope of this study. 143

However, since the novel engine system notionally uses the same hardware (intake ports, valves, piston and cylinder – note however that the intake valves may be shrouded), the model can be expected to provide useful prediction of the charging and combustion phenomena and emissions trends. Charging phenomena represents scavenging and supercharging in the case of the two-stroke cycle engine, and the heat release rate is required to estimate fuel efficiency. The emissions models can be used to estimate what effect a particular change may make on the emissions levels.

Chapter 5 - Results

5.1 Scavenging simulations 5.1.1 Shroud geometry In Section 2.2.4 the review of prior research indicated that an intake valve shroud subtending an angle of approximately 90° was optimum. Shrouds smaller than this allowed too much short-circuiting of the scavenging flow from the intake directly to the adjacent exhaust valves without the desired scavenging of residual gases, while a larger shroud excessively impeded the intake flow and established a vortex near the middle of the cylinder that trapped residual gases. Four shrouds were investigated using KIVA-ERC and the mesh of the entire Caterpillar SCOTE cylinder (Figure 4- 3). The first shroud was shaped and located based on the results of previous studies. Subsequent shrouds were adjustments to the first shroud aimed at reducing the short- circuit flow. It was expected that the largest (final) shrouds would give the best scavenging efficiency, but at the expense of considerable intake flow restriction.

The pre-processor file used to generate the mesh was unavailable, so the mesh specification file itself (ITAPE17) was modified to reflect the addition of a shroud. ITAPE17 is described in Amsden (1993) and Amsden (1997). The shroud was created by firstly identifying a group of cells that approximated the desired shroud shape. The cell numbers and orientation (each cell has “front”, “left”, “bottom” etc. faces) were determined, then the “F” flag was changed from 1.0 to 0.0, indicating that the cells are “deactivated”. The boundary conditions BCL, BCF and BCB for the shroud cells and some of their neighbours had to be altered to reflect the presence of the shroud surface. FV and IDREG for the shroud cells were unchanged because the shrouds were always only one cell thick. Shroud vertices were given an IDFACE value of –1 so that they behaved like valve stem vertices, i.e. they had the same velocity as the valve, but did not actually change their position with each time step. As the valve moved down and up, the top of the shroud maintained its position just inside the intake port, but the rest of the shroud grew and shrank to maintain a continuous barrier from the top of the shroud to the upper surface of the valve. This was done automatically by KIVA-ERC, using the same process that it uses for valve stems. The way that the valve shroud grows and shrinks as the valves move is 145 illustrated in Figure 5-1, which is a vertical cross section of the cylinder mesh through an intake and exhaust valve. Shroud

Figure 5-1: Cross-section through cylinder mesh showing a shroud on the intake (left) valve.

Simulations were performed with no shroud and four different shroud geometries. The shroud geometries studied are specified in Figure 5-2, Figure 5-3 and Table 5-1.

146

(a) Shroud 1 (b) Shroud 2

(c) Shroud 3 (d) Shroud 4 Figure 5-2: Cross-section of cylinder showing shroud geometries used in KIVA-ERC simulations. The intake poppet valves are in the lower half of the cylinder. The valve stems and shrouds appear white. 147 61

β2

β1

74 θ2 61 θ1

Figure 5-3: Definitions of shroud parameters. Intake valve diameter = 46.7 mm, exhaust valve diameter = 41.8 mm, bore = 137.2 mm

Table 5-1: Shroud parameters (see Figure 5-3 for definitions of symbols).

θ1 (deg) β1 (deg) θ2 (deg) β2 (deg) Shroud 1 110 6 100 -2 Shroud 2 135 18 122 -13 Shroud 3 135 18 147 -1 Shroud 4 170 0 165 9

5.1.2 Initial and boundary conditions Twelve cases were run with each valve shroud type, as well as with no shroud. The case conditions are outlined in Table 5-2.

148

Table 5-2: Scavenging simulation cases.

Speed Pin Tin Pex Valve Case (rpm) (kPa) (K) (bar) timing* 1 993 150 310 100 A 2 993 200 310 100 A 3 993 200 310 150 A 4 993 250 310 150 A 5 1789 200 310 100 A 6 1789 250 310 100 A 7 1789 300 310 200 A 8 1789 350 310 200 A 9 1789 350 360 200 A 10 1789 250 310 100 B Function 11 1789 310 100 A 1** Function 12 1789 310 100 A 2** * A: EVO = 100°, IVO = 130°, EVC = 250°, IVC = 270° ATDC B: EVO = 150°, IVO = 150°, EVC = 260°, IVC = 270° ATDC   CA − IVO   100 + 200 sin π  if IVO < CA < IVC ** Function 1: Pin ()CA =   IVC − IVO  100 otherwise   CA − IVO  300 −100sin π  if IVO < CA < IVC Function 2: Pin ()CA =   IVC − IVO  300 otherwise

In order to investigate the scavenging behaviour over a wide range of conditions, the cases covered low and high engine speeds and a wide range of intake and exhaust pressures. A substantially different valve timing and higher intake gas temperature were each tried to see whether they had significant effects on the scavenging behaviour.

All of the cases except 11 and 12 have constant intake port pressures. Case 11 has an intake pressure function that increases from 100 kPa at IVO to 300 kPa at maximum intake valve lift, then returns to 100 kPa at IVC. Case 12 has a pressure function that 149 decreases from 300 kPa at IVO to 200 kPa at maximum intake valve lift, then returns to 300 kPa at IVC. They are illustrated in Figure 5-4.

400

300

Case 11 200 Case 12

100 Intake port pressure (kPa)

0 0 100 200 300 Crank Angle (degrees ATDC)

Figure 5-4: Intake pressure vs crank angle for Cases 11 and 12.

The simulations were undertaken with a maximum time step of 10 µs. The initial cylinder conditions were estimated by the thermodynamic model described in Chapter 3, assuming perfect diffusion scavenging. The swirl ratio at EVO was set to zero. This is expected to introduce small errors into the results. One alternative is to allow the simulation run for one whole cycle before EVO, however this would increase the run time for each of the sixty cases from approximately three days to approximately nine days and was considered too expensive for the small improvement in accuracy.

5.1.3 Scavenging flow The KIVA-ERC code was modified to write data useful for measuring scavenging parameters to a file. The data include:

150

• the cumulative mass of gas delivered through the intake valves • the total instantaneous cylinder gas mass

• the instantaneous mass of CO2 in the cylinder • the cumulative mass of gas exhausted through the exhaust valves

• the instantaneous mass fraction of CO2 being exhausted

When used in conjunction with the regular KIVA-ERC output, many performance measures can be calculated, such as the delivery ratio, scavenging efficiency, retaining efficiency, exhaust gas purity and valve effective area.

KIVA-ERC runs failed (due to ‘tinvrt overflow’) for Cases 1 and 2 with Shrouds 1, 2 and 3. Restarts were attempted with different initial conditions and reduced time step sizes, however these failed as well. The reason(s) for the failed runs could not be determined during the course of the study. 54 of the 60 runs completed successfully.

To compare the performance of the shrouds, the scavenging efficiency was plotted against the delivery ratio. The delivery ratio was defined as the cumulative mass entering the cylinder through the intake valves between IVO and IVC normalised by the mass of air occupying the displaced volume of the cylinder at atmospheric pressure and 298 K. The results for all successful cases are shown in Figure 5-5.

0.8

No shroud 0.6 Shroud 1 Shroud 2 0.4 Shroud 3 Shroud 4

Scavenging Efficiency 0.2

0 01234 Delivery Ratio

Figure 5-5: Scavenging efficiency versus delivery ratio for all cases with each shroud. 151

Figure 5-5 shows that not having a shroud results in a higher delivery ratio but markedly lower scavenging efficiency that having a shroud. It also shows that as the shroud size is increased, both the delivery ratio and scavenging efficiency are decreased. The reduction in scavenging efficiency with increasing shroud size is most probably due to the reduction in delivery ratio.

Several graphical representations of scavenging simulations are shown in the following figures. The sections or cutplanes correspond to those shown in Figure 5-6. Generally, the figures show a favourable scavenging flow pattern. Fresh charge is directed down the back and sides of the cylinder. At the piston face the flow is diverted towards the centre and front of cylinder. Finally, the flow rises up the centre and front of the cylinder, efficiently pushing the residual gases out the exhaust valves. Small short circuit streams form around and between the pair of intake valve shrouds and flow towards the exhaust valves.

Inspection of gas velocity vectors (Figure 5-7) shows that only a small vortex is formed near the piston surface. Examination of the residual gas fraction contours (Figure 5-8) shows that little residual gas is trapped in the vortex. In fact, the contours do not form a closed loop around the vortex, which would indicate significant trapping of residual gases due to recirculation.

Figure 5-6: Caterpillar SCOTE cylinder sections.

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(a) 178° ATDC (b) 194° ATDC

(c) 206° ATDC (d) 223° ATDC Figure 5-7: Gas velocity vectors in section A-A for Case 6, Shroud 1. The intake valves are to the left. A small vortex is visible above the piston bowl.

153

(a) 178° ATDC (b) 194° ATDC

Figure 5-8: CO2 mass fraction contours in section A-A for Case 6, Shroud 1. Dark shading indicates low mass fraction. Intake valves are to the left. 154

(a) 178° ATDC (b) 194° ATDC

Figure 5-9: CO2 mass fraction contours in sections B-B to E-E for Case 6, Shroud 1. Dark shading indicates low mass fraction. The intake valves are to the left rear.

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Case 1, 160° ATDC Case 9, 160° ATDC

Case 1, 170° ATDC Case 9, 180° ATDC

Case 1, 180° ATDC Case 9, 190° ATDC

Case 1, 200° ATDC Case 9, 220° ATDC Figure 5-10: Comparison of gas composition through sections B-B to E-E during scavenging for Cases 1 (left column) and 9 (right column) with Shroud 4. Adjacent images have approximately equal scavenging gas volumes in the cylinder. 156

5.1.4 Valve flow The 1-D compressible gas flow equations described in Chapter 3 were used to calculate the effective valve areas from KIVA-ERC simulations. Recall that for the 0-D simulation, the valve effective areas were estimated using the valve curtain areas and a relationship for discharge coefficient versus valve lift reported by Heywood and Sher (1999, pp. 187-8) and represented in Figure 3-8. The estimated valve effective areas versus valve lift were plotted in Figure 3-9.

Using the KIVA-ERC-calculated valve flow rates, valve curtain area, intake port and cylinder pressures and gas temperature and composition, the effective valve areas in the KIVA-ERC simulations were calculated and compared with the 0-D estimates in Chapter 3. Note that the 0-D estimates were adjusted to account for the presence of the shroud. This was done by simply reducing the effective area by the same proportion as the reduction in the valve curtain area, so 90° shrouds would reduce the curtain area and effective area by 25%. The results for several cases are shown in Figure 5-11 (intake valves and Shroud 1) and Figure 5-12 (exhaust valves).

