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Numerical study on the spark ignition characteristics of hydrogen–air mixture using detailed chemical kinetics
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Numerical study on the spark ignition characteristics of hydrogeneair mixture using detailed chemical kinetics Jilin Han, Hiroshi Yamashita*, Naoki Hayashi Department of Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya-shi, Aichi, Japan
article info
abstract
Article history:
Hydrogen is a promising fuel and is expected to replace hydrocarbon fuels for its significant
Received 15 March 2011
potentials to reduce the pollutants and greenhouse gases. It is very important to investi-
Received in revised form
gate Minimum ignition energy (MIE) on safety standards and ignition process of hydro-
23 April 2011
geneair mixtures. Even though the formation of flame kernels in quiescent hydrogeneair
Accepted 25 April 2011
mixtures has been researched numerically and experimentally, the details of ignition
Available online 28 May 2011
mechanism have never been satisfactorily explained. In this study, the spark ignition of hydrogeneair mixture is investigated by using detailed chemical kinetics and considering
Keywords:
the heat loss to the electrode. The purpose of this study is emphasized in the effects of the
Spark ignition
energy supply procedure, the radius of the spark channel, electrode size and electrode gap
Hydrogeneair mixture
distance on the MIE. In addition, the effects of mixture temperature, electrode gap distance
Minimum ignition energy
and electrode size on relationship between the equivalence ratio and the MIE are
Equivalence ratio
examined.
Detailed chemical kinetics
Crown Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Hydrogen is a promising fuel that could replace hydrocarbon fuels due to its potential to reduce pollutants and greenhouse gases. In particular, easily applicable utilization of hydrogen is in the SI engine as a pure fuel [1,2] and fuel blends [3,4] to start the flame propagation for its near-zero engine-out emission and high flame speed. The latter is unique to hydrogen and able to ignite premixed mixture at low equivalence ratios to achieve high thermal efficiency [5,6]. Many complex chemical and physical processes occur simultaneously during spark ignition, and these processes interact with each other. The spark ignition mechanism has never been satisfactorily explained, despite many years of research. Experimental results change if one factor is altered,
but in many cases, there are insufficient experimental data on the subject to predict exactly what will happen. Numerical simulation is a convenient method for studying the specific effects of any factor on the spark ignition characteristics and for calculating important physical and chemical properties such as the instantaneous high temperature and the heat release rate, which are difficult to obtain experimentally. The minimum ignition energy (MIE) is the minimum amount of energy required to ignite a combustible vapor, gas, or dust cloud due to an electrostatic discharge. MIE is an important parameter for judging the ignition ability of combustion systems, and is considered to be an important safety criterion for combustible gases. Factors affecting the MIE play an important role in determining the subsequent behavior of the flame. These factors include the type and composition of the
* Corresponding author. Tel./fax: þ81 52 789 4470. E-mail address: [email protected] (H. Yamashita). 0360-3199/$ e see front matter Crown Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.04.190
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Nomenclature cp D h L Le m P q qmin Qtotal Qtotal,min R r Rc R
specific heat at constant pressure, J/(kg K) effective diffusivity, m2/s specific enthalpy, J/kg electrode gap distance, mm Lewis number molar mass, kg/mol pressure, Pa ignition energy density, GW/m3 minimum ignition energy density (MIED), GW/m3 total ignition energy, mJ minimum total ignition energy (MIE), mJ electrode radius, mm radial coordinate, mm radius of the spark channel, mm universal gas constant, J/(mol K)
mixture, spark duration, initial temperature, pressure, and velocity of the mixture, electrode size, electrode gap distance, and heat loss to the electrodes. Several numerical studies have examined the details of spark ignition. Yuasa et al. [7] performed a two-dimensional numerical analysis with elementary reactions, including ionemolecule reactions, to investigate the effect of the energy deposition schedule on the MIE during the composite spark ignition of methaneeair mixtures. Kravchik and Sher [8] simulated spark ignition and flame initiation in a quiescent methaneeair mixture numerically. Kono et al. [9] investigated the mechanism of flame kernel formation produced by shortduration sparks using a set of partial differential equations with unsteady and two-dimensional cylindrical coordinates. Thiele et al. [10] investigated the early development of a stable flame kernel during spark ignition based on a detailed model for coupling two-dimensional cylindrical reactive flows with electrodynamics. A previous study investigated the effect of the energy channel length on the relationship between the MIE and the equivalence ratio for methaneeair mixture without considering heat loss to the electrodes [11]. The effects of the electrode temperature on the relationship between the MIE and the equivalence ratio, and the effects of the electrode size, electrode gap distance, equivalence ratio, and spark duration on the MIE for a methaneeair mixture have also been examined [12]. From the point of view of safety, the hydrogen explosion prevention must be taken into consideration, because the MIE of hydrogeneair mixture is very small and it is easy to accidently to give rise to a disaster by spark ignition. Even though some experimental and computational research has been performed on hydrogeneair mixtures to determine the MIE for the spark ignition, the flame kernel development process, and the mass fractions of major radicals [13e17], the details of the ignition mechanism have not been satisfactorily explained. In this study, the spark ignition of a hydrogeneair mixture was investigated using detailed chemical kinetics and considering heat loss to the electrode. The purpose of this study was to analyze the effects of the energy supply
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time, ms spark duration, ms volume of the spark channel, m3 mass production rate, kg/(m3 s) mass fraction axial coordinate, mm
t ti V w Y z
Greek Symbols q angular coordinate l effective thermal conductivity, W/(m K) m effective viscosity, Pa s r density, kg/m3 s stress tensor, Pa F equivalence ratio Subscript i species
procedure, spark channel radius, electrode size, and electrode gap distance on the MIE. Additionally, the electrode gap distance, and electrode size on the relationship between the equivalence ratio and the MIE were examined.
2. Computational domain and numerical methods 2.1.
Simplifying assumptions
The following assumptions were made to simplify the mathematical treatment and accelerate the calculations. (1) The mixture gases are ideal gases. (2) The Soret, Dufour, and Pressure effects can be neglected because diffusion due to these effects is much smaller than that due to the temperature and concentration gradients. (3) The influence of the magnetic and electrical fields is negligible. (4) Viscous dissipation and DP/Dt can be neglected in the energy conservation equation. (5) Natural convection, heat transfer by radiation, and ionic species can be ignored.
2.2.
Governing differential equations
Spark ignition involves many simultaneous complex chemical and physical processes. The following series of equations was used to characterize the combustion process. (1) Equation of state, P ¼ rRT
X Yi i
mi
(2) Continuity equation, vr 1 vrur r vruz ¼0 þ þ vz vt r vr
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(3) Conservation of momentum equations, vðrur Þ 1 vðrrur ur Þ vðruz ur Þ 1 vðrsrr Þ vðsrz Þ sqq vP þ þ ¼ þ r vr vt r vr vz r vr vz vðruz Þ 1 vðrrur uz Þ vðruz uz Þ 1 vðrsrz Þ vðszz Þ vP þ þ ¼ þ vt r vr vz r vr vz vz (4) Species mass conservation equation, vYi vYi v rDi r v rDi vðrYi Þ 1 vðrrur Yi Þ vðrYi uz Þ 1 vr vz þ þ wi þ þ ¼ vr vz vt r vr vz r
(5) Energy conservation equation, vT vT v lr v l vðrTÞ 1 vðrrur TÞ vðruz TÞ 1 vr vz cP þ þ þ ¼ vr vz vt r vr vz r DP X þ hi wi þ q Dt i where vvr 2 1 vvr r vvz srr ¼ m 2 þ vr 3 r vr vz
m ¼ Pr l=cp where Pr is 0.75. The effective diffusivity of species i is given as Di ¼
1 l rLei cP
where Lei is constant for every species i.
2.3.
