Measurement of OH density and gas temperature in incipient spark-ignited hydrogen–air flame

Combustion and Flame 152 (2008) 69–79 www.elsevier.com/locate/combustflame

Measurement of OH density and gas temperature in incipient spark-ignited hydrogen–air flame Ryo Ono a,∗ , Tetsuji Oda b a High Temperature Plasma Center, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 227-8568, Japan b School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Received 8 January 2007; received in revised form 12 June 2007; accepted 26 July 2007 Available online 1 November 2007

Abstract To investigate the electrostatic ignition of hydrogen–air mixtures, the density of OH radicals and the gas temperature are measured in an incipient spark-ignited hydrogen–air flame using laser-induced predissociation fluorescence (LIPF). The assessment of the electrostatic hazard of hydrogen is necessary for developing hydrogenbased energy systems in which hydrogen is used in fuel cells. The spark discharge occurs across a 2-mm gap with pulse duration approximately 10 ns. First, a hydrogen (50%)–air mixture is ignited by spark discharge with E = 1.35Emin , where E is the spark energy and Emin is the minimum ignition energy. In this mixture, OH density decreases after spark discharge. It is 3 × 1016 cm−3 at t = 0 µs and 4 × 1015 cm−3 at t = 100 µs, where t is the postdischarge time. On the other hand, the gas temperature increases after spark discharge. It is 900 K at t = 30 µs and 1400 K at t = 200 µs. Next, a stoichiometric (hydrogen (30%)–air) mixture is ignited by spark discharge with E = 1.25Emin . In this mixture, OH density is approximately constant at 4 × 1016 cm−3 for 150 µs after spark discharge, and the gas temperature increases from 1000 K (t = 0 µs) to 1800 K (t = 150 µs). © 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Hydrogen–air mixture; Spark ignition; Incipient flame; OH radical density; Gas temperature; Laser-induced fluorescence

1. Introduction Hydrogen is sensitive to electrostatic discharge (ESD) compared with other flammable gases. The minimum ignition energy of hydrogen is less than 0.02 mJ in air, whereas that of other flammable gases such as methane, ethane, propane, butane, and benzene is usually higher than 0.2 mJ [1–3]. Hydrogen is a promising fuel for use in fuel cells and is expected to replace oil and natural gas for most uses, includ* Corresponding author.

E-mail address: [email protected] (R. Ono).

ing as a transportation fuel. However, in developing hydrogen-based energy systems, the electrostatic hazard of hydrogen should be assessed, because of its high sensitivity to ESD. To investigate the electrostatic hazard of hydrogen, the process of ignition of hydrogen–air mixtures by “capacitance spark discharge” should be elucidated, because this type of discharge is the most frequent electrostatic ignition source. The capacitance spark is produced by discharging a charged capacitor, which generates a spark with pulse duration typically 1 to 100 ns. Although the ignition process induced by the capacitance spark has been intensively studied for

0010-2180/$ – see front matter © 2007 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2007.07.022

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various flammable mixtures [1,4–7], two important parameters, the density of radicals and the gas temperature, have not been sufficiently measured in the ignition process. Only a few researchers have measured the relative density of radicals in the incipient flame [8–10], in which other types of discharges than the capacitance spark were used for ignition. As a result, the ignition process induced by the capacitance spark is not yet fully understood. In a steady-state hydrogen–air flame, the reaction proceeds via the well-known chain-branching process [1]: O + H2 → OH + H,

(1)

H + O2 → OH + O,

(2)

OH + H2 → H2 O + H,

(3)

Fig. 1. Electrical circuit used for spark discharge.

where O and H atoms are initially supplied by dissociation of O2 and H2 molecules, respectively. To sustain this chain-branching process, the gas temperature and the density of O, H, and OH radicals must be sufficiently high. Therefore, these parameters are important in the ignition process of the hydrogen–air mixture. In the present work, we measure the density of OH radicals and the gas temperature in an incipient hydrogen–air flame ignited by a capacitance spark. We use laser-induced predissociation fluorescence (LIPF) for the measurement. Our experimental data will contribute to the modeling and simulation of the electrostatic ignition of hydrogen–air mixtures, which is essential for the assessment of the electrostatic hazard of hydrogen. If we had used conventional laser-induced fluorescence (LIF) instead of the present LIPF, the uncertain quenching rate in the OH excited state would have caused considerable experimental error. LIPF is superior to LIF with regard to this point because it can considerably reduce the undesirable effect of quenching due to predissociation in the excited state [11,12] (see Section 2.2 for details).

