PDF-BASED MODELING OF AUTOIGNITION AND EMISSIONS FOR ADVANCED DIRECT-INJECTION ENGINES

Transcription

1 The Pennsylvania State University The Graduate School The Department of Mechanical and Nuclear Engineering PDF-BASED MODELING OF AUTOIGNITION AND EMISSIONS FOR ADVANCED DIRECT-INJECTION ENGINES A Dissertation in Mechanical Engineering by Eugene Hans Kung c 2008 Eugene Hans Kung Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2008

2 The dissertation of Eugene Hans Kung has been reviewed and approved by the following: Daniel C. Haworth Professor of Mechanical Engineering Dissertation Adviser Chair of Committee Stephen R. Turns Professor of Mechanical Engineering Domenic A. Santavicca Professor of Mechanical Engineering André L. Boehman Professor of Fuel Science Karen A. Thole Professor of Mechanical Engineering Head of the Department of Mechanical and Nuclear Engineering Signatures are on file in the Graduate School. ii

3 Abstract Transported probability density function (PDF) methods have shown promise in modeling canonical flame configurations. More recently, they have been applied to simple engine configurations to demonstrate their feasibility in more practical applications, and to demonstrate the importance of accurate accounting for turbulence/chemistry interactions (TCI) in IC engines. The research conducted here advances the stateof-the-art in two areas: advanced physical models and numerical methods for multiphase chemically reacting turbulent flows; and advanced combustion systems for direct-injection diesel engines. The hypotheses that are tested in this thesis are that turbulent fluctuations significantly impact heat release and emissions in advanced diesel engines and that PDF methods capture TCI effects in real engines. Contributions to modeling and algorithms include: 1) liquid fuel spray/pdf coupling; 2) real engine applications of PDF particle tracking through complex meshes; and 3) modularization of coupling among detailed thermochemistry and PDF methods. Contributions to engine combustion have included: 1) multiple-cycle calculations; 2) modeled premixed/direct-injection splits; 3) insight into the roles of turbulence and TCI on autoignition and emissions; 4) detailed information from the PDF method including spatial non-homogeneity, fluctuation effects, NOx and soot prediction, and detailed speciation; and 5) quantitative comparisons between CFD and experiment for a real engine. This research shows that turbulence/chemistry interactions in real engine applications are important to understanding and modeling engine combustion. The work allows for better analysis and performance prediction of advanced engine designs and points to how the models may be improved. Already, the PDF model s application to the real engine case here has shown appreciably better robustness and quantitative accuracy in ignition and emissions predictions compared to a conventional finite-volume approach where TCI is not considered. Ignition timing, heat release, and emissions are captured favorably with the PDF method. Directions for future improvement and research are suggested to address the remaining modeling issues. iii

4 Contents List of Figures viii List of Tables xi Acknowledgements xiii Chapter 1 Introduction Background Hypotheses and Objectives Thesis Outline Chapter 2 Advanced Direct-Injection Reciprocating-Piston Internal-Combustion Engines Direct-Injection Gasoline Engines Direct-Injection Diesel Engines Advanced Diesel-Based HCCI/PCCI Engines Review of HCCI/PCCI Research Efforts Summary Chapter 3 Fuels, Chemical Kinetics, and Soot Fuels Motivation for Detailed Chemical Mechanisms Gas-Phase Chemical Mechanisms Hydrocarbon Oxidation and Autoignition CO Oxidation NO x Formation Integrated Mechanisms Real Fuels CHEMKIN-Based Thermochemistry and Kinetics Soot Modeling iv

5 3.4.1 Two-Equation Soot Model Method of Moments Summary Chapter 4 Physical Models and Numerical Methods Advanced Diesel Modeling Challenges Formulations Governing Instantaneous Physical Equations Assumptions and Simplifications to the Governing Physical Equations Challenges of Turbulent Combustion Reynolds-Averaged Navier-Stokes Equations for CFD Composition PDF Method RANS Lagrangian Particle PDF Method Alternative Formulations Direct Numerical Simulation Large-Eddy Simulation Turbulent Transport in RANS/PDF Methods The k ε Turbulence Model Turbulence Wall Function Turbulent Transport Fokker-Planck Equation Scalar Dissipation and Mixing Models Turbulent Combustion Models PDF Method: Solution of the Mean Chemical Source Term Alternative Combustion Models Flamelet Models Bray-Moss-Libby Eddy Breakup Model Linear Eddy Model CMC Models Fuel Sprays Hybrid Particle/Mesh Solution Algorithm Finite-Volume Method Lagrangian Particle Method Particle Tracking Particle Number Density Control Mean Estimation Coupling and Consistency Additional Computational Considerations v

6 4.8.1 Meshing Chemistry Acceleration Parallelization Summary Chapter 5 Modeling Study and Experimental Comparison Scoping Studies for Simplified Engine Configurations Effects of Turbulence/Chemistry Interactions in a Real Engine Engine Configuration and Operating Conditions Global Results Pressure, Temperature, and Heat Release Profiles Emissions Discussion Parametric Studies Toward Improved Modeling Thermochemical Model Compression Ratio Initial and Boundary Conditions PDF Mixing Model Fuel Composition Spray/PDF Coupling Spray Parcel Number Spray Breakup Model Parameters Comparison with Experimental Data Results Overview CO Emissions % EGR and Full-Load Case Emissions Correlations Soot Emissions NO x Emissions Discussion Physical Modeling Considerations Ignition Timing: Effects of the PDF Model Numerical Issues Summary Chapter 6 Summary, Conclusions, and Further Study Scope and Technical Goals: Evaluation Contributions Recommendations for Future Work vi

7 Bibliography Appendix A Chemical Mechanisms A.1 n-heptane 34-Species Mechanism A.2 n-heptane 40-Species Mechanism with Added NO x Chemistry 178 vii

8 List of Figures 2.1 An illustration of the four major modes of internal engine combustion. The top-left shows a typical automotive spark-ignition engine. The top-right is a wall-guided direct-injection stratified-charge setup. The bottom-left illustrates the setup for homogeneous-charge compressionignition. Premixed-charge compression-ignition approaches this mode. The bottom-right illustrates the typical diesel engine combustion mode, a direct-injection compression-ignition Computed in-cylinder global temperature for consecutive cycles [20] Computed in-cylinder NO, NO 2, and N 2 O mole fractions versus crankangle for a 0.24 equivalence ratio n-heptane fueled premixed and directly-injected engine [21]. Left: CFD without the PDF method. Right: CFD with the PDF method. Note the difference in the ordinate scales for the two figures Pressure trace comparison between FV (i.e., no TCI) and PDF runs [21] Computed in-cylinder temperatures versus crankangle for n-heptane [21]. Left: Volume-averaged in-cylinder temperature and maximum finite-volume cell mean temperature for CFD without the PDF method. Right: Volume-averaged in-cylinder temperature, maximum finite-volume cell mean temperature, and maximum PDF notional particle temperature for CFD with the PDF method Schematic illustration of the profile of a piston sector representative of the configuration used for this work. The left side corresponds to the piston axis. The right side corresponds to the side of the piston. The curved section is the piston bowl Computed in-cylinder pressure versus crankangle. Left: 40% EGR; Right: 65% EGR Computed in-cylinder NO, NO 2, and N 2 O versus crankangle for 40% EGR. Left: FV; Right: PDF Sensitivity to chemical mechanism and TCI for the 65% EGR case, including comparison with experimental data viii

9 5.9 Sensitivity to compression ratio, run using the conditions from 65% EGR setup and the FV model. Clearance height was varied by ±0.1 mm from the baseline case to effect the changes Sensitivity to initial pressure and temperature for the 65% EGR condition. These are FV runs. The degree of variations for PDF runs is similar. Changes to temperature are indicated by the sign and number following a T. Changes to pressure are indicated by the sign and number following a P Sensitivity to mixing rate for PDF for the 65% EGR case. PDF 2 corresponds to C φ = 2, PDF 10 to C φ = 10, and PDF 20 to C φ = 20. PDF results approach the FV result as C φ Sensitivity to fuel composition (fuel mass) for the 40% EGR case. Results for pressure and heat release from two PDF runs are shown together with the experimental data Sensitivity to spray/pdf coupling for the 40% EGR case. Solid lines correspond to the creation of new PDF particles as spray parcels vaporize. Dashed lines correspond to distribution of newly vaporized fuel mass among existing PDF particles in each cell Sensitivity to spray/pdf coupling for the 40% EGR case. Here the minimum and maximum particle temperatures are plotted as a function of crankangle Sensitivity to number of spray parcels for the 65% EGR case using the FV model Sensitivity to spray model parameters for the 65% EGR case. KHRT Mod 1 corresponds to an increase in the breakup length constant, Cdist, from 1.9 to 2.5 and a reduction of B1 from 60 to 30. KHRT Mod 0 corresponds to a breakup length of 2.5 and B0 = 0.3 instead of the baseline value of B0 = EGR sweep from 40% to 70% comparison between experiment, FV, and PDF for pressure and heat-release Full-load case comparison between experiment, FV, and PDF for pressure and heat-release Comparison of CO at 90 atdc for FV and PDF models versus the engine-out measurements from the experiment Comparison of UHC at 90 atdc for FV and PDF models versus the engine-out measurements from the experiment Computed mean temperature [K] iso-contours for the 65% EGR case at 30 atdc (top) and at 90 atdc (bottom). PDF results are on the left and FV results are on the right ix

10 5.22 Computed mean CO mass fraction iso-contours for the 65% EGR case at 30 atdc (top) and at 90 atdc (bottom). PDF results are on the left and FV results are on the right Computed mean OH mass fraction iso-contours for the 65% EGR case at 30 atdc (top) and at 90 atdc (bottom). PDF results are on the left and FV results are on the right CO and OH total mass as a function of crankangle degrees for the 65% FV (a) and PDF (b) cases. The CO-OH line represents CO in cells that also have OH. OH-CO represents OH in cells that also have CO CO and UHC total mass as a function of crankangle degrees for the 65% FV (a) and PDF (b) case. The CO-HC line represents CO in cells that also have UHC. HC-CO line represents UHC in cells that also have CO Unburned hydrocarbon and methane total mass as a function of crankangle degrees for the 65% FV (a) and PDF (b) case CO and OH total mass as a function of crankangle degrees for the fullload FV (a) and PDF (b) case. The CO-OH line represents CO in cells that also have OH. OH-CO represents OH in cells that also have CO CO and UHC total mass as a function of crankangle degrees for the full-load FV (a) and PDF (b) case. The CO-HC line represents CO in cells that also have UHC. HC-CO line represents UHC in cells that also have CO Hydrocarbon and methane total mass as a function of crankangle degrees for the full-load FV (a) and PDF (b) case Comparison of soot at 90 atdc for FV and PDF models versus the engine-out measurements from the experiment. It should be noted that the experimental measurements, Exp PM, are smoke measurements and are measurements of particulate matter and not soot, which are a fraction of that measurement Comparison of NO x at 90 atdc for FV and PDF models versus the engine-out measurements from the experiment Comparison of NO:NO 2 ratio at 90 atdc for FV and PDF models. No data are available for this quantity from experiments x

11 List of Tables 4.1 Characteristics of Direct Numerical Simulation, Large Eddy Simulation, and Reynolds-Averaged Simulation approaches for turbulent combustion Turbulent combustion models for Reynolds-Averaged simulations Summary of global ignition timing and emissions results from [9]. CO and UHC values are global in-cylinder mass fractions at 40 o ATDC. Here FV denotes results obtained using cell-mean values of composition and temperature (neglecting TCI) and PDF denotes results obtained using the PDF method to account for TCI. TRLC denotes inclusion of a top-ring-land crevice Engine configuration and operating conditions for two EGR levels Key baseline model settings (dimensionless) Global results for 40% and 65% EGR and cases without turbulence/chemistry interactions (FV), with turbulence/chemistry interactions (PDF), and from experimental data (Exp). The timing and magnitude of the maximum rate of heat release are given in crankangle degrees atdc, CA dj/dθ max, and Joules per degree, (dj/dθ) max. Computed emissions are global in-cylinder emissions index values at 90 atdc, and UHC includes all hydrocarbons but the fuel Engine operating conditions for four EGR levels and a full-load case. The bore diameter is 103 mm and the squish height is 0.7 mm. There are 39,483 finite volume cells and a maximum of 987,075 gas-phase particles. Swirl ratio is defined as the angular velocity of the flow divided by the engine crankshaft angular rotational speed Global emissions results for full-load, 40%, 50%, 65%, and 70% EGR conditions. Computed emissions are global in-cylinder emissions index values at 90 atdc xi

12 5.7 Rates of reactions between OH radicals and selected other species in cm 3 -mol-sec-kcal units, taken from [63]. Note that these rates are different than the rates in the mechanism used for this work (see Section A.2) NO x and soot emissions results for full-load, 40% EGR, and 65% EGR conditions. Computed emissions are global in-cylinder emissions index values at 90 atdc. Experimental values for soot are smoke measurements and represent particulate matter, of which a fraction is soot. No data was available for the soot fraction xii

13 Acknowledgements My deepest thanks and gratitude go to my advisor, Professor Daniel Haworth. Seeing me through several years of graduate study as well as on other projects, he has provided me with a generously broad education and has always been helpful, attentive, patient, instructively critical, supportive, and encouraging. His guidance has been invaluable and I regard him as a role model for my academic career. It was his enthusiasm for engines and combustion that attracted me to pursue the Ph.D. I thank my Thesis Committee, Dr. Domenic Santavicca, Dr. Stephen Turns, and Dr. André Boehman for giving me their ears, helpful suggestions, and feedback. Dr. Turns has provided interested comments weekly as a member of our lab group meetings. I thank a former teacher, Professor Fred Dryer at Princeton University, for recommending Penn State to me and setting me on my graduate path. Dr. David Foster at the University of Wisconsin-Madison and Dr. Tanet Aroonrisopon provided the first engine experimental data with which I did initial comparisons. Several researchers at General Motors have provided helpful feedback including Dr. Diwakar Ramachandra, Dr. Shengming Chang, Dr. Bob Siewert, and Dr. Ronald Grover. I thank General Motors Research and Dr. Andreas Lippert for the experimental engine data for comparison and internships over summers during which I could apply our models in an engineering setting. xiii

14 Various discussions with post-docs, grad students, colleagues, and professors have helped to shape my understanding of engines and combustion and I thank them all for giving me their time. Dr. Ranjan Mehta, Dr. Kshitij Deshmukh, Dr. Yongzhe Zhang, Dr. Liangyu Wang, and Dr. Yuhui Wu provided feedback, mentorship, and suggestions. Ranjan has been especially helpful over the last year in providing the soot modeling capability in the code. Thanks to Dr. Ted Huang and Dr. Calvin Chan for keeping me on schedule and to Ted for help with proof reading. Thanks to Alex Yin for early proofing. I would also like to thank the Mechanical and Nuclear Engineering Department and their staff for their help with all the logistics and paperwork during my study here. Special thanks to John Raiser, Virginia Smith, and Jennifer Houser. I humbly thank my family for their continual support, love, and rebukes. Thank you Amazing Grace. The research funding, supported by the Department of Energy (DE-FC04-02AL67612 and DE-FC25-04NT42233), the National Science Foundation (CTS and DGE ), General Motors R&D Center, and CD-adapco, is gratefully acknowledged. xiv

15 Chapter 1 Introduction Of the remaining obstacles to understanding and controlling combustion, turbulence presents significant experimental and theoretical challenges. While turbulence itself remains an outstanding fundamental physical problem, the additional challenges of combustion in turbulent flows have spawned several approaches for turbulent combustion modeling. The tractable application of these detailed, high-end turbulent combustion models is crucial to the development of next-generation, clean, and efficient propulsion systems. 1.1 Background Market pressures, diminishing fuel resources, and pertinent global warming consequences continue to drive research and development towards reducing dependence on oil and reducing greenhouse-gas emissions. As a result, advanced engine combustion modes are receiving much attention. The research efforts range from homogeneous-charge compression-ignition (HCCI) to advanced direct-injection sparkignition (SIDI) operation [1, 2]. Engines running in these modes promise significant gains in thermal efficiency and lower engine-out emissions compared to current stateof-the-art production engines [3]. In the case of HCCI and quasi-hcci or premixed- 1

16 charge compression-ignition (PCCI) engine modes, this efficiency can be gained with a sizeable reduction in NO x and soot, a result of lower combustion temperatures and reduced regions of fuel-rich combustion. HCCI efficiency should be able to reach typical peak diesel efficiency of about 40-46% brake-specific fuel-conversion efficiency [4], if not somewhat higher because of leaner operation, while producing substantially lower emissions levels. In comparison, gasoline-engine fuel-conversion efficiency is typically around 30% while operating with far fewer regulated emissions than conventional diesel. HCCI engines have been fed with a wide range of fuels from conventional gasoline blends to diesel-type fuels. Efforts to understand and control these modes of operation are being aided by research into the fundamentals of flow structure and combustion behavior through experiments and modeling, from laser diagnostics to high-end computational fluid dynamics (CFD) [2]. Because of the highly complex nature of real production engines, experiments in representative systems are necessary to capture all the physics of the combustion event. However, an engine s complexity makes diagnostics very difficult. Through the use of laser diagnostics and highly instrumented research engines, much information can be gained about important flow characteristics and engine performance. Still, there are limits to the ability of experiments to capture a 3-D instantaneous description of the complex flow in the engine. High-end CFD complements experimental results by providing a complete picture of the flow in the engine without, for example, restrictions on the viewable area and measurable quantities. However, the accuracy of the physical models and numerical methods is critical to the relevance of CFD. There is a tradeoff between accuracy and runtime that is factored into the size of the computational mesh, the time steps, and the complexity of the algorithms and physical models used. To model chemistry, detailed mechanisms are required to capture autoignition and production of emissions species [5]. Trace emission species, such as carbon monoxide (CO) and NO x, can be 2

17 particularly hard to model. Mechanisms must be constructed to accommodate the regimes of temperatures and pressures that can be encountered in these combustion modes. For example, reaction pathways encompassing lean, low-temperature conditions, such as characterize HCCI combustion, must be considered to model NO x pathways other than thermal NO [6]. The complexity of the final mechanism must be manageable in order to allow the model to run within reasonable timeframes. Chemical kinetics calculations are computationally expensive to implement in 3- D time-dependent CFD using meshes typical of engineering applications ( cells). Zonal models [7] and hybrid CFD/zonal models [8], which have a small number of regions in which to compute chemistry, may be effectively used when flow/chemistry interactions are weak, such as during robust autoignition for highly homogeneous flows. However, detailed chemistry with greater physical resolution and direct consideration of turbulence/chemistry interactions (TCI) are necessary when modeling engine flows with less robust performance and/or stronger departures from homogeneity (e.g., late in-cylinder fuel injection) in order to accurately account for emissions and, in some cases, ignition timing [9]. One emissions species of particular importance is NO x. Predicting NO x accurately, besides benefitting the engine design process, also helps in understanding how to design aftertreatment systems that operate with high efficiency over the engine operating range. This range includes low-temperature and/or lean exhaust streams that characterize HCCI and direct-injection SIDI engines. Transitional and marginal engine operating regimes contribute to the problem of modeling engine-out NO x. Detailed chemistry can include the necessary NO x pathways that are active in the different regimes of operation. For example, the N 2 O pathway may be particularly active during low-temperature and lean operation [10]. Also, whereas engine-out NO x typically is characterized by a high NO:NO 2 ratio, experiments have shown that NO 2 may dominate under some HCCI conditions [11]. This ratio can be important for 3

18 proper aftertreatment function [12, 13]. It also has been reported that in-cylinder temperature, heterogeneity and stratification have strong influences on engine-out NO x [11, 14]. The research presented in this thesis uses a high-end (i.e., more physically accurate) CFD-based turbulent combustion model to accommodate detailed thermochemistry and turbulence/chemistry interactions. As always, it is important to maintain computational feasibility while providing greater detail and information than would be provided by less powerful models. Detailed chemical mechanisms are combined with a consistent hybrid particle/finite-volume transported composition probability density function (PDF) method that explicitly captures the influence of turbulent fluctuations on mean chemical source terms [15]. For purposes of chemistry calculation speedup, either a storage/retrieval-based scheme [16, 17] or parallel computing may be used. The consistent hybrid particle/finite-volume PDF algorithms for three-dimensional unsteady flows on unstructured and deforming meshes are described in [18]. Previous PDF-based modeling work has investigated autoignition and emissions in HCCI engines [9]. Through these studies it has been found that turbulence and turbulence/chemistry interactions always have a strong influence on the computed emissions. Cases with strong in-cylinder flow, strong spatial inhomogeneity, and/or marginal operating conditions show changes in the global combustion event (e.g., ignition timing and pressure traces) due to turbulence interactions. Other studies have looked at the effect of model coefficients [19], the importance of simulating several consecutive engine cycles to achieve a statistically stationary state [20], and the effect of mechanisms with detailed NO x pathways on computed engine-out emissions [21]. Here the PDF model is applied to a production-type engine geometry. This engine operates with a premixed-charge compression-ignition (PCCI) combustion mode, which utilizes directly injected fuel sprays. Analysis is applied to global quantities of 4

19 interest: pressure, heat release, and key emissions species. Understanding the coupling between the PDF model and the other relevant engine models is a major focus of the work as well as understanding the numerical and physical issues arising from the modeling of this engineering-scale system (as opposed to canonical flame simulations). Differences between models that do not account for TCI and the PDF model are examined in detail. 1.2 Hypotheses and Objectives This thesis addresses the following hypotheses: 1. Turbulent fluctuations have a significant impact on heat release and emissions in advanced diesel engines. 2. Models that account explicitly for turbulence/chemistry interactions give better agreement with experimental data over a broad range of conditions without model tuning. 3. PDF methods are an appropriate approach for modeling turbulence/chemistry interactions in advanced diesel engines. The use of transported PDF methods has provided improved accuracy for predicting combustion characteristics and emissions species in canonical flame simulations and simple engineering setups [15, 18]. PDF methods should also provide improved accuracy for device-scale simulations when the other physical models crucial to engine modeling are appropriately coupled. Through the application of PDF methods to real engine configurations, integrated with other physical sub-models such as liquid fuel sprays, an advance in the capability of engine modeling can be accomplished. 5

20 This research demonstrates the importance and analyzes the effects of turbulence/chemistry interactions in applications to real engine configurations. The focus is on modeling HCCI/PCCI combustion in direct-injection diesel engines. It is hypothesized that accounting for TCI using the PDF method will provide better agreement between the engine modeling effort and experimental data because more physics will be included in the framework. The use of the Lagrangian Monte Carlo method and associated procedures with the PDF method provides challenges in the coupling effort, as has already been seen in the preliminary work in coupling the fuel sprays with the PDF particles. By running the PDF method for realistic engine configurations, new insight can be extracted from the high-end, more physically realistic models. The objective is to have a CFD-based combustion model that will simultaneously treat a three-dimensional, time-dependent turbulent flow, realistic chemistry, turbulence/chemistry interactions, and multiphase systems, all in realistic internal-combustion engine configurations with realistic operating conditions. Using experimental data from industry, direct comparison is available to validate the model and the model integration. 1.3 Thesis Outline Chapter 2 reviews engine technologies and combustion modes. Direct-injection gasoline engines and direct-injection diesel engines are discussed. The homogeneouscharge compression-ignition combustion mode will discussed along with its potential benefits and the challenges to controlling it. Advanced diesel-based combustion modes will be discussed. These are the focus of the present modeling work. Chapter 3 will address the fuels and chemical kinetics. Models for fuel mechanisms are discussed, concerning the importance of capturing the myriad physical properties of hydrocarbon fuels that affect the combustion characteristics. Gas-phase chemical 6