Initial and boundary conditions
Two-dimensional cylindrical coordinates were used to calculate the ignition processes because the initial shape of the flame produced by sparks in a quiescent hydrogeneair mixture was presumed to be axisymmetric. We used analytical models with an electrode (Fig. 1). The computational domain shown in Fig. 1 contained the computational region, boundary conditions, electrode geometry, and location of the spark channel. The distance between the first 60 grid points around the electrode was set at 0.025 mm due to the smaller quenching distance of a hydrogeneair mixture compared to a methaneeair mixture in the r and z directions [11,12]. The computational region spanned 5.8 mm in both the r and z directions. The r and z axes were located on lines of symmetry for all variables. The other two boundaries were treated as outside boundaries, where the gradients of all variables are zero and the pressure can be assumed to be
vr 2 1 vvr r vvz þ sqq ¼ m 2 r 3 r vr vz vvz 2 1 vvr r vvz þ szz ¼ m 2 vz 3 r vr vz vvz vvr þ srz ¼ m vr vz GRI-mech 3.0, consisting of 53 species and 325 elementary reactions, was applied to the chemical kinetics model [18]. The specific heat at constant pressure was determined by a fourthorder polynomial approximation of the temperature, the coefficients of which were obtained from the JANAF table [19]. The enthalpy of a species is ZT hi ¼ h0i þ
cp;i dT T0
and the specific heat at constant pressure of the mixture is cp ¼
X
Yi cp;i
i
The simplified transport model proposed by Smooke et al. [20] was used for the transport properties. The effective thermal conductivity is l ¼ AcP
T T0
r
where T0 is the standard-state temperature, r ¼ 0.7, and A ¼ 2.58 104 g/(cm s). The effective viscosity is expressed as
Fig. 1 e Analytical model with electrode and boundary conditions for a hydrogeneair mixture.
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atmospheric. The radius of electrode R was varied from 0.3 to 1.5 mm to simulate different electrode sizes, and the electrode gap distance was varied from 0.3 to 1.2 mm to investigate the effect on the MIE. The electrode surface temperature was set to 300 K. The initially quiescent mixture of hydrogen and air in the computational domain had an initial temperature of 300 K and was at atmospheric pressure. For the electrode boundary conditions, no surface reactions and the no-slip condition were assumed on the electrode surface, and the gradient of the reaction chemical species i was zero. Because spark durations that give an optimum value of MIE are in the range of 3e100 ms [21], 20 ms was deemed long enough to avoid possible numerical problems that might occur due to the very rapid energy addition.
2.4.
Numerical method
The numerical method was the same as that used in previous studies [11,12] for methaneeair mixtures. The finite volume method [22] was used to discretize the above governing differential equations in space and time. This method is similar to the finite difference method or finite element method, and its values are calculated at discrete places on a meshed geometry. Finite volume refers to the small volume surrounding each node point on a grid. The grid size and the time step were chosen to be 0.05 mm and 1 ms, respectively. The semi-implicit method for pressure-linked equations (SIMPLE) method proposed by Patankar [23] was used to couple the velocity and pressure fields. The first-order upwind scheme was used for the convective terms, and the fully implicit Euler method was used to advance the time. The successive over-relaxation method was used to iterate each time step.
2.5.
Ignition behavior
The definition of successful ignition is very important when calculating the MIE. In this study, we defined successful ignition as when the flame ignited successfully in the section at z ¼ 0 mm based on the temperature time history. For example, the high temperature area extends to the ambient cold mixture in Fig. 2(a) for an ignition density of q ¼ 67.5 GW/m3, but it does not extend and the temperature decreases in Fig. 2(b) for q ¼ 65.0 GW/m3. Therefore, the hydrogeneair mixture ignited successfully in Fig. 2(a), but not in Fig. 2(b). It was assumed that the ignition energy was introduced into the spark channel at a certain constant ignition energy density q during the ignition duration. The total ignition energy was calculated from Qtotal ¼ q ti V, where V is the volume of the spark channel, ti is the ignition duration. In this manner, we can estimate the MIE in cases in which flame propagation succeeded or failed.
3.
Results and discussion
3.1.
Effects of the energy supply procedure on the MIE
The energy deposited during the short ignition duration time does not contribute to a temperature increase of the mixture,
Fig. 2 e Time history of temperature in section z [ 0 mm (F [ 1, L [ 1 mm, R [ 0.3 mm).
but rather increases the spark channel radius. That is, the spark channel radius increases with time during the spark duration. Test calculations in which the spark channel radius was allowed to increase with time for a methaneeair mixture during the spark duration have yielded results that differed by only a few percent or less from those obtained using a fixed spark channel radius [24]. To demonstrate the correctness of our code, we applied three models in which the spark channel radius changed with time (Fig. 3): the first had a constant spark channel radius during the spark duration (1-section), the spark channel radius in the second model increased halfway through the spark duration (2-section), and the spark channel radius in the third model increased in after four equal periods during the spark duration (4-section). Kravchik et al. [8] illustrated important factors that directly influenced the spark kernel expansion for a methaneeair mixture. These include the electrical and chemical power released and the power losses due to conduction to the electrode and the surrounding unburned mixture. In the early stages of spark development (about 100 ms), when the chemical power is smaller than the power loss, the electrical power
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Fig. 3 e Three energy supply procedure models.
supply determines the flame propagation. In the later stages when the chemical heat release dominates and the power losses from the cooler gas and electrode are much lower, the flame becomes self-sustaining. An interesting phenomenon during the early stages is that the electrical energy supply is almost constant with time. For that reason, the spark ignition energy densities are set on the right side of Fig. 3 according to the equation Q ¼ q ti V, where q is the ignition energy density, ti is the spark duration, and V is the volume of the spark channel. In this manner, the energy input in the spark channel during the spark ignition is the same for all three models. Fig. 4 shows the temperature histories of the three energy supply models for F ¼ 1, L ¼ 1 mm, and ti ¼ 80 ms, with the same ignition energy Qtotal,min ¼ 1.47 mJ. The temperature of the 4-section model was the highest (above 8000 K) for the large ignition energy density during the early stages of the spark ignition propagation. However, the temperature histories of the three models became almost the same when t > 100 ms, and they had the same MIE despite the different energy supply procedures. Thus, the energy supply procedure did not affect the values of the MIE for the methaneeair mixture. These computational results demonstrate the validity of the test calculations described earlier. Next, the effect of the energy supply procedure on the MIE for a hydrogeneair mixture was investigated. Thiele et al. [13] examined the electrical current and voltage traces
of a typical spark event for a hydrogeneair mixture. During the early stages, the electrical current and voltage are almost constant with time. According to the equation P ¼ VI, where V is the voltage and I is the electrical current, the power of the energy supply is nearly constant during the spark duration. For this reason, we applied the same spark channel radius change models that we used for the methaneeair mixture. The temperature history results for the hydrogeneair mixture are shown in Fig. 5 for F ¼ 1, L ¼ 0.5 mm and ti ¼ 20 ms, with the same ignition energy Qtotal,min ¼ 0.11 mJ. The temperature of the 4-section model was again the highest for the very large ignition energy density during the early stages of the spark ignition propagation. However, with increasing time, the temperature of the 4-section model remained higher and the mixture was successfully ignited. The temperatures of other models gradually decreased, and those mixtures were not ignited. Thus, the energy supply procedure dramatically affected the MIE values for a hydrogeneair mixture. According to our computational results, the MIE for the 4-section model was almost half that for the 1-section model. Thus, the energy supply procedure cannot be ignored for a hydrogeneair mixture. The effect of the energy supply procedure of a hydrogeneair mixture is totally different from that of a methaneeair mixture. For this reason, the 4-section model was used for all subsequent hydrogeneair mixture computations.
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0.6
MIE (mJ)
0.5 0.4 0.3 0.2 0.1 0
0
0.2
0.4
0.6
0.8
Rc (mm) Fig. 6 e Relationship between MIE and spark channel radius Rc (F [ 1, L [ 0.5 mm, R [ 0.3 mm, ti [ 20 ms).
Fig. 4 e Temperature history for the three energy supply models (F [ 1, L [ 1 mm, ti [ 80 ms, Qtotal,min [ 1.47 mJ).