2. Experiment 2.1. Spark ignition system The hydrogen–air mixture is ignited in a 1-L stainless steel chamber. The chamber is evacuated to less than 5 × 10−3 atm (0.5 kPa), then hydrogen and dry air [O2 (21%)–N2 mixture] are introduced up to a total pressure of 1 atm (100 kPa). The hydrogen concentration is determined from the partial pressures of hydrogen and air, which are measured using a Baratron vacuum gauge (MKS Instruments, Model 626A). The hydrogen concentration is fixed to 30% (stoichiometric mixture) or 50% (rich mixture). A lean mixture

is not considered due to the limitation of the sensitivity of our system. In a lean mixture, OH density is not sufficient to be measured using our system. The chamber is sealed with aluminum foil of diameter 30 mm. When an explosion occurs, the aluminum foil ruptures to release the explosion energy. The spark discharge occurs between needle-toneedle electrodes placed in the center of the chamber. The needles are made from tungsten and have a 1mm diameter and a 40◦ tip angle. The gap distance is 2 mm. Fig. 1 shows the electrical circuit used for generating the spark discharge. Cc is the capacitance of the ceramic capacitor connected in parallel with the spark gap and Ce is the capacitance of the electrode. The charge stored in the capacitance, C = Cc + Ce , is discharged at the spark gap. The capacitances are measured using an LCR meter (Kokuyo, KC-536). Ce is 1.8 pF and Cc is provided to cover the range from 2.5 to 200 pF. A high-voltage (HV) power supply is connected to the spark gap through a cable and a high-resistance resistor R = 500 M. The voltage of the HV power supply, Vp , increases from 0 to 5.5 kV at a low rate of increase (e.g., 0.1 kV/s). As Vp increases, the capacitance voltage Vc increases with a charging time constant of CR. When Vc exceeds the breakdown voltage of the spark gap, a discharge occurs at the spark gap. The resistance R is chosen so that the charging time constant becomes CR > 4 ms, which is much longer than the spark duration (∼ =10 ns). Therefore, almost no charge stored in the stray capacitance of the power supply cable flows into the spark gap during discharge; thus, the stray capacitance of the cable has no influence on the discharge. When the discharge occurs, the pulse generator detects the spark noise and sends trigger signals Strig to the HV power supply, the oscilloscope, and the laser for synchronization. Upon receiving the Strig signal, the HV power supply re-

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Fig. 2. Typical current waveform of spark discharge. C = 11.7 pF, Vs = 3.83 kV, and E = 0.0858 mJ.

duces its output to 0 V within 0.5 ms to prevent the occurrence of subsequent sparks. The spark voltage, Vs , is obtained from Vc immediately before the occurrence of the spark. However, the measurement of Vc with a high-voltage probe is undesirable because the input impedance of the probe affects the discharge. In the present experiment, Vc ∼ = Vp is applicable because the rate of increase in Vp is sufficiently low. Therefore, Vs can be obtained from Vp (∼ =Vc ) immediately before the occurrence of the spark. Vp is monitored with an oscilloscope (Tektronix, TDS3034B, 300 MHz) after being reduced by a factor of 10,000 with a voltage divider. The spark energy, E, is defined as CVs2 /2. Fig. 2 shows a typical current waveform of the spark discharge. The pulse width of the spark current is typically less than 10 ns. 2.2. LIPF of OH radicals A tunable KrF excimer laser (Lambda Physik COMPex 150T) with a 30-ns pulse width is used for exciting OH radicals [11]. The laser wavelength is tunable within the range from 247.8 to 248.7 nm with a spectral bandwidth of approximately 3 pm. The KrF laser excites ground-state OH radicals (X2 Π , v  = 0) to the (A2 Σ + , v  = 3) state. Three branches, P2 (8), Q1 (11), and O12 (6), are excited. The fluorescence from the excited OH radicals is measured with a photomultiplier tube (PMT, Hamamatsu, R212) through an interference filter (296 ± 5 nm). The filter is optimized to transmit the OH fluorescence from the (A2 Σ + , v  = 3) → (X 2 Π , v  = 2) band. The sensitivity of the PMT is calibrated with a calibrated xenon lamp (Hamamatsu, L7810-02). When the twodimensional LIPF technique is used for measuring the spatial distribution of OH density, an ICCD camera (ORIEL InstaSpec V) is used instead of the PMT for detecting the two-dimensional image of OH fluorescence intensity. The beam profile of the excimer laser is approximately uniform over the cross section. In all experiments, the laser energy flux at the measurement point between the spark gap is 70 mJ/cm2 .

