Quantitative Diagnostics of Hydroxyl (OH) Radicals in Methane–Air Flames Using Wavelength Modulation Spectroscopy with Correction for Water Spectral Interference

Abstract

Exhaust gases generated by fossil fuel combustion significantly contribute to air pollution and climate change, emphasizing the need for efficient combustion diagnostics. OH radicals are key indicators of flame behavior; however, conventional laser-induced fluorescence (LIF) techniques are impractical for industrial monitoring due to their complexity. In this study, wavelength modulation spectroscopy (WMS) employing a near-infrared laser at 1.49 μm was used to measure OH radical concentrations, incorporating a correction for spectral interference from H₂O. A wavelength division multiplexer (WDM) was used to enable the simultaneous operation of two lasers at 1.49 μm (OH) and 1.39 μm (H₂O, temperature), allowing for correction of water interference. OH concentrations were determined using both WMS and direct absorption spectroscopy (DAS), and the results were evaluated through comparison with CHEMKIN simulations. The proposed dual-laser system demonstrated reliable and interference-corrected quantification of OH radicals in methane (CH₄)/air premixed flames over a range of equivalence ratios. Comparisons with thermocouple-based temperature measurements and CHEMKIN-predicted species concentrations confirmed the reliability of the proposed technique. This study highlights the robustness and applicability of WMS-based OH diagnostics for combustion monitoring and demonstrates the potential for future implementation in industrial burner systems.

Graphical abstract

This is a visual representation of the abstract.

Keywords

Tunable diode laser absorption spectroscopy TDLAS wavelength modulation spectroscopy WMS OH radicals water spectral interference combustion diagnostics

Introduction

In response to increasingly stringent environmental regulations, combustion technologies are required to reduce pollutant emissions while maintaining or improving performance. Hydroxyl (OH) radicals play a crucial role in combustion chemistry, and their concentrations serve as sensitive indicators of flame structure and combustion dynamics. Therefore, accurate quantification of OH radical concentrations is essential for optimizing combustion processes and mitigating NO_X emissions. However, real-time measurement of OH radicals in high-temperature flames is particularly challenging due to their high reactivity and short lifetimes, which make conventional sampling-based techniques impractical. As a result, laser-based diagnostic methods have emerged as effective tools for OH detection in combustion environments.^1–5

Among these techniques, laser-induced fluorescence (LIF) has been widely used. This technique detects OH by exciting the molecule with a laser and collecting the resulting fluorescence emission, enabling visualization of flame structures. However, the complexity and bulkiness of LIF systems have limited their practical use in industrial combustion settings.^6–8 Chemiluminescence imaging, another method, uses optical filters to observe specific emission wavelengths, but it lacks both spatial resolution and quantitative accuracy.^9–11

In contrast, tunable diode laser absorption spectroscopy (TDLAS) provides a quantitative and species-selective approach based on the absorption of laser light at specific wavelengths. The simple and robust design of TDLAS makes it suitable for harsh environments. TDLAS has been successfully applied in numerous studies to measure OH radical concentrations. The OH radical absorption spectrum spans both the ultraviolet (UV) and near-infrared (NIR) spectral regions. Although UV absorption lines are strong and free from interference, UV laser systems are typically bulky and less suitable for practical diagnostics.^12–16 The NIR region allows for compact laser systems; however, OH absorption lines are significantly weaker and often overlap with water (H₂O) absorption, which is inherent in combustion products.^17–22

To address this challenge, various methods have been developed to correct for H₂O interference in OH measurements.^17–19 For example, Hayden et al. used dual-comb spectroscopy with three lasers at 1.49, 1.46, and 1.39 μm.¹⁷ Gao et al. applied wavelength modulation spectroscopy (WMS) using a single laser to alternate between OH and H₂O transitions.¹⁸ So et al. proposed a dual-laser direct absorption spectroscopy (DAS) method to isolate OH from overlapping H₂O signals.¹⁹

In this study, a dual-laser diagnostic method was employed, using a near-infrared laser at 1.49 μm to detect OH radicals and a second laser at 1.39 μm to measure flame temperature and H₂O concentration. A wavelength division multiplexer (WDM) was used to allow both beams to simultaneously probe the same flame region. Wavelength modulation spectroscopy (WMS) was applied to enhance sensitivity and to enable quantitative detection of OH radicals in the presence of spectral interference. The results obtained from DAS and WMS were compared with CHEMKIN simulations to examine the relative behavior of the measured species under identical conditions. The primary objective of this study is to demonstrate that wavelength modulation spectroscopy can be effectively applied to quantify OH radical concentrations under conditions with significant H₂O interference, while yielding results that are physically consistent with those obtained using direct absorption spectroscopy.

