High-speed OH-PLIF imaging of deflagration-to-detonation transition in H₂–air mixtures

Abstract

Planar laser-induced fluorescence (PLIF) is considered a standard experimental technique in combustion diagnostics. However, it has only been occasionally applied to explosion experiments with fast combustion regimes. It has been shown that single-shot OH-PLIF with high pulse energies yields clear fluorescence images of fast deflagrations and also detonations. This paper presents the first application of high-speed OH-PLIF at 20 kHz repetition rate to a deflagration-to-detonation transition experiment. Hydrogen–air mixtures at initial atmospheric pressure and ambient temperature are investigated. Satisfactory results are obtained for flame speeds up to about 500 m/s. Flame instabilities and turbulence–flame interactions are observed. Two factors limit the applicability of HS OH-PLIF toward higher flame speeds: excessive flame luminescence masking the HS OH-PLIF signal and strong absorption of laser light by the flame. The variation in OH-PLIF signal-to-background ratio across a DDT process is studied using a 1D laminar premixed flame simulation extended by spectroscopic models.

Appendices

Appendix 1: Fast flame in the obstructed channel

An additional experiment was performed to visualize the contributions of OH-PLIF and flame luminescence signals in case of a fast flame in the obstructed channel geometry. The camera and intensifier were operated at a framing rate of 40 kfps, whereas the OH-PLIF laser operated at 20 kHz so that every other camera frame experienced a laser pulse. Figure 12 presents three images from this sequence. Frames 1 and 3 show flame luminescence only, and frame 2 shows the sum of flame luminescence and OH-PLIF signal. The flame propagates at about 700 m/s toward the obstacle located at the end of the field-of-view. For a quantitative analysis, the images are Gauss-filtered $(\sigma =6)$ to reduce the influence of image intensifier noise. Intensities are then plotted in Fig. 13 for five vertical positions ($y=6$, 18, 30, 42, 54 mm), indicated in Fig. 12. In frame 1, the flame tip is located at $x\approx 50$ mm. Ahead of the flame, $x>50$ mm, registered intensities remain below 30 counts. Where the flame is present, $x<50$ mm, intensities fluctuate around 200–600 counts. In frame 2 both OH-PLIF signal and flame luminescence contribute to the registered intensity. Peak values reach 2500 counts at $y=54$ mm. The following two heights, $y=42$ and 30 mm, show similar peak intensities. At $y=18$ mm and $y=6$ mm, the peak intensity drops to 1420 counts and 1150 counts, respectively. This drop can be attributed to absorption of laser light as it passes through the flame and combustion products from top to bottom. Frame 3 again shows flame luminescence only with peak values of about 600 counts. Consistent with Eq. 2, the SBR is expressed as the ratio of OH-PLIF signal and flame luminescence signal, where the former is the difference between registered peak intensities in frame 2 (1150–2500 counts) and the background signal (600 counts). The latter is the background signal (600 counts). This leads to SBRs of 0.9, 1.4, 2.7, 3.0, and 3.2 for positions $y=6$, 18, 30, 42, 54 mm, respectively.

Fig. 12

Flame luminescence (frames 1 and 3) and OH-PLIF (frame 2) sequence of a fast flame ($\bar{{ v}}\approx 700$ m/s), $X_{\mathrm{H2}}=17.5$ vol.%, obstructed channel, ${1.96}\,{\hbox {m}}<x<{2.05}\,{\hbox {m}}$

Fig. 13

Intensity profiles for vertical positions $y=6, 18, 30, 42, 54$ mm in Fig. 12, frames 1–3

Appendix 2: Spectroscopic models for SBR evaluation

This section describes the spectroscopic models and approach employed to estimate the variation in the SBR between three cases representative of the experimental conditions. To estimate this ratio, we calculated the variation in the absorbed incident light intensity (or fluorescence intensity), on the one hand, and the variation in the concentration of chemically/thermally excited OH*, on the other hand.

