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Analysis of Mixing and Thermal Effectson Low-Temperature Combustion in ICEngine OperationYoungchul Ra a , Rolf D. Reitz a & Ramachandra Diwakar ba Engine Research Center , University of Wisconsin-Madison ,Madison, Wisconsin, USAb Powertrain Systems Research Laboratory , General Motors Researchand Development Center ,Published online: 19 Feb 2009.

To cite this article: Youngchul Ra , Rolf D. Reitz & Ramachandra Diwakar (2009) Analysis of Mixingand Thermal Effects on Low-Temperature Combustion in IC Engine Operation, Combustion Science andTechnology, 181:2, 274-309, DOI: 10.1080/00102200802426364

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ANALYSIS OF MIXING AND THERMAL EFFECTSON LOW-TEMPERATURE COMBUSTION IN ICENGINE OPERATION

Youngchul Ra1, Rolf D. Reitz1, and Ramachandra Diwakar2

1Engine Research Center, University of Wisconsin-Madison, Madison,Wisconsin, USA2Powertrain Systems Research Laboratory, General Motors Researchand Development Center

The effects of thermal and mixing conditions of the in-cylinder charge in internal combustion

(IC) engines on emissions in low-temperature combustion (LTC) regimes are analyzed

numerically. In the analysis, concepts of an equilibrium temperature (Teq), peak

temperature (Tpeak), and anticipated emissions (AE) are introduced. Also, mixture

condition representations in temperature (T) vs. temperature (T) space (called T 2 T plot)

and anticipated emissions (AE) vs. temperature (T) space (called AE 2 T plot) are

proposed to represent the in-cylinder mixture quality and emission characteristics of the

combustion. Five combustion pathways are identified using a Tpeak 2 Teq plot, and it is

applied to describe both HCCI and DI engine combustion. An optimal temperature window

and an optimal mixing window are defined and demonstrated in LTC engine operation. The

results show that stratification of mixture temperature due to evaporation cooling and wall

heat transfer significantly affects UHC/CO emissions of LTC engine operation. The T 2 T

and AE 2 T plots reveal information about mixture inhomogeneity, completeness of burning

of local mixtures, anticipated levels of emissions, and optimal timing of mixing that can

maximize improvements in emissions. The new method of analysis is useful to identify and

understand the evolution of in-cylinder mixture conditions in engine combustion.

Keywords: Detailed chemistry; Emissions; Low-temperature combustion; Mixing; Thermal effect

INTRODUCTION

Conventional compression ignition (CI) engines operate on a diesel cycle byinjecting fuel directly into the cylinder near top dead center (TDC). The injected fuelis mostly burned with the air in the diffusion combustion mode, which creates a hightemperature flame where the air and fuel mixture meets in near stoichiometric propor-tions. The locally high temperature regions produce oxides of nitrogen (NOx), whichare later emitted during the exhaust stroke; the fuel-rich regions near the flame producesoot, which is partially oxidized; and the remainder is emitted during the exhaust stroke.

Received 3 June 2008; revised 7 August 2008; accepted 15 August 2008

The authors acknowledge the financial support from the General Motors-University of Wisconsin

Collaborative Research Laboratory.

Address correspondence to Youngchul Ra, Engine Research Center, 1500 Engineering Drive, ERB

#1016B, Madison, WI 53706. E-mail: yra@wisc.edu

274

Combust. Sci. and Tech., 181: 274–309, 2009

Copyright # Taylor & Francis Group, LLC

ISSN: 0010-2202 print/1563-521X online

DOI: 10.1080/00102200802426364

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In order to continue usage of compression ignition combustion under currentpollutant emission regulations, many steps must be taken to lower the NOx andPM emissions of IC engines. Most advanced combustion techniques utilize avariation of injection timing and ignition delay to lower combustion temperaturesand=or enhance mixing times and=or intensity. If the mixing is accelerated viaeither increased swirl or shortened injection duration (i.e., increased injectionvelocity), or if the chemical reaction is slowed down, auto-ignition can be madeto occur after the fuel and air are better mixed and soot levels can be reduced.NOx emissions can be reduced by reducing the combustion temperature byrunning under highly dilute conditions (lean or using high levels of exhaust gasrecirculation [EGR]).

One of the attractive strategies for lowering emissions is premixed charge com-pression ignition (PCCI) (Iwabuchi et al., 1999; Kanda et al., 2005; Opat et al.,2007). This strategy is typically achieved with the use of more advanced injectiontiming than for conventional diesel. The fuel is injected into the combustion bowlwith the objective of providing a fully vaporized mixture of fuel and air, which formsmixture conditions close to a homogeneous charge. With a very high EGR (>60%)as dilution, not only is the ignition delay of the charge mixture prolonged, but alsothe combustion temperatures are lowered. This combustion regime is referred to aslow-temperature combustion (LTC) (Akihama et al., 2001). The combustion is typi-cally realized at mixture compositions just lean of stoichiometric, as opposed to themuch leaner conventional CI. Although LTC operation is useful in the reduction ofNOx and PM emissions, its use in regimes meeting current NOx and PM regulationsbegins to elevate UHC and CO levels.

Another strategy is to use relatively retarded injection timings to increase theignition delay and to allow for pre-mixing (Kimura et al., 1999, 2001, 2002; Kriegeret al., 1997). When heat release occurs after TDC, the pressure rise rate can bereduced for a given maximum heat release rate, which enables engine operation athigher load. However, if the heat release timings are retarded too much, the combus-tion becomes unstable and the engine efficiency decreases.

Other types of combustion use an early small injection (pilot injection) with alate injection of more fuel to keep temperatures low (Hashizume et al., 1998, Neelyet al., 2005). This method is able to combine the merits of the strategies using earlyand retarded injection timings. The maximum heat release rate can be reduced byspreading out the heat release through multiple injections (Sun and Reitz, 2006).

The process responsible for the formation of NOx and soot can be most easilydescribed using equivalence ratio (U) vs. temperature (T) space shown in Figure 1. Inthe U�T plot, it is evident how the requirement to achieve lower equivalence ratiosusing thorough mixing and low temperatures can simultaneously reduce NOx andsoot. Conventional diesel combustion travels through the soot and NOx islands,while LTC, PCCI, and homogeneous charge compression ignition (HCCI) all nar-rowly avoid the formation of these emissions. The shape and location of these islandsis a function of the in-cylinder conditions particular to the operating point, but thegeneral behavior remains unchanged.

The use of this form of combustion is currently restricted to light loads basedon the low cylinder temperature and pressures that are necessary to maintain thedecreased NOx. As the current LTC limit is pushed further by going to higher loads,

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lower inlet oxygen levels are required, which can be achieved by using higher EGRratios. However, at these very low O2 levels, substantial fractions of CO and UHCbegin to form. The mechanisms affecting UHC=CO formation and destruction withparametric variation were studied by Kook et al. (2005, 2006) in an optically access-ible laboratory engine. Also, Opat et al. (2007) studied the UHC=CO emission char-acteristics of LTC extensively in a single-cylinder engine converted from aproduction engine. They revealed that an optimum operating condition, called thesweet spot, exists that corresponds to minimum CO emissions. It results from aninteraction between the injection spray jet and the piston bowl lip, leading to an opti-mal split between fuel entering the squish region and fuel entering the piston bowl.This optimal split provides the most effective use of the limited oxygen available byaccessing oxygen from both the bowl and the squish region to burn out CO, whichwould otherwise be unable to find sufficient oxygen. In the study, a CFD model wassuccessful in predicting the parametric behavior of the experiments quantitatively aswell as qualitatively.

With a well-reported validation of the numerical models built in the previousstudies (Opat et al., 2007), the numerical approach is further utilized in the presentstudy to investigate and analyze mixing and thermal effects under LTC operatingconditions. The sweet spot operating condition is chosen for the analysis. In orderto help the analysis, several variables are introduced and applied to engine operationin the LTC regime.