Theoretical Principles

Direct Absorption Spectroscopy (DAS)

Calculation of Gas Concentration

Direct absorption spectroscopy (DAS) provides the advantage of relatively straightforward gas concentration retrieval without the need for external calibration. However, under certain measurement conditions, a reduction in the effective absorption area can hinder accurate concentration determination. In DAS, the laser wavelength is scanned with a ramp waveform of specified frequency and amplitude and passed through the target gas, where selective absorption occurs. The resulting absorption profile is then analyzed to retrieve the gas concentration and, in some cases, the temperature. The transmission coefficient $τ (ν)$ is defined as the ratio of the laser intensities after ( $I$ ) to that before $(I_{0}$ ) propagation through the target gas and can be expressed by Eq. 1.

τ (ν) = {(\frac{I}{I_{0}})}_{ν} = \exp (- α_{ν})

(1)

The expression for the absorbance,

α_{ν}

is given in Eq. 2, where P (atm) denotes the total pressure,

X_{abs}

is the mole fraction of species j and

L

(cm) represents the optical path length. The line strength for transition i of species j,

S_{i, j} (T)

(cm^–2 atm^–1) is a temperature-dependent parameter obtained from the HITRAN database,²³ and

Φ_{ν}

(cm) is the normalized line shape function for transition i of the species j, satisfying

\int_{- \infty}^{\infty} Φ_{ν} d ν \equiv 1

. The integrated absorbance area

A_{i}

is defined in Eq. 3.

α_{ν} = P \cdot X_{abs} \cdot S_{i, j} (T) \cdot Φ_{ν} \cdot L

(2)

A_{i} = \int_{- \infty}^{\infty} α_{ν} d ν = P \cdot X_{abs} \cdot S_{i, j} (T) \cdot L

(3)

Once the temperature is determined, the absorbance area can be calculated using Eq. 3, and the gas concentration can subsequently be derived using Eq. 4, which expresses the relationship between absorbance and concentration.

X_{abs} = \frac{A_{i}}{P \cdot S_{i, j} (T) \cdot L}

(4)

Calculation of Gas Temperature

Accurate gas temperature measurement using TDLAS requires two spectrally distinct absorption transitions. The temperature is inferred from the ratio of two spectrally resolved absorption signals, selected according to the prevailing measurement conditions. As in the concentration analysis, the integrated absorbance areas of the two selected transitions are computed using Eq. 3. The gas temperature is subsequently determined from the ratio of the two integrated absorbance areas, as expressed in Eq. 5.

R = \frac{A_{1}}{A_{2}} = \frac{\int P \cdot S_{1} (T) \cdot Φ_{ν_{1}} \cdot L d ν}{\int P \cdot S_{2} (T) \cdot Φ_{ν_{2}} \cdot L d ν} = \frac{S_{1} (T)}{S_{2} (T)} = \frac{S (T_{0}, ν_{1})}{S (T_{0}, ν_{2})} \exp [- \frac{hc}{k} (E_{1}^{″} - E_{2}^{″}) (\frac{1}{T} - \frac{1}{T_{0}})]

(5)

where P (atm) is the total pressure of the absorbing species, L (cm) is the optical path length of the laser beam through the absorbing medium.

Φ_{ν}

(cm) is the line shape function of the transition,

S (T_{0}, ν_{i})

(cm^–2 atm^–1) is the line strength of the transition centered at

ν_{i}

(cm^–1) at the reference temperature

T_{0} = 296 K

E ″

(cm^–1) is the lower state energy,

h

is the Planck constant,

c

is the speed of light in vacuum, and

k

is the Boltzmann constant. T (K) denotes the gas temperature. Based on the absorbance ratio, the temperature is ultimately determined using Eq. 6.

T = \frac{(\frac{hc}{k}) (E_{2}^{″} - E_{1}^{″})}{\ln (\frac{A_{1}}{A_{2}}) + l n (\frac{S_{2} (T_{0})}{S_{1} (T_{0})}) + (\frac{hc}{k}) \frac{(E_{2}^{″} - E_{1}^{″})}{T_{0}}}

(6)

Wavelength Modulation Spectroscopy (WMS)

Calculation of Gas Concentration

Wavelength modulation spectroscopy (WMS) applies a high-frequency sinusoidal modulation superimposed onto a low-frequency ramp waveform. Harmonic signals, specifically the first (1f) and second (2f) components, are extracted using a lock-in amplifier to obtain gas concentration information. Compared to direct absorption spectroscopy (DAS), WMS provides higher sensitivity, enabling the detection of trace gas concentrations; however, it requires additional calibration. The wavelength modulation applied in WMS is mathematically described by Eq. 7.

ν (t) = \bar{ν} (t) + a \cos (2 π f_{m} t)

(7)

In this equation,

\bar{ν} (t)

(cm^–1) represents the laser’s central wavenumber, a (cm^–1) denotes the modulation amplitude, and

f_{m} (Hz)

denotes the modulation frequency. The transmission coefficient can be expanded into a Fourier cosine series comprising multiple harmonic components, as expressed in Eq. 8.

τ (\bar{ν} + a \cos (2 π f_{m} t)) = \sum_{n = 0}^{n = + \infty} H_{n} (\bar{ν}, a) \cos (n 2 π f_{m} t)

(8)

The coefficients $H_{n} (\bar{ν}, a)$ represent the Fourier components of the absorbance signal, with the zeroth- and nth-order terms defined by Eqs. 9 and 10, respectively.

