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Mar 3, 2014 - High-speed schlieren photography was used to measure the critical radius for the onset of flame-front instability. Results show that, fo...
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Flame-Front Instabilities of Outwardly Expanding Isooctane/ n‑Butanol Blend−Air Flames at Elevated Pressures Xinyi Zhang, Chenglong Tang,* Huibin Yu, and Zuohua Huang* State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China ABSTRACT: Experiments were conducted in a constant volume bomb filled with isooctane/n-butanol blend−air mixtures over a wide range of n-butanol blending ratios, equivalence ratios, and initial pressures. High-speed schlieren photography was used to measure the critical radius for the onset of flame-front instability. Results show that, for a given n-butanol blending ratio, cellular instabilities appear earlier and the critical Peclet number, which represents the onset of instability, is decreased with the increase of the initial pressure and equivalence ratio. Under fuel-rich conditions, the critical Peclet number increases with the increase of the n-butanol blending ratio. Theoretical calculation of the critical Peclet number was also conducted to interpret the effects of nbutanol on the flame-front instabilities of the blends. Results show that, for rich mixture conditions, with the increase of the nbutanol blending ratio, the overall activation energy of the mixtures is decreased and, thus, the thermal−diffusional instabilities are suppressed. While under fuel-lean conditions, the thermal−diffusional instabilities are favored. As a consequence, with an increasing n-butanol blending ratio, the critical Peclet number is expected to be decreased under fuel-lean conditions and increased under fuel-rich conditions.

1. INTRODUCTION Bioalcohol has been emerging as an attractive substitute for gasoline because of its renewability. More than 95% of U.S. gasoline contains ethanol in a low level, and a high-level ethanol blend is also available in flexible fuel vehicles.1 In Brazil, the government has mandated that the minimum ethanol content must reach 22%.1 However, research interests have recently shifted to large alcohols, such as n-butanol, because in comparison to ethanol, n-butanol has higher energy density and is much less hydrophilic and, thus, less corrosive. Furthermore, n-butanol is easier to be mixed with gasoline and safer in storage and transportation because of a lower vapor pressure and also performs better in the cold start of engines.2−4 Moreover, in recent years, some notable achievements of the n-butanol production process in the microbiology field further promoted its possibilities as a main blending agent in gasoline engines in the future.2 Previously, many experiments on gasoline engines were carried out with n-butanol being a blending agent to assess the performance of these engines from both combustion and emission standpoints.5−10 Additionally, experimental studies on fundamental combustion characteristics of isooctane/n-butanol blends were also conducted. Dagaut and co-workers performed an experiment on the oxidation kinetics of isooctane/n-butanol blends in a fused silica jet-stirred reactor and provided the concentration profiles of reactants, stable intermediates, and final products under different conditions and blending ratios of n-butanol.11 Broustail et al. and Zhang et al.12,13 experimentally measured the laminar flame speeds of isooctane/n-butanol blends at different initial pressures and temperatures, separately, both using a constant volume bomb. More recently, Ma et al.14,15 have conducted an experimental work using high-speed schlieren photography on combustion characteristics of isooctane/2-methyfuran (MF) blends, and they found that the blended fuel flames are less stable than the flames of isooctane but more stable than the flames of MF at the © 2014 American Chemical Society

