Laser-induced fluorescence (LIF) is one of the most important and widely-used laser diagnostic techniques in combustion studies.^[1–5] It has been utilized to measure temperature^[1] and species concentration^[2] and to visualize flame structures,^[4,5] through the detection of intermediate species, such as OH, CH, and NO. Among them, OH benefits from its relatively high concentration in hydrocarbon combustion, strong absorption, and emission transitions in the ultraviolet, therefore it can be easily detected. More importantly, OH is a key intermediate in combustion kinetics,^[6] making it an ideal and popular candidate in LIF measurement.

The most attractive merit of LIF is the possibility to perform two-dimensional (2D) measurements, leading to planar laser-induced fluorescence (PLIF). OH-PLIF has become a standard diagnostic tool in combustion studies, and has been playing an increasingly important role in diagnosing practical combustion devices, such as internal combustion engines and gas turbines. All of these devices operate at high pressures above 1 bar (1 bar = 10⁵ Pa). Combustion diagnostics is therefore necessary to be carried out at high pressure to develop and validate combustion kinetic mechanisms.

However, it is not an easy task to interpret OH-PLIF in high-pressure combustion. The fluorescence is related to collisional energy transfer processes such as vibrational energy transfer (VET), rotational energy transfer (RET), and quenching. It is then a complex function of absolute OH concentration, pressure, temperature, and also the chemical composition of flame.^[7] At high pressure, LIF measurements are even heavily influenced by collision-induced effects, such as absorption lineshape broadening, central-frequency shifting, and collisional quenching, which are all enhanced as pressure rises. These effects should be taken into account in the analysis of the fluorescence signal, whether it is relative or absolute concentration measurement. Thus it is necessary to quantify the influence of those effects according to pressure as well as other flame conditions. Unfortunately, only a few studies focus on this issue, and some related topics are scattered in several published papers.^[7–9] Our previous study^[9] aims at the analysis of the absolute measurement of OH, and pressure only covers 1 bar–10 bar.

In the present work, specific attention is paid to estimate the effects of temperature and pressure on OH-LIF at high pressures via numerical analysis. A detailed theoretical analysis is carried out to reveal the physical processes of LIF. The temperature and pressure dependence of fluorescence is examined through three main parameters: Boltzmann fraction, overlap integral, and fluorescence yield. A suitable choice of the absorption line is done through calculation of Boltzmann fraction. High-pressure LIF measurements get complicated by the collision-induced effects, such as absorption lineshape broadening, central-frequency shifting, and collisional quenching. Absorption-line broadening and central-frequency shifting are calculated based on HITRAN database to evaluate the overlap integral. The fluorescence yield is estimated based on the LASKIN calculation, taking into consideration all energy transfer processes in the upper states of OH. Finally, OH-LIF measurements were conducted on flat stoichiometric CH₄/air flame at high pressures. The relationship between fluorescence and pressure was analyzed.

It is quite challenging to apply LIF to high-pressure combustion. One fundamental challenge comes from obtaining the fluorescence signal with an acceptable signal to noise ratio, since the fluorescence signal becomes much weaker at high pressures. A careful optimization of the excitation/detection scheme is needed, if one wanted to address the challenges of the high-pressure application of LIF. Many issues have to be considered, such as absorption line broadening and frequency shift, collisional transitions and quenching. It is of critical importance to understand the physical processes of LIF.

Laser-induced fluorescence originates from spontaneous emission of simulated atoms or molecules by laser radiation. In OH-LIF processes, the OH radicals are populated to an upper energy level by a laser beam with a wavelength tuning to a given transition line. The laser-populated OH radicals are not stable, some of which would directly return to the ground level through laser-induced stimulated emission. The population in the upper state would be re-distributed via rotational and vibrational energy transfer processes through collisions with other molecules. Also, collisions would make non-radiation transitions take place, which is referred to as collisional quenching. Spontaneous emissions take place when the OH radicals relax from the re-distributed upper states to the ground states, producing the fluorescence signal.

