EFFECTS OF TURBULENCE-CHEMISTRY INTERACTIONS IN DIRECT-INJECTION COMPRESSION-IGNITION ENGINES

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering EFFECTS OF TURBULENCE-CHEMISTRY INTERACTIONS IN DIRECT-INJECTION COMPRESSION-IGNITION ENGINES A Dissertation in Mechanical and Nuclear Engineering by Hedan Zhang c 2012 Hedan Zhang Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2012

2 The thesis of Hedan Zhang was reviewed and approved* by the following: Daniel C. Haworth Professor of Mechanical Engineering Dissertation Adviser, Chair of Committee, Graduate Program Chair Stephen R. Turns Professor of Mechanical Engineering James G. Brasseur Professor of Mechanical Engineering, Bioengineering, and Mathematics André L. Boehman Professor of Fuel Science and Mechanical Engineering Karen A. Thole Professor of Mechanical Engineering Head of the Department of Mechanical and Nuclear Engineering *Signatures are on file in the Graduate School.

3 Abstract Advanced combustion strategies are emphasized in modern compression-ignition engine systems, aiming at improving diesel engine efficiency and reducing pollutant emissions, especially soot and NOx, together with strategies to accommodate unconventional fuels. Recent studies have shown the importance of turbulence and turbulence-chemistry interactions on emissions from laboratory flames and compression-ignition engines. Constant-volume, high-pressure spray combustion is an important intermediate step for model validation and scientific understanding of combustion in direct-injection compressionignition engines. The Engine Combustion Network (ECN) provides a series of welldocumented experimental data for spray combustion under typical diesel-engine conditions, and this serves as a good resource for simulation and validation purposes. Here simulations for the ECN constant-volume, n-heptane spray configuration have been performed using OpenFOAM, an object-oriented C++ based code. The effects of exhaust-gas recirculation (EGR), ambient temperature and density on combustion were investigated computationally. The simulations demonstrate that the CFD model is capable of predicting sprays, mixing, ignition and combustion, quantitatively, for engine-relevant conditions reasonably well. The numerical results show that the ignition delay and lift-off lengths are strongly influenced by EGR, ambient gas temperature and ambient gas density, in agreement with measurements. Results from a model using a transported probability density function (PDF) method that explicitly accounts for turbulence-chemistry interactions have been compared to those from a model that simplistically accounts for turbulence-chemistry interactions, including mixture fraction profiles, ignition delays, lift-off lengths and flame structures under various ambient conditions. Significant differences between these two models have been observed, which iii

4 shows the importance of turbulence-chemistry interactions. The turbulent flame structure predicted by the PDF method is more realistic than that obtained from a simplistic model to account for turbulence-chemistry interactions. The choice of chemical mechanism also plays a strong role. Next, the high-fidelity CFD-based models have been used to simulate fuel effects and complex interactions between turbulence and gas-phase chemistry on emissions for biodiesel combustion and hydrogen-assisted diesel combustion in common-rail diesel engines. The sensitivity of predicted NOx emissions to variations in the physical properties of the fuel (density and viscosity) has been explored to determine the origins of the so-called biodiesel- NOx effect: the increase in NOx emissions that has been observed when petroleum-based diesel fuel is replaced with biodiesel fuel. Interactions between turbulence and gas-phase chemistry have been found to be important in the fuel density effect on NOx emissions. CFD also has been used to explore the changes in NOx emissions with hydrogen substitution that have been observed experimentally in hydrogen-enriched diesel combustion over a range of operating conditions. In spite of the significant simplifications and approximations, the model is able to reproduce the experimentally observed trends for some operating conditions. A model using a transported PDF method that explicitly accounts for turbulencechemistry interactions does somewhat better than a model using well-stirred reactor model which ignores turbulence-chemistry interactions, in low-speed conventional diesel combustion cases. The CFD results are consistent with the hypothesis that in-cylinder HO 2 levels increase with increasing H 2, which enhances the conversion of NO to NO 2. In close collaboration with engine experiments, this research shows that fuel physical properties and complex interactions between turbulence and chemistry have important effects on emissions. It has provided new physical insight into in-cylinder processes, which in turn allows better understanding for advanced engine development. iv

5 Contents List of Figures List of Tables List of Acronyms viii xv xvi 1 Introduction Background and Motivation Alternative Fuels for IC Engines in Transportation Turbulence-Chemistry Interactions in Chemically Reacting Flows Hypothese, Objectives and Approaches Organization of Thesis Turbulent Combustion in Direct-Injection Compression-Ignition Engines The Diesel Combustion Process Advanced Diesel Combustion Fuels Constant-Volume Turbulent Spray Combustion Mathematical Formulation, Physical Models, and Numerical Methods Gas-Phase Mean Equations Reynolds-Averaged Equations Turbulence Models Turbulence Wall Function v

6 3.2 Transported Composition PDF method Transported Composition PDF Equation Particle Equations Physical Models for the PDF Method Gas-Phase Chemistry Numerical Method Finite-Volume Codes Consistent Hybrid Lagrangian Particle/Finite Volume PDF Method Parallelization and In Situ Adaptive Tabulation Fuel Injector and Spray Models The Liquid Phase Physical Models Coupling of Spray Model with PDF Method Analysis of Spray and Spray Combustion in a Constant-Volume Chamber Engine Combustion Network (ECN) N-Heptane Cases Nonreacting N-Heptane Sprays Model vs Experiment Comparisons for the Baseline Model Parametric Studies Discussion Reacting n-heptane Sprays: Autoignition and Combustion With versus Without In Situ Adaptive Tabulation Model vs Experiment Comparisons Summary and Conclusions Analysis of Biodiesel and Hydrogen Effects on NOx Emissions in Direct- Injection Compression-Ignition Engines The Biodiesel NOx Effect in Common-Rail Diesel Engines Hydrogen-Assisted Diesel Combustion Computational Configuration and Model Setup vi

7 5.2.2 Computed vs Measured NOx without Hydrogen Enrichment Well-mixed Model with Hydrogen Enrichment PDF Model with Hydrogen Enrichment Discussion Summary Conclusions Summary Proposed Future Work Configurations Physical Modeling Numerical Algorithms Bibliography 112 Appendix A. Chemical Mechanisms 133 A.1 N-heptane 5-Species Mechanism A.2 N-heptane 29-Species Mechanism A.3 N-heptane 40-Species Mechanism A.4 N-heptane 71-Species Mechanism vii

8 List of Figures 1.1 Transportation Petroleum Use by Mode and the U.S. Production of Petroleum, An overview of internal combustion engine technologies, Average emission impacts of biodiesel for heavy-duty highway engines Summary of the quasi-steady diesel burning processes An example of a NOx-soot trade-off curve Φ-T regions with the highest NO and OH concentrations coincide LTC, PCCI and HCCI concepts on a Φ-T map Relative amounts of various chemical classes in diesel fuel Constant-volume chamber in the experiment Measured mean soot volume fraction contours Computational axisymmetric mesh for a constant-volume combustion chamber Computed (using a simplistic turbulence-chemistry interactions model) and measured penetration lengths versus time for a non-reacting n-heptane spray. (a) Liquid penetration length. (b) Vapor penetration length Computed and measured profiles of mean mixture fraction for a non-reacting n-heptane spray at 0.49 ms after the start of injection and an axial location of 17 mm Computed and measured profiles of mean mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and axial locations of 20 mm and 40 mm viii

9 4.5 Computed (with versus without PDF method) and measured mean profiles of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 20 mm Computed (with versus without PDF method) and measured mean profiles of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 40 mm Computed (with PDF method) and measured profiles of mixture fraction variance for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 20 mm Computed (with versus without PDF method and with variations in the PDF mixing model) and measured mean profiles of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 20 mm Computed (with versus without PDF method and with variations in the PDF mixing model) and measured mean profiles of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 40 mm Computed (with versus without PDF method and with variations in the PDF mixing model) and measured profiles of mixture fraction variance for a nonreacting n-heptane spray at 6 ms after the start of injection and an axial location of 20 mm Computed liquid and vapor penetration lengths with variations in turbulence model for a non-reacting n-heptane spray Computed liquid and vapor penetration lengths with variations in breakup model for a non-reacting n-heptane spray Computed liquid and vapor penetration lengths with variations in atomization model for a non-reacting n-heptane spray Computed liquid and vapor penetration lengths with variations in dispersion model for a non-reacting n-heptane spray ix

10 4.15 Computed liquid and vapor penetration lengths with variations in collision model for a non-reacting n-heptane spray Computed liquid and vapor penetration lengths with variations in spray model coefficient B 1 for a non-reacting n-heptane spray Computed liquid and vapor penetration lengths with variations in turbulence model coefficient C ϵ1 for a non-reacting n-heptane spray Computed liquid and vapor penetration with variations in the injector model for a non-reacting n-heptane spray Computational 3D quarter mesh for a constant-volume combustion chamber Computed liquid and vapor penetration lengths with variations in computational mesh for a non-reacting n-heptane spray Computed liquid and vapor penetration lengths with variations in computational time step for a non-reacting n-heptane spray Computed liquid and vapor penetration lengths with variations in the initial ϵ for a non-reacting n-heptane spray Computed liquid and vapor penetration lengths with variations in the criteria used to define liquid and vapor penetration lengths for a non-reacting n- heptane spray. (a) Liquid penetration definitions. (b) Vapor penetration definitions D computed mean temperature contours for a reacting n-heptane spray at baseline conditions of ambient temperature (1000 K), ambient density (14.8 kg/m 3 ) and O 2 level (21%), with versus without ISAT, for the 29-species mechanism D computed mean temperature contours for a reacting n-heptane spray at less robust combustion conditions of ambient temperature (1000 K), ambient density (14.8 kg/m 3 ) and O 2 level (8%), with versus without ISAT, for the 29-species mechanism x

11 4.26 2D computed temperature contours for a reacting n-heptane spray at conditions of ambient temperature (800 K), ambient density (14.8 kg/m 3 ) and O 2 level (21%), with versus without ISAT, for the 40-species mechanism Computed (with and without PDF) and measured ignition delay versus O 2 percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 14.8 kg/m Computed (with and without PDF) and measured lift-off length versus O 2 percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 14.8 kg/m Computed (with and without PDF) and measured ignition delay versus ambient temperature for a reacting n-heptane spray with 21% O 2 level and ambient density 14.8 kg/m Computed (with and without PDF) and measured lift-off length versus ambient temperature for a reacting n-heptane spray with 21% O 2 level and ambient density 14.8 kg/m Computed (with and without PDF) and measured ignition delay versus O 2 percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 30 kg/m Computed (with and without PDF) and measured lift-off length versus O 2 percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 30 kg/m Computed (without PDF) mean temperature distributions for a reacting n- heptane spray with ambient temperature 1000 K and ambient density 30 kg/m 3 at five different ambient oxygen concentrations at 6 ms Computed (with PDF) mean temperature distributions for a reacting n- heptane spray with ambient temperature 1000 K and ambient density 30 kg/m 3 at five different ambient oxygen concentrations at 6 ms xi

12 4.35 Computed (without PDF) mean temperature distributions for a reacting n- heptane spray with 21% O 2 level and ambient density 14.8 kg/m 3 at different ambient temperatures at 6 ms Computed (with PDF) mean temperature distributions for a reacting n- heptane spray with 21% O 2 level and ambient density 14.8 kg/m 3 at different ambient temperatures at 6 ms Computed (without PDF) mean temperature distributions for a reacting n- heptane spray with ambient temperature 1000 K and ambient density 30 kg/m 3 at 6 ms Computed (with PDF) mean temperature distributions for a reacting n- heptane spray with ambient temperature 1000 K and ambient density 30 kg/m 3 at 6 ms Scatter plots of temperature versus equivalence ratio for a reacting n-heptane spray at baseline conditions of ambient temperature 1000 K, ambient density 14.8 kg/m 3 and 21% O 2 level through the ignition period Scatter plots of temperature versus equivalence ratio for a reacting n-heptane spray at baseline conditions of ambient temperature 1000 K, ambient density 14.8 kg/m 3 and 21% O 2 level at quasi-steady state Constant-volume combustion bomb mesh Computed pressure versus time with variations in fuel density and viscosity. The reference case (ref) corresponds to conventional diesel fuel, den corresponds to a fuel mass density 1.16 times that of conventional diesel fuel, and vis corresponds to a fuel dynamic viscosity 1.90 times that of conventional diesel fuel, with all other fuel properties held fixed. Cases labeled fv correspond to calculations without the PDF method (ignoring the influence of turbulent fluctuations in composition and temperatures) xii

13 5.3 Computed NO mass versus time with variations in fuel density and viscosity. The reference case (ref) corresponds to conventional diesel fuel, den corresponds to a fuel mass density 1.16 times that of conventional diesel fuel, and vis corresponds to a fuel dynamic viscosity 1.90 times that of conventional diesel fuel, with all other fuel properties held fixed. Cases labeled fv correspond to calculations without the PDF method (ignoring the influence of turbulent fluctuations in composition and temperatures) Computed NO 2 mass versus time with variations in fuel density and viscosity. The reference case (ref) corresponds to conventional diesel fuel, den corresponds to a fuel mass density 1.16 times that of conventional diesel fuel, and vis corresponds to a fuel dynamic viscosity 1.90 times that of conventional diesel fuel, with all other fuel properties held fixed. Cases labeled fv correspond to calculations without the PDF method (ignoring the influence of turbulent fluctuations in composition and temperatures) Outer surface of the computational mesh, and computed contours of fuel vapor mass fraction at one instant Computed and measured pressure traces versus time for six combustion modes Computed and measured NO for 0% H 2 for six modes Computed and measured NO 2 for 0% H 2 for six modes Computed and measured NOx for 0% H 2 for six modes Computed (well-mixed model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for CD/1800 rpm/25% max load (Mode 1) Computed (well-mixed model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for CD/1800 rpm/75% max load (Mode 2) Computed (well-mixed model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for CD/3600 rpm/25% max load (Mode 3) Computed (well-mixed model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for CD/3600 rpm/75% max load (Mode 4) xiii

14 5.14 Computed (well-mixed model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for LTC/1800 rpm/25% max load (Mode 5) Computed (well-mixed model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for HECC/1800 rpm/25% max load (Mode 6) Computed (PDF model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for CD/1800 rpm/25% max load (Mode 1) Computed (PDF model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for CD/1800 rpm/75% max load (Mode 2) Computed (PDF model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for CD/3600 rpm/25% max load (Mode 3) Computed (PDF model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for CD/3600 rpm/75% max load (Mode 4) Computed (PDF model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for LTC/1800 rpm/25% max load (Mode 5) Computed (PDF model) and measured % changes (wrt/0% H 2 ) in NO and NO 2 w/h 2 addition for HECC/1800 rpm/25% max load (Mode 6) Computed (well-mixed model) maximum, minimum, and volume-averaged in-cylinder temperature versus crankangle for Mode 1 (CD/1800 rpm/25% max load) with 0% and 15% H 2 substitution Computed (well-mixed model) mass fraction of in-cylinder mixture having a temperature greater than 1700 K for Mode 1 (CD/1800 rpm/25% max load) with 0% and 15% H 2 substitution Computed (well-mixed model) global in-cylinder HO 2 level versus crankangle for Mode 1 (CD/1800 rpm/25% max load) with 0%, 7.5% and 15% H 2 substitution xiv