H_{0} (\bar{ν}, a) = \frac{1}{2 π} \int_{- π}^{+ π} τ (\bar{ν} + a \cos θ) d θ

(9)

H_{n} (\bar{ν}, a) = \frac{1}{π} \int_{- π}^{+ π} τ (\bar{ν} + a \cos θ) \cdot \cos (n θ) d θ

(10)

Under the weak absorption limit, the transmission coefficient can be approximated using Eq. 12 when the condition in Eq. 11 is satisfied, i.e., when the peak absorbance $P \cdot X_{abs} \cdot S_{i, j} (T) \cdot Φ_{ν} \cdot L$ is less than 0.05. Under the present experimental conditions ( $T =$ 1473 K, $L =$ 94 cm, $X_{OH} =$ 0.2%, estimated from CHEMKIN simulations), the peak absorbance was calculated using SpectraPlot to be approximately 0.046.²⁴ This value satisfies the weak-absorption criterion $(α_{peak} \leq 0.05$ ) commonly adopted in WMS analysis,²⁵ thereby justifying the use of Eq. 12.

P \cdot X_{abs} \cdot S_{i, j} (T) \cdot Φ_{ν} \cdot L \leq 0.05

(11)

τ (ν) \equiv {(\frac{I}{I_{0}})}_{ν} = e^{- α_{ν}} \approx 1 - α_{ν}

(12)

The nth harmonic Fourier coefficient reduces to the form given in Eq. 13. In this expression, the absorption coefficient determines the amplitude of each harmonic, and the peak magnitude of each measured harmonic is proportional to the concentration of the corresponding species.

\begin{aligned} H_{n} (\bar{ν}, a) = \frac{P \cdot X_{abs} \cdot S_{i, j} (T) \cdot L}{π} \int_{- π}^{+ π} Φ_{ν} (\bar{ν} + a \cos θ) \cdot \cos (n θ) d θ \end{aligned}

(13)

Analysis Procedure for OH Radicals, H₂O Concentration, and Flame Temperature

Figure 1 presents a schematic illustration of the analysis procedure used to isolate OH radical signals and correct for H₂O interference using both DAS and WMS techniques. The procedure includes signal acquisition, temperature determination, and concentration retrieval.

Figure 1.

Analysis process for measuring OH radicals while eliminating H₂O interference using DAS and WMS.

DAS Analysis Procedure

To eliminate H₂O interference in OH measurements using DAS, two lasers, designated as A (1.49 μm) and B (1.39 μm), are simultaneously directed through the same spatiotemporal region via a wavelength division multiplexer (WDM), which combines both beams into a single optical path, enabling the simultaneous acquisition of both absorption signals. The combined beam is collimated and directed through both a reference cell and the flame zone. The transmitted light is subsequently focused onto a photodetector, and the resulting signal is demodulated using a lock-in amplifier for harmonic extraction.

The procedure for isolating the OH radical signal from overlapping H₂O(1) interference is as follows (here, H₂O(1) denotes the H₂O transition overlapping with the OH absorption line). First, the integrated absorbance areas $A_{1}$ and $A_{2}$ of two H₂O absorption lines are measured using the B Laser, which selectively probes the H₂O(2) transitions used for temperature retrieval (here, H₂O(2) denotes a separate set of H₂O lines measured with laser B for temperature and H₂O diagnostics). The flame temperature $T_{flame}$ is then determined from the area ratio and the spectroscopic parameters of the two transitions according to Eq. 14. The retrieved temperature is subsequently used to evaluate the temperature-dependent line strength required for species concentration quantification.

T_{flame} = \frac{\frac{hc}{k} (E_{2, H_{2} O (2)}^{″} - E_{1, H_{2} O (2)}^{″})}{\ln (\frac{A_{1, H_{2} O (2)}}{A_{2, H_{2} O (2)}}) + \ln (\frac{S_{2, H_{2} O (2)} (T_{0})}{S_{1, H_{2} O (2)} (T_{0})}) + \frac{hc}{k} \frac{(E_{2, H_{2} O (2)}^{″} - E_{1, H_{2} O (2)}^{″})}{T_{0}}}

(14)

Second, the H₂O concentration is determined from the absorption area of the H₂O(2) transition measured with the B Laser, according to Eq. 15 and Eq. 16. In Eq. 15, the integrated absorbance

A_{H_{2} O (2)}

is related to the H₂O mole fraction

X_{H_{2} O (2)}

, the pressure P, the temperature dependent line strengths

S_{i, j} (T)

, and the optical path length L. Rearranging Eq. 15 yields Eq. 16, which expresses

X_{H_{2} O (2)}

explicitly in terms of

A_{H_{2} O (2)}

, P,

S_{i, j} (T)

, and L. Because the WDM combines both laser beams into a single optical path, the H₂O mole fraction probed by the B Laser,

X_{H_{2} O (2)}

, is identical to that probed by the A Laser,

X_{H_{2} O (1)}

, under identical spatial and temporal conditions.

