Effect of incident laser sheet orientation on the OH-PLIF imaging of detonations

Abstract

This study aims to investigate the effect of laser sheet orientation on the OH-planar laser-induced fluorescence (OH-PLIF) imaging of a detonation wave and to identify the potential benefit of using a transverse laser orientation, compared to the conventional frontal orientation. In this study, we developed a new laser-induced fluorescence (LIF) model, based on a preexisting one, to include a more fundamental calculation of the absorption lineshape and the effects of the laser orientation on the fluorescence signal. One- and two-dimensional simulations are used to validate this new LIF model for both laser orientations using OH-PLIF images from the literature. The effect of the two laser orientations on detonation imaging is investigated numerically on a two-dimensional OH field. Based on these results, the frontal orientation seems more suitable to collect information near the detonation front, while the transverse laser orientation can give more quantitative information far from the front and only for short optical paths. With the present laser configuration and experimental conditions, both laser orientations present the same limitation with a strong laser energy absorption for long optical paths. While these first results show a qualitative agreement with experimental data, new experimental data are required to quantitatively validate this promising transverse laser orientation and confirm its relevance for OH-PLIF imaging of detonations.

Appendices

Appendix 1: Sequence of images of the Voigt profile evolution along the detonation front

This appendix presents (Fig. 9) a more detailed evolution of the Voigt profiles presented in Fig. 1, with a higher spatial resolution to better illustrate the absorption lineshape evolution along the distance behind the leading shock (X). Similarly to the results presented in Fig. 1, the absorption lines are simulated based on Wang et al.’s [13] experimental conditions with a transverse laser orientation ($\delta _{\text {D}}=0$ and $\delta _{\text {Tot.}}=\delta _\mathrm{P}$). A movie presenting this sequence of images with intermediate positions is available in the supplementary material.

Appendix 2: Additional 1D validation cases with the transverse laser orientation.

Figure 10 presents two additional 1D validation cases extracted from Wang et al.’s OH-PLIF image [13]. As presented for areas 1 and 2, the LIF model reproduces qualitatively the overall intensity profile for both areas 3 and 4 when the correction accounting for the saturation of the camera is included. In area 3, the fluorescence decay has an overall offset of 2 mm, which is relatively small considering the non-ideality in the experimental image (the tilted detonation front). In area 4, the double peak structure is reproduced in the simulation with a local fluorescence intensity minimum located near 2 mm as observed experimentally. The double peak intensity is underestimated by 25% in area 4; this might indicate that the fluorescence signal attenuation is overestimated in the current model, or this might be due to an overestimated laser intensity attenuation. As discussed in Sect. 3.1 and emphasized in the conclusions, new experimental data are required to fully validate the LIF model for the transverse laser orientation.

Fig. 10

1D validation of the transverse laser orientation using an OH-PLIF image from Wang et al. [13], shown in a. 1D experimental (black symbols) and ZND (red and green lines) LIF profiles, obtained for area 3 and 4, are respectively shown in b and c. ZND OH mole fractions (blue lines) are represented for comparison. Conditions: 2H$_{2}$–O$_{2}$–10Ar at $P_{1}$ = 45.3 kPa and $T_{1}$ = 295 K

Fig. 11

Effect of the laser sheet orientation on the absorption line shifts in Wang et al.’s conditions [13]. Conditions: 2H$_{2}$–O$_{2}$–10Ar at $P_{1}$ = 45.3 kPa and $T_{1}$ = 295 K

Fig. 12

Effect of the initial pressure on the absorption lineshapes in Wang et al.’s experimental conditions [13] with a frontal laser orientation. Conditions: 2H$_{2}$–O$_{2}$–10Ar at $T_{1}$ = 295 K and both $P_{1}$ = 45.3 kPa and $P_{1}$ = 100 kPa shown, respectively, in a and b

Appendix 3: Relevance of the new LIF model

This appendix demonstrates the need to develop the new LIF model and to consider the improvements presented in this work, notably the absorption line shifts and the Voigt profile calculation. As explained in Sect. 3.2, the two laser orientations (the transverse and the frontal) must be considered independently as the Doppler shift is significantly different for these two orientations. Only three characteristic distances from the detonation front are presented in Figs. 11 and 12: von Neumann state ($X_{\text {vN}}$), induction length ($\varDelta _\mathrm{i}$), and CJ state ($X_{\text {CJ}}$).

Figure 11 emphasizes the contribution of the Doppler shift ($\delta _{\text {D}}$) for Wang et al.’s conditions, for both the two- and the five-line calculations of the Voigt profile. As the laser linecenter is constant, the $\delta _{\text {D}}$ contribution is observed by comparing the shift of the Voigt profile maximum with the laser linecenter between Fig. 11a and b for the three positions. As the value of $\delta _{\text {D}}$ decreases with the distance behind the leading shock and is mainly contributing to $\delta _{\text {Tot.}}$, it must be noted that the shift is the strongest for $X_{\text {vN}}$.

Figure 12 presents the evolution of both the two- and the five-line calculations of the Voigt profile at two different pressure conditions using a frontal laser orientation and for the three distances from the detonation front, defined previously: $X_{\text {vN}}$, $\varDelta _\mathrm{i}$, and $X_{\text {CJ}}$.

These figures show the need to consider the contribution of additional absorption lines for higher initial pressure in this specific spectral range.