3.2.
Effects of the spark channel radius on the MIE
Sloane et al. [24] investigated the effect of the spark channel radius on the MIE for a methaneeair mixture by using detailed first-step and third-step reaction models. They reported that even though the values of the MIE were different, the tendencies of the MIE versus spark channel radius were similar. The minimum ignition energies were much more sensitive to a larger spark channel radius, and leveled off at a constant value when the spark channel radius was smaller than a critical value. For a methaneeair mixture with detailed chemical reactions, this value was about 0.3 mm. We used our code to determine this value for a hydrogeneair mixture, as shown in Fig. 6, which illustrates the relationship between the MIE and spark channel radius. When the spark channel radius Rc decreased to 0.15 mm, the MIE leveled off at a value of 0.04 mJ.
A spark instantly establishes a small volume consisting of a hot kernel; its temperature decreases rapidly due to heat loss to the electrodes and ambient unburned gas. In the adjacent layer of ambient gas, the temperature rises and induces chemical reactions so that a flame kernel is formed, which propagates outwards with approximately spherical symmetry. Whether the flame kernel develops to a steady state depends on the number of radicals; this is important for flame propagation. If the ignition energy density is too small, the heat release rate within the inner spherical zone of the chemical reactions is insufficient to compensate for the heat loss rate to the outer zone of the preheated unburned gas. The radicals of the outer layer of the spark channel will then deactivate, and gradually the radicals of inner layer of the flame kernel will deactivate due to the large amount of heat dissipation. Thus, the flame is quenched and cannot become self-sustaining. To continue to propagate, the ignition energy density must grow to at least a level such that the gain of heat due to chemical reactions exceeds the heat lost to the unburned gas and electrodes. Then, enough intermediate radicals are generated, and the mixture is successfully ignited. This level of the ignition energy density corresponds to the horizontal section (Rc > 0.35 mm) shown in Fig. 7, which gives the relationship between the minimum ignition energy density and the spark channel radius.
160
MIED (GW/m3)
140 120 100 80 60 40
0
0.2
0.4
0.6
0.8
Rc (mm) Fig. 5 e Temperature history for the three energy supply models (F [ 1, L [ 0.5 mm, ti [ 20 ms, Qtotal,min [ 0.11 mJ).
Fig. 7 e Relationship between MIED and spark channel radius Rc (F [ 1, L [ 0.5 mm, R [ 0.3 mm, ti [ 20 ms).
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3.3. Profiles of major species, heat release rate of reactions, and chemical paths Fig. 8 shows the profiles of major species and the temperature distribution in the radial direction near the line of symmetry at t ¼ 20 ms and t ¼ 200 ms. At t ¼ 20 ms, the mass fractions of radicals, such as H, O and OH, were comparatively small, and they were located primarily inside the energy channel. The distribution of H2 and O2 indicate that the mass fractions of these chemical species were almost constant, regardless of location: only small amounts of H2 and O2 were consumed in the energy channel area. This behavior is similar to a methaneeair mixture if we do not consider the heat loss to the electrode during the incipient spark duration due to the comparatively low temperature (under 3000 K) in the spark channel, which cannot dissociate some radicals (H2, H2O). In contrast, when we do consider the heat loss to the electrode for a methaneeair mixture, the temperature near the electrode is over 4000 K, which is high enough to dissociate some radicals such as CH4, CO2 and H2O. At t ¼ 200 ms, high radical concentrations were found in the region between the energy channel and the surrounding unburned mixture (r ¼ 0.15e0.25 mm), and also in the energy channel area. The mass fraction profiles of H2 and O2 and the temperature distribution indicated the location of the flame front.
Because ignition involves the propagation of an exothermic wave, a more fundamental understanding of the combustion process can be obtained by checking the different contributions of the chemical reactions to the net heat release rate. The heat release rate of the main reactions and the net heat release rate along z ¼ 0 mm at different times for F ¼ 1, q ¼ 77.5 GW/m3 are illustrated in Fig. 9. These are the main reactions that play important roles in the heat release rate during the ignition process, including exothermic and endothermic processes. These reactions and their reaction numbers are as follows at different times: For t ¼ 10 ms H þ O2 þ M ¼ HO2 þ M
(R33)
H þ O2 þ N2 ¼ HO2 þ N2
(R36)
H þ O2 ¼ O þ OH
(R38)
H þ HO2 ¼ O2 þ H2
(R45)
H þ H2O2 ¼ HO2 þ H2
(R47)
H2 þ OH ¼ H þ H2O
(R84)
OH þ OH þ M ¼ H2O2 þ M
(R85)
For t ¼ 20 ms H þ O2 ¼ O þ OH
(R38)
H þ HO2 ¼ O2 þ H2
(R45)
H2 þ OH ¼ H þ H2O
(R84)
For t ¼ 200 ms
Fig. 8 e Profiles of major species concentrations and temperatures.
H þ O2 þ H2O ¼ HO2 þ H2O
(R35)
H þ O2 þ N2 ¼ HO2 þ N2
(R36)
H þ O2 ¼ O þ OH
(R38)
H þ HO2 ¼ O2 þ H2
(R45)
H þ HO2 ¼ OH þ OH
(R46)
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H2 þ OH ¼ H þ H2O
(R84)
For t ¼ 1000 ms
H þ O2 þ M ¼ HO2þ M
(R33)
H þ O2 þ H2O ¼ HO2 þ H2O
(R35)
H þ O2 þ N2 ¼ HO2 þ N2
(R36)
H þ O2 ¼ O þ OH
(R38)
H þ HO2 ¼ O2 þ H2
(R45)
H þ HO2 ¼ OH þ OH
(R46)
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H2 þ OH ¼ H þ H2O
(R84)
OH þ HO2 ¼ O2 þ H2O
(R87)
Fig. 9 shows that the behaviors of the net heat release rates were very different at different times. For t ¼ 10 and 20 ms, the net heat release rate was negative, i.e., the process was endothermic because of the high temperature in the spark channel. In particular, the backward reaction R45 was the chain initiation reaction and dominated the net heat release rate. As a result, intermediate radicals, such as H and HO2, were generated. In Fig. 9(c), the ignition process changed from endothermic to exothermic at t ¼ 200 ms. After the ignition delay time, exothermic reactions dominated the ignition process, and we could determine the position of the flame front based on the position of the peak heat release rate. Exothermic reactions R45 and R84 and endothermic reaction R38 made a fundamental contribution to the heat release rate during the entire spark ignition process. Reaction R38 was the chain-branching reaction, and played an important role in the entire spark ignition process with regard to generating O
Fig. 9 e Heat release rate of the main reactions along z [ 0 mm at different times (F [ 1, q [ 77.5 GW/m3).
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and H radicals, which are the characteristic radicals in the flame front and are consumed by exothermic reactions R45 and R84. Fig. 10 illustrates the history of the maximum mass fraction of O and OH radicals for F ¼ 1, q ¼ 77.5 GW/m3. Concentrations of the O and OH radicals were extremely high at t ¼ 50e60 ms when the ignition energy was supplied, then decreased rapidly and leveled out during the heat loss to the electrodes and ambient unburned mixture, and finally increased at about t ¼ 700 ms.
3.4.
