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Laminar burning velocities and flame instabilities of 2,5-dimethylfuran–air mixtures at elevated pressures
Combustion and Flame 158 (2011) 539–546
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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
Laminar burning velocities and flame instabilities of 2,5-dimethylfuran–air mixtures at elevated pressures Xuesong Wu a, Zuohua Huang a,⇑, Xiangang Wang a, Chun Jin a, Chenlong Tang a, Lixia Wei a, Chung K. Law b a b
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China Dept. of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 085405263, USA
a r t i c l e
i n f o
Article history: Received 20 May 2010 Received in revised form 13 August 2010 Accepted 7 October 2010 Available online 28 October 2010 Keywords: 2,5-Dimethylfuran Laminar burning characteristics Flame instabilities Elevated pressures
a b s t r a c t An experimental investigation on laminar burning velocities and onset of flame instabilities on spherically expanding flames in 2,5-dimethylfuran–air mixtures at elevated pressures was conducted over a wide range of equivalence ratios. The laminar burning velocities, laminar burning fluxes and Markstein lengths at different equivalence ratios and initial pressures were obtained. Furthermore, the diffusional–thermal and hydrodynamic effects on flame front instabilities were specified, and the onset of cellularity was reported. Results show that laminar burning velocities are decreased with increasing initial pressure due to the increase of the free-stream density and the progressively more important three-body termination reactions. With increasing initial pressure, Markstein length decrease, while the laminar burning flux increases. Onsets of flame instabilities, expressed in terms of critical radius or Peclet number, were found to be promoted with increasing equivalence ratio and initial pressures, due to the combined effects of diffusional–thermal and hydrodynamic instabilities. Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction 2,5-Dimethylfuran (DMF) is a new class of oxygenated biofuel, whose mass production from biomass has recently been made possible [1–3]. As a promising biofuel, DMF is of importance to energy diversification and environmental protection. Compared to bio-ethanol, DMF has a higher energy density (40% higher), a higher boiling point (20 K higher), and a higher research octane number (RON) and it causes no contamination to the groundwater due to its water insolubility [2,4]. Because of the above advantages, DMF is drawing an increasing interest from investigators throughout the world. Up to now, the published work mainly reported thermal decomposition and combustion characteristics of DMF. Grela et al. [5] studied very low-pressure pyrolysis of furan, 2-methylfuran, and DMF over the temperature range of 1050–1270 K. Lifshitz et al. [6] investigated the thermal decomposition kinetics of DMF over the temperature range of 1070–1370 K. Jiao et al. [7] studied the formation of ions from DMF by electron impact ionization and by ion–molecule reactions with Fourier transfer mass spectrometry. Wu et al. [8] studied the low-pressure premixed laminar DMF–O2– Ar flame with tunable vacuum ultraviolet synchrotron radiation photoionization and molecular-beam mass spectrometry. Possible reaction pathways of DMF, 2-methylfuran, and furan were proposed based on the intermediates identified. Zhong et al. [9] studied the ⇑ Corresponding author. Fax: +86 29 82668789. E-mail address: [email protected] (Z. Huang).
combustion and emissions performance of DMF in a direct-injection spark-ignition engine. They found that DMF has very similar combustion and emissions characteristics to gasoline. However, the fundamental combustion characteristics of DMF such as laminar burning characteristics are relatively less reported. Wu et al. [10] studied the laminar burning velocities and Markstein lengths of DMF–air–diluent premixed flames at atmospheric pressure. For a specific equivalence ratio, the laminar burning velocity shows a linear decreasing trend with the increase of dilution ratio. Tian et al. [11] using the schlieren optical method studied the flame propagation characteristics of DMF. They found the laminar burning velocity of DMF was very similar to gasoline and the difference was within 10% in the 0.9–1.1 equivalence ratio range. Laminar burning velocity is a fundamental physicochemical property of a combustible mixture [12]. It is usually used to partially validate the kinetic mechanism and is of practical importance in the design and optimization of various combustion devices [13,14]. Recognizing that there are sparse reported data on laminar burning velocities of DMF, especially at elevated pressure, one objective of the present study is to provide laminar burning velocities of DMF–air mixtures for the future reaction mechanism development. The outwardly propagating spherical flame, now, at elevated pressures is adopted because of its well defined configuration and dynamics, also because of its resemblance to flame propagation in internal combustion engines [14–18]. For rich DMF–air mixtures at high pressures, great care needs to be exerted in flame speed measurements, because over the years, flame front instabilities, both
0010-2180/$ - see front matter Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2010.10.006
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diffusional–thermal and hydrodynamic, have been theoretically predicted and experimentally observed [19–23]. This fascinating phenomenon will significantly affect the flame speed trajectory with respect to flame stretch rate and consequently affect the unstretched flame speed extraction [23,24]. Thus another objective of this work is to investigate the onset of flame front instabilities, represented by a critical flame radius (Rc), or critical Peclet number (Pec), after which the spontaneous formation of cells over the entire flame surface is observed. In the following, we first specified our experimentation and data reduction, followed by presentation and discussion of the results. Based on the experimental data, a formula was proposed to correlate the laminar burning velocities with experimental parameters. In addition, other flame properties, such as Markstein length (Lb), density ratio (r), laminar flame thickness (dl), critical flame radius (Rc), and critical Peclet number (Pec) were obtained over the experimental range for further analysis. 2. Experimental setup and procedures The experiments were conducted in a cylindrical constant volume combustion chamber. Detailed discussion on the instrumentation can be found in previous literature [18]. Briefly, a high-speed digital camera (HG-100K) with a frame speed of 10,000 frames/s was used to record the flame images during the flame propagation. The mixtures were prepared based on the partial pressures of the constituents, which were regulated by a mercury manometer when the initial pressure was 0.1 MPa, and were controlled by a pressure transmitter for higher initial pressures. A pressure transducer (Kistler 7001) was used to measure the pressure history during the flame propagation. The liquid fuel was injected into the chamber by a syringe through a valve, while the gases were introduced into the chamber through inlet/outlet valves. The entire chamber was heated by a 2.4 kW heating-tape wrapped outside the chamber body. The bomb was first heated to test temperature in a pre-experiment stage using heating tape, and left for approximately half an hour to ensure the bomb is heated uniformly. During the experiment, heating tape was switched on/off to maintain the temperature. After the mixture preparation, the chamber was left undisturbed for at least 10 min before ignition. Experiment shows that the 10-min interval before ignition at the high pressure is sufficient for the complete evaporation and mixing. After combustion, the chamber was vacuumed and flushed with fresh air to purge the residual gas. In these experiments, the initial temperature of 393 K was selected to ensure that DMF could be completely vaporized in the chamber before ignition. The initial pressure was set at 0.1, 0.25, 0.5 and 0.75 MPa, while the equivalence ratio varied from 0.8 to 1.5 with 0.1 intervals. To ensure repeatability, the experiment was repeated at least twice for each condition and the average value was used in the analysis. 3. Laminar burning velocity and Markstein length For an outwardly propagating spherical flame, the stretched flame propagation speed (Sn) can be calculated from the flame radius (ru) history [18,22,24],