Under most experimental conditions presently studied, the flame structure can be considered as essentially laminar. The Cantera software (Goodwin et al. 2016) is used to compute the freely propagating laminar flame structure. By including in the detailed reaction (Ó Conaire et al. 2004) the submechanism for OH* formation (Kathrotia et al. 2010), the contributions of the chemically/thermally excited OH* radical are directly obtained along the flame from the 1D flame calculation. The chemical and thermal pathways to form OH*, discussed by Fiala and Sattelmayer (2013), are, respectively, given by

$$\begin{aligned}&{\mathrm{{H}}}+{\mathrm{{O}}}+M \mathrel {\mathop {\rightleftarrows }^{{\mathrm{{Chem}}}}_{{\mathrm{{Diss}}}}} {\mathrm{{OH}}}*+M \end{aligned}$$

(3)

$$\begin{aligned}&{\mathrm{{OH}}}+M \mathrel {\mathop {\rightleftarrows }^{{\mathrm{{Therm}}}}_{{\mathrm{{Quen}}}}} {\mathrm{{OH}}}*+M \end{aligned}$$

(4)

where Chem is chemical excitation, Diss is dissociative de-excitation, Therm is thermal excitation, and Quen is quenching or collisional de-excitation.

To estimate the fluorescence intensity, we calculated the laser light absorption along the 1D flame using the Beer–Lambert law

$$\begin{aligned} I(d_{i}) = I(d_{i-1}) \exp (-\sigma _{{\mathrm{{OH}}}} f_{b} [{\mathrm{{OH}}}] \ell ) \end{aligned}$$

(5)

where ${I}_{{ d}}$ is the laser intensity at the distance ${d}_{{ i}}$, ${I}_{{ d}}$ is the laser intensity at the distance ${d}_{{ i-1}}$, $\sigma _{\mathrm{OH}}$ is the total local absorption cross section of OH radical over the optical pathlength $\ell ={d}_{{ i}}-({d}_{{ i-1}})$, i is the grid point number, and ${f}_{\mathrm{b}}$ is the Boltzmann fraction

$$\begin{aligned} f_{\mathrm{{b}}} = \frac{g'' \exp \left( -c_{2} \frac{E''}{T}\right) }{Q_{p}} \end{aligned}$$

(6)

where ${g}''$ is the statistical weight of the lower state, ${c}_{2}$ is the second radiative constant, $E''$ is the lower state energy, T is the temperature and ${Q}_{{ \mathrm p}}$ is the partition function.

Presently, we considered that the local intensity of fluorescence is proportional to the intensity of the incident light which is absorbed over $\ell$ divided by the collisional quenching rate, Q

$$\begin{aligned} I_{\mathrm{{Fluo}}}\propto \frac{I(d_{i-1}) - I(d_{i})}{Q} \end{aligned}$$

(7)

where Q is given by Paul et al. (1995)

$$\begin{aligned} Q = \frac{P}{kT} \left( \frac{8kT}{\pi m_{OH}}\right) ^{1/2} \sum {X_{i}\left( 1+\frac{m_{OH}}{m_{i}}\right) ^{1/2}\sigma _{Qi}}. \end{aligned}$$

(8)

The temperature dependence of the collisional quenching cross section, $\sigma _{{ Qi}}$, is described using the formalism of Lin et al. (1979)

$$\begin{aligned} \sigma _{Qi}(T) = \sigma _{Qi}(\infty ) \exp \left( \frac{\epsilon }{k_{Q}}\frac{1}{T}\right) \end{aligned}$$

(9)

where $\sigma _{{ Qi}}(\infty )$ is the collisional quenching cross section of the i species at infinite temperature, and $\frac{\epsilon }{{k}_{{ Q}}}$ is the temperature dependence parameter in the Lin et al. collisional quenching cross section expression.