Effects of the electrode gap distance on the MIE
MIE (mJ)
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0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
R=0.3 mm R=0.8 mm R=1.5 mm
0.3 0.4 0.5 0.6 0.7 0.8 0.9 Lewis and von Elbe [25] applied the same method used for methaneeair mixtures to measure experimentally the MIE values and quenching distance for a hydrogeneair mixture. The MIE was 0.02 mJ and the quenching distance was 0.66 mm for a stoichiometric hydrogeneair mixture. We compared our computational results with their experimental data to validate our numerical simulation code and to investigate factors that influence flame formation and the MIE. Fig. 11 illustrates our computational results used to determine the quenching distance and the effect of different sizes of electrodes on the relationship between the electrode gap distance L and the MIE in a stoichiometric hydrogeneair mixture. Three sizes of electrodes were chosen; the electrode radius R was set successively to 0.3, 0.8, and 1.5 mm. Although the quenching distance for hydrogeneair mixture was totally different from that for a methaneeair mixture, the computational results had similar tendencies; the MIE increased gradually for R ¼ 0.3 and 0.8 mm within the quenching distance, and the curves were similar to the experimental curve obtained with a free-tipped electrode. However, for R ¼ 1.5 mm, the curve at L ¼ 0.65 mm was almost vertical; thus, the combustible hydrogeneair mixture was hard to ignite within this distance for R ¼ 1.5 mm. This phenomenon is typical for experimental results with a flanged electrode. Thus, we identified 0.65 mm as the quenching distance, based on our computational results. This distance was almost the same as that obtained in the experiment. The MIE increased gradually below the quenching distance for a free-tipped electrode. However, when the electrode gap distances
Fig. 10 e History of the maximum mass fraction of H and OH (F [ 1, L [ 0.5 mm, q [ 77.5 GW/m3).
1
1.1 1.2
L (mm) Fig. 11 e Relationship between MIE and gap distance L (F [ 1).
became greater than the quenching distance, the curves had almost constant values over a considerable range of electrode gap distances for both types of electrodes. The start of the increasing trend of the curves in Fig. 11 moved forward (at L ¼ 0.45 mm for R ¼ 0.3 mm, L ¼ 0.60 mm for R ¼ 0.8 mm, and L ¼ 0.65 mm for R ¼ 1.5 mm) with decreasing electrode size. Fig. 12(a)e(d) show the temperature and velocity vector distributions of successful ignitions for the 0.3 mm electrode at an equivalence ratio F ¼ 1 for different electrode gap distances. In Fig. 12(a) and (b), the temperatures between the electrodes were very low. This indicates that the quenching effect of the cold electrode could significantly affect the formation of the flame kernel between electrodes, penetrating the small electrode gap distances of 0.3 and 0.4 mm. In contrast, in Fig. 12(c) and (d), the temperatures between the electrodes were relatively high for an electrode gap distance of 0.8 and 1.2 mm, respectively. The quenching effect did not affect the flame kernel between the electrodes for these large electrode gap distances. When the electrode gap distance was greater than 0.65 mm (Fig. 11), the curves of the computational results almost overlapped each other, indicating that the electrode size did not significantly affect the MIE. Fig. 13 illustrates the relationship between the MIE and the equivalence ratio for the 0.3 mm electrode at different distances. These computational results showed the same tendency as the experimental results reported by Ono and Oda [15]. This trend can be seen more clearly in Fig. 14, which provides data in terms of the minimum ignition energy density (MIED). Within a range between F ¼ 0.4 and 1.1, the MIED for L ¼ 0.5 mm was almost the same as the two other cases; thus, the MIE was almost proportional to the electrode gap distance L. However, the MIED was much larger for lean conditions (F ¼ 0.2) than for rich conditions (F ¼ 1.6 or 2). That is, the lean and rich conditions were more sensitive to heat loss to the electrode (Fig. 14). Fig. 15(a)e(c) show the temperature and velocity vector distributions of successful ignition for the same MIE densities for three different sizes of electrodes with an electrode gap distance of 1.2 mm. Although the electrode sizes were significantly different, there was no significant difference in
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Fig. 12 e Temperature distribution at t [ 500 ms (F [ 1, R [ 0.3 mm).
0.8 computation L=0.5 mm
0.7
experiment L=0.5mm
MIE (mJ)
0.6
computation L=1 mm
0.5
experiment L=1mm
0.4
computation L=2 mm experiment L=2mm
0.3 0.2 0.1 0 0
0.2 0.4 0.6 0.8
1
1.2 1.4 1.6 1.8
2
equivalence ratio Fig. 13 e Relationship between MIE and equivalence ratio for the R [ 0.3 mm electrode at different gap distances L.
Fig. 14 e Relationship between MIED and equivalence ratio for the R [ 0.3 mm electrode at different gap distances L.
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Fig. 15 e Temperature distribution at t [ 500 ms (F [ 1, L [ 1.2 mm).
the temperature distribution. This can also be observed in Fig. 16, which gives the maximum temperature histories for R ¼ 0.3, 0.8, and 1.5 mm. Especially for R ¼ 0.8 and 1.5 mm, the temperature distributions of the electrodes and the maximum temperature histories were almost the same. The computational results shown in Fig. 11 indicate that when electrode gap distance was greater than the quenching distance, the electrode radius did not significantly influence the value of the MIE. However, within the quenching distance, the effect of these factors was substantial (Fig. 16).
4.
Fig. 16 e Maximum temperature history for electrodes with R [ 0.3, 0.8 and 1.5 mm (F [ 1, L [ 1.2 mm, q [ 65 GW/ m3 [ qmin).
Conclusions
The quenching distance and the effects of the electrode gap distance and equivalence ratio on the MIE in a quiescent hydrogeneair mixture were investigated by numerical simulation using detailed chemical kinetics. The following conclusions were reached.
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1. The energy supply procedure dramatically affected the values of the MIE for a hydrogeneair mixture. 2. The computational results showed that as the spark channel radius Rc decreased to about 0.15 mm, the MIE leveled off at a value near 0.04 mJ. 3. The MIE increased gradually below the quenching distance for the free-tipped electrode, but increased sharply starting at the quenching distance. The size of the electrodes significantly affected the value of the MIE within the quenching distance, but did not affect it beyond the quenching distance.
Acknowledgments The authors are grateful to Professor K. Yamamoto and members of our research team for their helpful advice and assistance.
references
[1] Blarigan PV, Keller JO. A hydrogen fueled internal combustion engine designed for single speed/power operation. Int J Hydrogen Energy 1998;23(8):603e9. [2] White CM, Steeper RR, Lutz AE. The hydrogen-fueled internal combustion engine: a technical review. Int J Hydrogen Energy 2006;31(10):1292e305. [3] Hu EJ, Huang ZH, Liu B, Zheng JJ, Gu XL, Huang B. Experimental investigation on performance and emissions of a sparkignition engine fueled with natural gas-hydrogen blends combined with EGR. Int J Hydrogen Energy 2009;34(1):528e39. [4] Hu EJ, Huang ZH, Liu B, Zheng JJ, Gu XL. Experimental study on combustion characteristics of a spark-ignition engine fueled with natural gas-hydrogen blends combining with EGR. Int J Hydrogen Energy 2009;34(2):1035e44. [5] Hu EJ, Huang ZH, He JJ, Miao HY. Experimental and numerical study on laminar burning velocities and flame instabilities of hydrogen-air mixtures at elevated pressures and temperatures. Int J Hydrogen Energy 2009;34(20):8741e55. [6] Huang ZH, Zhang Y, Zeng K, Liu B, Wang Q, Jiang DM. Measurements of laminar burning velocities for natural gashydrogen-air mixtures. Combust Flame 2006;146(1e2):302e11. [7] Yuasa T, Kadota S, Tsue M, Kono M, Nomura H, Ujiie Y. Effects of energy deposition schedule on minimum ignition energy in spark ignition of methane-air mixture. Proc Combust Inst 2002;29:743e50. [8] Kravchik T, Sher E. Numerical modeling of spark ignition and flame initiation in a quiescent methane-air mixture. Combust Flame 1994;99(4):635e43.