Sn ¼
dr u dt
ð1Þ
where t is the elapsed time after ignition. The characteristics of the igniter will affect the initial flame development stage. Previous studies [12,13,18,24,25] showed that the flame speed was independent of ignition energy when the flame radius was greater than 6 mm. Therefore, this study disregards any data below 6 mm in
order to avoid the effect caused by the spark-ignition disturbance. Also, when the flame radius is less than 25 mm, the pressure increase in a constant volume combustion chamber is negligible [18] and the effect of cylindrical confinement on the determination of flame propagation speed can be neglected [26]. Thus, only the flame images with radius between 6 mm and 25 mm were used in the analysis. Besides, meaningful determination of the flame speed precludes instances exhibiting flame-front cellular structure [27], which will be shown in following sections. At the early stage of flame propagation (the constant pressure stage), the unstretched flame propagation speed (Sl) can be obtained [12,13,16,20,28],
a¼
dðln AÞ 2 dr u 2 ¼ ¼ Sn dt r u dt ru
Sl Sn ¼ Lb a
ð2Þ ð3Þ
The unstretched flame propagation speed can be obtained by linearly extrapolating the flame propagation speed to the zero flame stretch rate. The Markstein length of the burned gas, which indicates the effect of stretch rate on flame propagation speed and characterizes the instability of the flame front, is the negative value of the gradient from the best linear regression of the flame propagation speed against the stretch rate curve. The laminar burning velocity (ul) can be calculated by the following equation [12,18,24],
ul ¼
Sl
r
¼
qb S qu l
ð4Þ
qu and qb are the densities of the unburned and burned gases, respectively. And r is the density ratio which is the ratio of the density of the unburned gas to that of the burned gas. In this study, the laminar flame thickness is calculated using the equation [29], dl ¼ 2
0:7 Dth T a ul T u
ð5Þ
where Dth = k/(quCp) is the thermal diffusivity of the unburned mixture [30–32]; k is the thermal conductivity of the unburned gas; Cp is the specific heat capacity at constant pressure of the unburned gas; Ta and Tu are the adiabatic flame temperature and the initial temperature, respectively. Laminar burning flux (f), the eigenvalue of flame propagation, contains the basic information of reactivity, diffusivity, and exothermicity [33],
f ¼ u l qu
ð6Þ
In this study, the relative errors for the initial temperature and pressure are 0.76% and 0.40%, respectively. The relative error of measured radius has its maximum value of 1.35%. Based on the method of Kline and McClintock [34], the maximum standard errors are 16.6% for Markstein length, 4.5% for stretched flame propagation speed, 5.5% for unstretched flame propagation speed and 8.6% for unstretched laminar burning velocity. 4. Results and discussion 4.1. Flame morphology Schlieren images of stoichiometric DMF–air mixtures at different initial pressures are shown in Fig. 1. Because of the cooling effect of the electrodes, the flame propagation speed along the direction of the electrodes is slower than that in the vertical direction, thus the flame is not perfectly spherical at the early stage of
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Fig. 1. Schlieren images of flames of stoichiometric DMF–air mixtures at different initial pressures.
flame propagation and the flame radius in the vertical direction is used to calculate the flame propagation speed. When the initial pressure is less than 0.25 MPa, the flame surface remains smooth during flame propagation and no cracks were observed. The flame becomes wrinkled as the initial pressure increases. It is noted that although the electrodes may occasionally induce some cracks over the flame front, these cracks do not necessarily develop into cells [35]. The wrinkles could be observed over the flame surface when the initial pressures are 0.50 MPa and 0.75 MPa. However, no further cracking into small cells was observed as the flame expands. 4.2. Flame propagation and Markstein length 4.2.1. Flame propagation speed Figure 2a shows the stretched flame propagation speed versus stretch rate at Pu = 0.75 MPa and different equivalence ratios. The flame surface remains smooth except for some cracks at the equivalence ratios of 0.8 and 1.0, as shown in Fig. 3. However, these cracks do not branch and no further cracks appear on the flame surface and thus these cracks will not affect the flame propagation speed trajectory [17,24]. It is seen that a linear relationship between the stretched flame propagation speed and stretch rate still holds in these conditions. We further note that cellular flame front instabilities increase the flame front area on which the reaction takes place and the instabilities could lead to self-acceleration or even self-turbulization of a laminar flame, as predicted by Sivashinsky [36]. Figure 2b shows the stretched flame propagation speed versus stretch rate with flame schlieren images at the experimental condition of Pu = 0.75 MPa, u = 1.2. It is seen that there is a sharp increase on the stretched flame propagation speed trajectory, indicating the self-acceleration of the flame caused by flame front instabilities. Similar observations were reported in [14,16– 18,23,37]. As shown in Fig. 2b, cracks are appearing on the flame surface at the early stage of flame propagation. However, these cracks do not branch until flame ‘c’, where the cracks continue to branch and further develop to cellular structure. Meanwhile, the stretched flame propagation speed increases rapidly with the stretch rate. This critical state when cell development can no longer be suppressed is defined as the instant of transition to cellularity. And the corresponding flame radius is called critical flame radius. Figure 4 shows the stretched flame propagation speed versus stretch rate at u = 1.0 and different initial pressures. For a given
Fig. 2. Stretched flame propagation speed versus stretch rate (a) at Pu = 0.75 MPa and different equivalence ratios and (b) with schlieren images of flames at Pu = 0.75 MPa and u = 1.
initial pressure, the stretched flame propagation speed shows a decreasing tendency with increasing stretch rate. Thus, the burned Markstein length, the negative value of the slope from the best linear regression of flame propagation speed against stretch rate curve, is positive. As discussed above, the unstretched flame propagation
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Fig. 3. Schlieren images of flames for DMF–air mixtures at Pu = 0.75 MPa for different equivalence ratios.
