A NUMERICAL INVESTIGATION OF A TWO-STROKE POPPET …Two-stroke poppet-valved engines may combine the high power density of two - stroke engines and the low emissions of poppet-valved

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

v

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.

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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.

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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

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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

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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

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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

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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

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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

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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


1737 rpm) . Case numbers refer to Table 3-8. ................................................. 140


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

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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

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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



= 7 × 10-4. ......................................................................................................... 172





= 8 × 10-4. ......................................................................................................... 173





= 8.5 × 10-4. ...................................................................................................... 174





= 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

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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

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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


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


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

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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

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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

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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.

2

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.

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

Inlet poppet valve

Exhaust poppet valve

Piston

(a) Compression

(f) Supercharging (d) Blowdown

(c) Expansion (b) Combustion

(e) Scavenging

3

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.

Figure 1-2: Common scavenging arrangements

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

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

Figure 1-3: Schematic of Rotec engine prototype. Cylinders may not be in this order in a

practical engine block due to balancing considerations.

Figure 1-4: Intake valve shroud.

Intake Exhaust

Compressor Turbine

Intercooler

Air pump (2 x engine speed) Engine

Reed valvePoppet valve

Intake manifold Transfer manifold

Exhaust manifold

Shroud

Intake Exhaust

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.

7

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.

12

Table 2-1: Citations and author affiliations.

Citation Author affiliations (abbreviation)

(Nomura and Nakamura,

1993)

Toyota Motor Company (Toyota)

(Hundleby, 1990), (Stokes et

al., 1992)

Ricardo Consulting Engineers (Ricardo)

(Sato et al., 1981), (Nakano et

al., 1990), (Sato et al., 1992)

Shibaura Institute of Technology, Honda R&D Co.

(Shibaura/Honda)

(Das and Dent, 1993) Loughborough University of Technology

(Huh et al., 1993), (Kang et al.,

1996)

Pohang Institute of Science and Technology,

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

al., 1999)

Kanazawa University, Gunma University

(Kanazawa/Gunma)

(Rutherford and Dunn, 2001) Rotec Design Ltd (Rotec)

13

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

Toyo

ta

Ric

ardo

Shib

aura

/Hon

da

Kor

ean

Suzu

ki

Kan

azaw

a/G

unm

a

Rot

ec

Higher torque and power density compared to

four-stroke engines

Reduction of emissions from lubricant

consumption relative to ported two-stroke engines

Asymmetric valve timing, unavailable in ported

engines

The ability to be supercharged, difficult in ported

engines

Smoother operation due to the increased number

of firing strokes

Reduction of bore distortion due to asymmetric

cylinder heating, giving better piston ring and

liner durability

The possibility of combining manufacture with

four-stroke engines

Closer cylinder spacing (smaller engine size)

relative to uniflow engines due to the absence of

ports

Lower mechanical friction losses relative to four-

stoke engines due to lower peak pressures and

lower speed operation for the same torque output

Reduction in emissions and fuel consumption due

to higher turbulent kinetic energy in the trapped

cylinder gas at the point of fuel injection and

more available air and/or EGR

14

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).

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This figure is not available online. Please consult the hardcopy thesis available from the QUT Library

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16

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.

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This table is not available online. Please consult the hardcopy thesis available from the QUT Library

17

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.

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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.

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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).

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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.

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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.

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

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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.

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24

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).

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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.

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26

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

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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

drive

Hundleby (1990)

Suzuki Roots-type positive displacement Morita and Inoue (1996)

Rotec Reciprocating piston positive

displacement

Rutherford and Dunn (2001)

30

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.

31

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

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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.

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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.

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

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35

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.

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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.

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0

10

20

30

40

50

60

70

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

Pow

er d

ensi

ty (k

W/li

tre)

Suzuki

Toyota S-2

Toyota S-2D

Ricardo

Shibaura/Honda

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.

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

0

40

80

120

160

200

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

Torq

ue d

ensi

ty (k

W/li

tre)

Suzuki Toyota S-2

Toyota S-2D

Ricardo Shibaura/Honda

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.

250

300

350

400

450

500

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

bsfc

(g/k

Wh)

Suzuki

Toyota S-2

Toyota S-2D

Ricardo

Shibaura/Honda

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.

39

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

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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).

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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).

42

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.

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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.

45

Table 2-12: EU emissions standards for heavy-duty diesel engines.

Tier Date &

Category

Test

Cycle

CO

(g/kWh)

HC

(g/kWh)

NOx

(g/kWh)

PM

(g/kWh)

Smoke*

(m-1)

1992

<85 kW 4.5 1.1 8.0 0.612

Euro I 1992

>85 kW 4.5 1.1 8.0 0.36

1996.10 4.0 1.1 7.0 0.25 Euro II

1998.10

ECE

R-49

4.0 1.1 7.0 0.15

Euro III 2000.10 2.1 0.66 5.0 0.10 0.8

Euro IV 2005.10 1.5 0.46 3.5 0.02 0.5

Euro V 2008.10

ESC &

ELR

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.

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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).

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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

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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:

Delivery ratio rd = densityinletpumpvolumeswept

massdelivered×

Equation 2-1

Scavenging efficiency ηs = masstrappedretainedmassdelivered

Equation 2-2

Trapping efficiency ηt = massdeliveredretainedmassdelivered

Equation 2-3

Charging efficiency ηc = densityinletpumpvolumeswept

retainedmassdelivered×

Equation 2-4

Volumetric efficiency ηv = densityinletpumpvolumeswept

masstrapped×

Equation 2-5

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%

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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

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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.

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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.

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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.

Figure 2-29: Reciprocating piston supercharger.

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

One-way

valve

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Table 2-13: Summary of compressor characteristics.

Roots Vane Screw Rotary

piston

Spiral Centrif-

ugal

Recip.

piston

Overall efficiency

(%)

55 40 ~55 ~55 ~55 ~60 ~65

Max pressure

ratio

1.3 N/A* 1.5 1.8 1.8 3.5 >10

Positive

displacement

Yes Yes Yes Yes Yes No Yes

* 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.

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

Compressor

Plenum

Throttle valve

Plenum Plenum

Intake poppet valves

Exhaust poppet valves Cylinders

EGR valve

Turbine

Waste gate valve

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.

