Effect of Fuel Stratification on OH and ${\mathrm {CH}}_{2}\hbox {O}$ PLIF Multiplication of Turbulent Hydrogen-Enriched Flames

Abstract

Multiplication of hydroxyl and formaldehyde planar laser-induced fluorescence signals for turbulent hydrogen-enriched methane–air flames with compositionally inhomogeneous mixtures is investigated experimentally. Hydrogen-enriched methane–air flames with a global fuel–air equivalence ratio of 0.8 and hydrogen-enrichment percentage of 60% are examined. Two nozzles, each containing 4 fuel/air injection lobes are used in the experiments. The lobes of the first nozzle are straight, while those of the second nozzle are not, generating a swirling motion. The fuel is injected through several small diameter holes into the lobes. The amount of injected fuel flow rate varies between the lobes, generating stratified conditions. For each nozzle, two mean bulk flow velocities of 5 and 25 m/s are tested. Simultaneous hydroxyl and formaldehyde planar laser-induced fluorescence as well as separate stereoscopic particle image velocimetry are performed for the tested reacting conditions. For non-reacting flow tests, separate particle image velocimetry and acetone planar laser-induced fluorescence experiments are conducted to study the background turbulent flow characteristics and fuel/air mixing, respectively. The results show that stratification can lead to fragmentation of the flames and generation of islands with noticeable multiplication of hydroxyl and formaldehyde planar laser-induced fluorescence signals. Due to their significantly large number of occurrences, such flame structure can generate relatively large integral of the PLIF signals multiplication.

Appendices

Appendix A: Assessing Accuracy of PLIF Images Registration

In addition to the method related to the three-dimensional target plate discussed in Sect. 2, an alternative method was also used to assess the utilized registration technique. Specifically, a perforated and back-illuminated plate was used for the alternative registration technique, similar to Mohammadnejad et al. (2019). This plate is composed of 225 small diameter (less than 0.5 mm) through holes. The perforated plate was positioned at the burner exit plane ($x-y$ plane) and equidistant from both OH and formaldehyde cameras. The plate was back illuminated for both of the cameras, and an image was acquired by each camera. The small diameter holes serve as local light sources, whose positions are captured by both cameras. The images of these small light sources were collected by both the $\mathrm {CH}_{2}\hbox {O}$ and OH cameras and are shown by the cyan and green data points in Fig. 24a. In the figure, the overlap between the collected light (which is obtained by multiplying the OH and $\mathrm {CH}_{2}\hbox {O}$ camera images) is shown by the red colored pixels. An inset, highlighting the overlap in Fig. 24a, is enlarged and shown in Fig. 24c. Lack of overlap between the images prior to registration can be seen. The images from both cameras were anlalyzed using the “imwrap” function in MATLAB, and the $\mathrm {CH}_{2}\hbox {O}$ images were mapped onto the OH images. The results after registration are shown in Fig. 24b, with an inset shown in Fig. 24d. As can be seen, proper registration was achieved. Identical results were obtained using this alternative registration method and the three-dimensional target plate.

Fig. 24

a and b are images of a perforated and back-illuminated plate before and after registration, respectively. c and d are insets of (a) and (b), respectively

Appendix B: Sensitivity of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ to Registration, Global Thresholding, and Median-Based Filters

Effects of lack of accuracy in registration of the PLIF signals, varying the global threshold used in reduction of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ images, as well as the size of the median-based filters used for removing “salt-and-pepper” noise from the PLIF images on the results presented in Figs. 20 and 21 are discussed here.

The registered $\mathrm {CH}_{2}\hbox {O}$ PLIF images were displaced by one pixel towards left and right, the integral of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$, n, and $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ intensity were obtained, and the results were presented in Fig. 25a–c, respectively. For clarity purposes, only results pertaining to the smallest and largest Karlovitz numbers are presented in the figures. As can be seen, moving the registered $\mathrm {CH}_{2}\hbox {O}$ PLIF images towards left and right by one pixel does not significantly influence the PDFs of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ integral and intensity. The results show displacing the $\mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ PLIF images towards right moves the PDF of n towards left (smaller values of n). However, analyses of all test conditions show that the changes in the PDFs of n are significantly small, which do not influence the conclusions of the study.