equivalence ratios less than 1.0. However, up to now, no report on laminar flame instabilities of isooctane/n-butanol blends has been given. Flame instability was first experimentally observed in a Bunsen flame by Smithells and Ingle16 in the 19th century. It was shown by numerous observations that an initially smooth combustion wave in explosive gas mixtures would break or fold and finally exhibit the so-called cellular structure without apparent external interference in certain mixtures and pressures.17−22 Some theoretical work was carried out in the past few decades to clarify this fascinating phenomenon of laminar flames. Darrieus23 and Landau24 theoretically predicted that a planar flame is unconditionally unstable because of thermal expansion across the flame based on the assumption that the combustion layer is an infinitesimally thin discontinuity, which separates the burned and unburned gases that are incompressible. This kind of instability mechanism is called hydrodynamic instability or DL instability. Besides hydrodynamic instability, thermal−diffusive instability also needs to be taken into account when the perturbation wavelengths are of the order of the flame thickness, and thus, the transport process in the combustion layer must be considered. The first theoretical analysis of thermal−diffusive instability was made by Barenblatt et al.25 and then extended by Sivashinsky.26 It is shown that the flame is stable with respect to short-wave perturbations if the Lewis number Le is larger than Le* (Le* is the critical Lewis number, typically less than 1.0); otherwise, the flame is unconditionally unstable. Expanding spherical flames are closest to the real flames in gasoline engines, and it has been experimentally observed that, for the expanding spherical flames, at a critical state, cellular instability can no Received: December 25, 2013 Revised: March 3, 2014 Published: March 3, 2014 2258

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longer be suppressed by the curvature-induced stretch and cells will appear over the entire flame surface almost instantaneously. The flame radius and Peclet number at the critical state are called the critical flame radius and critical Peclet number, respectively.27−30 Bechtold and Matalon31 theoretically analyzed the stability of spherically expanding flames by incorporating both hydrodynamic and thermal−diffusional effects, and an explicit expression that depends upon the thermal expansion coefficient and Lewis number for the determination of the critical size or critical Peclet number was provided. However, transport properties in the theory of Bechtold and Matalon31 are assumed to be constant, whereas they, in fact, increase with the temperature through the flame zone. Subsequently, Addabbo et al.32 improved the theory and provided a revised expression, which is valid for variable transport properties on the basis of theoretical developments by Matalon et al.33 Law et al.27 and Jomaas et al.29 further combined the theoretical work with experiments on the cellular instabilities of expanding spherical flames, and their results showed that the predicted critical size or Peclet number well agree with experimental results qualitatively. In this work, a spherical expanding flame is established to observe the cellular instabilities of isooctane/n-butanol blend− air mixtures, and the experiment was implemented at elevated pressures because the phenomenon of cellular instabilities tends to be more obvious at elevated pressures. First, experimental and computational approaches are described. Results of flame morphology under different conditions and the critical Peclet number determined from the experiments are then presented, and the effects of the initial pressure, equivalence ratio, and nbutanol blending ratio on flame-front instability behaviors are analyzed qualitatively. Relevant theoretical calculations of the critical Peclet number are conducted in conjunction with the measurements to interpret the effect of the n-butanol blending ratio on the flame-front instability behaviors.

Figure 1. Laminar flame speeds for pure isooctane and n-butanol: (△) laminar flame speeds for isooctane at 433 K of the present work, (▲) laminar flame speeds for isooctane at 423 K by Broustail et al.,12 (○) laminar flame speeds for n-butanol at 433 K of the present work, (●) laminar flame speeds for n-butanol at 423 K by Broustail et al.,12 () simulated results for isooctane of model II at 433 K, and (- - -) simulated results for n-butanol of model II at 433 K.

Within the framework of Darrieus and Landau, the linear stability of a planar flame yields34

ω = SLkωDL ,

ωDL =

−σ +

σ3 + σ2 − σ σ+1

(1)