62

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:

∑=i

i

dtdm

dtdm

Equation 3-1

( ) ∑ −−=i

ioi dt

dQdtdVP

dtdm

hmudtd

Equation 3-2

mRTPV = 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:

mRTPVZ =

Equation 3-4

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.

64

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:

FASmm

a

f

⋅=φ Equation 3-5

halla


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:

∑ −−=+⋅∂∂

+⋅∂∂

i

ioi dt

dQdtdV

VmRT

dtdm

hdtdmu

dtdum

dtdT

tum φ

φ

Equation 3-6

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

Tum

dtdmu

dtdum

dtdQ

dtdV

VmRT

dtdm

h

dtdT i

ioi

∂∂

+⋅∂∂

−−−=

∑ φφ

Equation 3-7

The rate of change of the equivalence ratio in the control volume can be obtained by

differentiating Equation 3-5:

−

⋅=

dtdmm

dtdm

mmFASdt

df

f2

1φ Equation 3-8

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:

( ) ∑+=i

ii

f

dtdm

FASfueldtmfbd

dtdm

φ Equation 3-9

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:

( )

−+= ∑

i

ii dt

dmdt

dmdtmfbd

FASfuel

mdtd φφφ 1

Equation 3-10

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.

67

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

hytfytf

yy nnnnnn 2

),(),( 111

+++

++=

Equation 3-12

where:

dtdyytf =),(

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

ODEs have a Jacobian matrix (matrix of partial derivatives yf

∂∂ ) has one or more

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.

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

Initial conditions, method flag (stiff or non-stiff solver),

local and global error tolerances

Calculate derivatives dtdy

Set time for first solution point

Call VODE

End of solution interval?

Write solution point to file

Calculate and write

solution summary

End

Yes

No

Set time for next

solution point

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,

halla


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.

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Temperature (K)

Spec

ific

inte

rnal

ene

rgy

(kJ/

kg o

rigin

al a

ir)

1 bar3 bar10 bar30 bar100 bar

phi = 1

phi = 0

Figure 3-3: Calculated specific internal energy vs temperature for Fuel B-air mixtures at

thermochemical equilibrium at various pressures.

71

285

290

295

300

305

310

315

0 500 1000 1500 2000 2500 3000

Temperature (K)

Spec

ific

idea

l gas

con

stan

t (J/

kg*K

orig

inal

air)

1 bar3 bar10 bar30 bar100 bar

phi = 1

phi = 0

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 +

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)

Equation 3-15

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

73

-4000

-3000

-2000

-1000

0

1000

2000

0 500 1000 1500 2000 2500 3000

Temperature (K)

Spec

ific

inte

rnal

ene

rgy

(kJ/

kg o

rigin

al a

ir)

Data, phi=0Curve fit, phi=0Data, phi=0.5Curve fit, phi=0.5Data, phi=1Curve fit, phi=1

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

3-16 (“Function”).

285

290

295

300

305

310

0 500 1000 1500 2000 2500 3000

Temperature (K)

Spec

ific

idea

l gas

con

stan

t (J/

kg*K

orig

inal

air)

Data, phi=0

Function, phi=0

Data, phi=0.5

Function, phi=0.5

Data, phi=1

Function, phi=1

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.

74

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:

( ) 8.024.006.0

8.01 Cv

TVolPC

h pcyl

+= Equation 3-17

where:

h = heat transfer coefficient (W/m2·K)

P = cylinder pressure (bar)

Volcyl = instantaneous cylinder volume (m3)

T = instantaneous bulk gas temperature (K)

pv = mean piston speed (m/s)

C1,C2 = calibration constants

( )wTTAhQ −=& Equation 3-18

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.

75

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:

−

−

=

−k

k

o

k

oooeff P

PPP

kkPA

dtdm

12

11

2 ρ

Equation 3-19

whereas for choked flow:

11

12 −

+

+=

kk

ooeff kRT

kPAdtdm

Equation 3-20

Flow is choked if:

1

12 −

+≥

kk

o kPP

Equation 3-21

where:

k = ratio of specific heats = ( )TuR

∂∂+1 (from the ideal gas equation)

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

0

4

8

12

16

0 1

Valv

e lif

t (m

m)

IntakeExhaust

OPEN CLOSE

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.

0.4

0.5

0.6

0.7

0.8

0 0.1 0.2 0.3 0.4

Valve lift/diameter

CD Intake

Exhaust

Figure 3-8: Assumed poppet valve discharge coefficient vs valve lift/diameter ratio, based on

Heywood and Sher (1999, pp. 187-8).

77

The valve curtain areas were multiplied by the discharge coefficient to obtain

functions of valve effective area, shown in Figure 3-9.

0

0.0005

0.001

0.0015

0.002

0.0025

0 1

Effe

ctiv

e ar

ea (m

2 )

IntakeExhaust

OPEN CLOSE

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).

78

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):

−= ∑

i

ii dt

dmdt

dmmdt

d φφφ 1 Equation 3-22

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:

−∆+=ρPhhmU f

o Equation 3-24

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:

[ ]2

2O

fuel

O

fuel

fPfuel

fuelair

fuel

RThmmPhhu

mmm

mQ

−−

−∆+−

+=

ρo Equation 3-25

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

h°f (MJ/kg) -2.033 -0.728 0

Fuel ∆h (MJ/kg) 0 0 0

Heat of combustion

fuelmQ with H2O(l) (MJ/kg) 43.69 44.94 45.73

Discrepancy with measured

gross heat of combustion -3.0% -0.2% 1.6%

fuelmQ with H2O(g) (MJ/kg) 41.32 42.56 43.35

Discrepancy with measured

net heat of combustion (%) -2.7% +0.2% 2.1%

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:

( ) ( ) ),(, ffuelRairPair hmTumTumQ °+−= φφ Equation 3-26

where:

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

Dividing both sides by mfuel:

ffuel

air

fuel

humm

mQ

°+∂∂

= δφφ

Equation 3-27

Using Equation 3-5:

ffuel

huFASm

Q°+

∂∂

=φ

1 Equation 3-28

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):

( )dtdQ

dtdV

VmRTvPTTchROI

dtdum

dtdT

tum fuel

refinjpf −−

++−+°=⋅

∂∂

+⋅∂∂

2

2

ρφ

φ

Equation 3-29

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

83

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:

ROI = 0.051 + 6.8*10-4 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:

vfuel ROI/(ρfuel.Nnoz.π/4dnoz2) 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:

3

21 exp

),( Am

mmmID P

TAA

PTt

= Equation 3-32

65

40.1),( AID

AtrIDtr tFAtF −=β Equation 3-33

[ ] 2111)( ppCC

pM ττ −−= Equation 3-34

[ ]21exp1)( dC

dd CM ττ ⋅−−= Equation 3-35

)()1()()( τβτβτ dpt MMM −+= 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).

