Research Collection

Doctoral Thesis

Chemical kinetic mechanism reduction, multizone and 3D-CRFDmodelling of homgeneous charge compression ignition engines

Author(s): Barroso Raya, Gabriel

Publication Date: 2006

Permanent Link: https://doi.org/10.3929/ethz-a-005143585

Rights / License: In Copyright - Non-Commercial Use Permitted

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ETH Library

Diss. ETH No. 16437

Chemical Kinetic Mechanism Reduction,Multizone and 3D-CRFD Modelling of

Homogeneous Charge Compression IgnitionEngines

A dissertation submitted to theSwiss Federal Institute of Technology Zurieh

for the degree of

Doctor of Technical Sciences

presented byGabriel Barroso Raya

Dipl. Masch.-Ing. ETH

born 7 May 1975

citizen of Spain

Accepted on the recommendation of

Prof. Dr. K. BoulouchosProf. Dr. M. Bargende

2006

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Acknowledgments

This thesis was written during my work as reserch associate with theAerothermochemistry and Combustion Systenls Laboratory (LAV) at theSwiss Federal Institute of Technology in Zürich.

Above all, I thank Prof. Dr. Konstantinos Boulouchos for guidingmy work, his interest and support. My gratitude also goes to Prof. Dr.Michael Bargende for his interest in this work and for his time and effortsacting as co-examiner.

My thank also goes to the chairmen of the FVV-project MarkusWeßlau and Dr. Arne Schneemann for guiding the project. I thank theFVV and the Bundesanlt für Energie (BFE), Dr. A. Hinternlann, forfinancing the project.

I thank Yuri M. Wright, Luzi Valär and Marco Küng for the nicediscussions on nlY results. I thank all my colleagues of the lab for thegreat time I had. My gratitude also goes to Christian Weisskirch (THBraunschweig), Thomas Emmrich (HTW Dresden), Andreas Escher andSimon Haas (University of Stuttgart) for sharing with me experimentalresults to validate the models.

I thank Dominique Dietschweiler, Samuel Semadeni and AdrianSteinemann for their key contribution during their semester and diplomathesis for this work.

My special gratitude goes to my parents, my sister and my brotherand to Angelika Binz, for their support and patience during this years.

Gabriel Barroso Raya

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Abstract

The present work presents and validates new approaches for simulatinghomogeneous charged cOlllpressed ignited engines. The lllajor task, is thereduction of detailed chemistry to skeletallumped scheme. These mech­anisllls are then combined with a multi-zone model, and a 3-dimensionalfluid-mechanics model closed with a conditional moment closure assump­tion. The used lllethodologies for chemistry reduction are time resolvedheat released rate analysis of the individual reactions, and reaction pathanalysis with consequent species elimination, reaction elimination andlumping of elementary reactions to global ones. The first method could beused, to reduce the detailed starting mechanism with 385 species and 1895reactions, within a few iteration, to a lllechanism with 140 species and 456reactions. The agreement, between the detailed and the reduced one, wasexcellent. In a further step, using reaction path analysis with consequentspecies elimination, reaction elimination and lumping of elementary reac­tions to global ones, leaded to the smallest ever published, as much I amaware, n-butane mechanism for auto-ignition and combustion. The mech­anism has 22 species and 57 reactions. The lllechanism showed excellentagreement over a wide range of A and compression ratios. With the samemethodology, also a starting mechanism for n-heptane could successfullybe reduced, to the smallest n-heptane, as llluch as I am aware, skeletal n­heptane lllechanism for auto-ignition and combustion, which is completelydescribed with Arrhenius equations and does not have any steady stateassumption.

The work presents two different approaches to simulate the overallcombustion. Thc first model belongs to the group of stochastic multi­dimensional model. It takes into account, that different zones in thccombustion chamber have stochastic temperature and fuel concentrationaround a mean value. The zones communicate with their neighbor cellsvia boundary work. In each zone the creation and destruction of speciesand the successive heat release is calculated with detailed or reducedchemistry. The model shows good agreement with the experiment withinthe experilllental incertitude. With this kind of model, a slllOother heatrelease rate, as observed in the experiments, can be achieved.

The second model prescnted in this work is a 3-dimensional ftuid­mechanics model combined with reduced chemistry closed with aconditional moment closure assumption. The fluid-mechanics code solvesthe diffusion and convection of mass, momentum, energy, the mixturefraction and its variance. Additionally turbulence is closed by a K- - E

VB

model. The combustion source term is closed by a conditional momentassumption with skeletal chemistry, which also accounts for the influenceof turbulence on ignition delay and combustion. The fluid-mechanicscode solves the spray equation in a lagrange formulation, which allowsto simulate engines with internal mixture formation. This are the firstsimulations, as far as I am aware, which uses this methodology forsimulating direct injection HeeI diesel combustion with EGR rates up to60%. The model is able, to account for the high sensitivity on the changeof the EGR rate by only a few percents, when burning at this high EGRrates. The nlodel predicts the incomplete combustion in the vicinityto the wall, due to relaminarization of the flame. The first simulationssimulating nearly perfect homogeneous compressed ignited combustionwith the presented methodology are shown. The presented model givesgood agreement concerning overall experimental data as heat release rateand pressure curve.

A detailed analysis of spray simulation under different conditions in ahigh-temperature-pressure cell and sensitivity analysis with different en­gine meshes are performed. The widely used lagrangian-eulerian method­ology for spray calculations with its submodels for droplet breakup, evap­oration, coalescence, etc., did a reasonable job on nearly orifice resolvingmeshes in the near nozzle region combined with grids which are alignedin spray axis direction. Influence of Stokes number on droplet behavior,was physically reasonable reflected. Nevertheless, in engines simulations,the needed constraints on resolution an nlesh alignment is rarely fulfilled,so that spray simulation in engines are still uncertain.

Key Words: spray, multi zone model, conditional moment closure, ho­mogeneous charge compression ignition (HCCI), chemistry reduction, 3D­CFD engine simulation, reaction path analysis, lumping, n-butane, n­heptane

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Zusammenfassung

Die vorliegende Arbeit präsentiert und validiert neue Ansätze zur Simula­tion homogener kompressionsgezündeter Brennverfahren. Eine Kernauf­gabe ist die Reduktion detaillierter zu skelettartigen Reaktionsmecha­nismen. Die reduzierten Mechanismen werden mit einem stochastischenMehrzonenmodell und mit dreidimensionaler Strömungssimulation durcheinem CMC-Verbrennungsansatz gekoppelt. Die verwendeten Ansätze fürdie Reduktion der Chemie sind zeitaufgelöste Wärmefreisetzungsanalyseder individuellen Reaktionen, und Reaktionspfadanalyse mit darauf fol­gender Spezieseliminierung, Reaktioneneliminierung und Zusammenle­gung von Elementarreaktionen zu Globalreaktionen. Die erste Methodeermöglichte die Reduktion eines detaillierten Startmechanismus für n­Butan nlit 385 Spezies und 1895 Reaktionen, innerhalb weniger Itera­tionen, zu einem Mechanismus mit 140 Spezies und 456 Reaktionen. DieÜbereinstimmung zwischen der detaillierten Chemie und der reduziertenChemie ist hervorragend. In einem weiteren Schritt wurde mittels Reak­tionspfadanalyse mit darauf folgendenr Spezieseliminierung, Reaktionen­eliminierung und Zusammenlegung von Elementarreaktionen zu Global­reaktionen der kleinste publizierte - soweit mir bekannt - n-Butan Mecha­nismus für Selbstzündung und Verbrennung erstellt. Der Mechanismus hat22 Spezies und 57 Reaktionen. Der Mechanismus hat eine hervorragendeÜbereinstimmung mit der detaillierten Chemie in einem breiten ..\- undVerdichtungsverhältnis-Bereich. Mit der gleichen Methodik wurde eben­falls ein Startmechanismus für n-Heptan erfolgreich reduziert. Soweit mirbekannt, handelt es sich um den kleinsten Mechanismus für Selbstzündungund Verbrennung von n-Heptan, welcher vollständig mit Arrhenius Glei­chungen beschrieben ist. Dieser Mechanismus besitzt keine Spezies im sta­tionären Zustand oder im partiellen Gleichgewicht. Der Mechanismus hat24 Spezies und 63 Reaktionen.

Diese Arbeit stellt zwei Ansätze für die Simulation der Verbren­nung vor. Das erste Modell ist ein stochastisches Mehrzonenmodell.Es berücksichtigt die Existenz verschiedener Zonen im Brennraum, dieeine stochastische Initialisierung der Temperatur und des Luftkraftstoff­verhältnisses um einen Mittelwert aufweisen. Die Zonen kommunizierenmit den übgrigen Zonen mittels Volumenarbeit. In jeder Zone wird dieBildung und Zerstörung der Spezies mit detaillierter oder reduzierterChemie berechnet. Das Modell zeigte eine gute Übereinstimmung mit demExperiment innerhalb der Messunsicherheiten. Mit diesem Modell wirdeine weichere Wärmefreisetzung, wie häufig im Experiment festgestellt,berechnet, verglichen mit der Modellierung mit nur einem Reaktor.

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Das zweite in dieser Arbeit präsentierte Modell ist ein dreidimen­sionales fluidmechanisches Modell gekoppelt mit reduzierter Reaktions­kinetik und einem CMC-Ansatz für die Schliessung der Interaktionzwischen Turbulenz und Chemie. Der CFD-Code löst die Diffusion undKonvektion der Masse, des Impulses, der Energie, des Mischungsbruchesund deren Varianz. Für die Schliessung der Turbulenz wird ein K, - E Mo­dell verwendet. Das Verbrennungsmodell berücksichtigt auch den Einflussder Turbulenz auf Zündverzug und Verbrennung. Der CFD-Code löst dieSpraygleichung in einer Lagrangeformulierung, welche die Simulierungvon Verbrennungsmotoren mit innerer Gemischbildung ermöglicht. Eshandelt sich um die ersten Simulationen - soweit mir bekannt - welchediesen Ansatz für die Simulation direkteingespritzter HCCI Dieselrnoto­ren mit Abgasrückführraten bis 60 % verwenden. Das Modell zeigt diegrosse Sensitivität der Verbrennung auf kleinste Änderungen der AGR,wenn mit so hohen AGR-Raten verbrennt wird. Das Modell berechnetauch die unvollständige Verbrennung in der Nähe zur Wand infolge einerRelamisierung der Flamme voraus. Die ersten Simulationen eines fastperfekt homogenen, kompressionsgezündeten Brennverfahrens mit dervorgestellten Methodik werden gezeigt. Das vorgestellte Modell zeigt einesehr gute Übereinstimmung mit experimentellen Daten wie Druckverlaufund Wärmefreisetzung.

Eine detaillierte Analyse der Spraysimulation unter verschiedenen Be­dingungen in einer Hoch-Druck-Temperatur-Zelle und die Sensitivitätauf unterschiedliche Motornetze wird vorgestellt. Das weitverbreiteteLagrange-Euler-Verfahren für Spraysimulationen lieferte gute Ergebnissein numerischen Netze die den Düsendurchmesser auflösen und in Rich­tung der Sprayachse ausgerichtet sind. Der Einfluss der Stokes Zahl aufdas Verhalten der Tropfen wurde physikalisch vernünftig wiedergegeben.Dennoch werden diese Bedingungen in nlOtorischen Sinlulationen seltenerfüllt, so dass Spraysimulationen in Motoren immer noch einer gewissenUngenauigkeit unterliegen.

Schlüsselwörter: Spray, Mehrzonenmodellierung, Conditional MomentClosure, Homogeneous Charge Compression Ignition (HCCI), Reduktionvon Reaktionsmechanismen, 3D-CFD Motoren Simulation, Reaktionspfa­danalyse, n-Butan, n-Heptan

Contents

1 Introduction 11.1 Why Today's Technology Prevailed ? 11.2 State of the Art Homogeneous Charge Compression Ignition 4

1.2.1 Homogeneous Charge Compression Ignition InSnlall 2-Stroke Engines 5

1.2.2 Homogeneous Charge Compression Ignition in 4-Stroke Gasoline Type Engines . 6

1.2.3 Homogeneous Charge Compression Ignition in 4-Stroke Diesel Type Engines 81.2.3.1 HCCI with External Mixture Formation. 111.2.3.2 HCCI with Coexistent External and Inter-

nal Mixture Formation 121.2.3.3 HCCI with Internal Mixture Formation 131.2.3.4 Exhaust Gas Recirculation 141.2.3.5 Supercharging 151.2.3.6 Oxidation Katalyst 15

1.3 Cluster Project Homogeneous Diesel Combustion 161.4 Overview of Contents 16

2 Spray and Mixture Formation 192.1 State of the Art - Spray Modelling 192.2 Spray Fundamentals 222.3 Numerical Methodology 252.4 Setup for a High Pressure High Temperature Constant Vol-

ume Bomb. 302.5 Sensitivity Analysis of Discretization and Initial Gas Tur-

bulence 322.6 Sensitivity of Spray Prediction regarding Engines Sinlulations 452.7 Summary and Conclusions . 48

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CONTENTS Xl

2.8 List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . 49

3 Reduction of Detailed Chemistry3.1 State of the Art - Chemistry Reduction .. . .3.2 Used Methodologies for Mechanism Reduction3.3 Reduction of n-Butane ...3.4 Reduction of n-Heptane ..3.5 Summary and Conclusions .3.6 List of Symbols ....

53535456666970

4 Multizone HCCI Model 714.1 State of the Art - Multi Zone Modelling 714.2 Methodology of the Multi Zone Model . 724.3 Experimental and Numerical Setup . . . 744.4 Sensitivity Investigation of Model Parameters 76

4.4.1 Sensitivity Investigation of Temperature-Zones 764.4.2 Sensitivity Investigation of A-Zones . . . . . . . 774.4.3 Sensitivity Investigation of A- and Temperature Zones 784.4.4 Sensitivity investigation of Wall Heat Losses . . .. 784.4.5 Sensitivity Investigation of Initial Standard Devia-

tion of Temperature . . . . . . . . . . . . . . . . . . 804.4.6 Sensitivity Investigation of Initial Standard Devia-

tion of A-Distribution 804.4.7 Sensitivity of Joint Standard Deviation in Temper-

ature and A - Distribution. . . . . . . . . . . . 814.5 Verification with Experiments. . . . . . . . . . . . . . 824.6 Comparison Between the Behavior of n-Butane vs. n-

Heptane in Different Operating Points 854.7 Summary and Conclusions . 874.8 List of Symbols . . . . . . . . . . 88

5 CRFD with Reduced Chemistry 915.1 State of the Art - CRFD Modelling . . . . . . . . . . . . . . 915.2 Methodology of the CRFD Model with Reduced Chemistry 935.3 Used Reaction Mechanism for n-Heptane and n-Butane 955.4 Verification with Inhomogeneous Experiments. 965.5 Verification with Homogeneous Experiments. . 1055.6 Summary and Conclusions . . 1105.7 List of Symbols. . . . . . . 111

6 Summary and Conclusions 113

CONTENTS

Bibliography

A Skeletal n-butane mechanism

B Skeletal n-heptane mechanism

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133

137

Chapter 1

Introduction

In Sec. 1.1 a short historical overview about technical solutions to facili­tate transportation is given. Human being changed the main technology tosatisfy his needs for mobility. Today over 90 percent of the energy neededfor transportation is supplied by combustion process. The first section is asmooth transition to Sec. 1.2, where the state of the art of homogeneouscharge compression ignition (HCCI) technology is summarized. In Sec.1.3 the cluster project "homogeneous diesel cOlubustion" and the objec­tives of this work are presented. The contents of the subsequent chaptersare summarized in Sec. 1.4.

1.1 Why Today's Technology Prevailed ?

Transportation is one of the key necessities of society. Human being dis­covered this need early and used the help of animals to facilitate it. Thefirst not biological craft was the sailing ship. According to today's knowl­edge, the first sailor was constructed in the old Egypt. It was mainlyused for journeys on the Nile, the Mediterranean and the Red Sea, re­spectively. Already in the first century the Greek Heron of Alexandriainvented a stearll powered apparatus (Aeolipile), but only as a toy. Itis difficult and unfair to assign the invention of the stearll engine to asingle person, but a few highlights have to be emphasized. The first uti­lizable steam engine was designed by Thomas Newcomen to pump waterin amine. Its efficiency was 0.5%. The steam engine was further devel­oped by James Watt and Richard Trevithick and it was Nicolas Cugnot in1769 who first builded a steam power driven vehicular. In 1783 the first

1

CHAPTER 1. INTRODUCTION 2

steamship was constructed by Claude de Jouffroy d'Abbans. Trevithickconstructed in 1804 the first self-propelled railway steam engine - the firststeam locomotive was invented. In 1852 Henri Giffard builded the firstairship with a 2.2 kW steam engine. It can be said, that the 19th centurywas for transportation and also for industry the age of steam and coal,which was the main energy source to heat up the water.As for the steam engine, the internal COlllbustion engine was a co-inventionof many people. In the broadest sense, already in the 17th century, SirSamuel Morland used gunpowder to drive water pumps. Sadi Carnot es­tablished in 1824 the theory for conventional reciprocating internal com­bustion engines, whilst the American Samuel Morey received a patent in1826. In 1860 Lenoir constructed the first gas-engine. Nikolaus Otto wasgeared to Lenoir's engine. He started his first experiments in 1862 whichleaded in 1876 to the first 4-stroke gas-engine with cOlllpressed charge. Itwas Langen, Otto's partner, who employed Maybach and Daimler 1872in the new created enterprise "Gasmotorenfabrik Deutz", which todayis the famous "DEUTZ AG". 1882 after a dispute with Otto, Daimlerleft Deutz and created a new enterprise in Stuttgart. He constructed to­gether with Maybach the first motorbike 1885. In the same year Benzconstructed the first automobile, which had 3 wheels. The engine usedin the first motorbike and in the first automobile had externally-suppliedignition. Rudolf Diesel developed contemporaneous the compressed igni­tion engine. The first run of a diesel engine was in 1897 with an efficiencyof 26.2 percent. The first ships with diesel engines were built in 1903 andthe first trucks and locomotives propelled by diesel engines in 1908. In1933 Wankel patented the rotary piston engine. It needed nearly thirtyyears until Wankel could present in 1960 the first rotary piston engine ina adapted NSU Prinz. The greatest sensation was the two-disc unit in theNSU Ro 80. The oil crisis in the seventies of the last century dropped thepopularity of the rotary piston engine, because of its higher fuel consump­tion. Today this kind of engine is rarely used. After World War 11, alsothe use of gas turbines in automobiles was tried several times by differentmanufacturers. So presented e.g. Rover in 1962 the prototype T4. Themain issue of this propulsion system was its bad efficiency for automotiveapplications.It is interesting to notify, that the first electric vehicle was build by An­derson in 1839. So the electric propelled automotive is much older thanDaimler's car. Electric propelled 10ColllOtives and vehicles, respectively,are very successful in trains, tram, trolley-car and subways. They areestablished in applications were a contact wire is technical, economical

CHAPTER 1. INTRODUCTION 3

and scenic possible and safety. For individual transport this is nowadaysnot the case and the electricity has to be supplied by batteries. Becauseof their weight, their energy and power density, respectively, and theircharge time, they are not competitive to the internal combustion engine.Therefore the 20th century and the beginning of the 21th century are theage of crude oil.Nowadays 90 percent of the energy needed for transportation is gener­ated by combustion of fuels derived from crude oil. Because the price isprimarily set by the actual demand and offer, respectively, and latter isrestricted by the production limit of the wells, it is to expect, that dueto the increased demand of emerging economies, the costs for crude oilwill continuously increase. The rising price of crude oil will not force thehunlan being from one day to the other to change technologies or lifestyle.The rising fraction of diesel cars in Europe and hybrids in the UnitedStates are small indicators, that people in developed econonücs are softlyforced to more fuel efficient cars. Nevertheless, the economic wealth seemsto rise stronger then the energy prices. Additionally the inlprovement inefficiency is nearly abolished by the rise of the average car weight. Inenlerging markets the need for energy will continuously rise.Manufacturer of vehicles have to be concerned about short, medium andlong term environrnental legislation, costs of resources and needs of thecustomer. Both, gasoline and diesel passenger cars comply with the ac­tual legislation Euro 4 with standard technologies. Standard technologiesfor reduction of pollutants in spark ignited engines are exhaust gas re­circulation (EGR) and 3-way catalyst, whereas for diesel passengers carsengines is EGR. There are a few manufactures which have started usingparticle trap, but not because of the need by the actual legislation, morebecause of the actual justified fears of the society about the carcinogeneffect of particulate matter, which is caused by a significant amount bydiesel engines. The situation for vehicles for heavy duty applications isdifferent. Because this engines are frequently used in higher loads, thereduction of pollutants formation controlling the combustion, is more dif­ficult. Additionally the use of EGR is not so common, because on higherloads (without using modifications of the turbo charge system) the maxi­mum brake n18an effective pressure is reduced. There are two technologiesused by the manufacturers to comply with the EURO 4 regulation. Oneis cooled exhaust gas recirculation what lowers the NOx formation duringcombustion, and the other one is the use of a SCR-catalyst (selective cat­alytic reduction) which is an exhaust gas after treatment [2]. Nowadays itseems, that to comply with Euro 5 an SCR-catalyst will be indispensable.

CHAPTER 1. INTRODUCTION 4

It is important to comment that in 2002 Gärtner et al. [1] showed thepossibility of reducing NOx using EGR but the presented engine did notwith the Euro 4 regulations. Today there are manufacturer which do [2].

1.2 State of the Art Homogeneous ChargeCompression Ignition

It is to expect, that internal combustion engines will be the preferredpropulsion technology for the next decades. To comply with future enlis­sions legislation for diesel engines, the conlbination of aftertreatment andcombustion technology will be essential. Homogeneous Charge Compres­sion Ignition (HCCI) is a combustion process, which leads to low NOx

and low soot emissions. The main characteristics and properties of HCCIare, that mixture formation has finished before ignition occurs, that thecharge is diluted and that ignition is caused by auto ignition. Over theyears, manufactures, research centers and universities have made numer­ous publications giving different names to their combustion process. Theyall satisfy above definition and can only be differed by the way mixturefornlation occurs (internal, external, nozzle type, spread angle, injectiontime, etc.), the fuel and the type of exhaust gas recirculation (hot, cold,internal). In Sec. 1.2.1 the state of the art of HonlOgenous Charge Com­pression Ignition combustion in 2-stroke small engines is sunlmarized. InSec. 1.2.2 the same is done for 4-stroke gasoline type engines. In Sec.1.2.3 a literature overview for diesel type engines is given. The boundarybetween Sec. 1.2.2 and Sec. 1.2.3 is not sharp. The partition is donelooking on the type of engine, the injection system and the ignitability ofthe fuel. The strategies chosen for engines of the type of Sec. 1.2.2 is toinduce or hold thermal energy in order that the fuel, which in this case hasbad ignitability, combusts. In contrast the strategies chosen in Sec. 1.2.3are to withdraw thernlal energy so that the combustion does not occurto early. Because the nlain field of research of this work is HomogeneousCharge Compression Ignition of direct injected diesellike fuel, Sec. 1.2.1and Sec. 1.2.2 are only abrief overview of selected publications. Thethree mentioned sections are an introduction. Publications concerningabout the investigated topics, as spray simulations, chemistry reduction,multi zone modelling of compression auto ignition and 3-D simulationwith reduced chemistry of the homogeneous charge compression ignitionare summarized in Sec. 2.1, Sec. 3.1, Sec. 4.1 and Sec. 5.1, repectively.

CHAPTER 1. INTRODUCTION 5

1.2.1 Homogeneous Charge Compression Ignition inSmall 2-Stroke Engines

The roots of "modern" HCCI in "gasoline" engines ean be loeated in the2-stroke motorbike engine research in the late 70's. But before World WarII already Withrow [4] investigated non-knoeking auto ignition . In 1979Onishi et al. [5] ealled the thermal indueed auto ignition in 2-stroke en­gine "Aetive Thermo-Atmosphere Combustion (ATAC)" . He showed thatfor loads up to 2.5 bar he eould deerease the UHC-emissions and the eon­sumption. 2-stroke engines have hotter walls then 4-stroke engines, that iswhy they suffer of uneontrolled auto ignition. Seavenging effideney of twostroke engines with cross seavenging using delivery ratio between 1 and 2is in the range of 0.6 to 0.8 [6]. This eharaeteristie was used to auto ignitediluted gasoline-air-exhaust gas nlixtures. The eontrolled auto ignitionand the knoeking have similarities [7]. The main differenee is the dilutionand the temperature band were auto ignition oeeurs. In HCCI the loealenergy density is signifieantly lower than in the end gas of a SI-engine,that is the main reason, why auto ignition does not damage in HCCIeombustion proeess. Based on the promising results presented by Onishi,Ishibashi et al. [8], Iida et al. [9, 10], Gentili et al. [11] investigated autoignition in 2-stroke engines. Iida [9] showed that the hornogeneous chargeeompression teehnology was, using gasoline, utilizable above 2500 RPMand until 1.5 bar BMEP. Using methanol as fuel he showed that he eoulddrop the minimal RPM till 2000. This was already one indieation, thatthe eonventional charaeterization of fuels with the oetane number and theeetane number is not one-to-one applicable to the HCCI eombustion pro­eess. Iida [10] also showed, that the auto ignition loeation is only in a smallrange of the engine map perfect. Similar results he got with alternativefuels as nlethane, propane, Inethanol, ethanol and DME. With methaneand propane it was not possible to operate in HCCI mode with the in­vestigated engine under the published eonditions (RPM 3500) beeause ofits moleeular stability. With methanol and ethanol sueeessful operatingarea was little larger than for gasoline. And DME showed the possibil­ity of igniting lean mixtures (up to an equivalence ratio of 0.6, whereasfor methanol it was between 0.7 and 0.8, and for ethanol and gasolinebetween 0.8 and 0.9). DME has a eetan number between 55 and 60 andtherefore a higher ignitability. The maximum load for rieher mixtures wasbelow 1 bar BMEP beeause of to early autoignition. Gentili et al. [11]investigated the infiuenee of air-fuel ratio, eompression ratio and RPM.He performed his investigations at 2 bar BMEP. With leaner mixtures thecombustion duration was prolonged. The shortest eombustion duration

CHAPTER 1. INTRODUCTION 6

was at an air-fuel ratio lightly below stoichiometric (.\=0.85). Beneaththat the combustion duration was prolonged. The combustion durationwas for all cases between 150 and 200 CA. As expected, the combustionwith an compression ratio of 9 was shorter then the one with a compres­sion ratio of 7.8, because of the higher compression end temperatures ofthe first one. Interesting are the results of the RPM variation. It wasto expect that with increasing RPM the combustion duration would belonger and the start of combustion later, because the combustion dura­tion is only dependent on the characteristic chemical time. But his resultsshowed exactly the reverse. This could be because of the hotter walls athigher engine speed. Because the results were promising and the technicalsolution easy to manage (an additional throttle in the exhaust manifold),Honda sold this combustion technology in their 2-stroke motorbike en­gines. Nevertheless the emissions and consumption did not achieve thelevel of 4-stroke motorbike engines. Honda, who made a major researchcontribution in this field, produces nowadays practically only 4-stroke en­gines for nlOtorbikes.

1.2.2 Homogeneous Charge Compression Ignition in4-Stroke Gasoline Type Engines

Najt et al. [12] published in 1983 one of the first research results con­cerning HCCI in 4-stroke gasoline type engines. The publications whichsucceeded proposed different ways to auto ignite fuel with low ignitibility.Christensen et al. [23] enhanced the compression ratio up to 22. Withthis compression ratio he was able to auto ignite nüxtures of .\ = 3. Thislean nüxtures have a low power density and at loads of 3.9 bar BMEP thecylinder pressure fluctuations were significant. If the mixture is enrichedto increase the load, the heat is released violently and the engine knocks.By lowering the compression ratio the maximum load can be increased[14, 15]. The lower compression end temperature and end pressure delaysthe combustion begin and increases the combustion duration. Lower com­pression ratios have the disadvantage, that the compression end temper­ature is not sufficient to auto ignite the fuel [23]. This makes it necessaryto preheat the air. Nevertheless, with this strategy, it is not possible tosignificantly increase the load. GIsson et al. [15] showed, that with acompression ratio of 18 the maximum possible load is 5 bar BMEP. Theelectrical heating power, which is necessary to heat up the intake air, low­ers the overall efficiency. The use of a heat exchanger is because of the lowexhaust gas temperature not adequate. Additionally, for transient control

CHAPTER 1. INTRODUCTION 7

of the eombustion, a heater is unsatisfaetory beeause of the inertia of thesystem. The ignitability of the fuel, whieh as a first simplifieation (but asresults in Sec. 1.2.1 have shown, not satisfaetory) ean be derived from theoetane number, is also a parameter whieh was investigated to enhanee themaxinlum load. Olsson et al. [15] showed that with higher oetane num­ber the maximunl load eould be inereased. Using a fuel with an oetanenumber elose to 100 and no preheating a maximum load of 6 bar BMEPeould be reaehed. The advantage in the upper load nlap is a disadvantageon the lower load map. To be able to auto ignite the fuel at lower loads,the air had to be preheated. The maximum load with a fuel with an oe­tane number of 0 was elosed to 1.5 bar BMEP. With external hot EGR,and with an exhaust gas temperature whieh is sufficient, the preheatingof the intake air eould be redueed [12, 16]. Christensen et al. [17] showedthat although the effeetive intake air temperature is after the mixing withexhaust gas hotter, if operating with high amount of EGR in the rangeof 30% to 50%, the effeetive intake air temperature has to be hotter thanwithout EGR. He explains this phenomena with the slower reaetion kinet­ies due to the lower oxygen eoneentration. Additionally the eompressionend temperature is lower in the ease of an EGR-air-mixture beeause ofthe lower isentropic eoeffieient. However it was possible to renounce onpreheating in certain operating points. Christensen [17] and Oakley [16]showed that the use of external EGR delays the start of eombustion andinereases the eombustion duration. Therefore the pressure rise is lower.The maximum load is however far fronl the SI-engine maximum load.Christensen achieved a maximum load of 4 bar BMEP with 50 % EGR.The maximum pressure rise in this point was 4.6 bar / CA. This value isacceptable but is still more than the double of a conventional SI-engine.Compared to that, without EGR the maximum pressure rise was 26.6 bar/ CA and the maximum load 3.5 bar BMEP. The load dropped becauseof the bad loeation of start of eombustion. The eombustion duration waswith no EGR less than 10 degrees whereas with 50% EGR the durationwas 15 degrees. A main evolutionary step was the use of internal exhaustgas trapping [7, 18, 19]. The internal exhaust gas trapping was performedwith modified eanlshafts. One possibility is to elose the exhaust valve ear­lier than in conventional SI-engines, and the intake valve are opened laterthan in eonventional SI-engines. Consequently apart of the exhaust gasis trapped in the eylinder and a eompression in the gas-exchange eyele isperfornled. Law [18] proposed, as a seeond possible strategy, to inereasethe opening duration of the exhaust valve. The exhaust gas flows out,but beeause the exhaust valve are still open during the aspiration stroke,

CHAPTER 1. INTRODUCTION 8

the exhaust gas is re-aspirated. This second method seenlS to be lesspromising, because no results of consumption improvement can be foundin literature. Contrary to the use of external EGR, trapping the hot ex­haust gas leads to an earlier start of combustion because the mean gastemperature at compression begin is higher and therefore conlpression endtemperature also. This strategies allows the decrease of the compressionratio. Nevertheless the nlaximunl load is still limited to 4.5 bar IMEP.The limitation of the maxinlum load is a consequence of the nearly vol­ume reaetion of the whole cylinder mass. High ternperatures are neededto ignite the mixtures and the factors, which slow the combustion velocityare dilution [20, 21, 22] and thermal inhomogeneity. The thermal inho­mogeneity is given from the intake flow and the wall temperatures anddifficult to use as a control factor. A high dilution in an natural aspiredengine is only possible for partial load. Christensen [22] supercharged theengine with boost pressure of 2 bar. The maximum load he reached was14 bar IMEP with natural gas as fuel and a compression ratio of 17. Aat this point was 3. The leaner the mixture is, the longer is the com­bustion duration and the smaller is the pressure gradient. Christensen[22] made also an investigation with iso-oetane. The maxirnum load withthis fuel was between 9 and 10 bar IMEP. This load was reached witha A of 4.4. But it has to be mentioned, that this point is an academiclimit because the pressure rise is 31.8 bar / CA. Serial diesel cars havea nlaximum pressure rise of 6 bar / CA and SI-engines of about 2 bar/ CA. Christensen [21] proposes the use of high EGR (up to 50% and Aelose to 1) and a decrease of the conlpression ratio to 16. Christensen [23]proposed also the use of water injection to delay start of combustion andprolong combustion duration. Water is injeeted in the port. To achievegood evaporation the intake air had to be preheated. The water injectiondecreased NOx emissions without a large change of the efficiency. Butthe already high CO and UHC emissions were further increased.