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[9] Kono M, Niu K, Tsukamoto T, Ujiie Y. Mechanism of flame kernel formation produced by short duration sparks. Twenty-second Symposium on Combustion, 1988; 1643e1649. [10] Thiele M, Selle S, Riedel U, Warnatz J. A detailed twodimensional numerical study of spark ignition including Ionization, SAE Paper Series No. 2002-01-1110, 2002. [11] Han J, Yamashita H, Yamamoto K. Numerical study on spark numerical study on spark ignition characteristics of a methane-air mixture using detailed chemical kinetics (effect of electrode temperature and energy channel length on flame propagation and relationship between minimum ignition energy and equivalence ratio). J Therm Sci Technol; 2009:305e13. 09-0164. [12] Han J, Yamashita H, Hayashi N. Numerical study on the spark ignition characteristics of a methaneeair mixture using detailed chemical kinetics: effect of equivalence ratio, electrode gap distance, and electrode radius on MIE, quenching distance, and ignition delay. Combust Flame 2010;157:1414e21. [13] Thiele M, Warnatz J. Spark ignition hydrogen/air mixture: two dimensional detailed modeling and Laser based diagnostics. Combust Flame 2002;l28:74e87. [14] Owston R, Abraham J. Flame propagation in stratified hydrogen-air mixtures: spark placement effects. Int J Hydrogen Energy 2009;34:6532e44. [15] Ono R, Oda T. Spark ignition of hydrogen-air mixture. J Phys Conf Ser 2008;142:012003. [16] Lienesch F, Spilling M, Langer T, Markus D. Ignition of hydrogen/air mixtures through electric discharges at high frequency AC voltage. Chem Eng Technol 2009;32: 288e91. [17] Ono R, Oda T. Measurement of OH density and gas temperature in incipient spark-ignited hydrogen-air flame. Combust Flame 2008;152:69e79. [18] http://www.me.berkeley.edu/gri-mech. GRIemech 3.0. [19] Kee R, Lewis G, Warnatz J, Coltrin M, Miller A. Sandia Report, SAND86e8246 1986. [20] Smooke M. Reduced kinetic mechanisms and asymptotic approximations for methane-air flames. SpringereVerlag; 1991. 1e28. [21] Frendi A, Sibulkin M. Dependence of minimum ignition energy on ignition parameters. Combust Sci Technol 1990;73: 395e413. [22] Yamashita H. Numerical study on NOx production of transitional fuel jet diffusion flame. JSME Int J Ser B 2000;43: 97e103. [23] Patankar S. Numerical heat transfer and fluid flow. McGrawHill; 1980. [24] Sloane T. Numerical simulation of electric spark ignition in atmospheric pressure methane-air mixtures. Combust Sci Technol 1990;73:367e81. [25] Lewis B, von Elbe G. Combustion, flames and explosions of gases. 3rd ed. Academic Press; 1987. 333e347.
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Numerical study on the spark ignition characteristics of hydrogeneair mixture using detailed chemical kinetics Jilin Han, Hiroshi Yamashita*, Naoki Hayashi Department of Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya-shi, Aichi, Japan
article info
abstract
Article history:
Hydrogen is a promising fuel and is expected to replace hydrocarbon fuels for its significant
Received 15 March 2011
potentials to reduce the pollutants and greenhouse gases. It is very important to investi-
Received in revised form
gate Minimum ignition energy (MIE) on safety standards and ignition process of hydro-
23 April 2011
geneair mixtures. Even though the formation of flame kernels in quiescent hydrogeneair
Accepted 25 April 2011
mixtures has been researched numerically and experimentally, the details of ignition
Available online 28 May 2011
mechanism have never been satisfactorily explained. In this study, the spark ignition of hydrogeneair mixture is investigated by using detailed chemical kinetics and considering
Keywords:
the heat loss to the electrode. The purpose of this study is emphasized in the effects of the
Spark ignition
energy supply procedure, the radius of the spark channel, electrode size and electrode gap
Hydrogeneair mixture
distance on the MIE. In addition, the effects of mixture temperature, electrode gap distance
Minimum ignition energy
and electrode size on relationship between the equivalence ratio and the MIE are
Equivalence ratio
examined.
Detailed chemical kinetics
Crown Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Hydrogen is a promising fuel that could replace hydrocarbon fuels due to its potential to reduce pollutants and greenhouse gases. In particular, easily applicable utilization of hydrogen is in the SI engine as a pure fuel [1,2] and fuel blends [3,4] to start the flame propagation for its near-zero engine-out emission and high flame speed. The latter is unique to hydrogen and able to ignite premixed mixture at low equivalence ratios to achieve high thermal efficiency [5,6]. Many complex chemical and physical processes occur simultaneously during spark ignition, and these processes interact with each other. The spark ignition mechanism has never been satisfactorily explained, despite many years of research. Experimental results change if one factor is altered,
but in many cases, there are insufficient experimental data on the subject to predict exactly what will happen. Numerical simulation is a convenient method for studying the specific effects of any factor on the spark ignition characteristics and for calculating important physical and chemical properties such as the instantaneous high temperature and the heat release rate, which are difficult to obtain experimentally. The minimum ignition energy (MIE) is the minimum amount of energy required to ignite a combustible vapor, gas, or dust cloud due to an electrostatic discharge. MIE is an important parameter for judging the ignition ability of combustion systems, and is considered to be an important safety criterion for combustible gases. Factors affecting the MIE play an important role in determining the subsequent behavior of the flame. These factors include the type and composition of the
* Corresponding author. Tel./fax: þ81 52 789 4470. E-mail address: [email protected] (H. Yamashita). 0360-3199/$ e see front matter Crown Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.04.190
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Nomenclature cp D h L Le m P q qmin Qtotal Qtotal,min R r Rc R
specific heat at constant pressure, J/(kg K) effective diffusivity, m2/s specific enthalpy, J/kg electrode gap distance, mm Lewis number molar mass, kg/mol pressure, Pa ignition energy density, GW/m3 minimum ignition energy density (MIED), GW/m3 total ignition energy, mJ minimum total ignition energy (MIE), mJ electrode radius, mm radial coordinate, mm radius of the spark channel, mm universal gas constant, J/(mol K)
mixture, spark duration, initial temperature, pressure, and velocity of the mixture, electrode size, electrode gap distance, and heat loss to the electrodes. Several numerical studies have examined the details of spark ignition. Yuasa et al. [7] performed a two-dimensional numerical analysis with elementary reactions, including ionemolecule reactions, to investigate the effect of the energy deposition schedule on the MIE during the composite spark ignition of methaneeair mixtures. Kravchik and Sher [8] simulated spark ignition and flame initiation in a quiescent methaneeair mixture numerically. Kono et al. [9] investigated the mechanism of flame kernel formation produced by shortduration sparks using a set of partial differential equations with unsteady and two-dimensional cylindrical coordinates. Thiele et al. [10] investigated the early development of a stable flame kernel during spark ignition based on a detailed model for coupling two-dimensional cylindrical reactive flows with electrodynamics. A previous study investigated the effect of the energy channel length on the relationship between the MIE and the equivalence ratio for methaneeair mixture without considering heat loss to the electrodes [11]. The effects of the electrode temperature on the relationship between the MIE and the equivalence ratio, and the effects of the electrode size, electrode gap distance, equivalence ratio, and spark duration on the MIE for a methaneeair mixture have also been examined [12]. From the point of view of safety, the hydrogen explosion prevention must be taken into consideration, because the MIE of hydrogeneair mixture is very small and it is easy to accidently to give rise to a disaster by spark ignition. Even though some experimental and computational research has been performed on hydrogeneair mixtures to determine the MIE for the spark ignition, the flame kernel development process, and the mass fractions of major radicals [13e17], the details of the ignition mechanism have not been satisfactorily explained. In this study, the spark ignition of a hydrogeneair mixture was investigated using detailed chemical kinetics and considering heat loss to the electrode. The purpose of this study was to analyze the effects of the energy supply
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time, ms spark duration, ms volume of the spark channel, m3 mass production rate, kg/(m3 s) mass fraction axial coordinate, mm
t ti V w Y z
Greek Symbols q angular coordinate l effective thermal conductivity, W/(m K) m effective viscosity, Pa s r density, kg/m3 s stress tensor, Pa F equivalence ratio Subscript i species
procedure, spark channel radius, electrode size, and electrode gap distance on the MIE. Additionally, the electrode gap distance, and electrode size on the relationship between the equivalence ratio and the MIE were examined.