0.004

12 6

) 0.003

2 5 8 9 0-D 0.002 estimate 7 Error! 11 Referenc Effective area (m Effective 0.001

0 0 0.004 0.008 0.012 0.016

Time (s)

Figure 5-11: Calculated intake valve effective areas for shroud 1 based on KIVA-ERC results. Case numbers are indicated. The effective area estimated in Figure 3-9, reduced by the shroud area, is shown for comparison.

157

0.0025 0-D estimate 0.002 Error! Rf ) 2 11 6 0.0015 5 12 0.001

Effective area (m area Effective 8 4 9 5 . 10 7

0 0 0.004 0.008 0.012 0.016

Time (s)

Figure 5-12: Calculated exhaust valve effective areas for shroud 1 based on KIVA-ERC results. Case numbers are indicated. The effective area estimated in Figure 3-9, reduced by the shroud area, is shown for comparison.

Examining results for the shrouded intake valves (Figure 5-11), the KIVA-ERC valve effective areas rise more slowly than the 0-D estimate. There is a “knee” in the curves at an effective area of about 0.001 m2, approximately the same value as the knee in the 0-D estimate. Shortly after this point, in all cases but case 11, the KIVA- ERC effective areas climb much higher than the 0-D estimate, then briefly return to approximately the 0-D estimate.

The differences between the KIVA-ERC effective areas and the 0-D estimate can be partly attributed to gas dynamics. The effective area is based on the ratio of the intake port boundary pressure and the bulk cylinder pressure. When the intake flow is suddenly accelerated, the pressure at the valve deviates from that at the port boundary (the “ram effect” described in Heywood and Sher (1999, p. 193) and others).

The peaks in Figure 5-11 which apparently approach infinity coincide with rapid deceleration of the intake flow. These peaks are greatly magnified because they occur when the pressure ratio is close to unity, and small differences in the flow rate yield large differences in the calculated effective area. This hypothesis is supported 158 by case 11, in which the intake port boundary pressure rises and falls approximately with the valve lift. The intake flow is more constant in this case, and the KIVA-ERC effective area is approximately the same as the 0-D estimate for most of the valve open period. KIVA-ERC-calculated pressures in the intake and exhaust ports were examined at times when the calculated effective area differed from the 0-D estimation. Representative results are shown in Figure 5-13 and Figure 5-14. They clearly demonstrated significant differences between the pressures near the upper surfaces of the intake and exhaust valves and the imposed, constant pressure at the port boundaries. This is consistent with reasoning based on gas dynamics.

Figure 5-13: Pressure contours in the intake port for Shroud 1, Case 5 at 202 deg ATDC, showing the pressure gradient between the port boundary and the intake valves due to flow deceleration (the “ram effect”). Zero-dimensional modelling assumes constant pressure throughout the port. 159

Figure 5-14: Pressure contours in the exhaust port for Shroud 1, Case 5 at 175 deg ATDC. Here, the pressure difference between the region above the valve and the port boundary appears to be due to the port geometry.

Examination of Figure 5-12 shows that the KIVA-ERC effective areas vary significantly from the 0-D estimate, and vary significantly from case to case. The maximum KIVA-ERC effective areas are approximately half of the 0-D estimate, and some cases exhibit dips in the KIVA-ERC effective area at maximum valve lift. The maximum discharge coefficient is therefore approximately 0.3 – 0.4, which is much less than the experimentally-determined values reported by Heywood (1989).

The discrepancies in the intake and exhaust valve effective areas may be attributed to the relative coarseness of the mesh on the scale of the valves and the inability of KIVA-ERC to accurately model complex flow details that influence the effective area, especially flow separation.

The KIVA-ERC simulations generally predict lower air consumption than the 0-D simulations. The results for some cases with Shroud 1 are tabulated below. Agreement is within 20%. Note that the KIVA-ERC results are sensitive to the initial conditions that were estimated using 0-D modelling, whereas the 0-D simulations had run over at least ten cycles and had converged to a solution. 160

Table 5-3: Predicted air consumption for cases using KIVA-ERC and 0-D modelling. Case 3 4 5 6 7 8 9 10 KIVA 4.9 8.0 7.8 8.1 8.9 12.4 11.7 6.7 (kg/min) 0-D 6.0 8.9 7.1 10.5 9.1 11.8 14.1 8.1 (kg/min)

Experimentation is necessary to determine whether real air consumption more closely matches the 0-D model or KIVA-ERC model.

5.2 O-D Scavenging model 5.2.1 Description Examination of graphical representations of the KIVA-ERC scavenging simulations in the previous section revealed geometrical similarities in the scavenging flow entering the cylinder. For example, Figure 5-10 shows the concentration of CO2 at four horizontal cross-sections through the cylinder at four points in time for cases 1 and 9. These cases represent different speeds (993 rpm vs 1789 rpm) and different scavenging pressures (150 kPa vs 350 kPa), yet the scavenging flow appears similar in each case. This similarity suggested a simple scavenging model in which the only independent variable was the ratio of the instantaneous volume of fresh charge in the cylinder to the total instantaneous cylinder volume. This parameter was called the scavenging volume fraction. One sensitive measure of scavenging behaviour is the exhaust gas purity, α (Heywood and Sher, 1999). The exhaust gas purity is defined as the mass fraction of fresh charge in the exhaust gas at any given instant. Plots of α versus scavenging volume fraction for all cases using shroud 4 are summarised in Figure 5-15.

161

1 1 2 0.8 3 4 0.6 5 6 α 7 0.4 8 9 0.2 10 11 12 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Scavenging volume fraction Figure 5-15: α vs scavenging volume fraction for all cases with shroud 4.

Figure 5-15 shows that while there are similarities between the various cases, there is also significant variation that renders it inadequate. Examination of these plots and graphical output shows an apparent two-stage process occurring. The first stage is dominated by the exhaust of residual gases and the development of short-circuit flow. At a scavenging volume fraction of between 0.4 and 0.6 a relatively sharp transition begins to a second stage, in which the exhaust gas is a mixture of residual and intake gas, as well as the short circuit flow. The situation is represented graphically as in Figure 5-16.

162

Inlet Exhaust

m& sc m& 1e m& sc m& 2e m& i m& i

Zone 2 Zone 1

Zone 2

m& 12

Stage 1 Stage 2 Figure 5-16: Representation of two-stage scavenging process.

The model assumes that at IVO the cylinder contents, which are residual gases, are contained in zone 1. As intake gases enter the cylinder, a portion is short-circuited to the exhaust port at a rate m& sc that varies with time, and the remainder go into a second zone called zone 2. Some of the gas in zone 1 enters and mixes with the gas in zone 2 at a time-varying rate m&12 . The gas flowing through the exhaust valve is a mixture of the short-circuit flow and zone 1 gas. The transition to Stage 2 occurs when the mass in zone 1 is entirely depleted. The exhaust flow is then a mixture of the short-circuit flow and zone 2 gas.

In order to complete the model, functions for m& sc and m&12 were assumed.

Examination of KIVA-ERC simulations indicated that m& sc was a approximately a constant fraction of the intake flow m& i , or:

xm& i if m& e > xm& i m& sc =  Equation 5-1  m& e otherwise where: x = proportionality constant

m& e = total exhaust flow

163

One slight difficulty with Equation 5-1 is that the exhaust gas composition is a function of the exhaust gas rate, however the exhaust gas rate is a function of the exhaust gas composition (see Equation 3-19, Equation 3-20 and Equation 3-21). The system of equations Equation 3-19, Equation 3-20, Equation 3-21 and Equation 5-1 must therefore be solved. A simple iterative scheme was used to achieve this.

It was assumed that the volumetric rate of mixing of zone 1 into zone 2 was proportional to the speed of the engine, reflecting the variation of the level of turbulence in the cylinder with engine speed. The mass rate of zone 1 entering zone 2 can therefore be expressed:

m&12 = kωρ1 Equation 5-2 where: k = proportionality constant ω = engine speed

ρ1 = zone 1 density

The composition of zone 1 is constant, always being entirely composed of residual gases. The rate of change of mass in zone 1 is:

m& 1 = m& 1e + m& 12 Equation 5-3 where:

m& 1e = m& e − m& sc Equation 5-4

The rate of change of temperature in zone 1 can be derived by combining Equation 3-3, the perfect gas relation, and Equation 3-7, conservation of energy, and assuming the burned gas fraction is constant:

R()φ T T& = 1 1 P& 1  ∂u    + R(φ ) Equation 5-5 ∂T 1  T1 ,φ1 where: 164

T1 = temperature of the gas in zone 1 R = the specific gas constant (Equation 3-16) of the gas in zone 1 u = the specific internal energy (Equation 3-15) of the gas in zone 1 P =cylinder pressure

There is no need to explicitly determine the gas state in zone 2 if the bulk cylinder gas state (zone 1 + zone 2) is being calculated as described in Section 3. When zone 1 is exhausted, zone 2 simply becomes the bulk cylinder gas.

5.2.2 Comparison with KIVA-ERC calculations The model was compared with the sixty runs discussed in Section 5.1. The output of each run was processed using Mathcad to generate functions of time of the following quantities:

• Cylinder pressure P(t) • Mass of cylinder contents m(t)

• Cumulative mass flow through the intake valves mi(t)

• Cumulative mass flow through the exhaust valves me(t) • Bulk cylinder gas temperature T(t)

• Mass of CO2 in the cylinder mCO2(t)

• Mass fraction of CO2 flowing past the exhaust valves mfCO2e(t)

The exhaust gas purity is defined as the mass fraction of fresh charge in the exhaust gas at any instant (Heywood and Sher, 1999), so: mfCO2e (t) = α(t) mfCO2 f + [1−α(t)]mfCO2r Equation 5-6 where: mfCO2f = mass fraction of CO2 in fresh charge mfCO2r = mass fraction of CO2 in residual gases

Rearranging:

mfCO2e − mfCO2r α(t)= Equation 5-7 mfCO2 f − mfCO2r 165

m(0) Since mfCO2f = 0 for all KIVA cases and mfCO2r = where IVO occurs at t mCO2 (0) = 0: m(0) α(t)= 1− mfCO2e (t) Equation 5-8 mCO2 (0)

The scavenging efficiency is defined as the mass of fresh charge retained in the cylinder divided by the mass of the cylinder contents:

t m (t) − α(t) m (t) dt i ∫ & e η (t)= 0 Equation 5-9 sc m(t)

Substituting the expression for exhaust gas purity (Equation 5-8):

t  m(0)  mi (t) − 1− mfCO2e (t) m& e (t)dt ∫ mCO (0)  η (t)= 0  2  Equation 5-10 sc m(t)

Integrating and simplifying:

 mCO (t)  m (t) − m (t) + m(0)1− 2  i e  mCO (0)  η (t)=  2  Equation 5-11 sc m(t)

Since m(t) = mi(t) – me(t) + m(0):

m(0) mCO2 (t) ηsc (t)= 1− Equation 5-12 m(t) mCO2 (0)

166

The scavenging efficiency that would have been achieved if the residual cylinder gases were displaced by the intake gases with no mixing or short-circuiting (the “perfect displacement” model) was calculated using:

mi (t)  if mi (t) < m(t) ηsc.disp (t)=  m(t) Equation 5-13  1 otherwise

The scavenging efficiency that would have been achieved if the intake gas instantly mixed with the cylinder contents (the “perfect mixing” model) was also calculated. With perfect mixing, the exhaust gas purity is equal to the scavenging efficiency, or:

α(t)= η sc (t) Equation 5-14

So, from Equation 5-9:

t m (t) − η (t)m (t)dt i ∫ sc & e η (t)= 0 Equation 5-15 sc m(t)

Differentiating:

t m (t) − η (t) m (t) dt i ∫ sc & e m& i (t) −ηsc (t) m& e (t) 0 Equation 5-16 η&sc (t)= − m& (t) m(t) m(t) 2

Simplifying:

m& i (t) −ηsc (t) m& e (t) ηsc (t) η&sc (t)= − m& (t) m(t) m(t) Equation 5-17

Rearranging: 167

m& i (t) −ηsc (t)[]m& e (t) − m& (t) η&sc (t)= m(t) Equation 5-18

Since m& (t) = m& i (t) − m& e (t) and replacing ηsc with ηsc.diff to avoid confusion:

m& i (t) η&sc.diff (t)= ()1−ηsc.diff (t) m(t) Equation 5-19

This ODE was solved using Mathcad’s built-in 4th-order Runge-Kutta solver to obtain ηsc.diff(t).