15 List of Tables 2.1 Advanced modes of combustion in compression-ignition engines Earlier modeling work for the ECN n-heptane spray cases Turbulence models and coefficients Standard k ϵ turbulence model and wall function constants Spray models and coefficients Baseline n-heptane nonreacting spray case conditions Variations in ambient conditions for n-heptane reacting cases Physical and numerical models for baseline n-heptane nonreacting spray Computational wall time comparison with versus without ISAT for a baseline n-heptane case with the PDF method Comparison of computed ignition delays using different chemical mechanism Global parameters for six combustion modes with 0% H Global engine geometric parameters xv

16 List of Abbreviations AN L Cambridge CF D CM T DDM ECN EGR EM ST ERC U W HCCI HECC IC IEM ISAT KH RT LES LISA LLN L LT C P asr P CCI Argonne National Laboratory Cambridge University Computational fluid dynamics CMT-Motores Térmicos (Valencia) Discrete droplet method Engine combustion network Exhaust-gas recirculation Euclidean minimum spanning tree ERC-University of Wisconsin Homogeneous-charge compression-ignition High efficiency clean combustion Internal combustion Interaction by exchange with the mean In situ adaptive tabulation Kelvin-Helmholtz/Rayleigh-Taylor Large-eddy simulation Linearized instability sheet atomization Lawrence Livermore National Laboratory Low temperature combustion Partially stirred reactor Premixed-charge compression-ignition xvi

17 P enn.state P DF P ISO P OLIM I ppm P urdue RAN S RCCI rms RN G SIDI SIM P LE T AB T N F UNSW U RAN S Pennsylvania State University Probability Density Function Pressure implicit with splitting of operators Politecnico di Milano parts per million Purdue University Raynolds-averaged Navier-Stokes Reactivity controlled compression ignition Root-mean square Renormalized Group Spark-ignition direct-injection Semi-implicit method for pressure-linked equations Taylor analogy breakup Turbulent Nonpremixed Flames University of New South Wales Unsteady Reynolds-averaged Navier-Stokes xvii

18 Chapter 1 Introduction Piston engines have been widely used in transportation applications for decades, and continue to dominate in the transportation market. Complex interactions between turbulence and combustion present challenges to understanding and controlling the turbulent combustion process in piston engines. The application of detailed, high-end CFD-based turbulent combustion models is crucial for the development of next-generation clean and efficient combustion systems in engines. 1.1 Background and Motivation In 2010, the transportation sector used 27.4 quadrillion Btu of energy, accounting for 28% of total U.S. energy consumption [1]. Ninety-four percent of the energy consumed in this sector is from petroleum with small amounts of renewable fuels (4%) and natural gas (3%). Of the total petroleum consumption, 44% is gasoline, 14% is diesel, and 8% is aviation fuel. Conventional fuels for transportation are produced by refining petroleum-based sweet crude oil. However, petroleum consumption in the transportation sector surpassed U.S. petroleum production for the first time in 1989, and by the year 2035, transportation petroleum consumption is expected to grow to almost 17 million barrels per day, creating a gap of almost 7 million barrels per day if using only conventional sources of petroleum fuel, as shown in Fig The vast majority of motor vehicles in transportation rely on four-stroke internal 1

19 2 Figure 1.1: Transportation Petroleum Use by Mode and the U.S. Production of Petroleum, [2, 3]. Note: The U.S. production has two lines after The solid line is conventional sources of petroleum, including crude oil, natural gas plant liquids, and refinery gains. The dashed line adds in other non-petroleum sources, including ethanol, biomass, liquids from coal, other blending components, other hydrocarbons, and ethers. The sharp increase in values between 2009 and 2010 is caused by the data change from historical to projected values. The sharp increase in the value for heavy trucks between 2006 and 2007 is the result of a methodology change in the Federal Highway Administration data. combustion engines. These engines usually contain a reciprocating piston within a cylinder, two or more valves (intake and exhaust), and a spark plug in the case of a spark-ignition (SI) engine, which is typically fueled by gasoline or natural gas. Compression ignition engines do not have a spark plug and rely on autoignition of the fuel instead, typically diesel oil. The majority of the U.S. light-duty vehicle fleet is powered by SI gasoline engines. Substantial progress in gasoline engine efficiency in recent years has been the result of advances in engine technologies, including direct in-cylinder fuel injection, flexible valve systems, improved combustion-chamber design, and reduced mechanical friction. While all gasoline engines sold in the U.S. currently operate with stoichiometric combustion, other areas in the world are seeing the introduction of lean-burn gasoline engines [4]. Advances in leangasoline emission controls are critical for meeting emerging U.S. regulations, and ultimately it is expected that this technology will be introduced in the U.S. market [4]. Diesel engines are also well-suited for light-duty vehicle applications, with their considerably higher fuel

20 3 economy than comparable SI engines. However, light-duty diesel vehicles have limited market penetration in the U.S., accounting for only 1.7 percent of all U.S. sales of new light-duty vehicles in 2007 [4]; the majority of those are light trucks. Reducing the cost of emissions compliance continues to be addressed. The heavy-duty diesel is the primary engine for commercial vehicles because of its high efficiency and outstanding durability. More stringent federal and state standards for vehicle emissions have been proposed over the last decade. U.S. diesel engine emission standards in 2010 are 0.2 grams per horsepower-hour (g/hp-hr) for nitrogen oxides and 0.01 g/hp-hr for particulate matter [1]. The implementation of increasingly stringent heavy-duty engine emissions standards has held efficiency gains to a modest level. Current heavy-duty diesel engines have efficiencies in the range of 42-43%. Diesel comprised 73% of the class 3-8 trucks sold in 2010, down from 84% in 2006 [1]. An overview of the various development paths that internal combustion (IC) engines might take over the next 40 years is illustrated in Fig This shows the actual and proposed technologies for internal combustion engines in both light-duty and heavy-duty applications. The projections to 2020 are robust, due to the fact that eight-to-ten years are typically required for a new engine concept to fully penetrate the marketplace. The projections for are more speculative, and are based on predictions of technological maturity as well as evolution of the internal combustion engine marketplace. Compared to current engines, likely directions for next-generation clean and efficient combustion systems include higher pressures, lower temperatures, extremely lean and/or dilute mixtures, and different fuels including reactant mixtures with high levels of H 2, O 2, syngas (CO and H 2 ), and/or exhaust-gas recirculation (EGR). The combustion processes in these advanced combustion systems remain of research interest. Efforts to understand and control these processes are being aided by exploring the fundamentals of flow structure and combustion behavior through experiment and modeling ranging from homogeneous-charge compression-ignition (HCCI) to advanced direct-injection spark-ignition (SIDI) operation. These novel combustion strategies offer the potential for enabling engine systems with significantly increased fuel efficiency and dramatically reduced pollutant emissions. Fuel efficiency improvements are possible in the next 10 to 15 years [5], enabled by advanced combustion

21 4 Figure 1.2: An overview of internal combustion engine technologies, Actual and proposed technologies for internal combustion (IC) engines in both light-duty and heavy-duty applications. Information from Dennis Siebers, Sandia National Laboratories, Livermore, CA. technologies, of 50% or more for automotive engines relative to the spark-ignition engines dominating the road today in the U.S., and of 25% or more for heavy-duty truck engines relative to today s diesel truck engines Alternative Fuels for IC Engines in Transportation At the same time that efforts are underway to increase the fuel efficiency and decrease the environmental impact of engines for transportation, a new, diversified fuel source future is emerging in the marketplace. Currently light- and heavy-duty powertrains, composed of engines, fuels, and after-treatment devices, are highly optimized systems, and therefore less tolerant of variations in fuel composition. However, there is increasing pressure driven by government policy and high oil prices to accommodate a wider variety of replacement can-

22 5 didate fuels and/or fuel blends (non-petroleum-derived). These new fuels will be produced from oil sands, oil shale, and coal, as well as from variety of bio-materials. None of these future fuels are yet in wide use, but relatively small-scale efforts are underway to the extent that they can simply be combined with current fuels and used in conventional engines [5]. Bio-derived fuels are already being blended with gasoline and diesel fuel for automotive and heavy-duty ground transportation. Ethanol currently accounts for approximately 3% of the automotive fuel use in the U.S., and its usage is expected to rise significantly. Likewise, biodiesel use in the U.S., though very small, has undergone a 300-fold increase in six years. Diesel-fueled vehicles generally are more fuel-efficient than comparable gasoline-fueled vehicles. In fuel economy (miles per gallon) ratings published by the U.S. Environmental Protection Agency (EPA), diesel vehicles show a fuel economy advantage of 20 to 40 percent over gasoline vehicles, depending on the size and duty requirement of the vehicles. Penetration of even current-technology diesel engines into the light-duty truck market would reduce fuel use by 25-30% per gasoline vehicle replaced [6]. Diesel vehicles are inherently more fuel efficient in comparison with conventional gasoline vehicles for several reasons: 1. Diesel engines operate at higher compression ratios than do spark-ignited gasoline engines, creating higher in-cylinder temperatures before ignition, more complete combustion, and higher thermal efficiency. 2. The energy content of diesel fuel per gallon is 11 percent greater than the energy content of gasoline. 3. Diesel engines operate with fuel-lean equivalence ratios, while current SI engines in the U.S. require an equivalence ratio close to one. 4. In a diesel engine, the load is controlled by changing the amount of fuel that is injected. In contrast, in homogeneous stoichiometric engines, the load is controlled by throttling. Products that can be blended with diesel include: aviation fuel, bio-diesel, waste oils, used motor oil, alcohol, and alkylates [7].

23 6 The effects of fuel composition variations on autoignition, combustion and emissions can be subtle. For example, hydrogen has been used in conjunction with diesel fuel to power IC engines. This dual-fuel combustion is sometimes called diesel pilot-ignited hydrogen combustion. Diesel pilot-ignited hydrogen combustion at low quantities of hydrogen is beneficial since the diesel fuel is being replaced by hydrogen, which may stretch the supply of hydrocarbon fuels [8 15]. It has been suggested that hydrogen substitution may be a promising method to reduce undesired exhaust emissions, especially at high rates of hydrogen substitution. This will be discussed further in Chapter 5. A second example of the effects of fuel composition variations on emissions is the impact of biodiesel fuel on exhaust emissions. Biodiesel is a renewable oxygenated diesel fuel derived from vegetable oils or animal fats via transesterification. Since biodiesel can help to reduce the dependence on petroleum-based diesel fuels and can provide significant environmental benefits, it has become a promising alternative to conventional diesel fuels. Biodiesel can be used in its pure form (B100) or blended with petroleum diesel. Common blends include B2 (2% biodiesel), B5, and B20. It has been well documented that biodiesel can provide substantial reductions in unburned hydrocarbons, carbon monoxide, and particulate matter emissions. Biodiesel also has excellent lubricity and can reduce life-cycle CO 2 emissions. However, researchers have reported that there is generally an increase in NOx emissions when using biodiesel [16]. According to the comprehensive analysis of biodiesel impacts on exhaust emissions performed by the EPA, the concentration of biodiesel in conventional diesel fuel has been correlated with the changes in regulated and unregulated pollutants as shown in Fig On average, there is 2% NOx increase for soybean-based biodiesel B20 (i.e., a blend of 20 vol. % biodiesel in the baseline diesel fuel) and 10% NOx increase for neat biodiesel (B100) in heavy-duty highway diesel engines [17] Turbulence-Chemistry Interactions in Chemically Reacting Flows Turbulence-chemistry interactions and other nonlinear interactions such as turbulenceradiation interactions are known to strongly influence the local and global behavior of laboratory turbulent flames. Turbulence and combustion are intimately coupled. The effect

24 7 Figure 1.3: Average emission impacts of biodiesel for heavy-duty highway engines [17]. of turbulence on chemical reactions takes place through large-scale motions of the turbulent flow field. This enhanced transport effectively enhances the transport rates of chemical species and heat. Turbulent fluctuations in temperature and composition substantially influence the mean chemical reaction rates, which occur at molecular scales. The effect of chemical reactions on turbulence takes place through large density changes brought about by the heat release due to combustion. Turbulence-chemistry interactions and turbulence-radiation interactions that result from averaging highly nonlinear functions are briefly explained here. The principal focus of turbulent combustion modeling is the chemical source term in the mean (Reynolds averaged) species equations. The essence of the averaging problem is the strong nonlinearity of the chemical source term S = S ( ϕ ), where ϕ denotes the vector of physical quantities that is required to determine S (e.g., species mass fractions, pressure and temperature). While S = S ( ϕ ) is known (in principle) for a specified thermochemical system, the mean chemical source term S in general cannot be closed in terms of any finite number of moments of ϕ [18, 19]. The differences between S ( ϕ ) ) and S ( ϕ are manifestations of turbulence-chemistry interactions, and these differences are usually large in practical combustion systems.

