Coupling between premixed flame propagation and swirl flow during boundary layer flashback

Abstract

Flashback of premixed methane–air flames in the turbulent boundary layer of swirling flows is investigated experimentally. The premix section of the atmospheric model swirl combustor features an axial swirler with an attached center-body. Our previous work with this same configuration investigated the flame propagation during flashback using particle image velocimetry (PIV) with liquid droplets as seed particles that precluded making measurements in the burnt gases. The present study investigates the transient velocity field in the unburnt and burnt gas region by means of solid-particle seeding and high-speed stereoscopic PIV. The global axial and circumferential lab-frame flame propagation speed is obtained simultaneously based on high-speed chemiluminescence movies. By combining the PIV data with the global flame propagation speed, the quasi-instantaneous swirling motion of the velocity field is constructed on annular shells, which provides a more intuitive view on the complex three-dimensional flow–flame interaction. Previous works showed that flashback is led by flame tongues. We find that the important flow–flame interaction occurs on the far side of these flame tongues relative to the approach flow, which we henceforth refer to as the leading side. The leading side is found to propagate as a classical premixed flame front relative to the strongly modified approach flow field. The blockage imposed by flame tongues is not limited to the immediate vicinity of the flame base, but occurs along the entire leading side.

Appendix

1.1 PIV uncertainty analysis

The mean stereo reconstruction error was typically 0.1–0.2 pixel. The uncertainty associated with the random error was computed using the correlation statistics approach (Wieneke 2015; Sciacchitano et al. 2015). The mean uncertainties (one standard deviation) of the three components in the instantaneous velocity fields are reported in Table 1. The uncertainties corresponded to about 3% in the core flow of the in-plane velocity components (radial and axial) and about 5% in the out-of-plane velocity component (azimuthal). The relative uncertainty increases in the boundary layer and peaks at about 10% in the in-plane velocities and about 15% in the out-of-plane velocity.

Table 1 Uncertainty in PIV measurements associated with random error in the radial, axial and azimuthal velocity components

Peak-locking, thermophoresis and beam-steering effects may introduce a bias error in the present measurements (Sung et al. 1994; Westerweel 1997; Christensen 2004). Typical particle image diameters were 2–3 pixels in the current measurements. PDFs of the modulus of particle image pixel displacements indicated a moderate but acceptable level of peak-locking.

The micrometer-sized alumina particles employed in this work were found to have relaxations times that are two to three orders of magnitude smaller than the smallest time scales in the present turbulent flow and hence in general follow the flow accurately. However, across the flame front, where strong temperature gradients exist, particles experience thermophoresis affecting the accuracy of velocity vectors in the immediate vicinity of the flame front. The thermophoretic velocity, which is induced in the direction opposite to the local temperature gradient, may be estimated as ${u_{{\text{t}}.{\text{p}}.}}=0.5\nu \nabla T/T$ (Böhm et al. 2007). For the flames investigated in the current work the thermophoretic velocity was found to be at most 0.15 m/s, which is on the same order as the uncertainty due to the random error and significantly smaller than the absolute velocity along the flame front.

Beam-steering effects may introduce an additional error in the present configuration since the illuminating laser sheet passed through the flame and the imaged scattered light from alumina particles in the burnt gas passed through the flame front. The severity of beam-steering was tested by comparing the disparity map between non-reacting and reacting cases. No systematic disparity indicative of a coherent refraction of the laser sheet was found. Furthermore, the fluctuations in local and instantaneous disparity in the reacting cases was found to be on the same level as in the non-reacting cases, which suggests that beam-steering effects are negligible in agreement with previous investigations (Stella et al. 2001).

1.2 Flame front detection uncertainty analysis

Each velocity field was computed based on four particle images (two cameras with two frames per camera recorded $\Delta {t_{{\text{frame}}}}$ apart). Hence, four image frames were available at each time step to extract the flame front location, which are shown as blue and green solid and dotted lines in Fig. 11. Note that (for a given camera) a shift of 1–2 pixels between the flame front extracted based on frame 1 and 2, respectively, is expected owing to the lab-frame-of-reference flame propagation speed. Other deviations are due to imperfections in the camera calibration and image processing steps. The final flame front is defined as the 0.5 iso-surface based on the four binary images. The uncertainty, defined as the mean distance between the 0.5 iso-surface and any of the four individual flame front locations, ranges between 2 and 3 pixels (0.12–0.18 mm) with a standard deviation ranging between 1 and 2 pixels for different runs.