The delivery ratio is defined as the mass of fresh charge delivered divided by a reference mass, usually the displacement volume × the fresh charge density at ambient conditions:

m (t = IVC) m (t = IVC) Λ= i = i 2.44L ×1.185kg m −3 2.89g Equation 5-20

When comparing the 0-D model to KIVA-ERC calculations, the KIVA-derived valve flow rates, cylinder masses and pressures were used. For stage 1, when there are two zones in the cylinder, the following expressions were used: Zone 1 mass:

t m (t) = − m − m + m dt 1 ∫ ()& e & sc & 12 Equation 5-21 0 where: msc is defined in Equation 5-1 m12 is defined in Equation 5-2

For Stage 1, when m1(t) > 0:

168

m& sc α(t) = Equation 5-22 m& e

and from Equation 5-16 and Equation 5-22:

m& i (t) − m& sc (t) −ηsc (t) m& (t) η&sc (t) = m(t) Equation 5-23

For Stage 2, when m1(t) has reached zero:

m& sc + (1−ηsc )m& 2e α(t) = Equation 5-24 m& e

and from Equation 5-16 and Equation 5-24:

m& i (t) − m& sc (t) − ()1−ηsc m& 2e −ηsc (t) m& (t) η&sc (t) = m(t) Equation 5-25

To illustrate the application of these relations, take for example Case 4 (referring to the conditions in Table 5-2) with shroud 1 (described in Table 5-1). The quantities calculated by KIVA-ERC are shown in Figure 5-17.

169

1 Temperature × 10-3 K

Pressure × 10-6 Pa

-1 0.5 Mass × 10 kg

Cumulative exhaust -1 mass × 10 kg -2 CO2 mass × 10 kg Cumulative intake mass × 10-1 kg

0 0 0.014 0.029

Time (s) → Figure 5-17: KIVA-ERC-calculated cylinder quantities for Case 4, Shroud 1 from EVO to IVC.

The data represented in Figure 5-17 and several guesses of the calibration constants x and k were then tried until satisfactory matches of the exhaust gas purity and scavenging efficiency were achieved for all cases using a particular shroud. The calculated zone 1 quantities and the relevant equations used are shown in Figure 5-18. The calculated exhaust gas purities and scavenging efficiencies are shown in Figure 5-19.

170

1 Temperature × 10-3 K (Equation 5-5)

Mass × 10-1 kg (Equation 5-21)

0.5 m& 1 × kg/s (Equation 5-3)

m& 12 × kg/s (Equation 5-2)

m& sc × kg/s (Equation 5-1) 0 0 0.0084 0.0168

Time (s) →

Figure 5-18: Zone 1 quantities calculated from Figure 5-17 and matched calibration constants x = 0.1 and k = 8 × 10-4.

1 ηsc.disp (Equation 5-13)

ηsc.KIVA (Equation 5-12)

ηsc.0-D (Equation 5-25)

ηsc.diff (Equation 5-19) 0.5

αKIVA (Equation 5-7)

α0-D (Equation 5-24) 0 0 0.015 0.029

Time (s) →

Figure 5-19: Calculated exhaust gas purities and scavenging efficiencies for Case 4, Shroud 1.

171

This procedure was repeated for all sixty combinations of cases and shrouds (Figure 5-20 to Figure 5-24).

ηsc.0-D ηsc.KIVA ηsc.disp 1 1 1 ηsc.diff

0.5 0.5 0.5

0 0 0 0 0.015 0.029 0 0.015 0.029 0 0.014 0.029 (a) Case 1 (b) Case 2 (c) Case 3 1 1 1

0.5 0.5 0.5

0 0 0 0 0.014 0.029 0 0.008 0.016 0 0.008 0.016 (d) Case 4 (e) Case 5 (f) Case 6 1 1 1

0.5 0.5 0.5

0 0 0 0 0.008 0.016 0 0.008 0.016 0 0.008 0.016 (g) Case 7 (h) Case 8 (i) Case 9 1 1 1

0.5 0.5 0.5

0 0 0 0 0.005 0.01 0 0.008 0.016 0 0.008 0.016 (j) Case 10 (k) Case 11 (l) Case 12 Figure 5-20: Comparison of KIVA and two-zone scavenging model results for no shroud on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.34 and k =1.0. 172

ηsc.0-D ηsc.KIVA ηsc.disp 1 ηsc.diff

0.5 No data No data

0 0 0.015 0.029

(a) Case 1 (b) Case 2 (c) Case 3 1 1 1

0.5 0.5 0.5

0 0 0 0 0.015 0.029 0 0.008 0.016 0 0.008 0.016 (d) Case 4 (e) Case 5 (f) Case 6 1 1 1

0.5 0.5 0.5

0 0 0 0 0.008 0.016 0 0.008 0.016 0 0.008 0.016 (g) Case 7 (h) Case 8 (i) Case 9 1 1 1

0.5 0.5 0.5

0 0 0 0 0.005 0.01 0 0.008 0.016 0 0.008 0.016 (j) Case 10 (k) Case 11 (l) Case 12 Figure 5-21: Comparison of KIVA and two-zone scavenging model results for shroud 1 on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.12 and k = 7 × 10-4.

173

ηsc.0-D ηsc.KIVA ηsc.disp 1 ηsc.diff

0.5 No data No data

0 0 0.015 0.029   (a) Case 1 (b) Case 2 (c) Case 3 1 1 1

0.5 0.5 0.5

0 0 0 0 0.015 0.029 0 0.008 0.016 0 0.008 0.016   (d) Case 4 (e) Case 5 (f) Case 6 1 1 1

0.5 0.5 0.5

0 0 0 0 0.008 0.016 0 0.008 0.016 0 0.008 0.016 (g) Case 7 (h) Case 8 (i) Case 9 1 1 1

0.5 0.5 0.5

0 0 0 0 0.005 0.01 0 0.008 0.016 0 0.008 0.016 (j) Case 10 (k) Case 11 (l) Case 12 Figure 5-22: Comparison of KIVA and two-zone scavenging model results for shroud 2 on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.10 and k = 8 × 10-4.

174

ηsc.0-D ηsc.KIVA ηsc.disp 1

ηsc.diff

0.5 No data No data

0 0 0.015 0.029

(a) Case 1 (b) Case 2 (c) Case 3 1 1 1

0.5 0.5 0.5

0 0 0 0 0.015 0.029 0 0.008 0.016 0 0.008 0.016 (d) Case 4 (e) Case 5 (f) Case 6 1 1 1

0.5 0.5 0.5

0 0 0 0 0.008 0.016 0 0.008 0.016 0 0.008 0.016 (g) Case 7 (h) Case 8 (i) Case 9 1 1 1

0.5 0.5 0.5

0 0 0 0 0.005 0.01 0 0.008 0.016 0 0.008 0.016 (j) Case 10 (k) Case 11 (l) Case 12 Figure 5-23: Comparison of KIVA and two-zone scavenging model results for shroud 3 on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.09 and k = 8.5 × 10-4.

175

ηsc.0-D ηsc.KIVA ηsc.disp 1 1 1 ηsc.diff

0.5 0.5 0.5

0 0 0 0 0.015 0.029 0 0.015 0.029 0 0.015 0.029 (a) Case 1 (b) Case 2 (c) Case 3 1 1 1

0.5 0.5 0.5

0 0 0 0 0.015 0.029 0 0.008 0.016 0 0.008 0.016 (d) Case 4 (e) Case 5 (f) Case 6 1 1 1

0.5 0.5 0.5

0 0 0 0 0.008 0.016 0 0.008 0.016 0 0.008 0.016 (g) Case 7 (h) Case 8 (i) Case 9 1 1 1

0.5 0.5 0.5

0 0 0 0 0.005 0.01 0 0.008 0.016 0 0.008 0.016 (j) Case 10 (k) Case 11 (l) Case 12 Figure 5-24: Comparison of KIVA and two-zone scavenging model results for shroud 4 on the intake valves. Case numbers refer to conditions described in Table 5-2. Results for the perfect displacement and diffusion models are also indicated. The x-axis is time from EVO in seconds. For each case x = 0.07 and k = 9.0 × 10-4.

176

The results are summarised in Table 5-4.

Table 5-4: Comparison of scavenging efficiencies calculated using the 0-D model and KIVA- ERC. No shroud Shroud 1 Shroud 2 Shroud 3 Shroud 4 x = 0.34 x = 0.12 x = 0.10 x = 0.09 x = 0.07 k = 1 k = 7.0×10-4 k = 8.0×10-4 k = 8.5×10-4 k = 9.0×10-4 Case 0-D KIVA 0-D KIVA 0-D KIVA 0-D KIVA 0-D KIVA (Table 5-2) 1 0.78 0.78 ------0.90 0.88 2 0.81 0.81 ------0.92 0.92 3 0.72 0.71 0.87 0.86 0.85 0.85 0.85 0.84 0.84 0.83 4 0.77 0.76 0.91 0.90 0.89 0.90 0.89 0.89 0.88 0.88 5 0.61 0.61 0.77 0.77 0.74 0.75 0.74 0.74 0.72 0.73 6 0.55 0.56 0.74 0.75 0.76 0.78 0.77 0.78 0.76 0.77 7 0.51 0.51 0.68 0.68 0.65 0.66 0.64 0.64 0.62 0.63 8 0.58 0.57 0.74 0.74 0.71 0.72 0.71 0.71 0.69 0.69 9 0.60 0.60 0.78 0.78 0.75 0.76 0.74 0.74 0.73 0.73 10 0.55 0.55 0.64 0.63 0.62 0.61 0.62 0.60 0.60 0.58 11 0.58 0.59 0.78 0.78 0.76 0.76 0.75 0.76 0.75 0.74 12 0.68 0.69 0.82 0.82 0.79 0.80 0.79 0.79 0.77 0.78

Given the complex nature of the in-cylinder flow field, the widely-varying engine speeds, intake pressures valve timings and exhaust back pressures modelled, the agreement is very good in all cases. This gives confidence that other results within the wide range of parameters in Cases 1 to 12 will be similarly accurate. This model was incorporated in the zero-dimensional model described in Chapter 3. The zero- dimensional modelling results presented from this point on used this model, except where noted otherwise.

