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Proceedings of the Combustion Institute 35 (2015) 1451–1459

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Experimental investigation of Darrieus–Landauinstability effects on turbulent premixed flames

G. Troiani a, F. Creta b,⇑, M. Matalon c

a ENEA C.R. Casaccia, via Anguillarese 301, Rome, Italyb Dept. of Mechanical and Aerospace Engineering, University of Rome “La Sapienza”, Rome, Italy

c Dept. of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

Available online 15 August 2014

Abstract

The turbulent propagation speed of a premixed flame can be significantly enhanced by the onset ofDarrieus–Landau (DL) instability within the wrinkled and corrugated flamelet regimes of turbulent com-bustion. Previous studies have revealed the existence of clearly distinct regimes of turbulent propagation,depending on the presence of DL instabilities or lack thereof, named here as super- and subcritical respec-tively, characterized by different scaling laws for the turbulent flame speed.

In this study we present experimental turbulent flame speed measurements for propane/air mixtures atatmospheric pressure, variable equivalence ratio at Lewis numbers greater than one obtained within a Bun-sen geometry with particle image velocimetry diagnostics. By varying the equivalence ratio we act on thecut-off wavelength and can thus control DL instability. A classification of observed flames into sub/super-critical regimes is achieved through the characterization of their morphology in terms of flame curvaturestatistics. Numerical low-Mach number simulations of weakly turbulent two-dimensional methane/air slotburner flames are also performed both in the presence or absence of DL instability and are observed toexhibit similar morphological properties.

We show that experimental normalized turbulent propane flame speeds ST=SL are subject to two distinctscaling laws, as a function of the normalized turbulence intensity U rms=SL, depending on the sub/supercrit-ical nature of the propagation regime. We also conjecture, based on the experimental results, that at highervalues of turbulence intensity a transition occurs whereby the effects of DL instability become shadowed bythe dominant effect of turbulence.� 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Premixed turbulent flames; Bunsen flames; Darrieus–Landau instability; Turbulent propagation speed; Flamecurvature

http://dx.doi.org/10.1016/j.proci.2014.07.0601540-7489/� 2014 The Combustion Institute. Published by El

⇑ Corresponding author.E-mail addresses: guido.troiani@enea.it (G. Troiani),

francesco.creta@uniroma1.it (F. Creta), matalon@illinois.edu (M. Matalon).

1. Introduction

The search for a universal scaling law for theturbulent propagation speed of premixed flamesis still debated and systematically complicated bythe wide scatter of experimental results, often

sevier Inc. All rights reserved.

1452 G. Troiani et al. / Proceedings of the Combustion Institute 35 (2015) 1451–1459

due to the strong dependence from experimentalconditions [1–3], and by a general disagreementwith proposed theories.

In the context of flame–turbulence interaction,the presence of intrinsic Darrieus–Landau (DL)hydrodynamic instabilities, especially when theincident turbulence is weak, were recognized asan important factor influencing the propagatingcharacteristics of flames [4–6]. A number of exper-imental studies were performed [7–13] withemphasis on the role of DL instability. Althoughno final quantitative agreement yet exists on suchrole [1], there is mounting evidence that the bifur-cative transition to DL instability greatly influ-ences turbulent flame morphology and dynamics,hinting at the existence of a multiplicity of scalinglaws for the turbulent propagation speed.

In a laminar scenario [14,15] a planar flametransitions, upon onset of DL instability, to a typ-ical large scale cusp-like corrugated conformationsteadily propagating at a speed substantiallygreater than the unstretched laminar flame speedSL. Recently, in a series of numerical studies byCreta and Matalon [16–19], it was found that ina turbulent scenario a similar dichotomy persists.Thus, an originally laminar and stable planarflame will remain statistically planar, defining asubcritical turbulent mode (or regime) of propaga-tion, whereas an unstable flame in the presence ofturbulence will exhibit a more complex corruga-tion, with sharp cusps protruding into the burntmixture, hence defining a supercritical turbulentmode in which DL effects are dominant. For eachmode of propagation, such studies highlighted thepresence of clearly distinct scaling laws for theturbulent speed ST , expressed in the formST =SL � U rms=SLð Þn, with U rms the intensity ofthe turbulent field in terms of the r.m.s. of velocityfluctuations. In particular, indicating the twomodes with subscripts sub, sup it was observedthat ðiÞ ðST=SLÞsup > ðST=SLÞsub owing to increasedflame corrugation leading to a DL-enhancementof the turbulent speed, ðiiÞ scaling exponents aresubject to nsup < nsub indicating that the supercrit-ical mode is less sensitive to turbulence, and ðiiiÞDL effects are overpowered by the increasingwrinkling at high turbulent intensities, with thescaling exponent n reverting back to values similarto subcritical behavior.