\int_{- \infty}^{\infty} α_{H_{2} O (2)} d ν = P \cdot X_{H_{2} O (2)} \cdot \sum_{i, j} S_{i, j} (T) \cdot L = A_{H_{2} O (2)}

(15)

X_{H_{2} O (2)} = \frac{A_{H_{2} O (2)}}{P \cdot \sum_{i, j} S_{i, j} (T) \cdot L} \Rightarrow X_{H_{2} O (2)} = X_{H_{2} O (1)}

(16)

Finally, the known H₂O concentration is used in Eq. 17 to estimate the integrated absorbance of the H₂O(1) transition corresponding to laser A. This enables subtraction of the H₂O(1) contribution from the total absorbance, thereby isolating the OH radical absorption area

A_{OH}

. The resulting OH integrated absorbance is subsequently used in Eq. 18 to calculate the OH radical mole fraction

X_{OH}

, free from H₂O interference.

A_{H_{2} O (1)} = \int_{- \infty}^{\infty} α_{H_{2} O (1)} d ν = P \cdot X_{H_{2} O (2)} \cdot \sum_{i, j} S_{i, j} (T) \cdot L \Rightarrow \int_{- \infty}^{\infty} α_{OH} d ν = \int_{- \infty}^{\infty} (α_{OH} + α_{H_{2} O (1)}) d ν - \int_{- \infty}^{\infty} α_{H_{2} O (1)} d ν \Rightarrow \int_{- \infty}^{\infty} α_{OH} d ν = P \cdot X_{OH} \cdot \sum_{i, j} S_{i, j} (T) \cdot L = A_{OH}

(17)

X_{OH} = \frac{A_{OH}}{P \cdot \sum_{i, j} S_{i, j} (T) \cdot L}

(18)

WMS Analysis Procedure

In WMS, the first (1f) and second (2f) harmonic signals are extracted using a lock-in amplifier and are mathematically represented by Eq. 19 and Eq. 20.

S_{2 f (\bar{ν})} \approx \frac{G {\bar{I}}_{0}}{2} H_{2} (\bar{ν}) = - \frac{G {\bar{I}}_{0}}{2} \cdot \frac{P S_{i, j} (T) X_{abs} L}{π} \int_{- π}^{π} Φ_{ν} (\bar{ν} + a \cos θ) \cos 2 θ d θ

(19)

S_{1 f (\bar{ν})} \approx \frac{G {\bar{I}}_{0} i_{0}}{2}

(20)

In these expressions, the optoelectronic gain of the photodetection system was denoted by G, and

\bar{ν}

and

\bar{I_{0}}

were defined as the mean optical frequency and the mean laser intensity, respectively. The quantity

i_{0}

denotes the normalized intensity modulation coefficient at the modulation frequency.

H_{2} (\bar{ν})

was defined as the second Fourier coefficient of the transmission coefficient, P as the total pressure, and

X_{abs}

as the mole fraction of the absorbing species. The line strength for transition i of species j was expressed as

S_{i, j} (T)

(cm^–2 atm^–1). The function

Φ_{ν}

is the normalized line-shape function satisfying

\int_{- \infty}^{\infty} Φ_{ν} d ν \equiv 1

. The gas temperature is denoted by T (K), and the optical path length is denoted by L. The normalized harmonic amplitude

C = S_{2 f} / S_{1 f}

is defined from Eqs. 19 and 20, and its analytical expression is given in Eq. 21.

C = \frac{S_{2 f}}{S_{1 f}} = \frac{1}{i_{0}} H_{2} (\bar{ν}) = - \frac{P S_{i, j} (T) X_{abs} L}{i_{0} \cdot π} \int_{- π}^{π} Φ_{ν} (\bar{ν} + a \cos θ) \cos 2 θ d θ

(21)

The modulation depth is defined as $m = \frac{a}{Δ ν / 2}$ , where a denotes the frequency modulation amplitude and $Δ ν / 2$ represents the half-width of the selected transition. In the present experiment, the modulation depth was adjusted to approximately $m \approx 2.2$ , corresponding to the theoretical optimum for maximizing the 2f signal under weak-absorption conditions. The air-broadening coefficients at 1473 K are 0.0139 cm^–1/atm for OH and 0.0245–0.025 cm^–1/atm for the selected H₂O transitions.²³ Based on these values and the weak-absorption operating conditions adopted in the present study, the influence of differential pressure broadening on the harmonic peak amplitude ratio used for OH concentration retrieval is expected to be limited. The linear baseline component refers to slowly varying baseline contributions in the WMS signal (e.g., residual amplitude modulation, baseline slope in laser intensity, or detector drift) that can distort the measured harmonic peak amplitudes if not minimized.

Under weak-absorption conditions, the peak amplitudes of the OH and H₂O harmonic signals are proportional to the product of their respective line strengths and species concentrations. Based on this proportionality, the ratio of the normalized harmonic amplitudes for OH and H₂O can be expressed as shown in Eq. 22. The OH mole fraction is subsequently determined using Eq. 23.

