Ensemble-averaged dynamics of harmonically forced, turbulent premixed flames

Turbulent flames in practical devices are subject to a superposition of broadband turbulence and narrowband harmonic flow oscillations. In such cases, flames have a superposition of space–time correlated wrinkles, superposed with broadband turbulent disturbances that interact nonlinearly. This paper extends our prior experimental work to characterise and quantify these flame dynamics. We extract ensemble-averaged flame edge and velocity by ensemble-averaging the instantaneous data at the same phase with respect to the forcing cycle. This paper shows that the ensemble-averaged spatio-temporal dynamics of the flame changes significantly with turbulence intensity. From a spatial viewpoint, the ensemble-averaged flame at weak turbulence intensities exhibits clear cusps and a large ratio between curvature in concave and convex regions. In contrast, at high turbulence intensities, the concave and convex parts of the ensemble-averaged flame are nearly symmetric. From a temporal viewpoint, increasing turbulence intensity monotonically suppresses higher harmonics of the forcing frequency that are manifestations of flame nonlinearities. Taken together, these both point to the interesting observation that the ensemble-averaged flame exhibits increasingly linear dynamics with increasing turbulence intensities, in contrast to its very strong nonlinear behaviours at weak turbulence intensities and juxtaposed with the increasingly nonlinear nature of its instantaneous dynamics with increasing turbulence intensity. In addition, prior studies have shown clear coherent modulation of turbulent flame speed correlated with coherent curvature modulation and that this relationship could be quantified via a ‘turbulent Markstein number’, $M_{T}$ . We develop correlations for $M_{T}$ showing how it scales with turbulent and narrowband disturbance quantities, such as turbulent flame brush thickness and convective length scale.