2. Computational domain and numerical methods 2.1.
Simplifying assumptions
The following assumptions were made to simplify the mathematical treatment and accelerate the calculations. (1) The mixture gases are ideal gases. (2) The Soret, Dufour, and Pressure effects can be neglected because diffusion due to these effects is much smaller than that due to the temperature and concentration gradients. (3) The influence of the magnetic and electrical fields is negligible. (4) Viscous dissipation and DP/Dt can be neglected in the energy conservation equation. (5) Natural convection, heat transfer by radiation, and ionic species can be ignored.
2.2.
Governing differential equations
Spark ignition involves many simultaneous complex chemical and physical processes. The following series of equations was used to characterize the combustion process. (1) Equation of state, P ¼ rRT
X Yi i
mi
(2) Continuity equation, vr 1 vrur r vruz ¼0 þ þ vz vt r vr
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(3) Conservation of momentum equations, vðrur Þ 1 vðrrur ur Þ vðruz ur Þ 1 vðrsrr Þ vðsrz Þ sqq vP þ þ ¼ þ r vr vt r vr vz r vr vz vðruz Þ 1 vðrrur uz Þ vðruz uz Þ 1 vðrsrz Þ vðszz Þ vP þ þ ¼ þ vt r vr vz r vr vz vz (4) Species mass conservation equation, vYi vYi v rDi r v rDi vðrYi Þ 1 vðrrur Yi Þ vðrYi uz Þ 1 vr vz þ þ wi þ þ ¼ vr vz vt r vr vz r
(5) Energy conservation equation, vT vT v lr v l vðrTÞ 1 vðrrur TÞ vðruz TÞ 1 vr vz cP þ þ þ ¼ vr vz vt r vr vz r DP X þ hi wi þ q Dt i where vvr 2 1 vvr r vvz srr ¼ m 2 þ vr 3 r vr vz
m ¼ Pr l=cp where Pr is 0.75. The effective diffusivity of species i is given as Di ¼
1 l rLei cP
where Lei is constant for every species i.
2.3.
Initial and boundary conditions
Two-dimensional cylindrical coordinates were used to calculate the ignition processes because the initial shape of the flame produced by sparks in a quiescent hydrogeneair mixture was presumed to be axisymmetric. We used analytical models with an electrode (Fig. 1). The computational domain shown in Fig. 1 contained the computational region, boundary conditions, electrode geometry, and location of the spark channel. The distance between the first 60 grid points around the electrode was set at 0.025 mm due to the smaller quenching distance of a hydrogeneair mixture compared to a methaneeair mixture in the r and z directions [11,12]. The computational region spanned 5.8 mm in both the r and z directions. The r and z axes were located on lines of symmetry for all variables. The other two boundaries were treated as outside boundaries, where the gradients of all variables are zero and the pressure can be assumed to be
vr 2 1 vvr r vvz þ sqq ¼ m 2 r 3 r vr vz vvz 2 1 vvr r vvz þ szz ¼ m 2 vz 3 r vr vz vvz vvr þ srz ¼ m vr vz GRI-mech 3.0, consisting of 53 species and 325 elementary reactions, was applied to the chemical kinetics model [18]. The specific heat at constant pressure was determined by a fourthorder polynomial approximation of the temperature, the coefficients of which were obtained from the JANAF table [19]. The enthalpy of a species is ZT hi ¼ h0i þ
cp;i dT T0
and the specific heat at constant pressure of the mixture is cp ¼
X
Yi cp;i
i
The simplified transport model proposed by Smooke et al. [20] was used for the transport properties. The effective thermal conductivity is l ¼ AcP
T T0
r
where T0 is the standard-state temperature, r ¼ 0.7, and A ¼ 2.58 104 g/(cm s). The effective viscosity is expressed as
Fig. 1 e Analytical model with electrode and boundary conditions for a hydrogeneair mixture.
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atmospheric. The radius of electrode R was varied from 0.3 to 1.5 mm to simulate different electrode sizes, and the electrode gap distance was varied from 0.3 to 1.2 mm to investigate the effect on the MIE. The electrode surface temperature was set to 300 K. The initially quiescent mixture of hydrogen and air in the computational domain had an initial temperature of 300 K and was at atmospheric pressure. For the electrode boundary conditions, no surface reactions and the no-slip condition were assumed on the electrode surface, and the gradient of the reaction chemical species i was zero. Because spark durations that give an optimum value of MIE are in the range of 3e100 ms [21], 20 ms was deemed long enough to avoid possible numerical problems that might occur due to the very rapid energy addition.
2.4.
Numerical method
The numerical method was the same as that used in previous studies [11,12] for methaneeair mixtures. The finite volume method [22] was used to discretize the above governing differential equations in space and time. This method is similar to the finite difference method or finite element method, and its values are calculated at discrete places on a meshed geometry. Finite volume refers to the small volume surrounding each node point on a grid. The grid size and the time step were chosen to be 0.05 mm and 1 ms, respectively. The semi-implicit method for pressure-linked equations (SIMPLE) method proposed by Patankar [23] was used to couple the velocity and pressure fields. The first-order upwind scheme was used for the convective terms, and the fully implicit Euler method was used to advance the time. The successive over-relaxation method was used to iterate each time step.
2.5.
Ignition behavior
The definition of successful ignition is very important when calculating the MIE. In this study, we defined successful ignition as when the flame ignited successfully in the section at z ¼ 0 mm based on the temperature time history. For example, the high temperature area extends to the ambient cold mixture in Fig. 2(a) for an ignition density of q ¼ 67.5 GW/m3, but it does not extend and the temperature decreases in Fig. 2(b) for q ¼ 65.0 GW/m3. Therefore, the hydrogeneair mixture ignited successfully in Fig. 2(a), but not in Fig. 2(b). It was assumed that the ignition energy was introduced into the spark channel at a certain constant ignition energy density q during the ignition duration. The total ignition energy was calculated from Qtotal ¼ q ti V, where V is the volume of the spark channel, ti is the ignition duration. In this manner, we can estimate the MIE in cases in which flame propagation succeeded or failed.
3.
Results and discussion
3.1.
Effects of the energy supply procedure on the MIE
The energy deposited during the short ignition duration time does not contribute to a temperature increase of the mixture,
Fig. 2 e Time history of temperature in section z [ 0 mm (F [ 1, L [ 1 mm, R [ 0.3 mm).
but rather increases the spark channel radius. That is, the spark channel radius increases with time during the spark duration. Test calculations in which the spark channel radius was allowed to increase with time for a methaneeair mixture during the spark duration have yielded results that differed by only a few percent or less from those obtained using a fixed spark channel radius [24]. To demonstrate the correctness of our code, we applied three models in which the spark channel radius changed with time (Fig. 3): the first had a constant spark channel radius during the spark duration (1-section), the spark channel radius in the second model increased halfway through the spark duration (2-section), and the spark channel radius in the third model increased in after four equal periods during the spark duration (4-section). Kravchik et al. [8] illustrated important factors that directly influenced the spark kernel expansion for a methaneeair mixture. These include the electrical and chemical power released and the power losses due to conduction to the electrode and the surrounding unburned mixture. In the early stages of spark development (about 100 ms), when the chemical power is smaller than the power loss, the electrical power
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Fig. 3 e Three energy supply procedure models.