In the linear regime of OH-LIF, the detected fluorescence signal can be expressed as follows:^[7]

$$ \begin{eqnarray}{I}_{{\rm{F}}}=K{n}_{{\rm{OH}}}\left(\displaystyle \frac{{E}_{\nu }}{A}\right)\displaystyle \frac{{f}_{{\rm{B}}}{B}_{12}}{{c}^{2}}\displaystyle \int {\phi }_{{\rm{laser}}}{\phi }_{{\rm{abs}}}{\rm{d}}\nu \displaystyle \frac{{A}_{21}}{{A}_{21}+{Q}_{21}},\end{eqnarray}$$ (1)

LIF signal is a function of OH properties (concentration and temperature), from Eq. (1), but also related to energy transfer processes, such as vibrational energy transfer, rotational energy transfer, and collisional quenching. These processes are state-dependent, and evaluation of these processes cannot be done without the knowledge of the upper state population as a function of time. Therefore the LASKIN code^[10] is used to simulate the upper state population dynamic via solving the rate equations that govern the LIF process.

According to the previous theoretical analysis, the fluorescence signal in OH-LIF measurement depends on Boltzmann fraction, overlap integral, and fluorescence yield, which are all affected by pressure and temperature. The three factors will be numerically simulated and discussed in this section.

Usually, there are three exciting bands employed in OH-LIF applications: (0,0), (1,0), and (3,0) bands, because of the highest population in the ground X²π (ν″ = 0) state. Fluorescence of excitation within the (3,0) band is nearly free of quenching effect due to the rapid pre-dissociation of the OH A² Σ⁺ν’ = 3) state. Unfortunately, the high pre-dissociative rate would cause the fluorescence quantum efficiency to decrease, making the fluorescence signal even weak and difficult to detect. The main drawback of excitation in the (0,0) band is that the fluorescence signals are in the same band, and it is impossible to distinguish the signal and the scattered laser light. A practical solution is to employ the non-resonant excitation/detection scheme. The technique allows the use of optical filters to suppress the scattered light. This is why it is very popular to detect the (0,0) and/or (1,1) band after exciting the (1,0) band in OH-LIF applications. Therefore excitation of (1,0) band is discussed in the present simulation.

The Boltzmann fractions are calculated and illustrated in Fig. 1 for the lowest ten rotational levels in the state X²π (ν″ = 0) of OH using the Eq. (8) of Ref. [11]. The total partition function is obtained using Dunham coefficients given in Ref. [12]. It is notable that the Boltzmann equation is only valid in thermal equilibrium. The OH radicals in flames can be regarded as equilibrated because the chemical reaction rate is much slower than the rate of energy transfer processes. The Boltzmann fraction depends only on the temperature for a given level. As temperature increases, the OH radicals on the lower levels would jump to the higher levels. Consequently, the Boltzmann fraction declines on the low levels, while rises on the high levels. The Boltzmann fraction of level J″ = 8.5 presents the minimum temperature dependence over the common temperature domain of flames, 1500 K–2500 K. Considering that the Q₁ branch possesses the highest absorption coefficient, the Q₁(8) line is perfect for OH-LIF and employed in the following discussions.

The overlap integral ∫ ϕ_laserϕ_abs dν is an overall integral of spectrum overlap between the laser and absorption, revealing the excitation efficiency of the laser interacting with OH. It is common to assume that the lineshape of laser has a Lorentzian profile. The typical linewidth of a frequency-doubled dye laser is on the order of 0.1 cm⁻¹.^[13] In this simulation, the laser linewidth is therefore assumed to be 0.1 cm⁻¹. The assumed laser profile is shown and denoted with solid cycles in Figs. 2(a) and 2(b). The laser wavelength is at 283.636 nm where the absorption line Q₁(8) of A–X (1,0) band locates in vacuum.

The absorption lineshape of OH is usually described as Voigt profile that results from two broadening mechanisms, i.e., collisional broadening and Doppler broadening. The broadening parameter Γ₀ depends on temperature according to the power law, and can be expressed as follows:

$$ \begin{eqnarray}{\varGamma }_{0}(p,T)={\gamma }_{0}{T}_{{\rm{ref}}}{\left(\displaystyle \frac{{T}_{{\rm{ref}}}}{T}\right)}^{n}p,\end{eqnarray}$$ (2)

Also, the absorption lineshift would take place as a consequence of collision when the pressure or temperature changes. However, the data for evaluating lineshift is lacking in the HITRAN database. The research of Davidson et al.^[16] and Singla et al.^[9] demonstrates that the collision-induced lineshift obeys linear dependence of pressure and exponent dependence of temperature:

$$ \begin{eqnarray}\Delta {\nu }_{S}(p,T)=-0.0305\left(\displaystyle \frac{p}{{p}_{{\rm{ref}}}}\right){\left(\displaystyle \frac{{T}_{{\rm{ref}}}}{T}\right)}^{0.45},\end{eqnarray}$$ (3)

