Abstract

Spatially and temporally resolved temperatures are measured in counterflow diffusion flames with a tunable diode laser absorption spectroscopy (TDLAS) technique based on direct absorption of CO2 near 4.2 µm. An important aspect of the present work is the reduction of the beam diameter to around 150 µm, thus providing high spatial resolution that is necessary to resolve the high axial temperature gradient in counterflow flames. The temperature non-uniformity was taken into account through both hyperspectral tomography and the multiline technique with profile fitting, with the latter one being capable of providing temporally resolved data. The proposed methods were used to measure four counterflow flames with peak temperature ranging from 1654 to 2720 K, including both non-sooting and sooting ones.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Considering the worldwide thirsts for affordable energy, combustion of hydrocarbon fuels is still expected to play a major role in energy supply, especially in developing countries where population and economic growth are taking place at a rapid pace. Nevertheless, a consensus has been reached that combustion energy must be utilized in an efficient and environmentally friendly way. Knowledge on fundamental combustion and pollutant formation mechanisms are essential to achieve this goal, rationalizing the immense efforts devoted to combustion chemistry research in the past several decades [1].

Under realistic conditions, combustion kinetics are in complex interplay with convective transport, molecular diffusion as well as thermal radiation [2]. Therefore, practical combustion devices may not be suitable for detailed examination of combustion kinetics. Laboratory-scale reaction systems with well controlled boundary conditions are instead favored for kinetic research. Counterflow diffusion flame (CDF), where a flame front is established between two opposing streams of fuel and oxidizer, is a canonical flame configuration representative of many features of practical diffusion combustion systems [3]. In this regard, CDF has been routinely employed to investigate fundamental aspects of diffusion combustion such as flame structure [4,5], ignition [6], extinction [7], NOx [8] and soot formation [9]. In addition, CDF serves as a physical realization of the laminar flamelet concept which are widely used for the modelling of practical turbulent flames [10]. An additional advantage of CDF is its quasi-1D nature (with proper boundary conditions), meaning thermochemical properties such as temperature, species mole fractions and axial velocity in the core region of the flame does not vary in the radial directions. This property of CDF greatly facilitates data interpretation and numerical modelling with detailed chemistry.

Chemical reaction rates are critically dependent on temperature; accurate determination of flame temperature is an absolute necessity if reliable kinetic information is to be extracted from CDF experiments. Unfortunately, temperature measurements in CDFs have never been trivial, in particular for flames with high soot loadings. Frequently-used thermometry techniques for CDFs include thermocouple measurement [11] and two-color pyrometry based on either flame-generated soot particles or thin SiC filaments inserted inside the flame [12], and laser induced fluorescence of flame generated NO [13] or OH radicals [14]. Thermocouple measurements are subject to notable uncertainties from corrections for radiation cooling and conduction losses; they are also intrusive and may notably affect the thermochemical structures of the flames, a disadvantage shared by the technique of thin filament pyrometry. Here it may be important to point out that the issues of intrusiveness are notably more pronounced in CDF due to its much smaller flame area and stronger axial temperature gradient as compared to, for example, flat premixed flames or coflow jet flames. In addition, sooting CDFs with oxygen enrichment—such as those of the soot formation/oxidation type [9] that are relevant for soot research—can have peak temperature well beyond the upper limit (i.e., ∼2000K) for thermocouples. Soot pyrometry is a non-intrusive technique; however, measurement can only be made in regions where soot particles exist. The accuracy of the measurement is also highly dependent on knowledge of the optical properties of soot particles, which is by itself a complicated research topic [15]. In fact, in a recent work Gleason et al. [16] had to rely on temperature data measured with thermocouples to calibrate pyrometry data. The various LIF methods require bulky and costly laser sources and high-sensitivity detector systems, in addition to potential interferences from emissions from PAH and soot particles in the flames.

A promising non-intrusive technique for temperature sensing is laser absorption spectroscopy (LAS). When the laser wavelength is tuned to be resonant with closely spaced transitions of a target species from different rovibrational quantum states, the population ratio as inferred from the measured absorption spectrum can be used for thermometry. A minimum of two transition lines need to be measured to derive temperature and the number concentrations of the target species can be simultaneously obtained. A literature survey reveals that previous laboratory flame studies using LAS thermometry were typically based on near- or mid-infrared absorption of H2O [17], CO2 [18] or CO [19] molecules, and a majority of these studies were performed in flat premixed flame [20] or coflow diffusion flames [21]. Reports on temperature sensing with LAS in counterflow diffusion flames were surprisingly scarce. The only relevant work, as far as the authors are aware of, is a very recent one by Emmert et al. [22], who measured axial profiles and radial distributions of temperature of a series of highly diluted methane/acetylene counterflow diffusion flames. A close scrutinization of the reported data showed there was an uncertainty of around 500 µm in terms of axial position, indicating a relatively large diameter of the probing beam. We will come back to this point in a later section.

LAS is a line-of-sight (LOS) technique so that the temperature measured should be interpreted as a path-averaged result [23]. This poses no problems for cases where a uniform distribution of temperature is expected along the LOS. However, radial variations of temperature may be present even in simple laboratory flames such as the aforementioned quasi-1D CDF. Although the central region of a properly established CDF can be regarded as one-dimensional, a radial variation at the edge of the flame is unavoidable because of, for example, the thermal boundary layer, heat losses to the surrounding nitrogen curtain flow and buoyancy effects. Neglecting this non-uniformity would cause notable errors in LAS temperature measurements, as confirmed by previous studies of Zhou et al. [24]. in flat flames on a Hencken burner and also discussed in detail by Ma et al. [25] who investigated premixed flat flame stabilized on a McKenna burner.

Tomographic reconstruction is an effective method to deal with non-uniformity along the LOS [2628]; it can be used to obtain spatially resolved data from multiple LAS measurements along paths traversing different parts of the flames (and sometimes in different directions [29]). This would require sufficient optical access, sophisticated beam alignments and possibly expensive laser diode / detector arrays. For axisymmetric flames such as CDF, a simpler 1D tomography technique can be used for which LOS measurements are made at a discrete number of radial locations [30]; while there is no need to vary beam directions. A typical realization would involve radially traversing the flame relative to a fixed laser beam [31] so that only one pair of light source and detector is needed. However, since physically scanning the burner is a relatively slow process, only stable or unsteady flames with periodic variations [32] (through phase-locked measurements) can be measured. It would be challenging, if not impossible altogether, to use such method to obtain temporally resolved data in non-periodical transient processes. On the other hand, there is indeed a great need to study transient CDFs to gain fundamental understanding of 1) the interaction between turbulence and slow chemistries such as NOx and soot formation [3335]; 2) critical flame phenomena such as ignition and extinction [36].

Multiline thermometry is an alternative method to account for the non-uniformity along the LOS [37,38]. As opposed to the more traditional two-line technique, projections are made for a series of different absorption lines (could be for different species) to provide enough constraints for the derivation of the temperature distribution that are discretized along the LOS. In theory, the required number of absorption lines are dependent on the total number of unknowns (i.e., temperature and species mole fractions at each discretized grid points); therefore, for applications requiring high spatial resolution the large number of unknowns would demand many transition lines to be projected along the same LOS. This simply means that many laser sources (thus covering the transition lines) are needed, in addition to the challenge of aligning these beams to have the same path. More importantly, the correlation between temperature and concentration of the probed species, as well as their locations along the LOS, are in general not obtainable through 1D measurement [38], limiting the practical applicability of the method. Fortunately, there are cases in which temperature distribution along the LOS can be fitted reasonably well by functions dependent only on a small number of fitting parameters. For instance, simple trapezoid profiles and Boltzmann fitting profiles [25] have been proposed to characterize the radial variation of temperature in a Hencken burner and a flat premixed flame, respectively. With such a prior information on the general shape of the profile, the actual distribution of the temperature and species concentration can then be determined by multiline absorption measurements, provided the number of absorption features are larger than the number of unknown fitting parameters. If applicable, mutli-line thermometry has the distinct benefits that the non-uniform temperature can be determined by measuring along a single beam path, eliminating the need to scan different flame regions, and thus greatly reducing the measurement time. We will demonstrate in this work that a single laser would suffice to measure the non-uniform temperature in CDFs at kHz frequencies, enabling spatially and temporally resolved measurements at low cost. It may be useful to point out that, to the best of the authors’ knowledge, no previous work has applied mutli-line thermometry with profile fitting in CDFs.

There are additional challenges to apply LAS in CDFs. As compared to burner-stabilized premixed flames or coflow jet diffusion flames, a CDF is usually more confined in space and thus is featured with large gradients (along the axial direction) of temperature, species concentration and soot volume fractions. The gradient can be even stronger under high strain rate and/or high-pressure conditions. As a result, diagnostic technique for CDFs needs to have a high axial spatial resolution, necessitating a small beam diameter if LAS is to be employed. Indeed, a recent work on soot measurement in CDFs with light extinction [39] shows a beam diameter of ∼200 µm is required; larger beam size would induce notable measurement errors due to the smearing effect. In particular, it was shown that an increase of beam size from 200 to 600 µm led to a 30% error of peak soot volume fraction in an ethylene CDF. Therefore, additional efforts are needed to manipulate the optical setup for minimum beam diameter in the measurement volume. The high temperature (and thus density) gradient of CDF can induce notable beam steering effect, the correction of which may further complicate the optic setup. Details on this topic will be provided in the section on wavelength selection; here it suffices to note the requirement of beam manipulation for minimum beam size unavoidably increases the beam path in free space, making the absence of ambient absorption more critical for CDF applications.

We report in this work calibration-free, non-intrusive and spatially resolved temperature measurements in CDFs using a single interband cascade laser (ICL) based on direct absorption at the R-branch band head of ν3 fundamental of CO2 near 2397 cm−1 [21]. Special efforts were undertaken to reduce beam diameter to improve spatial resolution, which is necessary considering the high axial temperature gradient in CDFs. The proposed method was shown to be applicable to both non-sooting and sooting CDFs and was able to measure high temperature CDFs of the soot formation/oxidation type with peak temperature beyond 2600 K, for which the traditional thermocouple technique cannot be used. Non-uniformity along the LOS for CDFs was resolved through both hyperspectral tomography and multiline absorption with profile-fitting. Satisfactory agreements were obtained confirming the validity of both methods. The potential of using the multiline absorption for temporally resolved measurements under transient conditions were also demonstrated, which is a first attempt of this type in CDFs. The present experimental temperature and CO2 profiles can also be used for quantitative assessments of the uncertainty associated with the intrusiveness of thermocouples and gas-sampling mircro-probes, respectively, in CDFs where these effects of intrusiveness may not be trivial.

2. Theoretical background

This section begins with a brief review of the theory of LAS-based thermometry. Tomography inversion and multiline thermometry, both of which can account for the non-uniformity along the LOS, are then introduced. Subsequently, special requirements of applying LAS in CDF are discussed with specific absorption lines determined accordingly. Finally, it is shown that the radial distribution of temperature and species concentration in typical CDFs can be accurately represented by a simple Boltzmann fitting profile; with such a prior information on the shape of the temperature distribution, it is confirmed that multiline absorption performed along a single LOS can be used for spatially-resolved measurements of temperature in CDFs.

2.1 Laser absorption spectroscopy

2.1.1 Spectroscopic fundamentals

When a laser beam with frequency ν was sent through a gas medium with path length L, the fractional transmission, which can be directly measured, is expressed through the Beer-Lambert law as [40]:

$${(\frac{{{I_t}}}{{{I_0}}})_v} = \textrm{exp} \left( { - \int_0^L {{k_v}(x )dx} } \right)$$
from which the spectral absorbance αν can be obtained:
$${\alpha _v} ={-} \ln {(\frac{{{I_t}}}{{{I_0}}})_v} = \int_0^L {{k_v}(x)} dx$$

In the above equations, I0 and It are respectively the incident and transmitted light intensity; x is a position variable representing the location along the LOS; kν is the local spectral absorption coefficient due to all transitions of the target absorbing gas occurring at ν:

$${k_v}(x) = \sum\nolimits_j {P \cdot X(x)} \cdot {S_j}(T(x)) \cdot {\varphi _j}(v - {v_{0j}})$$
where P is gas pressure, X is mole fraction of the absorbing gas (we assume there is no other species interfering absorption at ν), Sj, φj and ν0j are the line strength, line shape function and central frequency of transition j, respectively. These parameters are typically available from spectroscopic databases such as HITEMP [41], although data regarding φj should be used with caution as they can be affected by complicated collisional broadening by surrounding gases. Note Sj depends on the local gas temperature T.

In typical experiments, a tunable laser would be set up to scan across a range of laser frequencies to cover several transition lines. If there are no overlapping transitions, the uncertainties related to φj can be avoided by integrating both sides of Eq. (3) over an individual absorption feature j:

$${k_j}(x) = \int_j {{k_v}(x)} dv = \int_j {P \cdot X(x) \cdot {S_j}(T(x)) \cdot {\varphi _j}(v - {v_{0j}})} dv = P \cdot X(x) \cdot {S_j}(T(x))$$
considering $\int_j {{\varphi _j}(v - {v_{0j}})} dv = 1$ by the definition of φj (i.e., the line-shape function is normalized).

To measure temperature, knowledge of the spectrally integrated absorption coefficient ${k_j}(x)$ needs to be known across a minimum of two separate absorption lines (e.g., 1 and 2) so that

$$\frac{{{S_\textrm{1}}(T(x))}}{{{S_\textrm{2}}(T(x))}} = \frac{{{k_1}(x)}}{{{k_2}(x)}}\frac{{P \cdot X(x)}}{{P \cdot X(x)}}\textrm{ = }\frac{{{k_1}(x)}}{{{k_2}(x)}} = R$$
becomes a known value. Local temperature T(x) can then be derived after consulting the line strength databases through Eq. (6).
$$T = \frac{{\frac{{hc}}{k}(E_2^{^{\prime\prime}} - E_1^{^{\prime\prime}})}}{{\ln (R) + \ln (\frac{{{S_2}({T_0})}}{{{S_1}({T_0})}}) + \frac{{hc}}{k}\frac{{(E_2^{^{\prime\prime}} - E_1^{^{\prime\prime}})}}{{{T_0}}}}}$$
where $(E_1^{^{\prime\prime}}$, $(E_2^{^{\prime\prime}}$ are low-state energy of the two absorption lines, T0 is a reference temperature. With temperature known, it is straightforward to obtain X(x) from Eq. (4) using data for either transition. LAS is line-of-sight technique; to apply Eq. (5) it is necessary to obtain local values of the spectrally integrated absorption coefficient (i.e., kj(x)) for the two transitions. Two approaches are available for this purpose. In the first method, we can integrate Eq. (2) over the absorption feature j to obtain absorbance Aj:
$${A_j} = \int_j {{\alpha _v}} dv = \int_j {\int_0^L {{k_v}(x)dx} } dv = \int_0^L {{k_j}(x)dx}$$

For axisymmetric CDFs, kj(x) can then be obtained through Abel inversion from a series of Aj evaluated along LOS traversing different radial locations of the flame (inversion algorithms to be described later). Alternatively, we can perform Abel inversion directly to αν to get kν(x), and spectrally integrate the latter to obtain kj(x). It should be noted that this second approach is more computationally intensive as the inversion algorithm needs to be run at every frequency; however, it has the advantage of being able to reconstruct frequency-resolved kν at each spatial grid point.

It is important to note Eq. (5) is only useful when the selected two absorption lines have isolated features (i.e., no overlapping line shape function from other transitions) so that the spectral integration over the absorption feature can be achieved. However, there are also cases in which many absorption lines center in a narrow spectral region, and the various line broadening mechanisms would result in significant line overlapping so that individual transition lines cannot be reliably deconvoluted. Under such conditions, it is necessary to first obtain local absorption spectra, i.e., kν(x), over a relatively broad spectral region (limited by the laser). A nonlinear least square fitting method can then be used to fit the measured spectra with T(x) and X(x) as free fitting parameters:

$$\mathop {\min }\limits_{T(x),X(x)} \int_{ - \infty }^{ + \infty } {{{(\sum\nolimits_j {PX(x){S_j}(T(x)){\varphi _j}(v - {v_{0j}}) - {k_v}{{(v;x)}^{measured}}} )}^2}} dv$$
where the line shape function φj(ν-ν0) is typically modeled via a Voigt profile. The line width parameters for φj can be obtained from spectroscopic databases; alternatively, they can also be determined as optimization parameters during the non-linear fitting process when the database is not appropriate to represent line broadening due to the complex gases in combustion applications.

2.1.2 One-dimensional tomography

As mentioned previously, due to non-ideal boundary conditions and/or edge effects CDFs may have temperature variations along the radial direction. Tomographic inversion is an effective method to reconstruct a spatial distribution of absorption coefficients from integrating projections along LOS. A schematic is shown in Fig. 1 to clarify the conversion from projection data (spectral absorbance αν) to local values (spectral absorption coefficient kν(x)), the two of which are related through:

$${\alpha _v}(x) = 2\int_x^R {\frac{{{k_v}(r)r}}{{\sqrt {{r^2} - {x^2}} }}} dr$$

For axisymmetric field, the domain to be reconstructed can be discretized into N nodes each of which represents a concentric ring around the symmetry axis, Fig. 1(b). With projections made at equally spaced radial positions, Eq. (9) can be numerically inverted using algorithms such as Onion-peeling (OP) or Abel-three-point (ATP) [30]. A general expression is:

$${\boldsymbol {Ab} = \boldsymbol {P}}$$
where A is a N×N matrix, b is a vector of the inversion results (i.e., kν at each node) and P is a vector of the N measured projection data. Such inversion algorithms typically involve ill-conditioned matrices and are sensitive to measurement noises. In this regard, methods such as Tikhonov regularization [42,43] can be used to stabilize the solution and reduce the inversion errors. In principle, new equations designed to ensure smoothness are added to the original Eq. (10) to form:
$$\left[ \begin{array}{c} {\boldsymbol {A}}\\ {\boldsymbol {\lambda} }{{\boldsymbol {L}}_{\boldsymbol {0}}} \end{array} \right]{\boldsymbol {b} = }\left[ \begin{array}{l} {\boldsymbol {P}}\\ {\boldsymbol {0}} \end{array} \right]$$
where λ is a regularization parameter to be obtained through the L-curve method [44]. L0 is a N×(N−1) matrix which serves as a gradient operator to ensure solution smoothness. As Eq. (11) represents an overdetermined system of equations, the solution b can be obtained through the least square fitting method.

 figure: Fig. 1.