where ω is the growth rate of wrinkles and σ is the thermal expansion coefficient. ω increases with the increase of σ, which is a primary parameter in measuring the hydrodynamic instabilities. When perturbation wavelengths are comparable to flame thickness, the influence of the perturbation curvature on the flame structure and flame speed or transport process needs to be taken into account, which were neglected in the hydrodynamic model by Darrieus23 and Landau.24 Zel’dovich further predicted that the effects of short wavelength curvature on the flame structure and speed varied to the ratio between thermal diffusivity and mass diffusivity of the component that controls the chemical reaction rate,35,36 namely, Lewis number. It has been verified by a lot of experimental studies as well as theoretical analysis that wrinkles in the flame front will be amplified if thermal diffusivity is less than mass diffusivity of deficient species relative to abundant inert gas in mixtures. That is to say, flames are thermal− diffusively unstable when Le < 1 and, in contrast, are thermal− diffusively stable when Le < 1; incidentally, the critical Le is slightly less than 1.0 in theoretical work.25,26 Hence, Le is the main parameter that reflects the thermal−diffusively instabilities. Small Le makes the flame deviate from neutral thermal diffusivity and is thermal−diffusively unstable. Kwon et al.30 pointed out that the cell development of the thermal−diffusionally unstable flame would be further facilitated by larger overall activation energy, and this is because the overall activation energy is an important parameter controlling the chemical reaction rate. Because both isooctane and n-butanol are heavy fuels and have very close Lewis number in the present work, the overall activation energy should also be taken into account to obtain the effects of n-butanol on the thermal−diffusional instabilities of the blends. Because curvature of disturbances with the dimension of flame thickness tends to stabilize the flame, the curvature-stabilization mechanism makes the dimensions of the diffusional−thermal cells and the smallest sizes of hydrodynamic driven cells are that of the flame thickness. Consequently, as flame thickness decreases, the diffusional− thermal and hydrodynamic cells are both promoted; thus, the stabilization effects of curvature recede.37

2. EXPERIMENTAL AND COMPUTATIONAL SPECIFICATIONS 2.1. Experimental Section. The experiment was conducted in a cylindrical constant volume bomb, which has a diameter of 180 mm and length of 210 mm. The premixed combustible mixture was sparkignited at the center of the bomb, and the spherical flame propagation sequence was imaged by a Redlake HG-100K high-speed camera operating at 10 000 frames/s, which was triggered 0.3 s earlier than the ignition timing for capturing the whole flame propagation process. Each test was repeated 3 times to ensure the reliability of the results. A detailed description of the experimental procedure can be found in the previous publication.13 A brief comparison of laminar flame speeds measured by the present experimental facility with previous measurements by Broustail et al.12 was given in Figure 1, and the two sets of results agree well with each other. Mixtures of isooctane, n-butanol, and air were used. The n-butanol volume fraction in isooctane/n-butanol blends varies from 0 to 1 with an interval of 0.2. The initial pressure was set as 1, 3, and 5 atm, and the equivalence ratio varies from 0.7 to 1.5, with an interval of 0.1. All tests were conducted at an initial temperature of 433 K to ensure the completed vaporization of liquid fuels. From the flame propagation sequences, the propensity of cell formation of flames is assessed and the critical flame radius or critical Peclet number is determined. 2.2. Specifications of Flame-Front Instability Parameters. Darrieus23 and Landau24 performed theoretical analysis, and their results demonstrated that hydrodynamic instability is caused by thermal expansion across the flame front, because the combustion process is typically accompanied with massive heat release, which results in thermal expansion; thus, flames are unstable in nature. 2259

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In present work, thermal expansion (σ), flame thickness (δ), Lewis number (Le), and overall activation energy (Ea) are considered as the parameters that interpret the instabilities of the spherically expanding flame. Calculation methods of the above four instability parameters are specified as follows: Thermal expansion is defined as σ = ρu /ρb

flame radius. This quantity was then non-dimensionalized by the flame thickness, and the critical Peclet number, Pecr, was defined. Smaller Peclet numbers refer to earlier appearance of flame instability. 3.1. Effects of the Pressure. Figure 2 exhibits the sequences of flame images at three initial pressures, an

(2)

where ρu is the density of the unburned gas mixture and ρb is the density of the burned gas mixture; both of them are calculated by the equilibrium program of Chemkin-II. Laminar flame thickness is defined on the basis of the temperature profile of the flame and is defined as

δ=

Tad − Tu (dT /dx)max

(3)

where Tad and Tu are the adiabatic temperature and initial temperature, respectively, and (dT/dx)max is the maximum gradient of the temperature profile of the flame. Both (dT/dx)max and Tad are obtained by the PREMIX code in Chemkin-II. The Lewis number known as the ratio of thermal diffusivity of the mixture to the mass diffusivity of the deficient reactant is expressed as Le = λ /(ρC pDm)

