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Re-assessing local structures of turbulent flames via vortex-flame interaction

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Re-assessing local structures of turbulent flames via vortex-flame interaction

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Content RE-ASSESSING LOCAL STRUCTURES OF TURBULENT FLAMES VIA VORTEX-FLAME INTERACTIONS by STEVEN LUNA A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MECHANICAL ENGINEERING) December 2022 Acknowledgments I would like to thank my advisor, Dr. Egolfopoulos, for guiding me through my time at USC, training me to do fundamental science, and exemplifying independent thought. I would like to thank my colleagues, in particular Laurel Paxton for show- ing me the ropes in the lab, Vyaas Gururajan for mentoring me through many a sagaciousdiscussion,andHibaKahouliforourinsightfulconversations. Iwouldalso like to thank Dr. Ronney for demonstrating a true passion for teaching and shaping the minds of many young engineers. I would like to thank my family - Mom, Dad, and Joey - for supporting me from the very beginning. Finally, I would like to thank Kat for putting up with long nights, library dates, and me in general. ii Table of Contents Acknowledgments ii List of Figures vi Abstract xi Chapter 1: Introduction 1 1.1 Literature Review 2 1.2 Objectives 8 Chapter 2: Background 11 2.1 Premixed Flames 11 2.1.1 Premixed Flame Theory 11 2.1.2 Oxidation of Methane 14 2.1.3 Flame Stretch 16 2.1.4 Karlovitz Number 17 2.1.5 Symmetric Counterflow Configuration 18 2.2 Turbulent Premixed Flames 19 iii 2.2.1 Basics of Turbulence 19 2.2.2 Turbulent Flame Regimes 22 Chapter 3: Numerical Setup 26 3.1 Vortex Flame Interaction 26 3.1.1 LaminarSMOKE 26 3.1.2 VFI Configuration 28 3.2 Cantera: 1D Flames 31 3.3 Pre-Processing 32 3.3.1 Mechanism Reduction 32 3.4 Post-Processing 34 3.4.1 Progress Variable 34 3.4.2 Flame Thickness 35 3.4.3 Isotherm Speed 37 3.4.4 Scalar Gradient Broadening 38 3.4.5 Mixture Properties 40 3.4.6 Distance From Flame 40 Chapter 4: Results and Discussion 42 4.1 Reactant Pool Modification Mechanisms 42 4.1.1 Flame Siphoning 42 4.1.2 Product-Side Annihilation 46 iv 4.2 The Modified Reactant Pool 50 4.2.1 Flame Siphoning Composition 51 4.2.2 Product-Side Annihilation Composition 52 4.3 Pollutant Effect on Flame 55 4.4 Implications for Experimental Observables 55 4.5 The Effect of Eddy Scale 57 4.6 Implications for Temperature Gradient Methods 59 4.7 Scaling with Pressure 68 4.8 Defining a Flame 70 4.9 Conclusions 72 Chapter 5: Future Work 75 Bibliography 77 Appendix A: Evaluating Numerical Dissipation 83 v List of Figures 1.1 Borghi-Peters turbulent combustion regime diagram [4, 5]. 3 2.1 CH 4 oxidation pathway [32] 14 2.2 Symmetric counterflow coniguration [33] 18 3.1 Initial conditions of VFI 31 3.2 Sample directed relation graph of a kinetic mechanism [36]. 33 3.3 A sample scatter plot of ∥∇c∥l F versus c. The vertical solid line is positioned where the conditional average line is at its maximum, which will be referred to as c = c max . The dashed horizontal line therefore refers to µ (∥∇c∥l F | c=c max ) 36 3.4 A sample d field where the light gray side represents the reactant side of the flame and the dark grey side represents the product side. 41 4.1 Left Column: Time series images of the temperature field for case L1 between2.75msand3.40ms. MiddleandRightColumns: Quantities along the black arrows shown in the left column. 45 vi 4.2 Time series images of the scaled CH 2 O field for case L1 between 2.75 ms and 3.50 ms. Arrows qualitatively denote fluid velocity direction andmagnitude. Greenlinesrepresentthe0.1iso-surfacesofthescaled HRR. 47 4.3 TimeseriesimagesoftheT fieldforcaseL5between2.4msand2.8ms. Arrows qualitatively denote fluid velocity direction and magnitude. Green lines represent the 0.1 iso-surfaces of the scaled HRR. 49 4.4 TimeseriesimagesofthescaledCH 2 OfieldforcaseL5between2.4ms and 2.8 ms. Arrows qualitatively denote fluid velocity direction and magnitude. Green lines represent the 0.1 iso-surfaces of the scaled HRR. 49 4.5 (a) Contours of the T field for case L1 at time 4.4 ms. Iso-surfaces of scaled HRR=0.1 are denoted by the green lines; (b) Global mixture properties variation with s/l F ; (c) Reactant and product scaled mass fraction variation with s/l F ; (d) Intermediate scaled mass fraction variation with s/l F . The variable s in the x-axis of Figs. 4.5b-4.5d is the distance along the black arrow shown in Fig. 4.5a starting from its tail. 53 vii 4.6 (a)ContoursofthetemperaturefieldforcaseL5attime4.02ms. Iso- surfacesofscaledHRR=0.1aredenotedbythegreenlines;(b)Global mixture properties variation with s/l F ; (c) Reactant and product scaledmassfractionvariationwiths/l F ;(d)Intermediatescaledmass fractionvariationwiths/l F . Thevariablesinthex-axisofFigs.4.6b- 4.6d is the distance along the black arrow shown in Fig. 4.6a starting from its tail. 54 4.7 (a) Contours of T field at time 4.08 ms for case L5. Green and black lines represent iso-surfaces of scaled mole-fraction CH 2 O = 0.1 andscaledHRR=0.5,respectively.(b)Histogramofscaleddistances, l/l F , between the iso-surfaces of CH 2 O and HRR shown in Fig. 4.7a 57 4.8 Temporal variation of (a) IMCM and (b) ICSD for all cases. 60 4.9 Scatter plots of instantaneous ∥∇c∥l F vs c for each case; the times selected correspond to the minimum values of IMCM for the L5, L2, and L1 cases, and to the peak IMCM value for case L0.5 shown in Fig. 4.8a. 62 4.10Hatchedregionscorrespondtothereactantsthatarewithin1.8l F and the of the 1500 K isotherm and the entirety of the products. ∥∇c∥l F fieldforallcases;thetimesselectedcorrespondtotheminimumvalues of IMCM for the L5, L2, and L1 cases, and to the peak IMCM value for case L0.5 shown in Fig. 4.8a. 63 viii 4.11 Contour plots of the T field on the left with corresponding scatter plots of ∥∇c∥l F on the right for case L5 at time corresponding to minimum IMCM, 2.96 ms. Scatter plots only consider diagonally hatched regions in contour plots which refer to (a) entire flow field (b) near-field to the flame (c) near-field with region of mutual flame annihilation removed. 65 4.12 Contour plots of the T field on the left with corresponding scatter plots of ∥∇c∥l F on the right for case L2 at time corresponding to minimum IMCM, 3.89 ms. Scatter plots only consider diagonally hatched regions in contour plots which refer to (a) entire flow field (b) near-field to the flame. 66 4.13 Contour plots of the T field on the left with corresponding scatter plots of ∥∇c∥l F on the right for case L1 at time corresponding to minimum IMCM, 5.65 ms. Scatter plots only consider diagonally hatched regions in contour plots which refer to (a) entire flow field (b) near-field to the flame (c) near-field with region of flame merging with recently extinct layers removed. 67 4.14TimeseriesimagesoftheT fieldforcaseL1between5.01msand5.65 ms. Arrows qualitatively denote fluid velocity direction and magni- tude. Green lines represent the 0.1 iso-surfaces of the scaled HRR. 68 ix 4.15 Contour plots of the T field on the left with corresponding scatter plots of ∥∇c∥l F on the right for case L0.5 at time corresponding to maximum IMCM, 1.60 ms. Scatter plots only consider diagonally hatched regions in contour plots which refer to (a) entire flow field (b) near-field to the flame. 69 A.1 Exact solution of maximum speed of vortex compared to simulation. 84 x Abstract Classicalturbulentflameregimeshavelongbeenusedasthebasisforunderstanding aturbulentflame’sstructureanddevelopingturbulentflamemodels. Theseregimes are defined by qualitative scaling arguments regarding the role of turbulence in modifying the shape of the flame surface and the internal flame structure. One of thesearguments,theKlimov-Williamscriterion,statesthatwhenthesmallesteddies intheturbulentflow,theKolmogorovscale,aresmallerthantheflamethicknessthey can enter the preheat zone and cause mixing thereby increasing the flame thickness. Manyexperimentalandnumericalworksshowanincreaseintheflamethicknesswith increasingturbulenceintensity. However,thereislittledirectevidenceregardingthe role of sub-flame-thickness scale eddies in broadening the flame structure. The goal of this work is to evaluate the effect of small eddies on the flame structureandexplorepossiblemechanismsthatleadtoabroadenedpreheatlayerby simulating several cases of high-speed vortex-flame interaction. This configuration consists of a lean atmospheric pressure methane/air flame interacting with vortices ranging from five times to half of the laminar flame thickness. Vortices smaller xi than the flame thickness were found to have minimal impact on the flame before dissipatingaway. Ontheotherhand,vorticesonthescaleoftheflameorlargerwere able to transport thermal energy, intermediates, and products to the reactant side of the flame. Two separate mechanisms were responsible for this, flame siphoning induced by large curvature of the flame front, and product-side flame annihilation which is analogous to extinction in a symmetric counter-flow burner. These results raisequestionsaboutthevalidityofclassicalscalingargumentsregardingbroadened preheat zone flames. xii Chapter 1: Introduction Combustion plays a major role in energy production and transport even as its use is being curbed due to the effect it has on the climate. The combustion process is involved in 83% of the total energy production budget of the US in 2020 [1]. With every coming year, the demand for energy has increased. Between 2020 and 2021 there was a 5% increase in energy demand, the majority of which was filled by carbon-based fuels [2]. This energy production is essential for the quality of life of thegeneralpopulationandisthebackboneofindustryandtheworldeconomy. The continued use of hydrocarbons as a source of energy considering the impact it has on the climate motivates increasing our understanding of combustion physics under conditions in practical combustors. Air-breathing propulsion systems heavily rely on combustion as a source of en- ergy due to the high energy density of liquid hydrocarbons. These propulsion sys- tems are an essential part of the transportation industry and of US defense. The airlineindustryaloneisacriticalpartoftheworldeconomyduetoitsspeedytrans- port of goods and people. 