21 mechanism basics are reviewed to provide the basis for the kinetic modeling underlying the detailed chemistry used here. Major mechanisms for oxidation and emissions formation are reviewed. Soot models are also discussed. Chapter 4 elaborates on the modeling challenges for engine applications and describes the models used here. Basic governing equations are given and methods of solution are described. Turbulence models and several combustion models are outlined. The transported PDF method and its application to the work here in a hybrid particle/mesh solution algorithm is explained. Fuel spray modeling is also described. Chapter 5 first presents the preliminary work that motivated this thesis. Parametric studies are given. A final set of results, based on model parameters determined through the parametric studies, compare the differences between running a finitevolume code with running the hybrid particle/mesh PDF solution. Differences in ignition timing and emissions are highlighted and discussion is given concerning the physical effects and numerical issues of the model. Chapter 6 summarizes the work in this thesis and suggests future paths for research based on the findings here. 7

22 Chapter 2 Advanced Direct-Injection Reciprocating-Piston Internal-Combustion Engines For the last several decades, the dominant modes of combustion in automotive engines have been either homogeneous-charge spark-ignition for gasoline-fueled engines or direct-injection compression-ignition for diesel-fueled engines. The strength of the former is low emissions, whereas the strength of the latter is high fuel efficiency. With increasing pressure to reduce both emissions and fuel consumption, engine researchers have been looking to new modes of combustion that represent hybrids of the two current systems [1]. Figure 2.1 provides an overview of internal engine combustion modes. These include gasoline direct-injection spark-ignition (DISI) and homogeneous-charge or premixed-charge compression-ignition (HCCI/PCCI) engines. The goals of engine research have not significantly changed over the last couple of decades: Heywood mentions both HCCI and DISI as the next steps in his volume on internal combustion engines from 1988 [4]. While both of these modes are still next steps, DISI has now taken the first step forward in its production development and HCCI production is also imminent. This development parallels the pace of combustion knowledge, which increases incrementally despite the major efforts undertaken to 8

23 understand this outstanding fundamental problem. The work here focuses on the development of HCCI/PCCI, specifically using diesel-type fuel, and represents a range of engine operating modes that include conditions such as a single injection event per engine cycle, multiple injections per cycle, and early and late injection timings. 2.1 Direct-Injection Gasoline Engines Direct-injection spark-ignition (DISI) combustion allows for the use of a stratified charge to shrewdly increase the thermodynamic potential of spark-ignited engines. A good review of the concept and research efforts is given by Zhao et al. [22]. The benefit of this setup is optimization of the compression ratio, at around 12 to 15, for efficiency [4] by: 1) directly injecting the fuel during compression, avoiding the issue of knock that occurs during the premixed-charge compression stroke; 2) igniting the charge with a spark, thus directly controlling ignition timing, which frees up the fuel ignition-quality requirement inherent with diesel engines; and 3) controlling engine power through fuel-injection amount, rather than through the use of a throttle, thereby reducing pumping losses typical with homogeneous-charge spark-ignition engines. Transient response and cold-start hydrocarbon emissions can also benefit by running in this combustion mode. The issues associated with these types of engines have been control and emissions. Standard spark-ignited premixed-charge gasoline engines have had a long history of development for combustion stability and emissions control. By providing the engine with appropriately formulated fuel, knock is generally a non-issue and combustion is easily controlled through the spark timing. The ubiquitous three-way catalyst is very efficient at reducing the main emissions species from these engines, that is, carbon monoxide, hydrocarbons, and nitrogen oxides. This catalyst is effective because the engine operates at an equivalence ratio of unity, which provides the best chemical mix 9

24 Premixed Flame Propagation Knock Key Emissions: UHC, CO, NOx ~Homogenous Autoignition Key Emissions: UHC, CO Homogeneous-Charge Spark-Ignition Ignition Homogeneous-Charge Compression-Ignition Liquid Fuel Fuel+Air +EGR Liquid Fuel Fuel, Air, EGR Stratified Flame Propagation Key Emissions: UHC, NOx, PM Non-Premixed Combustion Key Emissions: NOx, PM Stratified-Charge Spark-Ignition Ignition Stratified-Charge Compression-Ignition Liquid Fuel Air +EGR Liquid Fuel Air +EGR Figure 2.1: An illustration of the four major modes of internal engine combustion. The top-left shows a typical automotive spark-ignition engine. The top-right is a wall-guided direct-injection stratified-charge setup. The bottom-left illustrates the setup for homogeneous-charge compression-ignition. Premixed-charge compressionignition approaches this mode. The bottom-right illustrates the typical diesel engine combustion mode, a direct-injection compression-ignition. 10

25 for catalyst effectiveness. The move to directly injected fuel creates issues with the cycle-to-cycle variability and tendencies to misfire or have partial burns. Researchers at General Motors have experimentally diagnosed these issues in their engines, finding significant variation in fuel concentration near the spark plug, especially for highly stratified cases [23, 24]. Mixture preparation, when too lean near the spark plug, is a cause for misfire. While strategies such as high spray injection pressures, variable valve control, exhaust gas recirculation (EGR), and turbocharging are available to provide overall control of DISI combustion, the physical understanding of variability and its effect on combustion stability requires more research and investigation to sufficiently control the engine, preventing misfires and excessive emissions [22, 25]. CO and unburned hydrocarbon emissions are problems with fuel mixtures in locally lean regions that cause quenching of the flame and partial burns. Sooting and NO x emissions are results of overly rich fuel mixtures and locally rich combustion. Improvement in engine control may be able to assuage these emissions issues, but it is likely that improved exhaust emissions catalysts for lean operation will need to be used as well. Experimental diagnostics used to measure in-cylinder fuel and radical distributions include laser-induced florescence (LIF) and CN/OH radical chemiluminescence. High-speed film and heat-release analysis, high-speed photos of flow and spray and Schlieren-movies, planar-laser diagnostics, Laser-Mie scattering and phase-doppler anemometry for spray structure and drop-size distributions, and particle-image velocimetry are a sample of the various diagnostics used in engine research. Drake and Haworth provide a review into the varieties and applications of engine diagnostics [2]. These can be very difficult measurements, but can directly capture the physical phenomena. However, because of the limitations of each procedure, comparing experiments and simulations can be very difficult. The burden lies on both the experimenter and the modeler to produce data and analyses that are useful for the 11

26 other and push the state-of-the-art forward. 2.2 Direct-Injection Diesel Engines Most modern diesel engines use direct-injection technology for fuel metering and combustion timing. The discussion here will be restricted to this standard technology and the general characteristics and issues for the technology moving forward. A review of this and other diesel technologies is provided by Heywood [4]. Diesel engines operate with a combination of premixed and non-premixed modes, unlike the premixed flame mode used in modern spark-ignition engines. Liquid fuel is injected near the top of the compression stroke, with ignition shortly thereafter, in which a range of mixture stoichiometries ranging from rich to lean is created, rich near the spray core and leaner as the fuel-air mixture extends away from the center of the liquid spray plume. This type of combustion and flame structure affects how well the diesel engine will perform. A premixed rapid combustion occurs first, the result of fuel that has mixed with the air to within flammability limits, creating a characteristic high heat-release rate. Then, a mixing-controlled combustion phase begins, where burning is controlled by the rate at which burnable mixture becomes available. This phase includes fuel atomization, vaporization, fuel/oxidizer mixing, and chemical radical formation: it is dominated by the fuel vapor-air mixing process. A final late combustion phase may be seen if fuel is not fully burned and then continues to burn through expansion, or energy in soot and other combustion products are released. Combustion progresses, but the falling pressures and temperatures through expansion will significantly slow the kinetics. A prime benefit of diesel engines over their gasoline spark-ignition counterparts is higher efficiency. This is achieved in part by running without a throttle, since the mixture is not required to have equivalence ratio, φ, equal to unity, as with 12

27 homogeneous spark-ignition engines. Since there is no fuel in the engine chamber until fuel injection, knock is not a concern, so higher, and more efficient, compression ratios may be used, improving the fuel economy. Ignition delay is an important characteristic governed by the choice of fuel, which affects mixing by its volatility. Mixing rates control the fuel burning rate, affecting the timing and duration of the burn, and also limit engine speed. This mixingcontrolled combustion highlights the need to account properly for turbulence. Engine performance, i.e., global cylinder pressure and emissions, are highly dependent on fuel mixing. However, it is the emissions that are of greatest concern, because of the need to apply diesel engines more broadly to benefit from their inherent efficiency advantage, while meeting government regulations on air pollutants. Much work for achieving low diesel emissions has been focused on the aftertreatment end, in designing catalysts to capture the main emissions species of hydrocarbons, carbon monoxide, soot, and NO x (all of which have catalysts that require low-sulfur fuel to avoid poisoning). Such systems include soot filters, diesel hydrocarbon and carbon monoxide catalysts, and various NO x control strategies including lean-no x traps and urea selective catalytic reduction [26]. However, advances in fuel injection, including metering control and higher pressure injectors, and increased use of EGR (which reduces overall temperatures because of the higher heat capacities of the exhaust gases) have made progress in reducing in-cylinder soot and NO x. This direct-injection mode of diesel operation has been standard for the past decade as fuel injection systems have advanced in sophistication and spray pressure has increased, while spray control for precise injection timings, fuel metering, and injection profiles has also improved. Issues such as wall impingement, spray distribution (injection pressure), spray arrangement, piston geometry, and spray shape are all important to diesel performance and emissions [4]. 13

28 2.3 Advanced Diesel-Based HCCI/PCCI Engines Research on conventional diesel modes makes progress in part with new advances in the basic engine components such as the injection system, EGR control, and fueling strategies that push the combustion towards a more homogeneous-like system (e.g., see [27] for an example of an advanced diesel mode). The holy grail in compression-ignition engine research is the stable and flexible control of homogeneouscharge compression-ignition. Key advantages of diesel-based HCCI combustion systems are [1]: Low NO x emissions Low soot emissions High thermal efficiency Lower cost because of lower-pressure fuel-injection and less rigorous emissions aftertreatment equipment [3] These advantages are a result of running with a homogeneous charge (as in a conventional gasoline spark-ignition engine) and compression igniting a lean or dilute mixture. Because there is no spark, HCCI relies on autoignition (chemistry) to time the combustion event. Ignition occurs essentially simultaneously throughout the cylinder, or at several places within the cylinder, eliminating flame propagation. This combustion mode avoids the fuel-rich regions of combustion that are characteristic of diffusion flames and lead to high sooting. NO x production is low because the peak temperature is low. Also, the reliance on autoignition rather than flame propagation allows for significantly leaner or more dilute operation than conventional combustion modes. Running unthrottled with lean or dilute operation yields a high thermal efficiency. Engine-out emissions are low, although aftertreatment still generally is 14

29 required to meet the stringent European or U.S. tailpipe emissions standards. The combination of these benefits makes an attractive engine combustion system. Compared to SI gasoline engines, HCCI engines are more efficient because of the elimination of throttling losses, the use of a higher compression ratio, and the shorter combustion duration (because combustion no longer proceeds by flame propagation). For gasoline applications, the NO x emissions are comparably lower as well. Compared to CIDI diesel engines, the main advantages of HCCI engines are reduced particulate matter and NO x, the most problematic emissions species to meeting future regulations. Low-temperature and dilute operation help reduce these significantly, especially since higher dilution may be achieved because the need for flame propagation is eliminated as long as ignition is properly achieved (around 800 to 1100 K, depending on fuel). Thermal efficiency should also benefit from the reduced combustion duration, which is no longer primarily controlled by the rate of fuel/air mixing [3]. Control of HCCI combustion over a wide speed and load range has proven to be difficult and researchers are trying several strategies to reliably operate an engine in this mode [28 33]. HCCI does not provide a direct mechanism for ignition timing control, which is typically achieved with fuel-injection timing in the case of a conventional diesel engine, or ignition timing in the case of a conventional spark-ignition engine. Autoignition processes rely on pressure, temperature, and composition: temperature, in particular. These must all be properly controlled so that the combustion event will occur at the optimal timing for greatest efficiency. Low HCCI operating temperatures lead to incomplete combustion and high engine-out emissions of unburned hydrocarbons (UHC) and CO, which also can result from crevice volumes. Other issues include controlling the rate of heat release (which can be significantly higher than in conventional engines and is another reason for lean or dilute operation), cold start, high-load operation, and transient operation. Efficiency issues at low-load and knocking issues at high-load currently restrict the range of HCCI operation. An 15

30 optimal temperature range for HCCI combustion is K peak in-cylinder temperature. This is high enough to allow for complete CO-to-CO 2 conversion yet low enough to avoid significant NO x formation [34]. Major areas of research in HCCI revolve around controlling HCCI combustion over the operating range required for an automobile. Key areas include understanding the governing chemical kinetics [34] and applying appropriate engine controls, including optimal use of EGR as a diluent to control combustion by limiting the rate-ofpressure-rise and preventing significant flame propagation. Improved understanding of chemical kinetics is crucial because of the current uncertainty of low-temperature autoignition chemistry. This encompasses reaction pathways and rates for the range of candidate fuels and additives, which affects their local and global behaviors. For example, modeling the correct pool of radicals and resultant increase of the local gas temperature can be critical to pressure and emissions predictions [35]. Understanding the kinetics will help drive which fuels and additives to use and how to use them based on their response to temperature, pressure and composition. HCCI has been attempted with both diesel and gasoline-like fuel blends. Typical low-volatility diesel fuels can be used with high compression ratios but do not easily mix with the ambient gas to make a homogeneous charge. High-volatility gasoline fuels mix readily but require a high octane rating to avoid knocking at higher loads and thus cause problems for light-load ignition. Much fuel research, including research into additives and other fuels, is needed to find the optimal choice for this combustion mode. It is likely that HCCI will only be one operating mode for an engine, which may use more conventional operating modes for different regimes in its operating range. In that case, different fuels may be required for each combustion mode, requiring separate fuel tanks, or one fuel must be sufficiently flexible to be used in multiple combustion modes. Chapter 4 of [1] summarizes some of the technical challenges facing HCCI imple- 16

31 mentation. As with any new engineering approach, there are many considerations that must be addressed. Challenges to commercializing HCCI engines include: Start of combustion and burn-rate control Narrow operating regime (engine speed and load) Low power density Difficult operation at full load High rate of heat release at higher loads can lead to knock and engine damage Transient operation Excessive CO and UHC emissions Increased NO x at high loads Difficult cold starts While this partial list is substantial and daunting, the predicted fuel economy and emissions benefits and the lack of many alternatives has fueled research toward solutions for these obstacles. Research is underway in several areas of combustion control including: Fuel choice (e.g., the direct use of traditional diesel fuel in a truly homogeneous charge is not likely given its low volatility) Fuel preparations (premixed, direct-injection timing, split injections) Fuel blends Fuel additives 17

32 Fuel pre-conditioning (e.g., partial cracking) Residuals (and/or EGR) and their composition and effects on reactivity Water injection Pressure boosting Catalytic surface coating of combustion chamber for emissions reduction Intake heating Glowplug usage Thermal barriers Effective compression ratio Engine coolant temperature effects Heat transfer effects Engine speed and load Intentional charge stratification A combination of several of these control strategies and perhaps the development and implementation of others may be necessary to ensure that an HCCI engine could operate robustly under real-world conditions in a vehicle application. Most likely an HCCI-capable engine will need to run in other combustion modes for full-load and low-load operation [36]. As a step towards the practical implementation of HCCI, PCCI-type combustion systems are in development as a bridge to that combustion regime. These PCCI modes 18

33 will begin to approach some premixed-ness in operation. Through the controls mentioned above including earlier-than-conventional injection strategies and aggressive EGR use as a diluent (increasing mixture specific heat), more stringent low-emissions targets should be achievable, meeting future government regulations. Early injection strategies can enhance mixing with earlier vaporization, resulting in fewer fuel rich zones that are sources for soot emissions. Use of EGR helps limit peak cylinder temperatures, reducing production of thermal NO x. The PCCI mode is the type of engine combustion that is investigated in this thesis. 2.4 Review of HCCI/PCCI Research Efforts In this section we will review recent experimental and modeling studies of HCCI/PCCI engines to examine the impetus for better understanding engine combustion and the reasons for attempting detailed engine modeling. Sjöberg et al. [37] investigated the thermodynamic and chemical effects of EGR on HCCI ignition characteristics. They note that EGR can be used to help control combustion phasing. Using a variety of fuels (single-stage ignition fuels, gasoline and iso-octane; two-stage ignition fuels, PRF60 and PRF80) and EGR compositions (real, dry, and individual EGR constituents [N 2, CO 2, and H 2 O]), they performed both experimental and simulated (using the Senkin application of the Chemkin III kinetic rates code [38]) experiments to gauge the effects. In general, EGR addition would retard the start of combustion for fixed inlet temperatures and charge-to-fuel-mass ratio, with notable variations due to the fuel type and the kind of EGR supplied. Four major retarding mechanisms were observed in the experimental tests: 1) A thermodynamic cooling effect is provided by the addition of CO 2 and H 2 O, a result of the species high specific-heat capacities, which is expected for tri-atomic species as compared to diatomic air species, O 2 and N 2. Single-stage ignition fuels (iso- 19

34 octane and gasoline) proved more sensitive to this effect than two-stage ignition fuels (PRF80 and PRF60); 2) An O 2 reduction effect due to EGR displacement of fresh air (a dilution effect ) shows a strong retarding effect for two-stage ignition fuels but a weak effect for the single-stage ignition fuels; 3) Enhancement of autoignition due to H 2 O shows strong effects for two-stage ignition fuels, but much weaker effects for single-stage ignition gasoline and iso-octane fuels; and 4) Enhancement or suppression of autoignition due to the presence of trace species such as unburned hydrocarbons, carbon monoxide, and nitrogen oxide. Single-stage ignition fuels saw autoignition enhanced by the trace species while PRF80 showed retardation. While the simulations showed adequate thermodynamic treatment of EGR, the retard in autoignition seen experimentally was not matched. The authors believe that a main problem of the chemical mechanisms is insufficient sensitivity to the O 2 -reducing effect of added EGR, a characteristic that could be improved. These fuel effects are reasons for the emphasis placed on kinetic modeling and real fuel mechanism development, as will be discussed in Chapter 3. It should also be noted that the full effects of EGR may not be adequately captured by current EGR modeling efforts for real engines, as used in this work, since trace species are not included in the modeled EGR, thus potentially omitting some effects on ignition. However, the overall effects of EGR addition, combining the thermodynamic cooling effect, O 2 reduction, and autoignition timing effects can generally be captured by engine modeling as seen in [39] and shown later in this thesis. Work by Kuzuyama et al. represents some of the industry efforts towards making HCCI viable. The setup described in their experiments and simulations [36] show some of the tangible progress being made towards a reliable control of HCCI. Fuel choice in their setup was natural gas. They noted that the use of intake air heating used in previous studies [40, 41] for combustion control can be detrimental to the overall efficiency of the system. A heat exchanger between exhaust and intake gases 20

35 would be difficult to operate at low loads when HCCI exhaust temperatures are very low. If an electrical heater was used on the intake, the power consumption could likely reduce overall thermal efficiency. Efforts were made to effecting HCCI control through internal EGR in one study. Combustion-chamber geometry, turbocharging, and external EGR were investigated for expanding the operating range. High-load operation in HCCI mode was achievable through the use of internal and external EGR and turbocharging. However, high engine speeds, while more efficient because of reduced heat loss, proved problematic for stability because of the reduced time for autoignition. Whereas richer air-fuel ratios helped with stability, combustion noise became an issue. However, a combination of external cooled EGR and a hot spot in the cylinder, investigated both through simulation and with a ceramic glow plug, showed combustion stability with reduced combustion noise. The authors conclude that this is due to the cooler intake temperature combined with the temperature stratification produced by the glow plug that combines ignitability with a reduced rate of combustion. Combustion mode switching was also demonstrated. Cam profiles were varied without misfire in going from SI to HCCI operation, keeping combustion noise within acceptable levels through control of the throttle valve, fuel control valve, and exhaustvalve closing timing. This demonstrated the ability to capture an appropriate fuel/air mixture for HCCI operation on the first cycle of a combustion mode switch. Szybist and Bunting [42] also used intake air heating as a combustion control in their investigation of cetane number effects on HCCI performance. Blends of diesel secondary reference fuels used for cetane rating provided a cetane number range of 19 to 76, which was combined with an intake temperature sweep. They found that fuel blends with low cetane numbers required higher intake temperatures for ignition. The higher cetane number blends, however, exhibited strong low-temperature heatrelease (LTHR), an effect not noticeable for the low cetane number blends. These 21

36 high cetane number blends exhibited high CO emissions when run with retarded combustion phasing. Since the products of LTHR are high in CO, this seemed to suggest that the high cetane number blends would benefit from earlier combustion phasing in order to avoid cylinder expansion quenching effects. For low cetane number blends, retarded combustion phasing was suggested to avoid high pressure rise rates and the resulting higher NO x. Variable valve timing is also a key HCCI control parameter in work by Morikawa and Ishibashi [43]. They used variable valve timing for controlled auto-ignition, which allows for compression ratio and internal EGR control, focusing on a parameter that follows the difference between the adiabatic flame temperature and in-cylinder gas temperature before combustion. Other researchers have also looked at variable valve timing to control compression ratio and internal EGR, in particular Caton et al. [44] and Shaver et al. [33], all with a view towards HCCI control. Their work extends from the view of control theory and utilizes the effects that may be achieved through variable valve actuation to control compression ratios and the effects on efficiency in the work of [44], examining intake-valve opening and closing and exhaust-valve opening timings as the control parameters. Outputs such as composition, compression work, and exhaust temperature were all examined to assess their overall effects on HCCI phasing and stability of combustion. The work in [33] focused on physics-based control to utilize a fully variable valve actuation providing tight cycle-to-cycle HCCI control, which is important because of the lack of a direct ignition-control method. Coupling the valve timings to inducted gas composition and effective compression ratio, they developed a model for HCCI control. PCCI combustion has been investigated by Lilik et al. [45], using early fuel injection in a conventional common rail diesel engine to enhance ignition delay and increase premixing of fuel and air. This operation follows work by Wagner et al. [46], 22

37 Sluder et al. [47], and Sluder and Wagner [48] on a high efficiency clean combustion operating mode, utilizing single pulse injection, 50% EGR, early injection timing, and increased injection pressure. The higher injection pressure decreases the duration of the injection event, permitting more fuel to premix before ignition. Since the mixture is more locally lean than conventional diesel engines, particulate matter may be reduced. The dilution effect of EGR allows for reduction in NO x. Lilik et al. s experiments produced both results with an improvement in fuel economy, but with increases in hydrocarbon and carbon monoxide emissions, which have been commonly observed for PCCI and HCCI-type combustion modes. HCCI operating range expansion has been attempted through the use of stratified charge, as in the work by Aroonsrisopon et al. [49]. Using a Cooperative Fuels Research (CFR) engine, they expanded the lean limit of the operating range by using two injectors, one for creating a premixed charge and one for introducing fuel stratification. The proportion of fuel introduced between the two injectors was varied and showed that this approach helped significantly with indicated mean effective pressure (IMEP) and emissions at the lean limit. The rich limit, however, showed issues with high-pressure-rise rate and high CO and NO x emissions. This may have been exacerbated by the location of the stratifying injector, on the side of the cylinder, which caused significant wall wetting. The added complexity of engine control creates a higher level of engine management, where local fuel mixtures, flow dynamics, engine operating conditions, and other factors can be directly varied to optimize engine efficiency and emissions performance. Price et al. [50], noting that many gasoline HCCI engine tests seemed to show negligible soot emissions, while most diesel HCCI engine tests showed soot emission significantly lower that DI diesels, performed a study to more carefully track soot particles, especially ultra-fine soot particles that may escape detection from more 23

