Topology and flame speeds of turbulent premixed flame kernels in supersonic flows

Premixed flame kernels exposed to a mean expanding supersonic channel flow are examined using experiments and large-eddy simulations. Four cases, spanning three Mach numbers and two equivalence ratios, are explored. Numerical results are processed similarly to and compared with experimental data. Accuracy is assessed by comparing the numerically resolved flow field, flame growth, and internal flame structure with experimental data. Evolution of the flame topology, ascertained using these combined studies, confirms that the flame kernel morphs into a reacting vortex ring upon interaction with the supersonic mean flow expansion. The vortex ring topology assessment shows potentially significant errors in the turbulent flame speed based on line of sight (LOS) measurements. Modifications to the flame speed to correct the error associated with line of sight measurements are proposed. Two turbulent flame speed scalings are investigated: one with the RMS turbulent velocity, u′, and the other with the vortex propagation velocity, UT. It is shown that u′ fails to collapse the flame speed data but UT scaling does collapse the data from all four cases and produces a nearly linear scaling regime. This finding suggests turbulence plays a secondary role to the hydrodynamic instability in this particular problem. The conditions for displacement and consumption speed equivalency are explored further and it is found that the nature of the diagnostic used (LOS, planar, volumetric) and the progress variable isocontour measured play important roles and should be considered during interpretation of experimental data.