177

5.3 System simulations 5.3.1 Revision of combustion correlation constants In the absence of experimental heat release rate data from two-stroke poppet-valved heavy-duty diesel engines, KIVA-ERC simulations were used. Eighteen cases were run, representing three engine systems at each of the six modes of the FTP approximation. The three engine systems were: • The Caterpillar SCOTE adapted to a two-stroke cycle • A two-cylinder engine based on the SCOTE cylinder with a reciprocating air pump • A turbocharged and intercooled version of the system above

Conditions at IVC were estimated with the thermodynamic model using the combustion correlation constants estimated in Section 3.2.7.

The SCOTE 60° sector mesh described in Section 4.2.9. (especially Figure 4-2) was used. The simulations were run from IVC until EVO. The injection rate shape was calculated from Equation 3-30. The adjustable KIVA-ERC model constant values were those reported in Table 4-1.

Additionally, the initial swirl ratio and turbulence parameters were estimated from the KIVA scavenging simulations reported in Section 5.1 using the full SCOTE mesh. The calculated values of the parameters at IVC are shown in Table 5-5. They are reasonably insensitive to engine operating conditions, and mean values were used for all simulations using the SCOTE 60° sector mesh in this and subsequent sections for consistency. The initial swirl ratio was assumed to be 0.39, the turbulent kinetic energy parameter tkei was set at 6.6 and the length scale was 1.33 cm.

For four-stroke simulations, tkei is usually between 0.1 and 1.6 (Hessel et al., 2003). The higher value in the two-stroke cases reflects the higher intake gas flow rate and the turbulence-generating effect of the intake valve shroud.

178

Table 5-5: Turbulence and swirl values at IVC for the Shroud 1 cases listed in Table 5-2. Turbulent kinetic Turbulent kinetic Turbulence length Swirl Case energy (106cm2/s2) energy ratio scale (cm) ratio 1 - - - - 2 - - - - 3 1.02 6.7 1.40 0.43 4 1.15 7.5 1.44 0.30 5 3.10 6.3 1.36 0.38 6 3.01 6.1 1.47 0.33 7 2.57 5.2 1.30 0.33 8 2.96 6.0 1.34 0.37 9 3.12 6.3 1.33 0.41 10 4.23 8.5 0.96 0.21 11 3.35 6.8 1.44 0.85 12 3.26 6.6 1.29 0.28 Mean - 6.6 1.33 0.39

The procedure for determining the correlation constants was identical to that described in Section 3.2.7.

The ignition delay constants (Section 3.2.7.4) used are listed below.

A1 = 0.00385

A2 = 6580

A3 = 0.50

Previously, the constants were 2.33, 2230, 0.94. The higher apparent activation energy (A2) indicates a decline in the effect of physical processes such as evaporation and mixing, perhaps due to greater turbulence, and are closer to value determined for premixed fuel-air mixtures (Heywood, 1989, p. 544).

The correlation is compared with the KIVA-ERC results in Figure 3-13 and Figure 3- 14..

179

1.5

KIVA-ERC 1 Correlation

Ignition delay (ms) 0.5

0 800 900 1000 1100

Mean temperature T m (K)

Figure 5-25: Ignition delay vs mean temperature.

1.5

KIVA-ERC 1 Correlation

Ignition delay (ms) 0.5

0 20 30 40 50 60 70

Mean pressure P m (bar)

Figure 5-26: Ignition delay vs mean pressure.

The values used for the premixed combustion correlation (Section 3.2.7.5) were:

A4 = 0.41

A5 = 1.50

A6 = 1.17

180

A comparison of the data and the correlation is shown in Figure 3-15 and Figure 3- 16..

0.8

0.6 KIVA-ERC β Correlation 0.4

0.2

0 00.20.40.60.81 δ

Figure 5-27: Comparison of KIVA-ERC results and the β correlation vs δ.

0.8

0.6 KIVA-ERC β Correlation 0.4

0.2

0 00.511.52

Ignition delay t ID (ms)

Figure 5-28: Comparison of KIVA-ERC results and the β correlation vs ignition delay.

181

The expressions for the rate shape constants used in the model were:

Cp1 = 1.90

Cp2 = 5000 -1.07 -0.90 Cd1 = 0.079 + 1.47φ β -0.33 -0.40 Cd2 = -0.061 + 0.53φ β

τd = -0.14 + 0.081 Cp1

The diffusion burning rate shape parameters Cd1 and Cd2 reflect faster mixing due to the increased turbulence in two-stroke cycle operation.

5.3.2 Two-stroke adaptation of Caterpillar SCOTE The 0-D model described in Chapter 3 with the two-zone scavenging model developed in Section 5-2 and the multidimensional model described in Chapter 4 were used to predict the performance of the Caterpillar SCOTE (described in Figure 3-10 and Table 3-3) if it was converted to a two-stroke cycle. If this were to be performed experimentally, the following modifications would be required: a) The valve gear speed would have to be doubled, so that the camshafts rotated at the engine speed, rather than at half the engine speed. b) The valve timing would have to be altered. In practice, new camshafts would have to be manufactured. c) Shrouds would have to be attached to the intake valves. Some means would be required to prevent the shrouds from rotating. Valves are usually allowed to rotate to allow even wear. Kang et al. (1996) describes one method of preventing shrouds from rotating while allowing the valves to rotate. d) The fuel pump would have to be doubled in speed to allow injection once per engine revolution. If the same injection characteristics were required, the fuel pump cam would have to be altered to allow for the doubling of the pump speed. e) A pressure differential between the intake and exhaust ports is required for scavenging. Constant intake pressures of either 150 kPa or 200 kPa were used for initial studies. Later, the boost pressure was supplied by reciprocating air pumps and turbochargers which would better represent real engine systems. 182

For the numerical simulation, the following simple changes needed to be made to the Caterpillar SCOTE input files for the thermodynamic model: f) The cycle flag was changed from 4.0 (4-stroke) to 2.0 (2-stroke). g) The fuel mass injected per cylinder per cycle was reduced to maintain the same power output. h) The scavenging model flag was changed from 0.0 (perfect diffusion model, suitable for 4-stroke calculations) to 1.0 (two-zone scavenging model, suitable for 2-stroke poppet-valved engines). The scavenging model constants x and k was adjusted to be consistent with multidimensional calculations. i) The valve timings were altered. j) The intake and exhaust pressures were altered to give satisfactory scavenging flow. k) The combustion correlation constants were altered to better estimate the ignition delay, proportion of fuel in premixed combustion and the heat release rate.

For the simulations, Shroud 1 (referring to Table 5-1) was used, because it provided good scavenging with the least valve flow obstruction. The valve effective area was assumed to be due to the shroud was assumed to be proportional to the reduction in valve curtain area, or 29%.

Valve timing was explored parametrically, with engine speed, fuel rate, injection timing, intake pressure and temperature and exhaust pressure held constant. The following valve timing parameters were explored:

• EVO (° ATDC) = 90, 95 … 160 • IVC (° ATDC) = 240, 245 … 270 • IVO – EVO (° CA) = 0, 5 … 15 • IVC – EVC (° CA) = 0, 5 … 25

The total number of combinations of these parameters is 1,512. 183

The function to be maximised was simply the reciprocal of the brake specific fuel consumption (BSFC). This was so as to find the parameters giving the most fuel efficient system. In practice, emissions must also be taken into account. However, since there is currently no accurate means of predicting emissions in novel engine systems, emissions could not be included in the merit function.

There were additional constraints placed on the merit function: l) The predicted maximum burnt gas fraction was not to exceed 0.7, to ensure adequate available oxygen for high combustion efficiency and low emissions. m) The maximum cylinder pressure was not to exceed 15 MPa to avoid overstressing the engine, as suggested by Montgomery (2000). n) The root-mean-square difference between the predicted cylinder mass, burnt gas fraction and temperature at one degree intervals for two consecutive cycles at was to be less than 1%, indicating convergence towards a solution. RMS values much less than this were possible with the perfect diffusion scavenging model, however the two-zone scavenging model introduced some instability to the numerical solution, and values much smaller than 1% excluded too great a proportion of results, even when the calculation was set to run over 100 engine cycles. o) The predicted premixed fuel combustion fraction was to be less than 100%. Physically, values exceeding 100% are impossible, and predicted values greater than this were assumed to indicate that conditions were such that the ignition model was no longer valid and/or that conditions were not suitable for diesel autoignition.

The calculations with the 1,512 parameter combinations for each mode took less than two hours CPU time on a Silicon Graphics Origin 3000 computer. Approximately 20% of the combinations violated one of the four constraints or caused the ordinary differential equation integrator to fail.

Mechanical valve train considerations were considered outside the scope of this study. It is noted that a combination of high valve lift, short valve open period and 184 high engine speed could lead to unacceptable wear, spring surge and other unacceptable phenomena.

Combustion and emissions calculations were performed using KIVA-ERC and the SCOTE 60° sector mesh described in Section 4.2.9 (especially Figure 4-2). The simulations were run from IVC until EVO. Conditions at IVC (initial temperature, pressure and gas composition) were taken from the 0-D results. The injection rate shape was calculated from Equation 3-30.. The adjustable KIVA-ERC model constant values were those reported in Table 4-1.

The results are summarised and compared with 4-stroke “baseline” SCOTE data in Table 5-6. Note that the 4-stroke emissions values are not measured values but were calculated using KIVA-ERC. This was done to provide a more “apples with apples” comparison that might give more insight as to whether emissions would be increased or decreased. It should be noted that the two-stroke cases are possibly sufficiently different from the four-stroke cases that the KIVA-ERC model constants should be adjusted and direct comparisons are not necessarily valid. 185

Table 5-6: Predicted near-optimum valve timings, engine performance and combustion parameters for Modes 1-6 with the Caterpillar SCOTE engine running on a two-stroke cycle with Shroud 1 on the intake valves. Four-stroke results (italicised) are shown for comparison. Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Input parameters

Brake Power (kW) 0.5 7.9 31.3 38.5 30.0 12.7 (0.3) (7.6) (29.6) (38.4) (28.4) (12.7) BSFC (g/kWh) N/A 246 198 232 219 278 (266) (212) (264) (244) (303) Max. press. (MPa) 3.3 5.4 9.5 5.3 6.6 6.5 (5.6) (6.8) (10.3) (10.0) (8.1) (6.3) Ignition delay (ms) 4.2 1.83 0.69 0.60 1.03 1.12 (1.24) (0.91) (0.44) (0.50) (0.45) (0.64) Premixed burn 99 93 29 28 77 80 fraction (%) (77) (76) (8) (13) (9) (28) Max. burnt gas 0.11 0.23 0.62 0.67 0.40 0.22 fraction (0.14) (0.35) (0.69) (0.47) (0.39) (0.32)

On a practical engine system, the valve timing would be constant over all speeds and loads. To estimate these parameters, a 6-mode FTP cycle approximation similar to 186 that used by Montgomery and Reitz (1996) and Montgomery (2000) was used. From the former reference the mode weightings were calculated to be approximately: Mode 1 46.5% Mode 2 12.0% Mode 3 7.1% Mode 4 10.8% Mode 5 12.9% Mode 6 10.7%

The optimum parameters were those that minimised the cycle BSFC. The cycle BSFC for each combination of parameters was evaluated as follows:

∑()Fuelratemode ⋅Wmode Cycle BSFC = modes  Fuelrate  Equation 5-26  mode  ∑  ⋅Wmode  modes  BSFCmode 

Where Wmode is the weighting for each mode.