(4)

The method to calculate the Lewis number of the isooctane/n-butanol blends was given in a previous publication.13 According to Egolfopoulos and Law,38 the overall activation energy, Ea, is determined empirically as

⎧ ∂ln(m0) ⎫ ⎬ Ea = − 2R0⎨ ⎩ ∂[1/Tad] ⎭ p, φ

(5)

The differential is calculated by slightly varying the value of m0, namely, the mass burning rate, through adding a small amount of inert nitrogen in mixtures, and thus, the pressure can be considered to be constant. The mass burning rate is obtained by the PREMIX code in Chemkin-II. 2.3. Kinetic Model. To determine the theoretical critical Peclet number, the overall activation energy is needed and calculated using the PREMIX code of Chemkin-II with the detailed chemical kinetic combustion model. The chemical kinetic model used in this study is basically based on the latest chemical kinetic combustion model of nbutanol developed by Sarathy et al.39 As a start, using the PrincetonChemRC,40−43 the chemical kinetic combustion model by Sarathy et al. was simplified to a reduced n-butanol model, which contains 98 species and 737 reactions and is named model I. Because what we need is a chemical mechanism model to contain all necessary species and reactions to simulate laminar flame speeds for pure isooctane, nbutanol, and arbitrary blends of the two fuels, isooctane-associated reactions from Chaos et al.44 were added to model I. Finally, an integrated mechanism consisting of 133 species and 923 reactions, which can simulate laminar flame speeds for arbitrary blends of isooctane and n-butanol, is proposed and named model II. Figure 1 shows that the calculated laminar flame speeds with model II agree well with the experimental results. Thus, model II is used to calculate the activation energy, adiabatic temperature, laminar flame thickness, and thermal expansion coefficient in this study.

Figure 2. Schlieren image of isooctane/n-butanol blend−air mixtures at three initial pressures.

equivalence ratio of 1.3, and a n-butanol volume fraction of 0.4. Flame properties, such as the thermal expansion ratio, laminar flame thickness, global Lewis number, and overall activation energy, are also tabulated. At an initial pressure of 1.0 atm, the flame front expands in a very smooth way, which indicates that the flame front is a stable one at this pressure. When the pressure is increased, flame fronts become unstable and large cracks are observed on the flame front, as indicated at R = 9.1 mm and 0.3 MPa. These cracks subsequently branch, and more cracks are formed. At 0.5 MPa, the cracks branch even faster and a uniform cellular structure is formed at the flame radius larger than 16.6 mm. A comparison of flame front behaviors at different pressures clearly demonstrates that a high pressure tends to destabilize the flame. Mechanistically, at different initial pressures, the thermal expansion ratio and Lewis number are almost the same, and the significant decrease of the flame thickness resulting from the increase of the burning rate with an increasing pressure is the main cause for the destabilized effect of a high initial pressure. It is also noted that, when the initial pressure is increased, the increased overall

3. RESULTS Cellular instabilities can be visualized by capturing the flame images during flame propagation processes. To compare the flame-front instability behavior under different initial conditions in a more distinct way, the critical flame radius approach27 was adopted in this study. It defines the moment when the uniform cellular structure appears on the flame front as the instant when the flame loses stability. The flame radius, which corresponds to this transient state, is correspondingly defined as the critical 2260

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activation energy also contributes to the enhanced flame instability because flames are thermal−diffusively unstable under fuel-rich conditions. The fact that the critical radius, Rcr, decreases with an increasing initial pressure, as shown in Figure 3, is consistent with the observations in Figure 2. Figure

Figure 3. Experimental critical radius as a function of the n-butanol volume fraction at two initial pressures.

Figure 5. Schlieren images of isooctane/n-butanol blend−air mixtures at three blending ratios.