A rather similar scenario was recently pro-posed by Chaudhuri [20] where a limiting condi-tion was identified at which turbulencesuppresses the effects of DL instability. If, how-ever, DL instabilities can develop in weaker tur-bulence, then two distinct scaling laws for theturbulence speed, derived through spectral closuretechniques and self similarity arguments, indeedemerge.

In this work we present experimental evidencefor the above general dual behavior for turbulentflame speed, induced by the presence or absence of

intrinsic DL instabilities. We adopt a D ¼ 18 mmdiameter propane–air Bunsen flame at atmo-spheric pressure and variable equivalence ratio /and variable inflow turbulence intensity equippedwith particle image velocimetry (PIV) diagnostics.Results are supported by two dimensional low-Mach number direct numerical simulations ofmethane–air turbulent Bunsen flames, performedto investigate the morphological differencesbetween subcritical and supercritical modes ofpropagation.

2. Determination of stability limits

We defined super/subcritical turbulent regimesas flame propagation modes characterized respec-tively by the presence or absence of DL instability.Figure 1 displays Mie scattering images of pro-pane–air Bunsen flames, subject of the presentinvestigation, qualitatively illustrating the mor-phological differences of such propagative modes.We note smooth convex/concave wrinkling in thesubcritical regime as opposed to sharp cusp-likeprotrusions towards the burnt mixture typical ofDL corrugation which characterizes the supercrit-ical regime. A general guideline is thus needed todiscriminate between such regimes and possiblycontrol their onset as a function of the indepen-dent parameters available in the context of anexperimental setting.

Given a characteristic hydrodynamic length L,representative of the transverse dimension of theflame or device producing it, a planar laminarflame can become unstable to disturbances of longwavelength k if stabilizing effects, of thermal diffu-sive nature, are insufficient to the extent ofdecreasing the critical (cut-off) disturbance wave-length kc below L so that kc < k < L. Increasingthe pressure or driving the mixture compositiontowards stoichiometric conditions can indeedreduce the flame thickness and thus the Marksteinlength, which is of the same order, and which inturn decreases kc thus promoting instabilities. Inthe context of the hydrodynamic theory of pre-mixed flames the linear stability analysis of a pla-nar flame yields asymptotic dispersion relations[21–23] in the form of truncated series expansionsin powers of the transverse wavenumberk ¼ 2p=k, expressing the disturbance growth ratexðkÞ. As shown in [14], simplified Markstein-typeflame models can yield a closed form dispersionrelation yielding similar qualitative results. Suchmodels generally retain corrective diffusive effectsonly in the flame speed expressionSf ¼ SL �LK, where Sf is defined as the speedrelative to the unburnt mixture and where L isthe Markstein length and K is the flame stretch.The closed form dispersion relation yields a cut-off disturbance wavelength, defined at x ¼ 0 (seebold continuous and dashed lines in Fig. 2), which

Fig. 1. Mie scattering images (rotated 90�) of propane–air Bunsen flames at atmospheric pressure and Re ¼ 5000. 1.Subcritical regime, / ¼ 0:8;; 2. Supercritical regime, / ¼ 1:4.

Fig. 2. Growth rate xðk;/Þ for a propane–air planarflame at atmospheric pressure. Continuous lines:x ¼ const: > 0 (unstable planar flame), dotted lines:x ¼ const: < 0 (stable planar flame). Bold continuousline: cut-off wavelength kc defined as xðkc;/Þ ¼ 0 forpropane–air mixtures. Bold dashed line: cut-off wave-length for methane–air mixtures. Filled symbols: exper-imentally derived kc values for propane–air V-flames[27].

