Partial premixing and stratification in turbulent flames

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Proceedings of the Combustion Institute 35 (2015) 1115–1136

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Partial premixing and stratification in turbulent flames A.R. Masri ⇑ School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia Available online 26 September 2014

Abstract This paper reviews recent advances in understanding the structure of turbulent partially premixed and stratified flames. The term “partially premixed” refers here to compositionally inhomogeneous mixtures that include flammable and non-flammable fluid while “stratified” combustion refers to a reacting front propagating through a range of compositions within the flammable limits. An overview of relevant laminar flame concepts is first introduced. In laminar partially premixed flames, the interaction between rich and lean mixtures is significant leading to improvement in the flame’s resistance to extinction by straining. In lean back-supported laminar stratified flames, the flux of excess heat and radicals into the lean fluid results in higher flame speeds, broader reaction zones, and extended flammability limits compared to homogeneous counterparts. Rich stratified flames are more complex due to the combined fluxes of heat as well as reactive species such as H2 and CO. Recent research in turbulent partially premixed as well as stratified flames is reviewed. Detailed measurements in burners representative of those found in gas turbine combustors show that partial premixing at the lifted flame base increases with instability. Well-characterised laboratory burners where different fuel concentration gradients may be imposed at the jet exit plane show improved flame stability due to mixedmode combustion. Maximum stability is reached at some optimum level of compositional inhomogeneity. Highly resolved measurements in turbulent stratified flames show that the mass fractions of CO and H2 increase with stratification; a result that is consistent with laminar flame studies. Such experiments are, however, very difficult and require multi-level conditioning of the data. The paper concludes with a brief review of potential numerical approaches employed in the calculations of turbulent flames with inhomogeneous inlet conditions. A key challenge here is to reproduce the effects of increasing levels of stratification and/or inhomogeneity on the compositional structure of turbulent flames. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Partially premixed; Stratified flames; Inhomogeneous combustion; Composition gradients; Turbulent flames

1. Introduction While the broad classification of flames into premixed and non-premixed remains useful for

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academic purposes, the actual combustion process is much more complex particularly in practical devices where partial premixing is ubiquitous. Perfect mixing is generally hard to achieve especially in direct injection systems due to practical considerations associated with limited mixing lengths and combustion instabilities. A corollary of this is that a certain level of inhomogeneity remains

http://dx.doi.org/10.1016/j.proci.2014.08.032 1540-7489/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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in the mixture as is the case in gas turbine combustors where the flames are generally lifted [1–7]. Throughout this paper, the term “inhomogeneous” refers to the existence of composition (rather than velocity) gradients. Such compositional inhomogeneity may also be purposely introduced to reduce emissions and to extend the operational range as is done in stratified charge direct injection engines [8–17]. The base of a lifted turbulent “non-premixed” flame is known to be partially premixed [18–22] with the propagation of “edge flames” playing a key role in the stabilization process [23]. Non-premixed, burner-stabilized flames also involve significant partial premixing subsequent to the occurrence of local extinction which becomes prevalent as these flows gradually approach blow-off [24]. Piloted [25–32], bluff-body [33–35] as well as swirl-stabilized flames [36–39] are typical examples where such occurrences are common. The term “partially premixed” refers here to situations where the fluid parcel is compositionally inhomogeneous covering a wide range of mixture fractions including flammable as well as non-flammable fluid. Mixing continues to occur in this parcel so that diffusion-like reaction zones as well as premixed propagating layers may exist within close proximity. The inhomogeneity may be either induced at the inlets or may be generated within the combustor between the injector plane and the base of a lifted flame. The latter is a common scenario that exists in a range of applications from gas turbine combustors to hypersonic propulsion devices [1–7,40,41], and examples of these systems will be discussed later. Situations where the inlet conditions are designed to be compositionally inhomogeneous are less common and two burners are described as laboratory candidates for understanding the effects of imposed concentration gradients. Note that this is different from situations where the fuel is mixed with some air (but still outside the reactive limits) and issues as a homogenous mixture to burn like a classical non-premixed flame. Examples of such a situation include Sandia’s piloted flames [25–29] and some of Sydney’s swirling cases [37,38] where methane/air (1/3 and 1/2, by vol., respectively) is employed. Such flames should, strictly speaking, be referred to as “homogeneously partially premixed” although such a distinction is not made in the literature. The term “partially premixed” is used throughout this paper in the context of “inhomogeneous partial premixing” implying the existence of concentration gradients and, for simplicity, both terms “inhomogeneity” and “partial premixing” are used hereon interchangeably. Stratified flames may be viewed as a special case of partial premixing where the associated fluid samples are within the flammable limits (which may be extended due to stratification) so that the reaction front is propagating though a

range of equivalence ratios. Examples of this application include stationary gas turbines [1,5] as well as reciprocating direct injection stratified engines [8–17] where inducing mixture fraction gradients may lead to improved fuel efficiency and lower emissions. While the development of these engines is driving a renewed interest in the field, stratified combustion was studied much earlier in relation to explosion hazards in coal mines due to the formation of stratified layers of methane–air mixtures on the ceilings of mine galleries [42–46]. In the case of explosions caused by fast and slow fuel spills, some stratification may also exist in the vaporised fuel–air and this may explain some of the overpressures that result from such accidents [47,48]. Studying the combined effects of obstacles and stratification would be a topic of research interest that complements the existing literature on the overpressures and burning rates of deflagrations propagating past solid obstacles [49–51]. Modelling of turbulent premixed [52–54] and non-premixed [52,55,56] flames has advanced significantly over the past few decades, and key phenomena such as turbulence-chemistry interactions are now reproduced relatively well particularly in non-premixed configurations. A catalyst for this advance was the availability of extensive data sets for generic burners that formed a focus platform for modellers and experimentalists brought together in an international workshop series referred to as TNF [57]. The challenge remains, however, that models need to be “universal” in being able to account for conditions across the entire range of combustion modes from premixed to non-premixed. While very few numerical approaches can claim this capability, extensive data sets similar to those developed for the extremes of premixed and diffusion flames are evolving for turbulent partially premixed and stratified conditions. Figure 1 displays one of many regime diagrams available in the literature for turbulent combustion [58]. For two stream flows, the horizontal axis represents the mass fraction of fuel in one stream (where the balance is air) while the vertical axis shows the mass fraction of air in the second stream (where the balance is fuel). The third axis is for the burning index, Bi which illustrates the flame’s departure from blow-off such as Bi = 0 refers to unburnt fluid while Bi = 1 corresponds to the fully-burnt limit. Fully premixed flames lie within the lean and rich limits marked respectively by L and R on the main axes of Fig. 1. Stratified combustion may populate the dashed box which is within the nominal flammability limits while partially premixed flames can span a much broader domain that is not marked here. A range of flames studied by the TNF workshops [57] are marked in Fig. 1 and these include piloted (L, M, D, E, F) [25–32], bluff-body (HM1 and HM3) [33–35] and swirl-stabilised

A.R. Masri / Proceedings of the Combustion Institute 35 (2015) 1115–1136

E Flame D

1

Flames: L, HM1, SMH1

PM100

L

PM50

Stratified flows

R

Mass fraction of air in stream 2- balance is fuel

PM15

M, HM3, SMH3

F

PM200

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0 Burning Index 0

R L Mass fraction of fuel in stream 1-balance is air

1

Fig. 1. Regime diagram for turbulent combustion [58] in a two-stream flow: Stream 1 shows the mass fraction of fuel with the balance being air while stream 2 plots the mass fraction of air (balance is fuel). The third axis shows the burning index which is zero for unburnt fluid and one for the fully-burnt limit. Shown on the diagram are non-premixed piloted flames L, M, D, E, F [25–32], bluff-body flames HM1 and HM2 [33–35] and swirl-stabilised flames SMH1, SMH3 [36– 39]. Also shown are premixed flames in vitiated co-flows (PM50 to PM200) [59,60]. L, and R refer to lean, and rich flammability limits, respectively.