Fig. 25

PDFs of a $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ integral, b n, and c $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ intensity. In the figure legend, left and right pertain to the registered formaldehyde images displaced by one pixel to left and right

Changing the global threshold used for reducing the $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ images can influence the results presented Figs. 20 and 21e, f. However, our analyses show that the reported trends and conclusions do not change by changing the value of the utilized threshold. In order to investigate this, compared to the 30% threshold value used for generating results in Figs. 20 and 21e, f, 20% and 40% threshold values were also used and the results in Figs. 20 and 21e, f were reproduced. The results associated with the integral of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$, the number of pixels with significant $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$, and the intensity of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ are generated for all test conditions and are presented in Fig. 26a–c, respectively. The results related to 20% and 40% threshold values are shown by the dashed and solid curves, respectively. As can be seen, increasing the threshold value decreases the most probable value of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ integral and n, which is due to removing data when the large threshold value is applied. However, increasing the threshold value increases the most probable $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ intensity. Nevertheless, the results presented in Fig. 26 show that changing the threshold value from 20% to 40% does not influence the relative relations between the most probable values of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ integral and intensity as well as n. For example, the non-swirling nozzle at the mean bulk flow velocity of 25 m/s always features the largest most probable value of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ integral.

Fig. 26

Effects of threshold on a $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ integral, b n, and c $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ intensity

Median-based filters with $7 \times 7$ and $9 \times 9$ pixels$^2$ windows for filtering the OH and $\mathrm {CH}_{2}\hbox {O}$ PLIF images were used in the present study, respectively. Our analyses suggest changing the filter size does not influence the results presented in Figs. 20 and 21e, f. Figures 27a–c, present variations of the integral of $\mathrm {OH}_{\mathrm {PLIF}} \times {\mathrm {CH}}_{2}\hbox {O}_{\mathrm {PLIF}}$, n, and the $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ intensity, respectively. The results highlighted by the solid curves pertain to the OH and $\mathrm {CH}_{2}\hbox {O}$ PLIF images filtered by $7 \times 7$ and $9 \times 9$ median-based filters, respectively. The results shown by the dashed curves pertain to OH and $\mathrm {CH}_{2}\hbox {O}$ PLIF images filtered by smaller windows of $5 \times 5$ and $7 \times 7$ median-based filters, respectively. As can be seen, reducing the filter size does not significantly influence the PDFs presented in Fig. 27.

Fig. 27

a–c are variations of $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ integral, n, and $\mathrm {OH}_{\mathrm {PLIF}} \times \mathrm {CH}_{2}\hbox {O}_{\mathrm {PLIF}}$ intensity, respectively. The solid curves pertain to OH and $\mathrm {CH}_{2}\hbox {O}$ filtered by $7 \times 7$ and $9 \times 9$ median-based filters; and, the dashed curves pertain to OH and $\mathrm {CH}_{2}\hbox {O}$ filtered by $5 \times 5$ and $7 \times 7$ median-based filters

Appendix C: Uncertainty of the Velocity Data and the Related Statistics

The uncertainties related to estimation of the velocity data, the swirling strength, and the eddy turbulent kinetic energy are provided in Table 4. For all parameters listed below, the statistical uncertainty is negligible. The uncertainties listed in Table 4 were obtained considering the repeatability of the experiments. In order to estimate the velocity data and the related parameters uncertainties, the repeatability of each parameter provided below was calculated by dividing the velocity data into three sets and calculating the maximum deviation of the mean. The results provided in the table are listed based on the tested condition. The last row of the table presents the maximum percentile of the uncertainty by finding the maximum (among all tested conditions) of the uncertainty divided by the mean value of the parameter of interest. For V and W, since the mean value can be close to zero, the uncertainty is divided by the corresponding U value.

Table 4 Uncertainties of the velocity data statistics along with the swirling strength and the eddy turbulent kinetic energy