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86

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

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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.

88

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).

XY

0 1

01

2

3

4

5

6

7

8

9

10

-30 -2.607·10 -4

-29.869 -2.607·10 -4

-29.739 -2.607·10 -4

-29.608 -2.607·10 -4

-29.477 -2.607·10 -4

-29.346 -2.607·10 -4

-29.216 -2.607·10 -4

-29.085 -2.607·10 -4

-28.954 -2.607·10 -4

-28.824 -2.607·10 -4

-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)

30 20 10 0 10 20 30 40 500.01

0

0.01

0.02

0.03

0.04

0.05

XY 1⟨ ⟩

XY 0⟨ ⟩ Step 4: The result is graphed and checked against the original plot for accuracy.

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

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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.

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

tID ∫=

2

1

CA

CA

dCAAHRRβ

CA1 CA2

90

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:

∫+

=ID

ID

tSOI

SOItm dttTT )(1 Equation 3-37

∫+

=ID

ID

tSOI

SOItm dttPP )(1 Equation 3-38

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.

91

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

0.2

0.4

0.6

0.8

1

40 50 60 70 80 90Mean pressure Pm (bar)

Igni

tion

dela

y (m

s)

MeasuredCorrelation

Figure 3-13: Comparison of measured ignition delay and the ignition delay correlation vs mean

pressure.

93

0

0.2

0.4

0.6

0.8

1

840 860 880 900 920 940 960Mean temperature Tm (K)

Igni

tion

dela

y (m

s)

MeasuredCorrelation

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

( ) 1,

≥∑i iiID

i

PTttδ

Equation 3-39

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:

65

4),( AID

AID tAt δδδβ −= 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.

96

Table 3-5: Data used for calibration of β correlation (Equation 3-40).

Case Measured proportion of fuel

injection prior to ignition, δ

Measured proportion of fuel

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

97

0

20

40

60

80

0 20 40 60 80 100Proportion of fuel injected before ignition δ (%)

Prop

ortio

n of

fuel

in p

rem

ixed

com

bust

ion

β (%

) MeasuredCorrelation

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

0

20

40

60

80

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Ignition delay t ID (ms)

Prop

ortio

n of

fuel

in p

rem

ixed

com

bust

ion

β (%

) MeasuredCorrelation

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:

)()( τβτ pt MM = if τ < τd

)()1()()( ddpt MMM ττβτβτ −−+= if τ ≥ τd Equation 3-41

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.

99

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.

Watson et al.

Modified

Measurement

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

0 0.2 0.4 0.6 0.8 11.5

2

2.5

3

(a) Cp1 vs β

10 14 18 22 2610

20

30

40

(b) Cd1 vs φ -1.07β -0.90

2.2 2.6 3 3.4 3.81

1.4

1.8

(c) Cd2 vs φ -0.33β -0.40

2 2.2 2.4 0

0.02

0.04

0.06

(d) τd vs Cp1

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

Cd1 = 0.079 + 1.47φ -1.07β -0.90

Cd2 = -0.061 + 0.53φ -0.33β -0.40

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):

+−

=

−

11

1

1

2

12 η

γγ

PP

TT 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:

( )12 hhmW −= && 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:

=

2

1

PPf

PP

TTm

ref

ref& Equation 3-44

and

=

2

1

PPfη Equation 3-45

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

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):

−

+=

−

11

1

2

112

γγ

ηPPTT Equation 3-46

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:

( )ct

ctm

IIWW

++

=ωη

α&&

Equation 3-47

Efficiency

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:

iii tδαωω += −1 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):

ambin

outin

TTTT

−−

=ε Equation 3-49

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

22

2m

PAf

&

∆=

ρ Equation 3-50

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).

halla


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:

γγ 1

1

212

−

=

PPTT Equation 3-51

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

temperature (K)

419.7 425.2 430.0

Compressor outlet

density (kg/m3)

2.156 2.216 2.261

Charge air cooler

effectiveness

0.844 0.814 0.822

Charge air cooler

pressure loss factor (m-4)

1.232×105 1.270×105 1.378×105

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:

pvcb

Pafmep ++= max Equation 3-52

where:

fmep = friction mean effective pressure

Pmax = maximum cylinder pressure

pv = 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

1000 1400 1800

2.1

2.2

2.3

2.4

Correlation

Data Fmep (bar)

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

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

Equation 3-53

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.

Optimisation file

110.0 110.0 1 | EVO (deg ATDC)

270.0 270.0 1 | IVC (deg ATDC)

30.0 30.0 1 | IVO - EVO (deg)

20.0 20.0 1 | IVC - EVC (deg)

350.0 355.0 3 | SOI (deg ATDC)

194.0 194.0 1 | Air pump bore (mm)

-180. -120. 7 | Air pump phase (deg)

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

number

Engine

speed

(rpm)

Fuel rate

(kg/hr)

Start of

injection

(ºATDC)

Intake

temp (K)

Intake

pressure

(kPa)

Exhaust

pressure

(kPa)

EGR rate

(%)

Ref.

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 2 19 1600 8.064 -4.0 2 20 1600 8.064 -1.0 2 21 1600 8.064 2.0 2 22 1600 8.064 5.0

Conditions at 144º BTDC:

Pressure = 212.1 kPa

Temperature = 361.4 K

Burned gas fraction 0.007 2 23 1690 3.054 -9.0 2 24 1690 3.054 -6.0 2 25 1690 3.054 -3.0 2 26 1690 3.054 0.0 2 27 1690 3.054 3.0

Conditions at 144º BTDC:

Pressure = 148.4 kPa

Temperature = 334 K

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

delay

(ms)

Premixed

burn fract.

