The effects of multicomponent fuel droplet evaporation on the kinetics of strained opposed-flow diffusion flames

Combustion and Flame 160 (2013) 265–275

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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e

The effects of multicomponent fuel droplet evaporation on the kinetics of strained opposed-flow diffusion flames Chenguang Wang a, Anthony M. Dean a,⇑, Huayang Zhu b,c, Robert J. Kee b a

Chemical and Biological Engineering, Colorado School of Mines, Golden, CO 80401, USA Mechanical Engineering, Colorado School of Mines, Golden, CO 80401, USA c College of Petroleum Engineering, Xi’an Shiyou University, Shaanxi 710065, PR China b

a r t i c l e

i n f o

Article history: Received 23 July 2012 Received in revised form 9 October 2012 Accepted 13 October 2012 Available online 14 November 2012 Keywords: Multicomponent fuel droplets Fuel pyrolysis Opposed-flow nonpremixed flame Modeling

a b s t r a c t With the increasing use of alternative fuels, it becomes important to understand the impacts of their different chemical and physical properties on combustion processes. The objective of this paper is to explore the impact of the vaporization of a multicomponent liquid fuel on the combustion kinetics using an opposed-flow diffusion flame model. The model fuel consisted of a n-heptane, n-dodecane, and n-hexadecane mixture, selected to represent a Fischer–Tropsch fuel. A computational model is developed to describe the multicomponent vaporization process. Gas-phase chemical kinetics is modeled using a reduced mechanism containing 196 species. Results compare pre-vaporized fuel streams with those containing monodispersed initial droplet sizes of 20, 25 and 30 lm. The separation distance between the fuel and air inlets is either 5 and 10 mm. In all cases the fuel is carried in nitrogen, the pressure is 10 atm, and the fuel and air inlet velocities are 1 m s1. The fuel loading is set to achieve an overall equivalence ratio of unity. Results show that the finite evaporation rate significantly impacts the chemical kinetics. In particular, if the combination of separation length, stream velocity, and fuel volatility is such that fuel droplets penetrate into the higher temperature region near the flame-front, the rapid increase in evaporation rate significantly enhances the local vapor phase fuel mole fraction. The high temperature increases reaction rates, leading to higher peak temperatures as well as increased pyrolysis in the pre-flame region. For example, the peak temperature predicted for 30 lm droplets is 330 K higher than that for the pre-vaporized case. This increase occurs in spite of an initial decrease in temperature as a consequence of fuel vaporization. A similar effect is observed for the pre-flame pyrolysis products; ethylene, acetylene, and butadiene all increase by about a factor of two for the 30 lm droplet case. The implications of these findings regarding the use of alternative fuels is discussed. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction The objective of this paper is to analyze the impact of the vaporization of a multicomponent fuel on the kinetics of non-premixed strained flames. Such flames occur in diesel engines and turbines, where the vaporization process is most closely connected to the combustion event. Analysis of these flames is especially important with the advent of alternative fuels that might have significantly different chemical and physical properties than conventional ones. Such fuels (e.g., biomass-derived Fischer–Tropsch fuels) might have substantially different hydrocarbon compositions, such as a higher concentration of branched alkanes and different boiling point curves than petroleum-derived diesel fuels [1]. A convenient framework in which one can examine this coupling of physical and

⇑ Corresponding author. Tel.: +1 303 273 3643; Fax: +1 303 273 3730. E-mail address: [email protected] (A.M. Dean).

chemical properties of the fuel is an opposed-flow diffusion flame (Fig. 1). This provides the advantage of a well-defined flow field that can be modeled as a one-dimensional boundary value problem. As a result, this device is often used for combined experimental/modeling efforts, such as the analysis of pre-vaporized fuels [2,3]. Different models have been developed to predict the behavior of fuel evaporation [4–6]. In this work such efforts are extended by explicitly coupling the description of the evaporation of a multicomponent model fuel with the subsequent gas-phase kinetics of its components. To our knowledge, this is the first instance of such an analysis in an opposed flow diffusion flame. Of course, such coupling is frequently accomplished in CFD codes such as KIVA or Fluent to describe the combustion kinetics in engines and turbines [7,8]. In this work the goal is to develop a more explicit understanding of the impact of differential vaporization on the detailed kinetics in a diffusion flame environment. With a simpler physical configuration to model, it is possible to work with a more complex kinetic mechanism.

0010-2180/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.combustflame.2012.10.012

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dðquÞ þ 2qV ¼ SM ; dz

qu

ð1Þ

dV d þ qV 2 ¼ Kr þ dz dz



l

dV dz



þ SV  VSM ;

ð2Þ

  X K K X dT d dT ¼ k  ðu þ V k ÞY k cp;k x_ k W k hk  Q rad þ ST dz dz dz k¼1 k¼1

q



K X hk Sk ;

ð3Þ

k¼1

qu Fig. 1. Illustration of the opposed-flow nonpremixed-flame configuration.

This paper is an extension of an earlier effort [9] in which various single-component fuels, ranging from heptane to diesel fuel, were modeled with a very simplified kinetic mechanism. The vaporization model is extended to account for a multicomponent fuel, and a much more detailed kinetic mechanism is used to explore the impact of the various fuel components on the kinetics within the diffusion flame. A three-component fuel, consisting of n-heptane, n-dodecane, and n-hexadecane is used to create a simple surrogate for a Fischer–Tropsch fuel. This combination provides a wide range of vaporization rates to better define the impact of this parameter. A reduced version of the comprehensive n-alkane mechanism developed by Westbrook and co-workers [10] is used to predict the flame structure. The results of using monodispersed droplet sizes of 20, 25 and 30 lm are compared to those obtained using pre-vaporized fuel. The strain rate is varied by changing the separation distance of the inlet streams. This change has the added advantage of exploring the impact of different residence times of the fuel vapor in the hot nitrogen stream prior to entering the flame-front region. Calculations are carried out at a pressure of 10 atm, with room temperature liquid fuel droplets evaporating into a 950 K nitrogen stream. These conditions approximate those encountered when fuel is injected into a diesel engine. The results suggest that the variation in evaporation rate of the various components can produce surprisingly large variations in flame behavior, leading to large changes in the peak flame temperature as well as to substantial differences in the amount of pre-flame chemistry. These results are most pronounced when the evaporation of the heavier components occurs near the flame-front. The increased temperature in that region leads to a much higher rate of vaporization, producing an enhancement of the local fuel vapor mole fraction that increases the reaction rate. 2. Mathematical model As discussed in previous models, the overall approach is based upon an iterative algorithm, solving gas-phase conservation equations in an Eulerian framework and droplet tracking in a Lagrangian framework [9,11]. The coupling is accomplished by source terms in the gas-phase equations that are derived from the droplet equations. The droplet equations depend upon the local gas-phase environment. 2.1. Eulerian gas-phase conservation equations The conservation equations for gas-phase steady-state strained laminar axisymmetric opposed-flow flames in similarity form are well known [9,12–17]. A detailed derivation of the stagnation-flow similarity equations may be found in Kee et al. [17]. After incorporating the source terms associated with droplet vaporization, the equations can be summarized as

