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Ar flat flames
COMBUSTION A N D F L A M E 74: 221-231 (1988)
221
Concentration Measurements of Atomic Hydrogen in Subatmospheric Premixed C2H4/O2/Ar Flat Flames J. THADDEUS SALMON* and NORMAND M. LAURENDEAU Flame Diagnostics Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907
Absolute number densities of atomic hydrogen have been measured in subatmospheric, premixed C2I'L/O2/Ar flat t i m e s via two-photon excited fluorescence. The fuel-equivalence ratios of the flames were 1.0 and 1.7. The fluorescence measurements are calibrated by partial equilibrium calculations and corrected for quenching effects by assuming a constant average cross-section and using kinetic theory. A sensitivity analysis of the calibration procedure reveals that slightly rich flames appear to be the best candidates for calibrating fluorescence measurements of atomic hydrogen by partial equilibrium.
INTRODUCTION The hydrogen atom is a primary radical in the oxidation of all hydrocarbons. The high diffusivity and reactivity of this species make it important to the study of flame ignition and propagation. Hydrogen atoms may also play a significant role in chemical processes leading to the formation of soot [1]. Despite its importance to combustion, few methods existed for measuring concentrations of atomic hydrogen before the advent of high° powered lasers. These previous methods included resonant absorption [2-5], doping flames with lithium salts [6-8], and adding trace amounts of CO2 to hydrogen flames [9]. Resonant absorption is unfeasible in a flame as the absorption lines, which lie in the vacuum ultraviolet, are strongly absorbed by the combustion gases (most notably water vapor). Doping with lithium salts is impractical without a specially designed burner; moreover, the validity of this method is questionable at pressures below I00 Torr where kinetic studies of atomic hydrogen are most useful. Adding trace amounts of CO2 is useful only for hydrogen flames * Present address: Lawrence Livermore National Laboratory Livermore, CA 94550 Copyright © 1988 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 655 Avenue of the Americas, New York, NY 10010
as hydrocarbon flames produce copious amounts of carbon dioxide. With the development of high-powered lasers that are tunable in the far ultraviolet, atomic hydrogen can be excited via multiphoton absorption and then monitored by fluorescence [10-18] or by optogalvanic detection [19-22]. Fluorescence measurements of H-atom concentrations in premixed flames [12-16] were calibrated in the postflame region by partial equilibrium, and it was assumed that the rate coefficient for electronic quenching was independent of position within the flame. Such measurements have been largely confined to the postflame zone as the relative change in the actual quenching rate coefficient of atomic hydrogen is unknown within the preheat and reaction zones. Recent work [17] has compared conventional fluorescence measurements of atomic hydrogen, which assume a constant rate coefficient for quenching, to measurements using photoionization controlled-loss spectroscopy (PICLS), which are independent of quenching, in H2/O2/N2 flames at 20 Torr. This comparison demonstrated the need to account for quenching in the preheat zone when using conventional fluorescence. A subsequent study of the quenching of atomic hydrogen in H2/
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J.T. SALMON and N. M. LAURENDEAU
O2/N 2 flames
[23] established a T- i/2 dependence on temperature, in agreement with kinetic theory. Further studies showed that at higher pressures (72 Torr), conventional fluorescence measurements and PLCLS measurements agreed very well, except below 2 mm above the burner surface; hence, in such flames, the rate coefficient for quenching can be assumed to be nearly constant
. . . . . . . . . . . . . . . . . . . . . . .
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[24]. More recently, Bittner et al. [18] calibrated fluorescence measurements of atomic hydrogen to a known number density in a flow discharge cell. The difference in quenching rate between the two environments was accounted for by a correction factor that was determined by numerically solving the rate equations governing the excitation/relaxation dynamics at each point in the flame. Unfortunately, their results were not compared to those calibrated by partial equilibrium; in addition, they did not discuss the extent to which their correction factor varies with both position within the flame and flame stoichiometry. In this paper we report quantitative fluorescence measurements of atomic hydrogen in fiat, premixed, C2I'I4/O2/Ar flames for fuel-equivalence ratios of 1.0 and 1.7 at a pressure of 72 Torr. These conventional two-photon measurements are calibrated in the postflame zone by partial equilibrium and are corrected for the small variations in quenching near the burner surface by using the T-]/2 proportionality observed in subatmospheric H2/O2/N2 flames [23-25]. THEORY Excitation and relaxation of hydrogen atoms during fluorescence measurements can be described by the simple model shown in Fig. 1, where the ground state is level 1 and the directly excited state is level 3. Upon laser excitation, level 1 is depopulated by absorption of two photons and populated by collisional and radiative relaxation from levels 2 and 3. As shown later, two-photon absorption under our conditions is far below saturation. Hence, the change in the ground state population N~ is negligible. Furthermore, the energy of level 2 is 82259 cm-], thus making the equilibrium population of all excited electronic
." C o n t i n u u m
1
n=l
Fig. 1. Schematic drawing of the excitation/relaxation dynamics associated with fluorescence measurements of atomic hydrogen, where the respective rate coefficients (s- 1) are WI3 (two-photon absorption), (2o (total quenching from level i to level j), and A U(fluorescence). The wavelengths (nm) corresponding to excitation and fluorescence are given in parenthe~S.
levels negligible at flame temperatures. Therefore, N] = Nr, the total initial population of atomic hydrogen, throughout the laser pulse. Fluorescence is detected through radiative relaxation from level 3 to level 2. Hence, the measured fluorescence signal is directly proportional to the population of level 3, N3 (cm-3). Level 3 is populated via the absorption of two photons by atoms in the ground state (level 1) and depopulated by collisional transfer (quenching) and radiative relaxation (fluorescence). Photoionization via absorption of an additional photon by atoms in the directly excited state can be ruled out from a previous study of H2/O2/N2 flames [24]. The resulting rate of change of N3 can be taken as dN3
- - = N ] WI3-N3(Q3+ A3), dt
(1)
where W]3 is the rate coefficient for two-photon absorption, which is directly proportional to the square of the laser irradiance IL (W/cm 2) [25, 26], and (23 and A3 are the total rate coefficients for quenching (Q3] + (232) and spontaneous emission (A3] + A32), respectively. Chemical reactions by atoms in the directly excited state are not considered, but are implicitly accounted for by the quenching rate because both processes induce a loss from the directly excited state via collisions
H-Atom Fluorescence
223
and thus are indistinguishable when making fluorescence measurements. Quantitative fluorescence measurements are difficult if level 1 is strongly populated through photodissociation of an interfering species by the UV beam. Under these conditions, the population of level 1, N1, grows at a rate that is directly proportional to the population of the interfering species Np, resulting in dN1 dt = Np Wp,
(2)
where Np IVp is the rate of photodissociation that produces hydrogen atoms in the ground state. This process, which can lead to measured atomic concentrations that are artificially high, has been observed in fuel-lean hydrogen-oxygen flames at atmospheric pressure by Goldsmith [15]. In that case the interfering species was water vapor. Because the quantum efficiency for predissociation of water vapor by the absorption of one UV photon ()~ = 205 nm) is near unity [271, Eq. 2 shows that N~ oc Wj, ~ IL. Substituting this proportionality for NI into Eq. 1 yields N3 cx IL 3 at steady state, because Wl3 ~ IL2. This cubic proportionality has been observed by Goldsmith [15]. Because our fluorescence measurements of atomic hydrogen assume no laser-induced photochemistry, the measurements must be examined for possible nonquadratic dependence of the fluorescence signal on the UV laser power. At the temporal peak of the fluorescence pulse, dN3/dt = 0, and Eq. 1 reduces to N3 = N r Wl3/R3,
EXPERIMENTAL APPARATUS
(3)
where Ra -= Q3 + A3 is the rate coefficient for the total decay out of level 3. Relative changes in W~3 can be monitored by measuring variations in the power of the UV beam; however, direct temporal measurements of relative changes in Q3 are difficult as Q3 exceeds 3 × l0 s s-l at a pressure of 10 Torr [25]. Previous experiments using PICLS in H2/O2/N2 flames at 20 Torr showed that R3 ~ T- 1/2
portionality was the same for fuel-equivalence ratios of both 1.0 and !.4. Because Ra = Q3 + A3, these results suggest that Q3 ~" A3 at pressures greater than 20 Torr, and R3 can be successfully described by kinetic theory, with an effective cross-section in hydrogen flames that is independent of both stoichiometry and temperature. Because the pressure of the ethylene flames is 3.5 times that of the hydrogen flames, Eq. 4 can be used here to correct the fluorescence measurements of atomic hydrogen for any change in the local quenching rate coefficient. The inverse proportionality between R3 and T I/2 in Eq. 4 is also supported by the results of Meier et al. [28], who measured quenching rate constants for atomic hydrogen with H2, 02, and H20 as the quenching partners in a thermostatically controlled flow-discharge reactor. Because the concentration of H20 rises rapidly in a flame and the rate constant with 1-120 as the quencher is approximately four times that for either H2 or 02 [28], H20 is the dominant quenching species under combustion conditions. For reactor temperatures between 300 and 560 K, Meier et al. found that the product of the rate constant for the quenching of atomic hydrogen by H20 and T 1/2 was constant to within 10%, which is predicted by kinetic theory for a quenching cross-section that is independent of temperature. Thus, Eq. 4 is justified at least for hydrogen flames; full verification in hydrocarbon flames awaits publication of quenching rate constants for both CO and CO2.