Fig. 1. (a) Coordinate system for axisymmetric flames (radial slice at a specific burner height); (b) Discretization of the axisymmetric domain.

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As will be detailed later, we tested through numerical simulation several variants of the inversion algorithm and finally chose ATP with Tikhonov regularization, which was run for αν at every laser frequency with a resolution of 0.6 mm to obtain absorption spectra at each of the N spatial nodes.

2.1.3 Multiline thermometry with profile fitting

Tomography reconstruction requires physical movement of the flame relative to the beam and thus are not applicable in transient flames. Multiline thermometry is an alternative approach to resolve non-uniformity along the LOS with a potential to be used under conditions where temporal resolution is important. This is because for the multiline method, measurement along a single LOS would be sufficient provided the general functional form of the T and X radial distribution profile are known a prior. CDF is quasi-one-dimensional in nature, and the radial non-uniformity is mainly caused by edge effects. Therefore, it is reasonable to expect that the radial temperature (and species concentration) distribution can be divided into a core region where the scalars are relative constant, and an edge region where gradual transition towards ambient values takes place. As will be confirmed later, the radial profiles in CDF indeed have such characteristics; furthermore, radial distributions of temperature and species concentration can both be approximated by a Boltzmann profile with three function parameters. The purpose of the multiline measurement is to determine these function parameters.

To illustrate the procedures, we use generic distribution functions ${\cal T}$ (x;pr), ${\cal X}$ (x;qr) as an example to describe the radial profiles of temperature and the mole fraction of the target absorbing species, respectively, at a generic axial location (i.e., flame height). Here, x represents the radial distance, and pr and qr are the to-be-determined function parameters (both are 3×1 vectors in the case of Boltzmann distribution, to be elaborated later).

The determination of pr and qr from measured spectral absorbance αν is done via a nonlinear least-square fitting approach. First, an initial guess of the function parameter p0 and q0 is proposed; radial profiles of temperature and species mole fractions can then be calculated with the aforementioned distribution function ${\cal T}$ (x; p0), ${\cal X}$ (x, q0). With T and X distribution profiles known, it becomes relatively straightforward to calculate a local spectral absorption coefficient kν using Eq. (3). Numerically integrating kν along the LOS yields a first iteration of spectral absorbance Zν:

$${Z_v}(v;{{\boldsymbol {p}}_0},{{\boldsymbol {q}}_0}) = \sum\nolimits_i^N {\sum\nolimits_j {P{\cal X}} } ({x_i};{{\boldsymbol {p}}_0}){S_j}({\cal T}({x_i};{{\boldsymbol {q}}_0})){\varphi _j}((v - {v_{0j}});{x_i})$$
where N is the number of discrete spatial grids along the LOS. Note, the line shape function φj depends also on location because line broadening is related to local temperature and gas compositions. Obviously, with a pre-defined functional form of ${\cal X}$ and ${\cal T}$, different function parameters p0 and q0 would correspond to different absorption spectra. An optimization algorithm can be used to search pr and qr by minimizing the difference from the computed and the measured absorption spectra:
$$\mathop {\min }\limits_{{\boldsymbol {p}}\textrm{,}{\boldsymbol {q}}} \int_{ - \infty }^{ + \infty } {{{({Z_v}(v;{\boldsymbol {p}}\textrm{,}{\boldsymbol {q}}) - {\alpha _v}{{(v)}^{measured}})}^2}} dv$$

Such problems can be solved using either a brute-force enumeration method [25] or optimization algorithm such as the simulated annealing algorithm (SA) [45,46]; here wo chose to use the latter. In addition, in order to reduce the number of unknowns, we assume the distribution profiles of temperature and species mole fractions have the same functional form. Such assumption has been used in a previous work [47] and is confirmed to hold for the present CDFs.

2.2 Wavelength selection

The selection of appropriate absorption lines for LAS thermometry is influenced by temperature sensitivity, line strength and spectral isolation of the lines at the expected flame conditions. For our purpose, it is important to consider the special thermochemical features of CDFs when selecting target transition lines.

We first look at the requirement of temperature sensitivity. CDFs are frequently used for soot studies and in terms of sooting characteristics, they can be classified into soot formation (SF) and soot formation/oxidation (SFO) flames, depending on the relative position between the flame front and the stagnation plane [9]. SFO flame typically features a highly oxygen-enriched oxidizer stream so that the peak temperature in these flames may be much higher than that in typical hydrocarbon/air systems. It was shown in a previous study [48] that the computed peak temperature of a C2H4 SFO flames at critically sooting conditions could be as high as 2600 K. As a result, LAS thermometry designed to measure such CDFs need to have high temperature sensitivity at high temperature conditions. It may be worthwhile to mention here that considering the upper limit for thermocouple measurement are only around 1800K and the fact (to the best of our knowledge) that no previous studies have reported experimental temperature data using LAS for the aforementioned SFO flames, the need of an optic technique capable of accurately measure high temperature CDF is indeed pressing.

Regarding line strength, it is noted that typical laboratory CDF has a relatively small flame area with a diameter of around 1∼2 cm; this is to be compared to the ∼5 cm diameter of flat premixed flame on McKenna burner or diffusion flame on Hecken burner, both of which have been widely investigated with LAS. The small flame area directly translates to short absorption path, suggesting a strong line strength at high temperature is expected to ensure sufficient level of absorption along the LOS and thus a high signal to noise ratio (SNR). In addition, as we have already mentioned in the introduction section, CDFs are characterized by strong temperature gradient in the axial direction, especially under high strain rate and/or high-pressure conditions. To give an extreme example, a recent computation study [49] showed that for a C2H4 CDF with a strain rate of 200s−1 operated under 30 atm, the axial temperature gradient can reach as high as 3500 K / mm. To resolve such high gradient, it is essential to minimize the probing beam diameter. A simple pinhole is not sufficient due to beam diffraction; collimating optics along with a Galileo beam expander are helpful to reduce the angle of divergence of the beam from the laser source so that the expanded beam can then be refocused to a much smaller spot. Such optical arrangement would require a relatively long distance to be travelled by the beam before reaching the flame; therefore, it is essential to avoid absorption outside the flame. This means the selected lines should have negligibly small absorption under ambient conditions; if the ambient environment contains the target absorbing species, small line strength at room temperature is needed.

Transition lines that have isolated features are preferred in many cases as line overlapping could lead to difficulties for line deconvolution, which is necessary if Eqs. (4) and (5) are to be used for the derivation of temperature. However, since we would like to perform multiline absorption in the present work, it is beneficial to choose a spectral region in which several lines coexist. Even if these lines cannot be separated, Eq. (8) can still be used to obtain temperature and species concentration. However, it is preferred that the different lines are from transition of the same species to reduce the number of unknowns in the least square fitting process. It is also preferable if all the needed lines can be covered by a single laser to simply experimental setup and to facilitate beam alignment.

We finally chose to probe the R-branch band head of ν3 fundamental of CO2 near 2397 cm−1, the application of which in thermometry was first reported by Liu et al. [21]. This particular choice was made after a comprehensive survey of literature on mid-infrared LAS thermometry, with the above consideration regarding CDF in mind. Computed spectral absorption coefficients under the condition of 1 atm and 10% CO2 mole fraction are shown in Fig. 2 for various temperatures. As demonstrated by Liu et al. [21], the ν3 fundamental band head region has high temperature sensitivity at flame temperatures; absorption due to the high J transitions near the band head is also known to increase with temperature. These features are beneficial for measurement of high temperature flames. The chosen spectral region is also free from interference of other species. Furthermore, there are as many as 9 absorption peaks (although highly convoluted) within a narrow wavenumber range of 1 cm−1 that is easily accessible through a current sweep in a distributed feedback (DFB) laser, facilitating multiline absorption measurements. It can be seen in Fig. 2 that as the temperature goes below 600 K, there is almost no absorption. This means the selected line would have negligible absorption at ambient conditions, a feature that facilitates the additional efforts of beam manipulation needed to reduce beam sizes.

 figure: Fig. 2.

Fig. 2. Simulated CO2 absorption coefficients at various temperatures for XCO2 = 0.1 based on the HITEMP database.

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Note the spectral region selected for this work contains non-idealities so that the spectral lineshapes cannot be perfectly fitted by Voigt profiles. In particular, as a physical mechanism not considered by the Voigt fitting function, collisional narrowing was observed by Villarreal and Varghese [28] and Liu et al. [21] In addition, Spectral line mixing near the bandhead region were also confirmed to occur at high temperature under both atmospheric [50] and high pressure [51,52] conditions. These factors are expected to result in deviations between the experimental lineshapes and the Voigt fitted one. In consideration of this issue, Liu et al. [21] performed calibration studies in a high temperature static gas cell and adjusted the line position, line strength and broadening parameters to fit the spectra. Their data indeed confirmed the aforementioned non-idealities; meanwhile it also showed that the effects of these non-idealities on temperature measurement is rather limited. In particular, the temperature of the gases in the cell as obtained from a Voigt profile fitted spectra differed from that from a thermocouple measurement by less than 1.5%. In the present work, the spectral parameters adjusted by Liu et al. was used and we expect the issues of line narrowing and mixing would not incur unacceptable uncertainties in temperature measurement—a fact partially supported by the satisfactory agreements between our measured and predicted temperature profiles as shown in subsequent sections.

3. Experimental setup and methods

3.1 Burner and optical setup

The present counterflow burner is similar with the one used in Ref. [53]; thus, only a brief description is provided here. The burner consists of two identical 10 mm diameter nozzles that are arranged to vertically oppose each other with a separation distance of 8 mm. The fuel stream (fuel mole fraction XF, balanced by N2) is provided through the lower nozzle and the oxidizer stream (oxygen mole fraction XO, balanced by N2) through the upper one with the same exit velocity (V0). A curtain of N2 was provided through concentric slits encompassing the nozzle as shield gas, which is necessary to avoid ambient disturbances of the flame. Chilled recirculating water was provided through water jackets surrounding the nozzle to maintain the nozzle temperature at 25°C. All the gas flow rates were regulated through precision mass flow controllers (Sevenstar Flow Co.) that are field calibrated with digital positive displacement flow calibrators (Drycal, Mesa Labs). The whole burner assembly was mounted in a two-dimensional motored translating stage, facilitating the movement of the flame relative to the beam for tomography.

A schematic of the optical setup is shown in Fig. 3 with a magnified view of the flame in the upper-left corner. A factory collimated distributed feedback ICL (Nanoplus) was used as the light source providing emissions near 4172 nm. A laser diode controller (LDC 500, SRS) controls the temperature of the laser diode through thermoelectric cooling; it also provides the driving current that is modulated through a function generator (DS 340, SRS) to have a sawtooth profile repeated at 5k Hz.

 figure: Fig. 3.

Fig. 3. Schematic of the burner and optical setup; ICL: interband cascade laser; CVL: convex CaF2 lens; CCL: concave CaF2 lens; CCM: concave gold mirror; BS: beam splitter; MR: flat gold mirror.

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The laser beam was split to travel along a main path and a reference path. The latter is primarily used to monitor the laser energy; nevertheless, when a temperature-controlled Germanium etalon (8 cm long, FSR = 0.0154cm−1) is inserted it is also used to provide the relationship between laser driving current and emission wavelength. The reference beam was finally focused through a concave mirror into an MCT detector with 4-stage thermoelectric cooling (PVI-4TE, Vigo System).

Along the main path, a Galileo beam expander comprising a CaF2 plano-concave lens (f =−75 mm) and a plano-convex lens (f = 200 mm) was used to expand the collimated beam with a purpose of reducing its divergence angle (Note collimated beam with lower divergence angle can be focused into a smaller spot). Subsequently, a condensing lens (f = 250 mm) focused the beam at the central axis of the flame. Such optical arrangement was designed to minimize the beam diameter in the flame region for a maximization of measurement spatial resolution along the axial direction. The selection of these particular lenses system was based on considerations that take into account both the size of the burner and the limitation from diffraction. The optimized beam diameter at the burner axis was finally measured to be around 150 µm (FWHM), which is notably smaller than that in the work of Emmert et al. [22]. The beam starts to diverge after leaving the flame and an additional condensing lenes (f = 50 mm) helped to refocus the transmitted beam into an MCT detector. Voltage signals from the detectors representing light intensity are then digitized at 25 MHz by a 14-bit sampler (Gage) and are stored and processed using a PC. Note the MCT detector used in this work has a lower cutoff frequency at 100 Hz; as a result, flame emissions can be filtered out to avoid interference with the laser signals that are modulated at much higher frequencies.

3.2 Test procedures and flame conditions

The injection current of the ICL was modulated with a sawtooth waveform at 5k Hz to scan the laser from 2396.8 cm−1 to 2398.1 cm−1, covering the R-branch band head region of the CO2 ν3 fundamental. The range of the current was specially chosen so that laser emission can be divided into three regimes, as demonstrated in Fig. 4 where a representative transmitted light intensity (It) is shown for a complete scan period. In Regime I, the injection current was below the lasing threshold and thus no laser emission can be induced. This regime has the potential to provide a detector baseline for the subtraction of flame emissions, although the present MCT detector was found to be quite immune to flame radiation due to its 100 Hz lower cut-off frequency. In Regime II, there is laser emission but no gas absorption; therefore, It is essentially the same as the incident laser intensity (I0). Through nonlinear extrapolation, the measurement of It in this regime can be used to recover I0 in Regime III, in which the many CO2 absorption lines reside. Note, simply measuring I0 under flame-off conditions or using a reference beam was not sufficient as the flame may contain broadband absorbing medium such as soot particles, the influence of which should be subtracted when computing fractional transmission using Eq. (1). It is worthwhile to mention that due to hardware limitations, it was not possible for the laser to be tuned in an additional absorption-free regime on the other side of Regime III. In this regard, to ensure an accurate I0 extrapolation, a flame-off laser scan was performed immediately before each set of actual experiments so that I0 in Regime III was directly measured, which can then be used to adjust the extrapolation parameters.

 figure: Fig. 4.

Fig. 4. Typical transmitted laser intensity signal over a complete wavelength scan period.

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The optical setup and thus the beam are fixed in space, while the burner system is moved relative to the beam for both axial and radial scans (0.6 mm step size, only done when tomography is required). At a specific spatial location, data would be collected over a time interval encompassing 100 consecutive laser modulation periods and averaged in a phase-locked manner to enhance SNR. Note, such average can only be done for steady flames; special data pre-processing procedures for unsteady flames will be described in a later section on transient flame measurements.

In the present work, four CDFs with different boundary conditions were tested, consisting of one non-sooting flames (E1), one SF flame (E2), and two SFO flames (E3, E4) with peak temperatures beyond the limits of thermocouple measurements. The flow conditions are listed in Table 1.

Tables Icon

Table 1. Flame conditions and corresponding flow rates: Flame E1 is non-sooting, E2 is a SF flames, while E3 and E4 are SFO flames.

3.3 Method validation

A validation of the data reduction methodology is necessary before discussing the experimental data. Here we focus on the validation of the algorithms of 1) one-dimensional tomography; 2) nonlinear least square fitting represented by Eq. (8); and 3) the multiline technique and the simulated annealing algorithm to obtain T and X radial profiles through minimization of Eq. (13). By explicitly measuring the radial profiles with the 1D tomography approach, we will also confirm that radial distribution of T and X in CDFs can indeed be represented by Boltzmann fitting profiles.

3.3.1 Validation of the tomography algorithm

The purpose of the tomography algorithm is to reconstruct local spectra absorption coefficient from the LOS-integrated spectral absorbance. In this work, we utilized the Abel three point with Tikhonov regularization (TiK-ATP) method. The algorithm, as detailed in a previous section, was validated though numerical experiments targeted to invert a known virtual field.

A virtual field of temperature and CO2 concentration was first established through two-dimensional CFD modelling of an axisymmetric ethylene counterflow flames (XF = 0.5, XO = 0.2, V0 = 22 cm/s, referred to flame T1 throughout the text) using the opensource code of LaminarSMOKE [54,55] coupled with the UCSD chemical kinetic mechanism [56]. The LaminarSMOKE code was developed by Cuoci and coworkers [54,55] to solve Navier-Stokes equations for both steady and unsteady compressible reacting flows. The continuity and momentum conservation equations were solved with the PISO algorithm; while for the species and energy equations an operator-splitting methodology was applied to efficiently treat the high stiffness of the equations. Computations were performed in parallel using a Linux cluster with 72 CPU cores. After the virtual flame is established, spectral absorbance can be computed along various lines of sight radially distributed at an equal interval of 0.6 mm using Eqs. (2) and (3) with transition line related parameters taken from the HITEMP database [41]. The results are termed here as virtually measured spectral absorbance (VMSA). Random noises with a standard deviation of 1% were then added to the VMSA so the robustness of algorithm in treating noisy data can be tested. Tomography inversion using the TiK-ATP algorithm was applied to the VMSA at each frequency. An exemplary result of frequency-resolved reconstruction result is presented in Fig. 5 (green line, location reconstructed is on the center axis r = 0 and at an axial distance H of 4.65 mm above the fuel nozzle). The agreement between the reconstructed kν and the test reference kν (obtained directly using local temperature and CO2 mole fraction values) are seen to be satisfactory, confirming the performance of the inversion algorithm.

 figure: Fig. 5.