supply determines the flame propagation. In the later stages when the chemical heat release dominates and the power losses from the cooler gas and electrode are much lower, the flame becomes self-sustaining. An interesting phenomenon during the early stages is that the electrical energy supply is almost constant with time. For that reason, the spark ignition energy densities are set on the right side of Fig. 3 according to the equation Q ¼ q ti V, where q is the ignition energy density, ti is the spark duration, and V is the volume of the spark channel. In this manner, the energy input in the spark channel during the spark ignition is the same for all three models. Fig. 4 shows the temperature histories of the three energy supply models for F ¼ 1, L ¼ 1 mm, and ti ¼ 80 ms, with the same ignition energy Qtotal,min ¼ 1.47 mJ. The temperature of the 4-section model was the highest (above 8000 K) for the large ignition energy density during the early stages of the spark ignition propagation. However, the temperature histories of the three models became almost the same when t > 100 ms, and they had the same MIE despite the different energy supply procedures. Thus, the energy supply procedure did not affect the values of the MIE for the methaneeair mixture. These computational results demonstrate the validity of the test calculations described earlier. Next, the effect of the energy supply procedure on the MIE for a hydrogeneair mixture was investigated. Thiele et al. [13] examined the electrical current and voltage traces
of a typical spark event for a hydrogeneair mixture. During the early stages, the electrical current and voltage are almost constant with time. According to the equation P ¼ VI, where V is the voltage and I is the electrical current, the power of the energy supply is nearly constant during the spark duration. For this reason, we applied the same spark channel radius change models that we used for the methaneeair mixture. The temperature history results for the hydrogeneair mixture are shown in Fig. 5 for F ¼ 1, L ¼ 0.5 mm and ti ¼ 20 ms, with the same ignition energy Qtotal,min ¼ 0.11 mJ. The temperature of the 4-section model was again the highest for the very large ignition energy density during the early stages of the spark ignition propagation. However, with increasing time, the temperature of the 4-section model remained higher and the mixture was successfully ignited. The temperatures of other models gradually decreased, and those mixtures were not ignited. Thus, the energy supply procedure dramatically affected the MIE values for a hydrogeneair mixture. According to our computational results, the MIE for the 4-section model was almost half that for the 1-section model. Thus, the energy supply procedure cannot be ignored for a hydrogeneair mixture. The effect of the energy supply procedure of a hydrogeneair mixture is totally different from that of a methaneeair mixture. For this reason, the 4-section model was used for all subsequent hydrogeneair mixture computations.
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0.6
MIE (mJ)
0.5 0.4 0.3 0.2 0.1 0
0
0.2
0.4
0.6
0.8
Rc (mm) Fig. 6 e Relationship between MIE and spark channel radius Rc (F [ 1, L [ 0.5 mm, R [ 0.3 mm, ti [ 20 ms).
Fig. 4 e Temperature history for the three energy supply models (F [ 1, L [ 1 mm, ti [ 80 ms, Qtotal,min [ 1.47 mJ).
3.2.
Effects of the spark channel radius on the MIE
Sloane et al. [24] investigated the effect of the spark channel radius on the MIE for a methaneeair mixture by using detailed first-step and third-step reaction models. They reported that even though the values of the MIE were different, the tendencies of the MIE versus spark channel radius were similar. The minimum ignition energies were much more sensitive to a larger spark channel radius, and leveled off at a constant value when the spark channel radius was smaller than a critical value. For a methaneeair mixture with detailed chemical reactions, this value was about 0.3 mm. We used our code to determine this value for a hydrogeneair mixture, as shown in Fig. 6, which illustrates the relationship between the MIE and spark channel radius. When the spark channel radius Rc decreased to 0.15 mm, the MIE leveled off at a value of 0.04 mJ.
A spark instantly establishes a small volume consisting of a hot kernel; its temperature decreases rapidly due to heat loss to the electrodes and ambient unburned gas. In the adjacent layer of ambient gas, the temperature rises and induces chemical reactions so that a flame kernel is formed, which propagates outwards with approximately spherical symmetry. Whether the flame kernel develops to a steady state depends on the number of radicals; this is important for flame propagation. If the ignition energy density is too small, the heat release rate within the inner spherical zone of the chemical reactions is insufficient to compensate for the heat loss rate to the outer zone of the preheated unburned gas. The radicals of the outer layer of the spark channel will then deactivate, and gradually the radicals of inner layer of the flame kernel will deactivate due to the large amount of heat dissipation. Thus, the flame is quenched and cannot become self-sustaining. To continue to propagate, the ignition energy density must grow to at least a level such that the gain of heat due to chemical reactions exceeds the heat lost to the unburned gas and electrodes. Then, enough intermediate radicals are generated, and the mixture is successfully ignited. This level of the ignition energy density corresponds to the horizontal section (Rc > 0.35 mm) shown in Fig. 7, which gives the relationship between the minimum ignition energy density and the spark channel radius.
160
MIED (GW/m3)
140 120 100 80 60 40
0
0.2
0.4
0.6
0.8
Rc (mm) Fig. 5 e Temperature history for the three energy supply models (F [ 1, L [ 0.5 mm, ti [ 20 ms, Qtotal,min [ 0.11 mJ).
Fig. 7 e Relationship between MIED and spark channel radius Rc (F [ 1, L [ 0.5 mm, R [ 0.3 mm, ti [ 20 ms).
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3.3. Profiles of major species, heat release rate of reactions, and chemical paths Fig. 8 shows the profiles of major species and the temperature distribution in the radial direction near the line of symmetry at t ¼ 20 ms and t ¼ 200 ms. At t ¼ 20 ms, the mass fractions of radicals, such as H, O and OH, were comparatively small, and they were located primarily inside the energy channel. The distribution of H2 and O2 indicate that the mass fractions of these chemical species were almost constant, regardless of location: only small amounts of H2 and O2 were consumed in the energy channel area. This behavior is similar to a methaneeair mixture if we do not consider the heat loss to the electrode during the incipient spark duration due to the comparatively low temperature (under 3000 K) in the spark channel, which cannot dissociate some radicals (H2, H2O). In contrast, when we do consider the heat loss to the electrode for a methaneeair mixture, the temperature near the electrode is over 4000 K, which is high enough to dissociate some radicals such as CH4, CO2 and H2O. At t ¼ 200 ms, high radical concentrations were found in the region between the energy channel and the surrounding unburned mixture (r ¼ 0.15e0.25 mm), and also in the energy channel area. The mass fraction profiles of H2 and O2 and the temperature distribution indicated the location of the flame front.
Because ignition involves the propagation of an exothermic wave, a more fundamental understanding of the combustion process can be obtained by checking the different contributions of the chemical reactions to the net heat release rate. The heat release rate of the main reactions and the net heat release rate along z ¼ 0 mm at different times for F ¼ 1, q ¼ 77.5 GW/m3 are illustrated in Fig. 9. These are the main reactions that play important roles in the heat release rate during the ignition process, including exothermic and endothermic processes. These reactions and their reaction numbers are as follows at different times: For t ¼ 10 ms H þ O2 þ M ¼ HO2 þ M
(R33)
H þ O2 þ N2 ¼ HO2 þ N2
(R36)
H þ O2 ¼ O þ OH
(R38)
H þ HO2 ¼ O2 þ H2
(R45)
H þ H2O2 ¼ HO2 þ H2
(R47)
H2 þ OH ¼ H þ H2O
(R84)
OH þ OH þ M ¼ H2O2 þ M
(R85)
For t ¼ 20 ms H þ O2 ¼ O þ OH
(R38)
H þ HO2 ¼ O2 þ H2
(R45)
H2 þ OH ¼ H þ H2O
(R84)
For t ¼ 200 ms
Fig. 8 e Profiles of major species concentrations and temperatures.
