Transient Behavior of Turbulent Scalar Transport in Premixed Flames

Abstract

Transition from gradient to countergradient scalar transport in a statistically planar, one-dimensional, developing, premixed turbulent flame is studied both theoretically and numerically. A simple criterion of the transition referred to is derived from the balance equation for the combustion progress variable, with the criterion highlighting an important role played by flame development. A balance equation for the difference in velocitiesū b andū u conditioned on burned and unburned mixture, respectively, is numerically integrated. Both analytical and computed results show that; (1) The flux ρu c is gradient during an early stage of flame development followed by transition to countergradient scalar transport at certain instant t tr . (2) The transition time is increased when turbulence length scale L is increased or when the laminar flame speed S L and/or the density ratio are decreased. (3) The transition time normalized using the turbulence time scale is increased by u . Moreover, the numerical simulations have shown that the transition time is increased by u if a ratio of u /S L is not large. This dependence of t tr on u is substantially affected by (i) the mean pressure gradient induced within the flame due to heat release and (ii) by the damping effect of combustion on the growth rate of mean flame brush thickness. The reasonable qualitative agreement between the computed trends and available experimental and DNS data, as well as the agreement between the computed trends and the present theoretical results, lends further support to the conditioned balance equation used in the present work. Nomenclaturesimplified Bray number n = {n x , n y , n z } unit vector normal to flame surface p pressure Re t = u L/D u turbulent Reynolds number q an arbitrary quantity S L laminar flame speed t time U b mean normal velocity in products far behind flame U t turbulent burning velocityfully-developed turbulent burning velocity u = {u, v, w} = {u 1 , u 2 , u 3 } velocity vector and its components u rms turbulent velocity u t = U t /U t,∞ normalized turbulent burning velocity W mass rate of product creation in a turbulent flame X distance from flame stabilization region x = {x, y, z} = {x 1 , x 2 , x 3 } spatial coordinatesGreek symbols α parameter in the Bray number, see (2) see criterion given by (22) γ probability of finding flamelet t turbulent flame brush thickness u =ū b −ū u slip velocity vector δ t = t /L normalized turbulent flame brush thickness ε viscous dissipation rate θ = t/τ t normalized time κ molecular heat diffusivity ξ normalized distance, see (17) ρ density σ = ρ u /ρ b density ratio τ = ρ u /ρ b − 1 heat release factor τ c = κ u /S 2 L = δ L /S L laminar flame time scale τ ij viscous stress tensor τ t = L/u turbulent time scale ω = W t,∞ /(ρ u U t,∞ ) normalized mean rate of product creation Flow Turbulence Combust (2011) 86:609-637 611

Three-dimensional direct numerical simulation study of conditioned moments associated with front propagation in turbulent flows

“…Such an influence was known after the pioneering work by Corrsin 35 and was addressed in the combustion literature long time ago. 36 In particular, balance equations for conditioned velocities indicate that source and sink terms conditioned to flamelets reduce the magnitude of turbulent scalar flux even in the constant-density case, 37,38 with these terms being proportional to the mean rate of product creation W . Within the framework of the paradigm of infinitely thin flame front, W = ρ u S L f and the reduction effect is increased by the front speed, in line with the present DNS data.…”

Burning Rate in Impinging Jet Flames

“…and (iii) balance equations for g u and the difference in w b and w u , derived by the present author [30] and discussed in detail elsewhere [7,31]. Here, 2 ) r=0 and g 1 are tuning parameters reported in Table 2.…”

Transition from pulled to pushed fronts in premixed turbulent combustion: Theoretical and numerical study

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