Fig. 5. Frequency-resolved absorption features, shown are virtually measured spectral absorbance (VMSA) with random noise added, test reference kν and the reconstructed kν at axial distance of 4.65 mm above the fuel nozzle.

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Figure 5 only show reconstructed kν results for a location on the center axis. To further check the performance of the algorithm in reconstructing kν at other radial locations, we include in Fig. 6 the reconstructed radial profiles of kν at an exemplary frequency of (2397.28 cm−1, where absorption was the strongest) obtained from both ATP and Tik-ATP algorithms; the reference test data was also shown for comparisons. Note the error bar represents standard deviation from 100 trial runs. As can be seen, the reconstructed data agrees well with the test data and the employment of Tikhonov regularization notably inhibit noise propagation towards the center axis.

 figure: Fig. 6.

Fig. 6. Radial profiles of the absorption coefficient at 2397.28cm−1, comparisons among the reconstructed data with ATP, TiK-ATP and the test reference data are shown.

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3.3.2 Nonlinear least square fitting

With the reconstructed frequency-resolved kν available, it is now possible to extract local T and XCO2 values using Eq. (8). The results are shown in Fig. 7 where the agreements with the reference test data are seen to be satisfactory, especially in the flame core region (r < 4 mm). As we approach the edge of the flame, temperature drops and the deviation of the virtually measured value from the reference test data increases. This is in fact expected as the transition lines were intentionally selected not to be sensitive under low temperature conditions, as detailed in the previous section on wavelength selection. After additional analysis we came to the conclusion that the present method could give reliable measurement for temperature above 800 K.

 figure: Fig. 7.

Fig. 7. Reconstructed radial profiles of temperature (square) and CO2 mole fraction (circle) as compared with the test reference data (lines, directly from CFD results) for Flame T1 at H = 4.65 mm.

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Although the unsuitability of the present LAS method for measuring low temperature is a limitation, it poses no problems for our purpose to measure the temperature of CDFs where most interesting chemical reactions occur at a much higher temperature than 800 K. Furthermore, even if the low temperature region needs to be resolved, a thermocouple measurement would suffice. Note, under low temperature conditions, thermocouple measurement uncertainties due to radiation, conduction and catalytic effects would be much reduced.

3.3.3 Radial temperature profiles and validation of the multiline method

The application of multiline thermometry requires the general shape of T and X radial distribution profiles to be known a prior. In this regard, we perform a number of preliminary spatially resolved temperature measurements using the above-mentioned 1D tomography technique. Without loss of generality, we show in Fig. 8 exemplary radial temperature profiles for flame E1 at two different axial heights above the fuel nozzle. Much as expected, the profiles are seen to consist of a core region and an edge region. More importantly, they can both be represented with the following Boltzmann fitting profile:

$$y = {T_{amb}} + \frac{{{T_{core}} - {T_{amb}}}}{{1 + \textrm{exp} ((x - {x_0})/{G_1})}}$$
where Tcore, x0, and G1 are fitting parameters (i.e. components of the vector p or q, as mentioned in Section 2.1.3). Tamb and Tcore have physical interpretation as the ambient temperature (known at 300 K for this work) and core region temperature, respectively; x0 is the radical location where temperature drops to (Tcore- Tamb)/2, while G1 is a parameter that describes the gradient of the transition from Tcore to Tamb. The fitted profiles are shown as lines in Fig. 8, following the measured temperature profile very well.

 figure: Fig. 8.

Fig. 8. Experimentally measured radial temperature profiles for flame E1 at H = 4.65 (black symbol) and H = 4.2 mm (red symbols) with corresponding Boltzmann fitting profiles (lines).

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We next validate the optimization algorithm used for the multiline thermometry technique. As before, the test T and XCO2 fields were again obtained from CFD simulation of flame T1. To simulate measurement uncertainties, random noises of 1% were added to the CDF data. Solution procedure for the multiline thermometry is in fact a residue minimization process through Eq. (13). The parameters to be optimized are Tcore, x0, and G1 (and their counterparts for fitting CO2 mole fraction profiles) as given in Eq. (14). A robust simulated annealing algorithm [46] was used to search the optimal parameters which are exactly the solution we need. To avoid unnecessary search, the search domain was limited to a ±500 K region (in terms of Tcore) which can be easily estimated based on physical understanding of the flame structures.

Figure 9 shows the radial temperature profiles as obtained from the above multiline method for Flame T1 at H = 4.65 mm. The parameters used to create the profiles were optimized as Tcore = 1982K, x0 = 6.5 mm, and G1 = 0.69. Also shown are the test reference data directly available from the CFD results. As can be seen, the two profiles agree reasonably well in the flame core region (r < 4 mm) indicating the satisfactory performance of the present multiline thermometry method for measuring core region temperatures in CDFs. Notable disparities were observed near the edge of the flame (r > 6 mm) where the temperature drops below 800 K. Again, this is as expected due to the insensitivity of our selected transition lines under low temperature conditions. Nevertheless, the comparison in Fig. 9 shows the ability to measure high temperature flames through the multiline method would not be affected. Indeed, a hundred test runs were conducted with a standard deviation of Tcore to be only 36 K (averaged Tcore = 1975K as compared to the reference test value of 1968K). The stability of the simulated annealing algorithm and the multiline method itself were thus confirmed for applications in counterflow flames.

 figure: Fig. 9.

Fig. 9. Radial temperature profiles for Flame T1 and H = 4.65 mm, comparisons between the data obtained from multiline thermometry and the test reference data are shown.

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4. Results and discussions

4.1 Measurements in steady CDFs

In this section, we present measured temperature and CO2 mole fractions data for four representative counterflow flames referred to as Flame E1 to E4 with detailed flame conditions given in Table 1. Both tomography and multiline methods were applied for these four steady flames, which include a non-sooting flame (E1), a soot formation (SF) flame (E2) and two soot formation/oxidation (SFO) flames (E3 and E4).

A typical tomographically reconstructed experimental absorption spectrum is shown in Fig. 10 for flame E1 at H = 4.65 mm and r = 0 mm. To enhance SNR, the spectrum was obtained by averaging data over 100 consecutive wavelength scan periods. As can be seen, the experimental data can be satisfactorily fitted by theoretical model with a maximum residual of 0.00186. Note, as mentioned in the Section 2.2, spectroscopic constants that are experimentally determined by Liu et al. [21] in a high temperature cell were used during the fitting process. Absorption wings from neighboring transitions were also considered. Parameters related to collisional line broadening are highly dependent on local thermochemical environments and are challenging to calibrate; in this regard, following the suggestion of Emmert et al. [22], the Lorentzian line widths were freely fitted to the experimental absorption spectrum. In particular, to reduce the added computational cost we utilized two scaling factor γ1 and γ2 to scale Lorentzian line widths determined for air for each transition line and then fitted only γ1 and γ2. The fitting residual is comparable to or better than in the work of Liu et al. [21]., especially in the highly congregated spectral region from 2397.22 cm−1 to 2397.3 cm−1. For the multiline method, similar fitting approaches were used with the scaling factor applied to all the discretized regions.

 figure: Fig. 10.

Fig. 10. Experimental absorption spectrum for flame E1 at H = 4.65 mm and r = 0 mm, obtained through frequency-resolved tomography.

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As mentioned previously, counterflow flames are quasi one-dimensional and their thermochemical structures along the central axis are the most interesting to combustion research. Experimental results of axial profiles of temperature for Flame E1 to E4 are shown in Fig. 11, where data obtained from both Tik-ATP and the multiline technique are both presented. In addition, numerical predictions using OPPDIF module of the Chemkin package with a detailed chemical mechanism of KM2 [57] were also included for comparison purposes. As can be seen, the experimental temperature profiles show satisfactory agreement with the predicted ones for all the tested flame. The successful capture of the rather high temperature gradient on both sides of the flame front confirms that the present optical setup has sufficient spatial resolution. Furthermore, the Tik-ATP and multiline technique give similar results, serving as cross-validation for both techniques.

 figure: Fig. 11.

Fig. 11. Measured axial profiles of flame temperatures for flame E1, E2 (a) and E3, E4(b). Numerical results obtained through OPPDIF simulation were also included for comparison purposes. The locations of the gas stagnation plane are also marked as Hstg, g.

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The measured axial temperature profiles exhibit typical thermal structure of counterflow flames. For flames with stoichiometric mixture fraction smaller than 0.5 such as Flame E1 and E2, the flame front (i.e., location of Tmax) sits on the oxidizer side of the gas stagnation plane (marked as Hstg,g in Fig. 11(a) where axial velocity reduces to 0). The temperature profiles also show a higher gradient on the oxidizer side. With a fixed XF = 0.50, an increase of XO from 0.15 to 0.2 leads to an increase of peak flame temperature from 1654 K to 1946K, along with a transition of flame appearance from a blue non-sooting flame (Flame E1) to a reddish sooting one (Flame E2). This is much as expected as previous studies have shown that sooting tendencies of CDFs of the SF type increases with peak flame temperature due to enhanced fuel pyrolysis [58]. The results also demonstrate the presence of soot particles in the flame would not affect temperature measurement using the present LAS-based technique.

With a stoichiometric mixture fraction of 0.57 and 0.64 for Flame E3 and E4, respectively, the SFO flames shown in Fig. 11(b) have their flame fronts on the fuel side of the gas stagnation plane. An increase of XF from 0.15 to 0.2 lead to a temperature increase of 188 K. The temperature gradient near the flame front can be seen to be notably smaller as compared to that in SF flames. Due to their strongly oxygen-enriched oxidizer (i.e., XO = 0.9), Flame E3 and E4 have extremely high peak flame temperature of 2532 K and 2720 K, respectively. The sooting zone in SFO flames typically coincide with the high temperature flame front, leading to a flame with intense visible and infrared radiation. Therefore, it is critically important to minimize the interference from flame radiation on LAS signals. In this regard, the combinative usage of a thermal barrier (iris) in front of the detector and a signal conditioner with a lower cutoff frequency of 100 Hz proved to be effective.

Axial profiles of CO2 mole fractions (XCO2) measured with the tomography method for the four tested flames are shown in Fig. 12. The agreements between the measurements and numerical predictions are rather satisfactory. It may be worthwhile to mention that the XCO2 profiles measured optically here have the potential to be used for a quantitative assessment of the influence of probe intrusiveness in cases of probe sampling-based speciation method such as gas chromatography and mass spectrometry. Note the multiline method was not suitable for obtaining XCO2 especially for the high temperature flames E3 and E4 (uncertainty as high as 17%, not shown). This is because the multiline method requires non-linear fitting of a relatively larger number of unknowns including the 6 parameters and 4 parameters describing the radial distribution of temperature and CO2 mole fraction. The algorithm we employed (i.e., simulated annealing) tended to optimize all these parameters at the same time. As it turned out, the function to be optimized was significantly more sensitive to temperature as compared to CO2 mole fraction, thereby making the reconstructed CO2 mole fraction more susceptible to measurement noises as compared to temperature. Note similar observations were made by Liu et al. [38]. If accurate CO2 mole fraction is required, we should use the tomography method, as detailed in Section 2.1.2.

 figure: Fig. 12.

Fig. 12. Measured axial profiles of flame XCO2 for flame E1, E2 (a) and E3, E4(b).

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We further show in Fig. 13 radial temperature profiles measured for Flame E1 at two axial locations of H = 4.2 mm and 4.8 mm. Similar trends were observed for other tested flames and therefore are not repeatedly discussed. As expected, the flame can be seen to consist of a core region from the center axis to around r = 4 mm featuring a flat temperature profile, which confirms the one-dimensionality of counterflow flames. As r increases beyond 4 mm, temperature starts to drop towards ambient temperature indicating the presence of an edge region. The agreement between data obtained through tomography and the multiline method is again satisfactory. For a more complete description of the thermal structures of CDFs, a temperature contour plot for Flame E2 is given in Fig. 14 for a rectangular region of 3.45 < H < 5.40 mm and 0 < r < 6 mm. The edge region is seen to have a tendency to drift upwards, which is believed to be caused by buoyancy effects. The high temperature region was also slightly thinner at the edge of the flame as compared to that in the core region; this is due to the effect of concentric impinging N2 curtain flow.

 figure: Fig. 13.

Fig. 13. Measured radial temperature profiles for flame E1 at H = 4.2 mm and H = 4.8 mm, obtained from tomography (symbols) and the multiline method with profile fitting (lines).

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 figure: Fig. 14.

Fig. 14. Measured temperature contour plot of flame E2.

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4.2 Temporally resolved temperature measurements in CDFs

After demonstrating spatially resolved measurements, we next explore the possibility to perform temporally resolved measurements in CDFs. The tomography method as used in this work is not suitable for measurement under transient aperiodic conditions as it requires physical movement of the beam relative to the flame. On the other hand, with the multiline method a complete radial temperature profile can be obtained by measurement along a single LOS, allowing a possibility of instantaneous measurement.

In principle, for the multiline method, the maximum obtainable temporal resolution is determined by the laser scan frequency. For instance, the current ICL was scanned at a frequency of 5k Hz frequency; therefore, temperature profile can be obtained every 0.2 milliseconds. Nevertheless, it is important to note that without proper pre-processing, instantaneous signals obtained in a single scan period may have noise levels high enough to sabotage further analysis. This is exactly the reason why we averaged the data in a phase-locked manner over 100 scan periods to enhance SNR for measurements in steady flames. A comparison between instantaneous and phase-averaged transmitted light signals for Flame E1 at H = 4.65 mm is given in Fig. 15, where the relatively high random noise of the instantaneous signal can be clearly seen. Averaging effectively eliminate these noises, leading to a very smooth data that is beneficial for further spectroscopic fitting. To rely on the instantaneous data for temporally resolved temperature measurements, it is essential to perform signal conditioning to minimize random noises. In this regard, after testing several noise filtering methods, we finally chose to use the Savitzky–Golay algorithm (S–G) [59] for signal conditioning. The filtered data was also shown in Fig. 15 and it can be seen to have noise level comparable to the phase-averaged data.

 figure: Fig. 15.

Fig. 15. A comparison among instantaneous, phase-averaged and S-G filtered instantaneous signals.

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Temporally resolved measurement was performed based on the filtered instantaneous data; time evolution (resolution: 0.2 milliseconds) of axis temperatures (Tcore)is shown in Fig. 16(a) for Flame E1 and E2 at H = 4.65 mm. The tested flames were essentially steady; so, temperature measured from averaged data were also shown for comparison purposes. For completeness, we also show in Fig. 16(b) the other fitted parameters of x0 and G1. As can be seen, although the three parameters all fluctuate within a certain range, they in general show relatively good stability. Nevertheless, we note the level of fluctuation for x0 and G1 are higher than that for Tcore. This is actually as expected and can be explained by the fact that the spectral lines we selected in this work has low absorption at low temperatures (Fig. 2); The parameters of x0 and G1 determines the overall profiles of the radial temperature distribution needing information from both the high temperature flame core as well as the low temperature flame boundary. Since the low temperature region provides less information (i.e., constraints for fitting), it is not surprising to see x0 and G1 to have slightly higher fluctuation. However, we have made certain this would not notably affect the determination of Tcore – our primary target as shown in the section on the validation of multiline method (3.3.3). In conclusion, data shown in Fig. 16 demonstrates the validity of our approach using instantaneous absorption data along with the multiline method to measure temperature in CDFs.

 figure: Fig. 16.

Fig. 16. Instantaneous measurements for Flame E1 (red) and E2 (black) at H = 4.65 mm.(a) Tcore;(b) x0 and G1.

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The above demonstration should ideally be made on unsteady CDFs. Unfortunately, however, the apparatus needed for creating a well-controlled unsteady flame was not available at the moment. Nevertheless, after proving instantaneous absorption data can be used, it is possible as a proof of concept to use numerical experiments to demonstrate the present method in diagnosing CDFs under transient conditions. In this regard, we chose to numerically set up a transient flame with temperature evolving rapidly in the time scale of milliseconds. The initial flame condition of the numerical experiment was the same with Flame E1 with XF = 0.5, XO = 0.15 and V0 = 22 cm/s. At the instant of t = 0, boundary condition for XO was abruptly changed from 0.15 to 0.20, and the temporal evolution of the thermochemical structures of flames modeled through the open source LaminarSMOKE code [54,55]. Subsequently, temporally resolved VMSA were obtained through the computed temperature and CO2 mole fraction fields. Exemplary VMSA are given in Fig. 17(a) at representative H of 4.65 and 4.95 mm; note, 2% random noises was artificially added to simulate measurement noises.

 figure: Fig. 17.

Fig. 17. Time evolution of the virtually measured spectral absorbance (a) and temperature at the center axis (b) at two flame heights of H = 4.65 and 4.95 mm. Solid lines in (b) represent test reference temperature data directly from CFD simulations.