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The absolute density of OH radicals is determined using a three-level model. In this model, an OH radical in lower state 1 is excited to upper state 2 by laser irradiation, and then the subsequent fluorescence emitted in the 2 → 3 transition is measured. The rate equations are given by ⎧ dN1 (t) ⎪ ⎪ ⎨ dt = −B12 IL N1 (t) + (A21 + B21 IL )N2 (t), (4) ⎪ ⎪ ⎩ dN2 (t) = B I N (t) − (Γ + B I )N (t), 12 L 1 2 21 L 2 dt where Ni (t) is the number density of level i, Aij and Bij are the Einstein coefficients of i → j , and IL is the laser spectral intensity. Γ2 is the rate constant for all losses from state 2 without laser-stimulated emission; Γ2 ≡ P2 + Q2 + A2 , where P2 , Q2 , and A2 are the rates of predissociation, quenching, and spontaneous emission of state 2, respectively. Γ2 can be approximated as Γ2 ∼ P2 + Q2 since A2  P2 and A2  Q2 [11,13]. In our experiment, B12 IL N1 (t) (A21 + B21 IL )N2 (t) and Γ2 B21 IL , which lead to ⎧ ⎨ N1 (t) = N1 exp(−B12 IL t), (5) N (t) B12 IL ⎩ 2 = [1 − exp(−Γ2 t)], N1 (t) Γ2 where N1 = N1 (0). Equation (5) indicates that N1 (t) decreases during the laser irradiation. However, in fact, N1 (t) does not decrease in accordance with Eq. (5) due to rotational energy transfer (RET) within the lower vibrational level X 2 Π (v  = 0) [14]. When state 1 is pumped away by the laser irradiation, state 1 is refilled by the RET from all rotational levels of X 2 Π(v  = 0) at a rate of QRET . Equation (5) is applied only when QRET = 0. As discussed in Section 4.2, QRET ∼ = 2 × 109 s−1 in our experiment. Such a high RET rate allows N1 (t) to be approximated as a constant value (≡N1∗ ) during the laser irradiation. According to the model described in [14,15], N1∗ can be expressed as N1∗ N1

=

(B12 IL )−1

−1 Γ2−1 + Q−1 RET + (B12 IL )

.

(6)

The ratio N1∗ /N1 is between 0.95 and 1.0 under our experimental conditions. Accordingly, the LIPF signal intensity ILIPF can be expressed as τ ILIPF = cV

A23 N2 (t) dt 0

τ = cV 0

 B IL  A23 12 1 − exp(−Γ2 t) N1∗ dt Γ2

A23 ∼ B12 IL τ N1∗ , = cV Γ2

(7)

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where c is the collection efficiency of the LIPF signal, V is the volume of OH radicals, and τ is the laser pulse width (= 30 ns). From Eqs. (6) and (7), N1 can be determined from the measured ILIPF . All molecular constants except the quenching rate are obtained from [13]. If the rotational distribution reaches thermal equilibrium and corresponds to the Boltzmann distribution, the OH density N can be expressed in terms of N1 and the rotational temperature Tr as g exp[−E1 /(kTr )] N1 = 1 , N i gi exp[−Ei /(kTr )]

(8)

where Ei is the energy of state i, gi is the statistical weight of state i, and i represents the sum of all rotational levels in the lower state (X 2 Π , v  = 0). The quenching rate of the excited state (A2 Σ + , v  = 3), Q2 , is unfortunately unavailable. It is available only for the (A2 Σ + , v  = 0) state [16]. Therefore, we use the value of the v  = 0 state in the present experiment by assuming that the quenching rate of the v  = 3 state is equal to that of the v  = 0 state, as is often assumed elsewhere [14,17,18]. Actually, there must be some difference between the quenching rates of these two states. However, the error in the quenching rate has little influence on the results. For example, an error in the quenching rate of a factor of 3 leads to only 10% error in the estimated temperature and 40% error in the estimated OH density.