1 These cases involve combustion under highly turbulent conditions where the flameissubjecttoveryshortfluidmechanicaltimescalesandtheturbulentReynolds number can be as high as 10 5 , which implies extreme turbulence intensity. Interac- tion between the flame and this high-intensity turbulence makes flame stabilization difficult and can lead to flame blowout. Thelackoffundamentalunderstandingofhighlyturbulentcombustionanddiffi- culties modeling it lead to a mostly empirical design process. Improving our under- standing of the turbulent combustion process could pave the way to more efficient, stable, safe, and clean designs for combustors. 1.1 Literature Review Regimes of turbulent combustion can be characterized by comparing the relative length, time, and velocity scales of the flame and turbulence as in the Borghi-Peters diagram, Fig.1.1. Here, l istheintegrallengthscaleofturbulence, l F isthelaminar flamethickness, u ′ istherootmeansquared(RMS)ofvelocityfluctuations,and S 0 u is thelaminarflamespeed. OfparticularinterestaretheCorrugatedFlameletRegime (CFR) and the Thin Reaction Zone regime (TRZ). The CFR is characterized by a strongly wrinkled flame that maintains a consistent internal flame structure where asflamesintheTRZhavebroadenedpreheatlayerswhilemaintainingthinreaction layers. The Klimov-Williams criterion [3] is a qualitative scaling argument that separates the TRZ from the CFR along the unity Karlovitz number (Ka) line. It is 2 argued that when the Kolmogorov length scale (η ) is less than the flame thickness, whichcorrespondstoKa>1, thesmallesteddiesintheflowarecapableofentering thepreheatlayersoftheflame. Itisfurtherarguedthattheexistenceoftheseeddies in the preheat layer of the flame could enhance the effective diffusivity causing the layer to broaden. Significant effort has been made to evaluate these arguments, but there exists little direct evidence that sub-flame-thickness scale eddies are capable of entering the flame and cause this broadening of the preheat layer. 10 − 1 10 0 10 1 10 2 10 3 10 4 l/l F 10 − 1 10 0 10 1 10 2 10 3 u 0 /S L Re T = 1 Ka= 1 Ka d = 1 Broken Reaction Zone Thin Reaction Zone Corrugated Flamelet Wrinkled Flamelet Laminar Figure 1.1: Borghi-Peters turbulent combustion regime diagram [4, 5]. ArecentworkbySkibaetal. [6]experimentallyevaluatedunderwhatconditions turbulentmethane-airbunsenflamestransitionedfromathintoabroadenedpreheat zone. Simultaneousplanarlaserinducedflorescence(PLIF)imagesofformaldehyde, CH 2 O, and hydroxyl radical, OH, layers where processed to determine the flame thickness. IsosurfacesofCH 2 Owhereusedtoidentifytheleadingedgeofthepreheat 3 layer, i.e. the boundary with fresh reactants. A parametric study was conducted using a range of 4.2 <= u ′ /S 0 u <= 246 and 15 <= l/l F <= 215 and it was found that a unity Karlovitz number did not separate flames in the CFR and TRZ. The Re T = 2800 was found to better separate the thin flames from the broadened ones and broadening was attributed to Taylor scale eddies, which carry more kinetic energy than the Kolmogorov eddies. The presence of CH 2 O as a marker for the preheat zone of a hydrocarbon flame is a common experimental technique [6, 7]. However, there has been some evidence that CH 2 O may be linked to local extinction of the flame front. Numerical and experimental works of swirl burners have noted an increase in local extinction events just before flame blowout [8, 9]. In the experimental work, it was also noted that as blowout was approached the CH 2 O layer in the inner recirculation zone was much broader than that in a laminar unperturbed flame [8]. The broadened CH 2 O layer was likely ascribed to the increase frequency of local extinction events that coincided with blowout. Using simulated 1D flames, Paxton et al. also found that flames extinguished by oscillating stretch resulted in lingering CH 2 O [10]. This is contrasted with the concentrationofOHandtheheatreleaseratethatbothdrasticallyfellinmagnitude shortly after extinction. It is argued that the dominant consumption path of CH 2 O isthroughOHmeaningCH 2 Ocancontinuetomixwithitssurroundingsunhindered. A form of extinction in turbulent flames is product-side annihilation, which is 4 analogous to extinction in a symmetrical counter-flow burner. This type of extinc- tion can form product pockets, which are islands of products in the reactants. The formation of product pockets generally increases with an increasing turbulence [11, 12, 13], but the evolution and fate of product pockets has not been well studied nor has product-side annihilation in the context of turbulent flames. Recent numerical works by Xu et al. [14] and Krishmen et al. [15] used direct numericalsimulations(DNS)ofhighlyturbulentflamesofhighcarbon-numberfuels, and showed extinction by the collapse of product pockets inside of the reactant stream released thermal energy into the reactant pool. The introduction of thermal energy into the reactants coincided with modification of the composition of the reactant pool. Most notably, the products of pyrolysis of the high molecular weight fuels where found ahead of the flame in the reactants [15]. A few works have shown evidence of preheat layer broadening besides that by sub-flame-thickness scale eddies entering the flame. A study by Wang et al.[16] showedthatregionsoftheflamewithlargecurvaturetendtobebroaderanaverage, which was done by evaluating the magnitude of progress variable gradients, ∥∇c∥. The value of ∥∇c∥ is analogous to the inverse of the flame thickness, which will be discussed in more detail in Sec 3.4.2. A budget of the terms that influence the magnitude ∥∇c∥ was computed. In regions of significant flame curvature, it was found that curvature induced diffusion dominated the other terms and led to the broadening in these regions. 5 AnexperimentalworkbySkibaetal. performedhighspeedsimultaneousCH 2 O- /OH-PLIF and partical image velocimitry (PIV) and found that individual eddies on the order of the flame thickness where capable of locally broadening the flame [7]. Again, the leading edge of the flame was extracted by processing CH 2 O-PLIF images. This common event was found to broaden the flame thickness by up to three times. Leading up to broadening, the eddy pulls the flame into a highly curved peninsula and proceeds to separate the leading edge from the trailing edge of the flame. The remainder of the flame front was persistently thin even in the presencehomogeneouslydispersedsub-flame-thicknessscaleeddies, whichcouldnot be optically resolved Several DNS turbulent planar flames studies have investigated the effect of eddy scales on the flame structure. The first of these evaluated the effect of increasing the grid density to resolve finer eddies and found that this had little effect on the broadened flame structure, especially towards the higher temperature part of the flame [17]. Another set of works employ a band-pass filtering method to isolate strain rates of different eddy scales. From here, it was found that eddies between 2l F and 17l F account for over 80% of the total tangential strain rate on the flame [18, 19]. Few works have directly evaluated the effect of sub-flame-thickness scale eddies on the flame. One such numerical study by Blanquart and Bobbitt [20] and Bobbitt [21] conducted vortex flame interactions (VFI) with artificially reduced viscosity. 6 A VFI with u v /S 0 u >> 1 and l v /l F << 1 was simulated and it was found that the vortexcouldentertheflameandmixitslayers. Itshouldbenotedthatthereduction of viscosity by a factor 150 [21], neglects the effects momentum dissipation on these small eddies, which would be significant. Adissipationtimescaleforavortex, t D ,wasdevelopedbyCandelandcoworkers in a study evaluating a counter-rotating vortex pair’s ability to quench a flame [22]. The dissipation time scale grows with the square of the vortex size as in Eq. 1.1a and is inversely proportional to the kinematic viscosity, ν . Thus, it is expected that as the size of eddies approaches the flame thickness, t D will rapidly fall to the order of the flame time scale, t F , defined in Eq. 2.4. The ratio of these two time scales is defined as the vortex power, P V , as in Eq. 1.1c. If P V is less than one, then it is expected that the vortex will dissipate before it can pass through the flame. From here it is argued that eddies smaller than the flame thickness have a P V less than one and will not be effective at quenching the flame. t D =D 2 V /ν (1.1a) t F =l F /S 0 u (1.1b) P V =t D /t F (1.1c) 7 The effect of viscous dissipation has also been noted in DNS studies of Ka > 1 planar flames [23, 24]. The turbulent kinetic energy, k, decreased with increasing progress variable on average. This decrease in k was attributed to the increase in viscosity of the fluid as the temperature increased. It should be noted that a similar decrease was not found for experimental jet and Bunsen flames [25, 26]. 1.2 Objectives Based on the above discussion, a number of questions remain unanswered. Indi- rectexperimentalevidencehasshownthatsubstantiallybroadenedCH 2 Olayersare associated with extinction in swirl burners [8] as well as direct evidence that ex- tinction of 1D oscillating flame simulations [10] results in lingering CH 2 O. Direct evidence has also shown that thermal energy can be released into the reactant pool by flame extinction thereby increasing its reactivity [14]. Other experiments have shownvorticeslargerthanl F locallybroadentheflameupto3times[7]. Additional questions remain about the influence of sub-flame-thickness scale eddies. Driscoll has shown the Klimov-Williams criteria does not predict the transition from the TRZ and CFR and that flames remain locally thin in the presence of what should be homogeneously dispersed sub-flame-thickness scale eddies [7, 6]. Additionally, if the reaction layer remains thin and elevated concentrations of CH 2 O exist many l F away, how can these severely broadened layers any longer be considered part of the flame, or is a modified reactant pool a more fitting description? 