Every combination of valve timings was evaluated and the optimum was found to be: IVO = 145° ATDC IVC = 280° ATDC EVO = 140° ATDC EVC = 270° ATDC The cycle BSFC is 252 g/kWh and the modal BSFCs are shown in Table 5-9.

Note that the cycle BSFC for the baseline case is 272 g/kWh, the cycle NOx is 7.4 g/kWh and the cycle PM is 0.079 g/kWh.

187

Table 5-7: Modal BSFCs for valve timings optimised for a 6-mode FTP cycle approximation. (IVO=145, IVC=280, EVO=140, EVC=270ºATDC). Four-stroke baseline results are italicised. Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Input parameters

Speed (rpm) 750 953 993 1657 1737 1789 Intake air pressure 150 150 150 200 200 200 (kPa, absolute) Intake air 298 298 298 298 298 298 temperature (K) Exhaust pressure 100 100 100 100 100 100 (kPa, absolute) Fuel rate 0.013 0.034 0.104 0.102 0.063 0.033 (g/cyl/cycle) SOI (° ATDC) 352.0 359.5 354.5 367.5 361.5 354.5 Performance Brake power (kW) 0.1 7.8 31.2 37.9 29.6 12.1 BSFC (g/kWh) N/A 249 198 236 222 294 (266) (212) (264) (244) (303) Max. press. (MPa) 6.0 6.3 9.3 4.9 6.7 7.2 (5.6) (6.8) (10.3) (10.0) (8.1) (6.3) Ignition delay (ms) 1.51 1.33 0.93 1.22 0.63 0.61 (1.24) (0.91) (0.44) (0.50) (0.45) (0.64) Premixed burn 89 86 41 73 37 33 fraction (%) (77) (76) (8) (13) (9) (28) Max. burnt gas 0.08 0.22 0.67 0.73 0.37 0.21 fraction (0.14) (0.35) (0.69) (0.47) (0.39) (0.32)

NOx (g/kg fuel) 0.69 13 86 -* 5.5 21 (69) (64) (45) (15) (13.8) (22) Soot (g/kg fuel) 0.47 0.23 0.016 - 0.27 0.25 (0.16) (0.098) (0.18) (0.17) (0.47) (0.54) *No ignition predicted by KIVA-ERC.

5.3.3 Addition of Reciprocating Air Pump The Caterpillar SCOTE engine model was adapted to incorporate a reciprocating air pump, similar to that described in Figure 1-3. Assuming the air pump operates at twice the engine speed and each pump cylinder scavenges two engine cylinders, a six-cylinder engine can be considered as three sub-units in parallel, each sub-unit 188 comprising one pump cylinder and two engine cylinders (Figure 5-29). Therefore, only one of these sub-units need be modelled, saving much computational effort.

Engine

Air pump (2 x engine speed)

Reed valve Poppet valve Intake manifold Transfer manifold Exhaust manifold Figure 5-29: Engine sub-unit comprising one reciprocating pump cylinder and two engine cylinders.

The addition of a reciprocating air pump adds at least two major parameters to the system: the pump displacement and the pump phase. Other minor parameters included the transfer manifold volume (assumed to be 2 litres) and the reed valve effective area (assumed to be a generous 4×10-3 m2, or more than twice the effective area for two intake valves).

The work required to drive the pump was calculated by integrating the pump pressure with respect to pump cylinder volume. Pump friction was estimated using Equation 3-52, reduced by a factor of ten to account for the use of light metals, fewer and less stiff piston rings, and thin-walled components. The latter is due to the relatively light loads the pump components experience. A large bore/stroke ratio was assumed for the air pump to keep piston velocities, inertial forces and friction to a minimum. The air pump stroke was assumed to be fixed at half the engine stroke, or 82.55 mm. The assumed bore size therefore determined the pump displacement. The parameter space searched was:

189

• EVO (° ATDC) = 110, 120 … 160 • IVC (° ATDC) = 250, 260 … 300 • IVO – EVO (° CA) = 0, 10 … 30 • IVC – EVC (° CA) = 0, 10 … 30 • SOI (° ATDC) = -15, -10 … 0 • Air pump bore (mm) = 155.2, 174.6 … 232.8 (corresponding to a range of 64% … 144% of the engine cylinder displacement) • Air pump phase (° ATDC with one engine cylinder at TDC) = 180, 190 … 230

This totals 69,120 combinations. For each mode, the calculations for ten engine revolutions took approximately 50 hours CPU time on a Silicon Graphics Origin 3000 computer.

190

Table 5-8: Predicted near-optimum valve timings, engine performance and combustion parameters for Modes 1-6 for the arrangement in Figure 5-29 based on the Cat SCOTE engine with Shroud 1 on the intake valves. Four-stroke baseline results are italicised. Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Input parameters

Speed (rpm) 750 953 993 1657 1737 1789 Intake air pressure 100 100 100 100 100 100 (kPa, absolute) Intake air 298 298 298 298 298 298 temperature (K) Exhaust pressure 100 100 100 100 100 100 (kPa, absolute) Fuel rate 0.015 0.037 0.118 0.100 0.077 0.041 (g/cyl/cycle) Near-optimised parameters IVO (° ATDC) 170 180 170 150 160 150 IVC (° ATDC) 280 270 270 280 280 280 EVO (° ATDC) 160 160 150 130 140 150 EVC (° ATDC) 280 270 250 250 260 270 SOI (° ATDC) 350 355 355 355 355 350 Air pump bore 155.2 155.2 194.0 194.0 174.6 155.2 (mm) Air pump phase 200 180 170 170 170 180 (° ATDC)* Performance Brake Power (kW) 1.4 14.7 51.9 80.9 63.6 27.8 (0.6) (15.2) (59.2) (76.8) (56.8) (25.4) BSFC (g/kWh) N/A 287 230 246 253 317 (266) (212) (264) (244) (303) Air pump loss 0.6 1.1 3.5 8.6 6.1 3.5 (kW) Max. press. (MPa) 3.1 4.8 7.3 7.4 6.0 4.7 (5.6) (6.8) (10.3) (10.0) (8.1) (6.3) Ignition delay (ms) 3.49 0.97 0.39 0.24 0.29 0.53 (1.24) (0.91) (0.44) (0.50) (0.45) (0.64) Premixed burn 98 74 14 6 8 25 fraction (%) (77) (76) (8) (13) (9) (28) Max. burnt gas 0.16 0.41 0.69 0.70 0.65 0.47 fraction (0.14) (0.35) (0.69) (0.47) (0.39) (0.32) *When one engine cylinder is at TDC.

191

Every combination was evaluated, and the optimum values were: IVO = 160° ATDC IVC = 270° ATDC EVO = 130° ATDC EVC = 250° ATDC Pump bore = 194 mm (pump/engine cylinder displacement ratio = 1.00) Pump phase = 190° ATDC when one engine cylinder is at TDC. Cycle BSFC = 312 g/kWh

Cycle NOx = 9.9 g/kWh Cycle PM = 0.25 g/kWh

Modal data are shown in Table 5-9.

192

Table 5-9: Modal BSFCs for parameters optimised for a 6-mode FTP cycle approximation. Four-stroke baseline results are italicised. Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Input parameters

Speed (rpm) 750 953 993 1657 1737 1789 Intake air pressure 100 100 100 100 100 100 (kPa, absolute) Intake air 298 298 298 298 298 298 temperature (K) Exhaust pressure 100 100 100 100 100 100 (kPa, absolute) Fuel rate 0.017 0.037 0.118 0.100 0.077 0.041 (g/cyl/cycle) Injection timing SOI (° ATDC) 360 355 355 355 355 355 Performance Brake power (kW) 0.2 12.4 51.7 80.5 59.5 18.8 BSFC (g/kWh) N/A 341 231 247 270 469 (266) (212) (264) (244) (303) Air pump work 1.8 2.9 3.0 9.3 10.4 11.3 (kW) Max. press. (MPa) 4.7 5.4 7.2 7.7 7.0 6.0 (5.6) (6.8) (10.3) (10.0) (8.1) (6.3) Ignition delay (ms) 0.83 0.54 0.40 0.22 0.22 0.25 (1.24) (0.91) (0.44) (0.50) (0.45) (0.64) Premixed burn 64 27 14 5 4 0 fraction (%) (77) (76) (8) (13) (9) (28) Max. burnt gas 0.12 0.26 0.70 0.66 0.50 0.27 fraction (0.14) (0.35) (0.69) (0.47) (0.39) (0.32)

NOx (g/kg fuel) 28 54 40 25 28 36 (69) (64) (45) (15) (13.8) (22) Soot (g/kg fuel) 0.23 0.25 1.12 1.03 0.85 0.54 (0.16) (0.098) (0.18) (0.17) (0.47) (0.54)

The results indicate that the best efficiency is associated with the smallest air pump required to obtain sufficient air to avoid violating the maximum burned gas fraction constraint. Modes 2, 5 and 6 clearly suffer because the air pump is larger than necessary for these engine operating conditions. It would be desirable in a practical implementation to have a small air pump over all engine operating modes. One method of realising this is the use of a turbocharger and intercooler. At high speeds and loads this combination delivers compressed, cooled air to the air pump, so that the air pump has to deliver less air volume. 193

5.3.4 Addition of turbocharger The 0-D engine model was further modified to reflect the addition of a Caterpillar 3406E turbocharger and intercooler (described in Sections 3.2.8 and 3.2.9). Because only two engine cylinders were being modelled, the mass flow rate parameters on the turbine and compressor maps were reduced to one-third their original values. Thus the system approximated a turbocharged six-cylinder Caterpillar 3406E engine that had been retrofitted to two-cycle operation. It was recognised that there were some important differences: for example the amplitude and frequency of the flow pulsations in the intake and exhaust manifolds of the two-cylinder model would be different from a six-cylinder model, but the savings in computational time and effort would be worth a small loss of accuracy.