25 8 A variety of modeling approaches has been used to treat closure problem of species chemical source terms. The simpler ones are based on so-called characteristic time scales [20] and require additional modeling to treat the ignition process [21, 22]. Despite strong simplifications, these models can be effectively employed to obtain engineering quantities for a broad range of engine sizes [23] given careful consideration of model constants. Recently, more advanced models have been applied to treat the turbulence-chemistry interactions and allow inclusion of complex chemistry. Flamelet models [24, 25], originally based on precalculated lookup tables, have been successfully applied to study spray diffusion flames [26] and extended to engines [27]. The representative interactive flamelet (RIF) model, which uses two-way coupling between the flow-field solver and the transient flamelet integration, has been successful for autoignition of fuel sprays in combustion chambers [28] as well as in engines [29 31]. However, using one flamelet to represent the entire domain was found to be insufficient to accurately predict the premixed stage of the combustion and, in particular, heat-release rates, which poses problems in pollutant formation computation. Newer developments based on the Eulerian particle flamelet model (EPFM) [32, 33] therefore employ multiple RIFs and additionally solve an Eulerian transport equation to obtain the probability of finding the corresponding flamelet in each cell. More complex situations such as those with pilot injection have also been treated successfully with a flamelet formulation with two mixture fractions [34]. Alternative developments employing presumed PDFs and finite-rate chemistry have been proposed in [35, 36]. Alternative modeling based on conditional moment closure has been proposed [37, 38]. Successful use of conditional moment closure (CMC) for autoignition problems in simplified flow fields with both first- [39] and second-order [40] closure of the chemical source term has been reported, and its applicability to spray autoignition with first-order CMC closure has also been shown [41, 42]. In principle, a proper accounting of turbulence-chemistry interactions throughout the autoignition phase needs to include fluctuations of the scalar dissipation rate [43, 44], as in second-order CMC [40]. In practice, however, the computationally simpler first-order closure must be explored for engine calculations before the added complexity and cost of the second-order approach are justified. Other approaches for autoignition in the presence of

26 9 turbulence include models based on transport equations for flame surface density [45 47] and transported probability density function (PDF) methods [48, 49], both of which give overall good predictions. Transported PDF methods are particularly effective at capturing turbulence-chemistry interactions. A recent review of transported PDF methods in reactive turbulent flows can be found in [50]. Systematic investigations of turbulence-chemistry interactions have been carried out targeting configurations from the International Workshop on Measurement and Computation of Turbulent Non-premixed Flames (TNFs) [51 55], for example. Further information and data for the TNF workshop flames can be found at their website [56]. In addition, the importance of interactions between turbulence and thermal radiation has long been recognized [57 61]. Turbulence-radiation interactions arise from highly nonlinear coupling between temperature and composition fluctuations in both non-reacting and reacting turbulent flows. In this respect, turbulence-radiation interactions are akin to the turbulence-chemistry interactions that have been the subject of intense research for many years [62, 63]. The state-of-the-art in physical understanding and modeling of turbulenceradiation interactions in reacting turbulent flows has been reviewed by Modest [64] and by Coelho [65]. Complex interactions among turbulence, gas-phase chemistry, soot, and radiation have been shown to be important even in atmospheric-pressure, laboratory-scale flames [66 69]. Preliminary work in simulations accounting for turbulence-chemistry interactions in spark-ignition engines has been reported in [70, 71]. Turbulence-chemistry interactions have been shown to have strong influences on emissions and, in some cases, on ignition and heat release, in compression-ignition engines [72 80]. Numerical simulations that neglect these interactions, or treat them in a simplistic fashion, can fail to capture local and global flame ignition/extinction [52], and yield inaccurate predictions of temperature (by as much as several hundred Kelvin) and pollutant emissions [73]. The degree to which turbulence-chemistry interactions influence autoignition and emissions is expected to vary with the combustion system and operating conditions. Turbulent combustion in compression-ignition engines will be discussed further in Chapter 2.

27 10 The importance of finite-rate chemistry and turbulence-chemistry interactions, and of participating-medium radiation and turbulence-radiation interactions, is expected to be greater in next-generation combustion systems compared to current lean-to-stoichiometric hydrocarbon/air combustion systems. Computational fluid dynamics (CFD) simulations that account for these complex interactions will be necessary to develop next-generation, clean, and efficient propulsion systems. A principal requirement identified in a recent DOE workshop [5] is: To develop a validated, predictive, multiscale, combustion modeling capability to optimize the design and operation of evolving fuels in advanced engines for transportation applications. To meet this requirement, CFD modeling of fuel effects and turbulence-chemistry interactions will be addressed in this research. 1.2 Hypothese, Objectives and Approaches This thesis addresses the following hypotheses: 1. An accurate description of the effects of turbulence-chemistry interactions is important in numerial predictions of ignition characteristics, combustion and emissions in environments that are representative of those in advanced compression-ignition engines. 2. By explicitly accounting for turbulence-chemistry interactions, subtle fuel composition effects on emissions can be captured in CFD-based simulation with turbulent combustion modeling. Multi-dimensional, time-dependent CFD can complement experimental engine measurements. In contrast to engine experiments, detailed spatially- and temporally-resolved information on multiple physical quantities is readily extracted from a CFD simulation. On the other hand, significant simplifications and approximations are inherent in a CFD simulation. These include (i) simplifications in the geometric configuration, (ii) physical models that must be introduced for phenomena including liquid fuel sprays, hydrodynamic turbulence, and combustion, and (iii) inaccuracies that are associated with the numerical algorithms and discretization. A judicious blend of experiment and CFD simulations can yield deeper

28 11 insight than either tool used in isolation. Moreover, CFD modeling can provide a much easier way to isolate and vary one parameter at a time, which would be difficult to realize experimentally, especially for varying physical properties. Constant-volume, high-pressure spray combustion is an important intermediate step for model validation and scientific understanding of combustion in direct-injection compressionignition engines. The operating conditions explored in the Engine Combustion Network (ECN) workshop [81] are typical of diesel combustion, spanning or exceeding those typically experienced in a modern diesel engine. Also, constant-volume spray combustion allows the effect of each variable to be assessed independently, which helps to establish scientific understanding of combustion at conditions specific to engines. The objective of this thesis is to establish to what extent turbulence-chemistry interactions will influence ignition, combustion and emissions by comparing results from a model where turbulence-chemistry interactions are considered using a transported PDF method with results from a model where turbulence-chemistry interactions are either considered using a simplistic model or ignored altogether. Results will be shown for constant-volume turbulent spray combustion chambers under diesel-engine-like conditions, and for idealized and realistic compression-ignition engines. Quantitative comparisons will be made between model results and experimental measurements, where available. 1.3 Organization of Thesis 1. Chapter 2 reviews turbulent combustion in direct-injection compression-ignition engines. Advanced combustion systems in compression-ignition engines are reviewed, followed by discussions of diesel and surrogate fuels including n-heptane, and the constant-volume turbulent spray combustion configuration from the Engine Combustion Network. 2. Chapter 3 describes the governing equations, physical models and numerical methods that will be used in the CFD simulations. The emphasis is on the transported composition PDF method.

29 12 3. Chapter 4 shows quantitative comparisons of computed results with experiment for constant-volume turbulent spray combustion under conditions that are representative of those in modern compression-ignition engines. Systematic studies are performed for non-reacting n-heptane sprays and reacting n-heptane spray flames, and unsteady Reynolds-averaged (URANS) simulation results with and without PDF method are compared with experimental measurements. 4. In Chapter 5, the application of PDF models in URANS to idealized and realistic compression-ignition engines, and the capability to capture subtle differences in NOx emissions with variations in fuel composition, are explored for two cases: the biodiesel NOx effect in common-rail diesel engines, and hydrogen-assisted diesel combustion. 5. Chapter 6 concludes the thesis by summarizing the importance of turbulencechemistry interactions in the above configurations and key issues that remain unresolved. Future work is proposed.

30 Chapter 2 Turbulent Combustion in Direct-Injection Compression-Ignition Engines Compression-ignition engines have significantly higher efficiency compared to spark-ignition engines. However, NOx and soot emissions are a concern, and that concern is increasing as emission standards are tightened. Recently more advanced combustion strategies have been emphasized in efforts to realize further gains in efficiency and reductions in emissions. A series of computational studies and experimental tests has been carried out to explore advanced combustion systems for compression-ignition engines. Turbulence-chemistry interactions have been shown to have strong influence in local and global behavior of laboratory turbulent flames, and there is some evidence that they may be important for ignition, combustion and emissions characteristics in environments representative of those in advanced compression-ignition engines. In this work, we seek to quantify the extent to which turbulence-chemistry interactions influence autoignition and emissions for conditions that are representative of those in current and proposed compression-ignition engines. 13

31 The Diesel Combustion Process Diesel engines are of interest due to their higher efficiency in comparison to spark-ignited engines. In direct-injection diesel engines, fuel is injected directly into the combustion chamber at a pressure of MPa through a multi-hole nozzle which has several orifices with a diameter of mm. The temperature and pressure at compression top dead center are normally in the range of K and 4-12 MPa, respectively [82]. The diesel combustion process can be broken up into four different phases: ignition delay period, premixed combustion phase, mixing-controlled combustion phase, and the late combustion phase [8]. The ignition delay period begins at the start of injection. During the ignition delay period, the rate of heat release drops below zero due to the fuel absorbing heat while vaporizing [83]. Next is the premixed combustion phase where a rapid rate of heat release occurs. The portion of the fuel which has mixed with air forms a combustible mixture and ignites. After all of the premixed air-fuel charge is consumed, the mixingcontrolled combustion phase begins. Here the combustion transitions from a premixed flame to a diffusion flame. The rate of combustion is controlled by the fuel vaporization and mixing, in contrast to the fast burn of the kinetics-driven premixed flame. During the mixing-controlled combustion phase, the end of injection occurs. In the late combustion phase, unburned fuel seeks oxygen as it is turbulently mixing throughout the cylinder [84]. Dec [86] and Flynn et al. [85] have compiled the results of many studies into a complete picture of the structure of the diesel spray. A review of the conceptual model introduced by Dec [86] is given below. The conceptual model describes how the spray develops and combustion begins, and also the quasi-steady portion of the combustion. As liquid fuel is injected into the cylinder, high-temperature air is entrained into the fuel forming a cone-shaped spray. This high-temperature air vaporates and mixes with the fuel. There is a maximum penetration distance for the liquid fuel after which all the fuel has vaporized, called the liquid length. This varies with fuel properties, combustion chamber conditions, and injector geometry, but is basically the result of the energy balance between the energy of the air entrained and the energy required to vaporize the fuel. Higher air density and temperature in the cylinder cause more air to be entrained and thus reduce the

32 15 Figure 2.1: Summary of the quasi-steady diesel burning processes [85]. liquid length. Beyond the liquid length, the fuel vapor and air continue to mix and penetrate into the combustion chamber. With the high temperatures in the cylinder, autoignition begins when the fuel-air ratio and the temperature in the spray reach combustible limits. Combustion of this premixed, vaporized-fuel and air mixture occurs volumetrically in a premixed reaction. At the end of the initial premixed burn, a diffusion flame forms where the equivalence ratio of the mixture is close to one, surrounding the fuel-rich products of the premixed reaction. Because the liquid length and premixed burn location remain fixed until the end of combustion while the leading edge continues to move forward and expand radially, this portion of the combustion process is termed quasi-steady. A schematic diagram of a quasisteady diesel combustion flame jet is shown in Fig. 2.1, which includes a fuel-rich premixed core surrounded by a diffusion flame between the products of fuel-rich combustion and the surrounding air. During the quasi-steady phase, the liquid length shortens a small amount due to combustion that increases the energy of the air entrained into the jet. Beyond the liquid length, the mixture of vapor-phase fuel and hot entrained air increases in temperature until reacting in the fuel-rich premixed combustion zone, where the equivalence ratio is between 2

33 16 and 4 [86] under normal diesel operation. The fuel-rich premixed burn produces intermediate temperatures ( K), leaving unoxidized products such as CO and unburned hydrocarbons (HC) due to a lack of oxygen. A diffusion flame forms an envelope around the rich premixed zone and the liquid spray, forming a lifted diffusion flame. The distance from the nozzle to the edge of the diffusion flame is called the lift-off length, which is an extremely important characteristic of the flame, as it shows how much air is entrained into the rich premixed reaction zone where soot is initially formed. The lift-off length is typically shorter than the liquid length for the operating conditions of most modern diesel engines. Longer lift-off lengths allow more air entrainment, increasing oxygen in the rich premixed reaction zone and thereby reducing soot formation. The temperature of the diffusion flame sheath is near the stoichiometric adiabatic flame temperature. At the end of injection, the spray slows and stops, allowing the flame to move closer to the nozzle, shortening the lift-off length. The diffusion flame encircles the entire jet. At this point, a significant portion of the fuel energy remains unreacted, but the conceptual model is no longer well understood. The rich products within the jet appear to be carried toward the wall following the quasi-steady phase, splitting and forming large-scale turbulent structures that entrain air and continue to burn as a diffusion flame. Although diesel engines have the advantage of high efficiency, a limiting issue is criteria pollutant emissions: especially soot and NOx. A key diesel emissions issue is the soot/nox tradeoff: in general, strategies that reduce emission levels for one of these pollutants tend to increase the other [87]. An example is shown in Fig An equivalence ratio-temperature (Φ-T ) map is commonly used to describe how different combustion concepts affect pollutant formation. The typical regions in terms of temperature and equivalence ratio for NO formation and soot or particulate matter (PM) formation/oxidation are shown in the map. In Fig. 2.3, the highest NO concentrations coincide with the region of the highest OH concentrations, illustrating the soot-no dilemma : i.e., in the region with the high NO concentrations, plentiful OH radicals are available to oxidize the soot previously formed in the locally rich regions. However, outside this high temperature region, NO will not be

34 17 formed but soot may be, and only small amounts of OH radicals are available to oxidize it later. Fortunately, the tradeoff relationship between NOx and soot is only fixed for a specific engine. The soot/nox tradeoff can be broken by strategies that include variations in fuel composition (oxygenates) and fuel-injection scheduling. Advanced diesel combustion concepts (discussed in the following subsection) can break the tradeoff by altering the mixing and ignition parts of the combustion process. The use of exhaust gas recirculation (EGR) decreases the combustion temperature, and thereby the NOx formation. Recent combustion models accommodate both premixed and non-premixed burning and formation/destruction of the key pollutants, NOx and soot. Figure 2.2: An example of a NOx-soot trade-off curve [84]. 2.2 Advanced Diesel Combustion Advanced combustion strategies are of current interest to maintain or reduce fuel consumption while significantly reducing engine-out soot and/or NOx compared to conven-

35 18 Figure 2.3: Φ-T regions with the highest NO and OH concentrations coincide [88]. tional diesel combustion. These include homogeneous-charge compression-ignition (HCCI), premixed-charge compression-ignition (PCCI), low-temperature combustion (LTC), high efficiency clean combustion (HECC) and reactivity controlled compression ignition (RCCI). Figure 2.4 [89] shows soot and NOx formation zones and some advanced combustion modes on a Φ-T map. More advanced strategies are listed in Table 2.1. Figure 2.4: LTC, PCCI and HCCI concepts on a Φ-T map [89]. In a homogeneous-charge compression-ignition (HCCI) combustion system [137], a highly lean and/or dilute fuel/air/residual mixture is compression ignited. This results

36 19 Table 2.1: Advanced modes of combustion in compression-ignition engines. Advanced combustion concept HCCI (homogeneouscharge compressionignition) SRDC (smokeless locally rich diesel combustion) LTC (low temperature combustion) PCCI (partiallypremixed charge compression ignition) PPC (partially premixed combustion) PCI (premixed compression ignition) RCCI (reactivitycontrolled compression ignition) SCCI (stratification charge compression ignition) HECC (high efficiency clean combustion Primary focus reduced soot and NOx emissions reduced soot and NOx emissions reduced soot and NOx emissions lower soot emissions reduced soot and NOx emissions lower soot and NOx emissions Work and reference Early-DI HCCI: PREDIC (premixed lean diesel combustion) by Takeda et al. and Nakagome et al. [90, 91] with subsequent studies [92 96]; UNIBUS (Uniform Balky Combustion System) by Yanagihara et al. [97] with further studies [98]; MULINBUMP (multiple stage diesel combustion) by Su et al. [99 101]; NADI (narrow angle diesel injection) [ ]. Late-DI HCCI: MK (modulated kinetics) developed by Nissan [107, 108]. Premixed/direct-injected HCCI [ ] developed by Toyota [117, 118] Natti [119], Henein et al. [120] and Choi et al. [121], Aoyagi et al. [122], Colban et al. [123]. Genzale et al. [124]. Kook et al. [125], Opat et al. [126], Kumar and Zheng [127] Neely and coworkers [89], Kanda [128] and Araki [129], Sluder and coworkers [130], Lilik [8], Kook and Bae [125] and Aronsson et al. [131] Johansson [132], Hanson et al. [133] Okude et al. [134] high efficiency developed by Splitter, Reitz and Hanson [135] fuel consumption reduction im- efficiency provements Berntsson and Denbratt [88], Arronsrisopon et al. [115] developed by ORNL: Sluder et al. [136]