NUMERICAL APPROACH

Computational Conditions

The engine and injector simulated in this study are the same used by Opat et al.(2007). The operating conditions computed in the present study are for the sweetspot conditions of Opat et al. (2007) unless mentioned otherwise. In addition, a caseof conventional diesel combustion was considered to demonstrate the utility of the

Figure 1 Modern diesel combustion strategies plotted in U�T space (Neely et al., 2005).

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analysis method proposed in the present study. Detailed specifications of the engine,injector, and computed operating conditions are listed in Table 1.

Three-dimensional computational grids with the crevice volume resolved as anelongated top land region were employed. To save computation load, a 1=7th sectorof the full 360 degree mesh with periodic boundaries (corresponding to one plumefrom the seven-hole injector nozzle) was used. The average cell dimensions were1.2–1.8 mm and 0.6–4.1 mm in the radial and vertical directions, respectively. Twentycells were generated azimuthally. To resolve the crevice region, (i.e., the gap betweenthe piston and cylinder wall above the top ring), two radial cells were used along withthree vertical cells. The grid resolution was found to be fine enough to ensure the gridinsensitivity of the spray sub-models and combustion model employed in the presentstudy. The computational grid used in the present study is shown in Figure 2.

Numerical Sub-models

Computations were performed using the KIVA-3V Release 2 code (Amsden,1999) with an improved droplet vaporization model, which considers the droplettemperature range from flash-boiling conditions to normal evaporation (Ra andReitz, 2003, 2004). The improved model accounts for variable internal droplet tem-perature, and considers an unsteady internal heat flux with internal circulation, anda new model for the determination of the droplet surface temperature. The modeluses an effective heat transfer coefficient model for the heat flux from the surround-ing gas to the droplet surface. Also, the variable density of diesel fuel as a function oftemperature is considered in the governing equations and the relevant sub-models.

Table 1 Engine and injector specifications

Engine specification

Displacement [L] 0.4774

Bore�Stroke [mm] 82.0� 90.4

Compression ratio 16.6:1

Injector specification

Number of holes 7

Hole diameter [mm] 141

Included angle [�] 155

Injection pressure [bar] 860

Computational conditions

Engine speed [rev=min] 2000

Pressure @ IVC [bar] 1.62

Temperature @ IVC [K] 345

O2 @ IVC [%] 8.3,� 20.54y

Swirl ratio 2.2

Injection amount [mg=cycle] 15,� 20.4y

Actual start of injection [deg atdc] �28.2,� � 10.2y

Coolant temperature [�C] 90

Computation range [deg atdc] �132 (IVC)� 112 (IVO)

�Conditions for the sweet spot case of Opat et al. (2007).yConditions for the conventional diesel combustion simulation.

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A hybrid primary break-up model that is computationally effective as well ascomprehensive enough to account for the effects of aerodynamics, liquid propertiesand nozzle flows was employed (Beale and Reitz, 1999). In this model, the injectedfuel ‘‘blobs’’ are tracked by a Lagrangian method, while the break-up of each blob iscalculated from considerations of jet stability. For the secondary and further break-up processes, a Kelvin Helmholtz (KH) – Rayleigh Taylor (RT) hybrid model (Bealeand Reitz, 1999) was used.

A droplet collision model based on the stochastic particle method (Amsden,1999) was used, in which the collision frequency is used to calculate the probabilitythat a drop in one parcel will undergo a collision with a drop in another parcel,assuming all drops in each parcel behave in the same manner. The probability ofcoalescence is determined considering the Weber number, which includes the effectsof density and surface tension of the liquid droplets.

Droplet deformation in terms of its distortion from sphericity is modeled usinga forced, damped harmonic oscillator model, where the surface tension and viscosityof the droplet are the major properties used in the restoring force and dampingterms, respectively (Liu et al., 1993). Distortion of droplets affects the momentumchange between droplets and the ambient gas, and the subsequently drop velocities(or relative velocity between the drop and the gas) that are the governing parametersin the breakup and evaporation processes.

Effects associated with spray=wall interactions, including droplet splash, filmspreading due to impingement forces, and motion due to film inertia were consideredin a wall film sub-model, in addition to calculations of film transport on complexsurfaces with heating and vaporization of the film, and separation and re-entrain-ment of films at sharp corners (O’Rourke and Amsden, 1996).

In the two-phase transport equations, droplets are treated as point sources, andthe wall film fuel flow is not resolved on the computational grid. Therefore, it isassumed that in a computational cell where droplets or wall film parcels exist, theliquid vaporizes under the prevailing mixture conditions, and the vapor mixescompletely with the gaseous mixture within the cell. Thus, stratification of gaseousspecies within a single cell is not resolved.

Figure 2 Vertical cross-section view of the computational grid.

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For the turbulence calculation, the RNG k-e model (Han and Reitz, 1995) wasused. Wall functions obtained for simplified turbulence equations are used thatassume quasi-steady flow, fluid velocity that is directed parallel to a flat wall andvaries only in the direction normal to the wall, no streamwise pressure gradients,no chemical reactions, no spray sources, negligible dimensionless wall heat loss, largeReynolds numbers, and small Mach numbers (Amsden, 1999). The wall functionsare used to infer wall shear stresses and heat losses near walls.

Detailed chemistry was employed by coupling the KIVA-3V Release-2 codewith the Chemkin II library (Kee et al., 1989). A skeletal reaction mechanism forn-heptane fuel with 34 species and 74 reactions, which was further improved fromthe one developed by Patel et al. (2004), was used to calculate the detailed chemicalkinetics of fuel=air mixture burning. Various n-heptane mechanisms have beenwidely employed for diesel combustion calculations by many researchers becauseof its similar ignition characteristics to those of diesel fuel. While the n-heptanemechanism is used for reaction calculations in each cell, the physical properties ofthe fuel were represented with those of tetra-decane (C14H30) in the calculations ofspray processes and in gaseous species mixing. For the calculation of NOx forma-tion, a four-species (N, NO, N2O, and NO2) and nine-reaction NOx mechanismwas used that has been reduced from the GRI NOx mechanism (see http://www.me.berkeley.edu/gri_mech/) and added to the n-heptane reaction mechanism.

A phenomenological soot model (Kong et al., 2007) modified from theHiroyasu soot model (Hiroyasu and Kadota, 1979) was employed to predict sootemissions. In the modified model, acetylene (C2H2) is used as an inception speciesfor soot formation, which not only enables the soot model to be coupled with thedetailed chemistry calculation, but also improves the soot emission predictions.The soot oxidation rate was determined by the model by Nagle and StricklandConstable (1962).

Definition of Variables Used in Analysis

In order to help describe and analyze the thermal and mixing conditions in thecylinder, various gas temperatures and anticipated emissions are introduced. Fourdifferent gas temperatures are defined: gas temperature, Tg, burned gas temperature,Tb, equilibrium temperature, Teq, and anticipated peak temperature, Tpeak. Thesequantities are defined as follows:

. Gas temperature, Tg: temperature of the local gas mixture at the current time;

. Burned gas temperature, Tb: temperature of the gas mixture that is reached adia-batically through chemical reactions under constant volume from the currentmixture conditions;

. Equilibrium temperature, Teq: temperature of the gas mixture at the equilibriumstate corresponding to constant volume condition at the current mixture thermaland chemical conditions; and

. Anticipated peak temperature, Tpeak: the maximum temperature that the local gasmixture can reach though an adiabatic auto-ignition process that starts from thecurrent mixture conditions and proceeds along the rest of the volume change pro-file without mass exchange with neighboring gas mixtures.

