Paper # 070HE-0123 Topic: Heterogeneous Combustion, Sprays, and Droplets

8th U. S. National Combustion Meeting

Organized by the Western States Section of the Combustion Institute

and hosted by the University of Utah

May 19-22, 2013

Contributions of thermal and prompt NOx chemistry on NOx

formation near igniting oxygenated liquid fuel droplets

Torben Grumstrup1 Anthony J. Marchese

1 Frederick L. Dryer

2

Tanvir Farouk3

1Department of Mechanical Engineering,

Colorado State University, Fort Collins, CO

2Department of Mechanical and Aerospace Engineering,

Princeton University, Princeton, NJ

3Department of Mechanical Engineering

University of South Carolina, Columbia, SC

In emission measurement studies, diesel engines fueled by fatty-acid methyl ester biodiesel often exhibit slightly

increased production of oxides of nitrogen (NOx) in comparison to petroleum diesel. A number of explanations for this

increase have been proposed by the research community. One theory, which has been supported by optical engine test results, suggests that the presence of oxygen atoms in the methyl ester fuel molecule results in a leaner premixed

autoignition zone, thereby increasing in-cylinder temperatures and promoting thermal NOx production. In the present

study, this hypothesis is explored computationally by examining the contribution of thermal and prompt NOx mechanisms

on NOx formation in the vicinity of igniting liquid droplets. Non-oxygenated (heptane) and oxygenated (methyl

butanoate) fuel droplets are introduced into a hot (1150 K) air ambient whereupon the liquid vaporizes, thus producing a stratified fuel/air mixture that thermally autoignites after an ignition delay period. The spherically symmetric domain due to this single spatial dimension permits transient simulations involving detailed chemical kinetics and diffusive transport,

thereby permitting a special focus on low-temperature hydrocarbon and prompt NOx chemical kinetic effects during the

ignition and subsequent transition to quasi-steady (non-premixed) droplet burning. The transient autoignition and burning histories of each fuel in the same oxidative conditions and droplet size are analyzed to extract detailed historical evolution

characteristics of species and NOx as a function of fuel type. The computations show that the localized ignition event

occurs relatively far from the droplet surface (in a fuel lean region) and that the flame propagates inward, eventually stabilizing closer to the droplet surface. Because the autoignition event occurs in a stratified fuel/air mixture in the

vicinity of a liquid fuel, spherically symmetric droplet ignition represents a valuable physical analog to the premixed autoignition process of a diesel fuel spray. As such, the results of the computational study provide further analytical

insight into the oxygenated-fuel stoichiometry explanation for increased NOx in biodiesel-fueled engines.

1. Introduction

Because of the high energy density of liquid hydrocarbons, their amenability toward handling and the high power

density of energy conversion devices that combust liquid hydrocarbons with air, the combustion of liquid fuels will

continue to account for the overwhelming majority of energy consumption for the transportation sector . Combustion of

liquid fuels for transportation applications often proceeds via injection of the liquid spray into a high temperature

oxidizing environment [1]. In a compression ignition engine, for example, the liquid fuel has sufficient reactivity to

spontaneously ignite after an induction period during which a fraction of spray vaporizes, mixes with air and chemically

reacts with the air.

Although combustion of liquid sprays is pervasive in modern technology, it remains as a fertile topic of research

because of the challenges required in both experimentation and accurate numerical simulation. Liquid spray combustion

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is a multi-phase, turbulent, and chemically-complex phenomena for which all modes of heat transport are important [2].

While great strides have been made in chemically reacting flow modeling in recent decades, liquid spray combustion

simulations still employ numerous simplified sub-models (e.g. reduced chemical kinetic mechanisms, simplified spray

models, Reynolds averaged turbulence models, etc.) to facilitate reasonable computational times. In addition,

experimentation on combusting liquid sprays is similarly challenging, although the use of laser diagnostics and digital

imaging has been highly effective in increasing our understanding of diesel spray combustion in particular [3-5].

With the advantage of these relatively new optical diagnostic techniques, Dec [3] developed a conceptual model of

diesel spray combustion, which presents a more representative description of the autoignition process and transition to

non-premixed combustion than that conceptualized previously [6]. In this new conceptual model, Dec suggested that, as

the fuel jet penetrates into the cylinder, it entrains the ambient air, thereby creating a well-mixed, fuel rich mixture

directly downstream of the fuel jet with an equivalence ratio of 2 < < 4. After a short ignition delay period, the premixed fuel/air mixture spontaneously ignites creating a standing premixed autoignition zone, which subsequently

transitions into non-premixed combustion until the end of injection and the fuel supply is exhausted [3].