1.2.3 Homogeneous Charge Compression Ignition in4-Stroke Diesel Type Engines

On the diesel side it is unfair to assign the conlmencements of research toa single person. The border between "conventional" premixed diesel com­bustion for low loads and HCCI is diffuse. Already in 1958 Alperstein [3]published that fumigation of diesel leads to a decrease of soot emissions.HCCI research with modified SI-engines is mainly done to improve thepartial load effidency of SI-engines. The use of homogenous combustion

CHAPTER 1. INTRODUCTION 9

with auto ignition allows to ignite very lean mixtures and therefore reducepumping losses. Because the 3-way catalyst does not convert efficientlyunder lean conditions, the NOx have to be avoided controlling the com­bustion. For HCCI research with modified CI-engines the most importantissue is the reduction of NOx and soot. Because diesel engines do nothave a throttle, the pumping losses are in partial load practically inexis­tent compared to SI-engines. Because the principle of diesel engines needsglobal over stoichionwtric mixtures, the use of the 3-way catalyst tech­nology is not possible. In the conventional diesel combustion, the dieselis injected a few degrees before TDC. After a short ignition delay of therange of 0.5 to 1ms the diesel auto ignites. The fuel, which is already weIlmixed with air in this short time, combusts in apremixed flame. Thispart of the combustion is relatively fast and leads to a strong pressure risewith uncomfortable noise. This part of the combustion affects the N Oxemissions. The fuel, which is injected later, combusts in a diffusion flame.This part of combustion is mixing controlled. Because the mixing is notinfinitesimal fast, there are rich zones burning, which are responsible forthe soot enüssions. Homogeneous combustion can theoretically avoid thisdisadvantages, because the mixture is fornled significantly before com­bustion. 'This avoids rich zones, which lead to soot, and the strong overstoichionletric nüxture has a low energy density and therefore the com­bustion temperature is lower and avoids the production of thermal NOx .

This circumstances rnakes HCCr combustion very attractive in order toavoid costly exhaust gas after treatment technology. The idea is to havethe nüxture already formatted before start of combustion. The leaner andmore homogeneous the state of the mixture, the lower is the local energydensity. This leads to a decrease of the combustion temperature with thedirect consequence of lower NO x emissions. Additionally, a lean and ho­nlOgeneous mixture has no soot emissions. 'I'his novel combustion processhas also disadvantages. The literature about HCCr with diesel revealsthree main challenges. The first one is the control of combustion begin.The second one is the limited maximum load, which is a direct conse­quence of the absence of a control factor. The third nlain challenge is thebad evaporation of diesel if this is injected early. Diesel has compared togasoline worse evaporation properties [24, 25, 26]. This bad evaporationproperties lead, at early injection, to fuel accunlulation in the bowl andcylinder wall. The consequence is UHC enüssions and even soot can becreated.

Location Nozzle type: Pinj: Tin: EGR: Fuel: T Evap : CR: Source:of injection:Port Low-pressure 2.8 - 4.2 bar 160 - 205°e 0-60% Diesel (CN 45) 170 - 320 oe 8-13 [27]

gasoline type [28,29]or gas injection 8 bar 24 oe 0% DME (CN 55) -25 oe 15.7 [105]

Port + DI Low-pressure 8bar approx. 25°e 0% D~·/IE (CN 55) -25°e 14,16,18 [31]gas injection Methane (CN 0) -162°e

middle pressure 220bar Diesel (CN 54) 174-324°emultiple hole nozzle4 x 0.26 mm

Port + DI middle-pressure 50bar approx. 25°e 0-30% diesel (CN 54) 174-324°e 20.4 [32]GDI-type [33,34]

middle pressure 180barmultiple hole nozzle4 x 0.147 0.26 mm

DI high-pressure 1000bar approx. 25°e 0-30% n-pentane 36°e 16.5 [35,36J(PREDIC) pintle nozzle (CN 29)

area 0.28mm2

(PCI) multiple hole nozzle 800bar approx. 25°e 0% diesel (CN 54) 174-324°e 12 [37J5 x 0.21 mmimpingement 0-58%multiple hole nozzle2 x 5 x 0.21 mm

DI high-pressure approx. 25°e 0-30% diesel 178-279°e 16.5 [36]multiple hole nozzle (CN 19,30)

(MULDIC) (2 lateral injectors2 x 0.17 mm, 1000 bar1 central injector 1000 -6xO.17mm) 2000 bar

DI high-pressure 1600 bar approx. 25°e approx. 50% n.s. n.s. 18 [38]multiple hole nozzle

(MK) 5 x 0.22 mm

multiple hole nozzle 700 - 30-80 0 e 32-45 % 16 [39]5 x 0.23 mm 1300 bar

Table 1.1: Investigated HCCI configurations in literature.

@~'1j

~?:lI--.<

~;Ega~o~

f-'o

CHAPTER 1. INTRODUCTION 11

1.2.3.1 HCCI with External Mixture Formation

Because of the bad evaporation properties of diesel [24] for port injec­tion, special features have to be taken in account. In all experinlentalinvestigations with port injection of diesel, the intake air was pre-heated[23, 27, 28, 29]. The distance from the injection nozzle to the intake valveis in all cases at least 30 cm. This enhances the homogenization. Theminimal intake air temperature in [23] is 90 °c. Below this value, theevaporation is insufficient and leads to a bad combustion. To avoid theproduction of soot Gray et al. [28] proposed the pre-heating of the intakeair to 150°C. The Bosch smoke number is, with an intake air pre-heatingto 90 °C and a A of 3, 0.5 [23]. There is evidence that this is due to thebad evaporation. The UHC emissions are 37 g/kWh, the NOx emissions0.03 g/kWh and the CO enüssions 28 g/kWh. The low value of NO x

emissions indicate that the combustion temperature is low. But low com­bustion temperature leads to high CO and HC emissions. So it is difficultto distinguish, which part of the emissions is caused by the insufficientmixture formation and which part is caused by the cold combustion. Pre­heating the intake air to 90°C leaded to astart of combustion 5 °CABTDC (A = 3, E = 11.2). The combustion duration was 16 DCA andthe indicated mean pressure of the high pressure cycle approx. 2.6 bar.Ryan et al. [27] achieved similar results. He preheated the intake air upto 160°C and therefore had to decrease the compression ratio to 8. Heused approx. an external EGR ratio of 45% and was able to increase themaximal indicated mean pressure of the high pressure cycle to 3.8 bar.Iida et al. [105] used dimethyl ether (DME) which at room temperatureand pressure is gaseous and therefore easy to inject into the port. DMEhas a good ignitability which confirms its cetane number of 55. Iida usedan engine with a compression ratio of 15.7. The combustion started for allinvestigated air-fuel ratios at least 20 degrees before TDC. For all casesthe combustion was finished at TDC. The maximum mean effective pres­sure was 1 bar IMEP at a A of 3.5. A further decreasing of A leaded toknocking.Recapitulating, if using diesel fuel combined with port injection, the useof intake air pre-heating is mandatory to reach low soot enüssions. TheUHC emissions remain extensive. This is in general a weak point of thehomogenous charged auto ignited combustion. The compression ratio hasto be lowered notable, to avoid a to early start of combustion. This isdue to the high ignitability of diesel. The maximunI loads are deep. Thisconcept is nice for research, but does not seem to be practically applicable.

CHAPTER 1. INTRODUCTION 12

1.2.3.2 HCCI with Coexistent External and Internal MixtureFormation

In Sec. 1.2.3.1 the difficulties of the external mixture formation werepointed out. Port injection of gaseous fuel does not suffer of the evapora­tion difficulty. As shown by Kaimai [31] the maximum IMEP using fnelwith high ignitibility is in the order of 1 to 2 bar. Kaimai [31] proposesan coexistent external and internal mixtnre formation. DME is injectedin the port, whereas diesel is direct injeeted. Re investigated the inflnenceof the ratio between the energy supplied into the port and the one directinjected. For a load of 1 bar BMEP the whole energy conld be suppliedinto the port. Soot and NOx emissions where lowermost but URC andconsumption were worse than injecting the whole energy directly. AI­ready at 1.9 bar BMEP it was not possible to injeet the whole energy intothe port. At 3.9 bar BMEP the maximum ratio between energy snppliedinto the port and whole energy supplied was 0.5, afterwards the enginewas knocking. Additionally, at this limit, the NOx emissions started toincrease again. Probably the to early combnstion leaded to high temper­atnres and therefore NOx ' Odaka [32] investigated the use of a GDI-typeinjeetor to supply the Diesel into the port. The injection pressure was 50bar, to enhance the evaporation. The distance from the injector to theport was 40Clll and the injection occnrred during the aspiration cyde at60 deg. after TDC. With increasing anlOunt injected into the port theNOx emissions were lowered. The inflnence was much stronger, if the di­reet injection was performed at 10 BTDC than if the direct injeetion wasperformed at 3 BTDC. Postponing the direct injeetion from 10 BTDC to3 BTDC without port injection had mainly the same influence on NOx

reduction as having apremixed fuel ratio of 80%. Suzuki had similarresults. Increasing the premixed fuel ratio at low load (approx. 2.7 barBMEP) the NOx and the soot emissions were reduced. At higher loads(approx. 4.5 bar BMEP), starting replacing apart of the direet injeetedfuel by port injeetion, the NOx and the soot emissions decreased. At anpremixed fuel ratio of 80 % the increase again. Suzuki assurnes that thisbehavior is due to the increasing knocking. A knocking RCCI combustioncan be charaeterized by an early combustion an a high heat release rate.The 20 % diesel which is direct injected into a hot flame with low oxygenconcentration leads to NOx and soot. The URC emissions increase withincreasing premixed fuel ratio. The behavior of the consumption is idem.Odaka [32] investigates the possibility of the direct injection as a controlfactor. With 75% premixed fuel ratio, the time of direet injeetion hasonly little influence in the combnstion behavior. With 45 % premixed fuel

CHAPTER 1. INTRODUCTION

ratio the influence is larger.

1.2.3.3 HCCI with Internal Mixture Formation

13

The most acceptance by engine manufacturers have the approaches withdirect injection [40]. The engines must be able to run fullload, and lowestmodifications are preferable. Shimazaki [35] uses a central pintle nozzlewith two swirl dent. If the fuel is injected 180 degrees before TDC theNOx reduction is considerable (NOx = 1 ppm) having contemporaneouslya Bosch smoke degree of O. Shimazaki used n-pentane which has a boilingtemperature of 36°. The evaporation properties of this fuel is thereforebetter then the one of diesel. Therefore a conlparison with the smokedegree of diesel is inlproper. The UHC and the CO emissions are as ha­bitual for HCCI high (UHC = 1500 ppnl, CO = 1500 ppm) UHC emissionsare approximated 50 times higher than in conventional diesel combustionand CO enlissions about 5 times higher [41]. The indicated consump­tion was increased from 175 g/kWh for standard diesel combustion to 190g/kWh. The cetane number of n-pentane is 29 and therefore much lowerthan the one for diesel. Consequently ignition occurs inessential earlierthan in conventional DI operation. If the start of injection is moved to­wards TDC, at 80 degrees BTDC the UHC-enüssions drop to 600 ppnl.Contemporaneously the NOx emissions increase to 27 ppm. Between 80degrees BTDC and 20 degrees BTDC injection is not possible, becauseof knocking. The mixture is not anymore enough homogeneous, so thatthe ignition delay drops and an early combustion occurs which leads toknock. The maximunl IMEP is at a ,\ of 3.7 approx. 3bar. Iwabuchi [37]also investigates the direct injection. He uses a hole nozzle with a narrowaperture angle of 80 degrees. With this modification the impingement ofthe walls should be impeded. The nozzle has 5 wholes with a diameter of0.21. The injection pressure is 800 bar. The compression ratio is reducedto 12. At low load (,\ = 3.9) he varies the injection time between 40BTDC and 25 BTDC whereas at higher load (,\ = 2.6) an start of injec­tion variation from 80 degrees BTDC to 40 degrees BTDC is investigated.Remarkable is the high soot emissions at early injection, which for bothloads is always higher than the values for conventional diesel conlbustion.This must be due to a bad evaporation. The combustion must be leanbecause the NOx emissions are low (at least for the early injection points)and the UHC emissions high. To enhance the mixture formation specialimpingement nozzle were constructed. The collision of two jets prevents adeep penetration. The soot emissions dropped significantly with this newnozzle time. Also the UHC emission dropped, but not in such a scale as

CHAPTER 1. INTRODUCTION 14

the soot. Akagawa [36] investigated the use of two lateral nozzles. Thesenozzles had each two holes. At 150 degrees BTDC apart of the fuel wasinjected at apressure of 1000 bar. The main injection was carried outat TDC with an injection pressure of 2000 bar. The NOx emissions andthe soot emissions could be halved at a A of 1.4 without increasing signif­icantly the consumption by making a first injection at 150 degrees BTDCand a second injection at 14 degrees ATDC. The combination of a fuelwith a deeper cetane number and a lower compression ratio increases theignition delay and allows a good mixture formation. These benefits theNOx and the soot emissions. The UHC emissions are as usual high. Afurther disadvantage is the need of three injectors per cylinder. Contraryto the above investigations, where an early injection was chosen, to createa homogenous mixture, Kimura et al. [38, 39] proposed a late injection.The idea is to inject the whole fuel during the ignition delay. In low loads,the amount of fuel, which has to be injected during the ignition delay, islow. In higher loads the amount of fuel increases and combustion startsbefore the end of injection and a diffusion combustion occurs. To pro­long the ignition delay, cooled EGR is used and the compression ratio islowered from 18 to 16. The EGR can reach 45% [38]. To increase theanlOunt of fuel injected during the ignition delay, the injection pressure israised to a level between 1300 bar to 1600 bar. Additionally the diame­ter of the wholes of the nozzle is enlarged. To impede the impingementof the bowl, the piston bowl is broadened and a high swirl flow is used.Combustion occurs relatively late. This benefits the NOx emissions andthe pressure gradient. Because of the short combustion duration the fuelconsumption is in the order of a conventional diesel. With these combus­tion process, easily rnaximalloads of 7 bar IMEP are reachable. The usedinjectors have 5 wholes with diameter of 0.22 mnI. The high potentialof these conlbustion process, leaded NISSAN to introduce vehicles in theEuropean market.

1.2.3.4 Exhaust Gas Recirculation

Exhaust gas recirculation is used in conventional diesel engines to reducedNOx emissions. Basically the same effect ean be detected in HCCI eom­bustion. With increasing EGR rate the NOx emissions drop [28, 32].Widely more than the impact on NOx emissions is the possibility of con­trolling the combustion location. Iwabuchi [37] showed that increasingthe EGR rate the eombustion loeation moves towards later. IncrementingEGR rate leads to deeper eompression end ternperature, beeause of thesmaller isentropic exponent /'". Additionally the oxygen concentration in

CHAPTER 1. INTRODUCTION 15

the combustion chamber is deeper. Both leads to an increased ignitiondelay [36, 37, 38]. If the EGR is additionally cooled, the influence is evenmajor. A later start of combustion causes because of the deeper nlaximumpressure and tenlperature a prolongation of the combustion duration. Theslower reaction is also a consequence of the high concentration of inert gas.As described in Sec. 1.2.3.1, EGR can be used in external mixture forma­tion to preheating fresh mixture. A better evaporation of the fuel in theport can be reached.

1.2.3.5 Supercharging

If the complete fuel mass is injected before start of combustion, as in HCCIcombustion process has to be, the maximum loads are limited. The reasonis that start of combustion moves towards earlier with richer mixtures andtherefore the heat release rate becomes energy-intensive [31]. Supercharg­ing counteracts that, although the fuel mass is increased the mixture doesnot become to rich. A leaner mixture, due to the marginal local energydensity, burns slow. When combustion has started, the air excess acts as akind of thermal insulation between the burnt and the unburnt areas. Us­ing a intercooler the maximum potential is utilized. Iwabuchi [37] showedthat the behavior of emissions were equal to the behavior of them withoutsupercharging but on lower loads. Early injection leads to low NOx andsoot but high UHC emissions and a worse efficiency. Injecting the fuel at120 degrees BTDC the UHC emissions were 1600 ppm, with nearly zeroNOx and soot emissions. Injecting at 80 degrees BTDC leaded to 800ppm UHC, an opacity of 5 % and NOx of 600 ppm. 80 degrees BTDC isalso the latest start of injection without serious knocking. The maximumload using supercharging with internal mixture formation was of the orderof 7 bar [38] and 9 bar [37].

1.2.3.6 Oxidation Katalyst

The combustion temperature is in HCCI, due to the spatial distributedlean combustion, low. As already mentioned, this leads to deep NOx butto high UHC emissions. A modification of the spray [35, 36, 37] can helpto reduce the UHC emissions, which are caused by the impingement ofthe wall. Iwabuchi [37] advises that the UHC emissions are caused by thecold combustion and can hardly be solved by inner engine measures. Heinvestigated the conversion capacity of an oxidation catalyst with a palla­dium coat. Upon a catalyst inlet temperature of 2100 the UHC emissionsare in the range of a conventional diesel.

CHAPTER 1. INTRODUCTION 16

1.3 Cluster Project Homogeneous DieselCombustion

The cluster project homogeneous diesel combustion was financial sup­ported by the German "Forschungsvereinigung Verbrennungskraftmaschi­nen" . The project part at the Swiss Federal Institute of Technologywas additionally supported by the Swiss Office of Energy (BFE). In thisproject, the four participating Universities had different tasks. At the Uni­versity of Stuttgart, a one cylinder research engine was used, to analyzedifferent strategies for HCCI combustion in this direct injected passen­ger car diesel engine. The University of Braunschweig had a one cylinderheavy duty engine, to analyze different strategies for HCCI conlbustion inthis direct injected heavy duty diesel engine. The task of the Universityfor Applied Science HTW Dresden was to make wall heat losses measure­ments, to generate a large data base, for later create a new wall heat lossmodel for HCCI combustion. The task of the Swiss Federal Institute ofTechnology, was the reduction of reaetions mechanism and connect thenlto PSR, multi zone and 3D-CFD models, to analyze the combustion be­havior of the engines in Stuttgart and Dresden. This task, is also the taskof this work. Additionally, on the existing rapid compression machine,new findings about auto-ignition and combustion under perfect homoge­neous and inhomogeneous conditions, have to be carried out. This arereported in a parallel ongoing Ph.D thesis.

1.4 Overview of Contents

In chapter 2 an investigation about sensitivity of the used spray nlOd­eIs is done. In chapter 3 the used methodologies for chemistry reductionare presented. It is explained, as detailed at it is possible, how the pre­sented skeletal mechanism were constructed. In chapter 4 the stochasticmulti zone model with detailed or skeletal chemistry for simulation ofindirect injected homogeneous charge compression ignition engines is pre­sented and validated towards experimental measurement carried out atthe University of Stuttgart by Simon Haas under direct guidance of Prof.Michael Bargende. In chapter 5 the reduced chemistry is coupled witha 3-dinlensional fiuid-mechanics model closed with a conditional momentclosure assumption. The model is validated with experimental data of theUniversity of Stuttgart, for the case of direct injection HCCI combustion,and with data of the University for Applied Science HTW Dresden forthe case of indirect injection. The measurement at the HTW Dresden

CHAPTER 1. INTRODUCTION 17

were carried out by Mr. Thomas Emmrich under direct guidance of Prof.Wendelin Bach. In chapter the work is summarized and some suggestionsfor the future are given.

CHAPTER 1. INTRODUCTION 18

Chapter 2

Modelling of Spray andMixture Formation

Mixture formation is a key issue in HCCI. In this chapter an extensiveinvestigation is done, to get experienced about the sensitivity of the calcu­lations made in Sec. 5.4 to spray simulation weaknesses. As known fronlliterature [42, 52], diesel spray simulation with a lagrangian approach forthe dispersed phase and a eulerian approach for the continuum phase isknown to be sensitive to mesh resolution and its structure. In addition adependency to turbulent length scale at nozzle exit has been reported inthe computational literature. The ainl of this section is to quantify thesesensitivities and verify computational results.

2.1 State of the Art - Spray Modelling

Diesel engines are commonly used for heavy-duty application because of itshigh thermal efficiency. Additionally the acceptance to use them for pas­senger cars is growing. Compared to gasoline engines with 3-way-catalystthe emissions of NOx and particulate are higher. In stratified engines,pollution formation is strongly influenced by the condition of the mixtureduring combustion. The state of the mixture depends on the evolution ofthe fuel spray. To meet future emission legislation standards a strong de­crease in emissions is necessary. CFD simulation might be a powerful toolof investigation and improving the proper spatial and temporal distribu­tion of the mixture once the main shortcomings are reduced. In general,spray simulation can be divided in LHF- ('locally homogeneous flow') and

19

CHAPTER 2. SPRAY AND MIXTURE FORMATION 20

SF- ('separated flow') models. Contrary to the LHF approach does the SFmodel allow mass, momentum and energy exchange between the dropletsand the gas phase, which is indispensable for diesel spray calculations [42].Due to the large amounts of droplets in a diesel spray a stochastic descrip­tion of the parcels in a lagrangian space is widely used [44, 45]. Accordingto this methodology, all processes, which cannot be resolved deterministicon a parcel level, such as interaction with turbulence, droplet diameter,droplet collision, are solved with a Monte-Carlo-simulation. The conserva­tion equations for the continuum phase are usually the URANS-equations[42, 52]. Turbulence is modelled with the K, - E model. In the literature,a few modifications of the standard K, - E model have been proposed. Analternative is to use the LES methodology, which reproduces in a betterway the turbulence characteristics [53]. With a large-eddy-simulation thelarge turbulence scales are resolved whereas the small scales are lllodelled.Using the URANS-equations all scales of turbulence are modelled whichleads to a higher inaccuracy. The 'blob' method proposed by Reitz andDiwakar [54] is widely used for the simulation of the primary breakup.Literally, it is not a breakup model because large droplets with the diam­eter of the orifice are injected and the spray angle has to be prescribed.No information of inner nozzle flow is used. Alternatively, Huh and Gos­man [55] account for inner nozzle turbulence. The breakup time scale tBis a linear combination of the growth of instabilities tl and a turbulenttime scale tr. The spray angle is predicted. Both approaches are just amathematical simplification and do not represent the physical behaviorof spray in the near orifice area. Experinlental investigations observedligaments of fuel at the nozzle exit [59]. Nevertheless, because of thehigh spray density in this area, it is difficult to make c1ear statements.The secondary breakup of the initial droplets is caused by aerodynamicforces. The three-dimensional mathematical fornlulation of instabilitiesoccurring on the surface of the two-phase flow is areal challenge [49].These instabilities are usually the result of either a Raleigh-Taylor (R-T)or a Kelvin-Helmholtz (K-H) perturbation. The first is caused by theinertia of the denser fluid being exposed to acceleration; the second isa consequence of the viscous forces due to the tangential motion of thetwo phases. Based on the Reitz-Bracco analysis [60] Reitz and Diwakar[57] proposed a model which accounts for two breakup modes, namely the'bag' and the stripping breakup. Pilch and Erdman [56] proposed an ex­perimental correlation and divided the secondary breakup in five regimes.The breakup mode is depending on the Weber number. O'Rourke andAmsden used a different approach [58]. They made an analogy between a

CHAPTER 2. SPRAY AND MIXTURE FORMATION 21

droplet and a damped forced harmonie oscillator. Breakup occurred whenthe nondimensional droplet deformation y(t) was higher than one. Themajor drawback of the TAB model is that it only accounts for vibrationalbreakup whieh occurs for a Weber number between 6 and 12. For Dieselsprays the stripping breakup is predominant. Tanner [49] proposed theenhanced TAB (ETAB) model, which uses the droplet defornlation dy­namics from the standard TAB model, but provided a new strategy forthe description of the droplet breakup process. Tanner compared the com­puted droplet size and velocity between the TAB and the ETAB model.He found for the ETAB approach a good agreement between computationand experiment. With the TAB model the droplet size was under pre­dicted. He brought forward the argument that the original TAB modelhad not been designed to simulate the jet breakup. Tanner also madethe same calculations with the Wave breakup model and got similar goodresults as with the ETAB model. A study on grid dependency was notdone in that publication. Tanner made a grid sensitive study in [61]. Hemade a mesh refinement in axial direction to the spray axis. The refine­nlent had no infiuence on spray penetration. Larmi et al. [51] also madea comparison between the ETAB model and the WAVE model. The nleshwas refined near the point of injection using a geometrie distribution inradial and azimuthaI directions. He affirmed that spray simulations uti­lizing the discrete droplet model in conjunction with an Euler-Lagrangesolution approach are notoriously mesh sensitive. Nevertheless, it seemsthat using a very high resolution near the point of injection an asymp­totic behavior of the spray penetration can be achieved. For both modelsthe penetration is similar. Patterson and Reitz [48] included in the spraybreakup model Raleigh-Taylor instabilities, which were calculated siuml­taneously with Kelvin-Helmholtz wave model. The previous KH and newRT-KH spray models had only a small change in the predicted penetra­tion for a non-evaporating case, but the local droplet size was different inthe two models. The new nlOdel consistently gave higher drop size predic­tions near the nozzle. Because of the high experimental error, in the orderof 10 flm in the region where the spray is dense, it is difficult to chooseamong the models. For an evaporating case, the reduced breakup rate ofthe RT-KH model allowed the droplets to remain larger and penetrate far­ther. For this condition the difference between both model were larger andthe RT-KH model agreed better with the experiment. Comparing bothmodels in an engine simulation, only a small difference in the calculatedpressure curves was found but a large difference in the predicted soot andNOx emissions. It has to be mentioned, that the used mesh resolution

CHAPTER 2. SPRAY AND MIXTURE FORMATION 22

(2.1)

for the calculations in the constant volume bomb and the one used forengine calculations were different. However, comparison between the cal­culated spray penetration and optical measurement in the engine showedreasonable agreement. Bianchi and Pelloni [47] did a sensitivity analysisof grid resolution and remarked that the cell size used in common internalcombustion engine computations are inadequate to accurately resolve thetransient diesel spray dynamics. They also investigated the influence ofthe turbulence on spray dispersion. They proposed that the gas-phaseturbulence should take into account the anisotropy induced by liquid jetinjection. Schmidt [50] observed that there is a significant need to developmesh-independent momentum coupling between the gas and spray. Thecommonly used procedure for spray validation is to compare the simulatedsprays with experimental data in a high-pressure-temperature-bomb. Forthese simulations in most cases a cartesian grid [47, 52] is taken. Afterthe validation of the spray, engine calculations are made with apolargrid, which has a completely different resolution and cell aspect ratio.This chapter is a contribution to show, why the n18sh resolution and itsstructure are so inlportant for two-phase flow with a lagrangian-eulerianapproach. In a next step (taking a similar resolution) engine calculationshave been performed.

2.2 Spray Fundamentals

To estimate and characterize the way a jet will break-up, the followingthree major dimensionless nunlbers are important [62].

• Reynolds number:The Reynolds number characterizes the ratio between the inertialforces (u·p) to viscosity forces y. Osborne Reynolds (1842-1912)proposed this ratio in 1883 to provide a criterion for determiningdynamic similitude [77]. The droplet Reynolds number may be de­fined according to equation 2.1.

RPeD IUe - udl

ed=-----Me

The subscript c signifies quantities of the continuum phase, whereasthe subscript d signifies quantities of the droplet. An estimationof the droplet Reynolds number at thc nozzle exit for a spray withan injection pressure of 1300 bar and a nozzle diameter of 0.15 mmgives an approximate Reynolds nurnber of the order of 105 . Figure

CHAPTER 2. SPRAY AND MIXTURE FORMATION 23

2.6 shows the decrease of the droplet Reynolds number in the sprayaxis with increasing distance to the nozzle orifice.

• Weber number:The Weber number was introduced by Moritz Weber (1871-1951)and characterizes the ratio between inertial (or aerodynanüc) forceto the surface tension force. The droplet Weber number may bedefined according to equation 2.2.

We - Pe I ue - Ud 12

D d

(J"d(2.2)

The computed Weber number at nozzle exit for an injection pressureof 1300 bar and a nozzle orifice of 0.15 mm is according to figure 2.6also in the order of 105 .

• Ohnesorge number:The Ohnesorge number is the relation between the viscous forces andthe surface tension forces. The Ohnesorge nunlber may be definedaccording to equation 2.3.

(2.3)

The Ohnesorge number for diesel fuel at nozzle exit is of the orderof 10-2 .

The most used classification of the spray breakup regimes, was intro­duced by Ohnesorge in 1937 [62]. With the additional division of the windinduced break up into first and second wind induced breakup by Reitz,four different breakup regimes are today accepted. Namely this are theRayleigh break up, the first and the second wind induced break up andthe atomization breakup zones, respectively. The Rayleigh break up onlyoccurs at very low injection velocities. Disturbances lead to axisymmet­ric oscillations which produces a disintegration of the jet. The resultingdroplets have a larger diameter then the nozzle orifice. This behavior canbe viewed in a water tap. In the first wind induced break up reginle, thevelocity of the jet is increased. The jet is exposed to aerodynamic forceswhich lead to an earlier break up. The size of the resulting droplets are ofthe size of the nozzle orifice. A further increasing of the injection velocityyields to the second wind induced break up. In this reginle the influence ofthe aerodynamic forces and the surface tension is larger. The axisymmet­ric oscillations are strengthened and additional transversal oscillations can

CHAPTER 2. SPRAY AND MIXTURE FORMATION 24

1000000.001 +--<-----........I-.....;...;....:...;..I+--<-----.,....~...:.+~-'"---.;.....,.""':O';~

100

~ 0.100E:::JCGI01L-

o~ 0.01 01:=::=::=F.co

Reynolds number

Figure 2.1: Characterization of the break up regimes depending onReynolds and Ohnesorge number (source Schneider [62])

occur. Surface waves grow (Kelvin-Helmoltz instabilities) which lead tostripping of small droplets. The jet is fully disintegrated a few diametersof the nozzle orifices below. The resulting droplets are smaller than thenozzle orifice. A further increase of the injection velocity leads to the at­omization regime. This regime is characterized by existing liganlCnts anddroplets at nozzle exit. Because of the difficulty of measuring in this highdense regions, the scientific community is not unanimous about the exis­tence of a liquid core or not. Also different estimations exists about theWeber number, where atomization occurs. Miesse proposed 1956 astart ofatomization above a gas Weber nunlber of 40, whereas Ranz published in1953 a number of 13 [62]. As already mentioned above, and will be shownin section 2.5, the droplet Weber number at nozzle exit is of the order of104 to 105 and stays at values above 1000 within the spray. Therefore fordiesel direct injection systems, which are characterized by high injectionpressure, and for diesel fuel, with a given viscosity and surface tension atthe nozzle exit of the order of 10-3 and 10-2 , respectively, the prevalentbreak up regime is the atomization. By plotting the Ohnesorge numberand the Reynolds number in this double logarithmic Ohnesorge diagram(see figure 2.1), this four regimes are divided by a straight line. The regimeof direct diesel injection system is clearly in the atomization regime.