dY k dðqY k V k Þ _ k W k þ Sk  Y k SM : ¼x þ dz dz

ð4Þ

The axial coordinate z is the independent variable. The dependent variables include the axial velocity u, temperature T, and species mass fractions Yk. The scaled radial velocity V = v/r is also a dependent variable, with v and r being the radial velocity and radial coordinate, respectively. The mass density q is evaluated using an ideal-gas equation of state. Thermodynamic parameters include the species molar weights Wk, specific heats cp,k, and enthalpies hk. The pressure-gradient parameter Kr = (1/r)(dp/dr) is an eigenvalue that is determined during the course of the solution. Transport properties include mixture viscosity l and thermal conductivity k. The diffusion velocity is represented as

Vk ¼

K 1 X DT rT ; W j Dkj rX k  k q Yk T X k W j–k

ð5Þ

where Xk are the mole fractions, Dkj is the matrix of ordinary multicomponent diffusion coefficients, and DTk are the thermal diffusion coefficients [17]. The molar production rates of gas-phase species _ k . Radiation heat transfer by chemical reaction are represented as x between gaseous species and the environment is represented as Qrad [9,18]. Thermodynamic properties and reaction rates are evaluated through CHEMKIN software interfaces [17]. As noted above, the purely gas-phase equations are extended to include source terms associated with droplet vaporization. These terms include SM representing the net gas-phase mass addition, Sk representing the source of gas-phase species k, SV representing the source of radial momentum, and ST representing the source of thermal energy. The quantitative evaluation of these terms is discussed in a subsequent section. 2.2. Lagrangian droplets dynamics The present model assumes slow-vaporization-limit behavior [6], neglecting any spatial variations within individual droplets. Thus, the droplet trajectories, mass, temperature, and composition can be represented using a system of Lagrangian ordinary differential equations as

dzd ¼ ud ; dt

dr d ¼ rd V d ; dt

dmd _ d; ¼m dt dud Fz ; ¼ dt md

ð6Þ ð7Þ

dV d Fr ; ¼ V 2d þ dt md r d

q_ d dT d ; ¼ dt md cpd

ð8Þ ð9Þ

_d dY d;k m ðk  Y d;k Þ; ¼ dt md

ð10Þ

dF ¼ 2F V d : dt

ð11Þ

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In this formulation the independent variable is time t. The dependent variables are the droplet axial position zd, radial position rd, axial velocity ud, scaled radial velocity Vd = vd/rd, total mass md, temperature Td, mass fractions Yd,k, and the droplet flux-fraction _ d, function F . The total mass vaporization rate is represented as m with the mass vaporization rate of fuel species k being represented _ d;k ¼ k m _ d . Evaluation of the vaporization fraction k is disas m cussed in the subsequent section. The droplet heat capacity is cpd and heat transferred from the gas to the droplet is represented as q_ d . The axial and radial forces, Fz and Fr, which represent drag and thermophoretic forces, affect the droplet trajectories. As originally discussed by Continillo and Sirignano, the present formulation permits droplets to cross, and re-cross, the stagnation plane [19,9]. 2.3. Droplet vaporization Droplet vaporization is described with a thin-film model [12,13,15,20], which provides the needed quantitative relationships between droplets and the surrounding gas-phase environment. The model is first applied to evaluate the net vaporization rate, lumping the multicomponent fuel into a single effective species. Vapor-phase mass fractions for the effective fuel are needed at the droplet surface Yv,s and in the surrounding gas outside the droplet film Yv,g. These mass fractions are defined in terms of the individual multicomponent fuel species as

Y v;s ¼

K X Y v;s;k ;

Y v;g ¼

X Y v;g;k ;

ð12Þ

k

k¼1

where Yv,s,k and Yv,g,k are the mass fractions of the vapor species mixture at the droplet surface and in the gas far from the droplet, respectively. The summations consider only the fuel species in the gas phase. Using these equivalent fuel-vapor definitions, the net total droplet vaporization rate (i.e., including all of the component species) is evaluated as though the droplets were a single-component fuel [9]. That is,

_ d ¼ pdqf Dv;f Shv lnð1 þ Bv Þ; m

ð13Þ

where qf and Dv,f are the average mass density and vapor-phase diffusion coefficient within the thin film surrounding the droplet. A modified Sherwood number 

Shv ¼ 2 þ

Sh0  2 FðBv Þ

ð14Þ

accounts for variations in film thickness as a result of the Stefan flow associated with mass transfer at the droplet surface. The function

FðBv Þ ¼ ð1 þ Bv Þ0:7

lnð1 þ Bv Þ Bv

ð15Þ

Droplet vaporization is assumed to be sufficiently rapid such that the fuel-vapor concentration at the droplet surfaces are saturated. Thus, the vapor-phase mole fractions at the droplet surface can be evaluated from the species vapor pressures as

X v;s;k ¼ X d;k

pv;k ; p

ð19Þ

where pv,k is the saturation vapor pressure of the kth pure species at the droplet temperature of Td, Xd,k is the mole fraction of kth species of the liquid-phase mixture of the droplet, and p is the total gas _ d;k is evalpressure. The vaporization rate of an individual species m uated using the mass fraction of the vaporizing species k as _ d;k ¼ m _ d k , where the mass fraction k is evaluated based upon m the definition of the Spalding mass transfer number for individual species Bk as

k ¼ Y v;s;k þ

Y v;s;k  Y v;g;k : Bk

ð20Þ

The Spalding mass transfer number for each individual species Bk may be evaluated as a function of the mass-transfer number for the effective single-component fuel Bv as [21,22]

Bk ¼ ð1 þ Bv Þgk  1;   Dv;f Shv =Dk;f Shk ,

ð21Þ  Shk

where gk ¼ and is the modified Sherwood number for kth species. Because the relationships between Bk and Bv are nonlinear, an iterative process is needed to evaluate Bk. Heat transferred from the gas into the droplet is evaluated as

_d q_ d ¼ m

  cp;v ðT  T d Þ  Lv ; BT

ð22Þ

where BT is the Spalding heat-transfer number and T is the gasphase temperature outside the film surrounding the droplet. The Spalding heat- and mass-transfer numbers are related as

BT ¼ ð1 þ Bv Þ/  1;

ð23Þ

where 

/¼

cp;v Shv 1 : cp;f Nu Lef

ð24Þ

The effective latent heat Lv of vaporization is represented as

Lv ¼

X

k Lv;k ðT d Þ;

ð25Þ

k

where Lv,k(Td) is the latent heat of vaporization of the kth species at the droplet temperature. The average gas-phase specific heat within the film is represented as cp,f, and the heat capacity of the fuel-vapor mixture within the film cp,v is evaluated as

cp;v ¼

X

k cp;v;k :

ð26Þ

k

depends upon the overall Spalding mass-transfer number Bv as

Bv ¼

Y v;s  Y v;g : 1  Y v;s

ð16Þ

In the limiting case of nonvolatile droplets

Sh0 ¼ 2 þ 0:552Red1=2 Sc1=3 ;

ð17Þ

where the Schmidt number is Sc = lf/(qfDv,f) and lf is the viscosity of the film mixture. The droplet Reynolds number is defined in terms of the relative velocity as

Red ¼ qf jv  v d jd=lf ;

ð18Þ

where v and vd are the local gas-phase and droplet velocities, respectively and d is the droplet diameter.