Fig. 4. Stretched flame propagation speed versus stretch rate at u = 1.0 and different initial pressures.
Fig. 5. Laminar burning velocity (solid line) and laminar burning flux (dash dot line) versus equivalence ratio at different initial pressures.
speed is obtained by linearly extrapolating the flame propagation speed to the zero flame stretch rate. As shown in Fig. 4, the unstretched flame propagation speed decreases with increasing initial pressure due to the influence of the free-stream density and the chemical reaction.
laminar burning velocities and laminar burning flux under these conditions are not plotted in the figure, as mentioned earlier. The laminar burning velocities exhibit peak values near the equivalence ratio of 1.2, and they decrease with increasing initial pressure. The decreasing tendency of the laminar burning velocity with initial pressure is obvious when the initial pressure is smaller than or equal to 0.50 MPa; while further increasing the initial pressure shows little effect on the laminar burning velocity. The decrease of the laminar burning velocity with increasing initial pressure is due to the influence of the free-stream density and the chemical reaction. As the initial pressure increases, the threebody, inhibiting reactions become important with increasing pressure. This causes a slowdown in the kinetics and consequently the flame propagation rate [12]. Figure 5 then shows that the laminar burning flux exhibits peak values near the equivalence ratio of 1.2 and increases with increasing initial pressure. This reveals that the increase in the density of unburned gases with increasing initial
4.2.2. Laminar burning velocity and laminar burning flux Figure 5 shows the laminar burning velocity and the laminar burning flux versus equivalence ratio at different initial pressures. The results reported in [11] are also shown in Fig. 5. The initial pressure and temperature for their data are 0.1 MPa and 373 K, respectively. Their values are lower than those in this study except the equivalence ratio of 0.8. This may due to the different initial temperature and different calculated values of density ratio. A fully developed cellular structure can be observed over the flame surface soon after ignition when the initial pressure is 0.75 MPa and the equivalence ratio is larger than 1.2; thus, the inaccurate
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pressure overcomes the reduction of the laminar burning velocity. The combined effects of laminar burning velocity and density contribute to the increase of the laminar burning flux with increasing initial pressure. Laminar burning velocity can be correlated as the following formula, b
ul ¼ UPup
ð7Þ
where Pu is the initial pressure, and U and bp are empirical powerlaw fitting constants. Figure 6 shows the dependence of laminar burning velocities on initial pressure at equivalence ratios of 0.8, 1.0 and 1.2. Laminar burning velocity decreases with increasing initial pressure. The behavior of initial pressure to laminar burning velocity is similar to previous results [16,24,33,38]. As shown in Fig. 6, the fitted values agree well with the measured ones. Table 1 shows the value of U, bp and the standard deviation (SD) of experimental data to the fitted values. By using the corresponding formula (Eq. (7)), laminar burning velocities of DMF–air mixtures at different equivalence ratios and initial pressures can be calculated. Since ul xad1/2/qu p(1+n/2), the resulting reaction order, n, can be calculated by the equation, n = 2(bp + 1), where xad is the reaction rate [33]. Figure 7 shows the adiabatic flame temperature at the initial pressure of 0.10 MPa and the resulting reaction order versus equivalence ratio. The adiabatic flame temperature exhibits peak value near the equivalence ratio of 1.1. This rich shifting of the maximum Ta is due to the influence of product dissociation and reduced amount of heat release [39]. As shown in Fig. 7, the resulting reaction order first increases with equivalence ratio, and then it is insensitive to the increasing equivalence ratio. The resulting reaction order is larger than one and smaller than two over the experimental range. The branching reaction is temperature sensitive, while the three-body termination reaction (which has a negative influence on the net reaction order) is not temperature sensitive. For lean flame or stoichiometric flame, the flame temperature increases with increasing equivalence ratio as shown in Fig. 7. Thus
Fig. 7. Adiabatic flame temperature (square) and resulting reaction order (circle) versus equivalence ratio.
Fig. 8. Markstein length versus equivalence ratio at different initial pressures.
the branching reactions are progressively promoted; hence the reaction order increases with increasing equivalence ratio. This phenomena is also reported in [40].
Fig. 6. Laminar burning velocity versus initial pressure at equivalence ratios of 0.8, 1.0, and 1.2.
4.2.3. Markstein lengths Figure 8 shows the Markstein length versus equivalence ratio at different initial pressures. It is seen that the Markstein length of DMF–air mixtures decreases monotonically with increasing equivalence ratio. The Markstein length in most cases is positive in this study. One exception occurs at the equivalence ratios of 1.5, where the Markstein length is negative regardless of the initial pressure; another exception is at the initial pressure of 0.75 MPa, where the Markstein length decreased from positive to negative at the equivalence ratios of 1.0, as shown in Fig. 8. According to the asymptotic theory [41], the Markstein length depends on the Lewis number of the fuel in lean mixtures; while it depends on the Lewis number of oxidizer in rich mixtures. Thus, the Markstein length tends to increase monotonically with increasing equivalence ratio for light
Table 1 Values of U, bp and SD at different equivalence ratios. / U bp SD (m/s)
0.8 0.42 0.335 0.015
0.9 0.44 0.232 0.005
1 0.50 0.205 0.005
1.1 0.54 0.217 0.003
1.2 0.56 0.196 0.004
1.3 0.50 0.150 0.004
1.4 0.46 0.152 0.004
1.5 0.38 0.149 0.002
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where c1 and c2 are functions of r; Le the effective Lewis number of the mixture; Ze = Ea(Ta Tu)/R(Ta)2 the Zeldovich number; Ea the activation energy; R the universal gas constant. The initial pressure has little effect on the density ratio, as shown in Fig. 9. The extent of the variation of Ze with pressure is much smaller than that of dl [42]. Thus, the variation of Markstein length with pressure is dominated by the variation of dl and Le. For the positively stretched outwardly propagation flame, Lb is positive (negative) corresponding to Le > 1(Le < 1). As demonstrated in Fig. 9, the flame thickness decreases with increasing initial pressure. In the case of Le P 1, c1 and c2 are positive and dl is decreased with increasing initial pressure, so the Markstein length assumes positive values and decreases with increasing initial pressure.