Although challenging, experimentation with in-cylinder diagnostics on diesel engines certainly remains a

worthwhile avenue of research. However, difficulties remain in quantitative optical diagnostics because of the hostile

environment in a diesel engine cylinder. For example, quantitative in-cylinder measurements of species concentrations

such as nitric oxide (NO) or soot precursors in the vicinity of liquid diesel sprays represents a particular challenge [7].

Accordingly, just as steady, one-dimensional premixed laminar flames have played an important role in understanding

highly turbulent practical premixed combustion systems, isolated droplet ignition and combustion can be similarly effective to develop, test, and validate sub-models for combustion of liquid fuel sprays [8]. Specifically, as described

below, both the diesel spray and isolated spherically symmetric droplet produce compositionally and thermally stratified

fuel/air mixtures in the vicinity of a cold liquid fuel, which autoignites in a premixed autoignition event and subsequently

transitions to non-premixed combustion.

In the spherically symmetric droplet configuration, a cold liquid droplet is introduced into a hot oxidizing

environment. Heat is transferred from the oxidizing environment resulting in an increase in the droplet surface

temperature, which increases the gas phase mole fraction of fuel at the droplet surface. The fuel vapor diffuses from the

droplet surface into the hot oxidizer, creating a stratified fuel/air mixture. Since the droplet surface temperature remains

below the fuel boiling point, the presence of the liquid droplet also produces a highly stratified thermal boundary layer as

well. After sufficient time period governed by liquid droplet heating, diffusive transport, and chemical kinetic induction

period, the premixed fuel/air mixture autoignites. The resulting transient combustion event locally consumes the fuel

and air, resulting in a flame front that propagates toward the liquid droplet and then transitions to a stationary non-premixed flame [9]. A similar set of conditions occur when a diesel fuel is injected into the cylinder in a direct-injection

compression-ignition engine. However, computationally and experimentally, an important advantage exists in the case

of spherical symmetric droplet ignition configuration. Specifically, because of spherical symmetry, the liquid droplet,

the fuel vapor cloud, mass and thermal diffusive transport, Stephan flow velocity, transient flame front propagation and

resultant minor species concentrations can all be described spatially with a single radial variable. This critical aspect

enables transient simulations with detailed chemical kinetics and multicomponent mass transport that can be solved

without the need for extensive computational power.

As a specific example of the utility of spherically symmetric droplet ignition as a physical model for diesel spray

combustion, consider again the Dec [1] conceptual model of diesel spray combustion. Although there is substantial

evidence to support the presence of a standing rich premixed autoignition zone, it was not possible from the

chemiluminescence measurements to determine the precise location in the fuel vapor cloud wherein the actual ignition event was initiated [3]. In the spherically symmetric liquid droplet ignition case, both simplified asymptotic [10, 11] and

detailed transient numerical simulations [8, 12], clearly show that ignition event occurs in a fuel lean region and

propagates back toward the rich zone. Although there are clear differences in the fluid mechanics between the two

systems (which greatly affect the rates of thermal and mass transport), the overall similarities in the thermal and

equivalence ratio stratification suggest that the initial ignition event in a diesel spray might actually initiate in the outer

regions of the vapor cloud where the mixture is lean and hot.

A further use for spherically symmetric droplet ignition as a viable analog for diesel spray combustion is to better

understand the formation of oxides of nitrogen (NOx) during ignition and transition to non-premixed combustion in the

vicinity of a cold, condensed phase liquid fuel. Researchers, manufacturers, and regulators remain keenly interested in

NOx formation because it is a strictly regulated pollutant [13, 14] formed in most combustion systems. Diesel engines

have historically been heavy NOx emitters because the majority of the fuel consumption occurs in a non-premixed flame,

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which results in high local flame temperatures, thereby promoting NOx formation. In combustion systems in which air

is the oxidizer, nitric oxide (NO) is formed from atmospheric molecular nitrogen (N2) through three distinct chemical

pathways: thermal NO, prompt NO, and the N2O mechanism [15]. The thermal NO mechanism, also referred to as the

Zel’dovich mechanism [16], is comprised of three reactions:

N2 + O → NO + N (R1)

O2 + N → NO + O (R2)

N + OH → NO + H. (R3)