(4)
to within a few percent, where Tis the local flame temperature [23]. Moreover, the constant of pro-
Our experiments, shown in Fig. 2, use a dye laser (Molectron DL-18) pumped by a frequency-doubled, Q-switched Nd:YAG laser (Molectron MY34) to deliver nanosecond pulses of tuned radiation into flat premixed flames. The dye is Fluorescein548 in a basic (NaOH) solution of methanol. The frequency-doubled output from the dye laser, at a wavelength of 275 nm, is focused into a Rarnan cell having a length of 1 m and f-tiled with hydrogen at a pressure of 850 kPa. The output from the Raman cell is dispersed by a PellinBroca prism, and the third anti-Stokes component (205 nm) is directed over the center of a sintered-
224
J . T . SALMON and N. M. LAURENDEAU O-swit~ T.gqer Pulse
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instantaneous power of the laser beam is monitored with a UV-sensitive silicon PIN photodiode (Hamamatsu S1722-02); the output from the photodiode is sent to a second sampling module (Tektronix 7S14). This output also is digitized and stored by the microcomputer.
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Fig. 2. Experimental apparatus for two-photon fluorescence measurements of atomic hydrogen.
bronze flat-flame burner having a diameter of 6 cm. The pulse energy of the 205 nm beam is - 55 /zJ, and the line width (FWHM) is 2.0 cm- l [24]. The absorption line width (single photon) is essentially Doppler broadened with a FWHM of - 3 . 3 cm -1 at a temperature of 1550 K. The remaining Raman components and the fundamental beam are blocked. The 205-nm beam excites atomic hydrogen from the ground state (n = 1) to the second excited state (n = 3) (La transition) via a two-photon transition. Fluorescence from the directly excited state to the first excited state (n = 2) (Ha transition) at 656 nm is isolated by a Spex 3/4 m spectrometer having entrance and exit slit widths of 400 and 750 t~m, respectively; the height of the entrance slit is 5 mm. The output from the exit slit is monitored with a specially wired Hamamatsu R-955 photomultiplier tube [29], and the output is sent to a Tektronix 5S14N sampling module. The sampling window is set at the temporal peak of the fluorescence pulse. The peak fluorescence signal is digitized and stored by a microcomputer. The
The flames used for these experiments are shown in Table 1. Fluorescence profiles of atomic hydrogen were obtained in flames ranging from stoichiometric (4, = 1.0) to sooting (4, = 2.6). We were unable to obtain a temperature profile for the sooting flame and thus were unable to calibrate the measurements at that condition. Hence, absolute number densities were determined only for the nonsooting flames at 1.0 and 1.7. When conducting measurements on these flames, particularly the sooting one, the windows were isolated from the flame by plates with apertures that passed the UV beam. The volume between each window-plate combination was purged with nitrogen. When the plates were not used, condensation of a byproduct of the fuel-rich flames on the window strongly absorbed the UV radiation.
Laser-Induced Photochemistry Two tests were conducted to determine the extent of any photochemical effects induced by the laser beam: measuring the fluorescence signal as a function of UV laser power, and monitoring the TABLE 1 Flame Conditions Used in Experiments ° Equivalence Ratio
Flow Rates (mole/rain)
1.0 b'd 1.7
0.0130/0.0390/0.1455 0.0346/0.0622/0.2320 0.0528/0.0622/0.1240
2.6 b,c
° The flow rates are formatted as C2H4/O2/Ar. The pressure is 72 Torr. b Fluorescence vs. laser power. c Fluorescence spectrum. d Laser-saturated fluorescence measurements of OH calibrated by absorption.
H-Atom Fluorescence
225
fluorescence signal as a function of fluorescence wavelength. These measurements were conducted in the stoichiometric and sooting (4, = 2.6) flames at a height of 5 mm above the burner. This height was well below the position of visible soot formation, which was 17 mm above the burner. The height of 5 mm also corresponded to the position of maximum absorption of the UV beam by the sooting flame, which was about 20%; no absorption was observed in the stoichiometric flame. Because the sooting flame yielded the lowest measured fluorescence by atomic hydrogen, any interference by laser-induced photochemistry should be more detectable at cI, = 2.6. When measuring the fluorescence signal as a function of laser power, the laser is held at a constant power setting, and the laser beam is attenuated by quartz plates placed in the UV beam immediately before the primary focusing lens. The relative laser power is monitored with a UVsensitive photodiode and averaged over 600 laser shots. The fluorescence signal is averaged similarly, and the two averages are stored as ordered pairs for future processing. A quadratic dependence of the fluorescence signal on laser power is necessary but insufficient to establish a lack of detectable intrusion by the laser. Hence we also measured the fluorescence spectrum because it reveals possible sources of interference by molecules, such as polycyclic aromatic hydrocarbons, that fluoresce in the neighborhood of the H~ wavelength. Passing both tests provides evidence that possible interference from laser-induced chemistry is below the detection limit of the experimental system. Measurement of Number Density Before number densities can be measured, Eq. 3 must be developed further by considering radiative transfer from the probe volume to the photomultiplier tube. Fluorescence is collected at a right angle to the axis of the laser beam with the entrance slit opened to accept the entire width of the fluorescence volume. The observed fluorescence voltage out of the photomultiplier tube is related to ?43 by [30]:
V: = l~Gfic V:: ,
(Sa)
where the fluorescence emission ~: (W/cm 3 - sr) is
~:= hcp/A/ N3. 4~r
(5b)
In Eq. 5a, G(V/W) is the photomultiplier sensitivity, tic (sr) is the solid angle subtended by the collection optics, Vc (cm 3) is the fluorescence collection volume, and # accounts for various factors such as misalignment of the collection optics, reflectionand absorption by optical components, the throughput of the spectrometer, and nonuniform illumination of the fluorescence volume. In Eq. 5b, p/(cm-i) is the frequency of fluorescence, A/(s-l) is the Einstein coefficient for spontaneous emission to the intermediate level, and 4~r (sr) is the total solid angle for isotropic fluorescence. Equations 5 a, b show thatN3 ~ V:. Because Wl3 ~x IL 2 oc VL2 where VL is the measured laser voltage, Eqs. 3 and 4 yield
Nr= CVy/ VL2 T l/2,
(6)
where C is the calibration factor for the experimental system. This factor can be found by applying Eq. 6 at a point where N r is known and where Vf, VL, and T are measured. Once the system is calibrated at one point, the number density at any other location and in any other flame can be obtained from a fluorescence measurement and a temperature measurement. The stoichiometric flame was the first and last case investigated, which enabled us to determine if systematic errors were introduced by long-term drift in any unmeasured parameter. At each point, measurements of Vf and VL were averaged over 600 laser shots. Quenching was accounted for by measuring the local flame temperature with miniature thermocouples. Calibration of Fluorescence Measurements Quantitative fluorescence measurements of atomic hydrogen were obtained by measuring the OH concentration and flame temperature in the postflame zone, and determining the concentration of atomic hydrogen by assuming partial equilibrium. The elementary reactions in partial equilib-
226
J . T . SALMON and N. M. LAURENDEAU
rium used here are H2+O a=~ H + O H H2+OH ~ H + H 2 0
(7a) (7b)
O2+H ~:~ O + O H
(7c)
and C O + O H ~ CO2+H.