3. Results 3.1. Shape of incipient flame The shape of the incipient flame is observed by the two-dimensional LIPF of OH radicals. A laser beam with a 5 × 2 mm cross section is used for OH excitation, as shown in Fig. 3a. Fig. 3b shows the growth of the incipient H2 (50%)–air flame. The ignition energy E is three times higher than the minimum ignition energy Emin (E = 3.0Emin ), where Emin = 0.075 mJ [19]. The result for the H2 (30%)–air flame ignited by an E = 1.5Emin spark, where Emin = 0.048 mJ, is also shown in Fig. 3c. In this experiment, the OH distribution is measured by exciting only the P2 (8) branch. The rotational temperature Tr is not measured. Therefore, only the density of the lower state of the P2 (8) branch (N1 in Eq. (8)) is obtained and the OH density (N in Eq. (8)) is not obtained. As a result, the linear relation between the LIPF intensity and the OH density in Fig. 3 is not valid. Only a rough distribution of OH density can be obtained. Fig. 3 shows that the spark discharge produces a filament-shaped kernel between the gap. Then the kernel expands spherically at a velocity of approximately 10 m/s.

Fig. 4 shows the growth of the horizontal diameter of the incipient flame. The solid lines show the results for the H2 (50%)–air mixture ignited by E = 1.5, 3.0, and 11Emin sparks, and the broken line shows the result for the H2 (30%)–air mixture ignited by an E = 1.5Emin spark. The horizontal axis represents the postdischarge time t. The diameter for t  300 µs is measured by two-dimensional LIPF, as shown in Fig. 3d, and that for t > 300 µs is measured by taking photographs of light emission from the incipient flame using the ICCD camera. The incipient flame emits light from 304 to 325 nm via the A2 Σ + –X 2 Π (0,0) and (1,1) bands of OH radicals. The light emission is detectable using the ICCD camera for t > 300 µs, while that for t  300 µs is too weak to be detected. Fig. 5 shows examples of photographs of an incipient flame. 3.2. OH density and gas temperature OH density and gas temperature are measured in the incipient flame. In this experiment, the cross section of the laser beam is a 4 × 1.5-mm rectangle, as shown in Fig. 6. The height of the laser beam is shorter than the spark gap distance. This enables us to reduce the beam reflection at the electrode tips, which is undesirable for quantitative measurement. The gray area shown in Fig. 6 represents the observation volume. The density of OH radicals inside this volume is measured. To determine the OH density quantitatively, the volume of the incipient flame is required. It is assumed that the shape of the incipient flame in the observation volume is cylindrical with a height of 1.5 mm (= laser vertical width). The volume of the cylindrical flame is determined as 1.5π(d/2)2 mm3 , where d is the horizontal diameter of the flame obtained from Fig. 4. In our experiment, the spark voltage shows shotto-shot fluctuation between 3.3 and 4.0 kV. As a result, the spark energy fluctuates, leading to OH density fluctuation. When the range of the fluctuation is not too large, a linear relation is observed between the spark energy and the logarithm of the LIPF signal, as shown in Fig. 7. Hence, we first obtain the linear fitted line using the least-squares method and then determine the LIPF intensity at a desired spark energy from the fitted line. In the present experiment, the mean square of the residual in the least-squares fitting is less than 0.05, which corresponds to an error of approximately 20%. The incipient flame is produced by the spark discharge under a constant-volume condition. The gas density in the incipient flame immediately after ignition is approximately equal to that in the ambient gas. Then the incipient flame grows to a steady-state

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(a) Laser path

(b) H2 (50%)–air, E = 3.0Emin

(c) H2 (30%)–air, E = 1.5Emin

(d) LIPF signal intensity profile along the horizontal line shown in photograph (b) Fig. 3. (a)–(c) Two-dimensional LIPF of OH radicals. The LIPF signal intensity is normalized in each image. Since our system takes only one image per spark discharge, each image is for a different spark discharge. (d) Determination of horizontal flame diameter.

Fig. 5. Photographs of H2 (50%)–air flame ignited by E = 1.5Emin spark. The flame is observed using an ICCD camera with an optical gate of 20 µs.

Fig. 4. Horizontal diameter of incipient flames.

constant-pressure flame within a few hundred µs [4], at which point the gas density is much lower than that in the ambient gas. In the present experiment, the

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Fig. 6. Laser path and observation volume for LIPF measurement. Fig. 8. Boltzmann plots of OH rotational distribution. The hydrogen concentration is 30% and E = 1.25Emin . They are measured 10 µs after discharge.