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. Anticipated emissions, AE: emissions at the exhaust valve opening (EVO) time thatare calculated though an adiabatic auto-ignition process that starts from the cur-rent mixture conditions and proceeds along the rest of the volume change profilewithout mass exchange with neighboring gas mixtures.

The variables are described schematically on a typical gas temperature profile forHCCI operation in Figure 3. In order to obtain the temperature of the gas mixtureat the equilibrium state from the current conditions, two methods were considered:reaction progress calculation, and thermodynamic equilibrium calculation usingGibbs free energy minimization. Using the same chemistry mechanism (the presentn-heptane oxidation mechanism) employed in the combustion calculation, combus-tion of the local mixture was calculated assuming an adiabatic homogeneous com-pression ignition process until the burned mixture state reached equilibrium (i.e.,assuming that sufficient time was available for reactions to complete). The equilib-rium state is assumed to be reached when the gas temperature change becomes lessthan 0.01% after ignition occurs. Note, however, that the gas temperature may bestill changing at the calculated equilibrium point. Thus, the eventual equilibriumtemperature through reaction progress, which is expected to be identical to the ther-modynamic equilibrium temperature, may differ from the calculated equilibriumtemperature. The final thermodynamic equilibrium state was also calculated basedon Gibbs free energy minimization. The method developed by Pope (2003a,2003b) was used to find equilibrium gas temperature. The same species and thermo-dynamic data as those used in the reaction progress calculation were used.

In Figure 4, the equilibrium temperatures obtained using both methods arecompared for various initial temperatures and mixture compositions. The valuesobtained from thermodynamic equilibrium calculation may differ slightly from those

Figure 3 Gas temperatures defined in the present study. Dash-dotted line indicates the equilibrium tem-

perature, Teq; solid line indicates the gas temperature; and dash-double dotted line shows gas temperatures

at motoring conditions. The maximum value of Tg profile is defined as peak temperature, Tpeak, shown as

a dotted line.

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from the reaction progress calculation due to the error coupled with convergence cri-terion, as mentioned above. Another reason for the difference of the two equilibriumtemperatures is that the equilibrium constants for a certain reaction considered in thechemical reaction mechanism may differ from the thermodynamic equilibrium con-stants when the reaction rate constants for its reverse reaction are specified in themechanism. However, as expected, the computation time of the thermodynamicequilibrium calculation is tremendously shorter than that of the reaction progresscalculation. Due to this fact, the burned gas temperature of the local mixture wasapproximated with the thermodynamic equilibrium temperature, which is used inthe analysis in the present study.

RESULTS

Baseline Operating Condition

Figure 5 shows the sweet spot behavior of the CO and the variation of peakliquid fuel amounts found in the bowl and squish regions with injection timing vari-ation taken from Opat et al. (2007). The CO behavior exhibits a decrease as a start ofinjection command (SOIC) is advanced to earlier timings. After crossing a timingwith a minimum in CO, which is called the sweet spot (dashed line), there is aturn-up in the CO behavior. Both the peak heat release rate and ignition delaydecrease gradually with retarding injection timings from the earliest timing (Opatet al., 2007).

When the injection timing is retarded from the earliest case, the targeting pointof the spray at the start of injection moves from the piston top and squish region toenter the piston bowl. Because a large amount of the injected spray impinges on thepiston surface and is split into two parts, liquid fuel entering the squish region and

Figure 4 Comparison of equilibrium temperatures obtained from calculations of reaction progress and

thermodynamic equilibrium for various initial mixture temperatures and equivalence ratios.

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liquid fuel entering the piston bowl, the distribution of vapor fuel available for mix-ing in each region is expected to vary, depending on the injection timing. As can beseen in Figure 5B, the peak amount of liquid fuel entering the squish region increaseswhen the injection timing is advanced from the latest injection timing (SOIC¼�23degree after-top-dead-center (deg atdc)). For the sweet spot timing, an optimalamount of injected fuel is found in the squish region. Although the airflows inducedby the spray injection and by the squish flow both affect the mixing of the fuel andair significantly, the distribution of liquid droplets and wall film fuel still dominantlyinfluences the local mixture condition and determines the extent of utilization of airin each region for the subsequent ignition and combustion process.

UHC emissions also show similar trends to CO emissions and minima locationswith injection timing variation (Opat et al., 2007). Due to the fact that the CO must beformed from UHC through partial oxidation, an increase in CO magnitude is expectedwhen excess UHC begins to form. However, this does not mean that low UHCindicates high CO, because the CO oxidation occurs later in the combustion process.Similarly, increases in CO need not correlate to increases in UHC.

Effect of IVC Gas Temperature

For a homogeneous charge, the in-cylinder gas temperature at intake valveclosure (IVC) governs the ignition timing and subsequently affects the engine-outemissions. In order to estimate a favorable temperature window for the oxidationof UHC and CO in the cylinder, HCCI combustion was simulated for various gastemperatures at IVC with heat transfer between the gas and the cylinder walls con-sidered. The predicted profiles of pressure and emissions are shown in Figure 6.When the IVC temperature is higher than about 350 K, the UHC and CO emissionsdrop rapidly and are maintained at very low levels for higher IVC temperatures.Because the overall equivalence ratio of the charge is lean (phi¼ 0.64), the enhancedoxidation reactions with increasing gas temperature reduce both UHC and CO

Figure 5 Minimum emission behavior for a single injection timing sweep (Opat et al., 2007). (A) compari-

son of CO emissions between predicted and measured values. (B) CFD computed profiles of variation of

peak mass of liquid fuel in the bowl and squish regions. Note that for a given SOIC, the timing of

maximum liquid amount in each region may not be the same; thus, the curves do not total 100%.

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emissions. For the case with gas temperature of 354 K at IVC, the peak average andlocal maximum gas temperatures during the compression and expansion strokeswere 1472 and 1687 K, respectively. On the contrary, as the gas temperature atIVC decreases below 350 K, the combustion of charge mixture becomes more incom-plete, and the UHC and CO emissions increase substantially. It is interesting that therelative increase of CO emissions in the range between 298 and 345 K was predictedto be much lower than the increase of UHC emissions for the same temperaturerange. This is because the formation of CO from hydrocarbon species becomes lessactive at very low temperatures. For all the temperature variations considered in thepresent study, the soot and NOx emissions were predicted to be negligibly low, asshown in Figure 6B.

Operation with spray injection was also simulated for various IVC gas tem-peratures. In order to maintain a constant overall equivalence ratio of the chargemixture (the amount of injected fuel was fixed as 15 mg=cycle), the gas pressure atIVC was adjusted accordingly. Injection timings were fixed at the sweet spot timingof �32 deg atdc for all of the cases considered in the study. As shown in Figure 7,the effects of IVC gas temperature on engine-out UHC=CO variations have similartrends to those in the HCCI cases. However, the amount of variation in the CO emis-sions is much smaller than in the HCCI cases for IVC temperature higher than350 K. For IVC temperatures higher than 400 K, the CO emissions of spray injectioncases are more than one order of magnitude higher than in the corresponding HCCIcases. This indicates that the effects of IVC gas temperature variation are not as sig-nificant as in the HCCI cases. This is attributed to thermal and mixture preparationeffects.

When a spray is injected into the combustion chamber, evaporation of spraydroplets lowers the temperature of the local gas mixture surrounding the droplets.The decrease of local gas temperature by evaporation cooling is increased in fuel-richregions where more fuel vapor is available. In Figure 8, the distributions of gas tem-perature and fuel mass fraction in the plane of the spray at two different crank angles

Figure 6 Effects of gas temperature at the time of intake valve closure in HCCI engine operation.

Comparisons of (A) pressure profiles, (B) UHC, CO, soot, and NOx emissions.

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Figure 7 Effects of gas temperature at the time of intake valve closure on DI combustion. Comparisons of

(A) pressure profiles and (B) UHC and CO emissions. The gas temperature at IVC for the sweet spot

timing case was 345 K.