(SMH1, SMH3) [36–39] non-premixed flames as well as cases PM50–PM200 which correspond to turbulent premixed flames in hot vitiated co-flows [59,60]. The long term objective is to develop capabilities to calculate the structure of turbulent flames regardless of their location on this diagram. While RANS-based (Reynolds Averaged Navier Stokes) methods are still widely used in industry, large eddy simulation (LES) is evolving as a powerful tool, given its ability to account for transient processes as well as a wide range of flow scales. However, the issue of which sub-grid-scale (SGS) model can be reliably applied across the full range of combustion modes remains open. A brief discussion of the various modelling approaches employed with LES is presented in later sections. This paper presents a review of recent progress in current understanding of turbulent partially premixed and stratified combustion. The starting point is a section on laminar flames that defines some key concepts, describes relevant findings regarding the flame structure and sets the scene for the subsequent discussion. Section 3 introduces turbulent partially premixed flames in the context of practical combustors where inhomogeneity is induced by virtue of the fact that the flames are lifted. This section concludes by introducing laboratory burners stabilizing flames with inhomogeneous inlet conditions. Section 4 presents two

nominal families of stratified flames categorized, respectively, by low and high levels of turbulence. Section 5 gives a general discussion while Section 6, which precedes the conclusions, provides a brief account of some relevant direct numerical simulations (DNS) followed by an overview of recent advances in the modelling and calculations of turbulent partially premixed and stratified flames. 2. Laminar flame concepts A thorough knowledge of the structure of laminar flames forms an essential guide not only for interpreting data collected in turbulent counterparts but also for model development and validation. This section gives an overview of laminar partially premixed and stratified flames as provided by measurements and calculations. It is meant to be a summary of recent research relevant to the current topic rather than an extensive review of the vast literature that is available, particularly for laminar partially premixed flames. 2.1. Laminar partially premixed flames Laminar partially premixed flames can be easily established in a laboratory environment by bringing together two streams of fluid with one

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stream containing fuel with some oxidant and the other carrying mainly oxidant with some fuel. At the burner’s exit plane, both streams are generally outside, and on either side of the flammability limits so that mixing continues to occur further downstream. Up to three reaction zones may be established forming what is referred to as triple or tribrachial flames; terms first cornered by [61] and [62], respectively. A generalised representation of a one-dimensional partially premixed flame in mixture fraction space [63–65] is shown in Fig. 2, which is reproduced from [66]. The vertical axis represents temperature or the mass fraction of major product species (such as H2O or CO2). Using subscripts l and r to refer to the fuel-lean and fuel-rich streams, respectively, the mixture fraction, n may be given by [63–65]: n¼

Y F  Y F ;l Y o  Y o;l ¼ Y F ;r  Y F ;l Y o;r  Y o;l

ð1Þ

where Yi is the mass fraction of species i and subscript F refers to an element in the fuel such as carbon or hydrogen while subscript O refers to an element in the oxidant such as oxygen atoms. It should be noted that a more widely used formulation for mixture fraction is given by Bilger [67] with the advantage that it can preserve the stoichiometric value of n as that for the simple mixing case. The equivalence ratio in the inlet streams is given by ul = s YF,l/YO,l and ur = s YF,r/YO,r where s is the stoichiometric mass ratio of oxygen to fuel. At the fuel-lean inlet stream (n = 0), the equivalence ratio can range from ul = 0 (pure oxidant) to ul = 1 (stoichiometric) while at the fuel-rich inlet (n = 1), the range is from ur = 1 to ur = 1 which refers to pure fuel. Practically, both ul

Fig. 2. Representation of a generic one-dimensional partially premixed flame structure in mixture fraction space, n [66,91]. The vertical axis represents temperature or the mass fraction of major product species (such as H2O or CO2). Symbols F and O refer to fuel and oxidant elements, respectively. LPF and RPF refer to lean and rich premixed flames, respectively while NF refers to a non-premixed flame.

and ur are kept outside the flammable limits so that a triple flame structure may form, as illustrated in Fig. 2, with lean and rich premixed zones (LPF and RPF, respectively) surrounding a nonpremixed flame (NF). Double flames form when one of the inlets consists of pure oxidant or pure fuel. Lean premixed flames are investigated in a range of burners with the most common being the counterflow [65,68–74] and co-flow [75–84] geometries, which include axi-symmetric [75–82] as well as slot [83–85] burners. The inner edge of inverse flames [86–90] may also be classified as partially premixed given that the overall equivalence ratio is rich so that a range of compositions exist within the core. The purpose of many of these studies is to understand the extinction/ignition behaviour, given that these phenomena play an important role in the stabilisation of lifted flames. Seshadri and co-workers [65,70–73] performed extensive experimental and numerical research on laminar partially premixed flames using counterflow burners. Activation-energy asymptotics [65] and one-step mechanisms [71] were initially used but were found to be inadequate in reproducing the impact of partial premixing on extinction. In a later study [72], rate-ratio asymptotic analysis with a four-step mechanism was employed somewhat more successfully leading to the conclusion that, for pure fuel in the rich stream, the addition of fuel to the lean stream makes the flame more resistant to extinction caused by straining. This is due to the decrease of oxygen leakage from the reaction zone resulting in an increase in temperature. The reverse effect is noted when, for pure oxidant in the lean stream, air is added to the fuel stream [72]. This close interaction between the lean, rich, and stoichiometric wings of the flame is also established from the direct numerical simulations performed by Aggarwal’s group for a range of laminar partially premixed flames using slot [83,84], counterflow [68,74], and axisymmetric [75,77–80] burners. It was found that reactive radical species from the non-premixed section of the flames are transported both to the lean and rich premixed edges. Similarly, the rich premixed section supplies CO, H2 and potentially some hydrocarbon products, as is the case when n-heptane is used as parent fuel [68]. In an extensive review of extinction effects in laminar partially premixed flames, Aggarwal [91] confirms that, notwithstanding minor differences due to transport and chemical kinetics, the state relationships with respect to mixture fraction, as defined in Eq. (1) are valid for both counterflow and co-flow geometries [91] and that the flame structure in n-space is similar. Triple flames are first observed in counterflow burners [61] where the lean, rich, and diffusion flame zones are separated in physical space as