CHAPTER 2. SPRAY AND MIXTURE FORMATION

2.3 Numerical Methodology

25

The eomputations were earried out using the StarCD CFD code [45].The fuel is n-dodeeane. The properties for surface tension, liquid viscos­ity, latent heat of vaporization, vapor pressure and specifie heat capacityare modelIed as implemented in [44] and corresponds to DF2 diesel fuel.The eonservation equations for the eontinuum phase are the URANS­equations. Turbulence is modelIed with the standard K, - E model andstandard model parameters are used. In this section, only the relevantequations for the present investigation are listed.

Basic Conservation Equation for the Continuum Phase

The three dinlensional fluid solver used in this work, is StarCD [45]. Themass, momentum and energy conservation equations for general ineom­pressible and compressible fluid flows and a moving coordinate frame aregiven in equation 2.4 in eartesian tensor notation.

where, t is the time, Xi the eartesian coordinate, Ui the absolute fluidvelocity component in direction Xi, Uj the relative velocity between fluidand loeal (moving) eoordinate frame, p the pressure, p the density,Tijstress tensor eonlponents, Sm mass source, Si momentum source tenncomponent, T the temperature, Fh,j the diffusional energy flux in direc­tion X j and Sh the enthalpy souree term. The static enthalpy is definedaeeording to equation 2.7.

h - cpT - cp°To + L mmHm = ht + L mmHm (2.7)

where mm ist the mass fraction of mixture eonstituent m, Hm is the heatof formation of eonstituent m, cp the mean constant pressure specific heatat temperature T and cp

0 the reference specifie heat at temperature To.For newtonian turbulent flows, Ui, p, and other time dependent variables,including Tij, assume their ensemble average values, giving

CHAPTER 2. SPRAY AND MIXTURE FORMATION 26

(2.9)

2 8Uk _Tij = 2J-lSij - "3 J-l 8Xk 6ij - PUiUj (2.8)

where u' are fluctuations about the ensemble average, the overline denotesthe ensemble averaging process and <5 is the Kronecker delta, which is unitywhen i=j and zero otherwise. The rate of strain tensor Sij is defined as:

Sij = ~(8Ui 8uj)2 8xj 8Xi

The Reynolds stresses due to turbulent motion, last term on the righthand side of equation 2.8, and scalar fluxes are linked to the ensenlbleaveraged flow properties in an analogous fashion to their laminar flowcounterpart [45].

(2.10)

(2.11 )

(2.12)

where K, is the turbulent kinetic energy and J-lt the turbulent viscositydefined in equation 2.13.

U'·U'·K,_~

2C pfi2_ J1

J-lt-E

(2.13)

CJ1 is an empirical coefficient, which is set usually to 0.09. For fi andE the following transport equation are solved:

(2.14)

8 8 _ J-lt 8E-(pE) + -(pUjE - ---) =8t 8Xj O"E; 8Xj

CHAPTER 2. SPRAY AND MIXTURE FORMATION

where

/-lej j = /-l + /-lt

8UiP=2s··-- ~J 8x·J

PB--~~ 8pah, t p partialxi

27

(2.15)

For the nlOdel constant, standard values according to [45] where taken.

Basic Conservation Equations for the Dispersed Phase

According to [45] the momentum equation for a droplet of mass md isgiven by:

(2.16)

The first term on the RHS is the drag force, the second is the pressureforce, the third the virtual mass force and the last term the body forceternl. The drag force can be calculated from following equation:

(2.17)

The drag coefficient Cd is a function of the droplet Reynolds number.The gas velocity is the sum of the ensemble averaged gas velocity and itsfluctuation u' (2.22).

Atomization

Two atomization models are used for the primary breakup. The 'blob'nlethod proposed by Reitz and Diwakar [54] and the Huh and Gosman[55] model as implemented in [45]. First is literally not a breakup modelbecause large droplets with the diameter of the orifice are injected andthe spray angle has to be prescribed. The estimation of initial velocity foreach droplet is based on the assumption of equal probability of velocitydirection within a spray cone. Alternatively, Huh and Gosman account

OHAPTER 2. SPRAY AND MIXTURE FORMATION 28

for inner nozzle turbulence. The average turbulent kinetic energy, "'a andits dissipation rate, Ea at the hole exit are derived from force and energybalances. The breakup time scale TB is a linear combination of the growthof instabilities Tl and a turbulent time scale TT. In the application of themodel, the sizes of secondary droplets and their number are determinedfrom a randomly chosen value of a distribution function [45]. All dropletshave the same initial velocity. The spray angle is predicted and is used todetermine the upper limit for the initial radial velocity component. Identi­cal to the 'blob' method, the estimation of initial velocity for each dropletis based on the assumption of equal probability of velocity direction withina spray cone. Both approaches are just a mathenlatical simplification anddo not represent the physical behavior of spray in the near orifice area.

Secondary Break-Up

The WAVE breakup model is based on Kelvin-Helmoltz instabilities ofincompressible round liquid jets. The version utilized in this study is theReitz-Diwakar model [54] as implemented in the commercial CFD codeStarCD [45]. According to this model, droplet breakup due to aerody­namic forces occurs in the 'bag breakup' or in the 'stripping breakup'mode. The first is caused by non-uniform pressure field around thedroplet , which yields to a disintegration of the droplets when surface ten­sion forces are overcome. The critical value of the Weber number is givenby:

(2.18)

(2.20)

Where Cbl is an empirical coefficient given in table 2.3. The charac­teristic time of bag breakup can then be estimated as

C 1/2D3/2blPd d

Tb = 1/2 (2.19)4ad

Where the model constant Cb2 is given in table 2.3.'Stripping breakup' is a process in which liquid is sheared or stripped

from the droplet surface. The criterion for stripping breakup is

We >Cy/Red - sI

were 0 81 is a model constant. The characteristic time scale for thisregIme IS

CHAPTER 2. SPRAY AND MIXTURE FORMATION

Constant Explanation Default Rangevalue

Cbl eritical We for 'bag 6 3.6 -breakup' 8.4

Cb2 parameter for 7T

eharaeteristie time sealefor 'bag breakup'

C81 eriterion for 'stripping 0.5breakup'

C82 parameter for 20 2 - 20eharaeteristie time sealefor 'stripping breakup'

29

Table 2.1: Breakup model eonstants and the default values in StarCD [45]

Tb = C82 (Pd)~ D d2 P 111- Ud 1

where 0 82 is an empirieal eoefficient given in Table 2.:3.

Thrbulent Dispersion

(2.21 )

A droplet in a turbulent flow experienees a randomly varying velocity fieldto which it responds aeeording to its inertia. The stoehastie model pro­posed by Gosman et al. [66] assurnes that a droplet traversing a turbulentflow field interacts with a sequenee of turbulent eddies. The fluetuatingvelocity is assumed to be isotropie and to obey a Gaussian probabilitydensity function. Following these assumptions, the droplet experienees aninstantaneous fluid velocity

---> u---> +--->'U= U (2.22)

where 0- is is the loeal time averaged velocity and 71' is the random per­turbation. The latter is ealeulated from a Gaussian probability functionwith zero mean value and a standard deviation of (2t) ~ .

Inter Droplet Collision

The model for droplet-droplet eollisions follows that of 0 'Rourke [65].It distinguishes three types of interaction, eoaleseenee, separation, and

CHAPTER 2. SPRAY AND MIXTURE FORMATION 30

bouncing, respeetively. For eaeh pair of pareels, collisions only occur ifthey lie in the same computational eell. The droplets are eonsidered tobe uniformly distributed throughout the cell. The eollision frequeney, v ,of a eollector droplet with all droplets in the other pareel is given by:

The collision efficieney E 1,2 is evaluated from:

E = (1 0.75ln(2W) )-2. W 1.2141,2 + W - 1.214) , >

otherwise E 1,2 = O. W is a dimensionless parameter given by:

(2.23)

(2.24)

P l u u I D2W = d,2 d,l - d,2 d,2 (2.25)

9J-LDd, 1

The probability that the collector undergoes n collisions with dropletsfrom a donor parcel during the time interval 8t is taken to follow a Poissondistribution, with the mean value n' = v8t. If a eollision occurs, the prob­ability that the outcome is eoaleseenee, separation or bouneing, dependson the relative velocity and the diameter ratio of the eolliding droplets.

2.4 Setup for a High Pressure High Temper­ature Constant Volume Bomb

In previous published works by the author [70, 71, 72, 73] the eomparisonshave been performed for eases with different injection pressure, nozzle di­ameter, gas temperature and gas pressure. In this study only the resultsof an evaporating case will be shown. A deep analysis of the inside of thespray (droplet velocity, gas velocity, Weber number, Reynolds number,etc.) is presented, to show and understand the factors of eapital impor­tanee. This knowledge, may be extrapolated to the other cases, beeausethe undergoing physies and interaction between the two phases is c1arified.

Pinj TN2 PN2 Dn Pgas lid Kini Cini !-Ltini IIini

[bar] [K] [bar] [rnrn] [kg/m3] [-] [m2 182

] [m2183] [N8Im2

] [rn]1 1300 800 80 0.15 33.7 4 20 104 0.12 10-3

11 1300 800 80 0.15 33.7 4 0.1 0.05 0.61 10-1

111 1300 800 80 0.15 33.7 4 10 50 6.07 10-1

IV 1300 800 80 0.15 33.7 4 10 4000 0.076 10-3

V 1300 800 80 0.15 33.7 4 0 0 10 -2 * 0.0164 **

@~""rj

t;5~

!'-J

~"<~

~~~f-3§3tlJ

Table 2.2: Boundary conditions for the undergoing spray investigations 6(* Having K, and c equal to zero, no reasonable value for Mt is calculable, the code initializes /--lt with a low value, ** If the code is ~

initialized with K, and c equal to 0, the integral length scale corresponds to the distance from the nozzle orifice to the wall) ~~

~

~

CtJI-'

CHAPTER 2. SPRAY AND MIXTURE FORMATION 32

The used lengths of a computational cell for the calculations of thehigh-pressure-high-temperature cell are 0.125 mm, 0.5 mm and 1.0 nlnl,respectively. The aspect ratio of all cells is nearly one. The coarsestgrid resolution is a commonly used resolution for spray calculations in ahigh-pressure-temperature-cell [47, 52] and in engine calculations. Whenthe calculations were performed, the measured injection profiles were notavailable, therefore a simplified square injection profile was taken. Forthe calculations with the 'blob' method the half-cone angle of the sprayis set to 10. If not otherwise lllentioned, the initial value for K, andE is set to 20 and 104 respectively. This corresponds to the value of apassenger car diesel engine at TDC. Because in a combustion bomb noinitial turbulence is expected, calculation of case v has been performed.Nevertheless, a initialization of K, and E equal to 0 is dangerous. Usingthis value, no physical meaning of initial turbulent viscosity, turbulentlength and tinle scale is possible. For all calculations in this subsection aparcel injection rate of 3.5E+07 per lllinute was taken, this correspondsto 35'000 parcels per millisecond of injection.

2.5 Sensitivity Analysis of Discretizationand Initial Gas r:I'urbulence

The focus of this subsection is to understand and explain the influencesof droplet subnlodels or numerical issues. Comparison with experimentshave been carried out by the author [70] and a great nUlllber of otherresearchers(Le. [134]). The overall result, of this publication are similar,using fine grids and having a mesh, which is aligned in spray direction,reasonable results can be achieved concerning spray penetration, sprayangle and droplet size. Nevertheless, this conditions are rarely fulfilledfor engine calculations. Seldom, nearly nozzle orifice resolving meshesare used and rarely the meshes are aligned in spray axis. In this sectionis tried to show, under which conditions they really do a good work,showing for example a correct behavior on Stokes number. It is alsoexplained, why using comnlOn practice conditions, could prediction maynot be expected. It is shown, that fulfill the requirements of a perfect spraysimulation is theoretical possible, nevertheless, in practice, due to movingmesh generating issues and computational time, they can not always besatisfyingly fulfilled. For the presented analysis, computational results arecompared among each other, and in a further step, engine sinlulations arecompared to measured global results.

CHAPTER 2. SPRAY AND MIXTURE FORMATION 33

0.05

0.04

I0.03c

0'';:::C\'l"--Q) 0.02cQ)a.

0.01

00

.--...x--~

~­_.x"'"--.)(-

lt'"

"'x"'--x-"''''

Id" ..... x'" G----€> 0.125 mm, ...../ .....Y (3- --- -El 0.500 mm

, ;I

[;1' / )f---~ 1.000 mm, /, /

/?//

1/

0.0002 0.0004 0.0006 0.0008 0.001time [5]

Figure 2.2: Spray penetration for different spatial resolutions (case i, 8t= 1 J-LB)

Mesh Dependence

Fornler works have shown that simulations utilizing an Euler-Lagrangesolution approach for two-phase flows are mesh sensitive. The nlesh sen­sitivity study shown here is for case i (table 2.4. The chosen resolutionsare 0.125 mm, 0.5 mnl, and 1.0 mm. The simulated penetration depth isdefined as the location of the spray tip. In this study the leading particleon the cornputational side is considered to be the spray tip. This is anarbitrary assumption and has been analyzed in works of the author anco-workers [74]. Nevertheless, this is the most commonly used definition.In Figure 2.2 the penetration for the three different resolutions are shown.

With higher resolution a higher penetration is observed. This is awidely known behavior [47]. The cases with the highest and the secondmost highest resolution cover each other after 0.3 ms. Figure 2.3 showsthe simulated gas velocity over the radial distance to the spray axis, 18mm downstream of the orifice of the nozzle and 100 J-LB after SOl, forthree resolutions. It is to see that with the coarse grid, because the spraydid still not reach this region, the gas velocity is low. The case with the

CHAPTER 2. SPRAY AND MIXTURE FORMATION 34

150

130

110(j)-oS 90>.......'0 700ä)> 50(f)

ctlC>

30

1013-

-10-15

!G-------€l 0.125 mmG----iJ 0.500 mm*"~-~ 1.000 mm

"

_-----~-::;-_/- ~\t:::..~~-------- 10 -5 0 5 10 15

radial distance to spray axis [mm]

Figure 2.3: Simulated gas velocity over the radial distance to the sprayaxis, 18 mm downstream the orifice, 100 J.lS after SOl, fine, middle andcoarse resolution (case i, Jt = 1 J.ls)

highest resolutions has the highest gas velocity. An insufficient resolutionleads to an overestimation of the relative velocity between the dispersedand the continuous phase. A higher relative velocity causes higher dragforces and therefore the droplet penetrates less. Figure 2.4 shows again thesimulated gas velocity over the radial distance to the spray axis, 18 mmdownstream of the orifice of the nozzle, 0.4 millisecond later, for the threeresolutions. It is to see that for the finest resolutions the gas velocity is thehighest. A strong difference is to see between the both finer resolutionsand the coarser one.

The gas velocity reaches for the highest resolution after 250 J.lS at thisposition nearly steady state. Figure 2.5 shows the SMD for three differentspatial resolutions. The calculation with the finest grid has the smallestSMD after 100 J.lS. In the literature [e.g. [42]] it is mentioned, that a toofine grid could lead to an underestimation of droplet collision due to themethodology of the commonly used collision model of O'Rourke [58]. Asexplained above, only different parcel types in the same computationalcell can collide. The smaller the cell, the smaller is the probability of hav-

CHAPTER 2. SPRAY AND MIXTURE FORMATION 35

150

130

110(j)-E- 90>.......·0 700Q>> 50Cf)

ctlC)

30

10Go-

-10-15 - 10 -5 0 5 10 15

radial distance to spray axis [mm]

Figure 2.4: Simulated gas velocity over the radial distance to the sprayaxis, 18 mm downstream the orifice, 500 MS after SOl, fine, middle andcoarse resolution(case i, ot = 1 MB)

ing parcels of different types in this cell (assuming that the initial parcelamount is the f:'anle), and therefore the smaller is the collision probability.Thif:' could lead to Slllaller droplets because of the absence of coalescence.

In Figure 2.6 the values of the droplet velocity, the gas velocity, theWeber nUlllber, the droplet Reynolds number, and the characteristics tilllescales for stripping breakup and bag breakup are shown at the spray axisafter 100 MS, respectively. It is shown, that for the higher resolved case,at the same distance from the nozzle orifice, all values are lügher. Dueto the higher gaf:' velocity, the droplets are slowed down in a weaker way.Interesting, is that at the top of the spray the characteristic time scalefor droplet breakup of the higher resolved case undercuts the value of themiddle resolved case. Also it is to see, that bag breakup is important atlower relative velocity between both phases. At the beginning of injection,only the stripping breakup if:' significant. In both cases, the Weber numberis higher than the critical Weber number. So breakup occurs. As can beseen in figure 2.5 the difference of the SMD between both cases at 100MS is not large, nevertheless the SMD of the high resolved case is smaller.

CHAPTER 2. SPRAY AND MIXTURE FORMATION

1e-03 .------.-----.--~-,...------.---..---~-,...------.--.

36

Eo~(/)

1e-04

1e-05

G-----E> 0.125 mmG----iJ 0.500 mm)f---~ 1.000 mm

0.0002 0.0004 0.0006 0.0008 0.001time [5]

1e-06 L..-~_---,--_-,--_,---~_---,--_-,--_'---~_-J

o

Figure 2.5: SMD over time for three different spatial resolutions (case i, r5t= 1 j.Ls), Ruh Atomization Model

The data of figure 2.6 do not denlOnstrate that breakup occurs faster inthe case with higher resolution. So the difference between the SMD of thehigher resolved case and the coarser one, has to come from coalescence.As said above, the case with higher resolution undergoes less coalescence.

Figure 2.7 shows, that the case with higher resolution evaporatesfaster. This is due the smaller SMD and the deeper penetration. Nev­ertheless, this result is not self-evident. In the evaporation model, thesaturation pressure fronl the cell is taken. If the evaporated fuel concen­tration in a cell is high, evaporation occurs slowly. This effect seems notto be predominant.

Influence of Turbulent Viscosity on Spray SimulationBehavior

Abraham [52] showed, that using underresolved grids for jet computation,an unphysical behavior of the jet on initial gas turbulence was observed.Using meshes for the gas jet simulations, which resolved the gas jet orifice

CHAPTER 2. SPRAY AND MIXTURE FORMATION 37

0.500 mm Gl

0.125 mm €I

.:

:::i::gt::: ::::, 0'

:::t:gt:::::::..._:_--~--------

200 ,-----,------,-------,-r--.,....-.,-,..-----,------,------,180----,----- ----- ----16014012010080604020

"-----...L--""------'_-'--------'------'-_'-----...L-----'-------'

ü1

:>

0500 mm 0

0.125 mm ~

---- ----- -----,----- ----- ----

-- -- --- -- --- - -,- --- - - --- - --~.

.... .... ~ .~ -- -'. - - -- --- -- ---­

-- .. ----- -----,----- ----- ----

." ...:..... ~. ---- - ---

500 ~....,...--.-,---,--------,------.-,..--r----,--.,

45040035030025020015010050

o 10 20 30 40 50 60 70 80 90 100 o 10 20 30 40 50 60 70 80 90 100

100000

...!... 10000C-O>

.DE~ 1000zC-O>

.D100

~

10

, ,I • I I I I I I____ c r L L __ .L L L L __._

, I I " ": : Ir: ::, ", "

____ - __ ~ r~ •••• ~~ •• _~ ~----~----~----~---

I ::::

r I I I, + , I I__ ~ ~ l l l _

, 0'125'mm' GI0.500 mm 0

'------'-------'-----...L----'--------'-------'---_ L~,,_.

1E+006

100000

,

""I 100000>er

1000

100

I , I I " I I__ r r r L L L L L L _

: : : : : : : : :: : : : : : : :I I • , I I I I

: : : : : : : :- -~ --- -~- ---~- --- ~----~----~ -- - -~ -. - .~ ...

I I I I I II • I • ,

I I I I II • I I I

---r--)----~--O~i25~ ~~~- --~: 0500 mm GI

_..---l ..L__ ._.l-----'_'------'-------'-----...L----'-------.J

0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100

0.0001 0.001

~0> ~ 0.0001 I I I I I I • I

C •••• r - ~ - ~ r - - - - .. - - - - r - - - - r - - - - c - - - - r - - - - c - --

Ci 0> " ,

"- 1E-005 ."CD'C

0125 mm ' ,V5 €I ~ 1E-005

I I I ,

." -:-- -- -;-- -_.~ .. ~. ~- -~. ~ -- --~ --- -~ --- -~- --~ f- ' '0'125'mm' €I." 0500 mm (;If- 0.500 mm (;I

1E-006 1E-006

0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100

distance from orifice [rnm] distance from orifice [mm]

Figure 2.6: Droplet velocity (top left) , gas velocity (top right), We­ber number (middle left) , Reynolds number (middle right), characteristicstripping break up tinle scale, characteristic bag break up time scale overdistance to nozzle orifice after 100 MS after SOl for two resolutions (casei, Jt = 1 MS)

CHAPTER 2. SPRAY AND MIXTURE FORMATION 38

100

80~s.......Q)

60:::J-"'CQ)+-'co..... 400a.co>Q)

20

00

G-------€l 0.125 mmG----i] 0.500 mm)(-~~~ 1.000 mm

0.0002 0.0004 0.0006 0.0008 0.001time [5]

Figure 2.7: Evaporation over time for three mesh resolutions (case i, 5t =

1 J-LB)

with 8 points, leaded to no influence of the initial turbulent viscosityon the penetration and air entrainment of the jet. His work showed,that initial gas turbulence only has an influence on the spray, if it is atleast one order of magnitude higher than the jet diffusivity. In a internalcombustion engine, jet diffusivity is of the same order of magnitude or evenhigher then the air diffusivity [52]. They do not exist experimental datawith controlled initial turbulence, so it is difficult to estimate the regionwhen air diffusivity becomes important. Spray visualization of internalcombustion engines with optical access, do not show an influence of theair turbulence on spray behavior. Figure 2.8 shows the spray penetrationinitializing the turbulent viscosity according to table 2.4 for a fine resolvedmesh (left) and a coarse resolved mesh. The turbulent viscosity of case icorresponds to the value of a passenger car engine running at 4000 RPMat TDC. The turbulent viscosity of case iv corresponds to the value of apassenger car engine running at 2000 rpm at TDC. It is to see, that forboth resolutions, the results do not differ between this two initializations ofJ-Lt. Eut for the coarse resolution the initial gas viscosity has a tremendousinfluence on spray behavior.

CHAPTER 2. SPRAY AND MIXTURE FORMATION 39

0.05 .-----.--~_____.~-.,....--__.__-___,

0.04

E~ 0.03o~]1 0.02<l>a.

0.01

G----€) ease iG" tl ease ii><----->< ease iii+----+ ease iv...----. ease V

004

E~ 0.03o~

~ 0.02<l>a.

.-........... -_...

.D"'" -<3" G----€) ease i" ··tl ease ii><----->< ease iii+----+ ease iv,. ., ease v

o"'-~--'---~~~-~-'--~-'o 0.0002 0.0004 0.0006 00008 0.001

time[s]

O"'------~-----'-----~~-~~~~~---'

o 0.0002 0.0004 0.0006 0.0008 0.001time [s]

(2.26)

Figure 2.8: Influence of gas phase viscosity on spray behavior for twospatial resolutions (left 8xc = 0.125 mm, right 8xc = 1 mm

In the case of high resolution the influence is clearly smaller. Accordingto [68] the Stokes number establishes the degree of dispersion. The Stokesnumber is defined after equation 2.26.

STv ·8u

t = l

T v is the lnomentum response tüne, 8u the velocity difference over theshear layer and I is the size of the turbulent structure. For St « 1,the particle will follow the fluid motion. St » 1, the particle will moveessentially independent of the fluid. However particles with St '" 1 sill tendto centrifuged toward the peripheries of the flow structure. Consideringfigure 2.9 for all cases the Stokes number at exit ofthe nozzle is »1. So theparticle will not be influenced by the turbulent structure. Nevertheless,for the coarser resolution the Stokes number is clear lower then for thehigh resolution cases. For the case with coarser resolution the particleundercuts the border of Stokes number 1 earlier. Now, it is clear thatthe particle of ca1culations with lower spatial resolution, will easier followthe fluid motion. Looking on the tip of the spray, for all cases the Stokesnumber is beneath 1.

The particles in the front zone of the spray will follow the fluid motion.Between case i and case iii, so the cases with a level of turbulent viscosity ofthe order encountered in an engine and the high viscosity case, a differenceis noticeable. The case with higher turbulent viscosity has a slightly deeperStokes number. This forces the particle to follow the fluid nlOtion earlierthan in the lower viscosity case. Although, the turbulent viscosity is more

CHAPTER 2. SPRAY AND MIXTURE FORMATION 40

100000 .------.----------,.----------,---------y--------,---...........,

10000 ~

case i 0,5 mm 100mus •

case i 0.125 mm 100mus _

case lil 0125 mm 100mus X

­X~. ~. .,-. ~.... .~~.. ~..

•• X~-_••• X~.

•••. Xh.~ • X~ _. .....

•• "'XX-_ _ •

· XX··. . X X•• X· _ X

• ~X - •.. ... .-~ ­. ..X X~X••

X

01

0.01

1000

100.l.'-

'".<:l

E:J 10<:(Jl

'"-"0U5

30252015105

0.001 L-__-----''---__----' ------' ------' ------'- --.J

o

distance from nozzle orifice [mm]

Figure 2.9: Stokes number over distance to nozzle orifice for case i withtwo resolutions and case iii

then one order of magnitude lligher, it is not clear, if this is still aresolutionproblem or not. However, the influence is acceptable low. More, in figurc2.10 the values of turbulent dissipation rate (E), turbulent viscosity (J-Lt) ,turbulent Reynolds number and the characteristic time and length scalesof the investigatcd points of this study and the study by Abraham [52]and McCracken and Abraham [79] are visualized. It is to see, that notevery combination of initialization of turbulence is physically reasonable.From this figure and especially from figure 2.10 it can be seen, that valuesof turbulent viscosity in an engine are of the order of magnitude between10-2 to 10~1. The turbulent Reynolds nunlber at SOl is of the order ofmagnitude of 104 to 105 and the turbulent kinetic energy of the order of101 to 102 . Interesting is to see (figure 2.11), that the characteristic lengthscale is before SOl only dependent on the engine geometry.

CHAPTER 2. SPRAY AND MIXTURE FORMATION 41

1E+008_ 1E+006r 100002S 100E 1~ 0.01o 0.0001~ 1E-006'" 1E-008

1E-01 0

~~~~::--- ' , , ,•.J:::1 I I I I

,,~, - -- --- - ~ --- -- -- --- - ~ --- -- --- -- - ~ - -- -- -- -- -- ~" ,

c: 1000'" 100::;-E'Ul 10:l~

-'" 1um:;:; u 0.1.~ f,J)

'" <J) 0.01oE~:;:; 0.001~ 0.0001u 1E-00S

1E-006 0.0001 0.01

I I I I•• - ••••••• :•••••••••••• :•••••••••••• '1- •••••••••• ~

i*

100

I I , I••• _ •••••• 10 •• ~ ••••••• _ k ••• _. •• ...

, • ! I

• I I I, I I I

- - - - - - - _., - ~ - - - - •• - - - - - -, - - - - - - - - - - -. - - - - - - - - - - - T• I I I

1E-006 0.0001 0.01

1:' 1<J) 0.1:J~

-2 oS 0,01.2 ~ 0.001u""t; ~ 0.0001~:E 1E-005

- Ol&l :i5 1E-006~ - 1E-007

J::

u 1E-008

100

- : -.. :.----------~--:..i-._. ßlI"'"'C-',f-r

.~5·:

.k:..~~.~: --: - - -_. -" -_ .• : •.••.••••.• ; ••.•.. & •• ~-;

•••••••••• ~ _ • ~ L I-

~ ~ ~ :••••••••• _. _. ~ ~ L

• • I I

'" 100<-€ 10"' 1::;

0.1~ 001"' 00010u

0.0001.<,Q> 1E-00Sc: 1E-006Q)

:J 1E-007e 1E-0082

1E-006 0,0001 0.01 100

1E+0081E+007 ----------,--

~ 1E+006 ----------,--

i 1~!1I ,~;~-d~ 1 ~:---:"":----f-- 0.1 .. ---------

001 ----------<--o.001 • .__.1.-.

1E-006 0.0001 0.01 100

HPHT 80mb V'

LI" 0,15 mm

LI " 1.20 mm . ,.

LI" 110 mm _.•.._-.....-.---

Abraham HPHT 80mb loV'l viscosity *

1E-006 0.0001 0.01 100Abraham HPHT 80mb high viscosity 0

Abraham Engine •

kappa [m"2/s"2] c::J Engine relevant Zone

Figure 2.10: What are reasonable initializations of characteristic turbu­lence? A comparison between data from this work and fronl Abrahanl[52]

Time Step Dependence

Time step dependency studies have been done for case i and case v usingthe fine and the coarse resolution. The time step should resolve the timescales of the problem. The chosen time step should be smaller than theminimum of the momentum response time TM, the breakup time scalesTbag and Tstn the cell droplet time scale TC and the turbulent time scaleTt. The momentum response time may be defined by Eq. 2.27 [68].

Pd D2TM = (2.27)

18f.Lc

According to figure 2.12 the momentunI response time at nozzle exitIS of the order of 10-4 seconds and drops in the front part of the spray

CHAPTER 2. SPRAY AND MIXTURE FORMATION 42

-200 -150 -100 -00 50

0"::: ~-----~--~-- I=---..~00001 - .

1E-OOo .,C ----'------_-'------------'--_-----'

D.°O:~I(!mm~!imm,im=I····00001 -----------I------~1E~OD5 .."~ , i . .

-200 -150 ,100 -00 Ü 50

fJ±~-ul, ~

::::::IE1UUUUU -.... ,"'r'- "--'--------, --,--

10000 --- ------+-----------;----------- ,------- -:--- -------1000

-200 -150 -100 -50 0 50

,":::I(I~~-200 -150 -100 -50 0 50

~::::I±T~':::±+r~

0­

'"

ou

'"~

I HO Engine 1180 RPM-200 -150 -100 -50

• Passenger Car 4000 RPM• Passenger Car 2000 RPM

50 -200 -150 -100 -50 50

Figure 2.11: Characteristic turbulence values over crank angle for a pas­senger car diesel engine at two different RPM and a HD diesel engine.

to a level of 10-8 . The 'stripping breakup' time scale can be estimatedaccording to equation 2.28 [45] :

Cs2 (Pd) 1/2 DdTst = 2 P 111 _ üdl (2.28)

And the 'bag breakup' time scale can be evaluated from equation:

C 1/2D3/2b2Pd d ( )

Tbag = 1/2 2.294crd

Figure 2.13 shows the stripping and the bag break up time scale forcase i 100 IJB after SOL It is to see, that in the vicinity of the nozzle orificethe stripping break up is the predominant break up type. The break uptimes are of the order of 10-Ci to 10-4 •

The time a droplet needs to cross a computational cell is defined asthe cell droplet time scale. At the nozzle orifice the droplet velocity forcase i is 500 m/s. A computational cell has a length for the high resolvedcase of 0.125 mm.

CHAPTER 2. SPRAY AND MIXTURE FORMATION 43

0.001 ,---------,--------,-------,------,------....,.-------,

: :

0.0001 ~ ~ -.. ---.- ..i-.-------.-----------l--------------------!---------------------:-- _. ' , : ' :

•

30252015105

1E-00?

1E-006

1E-00S

• i.' :----------••-----~---------------------i-------------- -, -.. : :~.: .: ...•: .. ' , , :

••••.....•...•..... ~ •••......• -••. -.. -... --------------------~--------------------;---------------------i--------------------

: '.. : : :: i.. i : i: •• i :. :. '

, .."-------------------~---------------------:---------------------~.------------.. -.--:---------------- .. --.:-------------------.I I I • : I. :... ..:. : ,

• • ca!' i 0.125mm 100mus •1E-00S L..-__------' ~ ~ ~ ~__~

o

'"E

E::JC'"EoE

""Q)

'"coCL

'"2:

distance from nozzle orifice [mm]

Figure 2.12: Monlentum response time over distance to nozzle orifice forcase i 0.1 ms after SOl

(2.30)8xc 0.125 . 10-3 [m] _ []

Tc = - > [ /] - 0.25 /-18Ud 500 m 8

According to equation 2.30 the mininlal droplet time scale, which is ex­actly at the nozzle orifice, is 0.25 /-18. The droplet velocity drops withincreasing distance to the orifice, and therefore the droplet time scale willincrease. The turbulent time scale may be calculated and gives a theoret­ical value at nozzle orifice of 0.3 /-18.

