When a premixed flame propagates in a turbulent flow, not only does turbulence affect the burning rate (e.g., by wrinkling the flame and increasing its surface area), but also the heat release in the ...flame perturbs the pressure field, and these pressure perturbations affect the turbulent flow and scalar transport. For instance, the latter effects manifest themselves in the so-called countergradient turbulent scalar flux, which has been documented in various flames and has challenged the combustion community for approximately 35 years. Over the past decade, substantial progress has been made in investigating (
a
) the influence of thermal expansion in a premixed flame on the turbulent flow and turbulent scalar transport within the flame brush, as well as (
b
) the feedback influence of countergradient scalar transport on the turbulent burning rate. The present article reviews recent developments in this field and outlines issues to be solved in future research.
A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is ...performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U^{'} to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze=6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U^{'} is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.
The goals of the present review paper are; (i) to introduce experimental facilities and numerical tools applied to investigating inhomogeneously premixed flames, (ii) to summarize recent progress in ...revealing and understanding local phenomena (e.g. back-supported combustion or generation of flame surface area) that stem from the influence of mixture inhomogeneities on flame propagation through flammable reactants, (iii) to show state-of-the-art of unsteady multidimensional RANS and LES research into inhomogeneously premixed turbulent flames and to discuss models invoked for this purpose, and (iv) to highlight issues that still challenge researchers who develop such models.
Data obtained in recent direct numerical simulations (Lee et al.) of statistically one-dimensional and planar, lean complex-chemistry hydrogen-air flames characterized by three different Karlovitz ...numbers Ka ranging from 3 to 33 are further analyzed in order to explore local characteristics and structure of (i) extreme points characterized by the peak (over the computational domain) Fuel Consumption Rate (FCR) or Heat Release Rate (HRR) and (ii) leading points that are also characterized by a high FCR or HRR, but advance furthest into unburned reactants. Results show that, on the one hand, common characteristics of flame perturbations (curvature, strain and stretch rates, displacement speed) fluctuate significantly in the extreme or leading, FCR or HRR points and are different in different flames. Moreover, other two-point local quantities such as the local gradients of combustion progress variables or species (e.g., the radical H) mass fractions are different in different flames. Therefore, a common simple configuration of a perturbed laminar flame cannot be used as a catchall model of the entire local structure of zones surrounding the discussed points at various Ka. On the other hand, single-point local characteristics (temperature, species mass fractions, rates of their production) of the FCR extreme points are comparable in all three turbulent flames and in the critically strained planar laminar flame. In particular, the FCRs in the extreme points fluctuate weakly and are approximately equal to each other and to the peak FCR in the critically strained laminar flame. The latter finding implies that (i) the maximum FCR evaluated in the critically strained laminar flame could be used to characterize, in a first approximation, the local FCR in the extreme or leading points in turbulent flames, thus, supporting the leading point concept, and (ii) almost the same extreme FCR can be reached in substantially different local burning structures.
A Direct Numerical Simulation (DNS) study of statistically one-dimensional and planar, lean complex-chemistry hydrogen-air flames characterized by a low Lewis number Le and three different Karlovitz ...numbersKa ranging from 3 to 33 is performed, with the same complex-chemistry flames being also simulated by setting molecular diffusivities of all species equal to the heat diffusivity of the mixture. The simulations predict a significant increase in a ratio of turbulent burning velocity to the laminar flame speed in the former (Le<1) flames when compared to the latter (equidiffusive) flames. Extreme points characterized by the peak (over the computational domain) Fuel Consumption Rate (FCR) or Heat Release Rate (HRR) are found at each instant. In the equidiffusive flames, such extreme FCR and HRR are close to their peak values in the unperturbed laminar flame. If Le is low, the former rates are significantly higher than the latter ones due to an increase in the local temperature, equivalence ratio, and radical mass fractions, caused by diffusive-thermal effects. While the studied extreme points may appear sufficiently far from the leading edge of the instantaneous flame brush, leading points characterized by a lower, but still high (Le<1) FCR or HRR are observed close to the leading edge at each instant. Various local characteristics (temperature, equivalence ratio, species mass fractions and their gradients, reaction rates, etc.) of the extreme and leading points are explored and significant differences between zones characterized by high FCR or HRR are revealed. For instance, in the latter zones, major chemical pathways are changed. Moreover, while the extreme HRRs strongly fluctuate in time, with their mean and rms values being significantly increased by Ka, the extreme FCRs fluctuate weakly and are close at different Ka, thus, implying that almost the same extreme FCR can be reached in substantially different local burning structures.