(%)

Air flow

rate

(kg/min)

Maximum

pressure

(MPa)

Brake

power (kW)

BSFC

(g/kWh)

Ref.

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

-2

0

2

4

6

8

10

12

14

-30 -20 -10 0 10 20 30 40 50 60

Crank angle (deg ATDC)

Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(a) Case 1

-2

0

2

4

6

8

10

12

14

-30 -20 -10 0 10 20 30 40 50 60


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(b) Case 2

-2

0

2

4

6

8

10

12

14

-30 -20 -10 0 10 20 30 40 50 60Crank angle (deg ATDC)

Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(c) Case 3

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(d) Case 4

-2

0

2

4

6

8

10

12

14

-30 -20 -10 0 10 20 30 40 50 60


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(e) Case 5

Figure 3-24: Mode 3 (high load, mid speed). Case numbers refer to Table 3-8.

113

Experimental

Calculated

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(a) Case 6

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(b) Case 7

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(c) Case 8

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(d) Case 9

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(e) Case 10

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(f) Case 11

Figure 3-25: Mode 5 (mid load, high speed) . Case numbers refer to Table 3-8.

.

114

Experimental

Calculated

-1

0

1

2

3

4

5

6

7

8


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Hea

t rel

ease

rate

(nor

mal

ised

)

(a) Case 12

-1

0

1

2

3

4

5

6

7

8


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Hea

t rel

ease

rate

(nor

mal

ised

)

(b) Case 13

-1

0

1

2

3

4

5

6

7

8


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Hea

t rel

ease

rate

(nor

mal

ised

)

(c) Case 14

-1

0

1

2

3

4

5

6

7

8

-30 -20 -10 0 10 20 30 40 50 60


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Hea

t rel

ease

rate

(nor

mal

ised

)

(d) Case 15

-1

0

1

2

3

4

5

6

7

8


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Hea

t rel

ease

rate

(nor

mal

ised

)

(e) Case 16

-1

0

1

2

3

4

5

6

7

8


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Hea

t rel

ease

rate

(nor

mal

ised

)

(f) Case 17

Figure 3-26: Mode 6 (low load, high speed). Case numbers refer to Table 3-8.

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

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(a) Case 34, Mode 6 with high pressure injector

and 26.9% EGR

-1

0

1

2

3

4

5

6

7

8


Pres

sure

(MPa

)

-0.04

0

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

Hea

t rel

ease

rate

(nor

mal

ised

)

(b) Case 35, Mode 1 (idle)

-1

0

1

2

3

4

5

6

7

8


Pres

sure

(MPa

)

-0.04

0

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32H

eat r

elea

se ra

te (n

orm

alis

ed)

(c) Case 36, Mode 2 (low load, low speed)

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(d) Case 37, Mode 4 (high load, mid speed)

Notes:

1. 1002%2%

2%2%% ×−

−=

ambientexhaust

ambientinlet

COCOCOCOEGR

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.

halla


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

halla


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.

(a) Model for Table 3-11.

(b) Model for Table 3-12.

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

Plenum Plenum



Compressor

Plenum

Plenum Plenum



Turbine

Plenum

Charge air

cooler

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

pressure (kPa) 96.8 96.8 96.8

Assumed compressor intake

temperature (K) 293.8 293.8 293.8

Estimated intake manifold

pressure (kPa) 268.5 258.7 246.6

Estimated intake manifold

temperature (K) 320 322 317

Estimated exhaust manifold

pressure (kPa) 225.3 234.6 241.9

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.


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.


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:

( ) 513.2ln1.2

ln

+′

′

=y

TTTuc

q wp

w

ρ Equation 4-1

νyuy′

=′ Equation 4-2

21

41kCu µ=′ 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:

Dnozeff Cdd = 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:

( )000 rr

rrdtdr

≤−

−=τ

Equation 4-5

ΛΩ= 01726.3 rB

τ Equation 4-6

( )000 rBBr ≤ΛΛ= Equation 4-7

halla


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:

σρ 0

2

80

dVWe

We

ni

i

=

< Equation 4-8

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:

c

mmm

tYY

dtdY *−

= Equation 4-9

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:

εkCtt 2= Equation 4-11

where:

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

The coefficient f is calculated by:

111

−

−

−−

=eef

r

Equation 4-12

where:

2

222

1 N

HCOOHCO

YYYYY

r−

+++= Equation 4-13

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:

[ ] [ ][ ] [ ] [ ][ ]( )[ ] [ ] [ ]( )OHkOkNOk

NOKNONOk

dtNOd

ffbf

3221

222

21 11

2++

−=

b

f

b

f

kk

kk

K2

2

1

1=

Equation 4-17

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

fvsf

sfsf MRTE

PAM

−= exp2

1& Equation 4-18

where:

sfM& = 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:

( )XPKXPK

PKR OB

OZ

OAtot −+

+= 1

1 2

2

2

Where X is the proportion of A sites:

BTO

O

KKPP

X+

=2

2

Equation 4-19

PO2 = Oxygen partial pressure

K = various experimentally-determined rate constants

The soot mass oxidation rate is:

totsss

Csoso RM

dMW

CMρ

6=& Equation 4-20

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

name

Effect Typical value

or range

Model

value

af04 A larger value speeds up ignition,

reducing the ignition delay period.

104 – 5.0×105 1.25×105

denomc A larger value increases the proportion

of premixed combustion.

0.768×1010 0.768×1010

cm2 Turbulent timescale constant. A larger

value slows diffusion burning.

0.1 – 5.0 0.25

distant Initial break-up length 1.4 – 2.0 1.9

cnst22 Droplet break-up time constant before

impingement. Smaller value makes

smaller droplets which vaporise faster.