For the time step dependence study calculations of case iii, iv andcase v where performed with two different time steps, 0.5 /-18 and 1 /-18,respectively. Because the droplet velocity falls very fast (see Fig. 2.6)it can be assumed, that all time scales are resolved. The results weresome how complicated. The case with high resolution were not time stepdependent, which was expected. But the cases with low resolution, were

CHAPTER 2. SPRAY AND MIXTURE FORMATION 44

0.001case i 0 125 mm (stripping) ..case i 0 125 mm (bag) K

3025

,~ lSl MK

t.esz'W112"'~lC.....~K~

1E-006 .............__---'-----__-----L-__--' K--'-----"JI.<'------_----'----__---'

o 5 10 15 20

UJ

'; 0.0001('CIoUJ

Q)

E

0­::J

.::::t:.~ 1E-005I­.D

distance from nozzle orifice [mm]

Figure 2.13: Stripping and bag break up time scale over distance to nozzleorifice for case i 100 J1S after SOl

time dependent for the case v, but not for case iii and iv. This time stepdependency was not expected. More, Kaario [67] used the same code withthe identical nlethodology for engine calculations and observed, that a4 J1S tillle step could be used during the fuel injection period instead ofthe 2 J1S time step employed in an earlier study. The major differencebetween cases iii, iv and v is the initial turbulent viscosity. Case iv has aan integral viscosity of the order of a passenger car diesel engine runningat 2000 RPM, the one of case iii is nearly two orders of lllagnitude higher,and the one of case v rnore than an order of lllagnitude lower. Clearly is,that if a coarse resolution is used with turbulent viscosity of the order ofmagnitude of an engine, a time step of 1 J1s resolves the time scales and

CHAPTER 2. SPRAY AND MIXTURE FORMATION

no time step dependence is observed.

45

Theoretical Possibilities of Cornpensate U nderresolvedGrids

Because the individual droplets and the surrounding fluid is not resolved, abig number of submodels for the dispersed phase are used. If the cases arebad resolved, there is a need to decrease the deceleration of the droplet.For this purpose there exist mainly two possibilities for underresolvedgrids. The first is two drop the turbulent viscosity of the fluid. Differentworks have shown (i.e. [80]) that using less viscous turbulent lllOdels, as forexample the RNG - K, - E model, the spray penetrates further. The sameeffect can be achieved by decreasing OJ-t of the turbulence model. Thistype of tuning has two major disadvantages. First, different turbulencevalue will seriously influence the behavior of combustioll simulation, andsecondly, it is difficult to find a physical explanation for this type of tuning.The most frequently method is to modify the break up parameters. Figure2.14 shows, what happens, when the parameter for the characteristic breakup time is increased. As seen before, the stripping break up times scale isthe donlinant time scale in the vicinity to the nozzle orifice. Underresolvedgrids, suffer primary in this region. As can be seen in figure 2.2 the linearpenetration regime, is significantly lower, using underresolved grids.

Increasing the break up time scale for stripping break up leads to ahigher droplet dianleter (see figure 2.14). It is nice to see, that the dropletsize stays near constant, at a high level, llloving away frolll nozzle orifice,which is unphysical. Nevertheless, the capability of tuning with modelconstants is limited [134]. With the model constants, a kind of fine tuningcan be done.

2.6 Sensitivity of Spray Prediction regard­ing Engines Simulations

Looking on above results, one would expect, that spray calculation of en­gine are notoriously underresolved and strongly depending on mesh res­olution. Figure 2.15 shows the comparison between calculated pressurecurve and heat release rate between three mesh resolutions and experi­ment. Surprisingly, no severe mesh dependence is observed. For the finestgrid, in the nearly nozzle orifice region, nearly the nozzle dimension isresolved, whereas the coarsest grid, does not. Nevertheless, because for

CHAPTER 2. SPRAY AND MIXTURE FORMATION 46

0.001 ~r~-~'~'~'T-- 1000

"' - 1000' 0.0001

v0-

C ~ I

"g '"0:: 10 .....~'C

~U5~" 1E-005

case~rn 100mu, Cs2 20'" case~5 Olm 100mus Cs2 20 .. ~ .....case v 0~ OOmus Cs2 120 g case v 0.5 mm 100mu8 Cs2 120 g

case v 0.5 mm 300mus Cs2 120 \1 ease v 0.5 mm 300mus Cs2 120 \11E-006 ~-~...I. 0.1

10 15 20 25 30 35 10 15 20 25 30 35

0001 - 1E+006

100000~ 0.0001

'" -'" ..~ "', 10000m ....~" .... \1 ct'" 1E-005 '7f-

ease v"t 5 mm 100rnus Cs220 case y ~ffl 100mus Cs2 20.. 1000 ..case v 0.\'Ilm.,.100mU8 Cs2 120 Q case v 0.5 min 100mus Cs2 120 Q

case v 0.5~ 300mus Cs2 120 \1 case v 0.5 mm 300mu8 Cs2 120 \11E-006 ~.•. J-.. 100

10 15 20 25 30 35 10 15 20 25 30 35

100000 0.001·~-~-·I-~

- 10000

'" 00001.D

:[~ 1000 ~..z ..... '7 [5 ..... ~'" ~ '7 1E-005.D

case v~'" 1OOmus Cs2 20~ 100 case v~W 100mu, Cs2 20 .. ..case v 0.5 100mus Cs2 120 Q \1 case v 0.5 mrfi 100mus Cs2 120 Q

case v 0.5 mm 300mus Cs2 120 \1 \1 C<:::I58 V 0,5 mni 300mus C~2 120 \110 1E-006

10 15 20 25 30 35 10 15 20 20 30 35

Figure 2.14: TStripping, normalized Weber number for stripping break up,TBag, droplet Reynolds number, Weber number and droplet diameter foran underresolved case, with standard model paranleter Cs2 = 20 for strip­ping break up and an increased one Cs2 = 200 over distance to nozzleorifice for case i

engine sector calculations usually polar grids are used, the resolution inazimuthaI direction is in near orifice region for the coarsest grid thrice thenozzle orifice and for the finest grid, nearly the nozzle orifice. As has beenshown by the author in [70], to resolve the gas velocity gradients, onlya fine resolution in azimuthaI or in radial direction to the spray axis isneeded. Here, the first condition, is for all three grids approximately thesame.

Now, is everything done? The answer is definitive no. As has beenshown by the author [70] and also by Krüger [42], simulations with thelagrangian-eulerian method for spray calculation with a finite volume ap­proach for the continuum phase and the use of hexahedral grids, show

CHAPTER 2. SPRAY AND MIXTURE FORMATION 47

~·--T"--r·'-'T------r----'-----'----'-----'-----------T-----------T----'--------'----'-------'----'-------'--------',.,-----1

~ 190'000 cells / seclor".., 33'000 cells / seclor0--------<> 6'000 cells / seclor00------------> experiment

100

'7 90

~ 80:::::..

Q) 70

:: 60

~ 50a~ 40~

30

:il 20--<::

10

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

crank angle [deg]

: ~~ ~ e I -:~;;~~~~-~1;0~--7130>- -<> 33'000 cells / secloro 120~ 11 0 6---~ 6'000 cells / seclor~ 100 00------------> experiment~ 90~ 80~ 70lii 60

"0 50.'0 40~ 30

2010O...........-'-----------'-------'----'----------'-------'-----'-----..----'-----..-----'---------'-----'------'----.........l---'-----'------------A-60-50-40-30-20-10 0 10 20 30 40 50 60

crank angle [deg]

Figure 2.15: Influence of mesh resolution on engine calculation in operat­ing point 1 (see table 5.4) compared to experiments, left pressure curve,right heat release rate

not only resolution dependency for spray calculation, but also a strongdependence on the alignment of the grid to the spray axis. If, the sprayis injected in lets say 45 degrees to the alignment of the numerical fluidcells, numerical diffusion leads to a underprediction of spray penetration.This is a serious problem. Calculations have been perfornled by the au­thor, using different resolutions an injecting the spray with an angle of45 degrees to the alignment of the cell. The result was astonishing. Nomesh resolution was anymore observed, but the spray penetrated, due toincreased numerical diffusivity, less then the standard case, where the cellswhere aligned in spray directions. What does this mean? The lagrangian­eulerian method, can be used successfully, if the resolution near the nozzleorifice is increased until resolving nearly the nozzle orifice, and if the meshis aligned in spray direction. For practical purpose, the second criteria isdifficult to achieve, because a new mesh has to be generated for everyinjection direction. More, because nlOving meshes are needed for enginecalculations, creating such a mesh, is not straight forward. New meshgenerating tools are coming into market [135], which, at least for con­ventional diesel engines, do generate spray optimized meshes. For HCCrengines, where the injection direction is, at least in research, set more ver­tical, the generation of spray optimized moving meshes is nlOre difficult.Now, although this deficiency of spray numerics could be identified, inchapter 5, following standard practice, standard meshes are used. Thisis done, because the focus of this work is chemistry reduction and com­bustion rnodelling. In future, sever work has to be done, to handle thepresented deficiency.

CHAPTER 2. SPRAY AND MIXTURE FORMATION

2.7 Summary and Conclusions

48

Above results have shown, that lagrangian-eulerian coupling between thedispersed phase and the continuum phase can lead to physical correct re­sults, if the constraints of fine resolved mesh and mesh alignment in sprayaxis are fulfilled. It could be shown, that the Stokes number in the nearorifice region is significant above 1, and therefore the droplets are not in­fluenced by the surrounding gas flow and its turbulence. Stokes nUlnberdrops, towards the tip of the spray, where it can go below unity. Thismeans, that the droplets in the tip of the spray, may perceive an influenceof the surrounding flow. It was shown, that in the near nozzle orifice re­gion, the stripping break up time scale, is significant smalleI' then the bagbreak up time scale. The bag break up beconles important, at the tip ofthe spray. It could be shown, that the droplet Weber number, at least innear orifice region, is significant above the critical Weber number, so breakup has to occur. Analyzing engine ca1culation, no mesh dependency wasdetected. A severe influence of mesh alignment towards spray axis wasidentified, which was still in nozzle resolving meshes, tremendous. No re­finement is useful, if the meshes are not aligned in spray axis. For practicalpurpose, this criteria is difficult to achieve, because a new rnesh has to begenerated for every injection direction. More, because nlOving meshes areneeded for engine ca1culations, creating such a mesh, is not straight for­ward. New mesh generating tools are coming into market [135], which, atleast for conventional diesel engines, do generate spray optimized meshes.For HCCI engines, where the injection direction is, at least in research, setmore vertical, the generation of spray optimized moving meshes is moredifficult. Now, although this deficiency of spray nunl€rics could be identi­fied, in chapter 5, following standard practice, standard meshes are used.This is done, because the focus of this work is chenlistry reduction andcombustion modelling. It is also difficult to estinlate, how sensitive theoverall combustion reacts, on locally different mixture. McCracken andAbraham [79] showed in their particulary case, that the overall combus­tion (as pressure curve and heat release rate) did not react sensitive, onthe local state of the mixture, but emissions did. Nevertheless, in future,work has to be done, to handle the presented deficiency.

CHAPTER 2. SPRAY AND MIXTURE FORMATION

2.8 List of Symbols

Symbol Description UnitAd droplet area m

2

Cbl break up model constantCb2 break up model constantCEl nlodel constant turbulence modelCä model constant turbulence modelCE:~ model constant turbulence modelCE4 model constant turbulence modelCd drag coefficientCft model constant turbulence nlOdelCsI break up model constantCs2 break up model constantcp mean constant specific heat J/(kg·K)D droplet diarneter mD d droplet diameter mE collision efficiencyFh diffusional energy flux J/(m2 . s)F force Nh specific static enthalpy J/kg1 characteristic length scale III

1 size of the turbulent structure mmm mass fraction kg/kgOh Ohnesorge numberp pressure PaPDA phase doppler anemometryRed droplet Reynolds numberRNG renormalization groupSi momentulll source kg· m/s2

Sij rate of strain 1/S2

Sh enthalpy source J/(kg·s)Sm mass source kg/sSMD Sauter mean diameterSOl start of injection s, degSt Stokes NumberT temperature Ku velocity m/sU ensemble averaged velocity m/su relative velocity between fluid and mov- m/s

ing coordinate frame

49

CHAPTER 2. SPRAY AND MIXTURE FORMATION 50

unsteady reynolds averaged naVlerstokescollision parameterWeber numbercartesian coordinate m

N/m

m/sm

m2/s2

N· s/rn2

s

dissipation rateKronecker deltatime stepvelocity difference over shear layerspatial discretizationturbulent energydynamic viscositymlcrocollision frequencydensitymodel constant turbulence modelsurface tensionturbulent Prandtl numbermodel constant turbulence modelturbulent Schmidt numberstress tensorcharacteristic timescaleand Special Symbolsfluctuationsparcel 1parce12virtual massnozzlebody forcebag break upbag break upcontinuum phasecelldispersed phasedraggasenthalpycomponent in i directioninitial

12

WWe

URANS

p

CTm,t

T

T

Subscripts

amabbbagccddrgash1

1m

x

GreekE:

88t8u8xK,

CHAPTER 2. SPRAY AND MIXTURE FORMATION 51

InJ

J1In

mMN 2

overbarpsstrTttv

injectioncomponent in j directioninstabilitiesintegralnozzlemassmomentunlnitrogenensemble averagepressurestripping break upstripping break upturbulentturbulentthermalmomentum

CHAPTER 2. SPRAY AND MIXTURE FORMATION 52

Chapter 3

Systematic Reduction ofDetailed Chemistry

A chemical reaction kinetics mechanism describes a chemical process likecombustion with nlathematical functions. Such a systenl consist, for com­bustion of hydrocarbons, of hundreds to thousands elenlentary reactions,depending on the size (the number of C, 0, N and H atoms) of the com­bustion reactants [101, 102, 112, 113, 117, 115, 114, 116, 118]. Duringcombustion process hundreds of intermediate species are produced andreduced. For every species, an differential equation in time has to besolved. Simulation of a detailed reaction rnechanism causes an enormouscomputational effort, especially, when the species have to be transportedin a three dimensional domain. The biggest nunlerical problenl are theshort tinle scale of a large part of reactions. Applying a simple explicitintegration nlethod, which is direct connected to the timescale, for theabove nlentioned ODE's, a solution can not be reached in a feasible time.1'0 overcome this shortcoming, advanced numerical solvers for these stiffequation systems were developed. Nevertheless, the gain in computa­tion velocity, although it is significant, is not enough to simulate detailedchemistry coupled with three dimensional flow simulations.

3.1 State of the Art - Chemistry Reduction

Research community has developed a number of procedures to reducethe initial detailed mechanism to skeletal or even reduced ones. Skeletalmechanism, are mechanism which do include the main species and reaction

53

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 54

needed for the simulation of a specific problem. They consist in general of20 to 80 species reacting in less than 250 reactions [113, 119, 114, 120, 101].Whereas reduced mechanism, start from skeletal mechanism and reducedthis to 4 to 40 steps [113, 101,94, 121, 114]. This steps, are usuaHy globalreactions, whose reaction rates are computed from algebraic equation con­taining the reaction rates of elementary reactions. There exist also hy­brids, which do solve elementary reactions for a certain number of speciesand, the so called steady state species, are computed from algebraic rela­tion to the unsteady and steady species [94]. To obtain skeletal mechanismreaction path analysis or sensitivity analysis has been successfully used inthe past [113, 114]. The construction of this skeletal mechanism is seldomweH documented. Because, apriori, this methods are not based on linearalgebra theory as for example CSP [122, 123, 124, 125] or ILDM meth­ods [126]. CSP classifies, analyzing the lllatrix of ODE's, the species infast reacting and slow reacting ones. The fast reacting species are treatedwith quasi steady state assumption, whereas the slower, build a new dif­ferential equation system. Detailed description of the CSP method can befound in the publications of Lam [124, 125] and Massias et al. [122, 123].This methods, as much as I am aware, have never been used to reducemechanisllls with hundreds of species and thousands of reactions. An ad­vantage of the use of skeletal mechanislll, is that the chemistry describedby the mechanism, even if it simplified, is still chemical correct. Whereasreduced mechanism, are mathematical transformations, where the indi­vidual species, can lose it physical meaning [114]. Last, although this ismore a practical advantage and should not playamajor role in research,skeletal mechanism are still described by ordinary differential equation,and therefore can be used with the same programs as detailed chemistry.If using steady state assumption, usually, in the algebraic equations, thesearched species is computed as a relation of reaction rates where its ownconcentration is needed. This is usually solved by newton iteration whichcan annihilate the advantage of the reduced number of species and increaseCPU time to even higher than the detailed mechanism [113].

3.2 Used Methodologies for Mechanism Re­duction

The used methodologies for reduction of the initial chemical mechanismare the reaction path analysis, and the time resolved heat release rate anal­ysis of the individual reactions. The reaction path analysis, also known

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 55

as atomic-flux analysis, is a wide used [113] reduetion technique to geta skeletal mechanism, whereas the time resolved heat release rate anal­ysis of the individual reactions, as much as I am aware, has never beenpublished. Nevertheless, it is difficult to imagine, that people reduce amechanism with hundreds of species and thousands of reaetions with re­aetion path analysis, because the possible pathes a species can take areenormous, and it is easy to get lost. Müller [114] reduced a detailedn-heptane mechanism from Chevalier [111] from 172 species and 1011 re­actions to a skeletal one with 41 species and 83 elementary reaetions usingsensitivity analysis. He multiplied the reactions, he was interested in, witha faetor, and observed the influence on the ignition delay. If a significantinfluence could be observed, a decisive reaction was identified. For thereduetion, this had two meanings. First, the reaetion is in an importantreaction path, and second, the reaction is slow, because the timescale ofthe reaetion influences the overall process. In this way, he could easilyidentify, the most important reactions.

As it will be shown in section 3.3, the initial detailed n-butane mech­anism, was a sub-mechanism of the detailed iso-oetane mechanism fromCurran et al. [102]. This sub-mechanism consist of 385 species and 1895reaetions. To do sensitivity analysis for 1895 reaetions, is a though work.Nevertheless, if the time resolved heat release rate analysis of the individ­ual reaction had not worked, this had been my destiny. The famous PSRcode, which works with Chenlkin II libraries, has been slightly amplified,to calculate the time resolved individual heat release rate of every reac­tion. This tinle resolved heat release rate of every reaetion is analyzed inevery time step. With the modified code, a homogeneous reaetor is calcu­lated, under the conditions, the user wants to reduce the mechanism. Ifthe heat release rate exceeds in a single time step a threshold value set bythe user, a flag is put to one, which means that this reaction is important.A second code, which was baptized with the name readReactions, hadas input the ftag veetor and the old chemical kinetic reaetion rnechanisminput file. If the ftag of the reaction was 1, the reaetion was rewritten inthe new chemical reaction mechanism file, if not, the reaetion was deleted.Deleting reactions leaded also to the absence of the need of a few species.In section 3.3 nlOre details are given of practical interest.

Having a skeletal mechanism of the order of 150 species ore less, visualreaction path analysis can be carried out. 1 For this purpose the standardPSR with Chemkin II libraries [127] was used for the calculation and

1Theoretically, it can be carried out for arbitrary large mechanism, nevertheless inpractice, far large mechanism, the printed reaction path map becomes complex

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 56

8.8 Bore [cm]8.84 Stroke [cm]1200 RPM16.0 compression ratio1.365 pressure at IVC [atm]328 temperature at IVC [K]3.8 A

Table 3.1: Characteristics of the case, on what the reduction has beencarried out

Cantera [128] was used for the reaction path analysis. The standard casefor both reductions, n-butane and n-heptane, is a single zone adiabaticperfectly stirred reactor calculation with variable volume. The boundaryconditions are the one of a perfectly homogeneous HCCI engine. In table3.1 the characteristics of the standard case are given.

3.3 Reduction of n-Butane

First the detailed n-butane mechanism has been validated with existingexperimental data (figure 3.1. At high temperature, the agreement be­tween simulation and the shock tube experiments of Burcat et al. is good.In the temperature region below 900 K the discrepancy between simu­lation and the rapid compression nlachine experiments by Sochet et al.is higher. The cases are not unconditionally comparable, because in arapid compression rnachine, the temperature during conlpression is lowerthan the start temperature in a PSR. The later is kept constant, untilit is raised by the combustion. The proposed mechanism by Ogink andGolovitchev [130], but this mechanism had even a shorter ignition delaythen the one presented by Curran. The mechanism proposed by Marinovet al. [131] and the one proposed by Warth et al. [132] have also beentested. The ignition delay of both was significant longer then the exper­imental one. It has to be mentioned, that both mechanisms, the one ofMarinov and the one of Warth, have not been constructed for auto igni­tion phenomena. So it is unfair to disqualify them. Starting from detailedchemical nlechanisms, the in section 3.2 proposed time resolved heat re­lease analysis of the individual reactions was carried out. This methodwas used, because the starting mechanism, with 385 species and 1895 re­actions, was to complex for reaction path analysis. The alternative had

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 57

1.0E+00

1.0E-OlVi'......~ 1.0E-02CU

"c:1.0E-030

Ec:C)

1.0E-04

1. OE-OS

,....- --i'r-- C4H10 shock tube experiment Burcat (10 bar)

-e- C4H10 RCM experiment Sochet (10 bar)

-€l- C4H10 simulation PSR Curran mechanism (10 bar)

~~

"&........... SI

~ -... .......

'~.........

~

500 700 900 1100 1300 1500

temperature [K]

Figure 3.1: Validation ofthe detailed n-butane nlechanism from Curran et.al [102] with 385 species and 1895 reactions with published experiments[129]

been sensitivity analysis. But making sensitivity analysis with 1895 reac­tions, is a big piece of work. As above nlentioned, the PSR was slightlyextended to calculate the reaction rate of every individual reaction, anclassify them in important and unimportant reactions. This was done byusing a threshold value. If the heat release rate, in a single time step, washigher than this threshold value, the reaction was classified as important.The readReaction code was crucial to automatize this procedure. Becauseafter selecting the important reactions, it would be very time consurningto deselect them manually. The threshold value was set at the beginningto 1 J/s. It is to mention, that important reactions, especially in the coolflames, do not produce a lot of heat release. Most heat release is pro­duced by the reaction who lead to CO, H20 and 002' This procedurehelps also to identify reactions which are not used, because this one, willof course not produce any heat release. Nevertheless, it is quiet aston­ishing, that if areaction is present, it will be used. This procedure wasused in an iterative way. A new mechanism was computed, and with thisnew, reduced one, the same problem was recalculated. The new globalheat release rate (the one over all reactions) was compared with the one

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 58

-30 ·20

~ 120

:E 100:::1

-30 -20 -10 0 10 20 30crank angle [deg.)

100r------"'""::===1;;i' 0---0 delalled mechanism

i 80 1 reduced mechanisml'!GI

lQ 60GI

1!gj 40..i!!II 20.5 I--~=::::::::::::=::z.,l.-----I

20 30

140 0---0 detalled mechanism

""---+1 reduced mechanism

S 80l'!GIlQ 60GI

1! 40i.. 20

Figure 3.2: Comparison of the heat release rate (left) and the cumulativeheat release rate (right) of the skeletal mechanism reduced with time re­solved heat release rate analysis of the individual reactions to 140 speciesand 453 reactions with the initial mechanism by Curran et. al [102] with385 species and 1895 reactions at the operating point where reduction hasbeen carried out (table 3.1)

by the starting mechanism, and if the result was the same, a new itera­tion was started. The threshold value was kept at 1 J /s, until no reactionwas anynlOre eliminated. Elinlinating a few reactions, made it possible,that in the next iteration, even if the threshold value was kept constant,others reaction were eliminated. The threshold value was then increaseduntil it reached a value of 5 J /s. At this point the reaction mechanismwas reduced fronl the starting 385 species and 1895 reactions within a fewiterations to a nlechanism of 140 species and 453 reactions. It has to bementioned, that the nurnber of species was reduced to nearly a third ofthe initial ones, and the number of reactions to a fourth of the initial ones,without any apriori consideration of chenlistry. Figure 3.2 shows the com­parison between PSR calculations with the starting detailed mechanisnland the first reduced n-butane mechanism at the point of reduction (seetable 3.1).

The skeletal mechanism shows good agreement compared to the start­ing mechanism. The weak cool flames are weH predicted. At the hightemperature reaction the skeletal mechanism predicts a little less heat re­lease rate. Looking on the cumulative heat release rate the difference ismarginal.

Figure 3.3 shows the comparison over a wide range of ,,\ and compres­sion ratios, of the crank angle difference where the skeletal mechanismreaches 10% of the cumulative heat release and the detailed (left) and the

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 59

delta HRR 10 % delta HRR 50 %4.5 4.5

4.0 0.3~0.1- 4.0

Ä 3.5 Ä 3.50.13.0 0.0 0.0- 3.0

2.5 -0.1 -0.1 2.52 -0.3

2 1515 16 17 18 16 17 18compression ratio compression ratio

Figure 3.3: Comparison of the differenee in erank angle between the loea­tion where the skeletal meehanism (140 speeies, 453 reaetions)reaehes 10%of the eumulative heat release and the detailed meehanism (385 species,1895 reaetions) (left) and the loeation where 50% of the eUlllulative heatrelease is reaehed (right) for various A and eompression ratios. The RPMand the engine dimension are kept eonstant (table 3.1). A negative numbermeans, that ealculation with the skeletal seheme reaehes the eorrespond­ing point later.

loeation where 50% of the eumulative heat release is reaehed (right).TheRPM and the engine dimension are kept eonstant (table 3.1). The agree­ment between the skeletal meehanism and the detailed is over the wholeanalyzed range very good. It ean be said, that with the proposed method­ology, the main reaetions where identified. Inereasing the threshold value(as explained above) over 5 Jjs, leaded to an observable deviation in theheat release rate. This was therefore the starting meehanism for reaetionpath analysis. The skeletal meehanism had at this point 140 species and453 reaetions. The whole following reduction has been done two times.This is a disadvantage of the method. The user has to deeide, if thedeviation between the starting meehanism and the new ealculated is ae­eeptable. Sometimes, the solution with the new redueed one beeomesworse, but later, reducing it more, the agreement between the skeletalmeehanism and the starting detailed meehanism beeollles again better.This is especially the ease, when some intermediates are ereated, but theSehellle does not allow them to propagate. So the overall eumulative heatrelease rate ean drop. Eliminating this dead end, leads again to fuH eom­bustion. The fuH reduetion, from 140 species and 453 reaetions to the endllleehanism, with 22 speeies and 57 reactions, has been earried out, print­ing reaetion path maps, and analyzing the main pathes, lumping speeies

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 60

and deleting reactions. The reader has to excuse, that it is difficult todescribe every single step carried out, for the reduction. Because duringreduction, it is difficult to know if the chosen simplification will succeedor not. So writing down every step, will lead to a nonproductive work.Sometimes one has to accept, that the chosen simplification is bad, andrestart the analysis a few steps before. Nevertheless, indeed it sounds asa extremely time consuming work, using Cantera [128], it can be done ina reasonable time. Cantera reads the solution calculated with Chemkin,and plots without any further modification the reaction pathes. 2 To plotthe reaction pathes, it needs the pressure, temperature and the speciesconcentration over tinle, or in this case, over crank angle. The reductionhas been mainly carried out, by deleting or lumping a single species inevery step, recalculating the problem, and deciding by plotting the globalheat release rate, if the solution is acceptable. For reaction path analysis,only the flux of the C-atom has been visualized, on different crank angles,to allow the analysis of low temperature reactions and high temperaturereactions. The H-atom flux, was not analyzed, because the H 2 scheme isalready compact and plays a major role, especially for high temperaturereactions. So, no further simplification was expected. This experience wasalso done by Herrmann [133], where he tried to reduce an H2 and a CH4mechanism with CSP. The reduction of CH 4 had more success, than theone of H2 .

In addition to deleting species, the lumping of sub-mechanisms, be­comes early a major role. Lunlping is done, by generating a global re­action from several elementary reactions. For example at the stage ofa mechanism having 103 species and 338 reactions, the reaction pathanalysis showed, that one of the alkene isomer C4 H s propagated towardsCH3CHO passing towards one isomer of C4HsOH. C4H80H then re­acted to 02C4HSOH and the later to the final CH3 CHO. No branching ofthis path was observed. So, a global reaction C4Hs -----+ CH:3CHO was in­troduced. For the global reaction rates parameters, it was observed, whichof the reactions had the slowest time scale. The reaction rates parame­ters of these reaction where then taken. The estimation of the time scaleof the individual reaction, was done by comparing the pre-exponentialfactor A and the activation energy E A of the individual reactions. Thepre-exponential factor determines the collision frequency, so it is, the onewho determines the velocity of the reaction, having reached the activationtemperature. The activation energy, describes the energy, or if divided

2The solution can also be ca1culated by Cantera itself, but because the author wasmore familiar with Chemkin, Chemkin was used to ca1culate the problem

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 61

with the universal gas constant, at which temperature, this maximumvelocity will be reached. So the value of the exponential term can max­imally reach unity. An example, where the above simplification did notwork, was the reaction from the alkyl radical CH3 ---+ CH30. This pathwas branched into a second path CH 3 ---+ CH;~O2 ---+ CH 30 and a thirdpath following CH3 ---+ CH30 2 ---+ CH3 0 2H ---+ CH30. At this stage ofreduction, no simplification could be done.

Now, we make a jump to the reduced mechanism with 79 species and270 reactions. As know from theory [109], the fuel is first decomposedinto alkyl radicals, namely, this are the p - C4 H g and the s - C4 H g rad­icals in the presented reaction mechanism. This reaction is the typicalinitiation reaction for hydrocarbons. Both alkyl radicals propagate tohydro-peroxide isomers, namely the p - C4 H g 0 2 and s - C4 H g 0 2 , re­spectively. Additional, smaller alkyl radicals are created, which in thepresented skeletal mechanism is the C2 H s radical. Also alkene (olefin)isonlers are created, which are in this case two isomers of butene (C4H s ).This two butene isomers could be merged to one single isomer, withoutmajor error in the global reaction rate. The two hydro-peroxide isonlerswhere decomposed, into four isomers of C4 HsOOH. Two of theIn couldbe merged, and a third one neglected, because it was decomposed throughC4 HsO into fornlaldehyde and propyl. This path was not important. Apart of the above C4H sOOH isomers, propagated to four C4H sOOH02

isomers. Two of them could also be merged into a single one, withoutinfiuencing the global heat release rate. Eliminating a few species whichwere not on an important path, leaded to areaction mechanism with 70species and 238 reactions.

Arriving at a mechanism with 58 species and 213 reactions, made thcreaction pathes more clear. This is more a practical issue, but I wantto comment on that. The above more detailed mechanisms, where moredifficult to analyze, because the species propagated through a lot of pathesand the difference, between the importance of a pathes or an other was notso unambiguous. Cantera, prints arrows, which thickness is proportionalto the importance of a path. I have to repeat nwself, that without Cantera,a reduction, as presented here, would have been a nightmare. So I wantto thank at this position, Mr. David G. Goodwin, from the CalifornianInstitute of Technology, and his co-workers, to have made such a greattool freely available to the humanity. Merge both alkyl radicals, p - C4H g

and s - C4H g was at this point, still not possible, because a to earlyignition was observed. This would have been great, because then, a wholeseries of reactions, could have been deleted. At this point, the propyl

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 62

delta HRR 10 % delta HRR 50 %

1.5 1.0

compression ratio

4.5~------------'

4

A3.5

3

2.5

215

~O.5/

0.5 0.0

16 17 18compression ratio

4.5r--------------.