time. The beam diameter is obtained by passing a knife edge through the beam at the probe volume and assuming a Gaussian irradiance distribution [38]. Although this method is not very accurate (profile not Gaussian), it allows us to obtain a good estimate of the peak irradiance. The rate coefficient for photoionization is obtained from the peak irradiance and
(7d)
Partial equilibrium has been verified in the postflame zone of premixed fuel-lean hydrocarbon flames experimentally by Kaskan [31, 32] and in slightly fuel-rich hydrocarbon flames (4, = 1.07) by Iverach et al. [33]. Partial equilibrium of Reactions 7a-c for 0.6 ~< q, ~< 1.4 was also verified numerically by Peterson [34] using a onedimensional kinetic code for attached H2/O2/Ar flames. The equations for partial equilibrium include equilibrium constant (Kp) expressions for Reactions (7), and atom-balance expressions for hydrogen, carbon, oxygen, and argon [25]. Because Y.xi = 1 where xi is the mole fraction of the ith species, we have a nonlinear system of eight equations and nine unknowns: XH20, XCO2, XCO, XH2, XO2, XH, XO, Xor~, and XA,. For closure XoH is obtained from laser-saturated fluorescence measurements calibrated by absorption and from the flame temperature [35]. The temperature, also required for the equilibirum constants, is measured with miniature Pt/Pt-10%Rh thermocoupies that were silica coated [36] and corrected for radiation loss [37]. The resulting system of equations is solved by Newton's method, providing the mole fraction and number density for each of the eight remaining species. RESULTS AND DISCUSSION Before proceeding to the results of these experiments, a few comments should be made about the pulse characteristics of the laser that are shown in Table 2 and described further by Salmon and Laurendeau [24]. The pulse energy is measured with a power meter, and the peak power is obtained by dividing the pulse energy by the normalized pulse profile integrated with respect to
a3iIL W3i-
hcuL '
where the cross section a3i (cm 2) is approximately 10-2/(uL3n 5) for H atoms having a principal quantum number of n [12, 39]. The rate coefficient for two-photon absorption is given by [30]
Orl3./'L2 WI3--(hC~,L)2 ' where the cross-section al3 is 4.2 x 10 - ~ cm 4 s [40]. These pulse characteristics, in conjunction with the decay rate coefficient R3, indicate whether photoionization or saturation are important. The importance of these two processes can be evaluated from the ratios of W3i/R3 and WI3/R3. A conservative estimate of R3 for this flame is - 109 s-1, which is based on an estimated rate coefficient in a 10-Torr H2/O2/N2 flame of 3 x l0 s s- l [25]. The actual rate coefficient is probably higher. The ratios Wai/R3 and W13/R3 are on the order of 10 -3 and 10 -4 , respectively, which makes both photoionization and saturation negligible in these flames. TABLE 2 Pulse Parameters of the LaserBeam Used for the Two-Photon FluorescenceMeasurementsof Atomic Hydrogen Wavelength Pulse energy Peak power Diameter (FWHM) Peak It Peak W3i Peak W13
205 nm 55 13.6 kW 290/~m 1.5 x 107 W/cm 2 5 x 106s-1 1.3 x 105s i
H-Atom Fluorescence
227
Photochemistry Tests for interference by photochemistry revealed possible effects by the UV beam. The results of the first test, which measured the fluorescence signal as a function of laser power, are shown in Fig. 3 for the stoichiometric flame. The solid curve is a nonlinear least-square fit of the data to the function Vf=aVL 0
(8)
where a and b are the parameters of the curve fit. This fit yields b = 1.5 + 0.2 with a 95% confidence level obtained from the t distribution. A similar curve fit for the sooting flame yields b = 1.4 + 0.2, which shows that this result is independent of stoichiometry. Normally, strong photoionization of atoms in the directly excited state or saturation of the two-photon transition by the UV beam will cause b < 2, while photolysis, which results in the growth of atomic hydrogen, will cause b > 2 [25]. Previous measurements in hydrogen flames [24] showed a quadratic dependence of the fluorescence signal on the measured laser power, which indicates that photoionization of atoms in the directly excited state and saturation of the twophoton transition by the UV beam are insignifl140
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Number Density Measurements Our investigation of two-photon fluorescence by atomic hydrogen in premixed C2H4/O2/Ar flames was conducted at subatmospheric pressure for the following reasons. 1. Compared to flames at one atmosphere, subatmospheric pressure favors higher mole fractions of intermediates, such as atomic hydrogen. 2. Quenching is much lower, resulting in more fluorescence for the same number density. 3. Reactions occur at a slower rate, effectively spreading the flame front and increasing the spatial resolution within the reaction zone.
8 .,
cant. This conclusion is corroborated by the pulse characteristics given in Table 2. We also investigated the possibility of absorption by some hydrocarbon that subsequently pyrolyzes into species other than atomic hydrogen. The rates of absorption and pyrolysis required to simulate the observed dependence on the fluorescence signal significantly reduce the population of the absorbing species and thus violate Beer's law. A full analysis of this nonlinear absorption is given by Salmon [25]. Although this phenomenon may explain the observed nonquadratic dependence, further investigation is required to verify its significance in our experiments. The fluorescence spectrum revealed barely detectable radiation distributed over the entire spectral range. We also detected scattered radiation from the fifth Stokes component at 643 nm, which was generated by the Raman cell. These sources did not affect our measurements because we used a monochrometer for narrow-band detection. However, care is needed if dielectric bandpass filters are to avoid scattered radiation inadvertently transmitted through the filter, thus corrupting the fluorescence measurements.
20
0
I0 I I I I 5 I00 150 200 250 LASER VOLTAGE SQUARED(mV 2)
Fig. 3. Fluorescence signal as a function of the squared laser signal measured by a photodiode at 5 nun above the burner in the stoichiometric C21L/O2/Ar flame at a pressure of 72 Tort.
The favoring of intermediates at subatmospheric pressures ameliorates any photochemical effects that may be present and improves the signal-tonoise ratio of the measurements. A comparison of fluorescence measurements of atomic hydrogen and predictions from partial-
228
J . T . SALMON and N. M. LAURENDEAU
equilibrium calculations is shown in Fig. 4 for the stoichiometric flame at 72 Ton.. Also shown are profiles of the flame temperature and the number density of OH that were used in the partialequilibrium calculations. The H-atom measurements are calibrated by partial equilibrium at a height of 50 mm above the burner. The two Hatom profiles, which were the first and last ones measured in the experiments, show no long-term drift affecting the results. The fluorescence profiles in these flames are normalized by VL 3/2 rather than the VL 2 in Eq. 6, which reflects the measurement of fluorescence intensity as a function of laser power discussed in the previous section. Although the laser power was about the same for many of the points of the two profiles in Fig. 4, the laser power was somewhat erratic during the first profile, especially around a height of 5-10 mm above the burner. Normalizing by VL 3/2 results in the least scatter in the data, which is consistent with the nonquadratic behavior of the fluorescence signal with respect to the incident laser power. Although the fluorescence measurements are corrected for quenching by dividing by T 1/2, the temperature profile yields a maximum correction of about 2 %. Figure 4 also indicates that partial equilibrium is valid at heights greater than 25 mm from the burner and begins to break down below this height. The breakdown results in an underprediction of the number density of atomic hydrogen as I0
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the reaction zone is approached, which is the same trend found in previous hydrogen flames [24]. The peak concentration of atomic hydrogen is about four times the peak concentration of OH, whereas both profiles peak at about the same height above the burner. Vertical profiles of H-atom number densities in the fuel-rich (4, = 1.7) flame are shown in Fig. 5, along with profiles of the flame temperature and the number density of OH. As in the stoichiometric flame, the fluorescence measurements are calibrated by partial equilibrium at a height of 50 mm above the burner, and the pressure is 72 Ton'. The temperature profile is used again to correct for variations in quenching within the flame. This correction is less than 3 % at all positions in the flame. Atomic hydrogen concentrations predicted by partial equilibrium, also shown in Fig. 5, reveal the same trend as Fig. 4 except that partial equilibrium remains valid down to a height of 20 mm instead of 25 ram. The relative peak heights of the hydrogen atom and OH number densities are approximately 13:1 compared to 4:1 for the stoichiometric flame. In constrast to the results for the hydrogen flames [24], the number densities of atomic hydrogen in the ethylene flames are lower in the fuel-rich case than in the stoichiometric case. The higher flow rates in the fuel-rich flame resulted in less heat loss to the burner and thus a higher postflame temperature (1695 K in the fuel-rich
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flametemperatureand OH numberdensityprofiles.