The modified Nusselt number Nu⁄ is evaluated in a manner analo gous to Shv . The film Lewis number is defined as Lef = af/Dv,f, where af is the thermal diffusivity of the gas in the film and Dv,f is the mixture-averaged diffusion coefficient of the fuel-vapor species in the _ d ; Bv and BT, and thus evalfilm. Establishing consistent values of m uating q_ d , is an iterative process [12]. 2.4. Gas-phase source terms The influence of droplet vaporization on the gas-phase is represented in terms of mass, momentum, and energy sources SM, Sk, SV and ST in Eqs. (1)–(4). Sources for individual droplet are represented as

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C. Wang et al. / Combustion and Flame 160 (2013) 265–275

1

10 9

ð27Þ

k

The liquid-phase specific enthalpy of the droplet species is evaluated as hd,k = hg,k  Lv,k, where hg,k is the specific enthalpy of the vapor phase. This formulation assures self consistency between the liquid and gas-phase thermodynamics and the latent heat. If the thermodynamic properties for the liquid and gas phases are taken from independent data bases, such self consistency is not inherently assured. The source terms S = (SM, Sk, SV, ST)T for the control volume Dzj are evaluated as [9,14],

Sðzj Þ ¼

nd0 ud0 Dzj

XZ Nj

n¼1

t n þDt n

sF dt;

ð28Þ

tn

where N j is the number of times that a droplet enters control volume Dzj, and [tn, tn + Dtn] is the nth time interval that a droplet spends in the control volume Dzj. The variables nd0 and ud0 represent the droplet number density and velocity at the inlet. Although this formulation enables the droplets to cross the stagnation plane multiple times, multiple crossings do not occur in the present results. 2.5. Boundary and initial conditions The gas-phase problem is a boundary-value problem, with boundary conditions being specified at the inlet manifolds (cf. Fig. 1). At the left-hand manifold (i.e., z = 0),

u ¼ Uf ;

V ¼ 0;

T ¼ Tf ;

Y k ¼ Y k;f ;

V ¼ 0;

T ¼ To;

Y k ¼ Y k;o ;

10 7

C7H16

10 5 10

C12H26

3

C16H34

10 1 10

-1

10 -3 500

C7H16 400 300

C16H34

C16H34

C12H26

200

C7H16

100 0 100

200

300

400

500

600

700

Temperature (K) Fig. 2. Vapor pressure and latent heat as functions of temperature for the three surrogate fuel components.

fuel components. The markedly different evaporation rates for these components provide the opportunity to explore the impact of these differences in volatility on the subsequent chemistry. The choice of an all-alkane fuel is motivated by both the expected prevalence of such species in alternative fuels as well as the availability of reliable alkane kinetic mechanisms. 3.2. Counterflow flame conditions

ð29Þ

where the subscript ‘‘f’’ represents the fuel manifold. For the studies here, the gas-phase composition at the fuel inlet is dominantly N2, and sometimes includes low levels of O2. Typically, the fuel enters in the liquid phase, and thus does not directly contribute to the gas-phase boundary condition. At the right-hand manifold, (i.e., z = L),

u ¼ U o ;

Vapor pressure (Pa)

1 _d m sM C B _ d k m C B Bs C C B B kC s ¼ B C ¼ B m C; _ V þ F =r r d d d C B X @ sV A A @ _ md k hd;k þ q_ d sT 0

Latent heat (kJ kg-1)

0

ð30Þ

where the subscript ‘‘o’’ represents the oxidizer. For the studies here, the gas-phase composition at the oxidizer inlet is air. The droplets enter through the fuel manifold with the same axial velocity as the gas. However, the initial droplet temperature is typically around Td,0 = 300 K, which is substantially lower than the surrounding gas phase. The initial droplet composition is specified in terms of the liquid-phase volume fractions. The inlet droplet diameter is specified, which leads directly to an initial droplet mass. The initial droplet flux fraction is, by definition, F ¼ 1 [9]. 3. Chemical kinetics model 3.1. Surrogate fuel composition This study focuses on a three-component fuel mixture that serves as a relatively simple surrogate for a Fischer–Tropsch fuel. Specifically, the surrogate consists of n-heptane, n-dodecane, and n-hexadecane in a 1:4:1 mole ratio. This combination approximates the distribution of alkane species found in some synthetic aviation fuels [1]. Moreover, detailed validated chemical mechanisms for these alkanes are available [10]. The thermophysical properties of these alkanes are taken from NIST Standard Reference Database in the NIST Chemistry WebBook. Figure 2 shows the temperature-dependent vapor pressure and latent heat for the three

For the studies reported herein, the separation distance between manifolds is either L = 5 mm or L = 10 mm, and both inlet axial velocities are fixed at Uin = 1 m s1. This variation changes both the strain rate and the residence time for droplet vaporization prior to entering the high-temperature flame zone. The gas-phase temperatures at both inlets is 950 K and the pressure is 10 atm. These conditions approximate those expected in diesel engines at the point where the fuel is injected. Three initial droplet diameters (d0 = 20 lm, d0 = 25 lm and d0 = 30 lm) are considered. In all cases, the initial droplet temperature is Td,0 = 300 K, and the initial droplet velocity is the same as the gas-phase inlet velocity. The initial droplet number density must also be specified. With the droplet diameter specified, the inlet droplet number density is set such that the overall equivalence ratio would be unity if the fuel and oxidizer streams would be completely mixed. At the inlet, the fuel is diluted by nitrogen. For initially 20 lm droplets, these conditions lead to an inlet fuel-droplet loading density of nd0 ¼ 7:93  1010 m3, with the nominal droplet spacing being approximately 235 lm. If the fuel were fully vaporized at the inlet, these conditions would lead to inlet gas-phase fuel mole fractions of 0.192% for n-heptane and n-hexadecane and 0.767% for nhexadecane. Thus the fuel is highly diluted in the inlet carrier gas. When the initial droplet diameter is varied, the initial loading density is varied so as to maintain the same fuel mass loading and the overall equivalence ratio of unity. Simulations are also performed with the pre-vaporized fuel components in the nitrogen carrier stream. In this case the mass flow rate of nitrogen is approximately 1% lower than in the droplet cases. 3.3. Mechanism reduction procedure The alkane mechanism published by Westbrook et al. [10] contains 2115 species and 8130 reactions-much too large to use