38 typical soot measuring instruments. For a DI gasoline HCCI engine, they found that soot was non-negligible based on particle number, from which they expect nonnegligible soot mass. Chemical kinetic controls have also been examined, such as fuel additives or, as in work by Ogawa et al., separate additions of water or other chemicals to aid control and expand the combustion range [51]. In this work, the experiment utilized light naphtha, which has two-stage ignition, inducted through the intake manifold, and water or a low-ignitability fuel, which does not exhibit low-temperature oxidation, directly injected early in compression for ignition suppression for HCCI applications. This resulted in the ability to control emissions levels of NO x and smoke with stable combustion. Temperature increases were reduced when the water injection inhibited the low-temperature oxidation. They also found that with the direct injection of methanol, a strong chemical effect on radical reduction (i.e., primarily OH) is seen, producing a large suppression of oxidation rates. In general, alcohols exhibited stronger reaction suppression than other oxygenated fuels. Upatnieks and Mueller [52] have shown that the use of short-ignition-delay oxygenated fuel may help traditional direct-injection combustion strategies achieve lowtemperature combustion with near-zero engine-out NO x and smoke when combined with charge-gas dilution. Control is simplified because direct-injection of fuel can continue to be used as the ignition trigger. Diethylene glycol diethyl ether was used as the diesel oxygenate in tests run with an optical engine varying temperature, density, and nitrogen dilution of the charge gas, and varying fueling rate and injection timing. Both gasoline and diesel-type fuels are being investigated for HCCI use. In many cases, the type of fuel is chosen so that an additional combustion mode, either homogeneous spark-ignition or direct-injection compression-ignition, can be utilized for load ranges beyond that for which HCCI is suitable. As a result, significant efforts [53, 54] 24

39 are being focused on experiments and chemical kinetic models for surrogate gasoline and diesel fuels in view of the research that will require this knowledge and understanding to make the decision on how to use each type of fuel. 2.5 Summary This chapter has explained the nature of internal engine combustion and the different operating modes that are standard or are being developed. In general, four main avenues are available for combustion: 1) homogeneous-charge spark-ignition (the typical consumer engine mode); 2) stratified-charge compression-ignition (a modern engine combustion mode used for higher efficiency); 3) stratified-charge spark-ignition, which is a newer, promising combustion mode for gasoline engines; and 4) homogeneouscharge compression-ignition, which holds the promise of higher efficiency and low emissions. Issues concerning their performance include stability (misfire) and emissions control. The newer engine modes, the DISI and HCCI concepts, should improve over the current spark-ignition and compression-ignition engines in terms of efficiency and/or emissions. Given ideal conditions, the DISI engine mode should be able to attain higher efficiency than its homogeneous spark-ignition mode counterpart, but issues of cycle-to-cycle variability have created issues for its efficiency and emissions. Emissions are harder to control in DISI modes because of the overall fuel-lean stoichiometry. HCCI engines should be able to reduce soot and NO x emissions because of reduced fuel-rich regions and lower operating temperatures, respectively. There may also be some efficiency benefit due to running leaner. However, HCCI cycle-to-cycle variability is also an issue and its control is a major area of research. A review of the research shows several different approaches to achieving control of these combustion modes. Work is also being performed on what types of fuels would 25

40 be most appropriate for HCCI combustion modes. A combination of experimental and modeling tools are being used to help determine what control knobs best fit this application and the degree of each effect. Turbulence effects on HCCI and PCCI type engine modes are examined in this thesis. As some of the reviewed research shows, there is a need to understand better the interaction between turbulence and chemistry. Experiments have shown some of the effects of turbulence, such as with the use of different piston-top geometries. The use of CFD to examine these details can provide information to which engine diagnostics do not currently have access. 26

41 Chapter 3 Fuels, Chemical Kinetics, and Soot Fuel type is crucially important for the mode of combustion and the resulting combustion behavior. While fuel choice is ultimately important for the combustion mode, it also will influence detailed combustion behavior, including effects such as two-stage ignition, typical of a fuel like n-heptane, and autoignition, as will be discussed below. Such characteristics can have wide affects, such as how much EGR may be used or what peak pressures may be attained. Generally, there will be different limiting behaviors of fuels that recommend or demote their usability for a given combustion system. The fuel that provides the greatest operating range and overall performance would likely be the fuel of preference. However, with experimental research investigating several different fuels, there are only a limited number of surrogate fuels that have reliable chemical mechanisms for computational use. Thus, there is already a discrepancy between models and actual experiments that use novel fuels for which corresponding chemical kinetic reaction mechanisms are not available. Furthermore, even those mechanisms that do exist may still need further refinement, or may be too large to be used in an engineering-scale simulation. Skeletal mechanisms have been used, but these can also fall short in that they lose some detailed behavior. 27

42 3.1 Fuels Chemical energy stored in the bonds of molecules have long been a main source of energy. While nuclear energy and renewable energy from solar, wind, and geothermal sources will likely provide a greater proportion of energy, fossil fuels and biofuels will be the largest sources of energy for the foreseeable future. As a major transportation fuel source, it is necessary to understand the mechanisms of energy conversion from hydrocarbons to discover the most efficient means to use them and reduce their polluting potential. Mathematically, the general formulation of chemically reactive flows consist of equations for conservation of mass, momentum, energy, and some form of accounting for the fraction in the system of each chemical species, with equations of state and thermodynamic relations (see Chapter 4). The kinetics of chemical species provides the coupling between the species concentrations and the energy equation and these terms will generally define the space and times scales critical to the full system equation set, such as represented by the Damköhler number. The kinetics equations themselves are coupled and since each has its own characteristic timescale, a range of timescales in the set will create what is called a stiffness problem, which adds difficulty to solving the equations. Modern computer packages can handle this problem reasonably, but many methods are being undertaken to further overcome this, as will be discussed later. While the focus of this chapter is on the kinetics of fuel chemistry, some other physical properties are also highly important in the context of the modeling efforts for fuels. These are the liquid properties that affect fuel vaporization for fuel sprays. Modeling fuel sprays will be discussed in the next chapter. It should be noted that understanding the physics of fuel-spray breakup and evaporation is critical because it affects mixture preparation, which in turn has significant effects on combustion behavior. Fuels exhibit varied liquid properties that will in turn affect their spray 28

43 characterization. However most real fuels have multiple components, whereas most fuel models contain no more than a few. The efforts, therefore, in developing models for real fuels involve not only the kinetics of different and mixed fuels, but also the spray effects of different mixtures. When discussing fuel types for internal combustion engines, the focus will be on hydrocarbon fuels, primarily composed of paraffins (alkanes). These fuels are saturated, straight-chain or branched-chain, single-bonded hydrocarbons generally formulated as C n H 2n+2. Other hydrocarbons of interest include cycloalkanes and aromatics, which also comprise significant percentages of real fuels. There are advantages to hydrocarbons as well-known and convenient fuels. Hydrocarbon fuels have a relatively high volumetric energy density compared to alternatives such as hydrogen or battery energy storage. Emissions systems have been or are being developed to reduce the currently regulated pollutants of CO, UHC, NO x, and soot to low levels. However, zero emissions are a long-term target, and lower CO 2 emissions (higher efficiency) are being sought also. Fuel conversion and emissions production from fuels can be understood through the paths of fuel decomposition. These include the breakdown of the main fuel molecule along with the oxidation paths that result from the branching out of the reaction paths. The major mechanisms will be discussed below. There are two main types of hydrocarbon fuels for internal-combustion engine applications. Diesel-type fuels are characterized by low bulk volatility and are generally categorized with the cetane number. The fuels have not typically required significant volatility since compression-ignition engines that spray directly into the combustion chamber have operated with diffusion flames. However, quick vaporization and mixing with oxygen are necessary for combined combustion efficiency and emissions performance, a situation towards which advanced compression-ignition combustion modes are progressing. The steady move towards higher injection pressures has increased 29

44 spray atomization and the rate of fuel vaporization. Fuel-air mixing is thus mainly controlled by the injector and combustion chamber design, which affects the extent of liquid films on walls, since the volatility of diesel fuel is a relatively weaker factor [4]. The cetane number is a measure of ignition quality. It compares the fuel s ignition delay relative to a mixture of n-hexadecane (cetane) and alpha-methyl napthalene: conventional diesel is equivalent to a 50:50 ratio of the two chemicals. The shorter the ignition delay, the higher the cetane number, and the longer the available time for combustion. Ignition quality is highest for straight-chain paraffinic compounds, improving with increasing chain length. Gasoline-type fuels have a requirement for anti-knock qualities, quantified by an octane number, which measures their resistance to reaction as a homogeneous-charge under compression. Gasoline typically has high volatility relative to diesel fuels because of the need to vaporize quickly when used in port-injection configurations. However, in the case of direct-injection spark-ignition setups, the fuel requirements for gasoline may change to optimize the fuel to the combustion mode. Combustion characteristics, such as ignition and the related chemical kinetic pathways, are specific to the fuel type, though there are commonalities within hydrocarbon combustion that will be discussed later in this chapter. Because of the range of characteristics for different fuels, from molecule size to molecule arrangement, oxygenation, and other aspects, a need for appropriate chemical mechanisms has developed so that the questions of fuel choice can be answered for new combustion systems. Researchers including Farrell et al. on the diesel-fuels side [54] and Pitz et al. on the gasoline-fuel side [53] have developed targets for future research for experiments and kinetic databases and models to meet the demand for better fuel mechanisms. Since complete models for every fuel are likely not within reach for the short term, it makes sense to establish surrogates that can capture the major characteristics. Fuel properties are important and need better data, such as lower heating values and hydrogen-to-carbon ratios. Kinetic and fluid dynamic 30

45 knowledge such as elementary kinetic studies, combustion phasing for 10% and 50% mass-fraction burned, heat release, and spray vaporization must be expanded and improved. While some fuel components are well understood, such as n-heptane and iso-octane, several other components need further study. Newer types of fuels, synthetic fuels, oxygenated fuels, and biofuels, will introduce some new chemical components and require additional modeling and experimental effort. For example, biofuels, which are fatty acid esters produced by transesterification with methanol or ethanol of vegetable oil or animal fat, have, methyl oleate or, in the case of soy-derived biodiesel, methyl linoleate as the dominant component [55]. 3.2 Motivation for Detailed Chemical Mechanisms The mechanisms by which molecules decompose and recombine are critical to the physics of combustion. Indeed, Law s Combustion Physics [56] starts the discussion with chemical thermodynamics. Computational fluid dynamic simulations that include complex, realistic chemistry and emissions prediction should be able to significantly aid in development of combustion systems that are high efficiency and low-emissions. But the challenges of the chemical kinetics must first be overcome. Because of the complexity of the engineering system and the complexity of the chemical kinetics, a method using sufficient accuracy and reasonably fast computational time is needed. There are many aspects to producing a chemical mechanism for combustion systems. These include choosing the type of fuel that will be modeled. Most efforts up to now have focused primarily on single-fuel-component chemical mechanisms. There have been some efforts to develop real fuel mechanisms; an example is the diesel mechanism formed by the Integrated Diesel European Action program (IDEA) [57], which created a mechanism to model the binary mixture of 70 vol % n-decane and 31

46 30 vol % 1-methyl-naphthalene. In general, surrogate component selection will be necessary so that the important chemical characteristics are captured from the major species across a range of fuel mixtures, in a simpler representation than a complete fuel component mixture, which will include several hundreds of individual species [58,59]. Because of the local variability in fuel composition, capturing the characteristics of a very specific blend is not particularly useful. Broad combustion characteristics must be understood and modeled. The elementary chemical kinetic, thermochemical, and physical property data for the fuel mechanisms need to be further researched. Even for basic reaction paths, such as CO oxidation, new work continues to show that additional accuracy and precision are needed since there may still be significant uncertainty in the chemical parameters [60,61]. Accurate chemical kinetic models need to be developed that capture sufficient precision in reaction rates for these major pathways. These modeling studies will necessarily go hand in hand with good experimental laboratory tests to provide validation. The combined efforts to produce a valid chemical mechanism must then become subject to mechanism reduction or at least some form of chemistry calculation speedup such as tabulation or on-the-fly reaction tabulation, such as in [16] and [17]. Because of the size of the engineering system, complex chemistry provides a runtime barrier to its use as a development-level model. Increased computing power notwithstanding, methods will need to be developed to reduce the chemical complexity. Chemical mechanism reduction will be key to tractable simulations of reacting systems, as mentioned previously in Section 3.1, with work continuing on new mechanisms and on optimizing and improving current ones [5, 53, 54]. Work such as that by Zeppieri et al. [62] looks towards developing the models that will enable compact kinetic mechanisms of larger carbon number alkanes. Their method is aimed at producing partially reduced skeletal mechanisms and provides a process to help hone in 32

47 on the important pathways to oxidation and pyrolysis. In general, single-component fuel mechanisms have been used instead of multiple-component fuel mechanisms. This is an issue that the groups including [53] and [54] will seek to address in producing surrogate base mechanisms and real fuel mechanisms. 3.3 Gas-Phase Chemical Mechanisms There are several important aspects of chemical mechanisms for gas-phase reaction. For automotive fuels, a few major areas stand out, which are outlined below Hydrocarbon Oxidation and Autoignition Hydrocarbon oxidation has been well studied and the literature is rife with analyses of the processes by which hydrocarbon fuels are consumed. Westbrook and Dryer provide a good review in their 1984 paper [63], where they deal primarily with the higher temperature conditions encountered in flames and explosions (T 1000 K), and Turns and Law provide reviews in their recent books [56,64]. The combination of high temperatures and short time scales complicates analysis because spatial scales are small in turn, adding difficulty to experimental studies. But it is noted that the concepts of high-temperature reactions can be simpler than lower-temperature reactions that occur below 700 K, though even high-temperature kinetic studies remain difficult and much work is still required for turbulent combustion. Hydrocarbon chemistry below 1000 K is important for autoignition. Westbrook and Dryer [63] note the major aspects of hydrocarbon combustion, including sequential fragmentation of the primary fuel molecules into smaller intermediates that are eventually converted to final products, mostly water and carbon dioxide. Key sub-mechanisms and molecules include H 2 -O 2, O 3, CO, CH 2 O (formaldehyde), CH 4, C 2 H 6, C 2 H 4, C 2 H 2 (acetylene, a soot precursor), and aromatics. Some 33

48 of these are discussed in more detail below. Pollutant formation reactions must also be considered. Small hydrocarbons can exhibit very specific oxidation behavior, methane being one of the most studied and intriguing. Most of the higher hydrocarbons can eventually follow the oxidation patterns of the smaller hydrocarbons following the breakup of their larger chains, such as through β-scission (a rule that determines which C-C or C-H bond will be broken) and hydrogen-abstraction reactions. In general, three sequential processes are followed: 1) the fuel is broken up by O and H atoms, mainly forming olefins and hydrogen. The hydrogen can oxidize to water; 2) the unsaturated olefins will further oxidize to carbon monoxide or H 2. The H 2 will convert to water; 3) the carbon monoxide will then burn out. Most of the heat release due to the combustion is produced in this step CO Oxidation While the oxidation mechanism for CO has been well-studied [63 65] and is relatively straightforward, it remains difficult to predict CO emissions in engineering applications. Some of this is because of non-kinetic factors. However, there still may be some improvements to the current kinetic models, such as those proposed in a recent paper [60]. CO oxidation is an extremely important step in the complete oxidation of hydrocarbons. In turn, hydrocarbons can inhibit the oxidation of CO [63]. The first two oxidation reactions are: CO + O + M CO 2 + M, (3.1) CO + O 2 CO 2 + O. (3.2) These two steps are slow at typical combustion temperatures. However, in environments with hydrogen atoms even in amounts as small as 20 ppm [66], the CO mechanism becomes strongly coupled to another important mechanism, the H 2 -O 2 34

49 mechanism, and oxidation proceeds through: CO + OH CO 2 + H, (3.3) CO + HO 2 CO 2 + OH. (3.4) Reaction 3.3 is the most important reaction of these four, and most CO 2 results from it. While it is an elementary reaction, it is actually very complex [67]. This complexity means that the rate shows pressure dependence and variation with the efficiency of different third bodies. Because hydrocarbon species inhibit the chain branching that leads to OH radicals, CO oxidation is usually delayed until most of the hydrocarbon species have been consumed and the OH concentrations then rise. Reaction 3.3, however, is also a chain-propagating step, producing H atoms that react with O 2 to form OH and O: H + O 2 OH + O, (3.5) which, as can be seen, in turn fuels itself through reaction NO x Formation There are generally three major paths for NO x formation. Following Turns [64], these are thermal, prompt, and N 2 O-related paths. Thermal NO x generally becomes the dominant method of formation when temperatures exceed K, with NO x formation exponentially increasing with temperature. Thus, much engine research has aimed at reducing engine temperatures in order to avoid crossing into the temperature regime in which thermal NO x formation rapidly accelerates. The thermal, or Zeldovich, mechanism, includes two chain reactions: O + N 2 NO + N, (3.6) N + O 2 NO + O, (3.7) 35

50 and may be extended with a third reaction: N + OH NO + H. (3.8) The thermal mechanism is strongly dependent on temperature because of the high activation energy for the first reaction. Generally, this mechanism is considered unimportant below about 1800 K. However, its importance increases exponentially with temperature, strongly producing NO as temperatures rise above 1800 K. The coupling of the thermal mechanism to the concentrations of O 2, O, and OH species is important in cases where fuel combustion continues during NO formation. There are processes when NO formation takes place after fuel combustion, providing simpler conditions for analysis. In processes where fuel combustion and NO formation are concurrent there can be situations of super-equilibrium O and OH atoms that contribute significantly to increasing NO formation rates. N 2 O provides another path for NO x formation, called the N 2 O-intermediate mechanism, which is important in fuel-lean (φ < 0.8), low-temperature conditions. Three steps of this pathway are: O + N 2 + M N 2 O + M, (3.9) H + N 2 O NO + NH, (3.10) O + N 2 O NO + NO. (3.11) This NO x pathway may have particular importance for the newer engine technologies that utilize lean global mixtures, especially in the case of HCCI. The prompt NO, or Fenimore, mechanism is a path directly influenced by fuel chemistry. In general, the scheme takes hydrocarbon radicals and reacts them with molecular nitrogen to form amines or cyano compounds. These turn into intermedi- 36

51 ates that lead to NO production. For equivalence ratios above 1.2, the chain sequence can be very complex. For ratios less than 1.2, this general scheme has been proposed: CH + N 2 HCN + N, (3.12) C + N 2 CN + N, (3.13) HCN + O NCO + H, (3.14) NCO + H NH + CO, (3.15) NH + H N + H 2, (3.16) N + OH NO + H. (3.17) In addition, fuel-bound nitrogen is one other source of reaction paths for NO x formation, noted, for example, in [68], but this is not typically important for transportation fuels. Work by Glarborg and coworkers [6] and a paper by Glarborg [69] highlight the need for detailed chemical mechanisms for NO x formation. Several reaction paths may be necessary to properly capture NO x formation over the range of engine operation, especially with newer combustion modes that almost assuredly will reach operating conditions different from current modes. While typical models include only the major fuel components, small quantities of sulfur, chlorine, or potassium and sodium can be found in some fuels, and may be in higher quantities in fuels processed from cruder sources. These trace species can affect combustion and emissions, including NO x Integrated Mechanisms Here NO x chemistry from Glarborg etal. [6] has been incorporated in the n-heptane mechanism produced in Kung et al. [21]. The basic premise behind this work was to more accurately predict NO x formation by including a wider range of chemical path- 37

52 ways that affect its formation, including low-equivalence-ratio and low-temperature situations. With typical diesel operation, NO x formation has been dominated by thermal NO x. However, PCCI and HCCI combustion modes aim to keep temperatures below the threshold for significant thermal NO, i.e., 1700 K. In these cases, then, to accurately predict NO x it is reasonable to include the other major paths that may more significantly impact overall NO x. The numerical study in [21] found that this can be the case, agreeing with earlier work done by Mehresh et al. [10] and Correa and Smooke [70] Real Fuels Fuel choice can affect autoignition reactivity and the corresponding high-load limits of HCCI, as demonstrated by Sjöberg and Dec [71]. There they looked at three fuels: isooctane, PRF80 (an 80/20 volumetric mix of the primary reference fuels, iso-octane and n-heptane, respectively), and PRF60. Running in a single-cylinder HCCI research engine they found five load-limiting factors with different fuels: 1) wall-heating-induced run-away, 2) NO x -induced combustion-phasing runaway, 3) EGR-induced oxygen deprivation, 4) excessive exhaust NO x, and 5) wandering unsteady combustion. 1), 4), and 5) were issues for iso-octane, which has the highest resistance to autoignition. PRF60, a very reactive fuel, was limited by 3). Operation with PRF80 was limited by 2), which is perhaps understandable as it also had the highest IMEP for the study conditions. Trace amounts of NO x, even through recycled residuals, can act as an ignition enhancer, thus feeding the cycle for higher temperatures and increased NO x unless properly restrained. In general, the study found that PRF60 and PRF80 produced higher IMEP than iso-octane, which may be expected given the resistance to auto-ignition of a highoctane fuel. The two-stage ignition of the PRF fuels allows for a more retarded timing for 50% fuel mass burned. Their reactivity allows lower inlet temperatures, which 38

53 in turn means that more fresh oxidizer may be inducted. However, the efficiency of these fuels can lag that of the iso-octane because of the need for 50% fuel burned retardation. As can be seen from this and other studies into fuel choice, there are significant considerations that will need to be resolved for production engines CHEMKIN-Based Thermochemistry and Kinetics The CHEMKIN package, initially developed by Kee, Rupley, and Miller [72], can be used within the context of larger simulations of elementary chemical reactions in flows. CHEMKIN provides a standard interface that is multi-purpose and problemindependent. The user must provide a thermochemical database that includes the constant-pressure specific heat, standard-state enthalpy, and standard-state entropy polynomial curve-fit coefficients for each species in the mechanism. CHEMKIN uses the modified Arrhenius expression for elementary chemical reactions, though newer packages are more flexible and allow other options for how one may express the chemical formulas. In this thesis, CHEMKIN has been used to implement thermochemistry and chemical kinetics. 3.4 Soot Modeling In non-premixed hydrocarbon-air flames, soot may be generated. Soot is generally formed in the temperature range from 1300 K to 1600 K, a range that, for diesel engines, is available with the heterogeneous combustion typical of modern liquid-fuel direct-injection engines. The complexity of engine flows and combustion makes soot, which is already difficult to model in simple configurations, very difficult to model in engines. Some of the earliest engine soot modeling work was reported by Hiroyasu and 39

54 Kadota [73]. This modeling effort and subsequent variants were based on two empirical rate equations, one for formation and one for oxidation, that are functions of the key gas-phase reactant concentrations. The simplicity of this type of modeling makes it amenable to implementation and computationally efficient use in CFD engine codes. These types of models do not take into account particle growth and soot dynamics, leaving out some of the important physical processes of soot formation and destruction. The empirical nature prevents the model from being used extensively over a wide range of conditions unless there has been previous validation and tuning for these conditions. More physical models have been implemented while attempting to maintain computational tractability, utilizing the ever-more-powerful computers and improved algorithms and solvers that have been developed. Improvements and additions to soot modeling have included adding intermediate species for particle nucleation and particle growth and agglomeration [74]. For example, Frenklach and Wang estimate the nucleation rates of soot by looking at the collisions of higher polycyclic aromatic hydrocarbon (PAH) compounds [75]. Earlier work by Frenklach had already established the significant role of physical and chemical PAH coalescence to soot inception [76,77]. These additional soot features, however, are computationally expensive to use in engineering applications. As an example of one variable in soot formation, Law [56] discusses two pathways to soot growth, the H-abstraction C 2 H 2 -addition (HACA) path or benzene-ring combination. The dominant pathway seems to be dependent on which soot precursor (acetylene, C 2 H 2, or benzene) is more prevalent. While this may be examined in canonical laboratory flames, engine diagnostics provide no easy access to monitor the pathway of soot growth directly. That is one reason why modeling soot in engines is desirable. For the same reason, modeling soot in engines is difficult because of the lack of data against which to calibrate or compare. Most soot data are engine-out 40