A large compressor receiver (20 litres) was added to reduce the amplitude of pressure oscillations due to the air pump, and therefore the tendency of the compressor to surge. This also allowed more rapid convergence to a periodic solution. It was subsequently noted that Heywood and Sher (1999, p. 439) state that a relatively large compressor receiver is required when a turbocharger compressor is coupled with a reciprocating scavenge pump, which confirmed the observations of the behaviour of the numerical solution.

The turbocharged engine model is represented in Figure 5-30. The parameters searched were: • EVO (° ATDC) = 120, 130 … 170 • IVC (° ATDC) = 240, 260 … 300 • IVO – EVO (° CA) = 0, 10, … 30 • IVC – EVC (° CA) = 0, 10, … 30 • SOI (° ATDC) = -15, -10 … 0 • Air pump bore (mm) = 155.2, 174.6 • Air pump phase (° ATDC with one engine cylinder at TDC) = 100, 120 … 260

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This totals 1,944 combinations. For each mode, the calculations for two hundred engine revolutions took up to 50 hours CPU time on a Silicon Graphics Origin 3000 computer.

The results are summarised in Table 5-10.

Compressor Turbine

Intake

Intercooler

Engine

Air pump (2 x engine speed)

Reed valve Poppet valve Intake manifold Transfer manifold Exhaust manifold Figure 5-30: Turbocharged and intercooled engine subunit.

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Table 5-10: Predicted near-optimum valve timings, engine performance and combustion parameters for Modes 1-6 for the arrangement in Figure 5-30 based on the Cat SCOTE engine with Shroud 1 on the intake valves. Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Input parameters

Speed (rpm) 750 953 993 1657 1737 1789 Intake air pressure 100 100 100 100 100 100 (kPa, absolute) Intake air 298 298 298 298 298 298 temperature (K) Exhaust pressure 100 100 100 100 100 100 (kPa, absolute) Fuel rate 0.015 0.037 0.118 0.100 0.077 0.050 (g/cyl/cycle) Near-optimised parameters IVO (° ATDC) 180 180 180 160 160 160 IVC (° ATDC) 280 280 260 280 280 280 EVO (° ATDC) 170 170 170 150 150 150 EVC (° ATDC) 280 280 250 270 270 280 SOI (° ATDC) 355 360 360 355 355 355 Air pump bore 155.2 155.2 155.2 155.2 155.2 155.2 (mm) Air pump phase 180 180 180 180 180 180 (° ATDC)* Performance Brake Power (kW) 1.4 14.3 63.8 82.1 60.6 32.0 BSFC (g/kWh) N/A 294 221 242 265 336 (266) (212) (264) (244) (303) Air pump loss 0.4 1.2 1.7 7.2 7.7 7.1 (kW) Max. press. (MPa) 3.0 4.3 7.7 9.9 8.8 5.6 (5.6) (6.8) (10.3) (10.0) (8.1) (6.3) Ignition delay (ms) 2.28 1.22 0.29 0.19 0.22 0.30 (1.24) (0.91) (0.44) (0.50) (0.45) (0.64) Premixed burn 95 83 8 3 3 3 fraction (%) (77) (76) (8) (13) (9) (28) Max. burnt gas 0.19 0.42 0.69 0.53 0.44 0.44 fraction (0.14) (0.35) (0.69) (0.47) (0.39) (0.32) Turbo speed (rpm) 28,000 33,200 57,600 78,000 73,700 69,800 *When one engine cylinder is at TDC.

The best parameters for a 6-mode FTP cycle approximation are: 196

IVO = 170° ATDC IVC = 260° ATDC EVO = 170° ATDC EVC = 250° ATDC Pump bore = 155.2 mm (pump/engine cylinder displacement ratio = 0.64) Pump phase = 180° ATDC when one engine cylinder is at TDC. Cycle BSFC = 290 g/kWh

Cycle NOx = 6.1 g/kWh Cycle Soot = 0.17 g/kWh

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Table 5-11: Optimised parameters for a 6-mode FTP cycle approximation. Four-stroke cycle baseline results are italicised. Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Input parameters

Speed (rpm) 750 953 993 1657 1737 1789 Intake air pressure 100 100 100 100 100 100 (kPa, absolute) Intake air 298 298 298 298 298 298 temperature (K) Exhaust pressure 100 100 100 100 100 100 (kPa, absolute) Fuel rate 0.015 0.037 0.118 0.100 0.077 0.050 (g/cyl/cycle) Injection timing SOI (° ATDC) 360 355 360 355 355 355 Performance Brake power (kW) 0.7 13.5 63.6 80.0 57.6 29.6 BSFC (g/kWh) N/A 314 221 249 278 362 (266) (212) (264) (244) (303) Air pump work 0.7 1.6 1.5 9.4 9.8 8.7 (kW) Max. press. (MPa) 3.8 5.1 7.8 11.3 10.2 7.4 (5.6) (6.8) (10.3) (10.0) (8.1) (6.3) Ignition delay (ms) 0.97 0.48 0.27 0.15 0.17 0.20 (1.24) (0.91) (0.44) (0.50) (0.45) (0.64) Premixed burn 73 18 7 1 0 0 fraction (%) (77) (76) (8) (13) (9) (28) Max. burnt gas 0.15 0.42 0.69 0.46 0.39 0.35 fraction (0.14) (0.35) (0.69) (0.47) (0.39) (0.32) Turbo speed (rpm) 27,600 32,500 60,800 76,900 72,600 66,500

NOx (g/kg fuel) 33 33 18 19 20 17 (69) (64) (45) (15) (13.8) (22) Soot (g/kg fuel) 0.19 0.30 0.50 0.69 0.66 0.70 (0.16) (0.098) (0.18) (0.17) (0.47) (0.54)

The intercooled turbocharger reduced the estimated pump work in all modes, despite the increased backpressure.

Again, it is recognised that the emissions estimates are possibly inaccurate as the KIVA-ERC model constants, tuned for four-stroke cycle operation, are likely to require adjustment for the very different conditions associated with two-stroke cycle operation. 198

The predicted cylinder pressure and heat release rates for the operating conditions in Table 5-11 using both thermodynamic and KIVA-ERC models are compared in Figure 5-31.

KIVA 0-D

6 600 12 300

4 400 8 200

2 200 4 100 Pressure (MPa) Pressure (MPa) Heat release rate (J/deg) Heat release rate (J/deg) Heat

0 0 0 0 330 340 350 360 370 380 390 400 410 330 340 350 360 370 380 390 400 410 Crank angle (deg ATDC) Crank angle (deg ATDC)

(a) Mode 1 (b) Mode 2

12 300 12 300

8 200 8 200

4 100 4 100 Pressure (MPa) Pressure (MPa) Heat release rate (J/deg) Heat release rate (J/deg) Heat

0 0 0 0 330 340 350 360 370 380 390 400 410 330 340 350 360 370 380 390 400 410 Crank angle (deg ATDC) Crank angle (deg ATDC)

12 300 12 300

8 200 8 200

4 100 4 100 Pressure (MPa) Pressure (MPa) Heat release rate (J/deg) Heat release rate (J/deg) Heat

0 0 0 0 330 340 350 360 370 380 390 400 410 330 340 350 360 370 380 390 400 410 Crank angle (deg ATDC) Crank angle (deg ATDC)

(e) Mode 5 (f) Mode 6 Figure 5-31: Comparison of KIVA-ERC and thermodynamic models for the cases in Table 5-11.

The agreement between the two models in terms of pressure, ignition delay, premixed burn spike and heat release rate shape is reasonably good. The thermodynamic model was not calibrated for just these cases, but for the cases described in Table 5-7 and Table 5-9, otherwise better agreement could have been achieved. Chapter 6 - Discussion

6.1 Thermodynamic model performance

The aim of the thermodynamic model was to accurately and rapidly model a wide variety of two-stroke and four-stroke engine systems. Recalling Section 3.1, the requirements were:

• Speed • Flexibility • Accuracy

Each of these will be reviewed briefly in turn.

6.1.1 Speed The combination of the thermodynamic approach, the simplest practicable submodels (described in Section 3.2), an efficient stiff ODE solver and the use of the Fortran programming language resulted in an efficient and fast engine modelling program. Simple models representing engine systems like the Caterpillar SCOTE (Figure 3-10) took approximately six seconds to complete one hundred engine cycles. More complex systems, like a turbocharged, intercooled, two-cylinder engine with single-cylinder reciprocating air pump (Figure 5-30) took between thirty and sixty CPU seconds to complete one hundred engine cycles. These runtimes allow many thousands of parameter combinations to be investigated in a reasonable amount of time.

The runtimes could be further improved by testing for convergence to a periodic solution. In this way, the program would run only as many cycles as is needed to converge within a certain tolerance. The maximum number of cycles would also be limited in case the results converged too slowly or not at all.

Convergence can be accelerated by modifying the behaviour of some of the submodels, especially the two-zone scavenging model. The abrupt transition from zone 1 to zone 2 does not occur at precisely the same time on successive cycles 200 because of slight differences in conditions at the beginning of each cycle. Changes in the timing of the transition cause differences in the conditions at the beginning of the next cycle, which affect the timing of the next transition, and so on. A more gradual transition would reflect reality better (see Figure 5-20 to Figure 5-24) and probably increase the rate of convergence of solutions. The cost may be one or more additional model parameters. The perfect diffusion scavenging model, which had no zone transitions, converged noticeably more quickly than the two-zone model. Typically ten or twenty engine cycles were required for convergence to close tolerances, whereas approximately ten times as many cycles are required for the two-zone model. However, the two-zone model does appear to give much more accurate scavenging efficiencies (see Table 5-4).

Another sub-model that limited the speed of convergence was the turbocharger submodel. A reduction in the turbo moment of inertia could accelerate convergence to an equilibrium speed. On the other hand, the cyclic turbo speed fluctuations would also be magnified. Further investigation might suggest a reasonable compromise between speed and accuracy.

Little attempt at parallelisation of the code has been made to date. When used to explore parameter spaces, many slightly different problems are solved independently of each other, which suggests that efficient parallelisation is possible.

In the present study, the parameter space was divided into an n-dimensional regular grid and a merit function was evaluated at each grid point. This large mass of data is useful for optimisation over several operating modes, when operating conditions may not be optimised for each mode. Other optimisation schemes for individual modes may be used, and it may be possible to adapt these to multi-modal optimisation. These schemes include univariate searching, factorial analysis, Bayesian techniques, expert systems, Response Surface Methods and Genetic Algorithms. These are discussed briefly in (Montgomery, 2000). The application of Genetic Algorithms to engine optimisation with KIVA-ERC and experimentation is described in (Senecal et al., 2000). These methods aim to reduce the number of parameter combinations that require evaluation to approach an optimum.

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6.1.2 Flexibility The thermodynamic model is able to represent almost any combination of turbocharger, intercooler, valve, orifice, diesel engine cylinder, air pump cylinder and plenum with no alterations in the source code. In practice, changes were often made to the output subroutine to obtain the desired results.