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C. Wang et al. / Combustion and Flame 160 (2013) 265–275

Mole fraction (%)

4.0

1600

Pyrolysis

3.5

1500

3.0

1400

2.5

1300

C2H 4

2.0

1200

1.5

1100

n-C12H26

1.0

H2

0.5 0.0

1000

Temperature (K)

900 800

(a)

Mole fraction (%)

3.0

Oxidation

2.5 2.0

C2H4

1.5 Original Reduced

1.0

H2

0.5 0.0 0.1

0.12

0.14

0.16

0.18

0.2

Distance (mm)

(b)

C2H4 mole fraction (%)

Fig. 3. Comparison of the plug flow predictions of the complete and reduced mechanisms in the pre-flame region. (a) 3-component fuel diluted in nitrogen, (b) 3-component fuel/10% O2 diluted in nitrogen. Solid lines represent the complete mechanism; dashed lines represent the reduced 3-component mechanism.

1800

1.2

Original Reduced

Counterflow flame

1.0 0.8

1600 1400

0.6

1200

0.4 0.2 0

Temperature (K)

directly for the counterflow flame calculations. In fact, this mechanism is so large it is impractical to use it even to generate the target parameters needed for the mechanism reduction process. Thus, an alternative approach was used to develop a reduced reaction mechanism. First a smaller n-heptane mechanism, consisting of 654 species and 2827 reactions [23], was considered. An additional simplification, based on the high volatility of n-heptane, was to assume that the fuel was pre-vaporized. The counterflow diffusion flame code in CHEMKIN-PRO [24] was used to generate the species and temperature profiles for the counterflow case, using the conditions specified earlier with L = 5 mm. An interesting result was that, in addition to the expected reactions near the flame-front, there was substantial pyrolysis chemistry in the pre-flame zone, meaning that the reduced mechanism must account for this pre-flame chemistry for the three component fuel as well. To focus on the kinetics, two simplified cases were identified where the original large C8–C16 mechanism was used for plug-flow calculations. This much simpler plug-flow analysis enables the use of the original large mechanism with the 1:4:1 fuel ratio to generate targets for the subsequent mechanism reduction. The first case, chosen to account for the flame-front kinetics, assumed that both input streams used in the counterflow system were well mixed at a fixed temperature of 2000 K. The calculated n-heptane, n-dodecane, n-hexadecane, O2, CO, CO2, H2 and C2H4 concentration–time profiles over a 2 ms interval were selected as the targets. (Most of the reaction occurred within the first 0.1 ms.) The mechanism reduction was performed using the DRGEP method within CHEMKIN-PRO. The absolute error tolerance was set as 103 and the relative error tolerance was set as 5%. These criteria were satisfied with a reduced mechanism consisting of 117 species and 708 reactions. The second case, chosen to describe the kinetics in the preflame zone, was also a plug-flow calculation. Here it was important to attempt to account for the variation in temperature within the pre-flame zone. This temperature-distance profile was obtained from a counterflow diffusion flame calculation, using the multicomponent evaporation code described in this work, with an approximate reduced multicomponent mechanism. This mechanism was only used to generate an approximate temperature profile for the subsequent plug flow calculations. The approach was needed to account for the drop in temperature accompanying evaporation and the subsequent temperature changes due to reaction. This calculation predicted substantial pre-flame chemistry in a narrow zone where there was a rapid rise in temperature (895– 1560 K over 0.2 mm). This temperature-distance profile was then imposed on the plug-flow calculation with the initial composition corresponding to the fuel/nitrogen mixture. To generate a more robust mechanism, additional plug-flow calculations considered the impact of air entrainment. For this case, the equivalence ratio was set equal to 2 (10% O2). This combination of pyrolysis and partial oxidation conditions forced the reduced mechanism to properly account for the kinetics for both these conditions. The same target species were used as above. These cases required a more complex reduction scheme to suitably reduce the mechanism size. First the DRGEP method with absolute tolerance of 103 and a relative tolerance of 8% was employed to yield a mechanism with 310 species. Then a DRG-sensitivity method with the same tolerances was then used to produce a 161 species and 722 reactions mechanism. The two reduced mechanisms were then merged to generate a combined mechanism with 196 species and 907 reactions. Predictions using this combined mechanism for a variety of plug-flow conditions were compared to those obtained with the original large mechanism to assess the accuracy of the reduction. Such comparisons in the high temperature flame-front regime were virtually

1000 2

2.2

2.4

2.6

2.8

3

Distance (mm) Fig. 4. Comparison of the counterflow flame predictions for n-heptane as the fuel with the complete heptane mechanism to that of the reduced 3-component mechanism. Solid lines represent the complete heptane mechanism; dashed lines represent the reduced 3-component mechanism.

identical. Comparisons for the pre-flame pyrolysis conditions were very similar, as shown in Fig. 3a. Figure 3b compares the effect of adding 10% O2. The observed good agreement for both the pyrolysis and partial oxidation conditions is encouraging. A more demanding test of the accuracy of the reduced mechanism involved comparing the predictions of the counterflow flame using this reduced threecomponent mechanism considering only heptane as a fuel to those of the large heptane mechanism that had served as the basis for the mechanism reduction. Figure 4 illustrates the predicted results for temperature and ethylene production. The good agreement between the temperature profiles is particularly encouraging since temperature was not selected as a target during the reduction procedure. The ethylene comparisons are also reasonable, especially considering that the reduced mechanism was based on the C8–C16 rather than the C7 mechanism. A direct comparison of the C2H4 production under pre-flame plug-flow conditions using these two mechanisms showed similar differences, with approximately 10% less C2H4 produced using the complete C8–C16 than when using the complete C7 mechanism. These comparisons suggest the validity of this indirect reduction method; the 196 species reduced mechanism should be adequate to capture the major features of the kinetics in the 3-component counterflow diffusion flames in both the pre-flame and flame-front regions.