10 - 60 40

asf A larger value increases soot oxidation

rate, reducing the total soot produced

- 250

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

-2

0

2

4

6

8

10

12

14

-30 -20 -10 0 10 20 30 40 50Crank angle (deg ATDC)

Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(a) Case 1

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(b) Case 2

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(c) Case 3

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(d) Case 4

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(e) Case 5

3 5412

1 32

45

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

NOx (g/kg fuel)

Soot

(g/k

g fu

el)

MeasuredKIVA

(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


-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(a) Case 6

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(b) Case 7

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(c) Case 8

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(d) Case 9

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(e) Case 10

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(f) Case 11

7

910 11

86

116

79

810

0

0.2

0.4

0.6

0.8

0 10 20 30 40 50 60

NOx (g/kg fuel)

Soot

(g/k

g fu

el)

MeasuredKIVA

(g) Soot vs NOx emissions for cases 6-11


141


-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(a) Case 12

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(b) Case 13

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(c) Case 14

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(d) Case 15

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(e) Case 16

-2

0

2

4

6

8

10

12

14


Pres

sure

(MPa

)

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Hea

t rel

ease

rate

(nor

mal

ised

)

(f) Case 17

1214 17 161315

15131617

1412

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

NOx (g/kg fuel)

Soot

(g/k

g fu

el)

MeasuredKIVA

(g) Soot vs NOx emissions for cases 12-17


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.

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.

Shroud

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

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.

θ2

β2

θ1

β1

61

61

74

148

Table 5-2: Scavenging simulation cases.

Case Speed

(rpm)

Pin

(kPa)

Tin

(K)

Pex

(bar)

Valve

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

11 1789 Function

1** 310 100 A

12 1789 Function

2** 310 100 A

* A: EVO = 100°, IVO = 130°, EVC = 250°, IVC = 270° ATDC B: EVO = 150°, IVO = 150°, EVC = 260°, IVC = 270° ATDC

** Function 1: ( )

<<

−−

+=otherwise

IVCCAIVOifIVOIVCIVOCA

CAPin

100

sin200100 π

Function 2: ( )

<<

−−

−=otherwise

IVCCAIVOifIVOIVCIVOCA

CAPin

300

sin100300 π

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.

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:

0

100

200

300

400

0 100 200 300

Crank Angle (degrees ATDC)

Inta

ke p

ort p

ress

ure

(kPa

)

Case 11Case 12

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

0.2

0.4

0.6

0.8

1

0 1 2 3 4

Delivery Ratio

Scav

engi

ng E

ffici

ency

No shroudShroud 1Shroud 2Shroud 3Shroud 4

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.

152

(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

(c) 206° ATDC (d) 223° 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

(c) 206° ATDC

(d) 223° 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.

155

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 0.004 0.008 0.012 0.0160

0.001

0.002

0.003

0.004

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.

6 5 8

11

12

7 9 0-D

estimate Error!

Referenc

Effe

ctiv

e ar

ea (m

2 )

Time (s)

157

0 0.004 0.008 0.012 0.0160

5 . 10 4

0.001

0.0015

0.002

0.0025

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

6 5

8

11

12

7 9

0-D estimate Error!

R f

Effe

ctiv

e ar

ea (m

2 )

Time (s)

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

(kg/min) 4.9 8.0 7.8 8.1 8.9 12.4 11.7 6.7

0-D

(kg/min) 6.0 8.9 7.1 10.5 9.1 11.8 14.1 8.1

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

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Scavenging volume fraction

123456789101112

α

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

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 scm& 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 12m& . 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 scm& and 12m& were assumed.

Examination of KIVA-ERC simulations indicated that scm& was a approximately a

constant fraction of the intake flow im& , or:

>

=otherwisem

mxmifmxm

e

ieisc &

&&&& Equation 5-1

where:

x = proportionality constant

em& = total exhaust flow

Inlet Exhaust

Stage 1 Stage 2

Zone 2 Zone 1

Zone 2

em1&scm&im& em2&

im& scm&

12m&

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:

112 ωρkm =& 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:

1211 mmm e &&& += Equation 5-3

where:

scee mmm &&& −=1 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:

( ) PR

Tu

TRT

T

&&

)( 1,

111

11

φ

φ

φ

+

∂∂

= Equation 5-5

where:

164

1T = 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:

[ ] rfe mfCOtmfCOttmfCO 222 )(1)()( αα −+= Equation 5-6

where:

mfCO2f = mass fraction of CO2 in fresh charge

mfCO2r = mass fraction of CO2 in residual gases

Rearranging:

rf

re

mfCOmfCOmfCOmfCO

t22

22)(−−

=α Equation 5-7

165

Since mfCO2f = 0 for all KIVA cases and mfCO2r = )0(

)0(

2mCOm where IVO occurs at t

= 0:

)0()0()(1)(

22 mCO

mtmfCOt e−=α Equation 5-8

The scavenging efficiency is defined as the mass of fresh charge retained in the

cylinder divided by the mass of the cylinder contents:

)(

)()()()( 0

tm

dttmttmt

t

ei

sc

∫−=

&αη Equation 5-9

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

)(

)()0(

)0()(1)()( 0 2

2

tm

dttmmCO

mtmfCOtmt

t

eei

sc

∫

−−

=

&

η Equation 5-10

Integrating and simplifying:

)()0()(1)0()()(

)( 2

2

tmmCO

tmCOmtmtmt

ei

sc

−+−

=η Equation 5-11

Since m(t) = mi(t) – me(t) + m(0):

)0()(

)()0(1)(

2

2

mCOtmCO

tmmtsc −=η Equation 5-12

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:

<

=otherwise

tmtmiftmtm

t ii

dispsc

1

)()()()(

)(.η Equation 5-13

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:

)()( tt scηα = Equation 5-14

So, from Equation 5-9:

)(

)()()()( 0

tm

dttmttmt

t

esci

sc

∫−=

&ηη Equation 5-15

Differentiating:

)()(

)()()(

)()()()(

)( 20 tm

tm

dttmttm

tmtmttm

t

t

esciesci

sc &

&&&

&∫−

−−

=η

ηη Equation 5-16

Simplifying:

)()()(

)()()()(

)( tmtmt

tmtmttm

t scescisc &

&&&

ηηη −

−= Equation 5-17

Rearranging:

167

[ ])(

)()()()()(

tmtmtmttm

t escisc

&&&&

−−=

ηη Equation 5-18

Since )()()( tmtmtm ei &&& −= and replacing ηsc with ηsc.diff to avoid confusion:

( ))(1)()()( .. t

tmtmt diffsc

idiffsc ηη −=

&& 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:

g89.2)(

mkg185.1L44.2)(

3

IVCtmIVCtm ii ==

×=

=Λ − 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:

( )dtmmmtmt

sce∫ +−−=0

121 )( &&& Equation 5-21

where:

msc is defined in Equation 5-1

m12 is defined in Equation 5-2

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

168

e

sc

mm

t&

&=)(α Equation 5-22

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

)()()()()(

)(tm

tmttmtmt scsci

sc

&&&&

ηη

−−= Equation 5-23

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

( )e

escsc

mmmt

&

&& 21)( ηα −+= Equation 5-24

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

( ))(

)()(1)()()( 2

tmtmtmtmtm

t scescscisc

&&&&&

ηηη

−−−−= 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

0 0.014 0.0290

0.5

1

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.