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Temporal evolution of the center axis temperature, which was obtained through the multiline method based on the VMSA data, are shown in Fig. 17(b) for H = 4.65 and 4.95 mm. In Fig. 17(b), the open symbol was the instantaneous data; while the closed symbol and the error bar represent an ensemble average and standard deviation of 100 test runs, which are needed to assess the stability of the algorithm in dealing with the aforementioned simulated measurement noises. As can be seen, the standard deviations are within 2.5% and the agreement of the temperature retrieved from the multiline method and the reference test data are very good. As expected, the temperature remains nearly constant until the change of the boundary conditions reaches the reaction zone at t = 5 ms after which a quick temperature rise occurs until t = 20 ms; the temperature keeps unchanged afterwards, indicating the end of the transient process. The present results confirm the applicability of the multiline method in temperature measurement under transient conditions. We would like to point out that if in reality the transient experiment can be repeatedly performed multiple times, the ensemble averaged data would be considerably more reliable with higher signal-to-noise ratio.

Before concluding this work, it is necessary to mention that many unsteady laboratory flames can be non-symmetric. Our methodology is only proposed for axisymmetric flames, which is certainly a limitation. Nevertheless, the method can be applied to measure counterflow flames with unsteady boundary conditions (therefore unsteady strain rate or stoichiometric mixture fraction) while preserving symmetry. These flames are particularly useful for a fundamental understanding of the effects of hydrodynamics on slow chemistries such as NOx and soot formation.

5. Concluding remarks

In this work, we performed non-intrusive temperature measurements in counterflow diffusion flames using TDLAS. An interband cascade laser was used to provide incident infrared light for direction absorption by flame-generated CO2 at the R-branch band head of ν3 fundamental of CO2 near 2397 cm−1. Considering the high temperature gradient in counterflow flames, the optical arrangement and absorption lines were specially optimized to improve measurement spatial resolutions.

Measurements were performed on four representative counterflow flames including a non-sooting, SF and SFO flames. For the high temperature SFO flames, the peak flame temperature measured was 2700 K, which was beyond the high-temperature limit for traditional thermocouple measurements. Hyperspectral tomography was utilized to resolve the temperature non-uniformity along the line-of-sight. The measured temperature profiles are in excellent agreement with numerical predictions. In addition, it was found the radial temperature distribution of CDFs can be represented by a Boltzmann fitting profile, opening the possibility of using an alternative approach of multiline thermometry with profile fitting to resolve temperature non-uniformity in CDFs.

The spatially resolved temperature data from tomography and the multiline method agrees well with each other, cross validating both approaches. The multiline method was also confirmed to be applicable for temporally-resolved measurement under transient flame conditions. The present work is thought to be the first study of utilizing the multiline method for investigating the thermal structures of CDFs.

Funding

National Natural Science Foundation of China (51976142).

Acknowledgments

We gratefully acknowledge Dr. Xunchen Liu at Shanghai Jiaotong University for providing the Ge etalon that was used in this work along with his helpful suggestions. In addition, we are thankful to Dr. Liuhao Ma at The Chinese University of Hong Kong for insightful technical comments. YW would also like to express his gratitude to Dr. Aamir Farooq of KAUST for enlightening discussions regarding LAS.

Disclosures

The authors declare no conflicts of interest.

References

1. K. Kohse-Höinghaus, “Clean combustion: Chemistry and diagnostics for a systems approach in transportation and energy conversion,” Prog. Energy Combust. Sci. 65, 1–5 (2018). [CrossRef]  

2. F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014). [CrossRef]  

3. H. Tsuji, “Counterflow Diffusion Flames,” Prog. Energy Combust. Sci. 8(2), 93–119 (1982). [CrossRef]  

4. J. W. Ku, S. Choi, H. K. Kim, S. Lee, and O. C. Kwon, “Extinction limits and structure of counterflow nonpremixed methane-ammonia/air flames,” Energy 165, 314–325 (2018). [CrossRef]  

5. R. E. Padilla, D. Escofet-Martin, T. Pham, W. J. Pitz, and D. Dunn-Rankin, “Structure and behavior of water-laden CH4/air counterflow diffusion flames,” Combust. Flame 196, 439–451 (2018). [CrossRef]  

6. A. Ansari and F. N. Egolfopoulos, “Flame ignition in the counterflow configuration: Reassessing the experimental assumptions,” Combust. Flame 174, 37–49 (2016). [CrossRef]  

7. X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020). [CrossRef]  

8. K. C. Kalvakala, V. R. Katta, and S. K. Aggarwal, “Effects of oxygen-enrichment and fuel unsaturation on soot and NOx emissions in ethylene, propane, and propene flames,” Combust. Flame 187, 217–229 (2018). [CrossRef]  

9. Y. Wang and S. H. Chung, “Soot formation in laminar counterflow flames,” Prog. Energy Combust. Sci. 74, 152–238 (2019). [CrossRef]  

10. X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018). [CrossRef]  

11. C. S. McEnally, Ü. Ö. Köylü, L. D. Pfefferle, and D. E. Rosner, “Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples,” Combust. Flame 109(4), 701–720 (1997). [CrossRef]  

12. D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002). [CrossRef]  

13. A. Denisov, G. Colmegna, and P. Jansohn, “Temperature measurements in sooting counterflow diffusion flames using laser-induced fluorescence of flame-produced nitric oxide,” Appl. Phys. B 116(2), 339–346 (2014). [CrossRef]  

14. D. A. Santoianni, M. E. DeCroix, and W. L. Roberts, “Temperature imaging in an unsteady propane-air counterflow diffusion flame subjected to low frequency oscillations,” Flow, Turbul. Combust. 66(1), 23–36 (2001). [CrossRef]  

15. S. Zheng, L. Ni, H. Liu, and H. Zhou, “Measurement of the distribution of temperature and emissivity of a candle flame using hyperspectral imaging technique,” Optik 183, 222–231 (2019). [CrossRef]  

16. K. Gleason, F. Carbone, and A. Gomez, “Effect of temperature on soot inception in highly controlled counterflow ethylene diffusion flames,” Combust. Flame 192, 283–294 (2018). [CrossRef]  

17. Z. C. Qu, R. Ghorbani, D. Valiev, and F. M. Schmidt, “Calibration-free scanned wavelength modulation spectroscopy-application to H2O and temperature sensing in flames,” Opt. Express 23(12), 16492–16499 (2015). [CrossRef]  

18. R. M. Spearrin, W. Ren, J. B. Jeffries, and R. K. Hanson, “Multi-band infrared CO2 absorption sensor for sensitive temperature and species measurements in high-temperature gases,” Appl. Phys. B 116(4), 855–865 (2014). [CrossRef]  

19. C. Wei, D. I. Pineda, L. Paxton, F. N. Egolfopoulos, and R. M. Spearrin, “Mid-infrared laser absorption tomography for quantitative 2D thermochemistry measurements in premixed jet flames,” Appl. Phys. B 124(6), 123 (2018). [CrossRef]  

20. L. Ma, K.-P. Cheong, H. Ning, and W. Ren, “An improved study of the uniformity of laminar premixed flames using laser absorption spectroscopy and CFD simulation,” Exp. Therm. Fluid Sci. 112, 110013 (2020). [CrossRef]  

21. X. Liu, G. Zhang, Y. Huang, Y. Wang, and F. Qi, “Two-dimensional temperature and carbon dioxide concentration profiles in atmospheric laminar diffusion flames measured by mid-infrared direct absorption spectroscopy at 4.2 µm,” Appl. Phys. B 124(4), 61 (2018). [CrossRef]  

22. J. Emmert, M. Baroncelli, S. V. D. Kley, H. Pitsch, and S. Wagner, “Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner,” Energies 12(14), 2786 (2019). [CrossRef]  

23. C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energy Combust. Sci. 60, 132–176 (2017). [CrossRef]  

24. X. Zhou, X. Liu, J. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003). [CrossRef]  

25. L. H. Ma, L. Y. Lau, and W. Ren, “Non-uniform temperature and species concentration measurements in a laminar flame using multi-band infrared absorption spectroscopy,” Appl. Phys. B 123(3), 83 (2017). [CrossRef]  

26. W. Cai and C. F. Kaminski, “Tomographic absorption spectroscopy for the study of gas dynamics and reactive flows,” Prog. Energy Combust. Sci. 59, 1–31 (2017). [CrossRef]  

27. L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17(10), 8602–8613 (2009). [CrossRef]  

28. R. Villarreal and P. Varghese, “Frequency-resolved absorption tomography with tunable diode lasers,” Appl. Opt. 44(31), 6786–6795 (2005). [CrossRef]  

29. C. Liu, L. Xu, J. Chen, Z. Cao, Y. Lin, and W. Cai, “Development of a fan-beam TDLAS-based tomographic sensor for rapid imaging of temperature and gas concentration,” Opt. Express 23(17), 22494–22511 (2015). [CrossRef]  

30. C. J. Dasch, “One-dimensional tomography - A comparison of Abel, onion-peeling, and filtered backprojection methods,” Appl. Opt. 31(8), 1146–1152 (1992). [CrossRef]  

31. F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020). [CrossRef]  

32. X. Liu, G. Wang, J. Zheng, L. Xu, S. Wang, L. Li, and F. Qi, “Temporally resolved two dimensional temperature field of acoustically excited swirling flames measured by mid-infrared direct absorption spectroscopy,” Opt. Express 26(24), 31983–31994 (2018). [CrossRef]  

33. P. Rodrigues, B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha, “Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames,” Proc. Combust. Inst. 36(1), 927–934 (2017). [CrossRef]  

34. A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Formation of soot and nitrogen oxides in unsteady counterflow diffusion flames,” Combust. Flame 156(10), 2010–2022 (2009). [CrossRef]  

35. Y. Xuan and G. Blanquart, “A flamelet-based a priori analysis on the chemistry tabulation of polycyclic aromatic hydrocarbons in non-premixed flames,” Combust. Flame 161(6), 1516–1525 (2014). [CrossRef]  

36. H. G. Im, J. H. Chen, and J.-Y. Chen, “Chemical response of methane/air diffusion flames to unsteady strain rate,” Combust. Flame 118(1-2), 204–212 (1999). [CrossRef]  

37. S. T. Sanders, J. Wang, J. B. Jeffries, and R. K. Hanson, “Diode-Laser Absorption Sensor for Line-of-Sight Gas Temperature Distributions,” Appl. Opt. 40(24), 4404–4415 (2001). [CrossRef]  

38. C. Liu, L. Xu, and Z. Cao, “Measurement of nonuniform temperature and concentration distributions by combining line-of-sight tunable diode laser absorption spectroscopy with regularization methods,” Appl. Opt. 52(20), 4827–4842 (2013). [CrossRef]  

39. F. Yan, M. Zhou, L. Xu, Y. Wang, and S. H. Chung, “An experimental study on the spectral dependence of light extinction in sooting ethylene counterflow diffusion flames,” Exp. Therm. Fluid Sci. 100, 259–270 (2019). [CrossRef]  

40. R. K. Hanson, R. M. Spearrin, and C. S. Goldenstein, Spectroscopy and Optical Diagnostics for Gases (Springer International, 2016).

41. L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010). [CrossRef]  

42. K. J. Daun, K. A. Thomson, F. S. Liu, and G. J. Smallwood, “Deconvolution of axisymmetric flame properties using Tikhonov regularization,” Appl. Opt. 45(19), 4638–4646 (2006). [CrossRef]  

43. A. Guha and I. Schoegl, “Tomographic laser absorption spectroscopy using Tikhonov regularization,” Appl. Opt. 53(34), 8095–8103 (2014). [CrossRef]  

44. E. O. Akesson and K. J. Daun, “Parameter selection methods for axisymmetric flame tomography through Tikhonov regularization,” Appl. Opt. 47(3), 407–416 (2008). [CrossRef]  

45. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983). [CrossRef]  

46. W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008). [CrossRef]  

47. X. Liu, J. B. Jeffries, and R. K. Hanson, “Measurement of Non-Uniform Temperature Distributions Using Line-of-Sight Absorption Spectroscopy,” AIAA J. 45(2), 411–419 (2007). [CrossRef]  

48. Y. Wang and S. H. Chung, “Effect of strain rate on sooting limits in counterflow diffusion flames of gaseous hydrocarbon fuels: Sooting temperature index and sooting sensitivity index,” Combust. Flame 161(5), 1224–1234 (2014). [CrossRef]  

49. B. G. Sarnacki and H. K. Chelliah, “Sooting limits of non-premixed counterflow ethylene/oxygen/inert flames using LII: Effects of flow strain rate and pressure (up to 30 atm),” Combust. Flame 195, 267–281 (2018). [CrossRef]  

50. A. P. Nair, D. D. Lee, D. I. Pineda, J. Kriesel, and R. M. Spearrin, “MHz laser absorption spectroscopy via diplexed RF modulation for pressure, temperature, and species in rotating detonation rocket flows,” Appl. Phys. B 126(8), 138 (2020). [CrossRef]  

51. J. Lamouroux, L. Régalia, X. Thomas, J. Vander Auwera, R. R. Gamache, and J. M. Hartmann, “CO2 line-mixing database and software update and its tests in the 2.1 µm and 4.3 µm regions,” J. Quant. Spectrosc. Radiat. Transfer 151, 88–96 (2015). [CrossRef]  

52. D. D. Lee, F. A. Bendana, A. P. Nair, D. I. Pineda, and R. M. Spearrin, “Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures,” J. Quant. Spectrosc. Radiat. Transfer 253, 107135 (2020). [CrossRef]  

53. Y. Wang and S. H. Chung, “Strain rate effect on sooting characteristics in laminar counterflow diffusion flames,” Combust. Flame 165, 433–444 (2016). [CrossRef]  

54. A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Numerical Modeling of Laminar Flames with Detailed Kinetics Based on the Operator-Splitting Method,” Energy Fuels 27(12), 7730–7753 (2013). [CrossRef]  

55. A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “A computational tool for the detailed kinetic modeling of laminar flames: Application to C2H4/CH4 coflow flames,” Combust. Flame 160(5), 870–886 (2013). [CrossRef]  

56. . “University of California, San Diego Center for Energy Research, Combustion Division[DB/OL]. [2005-06-15]. http://maemail.ucsd.edu/combustion/cermech/.”

57. Y. Wang, A. Raj, and S. H. Chung, “A PAH growth mechanism and synergistic effect on PAH formation in counterflow diffusion flames,” Combust. Flame 160(9), 1667–1676 (2013). [CrossRef]  

58. L. Xu, F. Yan, M. Zhou, Y. Wang, and S. H. Chung, “Experimental and soot modeling studies of ethylene counterflow diffusion flames: Non-monotonic influence of the oxidizer composition on soot formation,” Combust. Flame 197, 304–318 (2018). [CrossRef]  

59. T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018). [CrossRef]  

References

  • View by:

  1. K. Kohse-Höinghaus, “Clean combustion: Chemistry and diagnostics for a systems approach in transportation and energy conversion,” Prog. Energy Combust. Sci. 65, 1–5 (2018).
    [Crossref]
  2. F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014).
    [Crossref]
  3. H. Tsuji, “Counterflow Diffusion Flames,” Prog. Energy Combust. Sci. 8(2), 93–119 (1982).
    [Crossref]
  4. J. W. Ku, S. Choi, H. K. Kim, S. Lee, and O. C. Kwon, “Extinction limits and structure of counterflow nonpremixed methane-ammonia/air flames,” Energy 165, 314–325 (2018).
    [Crossref]
  5. R. E. Padilla, D. Escofet-Martin, T. Pham, W. J. Pitz, and D. Dunn-Rankin, “Structure and behavior of water-laden CH4/air counterflow diffusion flames,” Combust. Flame 196, 439–451 (2018).
    [Crossref]
  6. A. Ansari and F. N. Egolfopoulos, “Flame ignition in the counterflow configuration: Reassessing the experimental assumptions,” Combust. Flame 174, 37–49 (2016).
    [Crossref]
  7. X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020).
    [Crossref]
  8. K. C. Kalvakala, V. R. Katta, and S. K. Aggarwal, “Effects of oxygen-enrichment and fuel unsaturation on soot and NOx emissions in ethylene, propane, and propene flames,” Combust. Flame 187, 217–229 (2018).
    [Crossref]
  9. Y. Wang and S. H. Chung, “Soot formation in laminar counterflow flames,” Prog. Energy Combust. Sci. 74, 152–238 (2019).
    [Crossref]
  10. X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018).
    [Crossref]
  11. C. S. McEnally, Ü. Ö. Köylü, L. D. Pfefferle, and D. E. Rosner, “Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples,” Combust. Flame 109(4), 701–720 (1997).
    [Crossref]
  12. D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002).
    [Crossref]
  13. A. Denisov, G. Colmegna, and P. Jansohn, “Temperature measurements in sooting counterflow diffusion flames using laser-induced fluorescence of flame-produced nitric oxide,” Appl. Phys. B 116(2), 339–346 (2014).
    [Crossref]
  14. D. A. Santoianni, M. E. DeCroix, and W. L. Roberts, “Temperature imaging in an unsteady propane-air counterflow diffusion flame subjected to low frequency oscillations,” Flow, Turbul. Combust. 66(1), 23–36 (2001).
    [Crossref]
  15. S. Zheng, L. Ni, H. Liu, and H. Zhou, “Measurement of the distribution of temperature and emissivity of a candle flame using hyperspectral imaging technique,” Optik 183, 222–231 (2019).
    [Crossref]
  16. K. Gleason, F. Carbone, and A. Gomez, “Effect of temperature on soot inception in highly controlled counterflow ethylene diffusion flames,” Combust. Flame 192, 283–294 (2018).
    [Crossref]
  17. Z. C. Qu, R. Ghorbani, D. Valiev, and F. M. Schmidt, “Calibration-free scanned wavelength modulation spectroscopy-application to H2O and temperature sensing in flames,” Opt. Express 23(12), 16492–16499 (2015).
    [Crossref]
  18. R. M. Spearrin, W. Ren, J. B. Jeffries, and R. K. Hanson, “Multi-band infrared CO2 absorption sensor for sensitive temperature and species measurements in high-temperature gases,” Appl. Phys. B 116(4), 855–865 (2014).
    [Crossref]
  19. C. Wei, D. I. Pineda, L. Paxton, F. N. Egolfopoulos, and R. M. Spearrin, “Mid-infrared laser absorption tomography for quantitative 2D thermochemistry measurements in premixed jet flames,” Appl. Phys. B 124(6), 123 (2018).
    [Crossref]
  20. L. Ma, K.-P. Cheong, H. Ning, and W. Ren, “An improved study of the uniformity of laminar premixed flames using laser absorption spectroscopy and CFD simulation,” Exp. Therm. Fluid Sci. 112, 110013 (2020).
    [Crossref]
  21. X. Liu, G. Zhang, Y. Huang, Y. Wang, and F. Qi, “Two-dimensional temperature and carbon dioxide concentration profiles in atmospheric laminar diffusion flames measured by mid-infrared direct absorption spectroscopy at 4.2 µm,” Appl. Phys. B 124(4), 61 (2018).
    [Crossref]
  22. J. Emmert, M. Baroncelli, S. V. D. Kley, H. Pitsch, and S. Wagner, “Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner,” Energies 12(14), 2786 (2019).
    [Crossref]
  23. C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energy Combust. Sci. 60, 132–176 (2017).
    [Crossref]
  24. X. Zhou, X. Liu, J. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
    [Crossref]
  25. L. H. Ma, L. Y. Lau, and W. Ren, “Non-uniform temperature and species concentration measurements in a laminar flame using multi-band infrared absorption spectroscopy,” Appl. Phys. B 123(3), 83 (2017).
    [Crossref]
  26. W. Cai and C. F. Kaminski, “Tomographic absorption spectroscopy for the study of gas dynamics and reactive flows,” Prog. Energy Combust. Sci. 59, 1–31 (2017).
    [Crossref]
  27. L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17(10), 8602–8613 (2009).
    [Crossref]
  28. R. Villarreal and P. Varghese, “Frequency-resolved absorption tomography with tunable diode lasers,” Appl. Opt. 44(31), 6786–6795 (2005).
    [Crossref]
  29. C. Liu, L. Xu, J. Chen, Z. Cao, Y. Lin, and W. Cai, “Development of a fan-beam TDLAS-based tomographic sensor for rapid imaging of temperature and gas concentration,” Opt. Express 23(17), 22494–22511 (2015).
    [Crossref]
  30. C. J. Dasch, “One-dimensional tomography - A comparison of Abel, onion-peeling, and filtered backprojection methods,” Appl. Opt. 31(8), 1146–1152 (1992).
    [Crossref]
  31. F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020).
    [Crossref]
  32. X. Liu, G. Wang, J. Zheng, L. Xu, S. Wang, L. Li, and F. Qi, “Temporally resolved two dimensional temperature field of acoustically excited swirling flames measured by mid-infrared direct absorption spectroscopy,” Opt. Express 26(24), 31983–31994 (2018).
    [Crossref]
  33. P. Rodrigues, B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha, “Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames,” Proc. Combust. Inst. 36(1), 927–934 (2017).
    [Crossref]
  34. A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Formation of soot and nitrogen oxides in unsteady counterflow diffusion flames,” Combust. Flame 156(10), 2010–2022 (2009).
    [Crossref]
  35. Y. Xuan and G. Blanquart, “A flamelet-based a priori analysis on the chemistry tabulation of polycyclic aromatic hydrocarbons in non-premixed flames,” Combust. Flame 161(6), 1516–1525 (2014).
    [Crossref]
  36. H. G. Im, J. H. Chen, and J.-Y. Chen, “Chemical response of methane/air diffusion flames to unsteady strain rate,” Combust. Flame 118(1-2), 204–212 (1999).
    [Crossref]
  37. S. T. Sanders, J. Wang, J. B. Jeffries, and R. K. Hanson, “Diode-Laser Absorption Sensor for Line-of-Sight Gas Temperature Distributions,” Appl. Opt. 40(24), 4404–4415 (2001).
    [Crossref]
  38. C. Liu, L. Xu, and Z. Cao, “Measurement of nonuniform temperature and concentration distributions by combining line-of-sight tunable diode laser absorption spectroscopy with regularization methods,” Appl. Opt. 52(20), 4827–4842 (2013).
    [Crossref]
  39. F. Yan, M. Zhou, L. Xu, Y. Wang, and S. H. Chung, “An experimental study on the spectral dependence of light extinction in sooting ethylene counterflow diffusion flames,” Exp. Therm. Fluid Sci. 100, 259–270 (2019).
    [Crossref]
  40. R. K. Hanson, R. M. Spearrin, and C. S. Goldenstein, Spectroscopy and Optical Diagnostics for Gases (Springer International, 2016).
  41. L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
    [Crossref]
  42. K. J. Daun, K. A. Thomson, F. S. Liu, and G. J. Smallwood, “Deconvolution of axisymmetric flame properties using Tikhonov regularization,” Appl. Opt. 45(19), 4638–4646 (2006).
    [Crossref]
  43. A. Guha and I. Schoegl, “Tomographic laser absorption spectroscopy using Tikhonov regularization,” Appl. Opt. 53(34), 8095–8103 (2014).
    [Crossref]
  44. E. O. Akesson and K. J. Daun, “Parameter selection methods for axisymmetric flame tomography through Tikhonov regularization,” Appl. Opt. 47(3), 407–416 (2008).
    [Crossref]
  45. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
    [Crossref]
  46. W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008).
    [Crossref]
  47. X. Liu, J. B. Jeffries, and R. K. Hanson, “Measurement of Non-Uniform Temperature Distributions Using Line-of-Sight Absorption Spectroscopy,” AIAA J. 45(2), 411–419 (2007).
    [Crossref]
  48. Y. Wang and S. H. Chung, “Effect of strain rate on sooting limits in counterflow diffusion flames of gaseous hydrocarbon fuels: Sooting temperature index and sooting sensitivity index,” Combust. Flame 161(5), 1224–1234 (2014).
    [Crossref]
  49. B. G. Sarnacki and H. K. Chelliah, “Sooting limits of non-premixed counterflow ethylene/oxygen/inert flames using LII: Effects of flow strain rate and pressure (up to 30 atm),” Combust. Flame 195, 267–281 (2018).
    [Crossref]
  50. A. P. Nair, D. D. Lee, D. I. Pineda, J. Kriesel, and R. M. Spearrin, “MHz laser absorption spectroscopy via diplexed RF modulation for pressure, temperature, and species in rotating detonation rocket flows,” Appl. Phys. B 126(8), 138 (2020).
    [Crossref]
  51. J. Lamouroux, L. Régalia, X. Thomas, J. Vander Auwera, R. R. Gamache, and J. M. Hartmann, “CO2 line-mixing database and software update and its tests in the 2.1 µm and 4.3 µm regions,” J. Quant. Spectrosc. Radiat. Transfer 151, 88–96 (2015).
    [Crossref]
  52. D. D. Lee, F. A. Bendana, A. P. Nair, D. I. Pineda, and R. M. Spearrin, “Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures,” J. Quant. Spectrosc. Radiat. Transfer 253, 107135 (2020).
    [Crossref]
  53. Y. Wang and S. H. Chung, “Strain rate effect on sooting characteristics in laminar counterflow diffusion flames,” Combust. Flame 165, 433–444 (2016).
    [Crossref]
  54. A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Numerical Modeling of Laminar Flames with Detailed Kinetics Based on the Operator-Splitting Method,” Energy Fuels 27(12), 7730–7753 (2013).
    [Crossref]
  55. A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “A computational tool for the detailed kinetic modeling of laminar flames: Application to C2H4/CH4 coflow flames,” Combust. Flame 160(5), 870–886 (2013).
    [Crossref]
  56. . “University of California, San Diego Center for Energy Research, Combustion Division[DB/OL]. [2005-06-15]. http://maemail.ucsd.edu/combustion/cermech/.”
  57. Y. Wang, A. Raj, and S. H. Chung, “A PAH growth mechanism and synergistic effect on PAH formation in counterflow diffusion flames,” Combust. Flame 160(9), 1667–1676 (2013).
    [Crossref]
  58. L. Xu, F. Yan, M. Zhou, Y. Wang, and S. H. Chung, “Experimental and soot modeling studies of ethylene counterflow diffusion flames: Non-monotonic influence of the oxidizer composition on soot formation,” Combust. Flame 197, 304–318 (2018).
    [Crossref]
  59. T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
    [Crossref]

2020 (5)

X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020).
[Crossref]

L. Ma, K.-P. Cheong, H. Ning, and W. Ren, “An improved study of the uniformity of laminar premixed flames using laser absorption spectroscopy and CFD simulation,” Exp. Therm. Fluid Sci. 112, 110013 (2020).
[Crossref]

F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020).
[Crossref]

A. P. Nair, D. D. Lee, D. I. Pineda, J. Kriesel, and R. M. Spearrin, “MHz laser absorption spectroscopy via diplexed RF modulation for pressure, temperature, and species in rotating detonation rocket flows,” Appl. Phys. B 126(8), 138 (2020).
[Crossref]

D. D. Lee, F. A. Bendana, A. P. Nair, D. I. Pineda, and R. M. Spearrin, “Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures,” J. Quant. Spectrosc. Radiat. Transfer 253, 107135 (2020).
[Crossref]

2019 (4)

F. Yan, M. Zhou, L. Xu, Y. Wang, and S. H. Chung, “An experimental study on the spectral dependence of light extinction in sooting ethylene counterflow diffusion flames,” Exp. Therm. Fluid Sci. 100, 259–270 (2019).
[Crossref]

J. Emmert, M. Baroncelli, S. V. D. Kley, H. Pitsch, and S. Wagner, “Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner,” Energies 12(14), 2786 (2019).
[Crossref]

Y. Wang and S. H. Chung, “Soot formation in laminar counterflow flames,” Prog. Energy Combust. Sci. 74, 152–238 (2019).
[Crossref]

S. Zheng, L. Ni, H. Liu, and H. Zhou, “Measurement of the distribution of temperature and emissivity of a candle flame using hyperspectral imaging technique,” Optik 183, 222–231 (2019).
[Crossref]

2018 (12)

K. Gleason, F. Carbone, and A. Gomez, “Effect of temperature on soot inception in highly controlled counterflow ethylene diffusion flames,” Combust. Flame 192, 283–294 (2018).
[Crossref]

C. Wei, D. I. Pineda, L. Paxton, F. N. Egolfopoulos, and R. M. Spearrin, “Mid-infrared laser absorption tomography for quantitative 2D thermochemistry measurements in premixed jet flames,” Appl. Phys. B 124(6), 123 (2018).
[Crossref]

X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018).
[Crossref]

K. C. Kalvakala, V. R. Katta, and S. K. Aggarwal, “Effects of oxygen-enrichment and fuel unsaturation on soot and NOx emissions in ethylene, propane, and propene flames,” Combust. Flame 187, 217–229 (2018).
[Crossref]

K. Kohse-Höinghaus, “Clean combustion: Chemistry and diagnostics for a systems approach in transportation and energy conversion,” Prog. Energy Combust. Sci. 65, 1–5 (2018).
[Crossref]

J. W. Ku, S. Choi, H. K. Kim, S. Lee, and O. C. Kwon, “Extinction limits and structure of counterflow nonpremixed methane-ammonia/air flames,” Energy 165, 314–325 (2018).
[Crossref]

R. E. Padilla, D. Escofet-Martin, T. Pham, W. J. Pitz, and D. Dunn-Rankin, “Structure and behavior of water-laden CH4/air counterflow diffusion flames,” Combust. Flame 196, 439–451 (2018).
[Crossref]

X. Liu, G. Zhang, Y. Huang, Y. Wang, and F. Qi, “Two-dimensional temperature and carbon dioxide concentration profiles in atmospheric laminar diffusion flames measured by mid-infrared direct absorption spectroscopy at 4.2 µm,” Appl. Phys. B 124(4), 61 (2018).
[Crossref]

X. Liu, G. Wang, J. Zheng, L. Xu, S. Wang, L. Li, and F. Qi, “Temporally resolved two dimensional temperature field of acoustically excited swirling flames measured by mid-infrared direct absorption spectroscopy,” Opt. Express 26(24), 31983–31994 (2018).
[Crossref]

B. G. Sarnacki and H. K. Chelliah, “Sooting limits of non-premixed counterflow ethylene/oxygen/inert flames using LII: Effects of flow strain rate and pressure (up to 30 atm),” Combust. Flame 195, 267–281 (2018).
[Crossref]

L. Xu, F. Yan, M. Zhou, Y. Wang, and S. H. Chung, “Experimental and soot modeling studies of ethylene counterflow diffusion flames: Non-monotonic influence of the oxidizer composition on soot formation,” Combust. Flame 197, 304–318 (2018).
[Crossref]

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

2017 (4)

P. Rodrigues, B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha, “Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames,” Proc. Combust. Inst. 36(1), 927–934 (2017).
[Crossref]

C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energy Combust. Sci. 60, 132–176 (2017).
[Crossref]

L. H. Ma, L. Y. Lau, and W. Ren, “Non-uniform temperature and species concentration measurements in a laminar flame using multi-band infrared absorption spectroscopy,” Appl. Phys. B 123(3), 83 (2017).
[Crossref]

W. Cai and C. F. Kaminski, “Tomographic absorption spectroscopy for the study of gas dynamics and reactive flows,” Prog. Energy Combust. Sci. 59, 1–31 (2017).
[Crossref]

2016 (2)

A. Ansari and F. N. Egolfopoulos, “Flame ignition in the counterflow configuration: Reassessing the experimental assumptions,” Combust. Flame 174, 37–49 (2016).
[Crossref]

Y. Wang and S. H. Chung, “Strain rate effect on sooting characteristics in laminar counterflow diffusion flames,” Combust. Flame 165, 433–444 (2016).
[Crossref]

2015 (3)

2014 (6)

Y. Xuan and G. Blanquart, “A flamelet-based a priori analysis on the chemistry tabulation of polycyclic aromatic hydrocarbons in non-premixed flames,” Combust. Flame 161(6), 1516–1525 (2014).
[Crossref]

R. M. Spearrin, W. Ren, J. B. Jeffries, and R. K. Hanson, “Multi-band infrared CO2 absorption sensor for sensitive temperature and species measurements in high-temperature gases,” Appl. Phys. B 116(4), 855–865 (2014).
[Crossref]

A. Denisov, G. Colmegna, and P. Jansohn, “Temperature measurements in sooting counterflow diffusion flames using laser-induced fluorescence of flame-produced nitric oxide,” Appl. Phys. B 116(2), 339–346 (2014).
[Crossref]

F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014).
[Crossref]

Y. Wang and S. H. Chung, “Effect of strain rate on sooting limits in counterflow diffusion flames of gaseous hydrocarbon fuels: Sooting temperature index and sooting sensitivity index,” Combust. Flame 161(5), 1224–1234 (2014).
[Crossref]

A. Guha and I. Schoegl, “Tomographic laser absorption spectroscopy using Tikhonov regularization,” Appl. Opt. 53(34), 8095–8103 (2014).
[Crossref]

2013 (4)

C. Liu, L. Xu, and Z. Cao, “Measurement of nonuniform temperature and concentration distributions by combining line-of-sight tunable diode laser absorption spectroscopy with regularization methods,” Appl. Opt. 52(20), 4827–4842 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Numerical Modeling of Laminar Flames with Detailed Kinetics Based on the Operator-Splitting Method,” Energy Fuels 27(12), 7730–7753 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “A computational tool for the detailed kinetic modeling of laminar flames: Application to C2H4/CH4 coflow flames,” Combust. Flame 160(5), 870–886 (2013).
[Crossref]

Y. Wang, A. Raj, and S. H. Chung, “A PAH growth mechanism and synergistic effect on PAH formation in counterflow diffusion flames,” Combust. Flame 160(9), 1667–1676 (2013).
[Crossref]

2010 (1)

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

2009 (2)

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Formation of soot and nitrogen oxides in unsteady counterflow diffusion flames,” Combust. Flame 156(10), 2010–2022 (2009).
[Crossref]

L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17(10), 8602–8613 (2009).
[Crossref]

2008 (2)

E. O. Akesson and K. J. Daun, “Parameter selection methods for axisymmetric flame tomography through Tikhonov regularization,” Appl. Opt. 47(3), 407–416 (2008).
[Crossref]

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008).
[Crossref]

2007 (1)

X. Liu, J. B. Jeffries, and R. K. Hanson, “Measurement of Non-Uniform Temperature Distributions Using Line-of-Sight Absorption Spectroscopy,” AIAA J. 45(2), 411–419 (2007).
[Crossref]

2006 (1)

2005 (1)

2003 (1)

X. Zhou, X. Liu, J. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
[Crossref]

2002 (1)

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002).
[Crossref]

2001 (2)

D. A. Santoianni, M. E. DeCroix, and W. L. Roberts, “Temperature imaging in an unsteady propane-air counterflow diffusion flame subjected to low frequency oscillations,” Flow, Turbul. Combust. 66(1), 23–36 (2001).
[Crossref]

S. T. Sanders, J. Wang, J. B. Jeffries, and R. K. Hanson, “Diode-Laser Absorption Sensor for Line-of-Sight Gas Temperature Distributions,” Appl. Opt. 40(24), 4404–4415 (2001).
[Crossref]

1999 (1)

H. G. Im, J. H. Chen, and J.-Y. Chen, “Chemical response of methane/air diffusion flames to unsteady strain rate,” Combust. Flame 118(1-2), 204–212 (1999).
[Crossref]

1997 (1)

C. S. McEnally, Ü. Ö. Köylü, L. D. Pfefferle, and D. E. Rosner, “Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples,” Combust. Flame 109(4), 701–720 (1997).
[Crossref]

1992 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

1982 (1)

H. Tsuji, “Counterflow Diffusion Flames,” Prog. Energy Combust. Sci. 8(2), 93–119 (1982).
[Crossref]

Aggarwal, S. K.