Production of thermal NO is dictated by the rate of reaction (R1), which breaks the N2 bond. The N2 bond energy is

quite high, so the (R1) reaction proceeds relatively rapidly only at high temperatures (greater than approximately 1800

K) [15, 17]. Prompt (or Fenimore [18]) NO formation is more complicated than the thermal NO formation path and is

not strictly limited to high temperature conditions. The first steps of the prompt NO main sequence are the reaction of

small fuel fragments with molecular nitrogen:

N2 + CH → NCN + H (R4)

N2 + CH2 → HCN + NH. (R5)

NCN, a product of (R4), reacts with O, OH, and O2 to form NO. The products of (R5) react with H, O, and OH over a

series of reactions, culminating in formation of atomic nitrogen (N), which in turn form NO by way of reactions (R2) and

(R3). Lastly, NO can be formed through N2O in the following reactions:

N2 + O + M → N2O + NO (R6)

N2O + O → NO + NO (R7)

A full NOx sub-mechanism that includes all three NOx production paths described above would typically include greater

than 35 species and 450 reactions. Moreover, it should also be recognized that even the most accurate full NOx sub-

mechanisms have only been tested against a data acquired for a limited number of fuels (e.g. H2 and C1 to C4

hydrocarbons) and in limited experimental configurations (i.e. steady, premixed, flat flame burners).

Given the inherent complexity of NOx formation, it might seem surprising that the overwhelming majority of

detailed numerical computations that attempt to accurately predict NOx formation include only reactions (R1) to (R3).

For example, many computational engine combustion studies employ the use of the computer codes such as Kiva [13](or

similar) to predict NOx formation. These computer models have been used to conduct numerous studies on piston-

cylinder engines, including diesel (e.g., [19]). Because of the computational requirements associated with large chemical

kinetic mechanisms, even the most ambitious Kiva modeling efforts have been restricted to approximately 50 species (e.g., [20, 21]). Accordingly, when NO-formation sub-models are employed it is typical to include only the thermal NO

mechanism, and in some cases adjustments are made to match experimental results [19]. The spherically symmetric

droplet ignition simulations presented in this paper demonstrate that NOx production during autoignition and transition to

non-premixed combustion in the vicinity of a liquid fuel is influenced by more than merely the 3-reaction step thermal

NO mechanism, and that realistic prediction of NOx formation under these conditions requires prompt and N2O

chemistry.

Mueller, et al. [5] reported on a series of experiments and analyses aimed at conclusively elucidating the origin of

NOx increases observed in diesel engines operating on methyl ester biodiesel in comparison to petroleum-derived diesel.

A specially-modified diesel engine with optical access for laser diagnostics and imaging was used with exhaust gas

instrumentation to support a number of explanations of the origins of NO at various loads, with various fuel blends,

injection timing, and rates of in-cylinder heat transfer. Among the results was the supposition that the oxygen present in

biodiesel fuel molecules (approximately C18H34O2) causes the otherwise richer premixed fuel-air mixture to be closer to stoichiometric. The leaner premixed autoignition zone leads to higher in-cylinder temperatures that favor NO production

by the thermal-NO mechanism (R1, R2, R3) [22].

In the present study, we examine this hypothesis in the context of the spherically symmetric droplet ignition

configuration. Specifically, given the similarities described above between the diesel spray and the droplet ignition

configuration, one would expect to observe similar differences in local temperatures and NOx formation between

oxygenated and non-oxygenated fueled droplets during autoignition and transition to the non-premixed flame. However,

as described below, in the spherically symmetric droplet ignition configuration, the oxygenated fuels produced neither

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higher local temperatures nor greater NOx production than a non-oxygenated fuel subjected to the same initial conditions

for computations that included detailed chemical kinetic mechanisms for both the fuel and NOx chemistry.

Two fuels were considered for the spherically symmetric droplet ignition simulations described herein: methyl

butanoate (MB) and n-heptane (nH). These fuels were chosen because they exhibit similar physical properties (see Table

1) and the chemical kinetics of methyl butanoate have been validated to a much greater extent than any of the larger

methyl esters. It should be noted that, although many of the physical properties of these two fuels are remarkably similar, methyl butanoate is less reactive (i.e. much lower Cetane Number) and has a lower heat of combustion than

either n-heptane or a larger methyl ester representative of biodiesel.

Table 1. Selected properties for methyl butanoate (MB) and n-heptane (nH).