4.3. Flame instability Fig. 9. Flame thickness (solid line) and density ratio (dash dot line) versus equivalence ratio at different initial pressures.
hydrocarbon–air mixtures, such as hydrogen–air and methane–air mixtures, while it tends to decrease with equivalence ratio for heavy hydrocarbon–air mixtures, such as ethanol–air, isooctane–air and propane–air mixtures [16,24,28,42,43]. The Markstein length of DMF–air mixtures decreases with increasing initial pressure for a given equivalence ratio. According to Bechtold and Matalon [28], the Markstein length can be expressed as,
Lb ¼ dl
1 2
2r pffiffiffiffi ; c2 ¼ 1þ r
c1 ¼
r1 c1 þ ZeðLe 1Þc2 ;
pffiffiffiffi pffiffiffiffi
4 r 1 ln½0:5ð r þ 1Þ r1
ð8Þ
There are three kinds of flame surface instabilities: the diffusional–thermal instability, the hydrodynamic instability (or Darrieus–Landau instability) and buoyancy-driven instability [33]. In this study, the laminar burning velocity is relatively high, thus only the diffusional–thermal instability and the hydrodynamic instability are observed. Diffusional–thermal instability is the combined effect of the nonequidiffusive and pure curvature instability. This instability can be characterized by the Markstein length or the Lewis number. The presence of this instability could be identified by irregular distortions of the flame surface relatively early in the flame propagation process when the deficient reactant is also the more diffusive one [44–47]. Hydrodynamic instability, an intrinsic instability of the flame, is induced by the density jump across the flame front. The controlling parameters of this instability are density ratio and flame thickness. Increasing density ratio across the flame or decreasing in flame thickness will promote this instability [23,42,48].
Fig. 10. Schlieren images of DMF–air flames at u = 1.2 and different initial pressures.
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hanced when the flame becomes thinner and diffusional–thermal stability is decreased with decreasing Markstein length. For a given initial pressure, the critical flame radius decreases with increasing equivalence ratio. This results from the decreasing diffusional– thermal stability of DMF–air mixtures with increasing equivalence ratio. For a given initial pressure, the critical Peclet number decreases nearly linearly with increasing equivalence ratio. Since both critical flame radius and flame thickness decrease with increasing initial pressure, the combined effects lead to unconspicuous variation of critical Peclet number to initial pressure, as shown in Fig. 11. 5. Conclusions
Fig. 11. Critical flame radius and critical Peclet number versus equivalence ratio.
As shown in Figs. 3 and 10, the flame is initially stable because of the strong curvature-induced stretch stabilizing effect. As the flame propagates outwardly and stretch rate decreases gradually, a critical state is reached at which cell development can no longer be suppressed and cellular structure appears almost instantaneously over the entire flame surface. In this study, this state is defined as the instant of transition to cellularity. This critical instant is almost consistent with the timing at the onset of cellular flame acceleration [49]. The flame radius of this state is defined as the critical flame radius, and the critical Peclet number (Pec) is the critical radius normalized by the laminar flame thickness of the mixtures. The instant of transition to cellularity depends on the combined effects of the hydrodynamic and diffusional–thermal instabilities [22,48]. 4.3.1. Effect of initial pressure and equivalence ratio Schlieren images of DMF–air flames at Pu = 0.75 MPa for different equivalence ratios are shown Fig. 3. With increasing equivalence ratio, the flame tends to be more unstable. The Markstein length decreases with increasing equivalence ratio, as shown in Fig. 8 and tabulated in Fig. 3. The decrease of Markstein length leads to the increase of the diffusional–thermal instability. The strong hydrodynamic instability cannot be stabilized by the weak diffusional–thermal stability and large cracks develop into cellularity on the flame surface. Thus, the interplay of hydrodynamic and diffusional–thermal instabilities makes the flame more unstable under the rich mixture condition. Figure 10 shows the schlieren images of DMF–air flames at different initial pressures and equivalence ratio of 1.2. It is seen that, with increasing initial pressure, the flame becomes more unstable and the instant of transition to cellularity is advanced. As tabulated in Fig. 10 and shown in Fig. 9, the density ratio is almost the same at the four different initial pressures and flame thickness decreases gradually with increasing initial pressure, so the controlling parameter of hydrodynamic instability is the flame thickness under these conditions. Since flame thickness and Markstein length decrease with increasing initial pressure, hydrodynamic instability is enhanced and diffusional–thermal stability is decreased. These two factors make the flame more unstable and the early occurrence of the cellular structure on flame surface with increasing initial pressure. 4.3.2. Critical flame radius and Peclet number Figure 11 shows critical flame radius and critical Peclet number versus equivalence ratio. It is seen that, for a given equivalence ratio, the critical flame radius decreases with increasing initial pressure. As discussed above, the hydrodynamic instability is en-
An experimental study on laminar burning velocities and flame instabilities of DMF–air mixtures was conducted using the spherically propagation flame at different equivalence ratios and initial pressures. The main conclusions are summarized as following: 1. Laminar burning velocities exhibit the peak values at the equivalence ratio of 1.2 and decrease with increasing initial pressure. Laminar burning fluxes increase with increasing initial pressure. Base on the experimental data, a correlation expression is obtained for the calculation of the laminar burning velocity of DMF–air mixtures over a wide range of equivalence ratios and pressures. 2. The Markstein lengths of DMF–air mixtures decrease with increasing equivalence ratio and initial pressure. 3. Increasing initial pressure and equivalence ratio destabilizes the flame front. The flame-front surface for rich DMF–air mixtures at high initial pressures is strongly affected by the combined effects of diffusional–thermal and hydrodynamic instabilities. 4. The critical flame radius decreases with increasing equivalence ratio and initial pressure. The critical Peclet number decreases with increasing equivalence ratio. Initial pressure has little influence on the critical Peclet number.
