9th Asia-Pacific Conference on Combustion, Gyeongju Hilton, Gyeongju, Korea 19-22 May 2013
Experimental and numerical studies on burning velocities and Markstein numbers of lean laminar H2/CH4/air flames Ekenechukwu C. Okafor1, Masashi Toyoda1, Akihiro Hayakawa1, Yukihide Nagano2, Toshiaki Kitagawa2 1Kyushu
University, Graduate School of Engineering,
2Kyushu
University, Faculty of Engineering,
744 Motooka, Nishi-Ku, Fukuoka, 819-0395, Japan
Abstract Experimental and numerical studies on the effects of hydrogen concentration on the unstretched laminar burning velocities and the Markstein numbers of premixed H2/CH4/air flames were conducted at equivalence ratio of 0.8. The experiments were conducted in a constant volume bomb at mixture temperature of 350 K and various initial mixture pressures up to 0.50 MPa. The mole fraction of hydrogen in the binary fuel was varied from 0 to 1.0. The unstretched laminar burning velocity increased non-linearly with increase in fraction of H2. It decreased with increase in initial mixture pressure. For each mixture pressure, the sum of concentrations of H and OH radicals in the numerically simulated flame were found to correlate strongly to the unstretched laminar burning velocity. The Markstein number obtained from the experiments varied non-monotonically with increasing hydrogen fraction at initial mixture pressure of 0.10 MPa. It decreased with increase in initial mixture pressure. Analytical evaluation of the Markstein number suggested that the Markstein number may vary nonmonotonically with hydrogen fraction due to non-monotonic variation of the effective Lewis number and may decrease with increase in mixture pressure due to increase in Zeldovich number. The propensity of flame instability varied nonmonotonically at 0.10 MPa
1 Introduction Hydrogen/methane binary fuel has attracted many research interests as an alternative fuel in internal combustion engines due to its promising combustion characteristics in comparison with methane or natural gas fuel [1, 2]. Laminar burning velocity is one of the most important fundamental properties of a fuel governing its combustion behavior. The laminar burning velocity of outwardly propagating flames is affected by flame stretch rate. The Markstein number or the Markstein length quantifies the sensitivity of the flame to stretch. It is related to the onset of flame instability due to thermo-diffusive effect and correlates to the Zeldovich and the Lewis numbers. Flame instability is caused by thermo-diffusive effects and hydrodynamic effects. The laminar burning velocity of H2/CH4/air flames has been reported to increase with increase in H2 fraction in the fuel and decrease with mixture pressure [3, 4]. Experimental studies
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have shown that addition of small quantities of H2 (mole fraction not greater than 0.2) to CH4 reduced the burned gas Markstein length [4]. Numerical studies, which varied the mole fraction of H2 in the fuel from 0 to 1.0 showed that the burned Markstein length varied non-monotonically with H2 fraction [5, 6]. However, this trend in Markstein length (Markstein number) of H2/CH4/air flames with increase in H2 fraction has not been given much research attention, especially at elevated mixture pressures. It is necessary to investigate the possibility of a nonmonotonic variation of onset of flame instability in the flames. Therefore, in this study, the unstretched laminar burning velocity, the Markstein number and the tendency of instability of H2/CH4/air flames were examined while varying the fraction of H2 from 0 to 1.0 at different initial mixture pressures. Local sensitivities analysis was carried out to study the reason for the variation in laminar burning velocity. The Markstein number was obtained from the experiment, and evaluated analytically to examine its non-monotonic trend with H2 concentration at different mixture pressures. The flame images were compared at different H2 fractions to investigate the propensity of flame instability.
2 Experimental and Numerical Procedures Spherically propagating laminar H2/CH4/air flames were examined by experiment using a constant volume fan-stirred combustion chamber shown in [7]. Procedure for experiments and data processing were also described in [7]. In this study, the equivalence ratio and initial temperature of the mixtures were kept constant at 0.8 and 350K, respectively. The concentration of hydrogen in the fuel was expressed in terms of mole fraction of hydrogen, xH2 in the binary fuel of methane and hydrogen defined by (1).
xH 2
nH
2
nH n CH 2
(1) 4
Here, nH2 and nCH4 are numbers of moles of H2 and CH4 in the binary fuel. The value of xH2 was varied from 0 to 1.0. The initial mixture pressures, Pi, were 0.10, 0.25 and 0.50MPa. Numerical simulation of one-dimensional unstretched premixed flames of the mixtures was carried out using GRI Mechanism version 3.0 [8] as the reaction mechanism in COSILAB software [9].