Figure 8 Distributions of gas temperature and fuel mass fraction in the plane of the spray axis for two

different IVC gas temperature conditions. Non-reacting spray injections were simulated. Iso-contours

of temperature and fuel mass fraction are also plotted. (A) Temperature distribution for Tivc¼ 345 K;

(B) fuel mass fraction distribution for Tivc¼ 345 K; (C) temperature distribution for Tivc¼ 450 K; and

(D) fuel mass fraction distribution for Tivc¼ 450 K.

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are shown for two different IVC gas temperatures. In order to examine the thermalcooling effect alone, non-reacting spray injections were simulated. The differencesbetween the average gas temperatures of the case with injection from those of themotoring case, and the local maximum and minimum gas temperatures in the bowland squish areas, are listed in Table 2.

As the IVC gas temperature increases, the decrease of the local gas temperaturethrough the evaporation process increases due to the enhanced evaporation. Thus,the stratification of the temperature field (difference of local maximum and mini-mum temperatures) caused by spray evaporation is increased. This reduces the posi-tive effects of the increased IVC gas temperature in the spray injection cases, and theresulting emissions become less sensitive to IVC gas temperature.

Effect of Wall Heat Transfer

In order to investigate the effects of heat transfer between the in-cylinder gasesand the cylinder walls, simulations were performed for both HCCI and spray com-bustion with adiabatic wall boundary conditions. The effects of radiation heat trans-fer were assumed to be negligible considering the low-temperature combustion.Figure 9 shows predicted pressure, heat release rate, and UHC=CO emissions pro-files obtained for the IVC conditions of the sweet spot case of Opat et al. (2007).

The effects of wall heat transfer are apparently seen from the difference ofpressure and temperature profiles of the HCCI cases between adiabatic and non-adiabatic wall boundary conditions, as shown in Figures 9A and 9B. In the adiabaticcase, there was a second peak in heat release rate curve that corresponds to theincrease of gas pressure and temperature seen near 10 deg atdc. This second peakof the heat release rate curve results from the rapid conversion of the accumulatedCO to CO2, as shown in Figure 9C. On the contrary, the non-adiabatic case showsslow oxidation of CO after TDC. The temperature differences at the time of firstignition (��10.5 deg atdc) and TDC between the adiabatic and non-adiabatic HCCIcases were calculated to be 18 and 112 K, respectively. Therefore, the relatively smallchange in temperature due to wall heat transfer significantly affects the engine-outemissions. From further investigation, it was found that the temperature aboutwhich the in-cylinder CO is rapidly consumed in the cylinder was about 1400 K.When the IVC mixture conditions are such that the maximum gas temperaturereaches this threshold, the engine-out UHC=CO emissions become very sensitiveto the wall heat transfer conditions.

In the spray injection cases, however, the effects of wall heat transfer are muchless than the corresponding HCCI cases. Although the peak cylinder pressure and

Table 2 Temperature decrease by spray injections

Tivc¼ 345 K Tivc¼ 450 K

CA¼�10 deg atdc CA¼TDC CA¼�10 deg atdc CA¼TDC

Tavg�Tmot [K] �28 �33.6 �40.9 �46.8

Tmax�Tavg [K] þ31 þ6 þ61 þ21

Tmin�Tavg [K] �82 �121 �125 �168

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average gas temperature increase significantly under the adiabatic condition, thereduction of UHC and CO is not as much as in the HCCI case. Because spray injec-tions cause the stratification of the fuel, plus the fact that it is more probable that gasmixtures near the cylinder walls are fuel-deficient (except for spray-impingingregions), the charge temperature decrease by wall heat loss is minimized. Therefore,the low temperature combustion emissions with spray injection are less sensitive tothe wall temperature boundary conditions. A comparison of pressure, average gastemperature, and UHC=CO emissions of DI and HCCI combustion under adiabaticand non-adiabatic wall boundary conditions is also shown in Figure 9.

Effects of Mixing

U 2 T Plot analysis. When the equilibrium temperature, Teq, and the peaktemperature, Tpeak, are used in a U�T plot, useful information about the mixtureconditions in the cylinder can be obtained. In Figure 10, the local equivalence ratioU based on the amount of reactants (including all species that contain carbon and

Figure 9 Effects of wall heat transfer on emissions. Comparison of profiles of (A) in-cylinder gas pressure;

(B) average in-cylinder gas temperature; (C) in-cylinder CO; and (D) in-cylinder UHC.

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hydrogen atoms) and oxygen was plotted with respect to local mixture temperature,equilibrium temperature, and anticipated peak temperature for the spray injectionsweet spot case of Opat et al. (2007) just before the first ignition. The local mixturetemperatures are governed by the evaporation process before the time of ignition, asdescribed in the previous section. Therefore, rich mixtures generally have lower tem-peratures than lean mixtures in U�Tg plot, as shown in Figure 10A. When the cor-responding equilibrium temperature is plotted, the in-cylinder charge conditions areseen to be distributed within two narrow regions that branch from the maximumequilibrium temperature stoichiometric point. Each branch of the distribution repre-sents the adiabatic flame temperature for lean or rich mixtures, which represents thethermodynamic state that could be reached regardless of time available for chemicalreactions. Therefore, the extent of mixing (or stratification) in the temperature andfuel concentration fields can be estimated from the ranges of equilibrium tempera-ture and equivalence ratio.

The peak temperature shown in Figure 10C includes the effect of engine oper-ating conditions such as engine speed, compression ratio, etc., and now accounts for

Figure 10 Analysis of in-cylinder mixture conditions using U�T plot. (A) U�Tg; (B) U�Teq; and (C)

U�Tpeak at �13 deg atdc, which is just before the first ignition (cool flame) occurs.

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the time available for chemical reactions during the cycle. As in the U�Teq plot, thein-cylinder mixture conditions are distributed in branch-like regions, though the dis-tributions of lean and rich mixtures are somewhat thicker than those on the U�Teq

plot. Extremely rich mixtures have long ignition delay times, and their anticipatedpeak temperatures are thus predicted to be very low. This is seen from the pointslocated on the rich side near Teq¼ 700 in Figure 10C. Note that the mixtures in thisregion contain chemical energy to be released; thus, the corresponding equilibriumtemperatures are about 1170 K in the U�Teq plot (see Figure 10B). Extremely leanmixtures are also located at low Tpeak. Therefore, the U�Tpeak plot reveals chargemixtures that may contribute to engine-out emissions significantly.

T 2 T Plot Analysis. Together with U�T plots, T�T plots using Tg, Teq, andTpeak are useful in the analysis of the in-cylinder conditions. Three combinations areshown in Figure 11 for the in-cylinder mixture distribution at the same crank angleof � 13 deg atdc of Figure 10 (just before the first ignition). Note that each numeri-cal cell is represented as a point, without considering the mass or volume of the cell

Figure 11 Analysis of in-cylinder mixture conditions using T�T plots. (A) Teq�Tg; (B) Tpeak�Tg; and

(C) Tpeak�Teq at � 13 deg atdc, which is just before the first ignition (cool flame) occurs.

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in both figures. As described above, from the range of the current gas temperature,Tg, the extent of stratification of the temperature distribution in the cylinder isrevealed, while the range of equilibrium temperature, Teq, indicates the mixture com-position distribution in the cylinder. The range of peak temperature, Tpeak, isanother indicator of mixture composition distribution, which includes the effectsof the engine operating condition, as the time available for reaction is accountedfor. Note that the range of Tpeak does not necessarily include the range of Teq.For example, when a rich charge mixture cannot burn within the time remainingin the cycle, the peak temperature of the charge mixture is expected to be close toits temperature at TDC, while its equilibrium temperature may be much higher thanthe peak temperature. This is clearly seen in the mixtures located at the end of therich branch in Figure 11B. As explained above, the local temperatures of rich mix-tures are located at the lower end of the range, while the lean mixtures are located athigher temperatures.