37 20 in low combustion temperatures and low engine-out NOx. There are no locally fuel-rich zones, hence little soot formed. Therefore, the system has the potential for diesel-like thermal efficiency with near-zero NOx and particulate-matter emissions. Technical issues with classical HCCI include a limited load-speed range over which an engine can operate in this mode, low efficiency at light loads, difficulty in controlling combustion phasing, high levels of engine-out unburned hydrocarbons (UHC) and carbon monoxide (CO), and noise. Premixed-charge compression-ignition (PCCI) can be seen as an intermediate step between conventional diesel combustion and HCCI. The charge in PCCI is not mixed as thoroughly as in HCCI, so that there will be some hot spots. Also, since in PCCI, the fuel is injected via the diesel fuel injector, the long ignition delay may result in diesel fuel penetration to the cylinder walls, resulting in incomplete combustion. HCCI and PCCI modes induce the engine to burn the fuel in the premixed phase, resulting in a globally fuel-lean charge and lowered combustion temperature, thus resulting in engine operation away from zones of NOx and soot formation. The difference is that the air-fuel charge in HCCI is homogeneous when it enters the cylinder. In PCCI, advanced in-cylinder injection of fuel leads to an extended premixed combustion phase. Low-temperature combustion (LTC) has been heavily explored in response to increasingly strict diesel emissions regulations. LTC is a generic term that refers to engine operating conditions that are below the temperatures that are required for the formation of NOx (Φ <2.5, T >2000 K) and/or soot (Φ 2.5, 1700 K< T <2400 K) [118]. The combustion temperature can be lowered by introducing EGR or by altering the combustion process to be locally fuel lean. EGR is introduced into the cylinder by displacing the intake air. With EGR, O 2 is reduced, which successfully reduces NOx. However, soot emissions increase due to the reduction in oxygen and the resulting inhibition of soot oxidation. HCCI-like conditions can be coupled with EGR to reduce soot emissions. In that case, a well mixed air-fuel charge is locally fuel lean. A fuel-lean charge will produce less heat and have more O 2 locally available to oxidize soot or prevent formation of soot. High efficiency clean combustion (HECC), formally known as efficient-ltc, is accomplished by a combination of a single-pulse injection, EGR ( 50%), early injection timing,

38 21 and increased injection pressure. The HECC mode provides a decrease in NOx emissions and soot emissions while maintaining or even increasing fuel efficiency. However, the HECC mode results in increased HC and CO emissions, which is common with HCCI-like combustion modes [130]. Reactivity-controlled compression ignition (RCCI) is a dual-fuel engine combustion technology developed at the University of Wisconsin-Madison Engine Research Center (ERC) [135]. RCCI is a variant of HCCI that provides more control over the combustion process and has the potential to dramatically lower fuel use and emissions. RCCI uses in-cylinder fuel blending with at least two fuels of different reactivities and multiple injections to control in-cylinder fuel reactivity to optimize combustion phasing, duration and magnitude. The process involves introduction of a low-reactivity fuel into the cylinder to create a well-mixed charge of low-reactivity fuel, air and recirculated exhaust gases. The high-reactivity fuel is injected before ignition of the premixed fuel occurs using single or multiple injections directly into the combustion chamber. Examples of fuel pairings for RCCI are gasoline and diesel, ethanol and diesel, and gasoline and gasoline with small additions of a cetane-number booster. In comparison to conventional diesel combustion, RCCI combustion exhibits significantly higher peak cylinder pressures and pressure-rise rates. 2.3 Fuels Gasoline and diesel fuels are composed of hundreds-to-thousands of individual compounds. Fundamental physical and chemical data are not available for all the components of interest, and even if they were available, simulations that account for that level of detail would be beyond the capability of current computational resources. The primary chemical classes of the components in diesel fuel are n-alkanes, iso-alkanes, cycloalkanes, and aromatics as shown in Fig Although the composition of diesel fuel is highly variable, there are some trends [138]: for example, the carbon numbers of the components range from approximately C10 to C22, with an average of 14 to 15. Considerable interest has been shown in surrogate fuels. A surrogate fuel is a fuel composed of a small number of pure compounds whose behavior matches certain characteristics of a target fuel that contains many compounds.

39 22 [139] The surrogate fuel should represent both the physical and chemical characteristics of the target fuel. Key physical properties include density, volatility, viscosity, surface tension and diffusion coefficients; key chemical properties include C/H/O content, ignition behavior, adiabatic flame temperature and sooting propensity. N-heptane is a primary reference fuel Figure 2.5: Relative amounts of various chemical classes in diesel fuel [138]. for octane rating in IC engines, and is often used as a single-component surrogate for diesel fuels. It has a cetane number of approximately 56, which is close to that of typical diesel fuels. Another characteristics of n-heptane is its two-stage ignition process, which is representative of diesel-like fuels. This is related to the cool flame phenomenon and the negative-temperature-coefficient behavior that are important in HCCI and LTC. Hence, extensive research has been published on measuring ignition delays and other quantities from experiments that employed n-heptane in engines [140, 141], as well as on developing chemical mechanisms for n-heptane [ ]. Most current chemical mechanisms have been derived from either the Chalmers mechanism [153] or a detailed n-heptane mechanism from Lawrence Livermore National Laboratory (LLNL) [154]. In this thesis, n-heptane gas-phase chemical mechanisms are used for multidimensional CFD simulations. 2.4 Constant-Volume Turbulent Spray Combustion Constant-volume turbulent spray combustion is an important intermediate step between laboratory flames and practical engines. Exploration of laboratory flames such as the TNF

40 23 Workshop flames emphasizes fundamental issues of turbulence-chemistry interactions in gaseous flames to establish basic scientific understanding of turbulent combustion. The liquid-fuel spray atomization and evaporation and fuel-air mixing processes are of great importance in many industrial applications, including internal-combustion engines [155, 156]. Detailed investigations of the main physical and chemical processes governing combustion in diesel engines, such as fuel-air mixing, auto-ignition, flame development [157, 158] and in-cylinder charge motions [124], are typically performed in simplified configurations such as constant-volume vessels. A key resource is an internet library of well-documented experiments, called the Engine Combustion Network (ECN This includes data obtained in a constant-volume chamber (Fig. 2.6) at typical conditions of diesel combustion. The goal of ECN is to facilitate validation of computational models at conditions appropriate for engines. The database includes key experimental data that have been acquired at well-defined boundary conditions over the past ten years, including spray liquid and vapor penetration, liquid length, lift-off length, ignition delay, pressure-rise rate, soot volume fraction, high-speed movies of chemiluminescence, effects of fuel type, and others. Much of the data have been obtained at the same conditions, making it suitable for model validation. A data searching utility provides experimental conditions such as fuel type, ambient con- Figure 2.6: Constant-volume chamber in the experiment [81].

41 24 ditions, injection pressure, injection mass and profile, nozzle size and other relevant data. The following ambient conditions at the time of fuel injection can be controlled, allowing the effect of each variable to be assessed: Ambient gas temperatures from 450 K to 1300 K Ambient gas densities from 3 to 60 kg/m 3 Ambient gas oxygen concentrations from 0% to 21% Figure 2.7: Soot volume fraction contours [81]. Ambient conditions: T a =1000 K, ρ a =14.8 kg/m 3, 21%O 2. Injector conditions: 1500 bar above ambient, 0.1 mm nozzle, n-heptane. Fuel is injected using modern common-rail fuel injectors with the following parameter ranges: Injection pressures above ambient from 40 to 200 MPa Nozzle diameters from 0.05 to 0.5 mm No. 2 diesel, single-component reference fuels (n-heptane, n-dodecane), and oxygenated fuels N-heptane sprays under different ambient conditions are of particular interest within the context of this thesis. For n-heptane sprays, different ambient compositions ranging from 0 to 21% O 2 represent various EGR levels that are relevant in many advanced combustion modes. Ambient temperatures from 750 K to 1300 K span conventional diesel engine

42 thermodynamic conditions and advanced combustion conditions including LTC. Two different ambient density conditions are included: 14.8 and 30 kg/m 3. Available data include liquid/jet penetration lengths, mixture fraction, lift-off length, ignition delay, and soot. Figure 2.7 is an example of experimental data of soot volume fraction for n-heptane. Earlier published computational modeling work for non-reacting and/or reacting n- heptane sprays in the Sandia constant-volume chamber are summarized in Table 2.2. Some have chosen a well-mixed model, which neglects turbulence-chemistry interactions. Exceptions include a conditional moment closure (CMC) model, an unsteady flamelet progressvariable (UFPV) model, a PDF model, a partially stirred reactor (PaSR) model and a 3-Zone Extended Coherent Flame Model (ECFM3Z). The PaSR model was developed at Chalmers Gothenburg [159], accounting for the unmixedness effect on chemical reaction rates. In this model, the chemical source term is described by 25 τ chem τ mix +τ chem ω i, where ω i is the chemical reaction rate of reaction i, τ chem is the chemical time and τ mix is the mixing time. The mixing time τ mix is calculated according to, τ mix = C mix µeff ρϵ, (2.1) where C mix is a constant set to 0.03, µ eff is the effective viscosity, ρ is density and ϵ is the rate of dissipation of turbulent kinetic energy. PDF and PaSR models have been applied for constant-volume n-heptane spray flames in this work.

43 26 Table 2.2: Earlier modeling work for the ECN n-heptane spray cases. Institution and reference Argonne National Laboratory (ANL) [160, 161] Cambridge University [162] CMT-Motores Térmicos (CMT) [163] T.U. Eindhoven (Eindhoven) [164] ERC-University of Wisconsin (ERC-UW) [143, 145, 165] Pennsylvania State University (Penn. State) [166, 167] Politecnico di Milano (POLIMI) [ ] Purdue University [ ] University of New South Wales (UNSW) [178] Okayama University [179] Imperial College [180] Chalmers University of Technology [181] Turbulence-chemistry interaction Well-mixed (no model) Conditional moment closure (CMC) Partially stirred reactor (PaSR) Well-mixed (no model) N/A PaSR, PDF Well-mixed (no model) Unsteady-flamelet progress variable (UFPV) Well-mixed (no model) 3-Zones Extended Coherent Flame Model (ECFM3Z) ECFM3Z PaSR

44 Chapter 3 Mathematical Formulation, Physical Models, and Numerical Methods Current computational simulations for engines range from zero- to three-dimensional to complement experimental studies by utilizing a variety of models for sprays, turbulence, chemical kinetics and combustion. Modeling these phenomena is critical to simulate modern engines and engine-like conditions. For example, spray characterizations are sensitive to spray models and parameters, and affect in-cylinder fuel distribution in direct-injection engines. Turbulence can significantly affect the species and enthalpy distributions, and thus heat release and emissions. Two three-dimensional CFD codes have been used here: OpenFOAM [182] and AC- Flux [183]. Reynolds-averaged forms of the governing equations are solved for ensembleaveraged mean quantities, which requires modeling the effects of turbulent fluctuations about local mean values. Simple models for turbulence-chemistry interactions may be sufficient for conditions where the effects of flow dynamics and spatial inhomogeneities are relatively small. However, under conditions with strong inhomogeneity, a sophisticated model is needed to deal with the turbulence-chemistry interactions. In this work, the transported composition PDF method is used to model turbulent com- 27

45 28 bustion. PDF methods have shown promise in canonical engine configurations and idealized engine-like geometries. The strength of the model lies in its capability to treat exactly the effects of turbulent fluctuations on mean chemical source terms. In this chapter, the numerical formulations and physical models of Reynolds-averaged conservation equations with a composition PDF method will be outlined and discussed. 3.1 Gas-Phase Mean Equations Reynolds-Averaged Equations A compressible, multiphase, chemically reacting turbulent flow is considered using a Reynolds-averaged formulation. Here angled brackets (<>) denote conventionally averaged mean quantities and tildes ( ) denote density weighted or Favre-averaged mean quantities. In the IC engine community, RANS refers to unsteady RANS, also known as URANS. In the context of piston engines, a simulation through a single engine cycle represents the ensemble average. Computed dependent variables represent ensemble- (phase-) averaged values at a given piston position. Simulations through multiple engine cycles should give same result on every cycle (after reaching statistically periodic state), which makes it appropriate to compare with experiment results that are likewise phase-averaged over many cycles. All fluctuations about the ensemble average are represented by the turbulence model. The principal mean partial differential equations for the gas phase (a multicomponent ideal-gas mixture) can be written using Cartesian tensor notation as follows. Here the liquid-phase source terms have been omitted for clarity. The detailed derivation for these

46 29 equations can be found in previous reviews of turbulent combustion modeling [18, 87]. ρ h t 2 p = 2 ρ x i x i t 2 2 ρ ũ i ũ j + 2 ( τ ij + τ T,ij ) ρ + g i (3.1) x i x j x i x j x j ρ ũ j + p ũ jũ i = ( τ ij + τ T,ij ) p + ρ g j (3.2) t x i x i x j ) ] h + p p + ũ i + Φ + Q rad (3.3) x i t x i [ ( + ρ Ỹαũ i = µ + µ ) ] T Ỹ α + ρ x i x i Sc α x S α (3.4) i + ρ hũ [ ( i = λ + µ T x i x i C p P r T ρ Ỹα t Sc T,α Here ũ i is a velocity component, p is pressure, ρ is density, g is a constant body force per unit mass, h is enthalpy, Y is mass fraction, subscript α denotes a chemical species, and µ and µ T are molecular viscosity and apparent turbulent viscosity, respectively. The viscous dissipation rate of kinetic energy to heat Φ is given by Φ = τ ij ũ i x j + ρ ϵ. S is a mass-based chemical source term, and C p is the constant-pressure specific-heat capacity. The viscous shear stress is τ ij ; τ T,ij is an apparent turbulent stress. Sc α is the molecular Schmidt number of species α, and P r T and Sc T,α are apparent turbulent Prandtl and Schmidt numbers, respectively. The mean density ρ is obtained using an ideal-gas equation of state. Note that the latter two equations (Eqs. 3.3 and 3.4) will be superseded by the transported PDF equations, for cases where the transported PDF method is used. The thermal equation of state and the caloric equation of state provide the density and temperature, respectively [87, 184]. The unaveraged forms of the equations of state are: ρ = ρ(p, h, Y ), (3.5) T = T (p, h, Y ). (3.6) Ideal-gas mixture properties are typically assumed. The state equations then are given by p = ρrt (R = R U ), (3.7) W