Laminar Burning Velocity
The variation of stretched laminar burning velocity, un with flame stretch rate, during flame propagation is shown in Fig.1. The difference between the unstretched laminar burning velocity, ul and the stretched one, un was considered proportional to stretch rate within the regime of stretch rate where the flame was stable, ul – un = L
(2)
where L is the Markstein length. By applying (2) to the measured relationship between and un, the unstretched laminar burning velocity, ul was obtained as the intercept value of un at = 0. [7, 10]. Non-linear correlation between the flame stretch rate and the stretched laminar burning velocity has been reported in literature [11, 12]. In this study, linear correlation was used in order to compare the present experimental results with those of previous researchers, and with the analytical result whose theory is based on the linear correlation. The linear correlation is reasonably adequate for hydrogen/air and methane/air mixtures [11]. The flames of xH2 > 0.5 at Pi = 0.25 MPa and xH2 > 0.3 at Pi = 0.50 MPa became cellular soon after ignition, as observed in the flame images (not shown here). Therefore, the stable flame regime of flame stretch rate was too narrow to apply (2) [7]. Hence, ul was obtained by numerical simulations. The simulated results agreed with experimental results at conditions where flame instability was not prominent. Therefore, the numerical simulation was considered reliable at all initial pressures and mole fractions of H2. Variation of the unstretched laminar burning velocity, ul, with
un cm/s
150 x = 0.7 H
Hydrogen-Methane = 0.8
2
100 ul 50
Onset of cellularity
500
1000 1/s
1500
Figure 1. Variation of un with at xH2 = 0.7
ul cm/s
0
Experimental Data 0.10 MPa 0.25 MPa 0.50 MPa Simulation
0.10 MPa 0.25 MPa 0.50 MPa
0.0 0
From relative sensitivity analysis, the following reactions showed highest sensitivity with respect to ul and concentrations of H and OH; H + O2 + H2O = HO2 + H2O H + O2 = OH + O H + HO2 = O2 + H2 H + HO2 = 2OH OH + H2 = H + H2O OH + CO = H + CO2
0.5 xH2
1.0
Figure 2. Variation of ul with xH2 and Pi
(R35) (R38) (R45) (R46) (R84) (R99)
The roles of these reactions involving H and OH in the combustion of H2/CH4 mixtures are well documented in the literature [13, 14, 15]. The main chain branching reaction (R38) had the highest positive sensitivity with respect to ul for xH2 ≤ 0.9 while reactions (R46) and (R84) had the highest positive sensitivities for xH2 = 1.0. Increase in the rates of (R38), (R46), (R84) and (R99) will result in increase in H and OH concentrations and ul. Reactions (R35) and (R45), which had the highest negative sensitivities with respect to ul are chain terminating reactions which reduce the concentration of the radicals in the flame.
Markstein Number
Markstein number, Ma is obtained by normalizing the Markstein length, L, with laminar flame thickness. In this study, the preheat zone thickness, l (= a/ul, a: thermal diffusivity of the mixture), was adopted. At initial mixture pressure of 0.10 MPa, the Markstein length varied non-monotonically with increasing xH2 (not shown here).
3
200 Hydrogen-Methane = 0.8
100
Figure 3 shows the correlation of ul to the concentration of H and OH in the flame. The concentration of H and OH at the point of maximum H concentration in the flame was employed in this study. It showed better correlation to ul than the maximum H concentration did. Although the maximum number of moles of H and OH increased with Pi, the maximum mole fractions decreased with Pi similar to ul. These radicals play important complementary roles in the rate-limiting elementary reactions in the combustion.
4
Pi MPa 0.10 0.50
0
mole fraction of H2, xH2, is shown in Fig. 2. The unstretched laminar burning velocity increased with increase in xH2 for the three initial mixture pressures. For the mixtures with xH2 ≤ 0.5, increase in ul with xH2 was gradual. However, ul increased rapidly as xH2 increased from 0.7 to 1.0. For fixed xH2, ul decreased with increase in initial mixture pressure. The pressure exponent or pressure index [7] was approximately equal to -0.45 for all mixtures of xH2 ≤ 0.7 and was equal to 0.37 and -0.22 for xH2 = 0.9 and 1.0, respectively.