55 observations (with smoke as the directly measured quantity, indicating particulate matter, of which soot is a fraction), and difficulties arise if soot evolves significantly downstream of the combustion chamber. Combustion simulations typically do not go beyond exhaust-valve opening. More detailed and multistep chemical models for soot have been developed for canonical systems that can be more easily set up and examined both experimentally and computationally. These include laminar flames [75], counterflow diffusion flames [78, 79], and turbulent non-premixed flames [80]. Detailed soot-modeling approaches have been applied in some engine applications, such as [81] and [74]. It is from this body of work that the soot modeling effort in this thesis derives. As soot is not the primary focus of this thesis, a comprehensive review is not included here. Rather, a skeletal framework is provided to allow the reader to explore further through the references Two-Equation Soot Model Two-equation models generally seem to provide reasonable accuracy along with highly desirable computational efficiency. The two-equation soot model as described in [82] provides a simplified reaction mechanism for formation, growth, and oxidation of soot particles. The model is based directly on the use of acetylene, C 2 H 2, which is intimately involved in soot inception. This starting point provides the link to detailed gas-phase chemistry. Two conservation equations must be solved, one for the soot mass-fraction and one for the number density. The model assumes spherical particle shapes, which, while unphysical, closes the model. Additional factors such as particle age and surface growth are not modeled. However, it has been suggested [83] based on experiments that soot mass growth is, to first order, based on acetylene concentration. The model will generally reduce particle size during oxidation while not modifying particle number, 41

56 another unphysical attribute, but overall one not too grievous since particle number is not strongly coupled to the reaction rates. Below are the four major reaction steps in this soot mechanism, where C(s) represents solid carbon, i.e., soot. The first two are steps for soot mass and number formation. The third is the soot oxidation. The fourth represents soot agglomeration, i.e., reduction of soot particle number Method of Moments C 2 H 2 2C(s) + H 2, (3.18) C 2 H 2 + nc(s) (n + 2)C(s) + H 2, (3.19) C(s) + 1/2O 2 CO, (3.20) nc(s) C n (s). (3.21) The method of moments soot model is a more involved and comprehensive model than the two-equation model; the reader is directed to [84] for more detail. What this model attempts to capture is additional mathematical and physical rigor with reasonable numerical economy to represent a particle undergoing simultaneous nucleation, coagulation, and surface growth. Based on solving Smoluchowski s master equations of Brownian coagulation, the equations for the evolution of the particle population may be written in terms of moments: dm r dt = d dt m r i N i, (3.22) i=1 where the subscript or superscript r represents the r-th moment order, t is time, and m i is the mass and N i is the particle number density of the i-th particle size class. Knowing all of these moments should, theoretically, provide complete knowledge of the particle size distribution, but in practice only the first few moments are really necessary. The method thus draws on the mathematical basis of a more general approach to problems in this class, but is able to approximate quite well with a small set 42

57 of lowest-order moments; here, six moments have been retained. Closure of the finite set is the crucial aspect of the model. That is accomplished by establishing expressions for the modification of the moments by the physical processes of soot formation and destruction. In the case of [84], this includes particle coagulation/nucleation, surface growth and aggregation. For engine applications, this should provide a more physically accurate model for soot emissions. Acetylene is used as the soot precursor for this thesis. Other researchers, such as Hong et al. [74], have applied the method of moments model to engine soot predictions. In their case, they apply it in a finite-volume solver using a skeletal n-heptane gas-phase reaction mechanism. Their studies showed good agreement between simulations and experiments in shock tubes and diesel engine smoke-number measurements. Studies such as this one show that a detailed soot model can be applied to engineering-scale systems. Here a method-of-moments soot model will be used in combination with the PDF method. 3.5 Summary Fuel effects and key oxidation pathways have been discussed in this chapter. Hydrocarbon oxidation, CO oxidation, and NO x formation were detailed. Soot and its formation and oxidation were discussed along with two models for its treatment in simulations. These chemical kinetic aspects are essential to modeling accuracy. In this work, chemical kinetics and thermochemistry are handled through the CHEMKIN libraries [72]. N-heptane often is used as a surrogate for diesel-like fuels. Several reduced n-heptane mechanisms are available, ranging from 29-species and 52- reactions to more than 100-species and 600-reactions. For this thesis, two mechanisms have been used (See Appendix A). The first is an n-heptane mechanism based on a 40-species skeletal mechanism from Chalmers and the University of Wisconsin [85 43

58 87]. This mechanism has 34 species and 74 reactions (including NOx chemistry) and includes an N 2 O pathway for low-temperature, lean NOx production. The second is a 71-species mechanism, assembled in [21], based on the 40-species skeletal mechanism from Chalmers [85] and incorporating the NO x chemistry from [6]. For both cases, parallel processing is used to accelerate the chemical reaction calculation. 44

59 Chapter 4 Physical Models and Numerical Methods Results from experimental tests have been complemented by computer simulations, from zero-dimensional to three-dimensional models, utilizing a variety of models for sprays, chemical kinetics, and combustion. CFD-based combustion modeling is the platform used in the recent research. The transported composition probability density function method is used to model turbulent combustion. PDF methods have shown promise in canonical configurations and simple engine-like geometries. The model s strength lies in its ability to treat exactly the effects of turbulent fluctuations on mean chemical source terms. This model is coupled with detailed chemical kinetics and a strategy for calculation acceleration. 4.1 Advanced Diesel Modeling Challenges Modeling an engine involves many factors, including, though not limited to, the spatial dimensionality, spray model, turbulence model, and chemical kinetics. Increasing spatial dimensionality generally increases complexity and the computational effort for the benefit of improved accuracy: e.g., going from a multi-zone model to a severalthousand-cell combustion chamber mesh. Spray characterization accuracy is critical 45

60 to simulating direct-injection engines that are sensitive to sprays and their effects on in-cylinder fuel distribution, i.e., mixture preparation. Turbulence can significantly affect the species and enthalpy distributions, and thus affects heat release and emissions. There remain significant uncertainties in chemical kinetics for practical hydrocarbon fuels. Studies [61, 88, 89] have shown that even simple species and reactions may have significant uncertainties in their thermodynamic properties and rate coefficients, enough to produce marked differences in computed ignition timings under HCCI conditions. Furthermore, there is a need for chemical mechanisms of surrogate fuels that can accurately model the behavior of real fuels [90]. An example of a modeling challenge that likely involves chemical kinetics, mixture preparation, and turbulence effects is carbon monoxide emissions prediction [39]. While the chemistry for CO formation and consumption have been extensively studied, this species seems to be harder to model than hydrocarbon emissions or even NO x emissions. Rate coefficients do continue to be updated for CO [60], but these changes may not be as significant a factor on computed CO emissions as others, which are investigated in Chapter 5. The effects of mixture preparation and turbulence/chemistry interactions are likely the greater sources of error in the calculation, and thus the areas where advances in the models would be very beneficial. These issues and others are important to engine modeling. The area that this work addresses is turbulence and how it affects combustion through turbulence/chemistry interactions in a 3-D CFD simulation. Presented here is a brief review of some of the modeling approaches that have been applied to HCCI engine combustion modeling. Zero-dimensional modeling does not take flow into account; the fluid is modeled as a perfectly mixed system with homogenous reaction and direct effect of boundaries on the whole. It can capture the general experimental trends in some cases but does not intrinsically capture details due to mixing and inhomogeneity [40, 91, 92]. Multi-zone models do better by taking into account combustion-chamber walls 46

61 and crevices [93 95]. These quasi-dimensional models add computational zones corresponding to different physical regions of the engine chamber, thus taking into effect spatial differences in composition and temperature. This added consideration, along with models for interaction between the zones, has shown improved accuracy compared to zero-dimensional models, while providing relatively fast simulation times. 3-D models take into account spatial inhomogeneities with a higher fidelity than multi-zone models. CFD codes typically solve the Reynolds-averaged form of the governing equations for ensemble-averaged mean quantities. This level of modeling is relatively efficient, but requires models for turbulent fluctuations about local mean values. For engine configurations where the effects of flow dynamics and spatial inhomogeneities are small, simple models for TCI may suffice. However, direct in-cylinder fuel injection and increased in-cylinder charge motion will only increase inhomogeneity and the impact of flow structure. Spatial inhomogeneities in composition and temperature are inevitable in a real engine, and intentional stratification is one strategy to reduce the peak rate of pressure rise in HCCI engines. The high-end models that are to be developed here directly address this need for accuracy in modeling turbulence/chemistry interactions. Modes of turbulent combustion include turbulent flame propagation, turbulent mixing-controlled combustion, and chemical-kinetics-controlled situations. Consideration of detailed chemical kinetics is required to capture autoignition and emissions [2]. Flame propagation is primarily a concern for spark-ignition modes, and flamelet models can be particularly useful to capture the physics in those simulations. Flamelet models also have been applied to premixed-charge compression-ignition engines [96]. For HCCI applications, transported PDF methods are appropriate in situations where turbulence/chemistry interactions become important, such as operating conditions with significant swirl or significant inhomogeneity in the composition [9]. There are higher-level models that can provide greater understanding of the un- 47

62 derlying physics of chemically reacting turbulent flows. Direct numerical simulation (DNS) may be used to provide insight into the physics of combustion, but only as a research tool and not as a device-scale modeling tool because of the prohibitive computational cost [97]. Large-eddy simulation with flamelet-based or filtered-density-function-based subfilter-scale models also may be applied to IC-engine combustion [2, 97]. The following sections will review turbulent combustions models, the theory behind these models, and then go into models and their applications to engine combustion. 4.2 Formulations Governing Instantaneous Physical Equations To establish the governing framework for turbulent combustion, the instantaneous partial differential equations (PDE s) that govern a multi-component chemically reacting gas-phase system with N S chemical species are outlined below using Cartesian tensor notation. A Roman index, i or j, will denote a component of a threedimensional vector, with the usual summation convention applying over repeated Roman indices in each term. The Greek index α will denote the chemical species. Conservation of Mass ρ t + ρu i x i = ρṡρ,liq (4.1) ρ is the mixture mass density and u i is the velocity in the i-th direction. Ṡ ρ,liq is the liquid-fuel-spray source term. The first term represents the change in density with time. The second term is the advection of density due to the velocity. The third term is the density source. 48

63 Conservation of Momentum ρu j t + ρu ju i x i = τ ij x i p x j + ρg j + ρṡj u,liq (j = 1, 2, 3) (4.2) τ ij is the viscous stress tensor, p is the pressure and g j is the body force. Ṡ j u,liq is the liquid-fuel-spray source term for momentum. The first term is the change in momentum with time. The second term is the advection of momentum by the velocity and is a nonlinear term. The third term is the effect on momentum of viscosity. The fourth term is the effect on momentum of pressure spatial gradients. The fifth term is the effect on momentum of body forces. The last term is the source term for momentum from the liquid-fuel-spray. Species Transport ρy α t + ρy αu i x i = J α i x i + ρs α + ρṡα Y,liq (α = 1, 2,..., N S ) (4.3) Y α is the mass fraction of species α, J α i is the molecular diffusive flux of species α and S α is the species α chemical source term rate per unit mass. Ṡ α Y,liq is the liquid-fuel-spray source term for species α. The first term is the change in species mass density with time. The second term is the advection of the species mass density by the velocity, a nonlinear term. The third term is the effect of diffusion on species mass density. The fourth term is the source of species mass density due to reaction. The last term is the source of species mass density due to liquid fuel spray. Conservation of Enthalpy (Energy) ρh t + ρhu i x i h is the mixture absolute enthalpy, J h i = J i h + Dp x i Dt + τ u j ij + x Q rad + ρṡh,liq (4.4) i is the molecular transport of enthalpy and Q rad is the radiative heat transfer. Ṡ h,liq is the liquid-fuel-spray source term 49

64 for enthalpy, h. The first term is the change in enthalpy with time. The second term is the advection of enthalpy by velocity, a nonlinear term. The third term is the effect on enthalpy of the diffusion of enthalpy. The fourth term is the effect on enthalpy due to work done by pressure. The fifth term is the effect of viscous dissipation. The sixth term is the effect of radiation. The last term is the effect of the liquid-fuel-spray source on energy. For each species α, the molar chemical production rate is ω α and molecular weight is W α. These can be combined to represent the 2nd term on the right-hand side of the species composition equation as: ρs α = W α ω α. Note that while the enthalpy equation is given here, alternative forms for the energy equation can be used [98]. The energy equation here is for absolute enthalpy (the summation of the sensible and formation enthalpies) and neglect a term for species body forces and diffusion velocities. Forms for the molecular transport terms τ ij, Ji α, and Ji h are not a focus in this work, but standard formulations are used to solve for these in the code, such as given in [72]. Thermal diffusion is typically neglected. Species transport can be modeled using a multicomponent form of Fick s law. Similarly, enthalpy transport may be modeled with a multicomponent form of Fourier s law. The standard approach for representing τ ij is in which µ is a multicomponent mixture viscosity. τ ij = µ( u i x j + u j x i ) 2 3 µ u l x l δ ij, (4.5) The thermal equation of state provides the density: ρ = ρ(p, h, Y ), (4.6) 50

65 and the caloric equation of state provides the temperature T = T (p, h, Y ). (4.7) Ideal-gas properties are typically assumed, giving the state equations and p = ρrt N S h = Y α ( h 0 f,α + α=1 (R = R U ), (4.8) W T T 0 C p,α (T )dt ), (4.9) where R U is the universal gas constant, W is the mixture molecular weight, h 0 f,α is the formation enthalpy for species α at T 0, the reference temperature, and C p,α is the constant-pressure specific heat for species α. Certain fluid properties are required to complete the equations, such as viscosity, species diffusivities and species thermal conductivities, and species constant-pressure and constant-volume specific heats. All these equations of state are standard and can be found in any thermodynamics text, such as [99]; they are also nicely summarized in [97]. A general expression for an arbitrary elementary chemical reaction mechanism with N S chemical species can be written in compact notation as a set of L reversible chemical reactions: ν l α and ν l α N S α=1 N S ν l αm α α=1 ν l αm α (l = 1, 2,..., L). (4.10) are stoichiometric coefficients on the reactant and product sides of the equation, respectively, for species α in the l th reaction. M α simply denotes a chemical species. The matrix forms of ν will be sparse for large numbers of species since any elementary reaction usually will involve no more than three reactant species. From this, the molar rate of production for species α, ω α, is given by the law of mass action: L ω α = {(ν l α ν l α) [ N S N S ] k l,f (T ) c ν lβ β k l,r (T ) c ν lβ }, (4.11) l=1 β=1 β=1 β 51

66 where k l,f (T ) and k l,r (T ) are the forward and reverse rate coefficients for the l th reaction, respectively, related through an equilibrium constant. c β is the molar concentration of species β. The rate coefficients are typically formed using the modified Arrhenius expression, k l,f (T ) = A l,f T b l,f exp{ E A l,f /(R U T )}, (4.12) developed from first principles [100], where three empirical coefficients the preexponential A l,f, temperature exponent b l,f, and activation energy E A l,f define the forward reaction rate for reaction l Assumptions and Simplifications to the Governing Physical Equations Some simplifications may be made to the governing equations. For low Mach number Ma and a high Reynolds number Re (i.e., Ma 2 Re 1 1), viscous dissipation (τ ij u j x i ) and spatial gradients ( p x i ) in pressure are negligible. Then, only p dp t dt needs to be considered for the pressure term in the enthalpy equation, though the spatial pressure gradient in the momentum equation must be retained since it drives the flow, being the countering force to the viscous effects and non-negligible in that context. Radiation will be neglected. While there is some radiation in engines, it should be insignificant compared to the other factors, given the type of operating environment. The combination of these simplifications allows for several quantities, such as fluid properties and ω α, to be functions of only the species mass fractions, energy (enthalpy in this case), and a reference pressure p 0 that is a function of time alone: Y, T, p Challenges of Turbulent Combustion The equations outlined in section are a complete description given the appropriate initial and boundary conditions. These equations will provide all quantities 52

67 of interest, such as temperature and species mass fractions, for a multicomponent reacting mixture in both laminar and turbulent flows. However, turbulent flows are generally not feasibly solved with this set of equations because of the large range of scales that must be resolved to accomplish this, requiring an inordinate amount of computing time. Typically, only fundamental studies on relatively simple configurations have been accomplished by this approach, though recent computing power advances have greatly enhanced this capability [101]. The reason for the intractability of these equations is their nonlinear nature (from the convective terms and pressure, when expressed in terms of velocity), which not only makes the solutions very sensitive to initial and boundary conditions, but, because of the lack of an analytical solution, makes the numerical solution scheme very difficult given the range of spatial and temporal scales required at high Reynolds numbers. Scaling arguments give the range of hydrodynamic scales, from smallest to largest, as Re 3 4, with time scales on the order of Re 1 2 [102]. Furthermore, for usefulness a full description of the flow is typically not necessary, and a probabilistic approach (mean values) is more appropriate for engineering applications. Length and time scales beyond the hydrodynamic scales may be pertinent when chemistry is considered in turbulent flow [103]. In these cases, the Damköhler number becomes very important. This dimensionless number is defined using the time-scales of flow and chemistry as Da τ flow τ chem, (4.13) and is typically large when considering the global characteristics of most engineering combustion systems. However, local values may range from smaller than unity to larger than unity. Regions of the flow that are important to combustion processes of interest, such as areas for flame stabilization and trace emissions species production, may have lower Da values. It is for values of Da 1 that turbulence-chemistry in- 53

68 Table 4.1: Characteristics of Direct Numerical Simulation, Large Eddy Simulation, and Reynolds-Averaged Simulation approaches for turbulent combustion. Approach DNS LES RANS Scale Resolution full large scales mean flow Modeling (theoretically) none subgrid scale all turbulent scales Mesh type very fine fine coarser Computational cost high medium low Applications research research/engin. research/engin. teractions are important. For very large Da one may assume fast chemistry, reducing the complexity of chemistry calculations in terms of computational effort and physical accuracy. For very small Da one may assume slow chemistry if the chemistry is only loosely or negligibly coupled with the flow, such as with emissions species. This allows for chemistry to be essentially post-processed, also reducing the complexity of chemistry calculations. Now we will outline the numerical formulation that is relevant to this thesis, Reynolds-averaged Navier Stokes together with a composition PDF method, and then look briefly at some of the other frameworks and models for combustion simulations. Table 4.1 summaries the three major methods and their applications Reynolds-Averaged Navier-Stokes Equations for CFD For any physical quantity represented by random variable Q = Q(x, t), a probabilistic mean or expected value can be defined. Here Q represents any physical random variable of interest in turbulent combustion including velocity, species composition, etc. There are several different ways of estimating a mean or expected value: spatially, temporally, cyclically, and phased are methods for approximating the mean values 54

69 from measurements. The method depends on the application. Statistically stationary flows will have different requirements than a four-stroke internal combustion engine. The expected value of Q will be denoted by Q. This mean value can be easily formed from the probability density function, PDF, of Q, f Q (ψ; x, t): Q = Q(x, t) = + ψf Q (ψ; x, t)dψ. (4.14) The PDF describes the probability that the value of Q will be in the range ψ to ψ + dψ. From the description of the PDF it follows that f Q (ψ; x, t) 0 and that + f Q(ψ; x, t)dψ = 1. The PDF is a function of space x and of time t, and is a density in the space ψ. A joint PDF may also be formed, i.e., the density function of multiple random variables. When describing turbulent flow, the joint PDF of velocity, u(x, t), and of the composition variables, φ(x, t) (which can be species mass fractions or a progress variable), can be particularly useful. With some simplifications, the composition variables can be well described by species mass fractions and the mixture enthalpy, not considering the reference pressure, p 0, for now. Thus, we can form the velocity-composition joint PDF: f uφ (V, ψ; x, t). (4.15) This is the one-point joint PDF of the event u(x, t) = V and φ(x, t) = ψ. What is important for purposes of turbulent combustion modeling is that the mean of any function of u and φ can easily be obtained from the joint PDF of those random variables. When modeling variable density flows it is useful to take density-weighted means, or Favre-averaged quantities, simply because it is easier to work with these forms of the equations. The mass density function, F uφ (V, ψ; x, t), the Favre-averaged PDF, f uφ (V, ψ; x, t), and the conventional PDF, f uφ (V, ψ; x, t), relate as: F uφ (V, ψ; x, t) = ρ(x, t) f uφ (V, ψ; x, t) = ρ(ψ)f uφ (V, ψ; x, t), (4.16) 55

70 where ρ is the mean mixture mass density. For the quantity Q, conventional means, denoted by Q, and density-weighted means, denoted by Q, are formed directly from the joint PDF. Fluctuations about a conventional mean are denoted by Q while fluctuations about the Favre-mean are denoted by Q. For a given function Q = Q(u, φ) we have, Q(V, ψ)f uφ (V, ψ; x, t)dv dψ = Q(x, t), (4.17) Q(V, ψ) f uφ (V, ψ; x, t)dv dψ = Q(x, t), (4.18) Q(x, t) = Q(x, t) + Q (x, t), (4.19) Q(x, t) = Q(x, t) + Q (x, t). (4.20) From the last two equations one can see how each quantity at a certain point in time can be decomposed into its mean and fluctuating part. By using this construct of equating the instantaneous quantity to mean and fluctuating components, one can recast the four main governing equations of mass, momentum, species composition, and enthalpy by rewriting them with the mean and fluctuating components substituted in for the instantaneous quantity. The and operators commute with differentiation in time and space. Then taking the mean yields the Reynolds-averaged Navier-Stokes (RANS) equations. The derivation for these equations is outlined in [97, 104]. Neglecting the liquid source term, the equations are: Reynolds Averaged Mass ρ t + ρ ũ i x i = 0. (4.21) Reynolds Averaged Momentum (j = 1, 2, 3) ρ ũ j t + ρ ũ jũ i x i = ρ ũ j u i + τ ij p + ρg j. (4.22) x i x i x j 56

71 Reynolds Averaged Chemical species (for N s species, α = 1, 2,..., N s ) ρ Ỹα t + ρ Ỹαũ i x i = ρ Y α u i J i α + ρ x i x S α. (4.23) i Reynolds Averaged Absolute enthalpy ρ h t + ρ hũ i = ρ h u i J i h x i x i x i + D p Dt + τ ij ũ j x i + Q rad. (4.24) This set of equations provides mean quantities. When solved on a finite-volume mesh, for example, they provide the cell-centered values of the mean quantities. Equations 4.21 to 4.24 with suitable closure models are similar to equations 4.1 to 4.4, except for the first terms on the right-hand side, which are the simplified versions of the following terms: ρ ũ j ũ i ρ ũ j u i = ρ ũ j u i, ρ Ỹαũ i ρ Ỹαu i = ρ Y α u i, ρ hũ i ρ hu i = ρ h u i. (4.25) These forms follow from the definitions of means and fluctuations outlined earlier. Thus we get terms that represent turbulent fluxes of momentum, species, and enthalpy. It is these terms, i.e., turbulent transport, along with the mean species source term, S α, that are the focus of modeling efforts in RANS Composition PDF Method The PDF method has been derived with different sets of independent variables that capture various levels of the turbulence effects on the flow, generally by choosing from velocity, composition, and frequency in order to form the probability density function. Perhaps the most comprehensive constructed PDF is one that uses a joint PDF of velocity, composition, and frequency. This allows for physical transport due 57

72 to turbulent velocity fluctuations to be solved without modeling, the mean chemical source term to be solved without modeling, and for a complete turbulence model to be formed with the information provided by frequency. The physical effect left to be modeled in this case is the molecular mixing. To more directly model the effects of mixing, scalar gradients would be required, which points to the need for multi-point and multi-time statistics, versus this one-point and one-time formulation, and for which the modeling effort would shift to that of modeling scalar gradients [105]. A multi-point, multi-time type of formulation is very difficult and its benefits are not yet evident. The velocity-composition-frequency PDF is itself a difficult approach. A velocity-composition PDF is notably more tractable than the velocitycomposition-frequency PDF. As a one-point statistical description of the flow, for low Mach number, the joint PDF of velocity and composition (species and enthalpy) fully describes the state of the fluid. However, because not all information on rates of change are provided by this PDF, fewer than the velocity-composition-frequency PDF, the evolution of this PDF, while well described, requires more modeling effort. What the PDF does provide is information to solve explicitly the composition source terms and turbulent velocity fluctuations while models are required for transport in velocity and composition space due to molecular processes associated with species diffusion and the stress tensor (the first and third terms on the right hand side of equation 4.29) and transport in velocity space due to pressure fluctuations (second term on the right hand side of equation 4.29). A composition PDF method will only use the joint PDF of the composition variables. While this requires models for turbulent diffusion and molecular mixing and relies on a turbulence model such as the k-ε model to treat the velocity field, it still solves explicitly for the turbulent fluctuations about the mean for the species source terms, thereby still providing significant turbulence/chemistry interaction modeling capability. While the higher dimension PDF equations can more directly account for 58