8 The objectives of this work are to identify and describe the mechanisms behind substantialbroadeningoftheCH 2 Olayersandtoevaluatetheinfluenceofsub-flame- thicknessscaleeddiesontheflame. Toachievethisgoal,highspeedtwodimensional (2D) VFI simulations were done. Vortices of various length scales spanning above and below l F will be submitted to a flame and a combination of local observations and global statistics will be extracted. This includes time series images of the mechanisms responsible for severe broadening of the CH 2 O layers as well as global statistics relating to the flame thickness of each VFI case. VFI simulations are a canonical case for studying turbulence on a local basis and can be used to establish an understanding that applies to more complex configurations. It should be noted that turbulence is an inherently three-dimensional (3D) phe- nomenon and that a 2D vortex can not fully represent the effects of turbulence on a flame. Regardless, a 2D vortex can still provide useful information regarding a subset of possible interactions between turbulence and the flame. The simplicity of this canonical configuration also lends itself to being less computationally expensive to simulate and simpler to visually interpret. This has been the motivation behind 2D computational VFI studies over the years by, among others, Candel, Poinsot, Bell, Ferziger, and Blanquart and coworkers (e.g., [27, 22, 28, 29, 30, 31]). This document is structured as: Chapter 2 establishes the fundamentals neces- sary to describe the flame broadening problem, Chapter 3 describes the numerical setup for the VFI configuration as well as pre- and post-processing, Chapter 4 lays 9 out results and discussion, and Chapter 5 goes over future work. 10 Chapter 2: Background 2.1 Premixed Flames 2.1.1 Premixed Flame Theory Premixed deflagration combustion involves a flame wave burning a fuel-oxidizer mixture at subsonic speeds. Mixtures are generally characterized by the stoichio- metric ratio which relates the concentration of fuel to oxidizer relative to the ratio of their stoichiometric concentrations which is shown in Eq 2.1 where F and O are the mole-fraction/mass-fraction of the fuel and oxidizer respectively and (F/O) st is the stoichiometric version of the (F/O) ratio. A mixture with a ϕ less than one is considered fuel lean while a ϕ great than 1 is fuel rich where fuel lean implies there will be leftover oxidizer from the combustion processes and vice versa. ϕ = (F/O) (F/O) st (2.1) In the reference frame of a laminar flame wave, the unburnt mixture is moving towards the flame surface with a speed S 0 u , the laminar flame speed. This unburnt 11 mixture is characterized by its equivalence ratio ϕ , unburnt temperature T u . As the unburntmixtureenterstheflameitispreheatedbydiffusionofthermalenergyfrom the downstream region of the flame. This region of the flame is labeled the Preheat Zone (PHZ) and it is characterized by a balance between convective and diffusive transport with little chemical activity. The reactants continue to be heated as they progress downstream and eventually end up in the reaction zone (RXZ) where most of the chemistry and heat release takes place. In this region the initial reactants are exothermically converted to the final products and heat is released which is then diffused upstream to heat the incoming reactants. The flame also has an associated thermal thickness that is computed using the temperature profile as in Eq 2.2 where T ad is the adiabatic flame temperature and (∂T/∂x) max is the maximum spatial gradient of the temperature profile in the di- rectionnormaltotheflame, x. TheT ad istakenfromadiabaticallyequilibratingthe reactantsunderconstantpressure. Assumingtherearenoheatlosses,themaximum temperature in the flame, T b , should be near T ad . l F = T ad − T u (∂T/∂x) max (2.2) Some parameters that govern S 0 u are given in Eq 2.3 where p is the pressure, n is the reaction order, λ is the heat conductivity, c p is the specific heat under constant pressure and T a is the activation temperature of the reactants. The activation 12 temperature can be stated as T a =E a /R 0 where E a is the overall activation energy of the reaction and R 0 is the universal gas constant. The dependence of flame speed on diffusive transport properties is felt through the p λ/c p term while the effect of chemistry, exothermicity, and Activation Energy is felt through the pressure and exponential terms. S 0 u ∼ p (n/2− 1) s λ c p exp − T a 2T b (2.3) The fundamental length and velocity scales of the flame are l F and S 0 u , respec- tively. Combining these, as in Eq 2.4, results in the characteristic flame time. This flame time is essentially the time it takes for a flame surface to burn through a length of reactants equal to its flame thickness. t F =l F /S 0 u (2.4) Theflamethicknessandflamespeedcanalsoberelatedtothethermaldiffusivity, α , in Eq. 2.5 by applying the balance between convective transport and diffusive transport in the PHZ. S 0 u l F ∼ α (2.5) 13 2.1.2 Oxidation of Methane The main consumption path of methane in a flame, Fig. 2.1, involves several key intermediates that will later become important in understanding the effect of tur- bulence on a flame. The thickness of the lines in Fig. 2.1 implies the proportion of the species that are consumed by that path. The section will focus on the major reaction pathway corresponding to the vertical path starting at CH 4 and ending in CO 2 . Figure 2.1: CH 4 oxidation pathway [32] 14 In a flame there exists a super-equilibrium of radicals in the RXZ including the hydrogen radical, H, oxygen radical, O, and OH that diffuse upstream and break down CH 4 into the methyl radical, CH 3 , through Reacs. R1-R3. This breakdown continues with the reaction of CH 3 with O in Reac. R4 to create formaldehyde, CH 2 O. Formaldehyde is mainly consumed through one of two paths, through OH in Reac. R6 or through H in Reac. R5, both producing the formyl radical, HCO. CH 4 + H CH 3 + H 2 R1 CH 4 + O CH 3 + OH R2 CH 4 + OH CH 3 + H 2 O R3 CH 3 + O CH 2 O + H R4 CH 2 O + H HCO + H 2 R5 CH 2 O + OH HCO + H 2 O R6 The formyl radical quickly decomposes into H and CO either through Reac. R7 or Reac. R8. Finally, oxidation of CO is catalyzed through reaction with OH to form carbon dioxide, CO 2 , a product, Reac. R9. This final oxidation of CO into CO 2 is important because it is responsible for the majority of heat release in the flame. 15 HCO + M H + CO + M R7 HCO + O 2 CO + HO 2 R8 CO + OH CO 2 + H R9 2.1.3 Flame Stretch The stretch rate, κ , of the flame surface is associated with the scaled lagrangian generation rate of surface area as in Eq. 2.6a, where A is the surface area of an in- finitesimalflameelement. Therearetwomainmechanismsbywhichflamesgenerate surface area. The first is given by the first term on the right-hand-side of Eq. 2.6b where∇ t is the del operator containing spatial derivatives in the directions tangent to the flame surface and u t is the tangential components of the fluid velocity at the flame surface. This term is the tangential strain rate ( a t ) and it generates surface areabytangentiallyconvectingelementsoftheflameawayfromeachotherandvice versa. The second term associated with stretching the flame is described by the second term on the right-hand-side of Eq 2.6b where V f is the local velocity of the flame surface and n is the unit vector normal to the local flame front. This term describes surface area generation by a curved flame element propagating in space. 16 κ = 1 A dA dt (2.6a) =∇ t · u t +(V f · n)(∇· n) (2.6b) Theprimaryeffectofthestretchontheflameisthroughtheflamespeed, S u ,and theflametemperature, T b ,bothofwhichdeviatefromtheirvaluesinanunperturbed laminar flame. Modification of the flame by the stretch rate is due to unequal thermal and reactant diffusivities is referred to as preferential diffusion. The ratio of these is represented by the Lewis number, Le = α/D k , where α is the thermal diffusivity and D k is the mass diffusivity of the deficient reactant k. Diffusion in the flame will always occur normal to the flame surface while the streamlines of the flow may not. In a stretched flame with non-unity Le, asymmetric diffusion will occur across external streamlines which leads to an imbalance between mass and thermal transport to and from the reacting layer. This imbalance is responsible for modifying T b which in turn modifies S u through Eq. 2.3. 2.1.4 Karlovitz Number The largest significant a t imposed by the fluid on the flame can be thought of as the inverse of the time scale of fluid mechanics where a t has units of 1/s. Multiplying this by t F results in a dimensionless number, the Karlovitz number, in Eq. 2.7. The 17 Karlovitznumberrepresentstherelativestrengthofthefluidmechanicstotheflame whereKa>>1impliesthefluidmechanicsaredominatingtheflameandviceversa. Ka=a t t F (2.7) 2.1.5 Symmetric Counterflow Configuration A common configuration for evaluating the effect of a t on a flame is the Symmet- ric Counterflow Burner configuration where two burners are facing each other, one facing up the other down. The bottom half is shown in Fig. 2.2 where the top diag- onally hatched surface is the symmetry plane. The equations in Fig. 2.2 represent thexandy componentsofthevelocityfield. Thecounterflowconfigurationimposes an a t =a which modifies the flame speed. The flame then stabilizes itself wherever the upstream velocity is S u . Figure 2.2: Symmetric counterflow coniguration [33] Due to preferential diffusion effects, non-unity Le flames will have the greatest 18 modificationto S u whereLe>1flameswillseetheir S u dropandviceversa. Asthe inletspeedofthefluidcomingfromtheburnersincreases,alarger a t willbeimposed on the flame and the flame will need to restabilize itself closer to the symmetry plane. Continuing to increase the inlet speed will eventually extinguish flames with Le > 1 due to the drop in T b no longer being able to sustain the high activation energy of reactions. Flames with Le≤ 1 will eventually be pushed up against the symmetry plane. Here, increasing the inlet speed will reduce the residence time of the reactants in the flame until chemistry cannot keep up and excessive incomplete reactions extinguish the flame. 