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shown in Fig. 3a. Tribrachial flames, shown in Fig. 3b and c refer to the situation when the three edges merge at a single point as seen in co-flow burners and at the base of laminar lifted flames. These flames were first observed by Phillips [45] in stratified layers of methane, but the term “tribrachial” was first coined by Buckmaster and Matalon [62]. While the distinction between triple and tribrachial flames is made in some quarters of the literature, it is not uniformly used particularly since it has already been established that these flames are structurally similar [92]. Therefore, the term triple flame will be used hereon to refer to both topologies. Triple flames are special cases of edge flames (see Fig. 3d) which play a key role in the stabilisation of lifted flames [23]. Edge flames propagate at well-defined speeds which could be positive (as in an ignition front) or negative (as in failure waves) [93]. Using a special counterflow slot-jet burner, Cha and Ronney [94] measured edge speeds (both positive and negative) over a range of conditions including varying global strain rates and mixture strengths. The propagation speed of triple flame edges may exceed that of

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the stoichiometric laminar burning velocity and this increase depends, amongst other factors, on the mixture fraction gradients in front of the edge [92]. Since the first theoretical analysis of triple flame propagation in mixtures of non-uniform concentrations by Dold [95], there has been a plethora of papers studying this phenomenon [94,96–102]. An extensive review of theoretical, numerical and experimental research on triple flames is given by Chung [92] while Buckmaster [93] provides a thorough review of edge flames. 2.2. Stratified flames Laminar stratified flames were first studied in the context of deflagrations propagating through layers of different fuel concentrations; scenarios that may eventuate at roofs of mine galleries or surfaces of liquid fuel pools [42–46]. Small-scale experiments duplicating such situations were constructed with concentration gradients of methane spilling outside the flammable limits and flame speeds up to eight times that of homogeneous mixtures [43,44] were observed. Stratified mixtures are

a

b

c

d

Fig. 3. Illustrations of triple flames stabilized on (a) counterflow [61], (b) slot (Wolfhard-Parker) [91], and (c) axisymmetric burners [91]. Also shown in (d) are illustrations of retreating (top) and advancing (bottom) edge flames [94]. The fuel used in (a) is butane while it is methane for the remaining cases.

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considered to be special cases of partially premixed flames where reaction fronts propagate through concentration gradients of mixtures that are generally within the flammable limits (this restriction is nominal since the homogeneous flammable limits may be extended due to stratification effects). Stratification may be referred to as large or small scale depending on the comparative measure of the flame thickness and the length scale over which concentrations are varying [103]. However, a more common characterisation of stratification refers to the alignment between the gradient of the reaction progress variable, rc and that of the equivalence ratio ru. This is illustrated in the schematic of Fig. 4 which is adopted from [104] where (a) is the angle formed between rc and ru. When both gradients are aligned (a = 0 or p), the flame front (line of constant c) is at its maximum stratification as it propagates across mixtures of different equivalence ratios. “Back-supported” stratification refers to situations where excess heat and radicals from the reaction zone feeds the mixture ahead of the propagating flame front as is the case when burning occurs from stoichiometric to lean fluid (a = p). The situation is more complex with rich mixtures: when the flame front propagates from rich to stoichiometric fluid, the temperature increases but back-support may still exist due to the diffusion of reactive species (such as H2 and CO) from the rich side. However, when burning from stoichiometric to rich mixtures, excess heat flux may also be sufficient to back-support the flame. Earlier investigations of laminar stratified flames have covered a range of burner geometries from counterflow to co-flow. Counterflow studies may be classified in two broad categories: (i) reactant to products (RTP) [105–114] where reactants of a given equivalence ratio, uR counter-flow into combustion products which are at up, and (ii) reactant to reactant (RTR) [111,115–120] where both streams are non-reacting and have different equivalence ratios (Ref. [111] studied both RTP and RTR

Fig. 4. A two-dimensional illustration of the alignment angle, a between the gradient of the reaction progress variable, rc and that of the equivalence ratio ru in stratified flames [104].

cases). Most studies of RTP flames are numerical [105–112,114] and employ one-dimensional flow configurations to report on the effects of equivalence ratio gradient and the concentration of the reacting stream. Recent papers of Coriton et al. [105] and Zhou and Hochgreb [114] report that heat flux plays a dominant role in lean flames while rich mixtures involve significantly higher complexities in chemical kinetics. Replacing oxygen molecules with CO2 or H2O for the same u in the product stream was found to lead to sudden extinction as reported by [105] due to the collapse of the HOH-O system of radicals. Reactant to reactant (RTR) studies cover a range of flow configurations and include both numerical [108,111,115] as well as experimental [114,116–120] investigations of back-supported as well as front-supported stratified flames. The common conclusions are that back-supported flames, compared to homogeneous counterparts, have (i) broader reaction zones, (ii) higher flame speeds, and (iii) extended flammability limits. For lean flames, these differences are due to higher flux of heat and radicals into the flame front while for rich flames, species such as H2 play a dominant role. Da Cruz et al. [115] reported that for flames with u changing from 1 to 2.5, the hydrogen cannot be consumed in the fresh rich mixture due to the lack of oxygen so that the flame slows down compared to the homogeneous limit. When u changes from 1.5 to 1.0, the produced hydrogen races to the fresh stoichiometric mixture where it assists in accelerating the flame. It should be noted that in stratified flames, defining the flame speed is not straightforward due to the varying equivalence ratio along the reacting surface. An alternative definition based on the displacement speed of a mixture fraction dependent progress variable is found to be more appropriate than that based on the fuel consumption through the thickness of the flame [111]. Recent experimental studies of stratified RTR flames were reported by Kang and Kyritsis [118– 120] and Balusamy et al. [116]. In the latter, a burst of propane is injected into a chamber containing a lean propane-air mixture (u = 0.6). After ignition, the evolution of specific sections of the flow were targeted for further analysis, and these correspond to back-supported flames with initial equivalence ratios of u = 1.24, 0.95 and 0.79. Measurements of flame speed, curvature, and stretch rates show that the stratified flames are more robust to stretch and propagate faster than the homogeneous counterparts. This is clear from Fig. 5a which shows the measured evolution of the laminar burning velocity for three, back-supported cases of stratification. All three curves asymptote to the burning velocity of 0.06 m/s at u = 0.6 (which is lower than that expected from the literature possibly due to the flow configuration [116]). Kang and Kyritsis [118–120] use a tubular chamber where a

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stratified mixtures due to the competition between heat flux and chemical kinetics. Stoichiometric to rich flames may be back-supported due to excess heat flux from the high temperature reaction zones. Propagation from rich to stoichiometric mixtures may also be back-supported by species such as H2 and CO which form in the rich zones and diffuse to leaner fluid where sufficient oxygen is found to burn. Further studies in rich stratified mixtures are needed to resolve such complexities. 3. Turbulent (compositionally inhomogeneous) partially premixed combustion