When the peak and equilibrium temperatures are plotted together, the in-cylinder mixture conditions are represented as two narrow strips, one each for the richand lean mixtures. When the mixture is lean enough, the ignition delay may be longerthan the available time, and the anticipated peak temperature of the mixture is likelyto be lower than the equilibrium temperature. A similar argument can be made fortoo rich mixtures. On the contrary, when the mixture is expected to ignite and releasethe available chemical energy completely, the anticipated peak temperature of themixture is predicted to approach the Tpeak¼Teq line (dotted 45� line in Figure 11C)during the combustion process. Note that if the mixtures ignite before TDC, the peaktemperatures of the mixtures are likely to be higher than corresponding equilibriumtemperatures due to the further compression of the ignited mixtures from the ignitionpoint to TDC. Therefore, these mixtures are located on the left-hand side of theTpeak¼Teq line. For crank angles after TDC, with HCCI-like combustion, the antici-pated peak temperatures of already ignited mixtures may be close to their equilibriumtemperatures; thus, both the peak and equilibrium temperatures decrease as crankangle proceeds. Therefore, based on the current mixture conditions, the Tpeak�Teq

plot not only indicates how incomplete the combustion of the in-cylinder mixture couldbe, but also how early before TDC the in-cylinder mixture ignites and is further com-pressed. The incompleteness of combustion at each local condition can be estimatedby the horizontal distance from the Tpeak¼Teq line, and the extent of compressionafter ignition can be estimated from the vertical distance from the Tpeak¼Teq line.

The Tpeak�Teq analysis was applied to simulation of adiabatic HCCI engineoperation. A characteristic path is demonstrated in Figure 12. The initially uniformmixture pressure and temperature at IVC were the same as in the correspondingspray injection case for the minimum CO injection timing of Opat et al. (2007).The overall equivalence ratio was 0.3, and 5% internal EGR was considered inthe initial mixture composition at IVC (equivalent to 20.4% oxygen mole fractionin the initial composition). The pressure and heat release profiles are shown in Figure12A. Main ignition was predicted to occur around �10 deg atdc. These operatingconditions correspond to path-B shown in Figure 13B, which will be described later.The Tpeak�Teq plots of the in-cylinder charge mixtures at various crank angles areshown in Figures 12B and 12C. The arrows in the figures indicate the direction ofincreasing crank angle (time).

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Before the time of ignition, Tpeak of the mixture is higher than the correspond-ing Teq of the mixture, as the burned gas undergoes additional compression. As thecrank angle proceeds, the points in the Tpeak�Teq plot move toward the Tpeak¼Teq

line while Tpeak is maintained constant. The points that represent the in-cylinder mix-ture align on the Tpeak¼Teq line after ignition and move along the Tpeak¼Teq lineduring the expansion stroke, as shown in Figures 12B and 12C, which means that thechemical energy of the mixture has been completely released.

Although the mixture conditions were assumed to be uniform over the entirecylinder region both in temperature and composition at IVC, it is seen that local mix-ture conditions deviate from a uniform distribution during the later stages of thecompression stroke due to the slight gradient of local gas temperature induced bythe piston motion. This results in a slight spread of the points at each crank angleshown, instead of a single point in the Tpeak�Teq plot. The spread of the pointsincreases with crank angle and becomes maximal at a certain time after ignition(e.g., see �4 deg atdc). This increase of spread is due to heat transfer from the hot

Figure 12 Analysis of in-cylinder mixture conditions in HCCI combustion. (A) Profiles of average cylinder

gas pressure and heat release rate. (B, C) Distribution of mixture conditions on Tpeak�Teq plot for various

crank angles. The mixture temperature and pressure at IVC are the same as in the minimum CO emission

point of Opat et al. (2007). Uniform mixture composition at IVC was equal to the overall equivalence of

the spray injection case.

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gases to the cold gases. The gases that received heat from hotter gases also ignitebefore TDC, and their Tpeak becomes higher than those obtained based on the initialcondition. At the same time, Tpeak values of mixtures that lose heat to colder gasesare decreased. However, after all of the gas in the cylinder ignites, mixing of theburned gases reduces the range of differences in temperature and species compositionof the in-cylinder gas. Therefore, the spread of points in the Tpeak�Teq plotdecreases again, as seen at TDC in Figure 12B.

In order to describe variations of the mixture condition in the cylinder on theTpeak�Teq plot, HCCI combustion paths are depicted in Figure 13. Figure 13Ashows five categories of pathways that can be considered in HCCI combustion.Among the five cases, case A is not possible because the peak gas temperature shouldbecome equal to the equilibrium gas temperature at some point in HCCI operation,according to the definition of peak gas temperature. Case E corresponds to the com-pression and expansion process of a mixture that does not contain fuel (motoring).Because no chemical energy is released, the profiles of current gas temperature, Tg,and the equilibrium gas temperature, Teq, are the same, which also fall on the tem-perature profile of the motoring process, as shown in Figure 13F.

Note that in case E, the anticipated peak gas temperature during the com-pression process is equal to the gas temperature at TDC; thus, the peak gas tempera-ture starts from the TDC gas temperature and follows the profile of current gastemperature during the expansion stroke. In the figure, the shaded area indicatesthe region that the mixture cannot reach during the process, the boundary of whichis determined by the pathway of case E.

Case B represents the HCCI process where ignition occurs before or at TDC,as shown in Figures 13B and 13C. Because the mixture releases chemical energy, theequilibrium gas temperature, Teq, is higher than the current gas temperature, Tg, andit increases during the compression stroke until the mixture ignites. When the currentmixture is at a condition where ignition is expected to occur after TDC, the equilib-rium temperature can exceed the anticipated peak temperature before the time ofignition. Therefore, the mixture condition point crosses the Tpeak¼Teq line andextends to the right half region of the Tpeak¼Teq line, reaching the highest equilib-rium temperature at TDC. Then, the pathway moves back toward the Tpeak¼Teq

line to approach the line when ignition occurs during the expansion stroke. Thispathway is shown in Figure 13D. If the mixture is so lean (or rich) that it burns par-tially and the burned gas temperature does not exceed the TDC gas temperature, theanticipated peak temperature becomes the TDC gas temperature until TDC. Then,Tpeak decreases during the expansion stroke while Teq remains higher than Tpeak dueto the unreleased chemical energy, as shown in Figure 13E.

Therefore, the location of the mixture conditions on Tpeak�Teq plot indicatehow incomplete the combustion of the local mixture is anticipated to be through aHCCI combustion process; it can be estimated qualitatively by the horizontal dis-tance from the Tpeak¼Teq line to the location of the mixture condition. It is alsonotable that the anticipated peak temperature reflects the local equivalence ratioof the mixture by comparing with case E; the closer the mixture equivalence ratiois to stoichiometry, the higher the anticipated peak temperature. Applying thisanalysis to the in-cylinder mixtures shown in Figure 11C, a few things can now bepointed out. The homogeneity of the mixtures can be estimated from the range of

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Figure 13 Adiabatic HCCI combustion paths for analysis of in-cylinder conditions using the Tpeak�Teq

plot. (A) Five pathway categories; (B) temperature profiles and pathway of case B with ignition occurring

before TDC; (C) temperature profiles and pathway of case B with ignition occurring at TDC; (D) tempera-

ture profiles and pathway of case C with ignition occurring after TDC; (E) temperature profiles and path-

way of case D with ignition occurring after TDC; (F) temperature profiles and pathway of case E with no

fuel. For case E, the equilibrium gas temperature is equal to gas temperature, and the shaded area indicates

the region that the gas mixture condition cannot reach in HCCI operation.