G. Troiani et al. / Proceedings of the Combustion Institute 35 (2015) 1451–1459 1453

is found to be kc ¼ 2pð3r� 1ÞL=ðr� 1Þ wherer ¼ qu=qb is the unburnt to burnt gas densityratio. This can be related to the equivalence ratio/ by determining the functions Lð/Þ and rð/Þ forpropane–air mixtures. The generalized hydrody-namic theory provides a comprehensive expres-sion for the Markstein length in terms offunctional parameters that can be extracted byexperimental data which reads

L=dD ¼r

r� 1

Z r

1

gðsÞs

dsþ ZeðLeeff � 1Þ2ðr� 1Þ

�Z r

1

gðsÞs

lnr� 1

s� 1

� �ds ð1Þ

where the diffusion length scale dD ¼ Dth=SL is ameasure of the laminar flame thickness, with Dth

taken as the thermal diffusivity, Ze the Zel’dovichnumber, gðT=T uÞ summarizes the temperature

dependence on transport and Leeff is a weightedaverage of the fuel and oxidizer Lewis numbers(details in [24,25]).

Figure 2 is a plot of the perturbation growthrate xðk;/Þ obtained using the closed formasymptotic dispersion relation [14] for a planarflame, inclusive of Eq. (1) and adopting experi-mental data by Tseng et al. [26] for propane mix-tures at atmospheric pressure which was fitted toestablish the dependence of all functional param-eters from /. We find that for such mixturesLð/Þ > 0, corresponding to large Leeff , rangingfrom 1.8 to 1.35 in the interval / 2 ½0:6; 1:6�,which excludes the possibility of thermal diffusiveinstabilities. Figure 2 shows that given a fixedhydrodynamic length L, representative of the lat-eral domain size, the condition L > kc defines anisland of instability in terms of flame compositionroughly centered at / ¼ 1. In other words when/ 2 ½/a;/b� the growth rate x > 0 for all distur-bances of wavelength kc < k < L, thus promotingDL instability. Experimental points in Fig. 2,obtained by harmonically forcing a premixedflame [27], confirm the existence of such an insta-bility /-interval albeit for a rod-stabilized V-flameconfiguration. We note that in the linear regime,any small disturbance on the planar flame growsexponentially in amplitude but is eventually stabi-lized by nonlinear effects into a large-scale, cusp-like conformation typical of DL instability.

Applying such reasoning to a Bunsen ratherthan a planar flame, the hydrodynamic length Lmay be assumed to be related to the nozzle diam-eter and to the outflow velocity, although someambiguity persists on its exact determinationand thus on the determination of the instabilityisland, given the lack of a general theory. Inspec-tion of Fig. 2 further suggests that for given oper-ating conditions a minimum nozzle diameterexists below which DL instability is not expectedat any /.

3. CFD of Bunsen flames

The foregoing section established the generalcriterion, derived for a planar flame, that DL

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instability, if present, will occur in a compositioninterval roughly centered about / ¼ 1. Such crite-rion, when extended to atmospheric pressure Bun-sen flames, thus proves only as a useful guidelinein triggering a supercritical propagative modefrom a subcritical one (such as those visible inFig. 1) by driving a lean mixture towards a richercomposition and vice versa, provided that for agiven outflow velocity, L, which can be consideredproportional to the Bunsen nozzle diameter, islarge enough to guarantee a finite instability com-position interval. Yet, the ambiguity on L andthus on the size of such interval makes the aboveguideline a necessary but not a sufficient conditionfor the existence of DL instability. In order to bet-ter distinguish supercritical configurations fromsubcritical an additional observable is needed.

In a mildly turbulent scenario, it was shown byCreta and Matalon in [18,19], through numericalsimulations, that a supercritical flame exhibitingDL instability manifests a characteristic morphol-ogy due to the interaction of turbulence with thecusp-like structures appearing on its surface andprotruding towards the combustion products. Inparticular, such interaction was shown to induceasymmetric flame curvature probability densityfunctions (p.d.f.), skewed towards negative curva-tures while a symmetric p.d.f. is generallyobserved for subcritical flames. Defining curva-ture as j ¼ �r � n, where n is the unit normal atthe flame surface pointing towards the burntgases, a negative skewness of curvature distribu-tion (defined as its third moment c) is indicativeof a flame being highly convex towards the burntside and only mildly convex towards the freshside. Such asymmetric morphological featureswere observed adopting both a weakly non linearmodel [19] and a hybrid front-capturing/Navier–Stokes model [18] of a planar flame assumed ofvanishing thickness with respect to the smallestfluid scales. In both cases a linear stability theoryexists in closed form yielding an unambiguousinstability criterion defined by the cut-off condi-tion L > kc, where L is uniquely defined as the lat-eral domain size. Thus, asymmetric curvature (aswell as flame position) distributions could belinked directly to the presence of DL effects. Inan experimental Bunsen setting, however, theskewness of flame curvature distribution, is onlyexpected to be an efficient qualitative marker forthe presence of DL instability. Still, we can inferthat supercritical regimes will be more likely ifcharacterized by highly skewed curvature p.d.f.’sand compositions close to stoichiometric, whilesubcritical regimes will be more likely to possessless skewed, if not symmetric p.d.f.’s and compo-sitions far from stoichiometric.