Fig. 11

Planar flame front detection based on solid seeding particle number density. a Raw image, b dewarped and masked image, c filtered image, d binarized image, e extracted flame fronts from Frame1/Camera1 (blue, solid), F2C1 (blue, dotted), F1C2 (green, solid), F2C2 (green, dotted) and 0.5 iso-surface flame front location (red, solid)

1.3 Flame base tracking and uncertainty associated with global flame propagation speeds

A set of image-processing steps was implemented in MATLAB to obtain the flame base location based on the chemiluminescence images. For each instant in time, the luminescence image was first filtered and then turned into a binary image based on a flame-dependent intensity threshold. The outline of the flame was extracted using an edge detection algorithm. The pixel location of the most upstream point on the extracted flame contour corresponded to the flame base. The pixel location was converted into physical coordinates by applying a previously obtained calibration based on a dot target.

The axial location of the flame base is tracked over time as the flame tongue swirls through the laser sheet and the global axial flame propagation velocity ${v_{\text{f}}}$ is obtained from a linear curve fit. An example is shown in Fig. 12. Similarly, the angular velocity ${\omega _{\text{f}}}$ of a flame tongue is determined by converting the horizontal position of the flame base in the luminescence image to the corresponding angular location and tracking it in time.

Fig. 12

Tracking of the axial and azimuthal flame base location and evaluation of the global flame propagation speed

The uncertainty in the global flame propagation velocity is evaluated based on the 95% confidence interval associated with the slope of the linear curve fit. The mean uncertainties obtained from five flashback events are given in Table 2. The mean axial and angular flame propagation velocities were 1.43 m/s and 383 rad/s, which leads to a relative uncertainty of 9 and 6%, respectively.

Table 2 Uncertainties associated with global lab-frame propagation velocities of the flame tongues

1.4 Combined uncertainties in flame base frame-of-reference

The three-component velocity fields obtained in the radial–axial plane of the laser sheet were converted to velocity fields on quasi-annular shells as described in Sect. 3.3.1. The velocity field in the vicinity of the leading side of a flame tongue was then transformed to a frame-of-reference moving with the flame base by subtracting the global flame propagation velocity. For this study, we did not aim at computing gradients in the velocity field along the circumferential direction (which would require invoking Taylor’s hypothesis). Instead, the main approximation introduced by the change of reference-frame, which was relevant for the analysis in the current work, is the following:

It was assumed that each velocity vector in Fig. 8 is the velocity relative to an observer moving with any point along the leading side flame front as opposed to just the flame base. The chemiluminescence movies showed that for the investigated operating condition the flame surface along the leading side of the flame tongues was smooth and steady in time for the duration it took a tongue to swirl through the laser sheet. Unsteady formation of small-scale bulges was generally not observed along the leading side in contrast to the trailing side. Therefore, to a good approximation, the entire leading side propagated with the lab-frame flame propagation velocity obtained by tracking the flame base. The combined uncertainty for the axial component of the velocity field in the flame-base frame-of-reference then was $\sigma _{{{u_z}}}^{{{\text{fb}}~{\text{FOR}}}}=\sqrt {\sigma _{{{u_z}}}^{2}+\sigma _{{{v_{\text{f}}}}}^{2}} =0.23\;{\text{m}}/{\text{s}}$. For the azimuthal velocity component, the uncertainty depended on the radial location of the annular shell of interest. For $r=13.8\;{\text{mm}}$ (corresponds to $\tilde {r}=1.1\;{\text{mm}},$ Fig. 8), $\sigma _{{{u_\theta }}}^{{{\text{fb}}~{\text{FOR}}}}=\sqrt {\sigma _{{{u_\theta }}}^{2}+{{\left( {{\sigma _{{\omega _{\text{f}}}}} \cdot r} \right)}^2}} =0.45\;{\text{m}}/{\text{s}}$.