K. C. Kalvakala, V. R. Katta, and S. K. Aggarwal, “Effects of oxygen-enrichment and fuel unsaturation on soot and NOx emissions in ethylene, propane, and propene flames,” Combust. Flame 187, 217–229 (2018).
[Crossref]

Akesson, E. O.

Ansari, A.

A. Ansari and F. N. Egolfopoulos, “Flame ignition in the counterflow configuration: Reassessing the experimental assumptions,” Combust. Flame 174, 37–49 (2016).
[Crossref]

Bai, X.-S.

X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018).
[Crossref]

Barber, R. J.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Baroncelli, M.

J. Emmert, M. Baroncelli, S. V. D. Kley, H. Pitsch, and S. Wagner, “Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner,” Energies 12(14), 2786 (2019).
[Crossref]

Bendana, F. A.

F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020).
[Crossref]

D. D. Lee, F. A. Bendana, A. P. Nair, D. I. Pineda, and R. M. Spearrin, “Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures,” J. Quant. Spectrosc. Radiat. Transfer 253, 107135 (2020).
[Crossref]

Blanquart, G.

Y. Xuan and G. Blanquart, “A flamelet-based a priori analysis on the chemistry tabulation of polycyclic aromatic hydrocarbons in non-premixed flames,” Combust. Flame 161(6), 1516–1525 (2014).
[Crossref]

Cai, W.

Cao, Z.

Carbone, F.

K. Gleason, F. Carbone, and A. Gomez, “Effect of temperature on soot inception in highly controlled counterflow ethylene diffusion flames,” Combust. Flame 192, 283–294 (2018).
[Crossref]

Castillo, J. J.

F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020).
[Crossref]

Caswell, A. W.

Chelliah, H. K.

B. G. Sarnacki and H. K. Chelliah, “Sooting limits of non-premixed counterflow ethylene/oxygen/inert flames using LII: Effects of flow strain rate and pressure (up to 30 atm),” Combust. Flame 195, 267–281 (2018).
[Crossref]

Chen, C.

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

Chen, J.

Chen, J. H.

H. G. Im, J. H. Chen, and J.-Y. Chen, “Chemical response of methane/air diffusion flames to unsteady strain rate,” Combust. Flame 118(1-2), 204–212 (1999).
[Crossref]

Chen, J.-Y.

H. G. Im, J. H. Chen, and J.-Y. Chen, “Chemical response of methane/air diffusion flames to unsteady strain rate,” Combust. Flame 118(1-2), 204–212 (1999).
[Crossref]

Cheong, K.-P.

L. Ma, K.-P. Cheong, H. Ning, and W. Ren, “An improved study of the uniformity of laminar premixed flames using laser absorption spectroscopy and CFD simulation,” Exp. Therm. Fluid Sci. 112, 110013 (2020).
[Crossref]

Choi, S.

J. W. Ku, S. Choi, H. K. Kim, S. Lee, and O. C. Kwon, “Extinction limits and structure of counterflow nonpremixed methane-ammonia/air flames,” Energy 165, 314–325 (2018).
[Crossref]

Chung, S. H.

Y. Wang and S. H. Chung, “Soot formation in laminar counterflow flames,” Prog. Energy Combust. Sci. 74, 152–238 (2019).
[Crossref]

F. Yan, M. Zhou, L. Xu, Y. Wang, and S. H. Chung, “An experimental study on the spectral dependence of light extinction in sooting ethylene counterflow diffusion flames,” Exp. Therm. Fluid Sci. 100, 259–270 (2019).
[Crossref]

L. Xu, F. Yan, M. Zhou, Y. Wang, and S. H. Chung, “Experimental and soot modeling studies of ethylene counterflow diffusion flames: Non-monotonic influence of the oxidizer composition on soot formation,” Combust. Flame 197, 304–318 (2018).
[Crossref]

Y. Wang and S. H. Chung, “Strain rate effect on sooting characteristics in laminar counterflow diffusion flames,” Combust. Flame 165, 433–444 (2016).
[Crossref]

Y. Wang and S. H. Chung, “Effect of strain rate on sooting limits in counterflow diffusion flames of gaseous hydrocarbon fuels: Sooting temperature index and sooting sensitivity index,” Combust. Flame 161(5), 1224–1234 (2014).
[Crossref]

Y. Wang, A. Raj, and S. H. Chung, “A PAH growth mechanism and synergistic effect on PAH formation in counterflow diffusion flames,” Combust. Flame 160(9), 1667–1676 (2013).
[Crossref]

Colmegna, G.

A. Denisov, G. Colmegna, and P. Jansohn, “Temperature measurements in sooting counterflow diffusion flames using laser-induced fluorescence of flame-produced nitric oxide,” Appl. Phys. B 116(2), 339–346 (2014).
[Crossref]

Cuoci, A.

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “A computational tool for the detailed kinetic modeling of laminar flames: Application to C2H4/CH4 coflow flames,” Combust. Flame 160(5), 870–886 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Numerical Modeling of Laminar Flames with Detailed Kinetics Based on the Operator-Splitting Method,” Energy Fuels 27(12), 7730–7753 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Formation of soot and nitrogen oxides in unsteady counterflow diffusion flames,” Combust. Flame 156(10), 2010–2022 (2009).
[Crossref]

Darabiha, N.

P. Rodrigues, B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha, “Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames,” Proc. Combust. Inst. 36(1), 927–934 (2017).
[Crossref]

Dasch, C. J.

Daun, K. J.

DeCroix, M. E.

D. A. Santoianni, M. E. DeCroix, and W. L. Roberts, “Temperature imaging in an unsteady propane-air counterflow diffusion flame subjected to low frequency oscillations,” Flow, Turbul. Combust. 66(1), 23–36 (2001).
[Crossref]

Denisov, A.

A. Denisov, G. Colmegna, and P. Jansohn, “Temperature measurements in sooting counterflow diffusion flames using laser-induced fluorescence of flame-produced nitric oxide,” Appl. Phys. B 116(2), 339–346 (2014).
[Crossref]

Dothe, H.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Dunn-Rankin, D.

R. E. Padilla, D. Escofet-Martin, T. Pham, W. J. Pitz, and D. Dunn-Rankin, “Structure and behavior of water-laden CH4/air counterflow diffusion flames,” Combust. Flame 196, 439–451 (2018).
[Crossref]

Egolfopoulos, F. N.

C. Wei, D. I. Pineda, L. Paxton, F. N. Egolfopoulos, and R. M. Spearrin, “Mid-infrared laser absorption tomography for quantitative 2D thermochemistry measurements in premixed jet flames,” Appl. Phys. B 124(6), 123 (2018).
[Crossref]

A. Ansari and F. N. Egolfopoulos, “Flame ignition in the counterflow configuration: Reassessing the experimental assumptions,” Combust. Flame 174, 37–49 (2016).
[Crossref]

F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014).
[Crossref]

Emmert, J.

J. Emmert, M. Baroncelli, S. V. D. Kley, H. Pitsch, and S. Wagner, “Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner,” Energies 12(14), 2786 (2019).
[Crossref]

Escofet-Martin, D.

R. E. Padilla, D. Escofet-Martin, T. Pham, W. J. Pitz, and D. Dunn-Rankin, “Structure and behavior of water-laden CH4/air counterflow diffusion flames,” Combust. Flame 196, 439–451 (2018).
[Crossref]

Ewing, D. J.

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008).
[Crossref]

Fan, J.

X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018).
[Crossref]

Faravelli, T.

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Numerical Modeling of Laminar Flames with Detailed Kinetics Based on the Operator-Splitting Method,” Energy Fuels 27(12), 7730–7753 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “A computational tool for the detailed kinetic modeling of laminar flames: Application to C2H4/CH4 coflow flames,” Combust. Flame 160(5), 870–886 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Formation of soot and nitrogen oxides in unsteady counterflow diffusion flames,” Combust. Flame 156(10), 2010–2022 (2009).
[Crossref]

Franzelli, B.

P. Rodrigues, B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha, “Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames,” Proc. Combust. Inst. 36(1), 927–934 (2017).
[Crossref]

Fraser, R. A.

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002).
[Crossref]

Frassoldati, A.

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “A computational tool for the detailed kinetic modeling of laminar flames: Application to C2H4/CH4 coflow flames,” Combust. Flame 160(5), 870–886 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Numerical Modeling of Laminar Flames with Detailed Kinetics Based on the Operator-Splitting Method,” Energy Fuels 27(12), 7730–7753 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Formation of soot and nitrogen oxides in unsteady counterflow diffusion flames,” Combust. Flame 156(10), 2010–2022 (2009).
[Crossref]

Gamache, R. R.

J. Lamouroux, L. Régalia, X. Thomas, J. Vander Auwera, R. R. Gamache, and J. M. Hartmann, “CO2 line-mixing database and software update and its tests in the 2.1 µm and 4.3 µm regions,” J. Quant. Spectrosc. Radiat. Transfer 151, 88–96 (2015).
[Crossref]

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

Ghorbani, R.

Gicquel, O.

P. Rodrigues, B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha, “Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames,” Proc. Combust. Inst. 36(1), 927–934 (2017).
[Crossref]

Gleason, K.

K. Gleason, F. Carbone, and A. Gomez, “Effect of temperature on soot inception in highly controlled counterflow ethylene diffusion flames,” Combust. Flame 192, 283–294 (2018).
[Crossref]

Goldenstein, C. S.

C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energy Combust. Sci. 60, 132–176 (2017).
[Crossref]

R. K. Hanson, R. M. Spearrin, and C. S. Goldenstein, Spectroscopy and Optical Diagnostics for Gases (Springer International, 2016).

Goldman, A.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Gomez, A.

K. Gleason, F. Carbone, and A. Gomez, “Effect of temperature on soot inception in highly controlled counterflow ethylene diffusion flames,” Combust. Flame 192, 283–294 (2018).
[Crossref]

Gord, J. R.

Gordon, I. E.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Guha, A.

Guider, O. L.

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002).
[Crossref]

Hagström, C. G.

F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020).
[Crossref]

Hansen, N.

F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014).
[Crossref]

Hanson, R. K.

C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energy Combust. Sci. 60, 132–176 (2017).
[Crossref]

R. M. Spearrin, W. Ren, J. B. Jeffries, and R. K. Hanson, “Multi-band infrared CO2 absorption sensor for sensitive temperature and species measurements in high-temperature gases,” Appl. Phys. B 116(4), 855–865 (2014).
[Crossref]

X. Liu, J. B. Jeffries, and R. K. Hanson, “Measurement of Non-Uniform Temperature Distributions Using Line-of-Sight Absorption Spectroscopy,” AIAA J. 45(2), 411–419 (2007).
[Crossref]

X. Zhou, X. Liu, J. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
[Crossref]

S. T. Sanders, J. Wang, J. B. Jeffries, and R. K. Hanson, “Diode-Laser Absorption Sensor for Line-of-Sight Gas Temperature Distributions,” Appl. Opt. 40(24), 4404–4415 (2001).
[Crossref]

R. K. Hanson, R. M. Spearrin, and C. S. Goldenstein, Spectroscopy and Optical Diagnostics for Gases (Springer International, 2016).

Hartmann, J. M.

J. Lamouroux, L. Régalia, X. Thomas, J. Vander Auwera, R. R. Gamache, and J. M. Hartmann, “CO2 line-mixing database and software update and its tests in the 2.1 µm and 4.3 µm regions,” J. Quant. Spectrosc. Radiat. Transfer 151, 88–96 (2015).
[Crossref]

Huang, Y.

X. Liu, G. Zhang, Y. Huang, Y. Wang, and F. Qi, “Two-dimensional temperature and carbon dioxide concentration profiles in atmospheric laminar diffusion flames measured by mid-infrared direct absorption spectroscopy at 4.2 µm,” Appl. Phys. B 124(4), 61 (2018).
[Crossref]

Huo, J.

X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020).
[Crossref]

Im, H. G.

H. G. Im, J. H. Chen, and J.-Y. Chen, “Chemical response of methane/air diffusion flames to unsteady strain rate,” Combust. Flame 118(1-2), 204–212 (1999).
[Crossref]

Jansohn, P.

A. Denisov, G. Colmegna, and P. Jansohn, “Temperature measurements in sooting counterflow diffusion flames using laser-induced fluorescence of flame-produced nitric oxide,” Appl. Phys. B 116(2), 339–346 (2014).
[Crossref]

Jeffries, J.

X. Zhou, X. Liu, J. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
[Crossref]

Jeffries, J. B.

C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energy Combust. Sci. 60, 132–176 (2017).
[Crossref]

R. M. Spearrin, W. Ren, J. B. Jeffries, and R. K. Hanson, “Multi-band infrared CO2 absorption sensor for sensitive temperature and species measurements in high-temperature gases,” Appl. Phys. B 116(4), 855–865 (2014).
[Crossref]

X. Liu, J. B. Jeffries, and R. K. Hanson, “Measurement of Non-Uniform Temperature Distributions Using Line-of-Sight Absorption Spectroscopy,” AIAA J. 45(2), 411–419 (2007).
[Crossref]

S. T. Sanders, J. Wang, J. B. Jeffries, and R. K. Hanson, “Diode-Laser Absorption Sensor for Line-of-Sight Gas Temperature Distributions,” Appl. Opt. 40(24), 4404–4415 (2001).
[Crossref]

Jiang, L.

X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020).
[Crossref]

Ju, Y.

F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014).
[Crossref]

Kalvakala, K. C.

K. C. Kalvakala, V. R. Katta, and S. K. Aggarwal, “Effects of oxygen-enrichment and fuel unsaturation on soot and NOx emissions in ethylene, propane, and propene flames,” Combust. Flame 187, 217–229 (2018).
[Crossref]

Kaminski, C. F.

W. Cai and C. F. Kaminski, “Tomographic absorption spectroscopy for the study of gas dynamics and reactive flows,” Prog. Energy Combust. Sci. 59, 1–31 (2017).
[Crossref]

Kang, J.

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

Katta, V. R.

K. C. Kalvakala, V. R. Katta, and S. K. Aggarwal, “Effects of oxygen-enrichment and fuel unsaturation on soot and NOx emissions in ethylene, propane, and propene flames,” Combust. Flame 187, 217–229 (2018).
[Crossref]

Kim, H. K.

J. W. Ku, S. Choi, H. K. Kim, S. Lee, and O. C. Kwon, “Extinction limits and structure of counterflow nonpremixed methane-ammonia/air flames,” Energy 165, 314–325 (2018).
[Crossref]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

Kley, S. V. D.

J. Emmert, M. Baroncelli, S. V. D. Kley, H. Pitsch, and S. Wagner, “Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner,” Energies 12(14), 2786 (2019).
[Crossref]

Kohse-Höinghaus, K.

K. Kohse-Höinghaus, “Clean combustion: Chemistry and diagnostics for a systems approach in transportation and energy conversion,” Prog. Energy Combust. Sci. 65, 1–5 (2018).
[Crossref]

F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014).
[Crossref]

Köylü, Ü. Ö.

C. S. McEnally, Ü. Ö. Köylü, L. D. Pfefferle, and D. E. Rosner, “Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples,” Combust. Flame 109(4), 701–720 (1997).
[Crossref]

Kraetschmer, T.

Kriesel, J.

A. P. Nair, D. D. Lee, D. I. Pineda, J. Kriesel, and R. M. Spearrin, “MHz laser absorption spectroscopy via diplexed RF modulation for pressure, temperature, and species in rotating detonation rocket flows,” Appl. Phys. B 126(8), 138 (2020).
[Crossref]

Ku, J. W.

J. W. Ku, S. Choi, H. K. Kim, S. Lee, and O. C. Kwon, “Extinction limits and structure of counterflow nonpremixed methane-ammonia/air flames,” Energy 165, 314–325 (2018).
[Crossref]

Kwon, O. C.

J. W. Ku, S. Choi, H. K. Kim, S. Lee, and O. C. Kwon, “Extinction limits and structure of counterflow nonpremixed methane-ammonia/air flames,” Energy 165, 314–325 (2018).
[Crossref]

Lamouroux, J.

J. Lamouroux, L. Régalia, X. Thomas, J. Vander Auwera, R. R. Gamache, and J. M. Hartmann, “CO2 line-mixing database and software update and its tests in the 2.1 µm and 4.3 µm regions,” J. Quant. Spectrosc. Radiat. Transfer 151, 88–96 (2015).
[Crossref]

Lau, L. Y.

L. H. Ma, L. Y. Lau, and W. Ren, “Non-uniform temperature and species concentration measurements in a laminar flame using multi-band infrared absorption spectroscopy,” Appl. Phys. B 123(3), 83 (2017).
[Crossref]

Law, C. K.

F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014).
[Crossref]

Lee, D. D.

D. D. Lee, F. A. Bendana, A. P. Nair, D. I. Pineda, and R. M. Spearrin, “Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures,” J. Quant. Spectrosc. Radiat. Transfer 253, 107135 (2020).
[Crossref]

A. P. Nair, D. D. Lee, D. I. Pineda, J. Kriesel, and R. M. Spearrin, “MHz laser absorption spectroscopy via diplexed RF modulation for pressure, temperature, and species in rotating detonation rocket flows,” Appl. Phys. B 126(8), 138 (2020).
[Crossref]

Lee, S.