The initial incident light intensity is expressed as a normalized spectrally resolved laser line shape, $L_{L}$, which is assumed to be Gaussian

$$\begin{aligned} L_{L} = \frac{1}{\varDelta \nu _{L}} \sqrt{\frac{4 \ln (2)}{\pi }} \exp \left( 4\ln (2) \left( \frac{\nu -\nu _{{\mathrm{{Inci}}}}}{\varDelta \nu _{L}}\right) ^{2}\right) \end{aligned}$$

(10)

where $\nu _{\mathrm{Inci}}$ is the frequency of the incident light, $35334.41483\hbox { cm}^{-1}$, and $\Delta \nu _{{ L}}=0.22\,\hbox{cm}^{-1}$ is the laser line width, as indicated from the laser supplier. Note that the integral of $L_{L}$ in the wavenumber space is equal to unity.

In addition to the absorption by the ${Q}_{1}$(6) absorption line, the contributions of the ${Q}_{2}$(1), ${Q}_{2}$(3), ${Q}_{12}$(1), ${Q}_{12}$(3) and ${Q}_{21}$(6) transitions were taken into account. For each line j, the spectrally resolved absorption cross section, $\sigma _{{\mathrm{{OH}}}}^{j}$, was calculated along the flame from

$$\begin{aligned} \sigma _{{\mathrm{{OH}}}}^{j}=S^{j} \varPsi ^{j} \end{aligned}$$

(11)

where ${S}^{{ j}}$ and $\varPsi ^{{ j}}$ are, respectively, the line strength and the line shape function of the transition j.

The line strength of a transition at a given temperature T is obtained from

$$\begin{aligned} S(T)=S(T_{{\mathrm{{ref}}}}) \frac{Q_{p}(T_{{\mathrm{{ref}}}})}{Q_{p}(T)} \frac{\exp \left( -c_{2} \frac{E''}{T}\right) }{\exp \left( -c_{2} \frac{E''}{T_{{\mathrm{{ref}}}}}\right) } \frac{1-\exp \left( -c_{2} \frac{\nu _{0}}{T}\right) }{1-\exp \left( -c_{2} \frac{\nu _{0}}{T_{{\mathrm{{ref}}}}}\right) } \end{aligned}$$

(12)

where ${T}_{\mathrm{ref}}=296\hbox { K}$ is the reference temperature, and $\nu _{0}$ is the absorption line center frequency.

The absorption line shape functions were described using the Voigt profile

$$\begin{aligned} \varPsi = 2 \sqrt{\frac{\ln (2)}{\pi }} \frac{V(a,x)}{\varDelta \nu _{D}} \end{aligned}$$

(13)

where V(a, x) is the Voigt function

$$\begin{aligned} V(a,x) = \frac{a}{\pi } \int _{- \infty }^{\infty } \frac{\exp (-y^{2})}{a^{2}+(x-y)^{2}} dy \end{aligned}$$

(14)

with

$$\begin{aligned} a = \sqrt{\ln (2)} \frac{\varDelta \nu _{C}}{\varDelta \nu _{D}} \end{aligned}$$

(15)

and

$$\begin{aligned} x = 2 \sqrt{\ln (2)} \frac{\nu -\nu _{0}}{\varDelta \nu _{D}} \end{aligned}$$

(16)

where $\Delta \nu _{\mathrm{D}}$ is the Doppler line width, $\Delta \nu _{\mathrm{C}}$ is the collision line width.

The Doppler and collision line widths were, respectively, calculated from

$$\begin{aligned} \varDelta \nu _{D} = \frac{2\nu _{0}}{c} \sqrt{\frac{2kT\ln (2)}{m_{A}}} \end{aligned}$$

(17)

and

$$\begin{aligned} \varDelta \nu _{C} = \sum 2\gamma _{i} P_{i} \end{aligned}$$

(18)

where $2\gamma _{{ i}}$ is the collision coefficient of the i species, and ${P}_{{ i}}$ is the partial pressure of the i species.

All spectroscopic parameters for each absorption line were taken from the HITRAN database (Rothman et al. 2009).