H-Atom Fluorescence case compared to 1480 K in the stoichiometric case). For the fuel-rich flame, Reactions 7b and 7d are the only reactions that have any effect on the calculated number density of atomic hydrogen. The higher temperature for the fuel-rich flame gives an equilibrium constant for Reaction 7b about half of that for the stoichiometric case, while the equilibrium constant for Reaction 7d is 40% of that for the stoichiometric case. The trend in both of these equilibrium constants favors less atomic hydrogen in the fuel-rich flame, despite the increased amount of total hydrogen atoms required by the stoichiometry. Because variations in quenching have been accounted for by using a temperature dependence in the number-density calculations, the calibration factors for the stoichiometric and fuel-rich flames should be equal to within the uncertainty of the calibration. The calibration factor for the fuel-rich flame, however, is about 27% higher than that for the stoichiometric flame. This difference could be caused by the following: 1. failure of kinetic theory to predict variations in the local quenching rate based on an average cross-section that is independent of the local composition; 2. uncertainties in the calibration introduced by the sensitivity of the predicted number density of atomic hydrogen to uncertainties in the input molar flow rates, the OH concentration, and the temperature; 3. concentrations of unburned hydrocarbons in the postflame gases that are not accounted for in the partial-equilibrium calculations. Failure of kinetic theory to predict the variation in the local quenching rate coefficient seems doubtful. Using PICLS, no measurable change in the quenching rate coefficient was observed in the postflame zone of premixed H2/O2/N2 flames at a pressure of 72 Torr for 0.6 ~< ,I, ~< 1.5 [23]. The calibration factor is sensitive to variations in the fuel-oxidizer ratio, the OH concentration, and the flame temperature [25]. These sensitivities are shown in Table 3 for both the stoichiometric and fuel-rich flames. Note that the uncertainties in the calibration factor owing to uncertainties in the fuel-oxidizer ratio, OH concentration, and flame
229 temperature are higher in the stoichiometric flame by about 200%, 100%, and 100%, respectively. Moreover, the measured difference in the magnitude of the calibration factor between the fuel-rich and stoichiometric flames (27%) is clearly within the estimated total uncertainty in the calibration factor for these two flame conditions (16-39%). We also investigated the sensitivity of the calibration factor to uncertainties in the fueloxidizer ratio and OH number density for a fuellean (~I, = 0.70) flame having the same flame temperature and OH number density as in the stoichiometric flame. For a 4% variation in the fuel-oxidizer ratio, the calibration factor varies by only 5 %; however, an 11% variation in the OH concentration yields a 31% variation in the calibration factor. We thus conclude that the sensitivity of the calibration factor to changes in the OH concentration and the fuel-oxidizer ratio in fuellean and stoichiometric flames makes fuel-rich flames most amenable to calibration by partial equilibrium. A possibly adverse effect on partial-equilibrium calculations in fuel-rich hydrocarbon flames lies in the failure of the technique to include unburned hydrocarbons, including soot, in highly fuel-rich and sooting flames. Failures to account for carbon and hydrogen atoms bound in these species is analogous to the introduction of additional fuel to the mixture, resulting in artificially high predictions of atomic hydrogen concentrations. For TABLE 3 Percent Uncertainty in Calibration Factor Owing to Uncertainties in the Experimental Parameters for the Stoichiometric and Fuel-Rich Flames a Equivalence Ratio 1.0
1.7
Fuel-oxidizerratio O H concentration
28% (4%) 24% (11%)
9 % (2%) 11% (11%)
Flame temperature Fluorescence measurements
11% (20K)
6 % (20K)
5% (5%) 39%
5% (5%) 16%
Total
*The experimental uncertainty responsible for each calibration factor effect is given in parentheses.
230 instance, failure to account for 5% of carbon and hydrogen in the form of unburned hydrocarbons results in a 20% overprediction of the calibration factor at an equivalence ratio of 1.7. Because the calibration factor for the fuel-rich flame is 27 % higher than that for the stoichiometric flame, part of the measured difference might be caused by this effect. Thus, slightly rich flames appear to be the best candidates for calibrating by partial equilibrium. Another possible answer to the dilemma of calibrating in fuel-rich to sooting flames lies in the use of PICLS. As described by Salmon and Laurendeau [17, 24], P I C L S o v e r c o m e s the effect of quenching by strongly photoionizing atoms in the directly excited state. The resulting measurements of number density are independent of quenching and, hence, only need to be calibrated at one flame condition. The calibration may be conducted even in a hydrogen flame. Because PICLS is independent o f quenching, there is no restriction on the flame used for calibration.
CONCLUSIONS We have quantitatively measured number densities of atomic hydrogen in flat, premixed, C2H4/O2/Ar flames by using two-photon-excited fluorescence. Two flames at a pressure of 72 Torr were investigated; the fuel-equivalence ratios were 1.0 and 1.7. The fluorescence measurements were calibrated by partial equilibrium at a height of 50 nun from the burner, which is well into the postflame zone, and were corrected for variations in quenching by employing the measured temperature and kinetic theory. The accuracy of the number densities is 40% for the stoichiometric flame and 15% for the fuel-rich flume. The uncertainty for atomic hydrogen in the fuel-rich flame may be higher because the partial-equilibrium calculations do not account for unburned hydrocarbons. The lack o f accuracy in the stoichiometric flame is caused by an increased sensitivity of the partial-equilibrium calculations to uncertainties in both the equivalence ratio and the measured OH concentration. Slightly rich flames appear to be the best candidates for calibrating
J . T . S A L M O N and N. M. L A U R E N D E A U measurements of atomic hydrogen by partial equilibrium. This research was supported by the U.S. Department o f Energy (Office o f Basic Energy Sciences). J. T. Salmon was also supported by a Newport Research A w a r d f u n d e d by Newport Corp. and administered by the Optical Society o f America.
REFERENCES
1. Harris, S. J., Weiner, A. M., Blint, R. J., and Goldsmith, J. E. M., Twenty-FirstSymposium (InternationaO on Combustion, The Combustion Institute, Pittsburgh, PA, 1988, 1033. 2. Dreyfus,R. W., Bogen, P., and Langer, H. in Proceedings AlP ConferenceNo. 90 (T. J. McIlrath and R. R. Freeman, Eds.), New York, AlP, 1972, p. 57. 3. Appel, D., and Appleton, J. P., Fifteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA, 1974, 701. 4. Lifshitz, A., Skinner, G. B., and Wood, D. R. J. Chem. Phys. 70:5607 (1979). 5. Wallenstein, R., Opt. Commun. 33:119 (1980). 6. Bulewicz, E. M., James, C. G., and Sugden, T. M. Proc. Roy. Soc. A235:89 (1956). 7. McEwan, M. J., and Phillips, L. F. Combust. Flame 9:420 (1965). 8. Neoh,,K. G., Howard, J. B., and Sarofun, A. F. in Particulate Carbon: Formation During Combustion (E. C. Siegla and C. W. Smith, Eds.), Plenum Press, New York, 1981, 261. 9. Dixon-Lewis, G., Sutton, M. M., and Williams, A. Trans. Faraday Soc. 61:255 (1965). 10. H~nsch, T. W., Lee, S. A., Wallenstein, R., and Wieman, C. Phys. Rev. Lett. 34:307 (1975). 11. Bokar, J., Freeman, R. R., White, J. C., and Storz, R. H. Phys. Rev. A24:612 (1981). 12. Lucht, R. P., Salmon, J. T., King, G. B., Sweeney, D. W., and Laurendeau, N. M., Opt. Lett, 8:365 (1983). 13. Alden,M., Schawlow, A. L., Svanberg, S., Wendt, W., and Zhang, P.-L. Opt. Lett. 9:211 (1984). 14. Goldsmith, J. E. M. Opt. Lett. 10:166 (1985). 15. Goldsmith, J. E. M. Opt. Lett. 11:416 (1986). 16. Goldsmith,J. E. M., and Anderson, R. J. M. Opt. Lett. 11:67 (1986). 17. Salmon, J. T., and Laurendeau, N. M. Opt. Lett. 11:419 (1986). 18. Bittner, J., Kohse-H/~oinghaus,K., Meier, U., Kelm, S., and Just, Th. Combust. Flame 71:41 (1988). 19. Bjorklund, G. C., Ausschnitt, C. P., Freeman, R. R., and Storz, R. H. Appl. Phys. Lett. 33:54 (1978).