2.2 Turbulent Premixed Flames 2.2.1 Basics of Turbulence Turbulence is characterized by chaotic fluid motion where the fluid velocity and pressure randomly fluctuate in space and time. Turbulence can be thought of as the superposition of many eddies, or rotating fluid elements, of various sizes and speeds being carried by the mean flow. In homogeneous isotropic turbulence (HIT), the statisticalpropertiesofturbulenceareindependentofspaceandtime. Thefollowing discussion will make this assumption. The largest eddies are associated with the length scale of the flow configuration such as the jet diameter. Just below that length scale is the integral length scale, 19 l, which contains most of the turbulent kinetic energy per unit mass (TKE), k, and has an associated velocity scale u ′ also known as the root mean squared of velocity fluctuations, Eq. 2.8. In Eq. 2.8 u is the velocity of the flow at a given point, u is the mean of this velocity, and the fluctuation in velocity associated with this point is u− u. u ′ = 1 3 ∥u− u∥ 2 1/2 (2.8) The Turbulent Reynolds number, Re T , is a dimensionless number that charac- terizes the turbulence intensity of the flow. It is based on u ′ and l in Eq. 2.9 where ν is the kinematic viscosity. Re T = u ′ l ν (2.9) Given that most of TKE is contained within the integral scale, u ′ and k are related by Eq. 2.10 where the 3 accounts for the three components of velocity. k∼ 3u ′ 2 2 (2.10) The turbulent energy cascade, first introduced by Richerson [34], is a range of eddy scales that are not affected by the diffusive nature of viscosity. In this inertial- subrange, eddies transfer TKE to smaller scales by breaking up into smaller scale 20 eddies within a timescale associated with their turnover time, such as τ for the integral length scale in Eq. 2.11. The transfer rate of TKE to and from eddies within the inertial-subrange must be equal otherwise energy would non-physically accumulate at a length scale. The transfer rate of TKE is therefore associated with the energy contained within that length scale divided by that eddies turn over time. For the integral scale, k ∼ u ′ 2 divided by τ from Eq. 2.11 results in Eq. 2.12. The third term in Eq. 2.12 enforces the idea that the TKE transfer rate applies to all scalesintheinertial-subrangewherer andu r arethelengthscaleandcorresponding velocity scales of eddies in this range, respectively. τ = l u ′ (2.11) ϵ ∼ u ′ 3 l ∼ u 3 r r (2.12) The smallest eddies found in a turbulent flow, the Kolmogorov scale, are sub- stantially modified by viscosity and will dissipate to heat before they have a chance to break down into smaller eddies. To represent momentum forces are competing withviscousforcesatthisscale, anewversionoftheReynoldsnumber, Eq.2.13a, is introduced where η is the length scale and v is the velocity scale. This Kolmogorov Reynolds’s number, Re η , is set equal to one representing this competition. The rate at which energy is dissipated away is represented by Eq. 2.13b which is equal to the 21 rate at which energy cascades down the inertial-subrange. Re η = η v ν ≈ 1 (2.13a) ϵ ∼ ν v 2 η 2 (2.13b) CombiningEqs.2.12,2.13a,and2.13btheKolmogorovlengthandvelocityscales can be solved for in Eqs. 2.14a and 2.14b, respectively. The Kolmogorov time scale is the ratio of η and v in Eq. 2.14c. η ∼ l u ′ l ν − 3/4 (2.14a) v∼ u ′ u ′ l ν − 1/4 (2.14b) τ η = η v ∼ l u ′ u ′ l ν − 1/2 (2.14c) 2.2.2 Turbulent Flame Regimes Interactions between turbulence and the flame involve the interaction of many time scales including the time scales of the eddies, the PHZ time scale, and the chemical timescaleforeachspecies. Oneattempttointerpretthesetimescalesinameaningful way is the Borghi-Peters diagram Fig. 1.1 which asserts that regimes of combustion can be characterized by u ′ /S 0 u and l/l F [35]. A few Dimensionless numbers are used to separate the regimes including, Re T , 22 Ka, and Ka δ which is the Karlovitz number with respect to the RXZ time scale. First, it is recognized that the kinematic viscosity and thermal diffusivity are pro- portional, ν ∼ α , which when combined with Eq. 2.5 results in Eq. 2.15. This relation allows the scales of the flame to be combined with those of turbulence. S 0 u l F ∼ ν (2.15) The turbulent Reynolds number, defined in Eq. 2.9, when combined with 2.15 results in Eq. 2.16. Re T ∼ u ′ S 0 u l l F (2.16) As mentioned in Sec. 2.1.4, the Karlovitz number is based on the highest signifi- cantstrainrateontheflame. Ofallthescalesintheturbulentcascade, thesmallest eddies impose the largest strain rates, which is proportional to the inverse of τ η . The Karlovitz number in a turbulent flame then becomes t F divided by τ η which is equal to the final term in Eq. 2.17. The third term in Eq. 2.17, l 2 F /η 2 , is created by combining Eqs. 2.4, 2.15, 2.14c, and 2.13a. Ka= t F τ η ∼ l 2 F η 2 ∼ l l F − 1/2 u ′ S 0 u 3/2 (2.17) Finally, Ka δ is computed from the Karlovitz number except using the charac- 23 teristic time of the reaction zone, t δ . The ratio of the RXZ layer thickness to the PHZ layer thickness is represented by δ which typically takes on a value around 0.1 [33]. Using this with Ka results in Eq.2.18. Ka δ =δ 2 Ka∼ δ 2 l 2 F η 2 (2.18) ThelaminarflameregimeinFig.1.1isdefinedby Re T <1wheretheturbulence is weak resulting in little warping of the flame surface. The next regime is the WrinkledFlameletRegimewhichischaracterizedbyRe T >1andu ′ /S 0 u <1. Inthis regime, the flame surface is now able to be warped by the eddies which moderately wrinkles the flame surface. Continuing into the Corrugated Flamelet Regime characterized by Ka < 1 and u ′ /S 0 u > 1, the vortices are now strong enough to strongly wrinkle the flame. The Ka < 1 boundary implies that all eddies within the turbulent cascade are larger than l F , or in other terms η >l F . Because Kolmogorov scale eddies are larger than theflamethickness, itisexpectedthattheycannotpenetratetheflameandmixthe inner layers which would result in an unmodified inner flame structure. The Thin Reaction Zone Regime is defined by the region Ka > 1, Re T > 1, and Ka δ < 1 and is identified by having a broadened PHZ while maintaining a ”thin reaction zone”. Now that Ka>1, the third term in Eq. 2.17 implies that the Kolmogorovscaleisnowη <l F andthesmallesteddiescannowpenetratetheflame 24 and mix layers. This effectively increases the scalar dissipation rate and therefore broadens the PHZ of the flame. The boundary Ka δ maintains that η > l F so the smallest eddies are still larger than the reaction layer. Thefinalregime,theBrokenReactionZoneRegime,containstheregion Ka δ >1 which implies that the smallest eddies now fit within the RXZ and can now locally extinguish the flame. 25 Chapter 3: Numerical Setup 3.1 Vortex Flame Interaction The2DVFIwassimulatedusingaCH 4 /airflameatanequivalenceratioof ϕ =0.7, unburnt temperature, T u =300 K, and atmospheric pressure. A 16 species directed relation graph (DRG) [36] reduced version of the USC Mech II [37] chemical kinetic model was used. Validation of the reduced model was done by comparing aspects of 1D flame solutions; specifically, S 0 u , l F , and species profiles between the two models. A1Dunperturbedlaminarflamesolutionusingthereducedmodelproduces a S 0 u =20.7 cm/s and l F =0.61 mm. 3.1.1 LaminarSMOKE Simulations were carried out by using laminarSMOKE, a multi-dimensional, com- pressible, reacting flow solver [38, 39]. This solver utilizes Strang operator split- ting [40] such that stiff chemical terms are solved using OpenSMOKE [39] and the non-stiff transport terms are solved using OpenFOAMS’s PISO algorithm [41]. A first-orderEulariantimediscretizationandasecond-orderspatialdiscritizationwere 26 used. AdaptivetimesteppingwasdonebasedontheCourantFriedrichsLewy(CFL) number set to 0.04 for all presented cases. Species diffusivity was modeled by using the mixture averaged coefficient formu- lation. Under the optically thin assumption, a gray gas radiation model [42, 43] was employed where carbon monoxide (CO), carbon dioxide (CO 2 ), nitrogen (N 2 ), and water (H 2 O) were the radiative species. Buoyancy and second order diffusion such as thermophoretic and Dufour effects where not considered. The conservation of mass, species, momentum, and energy equations are given in Eqs. 3.1a-3.1d where Y k is the mass fraction of the kth species, V k is the diffusion velocityofthekthspecies, ˙ ω k istheproductionrateofthekthspecies,pispressure, τ is the stress tensor, c p is the specific heat at constant pressure, c p,k is the specific heatofthekthspecies,λ isthethermalconductivity,h k isthetotalspecificenthalpy of the kth species, and q rad is the radiative heat transfer rate. ∂ρ ∂t +∇· (ρ u)=0 (3.1a) ∂ρY k ∂t +∇· (ρ (u+V k )Y k )= ˙ ω k (3.1b) ∂ρ u ∂t +∇· (ρ uu)=−∇ p+∇· τ (3.1c) 27 ρc p ∂T ∂t +ρ c p u+ X k c p,k Y k V k !! ·∇T =∇· (λ ∇T)+q rad − X k h k ˙ ω k (3.1d) The diffusive velocity for the kth species is computed using Eq. 3.2 where D k is the mixture-average formulation diffusion coefficient for the kth species [39]. A correction diffusion velocity is also applied to ensure mass conservation [44]. V k = D k Y k ∇Y k (3.2) The viscous stress tensor is also defined in Eq. 3.3 where the fluid bulk viscosity is assumed to be zero [45]. τ =µ ∇u+(∇u) T − 2 3 µ (∇· u)I (3.3) 3.1.2 VFI Configuration FourdifferentcasesofVFIwereconsidered,whicharelistedinTable3.1. Thevortex size,D V ,wasvariedfrom5timestohalfofthelaminarflamethicknesscorresponding to cases L5 through L0.5. Case L5 was set to have a maximum tangential velocity, U θ , of 300 times S 0 u as it was found that at this speed the vortex was capable of causing local extinction. The smaller vortices had their velocity scaled such that they would exist in the same inertial sub-range in HIT turbulence. Specifically, for 28 any two vortices U 3 θ /D V is proportional between them. Another configuration for VFI is a 2D counter-rotating pair of vortices inter- acting with the flame. A single vortex was used instead because counter-rotating vortices self-propagate along their axis of symmetry. The propagation speed is pro- portional to the the rotation speed of the vortex, which means high-speed vortices quickly propagate across the domain. By using a single vortex, a much smaller computational domain can be used to observe the full life-time of the interaction without the flame being push out of the domain by the vortex. The vortex power, as defined by Candel et. al. [22], is also shown in Tab. 3.1 along with the initial Karlovitz number of the vortex, K V0 , defined in Eq. 3.4. Ka V0 = t F D V /U θ (3.4) Each case uses a rectangular computation grid where both the domain and grid spacing are scaled based on D V as in Table 3.1. A uniform mesh is used such that 100 points are across D V and the height of the domain (H D ) is 5D V . The width of thedomain(W D )forthetwosmallestcaseswasrelativelyincreasedby50%because the flame thickness occupied a significant portion of the width. 