Fig. 5. (a) Evolution of unstretched values of the conditional laminar burning velocity measured in stratified flames of propane [116]. Cases C1, C2 and C3 correspond, respectively, to mixture stratification from u = 1.24, 0.95 and 0.79 to u = 0.6. (b) Laminar flame speed (circles) measured at various distances from the ignition point in stratified flame of methane propagating from about stoichiometric to u = 3.04 [119]. The solid line shows the equivalence ratio distribution in the unburnt mixture and the crosses refer to the measured flame speed corresponding to the local equivalence ratio.

fuel/air mixture on the ignition end counter-flows against air or fuel/air from the other end. One of their recent studies [119] investigated a range of cases where stoichiometric mixtures were ignited to propagate against rich ones (with u = 1.52, 2.28, 3.04 and 3.8) counterflowing from the other end. A sample result is shown in Fig. 5b for flame propagation from u 1.0 to 3.04. It is evident from this as well as other cases [119] that the flame speed in the stratified mixtures is higher than in the corresponding homogeneous ones and that the flammability limits are also extended. Heat flux from the near-stoichiometric front was argued to provide the back-support for these flames. In summary, the conclusions from both numerical and experimental studies of RTP and RTR flames are that stratified, back-supported flames have higher flame speeds, wider flammability limits, and more resistance to stretch than the homogeneous counterparts. In stoichiometriclean mixtures, excess heat and radicals provide the back-support if propagation is towards leaner fluid, otherwise the flame would be front-supported. The situation is more complex with rich

It is useful at the outset to re-iterate that reference to partial premixing is made here in the context of compositionally inhomogeneous mixtures that may span a wide range of mixture fractions within, as well as outside, the flammable limits. The word “compositionally inhomogeneous” is also imbedded in the title of this section to reinforce this distinction. The base of turbulent lifted flames provides a typical example of partial premixing and such occurrences were extensively discussed by Peters [121] as an extension of the laminar flamelets concept [63,122]. Lifted flames have since been studied both numerically and experimentally in a range of flow configurations and references [18,19] provide recent reviews on this topic. When the co-flow stream is heated [123–126], the flame base may transition from propagation to auto-ignition modes depending on the temperature of the co-flow. However, the nature of this transition is not fully understood [127,128]. Given the ubiquitous nature of partial premixing in turbulent combustion, laboratorybased lifted flames will not be considered any further and the remainder of this section focuses on inhomogeneous flames observed in burners that are more representative of gas turbine and propulsion systems. 3.1. Model gas turbine combustors Research on model combustors for gas turbine engines forms an intermediate level of complexity between simple laboratory flames and practical devices. Databases resulting from such studies [129–153] are essential to extend the capabilities of numerical tools to tackle issues that are otherwise not addressed in simple burners including combustion at high pressures. Two of the most outstanding issues related to gas turbines in general and to lean premixed combustion in particular are flame stability and blow-off [1,3]. Temme et al. [133] have recently classified experimental combustors into two broad categories burning liquid [129,130,132–135] or gaseous fuel [136–153], and a representative range of these combustors is shown in Fig. 6. The DLR model gas turbine combustor

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a

b

c

d

Fig. 6. Experimental gas turbine combustors stabilising turbulent partially premixed flames: (a) the DLR model gas turbine combustor [141]. (b) Combustor based on the Turbomeca design [139], (c) CNRS model combustor [137], (d) Twin annular premixed swirler (TAPS) combustor (University of Michigan) [130]. Note that CRZ, LRZ, and PRZ refer to corner, lip and primary recirculation zones, respectively.

shown in Fig. 6a [141–143,147–150,153] involves an annular ring of fuel injectors sandwiched between two swirling streams of air. An extensive data bank already exists for this combustor which has been used at atmospheric pressure. Another combustor based on the Turbomeca design is shown in

Fig. 6b [138,139,144] and uses a single swirling air stream surrounding a central fuel jet. This model combustor has been studied extensively at pressures elevated up to 6 bars [138,139]. The burner shown in Fig. 6c (referred to as the CNRS model combustor) [137] also uses a single swirling stream

Fig. 7. Scatter plots of temperature versus mixture fraction measured in a lean-premixed swirl methane combustor [144] of a quiet flame (left, u = 0.83) and a pulsating flame (right, u = 0.7). Here “h = 6 mm” refers to distance downstream of the exit plane, “r” to radial location and IRZ, ORZ to inner and outer recirculation zones, respectively. The solid curves are for laminar flame calculations and the vertical lines represent the global mixture fraction in the combustor.

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but recesses the fuel injection point upstream the jet exit plane. A combustion regime diagram is generated for this burner showing transition from flashback to a stable flame to blow-off. Unlike the burners discussed in Fig. 6a–c which use gaseous fuels, the combustor of Fig. 6d uses pre-vaporized liquid fuel and employs swirl both in the central pilot as well as the main fuel supply so it is known as the twin annular premixed swirler (TAPS) [130,132,133]. A common feature to all of these burners as well as others not shown here [136,146,151] is that the flames are lifted from the burner’s exit plane so that composition gradients form at the base. A comprehensive set of data now exists for most of the gaseous combustors shown in Fig. 6 using methane or propane as fuel [136–153]. The data from Meier’s group [141–145,147–151,153] include extensive measurements of velocity, mixing as well as reactive scalar fields. Sample scatter plots of temperature versus mixture fraction taken near the exit plane of the premixed version of the Turbomeca combustor [144] are shown in Fig. 7. As the global equivalence ratio decreases from 0.83 (Fig. 7a) to 0.7 (Fig. 7b) the flame starts to pulsate and, as is evident from Fig. 7b, the degree of scatter intensifies significantly with mixture fractions now covering almost double the range observed in the stable flame case. Calculations [154] discussed later in this paper corroborate this finding and confirm that pressure fluctuations, propagating back from the flame region perturb the flows in the fuel and air streams in different ways, leading to periodic fluctuations in the fuel-to-air ratio entering the flame. Flame instabilities constitute a very complex topic in combustion research, and this is well outside the scope of this paper. The reader is referred to others [1,7,133] where details about the types and dynamics of the various instabilities that occur in combustors are discussed. The Flame Index introduced by Takeno and his group [20–22] is a very convenient indicator of premixed and non-premixed combustion events occurring in turbulent flames that are either lifted or undergoing local extinction events. In its original form, the index was defined as GFO ¼ rY F  rY o but was later normalised and employed in the subgrid combustion models for LES of partially premixed combustion [155]. In its basic normalised form the index is defined as: b¼

rY F  rY O jrY F  rY O j

ð2Þ

where rY F , rY o are the gradients of the fuel and oxidant mass fractions so that values of b = 1 and 1 refer to the extremes of fully premixed and non-premixed flames, respectively. Modifications to this definition were proposed by Fiorina et al. [156] to account for partially premixed conditions where the gradients of fuel and oxidant are

