Quantitative measurement of atomic hydrogen in low-pressure methane flames using two-photon LIF calibrated by krypton
Introduction
Atomic species, in particular atomic hydrogen (H-atom), are involved in most elementary reactions of combustion chemistry. H-atoms are mostly formed from fuel H-abstraction, and participate in the dominant radical chain branching reaction, (R1) H + O2 ⇌ O+OH, and exothermic reaction (OH+CO ⇌ H+CO2) in flames. As with many small radicals, knowing their absolute concentration within the flame is important to better understand the kinetic reactions and detailed mechanisms. In stretched flames, the extinction strength rate and laminar flame speed directly interfere with these two reactions [1,2]. The reactions of formation and consumption of H-atoms compete strongly depending on the flame strain rate.
Two main categories of techniques can achieve quantitative detection of atoms, in particular H atom. The first is based on molecular beam mass spectrometry (MBMS) after gas probe sampling. The second relies on optical detection. In MBMS experiments, H-atom profiles were measured by ionizing H-atom slightly above its appearance ionization potential [3], [4], [5], [6], [7], [8]. The measurements were mainly carried out in laminar low-pressure premixed flames. The absolute quantification of atoms is performed assuming that partial equilibrium is reached in the burned gases [3,6] or by applying the method of relative cross‐sections for the ionization [7,9]. The absolute mole fraction of H-atom is reported within a factor of two using either methods of quantification [10]. Unlike the aforementioned probe sampling technique, the in situ optical detection of H atom is non-intrusive. However, this method is challenging due to the 10 eV gap between the ground and the first excited electronic states of atomic hydrogen. The single-photon excitation of H atom requires vacuum-ultraviolet radiation, which is strongly absorbed by most gases of the atmosphere, making it impractical in most combustion studies. Behind shock waves, this single absorption could be achieved by atomic resonance absorption spectroscopy (ARAS) [11], [12], [13], [14], [15], made possible by the specific configuration of the shock tube apparatus. The absolute concentration is then directly obtained from this absorption technique. The combination of ARAS/shock-tube is especially well suited for measuring the thermal dissociation rates of molecules of interest in combustion and producing H atoms or specific reaction rates involving the H-atom at high temperatures. Thus, Hanson's group measured the reaction rate constant of the reaction (R1) H + O2OH+O [16]. In another context, Rennick et al. [17] were able to measure the population on level n = 2 of H atom, largely populated due to the electronic excitation in their plasma. The calibration of the H atom concentration, probed at 656 nm (Balmer-β, n = 2 → n = 4) was carried out by using Cavity Ring-Down Spectroscopy (CRDS) in a H2/Ar arc jet discharge.
In plasma and flame environments, H-atom is mainly detected using techniques involving a two-photon excitation from the ground state (n = 1), such as two-photon laser induced polarization spectroscopy (TP-LIPS) [18], [19], [20] and two-photon laser induced fluorescence (TPLIF) [21], [22], [23], [24], [25], [26]. Several other multi-photon excitation variants have also been proposed [24,[27], [28], [29]. TP-LIPS is based on the direct measurement of the two-photon absorption, which gives it the advantage of not being affected by quenching. The technique has been applied in several plasma applications [18], and only in a few combustion environments [19,20,29]. We are indebted to Dux et al. [18] who have introduced an original way of calibrating the absolute density of the H-atom by using TP-LIPS from a standard response from xenon. The authors proposed to compare the two-photon absorption process of atomic hydrogen along the transition (1S→2S) at 243.2 nm, and the one of xenon along the transition 5p6→5p56p[1/2]0. This calibration method was later demonstrated in atmospheric flames by Grützmacher et al. [19]. It requires a removable xenon reference cell at room temperature. Even though it has a very interesting potential, the technique has only been used rarely in flames, maybe because of its complexity and, as pointed out by Grützmacher et al. [19], it is only accessible if pulsed UV laser radiation of sufficient peak power and single longitudinal mode spectral quality is available. In addition, the overlap configuration of the two required laser beams results in a long-length overlap volume, which in turn causes spatial averaging effects in flames. On the contrary, TPLIF at 205 nm is one of the most widespread methods for H-atom detection not only in flames [21], [22], [23],[30], [31], [32], [33], [34], [35], but also in plasmas [36], [37], [38], [39], [40]. It is a two-photon process between the states n = 1 and n = 3 of H-atom followed by the detection of fluorescence when it relaxes to the n = 2 state at 656.3 nm. Care must be taken to avoid interferences (photoionization, photolytic and photochemical effects [31,[41], [42], [43], [44], [45], [46]) and stimulated emission (SE) [21,47], which can each alter the linear relationship between the TPLIF signal and the atomic concentration. It was shown that the SE threshold is higher by using a ns-pulse laser compared to the shorter pulse lasers (ps or fs), while the photochemical effects (yielding to H formation) prevail with a longer pulse [30,44]. In the absence of these problems, the TPLIF signal should follow a quadratic regime with the laser energy. The TPLIF signal is then directly proportional to the atomic concentration, provided it has been corrected for the quenching rate Q. The quenching rate can be determined from the inverse of the fluorescence lifetime τ= 1/(A + Q) where A is the total spontaneous emission rate of the excited state of H-atom. However, due to its very short lifetime, the overall quenching rate is difficult to measure (especially when using a ns-pulse laser, and in atmospheric flames). Only few data obtained in low-pressure flames are reported [22]. Moreover, its calculation is obstructed by the lack of precise quenching cross-sections database determined at high temperatures [48,49]. Despite these difficulties, TPLIF has been recently reconsidered for measuring H-atom distributions in atmospheric flames (see e.g. [32], [33], [34], [35]). Except in [34], these studies used fs-lasers which may limit the impact of the quenching provided that they are combined with fast detections. Once measured, the TPLIF signals, corrected for quenching, can be converted into quantitative data. Only a few quantitative values of H-atom concentration are reported in flames and plasmas. Most are obtained after a comparison with a known or calculated concentration of H-atom measured in a separate set-up. Bittner et al. [22] converted the relative TPLIF signal in low-pressure H2/O2/Ar flames into an absolute H-atom density, based on a calibration performed with the titration of NO2 in a flow-tube. Juchmann et al. [50] have calibrated the H-atom density from a calorimetric determination in a dc-arcjet. Wouters et al. [51] undertook the calibration of H-atom density, from a time-resolved measurement of the fluorescence decay in a microwave discharge in H2. The TPLIF signal was also converted into an absolute H-atom density from the comparison of the experimental signal obtained in a Hencken burner with kinetic calculations performed assuming an adiabatic equilibrium [33], or in a Bunsen burner with adiabatic flame calculations [45].