C. Wang et al. / Combustion and Flame 160 (2013) 265–275

An initial set of calculations for the counterflow flame conditions with the separation distance L = 5 mm was performed with the three-component fuel pre-vaporized in the hot nitrogen stream. These simulations served as a basis to compare subsequent calculations where the fuel is introduced as liquid droplets. To facilitate comparison with the droplet results where evaporative cooling occurs, two calculations with inlet temperatures of 850 K and 950 K served to bracket the temperatures encountered in the droplet cases. Figure 5 shows predictions near the flame-front region. The computed temperature profiles and vapor phase residence times (calculated from the axial velocity profile) are shown in Fig. 5a. The peak temperature of 1690 K for the 850 K inlet temperature is increased to 1769 K for the 950 K case and the flame front shifts approximately 1 mm toward the fuel side for the higher temperature. These relatively low peak temperatures are the result of the nitrogen dilution of the fuel stream. The flames are quite narrow, approximately 0.3 mm wide at the temperature midpoint, due to the relatively high pressure of 10 atm. Figure 5b shows that significant consumption of all three fuel components begins at approximately the location where the temperature has increased to approximately 1000 K. Perhaps the most interesting feature of these calculations is the significant extent of reaction in the pyrolysis zone, as illustrated in Fig. 5c. Ethylene is produced very early in the nearly uniform inlet temperature region. The ethylene

10

Gas-phase flame

1600

8

1400

6

1200

4 2

1000

0

20

n-C12H26

0.6

15

0.5

O2

n-C7H16

0.4

10

0.3 0.2 0.1

5

Fuel components

n-C16H34

0.0

O2 mole fraction (%)

Mole fraction (%)

(a) 0.8 0.7

Residence time (ms)

Temperature (K)

1800

0

(b)

C2H2

Tin = 850 K

C4 H 6

0.0 2.2

2.4

Gas-phase alone, 950 K

85

Gas-phase alone, 850 K 80

(a)

0.20 0.15

Droplets

0.10 0.05

Gas 950K

850 K

Gas 950K

850 K

n-C7H16

0.00

(b)

0.80 0.60 0.40

n-C12 H26

0.20

Droplets

(c)

0.4

2

Two-phase (droplets)

90

0.25

Tin = 950 K

0.2

N2

95

75

Pyrolysis components

0.8 0.6

100

0.00

C2H 4

1.0

Calculations were performed with 20 lm diameter droplets to explore the impact of a finite vaporization rate. To attain the same overall equivalence ratio of unity used for the pre-vaporized case,

Mole fraction (%)

Mole fraction (%)

1.2

4.2. 20 lm Droplets

Mole fraction (%)

4.1. Pre-vaporized fuel results

production is due to the successive b-scission reactions of the alkyl radicals formed by radical abstraction reactions of the parent fuel components. There is sufficient reactivity in the pre-flame region to also produce acetylene and 1,3-butadiene. Vinyl radicals, formed by radical abstraction from ethylene, can either undergo b-scission to form acetylene or react with ethylene to form butadiene (C4H6). The temperature is increasing rapidly as these species are formed. Note that even at this point, the O2 mole fraction is negligible. The significant differences in the extent of pre-flame chemistry for the two cases reveals the importance of the inlet temperatures in driving the pyrolysis kinetics. One might expect more pre-flame chemistry for the pre-vaporized cases than for the droplet cases since the pre-vaporized fuel components will have spent more time in the hot nitrogen gas. However, as discussed below, the quantitative impact of the vaporization process is more complex and more interesting.

Mole fraction (%)

4. Results and discussion

Mole fraction (%)

270

2.6

2.8

3

Distance (mm)

(c) Fig. 5. Comparison of the effect on inlet fuel temperature on the counterflow diffusion flame profiles for the case where the fuel is all initially in the vapor phase. The separation distance and computational domain is 5 mm, but only the flamezone region is plotted.

0.20

Gas 950K

0.15

850 K

0.10

n-C16H34

0.05 0.00

0

0.5

Droplets 1.0

1.5

2.0

2.5

3.0

Distance (mm)

(d) Fig. 6. Comparisons of the counterflow diffusion flame profiles of vapor mole fractions of the fuel components for 20 lm droplets (solid lines) with the prevaporized cases (dashed lines).

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1400 1200

(a)

1000

1.2 1.0

(b) C2H4 Gas 950 K

0.6 0.4

Gas 850 K

0.2

Mole fraction

Mole fraction (%)

1400

10

1200

5

1000 0.4

0.8

1.2

1.6

2.0

2.4

2.8

Gas 850 K

1.0

(b) 20 µm

1800

n-C12H26

1600

0.6

1400

n-C16H34 n-C7H16

0.4

1200 1000

0.2

800 2000

1.0 0.8 0.6 0.4

Mole fraction

0.03 0.02

Gas 850 K

0.01 0.00

2.1

2.2 2.3 Distance (mm)

2.4

1800

n-C12H26

1600 1400

n-C16H34

n-C7H16

1200 1000

0.2

2.5

Fig. 7. Comparisons of the counterflow diffusion flame profiles of temperature, vapor phase residence time, and mole factions of selected pyrolysis products for 20 lm droplets (solid lines) to the pre-vaporized cases (dashed lines).

1.0

800 2000

(d) 30 µm

1800

n-C12H26

0.8

1600 1400

0.6 0.4 0.2 0.0 2.0

n-C7H16 2.1

n-C16H34

1200 1000

2.2

2.3

2.4

Gas Temp. (K)

0.04

(c) 25 µm

0.0

Gas 950 K

800

2000

0.8

1.2

(d) C4H6

3.2

Gas Temp. (K)

Mole fraction (%)

1600

1.2

Gas 950 K

1800

15

0.0

(c) C2H2

2000

Distance (mm)

0.06

2.0

20

0 0.0

0.0

0.05

2200

30 µm 25 20

(a)

25

1.2

0.8

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

30

Gas Temp. (K)

Mole fraction (%)

800

A series of calculations were performed wherein the droplet diameter was changed (with the droplet number density modified such that the amount of fuel was kept constant). Figure 8a compares the predicted temperatures and droplet-diameter profiles

Droplet diameter (µm)

1600

4.3. Effect of initial droplet diameter

Mole fraction

Temperature (K)

Two-phase (droplets) Gas-phase alone, 950 K Gas-phase alone, 850 K

Residence time (ms)

8 7 6 5 4 3 2 1 0

1800

Figure 7 shows the differences in the extent of pre-flame pyrolysis kinetics between the pre-vaporized and the 20 lm droplet cases. The peak temperature for the droplet case is 1738 K (Fig. 7a), between that for the pre-vaporized cases (1690 and1769 K). Interestingly, the peak temperature is higher than the 850 K pre-vaporized case, even though the temperature after the fuel has evaporated is actually slightly lower (835 K). Although the overall vapor phase residence time for the droplet case is slightly longer than the pre-vaporized cases, the time the fuel components spend in the vapor phase is shorter. The n-C7 vapor phase mole fraction approaches that for the pre-vaporized case at approximately 1 mm, meaning that it has approximately 1 ms less time in the heated gas. The time difference is approximately 2 ms for n-C12H26 and approximately 3 ms for n-C16H34. Nevertheless, the amount of pyrolysis is comparable to that predicted in the two pre-vaporized cases, as shown in Fig. 7b–d.