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aligned yet the burning rate remains controlled by diffusion. Additional modifications to b were provided by Briones et al. [78] and later by Som and Aggarwal [157] who replaced the gradient of fuel with that of carbon monoxide (rY CO ) arguing that, in many zones of partially premixed flames, the fuel may have been totally consumed. Knudsen and Pitsch [158] have questioned the validity of the definition for b (as in Eq. (2)) in three dimensional applications as well as for complex fuels. They have subsequently derived a more general model for distinguishing between premixed and non-premixed combustion events [158]. Despite the modifications and limitations discussed above, the Flame Index remains a useful tool to elucidate the extent of inhomogeneity in turbulent flames. Rosenberg et al. [159] have recently performed measurements of b in the combustor of Meier et al. [143,153] using joint LIF imaging of acetone and NO2, which are adopted as tracers for the fuel and oxidant streams, respectively. Figure 8 shows two instantaneous realizations taken at the exit plane of the combustor. While it is evident that both modes are present, the images reflect the time-varying dominance of premixed and non-premixed combustion modes depending on the occurrence of instabilities within the combustor. Such variability is expected to be a feature of many practical systems and accounting for it remains a challenge to modellers. 3.2. Flames with compositionally inhomogeneous inlets The burners discussed in the previous section stabilize flames that are all lifted from the burner’s lip resulting in partial premixing at the flame base. The extent of the induced inhomogeneity remains largely uncontrolled since this is dictated by many factors including the combustor design, the degree of instability, and the lift-off height. This section discusses two simple burners where the concentration gradients are imposed in a controlled way at the inlets. Additionally, the flames are stabilised to the burner’s exit plane such that conditions of intense turbulence-chemistry interactions can be formed downstream. Such configurations are designed with the intent of advancing knowledge of the effects of compositional inhomogeneity, yet also forming a data-base that may be used by modellers, such as in TNF workshops [57], in order to advance calculations of flows with concentration gradients in the boundary conditions. The process of introducing the inhomogeneity is rather simple and involves two concentric pipes where the inner one can be recessed to various distances upstream of the jet exit plane. One pipe carries fuel and the other carries air so that when the inner tube is sufficiently recessed, the fuel and air become homogeneously mixed. The other extreme,

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Fig. 8. Instantaneous images of the Flame Index reported by Rosenberg et al. [159] in the combustor of Meier et al. [143,153] (DLR model gas turbine combustor). Vertical axis (y) refers to distance downstream the burner’s exit while the horizontal axis (r) is radial distance from the centreline. A value of 1 (blue) implies a non-premixed flame while +1 (red) refers to premixed combustion: (a) Time when predominantly premixed flamelets occur, (b) time when both nonpremixed and premixed flamelets exist.

when both tubes are flush, represents the fully nonpremixed limit. The interesting conditions lie somewhere between these two limits where the issuing fluid mixtures are rather compositionally inhomogeneous, not unlike those found at the base of lifted flames. Two burners, shown in Fig. 9 were developed with this configuration. One uses a conical quarl (Fig. 9a) [160–165] to stabilise the flame to the burner while the other (Fig. 9b) is piloted [166] and forms a simple extension of the Sydney piloted burner [25–32]. Results from both burners show that an improvement in flame stability is obtained at some intermediate recess distance and for a given ratio of fuel/air issuing from the inner and outer pipes (a fixed global equivalence ratio, u). This is evident from the stability plots of Fig. 10 where the results from the quarled burner, replotted in Fig. 10a in the form of jet velocity versus recess distance [160–165] show peak stability at an optimal recess distance of L/D  6 over a range of quarl angles and equivalence ratios (D = 8 mm is the inner diameter of the outer tube). The fuel

used in both cases is compressed natural gas, CNG which is mostly methane). Note that the quarled burner uses the inverse flame configuration with fuel issuing from the annulus. Figure 10b shows the stability limits plotted versus L/D for the modified Sydney piloted burner with fuel issuing from the central tube and air from the annulus with D = 7.5 mm. These are referred to as FJ cases and show that, over the air/fuel ratios studied here, the optimal recess distance ranges from L/D 8 to 15 [166]. It should also be noted that with the piloted burner, the inverse flame configuration does not benefit from recessing the inner tube because the mixtures become quickly homogeneous due to higher shear rates between the inner and outer streams. Results presented in the remainder of this section refer to the Sydney piloted burner [166]. Figure 11 shows radial profiles of mean mixture fraction, and its rms fluctuations, n0 as well as mean axial velocity, and its rms fluctuations, u0 measured near the exit plane (x/D = 0.5) of two non-reacting CNG jets with a bulk velocity

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L

D L

Fuel

a

Air

b

Fig. 9. Schematics of two burners capable of providing inhomogeneous inlets by using two concentric pipes such that the inner pipe can slide for distance, L within the annulus. Flame stabilization is provided using either using (a) a quarl of D = 8 mm and angle h that can change from 10 to 40°. The inner pipe has ID = 5 mm and OD = 6 mm [160–165] or (b) a pilot annulus with a diameter of 18 mm. Here the inner pipe has ID = 4 mm, OD = 4.5 mm while the outer pipe has ID = 7.5 mm and OD = 8 mm [166].

(b)

60 o

θ = 30 , φ = 6.9

j

Jet Blowout Velocity U (m/sec)

(a)

50

o

θ = 25 , φ = 4.8 o

θ = 20 , φ = 3.4

o

θ = 15 , φ = 2.6

40

o

θ = 10 , φ = 2.1

30

0

2

4

6 8 L/D

10

12

14

Fig. 10. Stability plots showing the bulk jet velocity at blowoff versus the recess distance normalised by the jet diameter (L/D) for (a) the quarl stabilised flames (D = 8 mm) over a range of equivalence ratios, u and quarl angles, h (reproduced from earlier data [160–165]) (b) the piloted burner (D = 7.5 mm) [166] operating in FJ mode where fuel issues from the central pipe and air from the annulus. The curves (from highest to lowest) correspond to volumetric air/fuel ratios of 4.0, 3.0, 2.26, 2.0, 1.5, 1.0 and 0.44. The fuel used in both cases is compressed natural gas (CNG).

of 82 m/s at the jet exit plane, a volumetric air/fuel ratio of 2.0 but different recess distances. Case FJ200-100 (solid line) has a recess distance of L = 100 mm (L/D = 13.3) and shows a significant gradient in the fuel concentration as well as higher rms fluctuations, n0 compared to the near-homogeneous (and less stable) case FJ200-300 (dashed

line) were the recess is L = 300 mm (L/D = 40). Note that the mean axial velocity, and its rms fluctuations, u0 also shown in Fig. 11 are close for both cases. Scatter plots [167] of temperature versus mixture fraction measured near the jet exit plane (x/D = 1) as well as further downstream at x/D = 10 are shown in Fig. 12 for the same cases

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Fig. 11. Radial profiles of the (a) mean mixture fraction, and (b) its rms fluctuations, n0 (c) mean axial velocity, and (d) its rms fluctuations, u0 measured at x/D = 0.5 in non-reacting CNG jets FJ200 with a bulk jet velocity of 82 m/s and air/fuel ratio = 2, by volume. Solid lines are for FJ200-100 with recess distances of L = 100 mm (inhomogeneous) while dashed lines are for FJ200-300 with a recess distance L = 300 mm (which is close to homogenous) [166].

shown in Fig. 11 but reacting and using methane as fuel (left: FJ200-100 and right: FJ200-300). The vertical dashed line represents the location of stoichiometric mixture fraction. It is clear that, at optimal levels of inhomogeneity (Fig. 12a and b), premixed combustion seems to dominate the early stabilization region with fluid samples around stoichiometric burning in the vicinity of the pilot. This is contrasted with the near-homogeneous case (Fig. 12c and d) where mixing to stoichiometric conditions takes place as in a normal diffusion flame. Extensive measurements collected at Sandia’s Combustion Research Facility in these and similar flames at different departures from blowoff reveal more information [167]. The resulting data base is likely to form a good platform for the validation of models for finite-rate chemistry effects in flames with compositionally inhomogeneous inlets.