47 30 and N S h = α=1 Y α ( h 0 f,α + T ) C p,α (T )dt T 0, (3.8) 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. The averaged forms of the equations of state are discussed below after the composition PDF is introduced. Fluid properties that are required include transport properties (fluid viscosity, species diffusivities, thermal conductivities) and specific heats (constant-pressure). These are standard equations of state [87]. Standard formulations are adopted for molecular transport terms [185]. Thermal diffusion is typically neglected. Species transport is modeled using a multicomponent form of Fick s law, and heat conduction is modeled with a multicomponent form of Fourier s law. The viscous stress τ ij is written in a form that is appropriate for a Newtonian fluid, where µ is a multicomponent mixture viscosity. τ ij = µ( u i x j + u j x i ) 2 3 µ u l u l δ ij, (3.9) Turbulence Models In AC-Flux, a standard k ϵ turbulence model with wall functions is used to model turbulent transport in the mean equations. A renormalization group (RNG) k ϵ turbulence model is used in OpenFOAM, which is similar to the standard k ϵ, but with a modified form of the ϵ equation developed by Yakhot et al. [186] which attempts to account for the different scales of motion through changes to the production term. Other turbulence models explored include the Launder-Sharma k ϵ model [187] and a realizable k ϵ model [188]. Turbulence models and coefficients used in OpenFOAM are listed in Table 3.1. The standard k ϵ

48 31 equations are, ρ ϵ t ρ k t + ρ kũ j = x j x j + ρ ϵũ j x j = x j [( µ + µ T σ ϵ [( µ + µ T ) ϵ x j σ k ) k ] + τ T,ij ũ j x j ] C ϵ2 ρ ϵ2 k + C ϵ3 ρ ũ j x j ϵ ũ i +C ϵ1 x i ρ ϵ (3.10) k τ T,ij (3.11) x j where k is the turbulence kinetic energy and ϵ is the viscous dissipation rate of turbulence kinetic energy. Here σ k and σ ϵ are the turbulent Schmidt numbers, and C ϵ1, C ϵ2 and C ϵ3 are model constants (Table 3.2). The apparent turbulent stress is given by ( ũi τ T,ij = µ T + ũ ) j 2 x j x i 3 µ ũ l T δ ji 2 x l 3 ρ kδ ji. (3.12) Here µ T is an apparent turbulence viscosity that is given by µ T = C µ ρ k 2 /ϵ Turbulence Wall Function For RANS modeling, wall functions are usually adopted to deal with near-wall turbulence and to enforce the no-slip condition for the mean velocity. Standard wall functions using a logarithmic correlation [189] are used in AC-FLux at solid wall boundaries: ( ) 1 U = u z k ln y+ + B (3.13) ϵ = u3 z κy (3.14) uv = u 2 z = Cµ 1/2 k. (3.15) Here U is the mean velocity component parallel to the wall, u z is the wall shear velocity, B is a constant given by B = lne/κ where κ and E are log-law constants (see Table 3.2), y + is the distance y from the wall over the viscous length scale, u and v are the wall-parallel and wall-normal fluctuating velocity components, respectively, and C µ is a model constant. The values for the standard k ϵ turbulence model and wall functions constants in AC-FLux are summarized in Table 3.2.

49 32 Table 3.1: Turbulence models and coefficients. Standard k ϵ model C µ C ϵ1 C ϵ2 C ϵ3 σ k σ ϵ RNG k ϵ model C µ C ϵ1 C ϵ2 C ϵ3 σ k σ ϵ η β Launder-Sharma k ϵ C µ C ϵ1 C ϵ2 C ϵ3 σ k σ ϵ Realizable k ϵ C µ C 2 A 0 σ k σ ϵ Table 3.2: Standard k ϵ turbulence model and wall function constants. C ϵ C ϵ C ϵ C µ 0.09 σ k 0.7 σ ϵ 0.7 κ E RANS wall functions have been used here to determine the turbulent scales for the nearwall PDF particles as in Kung s work [73]. Dreeben and Pope applied a more sophisticated wall modeling approach for PDF particles in the velocity-frequency joint-pdf method [190]. 3.2 Transported Composition PDF method In the review by Veynante and Vervisch [18], various turbulent combustion models have been discussed. PDF methods offer the compelling advantage that the mean chemical

50 33 source term is closed in terms of the composition PDF: S α = S α (ψ) f ϕ (ψ; x, t)dψ, (3.16) where ψ is the sample-space vector corresponding to the composition variables ϕ. In a composition PDF method, an appropriate set of variables (here N S species mass fractions Y and the mixture specific enthalpy h) is treated as a vector denoted by ϕ of dimension N ϕ = N S + 1. The corresponding composition joint PDF represents the probability of ϕ taking on a particular value at spatial location x and time t, denoted by f ϕ. Thus, f ϕ (ψ; x, t)dψ = P rob{ψ ϕ < ψ + dψ}. (3.17) Mean values of any function of the composition variables, Q = Q(ϕ), can be expressed in terms of PDF: Q = Q(x, t) = Q = Q(x, t) = ρq / ρ = ρ 1 ρ(ψ)q(ψ)f ϕ dψ = Q(ψ)f ϕ dψ, (3.18) Q(ψ) f ϕ dψ, (3.19) where the Favre PDF f ϕ = ρ(ψ) f ϕ / ρ has been introduced, and the integration is over the entire composition sample space. The mean value of Q conditioned on the composition ϕ at location x and time t having the particular value ψ is denoted by Q(x, t) ϕ(x, t) = ψ = Q(x, t) ψ. For nonpremixed flames, the PDF of mixture fraction sometimes is presumed to be a beta distribution using an infinitely fast chemistry model. Other available models are the steady laminar flamelet model or conditional moment closure. The objective of transported PDF modeling is to relax as many assumptions as possible concerning the shape of the PDFs and other assumptions that are required in simpler turbulent combustion closures. The main advantage of a transported PDF method lies in the possibility of treating complex chemical sources directly. The PDF method has been derived using different sets of independent variables (e.g.,

51 34 velocity, composition and frequency) to form the probability density function. Several PDF methods with different choices of independent variables have been reviewed by Haworth [50, 191] and Kung [73], including a joint PDF of velocity, composition, and frequency, a velocitycomposition PDF and a composition PDF. A transported composition PDF method is used here to explicitly model the effects of turbulent fluctuations in species composition and enthalpy (hence temperature) relative to the local mean values. PDF methods can be implemented in both Eulerian [ ] and Lagrangian [195] contexts. A stochastic Eulerian field method and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure have been implemented in [193, 194] targeting a series of flames that exhibit different levels of local extinction. Eulerian PDF methods have not been applied to engine configurations, to date. A Lagrangian method distributes notional particles with scalar properties within the physical domain, and particles are associated with cells according to their physical positions. In this thesis, a Lagrangian framework is adopted following the implementation from Subramaniam and Haworth s work [195] Transported Composition PDF Equation The transport equation for the Favre-averaged composition PDF is: ρ f ϕ t = [ u i ψ ρ x ] f ϕ + i ψ α + ρ ũ if ϕ x i [ ρ 1 J α i x i ψ + ρ S αf ϕ ψ α ] ρ f ϕ. (3.20) Here summation is implied over indices i or α within a term, and denotes the probabilistic mean. J α is the molecular diffusive flux of composition variable ϕ α, and S α is the source term of composition variable ϕ α. ũ is the Favre-averaged mean velocity and u is the velocity fluctuation about ũ. On the left-hand side, the first term represents the temporal variation of the PDF, the second term is the advection of the PDF by mean velocity and the third term is the chemical source term. On the right-hand side are the transport term due to turbulent velocity fluctuations ( turbulent diffusion ) and the molecular transport

52 35 ( mixing ) term, which need closure models Particle Equations Here a Lagrangian particle Monte Carlo method is used to solve the modeled PDF equation [195]. In this approach, the Eulerian PDE (Eq. 3.20) can be recast in Lagrangian form. A system of notional particles is devised to represent a chemically reacting turbulent flow, whose one-point, one-time Eulerian joint PDF evolves according to the modeled PDF transport equation. The total number of notional particles is N P. The i th particle is assigned a mass m (i) with position coordinates x i (t) and N ϕ scalar variables ϕ (i) (t). Formally, a discrete mass density function F is introduced, Fϕx ( ) N P ψ, y; t m (i) δ(ψ ϕ (i) (t))δ(y x (i) (t)), (3.21) i=1 ( ) ( ) F ϕx ψ, y; t = F ϕ ψ, x; t = ρ(x, t) fϕ = ρ(ψ)f ϕ (ψ; x, t), (3.22) where δ(y x (i) (t)) is a three dimensional delta function at the particle location, and similarly for δ(ψ ϕ (i) (t)). In an infinitesimal time increment dt, the position and composition of each notional particle evolve according to, dx i = ũ i dt + dx i,turb (i = 1, 2, 3), dϕ α = S α (ϕ )dt + θ α,mixdt (α = 1, 2,..., N ϕ ), (3.23) The superscript refers to any particle, and dx i,turb is the increment in particle position resulting from turbulent velocity fluctuations about the local mean velocity ũ i, which usually is modeled by a gradient transport approximation. θα,mix dt is the increment in particle composition due to mixing. The transport equation of the one-point, one-time Eulerian

53 36 composition PDF g ϕ corresponding to Eq (3.23) is, ρg ϕ t + ρũ ig ϕ x i = x i [ u i ψ + ρs αg ϕ ψ α ] ρg ϕ [ θ ψ α,mix ψ (3.24) ] ρ(ψ)g ϕ. α To solve the PDF transport equation, an operator-splitting strategy is used, where each physical process (corresponding to each term in Eq. 3.23) is implemented sequentially. Local mean quantities are estimated as mass-weighted averages over nearby particle values. For example, the Favre-averaged value of a quantity of interest, Q = Q(ϕ), at the centroid of finite-volume cell c is, Q c,p p c m(p) Q (p) p c m(p), (3.25) where the summation is taken over all particles p in cell c. Here m (p) is the mass of particle p, and Q (p) = Q(ϕ (p) ) is the physical quantity carried by particle p. More elaborate algorithms can be found in [195]; however, those are expected to provide little benefit for the systems of interest here Physical Models for the PDF Method The effects of turbulent velocity fluctuations must be modeled in a composition PDF method. In this study, the gradient transport approximation is used [73, 196, 197]. This model simply takes the rate of transport to be proportional to the local gradient in the mean; this corresponds to a random walk in space at the particle level. diffusion model gives: The gradient [ u i ψ ρ x ] f ϕ = [ ] (ρf ϕ / ρ ) Γ t, (3.26) i x i x i where Γ t is the turbulent diffusivity, given by Γ t = µ t /σ t, µ t = C µ ρ k 2 /ϵ. (3.27)

54 Here σ t is the turbulent Schmidt number, usually taken to be 0.7, and C µ is a turbulence model constant (Table 3.1). A two-equation turbulence model is used to solve for k and ϵ, as discussed earlier (e.g., Eqs and 3.11). The scalar dissipation rate is a key quantity in tubulent combustion systems from the view of fundamental properties of the flame and of turbulent combustion modeling. One crucial aspect of PDF modeling is the choice of the mixing model, as it implicitly models the effects of scalar dissipation. Fox [198] states three constraints for evaluating the validity of a mixing model: 1. The scalar mean must remain unchanged. 2. The 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 = k/ϵ. 3. There must be no correlation with velocity at high Reynolds number. The interaction by exchange with the mean (IEM) model, also known as the Linear Mean Square Estimation (LMSE) model, was first proposed in the PDF context by Dopazo and O Brien [199]. IEM relaxes scalar values by interaction of each particle to the mean on a timescale computed by 1 C ϕ k ϵ, where C ϕ is a model constant, whose standard value is 2.0. It has been reported that IEM does not capture the time evolution of the PDF in homogeneous mixing problems [ ]. 37 Although it does not meet all of the mixing model requirements, IEM is a very simple and practical model for use in PDF calculations. Curl s model, or the coalescence-dispersion (CD) mixing model [204], is a stochastic mixing model. Two particles, randomly selected from particles in a finite-volume cell, mix with a given probability. The probability of a pair of particles interacting in a time interval dt is C ϕ Nωdt. Here C ϕ is a mixing model constant, N is the total number of particles, and ω is the turbulence frequency ω = ϵ/k = 1/τ. Scalar values of the initial particles are massweighted to form the mixed values. In contrast to IEM, Curl s model does not preserve the shape of the scalar PDF, although it does not relax toward a Gaussian distribution. Janika et al. [205] modified the CD model so that the degree of mixing is distributed as a

55 uniform random variable, to solve a key problem: namely, that it does not yield a continuous PDF, and to help reproduce the correct scalar dissipation rate. Pope [206] attempted to improve the shape of the PDF from the CD model by proposing a modified Curl s mixing model that more accurately captures the flatness of the PDF and the evolution towards a Gaussian PDF. Other improvements include introducing model parameters involving the element age to match the experimentally observed decaying fluctuations for passive scalars in homogeneous turbulence [207]. The Euclidean Minimum Spanning Trees (EMST) mixing model [208] attempts to remedy the issue of non-localness in reactive scalar space that the IEM and CD models have, although at increased computational cost. 38 A series of comparisons of these mixing models has been performed for canonical flames [194, ]. However, these results do not show that any one model is best for all combustion situations. Two mixing models, IEM and EMST, have been used in the PDF method in the present study. IEM is very simple and computationally fast, whereas EMST seeks locality in composition space, which is more physically realistic but is computationally expensive. With appropriate closures of the two terms on the right-hand side of Eq. (3.20), a modeled composition PDF transport equation can be written. For the gradient transport and IEM mixing models: ρ f ϕ t = x i + ρ ũ if ϕ x i ] [ (ρf Γ ϕ / ρ ) t x i + ρ S αf ϕ ψ α ψ α [ ] Cϕ ϵ k (ψ α ϕ α )ρf ϕ. (3.28) The first term on the right-hand side corresponds to the gradient transport model for the turbulent velocity fluctuations, and the second term corresponds to the IEM mixing model for molecular transport. The particle equations corresponding to Eq are, dx i = ũ i dt + ( ρ 1 Γ t x i ) dt + (2 ρ 1 Γ t ) 1/2 dw i (i = 1, 2, 3), dϕ α = S α (ϕ )dt 1 2 C ϕ(ψ α ϕ α )ωdt (α = 1, 2,..., N ϕ ), (3.29)

56 39 where the superscript * refers to any notional particle. Here W is a vector of independent isotropic Wiener processes. Properties of Wiener processes and related quantities are reviewed in Appendix J of [189]. In a numerical implementation, dw i normally is discretized as W i = W i (t + t) W i (t) = η i t 1/2, where η is a vector of three independent standardized Gaussian random variables and t is the computational time step. Thus turbulent transport is represented as a random walk of particles in physical space. 3.3 Gas-Phase Chemistry Various chemical mechanisms have been used in this work, depending on the configuration, research focus, and the computational effort. For the constant-volume spray combustion bomb (Chapter 4), three different n-heptane mechanisms have been used: a simple fivespecies one-reaction n-heptane mechanism provided in OpenFOAM [182], a 29-species 52- reaction n-heptane mechanism from the University of Wisconsin [142], which has been tuned for diesel engine conditions; and a 40-species n-heptane mechanism from Chalmers [153]. The need for detailed chemical mechanisms to accurately predict NOx formation over ranges of conditions that occur in advanced engines has been emphasized in recent work by Kung et al. [78]. For that purpose, a 71-species n-heptane/nox mechanism has been applied in recent work [73, 78, 79], which is based on a 40-species skeletal n-heptane mechanism from Chalmers [153], together with NOx chemistry from Glarborg et al. [213]. The mechanism includes multiple NOx formation pathways: the thermal NO mechanism, the N 2 O- intermediate mechanism and the prompt (Fenimore) NO mechanism. Engine-out NO usually is much higher than engine-out NO 2 for normal diesel combustion, and thermal NO usually dominates. However, for low-temperature homogeneous-charge compression ignition (HCCI)-like combustion modes, engine-out NO 2 can be higher than engine-out NO, and the NO 2 pathway can be important [78]. This is discussed further in Chapter 5.