In order to assess whether such morphologicalobservations preserve their validity for flames offinite thickness in a Bunsen burner configuration,we perform direct numerical simulations using the

full reactive Navier–Stokes equations. The simula-tions are carried out in a two-dimensional setting,effectively representing a slot rather than a Bunsenburner. As shown in [19], through a forcedMichelson–Sivashinsky model, valid forr� 1� 1, two-dimensional flames preserve thesame morphological and propagative features asthree-dimensional flames in the context of theinteraction of DL flame structures withturbulence.

The adopted numerical scheme is based on theunfiltered time-dependent low-Mach numberequations with detailed chemistry and withoutbuoyancy and radiation effects. An operator-splitstiff second-order predictor–corrector projectionscheme is employed, full details of which can befound in [28–30]. We choose a methane–air mix-ture described by a 16 species and 57 reactionschemical mechanism obtained via a Computa-tional Singular Perturbation (CSP) simplificationalgorithm [31] starting from a detailed Gri1.2mechanism. We employ a grid resolution of45 lm which accommodates a minimum of 10 gridpoints within the flame thickness defined on thebasis of the temperature profile. Burnt gases arefed externally of the fresh mixture nozzle outflowto stabilize the flame and to avoid Kelvin–Helm-holtz shear instabilities. A weak isotropic turbu-lent field is fed through the mean fresh Bunsenoutflow using a technique identical to thatdescribed in [18].

Two distinct simulations were performed, dis-played in Fig. 3 at various time instants, effectivelyrepresenting prototypical subcritical and super-critical configurations, which clearly exhibit a fun-damentally distinct morphology. Flame (a) inFig. 3 was obtained at atmospheric pressure fora nozzle diameter of 0.6 cm. A preliminary simu-lation of a spanwise periodic freely propagatinglaminar planar flame, of width L = 0.6 cm, exhib-ited stability when mildly perturbed at the samepressure level. This is indicative of the absenceof DL instability in flame (a) which indeed exhib-its subcritical features with a smooth flame surfacewrinkling. The flame surface is defined withoutloss of generality as the 1200 K temperature iso-contour and its curvature is displayed in the insetof Fig. 3, showing small positive/negative peakshinting to a quasi symmetric curvature p.d.f., pos-sibly moderately skewed towards negative valuesowing to the effect of the flame tip.

When the lateral domain is increased toL = 1.2 cm and the pressure raised to 2 atm, thepreliminary simulation involving a mildly per-turbed planar laminar flame was seen to exhibitinstability with formation of DL cusps. As aresult, flame (b) of Fig. 3, issuing from a nozzlediameter of 1.2 cm and appearing thinner due tothe higher pressure, clearly exhibits permanentcusp-like structures due to DL instability typicalof the supercritical regime. Such structures are

Fig. 3. Lower panel: two-dimensional simulation ofstoichiometric methane–air slot flames. Shown is formyl(HCO) radical mass fraction (Y HCO < 10�6 not shown)at various time instants. (a) Subcritical flame atp ¼ 1 atm, slot width d ¼ 0:6 cm, (b) supercritical flameat p ¼ 2 atm, d ¼ 1:2 cm. Inflow turbulenceUrms=SL ¼ 0:5. Fresh mixture bulk velocity is taken asffiffiffiffiffi

10p

SL so that the laminar Bunsen flame height is� 3=2d. Upper panels: instantaneous flame curvaturealong the flame curve s at a representative time instant.

G. Troiani et al. / Proceedings of the Combustion Institute 35 (2015) 1451–1459 1455

convected towards the tip, owing to the velocitycomponent tangent to the flame, and their effectis to introduce sharp negative curvature peaksclearly visible in the inset of Fig. 3 which appearfar larger in magnitude than in the subcriticalcase. We therefore conclude that the statisticalcharacterization of flame curvature and in partic-ular the skewness of its p.d.f. can act as an efficientmarker for the onset of DL instability in an exper-imental Bunsen flame.