Fig. 7. LIPF signal intensity as a function of spark energy for H2 (50%)–air mixture. t = 30 µs. P2 (8) and Q1 (11) are excited.

transitional flame between the constant-volume and the constant-pressure conditions is measured, and it is unclear which condition is applicable in our experiment. When the OH density is calculated from the LIPF signal intensity using Eq. (7), the two conditions give different OH densities because the quenching rate of the upper state is different for the two conditions. Therefore, the OH density is calculated under both conditions, and we assume that the actual density lies between the two calculated densities. Fig. 8 shows an example of temperature determination for the incipient H2 (30%)–air flame measured 10 µs after the spark. O12 (6), P2 (8), and Q1 (11) are excited. Two different temperatures are obtained under the constant-pressure and constant-volume conditions. The linear relations among the rotational levels indicate that the rotational distribution of OH radicals has reached thermal equilibrium 10 µs after the spark. In all the following experiments, thermal equilibrium is assumed and the temperature is determined from the ratio of only two LIPF intensities, P2 (8) and Q1 (11). Fig. 9 shows the time evolutions of OH density and OH rotational temperature (= kinetic tem-

Fig. 9. (— and -·-·-) time evolutions of (a) OH density and (b) OH rotational temperature of H2 (50%)–air mixture after spark discharge. (- - -) those of H2 O–air mixture at 90% relative humidity.

perature) in the incipient H2 (50%)–air flames for E = 3.0, 1.60, 1.35, and 0.95Emin . The mixture is ignited for E > Emin and not ignited for E = 0.95Emin . For comparison, the results for H2 O–air mixture (90% relative humidity), in which hydrogen is not contained, are also plotted with broken lines

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Fig. 11. Number of OH radicals contained in incipient H2 (50%)–air flame (—) and H2 (30%)–air flame (- - -).

4. Discussion 4.1. OH density and gas temperature in incipient flame

Fig. 10. Time evolutions of (a) OH density and (b) OH rotational temperature of H2 (30%)–air mixture after spark discharge.

for E = 0.95Emin . The two values obtained under the constant-pressure and constant-volume conditions are plotted with error bars. These densities and temperatures are spatially averaged. The spatial distribution of these parameters cannot be measured due to the low sensitivity of the LIPF measuring system. The results for the H2 (30%)–air mixture are also shown in Fig. 10. To determine the OH density of the H2 (50%)– air flame for E = 3.0Emin , the diameter of the E = 3.0Emin flame shown in Fig. 4 is used for estimating the OH volume. On the other hand, to determine these values for E = 1.60 and 1.35Emin flames, the diameter of the E = 1.5Emin flame shown in Fig. 4 is used because the diameter is approximately constant when E varies from 1.35 to 1.60Emin . Similarly, the OH densities in the H2 (30%)–air flames for E = 1.85 and 1.25Emin are determined using the diameter of the E = 1.5Emin flame shown in Fig. 4. For E = 0.95Emin , it is difficult to measure the diameter because the LIPF signal intensity is too weak for twodimensional LIPF. For this reason, the diameter of the E = 1.5Emin flame is used for the E = 0.95Emin mixtures.

In a steady-state hydrogen–air flame, OH density increases due to reactions (1) and (2) and decreases due to reaction (3), recombination reaction, reaction with atomic oxygen [1], and diffusion. Similarly, in the incipient hydrogen–air flame, there are production and decay processes of OH radicals. Reaction (3) is a dominant decay process of OH radicals that decreases OH density with a time constant of ∼100 ns under our experimental conditions. For example, in the initial phase (t < 50 µs) of H2 (50%)–air flame ignited by E = 1.35Emin , the temperature is approximately 1000 K, as shown in Fig. 9b. At this temperature, the rate coefficient of reaction (3) is 1.8 × 10−12 cm3 /s [20]. If the pressure of the flame is assumed to be 1 atm (i.e., gas density is 300/1000 of the ambient gas), the rate of reaction (3) is 6.5 × 106 s−1 . Fig. 9a shows that OH density decays much more slowly than this reaction rate. This indicates that a large number of OH radicals are produced simultaneously with decay via reaction (3). Fig. 9 also shows that OH density decays much more slowly than the rate of reaction (3) even when the mixture is not ignited (E = 0.95Emin ). This indicates that a number of OH radicals are produced even in the no-ignition case. OH density decreases for the initial 100 µs in the H2 (50%)–air mixture. On the other hand, the number of OH radicals contained in the flame does not show such a decrease. Fig. 11 shows the number of OH radicals contained in the flame obtained by multiplying OH density by flame volume, where the flame volume is measured by two-dimensional LIPF. In the H2 (50%)–air flames ignited by E = 1.35, 1.60, and 3.0Emin , the number of OH radicals is approximately