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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
Laminar burning velocities and flame instabilities of 2,5-dimethylfuran–air mixtures at elevated pressures Xuesong Wu a, Zuohua Huang a,⇑, Xiangang Wang a, Chun Jin a, Chenlong Tang a, Lixia Wei a, Chung K. Law b a b
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China Dept. of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 085405263, USA
a r t i c l e
i n f o
Article history: Received 20 May 2010 Received in revised form 13 August 2010 Accepted 7 October 2010 Available online 28 October 2010 Keywords: 2,5-Dimethylfuran Laminar burning characteristics Flame instabilities Elevated pressures
a b s t r a c t An experimental investigation on laminar burning velocities and onset of flame instabilities on spherically expanding flames in 2,5-dimethylfuran–air mixtures at elevated pressures was conducted over a wide range of equivalence ratios. The laminar burning velocities, laminar burning fluxes and Markstein lengths at different equivalence ratios and initial pressures were obtained. Furthermore, the diffusional–thermal and hydrodynamic effects on flame front instabilities were specified, and the onset of cellularity was reported. Results show that laminar burning velocities are decreased with increasing initial pressure due to the increase of the free-stream density and the progressively more important three-body termination reactions. With increasing initial pressure, Markstein length decrease, while the laminar burning flux increases. Onsets of flame instabilities, expressed in terms of critical radius or Peclet number, were found to be promoted with increasing equivalence ratio and initial pressures, due to the combined effects of diffusional–thermal and hydrodynamic instabilities. Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction 2,5-Dimethylfuran (DMF) is a new class of oxygenated biofuel, whose mass production from biomass has recently been made possible [1–3]. As a promising biofuel, DMF is of importance to energy diversification and environmental protection. Compared to bio-ethanol, DMF has a higher energy density (40% higher), a higher boiling point (20 K higher), and a higher research octane number (RON) and it causes no contamination to the groundwater due to its water insolubility [2,4]. Because of the above advantages, DMF is drawing an increasing interest from investigators throughout the world. Up to now, the published work mainly reported thermal decomposition and combustion characteristics of DMF. Grela et al. [5] studied very low-pressure pyrolysis of furan, 2-methylfuran, and DMF over the temperature range of 1050–1270 K. Lifshitz et al. [6] investigated the thermal decomposition kinetics of DMF over the temperature range of 1070–1370 K. Jiao et al. [7] studied the formation of ions from DMF by electron impact ionization and by ion–molecule reactions with Fourier transfer mass spectrometry. Wu et al. [8] studied the low-pressure premixed laminar DMF–O2– Ar flame with tunable vacuum ultraviolet synchrotron radiation photoionization and molecular-beam mass spectrometry. Possible reaction pathways of DMF, 2-methylfuran, and furan were proposed based on the intermediates identified. Zhong et al. [9] studied the ⇑ Corresponding author. Fax: +86 29 82668789. E-mail address: [email protected] (Z. Huang).
combustion and emissions performance of DMF in a direct-injection spark-ignition engine. They found that DMF has very similar combustion and emissions characteristics to gasoline. However, the fundamental combustion characteristics of DMF such as laminar burning characteristics are relatively less reported. Wu et al. [10] studied the laminar burning velocities and Markstein lengths of DMF–air–diluent premixed flames at atmospheric pressure. For a specific equivalence ratio, the laminar burning velocity shows a linear decreasing trend with the increase of dilution ratio. Tian et al. [11] using the schlieren optical method studied the flame propagation characteristics of DMF. They found the laminar burning velocity of DMF was very similar to gasoline and the difference was within 10% in the 0.9–1.1 equivalence ratio range. Laminar burning velocity is a fundamental physicochemical property of a combustible mixture [12]. It is usually used to partially validate the kinetic mechanism and is of practical importance in the design and optimization of various combustion devices [13,14]. Recognizing that there are sparse reported data on laminar burning velocities of DMF, especially at elevated pressure, one objective of the present study is to provide laminar burning velocities of DMF–air mixtures for the future reaction mechanism development. The outwardly propagating spherical flame, now, at elevated pressures is adopted because of its well defined configuration and dynamics, also because of its resemblance to flame propagation in internal combustion engines [14–18]. For rich DMF–air mixtures at high pressures, great care needs to be exerted in flame speed measurements, because over the years, flame front instabilities, both
0010-2180/$ - see front matter Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2010.10.006
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diffusional–thermal and hydrodynamic, have been theoretically predicted and experimentally observed [19–23]. This fascinating phenomenon will significantly affect the flame speed trajectory with respect to flame stretch rate and consequently affect the unstretched flame speed extraction [23,24]. Thus another objective of this work is to investigate the onset of flame front instabilities, represented by a critical flame radius (Rc), or critical Peclet number (Pec), after which the spontaneous formation of cells over the entire flame surface is observed. In the following, we first specified our experimentation and data reduction, followed by presentation and discussion of the results. Based on the experimental data, a formula was proposed to correlate the laminar burning velocities with experimental parameters. In addition, other flame properties, such as Markstein length (Lb), density ratio (r), laminar flame thickness (dl), critical flame radius (Rc), and critical Peclet number (Pec) were obtained over the experimental range for further analysis. 2. Experimental setup and procedures The experiments were conducted in a cylindrical constant volume combustion chamber. Detailed discussion on the instrumentation can be found in previous literature [18]. Briefly, a high-speed digital camera (HG-100K) with a frame speed of 10,000 frames/s was used to record the flame images during the flame propagation. The mixtures were prepared based on the partial pressures of the constituents, which were regulated by a mercury manometer when the initial pressure was 0.1 MPa, and were controlled by a pressure transmitter for higher initial pressures. A pressure transducer (Kistler 7001) was used to measure the pressure history during the flame propagation. The liquid fuel was injected into the chamber by a syringe through a valve, while the gases were introduced into the chamber through inlet/outlet valves. The entire chamber was heated by a 2.4 kW heating-tape wrapped outside the chamber body. The bomb was first heated to test temperature in a pre-experiment stage using heating tape, and left for approximately half an hour to ensure the bomb is heated uniformly. During the experiment, heating tape was switched on/off to maintain the temperature. After the mixture preparation, the chamber was left undisturbed for at least 10 min before ignition. Experiment shows that the 10-min interval before ignition at the high pressure is sufficient for the complete evaporation and mixing. After combustion, the chamber was vacuumed and flushed with fresh air to purge the residual gas. In these experiments, the initial temperature of 393 K was selected to ensure that DMF could be completely vaporized in the chamber before ignition. The initial pressure was set at 0.1, 0.25, 0.5 and 0.75 MPa, while the equivalence ratio varied from 0.8 to 1.5 with 0.1 intervals. To ensure repeatability, the experiment was repeated at least twice for each condition and the average value was used in the analysis. 3. Laminar burning velocity and Markstein length For an outwardly propagating spherical flame, the stretched flame propagation speed (Sn) can be calculated from the flame radius (ru) history [18,22,24],