MB nH

Fuel Property C5H10O2 C7H16

Molecular weight, [g/mol] 102.1 100.2

Boiling temperature, [K] 376 372

Density*, [kg/m3] 898.4 679.5

Specific heat*, [kJ/m3] 1.941 2.242

Thermal conductivity [W/(m*K)] 0.1403 0.1235

Heat of vaporization, [kJ/mol] 141.4 132.9

Heat of combustion, [kJ/mol] 2945.5 4849.2

Stoichiometric coefficient 7.5 11.0

Derived Cetane Number 6 53

*Density and specific heat are at 298 K

Derived Centane Numbers from [23, 24], all other quantities from [25].

For the computations reported herein, two different NOx sub-mechanisms were added to the existing chemical

kinetic mechanisms for the two fuels. The first NOx sub-mechanism contained only the three thermal NO reactions (R1,

R2, R3) and will be referred to henceforth as the, “thermal NO mechanism.” The second NOx sub-mechanism contained

the reactions of the thermal NO mechanism as well as those of the prompt and N2O pathways. This mechanism contains

main pathways initiated by reactions (R1) through (R7) and all the subsequent reactions necessary to describe these

reaction paths. The latter, more complete, mechanism referred to henceforth as the “full NOx mechanism” consisted of

36 species and 455 reactions. It should be noted that for the case of full NOx, we use “NOx” instead of “NO” because

the full NOx mechanism will produce several different oxides of nitrogen (NO, N2O, NO2, NO3, N2O3, N2O4), which are

generally abbreviated as NOx. The thermal NO mechanism only produces only nitric oxide. Thus, for two fuels with

two NOx mechanisms each, there are four total cases which are summarized in Table 2.

Table 2. Summary of simulation cases with the associated abbreviations used in this paper.

Abbreviation Fuel Thermal NO mechanism Full NOx mechanism

nHT n-heptane X

nHF n-heptane X

MBT methyl butanoate X

MBF methyl butanoate X

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2. Numerical Modeling

Simulations were conducted with an independently-developed comprehensive numerical model which is described

in detail elsewhere [26, 27]. The transient, spherically symmetric droplet combustion model features detailed gas-phase

kinetics, spectrally resolved radiant heat transfer, and multi-component gas transport. Mass and energy conservation is

solved in both the gas and liquid phase. The heat transfer within the droplet is of “finite” conduction prescribed by the

liquid phase thermal conductivity. Chemical kinetic mechanisms were created by appending thermal and full NOx

chemical kinetics to each fuel. Details of the fuel chemical kinetic mechanisms can be found in the associated

references: n-heptane [28], and methyl butanoate [25]. The thermal and full NOx chemical kinetics were obtained from

a small hydrocarbon mechanism with NOx chemistry by Konnov [29].

3. Results

A selection of results from simulations of spherically symmetric autoignition and transition to non-premixed

combustion of a single n-heptane (n-C7H16) droplet are shown in Figs. 1 through 3. Figure 2 contains the results of

computations with the full NOx mechanism, while Fig. 3 contains the results of identical simulations with only the

thermal NOx mechanism. Figure 1 is a plot of the gas phase initial conditions for both calculations, which were

performed for an initial droplet diameter of 200 m, ambient air at a fixed pressure 1 atm, droplet surface temperature of 300 K and ambient air temperature of 1150 K. Figure 1 represents the initial conditions for O2 and n-heptane mass

fraction, and temperature. At t = 0 s, the mass fraction of n-heptane at the droplet surface is specified by vapor-liquid

equilibrium at the surface and a relatively steep gas-phase n-heptane mass fraction profile is specified as an input to the

model. Similarly, a very narrow thermal boundary layer is also input into the model as initial conditions. Figure 2

shows results at selected times for t > 0 for computations with the full NOx mechanism. Each row of plots (labeled a, b,

and c) represent the same time step as indicated in the upper left corner of the leftmost plot. Plots in the first column show mass fraction for fuel, oxygen, major combustion products, and temperature. Plots in the second column show

mass fraction for NO, OH, O and local equivalence ratio . The plots in the third column show mass fraction for a number of oxides of nitrogen, including NO (which appears in both second and third column plots). For all plots, the

horizontal axis represents radial distance normalized by initial drop radius (r/ro).

Figure 1. Initial conditions for n-heptane droplet simulations.