Gas temperature (K)

the initial 3-component droplet number density was set at ndo  7:93  1010 m3 . These liquid droplets, initially at 300 K, were dispersed in the 950 K nitrogen stream flowing at 1 m s1, the same initial conditions used for the high temperature prevaporized case. Figure 6 compares the droplet predictions to those for the pre-vaporized cases. The slight drop in nitrogen mole fraction (Fig. 6a) between 0 and 2 mm for the droplet case reflects the increase in fuel vapor mole fraction as evaporation occurs. The subsequent drop in nitrogen mole fraction is quite similar for both cases, reflecting the increasing number of moles produced during the combustion process. Figure 6b–d shows vapor-phase mole fractions for the three fuel components as the liquid components evaporate. The most volatile n-heptane (Fig. 6b) is fully vaporized well before entering the flame-front region. Prior to entering the flame-front region, it achieves a uniform mole fraction that is slightly larger (3% relative change) than that for the pre-vaporized cases. This local enrichment, due to the fact that the fuel is now evaporating over a shorter time interval, is more evident with the less volatile fuels. The n-dodecane (Fig. 6c) begins to evaporate later, achieving a uniform mole fraction that is higher than that for the pre-vaporized cases by about 13%. This trend continues for the least volatile n-hexadecane (Fig. 6d) where the local enrichment is approximately 20%. The uniform vapor phase profile is significantly shorter than the more volatile components. For all three components, the fuel decay profiles fall between the those of the two pre-vaporized cases, consistent with the temperature-distance profiles shown in Fig. 7a.

800 2.5

Distance (mm) Fig. 8. Predictions of the impact of changing initial fuel droplet size on the counterflow diffusion flame profiles for liquid droplet size, temperatures and vapor phase mole fractions of the fuel components. Note distance scale in (a) is different from the other panels.

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for 20 lm, 25 lm and 30 lm droplets. It is interesting to note that during initial droplet vaporization, the droplet diameter actually increases slightly. This is the result of decreasing liquid-phase density as the droplet heats, which competes favorably with mass loss owing to little vaporization during the initial stages of vaporization. As the initial droplet size increases, the point at which the droplets are completely vaporized moves well into the high-temperature region. The peak flame temperature also increases dramatically, from 1738 K for the 20 lm case to 2102 K for 30 lm droplets, accompanied by a shift away from the fuel-inlet side. Figure 8b–d shows the vapor mole fractions for the fuel components near the flame-front. For the 20 lm case, all the fuel is evaporated and nearly uniform vapor mole fractions are established before any significant flame-influenced temperature increases. For the 25 lm case, only the most volatile n-C7 reaches a uniform pre-flame profile; the vapor mole fractions n-C12 and n-C16 are increasing and reaching levels well above those predicted for the 20 lm case. Again, these higher local vapor phase mole fractions can be attributed to the increasing vaporization rate as these droplets enter the high-temperature flame region. This trend continues for the 30 lm case; here the vapor mole fraction enhancement is even more pronounced. This increase in the fuel vapor mole fraction near the flame-front with the larger droplets results in a greater rate of heat release with the consequent increase in peak temperature. Another potential explanation for the increased temperature in the flame front region is that perhaps

Residence time (ms)

12 10

(a) 30 µm

8

20 µm 25 µm

6 4 2 0

Temperature (K)

2200 2000

(b)

30 µm

1800

25 µm

1600 1400

20 µm

1200

the delayed evaporation results in a higher O2 mole fraction in the region where these droplets evaporate. However, the O2 profiles for the 20 and 25 lm droplets fall in between those for the two pre-vaporized cases, while that for the 30 lm droplets are shifted about 1 mm downstream. The result is that, even for the largest droplets, the fuel is evaporating into a pyrolysis region and then swept into the oxidation zone. Figure 9 shows that the increase in fuel vapor mole fraction also leads to significant differences in the amount of pre-flame pyrolysis chemistry. Although the temperature is similar for the three droplet diameters for distances less than approximately 2.5 mm, the significant progressive increase in the amount of ethylene and hydrogen produced with increasing drop size is significant. This increase in C2H4 begins near 2 mm, where the temperature and residence time are similar for all three drop diameters. The one difference is the increased local vapor phase mole fractions in this region for the larger drops. Closer to the flame-front, the increased vapor phase residence time in the higher temperature region for the largest droplets could also contribute to increased reactivity. Not surprisingly, because of its higher diffusivity, the increases in the hydrogen mole fraction with larger droplets extend to larger distances. 4.4. Effect of separation distance The previous results illustrate the substantial impact on both the peak temperature and the extent of pre-flame pyrolysis chemistry if the evaporation rate is sufficiently slow that fuel droplets penetrate into the high temperature region. To explore this effect further, this sequence of calculations was repeated for cases where the separation distance is doubled to 10 mm, allowing more time for the droplet to evaporate before entering the high temperature region. Figure 10 compares predicted droplet-size profiles for the two separation distances. For both cases, the droplet diameter initially increases as a result of droplet heating (liquid density decreases) prior to the onset of evaporation in the hot nitrogen stream. The effect of increased separation distance gets progressively larger as the droplet size increases. In particular, note the almost vertical drop in diameter for the 30 lm case at 5 mm separation. This is due to droplet impingement into the hot flame region and subsequent very rapid evaporation. In contrast, the shapes of the profiles for the various drop sizes at 10 mm separation are similar to each other, reflecting the slower evaporation

1000 800

35

(c) H2

Droplet dia. (µm)

Mole fraction (%)

1.5

30 µm 25 µm

1.0

20 µm 0.5

20 µm

25

25 µm

20

30 µm

15

(a) 5 mm separation

10 5 0

0.0

35

2.0

(d) C2H4

Droplet dia. (µm)

2.5

Mole fraction (%)

30

30 µm 25 µm

1.5

20 µm

1.0 0.5

30 20

2.0

2.5

3.0

25 µm

15

20 µm

(b) 10 mm separation

10 5 0

0.0 1.5

30 µm

25

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Distance (mm)

Distance (mm) Fig. 9. Comparison of the effect of initial fuel droplet size on selected counterflow diffusion flame profiles.

Fig. 10. Comparison of the effect of changing the separation distance from 5 mm to 10 mm on the profile of liquid fuel diameter as the diameter varies from 20 lm to 30 lm.

273

700 650 600 550 500 450 400 350 300

C12H26 mole frac. (%)

700 650 600 550 500 450 400 350 300

20 µm 30 µm 25 µm

1.20 1.00 0.80

Gas

0.60

25 µm 20 µm

0.40 0.20

30 µm

0.00 0

(a) 5 mm separation

0.5

20 µm 30 µm

2.0

2.5

25 µm

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

1.20

850 K

1.00 0.80

Gas

0.60

30 µm

20 µm

0.40

25 µm

0.20

950 K

0.00 0

(b) 10 mm separation

1.0

2.0

3.0

4.0

5.0

Distance (mm)

Fig. 11. Comparison of the effect of changing the separation distance from 5 mm to 10 mm on the droplet temperature as the diameter varies from 20 lm to 30 lm.