2D simulations were initialized from 1D flame solutions computed with Cantera [46]. The flame was horizontally centered in the domain and the left boundary maintained the flames position with an inflow of reactants at a speed of S 0 u . The 29 Case D V /l F U θ /S 0 u Ka V0 P V W D /D V H D /D V ∆ x [m] l F /∆ x L5 5 300 60 188 13 5 3.03e-5 20 L2 2 221 111 30 13 5 1.24e-5 49 L1 1 175 175 7.6 19.5 5 6.24e-6 97 L0.5 0.5 139 278 1.88 19.5 5 3.12e-6 193 Table 3.1: List of conditions simulated. right boundary was set to be a wave transmissive outlet with a constant pressure of 1 atm [29]. The top and bottom boundaries were periodic. After this initialization, the flame was simulated in laminarSMOKE in the ab- sence of the vortex for around 10 ms until it reached steady state. This solution was then validated against the Cantera solution using S 0 u , l F , species profiles, and the temperature profile. The vortex was introduced by adding its velocity to the existing velocity field of the 1D flame. The vortex velocity distribution introduced by Rutland and Ferziger [29] was used, Eq. 3.5, due to the quick fall off in velocity away from the vortex center. This property of the vortex allowed it to be placed as close to the flame as possible without any significant modification of the velocity field in the preheat zone. The center of the vortex was placed 1.75D V from the 320 K isotherm on the reactant side of the flame as in Fig. 3.1. This placement method was found to consistentlyplacethevortexneartheflameacrossallcaseswithoutthevortexbeing initialized in the flame. 30 Figure 3.1: Initial conditions of VFI v θ (r)=U θ 2r D V exp 1 2 − 2r 2 D V 2 (3.5) 3.2 Cantera: 1D Flames The 1D laminar flames and their properties are computed using Cantera [46], an open-sourcesoftwarewithchemicalkinetic,thermodynamic,andtransportlibraries. The conservation equations solved for 1D laminar free flames with radiation are Eqs. 3.6a-3.6c. The present radiation model accounts for CO 2 and H 2 O as radiative species [47] and a mixture-averaged diffusion formulation was used. A combination ofNewtonsteppingandtimeintegrationisusedtosolvethediscretizedsteady-state differential equations. 31 ∂ρu ∂x =0 (3.6a) ρu ∂Y k ∂x =− ∂ ∂x (ρY k V k )+ ˙ ω k (3.6b) ρ c p u+ X k c p,k Y k V k !! ∂T ∂x = ∂ ∂x λ ∂T ∂x +q rad − X k h k ˙ ω k (3.6c) 3.3 Pre-Processing 3.3.1 Mechanism Reduction Mechanism reduction by Directed Relation Graph (DRG) was used to reduce the USCMechII[37]kineticmodelfrom114speciesdownto16species. Thereducedki- neticmodelwasvalidatedbasedonflamespeed, thermalprofile, andspeciesprofiles from solutions of lean methane flames. This method, introduced by Lu and Law [36], makes each species a vertex in a graph such as A-F shown in Fig. 3.2. These species can be connected to each other by edges which can take on a one-way connection such as A→ B or a two- way connection such as B ↔ D. The directional connection of species by an edge implies a dependence. For example, the connection A → B means that in order 32 Figure 3.2: Sample directed relation graph of a kinetic mechanism [36]. to accurately predict the production rates of species A, B must be included in the kinetic mechanism. A two-way connection implies that each species relies on the other. The connectivity of the graph is determined by evaluating the fractional sum of the absolute values of production rate of a species on another species. For example, the fractional dependence of A on B, r AB , is defined in Eq. 3.7 where i is the ith reaction, v A,i is the stoichiometric coefficient of species A, ˙ ω i is the progress rate of the ith reaction, and δ B,i is the Kronecker Delta function where it takes on a value of one if the ith reaction involves species B and takes on a value of zero otherwise. r AB = P i |v A,i ˙ ω i δ B,i | P i |v A,i ω i | (3.7) 33 Next, an error threshold is chosen as ϵ err and is compared to the fractional dependence of each species to every other species. For the dependence of species A onB,ifϵ err ≤ r AB thenwedeterminethatAdoesdependonB andanedgepointing from A to B is created. Once all of the edges are established, a few starting species are selected and a recursive search is made to find all species these starting species depend on. The reduced set of reactions only involve species from the reduced species set. Forthiswork, the ˙ ω i valueswerederivedfrom1Dlaminarflamesolutionsoflean methane-air flames. The progress rate of each reaction was integrated in space and the spatially mean values were used instead as defined in Eq. 3.8 where L is the length of the domain. ˙ ω i = 1 L Z L 0 ˙ ω i dx (3.8) 3.4 Post-Processing 3.4.1 Progress Variable A progress variable based on temperature, c, is defined in Eq. 3.9, where T ad is the adiabatic flame temperature. This normalized form of temperature is useful for studying the broadened flame structure as will be addressed in the following sections. 34 c≡ T − T u T ad − T u (3.9) 3.4.2 Flame Thickness In order to evaluate the effect of vortex power a method for determining the mean flame thickness was developed. The flame thickness of a laminar unperturbed flame is measured by using the temperature gradient method as in Eq. 3.10, where ∥∇T∥ max and∥∇c∥ max arethemaximummagnitudesofthetemperatureandprogress variable gradients, respectively. l F = T ad − T u ∥∇T∥ max = 1 ∥∇c∥ max (3.10) During the VFI, significant modification of scalar gradients in the flame will occur. A sample scatter plot of ∥∇c∥l F versus c is shown in Fig. 3.3 where the averageof∥∇c∥l F conditionedoncisshownastheredlineandunperturbedlaminar flame is shown as the blue line. The dashed horizontal line represents the maximum value of µ (∥∇c∥l F | c) which occurs at c = c max , which is represented by the solid vertical line. The magnitude of the c gradient is scaled by its maximum value in a 1D un- perturbed flame which is equivalent to multiplying by l F , as in Eq. 3.10. The 1D laminar flame solution in Fig. 3.3 peaks at a value of 1 which is associated with a 35 flame thickness of l F . The value∥∇c∥l F is also inversely proportional to the flame thickness; a larger value implies a thinner flame and vice versa. Similar reasoning is used to extract the mean flame thickness from the instan- taneous perturbed flame solution. The maximum value of the conditional mean of the c gradient, µ (∥∇c∥l F | c = c max ), is interpreted as the inverse of the scaled flame thickness. This measure will be referred to as the instantaneous maximum conditional mean (IMCM). Figure 3.3: A sample scatter plot of ∥∇c∥l F versus c. The vertical solid line is positioned where the conditional average line is at its maximum, which will be referredtoasc=c max . Thedashedhorizontallinethereforereferstoµ (∥∇c∥l F |c= c max ) The instantaneous conditional standard deviation (ICSD) is also computed at c = c max as σ (∥∇c∥l F | c = c max ). This is a measure of the variation in magnitude 36 of the gradient of c and will be used to determine which cases cause the most varied disruption of the scalar gradients in the flame. 3.4.3 Isotherm Speed The speed of the c isosurface with respect to the local fluid can be computed from thematerialderivativeofc,asinEq.3.11. Theisosurfacepropagatesinthedirection of the scalar gradient, which is the same direction as the unit normal vector to the flame ˆ n=−∇ c/∥∇c∥. Inthereferenceframeoftheisosurface,themagnitudeofthe scalar on the isosurface does not change with time, i.e. ∂c/∂t = 0. In addition, the velocity of the isotherm is equal in magnitude and opposite in direction to the fluid velocity in this reference frame. Applying these results in equation Eq. 3.12 where u is replaced with the negative isosurface displacement speed S d multiplied by ˆ n. Applying the fact that ˆ n is in the opposite direction of ∇c results in the equation for S d , Eq. 3.13 [48, 49, 50]. Dc Dt = ∂c ∂t +u·∇c (3.11) Dc Dt =(− S d ˆ n)·∇c (3.12) S d = 1 ∥∇c∥ Dc Dt =S d,c +S d,rd (3.13) 37 The material derivative in Eq. 3.13 can be expanded to the existing transport and chemistry terms present in the conservation of energy equation, Eq. 3.1d. The thermal diffusion term requires special treatment as it can be split into diffusion normal to the flame surface and curvature induced diffusion tangent to the flame [50]. Thefarright-hand-sideofEq.3.13includesthecontributionto S d ofcurvature induced diffusion, S d,c , and remaining transport and chemistry terms, S d,rd , which will be referred to as the kinematic restoration term [16]. The S d,c term is defined in Eq. 3.14a and the S d,rd in Eq. 3.14b [16]. S d,c =− α (∇· n) (3.14a) S d,rd =− n·∇ (λ ∥∇c∥) ∥∇c∥ρc p + P k h k ˙ ω k ρc p ∥∇c∥(T ad − T u ) + P k c p,k Y k V k ∥∇c∥c p ·∇c− ˙ q rad ρc p∥∇c∥(T ad − T u ) (3.14b) 3.4.4 Scalar Gradient Broadening The mechanics that govern the evolution of a scalar gradient such as the gradient of c in a flame is given by Eq. 3.15a [16], where a n is the local normal strain rate and ∂/∂nisaspatialderivativeinthedirectionof ˆ n. Thesetermsaremadedimensionless by multiplying each by l F t F resulting in Eq. 3.15b, where Ka V is the local Karlovitz 38 number of the vortex based on normal strain. As has been discussed previously, l F scales∇c. On the other hand, t F scales the a n and ∂S d /∂n terms. ∥ ˙ ∇c∥=− a n + ∂S d ∂n ∥∇c∥ (3.15a) t F l F ∥ ˙ ∇c∥=− l F Ka V ∥∇c∥+l F ∂S d ∂n ∥∇c∥t F ) (3.15b) t F l F ∥ ˙ ∇c∥=− l F Ka V ∥∇c∥+t F ∂S d,c ∂n ∥∇c∥l F +t F ∂S d,rd ∂n ∥∇c∥l F (3.15c) The S d term in Eq. 3.15b can be expanded into its curviture and kinematic restoration contributions which forms Eq. 3.15c [50]. A large positive l F Ka V ∥∇c∥ is indicative that convectivetransportcaused bythe vortex is broadeningthe flame. On the other hand, a large positive t F ∂S d,c ∂n ∥∇c∥l F indicates broadening caused by curviture of the flame. Finally, a large positive t F ∂S d,c ∂n ∥∇c∥l F means the restorative contributions of reactions and normal diffusion are broadening the flame. 39 3.4.5 Mixture Properties Effective Equivalence Ratio The effective equivalence ratio, ϕ eff , of a chemical state is evaluated using Eq. 3.16, where X k is the mole fraction of species k. C k , H k , and O k are the number of respective atoms in the species k. This method works based an atomic balance assuming all species will be converted to CO 2 , H 2 O, and O 2 as final products. ϕ eff = 1 X O 2 X k̸=CO 2 ,H 2 O,O 2 X k (C k +H k /4− O k /2) (3.16) Net Production Rate The reactivity of a mixture is measured using a net production rate, ˙ ω net , defined belowinEq.3.17. Thepurposeofthismeasurementistoshowthecompleteabsence of any reactivity. ˙ ω net = X k |˙ ω k | (3.17) 3.4.6 Distance From Flame A method was developed to determine the distance from the flame surface. The T = 1500 K isotherm, which is closely associated with the reaction layer of the flame, is chosen to represent the flame surface. A new field, d, is defined so that 40 each point in the field is set to its minimum distance to the 1500 K isotherm. If the given point in the field has T >= 1500K then it takes on a negative d where as points with T < 1500 have a positive d. Similar methods have been used in experimental [6] and numerical [51, 52] works. A sample d field is shown in Fig. 3.4. The 0 contour in Fig. 3.4 is the 1500 K isotherm and the other contours represent the distance from the 1500 K isotherm in mm with negative values being the reactant side of the flame and vice versa. Figure 3.4: A sample d field where the light gray side represents the reactant side of the flame and the dark grey side represents the product side. 41 Chapter 4: Results and Discussion Species mass/mole fractions, net production rates, and heat release rate (HRR) values will be scaled by their maximum value in a corresponding laminar free flame. Temperature will be displayed as c in cases where other established methods have used c. Otherwise the temperature will be used as is. 4.1 Reactant Pool Modification Mechanisms Two different mechanisms where responsible for transporting thermal energy, inter- mediates, and products into the reactant pool. The first of these is flame siphoning and the second is product-side annihilation. 