Effects of Lewis Number on the Evolution of Curvature in Spherically Expanding Turbulent Premixed Flames

Abstract

The effects of Lewis number on the physical mechanisms pertinent to the curvature evolution have been investigated using three-dimensional Direct Numerical Simulation (DNS) of spherically expanding turbulent premixed flames with characteristic Lewis number of L e = 0.8 , 1.0 and 1.2. It has been found that the overall burning rate and the extent of flame wrinkling increase with decreasing Lewis number L e , and this tendency is particularly prevalent for the sub-unity Lewis number (e.g., L e = 0.8 ) case due to the occurrence of the thermo-diffusive instability. Accordingly, the L e = 0.8 case has been found to exhibit higher probability of finding saddle topologies with large magnitude negative curvatures in comparison to the corresponding L e = 1.0 and 1.2 cases. It has been found that the terms in the curvature transport equation due to normal strain rate gradients and curl of vorticity arising from both fluid flow and flame normal propagation play pivotal roles in the curvature evolution in all cases considered here. The net contribution of the source/sink terms of the curvature transport equation tends to increase the concavity and convexity of the flame surface in the negatively and positively curved locations, respectively for the L e = 0.8 case. This along with the occurrence of high and low temperature (and burning rate) values at the positively and negatively curved zones, respectively acts to augment positive and negative curved wrinkles induced by turbulence in the L e = 0.8 case, which is indicative of thermo-diffusive instability. By contrast, flame propagation effects tend to weakly promote the concavity of the negatively curved cusps, and act to decrease the convexity of the highly positively curved bulges in the L e = 1.0 and 1.2 cases, which are eventually smoothed out due to high and low values of displacement speed S d at negatively and positively curved locations, respectively. Thus, flame propagation tends to smoothen the flame surface in the L e = 1.0 and 1.2 cases.

Effects of differential diffusion and stratification characteristic length-scale on the propagation of a spherical methane-air flame kernel

“…Indeed, small scale stratifications lead to a larger global heat release during the times following the forced ignition. Independently of the stratification scale, we notice that the burning extent, given here by Ω HRR , is more pronounced for the (CL) cases in comparison with the (VL) cases, which is consistent with the previous findings [9]. A possible explanation for the results exposed above relies on the evolution of the mixture fraction distribution on the flame front.…”

“…Previous homogeneous flame kernel development DNS analyses showed that differential diffusion tends to increase the flame speed and accelerate the overall flame expansion [8]. Furthermore, flame curvature dynamics was shown to be sensitive to Lewis number [9], in particular at low pressures [10]. On the other hand, flame kernel ignition dynamics have been shown to be strongly influenced by the fuel Lewis number, even in inhomogeneous mixtures [11].…”

Analysis of premixed flame kernel/turbulence interactions under engine conditions based on direct numerical simulation data

“…In figures 6 (d) and (f), the production of positive curvature by flow terms T u * and flame propagation terms T p * is depicted for both engine-relevant flame kernels. For (t > 1.0 · τ t ), only minor differences between flame kernel realizations persist and the present results are in good qualitative agreement with previous studies Alqallaf et al 2019). However, noticeable deviations between both flame kernels exist during the early development phase.…”

“…Note that the straining/bending balance due to flame propagation is reversed during this phase, which is a direct consequence of increased probability of high positive curvatures. As shown in previous studies Alqallaf et al 2019), the curvatureconditioned means of T p t and T p b exhibit a saddle point at κ = 0, while both terms substantially deviate from zero only at elevated curvatures (cf. figures S-4 (c) and (d) in the supp.…”

Numerical Simulations of Turbulent Combustion

“…Alqallaf et al [5] analyze direct numerical simulation data obtained from expanding, statistically spherical turbulent premixed flames characterized by three different Lewis numbers, i.e., Le = 0.8, 1.0, and 1.2, with all other things being equal. By processing the data, various terms in the transport equation for the local curvature of the instantaneous flame surface are evaluated and terms due to curl of vorticity and normal strain rate gradients are found to play the most important roles in the studied transport equation in all three cases.…”