4. Experimental setup

As stated, sub/supercritical regimes are soughtin a Bunsen flame in order to analyze their mor-phology and assess the influence of DL instabilityon turbulent flame speed. The Bunsen burner isoperated at two different bulk Reynolds numbersand variable equivalence ratio. The use of 3 lmalumina particles dispersed into the flow guaran-tees unbiased probing of flow velocity across theflame front within the PIV setting [32,33]. Thelaser source is a 54 mJ Nd:YAG equipped witha 60 mm focal length camera working at a resolu-tion of 1024 � 1280 pixels. The area recorded byCCD is 94:5� 118:6 mm2. Pulse to pulse delay isbetween 60 ls and 80 ls in order to attain a max-imum particle displacement less than one-quarter

of the interrogation window size (32 � 32 pixels)which presents 50% overlapping for velocity fieldestimation. Full details of the experimental setupmay be found in [33–35].

The flame front position is determined fromthe sudden particle number density jump causedby the steep temperature increase in the reactionzone of premixed flames [36]. Within Mie scatter-ing images this corresponds to zones at very differ-ent level of scattered light intensity. It follows thatthe locations with intensities higher than thethreshold are defined as unburnt, i.e. the reactionprogress variable c is set to zero and those withintensities lower than the threshold correspondto combustion products with c ¼ 1. Successiveaveraging of a number of 400 binarized imagesyields the mean progress variable hci, whose valuehci ¼ 0:5 is set to be mean front position. More-over, the turbulent intensity U rms acting on theflame front from the reactant side is evaluatedby taking the average of turbulent intensities con-ditioned to hci ¼ 0:02. Once the average flamefront position is defined, under the hypothesis ofaxisymmetricity of the mean field, the average sur-face area As is obtained and the turbulent speedfollows from ST ¼ _m=ðquAsÞ.

From any single binarized image of the instan-taneous flame front, the flame contour is extractedand a signed distance function w is evaluated withpositive and negative values indicating productsand reactants, respectively. The normal to theflame is constructed towards the products asn ¼ rw=jrwj so that flame curvature can beestablished as stated in Section 3. Note that thelargest absolute curvature that can be evaluatedis limited physically by flame thickness (dD), whichis of the order of 50–100 lm [26] and also byimage resolution that in this case is 90 lm.

5. Results and discussion

Mie scattering images of Bunsen flames shownin Fig. 4 reveal a variable number density of cusp-like structures as a function of equivalence ratio.As an example, examination of flames ‘a’ and‘I’, relative to lean mixtures, exhibit a clear sub-critical morphology with flame wrinkling appear-ing almost equally convex as it is concave. Onthe other hand, flames ‘c’, ‘d’ and ‘III’, relativeto richer mixtures, exhibit pointed structures pro-truding towards the burnt gases typical of thesupercritical regime. Further increasing the equiv-alence ratio, flames seem to regain a subcriticalmorphology, as with flame ‘VI’ and ‘h’, througha decrease in the number of cusp-like structures.

As can be observed in Fig. 5, relative to theRe ¼ 2500 case (flames I and III), these morpho-logical observations, translate into flame curva-ture p.d.f.’s being skewed towards negativecurvatures for supercritical flames.

Fig. 4. Mie scattering images of C3H8/air flames at varying equivalence ratios (/) and bulk Reynolds number,(Re ¼ 4 _m=Dlp) with _m mass flow rate. For the sake of clarity colors have been inverted so that dark zones correspond toreactants. Upper panels, Re ¼ 5000: a, / ¼ 0:8; b, / ¼ 1:1; c, / ¼ 1:4; d, / ¼ 1:5; h, / ¼ 1:7. Lower panels, Re ¼ 2500:I, / ¼ 0:7; II, / ¼ 0:9; III, / ¼ 1:4; V, / ¼ 1:6; VI, / ¼ 1:7. Flames e, / ¼ 1:55, f, / ¼ 1:6, g, / ¼ 1:65 and IV, / ¼ 1:5not shown for brevity.

Fig. 5. Curvature p.d.f.’s for Re ¼ 2500 flames. Squares:I, / ¼ 0:7 (subcritical), triangles: III, / ¼ 1:4(supercritical).