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constant for the initial phase (t < 50 µs) and then increases exponentially at a rate of 1.2 × 104 s−1 . In Fig. 9b, the gas temperature of the incipient hydrogen (50%)–air flames for E = 1.35 and 1.60Emin decreases from 1100 to 900 K in 30 µs after the spark and then increases at a rate of 3.2 K/µs for t > 30 µs. The initial temperature drop is due to heat conduction from the flame kernel to the ambient unburned gas [1]. The later temperature rise indicates that there are some heat-generating processes for t > 30 µs that exceed the heat loss to unburned gas. It is probably caused by some exothermic reactions. To elucidate the mechanism of the heat-generating process, the densities of other species such as O and H atoms are required. Since those densities are unknown, this is not discussed further in the present paper. In Fig. 9b, the gas temperature of the H2 (50%)– air mixture immediately after the spark is approximately equal to that of the H2 O–air mixture. This indicates that the temperature immediately after the spark does not strongly depend on the hydrogen concentration, while the OH density immediately after the spark strongly depends on the hydrogen concentration, as shown in Fig. 9a. Figs. 9 and 10 show that the OH density and gas temperature in the incipient H2 (30%)–air flame are higher than those in the H2 (50%)–air flame when they are ignited by the same ignition energy. For example, the OH density in the H2 (30%)–air flame ignited by E = 1.25Emin (= 0.060 mJ) is higher than that in the H2 (50%)–air flame ignited by the higher energy of E = 1.35Emin (= 0.10 mJ). Similarly, the gas temperature in the H2 (30%)–air flame is much higher than that in the H2 (50%)–air flame. The rate of temperature increase for t > 50 µs is 7.3 K/µs in the H2 (30%)–air flame, which is two times faster than that in the H2 (50%)–air flame. These results indicate that the chemical reaction in the stoichiometric flame (H2 = 30%) proceeds more rapidly than that in the H2 (50%)–air flame, as expected. The number of OH radicals in the incipient H2 (30%)–air flame is plotted in Fig. 11 with a broken line. It increases much more rapidly than in the H2 (50%)–air flame. This result also indicates the high speed of the reaction in the stoichiometric incipient flame. Fig. 4 shows that the flame velocity in the H2 (50%)–air mixture increases with the ignition energy in the early phase (t < 200 µs). It is 5.7 m/s for E = 1.5Emin and 10.0 m/s for E = 3.0Emin . The velocity increases with time and reaches a constant velocity (13.2 m/s) independent of the ignition energy. For the H2 (30%)–air flame ignited by E = 1.5Emin , the flame velocity is 8.8 m/s in the initial phase and eventually reaches 11.7 m/s. In Figs. 9 and 10, the spatial distribution of the OH density and gas temperature are assumed to be uni-

(a) H2 (50%)–air

(b) H2 (30%)–air

(c) Laser sheet

(d) LIPF intensity profile Fig. 12. Two-dimensional LIPF of OH radicals measured using thin laser sheet with 0.5-mm thickness for (a) H2 (50%)– air and (b) H2 (30%)–air mixtures. E = 1.5Emin . (c) Shape of laser sheet. (d) LIPF intensity profile along a line perpendicular to the spark gap obtained from (a) and (b).

form. The uniformity of the OH density is verified by two-dimensional LIPF. Figs. 12a and 12b show the two-dimensional LIPF images obtained using a thin laser sheet (0.5-mm thickness), as shown in Fig. 12c. The thin laser sheet enables us to observe the OH density distribution in the cross section of the flame. This experiment uses only P2 (8) excitation and gives only a rough distribution of OH radicals. Fig. 12d shows the LIPF intensity profile along a line perpendicular to the spark gap obtained from Figs. 12a and 12b. These results show that the OH distribution is approximately uniform in the early period of flame propagation (t = 200 µs for H2 (50%)–air and t = 100 µs