Pressure × 10-6 Pa

Temperature × 10-3 K

Mass × 10-1 kg

Time (s) →

Cumulative intake mass × 10-1 kg

CO2 mass × 10-2 kg

Cumulative exhaust mass × 10-1 kg

170

0 0.0084 0.01680

0.5

1

Figure 5-18: Zone 1 quantities calculated from Figure 5-17 and matched calibration constants

x = 0.1 and k = 8 × 10-4.

0 0.015 0.0290

0.5

1

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

Time (s) →

Temperature × 10-3 K (Equation 5-5)

Mass × 10-1 kg (Equation 5-21)

scm& × kg/s (Equation 5-1)

1m& × kg/s (Equation 5-3)

12m& × kg/s (Equation 5-2)

Time (s) →

α0-D (Equation 5-24)

αKIVA (Equation 5-7)

ηsc.disp (Equation 5-13)

ηsc.0-D (Equation 5-25)

ηsc.KIVA (Equation 5-12)

ηsc.diff (Equation 5-19)

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

0 0.015 0.0290

0.5

1

(a) Case 1

0 0.015 0.0290

0.5

1

(b) Case 2

0 0.014 0.0290

0.5

1

(c) Case 3

0 0.014 0.029 0

0.5

1

(d) Case 4

0 0.008 0.0160

0.5

1

(e) Case 5

0 0.008 0.0160

0.5

1

(f) Case 6

0 0.008 0.016 0

0.5

1

(g) Case 7

0 0.008 0.0160

0.5

1

(h) Case 8

0 0.008 0.0160

0.5

1

(i) Case 9

0 0.005 0.010

0.5

1

(j) Case 10

0 0.008 0.0160

0.5

1

(k) Case 11

0 0.008 0.0160

0.5

1

(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.

ηsc.diff ηsc.disp

172

ηsc.0-D ηsc.KIVA

No data

(a) Case 1

No data

(b) Case 2

0 0.015 0.0290

0.5

1

(c) Case 3

0 0.015 0.029 0

0.5

1

(d) Case 4

0 0.008 0.0160

0.5

1

(e) Case 5

0 0.008 0.0160

0.5

1

(f) Case 6

0 0.008 0.016 0

0.5

1

(g) Case 7

0 0.008 0.0160

0.5

1

(h) Case 8

0 0.008 0.0160

0.5

1

(i) Case 9

0 0.005 0.010

0.5

1

(j) Case 10

0 0.008 0.0160

0.5

1

(k) Case 11

0 0.008 0.0160

0.5

1

(l) Case 12

Figure 5-21: Comparison of KIVA and two-zone scavenging model results for shroud 1 on the



For each case x = 0.12 and k = 7 × 10-4.

ηsc.diff

ηsc.disp

173

ηsc.0-D ηsc.KIVA

No data

(a) Case 1

No data

(b) Case 2

0 0.015 0.0290

0.5

1

(c) Case 3

0 0.015 0.029 0

0.5

1

(d) Case 4

0 0.008 0.0160

0.5

1

(e) Case 5

0 0.008 0.0160

0.5

1

(f) Case 6

0 0.008 0.016 0

0.5

1

(g) Case 7

0 0.008 0.0160

0.5

1

(h) Case 8

0 0.008 0.0160

0.5

1

(i) Case 9

0 0.005 0.010

0.5

1

(j) Case 10

0 0.008 0.0160

0.5

1

(k) Case 11

0 0.008 0.0160

0.5

1

(l) Case 12




For each case x = 0.10 and k = 8 × 10-4.

ηsc.disp

ηsc.diff

174

ηsc.0-D ηsc.KIVA

No data

(a) Case 1

No data

(b) Case 2

0 0.015 0.0290

0.5

1

(c) Case 3

0 0.015 0.029 0

0.5

1

(d) Case 4

0 0.008 0.0160

0.5

1

(e) Case 5

0 0.008 0.0160

0.5

1

(f) Case 6

0 0.008 0.016 0

0.5

1

(g) Case 7

0 0.008 0.0160

0.5

1

(h) Case 8

0 0.008 0.0160

0.5

1

(i) Case 9

0 0.005 0.010

0.5

1

(j) Case 10

0 0.008 0.0160

0.5

1

(k) Case 11

0 0.008 0.0160

0.5

1

(l) Case 12




For each case x = 0.09 and k = 8.5 × 10-4.

ηsc.disp

ηsc.diff

175

ηsc.0-D ηsc.KIVA

0 0.015 0.029 0

0.5

1

(a) Case 1

0 0.015 0.0290

0.5

1

(b) Case 2

0 0.015 0.0290

0.5

1

(c) Case 3

0 0.015 0.029 0

0.5

1

(d) Case 4

0 0.008 0.0160

0.5

1

(e) Case 5

0 0.008 0.0160

0.5

1

(f) Case 6

0 0.008 0.016 0

0.5

1

(g) Case 7

0 0.008 0.0160

0.5

1

(h) Case 8

0 0.008 0.0160

0.5

1

(i) Case 9

0 0.005 0.010

0.5

1

(j) Case 10

0 0.008 0.0160

0.5

1

(k) Case 11

0 0.008 0.0160

0.5

1

(l) Case 12




For each case x = 0.07 and k = 9.0 × 10-4.