Fig. 12. Scatter plots of temperature versus mixture fraction measured at x/D = 1 (top: (a) and (c)) and x/ D = 10 (bottom: (b) and (d)) in piloted methane flames FJ200 (bulk jet velocity of 82 m/s, air/fuel ratio = 2, by volume) with recess distances of Lr = 100 mm (left, a and b) which corresponds to inhomogeneous conditions and L = 300 mm (right, c and d) which is close to homogenous [166]. The vertical dashed line marks the location of stoichiometric mixture fraction.

4. Turbulent stratified flames Experimental research in turbulent stratified flames may be loosely classified in two broad categories: (i) burners with low turbulence generated mostly by grids and (ii) high turbulence burners where velocity gradients, swirl, and/or bluffbodies are used to induce turbulence. The following sections describe key experiments in each of these categories and highlight recent conclusions. 4.1. Low-turbulence, stratified flames There is a bank of experimental research [48,103,168–176] in this area where the focus is generally on the effects of concentration gradients on the burning velocity as well as the topology of the flame with particular interest in issues of flame wrinkling, thickness, and curvature. The V-flame configuration is the most commonly used [171– 176] where the stratified mixture issuing towards the stabilising rod is formed in two ways. Either as shown in Fig. 13a (adopted from [174]) where a range of adjacent slots or channels carry mixtures

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a

b

c

d

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Fig. 13. Schematics of two low-turbulence ((a) and (b)) and two high-turbulence ((c) and (d)) stratified burners: (a) Vflame with turbulence generating grid and multi-channels feeding mixtures of different u [174]. (b) Burner with weak external swirling air used to stabilise stratified flames [48] (c) Darmstadt piloted stratified burner [104]. (d) Cambridge stratified swirl burner [182].

of different equivalence ratios [171,173–176] or by injecting pure fuel into a (generally lean) premixed co-flowing stream [172]. Another burner shown in Fig. 13b [48] adopts the same principle of flame stabilization as Be´dat and Cheng [177] using a low swirl stream surrounding two concentric pipes that carry mixtures of difference equivalence ratios. Other methods to induce stratification (not shown here) involve an enclosed chamber where concentration gradients are generated in various ways such as pulse injection of fuel into a homogenous mixture [103], fuel injection at two or more

locations [168] or simply by feeding a quantity of fuel and using a perforated plate to induce partial mixing [169,170]. Studies using these burners show some common findings in that the burning velocities and flame propagation rates increase for back-supported flames. This is generally associated with increases in flame wrinkling and hence flame surface density. Some contradictory results remain, however, regarding the effects of concentration gradients on some aspects of flame topology. Bonaldo and Kelman [48] report no change in the flame brush

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thickness due to stratification while Robin et al. [174] note a decrease of about 10% and others [171,175,176] report thicker flames. The effects of concentration gradients on flame curvature distributions are similarly controversial, with Vena et al. [176] measuring a slight decrease and others [171,173,175] reporting an increase, all for somewhat similar V-flame configurations. It should be noted that turbulence levels and scalar dissipation rates may vary between the various cases discussed here, and their magnitudes are not necessarily known. Similarly, the stratification level, S (which may be defined either by the u-ratio between adjacent streams [171], S = u1/u2, or using the local gradient of u) differs from one experiment to the other. It is important that studies in stratified flows, both laminar and turbulent, report results conditioned with respect to equivalence ratio so that only the effects of equivalence ratio gradients, for the same u, can be isolated [176]. 4.2. High-turbulence stratified flames Figure 13c and d shows two burners (respectively referred to as the Darmstadt and the Cambridge burners) that have become a TNFplatform for studying highly turbulent stratified flows. The Darmstadt burner, shown in Fig. 13c [104,178,179] is axi-symmetric and consists of three streams with the centre providing a pilot while the outer two annular channels, referred to as slot-1 and slot-2, supply mixtures at u1 and u2, respectively. The shear rate as well as the equivalence ratios u1 and u2 in the annular streams may be varied together or independently. Conditions studied with this configuration cover homogeneous as well as stratified cases with values of u0 /SL ranging from about 2.0 to 40 and Reynolds numbers well above 10,000 providing an extensive data set for model validation. The Cambridge burner (Fig. 13d) is also axisymmetric but with a bluff-body forming the central part of two-outer concentric streams supplying u1 and u2 [180–184]. This burner offers additional flow complexity over the Darmstadt version in the flow recirculation imposed by the central bluff-body as well as the ability to impart swirl to the outer stream. Values of u0 /SL higher than 10 may be achieved, and both swirling as well as non-swirling conditions were studied at different levels of stratification. Detailed measurements of temperature and reactive scalar fields were performed in both burners using line Raman–Rayleigh-LIF imaging available both at Sandia and Darmstadt [104,178,181,182] and these data, along with flow-field measurements, are available for modellers. Figure 14a shows sample scatter plots of temperature and the mass fractions of CH4 and CO versus equivalence ratio measured in swirling and stratified flames. A key conclusion from these

measurements is that stratification leads to values of H2 and CO within the reaction zone that are higher than those of homogeneously premixed flames [182]. This is clearly evident in Fig. 14b which shows measured profiles of CO and H2 conditioned on equivalence ratio at the location of peak CO mass fraction (deemed to be close to the location of peak heat release in lean mixtures at u = 0.75) [183]. Compared to the homogeneously premixed case (SwB3), the mass fractions of CO and H2 increase with increasing stratification (higher Du/Dr) under lean back-supported conditions in flame SwB7. It should be noted, however, that the measurements reported in Fig. 14 are taken close to the jet exit plane (10 and 30 mm) since stratification do not seem to survive further downstream. Another conclusion from these studies is that the flame surface density and scalar dissipation rates are not significantly affected by stratification. However, curvature distributions are broadened, albeit slightly, and this becomes evident when data are further conditioned on equivalence ratio [183]. Other high-turbulence stratified burners not shown here include a large scale dump combustor referred to as ORACLES (One Rig for Accurate Comparison with LES) [185]. The burner section uses two streams supplying mixtures of propane–air (at u1 and u2, respectively and a Reynolds number of 25,000) separated by a splitter plane. Another design is the bluff-body burner that simulates the effects of stratification induced in practical combustors due to the “close coupling” which occurs because of the proximity of fuel injectors to the flame holder [186] so that mixing is incomplete. Injectors positioned across the height of the combustor supply different levels of fuel so that a range of concentration gradients may be studied. It was found that stratification leads to a broadening in the blow-off limit and this is thought to be due to the “piloting” effects provided by the rich parts of the flame [186]. 5. Discussion It is evident from the preceding overview that, while there are some consistencies between the structures of laminar and turbulent flames with composition gradients, there are also subtle differences. The improved resistance to strain with partial premixing and the faster burning rates observed with laminar back-supported stratification may also be the reason for the improved stability in turbulent inhomogeneous flames. The edge and triple flame structures discussed in Section 2.1 are already well represented in the study of turbulent, laboratory-based lifted flames. It is not evident, however, that the role of these structures is as important in gas turbine combustors such as those shown in Fig. 6 where turbulence