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Fig. 13. LIPF signal intensity versus laser energy flux for Q1 (11) excitation of OH radicals.

for H2 (30%)–air). At a later time, the uniformity degenerates and the OH density increases with distance from the center of the flame, reaching a maximum at the shell of the flame. This OH density profile having a minimum at the center of the flame agrees with the results of Berglind and Sunner [8] and Thiele et al. [10], who observed spark-ignited incipient flames in methane–air and H2 (20%)–air mixtures, respectively. In all the experimental results shown in Figs. 9 and 10, it is verified that the spatial distribution of OH density is approximately uniform, except for the H2 (30%)–air flame at t = 150 µs. The uniformity of the temperature distribution cannot be confirmed at present and should be investigated in future work. 4.2. Uncertainty of LIPF measurement In this section, the uncertainty in the LIPF measurement is discussed. As described in Section 2.2, RET within the lower state X2 Π (v  = 0) may cause error in the LIPF measurement. If the RET rate is sufficiently high, the OH density in the lower state N1 is approximately constant during laser pumping, so that N1 is related to LIPF signal intensity ILIPF by Eqs. (6) and (7). On the other hand, if the RET rate is low, Eqs. (6) and (7) are not valid, and a complicated calculation is required to estimate N1 from ILIPF . Fig. 13 shows LIPF signal intensity versus laser energy flux when Q1 (11) is excited. Solid curves show theoretical values for various values of QRET calculated using the model described in [14]. When QRET is low, the LIPF signal intensity becomes saturated with increasing laser energy flux due to the depletion of OH radicals by laser pumping. Filled circles in Fig. 13 show experimental values measured 100 µs after ignition of the H2 (30%)–air mixture by E = 2.4Emin . Comparison between the experimental and theoretical values shows that QRET ∼ = 2 × 109 s−1 , which is sufficiently high for Eqs. (6) and (7) to be

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Fig. 14. (a) Fluorescence spectrum obtained by P2 (8) excitation measured 100 µs after ignition of H2 (30%)–air mixture by E = 2.4Emin . The spectral resolution is set to 0.4 nm. (b) (- - -) Represents the transparency of the interference filter used for LIPF measurement, (—) represents the “filtered” spectrum obtained by multiplying the spectrum shown in (a) by the filter transparency.

applicable. In the present work, QRET = 2 × 109 s−1 was assumed in all experiments. This assumption was not accurate because QRET depends on gas composition, temperature, and pressure and was only used for rough estimation. Nevertheless, the uncertainty in QRET does not cause a significant error in LIPF measurement if QRET is sufficiently high. For example, the variation of QRET between 5 × 108 s−1 and infinity leads to only a 6% error in the LIPF measurement. Vibrational energy transfer (VET) within the upper electronic state A2 Σ + may also cause error in the LIPF measurement [17]. A fraction of excited OH radicals in the A2 Σ + (v  = 3) level undergo VET into the lower vibrational levels A2 Σ + (v  = 2, 1, and 0) instead of predissociation and electronic quenching. Since those lower states do not have predissociation, their quantum yield is much higher than that of the v  = 3 state. Therefore, the lower levels generated by the VET yield relatively intense fluorescence in spite of their small populations. Fig. 14a shows the fluorescence spectrum obtained by P2 (8) excitation in the H2 (30%)–air mixture. The three lines labeled R2 (6), Q2 (7), and P2 (8) show the LIPF signal from the (v  = 3, v  = 2) transition. As well as the LIPF signal, some fluorescence caused by VET is observed from (0,0), (1,1), (1,0), and (2,1) transitions [11]. This VET is mostly caused by collision with N2 molecules, whose VET rate with the OH A2 Σ + state is much higher than that of H2 , O2 , and H2 O molecules [17,21]. The signals originating from VET cause error in the LIPF measurement because they increase the LIPF signal intensity. In the present experiment, the signals other than (3,2) are mostly eliminated us-

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the error for temperature and OH density measurement caused by laser polarization. They are defined as (Tiso − Tpol )/Tiso and (Niso − Npol )/Niso , where Tpol and Npol are temperature and OH density measured using a polarized laser, and Tiso and Niso are those measured without a polarization effect, respectively. If the depolarization of excited OH radicals is negligibly small in our experiments, the temperature becomes 10 to 20% higher than that shown in Figs. 9b and 10b. The error in OH density estimation is less than 5%, which is negligibly small. Fig. 15. Error for temperature and OH density measurement caused by laser polarization.