Referring to Fig. 2, at time t = 10 ms, the droplet surface temperature has increased sufficiently to raise the surface mass fraction of n-heptane to 0.8 and the fuel vapor has diffused and convected outward such that the location of

stoichiometry (= 1) is located at a normalized radius of approximately 8. Because of heat transfer to the liquid droplet surface, the thermal boundary layer has also increased substantially such that temperatures remain well below the

ambient temperature at normalized radii < 10. It is also notable that the increased mass fraction of fuel at the surface has

displaced the molecular oxygen and nitrogen (not shown) at the surface. Although the hot ignition has not yet occurred,

a subtle increase in temperature is discernible at a normalized radius of approximately 25 which is a result of the slow,

low-temperature exothermic reactions that will ultimately lead to hot ignition. The asymptotic nature of the ignition

event is evident from these early time plots. Specifically, although very little fuel appears to have diffused to the

normalized radius at the which the temperature rise appears, the residence time during which the evaporating fuel vapor

is exposed to oxygen at a high temperature increases with increasing normalized radius. Accordingly, the initial onset of

ignition (as signified by the slight increases in temperature at large normalized radii) occurs initially in a very fuel lean

location. The middle plot shows mass fraction for other species at t = 10 ms. Although only a slight increase in

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temperature is observed, a radical pool is already being established as evidenced by the presence of hydroxyl (OH) and

atomic oxygen (O) radicals in concentrations on the order of 1 parts per million (ppm). Nitric oxide (NO) mass fraction

is very small, with a peak value of YNO = 26e-9. In the right-hand plot, oxides of nitrogen are present in very low levels.

The maximum quantity is NO2 mass fraction at slightly over 30e-9.

At t = 12.5 ms (Fig. 2, second row of plots), the location of maximum temperature has moved inward to a

normalized radius of approximately 20 and a local depletion in molecular oxygen is also observable. The radical pool is also growing as the OH and O mass fractions have increased by 50%. Oxides of nitrogen in the right-hand plot remain

as small quantities, now less than 30e-9.

At t = 15.12 ms, the hot premixed ignition has occurred as evidenced by the temperature peak of 2400 K centered at

r/ro = 10. The location of peak temperature has also moved inward from r/ro = 20 to 10 as the combustion wave

propagated into the stratified fuel/air mixture toward the droplet surface (in the direction of increasing equivalence ratio).

The O2 mass fraction also exhibits substantial depletion in the vicinity of r/ro = 9, which indicates significant localized

O2 consumption. However, closer to the droplet surface (1 < r/ro < 9), a relatively high mass fraction of O2 remains

because the high equivalence ratio of the fuel/air mixture in this region prevents the combustion wave from propagating

closer to the droplet surface. At t = 15.12 ms, major combustion products and intermediates have also begun to form as

evidenced by the mass fraction curves for carbon monoxide (CO), carbon dioxide (CO2), and water (H2O). It is also

notable that the n-heptane, O2, and temperature profiles very near the droplet (1 < r/ro < 3) have yet to change

substantially in comparison to t = 12.5 ms. As indicated in the right-hand plot, the elevated temperatures of the premixed autoignition event have also resulted in a rapid increase in NOx formation, with NO and N2O having quickly increased in

concentration. At this time step, NO has a peak mass fraction of 290e-6.

At t = 15.41 ms, the premixed autoignition phase is nearly complete and the flame structure is transitioning toward

that of a quasi-steady non-premixed flame. The O2 mass fraction profile still exhibits a small amount of molecular

oxygen mixed with fuel between the droplet surface and flame (r/ro = 1 to ~6). The temperature and product mass

fraction profiles have broadened due to thermal diffusion and mass diffusion of hot combustion products away from the

flame in both directions. The mass fraction of NO has increased to 0.8e-3 and become the dominant oxide of nitrogen.

By t = 20 ms, the flame has transitioned completely to a stationary, quasi-steady non-premixed flame as evidenced

by n-heptane and oxygen mass fractions approaching zero on either side of the location of maximum flame temperature.

Now combustion is supported by fuel vapor diffusing from the droplet surface outward to the flame, and O2 diffusing

inward from the ambient. The peak temperature is 2300 K which is substantially lower than the peak temperature during the premixed autoignition phase. The mass fraction curves for CO, CO2, and H2O now extend to r/ro = 1, denoting the

presence of these species at the droplet surface. The peak value of NO mass fraction has increased further and the profile

has broadened as the NO is transported away from the droplet.