ηsc.diff ηsc.disp

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

x = 0.34

k = 1

Shroud 1 x = 0.12

k = 7.0×10-4

Shroud 2 x = 0.10

k = 8.0×10-4

Shroud 3 x = 0.09

k = 8.5×10-4

Shroud 4 x = 0.07

k = 9.0×10-4 Case

(Table 5-2) 0-D KIVA 0-D KIVA 0-D KIVA 0-D KIVA 0-D KIVA

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.

Case Turbulent kinetic

energy (106cm2/s2)

Turbulent kinetic

energy ratio

Turbulence length

scale (cm)

Swirl

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

0

0.5

1

1.5

2

800 900 1000 1100

Mean temperature Tm (K)

Igni

tion

dela

y (m

s)

KIVA-ERCCorrelation

Figure 5-25: Ignition delay vs mean temperature.

0

0.5

1

1.5

2

20 30 40 50 60 70

Mean pressure Pm (bar)

Igni

tion

dela

y (m

s)

KIVA-ERCCorrelation

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

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

δ

β KIVA-ERCCorrelation

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

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

Ignition delay t ID (ms)

β KIVA-ERCCorrelation

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

Cd1 = 0.079 + 1.47φ -1.07β -0.90

Cd2 = -0.061 + 0.53φ -0.33β -0.40

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

Speed (rpm) 750 953 993 1657 1737 1789 Intake air pressure

(kPa, absolute) 150 150 150 200 200 200

Intake air temperature (K)

298 298 298 298 298 298

Exhaust pressure (kPa, absolute)

100 100 100 100 100 100

Fuel rate (g/cyl/cycle)

0.013 0.034 0.104 0.102 0.063 0.033

SOI (° ATDC) 352.0 359.5 354.5 367.5 361.5 354.5 Valve timing

IVO (° ATDC) 120 150 140 140 155 130

IVC (° ATDC) 290 280 270 270 290 290

EVO (° ATDC) 120 150 140 140 140 130

EVC (° ATDC) 290 275 260 255 280 285

Performance

Brake Power (kW) 0.5 (0.3)

7.9 (7.6)

31.3 (29.6)

38.5 (38.4)

30.0 (28.4)

12.7 (12.7)

BSFC (g/kWh) N/A 246 (266)

198 (212)

232 (264)

219 (244)

278 (303)

Max. press. (MPa) 3.3 (5.6)

5.4 (6.8)

9.5 (10.3)

5.3 (10.0)

6.6 (8.1)

6.5 (6.3)

Ignition delay (ms) 4.2 (1.24)

1.83 (0.91)

0.69 (0.44)

0.60 (0.50)

1.03 (0.45)

1.12 (0.64)

Premixed burn fraction (%)

99 (77)

93 (76)

29 (8)

28 (13)

77 (9)

80 (28)

Max. burnt gas fraction

0.11 (0.14)

0.23 (0.35)

0.62 (0.69)

0.67 (0.47)

0.40 (0.39)

0.22 (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:

( )

∑

∑

⋅

⋅=

modesmode

mode

mode

modesmodemode

rateFuel

rateFuelBSFCCycle

WBSFC

W

Equation 5-26

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


(kPa, absolute) 150 150 150 200 200 200


298 298 298 298 298 298


100 100 100 100 100 100


0.013 0.034 0.104 0.102 0.063 0.033

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

(266) 198

(212) 236

(264) 222

(244) 294

(303) Max. press. (MPa) 6.0

(5.6) 6.3

(6.8) 9.3

(10.3) 4.9

(10.0) 6.7

(8.1) 7.2

(6.3) Ignition delay (ms) 1.51

(1.24) 1.33

(0.91) 0.93

(0.44) 1.22

(0.50) 0.63

(0.45) 0.61

(0.64) Premixed burn

fraction (%) 89

(77) 86

(76) 41 (8)

73 (13)

37 (9)

33 (28)


0.08 (0.14)

0.22 (0.35)

0.67 (0.69)

0.73 (0.47)

0.37 (0.39)

0.21 (0.32)

NOx (g/kg fuel) 0.69 (69)

13 (64)

86 (45)

-* (15)

5.5 (13.8)

21 (22)

Soot (g/kg fuel) 0.47 (0.16)

0.23 (0.098)

0.016 (0.18)

- (0.17)

0.27 (0.47)

0.25 (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.

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:

Air pump (2 x engine speed)

Engine



Exhaust manifold

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


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.


Input parameters


(kPa, absolute) 100 100 100 100 100 100


298 298 298 298 298 298


100 100 100 100 100 100


0.015 0.037 0.118 0.100 0.077 0.041

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

(mm) 155.2 155.2 194.0 194.0 174.6 155.2

Air pump phase (° ATDC)*

200 180 170 170 170 180

Performance

Brake Power (kW) 1.4 (0.6)

14.7 (15.2)

51.9 (59.2)

80.9 (76.8)

63.6 (56.8)

27.8 (25.4)

BSFC (g/kWh) N/A 287 (266)

230 (212)

246 (264)

253 (244)

317 (303)

Air pump loss (kW)

0.6 1.1 3.5 8.6 6.1 3.5


4.8 (6.8)

7.3 (10.3)

7.4 (10.0)

6.0 (8.1)

4.7 (6.3)


0.97 (0.91)

0.39 (0.44)

0.24 (0.50)

0.29 (0.45)

0.53 (0.64)


98 (77)

74 (76)

14 (8)

6 (13)

8 (9)

25 (28)


0.16 (0.14)

0.41 (0.35)

0.69 (0.69)

0.70 (0.47)

0.65 (0.39)

0.47 (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.



(kPa, absolute) 100 100 100 100 100 100


298 298 298 298 298 298


100 100 100 100 100 100


0.017 0.037 0.118 0.100 0.077 0.041

Injection timing SOI (° ATDC) 360 355 355 355 355 355 Performance


(266) 231

(212) 247

(264) 270

(244) 469

(303) Air pump work

(kW) 1.8 2.9 3.0 9.3 10.4 11.3


5.4 (6.8)

7.2 (10.3)

7.7 (10.0)

7.0 (8.1)

6.0 (6.3)


0.54 (0.91)

0.40 (0.44)

0.22 (0.50)

0.22 (0.45)

0.25 (0.64)


64 (77)

27 (76)

14 (8)

5 (13)

4 (9)

0 (28)


0.12 (0.14)

0.26 (0.35)

0.70 (0.69)

0.66 (0.47)

0.50 (0.39)

0.27 (0.32)

NOx (g/kg fuel) 28 (69)

54 (64)

40 (45)

25 (15)

28 (13.8)

36 (22)

Soot (g/kg fuel) 0.23 (0.16)

0.25 (0.098)

1.12 (0.18)

1.03 (0.17)

0.85 (0.47)

0.54 (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

194

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.