In order to minimise the user input, some program values such as constants related to fuel-air mixture properties were embedded as parameters in the Fortran source code. In future, many of these values may be made more accessible to the user by incorporating them in the model input file, or by creating a separate input file with seldom-adjusted model parameters.

The program design has been influenced by both the KIVA engine modelling program and the nature of the Fortran 77 programming language, with its text-based input and output files, driver routine and subroutines. There is undoubtedly scope for incorporation of features in the C, Fortran 90 and 95 languages.

During validation of the program, input files representing several engine systems were created. It was found that the fastest way to generate new engine models was to adapt an existing input file that most closely resembled the new engine system. In this way, new input files took only a few minutes to create. Most of the time taken in developing new input files was in doing a few runs to make sure the initial conditions in the engine system were reasonable. Good initial conditions improved the reliability and speed of convergence of the numerical integrator towards a periodic solution.

6.1.3 Accuracy At all stages of the development of the thermodynamic, parallel versions of the entire model or submodels were developed using Fortran and MathCAD, a mathematical software package. MathCAD’s symbolic language, built-in equation-solving and graphing features allowed the rapid generation and investigation of prototype submodels. MathCAD’s compact symbolic representations also provided a good 202 model for the subsequent Fortran implementation – it allowed concentration on the function of the subroutine without much of the distraction of how to implement it in a programming language. Drawbacks with MathCAD include slow execution of programs and the lack of a built-in stiff ODE solver that can automatically generate approximate Jacobian matrices (user-supplied Jacobians are impractical for this application). A built-in 4th-order Runge-Kutta solver was used to generate approximate solutions.

Once a prototype subroutine or submodel had been developed and tested in MathCAD, a Fortran implementation was developed. The behaviour of the Fortran version was compared with the MathCAD prototype, a process that caught errors in both the MathCAD and Fortran versions. Since all parts of the Fortran program were compared with a relatively independent MathCAD version, any remaining programming errors are expected to be few or minor.

The VODE ODE solver was usually used with absolute and relative tolerances of 10-6. Smaller tolerances resulted in longer runtimes, fewer errors in the submodels (possibly due to smaller time steps and consequently smaller changes in values between successive steps) and fewer failures with the VODE integrator.

The thermodynamic model was validated against published experimental data reported by Montgomery (2000) and Wright (2001). The former reference reported detailed measurements from a Caterpillar Single Cylinder Oil Test Engine (SCOTE) based on the Caterpillar 3406E heavy-duty diesel engine. The latter reference reported measurements taken from a production version of the six-cylinder Caterpillar 3406E engine. The agreement with the Caterpillar SCOTE calibration cases was good, with the calculated brake power and brake specific fuel consumption being within 5% of experimental data (Table 3-9). There were sometimes greater discrepancies in other estimated values, such as the ignition delay, premixed burn fraction and air flow rate. Some of the discrepancy was attributed to limitations in the semi-empirical correlations used to model the combustion behaviour. Some discrepancies, such as those between the reported and calculated air flow rates in cases 1-5 and 12-17, were difficult to explain, because all of the other results for these cases were in good agreement. A small error in the charging efficiency should 203 be magnified in the pressure trace. One explanation could be errors in the measurements.

In Section 3.2.3 is was argued that the maximum cylinder temperatures seldom exceeded 2000 K and the pressure was also high, so that dissociation could be neglected. Reviewing all of the cases, the maximum temperatures were calculated for mode3 in Table 5-11, in which the maximum bulk gas temperature was 1955 K at a pressure of 7 MPa (70 bar). Looking at Figure 3-3 and Figure 3-4, the errors in the specific internal energy and specific gas constant are very small, much less than 1%. The decision to simplify the gas property calculations by neglecting the effects of pressure (i.e. dissociation) would appear to be justified.

The thermodynamic model assumed a constant 100% combustion efficiency. Heywood (1989, p. 509) argued from the maximum allowable emissions that less than two percent of the fuel energy left the cylinder in the form of hydrocarbons, soot and carbon monoxide, so the assumption of complete combustion was a good approximation. This reasoning appears sound. KIVA-ERC sometimes predicts combustion inefficiencies greater than 2% (Hessel, 2003b) under operating conditions which would suggest that this figure is unreasonably high based on Heywood’s reasoning.

Improvements in accuracy could be achieved by giving to the ODE integrator all integration tasks in all submodels. Presently, only the equations for mass transfer, energy transfer and conservation of burned gas fraction are integrated using VODE. All other integration tasks used the approximation:

dX  X i ≈ X i−1 +   ()ti − ti−1 Equation 6-1  dt  i−1

where: X is any quantity t is time i (subscript) denotes the current time step 204

In practice, VODE occasionally stepped backwards in time when its error estimate exceeded the user-defined tolerances, so an array of previous values and the step times had to be maintained to avoid these errors being incorporated into the solution. Making VODE do all of the integration tasks would mean that all integrations would be subjected to error estimations and would influence the integrator step sizes. However, this would reduce the modularity of the thermodynamic model code and may significantly increase the computational effort required to do a simulation.

Examination of the gas flow rates through the intake valves (Section 5.1.4) suggests that gas dynamic effects are significant for even relatively short pipe runs. Rapid acceleration and deceleration of the gas flow induces pressure gradients that cause significant deviations from the zero-dimensional treatment. One such implementation is detailed in Zhu and Reitz (1999).

6.2 Scavenging of two-stroke poppet-valved engines

The KIVA-ERC scavenging simulations support conclusions in previous studies reported in the literature review that the optimum shroud size is in the vicinity of 100º. Shrouds much larger than this reduced the delivery ratio and the scavenging efficiency.

The smallest shrouds modelled had an average size of 105º and significantly improved the scavenging efficiency over having no shrouds at all. The scavenging efficiency approximated that of a uniflow engine. It was significantly better than the perfect diffusion model, which justified the effort in finding a better scavenging model. There was no evidence found for this shroud of significant vortex formation that might trap gases in the centre of the cylinder. This was used to explain combustion instabilities in spark-ignition prototypes.

The scavenging model described in Section 5.2 represents a novel contribution to engine modelling. It was inspired by the examination of KIVA-ERC scavenging simulations and by the three-zone model of Benson and Brandham (1969). The exhaust gas purity predicted by the KIVA-ERC simulations showed a definite two- 205 stage process, which suggested two zones. This is in contrast to the assertion in Heywood and Sher (1999, p. 130) that the exhaust gas purity curve is always a sigmoid (S-shaped) for all types of scavenging systems. The model was generalised to allow variations in the cylinder volume and pressure and the intake gas temperature and pressure. The model has just two calibration constants that are easy to determine from experiments or CFD simulations. The agreement between the two- zone model and KIVA-ERC simulation for a given shroud geometry was excellent over a wide range of engine speeds, intake and exhaust pressures and valve timings. This suggests that the two-zone model is a robust and accurate contribution to the modelling of poppet-valved two-stroke engines. The model may also be useful for other scavenging systems.

The model calibration constant x represents the proportion of intake flow short- circuited to the exhaust port. As would be expected, the magnitude of x was inversely proportional to the size of the shroud. Larger shrouds would be expected to shield the exhaust valves more effectively, reducing the value of x. This is reflected in the results of the optimisation in Section 5.2.2, reproduced in Table 6-1. Short-circuit flow was observed from simulations to occur largely around and between the intake valve shrouds. Optimum shroud turn angles would minimise x. As observed, x was fairly constant over a wide range of boost and exhaust pressures.

Table 6-1: Variation of x with average shroud angle. No shroud Shroud 1 Shroud 2 Shroud 3 Shroud 4 0° 105° 128° 138° 168° x = 0.34 x = 0.12 x = 0.10 x = 0.09 x = 0.07

The calibration constant k represents the volumetric rate of mixing of the residual gas and the fresh charge normalised against the engine speed. It varied with shroud size but was almost independent of engine speed or inlet and exhaust pressures and temperatures. The cylinder, valve and shroud geometry would be expected to influence the mixing rate within the cylinder. It is recommended that further work include a more detailed physical interpretation of k.

206

Minor improvements to the two-zone scavenging model may be possible. One that would yield a smoother and more realistic transition from zone 1 to zone 2 without introducing new calibration constants would be to assume two-way mixing between the two zones. This would then resemble some features of the Streit-Borman scavenging model (Streit and Borman, 1971), except with short-circuit flow added. Presently, zone 1 (the residual gas zone) donates its contents at a fixed volumetric rate to zone 2 (the fresh charge zone). This would also perhaps aid convergence to a cyclic solution.

6.3 Performance of two-stroke poppet-valved engines 6.3.1 Numerical modelling procedure The procedure used in this study to model a relatively novel engine system relied on both detailed experimental measurements and results obtained from detailed simulations based as much as possible on fundamental physical processes. The process of modelling two-stroke poppet-valved engines is illustrated in Figure 6-1.

The general approach was to start from well-studied physical systems and extrapolate in small steps towards the engine systems of interest. When empirical data was not available, for example for scavenging and combustion behaviour in two-stroke poppet valved engine cylinders, KIVA-ERC was used as the next best option. Its substantial basis in physical fundamentals and the relatively fine resolution of the computational mesh are expected to yield results of sufficient accuracy for the purposes of this investigation.

The approach in this study was to use the thermodynamic model to estimate initial conditions for the 3D KIVA-ERC model. The advantage of this approach was that the calculations can be performed relatively quickly. One limitation was that the thermodynamic model does not provide information on the spatial distribution of gas composition and temperatures at IVC. Since simulations showed the residual gas and fresh charge were mixed fairly quickly within the cylinder, the distribution of gas species and temperatures at injection was thought in most cases to be fairly uniform (see for example Figure 5-8d, Figure 5-9d and Figure 5-10, which show fairly uniform distributions well before IVC – substantial further mixing would occur 207 during compression and the ignition delay period). One possibility for further work would be to investigate the significance of the initial residual gas distribution on predicted emissions levels. As mentioned in Section 5.1.2, the calculations would require use of the 360° mesh and would have to encompass at least one full engine cycle, increasing the run time for from approximately three days to approximately nine days. 208

Development/ calibration/ validation of a thermodynamic model of a four-stroke engine system (Chapter 3)

Initial conditions

Four-stroke cycle gas exchange simulation using a full-cylinder KIVA-ERC model with valves and intake ports (Section 4.3)

Turbulence and Initial swirl parameters conditions

Calibration/validation of combustion and emissions model using KIVA-ERC and 60º sector cylinder mesh (Section 4.3)

Two-stroke cycle scavenging simulations using a full-cylinder KIVA-ERC model with valves and intake ports (Section 5.1)

Results

Development and validation of two- zone scavenging model (Section 5.2) Calibration constants Scavenging model

Preliminary modelling of two-stroke poppet-valved engine system (Section 5.3.1)

Calibration Turbulence and Initial constants swirl parameters conditions

Combustion and emissions modelling using KIVA- ERC and 60º sector mesh (Section 5.3.1)

Combustion model constants

Performance estimations using Initial Combustion and emissions thermodynamic model of two- conditions modelling using KIVA- stroke poppet-valved engine ERC and 60º sector mesh system (Sections 5.3.2-4) (Section 5.3.2-4)

Estimate of Estimate of combustion system behaviour and emissions

Figure 6-1: Flowchart of two-stroke poppet-valved engine modelling process. The boxes represent tasks and the arrows represent the flow of information from one task to the next.

