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This paper concerns the modeling of unresolved turbulent fluxes in premixed flames. Classically closed with a gradient assumption, this term may also contain a countergradient part, as detailed in other works. In a first section, the bibliographical resources giving details about the closure of the unresolved turbulent fluxes are investigated and confronted thanks to time-averaged direct numerical simulation databases. Large-eddy simulation is then performed to underline the possibility to integrate the counter-gradient transport in an industrial-like computation where the mesh may not be thin enough to capture all the turbulent transport at a resolved scale. Results given by the considered closures are compared with experimental points and analyzed.

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Some years ago, one of the authors (Proust, 2015) published the conclusions of a rather large experimental work devoted to the gas flame acceleration down a long pipe. It was concluded that the flame propagation could be represented by a constantly accelerating piston. The acceleration parameter seems to be primarily linked to the expansion velocity of the burnt product. Other parameters seemed of secondary importance questioning in particular the respective roles of the turbulence of the flame and of the instabilities. Further experiments were performed using perfectly smooth and rough tubes (figure 1), varying the diameter of the pipe (150 and 250 mm) and the reactivity of the mixtures (methane-air and hydrogen air at various equivalence ratios). The smooth pipe is transparent enabling a direct visualization of the flame during the flame propagation and a refined resolution of the flame trajectory (in the steel pipes standard flame sensors were used). The pressure was measured at various locations but also the flow velocities in the boundary to try and detect any turbulence development. Only homogeneous and quiescent mixtures were studied and the flame was propagated from a closed ignition end toward the other open end. The results of the parametric study are presented in this paper.