Figure 5-30: Turbocharged and intercooled engine subunit.

Air pump (2 x engine speed)

Engine



Exhaust manifold

Intake

Compressor Turbine

Intercooler

195


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.


Input parameters


(kPa, absolute) 100 100 100 100 100 100


298 298 298 298 298 298


100 100 100 100 100 100


0.015 0.037 0.118 0.100 0.077 0.050

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

(mm) 155.2 155.2 155.2 155.2 155.2 155.2

Air pump phase (° ATDC)*

180 180 180 180 180 180

Performance

Brake Power (kW) 1.4 14.3 63.8 82.1 60.6 32.0 BSFC (g/kWh) N/A 294

(266) 221

(212) 242

(264) 265

(244) 336

(303) Air pump loss

(kW) 0.4 1.2 1.7 7.2 7.7 7.1


4.3 (6.8)

7.7 (10.3)

9.9 (10.0)

8.8 (8.1)

5.6 (6.3)


1.22 (0.91)

0.29 (0.44)

0.19 (0.50)

0.22 (0.45)

0.30 (0.64)


95 (77)

83 (76)

8 (8)

3 (13)

3 (9)

3 (28)


0.19 (0.14)

0.42 (0.35)

0.69 (0.69)

0.53 (0.47)

0.44 (0.39)

0.44 (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

197

Table 5-11: Optimised parameters for a 6-mode FTP cycle approximation. Four-stroke cycle

baseline results are italicised.



(kPa, absolute) 100 100 100 100 100 100


298 298 298 298 298 298


100 100 100 100 100 100


0.015 0.037 0.118 0.100 0.077 0.050

Injection timing SOI (° ATDC) 360 355 360 355 355 355 Performance


(266) 221

(212) 249

(264) 278

(244) 362

(303) Air pump work

(kW) 0.7 1.6 1.5 9.4 9.8 8.7


5.1 (6.8)

7.8 (10.3)

11.3 (10.0)

10.2 (8.1)

7.4 (6.3)


0.48 (0.91)

0.27 (0.44)

0.15 (0.50)

0.17 (0.45)

0.20 (0.64)


73 (77)

18 (76)

7 (8)

1 (13)

0 (9)

0 (28)


0.15 (0.14)

0.42 (0.35)

0.69 (0.69)

0.46 (0.47)

0.39 (0.39)

0.35 (0.32)

Turbo speed (rpm) 27,600 32,500 60,800 76,900 72,600 66,500 NOx (g/kg fuel) 33

(69) 33

(64) 18

(45) 19

(15) 20

(13.8) 17

(22) Soot (g/kg fuel) 0.19

(0.16) 0.30

(0.098) 0.50

(0.18) 0.69

(0.17) 0.66

(0.47) 0.70

(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

0

2

4

6

330 340 350 360 370 380 390 400 410


Pres

sure

(MPa

)

0

200

400

600

Hea

t rel

ease

rate

(J/d

eg)

(a) Mode 1

0

4

8

12

330 340 350 360 370 380 390 400 410


Pres

sure

(MPa

)

0

100

200

300

Hea

t rel

ease

rate

(J/d

eg)

(b) Mode 2

0

4

8

12

330 340 350 360 370 380 390 400 410


Pres

sure

(MPa

)

0

100

200

300

Hea

t rel

ease

rate

(J/d

eg)

(c) Mode 3

0

4

8

12

330 340 350 360 370 380 390 400 410


Pres

sure

(MPa

)

0

100

200

300

Hea

t rel

ease

rate

(J/d

eg)

(d) Mode 4

0

4

8

12

330 340 350 360 370 380 390 400 410


Pres

sure

(MPa

)

0

100

200

300

Hea

t rel

ease

rate

(J/d

eg)

(e) Mode 5

0

4

8

12

330 340 350 360 370 380 390 400 410


Pres

sure

(MPa

)

0

100

200

300

Hea

t rel

ease

rate

(J/d

eg)

(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 sub-

models (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 sub-

model. 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.

201

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:

( )11

1 −−

− −

+≈ ii

iii tt

dtdXXX Equation 6-1

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

0°

x = 0.34

Shroud 1

105°

x = 0.12

Shroud 2

128°

x = 0.10

Shroud 3

138°

x = 0.09

Shroud 4

168°

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

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.

Development/ calibration/ validation of a thermodynamic model of a four-stroke engine system (Chapter 3)

Four-stroke cycle gas exchange simulation using a full-cylinder KIVA-ERC model

with valves and intake ports (Section 4.3)

Calibration/validation of combustion and emissions model using KIVA-ERC and 60º sector cylinder

mesh (Section 4.3)

Initial conditions

Initial conditions

Turbulence and swirl parameters

Preliminary modelling of two-stroke poppet-valved engine system (Section 5.3.1)

Two-stroke cycle scavenging simulations using a full-cylinder KIVA-ERC model with valves and

intake ports (Section 5.1)

Development and validation of two-zone scavenging model (Section 5.2)

Results

Calibration constants

Combustion and emissions modelling using KIVA-ERC and 60º sector mesh (Section 5.3.1)

Turbulence and swirl parameters

Initial conditions

Calibration constants

Performance estimations using thermodynamic model of two-stroke poppet-valved engine

system (Sections 5.3.2-4)

Combustion model constants

Scavenging model

Initial conditions

Combustion and emissions modelling using KIVA-

ERC and 60º sector mesh (Section 5.3.2-4)

Estimate of system behaviour

Estimate of combustion and emissions

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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Documents

A NUMERICAL INVESTIGATION OF A TWO-STROKE POPPET …Two-stroke poppet-valved engines may combine the high power density of two - stroke engines and the low emissions of poppet-valved