H+OH mol/m
3
0.6 Hydrogen-Methane 0.4
= 0.8
Pi MPa 0.10 0.25 0.50
0.2 0 0
100 ul cm/s
Figure 3. Correlation of ul with H + OH
200
It decreased as xH2 increased from 0 to 0.7, then increased as xH2 increased from 0.7 to 1.0. The Markstein number also showed a similar non-monotonic trend at 0.10 MPa as shown in Fig. 4. At Pi = 0.25 and 0.50 MPa, experimental data on L and Ma was not available at high xH2 values due to flame instability. As Pi increased from 0.10 to 0.50 MPa, the Markstein length and the Markstein number decreased for 0 ≤ xH2 ≤ 0.3. To understand the reason for the observed trends in Markstein number, the variation of Ma with xH2 and mixture pressure was investigated using an analytical expression correlating Ma to the Zeldovich number, Ze, the effective Lewis number, Leeff and the thermal expansion coefficient, expressed as the ratio of unburned mixture density, u, to the burned gas density, b [16]. Ma
2
1
2Ze( Leeff 1) 1 1 2 1 1 ln 1 2 (3)
This expression, derived from asymptotic analysis, suggests that the Markstein number is affected by hydrodynamic characteristics of the flame expressed by the thermal expansion ratio. Gas expansion influences the modification of the flame temperature by flame stretch [17], hence affects the Markstein number. In order to evaluate Ma using (3), Ze and Leeff were obtained.
Ze
E a Tb Tu R0Tb
(4)
2
Here Tb is the adiabatic flame temperature and R0 is the universal gas constant. The overall activation energy, Ea was derived by measuring the variation of uul due to slight perturbation of the adiabatic flame temperature as described in [17]. As shown in Fig. 5, the Zeldovich number decreased with increase in xH2 and increased with mixture pressure. The effective Lewis number of a mixture of a single component fuel and an oxidant for use in (3), is given by (5) [16]; Leeff 1
LeE
1 LeD 1A 1 A
(5)
where A = 1 + Ze( -1). The Lewis numbers LeE and LeD are those of the excess reactant and the deficient reactant, respectively. Here, is defined as the ratio of mass of excess-to-deficient reactants in the fresh mixture relative to their stoichiometric ratio. However, the fuel used in this study was a binary fuel. To obtain the effective Lewis number of the multi-component mixture of the binary fuel and the oxidant, the effective Lewis numbers obtained from (5) were applied in (6), which is a proposed expression for the Lewis number of a binary fuel by [19];
x CH xH 1 Leeff Leeff CH Leeff H
The Zeldovich number, Ze is the non-dimensional activation energy of the reaction and is defined according to (4).
4
2
4
(6)
2
where xCH4 (= 1-xH2) is the mole fraction of methane in the fuel.
Hydrogen-Methane = 0.8
0 Pi MPa 0.10 0.25 0.50
-2
0 0.0
0.5 xH2
For fixed xH2, LeE and LeD did not vary with Pi. However, Leeff decreased slightly with increasing mixture pressure due to the effect of Ze. The thermal expansion ratio did not vary significantly with Pi either. Hence, the calculated Ma decreased with increase in Pi for fixed xH2, mainly due to the increase in Zeldovich number. That could be the reason the measured Ma decreased with Pi.
1.0
Figure 4. Variations of the measured Markstein number
Hydrogen-Methane
= 0.8
1.2
8
1.0
Ze
4
Leeff
Pi MPa 0.10 0.25 0.50
0 0.0
Leeff
Ze
12
0.8 0.5 xH2
1.0
0.6
Figure 5. Variations of the Zeldovich number and the effective Lewis number
Calculated Ma
Ma
2
As also shown in Fig. 5, for fixed mixture pressures the effective Lewis number decreased as xH2 increased from 0 to 0.7 and then increased as xH2 increased from 0.7 to 1.0. The term Ze(Leeff - 1), which is the dominant term in (3) varied non-monotonically with xH2 for each Pi due to the non-monotonic variation of Leeff. Hence, Ma obtained from the analytical expression varied non-monotonically with xH2 at fixed mixture pressures, as shown in Fig. 6. Although the calculated Ma and the measured Ma did not agree quantitatively, their variations with xH2 showed good qualitative agreement at Pi = 0.10 MPa. The measured Ma may vary non-monotonically with xH2 mainly due to the effect of the non-monotonic variation of Leeff.
