Propagation of wrinkled turbulent flames in the context of hydrodynamic theory

Abstract

We study the propagation of premixed flames in two-dimensional homogeneous isotropic turbulence using a Navier–Stokes/front-capturing methodology within the context of hydrodynamic theory. The flame is treated as a thin layer separating burnt and unburnt gases, of vanishingly small thickness, smaller than the smallest fluid scales. The method is thus suitable to investigate the flame propagation in the wrinkled flamelet regime of turbulent combustion. A flow-control system regulates the mean position of the flame and the incident turbulence intensity. In this context we study the individual effects of turbulence intensity, turbulence scale, thermal expansion, hydrodynamic strain and hydrodynamic instability on the propagation characteristics of the flame. Results are obtained assuming positive Markstein length, corresponding to lean hydrocarbon–air or rich hydrogen–air mixtures. For stable planar flames we find a quadratic dependence of turbulent speed on turbulence intensity. Upon onset of hydrodynamic instability, corrugated structures replace the planar conformation and we observe a greater resilience to turbulence, the quadratic scaling being replaced by scaling exponents less than one. Such resilience is also confirmed by the observation of a threshold turbulence intensity below which the propagation speed of corrugated flames is indistinguishable from the laminar speed. Turbulent speed is found to increase and later plateau with increasing thermal expansion, this affecting the average flame displacement but not the mean flame curvature. In addition, turbulence integral scale is also observed to affect the propagation of the flame with the existence of an intermediate scale maximizing the turbulent speed. This maximizing scale is smaller for corrugated flames than it is for planar flames, implying that small eddies that will be unable to significantly perturb a planar front could be rather effective in perturbing a corrugated flame. Turbulent planar flames, and more so corrugated flames, were observed to experience a positive mean hydrodynamic strain, which was explained in terms of the overwhelming mean contribution of the normal component of strain. The positive straining causes a decrease in the mean laminar propagation speed which in turn can decrease the turbulent speed. The effect of the flame on the incident turbulent field was examined in terms of loss of isotropy and vorticity destruction by thermal expansion. The latter can be mitigated by a baroclinic vorticity generation which is enhanced for corrugated flames.