Shear-layer effects on the dynamics of unsteady premixed laminar counterflow flames

TL;DR

This work investigates how flow non-uniformity and unsteadiness affect premixed laminar counterflow flames, with a focus on off-center regions. Using a twin-nozzle counterflow, oscillatory inflow, Mie-scattering imaging, and PIV, the authors map centerline versus off-center flame dynamics under controlled frequencies ($f_e$) and amplitudes, revealing a two-regime response. They find that centerline flames are mainly driven by the excitation frequency $f_e$, while flames near the shear layer exhibit strong second-harmonic $2f_e$ and higher harmonics due to vortex shedding of counter-rotating pairs, with the vorticity intensity correlating with harmonic content. A critical radius, where $ig\langle \overline\omega^2\big\rangle$ reaches a threshold, aligns with the onset of $2f_e$ in flame oscillations, highlighting the pivotal role of shear-layer dynamics in off-center flame behavior. The results advance understanding of flame response in unsteady, non-uniform flows and have implications for modeling flamelets and extinction in practical combustors.

Abstract

The influence of flow non-uniformity and unsteadiness on premixed flames is of considerable interest due to its direct relevance to practical combustion systems. The steady counterflow flame has long served as a canonical configuration for investigating flame dynamics under controlled, spatially non-uniform conditions. A commonly studied variation, referred to as the unsteady counterflow, introduces a controlled temporal perturbation to the otherwise steady flow from the nozzles, thereby enabling the systematic examination of the coupled effects of unsteadiness and non-uniformity. Prior investigations have focused on flame dynamics along the line of symmetry, where the reduced dimensionality of the problem facilitates analysis. In the present study, we extend this perspective by experimentally examining flame behavior at off-center locations, where multi-dimensional effects of non-uniformity and unsteadiness are more pronounced. Results reveal markedly different dynamics away from the centerline, characterized by a dominant contribution from higher harmonic responses. Further analysis of the associated vortex dynamics in the shear layer demonstrates that the intensity of these vortical structures directly governs the strength of the observed higher harmonics, and thereby the altered flame behavior.

Figures (11)

• Figure 1: Illustration of the primary components of counterflow setup along with diagnostic instruments.
• Figure 2: Mie-scattering with superimposed PIV velocity field snapshot, for non-reactive (top) and reactive (bottom) data for $f_e$ = 137 Hz. Flame edge is illustrated in cyan, nozzle exits are depicted by grey rectangular boxes, and the coordinate system is illustrated in white in the bottom panel.
• Figure 3: Flame response along the center line ($r/R=0$) as a function of excitation frequency for both perturbation strategies: the constant amplitude method in black and the constant power method in red. The corresponding values of the Stokes number, $\mathit{St}=f_e t_F$ are shown on the secondary x-axis.
• Figure 4: Power spectral density of flame oscillation or displacement ($\hat{P}_{z_f}$) measured at (a) flame's center point ($r/R=0$), (b) flame location $r/R=1.0$, and (c) flame location $r/R=1.2$ accompanied by (d) radial profiles of first four harmonics of the $\hat{P}_{z_f}$ (markers are displayed every 6 data points for clarity). The radial location ($r_{2f_e}$) where $2f_e$ starts to increase is marked with a star and a vertical dashed line in (d). Four rows represent four excitation frequencies: (i.) $47~$Hz, (ii.) $137~$Hz, (iii.) $227~$Hz, and (iv.) $317~$Hz. The uncertainty in the computation of $z_f$ is $\pm 2$ pixel.
• Figure 5: Power spectral density of flame conditioned stretch rate due to tangential strain ($\hat{P}_{K_t}$) measured at (a) flame's center point ($r/R=0$), (b) flame location $r/R=1.0$, and (c) flame location $r/R=1.2$ accompanied by (d) radial profiles of first four harmonics of the $\hat{P}_{K_t}$ (markers are displayed every 6 data points for clarity). Four rows represent four excitation frequencies: (i.) $47~$Hz, (ii.) $137~$Hz, (iii.) $227~$Hz, and (iv.) $317~$Hz. The uncertainty in the computation of $\overline {K_t}$ is $0.01-0.02~$1/s.