H-Atom Fluorescence Ausschnitt, C. P., Bjorklund, G. C., and Freeman, R. R. Appl. Phys. Lett. 33:851 (1978). 21. Goldsmith, J. E. M. Opt. Lett. 7:437 (1982). 22. Goldsmith, J. E. M., Twentieth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA, 1984, 1331. 23. Salmon, J. T., and Laurendean, N. M. "Relative Fluorescence Quenching Measurements of Atomic Hydrogen in Subatmospheric H2/O2/N2 Flames with Photoionization Controlled-Loss Spectroscopy," in preparation for publication. 24. Salmon, J. T., and Laurendeau, N. M. Appl. Opt. 26:2881 (1987). 25. Salmon, J. T. "Quantitative Fluorescence Measurements of Atomic Hydrogen in Flames via Two-Photon Absorption." Ph.D. Thesis, Purdue University, West Lafayette, Indiana, 1986. 26. Loudon, R. The Quantum Theory of Light, 2nd Edition, Clarendon Press, Oxford, 1983. 27. Calvert, J. G., and Pitts, N. M., Jr. Photochemistry, John Wiley and Sons, Inc., New York, 1967. 28. Meier, U., Kohse-H6inghans, K., and Just, Th. Chem. Phys. Lett. 126:567 (1986). 29. Harris, J. M., Lytle, F. E., and McCain, T. C. Anal.
231
20.
30. 31. 32. 33.
34.
35. 36. 37. 38. 39. 40.
Chem. 48:2095 (1976). Goldsmith, J. E. M., and Laurendeau, N. M. Appl. Opt. 25:276 (1986). Kaskan, W. E. Combust. Flame 2:286 (1958). Kaskan, W. E. Combust. Flame 3:49 (1959). Iverach, D., Basden, K. S., and Kirov, N. Y. Fourteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA, 1973, p. 767. Peterson, R. C. "Kinetics of Hydrogen-Oxygen-Argon and Hydrogen-Oxygen-Argon-Pyridine Combustion using a Flat Flame Burner." Ph.D. Thesis, Purdue University, West Lafayette, Indiana, 1981. Lucht, R. P., Sweeney, D. W., and Lanrendeau, N. M. Combust. Sci. Technol. 42:259 (1985). Fristrom, R. M., and Westenbcrg, A. A. Flame Structure. McGraw-Hill, New York, 1965. Peterson, R. C., and Laurendeau, N. M. Combust. Flame 60:279 (1985). Mauck, M. Appl. Opt. 18:599 (1979). Bates, D. R. R. Astron. Soc. Mon. Notes 106:423 (1946). Bischel, W. K., Perry, B. E., and Crosley, D. R. Appl. Opt. 21:1419 (1982).
221
Concentration Measurements of Atomic Hydrogen in Subatmospheric Premixed C2H4/O2/Ar Flat Flames J. THADDEUS SALMON* and NORMAND M. LAURENDEAU Flame Diagnostics Laboratory, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907
Absolute number densities of atomic hydrogen have been measured in subatmospheric, premixed C2I'L/O2/Ar flat t i m e s via two-photon excited fluorescence. The fuel-equivalence ratios of the flames were 1.0 and 1.7. The fluorescence measurements are calibrated by partial equilibrium calculations and corrected for quenching effects by assuming a constant average cross-section and using kinetic theory. A sensitivity analysis of the calibration procedure reveals that slightly rich flames appear to be the best candidates for calibrating fluorescence measurements of atomic hydrogen by partial equilibrium.
INTRODUCTION The hydrogen atom is a primary radical in the oxidation of all hydrocarbons. The high diffusivity and reactivity of this species make it important to the study of flame ignition and propagation. Hydrogen atoms may also play a significant role in chemical processes leading to the formation of soot [1]. Despite its importance to combustion, few methods existed for measuring concentrations of atomic hydrogen before the advent of high° powered lasers. These previous methods included resonant absorption [2-5], doping flames with lithium salts [6-8], and adding trace amounts of CO2 to hydrogen flames [9]. Resonant absorption is unfeasible in a flame as the absorption lines, which lie in the vacuum ultraviolet, are strongly absorbed by the combustion gases (most notably water vapor). Doping with lithium salts is impractical without a specially designed burner; moreover, the validity of this method is questionable at pressures below I00 Torr where kinetic studies of atomic hydrogen are most useful. Adding trace amounts of CO2 is useful only for hydrogen flames * Present address: Lawrence Livermore National Laboratory Livermore, CA 94550 Copyright © 1988 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 655 Avenue of the Americas, New York, NY 10010
as hydrocarbon flames produce copious amounts of carbon dioxide. With the development of high-powered lasers that are tunable in the far ultraviolet, atomic hydrogen can be excited via multiphoton absorption and then monitored by fluorescence [10-18] or by optogalvanic detection [19-22]. Fluorescence measurements of H-atom concentrations in premixed flames [12-16] were calibrated in the postflame region by partial equilibrium, and it was assumed that the rate coefficient for electronic quenching was independent of position within the flame. Such measurements have been largely confined to the postflame zone as the relative change in the actual quenching rate coefficient of atomic hydrogen is unknown within the preheat and reaction zones. Recent work [17] has compared conventional fluorescence measurements of atomic hydrogen, which assume a constant rate coefficient for quenching, to measurements using photoionization controlled-loss spectroscopy (PICLS), which are independent of quenching, in H2/O2/N2 flames at 20 Torr. This comparison demonstrated the need to account for quenching in the preheat zone when using conventional fluorescence. A subsequent study of the quenching of atomic hydrogen in H2/
O010-2180/88/$03.50
222
J.T. SALMON and N. M. LAURENDEAU
O2/N 2 flames
[23] established a T- i/2 dependence on temperature, in agreement with kinetic theory. Further studies showed that at higher pressures (72 Torr), conventional fluorescence measurements and PLCLS measurements agreed very well, except below 2 mm above the burner surface; hence, in such flames, the rate coefficient for quenching can be assumed to be nearly constant
. . . . . . . . . . . . . . . . . . . . . . .
3
n=5
2
n=2 205.11
% Q= 1205.1)
[24]. More recently, Bittner et al. [18] calibrated fluorescence measurements of atomic hydrogen to a known number density in a flow discharge cell. The difference in quenching rate between the two environments was accounted for by a correction factor that was determined by numerically solving the rate equations governing the excitation/relaxation dynamics at each point in the flame. Unfortunately, their results were not compared to those calibrated by partial equilibrium; in addition, they did not discuss the extent to which their correction factor varies with both position within the flame and flame stoichiometry. In this paper we report quantitative fluorescence measurements of atomic hydrogen in fiat, premixed, C2I'I4/O2/Ar flames for fuel-equivalence ratios of 1.0 and 1.7 at a pressure of 72 Torr. These conventional two-photon measurements are calibrated in the postflame zone by partial equilibrium and are corrected for the small variations in quenching near the burner surface by using the T-]/2 proportionality observed in subatmospheric H2/O2/N2 flames [23-25]. THEORY Excitation and relaxation of hydrogen atoms during fluorescence measurements can be described by the simple model shown in Fig. 1, where the ground state is level 1 and the directly excited state is level 3. Upon laser excitation, level 1 is depopulated by absorption of two photons and populated by collisional and radiative relaxation from levels 2 and 3. As shown later, two-photon absorption under our conditions is far below saturation. Hence, the change in the ground state population N~ is negligible. Furthermore, the energy of level 2 is 82259 cm-], thus making the equilibrium population of all excited electronic
." C o n t i n u u m
1
n=l
Fig. 1. Schematic drawing of the excitation/relaxation dynamics associated with fluorescence measurements of atomic hydrogen, where the respective rate coefficients (s- 1) are WI3 (two-photon absorption), (2o (total quenching from level i to level j), and A U(fluorescence). The wavelengths (nm) corresponding to excitation and fluorescence are given in parenthe~S.