73 physics with a lower level of required modeling, it makes sense to try the composition- PDF model first with the benefit of reduced computation cost yet still a significant increase in theory over the standard finite-volume modeling with empirical or no models for TCI. In using the turbulent viscosity to determine the Reynolds stresses, the composition PDF method uses the isotropic viscosity hypothesis: ρ ũ i u j = µ T ( ũi + ũ ) j + 2 ( ) x j x i 3 δ ũ l ij ρ k + µ T. (4.26) x l This gradient diffusion model is used to solve for momentum transport and is the simplest possible consistent model. To solve for composition transport, a gradient diffusion model is also used: ρ u i φ α = Γ φ α T, (4.27) x i with a turbulent diffusion coefficient, Γ T = µ T σ φ, (4.28) where σ φ is the turbulent Schmidt number, usually taken to be 0.7, and µ T is an effective turbulent viscosity. With knowledge of the mean density in space and time, the k-ε equations and the mean velocities form a closed set. The mean density is computed from the solution of the modeled composition PDF equation. Here, a transported composition PDF method is used. One can derive a transport equation for the velocity-composition PDF from the conservation equations for density (continuity), velocity (momentum), composition, and energy [15]. Pope [15], using a somewhat arbitrary test function Q(u, φ), (u is the velocity vector and φ is the composition vector (i.e., species and enthalpy)), derives the result, expressed 59

74 in terms of the Favre (density-weighted) mean PDF, by equating two independent expressions for ρdq/dt. The first expression is essentially the expansion of the mean evaluation of the material derivative of Q. The second expression splits DQ(u,φ) Dt into Q Du j u j + Q Dφ α Dt φ α Dt and takes the mean of this expression. As a result of the setup of the equations, the arbitrariness of Q, the definitions of Du Dt and Dφ Dt given in the instantaneous governing equations, the ability to neglect some terms, and the use of integration by parts, the velocity-composition PDF is expressed as: [ ρ f uφ ] t + [ ρ V i f uφ ] x i + ( ρ g i p x i ) f uφ V i + [ ρ S α f uφ ] ψ α = V i [ ρ 1 ( τ ji x j + p x i ) V, ψ ρ f uφ ] + ψ α [ ρ 1 J α i x i V, ψ ρ f uφ ]. (4.29) Summation is performed over repeated indices i, j, or α within a term, and α = 1,..., N S + 1 (to include enthalpy with N S, the number of species); liquid spray and thermal radiation terms have been omitted, for clarity. The notation ρ 1 J α i x i V, ψ, for example, denotes the mean of the divergence of composition variable, α s, molecular flux J α, conditioned on the velocity, V, and the composition, ψ. Transport in physical space by the velocity V (including turbulent velocity fluctuations), transport in velocity space due to body forces and the mean pressure gradient, and transport in composition space by chemical reaction appear in closed form (left-hand side of Eq.(4.29)). On the right-hand side are the terms to be modeled. These represent transport in velocity and composition space due to molecular processes (terms involving τ ji and J α, respectively) and transport in velocity space due to pressure fluctuations (term involving p / x i ). The composition PDF f φ (ψ; x, t) is derived from the velocity-composition PDF 60

75 by integrating over velocity space: fφ (ψ; x, t) = fuφ (V, ψ; x, t)dv. Here φ denotes the vector of composition variables that characterize the thermochemical state (N s species mass fractions and mixture enthalpy) and tilde ( ) denotes a density-weighted (Favre-averaged) mean quantity. x is the position vector, u is the velocity vector, and time is t. The result is: [ ρ f φ ] t + [ ρ ũ f i φ ] + [ ρ S f α φ ] x i ψ α = [ u i ψ ρ x f φ ] i + ψ α [ ρ 1 J α i x i ψ ρ f φ ]. (4.30) Here summation is implied over repeated indices i or α within a term, and α = 1,..., N S + 1 (to include enthalpy). denotes the probabilistic mean. ρ is the density, J α is the composition variable α s molecular flux, and S α is the source term for composition variable α. ũ is the Favre-averaged mean velocity and u is the velocity fluctuation about ũ. For this implementation, only the mean velocity appears in a closed form: the effect of turbulent velocity fluctuations ( turbulent diffusion ) must be modeled (first term on the right-hand side of Eq.(4.30)). The other effect that must be modeled (second term on the right-hand side of Eq.(4.30)) represents molecular transport ( mixing ) RANS Lagrangian Particle PDF Method A transported composition PDF method is used here to model the effects of turbulent fluctuations. PDF methods may be implemented in both Eulerian and Lagrangian contexts. Work is currently being performed to develop tractable Eulerian frameworks for PDF methods [106, 107]. An Eulerian setup such as that in [106] uses a direct quadrature method of moments using scalar-type equations with source terms that evolve the PDF through a finite number of delta-functions. A Lagrangian setup 61

76 distributes notional particles with scalar properties throughout the physical domain associating particles with cells based on position. The work in this thesis follows the implementation of Subramaniam and Haworth [108] and uses a Lagrangian framework. PDF methods can explicitly account for the turbulent fluctuations in species composition and enthalpy (hence temperature) relative to the local mean value. A Lagrangian particle Monte Carlo method is used to solve the modeled PDF equation with use of a consistent hybrid particle/finite-volume method [18], which is necessary to ensure alignment between the dual representations of the gas phase. This hybrid scheme is more tractable than grid-based implementations because the increase in computational effort scales linearly with the number of independent variables, rather than exponentially as in the case of grid-based methods. The particles are a discrete, delta-function representation of the PDF and evolve by stochastic differential equations that account for changes in particle properties, such as position and composition. The Monte Carlo method is chosen in such a way that the evolution of the PDF due to these particles closely approximates the PDF evolution for the real fluid system. Coupling to the finite-volume solver provides the effects due to mean momentum in the particle equations, while models complete the effects of turbulent velocity fluctuations and mixing. A two-equation k ε turbulence model and a standard gradient transport approximation are used to account for transport by turbulent velocity fluctuations, and a simple pair-exchange model is used for molecular mixing [108, 109]. These models are addressed in Sections 4.3 and 4.4. Higher-level PDF methods are available by considering joint PDFs of more variables including velocity and frequency. 62

77 4.2.5 Alternative Formulations Direct Numerical Simulation In Section a complete description of the flow is provided. The solution of these equations without modeling should be able to reproduce the exact physical behavior of the flow, given appropriate numerical accuracy and exactly specified initial and boundary conditions, resolving all turbulence scales explicitly. This type of modeling falls under the category of direct numerical simulation (DNS) and is a valuable research tool. Realistically, some models and simplifications have been used even in DNS, including constant density, low Mach number, and simple chemistry. However, the order of the algorithms and the detail captured are still at a very high level. DNS is limited to a smaller range of physical scales and simpler physics than engineering-scale systems, which will be discussed shortly. The primary purpose of DNS so far has been to elucidate fundamental physical behavior and provide data that are not accessible to experimental measurement and diagnostics. Because the full range of turbulent scales must be captured by DNS, it is necessarily computationally expensive. However, because so much detail is simulated, DNS has provided information against which to build databases of useful turbulence quantities or to provide a benchmark against which to validate models. The usefulness of DNS, if it could be applied to engineering scale systems, is not necessarily a given. Most computational effort in DNS would be spent in resolving the smallest scales. The mean flow and the statistics of the device scale flow are only weakly dependent on the Reynolds number. The computation effort for DNS increases with Re 11/4 (see p. 102 in [103]). So far, computational and experimental studies seem to show that the smallest turbulence scales show little variation with Reynolds number, leading many researchers to attempt to more directly capture the larger scales, using large-eddy simulation with relatively simple models for the 63

78 unresolved sub-filter turbulence scales Large-Eddy Simulation Issues including cycle-to-cycle variability motivate the use of large-eddy simulation (LES) for internal-combustion-engine CFD. In LES, the governing equations are spatially filtered using a filter scale that is generally smaller than the turbulence integral scale. In the limit as the filter scale increases to the integral scale, one essentially recovers the Reynolds-averaged equations. Pitsch provides a review of LES for turbulent combustion [110] and Haworth gives a summary in the context of engine combustion [111]. LES has been shown to elucidate turbulent structures that are not captured by the standard RANS-based approaches [ ]. These details may be important to understanding cyclic fluctuations that can influence misfires, partial burns, and emissions issues. Furthermore, because the spatial distributions of flow velocities, energy (temperature), and composition have greater inhomogeneity and range, this provides reason to put more attention on the effects of turbulence/chemistry interactions (TCI), which have been shown to have a significant effect when the engineering system has significant inhomogeneity [9]. Research for direct-injection engines is currently focusing on these situations of greater in-cylinder inhomogeneity in order to approach the greater potential of running with stratified charge in these engines rather than the somewhat premixed charge being used in current SIDI engines. LES in combination with a good model for the sub-filter scales should be able to provide additional information concerning inhomogeneity and fluctuations and their effects on distinct combustion behavior for the modeling of an instantaneous, rather than an averaged, cycle. 64

79 4.3 Turbulent Transport in RANS/PDF Methods Turbulence modeling to provide closure for the turbulent fluxes through one, two, or more equations for key quantities has been a standard practice for quite some time. Pope s book provides additional detail about the variety and basis for these types of models [102]. Fox and Law provide good summaries of the relevant aspects for turbulent combustion [56,103]. The most widely used closures for RANS computations are either turbulent-viscosity-based models [103], which shift the problem from modeling the Reynolds stress tensor to the issue of specifying an effective turbulence viscosity µ T, or Reynolds-stress transport equation models, which more directly model the effects of the Reynolds-stress tensor. While these are all RANS closure models, they will continue to be used heavily since the computational cost of LES combined with the cost of complex chemistry, will likely keep RANS as the CFD model of choice for the near term, and so it is instructive to understand RANS models and worthwhile to work with them. Understanding the physical support for these models and their shortcomings is important, since the overall performance of the dependent coupled computations is significantly affected by these closures, which in the case of the k-ε model provides length-scale and time-scale information as well. A long standing method has been the two-equation turbulence model, typically using turbulent kinetic energy and dissipation as the quantities to solve for the turbulent viscosity. The aim of this section is to give an idea of what this model provides for closure of the equations in the form of a standard model from this field of study. The reader is referred to [102, 103] for more information concerning other models in this area, including more advanced models. 65

80 4.3.1 The k ε Turbulence Model The standard k-ε turbulence model is used to provide the turbulent fluxes of momentum, species, and enthalpy for the RANS equations. What needs to modeled in the mean momentum equation is the effective turbulent stress: ρ ũ j u i τ T,ji (4.31) which would be modeled using the assumption of the turbulent-viscosity hypothesis as: τ T,ji = ρ ũ j u i = µ T ( ũ j / x i + ũ i / x j ) 2 3 µ T ũ l / x l δ ji 2 3 ρ kδ ji. (4.32) The key quantity here is µ T, the effective turbulent viscosity, which is found by solving for C µ ρ k2 ε. C µ is a typical empirical k-ε model constant [115]. Equations are solved for the transport of k and ε. The physical basis for the solution of k derives quite well from the governing equations, while the equation for ε is more empirical, thus weakening the the model s robustness. Derivations may be found in [102], [56], and [103]. The k ε equations for variable density are given below: ρ k t + ρ kũ j x j = x j ( [µ + µ T σ k ] k x j ) + τ T,ij ũ j x i ρ ε, (4.33) and ρ ε t + ρ εũ j x j = x j ( [µ + µ T σ ε ] ε x j ) C ε2 ρ ε2 k + C ε3 ρ ε ũ j ε + C ε1 x j k τ ũ j T,ij. (4.34) x i σ k is a constant, typically taken to be 1.0. µ T is specified with C µ = 0.09, typically. 66

81 and where When density is constant, the following forms (from [103]) may be used: k t + u i k x i = ε t + u i ε = x i x i ( ν T σ k k x i ) + P k ε, (4.35) x i ( ν T σ ε ε x i ) + C ε1 ε k P k C ε2 ε 2 k, (4.36) P k = u i u j u i x j, (4.37) which, when taken with the turbulent viscosity hypothesis, is: ν T is specified by C µ k 2 ε P k = ν T ( u i + u j ) u i 2 x j x i x j 3 (ν u j T + k) u i. (4.38) x j x i = µ T ρ. As noted, the ε equation depends on three empirical constants for the three source terms on the right-hand side, representing: in order, gradient diffusion, production, and destruction. Typical values are σ ε = 1.3, C ε1 = 1.44, and C ε2 = The k-ε model has shown very good prediction capability for simple flows such as two-dimensional thin shear flows and flows with low pressure gradients and curvature. Limitations of k-ε include the inability to model flows with large pressure gradients or rapid changes in mean velocity. These limitations may be attributed in part to the different physics of turbulence and molecular processes. Reynolds-stress models may be more accurate for some cases, but there is still not enough robustness for these models to justify their computational cost (up to six, more complex, equations) in most engineering CFD applications. For the purposes of composition PDF methods, the k-ε quantities are used in calculating the mixing rate between particles, the model for molecular mixing effects. This coupling between models is significant in how it affects the evolution of the composition PDF. 67

82 4.3.2 Turbulence Wall Function For RANS modeling, wall functions are typically adopted for near-wall regions so that the k-ε equations do not need to be solved there. This reduces the computational expense of computing the wall effects, due to the steep gradients of mean velocity and turbulence dissipation rate, by using a logarithmic correlation for the near-wall region. The log-law is used for prescribing these turbulence wall functions and is provided in [102] for constant-density flows: U = u τ ( 1 κ ln y+ + B) (4.39) ε = u τ 3 κy (4.40) uv = u 2 τ = C 1/2 µ k (4.41) U is the mean velocity, u τ is the wall shear velocity, κ and B are log-law constants, y + is the distance y from the wall over the viscous length scale, ε is the turbulence dissipation rate, u and v are the tangential and wall-normal fluctuating velocities respectively, C µ is a model constant, and k is the turbulence kinetic energy. The above set is modeled instead by the below starred set of equations (where the subscript p indicates quantities evaluated at y p, which normally corresponds to the distance from the wall to the center of a computational cell adjacent), which provide a robust boundary condition solution for all situations and are equivalent to the nonstarred above equations under ideal conditions, though the physical soundness may deteriorate as conditions deviate from the ideal: u τ C 1/4 µ k 1/2 p (4.42) 68

83 y p y pu τ ν (4.43) U p = u τ( 1 κ ln y p + B) (4.44) uv p = u 2 U p τ U p (4.45) ε p = u τ 3 κy p (4.46) Here ν is the kinematic viscosity. The simplicity and computational economy of a set of wall functions makes their use widespread in commercial CFD modeling where the engineering-scale requires significant processing power for turbulent flows. There remain several flow conditions where the physical basis for the wall-function model is unclear or the accuracy will be poor [116]. In the context of our work, we apply the RANS wall functions to determine the turbulence scales for the relevant near-wall PDF particles. Work by Dreeben and Pope [117] directly applies a wall function approach for the PDF particles for the velocity-frequency joint-pdf method Turbulent Transport As explained in section 4.2.4, the effects of turbulent velocity fluctuations must be modeled when using the composition PDF. The gradient transport approximation is used here [15, 111]. This provides a reasonable model for the turbulent transport term, so-called turbulent diffusion, in the transported PDF equation. This model will simply provide a rate of transport based on gradients, akin to a random walk in space, using the expression in [15] (see also [118]): 69

84 ρ u i ψ f φ = Γ T f φ x i, (4.47) which may then be used to calculate the mean turbulent flux for composition transport, ρ Y α u i = Γ T Ỹα x i. (4.48) Whereas this approach may be quite accurate for simple free shear flows, its validity is questionable in variable density reactive flows (e.g., in situations where counter-gradient diffusion is important [119]). Assuming that reasonable accuracy is attainable, this model within the composition PDF framework allows for a simpler solution for the PDF, making the method more amenable to engineering-scale simulations Fokker-Planck Equation The evolution for a PDF in a diffusion process is governed by a well-known stochastic equation, the Fokker-Plank Equation (see [15] and also [102] for more detail): f(v ; t) t = V [f(v ; t)d(v, t)] [f(v ; t)b(v, t)]. (4.49) 2 V 2 This equation provides the basis for the Langevin equation, which generates the stochastic process called the Ornstein-Uhlenbeck process, whose PDF evolves by the Fokker-Planck equation. The Langevin equation is used in turbulent transport modeling in the velocity-composition PDF method by providing a good model for the velocity of a particle in turbulence, and is an example that through well-developed stochastic theory, PDF methods can properly capture physical processes. As one looks ahead to future development of models for engine usage, this is an aspect of the direction in which PDF methods may head if velocity-composition PDF s gain usage for engineering applications. 70

85 4.4 Scalar Dissipation and Mixing Models The choice of the mixing model is a crucial aspect of PDF modeling. It implicitly models the effect of scalar dissipation, which is the major common thread through all turbulent combustion models. Scalar dissipation has the unit of inverse time, s 1, and its inverse can be interpreted as the characteristic diffusion time across a flame. One can see that properly modeling scalar dissipation or its effects will directly affect the combustion model. The mixing models apply to the second term on the right-hand side of Equation In the context of this work, the Lagrangian mixing models apply locally, within each finite-volume cell, affecting the rate at which particles within a cell exchange composition of species and enthalpy. One can see that this will necessarily have a strong effect on the shape of the PDF. Taking the rate to the extreme, infinite mixing of particles in the composition PDF model should recover the behavior of a pure finite-volume model, where each cell is taken as a perfectly stirred reactor. The mixing model used here mixes composition and energy with the same rate for all species. A more accurate description would mix energy at a different rate than the compositions and account more directly for different diffusivities of species. Energy in a finite-volume context has the potential to mix significantly faster with the local composition than it would in the Lagrangian particle context. This might explain why, in general, it has been observed that the PDF model exhibits earlier ignition than either the finite-volume model or the experiment, as seen in the 5th chapter (and it remains to be seen whether a higher or lower rate would be the correct choice in this particular engineering system). Mixing allows segregated reactants to react when they are in the same computational volume or particle. When particles are used, specific Lagrangian mixing models have been developed that address the nature of this modeling. These models should 71

86 meet certain constraints to ensure that some level of realistic physics is captured, understanding that all appropriate models are still approximations to the actual phenomena. Fox [103] states three constraints for evaluating the validity of a mixing model: 1. The scalar mean must be unchanged; 2. Scalar dissipation rate evolves consistent with experimental observations for constant-density homogeneous flows, where the rate of change is equivalent to a mixing constant, C φ, over the turbulence time-scale, τ = κ/ε; 3. There must be no correlation with velocity at high Reynolds number. The Interaction by Exchange with the Mean (IEM) mixing model [120], or Linear Mean Square Estimation Model (LMSE) relaxes scalar values in each particle to the mean on a time-scale computed generally by 1 C φ κ ε, where C φ is generally 2.0. A linear, deterministic simulation of mixing is provided that is continuous in time, but that mixes all scalars at the same rate since differences in diffusion are not considered. Not all of the mixing model requirements are satisfied, though: 1) is fully satisfied, and 2) is partially satisfied. The model is very simple, however, and practical for use in PDF calculations. The Coalescence-Dispersion (C-D) mixing model [109] is a stochastic mixing model. Two particles, selected randomly from the particles in a finite-volume cell, mix with a given probability. The scalar values of the initial particles are used to form the mixed values, which are equal to the mass-weighted averaged of the two initial scalar values. The probability for mixing is proportional to the ratio of the time step to the turbulence time-scale, τ, the number of particles, and a mixing model constant, C φ. This type of model is discrete and loses a sense of continuity in the mixing process. Janika et al. [121] have modified the model so that the degree of mixing 72

87 is distributed as a uniform random variable, which helps to reproduce correctly the dissipation rate. Work by Pope [122] attempted to improve the shape of the PDF produced by the modified Curl s mixing model to more accurately capture the flatness of the PDF and the evolution towards a Gaussian PDF. Model parameters involving element age were introduced to provide a mixing bias, which resulted in the predictions more closely matching the experimental observations on the decaying fluctuations for passive scalars in homogeneous turbulence [123]. The Euclidean Minimum Spanning Trees (EMST) mixing model attempts to remedy the issue of non-localness in reactive scalar space [124]. This non-localness is the result of the transformation of an arbitrary initial PDF to a Gaussian PDF as seen in homogeneous turbulence, creating a physical requirement on mixing models that IEM or C-D do not meet. For example, these mixing models may result in the transfer of cold reactants across a reaction zone without being affected by the phenomenon of that zone. While spatial mixing is performed, it goes counter to what the scalar space would allow physically. The EMST model applies mixing of scalar particles governed by the closeness in reactive scalar space. Physical accounting is improved though computational time is also increased. Comparisons of mixing models for canonical flames have been performed that show the beneficial influence of EMST in certain setups [ ]. However, the results have not definitively singled out any one model as being the best for any one combustion situation. In [126], for example, the EMST model provides the best flame shape compared to the IEM and CD models but under-predicts the conditional variances of the thermochemical quantities due to a lack of extinction in the simulations. These models focus directly on maintaining restrictions in one particular space, with IEM and CD models preserving some locality in physical space and EMST and similar models seeking locality in composition space. It would be interesting to see if a 73

88 better mixing model would put appropriate emphasis on both spatial and composition space and the necessary effects and requirements of both into the physical modeling of mixing, without being a computational burden. This would be useful for modeling in realistic configurations where the cost of using compositionally local mixing models is prohibitive, but the somewhat physically weaker IEM and CD models balance out their beneficial run times. 4.5 Turbulent Combustion Models There are several approaches that attempt to provide the best approximation for the mean of the chemical source term in the context of non-dns simulations. Several of the more prominent methods will be discussed below, and are summarized in Table 4.2. Table 4.2: Turbulent combustion models for Reynolds-Averaged simulations Premixed Combustion Non-premixed Combustion Eddy Breakup (EBU) Eddy Dissipation Da 1 Bray Moss Libby (BML) Model Concept (EDC) Coherent Flame Model (CFM) Flamelet Model Flamelet Model using using G equation or Progress Variable Mixture Fraction Da 1 Linear Eddy Model (LEM) Conditional Momentum Closure (CMC) PDF methods Da 1 Arrhenius model 74

89 4.5.1 PDF Method: Solution of the Mean Chemical Source Term The PDF method explicitly solves for the mean chemical source term, which makes the model particularly attractive in turbulent combustion modeling. Solution of the composition PDF equation, Equation 4.30, provides source term information explicitly in the third term on the left-hand side of the equation. This allows the model to avoid making the incorrect assumption that the mean source term based on instantaneous independent variables (mass fraction, enthalpy, and pressure) is the same as the instantaneous source term based on the mean values of those independent variables: S α (Y, h, p) S α (Ỹ, h, p). (4.50) Instead, the mean chemical source term is solved directly as: S α = S α (ψ) f φ (ψ; x, t)dψ, (4.51) using the joint PDF of species composition for each finite-volume cell at each time step. This is the inherent strength of the model for turbulent combustion modeling Alternative Combustion Models Flamelet Models Currently, flamelet models such as the representative interactive flamelet (RIF) approach, G-equation approach, and others have shown good ability to predict trends in engine operation while providing detailed chemistry, using pre-computed tables for laminar flame speeds, s L (e.g., as a function of pressure, temperature, equivalence ratio), generated on a probability distribution function of the flame front, and computational efficiency, so that it can be reliably used as a design tool for production engines [27, 81, 129]. 75