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Fig. 14. (a) Scatter plots of temperature, and the mass fractions of CH4 and CO measured in the Cambridge stratified swirl burner [182]. Data are taken 10 mm downstream of the exit plane of stratified swirling flames SwB6 and SwB7 with swirl numbers of 0.45 and 0.79, respectively. Both flames have equivalence ratios of u = 1.0 and u = 0.5 in the inner and outer streams, respectively. Colour refers to radial location as per the colour bar shown on top. (b) Also, in the Cambridge stratified swirl burner, mean measured mass fractions of CO and H2 plotted versus temperature for cases SwB730 and SwB330 where the subscript refers to the measurement location of 30 mm downstream of the burner exit. Case SwB3 is not stratified with u = 0.75 in both inner and outer streams. Data are shown at 30 mm downstream of the jet exit plane and for various levels of Du/Dr (bin centres in parentheses). Data are conditioned to be within ±2.5% of the mean equivalence ratio at peak CO mass fraction in the SwB330 case. Laminar flame calculations at the global equivalence ratio are shown by a dashed line. The mean temperature at peak CO and peak H2 in the premixed cases is marked by a vertical grey line [183].

levels are generally high and precessing vortex cores as well as thermo-acoustic instabilities are much more dominant in determining the stability characteristics. The burners with controlled inhomogeneous inlets introduced in Section 3.2 may be good intermediate platforms to test aspects of turbulent partially premixed combustion without the added complexities of swirl and instabilities. It is worth noting that the burners shown in Section 3.2 may also be easily operated in stratified mode if the mixtures exiting the inner and outer jets are maintained within the flammability limits. Changes noted in the structure of the laminar and low-turbulence stratified flames in terms of curvature, thickness, and wrinkling are much

harder to detect in the turbulent counterparts and this may be partly due to turbulence which can shroud these effects. The flux of heat, reactive radicals as well as some reactive species such as CO and H2 noted in numerical studies of back-supported laminar flames are hardly reported in experimental studies of both laminar and turbulent partially premixed or stratified flames. A reason for this may be the limited access to diagnostics tools with sufficient accuracy and resolution to reliably measure these reactive minor species in flames. One exception here is the highly-resolved Sandia measurements in the Cambridge stratified burner where Sweeney et al. [181–183] reported higher levels of CO and H2 mass fractions in the initial

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regions of turbulent flames under lean back-supported stratification. It should also be noted that in these flows, turbulent transport may overwhelm the molecular processes so that stratification effects are generally short-lived and somewhat limited to regions close to where the stratification is induced. Two other aspects of partial premixing and stratification worth discussing here relate to the transient effects of ignition and the formation of pollutants. Briones et al. [187] studied laminar flames ignited downstream of an axisymmetric jet and reported that the flame front transitions from a triple to a double flame structure before stabilising on the burner. In turbulent spray flames, Pickett et al. [188] observed that upstream ignition changes the lift-off characteristics of the jet for a significant time before the lifted flame base resumes its natural position. Such transient scenarios remain only vaguely understood and warrant more experimental and numerical studies. The formation of pollutants such as NOx and soot is also significantly affected by the extent of partial premixing [189–193]. In a numerical study of laminar partially premixed of methane, Briones at el. [191] report that NOx formation reaches a minimum in the triple flame regime. In their experimental studies of both laminar and turbulent flames, Gore and co-workers [189,190,192,193] have shown that partial premixing has a strong effect on NOx as well as soot formation rates. They also note that soot plays a significant role in controlling NOx not only due to temperature changes but also through changes in the chemistry. It is evident, therefore, that partially premixed and stratified flames provide stringent tests for the chemical kinetic mechanisms particularly with respect to the formation of pollutants. Further research of these aspects is also warranted. 6. Numerical advances 6.1. DNS Direct numerical simulations are used quite effectively to resolve the structure of turbulent lifted, partially premixed [20,21,194–199] as well as stratified [200,201] flames. The 2D-DNS of Jimenez et al. [201] which employ detailed chemistry to simulate stratification effects in lean mixtures of propane–air, confirmed that the presence of inhomogeneities leads to significant differences in the heat release. Changes in the computed structure of the secondary reaction zone led to the conclusion that flamelet modelling may have limitations in stratified combustion and that conditional moment closure approaches may be more relevant. Three dimensional DNS of turbulent lifted flames of gaseous and spray fuels were performed using one-step reactions for n-heptane [196,199] and these simulations confirm the pres-

ence of edge-flame structures at the base of gaseous flames. Spray flames have a much higher level of complexity as is evident from the illustration of Fig. 15 where the calculations of Luo et al. [199] for n-heptane show composite structures of rich premixed flame parcels surrounded by diffusion flames (and vice versa). It is found that about 70% of the heat release is due to premixed combustion while the volumetric contribution of diffusion flames is more dominant [199]. The normalised Flame Index as modified by Domingo et al. [196] is found to be a useful marker of the combustion mode in these lifted flames as well as jets in hot cross-flow calculated by Grout et al. [198]. A modified, SGS expression for the normalised Flame Index is also developed for LES [196]. 6.2. LES and modelling issues Capabilities for accurate calculations of turbulent flames have advanced significantly over the past few decades and excellent reviews of this progress and the employed tools and approaches may be found elsewhere [52,54,56,202,203]. The TNF workshops [57] play positive roles as catalysts to resolve specific issues such as turbulence-chemistry interactions in non-premixed flames. The long term objective remains to expand such capabilities to cover the entire range of combustion modes and include partially premixed and stratified flames such as those considered here. Large eddy simulation is gradually maturing as the numerical approach capable of accounting for the flow complexities as well as the transient processes that are present in practical combustors. An outstanding challenge, however, is to develop reliable and computationally tractable subgrid-scale-models that can represent combustion across the full range of combustion modes [54,56,202]. Approaches based on pdf-like methods are very promising and these, according to Pope [56], include transported pdf’s [204–206] (with various implementation in LES [207–210]), MMC (multiple mapping conditioning) [211–213], the linear eddy model (LEM) [214,215] as well as stochastic field methods [216]. Other approaches include conditional moment closure (CMC) [217,218], and various formulations of the flamelet-like models [54,121] which are discussed in the next paragraph. In the context of flamelet modelling, the presence of inhomogeneities imposes additional challenges that include modelling the correlation between scalar dissipation of mixture fraction and reaction progress variable as well as the additional fluxes (of heat and radicals) through the reaction zone. Flamelet models used with LES include artificially thickened flamelets [219] with a dynamic application of the thickening factor so that it is employed at the flame front only. This approach has been used, somewhat successfully, in a number of burners [146,154] that involve