Figure 3 contains selected results from an n-heptane droplet ignition simulation with the same initial conditions to

that presented in Fig. 2, but with the full NOx mechanism replaced with only the 3 thermal NO reactions (R1 – R3). The

time steps plotted in Fig. 3 are not identical to those displayed in Fig. 2, but were chosen because they portray similar

features of the premixed autoignition event and transition to non-premixed combustion. As indicated by the left column,

the major features of the flame structure are still captured with the substitution of the thermal NO mechanism.

Specifically, the onset of ignition occurs in the fuel lean region at a normalized radius of greater than 20 and propagates

inward. Furthermore, the peak temperature during the premixed autoignition is higher than the quasi-steady non-

premixed flame temperature. The predicted NO formation, however, is vastly different between the two computations.

In particular, the peak level of NO mass fraction for the computations with thermal NO is 6 times less than that predicted in the computations with the full NOx mechanism. Moreover, the mass fraction profile of NO is much wider in the

thermal NO computations, with NO diffusing all the way back to the droplet surface as a consequence of the absence of

reactions to consume NO that are present in the full NOx mechanism.

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Figure 2. Gas phase species and temperature surrounding an n-heptane droplet at t = 10, 12.5, 15.12, 15.41, and 20 ms after injection into air at 1150 K and 1 atm for computations performed with full NOx mechanism.

x10-4

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Figure 3. Gas phase species and temperature surrounding an n-heptane droplet at t = 10, 12.8, 15.19, 15.45, and 20.0 ms after

injection into air at 1150 K and 1 atm for computations performed with the thermal NO mechanism.

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4. Discussion

As discussed in the introduction and illustrated in the detailed results plotted in Figs. 2 and 3, the spherically

symmetric autoignition of a liquid droplet and transition to a quasi-steady non-premixed flame is governed by many of

the same underlying physical phenomena as autoignition of a diesel spray and its transition into non-premixed

combustion. In the following section, we compare the results of computations with an oxygenated fuel (methyl

butanoate) with similar physical properties to that of n-heptane to determine if the differences in stoichiometry of the

stratified fuel/air mixture result in differences in flame temperature, thereby producing differences in thermal NO

formation.

Before presenting the methyl butanoate results, there are a number of insights that can be made from the simulation

results with n-heptane Firstly, comparing the computational results at t = 12.5 and 15.12 ms in Figure 2, it is clear that

ignition occurred at some time point in this interval because of the dramatic rise in temperature. A further indicator of

ignition is the even more dramatic increase in the peak OH mass fraction which increased by a factor of more than 1300

during this same interval. Such rapid increases in temperature and YOH can be explained only by the onset of ignition. Prior to the hot autoignition event, the peak temperature at t = 12.5 ms is located at r/ro = 20 and the stoichiometric

location ( = 1) in the stratified fuel/air mixture surrounding the droplet is located r/ro = 7. As such, the local region wherein the onset of autoignition occurs is clearly in the lean region. At t = 15.12 ms, after the premixed autoignition

has occurred, the location of peak temperature is located at r/ro = 10 and the stoichiometric location ( = 1) in the stratified fuel/air mixture surrounding the droplet remains fixed at r/ro = 7. This result confirms that, although a

combustion wave does propagate inward from the lean region of the stratified mixture in the direction of increasing

equivalence ratio, the flame front never propagates into a fuel rich zone. As shown below, this same result is observed

for computations performed with oxygenated fuel droplets.

Figure 4 shows how the location of peak temperature and location of stoichiometric equivalence ratio varies with

time for computations with methyl butanoate and n-heptane droplets under the same initial conditions as those presented

in Fig. 2. For both fuels, results are shown for computations performed with both the full NOx mechanism and thermal

NO mechanism. The upper pair of curves in both plots represents the location of peak temperature for the respective

fuels; the lower pair of curves represent the location of stoichiometric equivalence ratio ( = 1). For both the n-heptane and methyl butanoate computations, the results show that the premixed flame front propagates inward from a lean region

in the stratified mixture. The propagation begins slowly at larger normalized radii and then proceeds more rapidly as

indicated by the change in slope that occurs at 13.9 ms for n-heptane and 40 ms for methyl butanoate, respectively. The combustion wave very nearly reaches the stoichiometric location but never propagates into the rich region.

Figure 4. Location of maximum temperature and stoichiometric equivalence ratio for ignition and combustion of 200 m n-heptane

and methyl butanoate droplets in 1150 K air at 1 atm. Computations were performed with thermal NO and full NOx mechanisms. Arrows indicate the end of premixed burn and the transition to non-premixed combustion.