levels negligible at flame temperatures. Therefore, N] = Nr, the total initial population of atomic hydrogen, throughout the laser pulse. Fluorescence is detected through radiative relaxation from level 3 to level 2. Hence, the measured fluorescence signal is directly proportional to the population of level 3, N3 (cm-3). Level 3 is populated via the absorption of two photons by atoms in the ground state (level 1) and depopulated by collisional transfer (quenching) and radiative relaxation (fluorescence). Photoionization via absorption of an additional photon by atoms in the directly excited state can be ruled out from a previous study of H2/O2/N2 flames [24]. The resulting rate of change of N3 can be taken as dN3
- - = N ] WI3-N3(Q3+ A3), dt
(1)
where W]3 is the rate coefficient for two-photon absorption, which is directly proportional to the square of the laser irradiance IL (W/cm 2) [25, 26], and (23 and A3 are the total rate coefficients for quenching (Q3] + (232) and spontaneous emission (A3] + A32), respectively. Chemical reactions by atoms in the directly excited state are not considered, but are implicitly accounted for by the quenching rate because both processes induce a loss from the directly excited state via collisions
H-Atom Fluorescence
223
and thus are indistinguishable when making fluorescence measurements. Quantitative fluorescence measurements are difficult if level 1 is strongly populated through photodissociation of an interfering species by the UV beam. Under these conditions, the population of level 1, N1, grows at a rate that is directly proportional to the population of the interfering species Np, resulting in dN1 dt = Np Wp,
(2)
where Np IVp is the rate of photodissociation that produces hydrogen atoms in the ground state. This process, which can lead to measured atomic concentrations that are artificially high, has been observed in fuel-lean hydrogen-oxygen flames at atmospheric pressure by Goldsmith [15]. In that case the interfering species was water vapor. Because the quantum efficiency for predissociation of water vapor by the absorption of one UV photon ()~ = 205 nm) is near unity [271, Eq. 2 shows that N~ oc Wj, ~ IL. Substituting this proportionality for NI into Eq. 1 yields N3 cx IL 3 at steady state, because Wl3 ~ IL2. This cubic proportionality has been observed by Goldsmith [15]. Because our fluorescence measurements of atomic hydrogen assume no laser-induced photochemistry, the measurements must be examined for possible nonquadratic dependence of the fluorescence signal on the UV laser power. At the temporal peak of the fluorescence pulse, dN3/dt = 0, and Eq. 1 reduces to N3 = N r Wl3/R3,
EXPERIMENTAL APPARATUS
(3)
where Ra -= Q3 + A3 is the rate coefficient for the total decay out of level 3. Relative changes in W~3 can be monitored by measuring variations in the power of the UV beam; however, direct temporal measurements of relative changes in Q3 are difficult as Q3 exceeds 3 × l0 s s-l at a pressure of 10 Torr [25]. Previous experiments using PICLS in H2/O2/N2 flames at 20 Torr showed that R3 ~ T- 1/2
portionality was the same for fuel-equivalence ratios of both 1.0 and !.4. Because Ra = Q3 + A3, these results suggest that Q3 ~" A3 at pressures greater than 20 Torr, and R3 can be successfully described by kinetic theory, with an effective cross-section in hydrogen flames that is independent of both stoichiometry and temperature. Because the pressure of the ethylene flames is 3.5 times that of the hydrogen flames, Eq. 4 can be used here to correct the fluorescence measurements of atomic hydrogen for any change in the local quenching rate coefficient. The inverse proportionality between R3 and T I/2 in Eq. 4 is also supported by the results of Meier et al. [28], who measured quenching rate constants for atomic hydrogen with H2, 02, and H20 as the quenching partners in a thermostatically controlled flow-discharge reactor. Because the concentration of H20 rises rapidly in a flame and the rate constant with 1-120 as the quencher is approximately four times that for either H2 or 02 [28], H20 is the dominant quenching species under combustion conditions. For reactor temperatures between 300 and 560 K, Meier et al. found that the product of the rate constant for the quenching of atomic hydrogen by H20 and T 1/2 was constant to within 10%, which is predicted by kinetic theory for a quenching cross-section that is independent of temperature. Thus, Eq. 4 is justified at least for hydrogen flames; full verification in hydrocarbon flames awaits publication of quenching rate constants for both CO and CO2.
(4)
to within a few percent, where Tis the local flame temperature [23]. Moreover, the constant of pro-
Our experiments, shown in Fig. 2, use a dye laser (Molectron DL-18) pumped by a frequency-doubled, Q-switched Nd:YAG laser (Molectron MY34) to deliver nanosecond pulses of tuned radiation into flat premixed flames. The dye is Fluorescein548 in a basic (NaOH) solution of methanol. The frequency-doubled output from the dye laser, at a wavelength of 275 nm, is focused into a Rarnan cell having a length of 1 m and f-tiled with hydrogen at a pressure of 850 kPa. The output from the Raman cell is dispersed by a PellinBroca prism, and the third anti-Stokes component (205 nm) is directed over the center of a sintered-
224
J . T . SALMON and N. M. LAURENDEAU O-swit~ T.gqer Pulse
I
lL2, °m /l
I
I
I .........
I
instantaneous power of the laser beam is monitored with a UV-sensitive silicon PIN photodiode (Hamamatsu S1722-02); the output from the photodiode is sent to a second sampling module (Tektronix 7S14). This output also is digitized and stored by the microcomputer.
o,,,,,o,co,,
v,,,
High V~tOQe
I s°°°" I " Pellin.~'oca
PROCEDURE
.
Photodlode
.
.
.
, ~ Scotterlng Ptote
Fig. 2. Experimental apparatus for two-photon fluorescence measurements of atomic hydrogen.
bronze flat-flame burner having a diameter of 6 cm. The pulse energy of the 205 nm beam is - 55 /zJ, and the line width (FWHM) is 2.0 cm- l [24]. The absorption line width (single photon) is essentially Doppler broadened with a FWHM of - 3 . 3 cm -1 at a temperature of 1550 K. The remaining Raman components and the fundamental beam are blocked. The 205-nm beam excites atomic hydrogen from the ground state (n = 1) to the second excited state (n = 3) (La transition) via a two-photon transition. Fluorescence from the directly excited state to the first excited state (n = 2) (Ha transition) at 656 nm is isolated by a Spex 3/4 m spectrometer having entrance and exit slit widths of 400 and 750 t~m, respectively; the height of the entrance slit is 5 mm. The output from the exit slit is monitored with a specially wired Hamamatsu R-955 photomultiplier tube [29], and the output is sent to a Tektronix 5S14N sampling module. The sampling window is set at the temporal peak of the fluorescence pulse. The peak fluorescence signal is digitized and stored by a microcomputer. The
The flames used for these experiments are shown in Table 1. Fluorescence profiles of atomic hydrogen were obtained in flames ranging from stoichiometric (4, = 1.0) to sooting (4, = 2.6). We were unable to obtain a temperature profile for the sooting flame and thus were unable to calibrate the measurements at that condition. Hence, absolute number densities were determined only for the nonsooting flames at 1.0 and 1.7. When conducting measurements on these flames, particularly the sooting one, the windows were isolated from the flame by plates with apertures that passed the UV beam. The volume between each window-plate combination was purged with nitrogen. When the plates were not used, condensation of a byproduct of the fuel-rich flames on the window strongly absorbed the UV radiation.
Laser-Induced Photochemistry Two tests were conducted to determine the extent of any photochemical effects induced by the laser beam: measuring the fluorescence signal as a function of UV laser power, and monitoring the TABLE 1 Flame Conditions Used in Experiments ° Equivalence Ratio
Flow Rates (mole/rain)
1.0 b'd 1.7
0.0130/0.0390/0.1455 0.0346/0.0622/0.2320 0.0528/0.0622/0.1240
2.6 b,c
° The flow rates are formatted as C2H4/O2/Ar. The pressure is 72 Torr. b Fluorescence vs. laser power. c Fluorescence spectrum. d Laser-saturated fluorescence measurements of OH calibrated by absorption.