57 Numerical Method The finite-volume method is well suited and well developed for engine applications and other complex configurations. Features include robust schemes for dealing with arbitrary geometries using either structured or unstructured meshes, and guaranteed enforcement and local conservation of numerical fluxes. The Lagrangian PDF method is implemented using a consistent hybrid particle/finite-volume mesh algorithm. Details of these numerical algorithms follow Finite-Volume Codes A finite-volume solver has been used to solve the coupled partial differential equations for mean quantities which include mean continuity, momentum, scalar and enthalpy transport equations and also the equations for k and ϵ. Two different codes have been used. One is OpenFOAM [182], an open-source, object-oriented C++ code. The other CFD code, AC-Flux, uses an unstructured, deforming mesh and a finite-volume discretization [ ]. They are both capable of simulating turbulent spray combustion in engines and/or under engine-like conditions. For each code, the discretization is implicit and first-order in time and up to second-order in space (central differencing). A deferred correction approach is used to achieve second-order spatial accuracy. An iteratively implicit, pressure-based, sequential (segregated) solution procedure is used to solve the coupled system of governing equations; the pressure algorithm is patterned after SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) [217] and PISO (Pressure-Implicit Split Operator) [218, 219]. Additional Lagrangian particle algorithms and particle/mesh coupling strategies are used in both codes to solve the modeled composition PDF transport equation, in cases where the transported PDF method has been used [74, 183, 191, 195]. The basic differences between the codes are briefly discussed here. The programming language used in OpenFoam is C++, although the coupled Lagrangian PDF code uses Fortran. AC-Flux is a Fortran code. OpenFoam has advanced parallelization and syntax features compared to AC-Flux. However, the current OpenFOAM implementation does not allow for deforming meshes, as are required for piston engines. Regarding the PDF

58 41 implementations in these codes, there are differences in the details of the coupling between the finite-volume solver and the Lagrangian PDF solvers, and in the coupling between the PDF method and the dispersed-phase liquid spray. These are discussed in the following Consistent Hybrid Lagrangian Particle/Finite Volume PDF Method In a hybrid Lagrangian particle/finite-volume method, the finite-volume solver is used to solve the coupled partial differential equations for mean quantities. The principal coupling with the particle PDF method is through the mean density. This coupling is accomplished in different ways in the two codes. In AC-Flux, the mean density ρ is given by, ρ = p pw = Ru 1 RT T W Ru 1 p T (3.30) where R u is the universal gas constant and W is the mixture molecular weight; the quantity W T can be estimated from particle values according to Eq. (3.25). This approach may result in instabilities from statistical noise that is inherent in the particle values. An alternative approach called equivalent enthalpy has been used in OpenFOAM. There an equivalent enthalpy source term derived from particle data is passed to a PDE on the finitevolume side to filter the noise generated from the particle data. The equivalent enthalpy is defined as, h eq = γ γ 1 R ut N S α=1 Y α W α = γ p γ 1 ρ, (3.31) where γ = 1.4, R u is the universal gas constant, and Y α and W α are the mass fraction and molecular weight of species α. The source term accounts for the changes of equivalent enthalpy due to mixing, chemical reaction, and thermal radiation (where considered). Algorithms for mass, velocity, and energy consistency have been developed [72, 74, 183] to address coupling and consistency issues between finite-volume and Lagrangian particle sides for composition PDF methods. A variety of configurations has been tested for this method [74].

59 Parallelization and In Situ Adaptive Tabulation The simulations have been parallelized using a simple domain decomposition method to reduce computational cost. Computational effort is generally dominated by the chemical source term calculation, especially for the PDF method. Parallel processing has also been adopted to speed up the chemical reaction calculation on the particle side. The parallelization strategy used primarily for the work here is a load-balancing algorithm established based on equally dividing the cells or particles that must be computed in composition space. In this way, the number of cells or particles assigned to each processor is approximately the same, and the compositions are randomized to achieve approximately uniform load balancing. In situ adaptive tabulation (ISAT) is an example of a storage/retrieval strategy for chemistry acceleration. This approach has been applied primarily in the context of PDF methods for turbulent reacting flows, and has proven to be effective for reducing the computational cost by accelerating the computation of the chemical source terms. An improved ISAT algorithm [220] has been used here. A key parameter for ISAT is the global error tolerance ϵ; computational accuracy and computational cost vary with ϵ. Here ISAT has been implemented in OpenFOAM for the PDF method. 3.5 Fuel Injector and Spray Models The gas phase is solved in a hybrid Lagrangian/Eulerian framework, while the liquid spray is treated by a second Lagrangian approach, the standard discrete droplet method (DDM) [221]. In this approach, the spray droplets are described by stochastic particles, or parcels. Each parcel represents a class of identical, non-interacting droplets, and they are tracked though the physical domain in a Lagrangian manner according to the exchange of mass, momentum and energy with the gas phase. The mean conservation equations to solve for the continuous gas phase are the same as those given earlier in Chapter 3, except there is an additional source term for each equation due to spray interaction for mass, momentum and energy, respectively.

60 The Liquid Phase For a single evaporating droplet, the mass equation for the liquid is given by the expression dm d dt = πddρ v Sh ln p p v, p p v,s = πddρ v Sh ln(1 + X v,s X v, 1 X v,s ), (3.32) where p, p v, and p v,s are the gas pressure and the partial pressure of vapor in the droplet surroundings and at its surface, respectively, and X, X v, and X v,s are the corresponding mole fractions of the fuel vapor. Here the surface vapor pressure is assumed to be equal to the saturation pressure at the droplet temperature. D is the droplet diameter, D is the vapor diffusivity, and ρ v is the density of the fuel vapor close the surface of the droplet, estimated using the ideal gas law: ρ v = p R v T m, (3.33) where p is the gas pressure, which is assumed to be equal to the fuel vapor pressure close to the droplet surface, and T m is the mean (film) temperature given by T m = T d +(T T d )/3. R v is the mixture gas constant. Sh is the Sherwood number, which is dependent on Schmidt number Sc and Reynolds number Re, using the Ranz-Marshall correlation [222] for a single sphere in an undisturbed gas flow, Sh = Re 1/2 Sc 1/3, 0 Re < 200, 0 Sc < 250. (3.34) As Saffman, pressure and buoyancy forces are often neglected, the equation of motion for a discrete particle with mass m d is then, m d du d dt = πd2 8 ρc D u d u (u d u) + m d g. (3.35) The first term on the right-hand side is the drag force acting upon a particle surrounded by gas of density ρ and velocity u. The second term on the right-hand side of the equation is the gravitational body force. C D is the drag coefficient, an empirically determined param-

61 eter, depending on the geometrical shape of the particle as well as flow conditions and gas properties using the following expression: 44 C D = 24 Re d ( Re2/3 d ) forre < forre > 1000, (3.36) where the Reynolds number is given by The droplet energy equation is, Re d = ρ u d u D. (3.37) µ dt d dt = T T d τ h f 1 c l,d h v (T d ) τ e (3.38) where c l,d is the specific heat for the liquid. τ h is a characteristic heat transfer relaxation time, defined as τ h = m dc l,d πdκnu, (3.39) τ e is an evaporation relaxation time, defined as: τ e = where B is the Spalding mass transfer number given by, m d πddρ v Shln(1 + B), (3.40) B = X v,s X v, 1 Xv, s, (3.41) and f is a factor that corrects the rate of heat exchange due to the presence of mass transfer: f = z e z 1, (3.42) z = c p,vṁ d πdknu. (3.43) The Nusselt number N u is specified using a Ranz-Marshall correlation for a single sphere

62 45 in an undisturbed gas flow [222] here, with all the properties evaluated at the mean film temperature. P r is the Prandtl number, and c p and k are the specific heat and thermal conductivity of the gas, respectively: Nu = Re 1/2 P r 1/3, 0 Re < 200, 0 P r < 250, (3.44) P r = µ c p k. (3.45) When using a DDM approach, spray sub-models to describe atomization, breakup and dispersion are necessary. In the atomization process, the liquid core breaks up into tiny droplets at the nozzle exit; this is also referred to as primary breakup. The initial conditions of the spray parcels can either be given by an atomization model, or specified by a constant spray angle and a constant droplet size serving as a very simple atomization model; the latter approach is adopted in current work. Later on, the relatively large droplets can be further distorted and subsequently broken up into smaller secondary droplets. This is termed secondary breakup, which typically takes place further downstream of the nozzle Physical Models The physical models for the constant-volume spray combustion are described here. The initial spray angle and initial droplet size distribution from the nozzle are specified as constants with respect to time. The Ranz-Marshall correlation, which is obtained from experiment [222], was applied for the heat transfer model. A stochastic dispersion model accounts for random velocity perturbations. A standard drag model was used. The Ranz- Marshall model was also selected for droplet evaporation. Droplet collisions were neglected, due to their weak effect for the sprays of interest. The RNG k ϵ model [223, 224] with constant C 1 equal to 1.45 was adopted for turbulence. The Chalmers Partially Stirred Reactor (PaSR) model [159] is hard-coded in OpenFOAM for the non-pdf simulations. The secondary breakup model uses the Kelvin-Helmholtz/Rayleigh-Taylor (KH-RT) hybrid model [225, 226]. Two fundamental mechanisms, the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, govern the spray breakup process in this model. In the KH mode, new child parcels with size r c are stripped from the parent parcel. The rate of change of the radius

63 46 of the parent parcel is expressed as: where τ KH is the breakup time defined by, dr dt = r r c τ KH, (3.46) τ KH = 3.788B 1D Ω KH Λ KH. (3.47) Here B 1 is a model constant, and Ω and Λ are the frequency of the fastest growing wave and its corresponding wavelength, respectively. In the RT mode, if the wavelength Λ RT of the faster growing wave is smaller than the droplet radius, the RT waves start to grow on the surface of the droplets and the life time of the growing RT waves is tracked from then on. When the life time exceeds the characteristic breakup time τ RT, a catastrophic breakup occurs, immediately creating much smaller droplets with radii given by: r c = πc RT, K RT (3.48) τ RT = C τ, Ω RT (3.49) where Ω RT is the frequency of the fastest growing wave, K RT is the wave number, and C τ and C RT are model constants. Several spray models variants are explored in Chapter 4, include the breakup model, the injector model, the collision model and the dispersion model. The hollow-cone injector model adopts a Rosin-Rammler [227] PDF distribution for initial droplet size with scale parameter d and shape parameter n set to be m and 2, respectively. Minimum and maximum values are m and m, respectively. The Linearized Instability Sheet Atomization (LISA) [228] model use an empirical sheet constant value of 12. Other model coefficients used are summarized in Table 3.3. These models are all available in OpenFOAM. For the engine simulations in this thesis, the physical models used in AC-Flux are given as follows. A stochastic Lagrangian formulation again is used for liquid fuel sprays [230, 231].

64 47 Table 3.3: Spray models and coefficients. Blob model [229] B angle degree Taylor Analogy Breakup (TAB) model y 0 ẏ 0 C µ C ω W e crit Enhanced Taylor Analogy Breakup (ETAB) model C µ C ω W e crit K 1 K 2 W e transition Reitz-Diwakar (RD) model C bag C b C strip C s Trajectory model c space c time The principal models that are available in AC-Flux include droplet deformation, breakup, drag, turbulent dispersion, collision and coalescence, vaporization and spray-wall impingement. Here the deformation, drag, turbulent dispersion, vaporization and spray-wall impingement models were enabled, while the breakup, collision and coalescence models were disabled. In this study, the Taylor Analogy Breakup (TAB) [232] deformation model was used with the drag model of [79]. The spray model parameters and fuel-injector characterization were taken from Kung [73, 79]; these are representative of those for a modern light-duty direct-injection diesel engine Coupling of Spray Model with PDF Method The spray model is coupled with the PDF method in URANS through droplet vaporization. For a reacting multiphase flow, mass and energy source terms due to evaporation need to be considered in the context of the PDF method. In a hybrid Lagrangian particle/finite-volume method, the cell mean mass and enthalpy source terms due to evaporation are taken from the spray model on the finite-volume side, and then passed to the PDF side. To distribute these cell-level mean source terms among Lagrangian PDF particles in each cell, a simple

65 48 approach is to take an average of the source term over the number of particles in cell and to add this particle average mass/enthalpy source term to each particle in cell. Instead of simple averaging, the mass/enthalpy source term can be distributed proportional to the mass of the particle, which has been done in this work. The set of composition/enthalpy variables of the particles are then updated accordingly. Additionally, in the equivalent enthalpy approach [233, 234], the equivalent enthalpy source derived from the particle data must also account for changes due to spray evaporation.