4

Figure 3.4: Comparison of the differenee in erank angle between the loea­tion where the skeletal meehanism (43 species, 127 reactions) reaehes 10%of the eumulative heat release and the detailed meehanism (385 speeies,1895 reaetions) (left) and the loeation where 50% of the eumulative heatrelease is reaehed (right) for various A and eonlpression ratios. The RPMand the engine dimension are kept eonstant (table 3.1). A negative numbermeans, that ealculation with the skeletal seheme reaehes the eorrespond­ing point later.

radical C:i H 7 , the ethyl radical C2 H s, ethen C2 H 6 , HCCG, CH30H andCH20H eould be eliminated. Getting from this meehanism, whieh hadnow 53 species and 183 reaetions to smaller ones started being, a diffieulttask, beeause every speeies was important and no lumping or merging waspossible. This was the moment, similar to the one when Apollo 13 wasbehind the moon, without any radio eontact to the world. Even if allspecies had an influenee on loeation of the global global heat release rate,the meehanism was still to large, for using it later in 3D-eOlnputations.Looking on the reaetion path, it had to be estimated, which ones will beimportant at the end, and which ones not. The hope was, that eliminatingall unimportant species, as it was experieneed before, the llleehanism willagain prediet the overall eombustion weIl. An error is introdueed, whichwill be eorrected by the meehanism itself, when further redueed. It comeout even. The meehanism with 43 species and 127 reaetions showed verygood agreement with the starting meehanism.

Figure 3.4 shows the eomparison of the differenee in erank angle be­tween the loeation where the skeletal meehanism (43 species, 127 reae­tions) reaehes 10% of the eunlulative heat release and the detailed meeha­nism (385 species, 1895 reactions) (left) and the loeation where 50% of the

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 63

cumulative heat release is reached (right) for various A and compression ra­tios. The agreement is over a wide range lower than 1 degree crank angle.Onlyat low compression ratios, where the chemistry becomes slower, thedeviation is a little higher. Nevertheless, the result is very satisfying. Themechanism was coupled with the 3D-CRFD combustion model, presentedin chapter 5. But the computation time, were still to long. The task was,to build up a chemistry, which was able to compute a three dimensionalcase, within the order of magnitude of a day. With this chemistry, itwas still in the order of magnitude of weeks. Nevertheless, for calcula­tions in homogeneous reactors, the new reduced mechanism needed lessthan aminute, whereas the reduced mechanism with 140 species and 456reactions needed approximately three minutes, and the detailed startingmechanism approximately 15 minutes, in a standard Pentium IV PC run­ning with Windows 2000. The mechanism had still a few stiff reactions,which must have dropped significantly the time step. Further reductionwas needed. Now, the main reaction path were good visible. CH2CHO---+ C2H30 ---+ CH3 CO was areaction chain without branching. Thereforea lurnping was made to areaction from CH2CHO ---+ CH3CO. Below,the isomerization reaction are shown, before the lumping and after thelumping. The reaction rate parameters for both reactions are quite simi­lar. But analyzing the reaction path, the main reaction direction for theisomerization reaction CH2CHO ---+ C2H 30, is the backward direction(reaction 122 old). This is the case, because the backward reaction has antemperature exponent of 1.7. At 1000K the reverse reaction is about 18times as strong then the forward. For the new lumped reaction 121, theslower reaction rate from equation 121 old, are taken. At 1000 K they areabout half as strong then the 122 old backward reaction coefficient.

121 old. c2h301-2=ch3coReverse

122 old. c2h301-2=ch2choReverse

121 new. ch2cho=ch3coReverse

8.50E+141.14E+101.00E+141. 23E+11

8.50E+141.14E+10

0.02.10.01.7

0.02.1

14000.033500.014000.028300.0

14000.033500.0

An other simplification, which could be than, was the lumping of thereactions C2H 4 ---+ HCO ---+ CO by replacing HCO just with CO + Hin the equation. The same could be successfully done for the path fromformaldehyde CH20 ---+ HCO ---+ CO. In the same way lumping was

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 64

o216'd250 250

200 200

f15<l' f 150

~ 2" "~ 100 ~ 100

5<l 50

0~30.30 .20

Figure 3.5: Comparison of the heat release rate of the skeletal mechanismwith 22 species and 57 reactions to the detailed on with 385 species and1895 reactions for an operating point with € 16 and >'2 (left) and anoperating point with € 18 and >'4 (right). The RPM and the enginedimension are kept constant (table 3.1)

carried out to eliminate C2 HsO and C3 HsO. Lumping left the reactioninside the mechanism, only the reaction partners where somehow mod­ified. This leaded surely to errors, but after every sinlplification, a runwas made an checked if the global heat release rate, was in reasonableagreement with the starting mechanism. At arriving at 37 species and123 reactions, analyzing again the reaction path, elimination of unim­portant reactions was done. Reducing the number of reactions, do notgive the same perforrnance gain, as the elimination of species, becausethe number of differential equations which have to be integrated, is keptconstant. Nevertheless, a gain is achieved. Additionally, the species areforced, to follow the main pathes, which can facilitate further lumping.This reduced the mechanism from 123 reactions to 109 reactions keepingthe species number constant at 37. Now, because the species were forcedto take the main pathes, S - C4 H g , two isomers of C4 H sOOH02 , twoisomers of C4 H sOOH and s - C4 H g0 2 could be eliminated. Now themechanism had 31 species and 93 reactions. The reaction p - C4H g0 2

---+ C4 H sOOH ---+ C4 H s was lumped to aglobai reaction p - C4 H g0 2 ---+

C4H s. Additional the trajectory from C4 H s ---+ C2H s ---+ C2H 4 was mod­ified, to get directly from C4 H s ---+ C2H 4 . This trajectory change allowedin a next step to eliminate C2 H s. The mechanism had now 28 species.With some additionallumping the mechanism could finally be reduced toa mechanism with 22 species and 57 reactions.

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 65

delta HRR 10 0/04.5 _ ...................~;",;;"",;,;; ............................ 4.5 r""""r".....=.i;,w";,;~;"";,,;,,,;;O"'=";;;;..,,:,,,;;,-.....

3.5

Figure 3.6: Comparison of the difference in crank angle between the loca­tion where the skeletal mechanism (22 species, 57 reactions) reaches 10% ofthe cumulative heat release and the detailed mechanism (385 species, 1895reactions) (left) and the location where 50% of the cumulative heat releaseis reached (right) for various ,\ and compression ratios. The RPM and theengine dimension are kept constant (table 3.1). A negative number means,that calculation with the skeletal scheme reaches the corresponding pointlater.

Figure 3.5 shows the comparison of the heat release rate of the skeletalmechanislll with 22 species and 57 reactions to the detailed one with 385species and 1895 reactions for an operating point with E 16 and ,\ = 2(left) and an operating point with E 18 and ,\ = 4 (right). The RPMand the engine dimension are kept constant (table 3.1. The agreementis excellent, if one takes into account the tremendous reduction whichhas been carried out. Figure 3.6 shows the comparison of the differencein crank angle between the location where the skeletal mechanism (22species, 57 reactions) reaches 10% of the cumulative heat release and thedetailed lllechanism (385 species, 1895 reactions) (left) and the locationwhere 50% of the cumulative heat release is reached (right) for various,\ and cornpression ratios. The RPM and the engine dilllension are keptconstant (table 3.1). A negative number means, that calculation with theskeletal scheme reaches the corresponding point later. Again, the agree­ment is excellent over a wide range. It can be said, that the main reactionpathes were identified, and the lumping reactions were set reasonable. Thecomputational effort for a homogenous reactor and a physical calculationtime of 0.05 seconds could be dropped, frolll 15 minutes for the startingdetailed mechanism to a few seconds.

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 66

I -t':r- n-heptane Hewson Mechanismus (40 bar)

...... n·heptane shock tube experiment Clezkl93 (40 bar)

~-EI- n-heptane high pressure temperature cell ETH (40 bar)

...... Diesel high pressure temperature eell, Reuter89 (40 bar

-~~ ..,

,~,.

"- ,........." _._..~

1.0E~01

......1.0E-02/!J.,

~CLl 1.0E-03'0c:0E 1.0E-04c:tn

1.0E-05

600 700 800 900 1000 1100 1200

temperature [K]

Figure 3.7: Validation of the skeletal starting n-heptane mechanism fromHewson [101] with 67 species and 265 reactions with published data fromCiezki

3.4 Reduction of n-Heptane

First the starting mechanism was validated. In this case, the startingnlechanisnl is already a skeletal one. The choice of taking a skeletal one,was because, as shown in figure 3.7, the skeletal showed already very goodagreement with shock tube experiments by Ciezki.

The reduction was again done, under the homogeneous engine opera­tion conditions presented in table 3.1. The n-heptane mechanism by Hew­son included detailed NO reactions. Because, in the presented work, thetask was, to have a fast mechanism which predicts heat release rate rea­sonable, this reactions and species were eliminated. The resulting mecha­nism had now 53 species and 210 reactions and had, as expected, the sameglobal heat release rate. A consecutive reaction path analysis showed thatCH, one isomer of CH2 , C2 H 2 and C2 H could be neglected. A few degreesCA before any global heat is release is observed, n-heptane is decomposedinto four heptyl isomers C7H 15 . The initialization reaction is of the sametype, as already observed for n-butane and agrees with theory [109]. Thisreaction is one of the predominant until10° BTDC. The fuel is consumedto more than 70% to the heptyl isomers C7 H 15 - 2 and C7 H 15 - 3 at theobserved crank angles (24, 20, 18, 14 and 12 BTDC). At 11 degrees BTDC

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 67

the fuel is complete consunled. Therefore, only the two isomers C7 H 15 - 2and C7 H 15 - 3 where considered. The mechanism had now 47 species and160 reactions. Recakulating the case showed that the influence in globalheat release rate was negligible. The main chain at 14 BTDC is nown - C7 H 16 -----7 g~:z~:=~ -----7 C7 H 150 2 -----7 HEOOH -----7 00C700H -----7

HOOC700H -----7 OC700H -----7 OC7 H 130 -t C5H l1 -t n-C3H 7 -t C:~H6

-t CH20 -t CHO -t COThis chain remains important at 12° before TDC but the chains C7 H 15 - 2-t ~~~:i;9'" and C7 H 1S - 3 -t C6 H 12 ... start competing which eachother. At 12° BTDC the path trough p - C4 H g is stronger thanthe on through C6 H 12 and C3 H 6 . The species C6 H 12 could be elimi­nated. The main chain at this crank angle goes through p - C4H g -t

C4 H s -t C4H 7 -t C4 H 6 -t C3H s -t C3H 4 and through the parallel pathC2H 4 -t C2H 3 -t CH20 -t CHO. C3H 5 makes a chain branching withone arm going to CSHlO -t CsHg and then CsHg splits to C3H 6 ,C3H5and C2H 3 . The other arm gets direct to C3H 4 . The ratio of the nor­malized C-Atom flux is 0.15:0.35. Therefore, C5H lO , C5H g , C2H s andC2H 6 were set as candidates for elimination. The chain propagation fronlC3H 5 -t C5HlO -t C5H g , which then reacts to C3H 6,C3H 5,C2 H 4 andC2H 3 can be viewed as a delay cirde, which surely influences the velocityof heat release rate. The species C2 H 6 , one of the candidates, but noton this delay cirde, could be eliminated. At 10° BTDC the main chaingoes from C3 H 5 -t C3 H 4 -t C2H 4 -----7 C2H 3 which then is branched intoCH20 and CHO. CH3 0 2 and CH30H seenl to be of lower importanceand were elinlinated. The path from CH30 to CH20 had a 7.2 timeshigher normalized flux, then the path from CH30 -t CH20H -t CH20.Therefore, CH20H was eliminated. At 10° BTDC the main pathes arevery similar to the ones at 12° BTDC. At the end of combustion, it canbe seen, that the path through CH2 is not necessary, and therefore itwas eliminated. An additional candidate for further reduction, becauseit did not appear in any important reaction path from 24° BTDC toTDC, was HCCO and could be eliminated. 12° BTDC the two arms,C7H 12 - 2 -----7 P - C4H g -t C4 H g -t C4 H s -t C4 H 7 -t C4 H6 -t C3 H sand C7 H 12 - 2 -t C 3 H 6 -t C3 H s, where competing. At 10° BTDC andlater the second arm, is significant more important. Therefore, the speciescontained in the first arm were neglected. Now, reconlputing areactionpath analysis, it is seen, that the fuel C7 H 16 is equally consumed intoboth heptyl isomers C7H 1S - 2 and C7H 15 - 3. Both chain propagate tothe same products, therefore only one isomer is needed. Further C7H 14

seems to be a dead end, and the path through C6H 12 is not used anymore.

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 68

Both were eliminated. Prom 14° BTDC to the end of combustion, CH3

propagates directly to CH20 or via CH30. Eliminating the path throughCH3 0 shows not nluch infiuence on the global heat release rate. At 14°BTDC a few reaction pathes start competing which each other. The fiuxthrough CsHg , is compared to the other pathes, low and remains low un­til end of combustion. CsHg can therefore be eliminated. Because CSHlO

was only connected to CsHg , it becomes now superfiuous. The meclla­nism has now 31 species and 79 reactions. A new reaction path analysisshowed, that at 14° BTDC there were two competing pathes startingfrom C3H 6 . The first went through C2H s ---+ CH3 ---+ CH20, the secondthrough C3 H s ---+ C3H 4 ---+ CH20. Eliminating C3H s and C3H 4 less in­fiuence on the global heat release rate, then eliminating C2 H s, so, theywere elinünated. At this point, the nlechanism consisted of 29 species and70 reactions. No further reduction was possible, by eliminating species.Now, the mechanism was analyzed to look if lumping, unifying elementaryreactions to global reactions, was possible. One candidate chain for globalreaction was the chain n - C7 H 16 ---+ C7 H 1S ---+ C7 H 1S0 2 ---+ H EOOH ---+

00C700H ---+ HOOC700H ---+ OC700H ---+ OC7 H 130. AglobaI re­action was constructed C7H 1S - 3 + 202 ---+ OC7H 130 + 20H. Thespecies C7 H 1S0 2 , HEOOH, 00C700H, HOOC700H and OC700Hcan be now neglected and the result is a mechanism with 24 species and63 reactions.

Figure 3.8 shows the comparison of the difference in crank angle be­tween the location where the skeletal rnechanism (24 species, 63 reac­tions)reaches 10% of the cumulative heat release and the starting skeletalmechanism by Hewson [101](67 species, 265 reactions)(left) and the loca­tion where 50% of the cumulative heat release is reached (right) for variousA and compression ratios. The agreement of the crank angle, when 10% ofthe fuel is burned, is for the hole nlap within 2° crank angle, which corre­sponds, at the investigated engine revolutions, to 0.28 ms. The agreementof the crank angle, when 50% of the fuel is burned, is for a large area within1° crank angle, which corresponds at the investigated engine revolutions,to 0.14 ms. It can be said, that the overall agreernent is reasonable andthat the methodology of reaction path analysis with species eliminationand lumping of reactions, was successful used, and is a powerful tool, toreduce chemistry to the base needs.

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 69

--0 0-

-----0-__0--

18

2.52 --1

15 16 17compression ratio

delta HRR 50%4.5 t----~~--------t

___~-1-4.0 __ -1

3.5A

3.0

delta HRR 10%4.5 - . -1.4

40 -1.4~21-0_. -1.2 - -- .

A 3.5 -1.0~

3.0 -1.0 --------.=0.8--1.2_ -1.0

2.5 --1.4 _ --1.2-2 --1.4-

15 16 17 18compression ratio

Figure 3.8: Comparison of the difference in crank angle between the loca­tion where the skeletal mechanism (24 species, 63 reactions)reaches 10%of the cumulative heat release and the starting skeletal lllechanism byHewson [101] (67 species, 265 reactions) (left) and the location where 50%of the cumulative heat release is reached (right) for various ,\ and COlll­pression ratios. The RPM and the engine dimension are kept constant(table 3.1). A negative number means, that calculation with the skeletalscheme reaches the corresponding point later.

3.5 Summary and Conclusions

Analysis of the time resolved heat release rate of the individual reactionsand reaction path analysis has been used, to reduced starting mechanismsfor n-butane and n-heptane. It was shown, that the first method is rea­sonable for large starting mechanism, where reaction path analysis is notfeasible. With this method, which as much as I am aware, has neverbeen published, a detailed starting mechanism with 385 species and 1895reactions, could be reduced in a few iterations to a mechanism with 140species and 456 reactions. Further reduction with the method of " analysisof the time resolved heat release rate of the individual reactions" could notbe achieved. For the n-heptane starting mechanism, which was already askeletal one, this method failed. It seems, that the method is useful for afirst big reduction of the unnecessary species. This kind of species, are notany more present in skeletal mechanism. The consecutive reaction pathanalysis leaded, as much as I am aware, to the smallest lumped n-butanemechanism for auto-ignition and COlllbustion ever published. The mech­anism was reduced to 23 species and 57 reactions. More, the mechanismshowed excellent agreement compared with the starting detailed mech­anism. The gain in computing time was, for the calculation of a PSR

CHAPTER 3. REDUCTION OF DETAILED CHEMISTRY 70

setup with 0.05 seconds physical time, from originally 15 minutes to afew seconds, on a standard Pentium IV PC. Using reaction path analysisthe starting skeletal mechanism for n-heptane [101], could be reduced to amechanism with 24 species and 63 reactions. This is the slllallest, as llluchas I am aware, skeletal n-heptane mechanism for auto-ignition and COlll­bustion, which is completely described with Arrhenius equations and doesnot have any steady state assumption. It exist smaller ones, for examplea 14-step mechanism by Peters, which was reduced from a 33 species and97 reaction skeletal mechanism, by nlaking steady state assumption.

3.6 List of Symbols

Symbol3D-CRFD

CSPHHCCIHRRILDMPSRODE

Description U nitthree dimensional computational reactive fluiddynamicscingular perturbation modeheat release rate J / deghomogeneous charge compression ignitionheat release rate J / degintrinsic low-dimensional lllanifolds methodperfectly stirred reactorordinary differential equation

Chapter 4

Multizone HCCI Model

Numerical investigations and comparison with experiments are presentedwith regard to homogeneous-charge-compression-ignition for two differentfuels. N-heptane and n-butane are considered. N-Butane in particular,being gaseous under atmospheric conditions, is used to also guaranteeperfectly homogenous mixture composition in the combustion chamber.Starting fronl detailed chemical mechanisms for both fuels, reaction pathanalysis was used to derive reduced mechanisms, which are validated inhomogeneous reactors (see sections 3.3, 3.4). After reduction, reactionkinetics is coupled with multi zone modelling in order to predict autoigni­tion and heat release rates in an I.C. engine. Multi zone modeling is usedto simulate port injection HCCI technology with gaseous fuel. Compari­son with experinlental results for a passenger car engine - obtained at theUniversity of Stuttgart - yield good agreement.

4.1 State of the Art - Multi Zone Modelling

A wide used approach is the treatment of the combustion chamberas a perfectly stirred reactor with variable volullle and heat losses[81, 82, 83, 84, 85] . This approach is very useful if a valuation of suit­ability is perforllled and only the trends are essential [81, 82, 83, 84, 85].Chen et al. [82] performed an investigation of internal EGR. He showedthat using internal hot EGR leads to an earlier COlllbustion. Fiveland etal. investigated in [84] the influence of initial temperature, initial pressureof mixture, natural gas composition, heat transfer model, equivalence ra­tio and compression ratio on ignition behavior of an HCCI engine. As

71

CHAPTER 4. MULTIZONE HCCI MODEL 72

expected, an increase of initial temperature leaded to an earlier ignition.Similar was the behavior while increasing the inlet pressure keeping theequivalence ratio and the inlet temperature constant. Adding to methanehydrocarbons of higher order - such as ethane and propane - in a rangewhieh is absolutely possible in natural occurrence, the ignition delay couldbe shortened up to half a nlillisecond. In [85] the computational investi­gation of [84] was extended and was compared with experiments. Both,experinl€nts and simulation, showed again that adding a higher orderalkane leaded to an earlier ignition. For 100% methane simulation andexperiments agreed reasonable. But using gas mixture the difference be­tween simulation and experiments was increased. Because in reality thecombustion chamber is not homogeneous, models have been improved us­ing various zones, whieh can have stochastic [86, 87] initial conditions orthe use of models whieh divide the combustion chamber into an adia­batic core, a boundary layer and a crevice volume [88, 89]. Dependingon the model assumption the zones experience no interaction [87], volu­metrie work between the boundaries or mass and energy exchange due tostochastic collision [86]. In [88, 89] there is mass exchange between thecrevice zone, the boundary layer and the adiabatic core zone, respectively.Maiwald et al. [87] extrapolates from formaldehyde R2CO measurementsat start of combustion a standard deviation of the temperature at IVC of5K. They tell that their simulations show reasonable agreement with ex­periments under lean conditions (.\ > 2). Fiveland et al. [89]could predictadditional to pressure and temperature curves the emissions of URC withreasonable agreement. The deviation in CO prediction was a little higher.

4.2 Methodology of the Multi Zone Model

In this section a short overview of the used methodology for the stochasticmulti zone model is presented. As in a single zone model the sum ofthe volumes of all zones is calculated by the crank kinenlatics given byequation 4.1.

B 2

V(<p) = S(<p) . Jr' - + Vc4

(4.1)

(4.2)

Where S(<p) is the distance from to piston to the position at TDC.

1 L sS(<p) = H· 2(1 - cos(<p) + 4(1 - cos(2<p)))

And Vcis the cylinder volume at TDC.

CHAPTER 4. MULTIZONE HCCI MODEL

V_ VD

c-s-I

73

(4.3)

Equation 4.4 is the energy equation of a single homogenous reactor.

dTdt

I (dQß dV dQW)---P----m· Cv dt dt dt

(4.4)

dQß/dt is the heat release rate by ehemieal reactions whieh is ealcu­lated with detailed ehemistry.

dQ N s

~=V,"'w··M··u·dt ~ I I I

i=1(4.5)

wiis the souree or sink, respectively, of species i [mol/ (em:3·s)], Mds themolar weight [kg/mol], Ui is the internal energy [J/kg] and V [cm3 ] isthe VOIU111e of the reactor. For the ealculation of species produetion ordestruction rate the molar weight and the internal energy, Chemkin IIsubroutines are used. The stiff differential equation system is integratedwith the subroutine DVODE. For the ealculation of the heat losses themodel proposed by Woschni is taken,

dQw-d-=-t- = a w . A z . (T - Tw ) (4.6)

where the heat transfer coefficient is calculated with equation 4.7.

-0.2 0.8 -0.53 VH . Tl 0.8aw=ascaling·130·B ·p·T ·(CI ·Cm +C2 · V; . (p-pzs))

I . PI(4.7)

The value for ascaling can be varied for eonventional direct injecteddiesel engines in a range of +- 30%. In this work the parameter ascalinghas been varied in a range from 0.01 to 1. The constant Cl is set to 2.28+ 0.308 . eu/em. The swirl faetor eu/em is for the investigated engine1.23. For the constant C2 the standard value for direct injected engines istaken. rt is conscious to the authors that the model developed by Wosehniis unsuitable for the HCCr combustion process. Zoran et al. [98] adaptedthe eonstants of the model for use with HCCr engines. The adaptedversion has also been used during this work. No noticeable improvementwas detected looking on various operating points. The presented modelassumes that all zones have the equal probability to have heat losses to

CHAPTER 4. MULTIZONE HCCI MODEL 74

the wall. Therefore the calculated heat losses are proportional to the massfraction. The gas is modelled as ideal (Eq. 4.8).

p·V=m·R·T (4.8)

A simplified model for the fire land is taken. A new zone is introducedwhich represents the volume of the fire land. In this volume no chemistryis calculated. The fire land has a constant volume and the temperature isequal to the wall temperature. This assumption is supposed to be valid,because this small volume has a big conlmon surface. The pressure isequal to the cylinder pressure. Change of the mass in the fire land volun18is compensated by all the zones depending on their mass fraction.

The nmlti zone model consists of various reactors as described above.The reactors are coupled by pressure compensation an volume work be­tween the zones. The individual Zones are calculated as a homogeneousreactor during one time step. Afterwards the cylinder pressure is calcu­lated considering energy conservation (Eq. 4.9), the ideal gas law (Eq.4.8) and having the total cylinder volunle given by the crank kinematics(Eq. 4.1).

- "\;"'Nz

Cv . mcyl . Tcyl = L...Jj=l Cv,j . mj . Tj (4.9)

The sum of all individual zone volumes must be equal to the cylindervolume. The pressure of all zones is set after each tinle step to the cylinderpressure. To conserve the zone mass, volume work between the zones isdone. The zone temperature and air fuel ratio at intake valve elose iscalculated stochastic. A normal distribution is taken with user prescribedstandard deviation and mean value (Eqs. 4.10,4.11).

Nz

aT=Li=l

mioi(4.10)

Nz- "\;"' mi . TiT = L...J

i=l mioi

4.3 Experimental and Numerical Setup

(4.11 )

The results presented in this section focus on port-injected, four-strokeHCCI combustion with n-butane. Table 4.1 contains the basic data of thesingle cylinder research engine located at the University of Stuttgart. The

CHAPTER 4. MULTIZONE HCCI MODEL 75

Table 4.1: Characteristics of the single cylinder research engine of theUniversity Stuttgart (Germany)

Manufacturer Mercedes BenzOM611

Stroke 88.4 mmBore 88 mmVD 537.6 cm3connecting rod 149 mmlength

Ethermodynamic 16.6 piston bowl 114.7 piston bowl 2

swirl rate (Tip- 0.51pelmann)

Table 4.2: Initial- and boundary conditions of the operating points fueledwith n-butane

OP...

1 11 III IV

A [-] 3.8 4.2 5.4 3.1rpm [UImin] 1200 1200 1200 1200p @ IVC [bar] 1.36 1.75 2.25 1.24mp [mg] 9.6 11.6 11.7 11.6mAir [mg] 568 756 974 544T @ IVC [0 K] 352 352 352 348residual gas [%] 8.84 6.04 6.19 5.70

investigations with n-butane were all carried out with the thermodynamiccompression ratio of 16.6. Before starting to compare the simulations withthe experiments, a number of sensitivity analyses were performed.

In table 4.2 the analyzed operating points are shown. For all casesthe rpm was kept constant at 1200, because increasing the rpm leaded toincomplete combustion. The experimental data have a measurement un­certainties of the n-butane mass of von +- 5%, the pressure uncertaintiesis +- 0.02 bar and the air mass can be estimated with an accuracy of +­2%. Because the ignition and combustion in HCCI combustion processdepends strong on the locale mixture and temperature evolution, this un­certainties can worse the agreement between simulation an experiments.

CHAPTER 4. MULTIZONE HCCI MODEL 76

For all simulations in this chapter the reduced n-heptane mechanism with24 species and 63 reactions (see sec. 3.4) and the reduced n-butane mech­anism with 140 species and 385 (see sec. 3.3 reactions were used.

4.4 Sensitivity Investigation of Model Pa­rameters

The stochastic model presented in this chapter has a number of parame­ters, which can be adjusted to match optimal the experiment. The task ofthese sensitivity investigations is to find out the influence of the individualparameters. All investigations have been carried out in operating point iof table 4.2 with the reduced n-butane mechanism.

4.4.1 Sensitivity Investigation of Temperature-Zones

Figure 4.1 shows the influence of the number of temperature zones onpressure curve and heat release rate. The standard deviation of initialtemperature is 5° K. This value has been detected in experiments [87]and is used in this work as guidance level. With increasing zone numberthe amount of different initial zone temperature is amplified. Thereforea few zones, contrary to the single zone nlOdel, have a higher initial tem­perature, then the mean value. The consequence is a displacement of thecombustion phase towards earlier. It is interesting to see that the start ofheat release is not affected. The heat release rate is independent of thenumber of zones identical until a few degrees after TDC. It seems thatthe reactions responsible for ignition, are in this case in a kind of plateau,were a change of the temperature, does not lead to a influence in ignitiondelay. The cornbustion duration increases with additional zones, whereasthe maximum value of heat released drops. Combustion duration keepsbeing short. Looking on the results with 5 zones, it is to see, that theresolution is not enough. A discontinuity in the heat release rate can beobserved. After ignition of the hot zones, the heat release rate is inhibiteduntil the colder zones start burning.

The results with 25, 125 and 200 zones, respectively, do not differ.The number of zones, which has to be selected, depends on the standarddeviation of the initial temperature field. The higher the temperaturedifference between the zones is initialized, the higher zone resolution hasto be chosen to get smooth results.

CHAP1'ER 4. MULTIZONE HCCI MODEL 77

2010o-10

~ 1 Zone,>-------< 5 Zones,>-~ 25 Zone,>------< 125 Zone,- 200 Zone,

~ 20

o1! 10

""~ 50"'­.22 40~

~ 30o<IJ

~ 1 Zone-~-----~, 5 Zones

- --- _0 25 Zone,>-----< 125 Zones- 200 Zones

30

"2 50o

D

cronk ongle [deg) cronk ongle [deg]

Figure 4.1: Influence of the number of temperature-zones on the calculatedpressure curve (left) and the heat release rate (right) for operating pointii (1200 RPM, aT= 5K ~ 1.4 % , A = 3.8, Fuel = n-butane, reducedmechanism , CXscaling= 0.7)

4.4.2 Sensitivity Investigation of -\-Zones

Figure 4.2 shows the influence of the A zone number on pressure curve andheat release rate. Although the standard deviation has been set equal tothe temperature zone nUlllber investigation to 1.4 % of the mean value,nearly no difference can be observed. Ignition and combustion is llluchmore sensitive to thermal inhomogeneities than to inholllOgeneities in theair-fuel ratio.

The reaction rate changes several orders of magnitude in a relativeslllall temperature range (typically frolll 600K to 1500K), because thetemperature is in the exponent of the Arrhenius equation. Contrary, theinfluence of the concentration is in most elell18ntary reactions linear orquadratic, depending on the reaction order. To see an influence of the Azone number a larger standard deviation has to be taken. Nevertheless,usually in internal combustion engines, a correlation between temperatureand mixture is possible. In direct fuel injection, because of the coolingeffect of the evaporating fuel, an in indirect fuel injection, because ofthe different heat capacity of fuel compared to air. The first effect, isin this calculation not accounted for, because the fuel is already evapo­rated (n-butane is used) and has the same starting temperature as theair. The second effect, is accounted for, because the mixture propertiesare calculated depending on the mixture composition. The influence ofthe different heat capacity seems therefore for a homogeneous case with arelatively small standard deviation negligible.

CHAPTER 4. MULTIZONE HCCI MODEL 78

2010o-10

~ 1 Zone>- -<. 5 Zones

~ 25 Zone::;

--------- 125 Zone::;.._~ 200 Zone::;

60 r--r=====;---......--------,

Q) 30"'oQ)

~ 20

o1! 10

~ 1 Zone

" 5 Zones~ 25 Zones

>-----------<> 125 Zones

- 200 Zones

60 .....-------.----...,..----,---.....

30

Q)

540"'"'Q)

Q.

Qn

~50

cronk ongle [deg] cronk ongle [deg]

Figure 4.2: Influence of the number of A-zones on the calculated pressurecurve (left) and the heat release rate (right) for operating point ii (1200RPM, a>..= 0.05 ~ 1.4 % , A = 3.8, Fuel = n-butane, reduced mechanism, Qscaling= 0.7)

4.4.3 Sensitivity Investigation of A- and TernperatureZones

Figure 4.3 shows the influence of the resolution in the temperature andAspace. The nunlber of zones, at IVC, corresponds to the multiplicationof the temperature with the A zones. The behavior is practically identi­cal to the investigation with only variation of the thermal discretization(sec. 4.4.1), because as nlentioned above, the mixture is more sensitive onthernlal inhomogeneities then on concentration inhomogeneities.