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Tpeak; the mixtures are seen to be distributed in a wide range of equivalence ratio.There is a significant portion of the local mixture that is located in the right halfregion of the Tpeak¼Teq line; those mixtures potentially contribute to incompletecombustion. The points that are located in the region on the right-hand side ofthe Tpeak¼Teq line are mainly lean mixtures; UHC=CO emissions will be attributedto the partial combustion of those lean mixtures.

AE 2 T Plot analysis. When the anticipated emissions (AE) are plotted withrespect to average gas temperature, equilibrium, and peak temperatures, further use-ful information about the combustion process can be obtained. Figure 14 shows CO-temperature plots for the spray injection case. These plots were obtained using thein-cylinder mixture conditions at the time of cool flame combustion (�13 deg atdc)for the operating conditions of the spray injection minimum CO emission point. Theemissions are plotted on the basis of gram per unit gram of mixture. Three things arerevealed in this plot:

Figure 14 Analysis of anticipated CO emissions of in-cylinder charge at the time of first ignition (�13 deg

atdc). (A) Anticipated CO emissions vs. gas temperature, Tg; (B) anticipated CO emissions vs. equilibrium

temperature, Teq; and (C) anticipated CO emissions vs. peak temperature, Tpeak. The boxes in the figures

indicate the range of optimal temperature window.

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1. an estimation of the overall CO emissions, based on the current mixture con-ditions;

2. how the current mixture composition could potentially contribute to the COemissions; and

3. how the mixture quality can be improved from the current condition to reduceemissions.

First, it should be noted that, depending on the choice of temperature to plot, theshapes of the AE distributions can be significantly different. When the anticipatedCO emissions are plotted with Teq, the points that represent the conditions of themixture show a narrow-banded distribution, and the temperature ranges needed tominimize the anticipated CO emissions (or engine-out emissions) are clearly seen,as indicated by the box shown in Figure 14B. A similar shape of distribution is seenwhen the anticipated CO is plotted using Tpeak, as shown in Figure 14C. Tpeak higherthan 1400 K is seen to produce extremely low CO emissions, which can be defined asthe optimal temperature window in the anticipated CO�Tpeak plot. The corre-sponding temperature window in the anticipated CO�Teq plot is 1570 K and higher.Among the temperatures, Tpeak is considered to be the most informative; thus,AE�Tpeak is used in the analysis hereafter.

The maximum level of CO emissions that the current mixture conditions canpossibly reach can be roughly obtained from the maximum anticipated emissionvalue seen in the figures. Mixtures corresponding to the points beyond the optimaltemperature window are expected to significantly contribute to the overall engine-out CO emissions. Therefore, any possible ways to move these mixtures towardthe mixture conditions that fall within the optimal temperature window are expectedto be effective in the reduction of the engine-out CO emissions. Note that the currentAE�T plot does not consider the actual mixture mass that is represented by eachpoint in the plot, which makes it impossible to directly visualize quantitativeengine-out emissions from the plot.

It is interesting that the lean and rich mixtures are aligned on clearly differen-tiated branches of the distribution line that starts from the attainable maximum Teq

or Tpeak, based on the current charge mixture conditions. On the contrary, it is quitedifficult to distinguish the AE branches that result from lean and rich mixtures in theAE�Tg plot. It is clearly seen that the rich mixtures have a dominant contributionto the CO emissions. It is also notable that charge originating in the crevice regionare grouped in the plots due to their relatively similar thermal and composition con-ditions. Because the mixture in the crevice region is strongly affected by the heattransfer through the cylinder walls, the range of Tg and Tpeak of the mixtures is rela-tively low and thus is located near the lowest Tg=Tpeak values in the plots. In theAE�Teq plot, however, the crevice region is spread over a wider temperature range.This is due to the fact that the Teq of the mixture is governed by the mixture com-position as well as the current temperature, Tg, regardless of the time needed to reachthe equilibrium state.

In Figure 15, the anticipated UHC, soot and NOx emissions are plotted withrespect to Tpeak for the same conditions as in Figure 14. In all three figures (Figures15A–15C), the branches that correspond to lean and rich mixtures are clearly seen.As can be expected, the dominant contribution to UHC emissions by rich mixtures is

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seen (see Figure 15A). It is interesting that the effects of the crevice gas on UHCemissions can be easily seen from the UHC�Tpeak plot. The points are distributedvertically at Tpeak� 700 K.

As expected, soot emission is mostly produced by rich mixtures, as shown inFigure 15B. The figure also gives information about the contribution of the effectof temperature as well as the maximum level of soot emissions that the current mix-ture conditions can reach. On the contrary, lean mixtures contribute more to theNOx emissions, as shown in Figure 15C. However, for temperatures higher than1900 K, the anticipated NOx emissions increase rapidly for all mixtures. (The non-zero NOx at temperatures much lower than the NOx-forming temperature thresholdreflects the initial amount in the charge at IVC from the EGR.) Because the simu-lated operating condition (i.e., LTC) was engineered for low soot and NOx emis-sions, the anticipated levels of soot and NOx emissions are substantially lowcompared to conventional diesel combustion conditions. As noted above, similar

Figure 15 AE�Tpeak plots of anticipated UHC, soot, and NOx emissions of in-cylinder charge at the time

of first ignition (�13 deg atdc). (A) Anticipated UHC emissions; (B) anticipated soot emissions; and (C)

anticipated NOx emissions. The box in the UHC�Tpeak plot indicates the range of optimal temperature

window.

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plots can be obtained for UHC, soot, and NOx emissions with AE�Teq plots (notshown).

The AE�T analysis was also applied to time-varying mixture conditions. Theplotted crank angles are indicated in pressure profile shown in Figure 16. Based onthe pressure and heat release rate profile, eight crank angles were selected that rep-resent characteristic timings of the combustion: end of injection, start of cool flamecombustion, start of main ignition, TDC, peak cylinder gas pressure location, 89%heat release point, 96% heat release point, and 99% heat release point.

Figure 17 shows CO�Tpeak plots for the various crank angles. Before the mainignition timing, the mixture states are represented by two distinct narrow brancheson the plot, as shown in Figures 17A and 17B (also see Figure 14C). When the mainignition occurs, the distribution starts becoming thicker, especially in the rich mix-ture branch of the plot (see Figure 17C). In the meantime, the maximum anticipatedCO level decreases as more mixing of fuel=air proceeds. After the main ignition tim-ing, the burned gases mix with unburned or combusting gases, and thus the pointsare spread over a wider area. At the same time, the maximum Tpeak decreases asthe piston moves down after TDC. Note that, by definition, Tpeak of gases thatare already ignited becomes equal to the gas temperature, Tg. At the time of 99%heat release, it is seen that there still remains a significant extent of stratificationin the mixture temperatures and composition, although the in-cylinder gases are suf-ficiently mixed so that the anticipated CO points are distributed over a much nar-rower range than those at previous crank angles, and no distinct line-like branchesare seen (see Figure 17H). As the crank angle further proceeds, the reactivity ofthe mixtures decreases, and the distribution changes on the CO�Tpeak plot aremainly affected by the mixing process.

Similar variations are also seen in the anticipated UHC�Tpeak plot, as shownin Figure 18. Before the main ignition, the anticipated UHC emissions formed fromthe charge in the crevice regions are clearly seen at Tpeak¼�700 K. The anticipatedUHC values of these points decrease as crank angle proceeds and disappear at thetime of main ignition (see Figure 18C). This indicates that the conditions of the

Figure 16 Cylinder pressure and heat release rate reference points.