Sn ¼
dr u dt
ð1Þ
where t is the elapsed time after ignition. The characteristics of the igniter will affect the initial flame development stage. Previous studies [12,13,18,24,25] showed that the flame speed was independent of ignition energy when the flame radius was greater than 6 mm. Therefore, this study disregards any data below 6 mm in
order to avoid the effect caused by the spark-ignition disturbance. Also, when the flame radius is less than 25 mm, the pressure increase in a constant volume combustion chamber is negligible [18] and the effect of cylindrical confinement on the determination of flame propagation speed can be neglected [26]. Thus, only the flame images with radius between 6 mm and 25 mm were used in the analysis. Besides, meaningful determination of the flame speed precludes instances exhibiting flame-front cellular structure [27], which will be shown in following sections. At the early stage of flame propagation (the constant pressure stage), the unstretched flame propagation speed (Sl) can be obtained [12,13,16,20,28],
a¼
dðln AÞ 2 dr u 2 ¼ ¼ Sn dt r u dt ru
Sl Sn ¼ Lb a
ð2Þ ð3Þ
The unstretched flame propagation speed can be obtained by linearly extrapolating the flame propagation speed to the zero flame stretch rate. The Markstein length of the burned gas, which indicates the effect of stretch rate on flame propagation speed and characterizes the instability of the flame front, is the negative value of the gradient from the best linear regression of the flame propagation speed against the stretch rate curve. The laminar burning velocity (ul) can be calculated by the following equation [12,18,24],
ul ¼
Sl
r
¼
qb S qu l
ð4Þ
qu and qb are the densities of the unburned and burned gases, respectively. And r is the density ratio which is the ratio of the density of the unburned gas to that of the burned gas. In this study, the laminar flame thickness is calculated using the equation [29], dl ¼ 2
0:7 Dth T a ul T u
ð5Þ
where Dth = k/(quCp) is the thermal diffusivity of the unburned mixture [30–32]; k is the thermal conductivity of the unburned gas; Cp is the specific heat capacity at constant pressure of the unburned gas; Ta and Tu are the adiabatic flame temperature and the initial temperature, respectively. Laminar burning flux (f), the eigenvalue of flame propagation, contains the basic information of reactivity, diffusivity, and exothermicity [33],
f ¼ u l qu
ð6Þ
In this study, the relative errors for the initial temperature and pressure are 0.76% and 0.40%, respectively. The relative error of measured radius has its maximum value of 1.35%. Based on the method of Kline and McClintock [34], the maximum standard errors are 16.6% for Markstein length, 4.5% for stretched flame propagation speed, 5.5% for unstretched flame propagation speed and 8.6% for unstretched laminar burning velocity. 4. Results and discussion 4.1. Flame morphology Schlieren images of stoichiometric DMF–air mixtures at different initial pressures are shown in Fig. 1. Because of the cooling effect of the electrodes, the flame propagation speed along the direction of the electrodes is slower than that in the vertical direction, thus the flame is not perfectly spherical at the early stage of
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Fig. 1. Schlieren images of flames of stoichiometric DMF–air mixtures at different initial pressures.
flame propagation and the flame radius in the vertical direction is used to calculate the flame propagation speed. When the initial pressure is less than 0.25 MPa, the flame surface remains smooth during flame propagation and no cracks were observed. The flame becomes wrinkled as the initial pressure increases. It is noted that although the electrodes may occasionally induce some cracks over the flame front, these cracks do not necessarily develop into cells [35]. The wrinkles could be observed over the flame surface when the initial pressures are 0.50 MPa and 0.75 MPa. However, no further cracking into small cells was observed as the flame expands. 4.2. Flame propagation and Markstein length 4.2.1. Flame propagation speed Figure 2a shows the stretched flame propagation speed versus stretch rate at Pu = 0.75 MPa and different equivalence ratios. The flame surface remains smooth except for some cracks at the equivalence ratios of 0.8 and 1.0, as shown in Fig. 3. However, these cracks do not branch and no further cracks appear on the flame surface and thus these cracks will not affect the flame propagation speed trajectory [17,24]. It is seen that a linear relationship between the stretched flame propagation speed and stretch rate still holds in these conditions. We further note that cellular flame front instabilities increase the flame front area on which the reaction takes place and the instabilities could lead to self-acceleration or even self-turbulization of a laminar flame, as predicted by Sivashinsky [36]. Figure 2b shows the stretched flame propagation speed versus stretch rate with flame schlieren images at the experimental condition of Pu = 0.75 MPa, u = 1.2. It is seen that there is a sharp increase on the stretched flame propagation speed trajectory, indicating the self-acceleration of the flame caused by flame front instabilities. Similar observations were reported in [14,16– 18,23,37]. As shown in Fig. 2b, cracks are appearing on the flame surface at the early stage of flame propagation. However, these cracks do not branch until flame ‘c’, where the cracks continue to branch and further develop to cellular structure. Meanwhile, the stretched flame propagation speed increases rapidly with the stretch rate. This critical state when cell development can no longer be suppressed is defined as the instant of transition to cellularity. And the corresponding flame radius is called critical flame radius. Figure 4 shows the stretched flame propagation speed versus stretch rate at u = 1.0 and different initial pressures. For a given
Fig. 2. Stretched flame propagation speed versus stretch rate (a) at Pu = 0.75 MPa and different equivalence ratios and (b) with schlieren images of flames at Pu = 0.75 MPa and u = 1.
initial pressure, the stretched flame propagation speed shows a decreasing tendency with increasing stretch rate. Thus, the burned Markstein length, the negative value of the slope from the best linear regression of flame propagation speed against stretch rate curve, is positive. As discussed above, the unstretched flame propagation
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Fig. 3. Schlieren images of flames for DMF–air mixtures at Pu = 0.75 MPa for different equivalence ratios.