90 Beginning with the view of a turbulent diffusion flame as a collection of stretched laminar flamelets by Williams [130], flamelet equations have been developed based on mixture fraction and further developed for premixed and diffusion flames [ ]. The foundation of the flamelet models is the premise that in certain situations flamelets exist and dominate the mode of combustion, where chemistry is very fast in the flamelet, using chemistry tabulated ahead of time for a presumed shape PDF profile for the quantities of scalars. The laminar flamelet assumption works when the flame layer is thin relative to the size of the Kolmogorov eddy. If, however, the flame is thick relative to the eddy, the turbulent flow will break up the flame structure, essentially quenching the flame. Modeling focuses on mixture fraction, for diffusion flames, or the progress variable, c, or scalar G, which represents the premixed flame surface, for premixed flames. Models are also available for partially-premixed combustion. The flamelet approach tends to directly solve for scalar dissipation rate when considering the mixing processes. These models have their strength in that they maintain a strong coupling between the chemical kinetics and the molecular transport, while decoupling the kinetics and the hydrodynamics. They may not correctly describe all practical engineeringtype combustion systems, such as HCCI, but can properly describe situations where flamelets have been shown to be dominant, such as for homogeneous-charge sparkignited engines. Models have been developed to handle the increasing complexity and variety of engine combustion modes, such as multiple injections, partially-premixed combustion, and HCCI, and new work has adapted the model to overcome such limitations, such as the work on Representative Interactive Flamelets (RIF) by Weber et al. at Technische Universität Aachen [27] and the use of the Coherent Flame Model (CFM) [ ]. 76

91 Bray-Moss-Libby The classic Bray-Moss-Libby model is used for premixed turbulent combustion in conditions where the Damköhler number is high [138, 139]. This model creates a PDF as a function of the reaction progress variable and position that is a combination of contributions from the burnt, unburnt, and burning gases. It has been useful in elucidating physical aspects of flames such as counter-gradient diffusion and intermittency due to fluctuations between burnt and unburnt gases Eddy Breakup Model Eddy break-up (EBU) models for turbulent combustion [140] are useful for combustion systems where the turbulent mixing rate is slow compared to chemical reaction, i.e., the Damköhler number is high. This leads to the reasoning that the ratecontrolling process here is turbulent transport of the species and enthalpy, though one would expect the model to not perform well in low Damköhler number situations. As a result of the above assumption, the EBU concept takes the chemical source term to be proportional to the fluctuations of the reactant concentration or a progress variable. For example, the local mass fraction rate of fuel consumption can be expressed as: There are variants on this model, S F = C EBU(Ỹ 2 F ) 1 2 τ T. (4.52) including the eddy-dissipation concept (EDC) [141]. Since these types of models are based on known mean quantities without the need to solve additional equations they are computationally attractive. However, the model coefficients will need to be set up for each application, limiting predictive capabilities. 77

92 Linear Eddy Model The linear-eddy model (LEM) is a one-dimensional turbulence model (ODT) that has been developed by Kerstein [142] and applied in turbulent combustion. A notable example of a combustion application is the work by Sankaran and Menon [143]. LEM modeling captures molecular effects in turbulent flows, strengthening it over simpler models. Turbulent transport is treated with a simple stochastic model. The equations simulate a one-dimensional domain embedded in a turbulent flow, so that the reactive scalar field evolves according to a set of parabolic equations in a onedimensional approximation. The relatively low computational effort for modeling turbulent transport makes this an attractive approach for use in large-scale computations. However, the exact nature of the equation makes the overall system more stiff relative to most RANS computations. The one-dimensional, reaction-diffusion equation is of this form: φ t = φ Γ 2 + S(φ), (4.53) x2 with Γ representing a diffusion coefficient and S(φ) the reaction source term. LEM modeling may find use as a sub-grid scale model in LES calculations CMC Models The Conditional Moment Closure (CMC) model [144] provides the mean source terms by considering the PDF s of the scalars conditioned upon appropriate parameters given the problem. Typically, premixed or non-premixed combustion is considered, with conditioning on the progress variable, c, or the mixture fraction, z, respectively. The reasoning behind these choices of conditioning variables is that the fluctuations for the scalars will be strongly coupled to either progress variable or mixture fraction. Conservation equations are solved and usually higher moments are not considered. 78

93 The hypothesis behind this model is that the conditional average of the species source term, S α (Y, T ) z = η, is equal to that evaluated using the conditioned averages of composition, Y z = η, and temperature, T z = η : S α (Y, T ) z = η = S α ( Y z = η, T z = η ). (4.54) The unconditioned mean, S α, is formed by integrating the function over z. 4.6 Fuel Sprays The CFD code uses stochastic Lagrangian models for direct in-cylinder liquid fuel injection based on the KIVA spray formulation [145, 146]. The Lagrangian parcel spray model is coupled to the gas-phase PDF particle model through evaporation. Two methods have been developed. In the first, when spray parcels evaporate based on the spray model parameters, their location, vaporized mass, composition (pure fuel), and temperature are assigned directly to new PDF notional particles. This coupling naturally captures the high levels of local gas-phase fuel concentration and temperature fluctuations that arise from spray vaporization. More conventional treatments must model this effect or ignore it altogether [147,148]. In the second method, new PDF particles are not generated. The vaporized fuel mass is instead evenly distributed among the existing PDF particles. This mitigates the effect of vaporized spray spatial concentrations but still works within what, physically, should be a more appropriate local distribution of mass compositions. This approach to coupling the spray model and the PDF method is novel both for the type of application and the implementation. In a sense, what this coupling achieves is analogous to using a spray model with mesh refinement in order to capture more accurately the spray distribution for engine cases, for example in [146]. However, in that case the distribution of composition and enthalpy in those refined cells would 79

94 be more similar to that of the parent cells, with the exception in the end being the differences in fuel distribution. The PDF particle approach can capture both a more spatially refined fuel distribution as well as the distribution in composition and enthalpy of the existing mass. It is possible that further fidelity in this modeling approach could be achieved by increasing the maximum allowable number of particles in cells that have spray vaporization, then decreasing that cap afterwards to maintain computational feasibility. It is noted that this PDF/spray coupling approach has some potentially unphysical attributes. For example, when new PDF particles are generated for pure vaporized fuel mass, there is uncertainty at least as to whether fuel does vaporize without directly mixing with the gaseous boundary layer around the spray droplet. There is some reason to suspect that vaporized fuel would not have a local mass fraction of 1; however, Law notes that in realistic situations, fuel is sprayed into a hot oxidizing gas in such a way that, initially, there is very little or no oxidizer within the fuel spray. Only when the oxidizing gas is entrained in the spray jet interior can reaction be possible [56]. Thus, the rate of droplet vaporization to oxidizer entrainment affects combustion. In the case oxidizer entrainment is low and fuel vaporization is high, it is probable that the local mass fraction concentration of fuel around the spray would be high and perhaps even close to one. Then near-droplet mixing or fuel mass fraction concentration boundary layer thickness will be significant enough to control the rate of combustion. However, if entrainment is strong relative to droplet vaporization, the spray interior will be rapidly heated and enriched with oxidizer by the incoming hot gas. This will cause an environment that favors droplet burning, in which flames envelop the droplets. So the major issue involves properly predicting of mixing and flow rates near the spray jet, which may necessitate further modeling of the diffusion rates and turbulence and flow quantities near the sprays and droplets. The volatility of gaseous fuels leaves a range of conditions that must be considered for 80

95 droplet vaporization to entrainment rate, while two-phase combustion such as with coal particles would tend more heavily towards the dominating effects of oxidizer entrainment. The spray model used here also does not directly take into account droplet burning and the effect that that could have on vaporization and fuel mass fraction distribution. All vaporized fuel is directly transferred to gas phase volumes or particles that have no direct physical connection to the Lagrangian liquid fuel particles. Through collision modeling there is some droplet interaction, but the effects of that interaction on droplet burning is not considered. Overall one can see that spray modeling requires distinguishing between two main issues, that of heterogeneous droplet burning and homogeneous spray sheath combustion. This difference affects the mode of ignition and the extent to which burning is effected by diffusional burning around droplets versus premixed burning around the mixture of fuel and oxidizer within the spray interior. The stability of flames and combustion, rate of combustion, and pollutant formation will all be affected as a result. 4.7 Hybrid Particle/Mesh Solution Algorithm Hybrid particle/finite-volume mesh algorithms have provided a means to practically implement PDF methods in 3-D geometries. This section discusses the numerical aspects of the algorithm used to set up the foundation of the work in this thesis Finite-Volume Method There are a handful of practical ways to effectively solve the discretized governing equations. Numerical schemes are intrinsically important to the computational applications of flow solver, drawing on the mathematics and computer science fields to 81

96 develop the theory and algorithms. The finite-volume method is the method most commonly used in flow applications. Volumes, representing discretized portions of the flow evenly distributed over a defined space, are assembled to approximate the scales and features of the simulated flow region. These volume sizes are chosen so that the flow may be well approximated without requiring such small volumes as to make the flow intractable to computer solution. Linear equation solvers are then used to provide the coupled solution for all the volumes. The integral forms of the Navier-Stokes equations are used for these control volumes. For use in a hybrid scheme with the PDF method, the finite-volume solver is used to compute the coupled partial differential equations for a chemically reacting multicomponent gas mixture, the mean quantities of continuity, momentum, and enthalpy and the quantities for k and ε. In order to solve for these quantities, methods such as SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) [149] and PISO (Pressure-Implicit Split Operator) [150,151] may be employed to advance the solution through each time step. The solver used for this thesis employs a similar method, an iterative implicit pressure-based sequential solution. Both incompressible and compressible fluids, steady and transient flows are accommodated. While it is applicable for essentially arbitrary Mach number, more tightly coupled codes are generally required for high Mach number flows because of relationships between pressure and density that need to be more properly accounted. The reader is reminded that while this is an incompressible flow solver, we are generally not dealing with incompressible fluids in the internal combustion engine. Since the Mach number is low, the incompressible flow assumption is valid (e.g., given an engine stroke of 0.1 m and an engine RPM of 10,000, a characteristic velocity for fluids in the engine would be 33.3 m/s, significantly below the speed of sound in atmospheric air). The pressure/momentum/continuity coupling here uses a pressure-corrector method such as that in PISO. The steps for one iteration are as follows: 82

97 Velocity field is computed using the current pressure. A sparse implicit linear system is solved that corresponds to the discrete form of the momentum equations. Pressure and velocity fields are corrected to complete continuity. A sparse implicit linear system is solved that corresponds to the discrete form of the pressure equation. In the case of velocity, an explicit linear system is solved. Quantities such as enthalpy and species may be solved along with the correctors to tightly couple the system. The turbulence model s equations are solved. The finite-volume code discretization is first-order in time and up to second-order in space. The code can handle complex meshing, which includes complex geometry, moving meshes, non-aligned interfaces, and local mesh refinement Lagrangian Particle Method In the composition PDF method, the Lagrangian Particle Method is used to solve for the mean density and the mean composition to close the equation set in conjunction with the quantities provided by the finite-volume solver. In this context, they are the means by which Monte Carlo methods are applied to the problem, using the statistics generated by the stochastic nature built into the evolution of the particles and the resulting PDF of composition, in this work, or of composition, velocity, and/or frequency with other PDF methods. Monte Carlo methods provide the capability to solve problems of large dimensionality and slow convergence [152] that would otherwise be largely intractable with direct solution methods. Through appropriate models of the distribution, the physical problem can be approximated well, with statistical error minimized through the use of an appropriate sample size and algorithms. Be- 83

98 cause of the nature of the equations, the solution of the transported PDF equation for the composition PDF can avoid the more expensive direct solution methods by solving the transported PDF equations by Monte Carlo methods [153] Particle Tracking Particles must be convected through the mesh in a way consistent with the finitevolume code and the movement of the flow. In a velocity-composition PDF method approach, the velocity of each particle is specified and the particle will be moved accordingly. For a composition PDF method, as used here, the particle velocities are linked to the mean velocity of the cell and advected accordingly, modified by turbulent diffusion velocities specific to each particle, based on the cell mean velocity and a random component, and a mass consistency correction velocity, which is set to ensure that particle mass in a cell is consistent with the finite-volume cell mass. While particle tracking may seem straightforward, there are numerical issues that affect performance of the algorithm and the accuracy of the tracking. For example, depending on the algorithm, tracking may run into difficulties with abnormally shaped cells or cells with high aspect ratios. For engine meshes, cells can typically become flat close to walls in order to increase the fidelity of the calculation in these near-wall regions. The particle tracking scheme developed in [108] is used here. This method was developed for three-dimensional unstructured stationary or deforming meshes, large Courant numbers, and variable mesh cell sizes. Trilinear basis functions are used to map particles to the cells inside of which they should physically correspond. Particles are tracked from face to face based on the magnitude and vector of their motion over the time step, being tracked face to face until their calculated point of travel is reached. When a moving or deforming mesh is employed, the particles are first moved relative to any vertex movement, then they are moved as before based on their new 84

99 positions: a two-step procedure. This scheme by Subramaniam and Haworth has the advantage of being particularly robust over degenerate faces, different boundary conditions, non-aligned mesh interfaces, and for mesh refinement. It was noticed in the tests performed here that these near-boundary regions would generally show a drop in particle mass inconsistent with the corresponding finitevolume cell s mass. While the code is already set up with algorithms to ensure that these inconsistencies do not occur (see [18]), the peculiarities of an engineering-scale mesh seem to have elucidated some situations where the algorithms performance is insufficient. The number of particles and cells that exhibit mass inconsistency is relatively small, but can still create problems for the robustness of the code. This is an important issue that needs to be addressed, probably with an improved particle tracking algorithm that may more adequately place particles Particle Number Density Control In order to maintain sets of particles in the finite-volume cells that are a good representation of the distribution of composition, particle annihilation and cloning have been implemented [108]. The algorithm mainly tracks two particle statistics: 1) it accounts for the total number of particles in the domain, ensuring that it remains within a maximum and minimum limit, and 2) it ensures that the number of particles in a finite-volume cell remains within a maximum and minimum cell limit. These maxima and minima are set by the user dependent on the requirements of the problem. Particle cloning is performed when a cell s particle number is below the minimum. Large mass particles are preferentially split as needed until the required particle number is reached. The resultant cloned particles each have half the mass of the donor particle and have the same particle properties as the donor, such as mass fraction. Particles are annihilated when the total number of particles in a cell is above the 85

100 maximum. The mass from the annihilated particle is combined with another particle in the cell at random, with preference given to low-mass particles. Mass and mean particle properties should be preserved, though the particle property distributions will not be exactly preserved. Another method might attempt to preserve the distribution by combining particles close in composition space to prevent significant changes in the property distribution. In some cases, a cell may rob mass from a neighboring cell when its particle mass becomes zero. This can happen as a result of particle tracking even though consistency algorithms, discussed below, are employed to prevent this. Cell mass robbing helps to alleviate numerical issues in the algorithm, though it can introduce some artificial mass diffusion into the system. The robbed mass will be used to create new particles in the cell Mean Estimation Because of the stochastic nature of the solution, mean estimation is highly important and generally cannot be achieved by a simple straightforward averaging. The use of discrete particles to represent the flow allows for computer solutions but can introduce noise and error into the overall solution. One wants to be able to estimate not just the mean but the whole PDF for the quantities of interest. Otherwise, while means may be captured, other important moments may be significantly in error, which can easily cause incorrect solutions, since these outputs are also inputs in various elements of the solution algorithm [15]. There are some accurate schemes that have been implemented to more effectively produce mean estimates including least-mean-square cubic splines [154] and smoothed particle hydrodynamics [155]. However, in the context of engineering-scale 3-D simulations these algorithms are prohibitively expensive at this time. Therefore, the method developed by Subramaniam and Haworth [108] for 3-D flows in unstructured 86

101 deforming meshes is used here. This method is reasonably accurate and much more tractable for these types of simulations Coupling and Consistency Work done by Zhang and Haworth [9, 18, 156] addressed coupling and consistency issues between the finite-volume code and the Lagrangian particle representation of the PDF method. Algorithms for mass, velocity, and energy consistency have been developed. For velocity and energy consistency, the fluctuating components contained in the particle representation are used to establish a correction on the corresponding mean quantity of the finite-volume cell containing the particles. Composition PDF methods do not require the correction for the velocity, on the requirement that particles are advected with the mean flow. Energy consistency, however, needs to be maintained both on a global and a local level for the composition PDF so that details of combustion ignition and reaction are captured. In the framework of the hybrid FV/particle method used here, for a particle s enthalpy to change it must have contributions from a chemical source term (zero when considering absolute enthalpy), particle mixing, the mean pressure time derivative (important because of the reciprocating nature of an engine), mean viscous dissipation, and mean radiation (which is not considered here). As a result when the mean quantities are subtracted, the fluctuating enthalpy on a particle is due solely to particle mixing. One can calculate for the fluctuating enthalpy, whose average should be zero, on the particle side to capture the effect of the distribution while still computing energy solely on the finite-volume side, while maintaining consistency through the mean enthalpy. Mass consistency has been examined in work by Haworth and Pope and Muradoglu et al. [157,158]. The particle system s mass must be consistent with the mass 87

102 continuity equation, which will itself only be consistent if the mean pressure field satisfies the Poisson equation, which is the divergence of the mean momentum equation. For the composition PDF method, the particles are advected using the mean velocity of the finite-volume cell in which they reside. While consistency is maintained on the finite-volume side for the equations, there is a disconnect to the particles because of the discrete nature of the problem, thus creating the consistency problem in the coupling. A continuous velocity field needs to be formed from this discrete setup. Mass flux through cell faces, satisfied on the finite-volume side, should also be satisfied by the particles. Discretization errors and numerical issues add to the problem. The method developed by Zhang and Haworth [18] addresses the mass consistency problem so that the model may be robustly applied for engineering type meshes and systems. There are three stages to this algorithm. The first stage establishes a mean velocity field using trilinear interpolation based on vertex values of velocity. This sufficiently establishes a continuous velocity field that may be accessed by the particles. The second stage enforces the mass flux across each cell face so that the finitevolume mass flux and particle mass flux are equivalent. A velocity field for each cell face is computed and imposed on top of the mean field established in stage one. This helps to ensure consistency but numerical issues can still cause deviations, even in the limit of dense particles, when statistical errors should go to zero. Based on residuals, the third stage applies a corrector phase, in contrast to the predictor phases of the first two stages. Using the pressure algorithm from the finitevolume solver s corrector, dependent on a PISO or SIMPLE type scheme, this mass consistency stage applies the features of the solver to compute a set of element face mass flow rates to enforce mass consistency. The results from this method have been tested on a variety of configurations and have been presented in [9]. 88

103 4.8 Additional Computational Considerations Meshing Meshes need to be constructed prudently in order to avoid adding artifacts to the solution that result from the mesh geometry, properly capture features of the domain and the flow, and ensure convergence of the solution based on the size of the mesh. Refinement of the mesh must be made judiciously in order to balance the need for accuracy and the need for low computational cost. There are some methods for adaptive mesh refinement, such as for sprays [146], that help to capture details of the flow with finer meshing when needed, while eliminating the refinement when speed is more important. One must also satisfy a Courant number criterion to properly solve the flow, which puts another restraint on the size of the mesh. This is particularly important because the problem is not steady state but transient, making each step in time very important to the next iteration. The Courant number, C, is defined as C U t, where U is L the characteristic velocity (e.g., a particle velocity), t is the time step, and L is the characteristic length, normally the size of a cell. For this work, and in general for transient problems of this type that are highly coupled with the flow, a value of C 1 is typical. The mesh used in these studies is a section mesh and thus assumes azimuthal symmetry. This is a reasonable approximation for diesel engines that run with sprays that are evenly distributed and in cases where engine flow is fairly uniform, but would not be appropriate for many engine combustion modes. An accordion type mesh motion is utilized which preserves the number of finite-volume cells throughout the engine strokes, but cells at piston top-dead-center may have an undesirably high aspect ratio. 89

104 4.8.2 Chemistry Acceleration Use of detailed chemistry can be computationally expensive when applied to 3-D geometries. The cost increases with the size of the mesh, which is generally large for industrial applications. With the addition of PDF particles, chemistry calculation takes an even larger proportion of the runtime. Because of the percentage of the time spent doing chemistry calculation and the need to keep the simulation computationally tractable, a tabulative method was incorporated into the code to accelerate the chemistry calculations. Chemistry speedup through tabulative methods has been proposed in recent papers [16, 17]. Most applications have been for canonical configurations such as the Sandia laboratory flames. For these statistically stationary setups, they have shown significant speedup on the order of greater than 90% reduction in compute time. However, for highly non-stationary flows, such as reciprocating engine flows, the speedup has shown to be less significant [159]. Further work has been performed on parallelization of the algorithms [160] that show promise for improved performance for non-stationary systems and large problems. Here, as described further below, the issue of balancing computational load over the processors is a concern Parallelization Parallel processing can also be used to speed the chemical reaction calculation. This method takes advantage of multiple processors, decomposing the problem into parts and solving each part on a separate processor. When all processors have completed their task, the full solution is gathered together. In the context of this thesis, whereas the full CFD code itself is not parallelized, the calculations that require the most CPU time are the stiff linear system of chemical reactions and so significant overall speed-up is attained. For a given number of 90

105 processors, the domain is divided into sets of cells or particles, when the PDF particle method is used. The algorithm used for domain decomposition is very important as it can affect the efficiency of the parallelization. What one aims to do is to decompose the problem into parts that require the same amount of CPU effort (assuming that one is using processors of the same speed and type). This way, the load over the processors is balanced and the most efficient use of resources is achieved. There are two load-balancing algorithms that have been used here, both with decent load balancing. One simply randomizes the sets of decomposed regions so that no one set is biased to, say, a cold part of the domain that requires less CPU time, while another set may be biased to a hot part of the domain that requires more CPU time. Randomizing the sets of domains helps to homogenize the regions and should, for the most part, be an efficient an appropriate way to balance the load, though it is possible that a set of domains might be established that isn t well balanced simply because of the randomness. The other algorithm for load-balancing establishes sets based upon equally dividing the hot cells or particles that must be computed. Generally, this method will not divide numbers of cells or particles equally among the processors but will assign a set that is approximately computationally equivalent in effort to each of the other sets. While the latter algorithm has been used primarily for the work here, both should provide the same solution, though somewhat different speed-ups. 4.9 Summary This chapter outlined the modeling issues for turbulent combustion in an internal combustion engine system. Included in the review were the necessary physical governing equations. From this, three levels of modeling were presented that go from solving for every scale of the flow to solving only for mean flow: direct numerical 91

106 simulation, large-eddy simulation, and Reynolds Averaged simulation. PDF methods and their bearing on turbulent combustion, through modeling turbulence/chemistry interactions, were presented. Turbulence closures and other combustion models for the closure of the mean reaction rate were reviewed. Additional closures for turbulent transport and molecular mixing, necessary for composition PDF methods, were outlined. A three-dimensional, time-dependent Reynolds-averaged model is employed within an unstructured, deforming-mesh, compressible finite-volume CFD solver. A Lagrangian particle Monte Carlo method is used to solve the modeled composition PDF equation using a consistent hybrid particle/finite-volume method. This explicitly accounts for the turbulent fluctuations in species composition and enthalpy (hence temperature), relative to each finite-volume cell s mean value. A two-equation k ε turbulence model and a standard gradient transport approximation is used to account for transport by turbulent velocity fluctuations, and a simple pair-exchange model is used for molecular mixing [108]. Spray modeling and its effects on combustion were explained, noting that understanding and modeling mixture preparation is a major research need. Algorithms and methods for the hybrid particle/mesh solution used in this work were presented, concerning coupling and mesh and computing needs. Overall, one must realize the breadth of modeling required to realize a good solution of engine modeling problems. There are several issues, including turbulence/chemistry interactions, kinetics, flow scales, and mixture preparation that need to be properly captured to provide predictive capabilities for internal combustion engine solutions. With an understanding of this, the next chapter presents the work of this thesis to understand and quantify the effects of turbulence/chemistry interactions in the context of compression-ignition diesel engines. 92

107 Chapter 5 Modeling Study and Experimental Comparison This chapter presents results from simulations for simplified and real engine configurations. The first section summarizes key results from early scoping studies for simplified engine configurations. The next three sections present results obtained for a real engine configuration including quantitative comparisons with experimental measurements. It has been found that turbulence/chemistry interactions do have significant impacts on autoignition and emissions. However, there remain significant quantitative discrepancies between the model results and the experimental measurements. 5.1 Scoping Studies for Simplified Engine Configurations Early work explored the abilities of PDF-based CFD modeling on several fronts. The influence of TCI on emissions and autoignition was demonstrated in Zhang et al. [9] for a simplified engine configuration operating at a variety of conditions. The effects of crevice volumes, equivalence ratio, and wall temperatures were explored with and without a PDF method to account for TCI. Key results are summarized in 93