\frac{C_{OH}}{C_{H_{2} O}} = \frac{S_{OH} (T) \cdot X_{OH}}{S_{H_{2} O} (T) \cdot X_{H_{2} O}}

(22)

X_{OH} = \frac{C_{OH + H_{2} O}}{C_{H_{2} O}} \cdot \frac{S_{H_{2} O} (T) \cdot X_{H_{2} O}}{S_{OH} (T)}

(23)

Experimental

Line Selection

Precise selection of laser wavelengths is essential in TDLAS-based diagnostics because gas temperature and species concentrations are derived from spectrally resolved absorption signals. Figure 2a presents simulated absorption spectra of major reactants and products at 1473 K and 1 atm, generated using the HITRAN molecular spectroscopic database.²³ Within the 1.3–1.7 µm range, strong H₂O interference appears near the OH absorption features, and additional absorption from CH₄, CO, and N₂O is also observed. When the flame temperature is assumed to be approximately 1473 K, the HITRAN simulation indicates that H₂O absorption dominates the spectral region from 1400 to 1600 nm around the OH lines. Therefore, selecting wavelengths with sufficiently strong OH line strength while minimizing interference from other species is essential for quantitative OH concentration measurements.

Figure 2.

Simulated absorption spectra of OH radicals, H₂O, and other combustion-related species at 1473 K and 1 atm, calculated using the HITRAN database: (a) spectra in the 1.3–1.7 μm wavelength range; (b) enlarged view of the 1.39 μm H₂O transitions used for flame temperature and H₂O concentration measurements; and (c) enlarged view of the 1.49 μm OH transitions used for OH radical quantification.

In this study, two near-infrared (NIR) wavelengths were employed to measure the OH radical concentration. The 1.39 µm region, shown in Figure 2b, is dominated by strong H₂O absorption and was used to simultaneously determine the flame temperature and H₂O concentration, enabling quantitative correction of H₂O interference in the OH spectrum. Meanwhile, the 1.49 µm region, shown in Figure 2c, exhibits relatively stronger OH line strength and reduced spectral overlap with H₂O, making it more suitable for OH detection; however, the H₂O interference is still not negligible.

Experimental Setup and Conditions

The two lasers were combined into a single collimated beam on the transmission side using a wavelength-division multiplexer (MUX) and were routed together through the measurement region; a schematic of the optical setup is shown in Figure 3. At the receiver, the combined beam was separated by a demultiplexer (DEMUX) that exploits wavelength-dependent refractive-index differences, allowing independent detection of each channel. Because both wavelengths traverse essentially the same collimated path, turbulence-induced beam steering affects them equally and does not produce differential loss between the OH and H₂O signals.

Figure 3.

Experimental setup for OH radical measurement using TDLAS.

In the transmission unit, a 1.39 µm DFB laser (NTT Electronics, model NLK1E5GAAA, linewidth ≈ 2 MHz) was employed for flame-temperature and H₂O measurements, while a 1.49 µm diode laser (AeroDiODE, model 1491LD-2-0-0-1; optical output power 20 mW at an operating current of 90 mA) was used for OH quantification. Both lasers were driven by a custom function generator integrated with a laser controller that regulated injection current and device temperature while providing the modulation signals. To suppress low-frequency intensity fluctuations associated with turbulent flow and beam wander, high-frequency modulation schemes were applied: amplitude modulation at 4 kHz for DAS, and a 1 kHz wavelength ramp with a superimposed 60 kHz sinusoidal modulation for WMS harmonic detection.

The modulated beam was collimated and aligned to pass approximately 5 mm above the flame surface. To increase sensitivity for trace OH detection, the effective optical path length was extended by six mirrors to produce multiple reflections above the flame; after transmission the beam was re-collected by a collimation lens, spectrally separated by the DEMUX, and converted to electrical signals by photodetectors (Thorlabs PDA20CS2; 800–1700 nm). The detector outputs were demodulated using a lock-in amplifier (AMETEK Signal Recovery 7270 DSP Lock-in Amplifier), synchronized to the 60 kHz modulation frequency for harmonic extraction in the WMS measurements. Because a WDM-based common optical path was used, the geometric optical path length was identical (135 cm) for both wavelengths. However, OH radicals are confined to the thin flame-front region, so only the flame-intersecting portion of the beam (94 cm) contributes to OH absorption. Accordingly, an effective path length of 94 cm was used for OH quantification, whereas the full 135 cm path was used for H₂O. The DAS–WMS comparison for OH was therefore performed using the same effective OH path length (94 cm). Data acquisition and subsequent analysis were performed using a custom-developed analysis system. For all experiments, a laboratory-scale metal-fiber premixed burner was operated at a fixed heat load of 9000 kcal/h. The equivalence-ratio window ( $ϕ = 0.85 - 1.05$ ) was selected to ensure flame stability and reliable optical access; substantially leaner ( $ϕ \leq 0.6$ ) or richer ( $ϕ \geq 1.2$ ) operation was avoided because blow-off, local extinction, or sooting would compromise quantitative spectroscopic retrievals. Three equivalence-ratio conditions ( $ϕ$ = 0.85, 0.95 and 1.05) were tested, corresponding to a fuel flow of 18.82 L/min and air flows of 210.0, 188.5 and 170.5 L/min, respectively, as summarized in Table I. Under all tested conditions no signal clipping or discernible waveform distortion attributable to beam steering was observed. Flame-core temperature at 5 mm above the burner was additionally measured using an R-type thermocouple (Pt–13%%Rh/Pt) with a bare junction to provide a point-wise flame-core temperature for OH quantification (see the Results of Flame Temperature Measurements section below for the measurement map and comparison with TDLAS). Although measurements at more extreme lean or rich conditions (e.g., $ϕ \approx$ 0.75 or 1.15) are in principle feasible, the present study focuses on a direct and quantitative comparison between DAS and WMS under identical and stable combustion conditions. Because WMS harmonic detection is more sensitive to flame instability and spatial non-uniformity, the equivalence-ratio range was intentionally restricted to ensure robust signal retrieval. A wider equivalence-ratio range has already been investigated using an improved DAS approach.¹⁹