4.1.1 Flame Siphoning An example of flame siphoning is shown in Fig. 4.1 where the left most column shows the thermal layers of the flame pulled or ”siphoned” into the reactants. The green lines in Fig. 4.1 represent isosurface of heat release rate (HRR) that are 10% of the maximum in a 1D laminar flame. At the first time step of 2.75 ms, the flame 42 is relatively flat. As it interacts with the vortex it is pulled into a highly curved surface by 2.9 ms. At 3.1 ms, the flame experiences significant broadening in the region with large curvature. The flame then retreats toward the products and again becomes a flat flame by 3.4 ms. The initial Karlovitz number of all cases presented here is large as can be seen in Table 3.1. The case presented in Fig. 4.1, L1, has a Ka V0 = 175 so it may be expected that the convection dominates all other forms transport. The following analysis will compare the role of curvature, convection, and kinematic restoration terms in influencing the magnitude of the c gradient by Eq. 3.15c. The middle column represents the budget for the evolution of the magnitude of the c gradient as in Eq. 3.15c. These terms are plotted along the black arrow in the left most column starting from the tail and going to the head. In the initial two timesitappearsthattheconvectiontermismostlyresponsibleforbroadeningwhich ismostlybalancedbytherestorativeterm. Astheflamebecomesmorecurvedat2.9 ms, thecurvaturetermdominatesthebroadeningandisstillsomewhatbalancedby the restorative term. By 3.1 ms, the curvature term dominates all other terms and the preheat layers of the flame are effectively transported into the reactant stream. The curvature terms begins to recede as the flame returns to being a flat at 3.4 ms. Broadening in regions of large curvature have also been found by Sankaran et al. [52] and Wang et al. [16]. These works found that regions of large curvature where onaveragebroaderandthatthecurvaturetermofEq.3.15cwasresponsibleforthis 43 broadening. This work expands on these by showing an extreme local broadening eventcapableoftransportingthermalenergyintothereactantstreammany l F from the reacting layer thereby modifying the reactants. The right column of Fig. 4.1 shows S d and its curvature, S d,c , and restorative, S d,rd , components along the black arrow in the left column. These terms are mul- tiplied by the the local density to convert it to a local mass burning flux, which is then divided by the mass burning flux of an unperturbed laminar flame, f 0 u =S 0 u ρ u . This can also be thought of as the density weighted isotherm speeds that are scaled bythelaminarflamespeed. Asimilartrendisfoundhereaswiththescalargradient terms in themiddle column. At 2.75ms the flame propagates forward at close to S 0 u and the curvature term does little to slow the burning rate. By the next time, 2.8 ms, large portions of the flame along the black arrow have a negative mass burning flux on the order of f 0 u , which is caused the curvature term S d,c . Other works have shownthattheflametakesonanegativeflamespeedinregionswithlargecurvature [53, 54, 49, 55]. At 3.1 ms, the flame takes on a negative burning flux nearly 20 times that of a laminar flame and it quickly recedes backward and becomes nearly flat by 3.4 ms. The large negative flame speed in regions of large positive curvature imply that they are inherently unstable and that the flame will tend to return to being flat. Flame siphoning is also capable of pulling CH 2 O into the reactant stream as can be seen in Fig. 4.2 where CH 2 O contours are shown during the same period as 44 Figure 4.1: Left Column: Time series images of the temperature field for case L1 between 2.75 ms and 3.40 ms. Middle and Right Columns: Quantities along the black arrows shown in the left column. 45 Fig. 4.1. The black arrows overlaid on the CH 2 O contours qualitatively represent the fluid speed and direction in order to visualize the vortex. In the same fashion as thermal energy, the CH 2 O layers are pulled into a highly curved cusp and siphoned into the reactant pool where they may mix. Thethreelargestcases(L5,L2,andL1)werecapableofinducingflamesiphoning with cases L2 and L1 being the most effective. Case L0.5 could not induced flame siphoning as it dissipated before it made much of any modification to the flame. The effect of dissipation on the vortex will be explored in more detail in Sec 4.5. Cases L2 and L1 were likely so effective at causing flame siphoning due to their small scale while maintaining P V > 1. While a large a n is not directly responsi- ble for causing flame siphoning, the large velocity gradients they possess are likely responsibleforpullingtheflameintoasharplycurvedcuspthatinducesbroadening. The experimental findings by Skiba et al. [7], vortices just larger than the flame where found to locally cause broadening may be this flame siphoning phenomenon. Thatworkalsoshowsaneddypullingtheflameintoapositivelycurvedcusp, which thenpullstheleadingedgeoftheflameintothereactantsandawayfromthetrailing edge thereby locally broadening the flame. 4.1.2 Product-Side Annihilation Product-side annihilation also is capable of transporting thermal energy to the re- actant side of the flame as can be seen in Fig. 4.3 for case L5 where time series 46 Figure 4.2: Time series images of the scaled CH 2 O field for case L1 between 2.75 ms and 3.50 ms. Arrows qualitatively denote fluid velocity direction and magnitude. Green lines represent the 0.1 iso-surfaces of the scaled HRR. 47 temperature contours are shown and the scaled HRR = 0.1 is shown in green. Sim- ilar to flame siphoning, the flame surface is pulled into a curved cusp. Rather than broadening this cusp, at 2.55 ms the vortex causes the sides of cusp to come to- gether from the product side, i.e. product-side annihilation. This form of extinction is analogous to extinction of a flame in a symmetric counter-flow burner. This initial extinction event forms an island of products in the reactant stream, referred to as a product pocket, with a tail of extinct flame layers connecting this pocket the main flame at 2.6 ms. The product pocket, now entrained in the vortex, collapses by undergoing further product-side annihilation and releases its extinct layers into the reactant pool. By 2.8 ms the pocket is fully extinct and the thermal layers are free to mix in the reactants. Along with thermal energy, product-side annihilation also introduces CH 2 O into thereactantsascanbeseeninFig.4.4. Similartothethermalenergy,atailofCH 2 O isformedconnectingtheproductpockettothemainflameaswellaslingeringCH 2 O after the product pocket collapses. The largest vortex cases were the most effective at causing product-side annihi- lation, especially case L5 which had over 10 annihilation events within the first 5 ms. Case L2 also caused flame annihilation, but only two events occurred during the simulated time. The ability of the larger vortex to cause annihilation is likely due to its relatively large size compared the the flame thickness. Where the smaller vortices are able to wrap the surface into highly curved cusps that experience flame 48 Figure 4.3: Time series images of the T field for case L5 between 2.4 ms and 2.8 ms. Arrows qualitatively denote fluid velocity direction and magnitude. Green lines represent the 0.1 iso-surfaces of the scaled HRR. Figure 4.4: Time series images of the scaled CH 2 O field for case L5 between 2.4 ms and 2.8 ms. Arrows qualitatively denote fluid velocity direction and magnitude. Green lines represent the 0.1 iso-surfaces of the scaled HRR. 49 siphoning, the larger vortex produces a larger scale peninsula that is capable of annihilating with itself. As was mentioned in Sec. 1.1, there have been few studies that focus on the formation of product pocket formation and their evolution. Of the works that do exist, many of them conclude that the frequency of product pocket formation in- creases with increasing turbulence intensity [11, 12, 13]. The work by Xu et al. [14] also found that these product pockets are capable of collapsing and modifying the thermochemical state of the reactants. This work expands on these by showing that this mechanism can also be responsible for the introduction of important experi- mental observable, CH 2 O, that are normally associated with the preheat layer of the flame, but in this case are extinct layers/modified reactants. In particular, the work by Skiba et al. [6], which experimentally measured the transition from thin to broadened preheat layers using CH 2 O-PLIF, may have had some of its broadened layers attributed to product-side annihilation. 4.2 The Modified Reactant Pool The thermochemical state of the extinct/siphoned layers is explored in more detail in this section. Evaluating the modification to the reactants is of great importance because of the effect it could have the on the flame consuming it. 50 4.2.1 Flame Siphoning Composition In Fig. 4.5a a case of flame siphoning is shown where the contours of a temperature field are plotted along green lines representing HRR = 0.1. Several selections of scalar values are plotted along the black arrow from Fig. 4.5a starting from the tail to the head in Figs. 4.5b-4.5d. In Fig. 4.5b the temperature of the siphoned layers reach temperature as high as 900 K at s/l F = 1.5, which represents significantly elevated temperatures. The effectiveequivalenceratio, ϕ eff , alsodips toavalueas lowas0.6 ina similararea. It is expected that the equivalence ratio of the siphoned/extinct layers will drop due to excess O 2 left over from lean burning. The ˙ w net stays nearly zero throughout the entire line implying there is no reactivity in the siphoned layer whatsoever. MovingontoFig.4.5c,thescaledmassfractionofCH 4 andO 2 bothdrop,witha more significant drop in CH 4 which is in agreement with the decrease in ϕ eff . There is also a relative increase in the concentration of products, CO 2 and H 2 O, which reach as high as 20% of their peak value in a 1D laminar flame. Figure 4.5d shows intermediate species, which peak at values as high as 50% of their maximum mass fraction in a laminar flame except for OH. The absence of OH means the CH 2 O can exist in the reactants without being consumed because the main consumption path of CH 2 O is through OH. The same point was made by Paxton et al. [10] for their 1D numerical flames quenched by oscillating strain rate. It should also be noted 51 that the H 2 mass fraction seems to be elevated across the entire sampled line, which may be due to its large diffusivity compared to nearly all other species. 