4.4.4 Sensitivity investigation of Wall Heat Losses

Although Woschni developed his wall heat loss model for conventionaldiesel engine combustion, and therefore it has probably deficiencies forHCCI combustion, it is used in this work because of the nonexistence ofpromising alternatives. Zoran et al. [98] proposed some minor modifica­tions for HCCI. It was also tested in this work, without an improvementof the behavior. If the scaling factor (O:scaling) is decreased (Eq.4.7), thecombustion phase moves toward earlier, because of the higher zone tem­perature (see Fig.4.4. Combustion duration is decreased, because lessenergy is extracted from the system during combustion. If the scalingfactor is set to one, in this operating point, only marginal combustion isachieved. Figure 4.4 shows the significant influence of wall heat losses

CHAPTER 4. MULTIZONE HCCI MODEL 79

6060 r----.,....---.,....----.------,

~ lx 1 Zones,,' 5x 4 Zones

c 20x 10 Zonesc;::'50o-"

.,~ 40<n<n

~Cl.

30

20 '--------'-----~'----~-----'-~-----"

- 20 -10 0 10 20

cronk ongle [deg]

<:1>

~ 50

2:., 40

~., 30<no.,~ 20

o110

-10 ocronk ongle [deg]

10 20

Figure 4.3: Influence of the number of A and temperature zones on thecalculated pressure curve (left) and the heat release rate (right) for oper­ating point ii (1200 RPM, (JT= 5K ~ 1.4 %, (JJ\= 0.05 , A = 3.8, Fuel =n-butane, reduced nlechanism , Q;scaling= 0.7)

100 140

90o_scoling 0.01 0: 130 ~ o_scoling 0.01o_scoling 0.10 ., 120 0------0 o_scoling 0.10"D

80 tJ- ....•. . o_scoling 0.30 -......110 c o_scoling 0.300 o_scoling 0.50

.2 100 ------ o_scoling 0.50-" 70

.,90

~o_scoling 0.70 "2 80 o..scoling 0.70

:::J 60 o_scaling 1.00~ 70 o_scaling 1.00

<n<n 0 60., 50 .,

500. ~40 40

Ö 30.,30 . -'" 20

1020 0

-20 -10 0 10 20 -20 -10 20

crank angle [deg] crank ongle [deg]

Figure 4.4: Influence of wall heat losses on calculated pressure curve (left)and the heat release rate (right) for operating point ii (1200 RPM, 1 Zone,A = 3.8, Fuel = n-butane, reduced mechanism)

on nearly perfectly homogeneous combustion. Nevertheless, one has toadmit, that the chose of a scaling factor below 0.5, is a large intervention.Also, the use of only a single zone for this investigation, is a little un­fortunate. Eut, comparing with conventional combustion processes, werea good prediction of wall heat losses is only necessary to get the rightheat release rate and a meaningful efficiency calculation, the influence isremarkable.

CHAPTER 4. MULTIZONE HCCI MODEL 80

60 .----~---~

2010o-10

~ std. deviation 5 K, "std. deviation 10 K,~~ std. deviation 20 K

'" 30'"o'"'§ 20

o1! 10

/""

~50 ~~//.

D /.

~ 40 ,/

[ .~~ std. deviatian 5 K

30 / I~. ,. std. deviation lOK/ >-----u std. deviatian 20 K

20 '----'---->------~:------!- 20 - 10 0 10 20

crank angle [deg] uank angle [deg]

Figure 4.5: Influence of the thermal standard deviation at IVC on thecalculated pressure curve (left) and the heat release rate (right) for oper­ating point ii (1200 RPM, A = 3.8, Fuel = n-butane, reduced mechanism, CXscaling= 0.7)

4.4.5 Sensitivity Investigation of Initial Standard De­viation of Temperature

The intake flow in internal COlllbustion engines, leads to thermal inhomo­geneities in the cornbustion chamber. Experinlental investigations ?? haveshown, that the standard deviation of the temperature at intake valve closeis 5°K. Figure 4.5 shows, that increasing the thermal inhomogeneities atIVC leads to an earlier ignition. This is due to the increase of the exis­tence of zones with noticeable higher temperature then the mean value.The overall conversion decreases because of the simultaneous existence ofcolder regions.

The nlOdel allows temperature zones with a maximal temperature de­viation of the mean value corresponding to six standard deviations. Themass fraction of zones outside this regime, are included to the next allowedzone.

4.4.6 Sensitivity Investigation of Initial Standard De­viation of A-Distribution

Figure 4.6 shows the influence of standard deviation of the A-distribution.Increasing it, leads to a displacement of the high temperature reactionstowards earlier. This is due the higher reactivity of richer zones. The startof conlbustion remains unchanged. This behavior, allows the argumenta­tion, that the low-temperature reactions are not so sensitive on mixture

CHAPTER 4. MULTIZONE HCCI MODEL 81

60 r---~--~-~----, 60.----~--

:" -~; 40 L-/-'-"~-' ----,:c / ~...- std. deviotion 0.05::;, . .,.. . .•. std. deviotion 0.10

30 •..... 0 std. deviotion 0.20

o 10

~ std. deviotion 0.05~... ----" std. deviation 0.10o--..-.~ std. deviation 0.20

:ll 30o

'"~ 20

o~ 10

""~ 50.........2-'" 40"§

201020 '-:--~-----'-------

-20 -10

cronk ongle [deg] cronk ongle [deg]

Figure 4.6: Influence of the standard deviation of A at IVC on the calcu­lated pressure curve (left) and the heat release rate (right) for operatingpoint ii (1200 RPM, 100 Zones, A = 3.8, Fuel = n-butane, reduced mech­anism , O::scaling= 0.7)

compared to the high tenlperature reactions. But, it mayaiso be, thatthe chain reactions are boosted by the higher heat released in the richerzones. Concluding, it is unambiguous that temperature has a significanthigher influence the concentration of the reacting partners.

4.4.7 Sensitivity of Joint Standard Deviation in Tem­perature and A - Distribution

Now, the investigations performed in Sec.4.4.5 and are merged. Not onlya probability density function in teluperature- or A-space is analyzed, buta joint of both. The investigation starts with a standard deviation forboth of 1.4 % of the corresponding nlean value, which is in the case ofthe temperature 5°K, and in the case of the A distribution 0.05, continueswith a value of 2.8 %, which is in the case of the temperature looK, and inthe case of the A distribution 0.1, and ends with a value of 5.6 %, which isin the case of the temperature 20°K, and in the case of the A distribution0.2. Conlparing picture 4.7 and 4.5, nearly no difference is observable.The influence of the standard deviation of initial temperature superposesthe effect of the standard deviation of the A distribution.

CHAPTER 4. MULTIZONE HCCI MODEL 82

60 .----~-----.---~-_J

- std. deviotion in lambda & T 1.4 %-, std. deviotion in lambda & T 2.8 %

~-------~ std. deviation in lombdo & T 5.6 %

o110

'"~ 50:::;-'" 40 rL- ----.J 1

e'"'; 40<n<n

:':'0. _ std. deviotion in lombdo & T 1.4 %

30 ,___< std. deviatian in lombdo & T 2.8 %o std. deviatian in lombdo & T 5.6 %

~50

oL--~--"===-......--~~~- 20 -10 0 10 20

crank ongle [deg] cronk ongle [deg]

Figure 4.7: Influence of the joint standard deviation in A and tempera­ture distribution on pressure curve (left) and heat release rate (rig;ht) foroperating point ii(1200 RPM, 20 temperature zones, 10 A zones, A = 3.8,fuel n-butane, reduced mechanism, Q;scaling= 0.7)

4.5 Verification with Experiments

Figure 4.8 shows the comparison between the simulated and the experi­mental pressure curve (left) and the heat release rate (right), respectively,for operating point i. The cornputed heat release rate starts a few degreesearlier, but with low intensity. Therefore the peak pressure is a few barshigher and the peak value of the heat release rate also. The simulatedcombustion is a few degrees shorter. Nevertheless, the overall agreementis reasonable.

Figure 4.9 shows the comparison between the simulated and the exper­imental pressure curve (left) and the heat release rate (right), respectively,for operating point ii. The cool-flames at this operating point are for both,experiment and simulation, more pronounced. Again the simulated heatrelease starts more intensive. This leads to a higher peak pressure anda higher peak value of the heat release rate. The simulated combustionduration is also shorter then the measured one. An increase of the stan­dard deviation of the initial temperature of the zones, would lead to longercombustion duration but also to an earlier ignition. A higher standard de­viation leads to zones with a high initial temperature, which ignite earlier.Figure 4.10 shows the comparison between the simulated and the experi­mental pressure curve (left) and the heat release rate (right), respectively,for operating point iii. As in operating point ii the cool-flames are verypronounced. It seenlS that the leaner the mixture is, the better can the

CHAPTER 4. MULTIZONE HCCI MODEL 83

20 40 60

simulationexperiment

:;:0 60"t-0 40

'"L 20

0-60 -40 -20 0 20 40 60

~ 140'""~ 120

.2~ 100

e 80

110 r----';:::::::'====::;--~~~-I

10090

... 80on 70

~ 60~ 50'"E 40"-

302010o 1>.-----'---'---"----'----'----'

-60 -40 -20 0

crank angle [deg] crank angle [deg]

Figure 4.8: Comparison between the simulated and the experimental pres­sure curve (left) and the heat release rate (right), respectively, for oper­ating point i (1200 rpm, 20 temperature zones x 10 A zones, A= 3.8, (JT

= 2.5 K, (J).. = 0.05, fuel = n-butane, skeletal mechanism, O!scaling= 0.5 )

110100

simulation~ 140 :1:-: simulotion I'"90 '" experimentexperiment ~ 12080

0n 70 ~ 100

E 60 ~80::> 50 :;:'"'" 0 60'" 40 '"0- ~30 40-020 '"L 2010 )0 0

'}, .\

-60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60

cronk angle [deg] cronk angle [deg]

Figure 4.9: Comparison between the simulated and the experimental pres­sure curve (left) and the heat release rate (right), respectively, for oper­ating point ii (1200 rpm, 20 temperature zones x 10 A zones, A= 4.2, (JT

= 2.5 K, (J).. = 0.05, fuel = n-butane, skeletal mechanism, O!scaling= 0.5

cool-fiames be observed.For this operating point the pressure curve matches very weIl with the

experiment. The location of the heat release rate and the burn durationare also reasonable. Only the peak value of the heat release rate is toohigh compared to the experimental one. Figure 4.10 shows the comparisonbetween the simulated and the experimental pressure curve (left) and theheat release rate (right), respectively, for operating point iv. This is the

CHAPTER 4. MULTIZONE HCCI MODEL

110100 ~ 140

""90(l)

1:--: simulation I~ 120"- 80 2 experiment0 2 100.0 70

~ 60 280

:::l 50 ~'"'" " 60~ 40 ~

Cl. ~30 4020

0(l)

~-l ~.<:: 2010 ...-~

0 0-60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60

crank angle [deg] cronk angle [deg]

84

Figure 4.10: Comparison between the simulated and the experimentalpressure curve (left) and the heat release rate (right), respectively, foroperating point iii (1200 rpm, 20 temperature zones x 10 Azones, A= 5.4,O"T = 2.5 K, 0")., = 0.05, fuel = n-butane, skeletal lllechanism, CXscaling=

0.5 )

richest analyzed operating point. In this operating point neither for thesimulation nor for the experiments, cool flames are observable. Againthe computed heat release rate starts earlier, but at the beginning withlow intensity. A few degree after TDC there is a fast combustion witha high peak heat release rate compared to the experiments. Also thesimulated peak cylinder pressure is definitely higher than the experimentalone. Maiwald [87] already reported, that it is easier to simulate HCCrcombustion process under lean conditions than under riches one.

1'0 have the same initial and boundary conditions between experimentsand simulation is challenging. Fiveland et al. [85] made in his publicationa discussion of uncertainties in modelling and in experirnents. In this workthere are also a few uncertainties which could lead to differences betweencomputation and llleasurement. N-butane is applied continuously by agas tap and the fuel mass can only be determined by measurements ofthe exhaust gas and is therefore affiicted with an error of +- 10%. Inaddition there are llleasurement uncertainties in the cylinder pressure of+- 20 mbar and in the cylinder mass of +- 2%. If these uncertaintiesare corrected in the "right" direction, so a reasonable agreelllent betweenexperiment and simulation can be achieved also in this operating point.

CHAPTER 4. MULTIZONE HCCI MODEL 85

-- simulationf--...--. experiment

-- simulation m..fuel 90"

Il.J

11 0 r.=::::::I:===l:::::==:!::=~--'100 __ simulation

~ 90 .'-'_ experiment.! ~~ >---------< simulCllion m..fuel 90";

~ 601il 50~ 40n. JO

2010O ..........--..L.~-'-_a.----L..~....L..-.....--60 -40 -20 0 20 40 60

(;ronk; angle [deg]

~ 140"I:l

2: 120

.! 100Cl.. 80.,fIl

5l 60~ 40

1i 20-""

o-60 -40 -20 0 20 40 60

crank angle [deg]

Figure 4.11: Comparison between the simulated and the experimentalpressure curve (left) and the heat release rate (right), respectively, foroperating point iv (1200 rpm, 20 temperature zones x 10 ,\ zones, A= 3.1,(Jr = 2.5 K, 0'), = 0.05, fuel = n-butane, skeletal mechanism, CXscaling=

0.5 )

4.6 Comparison Between the Behavior of n­Butane vs. n-Heptane in Different Op­erating Points

The cetane number of n-heptane is 55 and is sinülar to the one of conven­tional diesel fuel. The cetane number for n-butane can be extrapolatedaccounting for the C-H-ratio and corresponds to 37. The octane num­ber for n-heptane is by definition 0 and the one for n-butane around 90.Therefore, an earlier ignition of n-heptane compared to n-butane is ex­pected. Picture 4.12 shows the pressure curve (left) and the heat releaserate (right) for operating point i using n-heptane and n-butane. As ex­pected the start of conlbustion is with n-heptane earlier. The cool flamesare in the case of n-heptane more pronounced. The maximum value of theheat release rate is for both cases identical. Figure 4.13 shows the pressurecurve (left) and the heat release rate (right) for operating point ii. As inthe first operating point, the n-heptane fueled engine starts combustingearlier. The difference is not as pronounced then in operating point i. Thecool flames are again for the case of n-heptane better visible as for theengine fueled with n-butane. The peak cylinder pressure is for both casesidentical.

In the richest of the investigated operating point, the n-heptane mix-

CHAPTER 4. MULTIZONE HCCI MODEL

110~ 140100 n-butane Cf>

(lJ

90 n-heptane ~ 120 n-butane

L 80 .2 n-heptane0

70 (lJ 100.D .,

~:" 60 0 80

(lJ::l 50 "'~ 0

:" 40 ~ 60Q. :"

30 -0 4020 (lJ

.<: 2010 ,., 6

0 0 ~ '. ~l

-60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60

crank angle [deg] crank angle [deg]

86

Figure 4.12: Comparison of the simulated pressure curve (left) and theheat release rate (right) with n-butane and n-heptane for operating pointi (RPM 1200, 20 temperature zones x 10 A zones,A = 3.8, eYT = 2.5 K, eY:>..

= 0.05, reduced mechanisms, CXscaling= 0.5)

110100 n-butane - 140 1:--: n-butane I0'

90 n-heptane Q) n-heptane

L 80 ~ 1200

.D 70 Q) 100

:" 60 "§80::l

~"' 50"' 0 60'" 40 ~Q. :"30 40-020 Q)

.<: 2010(1 ,,-)

0 o ...............- ;' ',ci

-60 -40 -20 0 20 40 60 -60 -40 -20 0 20 40 60

crank angle [deg] crank angle [deg]

Figure 4.13: Comparison of the simulated pressure curve (left) and theheat release rate (right) with n-butane and n-heptane for operating pointii (RPM 1200, 20 temperature zones x 10 A zones,A = 4.2, eYT = 2.5 K,eY:>.. = 0.05, reduced mechanisms, CXscaling= 0.5)

ture ignites significant earlier than the n-butane mixture. The whole com­bustion has finished for the case with n-heptane before TDC. This lead to asignificant higher pressure to the end of compression. Again, the expectedresult, that n-heptane has a better ignitability has been confirmed.

CHAPTER 4. MULTIZONE HCCI MODEL 87

20 40 60

,

~ n-butanen-heptane

..&.

<../o-60 -40 -20 0

~ 1400'>

'"~ 120.2'" 100e~ 80

~ 60e

40o

'".t:. 20

20 40 60

~.O.!;l,

n-butanen-heptane

110

10090

~ 800

70n

~ 60::>

50'"'"~ 400-

302010

0-60 -40

crank angle [deg] crank angle [deg]

Figure 4.14: Comparison of the simulated pressure curve (left) and theheat release rate (right) with n-butane and n-heptane for operating pointiv (RPM 1200, 20 temperature zones x 10 A zones,>' = 3.1, (jT = 2.5 K,(jA = 0.05, reduced mechanisms, CXscaling= 0.5)

4.7 Summary and Conclusions

The calculation with the stochastic multi zone model show, that the mix­ture is significant more sensitive on an increase of the standard deviationof temperature than on >. initialization. Temperature influences the re­action rates exponential, whereas the concentration has only a linear orquadratic influence in elementary reaetions, depending on the reaction or­der. Wall heat losses had a strong influence on the phase of combustionand its strength. The best results could be achieved by decreasing thescaling factor CXw to 0.5 of Woschni's heat loss model. A scaling of +­30% is usually needed in conventional diesel engines. The chosen numberof zones to get a sufficient resolution of the gaussian distributed initial­ization, depends on the standard deviation. The higher it is, the morezones have to be chosen to avoid a discontinuity in the heat release rate.20 temperature zones and 10 A zones, resolved, in the presented cases, thecombustion chamber sufficiently. The agreement with experiments wherefor the observed cases reasonable. The deviations are within measurementuncertainties. If the deviation are caused by measurement uncertainties,or if they are due to model deficiencies, can not be easily answered. Com­paring the results obtained in this chapter with the one obtained withthe more complex methodology applied in section 5.5, one has to admit,that a higher effort was needed in this chapter to chose the right modelconstants to fit the experiments. Nevertheless, for all analysed operating

CHAPTER 4. MULTIZONE HCCI MODEL 88

points, after choosing optimal model parameters, they have been kept con­stant. The calculations with n-heptane leaded as expected to an earliercombustion, because as known from theory, it has an higher ignitibilitycompared to n-butane. The cool flanles conlbusting n-heptane are signif­icantly more pronounced. This behavior is also none fronl theory, thatsmall alkanes have less pronounced cool flames then larger alkanes [109].In the case of n-butane the cool flames were not visible in every operatingpoint. Iida et al. [105] also noticed this behavior in experiments. Thepresented model, shows a reasonable agreement with experiments, andcan therefore be used for analyzing HeCr combustion process with exter­nal mixture fornlation. The model can easily be extended with reactionkinetics of other fuels and allows for a meaningful parametric study.

4.8 List of Symbols

SymbolBClC2

CvBQn

BBtQw

----atHHCCr

mMiNz

p

PIpzsRSTTlTw

ui

Descriptionboremodel constant wall heat lossesmodel constant wall heat lossesspecific heat at constant volumeheat release ratewall heat lossesstrokehomogeneous charge conlpression igni­tionratio crank angle to connecting rodlengthcylinder massmolar weight species inumber of zonespressurepressure at start of compressionisentropic pressurespecific gas constantpiston wayTemperaturetemperature at start of compressionwall temperatureinternal energy species i

Unitm

J/(kg·K)J/sJ/sm

kgkg/mol

Pa, barbarbarJ/(kg·K)mKKKJ/kg

CHAPTER 4. MULTIZONE HCCI MODEL 89

SymbolVVIVc

VDVH

Wi

Greek

a)..

aT

Subscriptscyl

Joverbarv

Descriptionvolunlevolume at start of compressioncompression end volumedisplacement volumedisplacement volumespecies production rate

wall heat transfer coefficientscaling factor wall heat lossescompression ratiocrank angleair fuel ratiostandard deviation ,.\standard deviation temperatureand Special Symbolscylinderspecies numbermean valuevolume

Unitm:3

m 3

m3

3mm 3

mol j (ern3 . s)

Jj(m2 . K· s)

deg.

CHAPTER 4. MULTIZONE HCCI MODEL 90

Chapter 5

CRFD Simulations withReduced Chemistry

Numerical investigations are presented and compared with experimentsregard to homogeneous-charge-compression-ignition for two different fu­eIs. N-heptane and n-butane are considered for covering an appropriaterange of ignition behavior typical for higher hydrocarbons. One fuel isdoser to diesel (n-heptane), the other doser to gasoline ignition properties(n-butane). Butane in particular, being gaseous under atmospheric condi­tions, is used to also guarantee perfectly homogenous mixture compositionin the combustion chamber. The reduced mechanisms are coupled with3D-CFD through the Conditional Moment Closure (CMC) approach inorder to predict autoignition and heat release rates in an I.C. engine. 3D­CFD with Conditional Moment Closure with n-heptane chemistry is usedto sinlulate direct injection HCCI technology with diesel. 3D-CFD withConditional Monlent Closure with n-butane chemistry is used to simulateport injection HCCI technology with n-butane. Comparison with exper­imental results for a common-rail-passenger car engine - obtained at theUniversity of Stuttgart and University for applied science Dresden - yieldgood agreenlent.

5.1 State of the Art - CRFD Modelling

In conventional diesel diffusion combustion, as the speed of the chemicalreaction is faster than the speed of the nlixing of the fuel and air, thecombustion reaction starts near stoichiometric air-fuel ratio and proceeds

91

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 92

across a wide-ranging region from lean to rich. NOx and soot are ac­cordingly generated and it is difficult to reduce these simultaneously. Tosolve this problem, it is desirable to complete the mixing process beforecombustion begins, and to burn the fuel in a lean homogeneous state. Tocomply with future emission standards, a combination of internal and ex­ternal reduction of exhaust gases is necessary. The purpose of this studyis develop and show the capability of 3D-CFD in combination with a con­ditional moment closure of the flame-turbulence interaction and reducedchemistry to predict HCCr combustion for direct injection and for portinjection (more or less completely homogeneous mixtures). To shortendevelopment time and to understand combustion processes, the use ofsimulation is increasing. The limited calculation capacities and the short­ened time from development to product need the modelling of the complexchemical and physical processes. In literature different complexity levelsto model three dimensional the HCCI combustion process can be found.In [90, 91, 92, 93] the initial conditions for detailed chemical kinetics cal­culation are taken from 3D-CFD calculations. This kind of models, arenot really CFD-HCCI models, because the main combustion is ca1culatedby a kind of multi zone model. Babajimopoulos et al. [90] simulates withKIVA-3V the gas exchange process and investigates strategies with vari­able valve actuation, anlOng other things negative valve overlap. Theyexperienced that for cases with high average temperature and with conl­bustion before TDC not nluch difference could be observed using a multizone model with temperature and phi distribution, a multi zone modelwith only temperature distribution or a single zone model. However forcases with marginal combustion, which often are cases with high EGR, thedifference was high. BabajinlOpoulos et al. validated the model proposedin [90] with experiments of a test engine in [91]. The proposed approachcould provide an accurate 10%, 50% and 90% nlass fraction burned within1-2 degrees CA. However, the nlOdel predicted near 100% combustion effi­ciency because it can not capture the cool regions in the cylinder. Aceveset al. [92] used a sinülar approach ca1culating the compression with KIVAuntil 20° BTDC without combustion and then using ten zones to ca1culatethe detailed chemistry. The ca1culations were smoother conlpared to theone with a single zone model. Similar to Babajimopoulos et al. [90, 91]and Aceves et al. [92] Amano ca1culated the intake and the compres­sion with 3D-CFD and then switched to multi zone nlOdeling to calculatecombustion. A disadvantage of this methodology is, that first a complete3D-CFD ca1culation has to be done. After that, a realistic temperature,air-fuel ratio and EGR distribution has to be extracted from the CFD

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 93

data. Then a calculation with the multi zone model can be performed.Bikas [94] developed a reduced kinetic mechanisnl and investigated theHCCI conlbustion process under different conditions with a single zonemodel. He used a representative interactive flamelet (RIF) model to cap­ture for spatial inhomogenities and compared the results with the obtainedby the OD-model for one operating condition with bad agreenlent. In thiswork, for the first time, a model is presented and validated, which con­siders spatial and temporal inhomogeneities by calculating the completehigh pressure cycle with 3D-CFD. The model can be used for direct injec­tion (the mixture in this case is not perfectly homogeneous) and also portinjection type HCCI where the mixture has asnlall standard deviation ofthe air fuel ratio, when compression starts. To solve the chemistry sourceterm only the mixture fraction and its variance is transported and reducedchemistry is solved in the mixture fraction space. The models accounts forcombustion turbulence interaction by conditional moment closure. Thismodel has been used in more fundamental research such as spray com­bustion by Mastorakos et al. [95], Wright et al. [96] and Weisser et al.[97].

5.2 Methodology of the CRFD Model withReduced Chemistry

The CMC modelling and the coupling with the commercial CFD codeStarCD used in this work, has been presented by previous works Mas­torakos et al. [95], Wright et al. [96] and [108]. Here a short summaryof the governing equations and the methodology is given. Using detailedchemistry in combination with 3D-CFD the conservation equation of lnass5.1 for each species has to be solved.

ar:p att + p. u· V"Yi - V . (pDiVYi) = Wi (5.1)

The first term on the LHS is the tenlporal change of species Yi, thesecond term on the LHS is the convection and the third ternl on the LHSis the diffusivity assuming Fick's law of diffusion with diffusivity Di . TheRHS is the species production rate by chemical reaction. and are thegradient and the divergence operators, respectively. Because turbulenceis modelled in our computation, velocity (u) and its fluctuation (u') areensemble averaged values. Conditional moments are averages, variances,etc., taken for only those members of the whole ensemble, which com­ply with a specified condition. Now we consider the conditional average

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 94

(an average, beeause our eomputation (URANS) only give a ensembleaveraged solution) and varianee of speeies mass fraetion Yi not only be­ing dependent on the loeation (x) and time (t) but also on the mixturefraetion. Although a new independent variable has been introdueed, thedimensionality of the problem ean often be redueed, assuming that notthe loeation but the mixture fraction at that loeation is important. Ae­eording to [95, 96, 99] the eonditional expeetation or average of the massfraetion Yi of species i and the eonditional expeetation or average QT oftemperature T are defined as

(5.2)

andQT(1], x, t) - (QT(X, t) I~(x, t) = 1]) - (QT 11]) (5.3)

where 1] is the sampIe variable for the eonserved sealar (in this easethe mixture fraetion) and denotes that the expectation or average of massfraction of Yi at loeation x to the time t having the mixture fraetion ~ inphysical spaee, eorresponds to the expeetation at 1] in the mixture fractionspaee. In other words, ~(x, t) must fulfill the eondition ~(x, t) = rJ andtherefore the average mass fraction of Qi at the physieal loeation x atthe time t depends only on the mixture fraction. The value of the massfraetion Yi of species i at the loeation x to the tinle t is

(5.4)

where Q(~(x, t), x, t) is the mean value and y(x,t) is the deviation whiehhas aeeording to equation 5.5 an expectation of O.

(5.5)

(5.6)

Bilger [99] inserts in equation 5.1 instead of Yi and its derivation equa­tion 5.2 and its derivation, respeetively. Following [95, 96, 99, 100], theeonservation equations for the eonditional species mass fractions (Eq. 5.6)(CMC equation) ean then be written as

pa~i + P (ul1]) \1Qi + P~ry) \1. [(u'YI1]) pP (1])]

= (wil1]) + pDi (\1~ . \1~I1]) ~

where is the probability density function (pdf). Full closure of equa­tion 5.6 requires modelling of the eonditional mean reaction rate,(wl1]) ,velocity (ul1]) , sealar dissipation rate (xl1]) = Cx . D(\1~ . \1~I1]) as weIl

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 95

as the turbulent flux. In this work the scalar dissipation rate is modelledaccording to [95, 96, 108]

_ C -"2 (X = Cx --=-~ 5.7)

K,

where Cx is set to 2, following standard practice. E is the turbulenceenergy dissipation rate, K, the turbulence kinetic energy and {'2 the vari­ance of the mixture fraction. Closure of the chemical source terms isperformed at first-order. This means, that the mean chemical source for agiven 1] is only a function of the conditional species concentration Qi(1]),the conditional temperature QT(1]) and the pressure P (Eq. 5.8).

(5.8)

The conditional turbulent fluxes are modelled with gradient fiuxes,while the conditional velocities are modelled based on a linear relationship[96] .

5.3 U sed Reactiün MechanismHeptane and n-Butane

für n-

Using the CMC approach for combustion modelling, detailed chenüstryhas to be solved for each node in the mixture fraction space. Additionalthe pdf has to be integrated for each species and each computational cellto get the unconditional species value. The use of skeletal mechanismreduces dranlatically the computational effort, without a large drop inaccuracy. A starting mechanism for n-heptane with 65 species and 285reactions [101] was succesfully reduced to a skeletal mechanism with 24species and 63 reactions (see section 3.4 using reaction path analysis.The starting mechanism for n-butane was a submechanism of the detailediso-octane mechanism of the Lawrence Livermore National Laboratory[102]. It consists of 385 species and 1895 reactions. This mechanismwas successfully reduced using heat release rate analysis of the individualreactions to a skeletal mechanism with 140 species and 453 reactions.After that, reaction path analysis has been used, to reduce the mechanismto 23 species and 63 reaction to be able to calculate with 3D-CFD in anaffordable tinle frame (see section 3.3).

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 96

5.4 Comparison of Simulations with 3D­CFD and Reduced Chemistry with In­homogeneous Experiments

The results presented in this seetion foeus on direct-injeeted, four-strokeHCCr eombustion with diesel. For the simulation the presented skeletaln-heptane meehanism is used. The model fuel n-heptane is taken, beeauseit has the same Cetane number as the diesel fuel taken in the experiments.The Cetane number is 55. The four operating points differ in the enginerevolution (RPM), the fuel mass injected, the injeetion pressure, the SOland the amount of EGR. Table 5.4 shows the eharaeteristies of the pas­senger eommon raH direet injection engine, whereas table 5.4 shows theeharaeteristies of the simulated operating points. It has to be mentioned,that the simulated operating points, do not represent best points of HCCI.This are somehow operating points, whieh had a eurious or unexpectedbehavior. To clarify the reason of this behavior simulations have beenearried out.

Analysis Operating Point 1

To aHow early injeetion without impingement of the eylinder liner thenozzle spread angle has been deereased, from 156°, whieh is the one usedin the serial engine, to an angle of 80°. Running the engine with 2000RPM, nearly the same fuH load eould be aehieved then with the serialapparatus. But inereasing the revolutions of the engine to 4000 RPM,the maximum fuH load was deereased to 5.76 IME PlI p. The fuH loadwas defined, as the load were the smoke emissions where higher then 2.5FSN, beeause this points are not applieable in a commercial passenger cardiesel engine. The simulations where carried out, to understand why thisbehavior occurred, and if it can be damped with lower swirl number. Inthe 1st and 2nd row of figure 5.1 a cut through the spray axis (side viewand top view) of A at 3° BTDC is shown. It is to see, that for the easewith 4000 RPM and the serial swirl number of 0.51, the distance fromnozzle orifice to the nlixture is the smaHest. The results without swirl,show a sligthly deeper penetration of the fuel mixture. But the differenceis nearly negligable. The case with the lowest RPM, shows the widestpenetration of the fuel-air mixtures. More air is entrained, and this ispossible the reason, why less soot is produced at lower RPM. Because thefuel injection pressure is kept constant, at a high value of 1550 bar, andtherefore the injeetion time also, the whole fuel is already injected and

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY

englne manufae- Mereedes Benzturerengme denomina- OM 611tionstroke 88.4 mmbore 88.0 mmdisplacement 537.6 cm"j

eonnecting rod 149 mmlengththermodynamic 14.7 -

eompression ratiobowl denomination M801 special shape for re-

searchswirl number (Tip- 0.51 -

pelmann)injection system Boseh eommon raH -

2nd Generationinjeetion hole num- 8 not serialberinjection hole diam- 0.104 lllm (not serial)eternozzle spread angle 80 degrees (not serial)

97

Table 5.1: Characteristics of the single eylinder research engine of theuniversity of Stuttgart

evaporated at TDC for the ease with lower RPM (see figure 5.1 3rd row,3rd eolumn). For the case with higher RPM, fuel is still injeeted afterTDC. The tumble motion, produeed by the quench flow in eOlllbinationwith the flow motion caused by the spray, transports the mixture towardsthe bowl bottom at lower RPM.