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Figure 17 Anticipated CO�Tpeak plots for various crank angles. (A) After the end of injection (�16 deg

atdc); (B) start of first ignition (�13.5 deg atdc); (C) start of main ignition (�5 deg atdc); (D) TDC; (E)

peak pressure point (þ6 deg atdc); (F) 89% heat release point (þ12 deg atdc); (G) 96% heat release point

(þ20 deg atdc); and (H) 99% heat release point (þ40 deg atdc).

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Figure 18 Anticipated UHC�Tpeak plots for various crank angles. (A) End of injection (�16 deg atdc);

(B) start of first ignition (�13.5 deg atdc); (C) start of main ignition (�5 deg atdc); (D) TDC; (E) peak

pressure point (þ6 deg atdc); (F) 89% heat release point (þ12 deg atdc); (G) 96% heat release point

(þ20 deg atdc); and (H) 99% heat release point (þ40 deg atdc).

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charge in the crevice region were changed by the gas flow from the main combustionchamber at the time of main ignition such that reactions occur to burn the availablefuel. It is notable that no group of points is seen in the corresponding UHC�Tpeak

plot (see Figure 17C). Therefore, the UHC in the crevice regions is expected to com-bust to final products such as H2O and CO2. Again, the lean and rich branches of theanticipated UHC distribution become thicker with crank angle and the anticipatedvalues of lean and rich mixtures become comparable, as can be seen in Figure 18H.

In Figure 19, the corresponding variation of Tpeak�Teq is shown for the eightcrank angles. It is seen at the end of injection (see Figure 19A) that a significant por-tion of both the lean or rich mixtures deviates from the Tpeak¼Teq line and arebeyond the optimal temperature window (Tpeak> 1400), which indicates that thosemixtures are likely to result in incomplete combustion. As time proceeds, the pointsbecome more aligned on the Tpeak¼Teq line, as can be seen by the time of 89% heatrelease in Figure 19F, but there are still a large number of points beyond the optimaltemperature window. Note that the proportion of lean mixture increases with crankangle due to the dilution of the rich mixture. From Figure 19H, it can be seen that asignificant amount of the charge will follow the path-D shown in Figure 12E.

Analysis of in-cylinder mixture conditions of the sweet spot operating con-dition using T�T and AE�T plots has been described. It is of interest to explorehow alteration of charge conditions during the combustion process can improvethe engine-out emissions. Methods to achieve enhancement of in-cylinder mixinghave been suggested by several researchers, such as the injection of air into combus-tion chamber (Kurtz and Foster, 2004) and valve actuation control (Reitz et al.,2004). The present analysis is useful to indicate optimal timings of alteration. Asan indication of the potential, sudden perfect mixing of the entire in-cylinder gascontents at specified time was considered. Together with the anticipated emissionsbased on the current mixture stratification condition (baseline case), the utility ofoptimal mixings can thus be assessed.

In the sudden mixing case, the combustion calculation was the same as in thebaseline case until a selected time for mixing. Therefore, the T�T and AE�T plotanalysis shown in Figures 16–19 is valid until the time of sudden mixing. At the timeof mixing, the entire in-cylinder is assumed to be perfectly mixed and homogeneousin both the temperature and fuel concentration fields. Then the computation is con-tinued for the newly homogeneous charge. Therefore, after the occurrence of suddenmixing, the T�T and AE�T plots become similar to those for the homogeneouscharge case shown in Figure 13. Liquid fuel existing at the time of mixing is keptin its current location and undergoes evaporation and combustion processes underthe altered ambient gas conditions.

Figure 20 shows a comparison of the variation of the total anticipated CO andUHC emissions at EVO when the mixing occurs at the specified crank-angle. Mix-ture modification was made at nine different crank angles (i.e., including at 30 degatdc in addition to the eight crank angles shown in Figure 16). For example, thebaseline anticipated CO emissions at TDC is about 648 g=kg-f (X at TDC in Figure20A). When the in-cylinder mixture is perfectly mixed with complete instantaneousmixing of the chamber gas occurring at TDC, the resulting anticipated CO emissionsare predicted to be about 814 g=kg-f (square). In the baseline case, the variation ofanticipated CO emissions for various mixing times indicates how the evolution of

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Figure 19 Tpeak�Teq plots for various crank angles. (A) End of injection (�16 deg atdc); (B) start of first

ignition (�13.5 deg atdc); (C) start of main ignition (�5 deg atdc); (D) TDC; (E) peak pressure point (þ6

deg atdc); (F) 89% heat release point (þ12 deg atdc); (G) 96% heat release point (þ20 deg atdc); and

(H) 99% heat release point (þ40 deg atdc).

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mixture stratification affects the anticipated emissions, while the mixing case showshow much the engine-out emissions could be improved and when the effective timesare to arrange enhanced mixing to reduce the engine-out emissions.

It is interesting to note that perfect mixing of the in-cylinder charge duringthe combustion can improve or deteriorate the engine-out emissions, dependingon the timing of mixing. When the mixing of the in-cylinder gas occurs beforeor at TDC, the anticipated CO emissions are significantly increased. On the con-trary, the anticipated CO emissions decrease substantially when the mixing occursat the time of the peak cylinder pressure (6 deg atdc) or at the 89% heat releasetime (12 deg atdc). The anticipated CO emissions increase again as the mixing isretarded further (e.g., later than 12 deg atdc) and approach the predicted level ofthe baseline engine-out CO emissions. In fact, the anticipated CO emission at þ40deg atdc is very close to the predicted engine-out CO of the baseline case, whichis 357 g=kg-f.

A similar argument can be made for the UHC emissions, though perfect mixingis predicted to improve the UHC emissions compared to the baseline case when themixing time occurs between the end of injection and the time of main ignition. Notethat, however, the level of the anticipated UHC emissions of the perfect mixing casein this period is much higher than the predicted engine-out UHC emissions.

The above results indicate that there is a range of optimal times to applyimproved mixing to reduce engine-out CO and UHC emissions by enhancing themixture homogeneity. The existence of this optimal time of mixing (i.e., optimal mix-ing window) can be explained by examining the variation of Tpeak. In Figure 20B,Tpeak of the in-cylinder charge in the mixing case is plotted together with the pre-dicted average and local maximum temperatures of the baseline case. In the figure,Tpeak of the homogeneous charge becomes greater than 1400 K (lower bound ofthe optimal temperature window in AE�Tpeak plot) when mixing occurs at

Figure 20 Effect of sudden complete mixing of the charge at the indicated crank angle. (A) Comparison of

anticipated CO and UHC emissions between the baseline and perfect mixing cases; (B) temperature pro-

files of average and local maximum temperatures in the baseline and Tpeak in the perfect mixing case. The

times of start and end of injection were �28.2 and �19.5 deg atdc, respectively. The box in Figure 20B

indicates the optimal mixing window location.

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optimal crank angles (indicated by the box in Figure 20B). In this case, the localhigh-temperature gases mix with neighboring low-temperature gases and enhancethe reactions of the low-temperature mixtures, in which CO and HC are otherwiseunlikely to be oxidized. It is seen that the Tpeak values cannot reach the optimalmixing window when the mixing occurs between the end of injection and TDC. Ifthe perfect mixing of the in-cylinder charge occurs later than the optimal mixingwindow, Tpeak of the altered mixtures decreases and never reaches the optimalmixing window as the cylinder volume expands. Note that Tpeak in this periodapproaches the average gas temperature of the baseline case, which means that theextent of mixing of the baseline case is close to being homogeneous.

Application of T 2 T and AE 2 T Plots to Conventional DieselCombustion

T�T and AE�T plot analysis was also applied to explain conventional dieselcombustion. In this case, the injection timing was set to �10 deg atdc and the injec-tion duration was 10.7 degree crank angle (deg CA). No EGR (except for 5% inter-nal EGR) was assumed. The initial pressure and temperature were the same as thosein the minimum CO operating case of Opat et al. (2007). The overall equivalenceratio was 0.4. Figure 21 shows the profiles of pressure, heat release rate, in-cylindersoot, and NOx. Ignition is seen to occur during the injection, and no cool flamebehavior is seen. A significant amount of fuel burns in the diffusion burning mode,which is seen from a long tail of the heat release rate profile. Soot rapidly increasesafter ignition and then oxidizes with mixing of the burned gases and the surroundinggases that have excess oxygen.

