Geometrical properties of turbulent premixed flames and other corrugated interfaces

Abstract

This study focuses on the geometrical properties of turbulent flame fronts and other interfaces. Toward that end, we use an original tool based on proper orthogonal decomposition (POD), which is applied to the interface spatial coordinates. The focus is mainly on the degree of roughness of the flame front, which is quantified through the scale dependence of its coverage arclength. POD is first validated by comparing with the caliper technique. Fractal characteristics are extracted in an unambiguous fashion using a parametric expression which appears to be impressively well suited for representing Richardson plots. Then it is shown that, for the range of Reynolds numbers investigated here, the scale-by-scale contribution to the arclength does not comply with scale similarity, irrespectively of the type of similarity which is invoked. The finite ratios between large and small scales, referred to as finite Reynolds number effects, are likely to explain this observation. In this context, the Reynolds number that ought to be achieved for a proper inertial range to be discernible, and for scale similarity to be likely to apply, is calculated. Fractal characteristics of flame folding are compared to available predictions. It is confirmed that the inner cutoff satisfactorily correlates with the Kolmogorov scale while the outer cutoff appears to be proportional to the integral length scale. However, the scaling for the fractal dimension is much less obvious. It is argued that much higher Reynolds numbers have to be reached for drawing firm statements about the evolution (or constancy) of the fractal dimension with respect to flame and flow parameters. Finally, a heuristic phenomenology of corrugated interfaces is highlighted. The degree of generality of the latter phenomenology is confirmed by comparing the folding of different interfaces including a turbulent-nonturbulent interface, a liquid jet destabilized by a surrounding air jet, a cavitating flow, and an isoscalar evolving in a turbulent medium. The latter outcome is likely to have strong implications for modeling the corrugation of turbulent interfaces occurring in many physical situations.

Isolating strain and curvature effects in premixed flame/vortex interactions

“…have also shown that the flame speed/flame stretch correlation is strongly affected by the flow forcing frequency and can even vanish at high forcing frequencies in agreement with the theoretical predictions of Joulin (1994), Clavin & Joulin (1997). Transient effects are also important for characterizing the flame geometrical properties, for instance flame stretch (Thiesset et al 2017). (iv) These effects might be smoothed when applying surface averaging.…”

“…2.1. The flame-vortex interaction burner (FVIB) Experiments are carried out at ICARE, Orléans, in the burner used by Thiesset et al (2017) and presented in figure 1. Fuel and oxidizer are mixed before being fed through the side of the burner.…”

“…There is a wealth of experimental (Roberts & Driscoll 1991;Roberts et al 1993;Mueller et al 1996;Sinibaldi et al 2003;Thiesset et al 2017) and numerical (Poinsot, Veynante & Candel 1991;Charlette, Meneveau & Veynante 2002;Bougrine et al 2014) studies devoted to FVIs. A review by Renard et al (2000) was also dedicated to this topic.…”

“…In addition, these results yielded expression of efficiency functions, i.e. the transfer function between vortex strength and flame stretch Charlette et al 2002;Bougrine et al 2014;Thiesset et al 2017) which are largely employed in LES of turbulent premixed combustion. It is also an archetypal situation in which some experimentally measurable surrogates of the heat release can be tested (Najm et al 1998).…”

Fractal scaling of the turbulence interface in gravity currents

“…developed and tested by Thiesset et al (2016) for exactly this purpose. The function smoothly connects the asymptotes L = const.…”