Fig. 4. Stretched flame propagation speed versus stretch rate at u = 1.0 and different initial pressures.
Fig. 5. Laminar burning velocity (solid line) and laminar burning flux (dash dot line) versus equivalence ratio at different initial pressures.
speed is obtained by linearly extrapolating the flame propagation speed to the zero flame stretch rate. As shown in Fig. 4, the unstretched flame propagation speed decreases with increasing initial pressure due to the influence of the free-stream density and the chemical reaction.
laminar burning velocities and laminar burning flux under these conditions are not plotted in the figure, as mentioned earlier. The laminar burning velocities exhibit peak values near the equivalence ratio of 1.2, and they decrease with increasing initial pressure. The decreasing tendency of the laminar burning velocity with initial pressure is obvious when the initial pressure is smaller than or equal to 0.50 MPa; while further increasing the initial pressure shows little effect on the laminar burning velocity. The decrease of the laminar burning velocity with increasing initial pressure is due to the influence of the free-stream density and the chemical reaction. As the initial pressure increases, the threebody, inhibiting reactions become important with increasing pressure. This causes a slowdown in the kinetics and consequently the flame propagation rate [12]. Figure 5 then shows that the laminar burning flux exhibits peak values near the equivalence ratio of 1.2 and increases with increasing initial pressure. This reveals that the increase in the density of unburned gases with increasing initial
4.2.2. Laminar burning velocity and laminar burning flux Figure 5 shows the laminar burning velocity and the laminar burning flux versus equivalence ratio at different initial pressures. The results reported in [11] are also shown in Fig. 5. The initial pressure and temperature for their data are 0.1 MPa and 373 K, respectively. Their values are lower than those in this study except the equivalence ratio of 0.8. This may due to the different initial temperature and different calculated values of density ratio. A fully developed cellular structure can be observed over the flame surface soon after ignition when the initial pressure is 0.75 MPa and the equivalence ratio is larger than 1.2; thus, the inaccurate
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pressure overcomes the reduction of the laminar burning velocity. The combined effects of laminar burning velocity and density contribute to the increase of the laminar burning flux with increasing initial pressure. Laminar burning velocity can be correlated as the following formula, b
ul ¼ UPup
ð7Þ
where Pu is the initial pressure, and U and bp are empirical powerlaw fitting constants. Figure 6 shows the dependence of laminar burning velocities on initial pressure at equivalence ratios of 0.8, 1.0 and 1.2. Laminar burning velocity decreases with increasing initial pressure. The behavior of initial pressure to laminar burning velocity is similar to previous results [16,24,33,38]. As shown in Fig. 6, the fitted values agree well with the measured ones. Table 1 shows the value of U, bp and the standard deviation (SD) of experimental data to the fitted values. By using the corresponding formula (Eq. (7)), laminar burning velocities of DMF–air mixtures at different equivalence ratios and initial pressures can be calculated. Since ul xad1/2/qu p(1+n/2), the resulting reaction order, n, can be calculated by the equation, n = 2(bp + 1), where xad is the reaction rate [33]. Figure 7 shows the adiabatic flame temperature at the initial pressure of 0.10 MPa and the resulting reaction order versus equivalence ratio. The adiabatic flame temperature exhibits peak value near the equivalence ratio of 1.1. This rich shifting of the maximum Ta is due to the influence of product dissociation and reduced amount of heat release [39]. As shown in Fig. 7, the resulting reaction order first increases with equivalence ratio, and then it is insensitive to the increasing equivalence ratio. The resulting reaction order is larger than one and smaller than two over the experimental range. The branching reaction is temperature sensitive, while the three-body termination reaction (which has a negative influence on the net reaction order) is not temperature sensitive. For lean flame or stoichiometric flame, the flame temperature increases with increasing equivalence ratio as shown in Fig. 7. Thus
Fig. 7. Adiabatic flame temperature (square) and resulting reaction order (circle) versus equivalence ratio.
Fig. 8. Markstein length versus equivalence ratio at different initial pressures.
the branching reactions are progressively promoted; hence the reaction order increases with increasing equivalence ratio. This phenomena is also reported in [40].
Fig. 6. Laminar burning velocity versus initial pressure at equivalence ratios of 0.8, 1.0, and 1.2.
4.2.3. Markstein lengths Figure 8 shows the Markstein length versus equivalence ratio at different initial pressures. It is seen that the Markstein length of DMF–air mixtures decreases monotonically with increasing equivalence ratio. The Markstein length in most cases is positive in this study. One exception occurs at the equivalence ratios of 1.5, where the Markstein length is negative regardless of the initial pressure; another exception is at the initial pressure of 0.75 MPa, where the Markstein length decreased from positive to negative at the equivalence ratios of 1.0, as shown in Fig. 8. According to the asymptotic theory [41], the Markstein length depends on the Lewis number of the fuel in lean mixtures; while it depends on the Lewis number of oxidizer in rich mixtures. Thus, the Markstein length tends to increase monotonically with increasing equivalence ratio for light
Table 1 Values of U, bp and SD at different equivalence ratios. / U bp SD (m/s)
0.8 0.42 0.335 0.015
0.9 0.44 0.232 0.005
1 0.50 0.205 0.005
1.1 0.54 0.217 0.003
1.2 0.56 0.196 0.004
1.3 0.50 0.150 0.004
1.4 0.46 0.152 0.004
1.5 0.38 0.149 0.002
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where c1 and c2 are functions of r; Le the effective Lewis number of the mixture; Ze = Ea(Ta Tu)/R(Ta)2 the Zeldovich number; Ea the activation energy; R the universal gas constant. The initial pressure has little effect on the density ratio, as shown in Fig. 9. The extent of the variation of Ze with pressure is much smaller than that of dl [42]. Thus, the variation of Markstein length with pressure is dominated by the variation of dl and Le. For the positively stretched outwardly propagation flame, Lb is positive (negative) corresponding to Le > 1(Le < 1). As demonstrated in Fig. 9, the flame thickness decreases with increasing initial pressure. In the case of Le P 1, c1 and c2 are positive and dl is decreased with increasing initial pressure, so the Markstein length assumes positive values and decreases with increasing initial pressure.