Table I.

Combustion conditions for the experiment.

Heat load (kcal/h)	9000
Equivalence ratio ( $ϕ$ )	0.85	0.95	1.05
Fuel (L/min)	18.82
Air (L/min)	210.0	188.5	170.5

Results and Discussion

Results of Flame Temperature Measurements

First, the results of flame temperature measurements obtained using H₂O absorption spectroscopy are presented. The flame temperature was calculated using DAS by analyzing the integrated-area ratio of two selected H₂O absorption lines. Experiments were conducted at equivalence ratios of 0.85, 0.95, and 1.05 to evaluate the influence of combustion conditions on flame temperature. For comparison, flame temperatures were also measured at the same height above the burner using an R-type thermocouple, and the results are summarized in Table II. The thermocouple junction was mounted on an unshielded probe and positioned 5 mm above the burner surface along the laser beam axis. As illustrated in Figure 4a, temperature measurements were conducted at three positions, i.e., center, left, and right on the burner. The thermocouple temperature reported in Table II represents the average of these three measurement locations. Radiative heat loss at the thermocouple junction was recognized as a potential source of measurement uncertainty; however, no quantitative radiation correction was applied in this study. As a result, the measured thermocouple temperature may deviate from the actual gas temperature depending on local heat-transfer conditions, including radiative and convective effects. Figure 4b compares the temperatures measured by the two techniques.

Figure 4.

(a) Thermocouple temperature measurement locations, (b) Comparison of temperature measurement results between thermocouple and TDLAS.

Table II.

Results of flame temperature measurements.

Equivalence ratio ( $ϕ$ )	TDLAS ( $^{\circ} C$ )	Thermocouple average ( $^{\circ} C$ )
0.85	1067.6	1088.9
0.95	1114.3	1138.0
1.05	1105.9	1143.6

A comparison between thermocouple and TDLAS measurements showed that the maximum flame temperature occurred at an equivalence ratio of 0.95 for both techniques. Although similar trends were observed, a systematic discrepancy in absolute temperature values was present. This difference primarily arises from the line-of-sight, path-integrated nature of TDLAS, which yields a temperature averaged over both reactive and post-flame regions along the optical path. In contrast, thermocouple measurements reflect local temperatures within the flame region at the measurement height. To account for the distinct spatial distributions of absorbing species, different temperature descriptors were employed for OH and H₂O quantification. Because OH radicals are confined to the thin reaction zone near the flame front, the local flame temperature obtained from thermocouple measurements at 5 mm above the burner was used for OH concentration calculations. In contrast, H₂O contributes to absorption over an extended post-flame region along the optical path; therefore, the path-averaged temperature derived from DAS-based TDLAS measurements was used for H₂O quantification. Despite differences in absolute values, the overall temperature trends obtained from both techniques were consistent, supporting the reliability of the combined diagnostic approach.

Results of DAS

The OH radical concentration was determined using the DAS method after correcting for H₂O interference, based on the measured flame temperature. The raw absorption signals simultaneously acquired from the two lasers are presented in Figure 5. Figure 5a displays the OH absorption spectrum, which contains overlapping contributions from H₂O absorption. Figure 5b shows the H₂O absorption signal, which was used both for flame temperature determination and for isolating the overlapping H₂O(1) component from the OH absorption signal. To achieve this, a spectrally isolated H₂O(2) absorption line was employed.

Figure 5.

(a) OH absorption signal affected by H₂O interference; (b) Isolated H₂O absorption signal used for temperature measurement and correction.

As illustrated in the experimental setup schematic (Figure 3), both lasers propagate through the same spatial and temporal region. Consequently, although the signal intensities of H₂O(1) and H₂O(2) differ due to variations in line strength, the measured H₂O concentration is identical for both transitions. Taking advantage of this property, the H₂O concentration was first derived from the absorption area of the H₂O(2) line using Eqs. 15–16. The OH absorption signal, free from H₂O interference, was subsequently obtained by subtracting the estimated H₂O(1) contribution from the total OH + H₂O absorption signal. Table III summarizes the DAS-derived H₂O concentrations, the H₂O(1) absorption area, the combined OH + H₂O absorption area, and the isolated OH absorption area for each equivalence ratio condition.

