DNS Study of the Bending Effect Due to Smoothing Mechanism

Abstract

Propagation of either an infinitely thin interface or a reaction wave of a nonzero thickness in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is simulated by solving unsteady 3D Navier–Stokes equations and either a level set (G) or a reaction-diffusion equation, respectively, with all other things being equal. In the case of the interface, the fully developed bulk consumption velocity normalized using the laminar-wave speed SL depends linearly on the normalized rms velocity u′/SL. In the case of the reaction wave of a nonzero thickness, dependencies of the normalized bulk consumption velocity on u′/SL show bending, with the effect being increased by a ratio of the laminar-wave thickness to the turbulence length scale. The obtained bending effect is controlled by a decrease in the rate of an increase δAF in the reaction-zone-surface area with increasing u′/SL. In its turn, the bending of the δAF(u′/SL)-curves stems from inefficiency of small-scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles characterized by a high local curvature are smoothed out by molecular transport within the reaction wave.

Effects of turbulent length scale on the bending effect of turbulent burning velocity in premixed turbulent combustion

“…This suggests that the parameterisations of 𝑆 𝑇 /𝑆 𝐿 which are only functions of 𝑢 ′ /𝑆 𝐿 [20,45,46] are unlikely to be accurate and the role of integral scale in increasing the flame area has been reported before based on theoretical [47], numerical [48][49][50] and experimental [51] findings. Moreover, a decrease in 𝑆 𝑇 /𝑆 𝐿 with decreasing 𝑢 ′ 𝑆 𝐿 ⁄ is consistent with constant-density simulation results by Yu et al [13,14,16] and analytical results by Denet [8].…”

“…This behaviour is commonly referred to as bending in premixed turbulent combustion literature [3][4][5][6][7][8][9][10][11][12]. The physical origin of bending is not completely understood but significant physical insights have been provided in recent years based on the analysis of the propagation of reaction waves in constant density turbulent flow conditions [13][14][15][16], and some of the conclusions made from these constant density Direct Numerical Simulations (DNS) have subsequently been confirmed by variable density DNS of turbulent premixed flames [11]. Ahmed et al [11] used the statistical behaviours of the volume-integrated values of the different terms of the Flame Surface Density (FSD) transport equation to explain the bending behaviour using DNS data of statistically planar turbulent premixed flames with unity Lewis number subjected to forced unburned gas turbulence.…”

A New Mathematical Framework for Describing Thin-Reaction-Zone Regime of Turbulent Reacting Flows at Low Damköhler Number

“…The major results of the present work are as follows. First, exact, unclosed transport equations for the unconditioned, see Equations (35) and (36), and conditioned (to c < 1), see Equations (26)- (29), first and second-order moments of the reaction-progress-variable moments are derived.…”

“…Consequently, the wrinkle is rapidly smoothed out. A recent DNS study [34,35] does show that small-scale (when compared to δ L ) wrinkles of a reaction-zone surface are efficiently smoothed out by molecular mixing, with this effect significantly reducing U T when compared to a linear dependence of U T ∝ u simulated in the case of front propagation in the statistically same turbulence [36].…”

Numerical Simulations of Turbulent Combustion

“…Yu and Lipatnikov [6] compare direct numerical simulation data computed by studying two model problems relevant to premixed turbulent combustion. These are (i) motion of a self-propagating interface in a constant-density turbulence and (ii) propagation of a reaction wave of a finite thickness in a constant-density turbulence.…”