(b) 10 mm separation Fig. 13. Comparison of the effect of changing the separation distance from 5 mm to 10 mm on vapor phase mole fraction of n-C12 as the diameter varies from 20 lm to 30 lm.

0.25 0.20

Gas

0.15

20 µm

0.10

30 µm 25 µm

0.05 0.00

0

0.5

1.0

1.5

2.0

2.5

Distance (mm)

(a) 5 mm separation

C16H34 mole frac. (%)

C7H16 mole frac. (%)

1.5

(a) 5 mm separation

Distance (mm)

0.35

25 µm

0.30 0.25

Gas

0.20 0.15

20 µm

0.10

30 µm

0.05 0.00

0.25

0

0.5

1.0

1.5

2.0

2.5

Distance (mm) 0.20

Gas

0.15

(a) 5 mm separation

30 µm Two-phase Gas, 950 K Gas, 850 K

25 µm

0.10 0.05

20 µm

0.00 0

1.0

2.0

3.0

4.0

5.0

Distance (mm)

(b) 10 mm separation Fig. 12. Comparison of the effect of changing the separation distance from 5 mm to 10 mm on vapor phase mole fraction of n-C7 as the diameter varies from 20 lm to 30 lm.

of the larger droplets. For this case the droplets completely evaporate prior to entering the hot region. Figure 11 shows analogous droplet-temperature trends. As a consequence of the larger separation distance with the associated lower droplet temperatures at a given distance, the evaporation rate is slower, resulting in less enhancement of the vapor phase mole fractions of the three fuel components. This results in vapor phase fuel mole fractions closer to those predicted for the pre-vaporized cases, as seen in Figs. 12–14. With the most volatile component (n-C7), Fig. 12 shows that, for the 20 lm case, the vapor phase mole fractions closely approach those for the pre-vaporized cases at both separation distances. However, even for this volatile component, the evaporation rate is sufficiently slow for larger droplet diameters to observe differences. For the shorter separa-

C16H34 mole frac. (%)

C7H16 mole frac. (%)

1.0

Distance (mm)

C12H26 mole frac. (%)

Drop Temp. (K)

Drop Temp. (K)

C. Wang et al. / Combustion and Flame 160 (2013) 265–275

0.35 0.30 0.25 0.20

Gas

0.15

950 K

20 µm

0.10

30 µm 25 µm

0.05 0.00

0

1.0

2.0

3.0

4.0

5.0

Distance (mm)

(b) 10 mm separation Fig. 14. Comparison of the effect of changing the separation distance from 5 mm to 10 mm on vapor phase mole fraction of n-C16 as the diameter varies from 20 lm to 30 lm. Long dashed line shows prediction for pre-vaporized fuel entering at 950 K; short dashed line for 850 K.

tion, significant enhancement is observed, more so for the 30 lm case. Such enhancements are much diminished at the larger separation. For the mid-volatile n-C12, Fig. 13 shows a more pronounced effect of both droplet size and separation distance, with substantial deviations from the pre-vaporized cases for all droplet sizes at 5 mm separation. The deviations are smaller at 10 mm separation, but still significant. For the 5 mm case, neither the 25 lm or 30 lm droplets have fully vaporized before reaching the flame-front. In contrast, all of the components for the larger separation have

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30 µm 25 µm 20 µm

(a) 5 mm separation Two-phase Gas, 950 K Gas, 850 K

Gas 0

0.5

1.0

1.5

2.0

2.5

3.0

1800

Temperatrue (K)

Temperature (K)

2200 2000 1800 1600 1400 1200 1000 800

(c) 10 mm separation

1600

Two-phase Gas, 950 K Gas, 850 K

1400 1200

Gas

1000 800

3.5

1.0

0

2.0

(b)

Temperatrue (K)

Temperature (K)

960 940 920 900 880 860 840 820 800

Gas, 950 K 30 µm

25 µm 20 µm 5 mm separation 0

0.5

1.0

3.0

4.0

5.0

6.0

Distance (mm)

Distance (mm)

1.5

2.0

960 940 920 900 880 860 840 820 800

(d) 30 µm 20 µm

Gas, 950 K 25 µm

10 mm separation 0

1.0

2.0

Distance (mm)

3.0

4.0

Distance (mm)

Fig. 15. Comparison of the effect of changing the separation distance from 5 mm to 10 mm on the temperature profile. The lower panels expand the temperature range to show the temperature drop during the evaporation process.

(a) Residence time 5 mm separation

Residence time (ms)

10 9 8 7 6 5 4 3 2

30 µm

Two-phase Gas, 950 K Gas, 850 K

Gas

2.5 2.0

(b) C2H4

1.5

30 µm

25 µm

20 µm

1.0 0.5

two pre-vaporized cases. Although the magnitude of the differences relative to the gas phase are much smaller than for the 5 mm separation, the trend is the same, with the largest droplets having the highest peak temperature. The variation in the cooling rate during evaporation, shown in the lower panels of Fig. 15, is directly related to the evaporation rate. The increased surface-tovolume ratio for the smaller droplets leads to increased evaporation rates and faster cooling. In the lower panel for the 10 mm case, note that even the 30 lm droplet has completely evaporated

Mole fraction (%)

Mole fraction (%)

Residence time (ms)

reached uniform pre-flame profiles. As illustrated in Fig. 14, the trend of increasing vapor mole fraction enhancement with increasing droplet size continues for the least volatile component n-C16. Figure 15 illustrates the impact of different evaporation rates on the peak flame temperature, due to different separation distances. The 10 mm separation distance leads to peak temperatures much closer to those predicted for the pre-vaporized cases. The peak temperatures were 1796 K, 1749 K, and 1724 K for the 30 lm, 25 lm, and 20 lm droplet sizes respectively. These can be compared to peak temperatures of 1804 K and 1729 K for the

Gas

0.12 0.10 0.08 0.06 0.04 0.02 0.00 2.0

(c) C2H2

Mole fraction (%)

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

30 µm 25 µm 20

Gas

12 10 8

(e) Residence time 10 mm separation

30 µm

Two-phase Gas, 950 K Gas, 850 K

Gas, 850 K

6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

30 µm 25 µm 20 µm

(f) C2H4

Gas, 950 K 850 K

0.5 0.4

(g) C2H2

30 µm 25 µm 20 µm

0.3 0.2

Gas, 950 K

0.1 0.0 0.06

(d) C4H6

Mole fraction (%)

Mole fraction (%)

Mole fraction (%)

0.0

14

30 µm 25 µm 20 µm Gas

2.1

2.2

2.3

Distance (mm)

2.4

2.5

0.05

30 µm

(h) C4H6

25 µm 20 µm

0.04 0.03 0.02 0.01 0.00 4.0

Gas, 950 K 4.2

4.4

4.6

4.8

5.0

Distance (mm)

Fig. 16. Comparison of the effect of changing the separation distance from 5 mm to 10 mm on the vapor phase residence time and selected pyrolysis products as the diameter varies from 20 lm to 30 lm.