In Figure 22, Tpeak�Teq plots are shown for various crank angles during com-bustion. At �4 deg atdc (see Figure 22A), some of the rich mixture has alreadyburned; thus, the Tpeak values become higher than the corresponding Teq valuesdue to compression during the remaining compression stroke. This applies for mix-tures that ignite before TDC. At the same time, there is some mixture that is too richto burn with Tpeak lower than the corresponding Teq values. Because Figure 22A isduring the injection period with insufficient time for mixing of the fuel and air, muchof the mixture is richer than stoichiometric.

As time proceeds, more of the mixture becomes aligned on the Tpeak¼Teq

line due to further dilution of the rich mixtures and mixing of the burned gaseswith unburned charge. At þ4 deg atdc (see Figure 22D), when the cylinder gaspressure is about the peak value and 70% of the total heat has been released,it is seen that most of the charge is aligned on the Tpeak¼Teq line, which indi-cates that the in-cylinder charge is expected to burn almost completely, and thusthe UHC and CO emissions are expected to be extremely low. As the expansionstroke further proceeds, the maximum Tpeak (or Teq) of the local in-cylinder chargedecreases and amount of rich mixture is reduced. Eventually, the entire in-cylindermixture becomes lean while stratification remains in both temperature and compo-sition, as shown in Figure 22H.

AE�Tpeak plots for the corresponding crank angles are shown in Figures 23and 24. Because the UHC and CO emissions are not a concern in conventional diesel

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combustion, anticipated soot and NOx emissions are shown. The anticipated sootlevels increase during the injection period (see Figures 23A and 23B) and thendecrease with crank angle. It is clearly seen that the rich mixtures are the main con-tributor of soot formation during the ignition and combustion period. During theexpansion stroke, mixing of the burned gases and available air reduces the mixturestratification and helps soot oxidation, resulting in a fast decrease of in-cylinder sootlevels (see Figures 23C–23H). For the operating conditions considered in the presentstudy, the soot emission levels were predicted to be low.

On the contrary, the anticipated NOx emissions remain at high levels over allcrank angles, as shown in Figure 24. The engine-out NOx emission level was

Figure 21 Conventional diesel combustion. Injection timing �10 deg atdc. No EGR. Initial pressure

and temperature at IVC 1.91 bar and 348.6 K, respectively. (A) Pressure and heat release rate profiles;

(B) in-cylinder soot and NOx profiles. Figure 21A also shows the seven crank angles at which T�T

and AE�T plots are made, as shown in Figures 22 and 23.

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Figure 22 Tpeak�Teq plots at various crank angles for conventional diesel combustion. Injection timing

�10.2 deg atdc. No EGR. Initial pressure and temperature at IVC 1.91 bar and 348.6 K, respectively.

(A) ca¼�4; (B) ca¼�2; (C) ca¼TDC; (D) ca¼þ4; (E) ca¼þ10; (F) ca¼þ20; (G) ca¼þ30; and

(H) ca¼þ50 deg atdc.

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Figure 23 Anticipated soot�Tpeak plots at various crank angles for conventional diesel combustion.

Injection timing �10.2 deg atdc. No EGR. Initial pressure and temperature at IVC were 1.91 bar and

348.55 K, respectively. (A) ca¼�4; (B) ca¼�2; (C) ca¼TDC; (D) ca¼þ4; (E) ca¼þ10; (F) ca¼þ20;

(G) ca¼þ30; (H) ca¼þ50 deg atdc.

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Figure 24 Anticipated NOx�Tpeak plots at various crank angles for conventional diesel combustion.

Injection timing �10.2 deg atdc. No EGR. Initial pressure and temperature at IVC were 1.91 bar and

348.55 K, respectively. (A) ca¼�4; (B) ca¼�2; (C) ca¼TDC; (D) ca¼þ4; (E) ca¼þ10; (F) ca¼þ20;

(G) ca¼þ30; (H) ca¼þ50 deg atdc.

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predicted to be 69 g=kg-fuel. After ignition occurs during the injection, the contri-bution to NOx from lean mixtures increases (see Figures 24A and 24B). Then themaximum anticipated NOx decreases while more mixture is diluted from rich to leanand is subject to NOx formation (see Figure 24C). As time further proceeds, both themaximum anticipated NOx and the amount of lean mixture increase (see Figures24D–24G) and finally settle at the engine-out emission level (see Figure 24H). Notethat a significant amount of NOx is also potentially formed from rich mixtures atextremely high temperatures, as can be clearly seen in Figures 24A–24D. It is inter-esting that the distribution of anticipated NOx emissions varies significantly after 20deg atdc, while the overall in-cylinder NOx amount becomes saturated, as is seenfrom Figure 24B. This indicates that the NOx is not newly formed actively, butrather that the existing NOx is redistributed by mixing of in-cylinder gases after acertain time in the engine cycle.

SUMMARY AND CONCLUSIONS

The effects of thermal and mixing conditions of in-cylinder charge on emissionswere analyzed in LTC regime. In the analysis, equilibrium temperature (Teq), peaktemperature (Tpeak), and anticipated emissions (AE) were introduced, and T�Tplots and AE�T plots were proposed as ways to present in-cylinder mixture qualityand anticipated emission characteristics of the combustion. Five HCCI pathwayswere identified using the Tpeak�Teq plot, and the plot was applied to describe bothHCCI and DI engine combustion in the LTC regime. The method was also appliedto conventional diesel combustion. An optimal temperature window and an optimalmixing window were defined and demonstrated in LTC engine operation.

Based on the results, the following conclusions were drawn.

1. Wall heat transfer was found to significantly affect UHC=CO emissions of LTCengine operation.

2. Together with the standard U�T plot, T�T and AE�T plots are useful methodsto analyze the evolution of in-cylinder mixture conditions in engine combustion.

3. The Tpeak�Teq plot gives information about the inhomogeneity of the currentmixture and the potential deviation of the mixture from complete release of avail-able chemical energy. Variation of the Tpeak�Teq plot details with crank anglecan be used to show how the mixture conditions evolve.

4. AE�Tpeak plot gives information about the engine-out emissions that areexpected based on the current mixture conditions.

5. In order to reduce the UHC=CO emissions, the condition of charge mixtureshould be in optimal thermal conditions, which is called the optimal temperaturewindow. In terms of Tpeak, the lower bound of the optimal temperature windowwas found to be 1400 K.

6. There are optimal timings of mixing during combustion that can improve engine-out emissions. This is defined as the optimal mixing window. For example, for theminimum-CO operating condition considered in the present study, the optimalmixing window was found to be between 3 and 12 deg atdc.

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NOMENCLATURE

AE emissions at exhaust valve opening resulting from an adiabatic combustionprocess from the current mixture conditions without mass exchange withneighboring gas mixtures

atdc after top dead centerCI compression ignitionEVO exhaust valve openHCCI homogeneous charge compression ignitionIVC intake valve closureLTC low-temperature combustionNox nitric oxidesPCCI premixed charge compression ignitionSOIC start of injection commandTeq temperature of the gas mixture at the equilibrium state corresponding to

constant volume condition at the current mixture thermal and chemicalconditions

Tg temperature of the local gas mixture at the current timeTpeak maximum temperature that the local gas mixture can reach though an

adiabatic combustion process without mass exchange with neighboring gasmixtures

TDC top dead centerUHC unburned hydrocarbon

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