Figure 4. Experimental critical Peclet number as a function of the nbutanol volume fraction at two initial pressures.

4 further indicates that the values of Pecr at different pressures are very close, and this suggests that the decreased flame thickness is the primary cause for the more unstable flame front at higher pressures. 3.2. Effects of the Equivalence Ratio. As shown in Figure 5, the flame front remains smooth under fuel-lean conditions but cellular structures appear under fuel-rich conditions. Because both isooctane and n-butanol are typically heavy fuels, it is well-understood that the equivalence ratio has a significant effect on the cellular instability of the flame. With the increase of the equivalence ratio, flames tend to be more unstable. The Lewis number decreases remarkably from fuellean to fuel-rich, as expected. As shown in Figure 6, Pecr

Figure 6. Experimental critical Peclet number as a function of the nbutanol volume fraction at three equivalence ratios.

decreases significantly when the equivalence ratio changes from 1.3 to 1.5, and this is consistent with the result in Figure 5. It is noted that Pecr in the fuel-lean case is not provided in Figure 6 because the flame front remains smooth and no cellular structure is observed in fuel-lean cases within the pressure range of this study. 3.3. Effects of the n-Butanol Blending Ratio. Figure 7 exhibits the sequences of flame images with the increase of the 2261

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decreased, indicating the enhancement of thermal−diffusional instability and that the stabilization effect of curvature is weakened. However, with the increase of the n-butanol volume fraction, the overall activation energy decreases; hence, the thermal−diffusive cell development in the flame front is suppressed. Therefore, the decreased overall activation makes the flame become less unstable with the increase of the nbutanol volume fraction. On the contrary, it is inferable that, for fuel-lean flames, with the increase of the n-butanol volume fraction, the cell development at the flame front will be facilitated because flames are thermal−diffusionally stable and the decreased activation energy favors the cell development. The inference can be experimentally validated only if the initial pressure is high enough for the appearance of the cell structure under fuel-lean conditions. Figures 4 and 6 quantify the result in Figure 7 by showing the critical Peclet number, Pecr, of isooctane/n-butanol blend−air flames under different initial conditions. The experimental observations of flame front behaviors under different pressures, equivalence ratios, and blending ratios are theoretically interpreted in Table 1.

4. THEORETICAL ANALYSIS Theoretical expression for the determination of the critical Peclet number of the expanding spherical flames was provided by linear stability analysis by Bechtold and Matalon.31 Subsequently, Addabbo et al.32 re-examined the results by Bechtold and Matalon31 and proposed a modified expression, which is more general to be valid for variable transport properties and allowed for mixtures spanning from lean to rich conditions. According to Addabbo et al.,32 the critical Peclet number for the transition to cellularity is expressed as Pecr = Pe1(σ ) + β(Le − 1)Pe 2(σ ) + PrPe3(σ ) Figure 7. Schlieren image of isooctane/n-butanol blend−air mixtures at three equivalence ratios.

(6)

where β = Ea(Tad − Tu)/R is the Zel’dovich number, Ea is the overall activation energy, Tu is the initial temperature, Tad is the adiabatic temperature, R0 is the universal gas constant, and Le is the Lewis number. Pr is the Prandtl number, which is defined as Tad2

0

n-butanol volume fraction, f vb, at an equivalence ratio of 1.3 and initial pressure of 0.5 MPa. It can be distinguished from the flame morphology that, when the n-butanol volume fraction is increased, the flame tends to be more stable. To give a qualitative explanation, four instability parameters were calculated. As shown in Figure 7, with the increase of the nbutanol volume fraction, the thermal expansion coefficient is increased, indicating the enhancement of hydrodynamic instability. Additionally, with the increase of the n-butanol volume fraction, the flame thickness and Lewis number are

Pr = ηmc p,m/λm

(7)

in which ηm, cp,m, and λm are the dynamic viscosity, specific heat, and heat conductivity coefficient of the mixture, respectively. The theoretical expression of the critical Peclet number in eq 6 indicates that flame-front instability arises from three mechanisms. The first term on the right-hand side of eq 6,