C. Wang et al. / Combustion and Flame 160 (2013) 265–275

before entering the high-temperature region, whereas only the 20 lm droplet vaporized completely with 5 mm separation. Figure 16 shows the impact of the variations in vapor-phase mole fractions on the pre-flame pyrolysis chemistry at different separation distances. Note that the residence times are significantly longer at the larger separation (Fig. 16 a and e). As expected, the extent of reaction for the pre-vaporized cases is slightly larger at the larger separation distance due to the increased time in the vapor phase. In contrast, there is significantly less pre-flame reaction for the droplet cases at the larger separation, and the variation of the extent of reaction with droplet size is much smaller than it is for the smaller separation. The larger enhancements of local fuel vapor mole fractions with the droplets for the smaller separation cases more than offset the decreased residence time for this case. The effect of varying droplet size is much less at the larger separation distance where even the heaviest component in the largest droplet has time to vaporize before entering the flame-front. The greatly enhanced vaporization rates that result if the droplets penetrate into the high temperature region near the flame-front thus may have profound effects upon the extent of both the pre-flame and flame-front chemistry. 5. Summary and conclusions An opposed-flow diffusion flame model was used to explore the impact of the evaporation of a multicomponent fuel on the kinetics in the pre-flame and flame-front regions. The fuel consisted of three alkanes with much different volatilities, selected to cover the range expected in a typical aviation fuel. The advantage of using the alkanes is that validated kinetic mechanisms are available. A reduced kinetic mechanism containing 196 species was derived from an initial mechanism containing 2115 species. Results were obtained comparing pre-vaporized fuel streams to those containing monodispersed droplet sizes of 20, 25 and 30 lm carried in nitrogen at separation distances of 5 and 10 mm with both inlet velocities at 1 m s1. In all cases the overall equivalence ratio was set to be unity and the pressure was 10 atm. It was observed that finite evaporation rates significantly impacted the kinetics. In particular, if the combination of separation length, stream velocity, and fuel volatility was such that the fuel droplets entered the higher temperature region near the flamefront, the rapid increase in evaporation rate in that region significantly enhanced the local vapor phase fuel mole fraction. This in turn increased the reaction rates, leading to higher peak temperatures as well as increased pyrolysis in the pre-flame region. For example, the peak temperature predicted for the 30 lm droplet was 330 K higher than a pre-vaporized case at the same inlet temperature. This increase occurred in spite of an initial decrease in temperature as the droplet evaporates. A similar effect is observed

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for the pre-flame pyrolysis products; ethylene, acetylene, and butadiene all increased about a factor of two for the 30 lm droplet case. These variations in temperatures and species concentrations resulting from droplet evaporation could have significant implications for various combustion applications. The importance of the local fuel mole fraction in terms of dramatically changing the reaction rate requires careful attention to details of the fuel evaporation rate. Even when combustion kinetics is a primary focus, it is clearly important to consider fuel volatility characteristics when designing surrogate fuel blends [25]. Acknowledgment This effort was supported by the Office of Naval Research via Grant N00014-08-1-0539. References [1] B.L. Smith, T. Bruno, J. Propul. 24 (2008) 618–623. [2] J.A. Cooke, M. Bellucci, M.D. Smooke, A.A. Gomez, A. Violi, T. Faravelli, E. Ranzi, Proc. Combust. Inst. 30 (2005) 439–446. [3] A. Holley, Y. Dong, F. Egolfopoulous, Combust. Flame 144 (2006) 448–460. [4] M. Arias-Zugasti, D.E. Rosner, Combust. Flame 135 (2003) 271–284. [5] S.S. Sazhin, A.E. Elwardany, E.M. Sazhina, M.R. Heikal, Int. J. Heat Mass Transfer 54 (2011) 4325–4332. [6] W.A. Sirignano, G. Wu, Int. J. Heat Mass Transfer 51 (2008) 4759–4774. [7] Y. Ra, R.D. Reitz, Combust. Flame 155 (2008) 713–738. [8] Y. Ra, R.D. Reitz, Combust. Flame 158 (2011) 69–90. [9] R.J. Kee, K. Yamashita, H. Zhu, A.M. Dean, Combust. Flame 158 (2011) 1129– 1139. [10] C.K. Westbrook, W.J. Pitz, O. Herbinet, H.J. Curran, E.J. Silke, Combust. Flame 156 (2009) 181–199. [11] H. Zhu, R.J. Kee, L. Chen, J. Cao, M. Xu, Y. Zhang, Combust. Theory Model 16 (2012) 715–735. [12] B. Abramzon, W.A. Sirignano, Int. J. Heat Mass Transfer 32 (1989) 1605–1618. [13] E. Gutheil, W.A. Sirignano, Combust. Flame 113 (1998) 92–105. [14] A.M. Lentati, H.K. Chelliah, Combust. Flame 115 (1998) 158–179. [15] W.A. Sirignano, Fluid Dynamics and Transport of Droplets and Sprays, second ed., Cambridge University Press, 2010. [16] A.U. Modak, A. Abbud-Madrid, J. Delplanque, R.J. Kee, Combust. Flame 144 (2006) 103–111. [17] R.J. Kee, M.E. Coltrin, P. Glarborg, Chemically Reacting Flow: Theory and Practice, Wiley, Hoboken, NJ, 2003. [18] R.S. Barlow, A.N. Karpetis, J.H. Frank, J.Y. Chen, Combust. Flame 127 (2001) 2102–2118. [19] G. Continillo, W.A. Sirignano, Combust. Flame 81 (1990) 325–340. [20] S.S. Sazhin, Prog. Energy Combust. Sci. 32 (2006) 162–214. [21] H. Watanabe, Y. Matsushita, H. Aoki, T. Miura, Combust. Flame 157 (2010) 839–852. [22] E. Rivard, D. Brüggemann, Chem. Eng. Sci. 65 (2010) 5137–5145. [23] M. Mehl, W.J. Pitz, C.K. Westbrook, H.J. Curran, Proc. Combust. Inst. 33 (2011) 193–200. [24] CHEMKIN-PRO Release 15101. Reaction Design, Inc., San Diego, CA, 2010. [25] C.J. Mueller, W.J. Cannella, T.J. Bruno, B. Bunting, H.D. Dettman, J.A. Franz, M.L. Huber, M. Natarajan, W.J. Pitz, M.A. Ratcliff, K. Wright, Energy Fuels 26 (2012) 3284–3303.