Goehlich et al. [52] have transposed the aforementioned method of calibration of TP-LIPS signals to atomic species detected by TPLIF by comparing their signal with that of a rare gas (xenon) at room temperature. Krypton has also been considered as a good candidate for the calibration, because it exhibits a two-photon resonance with excitation energies close to those of H-atom and it presents a relative absorption cross-section half that of H according to Niemi et al. [37] and Boogaarts et al. [38]. The ratio of the two-photon absorption cross-sections of Kr and Xe was measured by Elliott et al. [53]. The calibration approach of H-atom TPLIF signals has been widely applied in plasmas [37], [38], [39], [40],[54], [55], [56], [57], however, to the best of our knowledge, never in flames.
Following our previous study undertaken for O-atom calibration [58], the present work aims to measure the absolute concentration of atomic H species in flames previously stabilized in our laboratory. The absolute calibration of the H-atom requires a well-defined calibration flame where the H-TPLIF signal is directly related to that emitted by the noble gas, Kr according to [37,38]. In order to convert the relative signal into an absolute mole fraction, attention was paid to avoid interference effects or SE, and to the control of the quenching variation along the vertical axis of the flame. The experimental atomic hydrogen profiles were compared with the simulated ones by using the Premix code [59] with the detailed kinetic model developed in our laboratory [60].
Section snippets
Low-pressure burner and gas supply
Experiments were undertaken in laminar low-pressure methane flames stabilized on a 6-cm diameter bronze water-cooled McKenna burner. Temperature of the porous burner was stabilized at 293 K and 333 K in N2 and Ar diluted flames, respectively. The pressure is regulated within ±0.3% by using an automatic valve (Oerlikon CMOVE/MOVE1250). The burner is mobile in translation in the vertical axis allowing the measurements of species profiles as a function of the height above the burner (HAB). Details
Method for absolute calibration of TPLIF signals of atomic hydrogen
According to [37,52], the H-atom TPLIF signal can be converted into an absolute mole fraction by intercomparing with the TPLIF signal of krypton. In this section, we present the spectroscopy of H and Kr atoms and the related spectroscopic constants and coefficients, which are required for the quantitative measurement of H-atom concentration. Then, we briefly explain the basic equations, which were used to obtain the concentration from the LIF signals of H and Kr atoms.
Quenching rates
One of the main difficulties in the calibration procedure lies in the evaluation of the quenching rate of the two atoms (H and Kr) in Eq. (2). The quenching rate is defined by where Nt is the total density, is the collider mole fraction and is the quenching coefficient that is equal to the product between the quenching cross-section and the relative mean speed . is the reduced mass, is the Boltzmann constant and T is the temperature.
The quenching
Quantification of TPLIF signal in the calibration flame
TPLIF measurements require that some conditions to be fulfilled. Particularly, Eq. (2) used in the calibration procedure implicitly relies on the fact that photolytic effects, photoionization and stimulated emission (SE) are very limited if not absent. If such, a quadratic regime is effectively reached. The LIF signals plotted against the laser energy on a logarithmic scale makes it easy to verify the fluorescence regime. These plots were performed for H and Kr atoms and provided in Fig. S2 of
Conclusions
In this work, the two-photon laser induced fluorescence technique was applied to measure the concentration profiles of atomic hydrogen in laminar low-pressure premixed flames. Excitation of the transition from its ground state to state n = 3 was performed by two-photon absorption at 205 nm and collecting the fluorescence from n = 3 to n = 2 at 656.3 nm. For the first time in flames, the TPLIF signals from the H-atom have been calibrated by using the TPLIF signal from krypton, excited at
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work is a contribution to the CPER research project CLIMIBIO. The authors thank the French Ministère de l'Enseignement Supérieur et de la Recherche, the Hauts-de-France Region and the European Funds for Regional Economical Development for their financial support to this project.
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