Table III.

Derivation of single OH radical absorbance by removing interference from H₂O absorbance.

Equivalence ratio( $ϕ$ )	$X_{H_{2} O (2)} = X_{H_{2} O (1)}$ (Conc. %)	$A_{H_{2} O (1)}$ (cm^–1)	$A_{OH + H_{2} O (1)}$ (cm^–1)	$A_{OH}$ (cm^–1)
0.85	10.57	0.0029	0.0054	0.0025
0.95	12.12	0.0034	0.0060	0.0026
1.05	11.22	0.0033	0.0058	0.0025

After subtracting the H₂O absorption contribution, the net OH absorption area was extracted, from which the OH radical concentration was calculated. Numerical simulations were performed using CHEMKIN-PRO PREMIX, a one-dimensional laminar burner-stabilized flame model, with the GRI-3.0 reaction mechanism, which is suitable for CH₄/air flame analysis.^26,27 The OH radical concentrations predicted by the GRI 3.0 mechanism were obtained as a function of the equivalence ratio. In the combustion experiments, the light source transmitted through the surface of a metal fiber-type burner at a distance of 5 mm above the flame; therefore, the numerical predictions were compared with the OH radical concentrations measured at the corresponding 5 mm location in the flame. The H₂O and OH concentrations measured by DAS were then compared with the CHEMKIN simulation results, as illustrated in Figure 6.

Figure 6.

Concentration measurements by DAS compared with CHEMKIN simulations. (a) H₂O and (b) OH radicals.

Figure 6a displays the measured H₂O concentrations as a function of equivalence ratio, while Figure 6b presents the corresponding OH radical concentrations compared with CHEMKIN simulations. The H₂O concentrations measured by TDLAS averaged approximately 11% and were generally lower than the corresponding CHEMKIN simulations, while showing qualitative agreement across the examined equivalence-ratio range. The discrepancy in H₂O concentration can be attributed to the line-of-sight nature of TDLAS measurements, which average over both reactive and non-reactive regions. Simulations of the absorption path indicate that inclusion of non-reactive zones may lead to an underestimation of the H₂O concentration by up to 2.78%. The peak H₂O concentration was observed at an equivalence ratio of 0.95, in good agreement with the CHEMKIN simulations. Because no independent quantitative diagnostic for OH was available, absolute validation of the retrieved OH concentrations was not possible; therefore, the OH results were evaluated through comparison with CHEMKIN simulations. The lowest OH radical concentration was recorded under fuel-lean conditions ( $ϕ =$ 0.85), while the maximum was observed at $ϕ =$ 0.95. Similar to the H₂O results, the measured OH radical concentrations were slightly lower than the simulation values but exhibited a consistent dependence on equivalence ratio.

Results of WMS

This section presents the quantitative analysis of OH radical concentrations using the WMS method under conditions of significant H₂O interference. As illustrated in Figure 7, superimposing a high-frequency sinusoidal wave onto a low-frequency sawtooth waveform produces a composite second harmonic (2f) signal, which represents the combined contributions of the two absorption features. To eliminate background noise and signal drift, the second harmonic (2f) signal was normalized using the simultaneously acquired first harmonic (1f) signal prior to analysis.

Figure 7.

WMS signal of OH radicals with interference from H₂O.

The peak values of the normalized 2f/1f signals for OH + H₂O ( $C_{OH + H_{2} O}$ ) and H₂O ( $C_{H_{2} O}$ ) are presented in Table IV. For quantitative retrieval of OH concentration using WMS, the line strengths were calculated by substituting the DAS-derived flame temperatures into the temperature-dependent line strength expressions for H₂O. Similarly, thermocouple-measured temperatures were used to determine the OH line strength. Finally, the OH concentration was calculated using Eq. 23 with H₂O concentration obtained from DAS. The parameters used in these calculations are summarized in Table IV.

Table IV.

Calculation parameters and results for OH radical quantification using WMS.

Equivalence ratio ( $ϕ$ )	2f/1f signal OH + H₂O peak height	2f/1f signal H₂O peak height	OH radical Line strength (cm^–2 atm^–1)	H₂O Line strength (cm^–2 atm^–1)	H₂O Concentration (%)
0.85	0.3874	0.2765	0.0239	2.002E-04	10.57
0.95	0.5130	0.3917	0.0217	2.039E-04	12.12
1.05	0.4879	0.3655	0.0220	2.079E-04	11.22

Under conditions with H₂O interference, OH concentrations were quantitatively determined using wavelength modulation spectroscopy (WMS). The results were compared with CHEMKIN simulation predictions and further evaluated against OH concentrations obtained using direct absorption spectroscopy (DAS). A summary of these results is provided in Figure 8 and Table V.