4.3. Flame instability Fig. 9. Flame thickness (solid line) and density ratio (dash dot line) versus equivalence ratio at different initial pressures.
hydrocarbon–air mixtures, such as hydrogen–air and methane–air mixtures, while it tends to decrease with equivalence ratio for heavy hydrocarbon–air mixtures, such as ethanol–air, isooctane–air and propane–air mixtures [16,24,28,42,43]. The Markstein length of DMF–air mixtures decreases with increasing initial pressure for a given equivalence ratio. According to Bechtold and Matalon [28], the Markstein length can be expressed as,
Lb ¼ dl
1 2
2r pffiffiffiffi ; c2 ¼ 1þ r
c1 ¼
r1 c1 þ ZeðLe 1Þc2 ;
pffiffiffiffi pffiffiffiffi
4 r 1 ln½0:5ð r þ 1Þ r1
ð8Þ
There are three kinds of flame surface instabilities: the diffusional–thermal instability, the hydrodynamic instability (or Darrieus–Landau instability) and buoyancy-driven instability [33]. In this study, the laminar burning velocity is relatively high, thus only the diffusional–thermal instability and the hydrodynamic instability are observed. Diffusional–thermal instability is the combined effect of the nonequidiffusive and pure curvature instability. This instability can be characterized by the Markstein length or the Lewis number. The presence of this instability could be identified by irregular distortions of the flame surface relatively early in the flame propagation process when the deficient reactant is also the more diffusive one [44–47]. Hydrodynamic instability, an intrinsic instability of the flame, is induced by the density jump across the flame front. The controlling parameters of this instability are density ratio and flame thickness. Increasing density ratio across the flame or decreasing in flame thickness will promote this instability [23,42,48].
Fig. 10. Schlieren images of DMF–air flames at u = 1.2 and different initial pressures.
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hanced when the flame becomes thinner and diffusional–thermal stability is decreased with decreasing Markstein length. For a given initial pressure, the critical flame radius decreases with increasing equivalence ratio. This results from the decreasing diffusional– thermal stability of DMF–air mixtures with increasing equivalence ratio. For a given initial pressure, the critical Peclet number decreases nearly linearly with increasing equivalence ratio. Since both critical flame radius and flame thickness decrease with increasing initial pressure, the combined effects lead to unconspicuous variation of critical Peclet number to initial pressure, as shown in Fig. 11. 5. Conclusions
Fig. 11. Critical flame radius and critical Peclet number versus equivalence ratio.
As shown in Figs. 3 and 10, the flame is initially stable because of the strong curvature-induced stretch stabilizing effect. As the flame propagates outwardly and stretch rate decreases gradually, a critical state is reached at which cell development can no longer be suppressed and cellular structure appears almost instantaneously over the entire flame surface. In this study, this state is defined as the instant of transition to cellularity. This critical instant is almost consistent with the timing at the onset of cellular flame acceleration [49]. The flame radius of this state is defined as the critical flame radius, and the critical Peclet number (Pec) is the critical radius normalized by the laminar flame thickness of the mixtures. The instant of transition to cellularity depends on the combined effects of the hydrodynamic and diffusional–thermal instabilities [22,48]. 4.3.1. Effect of initial pressure and equivalence ratio Schlieren images of DMF–air flames at Pu = 0.75 MPa for different equivalence ratios are shown Fig. 3. With increasing equivalence ratio, the flame tends to be more unstable. The Markstein length decreases with increasing equivalence ratio, as shown in Fig. 8 and tabulated in Fig. 3. The decrease of Markstein length leads to the increase of the diffusional–thermal instability. The strong hydrodynamic instability cannot be stabilized by the weak diffusional–thermal stability and large cracks develop into cellularity on the flame surface. Thus, the interplay of hydrodynamic and diffusional–thermal instabilities makes the flame more unstable under the rich mixture condition. Figure 10 shows the schlieren images of DMF–air flames at different initial pressures and equivalence ratio of 1.2. It is seen that, with increasing initial pressure, the flame becomes more unstable and the instant of transition to cellularity is advanced. As tabulated in Fig. 10 and shown in Fig. 9, the density ratio is almost the same at the four different initial pressures and flame thickness decreases gradually with increasing initial pressure, so the controlling parameter of hydrodynamic instability is the flame thickness under these conditions. Since flame thickness and Markstein length decrease with increasing initial pressure, hydrodynamic instability is enhanced and diffusional–thermal stability is decreased. These two factors make the flame more unstable and the early occurrence of the cellular structure on flame surface with increasing initial pressure. 4.3.2. Critical flame radius and Peclet number Figure 11 shows critical flame radius and critical Peclet number versus equivalence ratio. It is seen that, for a given equivalence ratio, the critical flame radius decreases with increasing initial pressure. As discussed above, the hydrodynamic instability is en-
An experimental study on laminar burning velocities and flame instabilities of DMF–air mixtures was conducted using the spherically propagation flame at different equivalence ratios and initial pressures. The main conclusions are summarized as following: 1. Laminar burning velocities exhibit the peak values at the equivalence ratio of 1.2 and decrease with increasing initial pressure. Laminar burning fluxes increase with increasing initial pressure. Base on the experimental data, a correlation expression is obtained for the calculation of the laminar burning velocity of DMF–air mixtures over a wide range of equivalence ratios and pressures. 2. The Markstein lengths of DMF–air mixtures decrease with increasing equivalence ratio and initial pressure. 3. Increasing initial pressure and equivalence ratio destabilizes the flame front. The flame-front surface for rich DMF–air mixtures at high initial pressures is strongly affected by the combined effects of diffusional–thermal and hydrodynamic instabilities. 4. The critical flame radius decreases with increasing equivalence ratio and initial pressure. The critical Peclet number decreases with increasing equivalence ratio. Initial pressure has little influence on the critical Peclet number.
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