ing the interference filter, whose transparency profile is plotted in Fig. 14b with a broken line. The solid line in Fig. 14b represents the “filtered” spectrum obtained by multiplying the spectrum shown in Fig 14a by the filter transparency. It shows that almost no signals except for (3,2) are observed after passing through the interference filter. This indicates that VET has no significant influence on the present experiment. If the VET rate, V2 , is not negligibly small compared with the predissociation and quenching rates, then Γ2 in Eq. (7) should be Γ2 = P2 + Q2 + V2 instead of Γ2 = P2 + Q2 . In the present mixtures, V2  P2 , Q2 can be assumed [17,21]; hence Γ2 = P2 + Q2 is applicable. The KrF laser used in the present experiment is horizontally polarized. The polarization of the exciting laser causes error in the LIPF measurement [14,22]. When OH radicals are excited by a polarized laser, those radicals having a transition dipole parallel to the laser beam polarization vector are preferentially excited. Thus, the excited radicals have a spatial orientation related to the laser polarization direction. These oriented radicals emit polarized fluorescence whose intensity has an anisotropic spatial distribution. This causes experimental error because an isotropic fluorescence distribution is assumed in the measurement. If the oriented excited radicals undergo collisions, the polarization is destroyed and isotropic fluorescence is observed. In conventional LIF at atmospheric pressure, the polarization effect is usually negligible because a number of collisions destroy the oriented excited species. In LIPF, however, the excited radicals undergo few collisions because most of the excited radicals predissociate before collision with other molecules. The polarization effect is maximized when no collisions occur. In this worst case, based on [22], the LIPF signal intensity using P2 (8) excitation is overestimated by 5% and that using Q1 (11) excitation is underestimated by 10% compared with the case of no polarization under our experimental conditions. Fig. 15 shows

5. Conclusions To investigate the electrostatic ignition of hydrogen–air mixtures, the density of OH radicals and the gas temperature were measured in an incipient sparkignited hydrogen–air flame using LIPF. A rich mixture (H2 (50%), Emin = 0.075 mJ) and a stoichiometric mixture (H2 (30%), Emin = 0.048 mJ) were ignited using a capacitance spark discharge generated across a 2-mm point-to-point gap. The ignition energy was set to near Emin because ignition near Emin is the most important factor in the safety assessment of electrostatic hazards. The spatial distribution of OH density in the incipient flame was observed by two-dimensional LIPF. The OH distribution was approximately uniform in the early period of flame propagation, while it increased with distance from the center of the flame at a later time. In the incipient H2 (50%)–air flame ignited by an E = 1.35Emin spark, OH density decreased from 3 × 1016 to 4 × 1015 cm−3 in 100 µs; then it was approximately constant for the next 100 µs. On the other hand, the number of OH radicals contained in the incipient flame was approximately constant at 1 × 1013 for 100 µs after the spark, and then increased exponentially for the next 100 µs up to 5 × 1013 . It was shown that a rapid decay process of OH radicals occurred including reaction (3) as well as a rapid production process whose rate was approximately equal to that of the decay process in the early period of incipient flame propagation. In this incipient flame, the gas temperature immediately after the spark was 1100 K. The temperature decreased to 900 K in 30 µs, then increased to 1400 K at t = 200 µs. The same measurement was also carried out for E = 3.0, 1.60, and 0.95Emin sparks. In the stoichiometric mixture ignited by an E = 1.25Emin spark, OH density was approximately constant at 4 × 1016 cm−3 for 150 µs after the spark, and the number of OH radicals increased from 1 × 1013 to 7 × 1014 in 150 µs after the spark. The gas temperature in this incipient flame increased from 1000

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to 1800 K in 150 µs after the spark. The OH density and gas temperature were higher than those of the H2 (50%)–air flame. This indicates that the chemical reaction in the stoichiometric flame proceeded more rapidly than that in the H2 (50%)–air flame, as expected. Flame velocity was also measured. It was shown that the velocity increased with ignition energy in the early phase (e.g., t < 200 µs for H2 (50%)–air). It increased with time and reached a constant velocity, which was independent of ignition energy.

Acknowledgment The authors acknowledge support from the New Energy and Industrial Technology Development Organization (NEDO).

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