0.8
Hydrogen-Methane = 0.8
0.4 0 -0.4 -0.8
Pi MPa 0.10 0.25 0.50
0 0.0
0.5 xH2
1.0
Figure 6. Variations of the calculated Markstein number
5 Flame instability Positive flame stretch tends to inhibit the evolution of flame instability [18]. The propensity of flame instability with increasing xH2 was studied by comparing the images of the flames at constant stretch factor, K (=l/ul). At Pi = 0.10 MPa, the flame images showed an increase in the propensity of the flames to become unstable as xH2 increased from 0 to 0.7. This was expected since lean H2 flame is more unstable than lean CH4 flame. However, the propensity of flame instability decreased as xH2 increased from 0.7 to 1.0. Shown in Fig. 7 is a comparison of the flame images at constant K for the flames with xH2 ≥ 0.5 at Pi = 0.10 MPa. Of the four flames, the one of xH2 = 0.7 had the most wrinkled front indicating that it was the most unstable flame. The propensity of flame instability varied non-monotonically as H2 fraction increased. This observation agreed with the variation of the Markstein number and the effective Lewis number. The instability could be predominantly due to thermo-diffusive effects on the flame. Jomaas et al. [18] reported that the critical Peclet number for the onset of instability depends only on and the wavenumber for pure hydrodynamic instability, manifested for equidiffusive mixtures, and on Ze(Leeff - 1) for non-equidiffusive mixtures. As pressure increased the flames became more unstable, as shown in Fig. 8 for the flame of xH2 = 0.3. This may be due to decrease in flame thickness in addition to decrease in Ma. Hydrodynamic instability is promoted by decrease in flame thickness. At Pi = 0.25 and 0.50 MPa, the propensity of flame instability increased as xH2 increased from 0 to 0.7. Although a
comparison of the propensity at xH2 ≥ 0.7 was not possible because the intensity of cellularity was too high to be distinguishable, the non-monotonic variation of Ze(Leeff - 1) suggested that the propensity of instability could vary nonmonotonically at 0.25 and 0.50 MPa.
6
The effects of hydrogen concentration on laminar burning velocities and Markstein numbers of H2/CH4/air flames were studied at different initial mixture pressures. The unstretched laminar burning velocity increased with increase in H2 fraction in the fuel. The concentration of H and OH may have a strong influence on ul due to the relevance of the radicals to the dominant elementary reactions. The Markstein number varied non-monotonically with increasing xH2 and decreased with increase in initial mixture pressure mainly due to the effect of the effective Lewis number and the Zeldovich number, respectively. The propensity of flame instability may vary nonmonotonically with xH2 due to the non-monotonic variation of the effective Lewis number.
References [1] [2] [3] [4]
K = 0.013, Pi = 0.10 MPa xH2 = 0.5 xH2 = 0.7 xH2 = 0.9 xH2 = 1.0 l = 0.067mm l = 0.052mm l = 0.035mm l = 0.029mm
[5] [6] [7]
[8]
(rsch, t) (rsch, t) (rsch, t) (rsch, t) (61mm, 18.5ms)(51mm, 10.4ms) (32mm, 3.6ms) (24mm, 2.0ms)
Figure 7. Comparison of flame images of xH2 ≥ 0.5. Here rsch is flame radius while t is time from ignition
[9]
[10] [11]
K = 0.015, xH2 = 0.3 0.10 MPa l = 0.083mm
0.25 MPa l = 0.050mm
0.50 MPa l = 0.032mm
[12] [13] [14] [15] [16] [17]
(rsch, t) (62mm, 26.5ms)
(rsch, t) (44mm, 25.5ms)
(rsch, t) (32mm, 22.5ms)
Figure 8. Comparison of flame images at different Pi. Here rsch is flame radius while t is time from ignition
Conclusions
[18] [19]
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