Table 1 Pu = 0.3 MPa, Tu = 433 K ϕ = 0.8

f vb = 0

f vb = 0.2

f vb = 0.4

f vb = 0.6

f vb = 0.8

f vb = 1.0

Ea (kJ/mol) Tad (K) σ Le Pr ϕ = 1.4

189.3 2151.9 5.208 2.923 0.729 f vb = 0

187.6 2150.8 5.213 2.692 0.730 f vb = 0.2

185.1 2149.7 5.217 2.506 0.730 f vb = 0.4

183.1 2148.4 5.222 2.352 0.730 f vb = 0.6

180.3 2147.2 5.228 2.221 0.731 f vb = 0.8

178.8 2145.8 5.234 2.108 0.731 f vb = 1.0

Ea (kJ/mol) Tad (K) σ Le Pr

270.0 2150.4 5.775 0.886 0.750

263.1 2149.0 5.782 5.882 0.750

250.3 2147.6 5.788 5.878 0.751

242.2 2146.1 5.795 5.874 0.751

235.3 2144.6 5.802 5.870 0.752

223.4 2143.0 5.810 0.865 0.752

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Pe1(σ), which is determined only by the thermal expansion coefficient, stands for the pure hydrodynamic effect on the critical Peclet number. The second term demonstrates that the thermal−diffusion effect also plays an important role on the critical transient state of expanding spherical flames. For Le > 1, the critical transient state is delayed and the thermal−diffusion effect tends to stabilize the flames, whereas for Le < 1, the thermal−diffusion effect tends to destabilize the flames because the Lewis number now exerts a negative effect on the critical Peclet number. This explains the phenomenon of the early appearance of the cellular structure under fuel-rich conditions compared to that under fuel-lean conditions for the heavy fuels and is in accordance with the experimental observations in Figure 5. Furthermore, the second term on the right-hand side of eq 6 indicates that high activation energy will facilitate the cell development of thermal−diffusional unstable flames. The third term on the right-hand side of eq 6 represents the extra contribution of the viscosity effect, which was not considered in the result by Bechtold and Matalon31 and tends to stabilize flames. Figures 8−13 show the theoretical calculations for the first, second, and third terms on the right-hand side of eq 6, as a

Figure 9. PrPe3 as a function of the n-butanol volume fraction at two equivalence ratios.

Figure 10. Pe2 as a function of the n-butanol volume fraction at two equivalence ratios. Figure 8. Pe1 as a function of the n-butanol volume fraction at two equivalence ratios.

function of the n-butanol blending ratio. As shown in Figures 8−10, Pe1(σ), Pe2(σ), and Pe3(σ) remain almost the same when the n-butanol volume fraction increases from 0 to 1 under both fuel-lean and fuel-rich conditions. This indicates that hydrodynamic and viscosity effects on flame-front instabilities vary little with the increase of the n-butanol volume fraction. Figures 11 and 12 show that both β and Le − 1 are decreased when the n-butanol volume fraction is increased under both fuel-lean and fuel-rich conditions, which explains that, under fuel-lean conditions, blending n-butanol into isooctane weakens the stabilization effect of thermal diffusion on flame-front instabilities and, thus, decreases the critical Peclet number, as shown in Figures 13 and 14. However, the variation trend may be inverted under fuel-rich conditions because, although both β and Le − 1 are decreased with the increase of the n-butanol blending ratio, Le − 1 becomes negative under fuel-rich conditions; therefore, the direction of the change in β(Le − 1) will depend upon the relative dominance between the two effects. Indeed, as shown in Figure 13, β(Le − 1) shows an

Figure 11. (Leeff − 1) as a function of the n-butanol volume fraction at two equivalence ratios.

increase with n-butanol blending under fuel-rich conditions. As shown in Figure 14, blending n-butanol into isooctane under 2263

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number. This is in agreement with the experimental results in Figure 7. Under fuel-lean conditions, the critical Peclet number decreases with the increase of the n-butanol volume fraction, whereas under fuel-rich conditions, the critical Peclet number increases and thermal−diffusional instabilities of flame tend to be suppressed with the increase of the n-butanol volume fraction. The addition of n-butanol has an opposite effect on flame-front instabilities under fuel-lean and fuel-rich conditions. This resulted from the opposite influences of the overall activation energy on thermal−diffusional instabilities of the two conditions.