Fig. 6. Top curves: skewness of flame curvature p.d.f.’s.Circles: Re ¼ 2500, diamonds: Re ¼ 5000 (Experimentalpoints labels correspond to Fig. 4 nomenclature). Errorbars proportional to standard deviation of the measure(see [38] for details). Filled/empty symbols refer toscaling laws in Fig. 7. Bottom curves: representativehydrodynamic length L (taken as L ¼ 5 mm) and cut-offwavelength kc for a planar flame, normalized with flamethickness dD. Expression of kc appearing in Section 2 wasused.

1456 G. Troiani et al. / Proceedings of the Combustion Institute 35 (2015) 1451–1459

The curvature analysis, in terms of p.d.f. skew-ness, was carried out on all performed experi-ments and is shown in Fig. 6 as a function of /.We note higher absolute skewness for near stoi-chiometric values of /, indicating likely presenceof DL-type cusps, while smaller absolute valuesare attained for off stoichiometric compositions,hinting at a lower cusp number density. Alsoshown in Fig. 6 is the analytical linear stability cri-terion L > kc for a planar propane flame, similarlyto that shown in Fig. 2, clearly indicating theinstability / islands for a representative value ofL. Although no threshold value for the skewnesscan be defined in this experimental setting, dis-criminating between sub- and supercritical flames,

G. Troiani et al. / Proceedings of the Combustion Institute 35 (2015) 1451–1459 1457

similarly to the ambiguity existing on L, Fig. 6clearly shows that in near-stoichiometric condi-tions (a necessary condition for DL instability)all flames exhibit highly skewed curvatures indi-cating a higher occurence of DL-type structureswhich define the supercritical regime.

An additional finding, visible in Fig. 6, is thatthe effect of / on skewness appears to be less pro-nounced at a higher Re number. While a largelynon uniform skewness, at the lower Re number,underlines the distinct presence of DL-inducedcusp structures which survive the effect of incidentturbulence, a more uniform skewness distribution,occurring at a higher Re, is a symptom of turbu-lence being the dominating factor in determiningthe flame morphology, with DL structures thusplaying a lesser role. In this context we note thatthe bulk Re is linearly related to the turbulentReynolds number, based on the integral scale,and thus to the turbulence intensity [37]. Extrapo-lating this concept to higher Re numbers, weshould ultimately expect little or no effect of /on skewness and thus on flame morphology, a factthat hints at the existence of an additional regimein which turbulence is the sole dominating factorirrespective of the presence of underlying DLinstability whose effects are therefore partially orcompletely shadowed. The existence of thisadditional third regime of propagation was alsoobserved experimentally by Al-Shahrany et al.[12], numerically in [19] and was conjectured byChaudhuri et al. in [20]. Further evidence wasfound by Kobayashi et al. [10] who noted thatthe flame’s fractal dimension is sensitive to pres-sure increase, responsible for triggering DL insta-bilities, only at low turbulence intensity whereasat higher intensity fractal dimension plateaus toa universal value irrespective of DL effects.

Fig. 7. Normalized turbulent propagation speed as afunction of normalized turbulence intensity. Circles:Re ¼ 2500, diamonds: Re ¼ 5000 (experimental pointslabels correspond to Fig. 4 nomenclature).

We now proceed to analyze flame behavior interms of turbulent flame speed as a function ofturbulence intensity. Results are shown in Fig. 7where we observe that the normalized turbulentflame speed data are best fitted by two distinctscaling laws, within the range of Re numbersunder investigation. In particular, the concurrentanalysis of Fig. 6 and Fig. 7 shows that flamesconjectured to be supercritical, owing to highlyskewed curvatures and near stoichiometric com-positions, populate the scaling law associated tofaster turbulent speeds (filled symbols, dashedline), which is thus named ‘supercritical’. In otherwords, the turbulent flame speed is enhanced bythe presence of DL instability (DL-enhancement)which, as we have seen, induces a characteristicmorphology to the flame surface in terms ofsharp, cusp-like structures. It can therefore beargued that such corrugation, which can bethought of as an additive effect to the turbulentwrinkling, is responsible for a systematic increasein flame area per unit flame-brush length which isin turn the cause for the enhancement in ST=SL.Subcritical flames, on the other hand, are deprivedof the additional DL-driven corrugation mecha-nism and for this reason are observed to followa different scaling law for ST=SL. Figure 7 alsoseems to reveal that the DL-enhancementdecreases with turbulence intensity until it is com-pletely depleted beyond some intensity threshold,thus leaving a single scaling law for ST=SL athigher intensity. Although additional data athigher Re would be needed to corroborate the lat-ter statement, this would substantiate the exis-tence of a third unique turbulence-driven regimeof propagation, independent of DL effects asobserved in [19,20].