H-Atom Fluorescence
225
fluorescence signal as a function of fluorescence wavelength. These measurements were conducted in the stoichiometric and sooting (4, = 2.6) flames at a height of 5 mm above the burner. This height was well below the position of visible soot formation, which was 17 mm above the burner. The height of 5 mm also corresponded to the position of maximum absorption of the UV beam by the sooting flame, which was about 20%; no absorption was observed in the stoichiometric flame. Because the sooting flame yielded the lowest measured fluorescence by atomic hydrogen, any interference by laser-induced photochemistry should be more detectable at cI, = 2.6. When measuring the fluorescence signal as a function of laser power, the laser is held at a constant power setting, and the laser beam is attenuated by quartz plates placed in the UV beam immediately before the primary focusing lens. The relative laser power is monitored with a UVsensitive photodiode and averaged over 600 laser shots. The fluorescence signal is averaged similarly, and the two averages are stored as ordered pairs for future processing. A quadratic dependence of the fluorescence signal on laser power is necessary but insufficient to establish a lack of detectable intrusion by the laser. Hence we also measured the fluorescence spectrum because it reveals possible sources of interference by molecules, such as polycyclic aromatic hydrocarbons, that fluoresce in the neighborhood of the H~ wavelength. Passing both tests provides evidence that possible interference from laser-induced chemistry is below the detection limit of the experimental system. Measurement of Number Density Before number densities can be measured, Eq. 3 must be developed further by considering radiative transfer from the probe volume to the photomultiplier tube. Fluorescence is collected at a right angle to the axis of the laser beam with the entrance slit opened to accept the entire width of the fluorescence volume. The observed fluorescence voltage out of the photomultiplier tube is related to ?43 by [30]:
V: = l~Gfic V:: ,
(Sa)
where the fluorescence emission ~: (W/cm 3 - sr) is
~:= hcp/A/ N3. 4~r
(5b)
In Eq. 5a, G(V/W) is the photomultiplier sensitivity, tic (sr) is the solid angle subtended by the collection optics, Vc (cm 3) is the fluorescence collection volume, and # accounts for various factors such as misalignment of the collection optics, reflectionand absorption by optical components, the throughput of the spectrometer, and nonuniform illumination of the fluorescence volume. In Eq. 5b, p/(cm-i) is the frequency of fluorescence, A/(s-l) is the Einstein coefficient for spontaneous emission to the intermediate level, and 4~r (sr) is the total solid angle for isotropic fluorescence. Equations 5 a, b show thatN3 ~ V:. Because Wl3 ~x IL 2 oc VL2 where VL is the measured laser voltage, Eqs. 3 and 4 yield
Nr= CVy/ VL2 T l/2,
(6)
where C is the calibration factor for the experimental system. This factor can be found by applying Eq. 6 at a point where N r is known and where Vf, VL, and T are measured. Once the system is calibrated at one point, the number density at any other location and in any other flame can be obtained from a fluorescence measurement and a temperature measurement. The stoichiometric flame was the first and last case investigated, which enabled us to determine if systematic errors were introduced by long-term drift in any unmeasured parameter. At each point, measurements of Vf and VL were averaged over 600 laser shots. Quenching was accounted for by measuring the local flame temperature with miniature thermocouples. Calibration of Fluorescence Measurements Quantitative fluorescence measurements of atomic hydrogen were obtained by measuring the OH concentration and flame temperature in the postflame zone, and determining the concentration of atomic hydrogen by assuming partial equilibrium. The elementary reactions in partial equilib-
226
J . T . SALMON and N. M. LAURENDEAU
rium used here are H2+O a=~ H + O H H2+OH ~ H + H 2 0
(7a) (7b)
O2+H ~:~ O + O H
(7c)
and C O + O H ~ CO2+H.
time. The beam diameter is obtained by passing a knife edge through the beam at the probe volume and assuming a Gaussian irradiance distribution [38]. Although this method is not very accurate (profile not Gaussian), it allows us to obtain a good estimate of the peak irradiance. The rate coefficient for photoionization is obtained from the peak irradiance and
(7d)
Partial equilibrium has been verified in the postflame zone of premixed fuel-lean hydrocarbon flames experimentally by Kaskan [31, 32] and in slightly fuel-rich hydrocarbon flames (4, = 1.07) by Iverach et al. [33]. Partial equilibrium of Reactions 7a-c for 0.6 ~< q, ~< 1.4 was also verified numerically by Peterson [34] using a onedimensional kinetic code for attached H2/O2/Ar flames. The equations for partial equilibrium include equilibrium constant (Kp) expressions for Reactions (7), and atom-balance expressions for hydrogen, carbon, oxygen, and argon [25]. Because Y.xi = 1 where xi is the mole fraction of the ith species, we have a nonlinear system of eight equations and nine unknowns: XH20, XCO2, XCO, XH2, XO2, XH, XO, Xor~, and XA,. For closure XoH is obtained from laser-saturated fluorescence measurements calibrated by absorption and from the flame temperature [35]. The temperature, also required for the equilibirum constants, is measured with miniature Pt/Pt-10%Rh thermocoupies that were silica coated [36] and corrected for radiation loss [37]. The resulting system of equations is solved by Newton's method, providing the mole fraction and number density for each of the eight remaining species. RESULTS AND DISCUSSION Before proceeding to the results of these experiments, a few comments should be made about the pulse characteristics of the laser that are shown in Table 2 and described further by Salmon and Laurendeau [24]. The pulse energy is measured with a power meter, and the peak power is obtained by dividing the pulse energy by the normalized pulse profile integrated with respect to
a3iIL W3i-
hcuL '
where the cross section a3i (cm 2) is approximately 10-2/(uL3n 5) for H atoms having a principal quantum number of n [12, 39]. The rate coefficient for two-photon absorption is given by [30]
Orl3./'L2 WI3--(hC~,L)2 ' where the cross-section al3 is 4.2 x 10 - ~ cm 4 s [40]. These pulse characteristics, in conjunction with the decay rate coefficient R3, indicate whether photoionization or saturation are important. The importance of these two processes can be evaluated from the ratios of W3i/R3 and WI3/R3. A conservative estimate of R3 for this flame is - 109 s-1, which is based on an estimated rate coefficient in a 10-Torr H2/O2/N2 flame of 3 x l0 s s- l [25]. The actual rate coefficient is probably higher. The ratios Wai/R3 and W13/R3 are on the order of 10 -3 and 10 -4 , respectively, which makes both photoionization and saturation negligible in these flames. TABLE 2 Pulse Parameters of the LaserBeam Used for the Two-Photon FluorescenceMeasurementsof Atomic Hydrogen Wavelength Pulse energy Peak power Diameter (FWHM) Peak It Peak W3i Peak W13
205 nm 55 13.6 kW 290/~m 1.5 x 107 W/cm 2 5 x 106s-1 1.3 x 105s i
H-Atom Fluorescence
227
Photochemistry Tests for interference by photochemistry revealed possible effects by the UV beam. The results of the first test, which measured the fluorescence signal as a function of laser power, are shown in Fig. 3 for the stoichiometric flame. The solid curve is a nonlinear least-square fit of the data to the function Vf=aVL 0
(8)
where a and b are the parameters of the curve fit. This fit yields b = 1.5 + 0.2 with a 95% confidence level obtained from the t distribution. A similar curve fit for the sooting flame yields b = 1.4 + 0.2, which shows that this result is independent of stoichiometry. Normally, strong photoionization of atoms in the directly excited state or saturation of the two-photon transition by the UV beam will cause b < 2, while photolysis, which results in the growth of atomic hydrogen, will cause b > 2 [25]. Previous measurements in hydrogen flames [24] showed a quadratic dependence of the fluorescence signal on the measured laser power, which indicates that photoionization of atoms in the directly excited state and saturation of the twophoton transition by the UV beam are insignifl140
i
i
i
i
120
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Number Density Measurements Our investigation of two-photon fluorescence by atomic hydrogen in premixed C2H4/O2/Ar flames was conducted at subatmospheric pressure for the following reasons. 1. Compared to flames at one atmosphere, subatmospheric pressure favors higher mole fractions of intermediates, such as atomic hydrogen. 2. Quenching is much lower, resulting in more fluorescence for the same number density. 3. Reactions occur at a slower rate, effectively spreading the flame front and increasing the spatial resolution within the reaction zone.
8 .,
cant. This conclusion is corroborated by the pulse characteristics given in Table 2. We also investigated the possibility of absorption by some hydrocarbon that subsequently pyrolyzes into species other than atomic hydrogen. The rates of absorption and pyrolysis required to simulate the observed dependence on the fluorescence signal significantly reduce the population of the absorbing species and thus violate Beer's law. A full analysis of this nonlinear absorption is given by Salmon [25]. Although this phenomenon may explain the observed nonquadratic dependence, further investigation is required to verify its significance in our experiments. The fluorescence spectrum revealed barely detectable radiation distributed over the entire spectral range. We also detected scattered radiation from the fifth Stokes component at 643 nm, which was generated by the Raman cell. These sources did not affect our measurements because we used a monochrometer for narrow-band detection. However, care is needed if dielectric bandpass filters are to avoid scattered radiation inadvertently transmitted through the filter, thus corrupting the fluorescence measurements.
20
0
I0 I I I I 5 I00 150 200 250 LASER VOLTAGE SQUARED(mV 2)
Fig. 3. Fluorescence signal as a function of the squared laser signal measured by a photodiode at 5 nun above the burner in the stoichiometric C21L/O2/Ar flame at a pressure of 72 Tort.