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The fact that the fuels considered herein ignite in the lean, high temperature region far from the surface of the

droplet is supported by asymptotic ignition theory which states that a sufficiently high Damköhler number is required for

ignition [30]. The reaction Damköhler number in this case represents a ratio of the residence time available for a

chemical reaction to proceed to that the chemical kinetic induction period [30]. Thus, both sufficiently long residence

time and sufficient chemical reactivity are required for ignition to occur. Long residence time is experienced by those reactants that have traveled a long distance, such as fuel vapor diffusing from the droplet surface to the hot ambient.

Sufficient chemical reactivity is achieved in regions of elevated temperature, which cannot exist in the vicinity of a

vaporizing liquid fuel. Accordingly, the only location where ignition can occur is far from the droplet surface where

temperatures are high and residence times are long. While it is recognized that there are vast differences in the

mechanisms of mass and energy transport between the quiescent spherically symmetric configuration described herein

and the diesel spray configuration, both configurations produce stratified fuel/air mixtures that are cold and rich in the

vicinity of the condensed phase and hot and lean in the far field. Therefore, the underlying Damköhler number

arguments should still apply in the more complex diesel spray configuration. As such, based on the results of the droplet

simulations, coupled with the inherent difficulties of actually measuring the location of the onset of ignition in a direct

injection diesel engine, it is reasonable to hypothesize that the onset of ignition for diesel spray combustion will initiate

in a fuel lean region in the periphery of the vapor cloud surrounding the liquid jet. It should be noted, however, that

although these computations clearly show that the flame front never penetrates the fuel rich zone in the quiescent, spherically-symmetric droplet ignition configuration, these computations cannot rule out that possibility in the diesel

spray case given the complexity of the fluid mechanics.

Figure 5. Mass of NO produced by droplet flame with respect to time. Simulations

with full NOx chemistry show significantly more NO production.

The four simulation cases can also be used to investigate the influence of the prompt NOx and/or N2O chemical

kinetic sub-mechanisms on the total NO mass emissions during the premixed autoignition and non-premixed burn phase

in the spherically-symmetric droplet combustion configuration. As discussed in the introduction, it is common practice in even the most sophisticated CFD modeling efforts on internal combustion engines to include only the thermal NO

reactions (R1) to (R3). Accordingly, even if CFD computations with reduced chemical kinetic mechanisms and

reasonably realistic spray models were to accurately predict the onset of autoignition and propagation of a combustion

wave in the vicinity of the diesel spray, the NOx results presented herein strongly suggest that such computations cannot

be predictive if only thermal NO is considered. This result is illustrated further in Fig. 5, which is a plot of NO mass

emissions as a function of time for n-heptane and methyl butanoate droplet computations with the full NOx and thermal

NO sub-mechanisms. Note that because of the differences in chemical reactivity (as indicated by the large difference in

Derived Cetane Number in Table 1), the methyl butanoate exhibits a much longer ignition delay period (approximately

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40 ms vs. 15 ms for n-heptane). The results clearly show that the computations that consider full NOx chemistry (i.e.,

thermal, prompt, and N2O) predict substantially higher NO mass emissions. Specifically, the full NOx mechanism

computations with n-heptane predict 4.8 times higher NO mass emissions than those computations performed with the

thermal NO mechanism only. Similarly, the methyl butanoate computations with full NOx chemistry predict 3.3 times

higher NO mass emissions than those computations performed with the thermal NO mechanism only. These results

underscore the fact that prompt and/or N2O pathways to NOx formation are critical in autoignition and transition to non-premixed combustion of liquid fuels and should not be omitted from computations.

Finally, the results plotted in Fig. 5 also show that the methyl butanoate droplet ignition and combustion results in

decreased NO mass emissions in comparison with the n-heptane droplets under the same conditions for both the full NOx

and thermal NO computations. The reason for this result, which is contradictory to the explanation by Mueller and

coworkers [15] for increased NOx formation in methyl ester combustion in diesel engines, can be explained by

examining the instantaneous maximum gas phase temperature during autoignition and transition to non-premixed

combustion for both fuels, as discussed below.