J. W. Ku, S. Choi, H. K. Kim, S. Lee, and O. C. Kwon, “Extinction limits and structure of counterflow nonpremixed methane-ammonia/air flames,” Energy 165, 314–325 (2018).
[Crossref]

Li, L.

Li, X.

X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020).
[Crossref]

Lin, Y.

Liu, C.

Liu, F. S.

Liu, H.

S. Zheng, L. Ni, H. Liu, and H. Zhou, “Measurement of the distribution of temperature and emissivity of a candle flame using hyperspectral imaging technique,” Optik 183, 222–231 (2019).
[Crossref]

Liu, X.

X. Liu, G. Wang, J. Zheng, L. Xu, S. Wang, L. Li, and F. Qi, “Temporally resolved two dimensional temperature field of acoustically excited swirling flames measured by mid-infrared direct absorption spectroscopy,” Opt. Express 26(24), 31983–31994 (2018).
[Crossref]

X. Liu, G. Zhang, Y. Huang, Y. Wang, and F. Qi, “Two-dimensional temperature and carbon dioxide concentration profiles in atmospheric laminar diffusion flames measured by mid-infrared direct absorption spectroscopy at 4.2 µm,” Appl. Phys. B 124(4), 61 (2018).
[Crossref]

X. Liu, J. B. Jeffries, and R. K. Hanson, “Measurement of Non-Uniform Temperature Distributions Using Line-of-Sight Absorption Spectroscopy,” AIAA J. 45(2), 411–419 (2007).
[Crossref]

X. Zhou, X. Liu, J. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
[Crossref]

Luo, K.

X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018).
[Crossref]

Luo, Y.

X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018).
[Crossref]

Ma, L.

L. Ma, K.-P. Cheong, H. Ning, and W. Ren, “An improved study of the uniformity of laminar premixed flames using laser absorption spectroscopy and CFD simulation,” Exp. Therm. Fluid Sci. 112, 110013 (2020).
[Crossref]

L. Ma, W. Cai, A. W. Caswell, T. Kraetschmer, S. T. Sanders, S. Roy, and J. R. Gord, “Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy,” Opt. Express 17(10), 8602–8613 (2009).
[Crossref]

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008).
[Crossref]

Ma, L. H.

L. H. Ma, L. Y. Lau, and W. Ren, “Non-uniform temperature and species concentration measurements in a laminar flame using multi-band infrared absorption spectroscopy,” Appl. Phys. B 123(3), 83 (2017).
[Crossref]

McEnally, C. S.

C. S. McEnally, Ü. Ö. Köylü, L. D. Pfefferle, and D. E. Rosner, “Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples,” Combust. Flame 109(4), 701–720 (1997).
[Crossref]

Meng, D.

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

Mu, Z.

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

Nair, A. P.

A. P. Nair, D. D. Lee, D. I. Pineda, J. Kriesel, and R. M. Spearrin, “MHz laser absorption spectroscopy via diplexed RF modulation for pressure, temperature, and species in rotating detonation rocket flows,” Appl. Phys. B 126(8), 138 (2020).
[Crossref]

D. D. Lee, F. A. Bendana, A. P. Nair, D. I. Pineda, and R. M. Spearrin, “Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures,” J. Quant. Spectrosc. Radiat. Transfer 253, 107135 (2020).
[Crossref]

Ni, L.

S. Zheng, L. Ni, H. Liu, and H. Zhou, “Measurement of the distribution of temperature and emissivity of a candle flame using hyperspectral imaging technique,” Optik 183, 222–231 (2019).
[Crossref]

Ning, H.

L. Ma, K.-P. Cheong, H. Ning, and W. Ren, “An improved study of the uniformity of laminar premixed flames using laser absorption spectroscopy and CFD simulation,” Exp. Therm. Fluid Sci. 112, 110013 (2020).
[Crossref]

Padilla, R. E.

R. E. Padilla, D. Escofet-Martin, T. Pham, W. J. Pitz, and D. Dunn-Rankin, “Structure and behavior of water-laden CH4/air counterflow diffusion flames,” Combust. Flame 196, 439–451 (2018).
[Crossref]

Paxton, L.

C. Wei, D. I. Pineda, L. Paxton, F. N. Egolfopoulos, and R. M. Spearrin, “Mid-infrared laser absorption tomography for quantitative 2D thermochemistry measurements in premixed jet flames,” Appl. Phys. B 124(6), 123 (2018).
[Crossref]

Perevalov, V. I.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Pfefferle, L. D.

C. S. McEnally, Ü. Ö. Köylü, L. D. Pfefferle, and D. E. Rosner, “Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples,” Combust. Flame 109(4), 701–720 (1997).
[Crossref]

Pham, T.

R. E. Padilla, D. Escofet-Martin, T. Pham, W. J. Pitz, and D. Dunn-Rankin, “Structure and behavior of water-laden CH4/air counterflow diffusion flames,” Combust. Flame 196, 439–451 (2018).
[Crossref]

Pineda, D. I.

F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020).
[Crossref]

D. D. Lee, F. A. Bendana, A. P. Nair, D. I. Pineda, and R. M. Spearrin, “Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures,” J. Quant. Spectrosc. Radiat. Transfer 253, 107135 (2020).
[Crossref]

A. P. Nair, D. D. Lee, D. I. Pineda, J. Kriesel, and R. M. Spearrin, “MHz laser absorption spectroscopy via diplexed RF modulation for pressure, temperature, and species in rotating detonation rocket flows,” Appl. Phys. B 126(8), 138 (2020).
[Crossref]

C. Wei, D. I. Pineda, L. Paxton, F. N. Egolfopoulos, and R. M. Spearrin, “Mid-infrared laser absorption tomography for quantitative 2D thermochemistry measurements in premixed jet flames,” Appl. Phys. B 124(6), 123 (2018).
[Crossref]

Pitsch, H.

J. Emmert, M. Baroncelli, S. V. D. Kley, H. Pitsch, and S. Wagner, “Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner,” Energies 12(14), 2786 (2019).
[Crossref]

Pitz, W. J.

R. E. Padilla, D. Escofet-Martin, T. Pham, W. J. Pitz, and D. Dunn-Rankin, “Structure and behavior of water-laden CH4/air counterflow diffusion flames,” Combust. Flame 196, 439–451 (2018).
[Crossref]

Qi, F.

X. Liu, G. Zhang, Y. Huang, Y. Wang, and F. Qi, “Two-dimensional temperature and carbon dioxide concentration profiles in atmospheric laminar diffusion flames measured by mid-infrared direct absorption spectroscopy at 4.2 µm,” Appl. Phys. B 124(4), 61 (2018).
[Crossref]

X. Liu, G. Wang, J. Zheng, L. Xu, S. Wang, L. Li, and F. Qi, “Temporally resolved two dimensional temperature field of acoustically excited swirling flames measured by mid-infrared direct absorption spectroscopy,” Opt. Express 26(24), 31983–31994 (2018).
[Crossref]

F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014).
[Crossref]

Qu, Z. C.

Raj, A.

Y. Wang, A. Raj, and S. H. Chung, “A PAH growth mechanism and synergistic effect on PAH formation in counterflow diffusion flames,” Combust. Flame 160(9), 1667–1676 (2013).
[Crossref]

Ranzi, E.

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Numerical Modeling of Laminar Flames with Detailed Kinetics Based on the Operator-Splitting Method,” Energy Fuels 27(12), 7730–7753 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “A computational tool for the detailed kinetic modeling of laminar flames: Application to C2H4/CH4 coflow flames,” Combust. Flame 160(5), 870–886 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Formation of soot and nitrogen oxides in unsteady counterflow diffusion flames,” Combust. Flame 156(10), 2010–2022 (2009).
[Crossref]

Régalia, L.

J. Lamouroux, L. Régalia, X. Thomas, J. Vander Auwera, R. R. Gamache, and J. M. Hartmann, “CO2 line-mixing database and software update and its tests in the 2.1 µm and 4.3 µm regions,” J. Quant. Spectrosc. Radiat. Transfer 151, 88–96 (2015).
[Crossref]

Ren, W.

L. Ma, K.-P. Cheong, H. Ning, and W. Ren, “An improved study of the uniformity of laminar premixed flames using laser absorption spectroscopy and CFD simulation,” Exp. Therm. Fluid Sci. 112, 110013 (2020).
[Crossref]

L. H. Ma, L. Y. Lau, and W. Ren, “Non-uniform temperature and species concentration measurements in a laminar flame using multi-band infrared absorption spectroscopy,” Appl. Phys. B 123(3), 83 (2017).
[Crossref]

R. M. Spearrin, W. Ren, J. B. Jeffries, and R. K. Hanson, “Multi-band infrared CO2 absorption sensor for sensitive temperature and species measurements in high-temperature gases,” Appl. Phys. B 116(4), 855–865 (2014).
[Crossref]

Roberts, W. L.

D. A. Santoianni, M. E. DeCroix, and W. L. Roberts, “Temperature imaging in an unsteady propane-air counterflow diffusion flame subjected to low frequency oscillations,” Flow, Turbul. Combust. 66(1), 23–36 (2001).
[Crossref]

Rodrigues, P.

P. Rodrigues, B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha, “Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames,” Proc. Combust. Inst. 36(1), 927–934 (2017).
[Crossref]

Rosner, D. E.

C. S. McEnally, Ü. Ö. Köylü, L. D. Pfefferle, and D. E. Rosner, “Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples,” Combust. Flame 109(4), 701–720 (1997).
[Crossref]

Rothman, L. S.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Roy, S.

Sanders, I. C.

F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020).
[Crossref]

Sanders, S. T.

Santoianni, D. A.

D. A. Santoianni, M. E. DeCroix, and W. L. Roberts, “Temperature imaging in an unsteady propane-air counterflow diffusion flame subjected to low frequency oscillations,” Flow, Turbul. Combust. 66(1), 23–36 (2001).
[Crossref]

Sarnacki, B. G.

B. G. Sarnacki and H. K. Chelliah, “Sooting limits of non-premixed counterflow ethylene/oxygen/inert flames using LII: Effects of flow strain rate and pressure (up to 30 atm),” Combust. Flame 195, 267–281 (2018).
[Crossref]

Schmidt, F. M.

Schoegl, I.

Smallwood, G. J.

K. J. Daun, K. A. Thomson, F. S. Liu, and G. J. Smallwood, “Deconvolution of axisymmetric flame properties using Tikhonov regularization,” Appl. Opt. 45(19), 4638–4646 (2006).
[Crossref]

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002).
[Crossref]

Snelling, D. R.

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002).
[Crossref]

Spearrin, R. M.

F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020).
[Crossref]

A. P. Nair, D. D. Lee, D. I. Pineda, J. Kriesel, and R. M. Spearrin, “MHz laser absorption spectroscopy via diplexed RF modulation for pressure, temperature, and species in rotating detonation rocket flows,” Appl. Phys. B 126(8), 138 (2020).
[Crossref]

D. D. Lee, F. A. Bendana, A. P. Nair, D. I. Pineda, and R. M. Spearrin, “Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures,” J. Quant. Spectrosc. Radiat. Transfer 253, 107135 (2020).
[Crossref]

C. Wei, D. I. Pineda, L. Paxton, F. N. Egolfopoulos, and R. M. Spearrin, “Mid-infrared laser absorption tomography for quantitative 2D thermochemistry measurements in premixed jet flames,” Appl. Phys. B 124(6), 123 (2018).
[Crossref]

C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energy Combust. Sci. 60, 132–176 (2017).
[Crossref]

R. M. Spearrin, W. Ren, J. B. Jeffries, and R. K. Hanson, “Multi-band infrared CO2 absorption sensor for sensitive temperature and species measurements in high-temperature gases,” Appl. Phys. B 116(4), 855–865 (2014).
[Crossref]

R. K. Hanson, R. M. Spearrin, and C. S. Goldenstein, Spectroscopy and Optical Diagnostics for Gases (Springer International, 2016).

Tashkun, S. A.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Tennyson, J.

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Thomas, X.

J. Lamouroux, L. Régalia, X. Thomas, J. Vander Auwera, R. R. Gamache, and J. M. Hartmann, “CO2 line-mixing database and software update and its tests in the 2.1 µm and 4.3 µm regions,” J. Quant. Spectrosc. Radiat. Transfer 151, 88–96 (2015).
[Crossref]

Thomson, K. A.

K. J. Daun, K. A. Thomson, F. S. Liu, and G. J. Smallwood, “Deconvolution of axisymmetric flame properties using Tikhonov regularization,” Appl. Opt. 45(19), 4638–4646 (2006).
[Crossref]

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002).
[Crossref]

Tsuji, H.

H. Tsuji, “Counterflow Diffusion Flames,” Prog. Energy Combust. Sci. 8(2), 93–119 (1982).
[Crossref]

Valiev, D.

Vander Auwera, J.

J. Lamouroux, L. Régalia, X. Thomas, J. Vander Auwera, R. R. Gamache, and J. M. Hartmann, “CO2 line-mixing database and software update and its tests in the 2.1 µm and 4.3 µm regions,” J. Quant. Spectrosc. Radiat. Transfer 151, 88–96 (2015).
[Crossref]

Varghese, P.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

Vicquelin, R.

P. Rodrigues, B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha, “Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames,” Proc. Combust. Inst. 36(1), 927–934 (2017).
[Crossref]

Villarreal, R.

Wagner, S.

J. Emmert, M. Baroncelli, S. V. D. Kley, H. Pitsch, and S. Wagner, “Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner,” Energies 12(14), 2786 (2019).
[Crossref]

Wang, G.

Wang, H.

X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018).
[Crossref]

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

Wang, J.

Wang, S.

Wang, X.

X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020).
[Crossref]

Wang, Y.

Y. Wang and S. H. Chung, “Soot formation in laminar counterflow flames,” Prog. Energy Combust. Sci. 74, 152–238 (2019).
[Crossref]

F. Yan, M. Zhou, L. Xu, Y. Wang, and S. H. Chung, “An experimental study on the spectral dependence of light extinction in sooting ethylene counterflow diffusion flames,” Exp. Therm. Fluid Sci. 100, 259–270 (2019).
[Crossref]

L. Xu, F. Yan, M. Zhou, Y. Wang, and S. H. Chung, “Experimental and soot modeling studies of ethylene counterflow diffusion flames: Non-monotonic influence of the oxidizer composition on soot formation,” Combust. Flame 197, 304–318 (2018).
[Crossref]

X. Liu, G. Zhang, Y. Huang, Y. Wang, and F. Qi, “Two-dimensional temperature and carbon dioxide concentration profiles in atmospheric laminar diffusion flames measured by mid-infrared direct absorption spectroscopy at 4.2 µm,” Appl. Phys. B 124(4), 61 (2018).
[Crossref]

Y. Wang and S. H. Chung, “Strain rate effect on sooting characteristics in laminar counterflow diffusion flames,” Combust. Flame 165, 433–444 (2016).
[Crossref]

Y. Wang and S. H. Chung, “Effect of strain rate on sooting limits in counterflow diffusion flames of gaseous hydrocarbon fuels: Sooting temperature index and sooting sensitivity index,” Combust. Flame 161(5), 1224–1234 (2014).
[Crossref]

Y. Wang, A. Raj, and S. H. Chung, “A PAH growth mechanism and synergistic effect on PAH formation in counterflow diffusion flames,” Combust. Flame 160(9), 1667–1676 (2013).
[Crossref]

Weckman, E. J.

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002).
[Crossref]

Wei, C.

C. Wei, D. I. Pineda, L. Paxton, F. N. Egolfopoulos, and R. M. Spearrin, “Mid-infrared laser absorption tomography for quantitative 2D thermochemistry measurements in premixed jet flames,” Appl. Phys. B 124(6), 123 (2018).
[Crossref]

Wen, X.

X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018).
[Crossref]

Xu, L.

Xuan, Y.

Y. Xuan and G. Blanquart, “A flamelet-based a priori analysis on the chemistry tabulation of polycyclic aromatic hydrocarbons in non-premixed flames,” Combust. Flame 161(6), 1516–1525 (2014).
[Crossref]

Yan, F.

F. Yan, M. Zhou, L. Xu, Y. Wang, and S. H. Chung, “An experimental study on the spectral dependence of light extinction in sooting ethylene counterflow diffusion flames,” Exp. Therm. Fluid Sci. 100, 259–270 (2019).
[Crossref]

L. Xu, F. Yan, M. Zhou, Y. Wang, and S. H. Chung, “Experimental and soot modeling studies of ethylene counterflow diffusion flames: Non-monotonic influence of the oxidizer composition on soot formation,” Combust. Flame 197, 304–318 (2018).
[Crossref]

Zhang, G.

X. Liu, G. Zhang, Y. Huang, Y. Wang, and F. Qi, “Two-dimensional temperature and carbon dioxide concentration profiles in atmospheric laminar diffusion flames measured by mid-infrared direct absorption spectroscopy at 4.2 µm,” Appl. Phys. B 124(4), 61 (2018).
[Crossref]

Zhang, J.

X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020).
[Crossref]

Zhang, T.

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

Zhang, X.

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

Zhao, D.

X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020).
[Crossref]

Zheng, J.

Zheng, S.

S. Zheng, L. Ni, H. Liu, and H. Zhou, “Measurement of the distribution of temperature and emissivity of a candle flame using hyperspectral imaging technique,” Optik 183, 222–231 (2019).
[Crossref]

Zhou, H.