209

6.3.2 System simulation results As discussed in Chapter 4, KIVA-ERC seemed better able to predict trends in emissions rather than absolute values in the absence of empirical data. If a genuine emissions prediction capability for novel engine systems is required, then better emissions models need to be developed, which is a significant undertaking (Kong, 2003). The thermodynamic model has no emissions prediction capability. The limited emissions prediction capability and the relatively good BSFC prediction capability (Section 3.3) suggested an approach whereby engine system parameters were optimised for fuel efficiency alone. Should physical engine systems be constructed, these parameter combinations could be used as a starting point. Once emissions have been measured, they could be compared with target levels and computer models could be calibrated. Further experiments and computer simulations could then be used to refine engine system parameters.

Comparisons between four-stroke and two-stroke engine systems assumed substantially the same engine hardware was used in each case. The engine cylinder, piston, injector, valves (excepting the addition of a shroud for two-stroke operation) and intake ports were the same for all cases. Additionally, the engine operating loads and speeds were the same for each case. This approach was taken for the following reasons:

• Computational model constants calibrated for the four-stroke cycle are more likely to apply to the two-stroke cases. • The number of parameters that need to be optimised are limited to a manageable set. • Any future experimentation is likely to start off with this approach, as has past experimentation (Section 2.2.2). • There is commercial interest in adapting four-stroke engines to two-stroke cycles, especially if fuel efficiency or emissions levels can be improved. • It has been hypothesised that operating a two-stroke poppet-valved diesel engine at loads similar to that of a four-stroke engine of the same displacement could result in low emissions (see Section 1.2).

210

The disadvantages of this approach are: • Significant advantages may be overlooked by restricting the number of dimensions in the parameter space. • The 6-mode FTP approximation is of limited value to non-vehicle applications, such as aeronautical engine or stationary generator applications. • This approach did not investigate the potential for improved power density, since the power levels were the same as for the four-stroke engine. An engine system optimised for a certain cycle is not likely to perform as well on a different cycle.

Future studies could expand understanding of two-stroke poppet-valved engine systems. A large proportion of this study was devoted to development of the unique tools and techniques required to simulate these systems.

The thermodynamic and KIVA-ERC models predict good fuel economy from a two- stroke adapted Caterpillar Single Cylinder Oil Test Engine (SCOTE, described in Figure 3 10 and Table 3 3). The thermodynamic modelling predicts better fuel economy than the baseline engine (Table 5 6 and Table 5 7) and a 7% reduction in BSFC over a 6-mode FTP cycle approximation. However, the parasitic scavenging pump losses were not accounted for in this case and the baseline engine was optimised for emissions and fuel economy rather than fuel economy alone. This numerical exercised indicated that such an apparatus should not be difficult to construct and that the scavenging and combustion behaviour should yield good performance. Such an apparatus would be an ideal test bed for experimentally investigating emissions from two-stroke poppet-valved diesel engines.

When the scavenging pump work is accounted for as in Sections 5.3.3 and 5.3.4, the predicted cycle BSFC is 15% greater than for the baseline case without a turbocharger and 7% greater when a turbocharger is added. The most efficient operating modes were the high load cases (modes 3, 4 and 5 in the 6-mode FTP cycle approximation). This is perhaps because the scavenging pump load, which was mainly a function of speed, was proportionally less in these cases.

211

Two-stroke poppet-valved engines have been shown to operate at idle speeds approximately half that of equivalent four-stroke engines (Rutherford and Dunn, 2002). If the turbocharged system idle speed is reduced from 750 rpm to 450 rpm, the cycle BSFC is reduced from 290 g/kWh to 280 g/kWh, which is close to the baseline four-stroke engine cycle BSFC of 272 g/kWh.

Modelling showed that a Caterpillar 3406E turbocharger could be used without modification on an engine retrofitted to two-stroke cycle operation, significantly simplifying and reducing the cost of the retrofit. Additionally, the turbocharged system required a considerably smaller air pump than the unturbocharged system. The best turbocharged parameter combination had an air pump cylinder displacement 64% of the engine cylinder displacement, whereas the ratio for the unturbocharged system was 100%. This could reduce the cost and mass of a retrofitted engine while improving performance.

The predicted two-stroke emissions levels generally showed no clear advantage over four-stroke operation; however the engine parameters were not optimised for emissions. The question of whether two-stroke poppet-valved diesel engines can run more cleanly than four-stroke equivalents without an excessive fuel consumption penalty can presently only be addressed with the assistance of experimentation. Of particular interest is whether the internal EGR (unscavenged residual gases) would suppress NOx and the high turbulence intensity would reduce PM, CO and HC emissions.

Some of the best-case valve motion may be difficult to achieve while retaining adequate durability. The analysis of the turbocharged system (Section 5.3.4) suggested intake and exhaust valve open periods of 90º CA and 80º CA respectively while assuming the same lift profile and maximum lift as the four-stroke cases which had valve open periods of 242 and 235. The valve acceleration is therefore increased by (242÷90)2 and (235÷80)2 or approximately 7-fold and 9-fold, respectively. Nevertheless, it is useful to know what the ideal case is.

Chapter 7 - Conclusions and Further Work

7.1 Summary

The performance of a four-stroke direct-injection diesel engine converted to a two- stroke cycle and scavenged by a reciprocating air pump has been estimated using a combination of four-stroke experimental data, multidimensional modelling of the cylinder, valves and intake ports, and zero-dimensional thermodynamic modelling of the entire engine system.

A fast, flexible zero-dimensional model was developed, calibrated and validated for four-stroke cycle operation using experimental data. The model is robust and capable of automatically evaluating tens of thousands of simulations of relatively complex engine systems in a few days. The model is therefore useful gaining an understanding of novel engine systems with complex behaviour. It was used to estimate near-optimum engine system parameters at single engine operating points and over a six-mode engine cycle. The model was also used to provide boundary conditions to a multidimensional engine model for more detailed simulations.

The multidimensional model was used for detailed scavenging and combustion simulations and to provide estimates of emissions levels. The combustion simulations were used to adjust zero-dimensional combustion correlations when experimental data was not available. Scavenging simulations were performed with shrouded and unshrouded intake valves.

7.2 Conclusions

Several conclusions can be drawn from the simulations performed in this study: a) Experimental investigations of novel engine systems are greatly enhanced by prior use of thermodynamic and multidimensional modelling to guide the design of prototypes.

213 b) The use of thermodynamic and multidimensional modelling in parallel with experimental investigations should greatly reduce the time and cost of prototype development compared with experimentation alone. c) Thermodynamic and multidimensional modelling of novel engine systems without validation by experiments provides useful predictions of behaviour throughout the system with the exception of emissions predictions. d) A novel two-zone scavenging model has been developed and validated by multidimensional modelling. It provides very accurate estimates of scavenging efficiencies over a very broad range of engine speeds and boost pressures. e) Multidimensional scavenging simulations confirm previous studies that indicate scavenging performance approaching that of a uniflow-scavenged cylinder is possible. To achieve this, an intake shroud or other means of reducing short-circuit flow is necessary. Intake shrouds larger than approximately 105º reduce both the delivery ratio and scavenging efficiency. This supports previous studies that concluded shrouds of approximately 90º were optimum. f) Two-stroke poppet-valved engine systems can have a lower indicated specific fuel consumption than equivalent four-stroke engines. This is because the turbulence generated by high flow rates past the shrouded intake valve increases the rate of combustion of fuel. This in turn means that a greater fraction of heat release occurs at higher pressures, and the piston can extract more work. g) Parasitic losses from the external air pump were significant at low loads, leading to increased brake specific fuel consumption relative to the four- stroke cycle. Air pump losses were mitigated by the use of turbocharging followed by charge air cooling, which reduced the specific volume of the fresh charge. This in turn allowed the air pump size to be reduced by approximately 36% compared to the un-turbocharged engine system. 214

Two-stroke poppet-valved engine systems are likely to achieve substantially the same fuel efficiency as equivalent four-stroke engine systems. h) Two-stroke poppet-valved engine parameters can not accurately be optimised for both fuel consumption and emissions in the absence of experimental data from a similar two-stroke poppet-valved engine. If such optimisation is required, then it entails the construction and instrumentation of one or more prototypes. i) Two-stroke poppet-valved engine systems will have much greater demands on the valve train than four-stroke engine systems.

7.3 Further work 7.3.1 Improvements to the thermodynamic model The use of one-dimensional elements in the thermodynamic model should be investigated. The overall air consumption and pressure traces showed satisfactory agreement with experimental data and multidimensional modelling, but KIVA-ERC modelling showed that significant variations do occur in intake and exhaust ports. A trade-off analysis would have to be performed to determine whether any improvements in system behaviour were worth the reduction in program speed.

Presently, the thermodynamic model is capable of automatically surveying the user- defined parameter space. The implementation of an efficient automatic optimisation scheme capable of optimising engine system parameters for multi-mode engine cycles would be a great improvement.

One significant improvement to the thermodynamic model would be parallelisation on a machine such as the Silicon Graphics Origin 3000.

A review of submodel behaviour would be desirable to identify ways to reduce the computational effort of the ordinary differential equation integrator and speed convergence to a periodic solution without affecting the overall model accuracy. 215

Numerous small improvements to the user interface and program source code can be made.

7.3.2 Improvements to multidimensional modelling Attempts to calibrate KIVA-ERC with experimental data indicated that trends were reliably predicted, but that model constants required adjusting at different engine operating conditions. The emissions estimates available from the multidimensional modelling of the two-stroke poppet-valved engine systems must be considered tentative until experimental data becomes available.

The effects of initial residual gas distribution on ignition delay, combustion and emissions should be investigated further to determine whether the current approach – assuming a uniform distribution based on thermodynamic modelling – is sufficiently accurate. One alternative is to do full cycle simulations with a 360° mesh which may entail a prohibitive amount of computational effort for some applications.

7.3.3 Two-zone scavenging model Two-way mass transfer between the two zones should be investigated. This has the potential to improve the exhaust gas purity curve. If this can be achieved without compromising the presently excellent agreement with multidimensional scavenging simulations, it would be a substantial improvement.

The physical interpretations of the scavenging parameters x and k should be investigated further.

The applicability of the two-zone scavenging model to other scavenging arrangements (e.g. cross-flow, loop, uniflow) could be investigated.

7.3.4 Further system studies The systems reported in this study are applicable to the retrofitting of a diesel engine to two-stroke operation and re-use at the same operating conditions. The two-stroke poppet-valved engine system is likely to have substantially different operating 216 characteristics to a four-stroke engine, so different load-speed conditions may yield much better results. Much further work is required to evaluate the overall potential of two-stroke poppet-valved engine systems. In particular, the potential of this type of engine for increases in power density should be investigated. 217

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