The foregoing scenario thus furnishes experi-mental evidence for the existence of a dual modeof propagation for weakly turbulent premixedflames which was observed numerically in [18,19]and conjectured by Chaudhuri et al. in [20]. Inparticular, in this latter study, the existence of aDL-enhanced turbulent propagation regime issubject to the condition that, given a flame pertur-bation wavenumber k, its linear growth rate x,given by the dispersion relation, be greater thanthe characteristic eddy frequency xturb ¼ 2p=sturb

where sturb is the eddy turnover time estimatedas the ratio of turbulent kinetic energy to meandissipation rate. Defining the non dimensionalparameter b ¼ xturb=x for all scales smaller thanthe integral length scale, then the region b < 1indicates that a DL instability can indeed developin a turbulent environment and thus a supercriti-cal propagation mode can exist. Figure 8 showsthe locus b ¼ 1, estimated following [20] for a/ ¼ 1 propane–air mixture, within a turbulentcombustion diagram populated by the experimen-tal points of the present study. We note thatsupercritical flames (shown with filled symbols)

Fig. 8. Modified premixed turbulent combustion dia-gram with superimposed experimental points. Dash–dotcurve is the b ¼ 1 locus (calculated at / ¼ 1); Circles:Re ¼ 2500 ; Diamonds: Re ¼ 5000 ; Filled/empty sym-bols refer to super/subcritical scaling laws in Fig. 7.

1458 G. Troiani et al. / Proceedings of the Combustion Institute 35 (2015) 1451–1459

have the tendency to fall within the b < 1 regionthus confirming the validity of the conjectured cri-terion defining the DL-enhanced regime.

Fits of the kind ST=SL � ðU rms=SLÞn can besought for the scaling laws of Fig. 7. We find forthe subcritical propagation mode a scaling expo-nent nsub � 0:4 which confirms previous experi-mental studies [9] and is close to the analyticalexpression proposed in [20] where nsub ¼ 0:5. Forthe supercritical propagation mode we findnsup � 0:25 which is substantially smaller thannsub. This indicates that the DL-induced structuresof the supercritical case appear to be less sensitiveto turbulence in spite of the fact that their highercorrugation causes an enhancement of turbulentflame speed. This property of supercritical flameswas repeatedly observed in [18,19,16] using differ-ent numerical approaches and where it wastermed ‘resilience’ to the incident turbulence.

6. Conclusions

An experimental investigation of Darrieus–Landau (DL) hydrodynamic instability effects onturbulent premixed flame propagation was per-formed using propane–air Bunsen flames at atmo-spheric pressure. Measurements of turbulentflame speed and flame curvature statistics werecarried out. Two distinct scaling laws wereobserved for the turbulent flame speed as a func-tion of turbulence intensity. A law exhibitinghigher turbulent flame speed is observed forflames closer to stoichiometric composition andpossessing enhanced negative skewness of curva-ture p.d.f.’s. Flames with such characteristics areshown to be more likely to exhibit typical DLinstability effects in terms of cusp-like corruga-tion. Super- and subcritical modes of propagationcan thus defined, respectively based on the pres-ence or absence of such effects. Increased flamecorrugation is therefore conjectured to cause aDL-induced enhancement of the turbulent flame

speed in the supercritical mode which is absentin the subcritical mode. The morphological fea-tures of the two modes of propagation were alsoinvestigated and observed by means of directnumerical simulations of methane–air Bunsenflames, confirming the presence of DL cusp-likecorrugation in the supercritical case, introducingsharp negative bursts in flame curvature.

Power law fits ST =SL � ðU rms=SLÞnsub;sup revealnsub < nsub � 0:4 which confirm previous numeri-cal [16,19] and analytical [20] studies. Results alsosuggest that at higher intensity, turbulence is theprevailing phenomenon, shadowing any DL-dri-ven effects and therefore unifying the dual propa-gation mode into a single turbulence-driven mode.In a future study, additional data will be gatheredto corroborate the existence of such turbulence-driven mode.

Acknowledgments

F. Creta is grateful to Dr. H.N. Najm for hisvaluable comments and scientific feedback andfor providing precious assistance with the dflamecode.

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