Hydroxyl (OH) is known to be a tracer of the high temperature reac­tions. Looking on the loeation of it, gives the opportunity to estimate theloeation of eOlllbustion. Figure 5.2 shows the hydroxyl eoneentration forthe base case at 4000 RPM (with swirl, F t row, 1st column), the one forthe ease without swirl at 4000 RPM (without swirl, 1st row, 2nd column)and for the ease with swirl but at engine revolutions of 2000 RPM (withswirl, 1st row, 3rd column). The eombustion occurs for the base case in anear region to the nozzle orifiee. Deereasing the swirl leads to a combus-

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 98

OP1 OP2 OP3 OP4RPM 4000 2000 2000 2000 l/minfuel mass in- 16.4 15.5 15.5 15.5 mgjected

Pinj 1550 1200 1200 1200 barSOl 25 20 35 60 deg.

BTDCEGR 0 53 60 58 barresidual gas 4 2 4 4 %NO* 211 13 7 17 ppmx

CO* 407 10000 20600 11200 ppmUHC* 115 470 1240 3073 ppmFSN* 2.36 2.87 0.06 0 -

Table 5.2: Characteristics of the investigated operating point with directfuel injection (* experimental values)

tion deeper in the bowl. The swirl influences the small droplets at the tipof the spray. In this spray region, as has been shown in section 2.5, theStokes number drops beneath 1, and therefore the droplets are deflectedby the main flow. If the gas flow has swirl, the penetration is decreased.The calculation at 2000 RPM (with swirl, 1st row, 3st column) showscombustion in a wide region inside the bowl. Because more air can beentrained less soot is expected. Overall, a reduction of the swirl will helpto decrease the soot emissions. Nevertheless, the air exploitation is for allthree cases inadequate. A large part of the air in the combustion chamber,does not participate on the combustion. It seems, that the small nozzleorifice diameter of 0.104 mm, which is adequate for a fast evaporation inHCCI nlOde, is disadvantageous for conventional diesel combustion.

Analysis Operating Point 2

Operating point 2 had in the experiment high soot emissions. The simu­lation of this case should clarify if before start of combustion a large areain the combustion chamber has a A below 0.5.

As can be seen in figure 5.3 at TDC a large area of the combustionchamber has a A below 0.5. The suspicion was therefore right. It isalso to see, that the OH concentration is high, when the temperaturereaches it maximum. Formaldehyde is produced earlier then hydroxyl.

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 99

~I ~I ~I0.1 g ~ 0.1 I ~0.1 I

RPM 4000, SN 0.51 (base) RPM 4000, SN 0.0 RPM 2000, SN 0.51

11 C '",' ., '•• ~ • , .•..•.• ,,,. .".' .,.• ".+" ,"'-,.,."""•.•

~ '~~"i) eo.2 7."C ""'" 50l! 4.o 3.D.. ""~ 10

liD °-8'b'QI~-~'O"",,-·I.:~ ." ·0···· ··'~@·-·'···4iJ-·'_··""··ao

ILambda

I......SN 0.51 RPM 4000+-+ SN 0.00 RPM 4000~ SN 0.51 RPM 2000

Lambda

ILambda

...... SNO.51 RPM4000 ........ SNO.51 RPM4000+-+ SN 0.00 RPM 4000 +-+ SN 0.00 RPM 4000~ SN 0.51 RPM 2000 ~ SN 0.51 RPM 2000)IHI( Experiment JHIE Experiment

~ ~:g ..,,'+,,+ _H.' '.•"~._.".'._"."--'.".~-'-".'.."."- ~ ~: .,"""',- '. , .•. '.0"" ."" , •••• 'T ~.. ~,..,."~,,.."""..'+.~ -, "-,,. - -"~

ru tlilO ~ ,...... 1010 ~.c 110 ~'-< 110 i~ 1(](1 ~ 0 100 1

~:g =,:i: ]"::J70 '~10

g::g :[2: i~~g :::t::::c. iilO 20

·~Z·_·· --40 _20·""'" "O-,·_····'2·0""-·_-:jQ_·_'~......: 1:_6\)-I>l' ~O"'·'4·;:'20-o "·0' 20 40 ..J60

crank angle [deg] crank angle [deg] crank angle [deg]

Figure 5.1: Operating point 1: ..\ at 3° BTDC for the base case at 4000RPM with swirl (SN = 0.51, 1S t column, pt&2nd row) , for 4000 RPMwithout swirl (SN = 0.0, 2nd column, 1st&2nd row) and for the baseconfiguration but at 2000 RPM (SN = 0.51, 3rd column, pt&2nd row).The 3rd row shows the comparison of pressure curve, heat release rate andevaporated fuel

For experimentalist, this means, that tracing OH will show the start andduration of the high temperature combustion, whereas formaldehyde is atracer of low temperature reactions. At 10° ATDC the fornlaldehyde hasnearly disappeared. In the second row of figure 5.3 the pressure curve andthe heat release rate can also be shown. It is to see, that the agreementof global values is reasonable. Nevertheless, the cool flames could not bepredicted and the heat release rate is little shorter and stronger. Thereduced reaction mechanism can predict cool flames, nevertheless it hasbeen observed, that for cases with high EGR, where the global..\ is low, thereduced mechanism has some difficulties. Conlbustion of lean mixtures,showed pronounced cool flames.

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 100

O~ 0.0

::. 4000, SN00':::.1__SN 0.51 RPM4000++ SN 0.00 RPM 4000~ SN 0.51 RPM 2000~ Experiment

OH

RPM 4000, SN 0.0

..........SN 0.51 RPM 4000++ SN 0.00 RPM 4000~ SN 0.51 RPM 2000~ Experiment

I OH / 0.2E.j)2iRPM 2000, DZ 0.51

........ SNO.51 RPM4000++ SN 0.00 RPM 4000*'* SN 0.51 RPM 2000

crank angle [deg] crank angle [deg]

1tO ~"-" .",., _'0 _._-'-'.' - - ,.,":"

........ 100" .,".",,no,,,,,.e':. 9D: '/- ... I.2 '0:...~ 50-- 40·'~ >0'

c.. "". i~ 10 .CD D" 0' ~' 1"i' "~"r e-.J ,

00 ~ao...oloO-i!CIO 4080

crank angle [deg]

Figure 5.2: Operating point 1: Hydroxyl concentration (OH) at 17° ATDCfor the base case at 4000 RPM with swirl (SN = 0.51, 1S t column, pt row),for 4000 RPM without swirl (SN = 0.0, 2nd column, 1st row) and for thebase configuration but at 2000 RPM (SN = 0.51, 3rd colunln, pt row).The 3rd row shows the eomparison of pressure eurve, heat release rate andevaporated fuel

Analysis Operating Point 3

Operating point 3 seemed to be an optinlal point, if it had not the highcarbon-monoxide emissions. The question was, are the CO emissions ere­ated in the squish region? Before we analyze that, we will make a shortremark about the high sensitivity of combustion on high EGR rates. Inexperiments, has been found, that changing the EGR rate of only 1 %leaded to a strong change in eombustion. This sensitivity is due to thelow global A at this high rates. When the EGR rate is somehow be­tween 50% and 60%, depending on the operating point, the global Areaehes nearly the value of 1. It this is the case, no eombustion will oc­euro It is somehow astonishing, that the border is so sharp. More, in thecombustion ehamber, the mixture is not homogeneous, so there will existregions with air excess and others without. Additionally, and this makes

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY

~I VA 0.779

i< %.'~ lOt I E-4

---0.1 2000.2E·

Lambda3

temperature OHTDC 10ATDC 10ATDC

101

Formaldehyde

5ATDC

0.73E·3 i0.S4E.2

1

100 150 ,"' +'" _. +"",."._"_".,,.

!lO ........ Slmulalion :;g: Slmulatlon'jij 80: +-+ Experiment ~ '20 c +-+ Experiment

~:~/\ J~:~~~ ~ ::J ....... 70 ~

11140~ ~~60-V... ""., " "I ~O; III .

'40- I -a. 20" .... - 30- l-1O~ -.",,; 20- "

o_!:: -40 . ·-20 ~ Ö- ro .w ic 'g:: ob L! j 9 _l 'i Ji! M..MAjk

-60-40-20 0"" 40 60eran angle [deg] erank angle [deg]

Figure 5.3: Operating point 2: ). at TDC (1 st colunln, pt row) , tenlper­ature at 10° ATDC (2 nd column, pt row) , hydroxyl concentration at 10°ATDC (3rd column, pt row) , fornlaldehyde concentration at 5° ATDC1st COlunln, 2nd row) , conlparison between simulated and experimentalpressure curve and heat release rate ( 2nd&3rd column, 2nd row).

this behavior really amazing, the same behavior has been experienced ingasoline HCCI engines, with internal exhaust gas trapping [110]. In thistype of engines, the mixture, because of an earlier injection and betterevaporation properties of the fuel, should be more homogeneous. Figure?? shows the sensibility of the phase of combustion on the EGR rate.The simulation shows the same sensibility as experiments. The EGR ratefor the experiment was 60%. At this EGR rate the simulation did notburn. Nevertheless, the measurement of the experimental EGR rate hasan measurement uncertainty of +- 5 %, so that the achieved results arereasonable.

Figure 5.5 shows). at TDC, the temperature and the carbon-monoxideemissions 41° ATDC and the pressure curve and heat release rate compar­ison between sinlulation and experiment. Comparing local ). of operatingpoint 2 with operating point 3 prior to conlbustion, it can be clearly deter­mined, that the mixture in the second case is much leaner. This explainsthe big difference in soot emissions, where for operating point 2 the mea-

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 102

........ simulation (EGR 55 %)++ simulation (EGR 56 %)13--8 simulation (EGR 57 %)x-x Experiment (EGR 60 %)

100

90

's....' BQca

70.c.......Q.) 60

s.... 50:::scn 40cnQ.) 30s....a. 20

10

0-60 -40 -20 0 20

crank angle [deg]40 60

Figure 5.4: Operating point 3: Influence of EGR rate on phase of com­bustion (Experimental EGR was 60%)

sured smoke filter number is 2.87 whereas in operating point 3, it is 0.06.The CO emissions are produced in the near wall region. It is in a firstview astonishing, that the used model can predict in a physical expectedway, the region of pollution formation.

The used model, reduces the dimensionality of the problem, by makingthe simplification, that every point with the same mixture fraction has thesame expectation of species concentration. In an mathematical way thismeans:

(5.9)

Where the first term in the RHS is the diffusion of species a in 'J]

(mixture fraction) space and the second term is the species productionrate for this 'J] (mixture fraction). The species production rate is only a

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 103

~I0.5

lambda

TDC

100 ,... ,,'" ""'.~;_.""".~-~.'~'--I'"""-'-.' r""·"

"'"- ---"Simulatlon1ij ,,~ ++ Experimente... 70-

(I) '" "S 51] ~lJl •• r~ ,ro ~

C. 20 r1~ I,"'

o ...............I........o...------.........,,"'~"', •• \ • ,,_.~_.J__~.""""""'"-ftO --l-O -.:1(1 0 20 "0. GO

crank angle [degJ

temperature

41ATDC

CO41 ATDC

O.77E.J0.1 E-1

Figure 5.5: Operating point 3: A at TDC (1st column, pt row), tempera­ture at 41 0 ATDC (2 nd column, 1st row), carbon monoxide concentrationat 41 0 ATDC (3 r-d column, 1st row) and cornparison between simulatedand experimental pressure curve and heat release rate ( 1st&2nd column,2nd row).

function of the TJ and implicitly of the corresponding tenlperature at theobserved TJ. The diffusion in TJ space is modelIed according to the AMCmapping model [96].

(NITJ) = NoG(TJ)G(TJ) = exp(-2[erj-l(2TJ _1)]2)

XNo = 1 -

2 Jo G(TJ)P(TJ)8TJ

(5.10)

(5.11)

(5.12)

The mean scalar dissipation rate X is computed from the mean turbu­lence quantities of the flow field.

(5.13)

Here, we use cx =2.0 following standard practice and in the absence ofany detailed measurements of mixture fraction variance that could allow

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 104

adjustment of this constant. Therefore the diffusion (or scalar dissipation)is also a mean value of the observed flow field. The reason, why uncom­pleted combustion is found in the near wall zone is the following. First,the region needs to have fuel (in effect nlixture fraction). That is why weobserve CO emissions in the piston region and not in the cylinder headregion. Second, the expected quantities following equation 5.9 are inte­grated over a probability density function. The used probability densityfunction is a beta function distribution give by [100]

where

r~l(l _ )8-1P(1]) = 1] I

b1] ; 0 < 1] < 1 (5.14)

h _ (I 1]1'-1(1 -1])8-151] = r(r)r(s) (5.15)io r(r+s)

and r(x) is the Gamma function. The parameter rand s are directlyrelated to the mixture fraction mean, (~), and variance,((/2), by

1 - (~)r = (~)( (~) ((/2) - 1);

1 - (~)

s = r (~) (5.16)

For the mixture fraction variance,(/2 the following transport equationis solved

"2o "2 0 _ "2 J-lt ~ 2J-lt O~ E "2-(p( ) = --[P'Uj~ - (pDg + -)-,-] + -(-) - CxP-~ot OXj (}g OXj a g OXj K,

(5.17)where ag should be assigned to the same value as the Schnlidt number.After this elevated number of equations, the explanation is really sinlple.Assuming that the nlixture fraction is equally distributed, this will be thecase in section 5.5, the only difference in a OD-CMC approach betweena cell in the near wall region and a cell in the center of the combustionchamber, is the mixture fraction variance (2. As can be seen in equation5.17 the mixture fraction variance is strongly influenced by the turbulentviscosity J-lt. The turbulent viscosity is defined in a K,-E nlOdel as following:

C pK,2ILt = !J (5.18)

E

In the vicinity to the wall molecular and turbulence effects are of com­parable magnitude [45]. Because the turbulent viscosity inside the com­bustion chamber is three orders of nlagnitude higher than the molecular

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 105

viscosity, in near wall region the viscosity is significant lower than in thecenter of the combustion chamber. Because the mixture fraction varianceproduction, assuming homogeneous mixture, is increased with higher vis­cosity, if the viscosity drops to laminar level, the mixture fraction variancehas also to drop. This can be seen plotting the mixture fraction varianceand the turbulent viscosity. A low mixture fraction variance, leads toa sharp pdf around the mean value. If at this location the mixture islean, integrating over the pdf, makes that lean conditions are significantmore considered for. Burning under lean conditions leads to incompletecombustion and therefore to carbon monoxide and unburnt hydrocarbons.The model predicts at the wall the emissions caused by the extinction ofthe lean flame and not explicitly the one caused by the cold wall. Nev­ertheless, the temperature of this lean region is also much colder in themixture fraction space then the nlean temperature. It is to expect, thatthe model underestimates the emissions due to uncomplete combustion.

Analysis Operating Point 4

The investigated question in operating point 4, is difficult to be answeredwith the presented models because, as has been shown in section 2, thereexist sever model or numerical uncertainties concerning spray sinlulation.The simulations give reasonable overall mixture prediction, but if detailsabout the spray are needed, the results have to be interpreted carefully. Inexperiments an inlpingement of the cylinder liner with fuel was supposed.This was assunled to cause an oil dilution. Could the sirnulation verifythis behavior?

Figure 5.6 shows the liquid spray and the A at 49° BTDC, at 40°BTDC, at 30° BTDC, at 20° BTDC, at 10° BTDC and at TDC. It isto see, that the spray penetrates far into the combustion chamber andimpinges the bowl at 40° BTDC. The simulation could not confirm thesupposition by the experiment.

5.5 Comparison of Simulations with 3D­CFD and Reduced Chemistry and Ho­mogeneous Experiments

In this section fully premixed n-butane HCCI combustion is three dimen­sional simulated. The investigated engine is a HD diesel engine with 1991cm3 displacement. The engine characteristics can be observed in table 5.5.

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 106

I I49 BTDC 40 BTDC 30 BTDC

I EQ"6 I ~I0.53 1.183

20 BTDC 10 BTDC TDC

Figure 5.6: Operating point 4: A and liquid spray at 49° BTDC, at 40°BTDC, at 30° BTDC, at 20° BTDC, at 10° BTDC and at TDC

The investigated operating point has an indicated mean effective pressureof the high pressure cycle (without gas exchange) of 4 bar operating witha global A of 5.13. More details about the operating point can be see intable 5.5. N-butane is injected at a great distance from intake port toguarantee a perfectly homogeneous mixture.

On the computational side, a homogeneous mixture, with mean mix­ture fraction of 0.013 and a standard deviation of 10% of this n18an valueis initialized. To guarantee a fully uncorrelated initial mixture state, arandom number generater has been implemented, which produces num­ber with a gaussian distribution and given standard deviation and meanvalue. The generator is the same as the used in chapter 4. Neverthe­less, according to chapter 4 not a great influence of the A fluctuation isexpected.

Figure 5.7 shows the comparison between the measured and the sim­ulated pressure curve. It can be seen, that the start of combustion of thesimulation, is a few crank angle degrees later and the simulated combus­tion seems to be shorter. The simulated heat release rate shows weak coolflames, which agrees with the results presented in chapter 4, where thecool flames of n-butane could only be identified in lean combustion. Thediscrepancy between simulation and experiment, could be due to the use

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY

engine manufac- Mercedes Benzturerenglne denomina- OM 611tionstroke 150.0 mmbore 130.0 mmdisplacement 1991 cm:1

connecting rod 0.273 mmlengthcompression ratio 17.2 -

swirl number (Tip- 0.00 -

pelmann)

107

Table 5.3: Characteristics of the single cylinder research engine of theHTW Dresden

OP1RPM 1420 l/minfuel mass injected mgSOl port injectionEGR 0 %residual gas 4 %NO* 1 ppmxCO* 2024 ppmUHC* 894 ppnlFSN* 0.0 -

Table 5.4: Characteristics of the investigated operating point with homo­geneous mixture (* experimental values)

of only a OD-CMC model. This means that, the initialization of chem­istry is done with a single mean temperature for the air side, and a singlemean temperature for the fuel side. In this investigation, both, air andfuel, have the same initial temperature, because it is supposed that duringintake the temperature of both relax to a mean value. After start of com­bustion, the temperature in the mixture fraction space, evolves accordingto the chemistry for the specific nlixture fraction and a overall pressurecontribution from the CFD side, which is due to compression/expansion

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 108

60

4

150

350 '--

500 r' ,,,' ,,,''50 [+--+,"," "O[;O,,,,J. 1-''''---400 :-

j 300 -

'"2. 250

'"~ 200

130:'" L--='--'..J

120 L

I ~~~ 'll~ 80~ 70~ 60~ 50 f-

40 '-­30 :...

20 =- .0,02'

10 te-e·e-30,1, , Ln,,"', l I I • l • J o~.......L-~'-"

-60 -40 -20 0 20 40

crank angle [deg]

Figure 5.7: Comparison of pressure eurve (left) and heat release rate(right) between simulation and experiment for operating point i (RPM1420, IMEPHP=4.02 bar, A 5.13, n-butane, homogeneous)

lambda 4.33 temperature 1000 co 0.0

......simulation- experiment

1:"------r--------;r---. 130 ~"- 12C ~ftI i10 ~.0 '00 l'";;; ""00 t I

~ :~ I~ :fL. 30 ~

a. ~~."dD i.. •. , ."".,~ ., .. , ." ••.• ,'_",•.~ •. ._.• _~,_"'_-80 -4G _21 D 2D 40

"'CO ,900~

100:~"""~ ""'r~-,a:: 4Cl(J ~0::: ,..;I I!M~

~QO ~

o_i:---<o::::--'b"".JI'o·!O·'~'·2C-'''·''-'..:o ' ~

crank angle [degj crank angle [deg]

Figure 5.8: 3D-simulation of homogeneous n-butane eombustion at 20°BTDC (RPM 1420, IMEPHP=4.02 bar, A 5.13, n-butane, homogeneous)

and eonlbustion. Therefore, having the same mean mixture fraction, thesame ehemistry is expeeted, independent if the fuel is in the center of theeombustion ehamber or near a wall. Nevertheless, as ean be seen in figures5.8,5.9,5.10 there is a strong influenee of the loeation in the eombustionehamber in combustion behavior. The reason will be explained a few linesbelow. Figure 5.8 shows the state of the mixture before ignition oeeurs.

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 109

lambda /.33

..,16.5

temperature 1100

1000I

co 0.0015

~I.

' .'!II"'w, .... ~,;., -.l.. . _."" ,: ..

~ , ','..," ' .,,, ' ".--.'\ ... " ',:':, -:, ';.~. .~

0.011 0.0098

......simulation- experiment

:: ~-~'~"'~""""''''''"'.'''''+,.,.+.•"j ,••• - ••••••• '-.-.- •• " ......~~'-••~ -: [.~.-.-.,.__.~~-. ",- .~-.~-I~~~.-.-.-,."J

,...., 130 I

m~~ ...... soor ~..c1oo <7(lO~ -!-; O. l.2 so.,S;~ ::2o!ilO~lIl"· o:: ·flIl". 0:: ,~ : I *~

C. : 100 'i-:~~...~~~;~ ~~ ~ 0 ~ ~ ~

crank angle [degl crank angl e [degl

Figure 5.9: 3D-simulation of homogeneous n-butane combustion at 13°BTDC (RPM 1420, IMEPHP=4.02 bar, >. 5.13, n-butane, homogeneous)

The mean value for >. is 5.13, which corresponds to a fuel concentrationof 0.013 [kgjkg]. The temperature is in the center of the combustionchamber around 1000 K, whereas in the crevice and in the region nearto the cylinder liner it is around 900K. After the cool flame (figure 5.9)the temperature has increased around lOOK, but it has to be said thatapart of this lOOK is caused by the compression. Carbon monoxide isalready detectable, and the fuel concentration decreases, whereas >. in­creases. Most part of carbon monoxide is created in the cylinder center,where combustion is stronger. At TDC (figure 5.10) combustion is alreadyover. The conlbustion duration, including the cool flanles, is of the orderof 200 degrees, whereas looking only on the high temperature reactions,the combustion duration is of the order of 100 degrees. Changing thescaling for the fuel concentration, it can be seen, that some part of thefuel, in the vicinity to the wall did not burn. Also later in the expansion,unburned fuel will be visible in this regions. Contrary to the cases withdirect injection, the largest amount of carbon monoxide is in the center ofthe combustion chamber and not in the squish zone or in the crevice. Laterin the expansion carbon monoxide concentration will slowly decrease, butstill exist.

As mentioned above, the model can account for emissions formationdue to incomplete combustion in the vicinity of the walls. This is, asdetailed explained, deduced and shown in section 5.4, due to the drop of

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 110

lambda> 7.0

Itemperature co E-3

...... simulation- experim ent

~= .' ... '. .0"""''''',,_.,,', "•.••""_"".""'.""~""_.'.""_._ _: ~ .,,"'_,,~""."'_, ,.,_,,'•. _ ._. "! _,,_ ,...• ,.. _.... '~, _'_"~

~ I~ 120 WQ ~ ~R:I 110 - 1"""""1 700 ~ , J

1!2. ': : ~ "",.~ I 1l!! ;: '..., "",: I 1~ .. :i[""'~!i

l ~, , ,..,·I~Ul~..~~j~ ~ ~ 0 m ~ ~ ~ -~ 0 ~ ~ ~

crank angle [deg) crank angle [deg]

Figure 5.10: 3D-simulation of honlogeneous n-butane combustion at TDC(RPM 1420, IMEPHP=4.02 bar, ,\ 5.13, n-butane, homogeneous)

mixture fraction variance with decreasing turbulent viscosity. The modelpredicts at the wall the emissions caused by the extinction of the leanflame and not explicitly the one caused by the cold wall. Nevertheless,the temperature of this lean region is also much colder in the mixturefraction space then the mean temperature. It is to expect, that the nlOdelunderestinlates the emissions due to incomplete combustion.

5.6 Summary and Conclusions

The presented model, with skeletal chemistry and turbulence flame inter­action closure with conditional moments showed reasonable agreement toexperiments, cornparing global quantities as pressure curve and heat re­lease rate. This are the first simulations, as far as r am aware, which usesthis methodology for simulating direct injection HCCr diesel combustionwith EGR rates up to 60%. The model is able, to account for the highsensitivity on the change of the EGR rate by only a few percents, whenburning at this high EGR rates. The model predicts the incomplete com­bustion in the vicinity to the wall, due to relaminarization of the flame.The first simulations simulating nearly perfect homogeneous compressedignited combustion with the presented methodology are shown. Again inthe vicinity to the wall, incomplete combustion occurs due to the absence

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 111

of turbulence which helps to complete the combustion. If this is the realphysical reason, why incomplete combustion occurs in the near wall re­gions can be questioned. Because for perfectly homogeneous combustion,Damköhler number is « 1, and therefore the characteristic chemical timescale determines combustion behavior. An enhancement will be the useof two [96, 108] or even three dimensional CMC. For engine calculationsthis is at the moment computational to expensive. Bilger and Klimenko[100] proposed some enhancement of the model with additional terms forthe effects of conductive/convective heat transfer at the wall, but also incombination with a more dimensional CMC approach.

5.7 List of Symbols

Symbol3D-CRFD

ATDCBTDCCxGMD·~EGRHeCr

IMEPHP

QT

Description U nitthree dimensional computational reac-tive fluid dynamicsafter top dead centerbefore top dead centermodel constant scalar dissipation ratemodel constant turbulence modeldiffusivity species iexhaust gas recirculation %homogeneous charge compression igni-tionindicated mean effective pressure of the barhigh pressure cydeprobability density functionprobability density functionconditional expectation of reactive kg/kgscalar aconditional expectation of reactive kg/kgscalar iconditional expectation of temperature kg/kg

CHAPTER 5. CRFD WITH REDUCED CHEMISTRY 112

Symbol Description UnitRIF representative interactive flameletRPM engine revolutions per minute l/sSN swirl number TippelmannSOl start of injection degTDC top dead centeru velocity m/sYi mass fraction species i kg/kgYi(X,t) deviation of reactive scalar i kg/kgWo: species Ct production rate kg/(m3

. s)w· species i production rate kg/(m3

. s)t

Greek

X scalar dissipation rateE dissipation rate m 2 /s3

7J sample space variable for ~ kg/kgK, turbulent energy m 2 /s 2

A air fuel ratio

Mt turbulent viscosity N· s/m2

p density kg/m3

{jg Schmidt number

~ conserved scalar or mixture fraction kg/kg('2 variance of conserved scalar or mixture kg/kg

fractionSubscripts and Special Symbols

fluctuationsfavre averaging

0 ensemble averaging(xIY) conditional expectation of x on y

Chapter 6

SummaryandConclusions

In this final chapter, present work and major conclusions are sUlllmarized,and suggestions for future work are made.

Summary

The presented work has examined different modelling aspects of dieselengines, emphasizing the requirements needed for homogeneous chargecompression ignition COlllbustion sinlulations. The main in-cylinder simu­lation processes in direct injection diesel engines are, mixture fornlation,which includes spray and air fiow simulation, ignition and combustion.This processes can not be viewed as isolated, since the state of the mixtureinfiuences the ignition and the mean fiow fiuctuations the combustion be­havior. The presented models use skeletal chemistry which includes auto­ignition chemistry, therefore ignition and combustion are treated with thesame models.

Spray simulation is achallenging issue. This work nlade investigationsconcerning numerical deficiencies. It could be shown, that using nearlyorifice resolving meshes and an alignment of the mesh in spray axis di­rection, physical reasonable results can be achieved. It could be shown,that the Stokes number at nozzle exit, is significant higher then one, andtherefore the droplet is not infiuenced by the air fiow and its turbulence.Travelling on the spray axis to the tip of the spray, the Stokes numberstarts to decrease and reaches in spray tip region unity, or even below. Be-

113

CHAPTER 6. SUMMARY AND CONCLUSIONS 114

cause the droplets at spray tip are small, now the mean fiow can inftuenceits trajectory. It was shown, that using coarser resolved grids, the Stokesnumber was lower, and therefore the spray was (unphysical) inftuenced bythe turbulence of the surrounding fiow. It was also shown, that using un­derresolved grids, leads to a large velocity gradient between the dispersedand the continuum phase. This increased velocity gradient leads to higherdrag forces and impedes correct droplet penetration. Astonishing, was thelarge inftuence of the alignment of the numerical grid compared to spraydirection. Using a grid which was not aligned in grid direction, in thespecial case of 45 degrees, no mesh dependence was observed, and spraytip penetration was underpredicted, even if the mesh resolved the nozzleorifiee.

Using analysis of the heat release rate of every individual reaction, amethodology, as mueh I am aware, has never been published before, adetailed chemieal reaction mechanism of n-butane, containing 385 speciesand 1895 reactions could be redueed, within a few iterations, to a skele­tal one, with 140 species and 456 reaetions. The mechanism showed,compared to the initial detailed one, over a wide range of A and eom­pression ratios excellent agreement. This methodology eould not be used,to reduee the meehanism more. Therefore, reactions path analysis witheonsequent speeies elimination, reaction elimination and lumping of ele­mentary reaetions to global ones, leaded to the smallest, as nmeh as Iam aware, n-butane mechanism for auto-ignition and combustion. Themechanism eonsists of 22 species and 57 reaetions and showed comparedto the detailed one over a wide range of A and compression ratios exeellentagreement. The ca1culation of a single PSR with a physieal ea1culationtime of 0.05 seconds, eould be dropped, frorn initially 15 minutes to a fewseconds. Reaction path analysis with consequent speeies elimination, re­action elimination and lumping of elementary reaetions to global ones, wasalso successfully used to reduee a starting skeletal n-heptane mechanismwith 67 species and 265 reactions, to the smallest, as nluch as I anl aware,skeletal n-heptane mechanism for auto-ignition and combustion, which isconlpletely described with Arrhenius equations and does not have anysteady state assumption. The mechanism has 24 speeies and 63 reactions.There do exist smaller ones, but with steady state assumption, which canbe, either they are snlaller, computational more expensive.

A stochastie model, which uses various perfectly stirred reaetors eon­nected through pressure work which each other, was presented. The eal­culation with the stoehastic multi zone model showed, that the mixtureis significant more sensitive on an inerease of the standard deviation of

CHAPTER 6. SUMMARY AND CONCLUSIONS 115

temperature than on Ainitialization. Temperature influences the reactionrates exponential, whereas the concentration has only a linear or quadraticinfluence in elenlentary reactions, depending on the reaction order. Thechosen number of zones to get a sufficient resolution of the gaussian dis­tributed initialization, depends on the standard deviation. The higher itis, the more zones have to be chosen to avoid a discontinuity in the heatrelease rate. The agreement with experiments where for the observedcases reasonable. The deviations are within measurenlent uncertainties.If the deviation are caused by measurement uncertainties, or if they aredue to model deficiencies, can not be easily answered. Comparing theresults obtained with the multi zone model with the one obtained withthe more complex methodology of CMC combined with 3D-CFD and re­duced chenlistry, one has to admit, that a higher effort was needed withthe multi zone nlethodology to chose the right model constants to fit theexperiments. Nevertheless, for all analyzed operating points, after choos­ing optirnal model parameters, they have been kept constant. The coolflames combusting n-heptane are significantly more pronounced then theones of n-butane. This behavior is also none from theory, that small alka­nes have less pronounced cool flames then larger alkanes. In the case ofn-butane the cool flames were not visible in every operating point, whatalso agrees with experimental experience. The presented model, shows areasonable agreement with experiments, and can therefore be used for an­alyzing HCeI conlbustion process with external mixture formation. Themodel can easily be extended with reaction kinetics of other fuels andallows for a meaningful parametric study.