Figure 6 shows maximum temperature as a function of time for n-heptane and methyl butanoate droplet

computations with the full NOx and thermal NO sub-mechanisms. For both computations, the maximum temperature

starts out at the ambient temperature of 1150 K and, after an initial induction period, the temperature begins to rise at

some location in the gas phase (as shown above in Fig. 4) and transitions to a hot autoignition as demonstrated by the

very rapid temperature rise at t = 15 ms and t = 40 ms for n-heptane and methyl butanoate, respectively. During the premixed autoignition event, the temperature exceeds the quasi-steady non-premixed flame temperature by a substantial

margin (on the order of 100 K for both fuels). The end of premixed burn and transition to non-premixed flame for the

respective fuels is indicated by arrows in the plot. After transition to the non-premixed flame, the temperature is

relatively constant but slowly decreases because leakage of reactants through the flame increases as the droplet size

decreases. Although both fuels exhibit higher peak temperatures during the premixed autoignition event, the results

clearly show that, in the droplet ignition configuration, the peak flame temperatures are substantially higher for n-

heptane in comparison to methyl butanoate. This result is observed irrespective of the NOx mechanism used. This result

is contrary to what might be expected from the hypothesis of Mueller, et al. [31] that oxygenated fuels should produce a

higher temperature during the premixed autoignition phase because the presence of oxygen atoms in fuel molecule

results in a leaner (but still rich) premixed autoignition zone, thereby increasing in-cylinder temperatures and promoting

thermal NO production.

Figure 6. Maximum temperature with respect to time. Arrows indicate the end of premixed burn and the beginning of the diffusion flame. N-heptane

exhibits higher temperatures than methyl butanoate.

12

The reason that the results presented herein are contradictory to that hypothesized for the diesel spray can be easily

explained by the fact that the location of maximum temperature (Figure 4) never propagates into a rich zone for either

the oxygenated or non-oxygenated fuel. Accordingly, in the spherically symmetric droplet ignition configuration,

oxygenated fuels will exhibit premixed autoignition zones that are further from stoichiometric, which is the opposite of

the theory of Mueller, et al. [15], in which a standing rich premixed autoignition zone is observed.

The results presented in this paper are not intended to refute the proposed explanation of Mueller, et al. [15] of increased NOx in biodiesel-fueled engines, which was based on a very thorough set of experiments conducted in an

optical engine, accompanied by sound reasoning and analytical modeling. The authors of that study do, however, point

out the limitations of their study, such as the fact that the bulk mean in-cylinder temperatures calculated from a first law

energy balance do not represent local temperatures in the spray. Nor was the intent of this study to disparage diesel

combustion simulations that stretch the limits of computational power by considering chemical kinetic mechanisms of 40

or more species, but cannot possibly afford to double the size of the mechanism by considering full NOx chemistry.

Rather, our intent was to suggest that further examination of NOx formation in autoignition of stratified fuel/air mixtures

in the vicinity of a liquid fuel is clearly warranted. Indeed, we acknowledge the differences between the complexities of

a direct injection diesel spray and the simple geometrical configuration of the spherically symmetric autoignition that

enables these computations to consider detailed fuel chemical kinetic mechanisms with full NOx chemistry. However,

despite their inherent differences, we also believe that the two environments share many of the same fundamental

phenomena and based on those similarities, we believe that spherically symmetric droplet ignition and combustion is a useful tool for improving understanding of NOx formation in engines.

5. Conclusions

Isolated, spherically-symmetric liquid droplet ignition and combustion simulations were conducted for n-heptane

and methyl butanoate droplets to determine the influence of the oxygenated fuel on the stoichiometry of the stratified

fuel/air mixture and its effect on the local flame temperatures during ignition and transition to non-premixed combustion.

For both fuels, computations were performed by integrating existing chemical kinetic mechanisms with a simplified NOx chemistry (containing only thermal Zel’dovich NO chemistry) and with full NOx chemistry that included thermal,

prompt (Fenimore), and N2O mechanisms. The results showed that ignition occurred relatively far from the droplet

surface where the fuel-air mixture was very lean. This result is consistent with asymptotic ignition theory which states

ignition requires high temperatures and long diffusion times. Temperatures achieved during the premixed burn period

prior to the establishment of the diffusion flame showed that n-heptane exhibited higher temperatures than methyl

butanoate. Comparisons between the two NO mechanisms for the same fuel showed substantial increases in NO mass

emissions for computations performed with the full NOx mechanism that those performed with the simple thermal NO

mechanism. A comparison of NO production among the two fuels showed that n-heptane produced higher NO mass

emissions than methyl butanoate.

Acknowledgements

The work at Colorado State University was supported by grants from the National Science Foundation (NSF CBET-

0854134) and the U.S. Department of Energy (under contract DE-EE0003046 awarded to the National Alliance for

Advance Biofuels and Bioproducts).

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