S. Zheng, L. Ni, H. Liu, and H. Zhou, “Measurement of the distribution of temperature and emissivity of a candle flame using hyperspectral imaging technique,” Optik 183, 222–231 (2019).
[Crossref]

Zhou, M.

F. Yan, M. Zhou, L. Xu, Y. Wang, and S. H. Chung, “An experimental study on the spectral dependence of light extinction in sooting ethylene counterflow diffusion flames,” Exp. Therm. Fluid Sci. 100, 259–270 (2019).
[Crossref]

L. Xu, F. Yan, M. Zhou, Y. Wang, and S. H. Chung, “Experimental and soot modeling studies of ethylene counterflow diffusion flames: Non-monotonic influence of the oxidizer composition on soot formation,” Combust. Flame 197, 304–318 (2018).
[Crossref]

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

Zhou, X.

X. Zhou, X. Liu, J. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
[Crossref]

AIAA J. (2)

D. R. Snelling, K. A. Thomson, G. J. Smallwood, O. L. Guider, E. J. Weckman, and R. A. Fraser, “Spectrally resolved measurement of flame radiation to determine soot temperature and concentration,” AIAA J. 40(9), 1789–1795 (2002).
[Crossref]

X. Liu, J. B. Jeffries, and R. K. Hanson, “Measurement of Non-Uniform Temperature Distributions Using Line-of-Sight Absorption Spectroscopy,” AIAA J. 45(2), 411–419 (2007).
[Crossref]

Appl. Opt. (7)

Appl. Phys. B (6)

L. H. Ma, L. Y. Lau, and W. Ren, “Non-uniform temperature and species concentration measurements in a laminar flame using multi-band infrared absorption spectroscopy,” Appl. Phys. B 123(3), 83 (2017).
[Crossref]

X. Liu, G. Zhang, Y. Huang, Y. Wang, and F. Qi, “Two-dimensional temperature and carbon dioxide concentration profiles in atmospheric laminar diffusion flames measured by mid-infrared direct absorption spectroscopy at 4.2 µm,” Appl. Phys. B 124(4), 61 (2018).
[Crossref]

A. Denisov, G. Colmegna, and P. Jansohn, “Temperature measurements in sooting counterflow diffusion flames using laser-induced fluorescence of flame-produced nitric oxide,” Appl. Phys. B 116(2), 339–346 (2014).
[Crossref]

R. M. Spearrin, W. Ren, J. B. Jeffries, and R. K. Hanson, “Multi-band infrared CO2 absorption sensor for sensitive temperature and species measurements in high-temperature gases,” Appl. Phys. B 116(4), 855–865 (2014).
[Crossref]

C. Wei, D. I. Pineda, L. Paxton, F. N. Egolfopoulos, and R. M. Spearrin, “Mid-infrared laser absorption tomography for quantitative 2D thermochemistry measurements in premixed jet flames,” Appl. Phys. B 124(6), 123 (2018).
[Crossref]

A. P. Nair, D. D. Lee, D. I. Pineda, J. Kriesel, and R. M. Spearrin, “MHz laser absorption spectroscopy via diplexed RF modulation for pressure, temperature, and species in rotating detonation rocket flows,” Appl. Phys. B 126(8), 138 (2020).
[Crossref]

Combust. Flame (15)

Y. Wang and S. H. Chung, “Effect of strain rate on sooting limits in counterflow diffusion flames of gaseous hydrocarbon fuels: Sooting temperature index and sooting sensitivity index,” Combust. Flame 161(5), 1224–1234 (2014).
[Crossref]

B. G. Sarnacki and H. K. Chelliah, “Sooting limits of non-premixed counterflow ethylene/oxygen/inert flames using LII: Effects of flow strain rate and pressure (up to 30 atm),” Combust. Flame 195, 267–281 (2018).
[Crossref]

Y. Wang and S. H. Chung, “Strain rate effect on sooting characteristics in laminar counterflow diffusion flames,” Combust. Flame 165, 433–444 (2016).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “A computational tool for the detailed kinetic modeling of laminar flames: Application to C2H4/CH4 coflow flames,” Combust. Flame 160(5), 870–886 (2013).
[Crossref]

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Formation of soot and nitrogen oxides in unsteady counterflow diffusion flames,” Combust. Flame 156(10), 2010–2022 (2009).
[Crossref]

Y. Xuan and G. Blanquart, “A flamelet-based a priori analysis on the chemistry tabulation of polycyclic aromatic hydrocarbons in non-premixed flames,” Combust. Flame 161(6), 1516–1525 (2014).
[Crossref]

H. G. Im, J. H. Chen, and J.-Y. Chen, “Chemical response of methane/air diffusion flames to unsteady strain rate,” Combust. Flame 118(1-2), 204–212 (1999).
[Crossref]

Y. Wang, A. Raj, and S. H. Chung, “A PAH growth mechanism and synergistic effect on PAH formation in counterflow diffusion flames,” Combust. Flame 160(9), 1667–1676 (2013).
[Crossref]

L. Xu, F. Yan, M. Zhou, Y. Wang, and S. H. Chung, “Experimental and soot modeling studies of ethylene counterflow diffusion flames: Non-monotonic influence of the oxidizer composition on soot formation,” Combust. Flame 197, 304–318 (2018).
[Crossref]

K. Gleason, F. Carbone, and A. Gomez, “Effect of temperature on soot inception in highly controlled counterflow ethylene diffusion flames,” Combust. Flame 192, 283–294 (2018).
[Crossref]

R. E. Padilla, D. Escofet-Martin, T. Pham, W. J. Pitz, and D. Dunn-Rankin, “Structure and behavior of water-laden CH4/air counterflow diffusion flames,” Combust. Flame 196, 439–451 (2018).
[Crossref]

A. Ansari and F. N. Egolfopoulos, “Flame ignition in the counterflow configuration: Reassessing the experimental assumptions,” Combust. Flame 174, 37–49 (2016).
[Crossref]

K. C. Kalvakala, V. R. Katta, and S. K. Aggarwal, “Effects of oxygen-enrichment and fuel unsaturation on soot and NOx emissions in ethylene, propane, and propene flames,” Combust. Flame 187, 217–229 (2018).
[Crossref]

X. Wen, X.-S. Bai, K. Luo, H. Wang, Y. Luo, and J. Fan, “A generalized flamelet tabulation method for partially premixed combustion,” Combust. Flame 198, 54–68 (2018).
[Crossref]

C. S. McEnally, Ü. Ö. Köylü, L. D. Pfefferle, and D. E. Rosner, “Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples,” Combust. Flame 109(4), 701–720 (1997).
[Crossref]

Comput. Phys. Commun. (1)

W. Cai, D. J. Ewing, and L. Ma, “Application of simulated annealing for multispectral tomography,” Comput. Phys. Commun. 179(4), 250–255 (2008).
[Crossref]

Energies (1)

J. Emmert, M. Baroncelli, S. V. D. Kley, H. Pitsch, and S. Wagner, “Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner,” Energies 12(14), 2786 (2019).
[Crossref]

Energy (1)

J. W. Ku, S. Choi, H. K. Kim, S. Lee, and O. C. Kwon, “Extinction limits and structure of counterflow nonpremixed methane-ammonia/air flames,” Energy 165, 314–325 (2018).
[Crossref]

Energy Fuels (1)

A. Cuoci, A. Frassoldati, T. Faravelli, and E. Ranzi, “Numerical Modeling of Laminar Flames with Detailed Kinetics Based on the Operator-Splitting Method,” Energy Fuels 27(12), 7730–7753 (2013).
[Crossref]

Exp. Fluids (1)

F. A. Bendana, I. C. Sanders, J. J. Castillo, C. G. Hagström, D. I. Pineda, and R. M. Spearrin, “In-situ thermochemical analysis of hybrid rocket fuel oxidation via laser absorption tomography of CO, CO2, and H2O,” Exp. Fluids 61(9), 190 (2020).
[Crossref]

Exp. Therm. Fluid Sci. (2)

F. Yan, M. Zhou, L. Xu, Y. Wang, and S. H. Chung, “An experimental study on the spectral dependence of light extinction in sooting ethylene counterflow diffusion flames,” Exp. Therm. Fluid Sci. 100, 259–270 (2019).
[Crossref]

L. Ma, K.-P. Cheong, H. Ning, and W. Ren, “An improved study of the uniformity of laminar premixed flames using laser absorption spectroscopy and CFD simulation,” Exp. Therm. Fluid Sci. 112, 110013 (2020).
[Crossref]

Flow, Turbul. Combust. (1)

D. A. Santoianni, M. E. DeCroix, and W. L. Roberts, “Temperature imaging in an unsteady propane-air counterflow diffusion flame subjected to low frequency oscillations,” Flow, Turbul. Combust. 66(1), 23–36 (2001).
[Crossref]

Fuel (1)

X. Li, J. Zhang, J. Huo, X. Wang, L. Jiang, and D. Zhao, “C-shaped extinction curves and lean fuel limits of methane oxy-fuel diffusion flames at different oxygen concentrations,” Fuel 259, 116296 (2020).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (3)

J. Lamouroux, L. Régalia, X. Thomas, J. Vander Auwera, R. R. Gamache, and J. M. Hartmann, “CO2 line-mixing database and software update and its tests in the 2.1 µm and 4.3 µm regions,” J. Quant. Spectrosc. Radiat. Transfer 151, 88–96 (2015).
[Crossref]

D. D. Lee, F. A. Bendana, A. P. Nair, D. I. Pineda, and R. M. Spearrin, “Line mixing and broadening of carbon dioxide by argon in the v3 bandhead near 4.2 µm at high temperatures and high pressures,” J. Quant. Spectrosc. Radiat. Transfer 253, 107135 (2020).
[Crossref]

L. S. Rothman, I. E. Gordon, R. J. Barber, H. Dothe, R. R. Gamache, A. Goldman, V. I. Perevalov, S. A. Tashkun, and J. Tennyson, “HITEMP, the high-temperature molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 111(15), 2139–2150 (2010).
[Crossref]

Meas. Sci. Technol. (1)

X. Zhou, X. Liu, J. Jeffries, and R. K. Hanson, “Development of a sensor for temperature and water concentration in combustion gases using a single tunable diode laser,” Meas. Sci. Technol. 14(8), 1459–1468 (2003).
[Crossref]

Opt. Express (4)

Optik (1)

S. Zheng, L. Ni, H. Liu, and H. Zhou, “Measurement of the distribution of temperature and emissivity of a candle flame using hyperspectral imaging technique,” Optik 183, 222–231 (2019).
[Crossref]

Proc. Combust. Inst. (1)

P. Rodrigues, B. Franzelli, R. Vicquelin, O. Gicquel, and N. Darabiha, “Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames,” Proc. Combust. Inst. 36(1), 927–934 (2017).
[Crossref]

Prog. Energy Combust. Sci. (6)

W. Cai and C. F. Kaminski, “Tomographic absorption spectroscopy for the study of gas dynamics and reactive flows,” Prog. Energy Combust. Sci. 59, 1–31 (2017).
[Crossref]

C. S. Goldenstein, R. M. Spearrin, J. B. Jeffries, and R. K. Hanson, “Infrared laser-absorption sensing for combustion gases,” Prog. Energy Combust. Sci. 60, 132–176 (2017).
[Crossref]

K. Kohse-Höinghaus, “Clean combustion: Chemistry and diagnostics for a systems approach in transportation and energy conversion,” Prog. Energy Combust. Sci. 65, 1–5 (2018).
[Crossref]

F. N. Egolfopoulos, N. Hansen, Y. Ju, K. Kohse-Höinghaus, C. K. Law, and F. Qi, “Advances and challenges in laminar flame experiments and implications for combustion chemistry,” Prog. Energy Combust. Sci. 43, 36–67 (2014).
[Crossref]

H. Tsuji, “Counterflow Diffusion Flames,” Prog. Energy Combust. Sci. 8(2), 93–119 (1982).
[Crossref]

Y. Wang and S. H. Chung, “Soot formation in laminar counterflow flames,” Prog. Energy Combust. Sci. 74, 152–238 (2019).
[Crossref]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983).
[Crossref]

Sensors (1)

T. Zhang, J. Kang, D. Meng, H. Wang, Z. Mu, M. Zhou, X. Zhang, and C. Chen, “Mathematical Methods and Algorithms for Improving Near-Infrared Tunable Diode-Laser Absorption Spectroscopy,” Sensors 18(12), 4295 (2018).
[Crossref]

Other (2)

. “University of California, San Diego Center for Energy Research, Combustion Division[DB/OL]. [2005-06-15]. http://maemail.ucsd.edu/combustion/cermech/.”

R. K. Hanson, R. M. Spearrin, and C. S. Goldenstein, Spectroscopy and Optical Diagnostics for Gases (Springer International, 2016).

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Figures (17)

Fig. 1.
Fig. 1. (a) Coordinate system for axisymmetric flames (radial slice at a specific burner height); (b) Discretization of the axisymmetric domain.
Fig. 2.
Fig. 2. Simulated CO2 absorption coefficients at various temperatures for XCO2 = 0.1 based on the HITEMP database.
Fig. 3.
Fig. 3. Schematic of the burner and optical setup; ICL: interband cascade laser; CVL: convex CaF2 lens; CCL: concave CaF2 lens; CCM: concave gold mirror; BS: beam splitter; MR: flat gold mirror.
Fig. 4.
Fig. 4. Typical transmitted laser intensity signal over a complete wavelength scan period.
Fig. 5.
Fig. 5. Frequency-resolved absorption features, shown are virtually measured spectral absorbance (VMSA) with random noise added, test reference kν and the reconstructed kν at axial distance of 4.65 mm above the fuel nozzle.
Fig. 6.
Fig. 6. Radial profiles of the absorption coefficient at 2397.28cm−1, comparisons among the reconstructed data with ATP, TiK-ATP and the test reference data are shown.
Fig. 7.
Fig. 7. Reconstructed radial profiles of temperature (square) and CO2 mole fraction (circle) as compared with the test reference data (lines, directly from CFD results) for Flame T1 at H = 4.65 mm.
Fig. 8.
Fig. 8. Experimentally measured radial temperature profiles for flame E1 at H = 4.65 (black symbol) and H = 4.2 mm (red symbols) with corresponding Boltzmann fitting profiles (lines).
Fig. 9.
Fig. 9. Radial temperature profiles for Flame T1 and H = 4.65 mm, comparisons between the data obtained from multiline thermometry and the test reference data are shown.
Fig. 10.
Fig. 10. Experimental absorption spectrum for flame E1 at H = 4.65 mm and r = 0 mm, obtained through frequency-resolved tomography.
Fig. 11.
Fig. 11. Measured axial profiles of flame temperatures for flame E1, E2 (a) and E3, E4(b). Numerical results obtained through OPPDIF simulation were also included for comparison purposes. The locations of the gas stagnation plane are also marked as Hstg, g.
Fig. 12.
Fig. 12. Measured axial profiles of flame XCO2 for flame E1, E2 (a) and E3, E4(b).
Fig. 13.
Fig. 13. Measured radial temperature profiles for flame E1 at H = 4.2 mm and H = 4.8 mm, obtained from tomography (symbols) and the multiline method with profile fitting (lines).
Fig. 14.
Fig. 14. Measured temperature contour plot of flame E2.
Fig. 15.
Fig. 15. A comparison among instantaneous, phase-averaged and S-G filtered instantaneous signals.
Fig. 16.
Fig. 16. Instantaneous measurements for Flame E1 (red) and E2 (black) at H = 4.65 mm.(a) Tcore;(b) x0 and G1.
Fig. 17.
Fig. 17. Time evolution of the virtually measured spectral absorbance (a) and temperature at the center axis (b) at two flame heights of H = 4.65 and 4.95 mm. Solid lines in (b) represent test reference temperature data directly from CFD simulations.

Tables (1)

Tables Icon

Table 1. Flame conditions and corresponding flow rates: Flame E1 is non-sooting, E2 is a SF flames, while E3 and E4 are SFO flames.

Equations (14)

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( I t I 0 ) v = exp ( 0 L k v ( x ) d x )
α v = ln ( I t I 0 ) v = 0 L k v ( x ) d x
k v ( x ) = j P X ( x ) S j ( T ( x ) ) φ j ( v v 0 j )
k j ( x ) = j k v ( x ) d v = j P X ( x ) S j ( T ( x ) ) φ j ( v v 0 j ) d v = P X ( x ) S j ( T ( x ) )
S 1 ( T ( x ) ) S 2 ( T ( x ) ) = k 1 ( x ) k 2 ( x ) P X ( x ) P X ( x )  =  k 1 ( x ) k 2 ( x ) = R
T = h c k ( E 2 E 1 ) ln ( R ) + ln ( S 2 ( T 0 ) S 1 ( T 0 ) ) + h c k ( E 2 E 1 ) T 0
A j = j α v d v = j 0 L k v ( x ) d x d v = 0 L k j ( x ) d x
min T ( x ) , X ( x ) + ( j P X ( x ) S j ( T ( x ) ) φ j ( v v 0 j ) k v ( v ; x ) m e a s u r e d ) 2 d v
α v ( x ) = 2 x R k v ( r ) r r 2 x 2 d r
A b = P
[ A λ L 0 ] b = [ P 0 ]
Z v ( v ; p 0 , q 0 ) = i N j P X ( x i ; p 0 ) S j ( T ( x i ; q 0 ) ) φ j ( ( v v 0 j ) ; x i )
min p , q + ( Z v ( v ; p , q ) α v ( v ) m e a s u r e d ) 2 d v
y = T a m b + T c o r e T a m b 1 + exp ( ( x x 0 ) / G 1 )

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