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Fig. 15. Instantaneous structure of the reactive region of a lifted lean spray flame of n-heptane computed by DNS [199] (Purple: iso-line of stoichiometric mixture fraction, green: diffusion flames, red: premixed flames). The flow configuration uses central and annular swirling air issuing from concentric pipes at a temperature of 500 K. Spray droplets with a lognormal distribution spanning the range 1–20 lm (mean 10 lm) are issuing from the tip of wall region between the annular pipes. Further details may be found in [199].

unstable combustion regimes. A key finding here is that the assumption of perfect mixing at the combustor inlet is inadequate particularly in the unstable regime and full meshing of the injectors is required to compute the history of fuel/air mixing [154]. Calculations that include the flow

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through the injectors reveal the existence of a self-exited mode where the velocity pulses result in an intermittent accumulation and subsequent release of fuel; and hence unsteady combustion similar to what is observed experimentally [144]. The same approach is also used to compute the Darmstadt stratified flames [104] and the results compare well with measurements. Figure 16 shows computed snapshots of a source term isosurface coloured with equivalence ratio. It is evident that vortices induce flame wrinkling and that stratification starts with lean pockets that grow as they travel downstream. Another LES-flamelet approach that uses filtered tabulated chemistry (F-TACLES) [220] has been applied by Schmitt et al. [221] to compute the structure of a highly swirling combustor. More recently, Nambully et al. [222] extended the filtered laminar flamelet–PDF approach [223] to enable explicit filtering with a sub-grid wrinkling factor linked to the laminar flame speed and the sub-grid kinetic energy. This approach, which is also formulated to account for differential diffusion, has been used successfully to compute the structure of turbulent stratified flames stabilized on the Cambridge burner [222,224]. It is worth noting here that accounting for multi-component molecular transport is particularly important in computing the stratification effects given the potential significance of differential diffusion in enhancing the stability of back-supported stratified flames. The flamelet/progress variable model (FPV) developed by Pierce and Moin [225] has been extended by others to enable its application with LES to flames with transient processes such as local extinction and auto-ignition [226,227]. The extension includes a closure model for the residual scalar dissipation rates of mixture fraction and the reaction progress variable. The level-set G-equation model developed by Peters [121] has also been

Fig. 16. Time-sequence of snapshots for the iso-surface of CO2 computed using LES for the Darmstadt stratified flame (TSF-A-r, with equivalence ratios of 0.9 and 0.6 in the inner and outer streams, respectively). The contours are colourcoded with respect to equivalence ratio. Circles mark the evolution of lean pockets [104].

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inhomogeneity in the inlets on the compositional structure of turbulent flames [182,183]. 7. Concluding remarks While significant advances were made in understanding the structure of laminar and turbulent stratified as well as partially premixed flames, significant challenges remain. This paper reviews recent developments in these fields drawing the following conclusions:

Fig. 17. Scatter plots of gradient of mixture fraction versus the gradients of reaction progress variable computed using LES for the Darmstadt stratified flame (TSF-A-r) [231]. Symbols FS, BS refer, respectively to front- and back-supported conditions while NO refers to no stratification.

extended and applied with LES to compute a low swirl burner [228]. Closure based on flame surface density has been developed for inhomogeneous flows and applied to the ORACLES dump combustor [229,230] as well as to the Darmstadt stratified burner [231]. An effective diffusivity approach is employed to model the cross scalar dissipation rate term (in the progress variable equation) that accounts for diffusive flux through the flame front. Figure 17 shows scatter plots for the gradients of mixture fraction and reaction progress variable computed for a selected Darmstadt stratified flame [231]. It is evident that while frontsupported as well as non-stratified samples are encountered, the dominant stratification is due to back-supported flame propagation. With PDF-like methods, and not withstanding issues of molecular mixing and relatively higher computational costs, the transition from non-premixed to partial premixed and premixed combustion is rather seamless. Monte Carlo-based approaches were used successfully to compute the structure of turbulent lifted as well as premixed flames in hot vitiated co-flows [128,209,232]. Such approaches are potentially capable of accounting for turbulent flames with compositional inhomogeneities such as those discussed in Section 3. This is evident from the recent calculation of Bulat et al. [233] which use LES with stochastic fields-pdf method to compute the flame structure in an industrial gas turbine combustor. Given their potential, pdf-like methods should be much more widely used in the calculations of turbulent flames with inhomogeneous inlets as well as turbulent stratified burners similar to those discussed in Sections 3.2 and 4.2. An outstanding challenge to all modelling approaches discussed above is to reproduce the effects of different levels of stratification and/or

 In laminar partially premixed flames, concentration gradients enhance the interaction between the rich, stoichiometric and lean parts potentially leading to situations where the flame is more resistant to extinction caused by straining.  In laminar lean back-supported stratified flames, the flux of excess heat and radicals into the lean fluid leads to higher flames speeds, broader reaction zones, and extended flammability limits compared to the homogeneous counterparts. The situation is more complex when rich mixtures are present due to the potentially competing fluxes of heat as well as reactive species such as H2 and CO.  Turbulent partial premixing is ubiquitous in practical combustors where the flames are mostly lifted and the compositional inhomogeneity induced at the flame base can vary in time due to flow instabilities as confirmed by various measurements including those of the Flame Index.  Well-designed laboratory burners with inhomogeneous inlets show improved stability at an optimum level of inhomogeneity. Such burners form an excellent platform for further understanding the compositional structure of these turbulent flows and for advancing current modelling capabilities.  Measurements of species concentrations in stratified and partially premixed flames require a high level of accuracy and resolution since the data must be processed with multiple level of conditioning. Such highly resolved measurements in turbulent stratified flames show that CO and H2 increase with stratification; a result that is consistent with laminar flame studies.  LES with various SGS-combustion models is gradually evolving as a reliable tool for computing the structure of turbulent flames with compositionally inhomogeneous boundary conditions. Various formulations of laminar flamelet modelling have evolved to account for the transport processes that occur across the flame surface. PDF-like methods are potentially capable yet not extensively used perhaps due to excessive computational resources.

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Acknowledgments Thanks to Professors Thierry Poinsot and SukHo Chung for inviting me to present this review. I am eternally grateful to the Australian Research Council for supporting my ARC-Australian Professorial Fellowship (ARC-DP110105535). My research is also generously funded by the Australian Research Council (ARC) through Grants: DP0772408, DP1097125, DP110105535, and DP130104904. Sincere thanks to all members of my research team and in particular to Mr. P.X. Pham for extensive assistance with the figures and references and to Mr. Shaun Meares for providing Figs. 9b, 10b, 11 and 12. I am grateful to Professor S.B. Pope and Dr. R.S. Barlow for thoughtful comments on the manuscript and subsequent stimulating discussions. Thanks to Professor Mohy Mansour for providing Figs. 9a and 10a. The constructive feedback of the anonymous reviewers, Professors Bob Bilger and Jim Driscoll and Drs. Matthew Cleary, Matthew Dunn and Agisilaos Kourmatzis is also greatly appreciated.

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