5. CONCLUSION Cellular instability of the n-butanol/isooctane expanding spherical flame was studied experimentally and theoretically. The cell structure appears earlier at the flame front, and the flame tends to lose stability earlier with the increase of the initial pressure and equivalence ratio, because the flame thickness decreases dramatically with the increase of the pressure and the flame becomes more thermal−diffusionally unstable with the increase of the equivalence ratio. Flame cellular instability is suppressed with n-butanol blending under fuel-rich conditions because high activation energy facilitates the thermal−diffusional instabilities and the overall activation energy is decreases with the increasing n-butanol volume fraction. Theoretical analysis shows that the hydrodynamic and viscosity effects on flame instabilities vary little with n-butanol blending. However, thermal−diffusional instability is facilitated with n-butanol blending under fuel-lean conditions, whereas it is suppressed with n-butanol blending under fuel-rich conditions. The calculated critical Peclet number decreases with the increase of the blending ratio under fuel-lean conditions but shows an increase under fuel-rich conditions. This is in agreement with the experimental results.

Figure 12. β as a function of the n-butanol volume fraction at two equivalence ratios.

■

Figure 13. β(Leeff − 1) as a function of the n-butanol volume fraction at two equivalence ratios.

AUTHOR INFORMATION

Corresponding Authors

*Telephone: 86-29-82665075. Fax: 86-29-82668789. E-mail: [email protected]. *Telephone: 86-29-82665075. Fax: 86-29-82668789. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This study was supported by the National Natural Science Foundation of China (51136005 and 51121092), the Ministry of Education of China (20120201120067), and the National Basic Research Program (2013CB228406).

■ Figure 14. Theoretical calculated critical Peclet number as a function of the n-butanol volume fraction at two equivalence ratios.

fuel-rich conditions suppresses the thermal−diffusional cell development at the flame front and increases the critical Peclet 2264

NOMENCLATURE ω = growth rate of wrinkles σ = thermal expansion coefficient Le = Lewis number Le* = critical Lewis number δ = flame thickness (mm) Ea = overall activation energy (kJ/mol) ρu = density of unburned gas mixtures (g/m3) ρb = density of burned gas mixtures (g/m3) Tad = adiabatic temperature (K) dx.doi.org/10.1021/ef4025382 | Energy Fuels 2014, 28, 2258−2266

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Tu = initial temperature (K) R0 = universal gas constant (J mol−1 K−1) m0 = mass burning rate (g m−2 s−1) Pe = Peclet number Pecr = critical Peclet number R = flame radius (mm) Rcr = critical flame radius (mm) f vb = volume fraction of n-butanol ϕ = equivalence ratio Pu = initial pressure (MPa) β = Zel’dovich number Pr = Prandtl number η = dynamic viscosity (N S m−2) cp,m = specific heat (J mol−1 K−1) λ = thermal conductivity (W m−1 K−1)

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dx.doi.org/10.1021/ef4025382 | Energy Fuels 2014, 28, 2258−2266

Energy & Fuels

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(43) Lu, T.; Ju, Y.; Law, C. K. Complex CSP for chemistry reduction and analysis. Combust. Flame 2001, 126 (1), 1445−1455. (44) Chaos, M.; Kazakov, A.; Zhao, Z.; Dryer, F. L. A hightemperature chemical kinetic model for primary reference fuels. Int. J. Chem. Kinet. 2007, 39 (7), 399−414.

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dx.doi.org/10.1021/ef4025382 | Energy Fuels 2014, 28, 2258−2266