66 Chapter 4 Analysis of Spray and Spray Combustion in a Constant-Volume Chamber In-cylinder combustion process in modern diesel engines are complex. Driven by the need for reductions in fuel consumption and engine-out emissions while accommodating alternative fuels, next-generation clean and efficient combustion systems are likely to feature higher pressures, lower temperatures, extremely lean and/or dilute mixtures, and different fuels. Combustion characteristics in such advanced engine conditions are still largely unknown and are challenging to model. Experimental and computational efforts have been initiated to understand the fundamentals of these advanced combustion systems, such as the ECN workshop [81]. In this chapter, the transported PDF method is applied in URANS to explore the effects of turbulence-chemistry interactions on autoignition and combustion under modern diesel-engine-like conditions. The targeted configuration is a constant-volume combustion chamber, without the complications of moving pistons and/or valves, where measurements are available for a wide range of thermochemical conditions representative of modern diesel engines [81]. A surrogate of diesel fuel, n-heptane, is the focus in this work. Systematic parametric studies have been performed to explore the importance or lack thereof of turbulence-chemistry interactions under engine-relevant conditions. 49

67 4.1 Engine Combustion Network (ECN) N-Heptane Cases 50 The Engine Combustion Network (ECN) [81] provides a platform for collaboration among experimentalists and computational researchers in engine combustion with measurements available for multiple fuels and operating conditions. The ECN non-reacting n-heptane baseline case and reacting n-heptane cases in a constant-volume chamber under various ambient environments are targeted in this work. For non-reacting n-heptane sprays, validation is done for liquid and vapor penetration, and for mean mixture fraction profiles. For reacting n-heptane sprays, computed and measured ignition delays, lift-off lengths and flame structures are compared. The baseline n-heptane nonreacting spray case (Table 4.1) has an initial ambient gas temperature of 1000 K, initial density of 14.8 kg/m 3, initial pressure of 4.21 MPa and inert ambient (0% O 2 in the initial ambient gas composition). Liquid n-heptane fuel is injected at a temperature of 373 K with a square-shaped injection-rate profile (constant injection rate over specified duration). Table 4.2 shows various ambient conditions that have been studied for reacting cases, including O 2 percentage ranging from 0% to 21%, initial ambient gas temperature ranging from 750 K to 1300 K, and initial density of 30 kg/m 3. Measured data available include liquid and jet penetration lengths, pressure versus time, mixing images, soot volume fraction and various high-speed movies. The combustion vessel for the experiment is a cubic chamber with a characteristic length of 108 mm. Liquid fuel is injected from the top center of the vessel. For computational expediency, this is modeled as a one-degree axisymmetric wedge with a single layer of cells in the azimuthal direction (shown in Fig. 4.1). The total number of cells for the nonuniform axisymmetric mesh is 6372, with approximately 0.56 mm minimum cell size in the axial direction. The axial direction length of the computational domain is 108 mm and the radial dimension has been adjusted to ensure the same total volume as that of the experimental chamber. A set of model parameters has been selected to match the global spray characteristics for the nonreacting case. The sensitivity of results to variations in model parameters is discussed in Section below. For the baseline model, the initial spray angle was specified

68 51 Table 4.1: Baseline n-heptane nonreacting spray case conditions. Fuel n-heptane Nozzle diameter mm Fuel injection temperature 373 K Fuel injection pressure 150 MPa Total fuel mass injected 17.8 mg Injection duration 6.8 ms Ambient gas pressure 4.33 MPa Ambient gas temperature 1000 K Ambient gas density 14.8 kg/m 3 Ambient gas composition 0% O 2, (mole fraction) 89.71% N 2, 6.52% CO 2, 3.77% H 2 O Table 4.2: Variations in ambient conditions for n-heptane reacting cases. Ambient O 2 Ambient temperature Ambient density (%) (K) (kg/m 3 ) as a constant 12.6 degrees and the initial droplet diameter was mm; the latter was derived from the injector diameter and given area contraction coefficient [225]. The spray breakup was described with the KH-RT model by Reitz (see Section 3.5.2) with B 1 equal to 6.4. The Ranz-Marshall correlation was applied for the heat transfer model. A stochastic dispersion model accounts for turbulent velocity fluctuations and a standard drag model was used. The Ranz-Marshall model was selected for droplet evaporation. Droplet collisions were neglected as their effects are weak for these sprays. A renormalization group (RNG)

69 52 Figure 4.1: Computational axisymmetric mesh for a constant-volume combustion chamber. k ϵ turbulence model [223, 224] was used, with the model constant C 1 equal to 1.45, with initial values of k and ϵ estimated as m 2 /s 2 and 3.5 m 2 /s 3, respectively. Here, the radius of the domain was used to characterize the initial turbulence length scale l, and the initial value of ϵ was calculated as ϵ = C 0.75 µ k 1.5 /l. The initial value of k was estimated from k = 1.5 u 2 rms where u rms is approximately 0.7 m/s according to the description of the experimental data. The computational time step is s for this axisymmetric mesh (shown in Fig. 4.1). A constant wall temperature boundary condition of 850 K is used to match the measured pressure trace. Other initial conditions are specified according to Tables 4.1 and 4.2 and the experimental conditions listed at the ECN website [81]. 4.2 Nonreacting N-Heptane Sprays The first step in the constant-volume chamber study was to establish a baseline set of physical and numerical parameters to match the experimentally measured global spray characteristics for a nonreacting, vaporizing n-heptane spray (Table 4.1). Key spray characteristics are computed and compared with the experimental data, including liquid and

70 53 vapor penetration lengths and mixture fraction profiles [166, 167]. Computed mean mixture fraction and its variance (the latter for cases where turbulence-chemistry interactions are considered using the PDF method) are compared with experiment. The criteria for defining liquid and vapor penetration lengths follow the recommendations given on the ECN website [81]: Liquid length: The distance from the injector exit along the injection axis to the location where the local liquid volume fraction has fallen to a value of 0.15%. Vapor penetration: The distance from the injector exit along the injection axis to the location where the fuel vapor mixture fraction has fallen to Mixture fraction: For the nonreacting n-heptane spray, mixture fraction is equal to the fuel mass fraction of n-heptane (C 7 H 16 ); for reacting n-heptane sprays, mixture fraction z is defined as: z = Y CH Y CH,O Y CH,F Y CH,O, (4.1) where Y CH is the total elemental mass fraction of C and H; subscripts F and O denote fuel stream and oxidizer stream, respectively. A fuel-based local equivalence ratio Φ is defined as: Φ = z 1 z where subscript st denotes stoichiometric reactants. 1 z st z st, (4.2) A systematic parametric study has been performed to establish sensitivities of the computed liquid and vapor penetration lengths to variations in physical models, numerical parameters, initial conditions and criteria for definition of penetration lengths. These parametric studies were conducted using a simplistic model for turbulence-chemistry interactions. In the following, results obtained from a simple model for turbulence-chemistry interactions are labeled FV ( finite-volume, to indicate that chemistry is computed using cell-level mean values of composition and temperature).

71 Model vs Experiment Comparisons for the Baseline Model (a) (b) Figure 4.2: Computed (using a simplistic turbulence-chemistry interactions model) and measured penetration lengths versus time for a non-reacting n-heptane spray. (a) Liquid penetration length. (b) Vapor penetration length. Results of liquid and vapor penetration are shown in Fig As can be seen, the computed liquid penetration matches the measured data reasonably well during the quasisteady period, while over-predicting during the early developing period. The computed vapor penetration generally follows the experimental curve with slight over-prediction at 1 ms, but under-predicting after 2 ms. Computed and measured mean mixture fraction profiles are compared in Figs. 4.3 and 4.4. Good agreement of mean mixture fraction profiles was found at 0.49 ms after injection at the 17 mm axial location, and at 6 ms after injection at the 40 mm axial location, where measured data are available. The mean computed mixture fraction profile is also acceptable at 6 ms after injection at the 20 mm axial location, although it is slightly over-estimated along the injection axis. The influence of turbulence-chemistry interactions for nonreacting sprays is explored by comparing results using a simplistic turbulence-chemistry interactions model versus those

72 55 Figure 4.3: Computed and measured profiles of mean mixture fraction for a non-reacting n-heptane spray at 0.49 ms after the start of injection and an axial location of 17 mm. Figure 4.4: Computed and measured profiles of mean mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and axial locations of 20 mm and 40 mm. using the PDF method. The influence on computed mean mixture fraction profiles is shown in Figs. 4.5 and 4.6. Large differences can be seen with the PDF method versus without the PDF method, with the PDF method giving higher on-axis values: 20% higher at 20

73 56 mm, and 50% higher at 40 mm. The reported measured mixture fraction variance profiles (Fig. 4.7) were based on 40 samples, and are not expected to be quantitatively accurate. The general shape of the mixture fraction variance profile is captured by the model, but quantitative accuracy cannot be assessed until more complete data are available. Figure 4.5: Computed (with versus without PDF method) and measured mean profiles of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 20 mm. The influence of the mixing model and the value of the mixing model coefficient have been explored in the PDF method. Comparisons of the computed mixture fraction profiles with variations in the mixing model are shown in Figs These include results with two different mixing models (IEM and EMST) and with different values of C ϕ. In general, mixing model constants have relatively small effect on the mean mixture fraction profiles. The computed mixing fraction variance decreases with increasing C ϕ as expected, and for a given value of C ϕ, is lower for EMST compared to IEM. Here the computed mean mixture fraction profiles are closer to experiment with a simple model for turbulence-chemistry interactions. It is emphasized that this is because the model calibration exercise to arrive at the base model was done without the PDF method, for computational expediency. As will be shown in following subsection, results are highly sensitive to the spray and turbulence models, in particular.

74 57 Figure 4.6: Computed (with versus without PDF method) and measured mean profiles of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 40 mm. Figure 4.7: Computed (with PDF method) and measured profiles of mixture fraction variance for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 20 mm Parametric Studies Physical models and numerical parameters for the baseline n-heptane case are selected to match the measured data through tuning process. Sensitivities of model results to variations

75 58 Figure 4.8: Computed (with versus without PDF method and with variations in the PDF mixing model) and measured mean profiles of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 20 mm. Figure 4.9: Computed (with versus without PDF method and with variations in the PDF mixing model) and measured mean profiles of mixture fraction for a non-reacting n-heptane spray at 6 ms after the start of injection and an axial location of 40 mm. in physical models and numerical parameters are explored by varying one parameter at a time, to isolate its effect (Table 4.3).

76 59 Figure 4.10: Computed (with versus without PDF method and with variations in the PDF mixing model) and measured profiles of mixture fraction variance for a non-reacting n- heptane spray at 6 ms after the start of injection and an axial location of 20 mm. Influence of physical models Figure 4.11 shows that computed liquid and vapor penetration lengths are both quite sensitive to the choice of turbulence model. All other turbulence models generate lower liquid penetration lengths compared to the RNG k ϵ model. For the Launder-Sharma k ϵ (LSKE) model, vapor penetration length is extremely high, while liquid penetration is significantly low. The other two models (standard k ϵ model and realizable k ϵ model), give relatively low vapor penetration lengths. Significant differences in computed liquid penetration lengths can be observed in Fig for different breakup models. The liquid penetration length is much higher for the Reitz-Diwakar model and is lower for the other models. Relatively minor differences in computed vapor penetration lengths are seen for the different breakup models. The LISA atomization model gives low liquid penetration length (Fig. 4.13), while results for the other atomization models are similar. The dispersion and collision models have relatively small influences on computed liquid and vapor penetration lengths (Figs and 4.15). In Figs and 4.17, it can be seen that the computed liquid penetration length increases with increasing B 1 and vapor penetration length increases with increasing C ϵ1. Thus B 1 and C ϵ1 are key parameters that affect liquid and vapor pen-

77 60 Table 4.3: Physical and numerical models for baseline n-heptane nonreacting spray. Model and parameters Baseline model (FV-PDF) Variations performed (FV) atomization none Linearized Instability Sheet Atomization (LISA) model, Blob model collision none O Rourke (OR), trajectory dispersion stochastic gradient, none breakup KH-RT Reitz-Diwakar (RD), Taylor Analogy Breakup (TAB), Enhanced Taylor Analogy Breakup (ETAB) turbulence RNG k ϵ standard k ϵ, Launder-Sharma k ϵ (LSKE), realizable k ϵ (realizable KE) injector model constant hollow cone mesh axisymmetric quarter time step [s] , initial ϵ [m 2 /s 3 ] , 4.5 B 1 in KH-RT model , 4.3 C ϵ1 in RNG k ϵ model , 1.63 liquid penetration definition liquid fuel mass percent= , 0.97 vapor penetration definition fuel vapor mass percent= , 0.97 etration lengths, respectively. The computed liquid penetration length does not vary much with injector models, while the hollow-cone model gives slightly higher vapor penetration lengh than the Blob model (Fig. 4.18). Influence of numerical parameters A three-dimensional quarter mesh in Fig with comparable mesh size to that used in the axisymmetric mesh has been implemented for comparison as shown in Fig The computed liquid penetration length is approximately 2 mm lower for 3D mesh than for the 2D axisymmetric mesh, while the computed vapor penetration length is essentially the same. Figure 4.21 shows that an overly large computational time step size can cause instability

78 61 (a) Liquid penetration length (b) Vapor penetration length Figure 4.11: Computed liquid and vapor penetration lengths with variations in turbulence model for a non-reacting n-heptane spray. (a) Liquid penetration length (b) Vapor penetration length Figure 4.12: Computed liquid and vapor penetration lengths with variations in breakup model for a non-reacting n-heptane spray. to the computed liquid penetration length, and can lead to extreme vapor penetration to the wall of the chamber. Further refinement of the timestep decreases the computed liquid

79 62 (a) Liquid penetration length (b) Vapor penetration length Figure 4.13: Computed liquid and vapor penetration lengths with variations in atomization model for a non-reacting n-heptane spray. (a) Liquid penetration length (b) Vapor penetration length Figure 4.14: Computed liquid and vapor penetration lengths with variations in dispersion model for a non-reacting n-heptane spray. penetration length slightly, and results in little change in the computed vapor penetration length.