4.2.2 Product-Side Annihilation Composition Because case L5 has the most flame annihilation events, the thermochemical state ofitsextinctlayersareevaluatedinFig.4.6,wheretheFigs.4.6b-4.6dshowselected scalar values plotted along the arrow in Fig. 4.6a. In Fig. 4.6b the temperature of the recently extinct layers is significantly raised to as high as 1300 K and ϕ eff is as low as 0.5 at s/l F =7.5. Again, the ˙ ω net is nearly zero across the entire sampled line which implies no reactivity in the extinct layers. The reactants and products along the arrow are shown in Fig. 4.6c where the CH 4 andO 2 droptovaluesaslowas0.3. Theproducts, CO 2 andH 2 O,reachscaledmass fractions as high as 0.6. Figure 4.6d shows intermediates along the arrow where nearly all plotted species are elevated except for OH, which allows for the continued existence of CH 2 O. The scaled mass fraction of H 2 does not appear to be much more elevated then the other intermediates like it was in the siphoning case. 52 (a) (b) (c) (d) Figure 4.5: (a) Contours of the T field for case L1 at time 4.4 ms. Iso-surfaces of scaled HRR=0.1 are denoted by the green lines; (b) Global mixture properties variation with s/l F ; (c) Reactant and product scaled mass fraction variation with s/l F ; (d) Intermediate scaled mass fraction variation with s/l F . The variable s in the x-axis of Figs. 4.5b-4.5d is the distance along the black arrow shown in Fig. 4.5a starting from its tail. 53 (a) (b) (c) (d) Figure 4.6: (a) Contours of the temperature field for case L5 at time 4.02 ms. Iso-surfaces of scaled HRR=0.1 are denoted by the green lines; (b) Global mix- ture properties variation with s/l F ; (c) Reactant and product scaled mass fraction variation with s/l F ; (d) Intermediate scaled mass fraction variation with s/l F . The variablesinthex-axisofFigs.4.6b-4.6disthedistancealongtheblackarrowshown in Fig. 4.6a starting from its tail. 54 4.3 Pollutant Effect on Flame 4.4 Implications for Experimental Observables Sections 4.1 and 4.2 demonstrate the introduction of thermal energy, CH 2 O, other intermediates, and products into the reactant stream by means other than sub- flame-thickness scale eddies broadening the flame. The existence of CH 2 O in the reactant stream has significant implications for experimental methods that utilize CH 2 O to identify the preheat layer of the flame. A common method of experimentally evaluating preheat layer thickness is pro- cessing CH 2 O-PLIF images where isosurfaces of CH 2 O identify the leading edge of the flame (the boundary between the flame and reactants) [6, 7]. The trailing edge of the flame may be identified by the product of the CH 2 O and OH [6, 7] which is associated with the heat release and therefore the reacting layer of the flame [56, 6, 57, 10]. The mean distance between these isosurfaces is taken to be the mean flame thickness. This method for determining the flame thickness is investigated in Fig. 4.7a where temperature field contours for case L5 at 4.0 ms are pictured. This time was selected due to the large scale modifications to reactant pool. The black isosurface signifies the scaled CH 2 O mass fraction equal to 10% of that in a laminar flame and thegreenlinerepresentsthescaledHRRat50%ofthemaximuminalaminarflame. Each of these isosurfaces occur twice in the flame surface, one on the reactant side 55 and another on the product side of their respective peaks in the flame. Only the reactant side isosurface of CH 2 O and the product side isosurface of HRR are shown in Fig. 4.7a and considered in the following analysis. A similar technique to what was done by Skiba et al. [6] is performed. These two isosurfaces that bound the so-called ”broadened preheat layer” are each made up of points. Each point on an isosurface is matched with the closest point on the other isosurface to form point-pairs. The distance between every unique point-pair, l, is measured and plotted as a histogram in Fig. 4.7b where the l is scaled by l F . ThehistograminFig.4.7bshowsthemostcommondistancebetweenisosurfaces is l/l F =1 implying that most of the flame is at the laminar flame thickness. There isalsoasignificantportionoftheflamewith l/l F <1thatwouldmeanlargeregions oftheflameareexperiencingthinning. Thereisalargetailofthehistogramtowards l/l F >1 with values as high as l/l F =8. These values are associated with modified regions of the reactant stream rather than locally broadened flames. This tail tends to skew the mean flame thickness towards larger values; in this case the mean flame thickness was 1.68l F . Modification of the reactant stream by either product-side annihilation or flame siphoningwillintroducethermalenergyandCH 2 Omanyflamethicknessesfromthe reacting layer. In particular, product-side annihilation is especially capable of this of due to the creation of product-pockets which can be transported upstream of the flame before they collapse. Measurements of the turbulent flame thickness by this 56 (a) (b) Figure 4.7: (a) Contours of T field at time 4.08 ms for case L5. Green and black lines represent iso-surfaces of scaled mole-fraction CH 2 O = 0.1 and scaled HRR = 0.5, respectively.(b) Histogram of scaled distances, l/l F , between the iso-surfaces of CH 2 O and HRR shown in Fig. 4.7a distancing method will need to consider if these phenomena are taking place and how they may influence their results. 4.5 The Effect of Eddy Scale ScalingargumentsmadebyDomk¨ ohler[58]andWilliams[3]regardingthetransition fromthethintothebroadenedpreheatzonebothassertthatthesub-flame-thickness scale eddies are responsible. Specifically, it is argued that their ability to enter the flameincreasestheeffectivescalardiffusivitytherebydecreasingscalargradientsand increasing the flame thickness. Another distinct method for determining the flame thickness is considered to evaluatethesearguments. As wasdiscussedingreatdetailinSec3.4.2, thegradient 57 in temperature, which can be expressed as the progress variable c, can be thought of as inversely proportional to the flame thickness. This method has been used to measureflamebroadening/thinninginotherliterature[16]. Itshouldbenotedthat, similar to the isosurface distancing technique, modification of the reactant stream can also cause this measurement to be misleading. This will be discussed in more detail in Sec. 4.6. A measure of the mean flame thickness (IMCM) versus time was performed to evaluatethisreasoningforallcasesasshowninFig.4.8a. CaseL5showsthelargest increase in the IMCM with values as high as 1.4 implying the mean flame thickness, whichisinverselyproportional,is70%ofl F . Thisislikelycausedbyalargenegative a n which is capable of thinning the flame as in Eq. 3.15a. Cases L2 and L1 show similar spikes in the IMCM, but they are not as large. On the other hand, case L2 shows the largest dip in the magnitude of the IMCM with a value of around 0.7, which implies a mean flame thickness is 40% larger than l F . Similar dips are seen for cases L5 and L1. The cause of these dips in the value of IMCM will be further evaluated in Sec. 4.6. The outlier in Fig. 4.8a, Case L0.5, shows very little deviation of the IMCM from a values of 1, which is associated with a flame thickness of l F . It could be that some portions of the flame are significantly broadened and others equivalently thinned which would cancel when evaluating the IMCM producing a misleading value of IMCM = 1. Fig. 4.8b shows the ICSD, which is a conditional measure of 58 the standard deviation of∥c∥l F at c=c max as discussed in Sec. 3.4.2. This measure ofvariationoftheflamethicknessshowsthat,onceagain,caseL0.5doesnotdeviate far from its mean value which is already close to l F . This is due to the fact that the smallest vortex has the lowest vortex power of 1.88 as shown in Table 3.1. A vortex power on the order of 1 implies the vortex will dissipate at the same time scale as it takes the flame to burn over a distance of l F . In effect, the vortex will dissipate away before the flame has an opportunity to interact with it. 4.6 Implications for Temperature Gradient Methods The cause of the large dips in the IMCM for cases L5, L2, and L1 is of interest. There exists no sub-flame-thickness scale eddies for these cases, so the mechanisms responsible are investigated. Figure 4.9 shows the∥∇c∥l F versus c scatter plots for every case where the red line is the mean of∥∇c∥l F conditioned on c and the blue line corresponds to a 1D laminar flame. The selected times correspond to when the IMCM is minimum for cases L5, L2, and L1 and where the IMCM peaks for L0.5. The conditional mean of case L5 shows significant deviation from the 1D flame solution through 0.2 < c < 0.7 where it is tends take on lower values. Case L2 shows even more deviation from the 1D solution over the same range, where the conditional mean takes on a maximum value (IMCM) of around 0.7. The conditional mean of case L1 show substantial deviation from the 1D flame 59 Figure 4.8: Temporal variation of (a) IMCM and (b) ICSD for all cases. over the range 0.05 < c < 0.3, especially at c = 0.3. The conditional mean quickly rises and peaks at c=0.6 taking on a maximum value of 0.8. Finally, the conditional mean of case L0.5 fairly closely follows the 1D flame solution across the full range of c. Keeping in mind that this plot represents the peak deviation of the IMCM from 1, the scatter plot does show some variation, but 60 not nearly as much as any of the larger vortex cases. Thecauseforthelargedipsintheconditionalmeanof∥∇c∥couldbethatextinct and siphoned layers of the flame that are now mixing in the reactant stream still contain temperature