108 Table 5.1. The study concluded that for homogeneous reactants with low-to-moderate swirl, ignition timing was negligibly affected by TCI. However, emissions did show a significant response to the inclusion of the high-end turbulence/chemistry interactions model. Cases with high swirl, high inhomogeneity, and significant crevice volumes showed that emissions and ignition timing were all affected by TCI. Unburned fuel was noted as a contributor to UHC in cases of high swirl or significant crevice volume only. Kung et al. focused on the effects of simulating multiple consecutive engine cycles [20]. It was found that it is necessary to simulate several engine cycles including intake and exhaust strokes to achieve a representative cyclic steady-state condition (see Figure 5.1). Strong emissions sensitivity was found to be related to high levels of in-cylinder inhomogeneity, further making the case for inclusion of a model for TCI effects. Such numerical studies inherently rely on the setup of the initial and boundary conditions, creating a greater need for good experimental data. However, such data is not currently available for some details such as EGR distribution. A study by Zhang et al. investigated the sensitivity of simulations to variations in the PDF method s model coefficients [19] for the key physical effects of molecular mixing and turbulent diffusion. It was found that enhanced molecular mixing led to a more homogeneous composition distribution and delayed ignition. Similar effects were seen for variations in the turbulent diffusion model. Recent work by Kung et al. [21] emphasized the need for detailed chemical mechanisms that accurately predict NO x formation over the ranges of temperature, pressure, and equivalence ratio that occur in HCCI engines (Figure 5.2). Detailed chemical kinetic pathways for NO x formation were added to an n-heptane fuel mechanism. Significant differences in predictions are seen, as emphasized by the different scales for the case without the PDF method and the case with the PDF method. Note how N 2 O dominates, while NO x is extremely low for the case without the PDF method, 94

109 Table 5.1: Summary of global ignition timing and emissions results from [9]. CO and UHC values are global in-cylinder mass fractions at 40 o ATDC. Here FV denotes results obtained using cell-mean values of composition and temperature (neglecting TCI) and PDF denotes results obtained using the PDF method to account for TCI. TRLC denotes inclusion of a top-ring-land crevice. Case Equiv. Twall[K] IVC Premixed TRLC Ignition YCO YUHC YUHC ratio liner/ swirl or SOI Y/N timing φ head & ratio [ o BT DC] [ o AT DC] (fuel) (non-fuel) piston FV/PDF FV/PDF FV/PDF FV/PDF PHI / premixed N 1.5/ / / /2.03 PHI / premixed N -3.5/ / / /0.92 PHI / premixed N -3.9/ /0.25 0/ /0.41 TWAL / premixed N -0.8/ / / /1.23 SWRL / premixed N 1.6/ / / /2.76 SOI / o N -6.5/ /0.46 0/ /0.52 SOI / o N -7.4/ / / /0.61 SOI / o N -9.0/ / / /0.68 TRLC / o Y -6.9/ / / /

110 which is in sharp contrast with the results using the PDF method (the model conditions represent a low equivalence ratio case). Again, the need for accurate modeling of TCI effects is demonstrated through comparisons between CFD with and without PDF-based TCI modeling (Figures 5.3 and 5.4). 5.2 Effects of Turbulence/Chemistry Interactions in a Real Engine Preliminary tests are presented here. The tests are for RANS simulations without TCI and with TCI consideration (i.e., with the PDF method). Comparing these results to experiments, key differences can be discerned between the models and between the simulations and experiments. This permits us to account for both the effects of turbulence/chemistry interactions and the disparities between model and experiment Engine Configuration and Operating Conditions The test has been set up to model a real engine configuration, with experimental data made available by General Motors Corporation. This data was acquired from a single-cylinder engine using direct common-rail injection and cooled EGR, based on a production engine setup. Pressure, apparent heat-release rates, and emissions indices are provided from the experiments. A 1/7th sector mesh is used to represent a bowl-in-piston diesel engine (see Figure 5.5 and Table 5.2). The mesh includes a top-ring-land crevice, which can be important in determining unburned hydrocarbon (UHC) and CO emissions [9, 161, 162]. Intake and exhaust ports and valves are not modeled. Simulations begin at 138 btdc (post intake-valve closure) and continue to 90 atdc (before exhaust-valve opening). Two operating conditions are run to examine the effect of EGR and the response of the models at part load. EGR is represented by the inclusion of appropriate fractions 96

111 Initial Cycle 2nd Cycle 3rd Cycle Temperature (K) Crank (deg) Figure 5.1: Computed in-cylinder global temperature for consecutive cycles [20] Mole Fraction [ppm] NO NO2 N2O Mole Fraction [ppm] NO NO2 N2O Crankangle Degrees [360 = TDC compression] Crankangle Degrees [360 = TDC compression] Figure 5.2: Computed in-cylinder NO, NO 2, and N 2 O mole fractions versus crankangle for a 0.24 equivalence ratio n-heptane fueled premixed and directly-injected engine [21]. Left: CFD without the PDF method. Right: CFD with the PDF method. Note the difference in the ordinate scales for the two figures. 97

112 Pressure [bar] CFD wo/pdf CFD w/pdf Crankangle Degrees [360 = TDC compression] Figure 5.3: Pressure trace comparison between FV (i.e., no TCI) and PDF runs [21] Temperature [K] Volume averaged Max FV cell value Crankangle Degrees [360 = TDC compression] Temperature [K] Volume averaged 800 Max FV cell value Max PDF particle value Crankangle Degrees [360 = TDC compression] Figure 5.4: Computed in-cylinder temperatures versus crankangle for n-heptane [21]. Left: Volume-averaged in-cylinder temperature and maximum finite-volume cell mean temperature for CFD without the PDF method. Right: Volume-averaged in-cylinder temperature, maximum finite-volume cell mean temperature, and maximum PDF notional particle temperature for CFD with the PDF method. 98

113 Table 5.2: Engine configuration and operating conditions for two EGR levels. Displacement volume l/cyl Stroke 99 mm Bore 103 mm Squish 0.7 mm Engine Speed 1891 rpm Connecting rod length 188 mm Offset 0.5 mm Compression ratio 16:1 Swirl ratio 1.5 Start of injection 23 btdc EGR 40% or 65% # of cells in mesh Maximum # of PDF particles of CO 2 and H 2 O. The fuel injector is mounted near the top of the chamber on the centerline, with the spray directed along the bisecting plane and angled down towards the bowl at Start of injection (SOI) is at approximately 23 btdc. Figure 5.5: Schematic illustration of the profile of a piston sector representative of the configuration used for this work. The left side corresponds to the piston axis. The right side corresponds to the side of the piston. The curved section is the piston bowl. 99

114 5.2.2 Global Results To determine the importance of turbulence/chemistry interactions for this configuration, two sets of calculations were performed: one with the transported PDF method ( PDF ) and one where cell-mean values are used directly in the chemical mechanism ( FV ). Some baseline model parameters are given in Table 5.3. Global results are summarized in Table 5.4. There, the differences between FV and PDF are marked with regards to ignition and heat release rates and emissions predictions. When compared to experiment, computed emissions values require additional accuracy, though pressure traces between model and experiment are satisfactory Pressure, Temperature, and Heat Release Profiles 100 FV PDF Experimental 80 FV PDF Experimental 80 Pressure (bars) Pressure (bars) Crankangle Degrees [0 = TDC] Crankangle Degrees [0 = TDC] Figure 5.6: Computed in-cylinder pressure versus crankangle. Left: 40% EGR; Right: 65% EGR. For the 40% EGR case (left on Figure 5.6), the experimental pressure curve peaks at 0 CAD; the FV pressure peaks almost 2 degrees later and the PDF curve peaks 100

115 Table 5.3: Key baseline model settings (dimensionless). Spray: KH B0 (radius) 0.61 Spray: KH B1 (breakup time) 40.0 Spray: KH A Spray: KH (particle mass shedding factor) 0.2 Spray: RT τ (breakup time) 10.0 Spray: RT C (effective wavelength) 0.60 Spray: RT C dist (breakup length) 1.9 PDF: C φ (pdf mixing coefficient) 2.0 Chemical Mechanism: 34-species n-heptane (Appendix A.1) at 2 degrees later. The experimental pressure curve lies between the two computed traces, with FV over-predicting the peak pressure and PDF under-predicting. For 65% EGR (right on Figure 5.6), both FV and PDF show early ignition compared to the experiment. The FV pressure trace matches the experimental peak well (peak pressure about 1 bar below the experiment), whereas the PDF peak pressure is 6 to 7 bars below. Timing of the peak pressure is the same in all cases at about 2 atdc. Overall, the PDF results show lower maximum heat release rates that occur earlier than those in the FV cases. Temperature traces (not shown) show global trends that are similar to the pressure traces. However, there is a larger range in finite-volume cell-mean temperatures when using the PDF method, with significantly higher maximum cell temperatures through the 40% EGR expansion stroke and somewhat higher maximum cell temperatures towards the middle of the expansion stroke for 65% EGR. This increased range of temperature is an indication of temperature inhomogeneity that can have a significant influence on emissions. 101

116 10 2 NO NO2 N2O 10 2 NO NO2 N2O PPM 10 1 PPM Crankangle Degrees [0 = TDC] Crankangle Degrees [0 = TDC] Figure 5.7: Computed in-cylinder NO, NO 2, and N 2 O versus crankangle for 40% EGR. Left: FV; Right: PDF Emissions Emissions values are taken from the end of the run (90 atdc); there is little further change in computed emissions after that time. PDF CO and UHC emission indices are higher than those computed using FV, while PDF NO x values are lower, as seen in Table 5.4. Time evolution of in-cylinder NO, NO 2, and N 2 O is shown in Figure 5.7 for the 40% EGR case. For this operating condition, engine-out NO x is dominated by NO. Values of NO x and N 2 O for 65% EGR (not shown) are extremely low: less than 1 ppm. In this case there is more N 2 O than NO at 90 atdc. For the 40% EGR case, PDF CO values are about 40% of the experimental emissions index, while FV CO is about 10% of the experimental value. Both FV and PDF unburned hydrocarbon values are several orders of magnitude lower than the experimental values. NO x is correspondingly higher for the FV case relative to PDF, but both are lower than the experiment, though on the same order. Here the NO x emission index is a combination of NO and NO

117 Table 5.4: Global results for 40% and 65% EGR and cases without turbulence/chemistry interactions (FV), with turbulence/chemistry interactions (PDF), and from experimental data (Exp). The timing and magnitude of the maximum rate of heat release are given in crankangle degrees atdc, CA dj/dθ max, and Joules per degree, (dj/dθ) max. Computed emissions are global in-cylinder emissions index values at 90 atdc, and UHC includes all hydrocarbons but the fuel. Case Model CA dj/dθ max (dj/dθ) max CO UHC NO x [ atdc] [J/CA ] [g/kg fuel] [g/kg fuel] [g/kg fuel] 40% EGR FV e PDF e Exp % EGR FV PDF Exp The 65% EGR case shows significantly higher values of CO for the simulated cases relative to experiment. PDF computations show the highest CO value. Unburned hydrocarbons are correspondingly higher for the PDF case relative to the FV case and experiment. NO x values are higher for the FV case relative to the PDF case, but both are an order of magnitude below the experimental values Discussion The results shown here represent preliminary attempts to apply PDF methods to a practical direct-injection diesel engine. In these cases, computed pressure traces without the PDF show better agreement with experiment than those with the PDF. Emissions results also fared poorly in comparison to experiments for PDF cases, though the cases without PDF did not do much better. These results may appear disappointing, but they are not surprising. The thermochemical model and other models (sprays, in particular) that have been used here have been tuned to give good agreement with experiment without a PDF method. This has included adjustments 103

118 by other researchers to kinetic rate coefficients in the chemical reaction mechanism (see Appendix A). Thus, the more important conclusion is that there are significant differences between results that ignore and the results that include the effect of turbulence/chemistry interactions. These results suggest that turbulence/chemistry interactions are important, even in determining the mean pressure trace. The more satisfactory treatment of turbulence/chemistry interactions permitted by using the PDF method should allow a more systematic approach to modeling in-cylinder thermochemical processes, where one physical submodel is not tuned to make up for deficiencies in another. This initial study prompted a systematic parametric study to examine in more detail the interplay between the various models, such as sprays and chemical kinetics. A broader range of experimental conditions also was considered to compare and contrast the effects of models and turbulence/chemistry interactions on global-averaged performance and emissions. The evolution of key chemical species also was examined. 5.3 Parametric Studies Toward Improved Modeling In the following subsections, examples of results from sensitivity studies are presented. These are followed by detailed quantitative comparisons with the experimental data provided by General Motors for the operating conditions specified in Table 5.5. This data is the same experimental data set detailed earlier. As before, two sets of calculations are performed: one with the transported PDF method ( PDF ) and one where cell-mean values are used directly in the chemical mechanism ( FV ). Comparison between the two allows for the determination of the importance of turbulence-chemistry interactions. 104

119 Table 5.5: Engine operating conditions for four EGR levels and a full-load case. The bore diameter is 103 mm and the squish height is 0.7 mm. There are 39,483 finite volume cells and a maximum of 987,075 gas-phase particles. Swirl ratio is defined as the angular velocity of the flow divided by the engine crankshaft angular rotational speed. Engine condition 70% EGR 65% EGR 50% EGR 40% EGR Full-Load Displacement volume l/cyl Swirl ratio 1.5 Baseline compression ratio for 0.7 mm clearance 16:1 Engine RPM Baseline initial pressure (bars) Baseline initial temperature (K) Start of injection 23 btdc 23 btdc 23 btdc 23 btdc 3.5 btdc External EGR 70% 65% 50% 40% 0% Equivalence ratio (based on in-cylinder O2 to fuel) Equivalence ratio (based on fresh air to fuel ratio) Initial O2 %

120 5.3.1 Thermochemical Model Previous results [163] have shown consistently early ignition timings for both FV and PDF runs compared with the experimental results. The difference between the results of the 34-species and 40-species n-heptane chemical mechanisms (Figure 5.8) suggests that the discrepancy is largely due to the chemical kinetics (see Appendix A for the reaction mechanisms). The 40-species n-heptane mechanism has not been tuned with respect to engine data. The significantly better ignition timing of the 40-species mechanism led to the use of this mechanism for the remaining sensitivity studies. Figure 5.8 also shows significant differences between the FV and PDF results; this again illustrates the importance of TCI. In this case, FV matches the experimental pressure trace better than PDF. This is not unexpected. In the absence of good models for TCI, engine models have been tuned by adjusting parameters in other models to account for this missing physics Compression Ratio A second example is sensitivity to engine geometry. The baseline clearance height for this engine configuration is 0.7 mm. An increase or decrease of 0.1 mm causes the geometric compression ratio to change from 16 to 15.8 or 16.2, respectively. The computed peak pressure increases or decreases between 2 and 3 bars (Figure 5.9) in response to this variation, demonstrating a strong sensitivity to this parameter Initial and Boundary Conditions Changes to initial pressure and temperature were also explored. A ± 8 kpa change in initial pressure resulted in correspondingly higher or lower pressure throughout the cycle, with the peak pressure changing by about +/- 4-5 bars (Figure 5.10). 106

121 80 Pressure (bars) Experimental Data FV 34-species PDF 34-species FV 40-species PDF 40-species Crankangle Degrees [0 = TDC] Figure 5.8: Sensitivity to chemical mechanism and TCI for the 65% EGR case, including comparison with experimental data. 107

122 90 80 Pressure (bars) Crankangle Degrees [0 = TDC] Figure 5.9: Sensitivity to compression ratio, run using the conditions from 65% EGR setup and the FV model. Clearance height was varied by ±0.1 mm from the baseline case to effect the changes. 108

123 Overall the initial and peak pressures for higher initial temperatures are lower, with peak pressure approximately 2 bars lower for each 10 K increase in initial temperature. This is because of the decrease in trapped mass with increasing initial temperature. However, the higher initial temperature gives a steeper rate of pressure rise (Figure 5.10). Changes to the wall temperatures, which are set constant throughout the run, showed very little effect on global pressure and heat release for an increase or decrease of 10 K. Changes to swirl, start of injection timing, wall temperature, and fuel temperature were also explored and showed expected but not significant effects on global results PDF Mixing Model A key model coefficient in PDF methods is the mixing rate, C φ. This coefficient is the ratio of a turbulence (hydrodynamic) timescale to a scalar timescale, and is related to the scalar dissipation rate. It should not be regarded as a universally applicable constant. The usual value for passive scalars in homogeneous turbulence is C φ 2; even there, variations have been reported in canonical experiments (e.g., C φ 1-3 [164]). In reacting flows, a wider range of values has been reported. For example, the recent comprehensive study of mixing models by Cao, Wang and Pope [165] reported values ranging from 1.5 to 3.8, depending on the specific models used. In LES-based modeling studies, values in the literature include C φ = 8 [166] to values as high as C φ = 10 [167]. These large variations in C φ likely result from a combination of the failure to compute the hydrodynamic time scale (or dissipation rate) correctly, and the inherent limitations of single-timescale models. Here the hydrodynamic timescale τ is determined by a standard k ε turbulence model (τ = k/ε), and the shortcomings of such models are well known. In the limit C φ, the PDF result should be the same as that from the FV 109

124 80 P(bars) 60 T+20 K T+10 K Baseline T-10 K T-20 K P+8kPa (4.5%) P-8kPa (4.5%) Crankangle Degrees [0=TDC] Figure 5.10: Sensitivity to initial pressure and temperature for the 65% EGR condition. These are FV runs. The degree of variations for PDF runs is similar. Changes to temperature are indicated by the sign and number following a T. Changes to pressure are indicated by the sign and number following a P. 110

125 model: this corresponds to a perfectly stirred reactor model for each cell. At the other extreme (C φ 0), there is no mixing at all. In that case, particle compositions change only as a result of chemical reaction, while cell compositions are the result of averaging those separate reacting fluid representations. This would not resolve any of the effects of mixing. The sensitivity of global pressure to the mixing rate parameter is significant, and as C φ increases, the PDF results approach the FV result (Figure 5.11). This is evidence for the important effect of mixing rate and turbulence/chemistry interactions on combustion results. It is unreasonable to assume infinite mixing with the relatively large finite-volume cells. The reduced rate of mixing provided by the PDF method and the mixing model help to improve the physical modeling, capturing the effects of turbulence on timescales Fuel Composition Chemical differences exist between experiment (diesel fuel) and model (n-heptane fuel). For example, use of the experimental fuel mass in the model will result in a different equivalence ratio because of the discrepancy in C/H ratio between n-heptane and diesel fuel. However, as Figure 5.12 shows, this difference does not result in a large deviation in the computed global pressure and heat release. There the n-heptane mass of the ER Equivalent case is kg lower than the experimental diesel fuel mass to maintain the same equivalence ratio. For the remaining runs in this thesis, the fuel mass was kept consistent with the experiment Spray/PDF Coupling The two methods described earlier (see Section 4.6) for spray and PDF particle interaction are compared in Figure Differences in global heat release and pressure traces are small. There is a slightly higher rate of heat release when the vaporized 111

126 P(bars) FV PDF 20 PDF 10 PDF Crankangle Degrees [0 = TDC] Figure 5.11: Sensitivity to mixing rate for PDF for the 65% EGR case. PDF 2 corresponds to C φ = 2, PDF 10 to C φ = 10, and PDF 20 to C φ = 20. PDF results approach the FV result as C φ. 112

127 P(bars) Experimental Data Fuel Mass Equivalent ER Equivalent HR(J/deg) Crankangle Degrees [0 = TDC] 0 Figure 5.12: Sensitivity to fuel composition (fuel mass) for the 40% EGR case. Results for pressure and heat release from two PDF runs are shown together with the experimental data. 113

128 spray is distributed among the existing PDF particles, resulting in a higher rate of pressure rise. The differences in particle temperature distributions are more pronounced (Figure 5.14). The distributed-spray case s coldest particles are significantly higher in temperature than those associated with new particle creation. When new particles are created directly from the newly vaporized fuel, low particle enthalpies (temperature) can result because of the explicit vaporization model. This low-enthalpy mass is spread over existing particles in the other approach. The cold particles are a small portion of the total mass in the cylinder, but may be important to the production of trace emissions species. The distributed coupling algorithm has been adopted for the quantitative comparisons with experiment that follow in Section Spray Parcel Number Sensitivity of model results to grid resolution and the number of spray parcels has been noted in earlier modeling studies [146]. Figure 5.15 compares a run using 20,000 spray parcels with one using 40,000 parcels. The difference is small. Subsequent runs use 20,000 spray parcels Spray Breakup Model Parameters Many model coefficient variations in the spray breakup model were explored. Variations in the KH-RT spray breakup model are examined in Figure Model parameters include the breakup distance (C dist), the Kelvin-Helmholtz (KH) wave breakup model constant to calculate radius (B0), the KH wave breakup model constant to calculate breakup time (B1), and the KH mass criterion for the creation of child droplets. Only a small subset of the results is shown. Increasing the breakup length improved the prediction of ignition timing, but resulted in high and unacceptable wall wetting. Inclusion of additional droplet drag effects reduced the computed 114

129 P(bars) New Particles Distributed Spray HR(J/deg) Crankangle Degrees [0 = TDC] 0 Figure 5.13: Sensitivity to spray/pdf coupling for the 40% EGR case. Solid lines correspond to the creation of new PDF particles as spray parcels vaporize. Dashed lines correspond to distribution of newly vaporized fuel mass among existing PDF particles in each cell. 115

130 Temperature (K) New Particles Distributed Spray Crankangle Degrees [0 = TDC] Figure 5.14: Sensitivity to spray/pdf coupling for the 40% EGR case. Here the minimum and maximum particle temperatures are plotted as a function of crankangle. 116

131 P(bars) PDF 20,000 parcels PDF 40,000 parcels 20 HR(J/deg) Crankangle Degrees [0 = TDC] 0 Figure 5.15: Sensitivity to number of spray parcels for the 65% EGR case using the FV model. 117

132 P(bars) Experimental Data Baseline PDF KHRT Mod 1 KHRT Mod HR(J/deg) Crankangle Degrees [0 = TDC] Figure 5.16: Sensitivity to spray model parameters for the 65% EGR case. KHRT Mod 1 corresponds to an increase in the breakup length constant, Cdist, from 1.9 to 2.5 and a reduction of B1 from 60 to 30. KHRT Mod 0 corresponds to a breakup length of 2.5 and B0 = 0.3 instead of the baseline value of B0 =

133 peak pressure. The control parameter for creation of child droplets had a minor effect on the timing of the heat release peak. Both B0 and B1 showed significant changes in the computed peak pressure and maximum rate of pressure rise. 5.4 Comparison with Experimental Data Four PCCI (high EGR) modes and a full-load mode (Table 5.5) are simulated using the same set of model parameters. Two sets of calculations are shown (FV and PDF) to emphasize the role of TCI. Based on the results of the sensitivity study, the mixing coefficient in the PDF mixing model was set at 6.0, the geometric compression ratio was increased to 16.2, and the KH-RT model constant B1 was set at 10. The spray/pdf particle coupling was set to distribute vaporized spray mass among existing particles instead of creating new particles. These settings apply to all the PDF and FV runs, where applicable. In general, the agreement between computed and measured pressure and heat-release traces is acceptable, and the model responds correctly to the variations in operating conditions. Two sets of calculations are shown (FV and PDF) to emphasize the role of TCI. Pressure and heat release data are examined first. Then, emissions results (CO, UHC, soot, and NO x ) are discussed. Figures 5.17 and 5.18 show computed and measured pressure and heat-release traces for 70% EGR, 65% EGR, 50% EGR, 40% EGR, and full-load cases, respectively Results Overview There are prominent differences between FV and PDF simulations. For example, peak pressure for FV and PDF cases for the 65% EGR case bracket the experimental value, with the FV case tracking a bit higher and the PDF case tracking lower. However, the PDF case better matches the experimental pressure trace through expansion. The 119