The absorption spectra of the A–X (1, 0) Q₁(8) line are calculated at temperatures varying from 1000 K to 3000 K and at high pressures varying from 1 bar to 30 bar. The calculation has counted in the effect of line-shift using a modified Python function base on the HAPI Python library.^[17] Figures 2(a) and 2(b) show the cases of absorption spectra at different pressures and different temperatures, respectively. As the pressure rises, the absorption spectra become broad and red-shifted due to collision effects. But the situation is converse when the temperature increases. Increasing the temperature would narrow the absorption spectra, because the effect of Doppler broadening increases while that of collisional broadening decreases since the density decreases. Also the absorption spectra blue-shift when increasing temperature as a result of smaller lineshift due to the decreasing effect of collision broadening.

The calculated overlaps are shown in Figs. 2(c) and 2(d). The overlap decreases obviously when the pressure increases, which indicates that the collisional broadening dominates in the decrease of overlap. It is interesting that the overlap increases with the increase of temperature at low pressure, but decreases at high pressure. This is a consequence of competition between Doppler broadening and collisional broadening. The turning point of the trend is at a pressure of about 5 bar. Because the overlaps are very close at this pressure when temperature varying from 1000 K to 3000 K as it is demonstrated in Fig. 2(d) that all the lines cross near 5 bar.

In many practical applications of OH-LIF, such as gas turbines and engines, the pressure varies quickly with time and space, and is hardly determined. Therefore the excitation wavelength for OH-LIF is usually chosen according to the line position database of LIFBASE,^[18] without considering the influence of lineshift, even at high pressure. The lineshift induced by collisions, however, would decrease the excitation efficiency. The overlaps and the corresponding overlap decreases are calculated for the tuning and detuning of laser frequency according to the line position of Q₁(8) at 2000 K and 10 bar. For detuning case, the laser wavelength is tuned to 283.636 nm, the absorption line of Q₁(8) in the vacuum. The calculated results are shown in Fig. 3(a), where the laser linewidth varies from 0 to 1 cm⁻¹. (The laser lineshape for a zero linewidth is a Dirac δ function.) The overlap decrease falls when laser linewidth increases, however the overlap declines quickly. The overlap for a laser linewidth of 1 cm⁻¹ is less than one third of that for 0.1-cm⁻¹ linewidth. It is notable that, the detuning makes the overlap decrease about 13 % for 0.1-cm⁻¹ linewidth due to the lineshift, which would lead to an obvious decrease in excitation efficiency. A larger laser bandwidth is less sensitive to detuning, but would reduce the excitation efficiency. The overlap decreases are also calculated for different temperatures and pressures with a 0.1-cm⁻¹ linewidth, as illustrated in Fig. 3(b). As the pressure rises, the overlap decrease grows quickly and reaches about 30 % at 30 bar. Increasing temperature would slightly ease the growth of overlap decrease. Therefore, in order to maximize the excitation efficiency, it requires considerable attention to mitigate the effect of collision-induced lineshift, especially at high pressure. And the laser frequency should be tuning to the center of the absorption spectrum according to the predetermined or estimated pressure.

The fluorescence yield represents the fraction of laser-excited molecules that emit fluorescence photons before returning to the ground state. The quantification of the fluorescence yield requires the determination of collisional quenching coefficient. The calculation of collisional quenching, however, is very complicated because it depends on the detailed information of energy transfer. The LASKIN code is employed to simulate the energy transfer in OH-LIF, including collisional quenching, VET, RET, etc. A stoichiometric CH₄/air flame is taken as an example to analyse the influence of temperature and pressure on fluorescence yield. The exhaust gases of the flame in chemical equilibrium consist of 71.43 % N₂, 0.46 % O₂, 18.3 % H₂O, 0.36 % H₂, 8.53 % CO₂, and 0.90 % CO, computed by the open-source code Cantera^[19] with the GRI-Mech 3.0 chemical mechanism.^[20] It should be noted that the gas composition of the flame varies very little in chemical equilibrium for different temperatures and pressures, which can be omitted. The temperature is varied between 1000 K and 2300 K and the pressure is varied from 1 bar to 30 bar. In our case, the OH fluorescence is collected including the overall emission from the A–X (0,0) and (1,1) bands, under excitation of Q₁(8) line in A–X (1, 0) band. The laser pulse is assumed to have the form of I(t) ∝ t^a exp (–bt), with values of a = 2.5 and b = 2 × 10⁸ s⁻¹, which provides a good approximation of typical laser pulse adopted in OH-LIF measurements.