80 63 (a) Liquid penetration length (b) Vapor penetration length Figure 4.15: Computed liquid and vapor penetration lengths with variations in collision model for a non-reacting n-heptane spray. (a) Liquid penetration length (b) Vapor penetration length Figure 4.16: Computed liquid and vapor penetration lengths with variations in spray model coefficient B 1 for a non-reacting n-heptane spray. Influence of initial conditions The assumed initial turbulence level does not have a strong influence on the computed liquid or vapor penetration lengths, as shown in Fig

81 64 (a) Liquid penetration length (b) Vapor penetration length Figure 4.17: Computed liquid and vapor penetration lengths with variations in turbulence model coefficient C ϵ1 for a non-reacting n-heptane spray. (a) Liquid penetration length (b) Vapor penetration length Figure 4.18: Computed liquid and vapor penetration with variations in the injector model for a non-reacting n-heptane spray. Influence of thresholds used to define penetration lengths In Fig. 4.23, it can be seen that slight variations in the threshold volume fraction values used to define the computed liquid and vapor penetration result in little change in the computed

82 65 Figure 4.19: Computational 3D quarter mesh for a constant-volume combustion chamber. (a) Liquid penetration length (b) Vapor penetration length Figure 4.20: Computed liquid and vapor penetration lengths with variations in computational mesh for a non-reacting n-heptane spray. values. However, computed results defined by 98% of liquid fuel mass and 99% of fuel vapor mass are relatively lower compared to those defined by fuel volume fraction and mixture fraction thresholds of

83 66 (a) Liquid penetration length (b) Vapor penetration length Figure 4.21: Computed liquid and vapor penetration lengths with variations in computational time step for a non-reacting n-heptane spray. (a) Liquid penetration length (b) Vapor penetration length Figure 4.22: Computed liquid and vapor penetration lengths with variations in the initial ϵ for a non-reacting n-heptane spray Discussion The ECN website [81] provides a good summary of ongoing computational work for the constant-volume n-heptane spray. Several other groups have shown as good agreement

84 67 (a) Liquid penetration length (b) Vapor penetration length Figure 4.23: Computed liquid and vapor penetration lengths with variations in the criteria used to define liquid and vapor penetration lengths for a non-reacting n-heptane spray. (a) Liquid penetration definitions. (b) Vapor penetration definitions. with experiment as we have found here, except that many models tend to under-predict at later times for vapor penetration lengths. The level of success in agreement with experiment is most likely due to adjustment of model constants and/or other factors. Most groups show reasonable agreement of mean mixture fraction profiles with experimental data, and some noticeable issues with grid convergence and/or statistical convergence have been mentioned at the 20 mm axial location at 6 ms. Since most of the groups do not account for the influence of turbulent fluctuations on chemistry, only one group (POLIMI) has shown results of mixture fraction variance, which are reasonably well predicted with sufficient grid refinement. 4.3 Reacting n-heptane Sprays: Autoignition and Combustion In this section, reacting n-heptane sprays are simulated over a wide range of initial O 2 levels (8%, 10%, 12% and 21%), ambient temperatures (750 K, 800 K, 850 K, 900 K, 950

85 68 K, 1000 K, 1100 K, 1200 K and 1300 K), and ambient gas densities (14.8 kg/m 3 and 30 kg/m 3 ). The spray and turbulence models were kept the same as the baseline model from the nonreacting n-heptane spray simulations of the preceding subsection. As summarized in ECN proceedings, a variety of chemical mechanisms have been applied for this configuration, ranging from 23 species to 159 species, and involving skeletal and reduced mechanisms. These include the Engine Research Center (ERC) 29-species skeletal mechanism (Appendix A.2) used by three groups (CMT, POLIMI and UNSW), Golovitchev s 42-species skeletal mechanism [153], Lu s 63- and 52-species reduced mechanisms [235], Pitsch s 23-species reduced mechanism [236], Zeuch s 110-species skeletal mechanism [237], the ERC-PRF 41-species skeletal mechanism [238], Seiser s 159-species skeletal mechanism [141], Peters 37-species skeletal mechanism and a 42-species skeletal mechanism [239]. In this section, the ERC 29-species, 52-reactions n-heptane mechanism (Appendix A.2) was the main chemical mechanism used for reacting n-heptane spray cases, except that some cases with less robust combustion were simulated using a 40-species n- heptane mechanism (Appendix A.3) to explore the influence of the chemical mechanism. The primary global quantities of interest for comparison with experiment are the ignition delays and lift-off lengths. Results of simulations with the PDF method and without the PDF method are compared to determine the extent to which turbulence-chemistry interactions influence the results With versus Without In Situ Adaptive Tabulation The reacting cases used ISAT to accelerate the chemistry calculations. The ISAT global error tolerance ϵ was set to , as an acceptable compromise between accuracy and efficiency. Here the influence of ISAT is shown, to justify this choice. For the 21% O 2, 1000 K and 14.8 kg/m 3 ambient condition case, the computed ignition delay with the PDF method is ms with ISAT and ms without ISAT. In Fig. 4.24, the computed mean temperature fields at early times show some differences with versus without ISAT. However, the quasi-steady-state mean temperature fields with ISAT versus without ISAT are quite similar to each other. The computational wall time for a single-processor run to

86 Table 4.4: Computational wall time comparison with versus without ISAT for a baseline n-heptane case with the PDF method Single-processor wall time with ISAT Six-processor wall time without ISAT 133,402 s 306,407 s 69 3 ms with ISAT is less than half that for a 6-processor run without ISAT (Table 4.4). The wall time for a single-processor run using ISAT is less than that of a parallel computation without ISAT. (a) t=1 ms without ISAT (b) t=2 ms without ISAT (c) t=3 ms without ISAT (d) t=1 ms with ISAT (e) t=2 ms with ISAT (f) t=3 ms with ISAT Figure 4.24: 2D computed mean temperature contours for a reacting n-heptane spray at baseline conditions of ambient temperature (1000 K), ambient density (14.8 kg/m 3 ) and O 2 level (21%), with versus without ISAT, for the 29-species mechanism. Results for a less robust combustion case are shown in Fig (8% O 2, 1000 K and 14.8 kg/m 3 ). There the computed ignition delay with ISAT is ms versus ms without ISAT. Compared to the result without ISAT, the mean temperature contours with ISAT have a higher maximum temperature by approximately 77 K at 4 ms and 15 K at 5 ms,

87 70 respectively. For low ambient temperature, the 29-species n-heptane mechanism does not perform well. Results with versus without ISAT for the 40-species n-heptane mechanism at 800 K ambient temperature are shown in Fig There the computed ignition delay is ms with ISAT compared to ms without ISAT. These results suggest that while there are some quantitative differences between results obtained with versus without ISAT, the differences are not large, even for non-robust combustion conditions, and the results obtained with ISAT will be sufficient if an appropriate chemical mechanism is chosen. All subsequent PDF results shown in this chapter were obtained using the same chemical mechanism - the 29-species n-heptane mechanism - so ISAT has not been used here Model vs Experiment Comparisons According to the description of the experiment on the ECN website, ignition delay is defined as the time from the start of injection until the high-temperature ignition and combustion (the premixed burn). Specifically, a documented constant or manually chosen noise threshold on the smoothed pressure-rise-versus-time trace defines the ignition-delay time. The lift-off length is defined as the axial distance from the injector to the location of the hightemperature reaction zone in the quasi-steady flame. This is defined quantitatively by taking the average of two axial distances: the distance between the injector and the axial location where chemiluminescence from excited-state OH (OH ) reaches a leveling-off value, and the distance between the injector and the spray centerline with an intensity greater than approximately 50% of the leveling-off value. Among computational researchers, definitions of ignition time vary widely, with most being temperature-based. The lift-off length is also defined differently in computations, with some using temperature-based and some using OH mass-fraction-based definitions. Here the ignition delay and lift-off length definitions are taken as follows: Lift-off length: The axial distance from the injector to the nearest location where a cell-centered mean OH mass fraction value of has been reached. Ignition delay: The time after injection when the local temperature rises by 400 K

88 71 (a) t=4 ms without ISAT (b) t=5 ms without ISAT (c) t=4 ms with ISAT (d) t=5 ms with ISAT Figure 4.25: 2D computed mean temperature contours for a reacting n-heptane spray at less robust combustion conditions of ambient temperature (1000 K), ambient density (14.8 kg/m 3 ) and O 2 level (8%), with versus without ISAT, for the 29-species mechanism. from the initial ambient temperature of the domain. Quantitative comparisons of two sets of computational results with experimental data are provided below: one set that uses a simple model for turbulence-chemistry interactions (denoted by FV ) and one that takes turbulence-chemistry interactions into account by using a Lagrangian particle/eulerian finite-volume PDF method (denoted by PDF ). Figure 4.27 shows that both models follow the experimental trend with variations in O 2 level qualitatively, with better predictions at higher O 2 levels. However, there are significant quantitative differences between PDF and non-pdf results. With the PDF method, ignition

89 72 (a) t=3 ms without ISAT (b) t=3 ms with ISAT Figure 4.26: 2D computed temperature contours for a reacting n-heptane spray at conditions of ambient temperature (800 K), ambient density (14.8 kg/m 3 ) and O 2 level (21%), with versus without ISAT, for the 40-species mechanism. is delayed at lower O 2 levels by about 1 ms for 10% O 2 and 1.8 ms for 8% O 2, respectively. Computed lift-off lengths with the PDF method are generally higher compared to the non- PDF model, although the trends still follow the measured data qualitatively (Fig. 4.28). Figure 4.27: Computed (with and without PDF) and measured ignition delay versus O 2 percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 14.8 kg/m 3.

90 73 Figure 4.28: Computed (with and without PDF) and measured lift-off length versus O 2 percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 14.8 kg/m 3. With variations in ambient temperature, the computed ignition delays for both models follow the general experimental trend well, except for extremely low ambient temperatures (Fig. 4.29). Longer ignition delays are observed for low-ambient-temperature conditions. For an ambient temperature of 800 K, the ignition delay is over-predicted by 2 ms for the non-pdf model and by 2.6 ms for the PDF model, respectively. For lower temperatures (750 K), the 400 K temperature rise criterion is not reached computationally. For ambient temperatures of 900 K and above, the models match the measured ignition delays quite well. In Fig. 4.30, the computed lift-off lengths for both models follow the measured data. Computed lift-off lengths for the non-pdf model are under-estimated by approximately 6 mm at ambient temperatures above 1000 K, but match the measured data well below 1000 K, except for the lowest temperature of 750 K. The PDF lift-off length curve follows the general trend of the measured data, but over-estimates by 8-15 mm across the full temperature range. At the higher ambient density of 30 kg/m 3, the computed ignition delay rises slightly with decreasing ambient O 2 percentage for the non-pdf model. For the PDF method, the computed ignition delays with 12% and 15% initial ambient O 2 match the experimental

91 74 Figure 4.29: Computed (with and without PDF) and measured ignition delay versus ambient temperature for a reacting n-heptane spray with 21% O 2 level and ambient density 14.8 kg/m 3. Figure 4.30: Computed (with and without PDF) and measured lift-off length versus ambient temperature for a reacting n-heptane spray with 21% O 2 level and ambient density 14.8 kg/m 3. results closely. However, at low ambient O 2 levels of 10% and 8%, the PDF results show significantly longer ignition delay compared to the non-pdf model and experiment, with a 200% over-prediction at 8% O 2. The lift-off lengths, as in Fig. 4.32, are not well as predicted

92 75 as the ignition delays. The computed lift-off lengths for the non-pdf model are consistently under-predicted, although they follow the experimental trend of decreasing lift-off length with increasing ambient density for the same ambient O 2 level (compared to Fig. 4.28). In Fig. 4.28, only the non-pdf model results are shown for 10% and higher O 2. The reason is that for 8% O 2 in the non-pdf model, and for all cases with the PDF method, the computed OH mass fraction does not reach , and a different criterion needs to be used. Figure 4.31: Computed (with and without PDF) and measured ignition delay versus O 2 percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 30 kg/m 3. There is limited experimental data on the turbulent flame structures, such as high-speed movies of chemiluminescence imaging. Simulations were performed under various ambient conditions. Here the computed flame structures are illustrated for different ambient oxygen percentages, ambient densities and ambient temperatures. Mean temperature contours are compared at quasi-steady state with and without the PDF method in Figs As seen in Figs and 4.34, computed mean temperatures distributions for different ambient oxygen levels (8%, 10%, 12%, 15% and 21%) show clear differences between PDF and non-pdf results. With increasing ambient oxygen concentration, the computed peak temperature rises. In general, the non-pdf model shows higher temperatures in the high-

93 76 Figure 4.32: Computed (with and without PDF) and measured lift-off length versus O 2 percentage for a reacting n-heptane spray with ambient temperature 1000 K and ambient density 30 kg/m 3. temperature region than the PDF method. The computed flame structure for the non-pdf model is thinner than that of PDF method. The PDF model results are more consistent with the broadened turbulent flame brush that is expected for these highly turbulent flames. Figures 4.35 and 4.36 show the computed mean temperature distributions for different ambient temperatures: 750 K, 800 K, 850 K, 900 K, 950 K, 1100 K, 1200 K and 1300 K. With increasing ambient temperature, the flame becomes thinner and longer, and the peak flame temperature rises. Results with and without the PDF method are again quite different from each other, with the flame structures of the PDF method being much wider and usually located further downstream compared to that of the non-pdf model. Temperatures in the flame are relatively low for the PDF method. For the lowest ambient temperature (750 K), the fuel does not ignite (temperature rise of 400 K is not reached). At the high ambient density of 30 kg/m 3, for ambient oxygen levels ranging from 8% to 15%, the flame structures look quite different compared to those for the same ambient oxygen percentage at the low ambient density of 14.8 kg/m 3. In general, the flames are shorter for the high-density ambient conditions. The computed flame shapes and lift-off locations do not vary as much as those for the lower ambient density with variations in

94 77 (a) O 2=8% (b) O 2=10% (c) O 2=12% (d) O 2 =15% (e) O 2 =21% Figure 4.33: Computed (without PDF) mean temperature distributions for a reacting n- heptane spray with ambient temperature 1000 K and ambient density 30 kg/m 3 at five different ambient oxygen concentrations at 6 ms. ambient oxygen level. The computed peak temperatures are also reduced by up to 200 K for the higher ambient density. The PDF method produces shorter and wider flames, compared to those of the non-pdf model for the same ambient oxygen percentage. Results from other groups in the ECN proceedings also showed poor agreement at the less robust combustion conditions, especially for the lower O 2 percentages. In general, a common trend of over-predicted ignition delay has been shown among most modeling groups under varying ambient O 2 conditions. This may in part be due to the lack of appropriate definitions for low ambient O 2. Both the computed lift-off length and ignition delay from one group (ANL) were well predicted using a different chemical mechanism (Golovitchev mechanism). In some cases, results for either ignition delay or lift-off length were relatively good, while those for the other were not as good. Significant qualitative structural differences were

95 78 (a) O 2=10% (b) O 2=12% (c) O 2 =15% (d) O 2 =21% Figure 4.34: Computed (with PDF) mean temperature distributions for a reacting n- heptane spray with ambient temperature 1000 K and ambient density 30 kg/m 3 at five different ambient oxygen concentrations at 6 ms. reported between models that neglect turbulence-chemistry interactions and those that consider turbulence-chemistry interactions. In particular, well-mixed models tend to give unrealistically thin laminar-like flame structures. Here significant differences have been found between results from the PDF method and a non-pdf model. The computed turbulent flame structures with the PDF are more realistic, while quantitative comparisons in lift-off length and ignition delay are generally better for the non-pdf method at low O 2 and low T. One reason for this poor performance of the PDF method at low ambient O 2 and/or low ambient T may be the chemical mechanism. The 29-species chemical mechanism that has been used here has been tuned by the Wisconsin-ERC to match the global engine data in a model that neglects turbulence-chemistry interactions. Therefore, it may not be surprising

96 79 (a) T =750 K (b) T =800 K (c) T =850 K (d) T =900 K (e) T =950 K (f) T =1100 K (g) T =1200 K (h) T =1300 K Figure 4.35: Computed (without PDF) mean temperature distributions for a reacting n- heptane spray with 21% O 2 level and ambient density 14.8 kg/m 3 at different ambient temperatures at 6 ms. that it performs better with a non-pdf model. To explore sensitivity of computed results to the chemical mechanism, a 40-species n- heptane mechanism was used for some cases: a low-ambient-temperature (800 K) case, and a low-ambient-o 2 (8%) case, where ignition delay predictions are less robust. Results are