134 40% EGR plots show slightly better ignition timing for FV, but better peak-pressure match for PDF. PDF under-predicts peak heat release while FV over-predicts peak heat release. Both FV and PDF pressure traces track higher than the experimental pressure trace through expansion. The trend is increasingly early ignition timing with more pronounced heat release differences and decreasing peak pressure with increasing EGR. For the full-load case (Figure 5.18), FV shows a sharp spike in heat release at about 1 CAD btdc that is absent in the experimental data and in the PDF results. This leads to a greater rate of pressure rise and a higher overall peak pressure relative to both experiment and PDF results. Both FV and PDF pressure traces fall below the experimental trace as the cylinder expands. Though the geometric compression ratio is higher than in the experiment, the simulated pressure trace is in line with experiment through compression. The EGR sweep, from 40% to 70%, and full-load comparison, Figures 5.17 and 5.18, show that the FV model seems to match peak pressure better than the PDF model when running at high EGR rates. This is reversed for lower EGR rates, with the PDF model matching peak pressure better at 40% and full-load conditions. However, it is curious that the FV model shows pressure traces that are more robust than the experimental trace at the 65% and 70% EGR levels than its CO emissions would lead one to expect, which are higher than the experiment (see Table 5.6). The 70% and 65% EGR initial heat-release peaks for the simulated traces are consistently early for both FV and PDF models relative to experiment (Figure 5.17 (a) and (b)). In the 50% and 40% EGR cases, the primary heat release trace approaches that of the experiment and there is less initial heat release, though FV and PDF show heat release earlier than the experiment. FV has a tendency to ignite later than the PDF case. For the full-load case, one broad heat-release event is exhibited. This is captured by the PDF model, while FV shows a sharp early spike. These results show that the models are able to span combustion regimes from con- 120

135 P(bars) HR(J/deg) P(bars) HR(J/deg) 20 Experimental FV PDF Experimental FV PDF Crankangle Degrees [0 = TDC] Crankangle Degrees [0 = TDC] (a) 70% EGR (b) 65% EGR P(bars) HR(J/deg) P(bars) HR(J/deg) 20 Experimental FV PDF Experimental FV PDF Crankangle Degrees [0 = TDC] Crankangle Degrees [0 = TDC] (c) 50% EGR (d) 40% EGR Figure 5.17: EGR sweep from 40% to 70% comparison between experiment, FV, and PDF for pressure and heat-release. 121

136 P(bars) Experimental FV PDF HR(J/deg) Crankangle Degrees [0 = TDC] 0 Figure 5.18: Full-load case comparison between experiment, FV, and PDF for pressure and heat-release. 122

137 Table 5.6: Global emissions results for full-load, 40%, 50%, 65%, and 70% EGR conditions. Computed emissions are global in-cylinder emissions index values at 90 atdc. Case Model CO UHC [g/kg fuel] [g/kg fuel] Full load FV PDF Exp % EGR FV PDF Exp % EGR FV PDF Exp % EGR FV PDF Exp % EGR FV PDF Exp ventional full-load diesel to low-temperature PCCI modes. The differences between the different EGR levels and the full-load case are marked, comparing Figures 5.17 and Both FV and PDF follow the trends in heat-release rate and pressure exhibited by the experimental results. These simulations have been performed with a view towards finding appropriate and robust parameters to achieve pressure traces in reasonable agreement with engine data over a broad range of operation and to explore the complexities of this level of modeling. These cases demonstrate the applicability of the PDF model without tuning for each operating condition. Results for emissions indices across the run conditions reveal a non-monotonic behavior (Table 5.6 and Figures 5.19 and 5.20). There, two trace emissions species are examined: CO and UHC. The PDF model significantly over-predicts CO in the 123

138 g/kg fuel 10 1 Exp CO FV CO PDF CO 0.1 Full Load 40% EGR 50% EGR 65% EGR 70% EGR Figure 5.19: Comparison of CO at 90 atdc for FV and PDF models versus the engine-out measurements from the experiment. 124

139 g/kg fuel 10 1 Exp HC FV HC PDF HC 0.1 Full Load 40% EGR 50% EGR 65% EGR 70% EGR Figure 5.20: Comparison of UHC at 90 atdc for FV and PDF models versus the engine-out measurements from the experiment. 125

140 full-load and 65% EGR cases, while slightly under-predicting CO for 40% EGR. For the same conditions, the FV model predicts lower levels of CO than the PDF model, but with numbers significantly different from both PDF and experimental values. The trend for PDF CO better tracks the experimental CO for cases with EGR. UHC modeling fares somewhat better, with PDF predictions coming close to experiment for full-load and 40% EGR cases, while significantly over-predicting for 65% EGR. FV also over-predicts for 65% EGR, and significantly under-predicts for the other two cases. It is curious that some cases such as the 65% EGR case and the full-load case both have high computed CO, while the 40% EGR case does not. One might expect high CO at the lower temperatures of the 65% EGR case, but the full-load case should have sufficiently robust combustion to burn out the CO. Figure 5.21 compares PDF and FV iso-surfaces of mean temperature at 30 and 90 CAD atdc for the 65% EGR case. The PDF iso-surfaces exhibit small-scale wrinkling resulting from stochastic errors from the use of a finite number of particles. More importantly, the general structure and arrangement of the surfaces differ substantially between PDF and FV. The lower left figure depicts local hot spots near the crevice and in the bowl that are not present in the FV plot. Cold tongues from the head and from the liner are noticeable in the 30 CAD and 90 CAD PDF plots; these are absent in the FV plots. Because of the extreme sensitivity of the trace emissions species to temperature, these temperature differences are expected to result in differences in CO and UHC. Corresponding CO iso-surfaces are shown in Figure For both PDF and FV there is high CO in the squish region of the piston top. The iso-surfaces appear to be attached to the flat portion of the piston top. These surfaces stretch almost to the head and also extend into the bowl for the PDF case at 90 CAD atdc. The structure appears to correlate with the structure of the temperature iso-contours. 126

141 Figure 5.21: Computed mean temperature [K] iso-contours for the 65% EGR case at 30 atdc (top) and at 90 atdc (bottom). PDF results are on the left and FV results are on the right. 127

142 Figure 5.22: Computed mean CO mass fraction iso-contours for the 65% EGR case at 30 atdc (top) and at 90 atdc (bottom). PDF results are on the left and FV results are on the right. 128

143 Figure 5.23: Computed mean OH mass fraction iso-contours for the 65% EGR case at 30 atdc (top) and at 90 atdc (bottom). PDF results are on the left and FV results are on the right. 129

144 5.4.2 CO Emissions Westbrook and Dryer [63] noted that the CO oxidation mechanism required the addition of HO 2 and H 2 O 2 to prior models in order to match experimental results for CO oxidation in a turbulent flow reactor [168] (HO 2 and H 2 O 2 are included in the mechanism used here). The high CO that we see in these results may be a result of a similar hole in the reaction pathways for this reduced mechanism. Other possibilities may be quenching due to thermal boundary layers and coupled effects with the spray model. A key reaction pathway for CO oxidation is CO + OH = CO 2 + H [63]. Absence of OH would almost completely inhibit CO burn out, greatly affecting heat release as well. Figure 5.23 suggests that for the 65% EGR case, the absence of significant quantities of OH in regions where the CO concentrations are greatest may contribute to the continued presence of CO. The FV run also has high CO relative to experiment and relative to the availability of OH. In [63], it was noted that even small amounts of hydrocarbons can significantly inhibit the oxidation of CO. The reasoning started with the fact that CO depends strongly on the presence of OH radicals. However, hydrocarbon species inhibit chain branching because the rate of reaction for the major OH-producing reaction, reaction 3.5, is much less than the rate between H atoms and hydrocarbon species. The presence of hydrocarbons can thus inhibit the formation of OH radicals, whose paucity in turn inhibits the oxidation of CO. Similarly, the rate of reaction 3.3 is much less than the rate of the reactions between OH radicals and common hydrocarbons, shown in Table 2 of [63], in which several reactions between OH and hydrocarbons have rates an order of magnitude higher. As a result, hydrocarbon oxidation will produce CO, but CO will not be oxidized significantly until the hydrocarbon species and fragments are completely consumed. Only then will the OH radical fraction grow sharply and 130

145 consume the CO. It is possible that the over-prediction of CO is affecting not only the heat release calculation but also the hydrocarbon, NO x, and soot predictions. It may be that the above sequence of events is at the heart of the inability of the model to predict CO emissions. Perhaps there are key reaction paths missing in the reaction mechanism, but as can be seen in Appendix A.2, the current mechanism is complete with regards to the standard CO consumption pathways and does include such important species as HO 2 and H 2 O 2 in the species list. There are possible issues concerning the fuelspray distribution modeling. Turbulence/chemistry interactions do play a role in the predictions, and it may be that there is some transport process that is either enhancing or inhibiting CO oxidation, probably linked to the mixing model used. It should be stressed that the FV model has an inherent perfectly stirred reactor model built-in for each finite-volume cell. The PDF model limits this aspect of the mixing and in so doing may be inhibiting the combustion by reducing the reaction rate of CO. This will cause previously unseen (i.e., with finite-volume modeling) species transport differences affecting CO oxidation and OH production due to the distribution of species concentrations and local enthalpies. Hydrogen also plays a significant role in CO oxidation. It has been well documented that the diffusion of hydrogen is very high and species-specific diffusion might have an effect on the role of hydrogen in emission modeling. Given the importance of hydrogen to the reactions leading to CO oxidation, there is a strong need to have hydrogen present with CO in cells or particles. Results such as the 3-D plot of CO mass fraction in Figure 5.22 open up many questions. While the disparity between the FV and PDF models is fairly stark, some similarities can be seen. The magnitude of CO is a notable difference, but the general region of the emission species is similar between both cases. Is this the result of thermal boundaries on the piston top? Why does the PDF model show 131

146 higher amounts of CO than the FV case even though both seem to originate the CO from the same region? Are crevice volumes being adequately modeled concerning their contribution to emissions? How well is the fuel spray being modeled so that fuel penetration and distribution is appropriate? Is CO prevented from oxidizing even relatively far from the thermal boundaries (this may be the result of charge quenching when the piston is closer to TDC and the resulting charge distributing over that region during expansion)? Is the CO mass fraction result primarily a symptom of flow physics or kinetic rates for hydrocarbon species? If it is the kinetic rates, would improvement to the mechanism benefit the FV or PDF model more? If it is not the kinetic rates, why do the flow and thermal boundary effects seem to be more prominent in the PDF case than the FV case? Figures 5.22 and 5.23 show that the regions of highest CO concentration are separate from the regions of highest OH concentration, and that this is the case for both FV and PDF models, but much more prominent in the case of the PDF model. It would be reasonable to assume that CO over-prediction would not be as stark if these regions shared the same physical space. Is their separation the reason for the CO over-prediction or is that due primarily to slow UHC oxidation in the high CO region? If it is because the two regions are kept apart, there may be some engine flow effects or mixing/diffusion effects that are not being properly captured and this should be examined for future modeling efforts. Because these cases all run with SOI fairly close to TDC, fuel should be prevented from reaching the near-wall and crevice regions [169], limiting hydrocarbon emissions, which is perhaps evidenced by the low fuel species emissions. Dec et al. [169] note, in experiments, that overly lean regions tend to produce oxygenated and unburnt hydrocarbons in greater amounts than richer regions. This is also seen by Drake et al. [25] in a two-stroke DISI configuration. It may be that the PDF model is producing more locally lean regions because of the PDFs produced 132

147 for each cell, which allow for unburnt hydrocarbons to continue longer than in a FV reaction model. While this may produce higher emissions levels in the PDF model, this would suggest that the UHC kinetic rates need to be improved to allow for UHC oxidation to occur more expediently, so as to allow for CO oxidation at rates more consistent with experiments. Drake et al. also note that, while incomplete combustion of the injected fuel cloud may be a major source of the UHC emission, late release of fuel trapped in the injector nozzle-exit crevice is another probable dominant UHC source (while crevice volumes are not, as evidenced by the 3-D plots shown here). Thermal boundary layers may play a significant role, especially in high EGR cases, where low temperatures, utilized to reduce NO x, may increase UHC s. Such a situation was noted in a computational study by Cook et al. [170], who showed that methane was a primary component of the UHC emissions. Here, the thermal boundary layers may be playing a similar role, also producing high levels of methane. However, they reported high CO and UHC only in fuel-lean mixtures and attributed methane production to rich, poorly mixed regions. This study shows high levels of CO and methane as a significant proportion of the unburned hydrocarbon emissions in a full-load case and in high EGR cases, suggesting limited importance, in these cases and with these models, of the thermal boundary layer to CO emissions. Since the Cook work was also computational, one may wonder if an underlying deficiency may be the capability of the kinetic mechanism. Therefore, concerning incomplete combustion regardless of kinetics, perhaps two particular conditions are in play here. Either the regions are too lean or too rich, leading to incomplete combustion because of leanness or incomplete combustion in rich regions because of a lack of sufficient mixing before the cylinder expands and pressure drops, quenching the reactions. These two sides of the equivalence-ratio distribution that lead to incomplete combustion is what the PDF model will most likely enhance through its composition PDF, making it more susceptible to higher 133

148 UHC emissions. This could be problematic because of the significant effect that even small quantities of UHC have on the CO emissions predictions and, likewise, the predictions of NO x and soot. If the PDF model is capturing more physics, then the higher emissions predictions may point to the need for improved kinetic rate modeling. In cases where UHC predictions might decrease with increased oxidation rates for UHC s (and depart, in some cases, from a good match with experiments), it may be necessary to more carefully consider the effects of UHC sourced from the fuel injector nozzle regions, especially considering the low amounts seen in the experiments % EGR and Full-Load Case Emissions Correlations The simultaneous presence of CO, hydrogen, OH, and/or hydrocarbon species in computational cells (FV) or computational particles (PDF) is examined next. The goal in performing this analysis is to see what differences there are between the FV and the PDF models, which model seems to be more physical, and what steps may be taken to improve the modeling capabilities. For example, if hydrocarbon species exist concurrently with CO or soot, the presence of the emissions species may be attributed to the hydrocarbon presence dominating the competition for H atoms. If H atoms are non-existent, there is a fundamental hole in the reaction pathway. If OH is not present, there is again a hole in the reaction pathway. If OH and UHC are present with CO or soot, the UHC may be the dominating reaction rate. If H atoms and/or OH atoms exist but the emissions species is still there, it may be that earlier this situation was not the case, delaying the consumption of CO or soot until the pressure and temperature decreased to the extent that the reaction rates also decreased, leading to engine-out emissions predictions that are high relative to experiment. These combinations of reactant mixtures are dependent on turbulence/chemistry interactions that will affect the distribution of species and enthalpy. In the finite-volume case, this distribution is a delta function for each cell, 134

149 while for the particle model it is a delta function for each particle, with particles per cell representing a distribution within that cell. Both the 65% EGR and the full-load cases showed that throughout most of the modeled engine cycle, the presence of CO in a finite-volume cell or a PDF particle coincided with the presence of UHC. This undoubtedly hinders the oxidation of CO, blocking any significant reduction in that emissions species as can be seen from Figures 5.24, 5.25, 5.27, and To create these figures, each cell or particle is checked for the existence of CO. If CO exists, the cell or particle is then checked for a corresponding species such as OH. The reverse is then done for the corresponding species, providing information on the co-existence of species and the extent to which this applies globally. Currently, any amount is registered though a threshold minimum value may be useful. These x-y plots, combined with Figures 5.22 and 5.23, indicate that while the colocation of CO and OH is common, there are some regions where one or the other species is in very low supply. There also appears to be an issue of methane oxidation, since methane becomes the dominant hydrocarbon species as the cycle progresses (Figures 5.26 and 5.29). Methane is not an easy species to oxidize in most environments, especially in a less robust operating condition such as the 65% EGR case with cooler overall and boundary temperatures. Inadequacy in the chemical mechanism may be the cause for the high computed levels of methane. State-of-the-art methane mechanisms such as GRI- Mech 2.11 [171] have as many as 279 reactions for C 1 hydrocarbon oxidation, while the mechanism used here has 165 reactions for C 1 through C 7 hydrocarbon oxidation, a much larger range of reactions to model (210 reactions in the mechanism are used for very detailed NO x modeling) with different values for the rate coefficients of reactions that match those from GRI-Mech Methane is also a major inhibitor to CO oxidation, as noted in Table 2 of Westbrook and Dryer [63]. It has more than an order-of-magnitude greater reaction rate than CO at 1000 K, with a temperature 135

150 Mass (kg) CO-OH OH-CO Total CO mass Total OH mass Crankangle Degrees [0 = TDC] (a) FV 65% EGR Mass (kg) CO-OH OH-CO Total CO mass Total OH mass Crankangle Degrees [0 = TDC] (b) PDF 65% EGR Figure 5.24: CO and OH total mass as a function of crankangle degrees for the 65% FV (a) and PDF (b) cases. The CO-OH line represents CO in cells that also have OH. OH-CO represents OH in cells that also have CO. 136

151 Mass (kg) CO-HC HC-CO Total CO mass Total UHC mass Crankangle Degrees [0 = TDC] (a) FV 65% EGR Mass (kg) CO-HC HC-CO Total CO mass Total UHC mass Crankangle Degrees [0 = TDC] (b) PDF 65% EGR Figure 5.25: CO and UHC total mass as a function of crankangle degrees for the 65% FV (a) and PDF (b) case. The CO-HC line represents CO in cells that also have UHC. HC-CO line represents UHC in cells that also have CO. 137

152 Mass (kg) Total UHC mass Total CH4 mass Crankangle Degrees [0 = TDC] (a) FV 65% EGR Mass (kg) Total UHC mass Total CH4 mass Crankangle Degrees [0 = TDC] (b) PDF 65% EGR Figure 5.26: Unburned hydrocarbon and methane total mass as a function of crankangle degrees for the 65% FV (a) and PDF (b) case. 138

153 Mass (kg) CO-OH OH-CO Total CO Mass Total OH Mass Crankangle Degrees [0 = TDC] (a) FV full-load Mass (kg) CO-OH OH-CO Total CO Mass Total OH Mass Crankangle Degrees [0 = TDC] (b) PDF full-load Figure 5.27: CO and OH total mass as a function of crankangle degrees for the fullload FV (a) and PDF (b) case. The CO-OH line represents CO in cells that also have OH. OH-CO represents OH in cells that also have CO. 139

154 Mass (kg) CO-HC HC-CO Total CO Mass Total HC Mass Crankangle Degrees [0 = TDC] (a) FV full-load Mass (kg) CO-HC HC-CO Total CO Mass Total HC Mass Crankangle Degrees [0 = TDC] (b) PDF full-load Figure 5.28: CO and UHC total mass as a function of crankangle degrees for the full-load FV (a) and PDF (b) case. The CO-HC line represents CO in cells that also have UHC. HC-CO line represents UHC in cells that also have CO. 140

155 Mass (kg) Total HC Mass Total CH4 Mass Crankangle Degrees [0 = TDC] (a) FV full-load Mass (kg) Total HC Mass Total CH4 Mass Crankangle Degrees [0 = TDC] (b) PDF full-load Figure 5.29: Hydrocarbon and methane total mass as a function of crankangle degrees for the full-load FV (a) and PDF (b) case. 141

156 Table 5.7: Rates of reactions between OH radicals and selected other species in cm 3 - mol-sec-kcal units, taken from [63]. Note that these rates are different than the rates in the mechanism used for this work (see Section A.2). Reaction Rate Expression Rate at 1000K CO + OH CO 2 + H T 1.3 exp(+765/rt ) CH 4 + OH CH 3 + H 2 O T 3.08 exp( 2000/RT ) exponent of 3.08 compared to 1.3 for the CO and OH combination (Table 5.7). A review of more recent literature (e.g., Turns 2000 [64] and Law 2006 [56]) has not found significant updates to the mechanisms for methane or CO oxidation, though there has been some work to update rate coefficients [60]. Appendix A.2 shows that the chemical mechanism used here employs somewhat different rate coefficients, a result of mechanism reduction. This may be a deficiency that would need to be addressed. The over-prediction of CO emissions may lie primarily with the rate of hydrocarbon consumption, which is essential to the core of the fuel-specific n-heptane kinetic mechanism used here. UHC modeling must more carefully take into account wall effects from wall wetting, resolution of all crevice volumes including those in the head and around the valves, and injector geometry and design effects that may contribute to unburned hydrocarbon emissions, but hydrocarbon sources that do not significantly affect CO oxidation. It may be that if the core region of the cylinder oxidized hydrocarbons sufficiently fast in the cases modeled here, then CO could be oxidized more completely. Until hydrocarbons are used up, the chain branching reactions necessary for CO oxidation cannot take place. 142

157 1 0.1 g/kg fuel Exp PM FV Soot PDF Soot Full Load 40% EGR 65% EGR Figure 5.30: Comparison of soot at 90 atdc for FV and PDF models versus the engine-out measurements from the experiment. It should be noted that the experimental measurements, Exp PM, are smoke measurements and are measurements of particulate matter and not soot, which are a fraction of that measurement. 143

158 5.4.3 Soot Emissions PDF-based soot emissions predictions (Table 5.8 and Figure 5.30) are reasonably close to experiment for the three modeled cases: the 65% and 40% EGR cases and the full-load case. The furthest departures from the experiment come from the FV model in the 40% and 65% EGR cases. There the predictions are off by several orders of magnitude and are always low compared to experiment. The PDF predictions are, at worst, off by an order of magnitude. The low soot predictions from the FV case are perhaps to be expected, given the robustness of its predicted combustion for all cases. Lower CO, higher heat-release rates, and higher average pressure curves would seem to indicate that the fuel has burned more completely. Furthermore, because of the inaccurate physics of infinite mixing in each finite-volume cell, what may be true physical regions of low mixedness will not be captured. The PDF model tends to over-predict soot, although it under-predicts slightly in the 65% EGR case. The over-prediction is by a factor of two for the full-load case, and by one order of magnitude for the 40% EGR case. These results, however, are still relatively close compared to those from the FV model. Furthermore, it is possible that the over-predictions are a direct result of the inaccurate predictions of trace species such as CO and OH: CO is a major contributor to heat release, and OH is a major actor in soot oxidation kinetics. It is probably reasonable to expect soot predictions to decrease once the CO numbers improve. It should also be noted that the experimental soot values are actually smoke measurements, which are more representative of particulate matter, of which a fraction is the soot emission. No data was available for the soot fraction. This discrepancy will have some effect on the comparisons, but the overall trend is not expected to change. Given that this is the first application of the method-of-moments soot model to real engines using a PDF method, the level of agreement between model and 144

159 Table 5.8: NO x and soot emissions results for full-load, 40% EGR, and 65% EGR conditions. Computed emissions are global in-cylinder emissions index values at 90 atdc. Experimental values for soot are smoke measurements and represent particulate matter, of which a fraction is soot. No data was available for the soot fraction. Case Model NO x Soot NO: [g/kg fuel] [g/kg fuel] NO2 Full load FV PDF Exp N/A 40% EGR FV PDF Exp N/A 65% EGR FV PDF Exp N/A measurements is quite encouraging especially since no tuning has been performed NO x Emissions NO x computations were performed for only three cases (Table 5.8 and Figure 5.31) because of the additional computational cost of the comprehensive NO x formation mechanisms that were used. The comprehensiveness of the NO x formation pathways included in the kinetic mechanism gives confidence that all important pathways are available. It should be noted that in the experiment, NO concentration was measured and converted to a mass-based value using the molecular weight of NO 2, since most NO will oxidize to NO 2 in air. The computed results have been adjusted accordingly. While both models consistently under-predict NO x compared to experiment, the values for full-load and 40% EGR are within 50% of experiment. The 65% EGR case shows a difference of an order of magnitude. Except for the 40% EGR case, FV and PDF results are close: there the FV prediction is somewhat closer to the experimental measurement. It may be that as a result of the discrepancies in ignition timing, peak 145

160 10 g/kg fuel Exp NOx FV NOx PDF NOx 0.01 Full Load 40% EGR 65% EGR Figure 5.31: Comparison of NO x at 90 atdc for FV and PDF models versus the engine-out measurements from the experiment. 146