Figure 4 shows the temporal profiles of the simulated fluorescence for CH₄/air flame. And figure 5 illustrates the relative fluorescence yield as a function of pressure and temperature, respectively. The fluorescence signal lags just behind the laser pulse. As the pressure increases, the fluorescence drops sharply, and its duration reduces, which implies a shorter lifetime of fluorescence. From Fig. 5(a), the fluorescence yield is approximately inversely proportional to pressure at a certain temperature. This is due to the fact that the quenching rate is proportional to the total density population which increases linearly with pressure. As shown in Fig. 4(b), the fluorescence signal varies for different temperatures, but its lifetime remains almost the same. At a certain pressure, the trend of fluorescence yield when increasing temperature has a downward-parabola-like profile, and there appears a peak value at about 1500 K. This is a natural result of the characteristic of RET.^[7]

It should be pointed out that, the temperature alters the fluorescence yield at an acceptable level, but the high pressure heavily affects the fluorescence yield. The fluorescence yield at 10 bar is only about 1/10 of that at 1 bar and increasing pressure would further decrease the fluorescence yield. Thus it is not easy to detect OH-LIF at high pressure.

The OH-LIF measurements of stoichiometric CH₄/air flame were conducted on McKenna flat burner placed in a home-made high-pressure chamber, which can operate at a maximum pressure of 15 bar, as reported in Ref. [22]. The pressure of the high-pressure chamber can stabilize at a certain pressure with a deviation less than 1 %. The exit velocities were fixed to 5 cm/s in each flame through changing the flow rates of CH₄ and air. The LIF measurement set-up is similar to our previous studies.^[23,24] The excitation line for OH was chosen to be Q₁(8) of A–X (1,0), near 283.636 nm. But the exact exciting wavelength was carefully tuning while monitoring the LIF signal, in order to eliminate pressure-dependent frequency-shift effect. The fluorescence was collected with an intensified CCD camera at about 5 mm above the burner surface at pressures from 1 bar to 10 bar with a step of 1 bar. Figure 6 shows the pressure dependence of fluorescence intensity obtained by averaging 50 individual measurements, and the error bars represent the standard derivations. The fluorescence intensity decreases with increasing pressure, which resembles an inverse dependence of pressure. Such behavior is similar to that of fluorescence yield as analyzed in Subsection 3.3. It is experimental validated that the collisional quenching plays a decisive role in fluorescence decrease at high pressure, although the line shape and absorption of OH vary a little at different pressures.

In summary, the effects of temperature and pressure on OH-LIF are numerically studied under the common excitation of A–X (1,0) transition at high pressures. The study firstly analyses the physical processes of LIF in detail. It is found that the fluorescence signal is a complex function of absolute OH concentration, pressure, temperature, and the chemical composition of flame. Operations at high pressures require a careful choice of excitation line. Through the calculation of Boltzmann fraction, the Q₁(8) line in A–X (1,0) band of OH presents the minimum temperature dependence, and is perfect for OH-LIF. At high pressures, LIF measurements suffer from the collision-induced effects, such as absorption lineshape broadening, central-frequency shifting and collisional quenching. The absorption spectra of OH are calculated using HITRAN database with a modified HAPI-based Python function. The overlap integral gets lower due to the absorption lineshape broadening as pressure increases, which leads to smaller excitation efficiency. It is of great importance to take into account central-frequency shifting that cannot be omitted at high pressures. And the laser frequency should be tuned to the center of the absorption spectrum according to the predetermined or estimated pressure. The fluorescence yield is estimated based on the LASKIN calculation, taking into considering collisional quenching, VET, RET in the upper states. It is illustrated the fluorescence yield is approximately inversely proportional to pressure at a certain temperature. And the temperature would alter the fluorescence yield, but at an acceptable level. The OH-LIF measurements of flat CH₄/air in high-pressures chamber validate the decisive contribution of collisional quenching on fluorescence decrease at high pressure. To summarize, it is important to keep in mind that, the temperature dependence of fluorescence is dominated by the Boltzmann fraction, and the pressure dependence is primarily governed via the overlap integral and fluorescence yield. And the collisional quenching plays a decisive role in fluorescence decrease at high pressure. These results illustrate the physical processes of OH-LIF, and would provide useful suggestions for high-pressure application of OH-LIF.

Acknowledgment. The authors would like to thank the LASKIN group for providing the software.