The favoring of intermediates at subatmospheric pressures ameliorates any photochemical effects that may be present and improves the signal-tonoise ratio of the measurements. A comparison of fluorescence measurements of atomic hydrogen and predictions from partial-
228
J . T . SALMON and N. M. LAURENDEAU
equilibrium calculations is shown in Fig. 4 for the stoichiometric flame at 72 Ton.. Also shown are profiles of the flame temperature and the number density of OH that were used in the partialequilibrium calculations. The H-atom measurements are calibrated by partial equilibrium at a height of 50 mm above the burner. The two Hatom profiles, which were the first and last ones measured in the experiments, show no long-term drift affecting the results. The fluorescence profiles in these flames are normalized by VL 3/2 rather than the VL 2 in Eq. 6, which reflects the measurement of fluorescence intensity as a function of laser power discussed in the previous section. Although the laser power was about the same for many of the points of the two profiles in Fig. 4, the laser power was somewhat erratic during the first profile, especially around a height of 5-10 mm above the burner. Normalizing by VL 3/2 results in the least scatter in the data, which is consistent with the nonquadratic behavior of the fluorescence signal with respect to the incident laser power. Although the fluorescence measurements are corrected for quenching by dividing by T 1/2, the temperature profile yields a maximum correction of about 2 %. Figure 4 also indicates that partial equilibrium is valid at heights greater than 25 mm from the burner and begins to break down below this height. The breakdown results in an underprediction of the number density of atomic hydrogen as I0
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the reaction zone is approached, which is the same trend found in previous hydrogen flames [24]. The peak concentration of atomic hydrogen is about four times the peak concentration of OH, whereas both profiles peak at about the same height above the burner. Vertical profiles of H-atom number densities in the fuel-rich (4, = 1.7) flame are shown in Fig. 5, along with profiles of the flame temperature and the number density of OH. As in the stoichiometric flame, the fluorescence measurements are calibrated by partial equilibrium at a height of 50 mm above the burner, and the pressure is 72 Ton'. The temperature profile is used again to correct for variations in quenching within the flame. This correction is less than 3 % at all positions in the flame. Atomic hydrogen concentrations predicted by partial equilibrium, also shown in Fig. 5, reveal the same trend as Fig. 4 except that partial equilibrium remains valid down to a height of 20 mm instead of 25 ram. The relative peak heights of the hydrogen atom and OH number densities are approximately 13:1 compared to 4:1 for the stoichiometric flame. In constrast to the results for the hydrogen flames [24], the number densities of atomic hydrogen in the ethylene flames are lower in the fuel-rich case than in the stoichiometric case. The higher flow rates in the fuel-rich flame resulted in less heat loss to the burner and thus a higher postflame temperature (1695 K in the fuel-rich
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H-Atom Fluorescence case compared to 1480 K in the stoichiometric case). For the fuel-rich flame, Reactions 7b and 7d are the only reactions that have any effect on the calculated number density of atomic hydrogen. The higher temperature for the fuel-rich flame gives an equilibrium constant for Reaction 7b about half of that for the stoichiometric case, while the equilibrium constant for Reaction 7d is 40% of that for the stoichiometric case. The trend in both of these equilibrium constants favors less atomic hydrogen in the fuel-rich flame, despite the increased amount of total hydrogen atoms required by the stoichiometry. Because variations in quenching have been accounted for by using a temperature dependence in the number-density calculations, the calibration factors for the stoichiometric and fuel-rich flames should be equal to within the uncertainty of the calibration. The calibration factor for the fuel-rich flame, however, is about 27% higher than that for the stoichiometric flame. This difference could be caused by the following: 1. failure of kinetic theory to predict variations in the local quenching rate based on an average cross-section that is independent of the local composition; 2. uncertainties in the calibration introduced by the sensitivity of the predicted number density of atomic hydrogen to uncertainties in the input molar flow rates, the OH concentration, and the temperature; 3. concentrations of unburned hydrocarbons in the postflame gases that are not accounted for in the partial-equilibrium calculations. Failure of kinetic theory to predict the variation in the local quenching rate coefficient seems doubtful. Using PICLS, no measurable change in the quenching rate coefficient was observed in the postflame zone of premixed H2/O2/N2 flames at a pressure of 72 Torr for 0.6 ~< ,I, ~< 1.5 [23]. The calibration factor is sensitive to variations in the fuel-oxidizer ratio, the OH concentration, and the flame temperature [25]. These sensitivities are shown in Table 3 for both the stoichiometric and fuel-rich flames. Note that the uncertainties in the calibration factor owing to uncertainties in the fuel-oxidizer ratio, OH concentration, and flame
229 temperature are higher in the stoichiometric flame by about 200%, 100%, and 100%, respectively. Moreover, the measured difference in the magnitude of the calibration factor between the fuel-rich and stoichiometric flames (27%) is clearly within the estimated total uncertainty in the calibration factor for these two flame conditions (16-39%). We also investigated the sensitivity of the calibration factor to uncertainties in the fueloxidizer ratio and OH number density for a fuellean (~I, = 0.70) flame having the same flame temperature and OH number density as in the stoichiometric flame. For a 4% variation in the fuel-oxidizer ratio, the calibration factor varies by only 5 %; however, an 11% variation in the OH concentration yields a 31% variation in the calibration factor. We thus conclude that the sensitivity of the calibration factor to changes in the OH concentration and the fuel-oxidizer ratio in fuellean and stoichiometric flames makes fuel-rich flames most amenable to calibration by partial equilibrium. A possibly adverse effect on partial-equilibrium calculations in fuel-rich hydrocarbon flames lies in the failure of the technique to include unburned hydrocarbons, including soot, in highly fuel-rich and sooting flames. Failures to account for carbon and hydrogen atoms bound in these species is analogous to the introduction of additional fuel to the mixture, resulting in artificially high predictions of atomic hydrogen concentrations. For TABLE 3 Percent Uncertainty in Calibration Factor Owing to Uncertainties in the Experimental Parameters for the Stoichiometric and Fuel-Rich Flames a Equivalence Ratio 1.0
1.7
Fuel-oxidizerratio O H concentration
28% (4%) 24% (11%)
9 % (2%) 11% (11%)
Flame temperature Fluorescence measurements
11% (20K)
6 % (20K)
5% (5%) 39%
5% (5%) 16%
Total
*The experimental uncertainty responsible for each calibration factor effect is given in parentheses.
230 instance, failure to account for 5% of carbon and hydrogen in the form of unburned hydrocarbons results in a 20% overprediction of the calibration factor at an equivalence ratio of 1.7. Because the calibration factor for the fuel-rich flame is 27 % higher than that for the stoichiometric flame, part of the measured difference might be caused by this effect. Thus, slightly rich flames appear to be the best candidates for calibrating by partial equilibrium. Another possible answer to the dilemma of calibrating in fuel-rich to sooting flames lies in the use of PICLS. As described by Salmon and Laurendeau [17, 24], P I C L S o v e r c o m e s the effect of quenching by strongly photoionizing atoms in the directly excited state. The resulting measurements of number density are independent of quenching and, hence, only need to be calibrated at one flame condition. The calibration may be conducted even in a hydrogen flame. Because PICLS is independent o f quenching, there is no restriction on the flame used for calibration.
CONCLUSIONS We have quantitatively measured number densities of atomic hydrogen in flat, premixed, C2H4/O2/Ar flames by using two-photon-excited fluorescence. Two flames at a pressure of 72 Torr were investigated; the fuel-equivalence ratios were 1.0 and 1.7. The fluorescence measurements were calibrated by partial equilibrium at a height of 50 nun from the burner, which is well into the postflame zone, and were corrected for variations in quenching by employing the measured temperature and kinetic theory. The accuracy of the number densities is 40% for the stoichiometric flame and 15% for the fuel-rich flume. The uncertainty for atomic hydrogen in the fuel-rich flame may be higher because the partial-equilibrium calculations do not account for unburned hydrocarbons. The lack o f accuracy in the stoichiometric flame is caused by an increased sensitivity of the partial-equilibrium calculations to uncertainties in both the equivalence ratio and the measured OH concentration. Slightly rich flames appear to be the best candidates for calibrating
J . T . S A L M O N and N. M. L A U R E N D E A U measurements of atomic hydrogen by partial equilibrium. This research was supported by the U.S. Department o f Energy (Office o f Basic Energy Sciences). J. T. Salmon was also supported by a Newport Research A w a r d f u n d e d by Newport Corp. and administered by the Optical Society o f America.
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