In the combustion literature, contradictory results on the influence of turbulence on the local thickness of a premixed flame can be found and the present paper aims at contributing to reconcile this ...issue. First, different measures of local flame thickness in a turbulent flow, e.g. area-weighted and unweighted surface-averaged values of (i) |∇c|, i.e., the absolute value of 3D gradient of the combustion progress variable c, or (ii) 1/|∇c|, are studied and analytical relationships/inequalities between them are obtained. Second, the evolution of the different flame thickness measures is explored by numerically evaluating them, as well as various terms in relevant evolution equations derived analytically. To do so, various measures and terms are extracted from DNS data obtained from (i) a highly turbulent, constant-density, dynamically passive, single-reaction wave, (ii) moderately and highly turbulent, single-step-chemistry flames, and (iii) moderately and highly turbulent, complex-chemistry lean methane-air flames. In all those cases, all studied flame thickness measures are reduced during an early stage of premixed turbulent flame development, followed by local flame re-broadening at later stages. Analysis of various terms in the aforementioned evolution equations shows that the initial local flame thinning is controlled by turbulent strain rates. The subsequent local flame re-broadening is controlled by (i) curvature contribution to the stretch rate, which counter-balances the strain rate, (ii) spatial non-uniformities of the normal diffusion contribution to the local displacement-speed vector Sdn, and (iii) dilatation, which plays an important role in moderately turbulent flames, but a minor role in highly turbulent flames. Moreover, the present study shows that differently defined measures of a local flame thickness can be substantially different. This difference should also be borne in mind when comparing data that indicate local flame thinning with data that indicate local flame broadening.
•Ambiguity exists in extracting surface-averaged quantities from reacting-flow DNS.•Differently defined averaged quantities are compared analytically and numerically.•Difference between them is ...significant in highly turbulent reacting flows.•This difference in part explains controversy in flame thinning/broadening.
The paper aims at clarifying some issues associated with evaluation of surface-averaged quantities in Direct Numerical Simulation (DNS) of a turbulent reacting flow. For a quantity ϕ(t, x) averaged over an isosurface c(t,x)=c^ of a reaction progress variable c, there exist at least two different definitions of surface averages; an area-weighted surface average 〈ϕ〉s|c^,t and an unweighted surface average 〈ϕ〉v|c^,t. These two fine-grained averages can also be extended to coarse-grained surface averages 〈ϕ〉S|c^,ϵ,t and 〈ϕ〉V|c^,ϵ,t over an interval of c^≤c(t,x)≤c^+ϵ. In a highly turbulent medium, the difference 〈ϕ〉s−〈ϕ〉v between the area-weighted and unweighted surface averages can be significant for most quantities ϕ of basic interest. The sign of this difference depends on the sign of the correlation between ϕ and |∇c|, can be opposite for different ϕ or even for different isosurfaces of the same scalar field ϕ. For a quantity ϕ that can become singular in the zero-gradient points |∇c|(t,x)=0, its unweighted or area-weighted surface averages can still be bounded. The difference between area-weighted and unweighted surface averages of 1/|∇c| or |∇c| is relevant to explaining the well-known, but still challenging controversy between available data on the influence of turbulence on the local flame thickness.
The structure of premixed turbulent flames and governing physical mechanisms of the influence of turbulence on premixed burning are often discussed by invoking combustion regime diagrams. In the ...majority of such diagrams, boundaries of three combustion regimes associated with (i) flame preheat zones broadened locally by turbulent eddies, (ii) reaction zones broadened locally by turbulent eddies, and (iii) local extinction are based on a Karlovitz number Ka, with differently defined Ka being used to demarcate different combustion regimes. The present paper aims to overview different definitions of Ka, comparing them, and suggesting the most appropriate choice of Ka for each combustion regime boundary. Moreover, since certain Karlovitz numbers involve a laminar flame thickness, the influence of complex combustion chemistry on the thickness and, hence, on various Ka and relations between them is explored based on results of complex-chemistry simulations of unperturbed (stationary, planar, and one-dimensional) laminar premixed flames, obtained for various fuels, equivalence ratios, pressures, and unburned gas temperatures.
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