Figure 8.

Comparison of OH concentration measurements obtained by DAS and WMS.

Table V.

Comparison of OH concentrations obtained by DAS and WMS.

Equivalence ratio ( $ϕ$ )	OH concentration_DAS (%)	OH concentration_WMS (%)
0.85	0.140	0.142
0.95	0.153	0.154
1.05	0.147	0.149

As stated in the objective of this study, the agreement between DAS and WMS results under the present conditions is not intended to demonstrate the superiority of WMS over DAS, but rather to validate the applicability of WMS for quantifying OH concentrations under conditions with H₂O interference. Comparison of OH concentrations obtained using WMS and DAS showed overall similar behavior, with the lowest OH concentration observed under fuel-lean conditions ( $ϕ =$ 0.85) and a maximum at $ϕ =$ 0.95. These observations indicate that WMS provides physically consistent OH concentration values even in the presence of H₂O spectral interference. Based on typical temperature uncertainties of ±2–3% associated with TDLAS measurements in similar flame environments,^19,28 and considering the weak-absorption regime of the present measurements, the propagated uncertainty in the derived OH concentration is estimated to be within approximately ±5%.

Conclusion

This study introduced a dual-laser diagnostic methodology integrating direct absorption spectroscopy (DAS) and wavelength modulation spectroscopy (WMS) for quantifying OH concentrations in methane–air premixed flames. The approach demonstrated accuracy even in the presence of significant H₂O interference. By implementing wavelength division multiplexing (WDM) in the near-infrared region, simultaneous measurements were conducted under identical spatial and temporal conditions. The DAS measurement at 1.39 μm provided both flame temperature and H₂O concentration, which were necessary for correcting H₂O interference, thereby enabling reliable estimation of OH concentrations (mole fraction) in the range of 0.12–0.15%. The WMS analysis, using 1f-normalized 2f signals, corroborated the OH concentrations measured by DAS.

Comparisons with CHEMKIN simulation results showed strong agreement in both spatial trends and equivalence ratio dependence, thereby confirming the accuracy and reliability of the proposed diagnostic method. Although absolute validation of OH concentrations was limited due to the lack of a calibration reference, the observed trends were consistent with the CHEMKIN simulations. While radiative heat loss is inherently present at the thermocouple junction, manufacturer-specific correction tables were not applied because their direct applicability to the present open flame environment cannot be assured. Comparison with DAS-derived path-averaged temperatures showed consistent equivalence-ratio trends with only a modest systematic offset. Owing to the line-of-sight weighted nature of absorption spectroscopy and the strong localization of OH in the high-temperature reaction zone, the resulting temperature bias has only a limited impact on the derived OH and H₂O concentrations. Therefore, the main conclusions of this work are robust in terms of relative trends and DAS–WMS consistency.

Moreover, the DAS and WMS measurements exhibited strong mutual agreement. These findings confirm the robustness of the proposed method and its applicability for real-time monitoring of reactive species in practical combustion systems, such as industrial burners and engines operating under variable fuel and flow conditions. Future work will focus on developing in-situ calibration methodologies to enable accurate absolute quantification of OH radicals under realistic combustion conditions.

Footnotes

Consent for Publication

All authors have read and approved the final version of the manuscript and consent to its publication.

CRediT Author Statement

Jiyeon Park: Conceptualization, Methodology, Investigation, Data curation, Formal analysis, Writing – original draft. Aran Song: Investigation, Formal analysis, Validation. Changkook Ryu: Supervision, Writing – review and editing. Daehae Kim: Methodology, Resources, Validation Miyeon Yoo: Methodology, Resources, Validation Changyeop Lee: Conceptualization, Methodology, Supervision, Project administration, Writing – review and editing.

Funding

This work was supported by the Technology Innovation Program (Development and demonstration of 2 ton/hr industrial hydrogen boiler, 20023380) funded By the Ministry of Trade, Industry & Energy (MOTIE, Korea).

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

ORCID iDs

Jiyeon Park

Aran Song

Changkook Ryu

Daehae Kim

Miyeon Yoo

Changyeop Lee

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Quantitative Diagnostics of Hydroxyl (OH) Radicals in Methane–Air Flames Using Wavelength Modulation Spectroscopy with Correction for Water Spectral Interference

Abstract

Keywords

Introduction

Theoretical Principles

Direct Absorption Spectroscopy (DAS)

Calculation of Gas Concentration

Calculation of Gas Temperature

Wavelength Modulation Spectroscopy (WMS)

Calculation of Gas Concentration

Analysis Procedure for OH Radicals, H2O Concentration, and Flame Temperature

DAS Analysis Procedure

WMS Analysis Procedure

Experimental

Line Selection

Experimental Setup and Conditions

Results and Discussion

Results of Flame Temperature Measurements

Results of DAS

Results of WMS

Conclusion

Footnotes

Consent for Publication

CRediT Author Statement

Funding

Declaration of Conflicting Interests

ORCID iDs

References

Analysis Procedure for OH Radicals, H₂O Concentration, and Flame Temperature