H þ O2 þ H2O ¼ HO2 þ H2O
(R35)
H þ O2 þ N2 ¼ HO2 þ N2
(R36)
H þ O2 ¼ O þ OH
(R38)
H þ HO2 ¼ O2 þ H2
(R45)
H þ HO2 ¼ OH þ OH
(R46)
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H2 þ OH ¼ H þ H2O
(R84)
For t ¼ 1000 ms
H þ O2 þ M ¼ HO2þ M
(R33)
H þ O2 þ H2O ¼ HO2 þ H2O
(R35)
H þ O2 þ N2 ¼ HO2 þ N2
(R36)
H þ O2 ¼ O þ OH
(R38)
H þ HO2 ¼ O2 þ H2
(R45)
H þ HO2 ¼ OH þ OH
(R46)
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H2 þ OH ¼ H þ H2O
(R84)
OH þ HO2 ¼ O2 þ H2O
(R87)
Fig. 9 shows that the behaviors of the net heat release rates were very different at different times. For t ¼ 10 and 20 ms, the net heat release rate was negative, i.e., the process was endothermic because of the high temperature in the spark channel. In particular, the backward reaction R45 was the chain initiation reaction and dominated the net heat release rate. As a result, intermediate radicals, such as H and HO2, were generated. In Fig. 9(c), the ignition process changed from endothermic to exothermic at t ¼ 200 ms. After the ignition delay time, exothermic reactions dominated the ignition process, and we could determine the position of the flame front based on the position of the peak heat release rate. Exothermic reactions R45 and R84 and endothermic reaction R38 made a fundamental contribution to the heat release rate during the entire spark ignition process. Reaction R38 was the chain-branching reaction, and played an important role in the entire spark ignition process with regard to generating O
Fig. 9 e Heat release rate of the main reactions along z [ 0 mm at different times (F [ 1, q [ 77.5 GW/m3).
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and H radicals, which are the characteristic radicals in the flame front and are consumed by exothermic reactions R45 and R84. Fig. 10 illustrates the history of the maximum mass fraction of O and OH radicals for F ¼ 1, q ¼ 77.5 GW/m3. Concentrations of the O and OH radicals were extremely high at t ¼ 50e60 ms when the ignition energy was supplied, then decreased rapidly and leveled out during the heat loss to the electrodes and ambient unburned mixture, and finally increased at about t ¼ 700 ms.
3.4.
Effects of the electrode gap distance on the MIE
MIE (mJ)
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0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
R=0.3 mm R=0.8 mm R=1.5 mm
0.3 0.4 0.5 0.6 0.7 0.8 0.9 Lewis and von Elbe [25] applied the same method used for methaneeair mixtures to measure experimentally the MIE values and quenching distance for a hydrogeneair mixture. The MIE was 0.02 mJ and the quenching distance was 0.66 mm for a stoichiometric hydrogeneair mixture. We compared our computational results with their experimental data to validate our numerical simulation code and to investigate factors that influence flame formation and the MIE. Fig. 11 illustrates our computational results used to determine the quenching distance and the effect of different sizes of electrodes on the relationship between the electrode gap distance L and the MIE in a stoichiometric hydrogeneair mixture. Three sizes of electrodes were chosen; the electrode radius R was set successively to 0.3, 0.8, and 1.5 mm. Although the quenching distance for hydrogeneair mixture was totally different from that for a methaneeair mixture, the computational results had similar tendencies; the MIE increased gradually for R ¼ 0.3 and 0.8 mm within the quenching distance, and the curves were similar to the experimental curve obtained with a free-tipped electrode. However, for R ¼ 1.5 mm, the curve at L ¼ 0.65 mm was almost vertical; thus, the combustible hydrogeneair mixture was hard to ignite within this distance for R ¼ 1.5 mm. This phenomenon is typical for experimental results with a flanged electrode. Thus, we identified 0.65 mm as the quenching distance, based on our computational results. This distance was almost the same as that obtained in the experiment. The MIE increased gradually below the quenching distance for a free-tipped electrode. However, when the electrode gap distances
Fig. 10 e History of the maximum mass fraction of H and OH (F [ 1, L [ 0.5 mm, q [ 77.5 GW/m3).
1
1.1 1.2
L (mm) Fig. 11 e Relationship between MIE and gap distance L (F [ 1).
became greater than the quenching distance, the curves had almost constant values over a considerable range of electrode gap distances for both types of electrodes. The start of the increasing trend of the curves in Fig. 11 moved forward (at L ¼ 0.45 mm for R ¼ 0.3 mm, L ¼ 0.60 mm for R ¼ 0.8 mm, and L ¼ 0.65 mm for R ¼ 1.5 mm) with decreasing electrode size. Fig. 12(a)e(d) show the temperature and velocity vector distributions of successful ignitions for the 0.3 mm electrode at an equivalence ratio F ¼ 1 for different electrode gap distances. In Fig. 12(a) and (b), the temperatures between the electrodes were very low. This indicates that the quenching effect of the cold electrode could significantly affect the formation of the flame kernel between electrodes, penetrating the small electrode gap distances of 0.3 and 0.4 mm. In contrast, in Fig. 12(c) and (d), the temperatures between the electrodes were relatively high for an electrode gap distance of 0.8 and 1.2 mm, respectively. The quenching effect did not affect the flame kernel between the electrodes for these large electrode gap distances. When the electrode gap distance was greater than 0.65 mm (Fig. 11), the curves of the computational results almost overlapped each other, indicating that the electrode size did not significantly affect the MIE. Fig. 13 illustrates the relationship between the MIE and the equivalence ratio for the 0.3 mm electrode at different distances. These computational results showed the same tendency as the experimental results reported by Ono and Oda [15]. This trend can be seen more clearly in Fig. 14, which provides data in terms of the minimum ignition energy density (MIED). Within a range between F ¼ 0.4 and 1.1, the MIED for L ¼ 0.5 mm was almost the same as the two other cases; thus, the MIE was almost proportional to the electrode gap distance L. However, the MIED was much larger for lean conditions (F ¼ 0.2) than for rich conditions (F ¼ 1.6 or 2). That is, the lean and rich conditions were more sensitive to heat loss to the electrode (Fig. 14). Fig. 15(a)e(c) show the temperature and velocity vector distributions of successful ignition for the same MIE densities for three different sizes of electrodes with an electrode gap distance of 1.2 mm. Although the electrode sizes were significantly different, there was no significant difference in
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Fig. 12 e Temperature distribution at t [ 500 ms (F [ 1, R [ 0.3 mm).
0.8 computation L=0.5 mm
0.7
experiment L=0.5mm
MIE (mJ)
0.6
computation L=1 mm
0.5
experiment L=1mm
0.4
computation L=2 mm experiment L=2mm
0.3 0.2 0.1 0 0
0.2 0.4 0.6 0.8
1
1.2 1.4 1.6 1.8
2
equivalence ratio Fig. 13 e Relationship between MIE and equivalence ratio for the R [ 0.3 mm electrode at different gap distances L.
Fig. 14 e Relationship between MIED and equivalence ratio for the R [ 0.3 mm electrode at different gap distances L.
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 9 2 8 6 e9 2 9 7
Fig. 15 e Temperature distribution at t [ 500 ms (F [ 1, L [ 1.2 mm).
the temperature distribution. This can also be observed in Fig. 16, which gives the maximum temperature histories for R ¼ 0.3, 0.8, and 1.5 mm. Especially for R ¼ 0.8 and 1.5 mm, the temperature distributions of the electrodes and the maximum temperature histories were almost the same. The computational results shown in Fig. 11 indicate that when electrode gap distance was greater than the quenching distance, the electrode radius did not significantly influence the value of the MIE. However, within the quenching distance, the effect of these factors was substantial (Fig. 16).
4.
Fig. 16 e Maximum temperature history for electrodes with R [ 0.3, 0.8 and 1.5 mm (F [ 1, L [ 1.2 mm, q [ 65 GW/ m3 [ qmin).
Conclusions
The quenching distance and the effects of the electrode gap distance and equivalence ratio on the MIE in a quiescent hydrogeneair mixture were investigated by numerical simulation using detailed chemical kinetics. The following conclusions were reached.
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1. The energy supply procedure dramatically affected the values of the MIE for a hydrogeneair mixture. 2. The computational results showed that as the spark channel radius Rc decreased to about 0.15 mm, the MIE leveled off at a value near 0.04 mJ. 3. The MIE increased gradually below the quenching distance for the free-tipped electrode, but increased sharply starting at the quenching distance. The size of the electrodes significantly affected the value of the MIE within the quenching distance, but did not affect it beyond the quenching distance.
Acknowledgments The authors are grateful to Professor K. Yamamoto and members of our research team for their helpful advice and assistance.
references
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