The presented model, with skeletal chemistry and turbulence flame in­teraction closure with conditional moments showed reasonable agreementto experiments, comparing global quantities as pressure curve and heatrelease rate. This are the first simulations, as far as I am aware, which usesthis methodology for simulating direct injection HCCr diesel combustionwith EGR rates up to 60%. The model is able, to account for the highsensitivity on the change of the EGR rate by only a few percents, whenburning at this high EGR rates. The model predicts the incomplete com­bustion in the vicinity to the wall, due to relanlinarization of the flame.The first simulations simulating nearly perfect homogeneous compressedignited conlbustion with the presented methodology are shown. Again inthe vicinity to the wall, incomplete combustion occurs due to the absenceof turbulence which helps to complete the combustion. If this is the realphysical reason, why incomplete combustion occurs in the near wall re­gions can be questioned. Because for perfectly homogeneous combustion,

CHAPTER 6. SUMMARY AND CONCLUSIONS 116

Damköhler number is « 1, and therefore the characteristic chemical timescale determines combustion behavior.

Conclusions

Regarding spray simulations, it can be said, that the widely usedlagrangian-eulerian methodology for spray calculations with its submod­els for droplet breakup, evaporation, coalescence, etc., do a reasonablejob on nearly orifice resolving meshes in the near nozzle region combinedwith grids which are aligned in spray axis direction. In engines simula­tions, this constraints are rarely fulfiUed, so that major deviance to theexpected physical correct behavior exist.

The presented reduction techniques are easy to use, and do not needdeep chemical knowledge, to be applied. Using them, fast skeletal mech~anisnl for n-butane and n-heptane were developed, which agree very weIlover a wide range of A and compression ratio with the starting mechanism.They were successfully used in the presented multi zone model and the3D-CFD-CMC model.

The presented multi zone model, agreed reasonable with the exper­iments. Nevertheless, one has to admit, that the physics ongoing in acombustion chamber, are quit simplified, and the model is useful for anal­ysis and potential calculations. Predictions have to be considered withsome tolerances.

The presented OD-CMC model with reduced chemistry showed excel­lent agreement to experiments. No model tuning, outside nleasurementuncertainties is needed, an the predicted global quantities, as heat releaserate and pressure curve are good. The nlOdel predicts incornplete com­bustion in the vicinity to the wall, due to relaminarization of the flame.If this is the physical main reason, why incomplete conlbustion occurs innear wall regions, can be discussed. A major part, will probably also be,due to the colder temperature in near wall regions.

Suggestions for the Future

Regarding spray sinlulation three alternative ways are proposed for thefuture. First: A new methodology for spray simulation is developed, whichis not influenced by the use of arbitrary grids. This can be probably findin Neverland. Second: Enhanced grid generators are developed. The gridresolves in the near nozzle region nearly the nozzle orifice. The generatedmesh is aligned in spray axis direction. This method is promising, and

CHAPTER 6. SUMMARY AND CONCLUSIONS 117

already some enterprises have seen the need, and brought a product intomarket [135]. Third: Multi grid methods are developed, where the sprayis calculated in an independent mesh, and every time step, a kind ofmapping is fulfilled. For collision model, such suggestion has already beenimplemented [136]

The reaction path analysis is a powerful tool, for reducing chemistry.The skeletal mechanism which are achieved, represent the nlain chemistry.At the moment, the user has to select the species he wants to eliminate,and the reactions he wants to lunlp. It would be nice, to develop a tool,which reduces using this nlethodology automatically. So, arbitrary diffi­cult mechanism could be reduced. It is difficult to estimate, if such a toolis realizable.

The derived skeletal mechanism for n-heptane could be enhanced with"simplified" soot chemistry, to alow also predictions of soot emissions.

An enhancement of the presented CMC model will be the use of twoor even three dimensional CMC. For engine calculations this is at themoment computational to expensive. Also an enhancement, to accountfor local wall heat losses, would be recommendable. Bilger and Klimenko[100] proposed some enhancement of the model with additional terms forthe effects of conductive/convective heat transfer at the wall, but also incombination with a more dimensional CMC approach.

CHAPTER 6. SUMMARY AND CONCLUSIONS 118

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[114] VIf Christina Müller, "Reduzierte Reaktionsmechanisnlen für dieZündung von n-Heptan und iso-Oktan unter motorrelevanten Be­dingungen", Ph. D. Thesis, Rheinisch-Westfälischen TechnischenHochschule Aachen, 1993

[115] E. Ranzi, A. Sogaro, P. Gaffuri, G. Pennati, C.K. Westbrook, W.J.Pitz, "A New Comprehensive Reaction Mechanism for Combustionof Hydrocarbon Fuels", Combustion and Flame 99:201-211, 1994

[116] Elisio Ranzi, Tiziano Faravelli, Paolo Gaffuri, Angelo Sogaro, "Low­Temperature Combustion: Automatie Generation of Primary Oxi­dation Reactions and Lumping Procedures", Combustion and Flame102:179-192, 1995

[117] R. Minetti, M. Ribaucour, M. Carlier, C. Fittschen, L.R. Socher,"Experimental and Modeling Study of Oxidation and Autoignitionof Butane at High Pressure" , Combustion and Flame 96:201-211,1994

[118] F. Battin-Leclerc, P.A. Glaude, V. Warth, R. Fournet, G. Scacchi,G.M. Come, "Computer tools for modelling the chemieal phenomenarelated to combustion" , Chemical Engineering Science 55 2883-2893,2000

[119] Shigeyuki Tanaka, Ferran Ayala, Janles C. Keck, "A reduced chem­ieal kinetic model for HCCr combustion of primary reference fuel ina rapid compressio machine", Combustion and Flame 133, 467-481,2003

BIBLIOGRAPHY 130

[120] T. Rente, V. L Golovitchev, L Denbratt, "Numerical Study of n­Heptane Spray Auto-Ignition at Different Levels of Pre-IgnitionThrbulence", The Fifth International Symposiunl on Diagnosticsand Modeling of Combustion in Internal Combustion Engines (CO­MODIA 2001), July 1 4, 2001

[121] N. Peters, G. Paczko, R. Seiser, K. Seshadri, "Temperature Cross­Over and Non-Thermal Runaway at Two-Stage Ignition of N­Heptane", Combustion and Flame 128:3859, 2002

[122] Massias, A., Diamantis, D., Mastorakos, E., Goussis, D.A., "Globalreduced mechanisms for methane and hydrogen combustion with ni­tric oxide formation constructed with CSP data", Combustion The­ory Modelling 3, 233-257, 1999

[123] Massias, A., Diamantis, D., Mastorakos, E., Goussis, D.A., "An Al­gorithm for the Construction of Global Reduced Mechanisllls WithCSP Data", Combustion and Flame 117:685-708, 1999

[124] Lam, S.H.,"Using CSP to understand complex chemieal kinetics",Combustion Science and Technology 89, pp. 375-404, 1993

[125] Lam, S.H, Goussis, D.A., "The CSP Method for Simplifying Ki­netics", International Journal of Chemical Kinetics 26, pp. 461-486,1994

[126] Gorban, A.N., Karlin, LV., Zinovyev, A.Y., "Constructive methodsof invariant manifolds for kinetic problems", Physics Reports 396,194-403, 2004

[127] James A. Miller, "Chemkin 11: A FORTRAN chernical kinetics pack­age for the analysis of gasphase chenücal and plasma kinetics" , San­dia National Laboratories, Livermore, USA

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BIBLIOGRAPHY 131

[130] Ogink, R. and Golovitchev, V., Reaction Mechanisms for NaturalGas and Gasoline in Homogeneous Charge Compression Ignition(HCCI) Engine Modeling , Presented at 6th Int. Conf. on Enginesfor Autmobile, SAE Naples, ICE2003, Italy, September, 2003

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[132] Warth, V., Stef, N., Glaude, P.A., Battin-Leclerc, F., Scacchi, G.,"Computer-Aided Derivation of Gas-Phase Oxidation Mechanism:Application to the Modelling of the Oxidation of n-Butane", Com­bustion and Flame 114:81-102, 1998

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[134] Pizza, G.M., Wright, Y., Boulouchos K., "Evaporating and Non­Evaporating Diesel Spray Simulation: Comparison between theETAB and Wave Break-Up Model", International Journal of Ve­hicle Design, submitted for publication, 2005

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[136] Simone E. Hieber, "An Investigation of the mesh dependence of thestochastic discrete droplet model applied to dense sprays", masterthesis, Michigan Technological University, 2001

BIBLIOGRAPHY 132

Appendix A

Skeletal n-butanemechanism

CHEMKIN INTERPRETER OUTPUT: CHEMKIN~II Version 3.9 Aug. 1994DOUBLE PRECISIoN

ELEMENTS AToMICCoNSIDERED WEIGHT

1. H 1.007972. C 12.01123. 0 15.99944. N 14.0067

------------------------------------~-~~--------------------~------------------

CP HH AA R

SPECIES S G MoLECULAR TEMPERATURE ELEMENT COUNTCoNSIDERED E E WEIGHT LQW HIGH H C 0 N------------------~------~-~---------------------------------------------------

1. H G 0 1.00797 300 5000 1 0 0 02. H2 G 0 2.01594 300 5000 2 0 0 03. 0 G 0 15.99940 300 5000 0 0 1 04. 02 G 0 31.99880 300 5000 0 0 2 05. oH G 0 17.00737 300 5000 1 0 1 06. H20 G 0 18.01534 300 5000 2 0 1 07. N2 G 0 28.01340 300 5000 0 0 0 28. C4H10 G 0 58.12430 300 5000 10 4 0 09. CO G 0 28.01055 300 5000 0 1 1 0

10. C02 G 0 44.00995 300 5000 0 1 2 011. CH3 G 0 15.03506 300 5000 3 1 0 012. H02 G 0 33.00677 300 5000 1 0 2 013. H202 G 0 34.01474 300 5000 2 0 2 0

133

APPENDIX A. SKELETAL N-BUTANE MECHANISM

14. CH20 G 0 30.02649 300 5000 2 1 1 015. C2H3 G 0 27.04621 300 5000 3 2 0 016. CH3CO G 0 43.04561 300 5000 3 2 1 017. pC4H9 G 0 57.11633 300 5000 9 4 0 018. C4H800H1 302 G 0 121.11393 300 5000 9 4 4 019. C4H800H1_3 G 0 89.11513 300 5000 9 4 2 020. C4H801~3 G 0 72.10776 300 5000 8 4 1 021. pC4H902 G 0 89.11513 300 5000 9 4 2 022. C3H53 G 0 41.07330 300 5000 5 3 0 0----~-----------~-------~~~---------------------------------~~-----------------

(k = A T**b exp(-E/RT))REACTIONS CONSIDERED A b E

1. C2H3+H+02=CH20+CH20 1. 25E+10 0.0 18900.0Reverse Arrhenius coefficients: O.OOE+OO 0.0 0.0

2. H+CO+OH=CO+H20 1.02E+14 0.0 0.0Reverse Arrhenius coefficients: 2.90E+15 0.0 105000.0

3. CO+OH=C02+H 1.40E+05 2.0 -1350.0Reverse Arrhenius coefficients: 1.57E+07 2.0 21000.0

4. H+02=O+OH 1.97E+14 0.0 16500.0Reverse Arrhenius coefficients: 1.56E+13 0.0 425.0

5. O+H2=H+OH 5.08E+04 2.7 6290.0Reverse Arrhenius coefficients: 2.23E+04 2.7 4200.0

6. O+H20=OH+OH 2.97E+06 2.0 13400.0Reverse Arrhenius coefficients: 3.01E+05 2.0 -3850.0

7. OH+H2=H+H20 2. 16E+08 1.5 3430.0Reverse Arrhenius coefficients: 9.35E+08 1.5 18600.0

8. H202+0H=H20+H02 1.00E+12 0.0 0.0Reverse Arrhenius coefficients: 1.69E+11 0.3 31500.0

Declared duplicate reaction ...9. CO+H02=C02+0H 3.01E+13 0.0 23000.0

Reverse Arrhenius coefficients: 6.43E+15 -0.3 84600.010. H20+m=H+OH+m 1. 84E+27 ~3.0 123000.0

Reverse Arrhenius coefficients: 2.25E+22 -2.0 0.0H2 Enhanced by 2.500E+00H20 Enhanced by 1.200E+01CO Enhanced by 1.900E+00C02 Enhanced by 3.800E+00

11. H+02(+m)=H02(+m) 1. 48E+12 0.6 0.0Low pressure limit: 0.35000E+17 -0.41000E+00 -0. 11200E+04TROE centering: 0.50000E+00 0.10000E-29 0.10000E+31 0.10000+101

H2 Enhanced by 2.500E+00H20 Enhanced by 1.200E+01CO Enhanced by 1.900E+00C02 Enhanced by 3.800E+00

12. CO+O(+m)=C02(+m) 1.80E+10 0.0 2380.0Low pressure limit: 0.13500E+25 -0.27900E+01 0.41900E+04

H2 Enhanced by 2.500E+00H20 Enhanced by 1.200E+01CO Enhanced by 1.900E+00C02 Enhanced by 3.800E+00

13. CO+02=C02+0 1. 07E-15 7.1 13300.0Reverse Arrhenius coefficients: 9.44E-15 7.1 19500.0

14. CH20+0H=H+CO+H20 3.43E+09 1.2 -447.0Reverse Arrhenius coefficients: 1. 19E+09 1.2 29400.0

15. CH20+H=H+CO+H2 9. 33E+08 1.5 2980.0Reverse Arrhenius coefficients: 7.45E+07 1.5 17600.0

134

APPENDIX A. SKELETAL N-BUTANE MECHANISM

16. CH2o+o=H+Co+oH 4.16E+11 0.6 2760.0Reverse Arrhenius coefficients: 1.46E+10 0.6 15300.0

17. CH3+oH=CH2o+H2 2.25E+13 0.0 4300.0Reverse Arrhenius coefficients: 6. 76E+14 0.0 76000.0

18. CH3+o=CH2o+H 8.00E+13 0.0 0.0Reverse Arrhenius coefficients: 1.06E+15 0.0 69600.0

19. Ho2+o=oH+o2 3.25E+13 0.0 0.0Reverse Arrhenius coefficients: 7.86E+14 -0.3 55400.0

20. H+Co+H02=CH2o+o2 2.97E+10 0.3 -3860.0Reverse Arrhenius coefficients: 2.05E+13 0.0 39000.0

21. H+Co+o2=Co+Ho2 7.58E+12 0.0 410.0Reverse Arrhenius coefficients: 9.03E+11 0.3 32900.0

22. Ho2+H=oH+oH 7.08E+13 0.0 300.0Reverse Arrhenius coefficients: 1. 35E+14 -0.3 39600.0

23. Ho2+H=H2+o2 1.66E+13 0.0 820.0Reverse Arrhenius coefficients: 9.14E+14 -0.3 58300.0

24. H02+oH=H2o+o2 2.89E+13 0.0 -500.0Reverse Arrhenius coefficients: 6.89E+15 -0.3 72100.0

25. H202+o2=Ho2+Ho2 5.94E+17 ~0.7 53200.0Reverse Arrhenius coefficients: 4.20E+14 0.0 12000.0

Declared duplicate reaction ...26. oH+oH(+m) =H202 (+m) 1.24E+14 -0.4 0.0

Low pressure limit: 0.30400E+31 -0.46300E+01 0.20500E+04TRoE centering: o.47000E+00 0.10000E+03 0.20000E+04 0.10000E+16

H2 Enhanced by 2.500E+00H20 Enhanced by 1.200E+01CO Enhanced by 1.900E+00C02 Enhanced by 3.800E+00

27. H202+H=H20+0H 2.41E+13 0.0 3970.0Reverse Arrhenius coefficients: 7.75E+12 0.0 74700.0

28. CH20+H02=H+CO+H202 5.82E~03 4.5 6560.0Reverse Arrhenius coefficients: 1. 19E-02 4.2 4920.0

29. oH+m=o+H+m 3.91E+22 -2.0 105000.0Reverse Arrhenius coefficients: 4.72E+18 -1.0 0.0H2 Enhanced by 2.500E+00H20 Enhanced by 1.200E+01CO Enhanced by 1.900E+00C02 Enhanced by 3.800E+00

30. o2+m=o+o+m 6.47E+20 -1. 5 122000.0Reverse Arrhenius coefficients: 6.17E+15 -0.5 0.0H2 Enhanced by 2.500E+00H20 Enhanced by 1.200E+01CO Enhanced by 1.900E+00C02 Enhanced by 3.800E+00

31. H202+0=OH+H02 9. 55E+06 2.0 3970.0Reverse Arrhenius coefficients: 2.54E+07 1.7 19900.0

32. C2H3+o2=CH2o+H+Co 1.70E+29 -5.3 6500.0Reverse Arrhenius coefficients: 1.66E+29 -5.3 93000.0

33. CH3Co(+m) =CH3+Co (+m) 1.20E+08 0.0 16700.0Low pressure limit: 0.12000E+16 O.OOOOOE+OO 0.12500E+05

34. pC4H9=C2H3+C2H3+3H 7.50E+15 -1.4 29600.0Reverse Arrhenius coefficients: 3.30E+11 0.0 7200.0

35. C4H10+o2=pC4H9+Ho2 2.50E+13 0.0 49000.0Reverse Arrhenius coefficients: 2.50E+12 0.0 ~2200.0

36. C4H10+H=pC4H9+H2 1.88E+05 2.8 6280.0Reverse Arrhenius coefficients: 2.81E+01 3.4 10000.0

37. C4H10+oH=pC4H9+H2o 1.05E+10 1.0 1590.0Reverse Arrhenius coefficients: 6.82E+06 1.7 20500.0

38. C4H10+o=pC4H9+oH 1. 13E+14 0.0 7850.0Reverse Arrhenius coefficients: 1. 48E+13 0.0 12200.0

135

APPENDIX A. SKELETAL N-BUTANE MECHANISM

39. C4Hl0+H02=pC4H9+H202 1.70E+13 0.0 20500.0Reverse Arrhenius coefficients: 4.58E+12 0.0 9810.0

40. H202+H=H2+H02 4.82E+13 0.0 7950.0Reverse Arrhenius coefficients: 1. 88E+12 0.3 24300.0

41. H+CO+O=C02+H 3.00E+13 0.0 0.0Reverse Arrhenius coefficients: 9.68E+15 0.0 110000.0

42. H202+02=H02+H02 1.84E+14 -0.7 39600.0Reverse Arrhenius coefficients: 1.30E+ll 0.0 -1630.0

Declared duplicate reaction ...43. C2H3+02=CH3CO+O 3.50E+14 -0.6 5260.0

Reverse Arrhenius coefficients: 2.59E+12 0.1 6460.044. H202+0H=H20+Ho2 5.80E+14 0.0 9560.0

Reverse Arrhenius coefficients: 9.77E+13 0.3 41000.0Declared duplicate reaction ...

45. C3H5_a+OH=C2H3+CH20+H 2.03E+12 0.1 23600.0Reverse Arrhenius coefficients: 1.50E+11 0.0 10600.0

46. C3H5_a+H02=C2H3+CH20+0H 7.00E+12 0.0 -1000.0Reverse Arrhenius coefficients: 2.04E+13 -0.2 12300.0

47. C4H800Hl_302=C4H800Hl_3+02 8.09E+21 -1.9 37800.0Reverse Arrhenius coefficients: 7.54E+12 0.0 0.0

48. C4H80oHl_302=CH3Co+CH3Co+H2o+0H 2.50E+l0 0.0 21400.0Reverse Arrhenius coefficients: 6.51E+04 1.1 44400.0

49. C4H800Hl_3=C4H801_3+oH 5.00E+l0 0.0 15200.0Reverse Arrhenius coefficients: O.OOE+OO 0.0 0.0

50. C4H801_3+0H=CH20+C3H5_a+H20 5.00E+12 0.0 0.0Reverse Arrhenius coefficients: O.OOE+OO 0.0 0.0

51. C4H801_3+H=CH20+C3H5_a+H2 5.00E+12 0.0 0.0Reverse Arrhenius coefficients: O.OOE+OO 0.0 0.0

52. C4H801_3+o=CH20+C3H5_a+OH 5.00E+12 0.0 0.0Reverse Arrhenius coefficients: O.OOE+OO 0.0 0.0

53. C4H801_3+H02=CH20+C3H5_a+H202 1.00E+13 0.0 15000.0Reverse Arrhenius coefficients: O.OOE+OO 0.0 0.0

54. pC4H902=C4H800Hl_3 2.00E+l0 0.0 20800.0Reverse Arrhenius coefficients: 1.74E+09 -0.1 8190.0

55. pC4H902=pC4H9+02 7.60E+18 -1.2 35800.0Reverse Arrhenius coefficients: 4.52E+l0 0.0 0.0

56. C3H5_a+02=CH3Co+CH20 7. 14E+15 -1.2 21000.0Reverse Arrhenius coefficients: 4.94E+16 -1.4 88600.0

57. CH3+02=CH20+0H 7.47E+ll 0.0 14300.0Reverse Arrhenius coefficients: 7.78E+ll 0.0 67800.0

NOTE: A units mole-cm-sec-K, E units cal/mole

NO ERRoRS FOUND ON INPUT ... CHEMKIN LINKING FILE WRITTEN.

WORKING SPACE REQUIREMENTS AREINTEGER: 1786REAL: 1375CHARACTER: 26

136

Appendix B

Skeletal n-heptanemechanism

CHEMKIN INTERPRETER OUTPUT: CHEMKIN-II Version 2.5 Dec. 1990DOUBLE PRECISION

ELEMENTS AToMICCoNSIDERED WEIGHT

1. H 1.007972. 0 15.99943. C 12.01124. N 14.0067

SPECIESCoNSIDERED

CP H

H AA RS G MoLECULAR TEMPERATURE ELEMENT COUNTE E WEIGHT LoW HIGH HOC N

1. 02 G 0 31.99880 200.0 3500.0 0 2 0 02. H G 0 1.00797 200.0 3500.0 1 0 0 03. oH G 0 17.00737 200.0 3500.0 1 1 0 04. 0 G 0 15.99940 200.0 3500.0 0 1 0 05. H2 G 0 2.01594 200.0 3500.0 2 0 0 06. H20 G 0 18.01534 200.0 3500.0 2 1 0 07. H02 G 0 33.00677 200.0 3500.0 1 2 0 08. H202 G 0 34.01474 200.0 3500.0 2 2 0 09. CO G 0 28.01055 200.0 3500.0 0 1 1 0

10. C02 G 0 44.00995 200.0 3500.0 0 2 1 011. CHO G 0 29.01852 200.0 3500.0 1 1 1 012. CH20 G 0 30.02649 200.0 3500.0 2 1 1 013. CH3 G 0 15.03506 200.0 3500.0 3 0 1 014. C2H4 G 0 28.05418 200.0 3500.0 4 0 2 015. CH4 G 0 16.04303 200.0 3500.0 4 0 1 0

137

APPENDIX B. SKELETAL N-HEPTANE MECHANISM

16. C2H5 G 0 29.06215 200.0 3500.0 5 0 2 017. C2H3 G 0 27.04621 200.0 3500.0 3 0 2 018. C3H6 G 0 42.08127 300.0 5000.0 6 0 3 019. NC3H7 G 0 43.08924 300.0 5000.0 7 0 3 020. C5Hl1 1 G 0 71.14342 300.0 5000.0 11 0 5 021. C7H15_3 G 0 99.19760 300.0 5000.0 15 0 7 022. C7H16 G 0 100.20557 300.0 5000.0 16 0 7 023. oC7H13o G 0 129.18046 300.0 5000.0 13 2 7 024. N2 G 0 28.01340 300.0 5000.0 0 0 0 225. NO G 0 30.00610 200.0 6000.0 0 1 0 126. N G 0 14.00670 200.0 6000.0 0 0 0 1--------~~--~------------------------------------------------------------------

(k = A T**b exp(-E/RT))REACTIONS CONSIDERED A b E

1. 02+H=>OH+0 8.76E+13 0.0 14842.32. oH+0=>02+H 1.25E+13 0.0 700.33. H2+o<=>OH+H 5.83E+04 2.7 6285.84. H2+0H<=>H2o+H 1. 18E+08 1.6 3298.35. 2oH<=>H2o+0 1.20E+09 1.1 100.46. 2H+M<=>H2+M 1.95E+18 -1.0 0.0

02 Enhanced by 4.000E-OlH20 Enhanced by 6.500E+00CO Enhanced by 7.500E-OlC7H16 Enhanced by 3.000E+00N2 Enhanced by 4.000E~01

7. 2o+M<=>02+M 3. 15E+17 ~1.0 0.002 Enhanced by 4.000E~01

H20 Enhanced by 6.500E+00CO Enhanced by 7.500E-OlCH4 Enhanced by 3.000E+00C7H16 Enhanced by 3.000E+00N2 Enhanced by 4.000E-Ol

8. H+oH+M<=>H2o+M 2.64E+22 ~2.0 0.002 Enhanced by 4.000E-OlH20 Enhanced by 6.500E+00CO Enhanced by 7.500E-OlCH4 Enhanced by 3.000E+00C7H16 Enhanced by 3.000E+00N2 Enhanced by 4.000E-Ol

9. H+02+M<=>H02+M 5.95E+19 -1.4 0.0H2 Enhanced by 2.500E+00H20 Enhanced by 1.200E+OlCO Enhanced by 1.900E+00C02 Enhanced by 3.800E+00

10. H02+H=>2oH 1. 47E+14 0.0 1003.811. H02+H=>H2+o2 2.54E+13 0.0 693.112. H02+H=>H2o+o 2.44E+13 0.0 1720.813. H02+o=>OH+02 2. 15E+13 0.0 -406.314. H02+oH<=>H2o+o2 4.94E+13 0.0 0.015. 2H02=>H202+02 2.87E+11 0.0 -1242.816. 20H+M<=>H202+M 2.73E+22 ~2.0 0.0

02 Enhanced by 4.000E-OlH20 Enhanced by 6.500E+00CO Enhanced by 7.500E-OlCH4 Enhanced by 3.000E+00C7H16 Enhanced by 3.000E+00

138

APPENDIX B. SKELETAL N-HEPTANE MECHANISM

N2 Enhanced by 4.000E-0117. H202+H=>H20+0H 1. 17E+13 0.0 3585.118. H202+0<=>OH+H02 2.75E+13 0.0 6405.419. H202+0H<=>H20+H02 4.53E+12 0.0 1003.820. CO+OH<=>C02+H 5.99E+06 1.5 -497.121. CO+H02=>C02+0H 1.50E+14 0.0 23589.922. CO+0+M=>C02+M 7.36E+13 0.0 -4541.1

02 Enhanced by 4.000E-01H20 Enhanced by 6.500E+00CO Enhanced by 7.500E-01CH4 Enhanced by 3.000E+00C7H16 Enhanced by 3.000E+00N2 Enhanced by 4.000E-01

23. CHO+M=>CO+H+M 3. 73E+14 0.0 15774.402 Enhanced by 4.000E-01H20 Enhanced by 6.500E+00CO Enhanced by 7.500E-01CH4 Enhanced by 3.000E+00C7H16 Enhanced by 3.000E+00N2 Enhanced by 4.000E-01

24. Co+H+M=>CHO+M 5.25E+14 0.0 733.802 Enhanced by 4.000E-01H20 Enhanced by 6.500E+00CO Enhanced by 7.500E-01CH4 Enhanced by 3.000E+00C7H16 Enhanced by 3.000E+00N2 Enhanced by 4.000E-01

25. CHo+H=>Co+H2 8.99E+13 0.0 0.026. CHo+oH=>Co+H2o 1.20E+14 0.0 0.027. CHO+02=>CO+H02 3.35E+12 0.0 0.028. CH2o+M=>CHo+H+M 1.58E+36 -5.5 96696.9

02 Enhanced by 4.000E-01H20 Enhanced by 6.500E+00CO Enhanced by 7.500E-01CH4 Enhanced by 3.000E+00C7H16 Enhanced by 3.000E+00N2 Enhanced by 4.000E~01

29. CH2o+H=>CHo+H2 1. 17E+08 1.6 2165.430. CH20+0=>CHO+OH 3.33E+11 0.6 2772.531. CH2o+0H=>CHO+H2o 3.32E+09 1.2 -454.132. CH20+H02=>CHO+H202 3.30E+12 0.0 13073.633. CH3+o=>CH20+H 1.01E+14 0.0 0.034. CH3+H(+M) <=>CH4(+M) 2.21E+14 0.0 0.0

Low pressure limit: 0.62570E+24 -0. 18000E+01 O.OOOOOE+OOTROE centering: 0.42000E+00 0.23700E+04 O.OOOOOE+OO

35. CH3+02=>CH20+0H 2. 89E+11 0.0 8938.836. CH3+H02=>CH4+02 3.83E+12 0.0 0.037. 2CH3=>C2H4+H2 1. 14E+14 0.0 32026.838. 2CH3<=>C2H5+H 3.38E+13 0.0 14674.939. CH4+H<=>H2+CH3 1.07E+04 3.0 8030.640. CH4+0<=>OH+CH3 5.81E+08 1.6 8484.741. CH4+0H<=>H20+CH3 1.42E+07 1.8 2772.542. C2H3+o2=>CH20+CHO 5.76E+12 0.0 0.043. C2H4+H<=>C2H3+H2 6.07E+14 0.0 15033.544. C2H4+0=>CHO+CH3 1.61E+07 1.9 178.845. C2H4+0H<=>C2H3+H2o 2.04E+13 0.0 5951.246. C2H5(+M)=>C2H4+H(+M) 1. 48E+13 0.0 39914.0

Low pressure limit: 0.10000E+17 O.OOOOOE+OO 0.30115E+05TROE centering: O.OOOOOE+OO 0.42280E+03 O.OOOOOE+OO

47. C2H4+H(+M) =>C2H5 (+M) 1.05E+12 0.5 1820.0

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APPENDIX B. SKELETAL N-HEPTANE MECHANISM

Low pressure limit: 0.12000E+43 -0. 76200E+01 0.69694E+04TROE centering: O.OOOOOE+OO 0.42280E+03 O.OOOOOE+OO

48. C3H6<=>C2H3+CH3 3.65E+15 0.0 85803.149. C3H6+0=>C2H4+CH20 7.03E+13 0.0 5019.150. C3H6+0=>C2H5+CHO 2.90E+12 0.0 0.051. C3H6+0H=>C2H5+CH20 8.89E+12 0.0 0.052. NC3H7<=>CH3+C2H4 9.57E+13 0.0 31022.953. NC3H7<=>H+C3H6 1.06E+14 0.0 37022.054. NC3H7+02=>C3H6+H02 9.69E+11 0.0 4995.255. C5H11_1=>C2H4+NC3H7 2.71E+13 0.0 28417.856. C7H16+H=>C7H15_3+H2 1.65E+07 2.0 4995.257. C7H16+0=>C7H15_3+0H 5.16E+13 0.0 5210.358. C7H16+0H=>C7H15_3+H20 2.31E+09 1.3 693.159. C7H16+H02=>C7H15_3+H202 5.96E+12 0.0 17017.260. C7H16+CH3=>C7H15_3+CH4 7.42E+11 0.0 9512.461. C7H16+02=>C7H15_3+H02 3.46E+13 0.0 47633.862. C7H15_3+202=>OC7H130+20H 1. 86E+12 0.0 0.063. OC7H130=>CH20+C5H11_1+CD 1.80E+13 0.0 15009.664. N+NO<=>N2+0 2.70E+13 0.0 355.065. N+02<=>NO+O 9.00E+09 1.0 6500.066. N+OH<=>NO+H 3.36E+13 0.0 385.0

NOTE: A units mole~cm-sec-K, E units cal/mole

NO ERRORS FOUND ON INPUT ... CHEMKIN LINKING FILE WRITTEN.

WORKING SPACE REQUIREMENTS AREINTEGER: 1908REAL: 1305CHARACTER: 30

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Curriculum Vitae

19751982-19871987-19901990-19951995-200120012001-2006

born on May, 7th in Zug ZG, SwitzerlandElementary school in Steinhausen, SwitzerlandSecondary school in Steinhausen, Switzerlandgrammar school (typus economy) Zug, SwitzerlandStudy of mechanical engineering at ETH ZürichDiploma in nlechanical engineering at ETH ZürichDoctoral student and teaching assistant at theInstitute of Energy Technology/LAV at ETH Zürich

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