gradients. Figure 4.10 shows contours of the∥∇c∥l F fields for each case at the same times considered in Fig. 4.9. The diagonally hatched regions correspond to regions where the distance to the flame field, d, is d < 1.8l F . In simpler terms, the hatched region is made of reactants that are within 1.8l F of the flame surface, the flame itself, and the entire product pool. This hatched region will be referred to as the near-field to the flame, the non-hatched region as the far-field, and their combination as the entire-field. Based on Fig. 4.10, cases L5 and L2 have significant c gradients in the far-field of the flame. These temperature gradients are no longer associated with the flame, however they are still considered when evaluating the IMCM and could potentially skew the IMCM towards smaller values. Case L1 also appears to have some tem- perature gradients in the far-field, but not to the extent of L5 and L2. Case L0.5 sees very little modification to the far-field at all. The effect of these gradients in the far-field on the conditional mean statistics of case L5 is considered in Fig. 4.11a and b. In each row of Fig. 4.11, only the diagonally hatched region of the temperature field on the left is sampled in the scatter plot on the right. The same applies for Fig. 4.12-4.15. Fig. 4.11a shows the entire-field sampled in the scatter plot while Fig. 4.11b shows only the near-field to 61 Figure 4.9: Scatter plots of instantaneous ∥∇c∥l F vs c for each case; the times selected correspond to the minimum values of IMCM for the L5, L2, and L1 cases, and to the peak IMCM value for case L0.5 shown in Fig. 4.8a. the flame considered. When only the near-field is considered, the conditional mean is raisedtomatchthe1Dflameoverarangeof0 .1<c<0.4. However, near c=0.6 wherethe1Dlaminarflamepeaks,thereisstillasignificantdipinconditionalmean. Anothermeansbywhichthetemperaturegradientcanbesuppressedattemper- atures normally associated with the preheat layer is mutual flame annihilation, also 62 Figure 4.10: Hatched regions correspond to the reactants that are within 1.8l F and the of the 1500 K isotherm and the entirety of the products. ∥∇c∥l F field for all cases; the times selected correspond to the minimum values of IMCM for the L5, L2, and L1 cases, and to the peak IMCM value for case L0.5 shown in Fig. 4.8a. referred to reactant-side annihilation. As two flames propagate towards each other and consume the reactants between them, the temperature along the plane of sym- metry separating them will rise. In an ideal case, the temperature gradient along the plane of symmetry will be equal to zero throughout this interaction. Analysis of measured broadening of the flame thickness due to mutual flame annihilation has not been considered in literature to the author’s knowledge. The temperature field pictured on the left in Fig. 4.11 shows a product pocket 63 that is merging with the main flame surface near y = 15 mm. In Fig. 4.11c the near-field of the flame is again considered except with the region of mutual flame annihilationisremove. Thescatterplotexcludingtheseregionsshowtheconditional mean has been raised and now matches the 1D flame across the full range of c. The effect of temperature gradients in the free stream for case L2 is shown in Fig. 4.12. In Fig. 4.12b, where only the near-field to the flame is considered, the conditionalmeanisraisedacrossnearlythewholerangeofccomparedtoFig.4.12a, where the entire-field is considered. While some deviation from the 1D solution remains around c=0.25, nearly the whole conditional mean line closely follows the 1D laminar flame solution. CaseL1isconsideredinFig.4.13wheretheentire-fieldisconsideredinFig.4.13a and the near field is considered in Fig. 4.13b. There is little difference in the scatter plots between these two for c > 0.4. However, in the near-field scatter plot there exist no points below c < 0.1, which implies that the entire near-field of the flame has been modified. AswasdiscussedforcaseL5,mutualflameannihilationcancausethesuppression of temperature gradients. Case L1 experiences a similar phenomenon except with merging between recently siphoned layers and the flame front. Figure 4.14 shows a timeseriesofthetemperaturefieldcontoursforcaseL1leadinguptothisevent. At 5.33 ms the siphoning event is initiating in the top half of the domain and by 5.49 ms the siphoned layers are being pulled from the flame. At 5.46 ms the siphoned 64 Figure4.11: ContourplotsoftheT fieldontheleftwithcorrespondingscatterplots of∥∇c∥l F on the right for case L5 at time corresponding to minimum IMCM, 2.96 ms. Scatter plots only consider diagonally hatched regions in contour plots which refer to (a) entire flow field (b) near-field to the flame (c) near-field with region of mutual flame annihilation removed. layers are now merging with the flame. In Fig. 4.13c the regions of the flame that experience merging with recently 65 Figure4.12: ContourplotsoftheT fieldontheleftwithcorrespondingscatterplots of∥∇c∥l F on the right for case L2 at time corresponding to minimum IMCM, 3.89 ms. Scatter plots only consider diagonally hatched regions in contour plots which refer to (a) entire flow field (b) near-field to the flame. extinct layers are removed from consideration. The scatter plot of these regions showtheconditionalaverageisraisedtobeclosertothe1Dflamesolutionespecially near the peak value at c=0.6. The effect of gradients in the far-field for case L0.5 in Fig. 4.15 where Fig. 4.15a considers the entire-field and Fig. 4.15b considers the near-field. The difference between the two scatter plots only exists for c < 0.05, but the deviation from the 66 Figure4.13: ContourplotsoftheT fieldontheleftwithcorrespondingscatterplots of∥∇c∥l F on the right for case L1 at time corresponding to minimum IMCM, 5.65 ms. Scatter plots only consider diagonally hatched regions in contour plots which refer to (a) entire flow field (b) near-field to the flame (c) near-field with region of flame merging with recently extinct layers removed. 1D flame is minimal to start with. 67 Figure 4.14: Time series images of the T field for case L1 between 5.01 ms and 5.65 ms. Arrows qualitatively denote fluid velocity direction and magnitude. Green lines represent the 0.1 iso-surfaces of the scaled HRR. 4.7 Scaling with Pressure ValuesofP V >1(P V asdefinedinEq.(1.1c))seemtobeagoodindicatorofwhether a vortex will modify the flame structure, as discussed earlier. The smallest vortex, case L0.5, has P V ≈ 1, as shown in Table 3.1, and has minimal impact on the flame structure before it dissipates away. Larger vortices have P V >>1 and substantially modify the flame structure and even the free-stream composition. This work only considers conditions at atmospheric pressure, but it is of interest to see how vortex power scales with pressure and whether sub-flame-thickness scale eddies can have P V >1. If so, these eddies may be capable of stirring the flame’s thermal layer that 68 Figure4.15: ContourplotsoftheT fieldontheleftwithcorrespondingscatterplots of∥∇c∥l F ontherightforcaseL0.5attimecorrespondingtomaximumIMCM,1.60 ms. Scatter plots only consider diagonally hatched regions in contour plots which refer to (a) entire flow field (b) near-field to the flame. was not observed in this work. To evaluate how the vortex power of eddies with D V < l F scales with pressure we will first consider eddies with D V = l F . Recalling the definition of t D , t F , and P V in Eqs. (1.1a)-(1.1c) and setting D V =l F we end up with: P V = l F S 0 u ν (4.1) 69 The next step is to apply scaling laws of pressure to each term on the right-hand- side of Eq. (4.1). The l F and S 0 u terms each scale with pressure based on the overall reaction order, n, as: l F ∼ p − n/2 (4.2a) S 0 u ∼ p n/2− 1 (4.2b) and the kinematic viscosity scales with pressure as: ν ∼ p − 1 (4.3) Combining Eqs. (4.1)-(4.3) we arrive at: P V ∼ p 0 (4.4) where the vortex power of eddies with D V = l F is rather insensitive to pressure. Therefore, the P V < 1 of sub-flame-thickness scale eddies should apply to similar conditions at higher pressures. 4.8 Defining a Flame The introduction of thermal energy and temperature gradients into the free stream raisequestionsregardinghowtodefinetheflameandwhatshouldbeconsideredpart 70 of the flame. Basic combustion theory mandates that in order for a flame to exist their must be (a) temperature gradients that transport thermal energy upstream and (b) heat release that can sustain these temperature gradients. A possible interpretation of the flame structure, and one that has been the base of reasoning for most of this work, is that the this thermal energy that is many l F in distance from the reacting layer should be considered as the modified reactant stream. These modified reactants are not considered part of the flame, but as a part of the reactants. This point of view becomes complicated as the flame begins to consume these modified reactants potentially modifying the flame structure and the entire near-field of the flame. Another potential mode of understanding combines the classical broadened pre- heat zone view with the above mentioned modified reactants point of view. These modified reactants could be considered as a part of the turbulent flame structure; potentially as a third zone to the flame structure. This intermediate zone would be characterized by elevated temperature, modified composition, and significant dis- tance from the reacting layer regardless of whether temperature gradients exist. Large gradients in this intermediate zone will quickly dissipate due to the lack of heat release and reactions in general. 71 4.9 Conclusions Canonical vortex flame interaction simulations were carried out aiming to investi- gate quantitatively the effects of eddies of various scales on the topology and local structure of a lean atmospheric methane/air flame, and to provide further insight intothemechanismsthatareresponsiblefortheso-calledflamebroadeningofhighly turbulent premixed flames. To that end, four different eddy sizes were considered ranging from 0.5 to 5 times the laminar flame thickness computed for the original state of the reactants. The velocity scale of the largest eddy was chosen so that lo- cal extinction could occur while the smaller vortices were scaled so that they would exist in the same inertial sub-range of homogeneous isotropic turbulence. It was determined that due to severe change of flame topology and local extinc- tion events, unreacted formaldehyde and thermal energy would be transported and accumulate in the reactant pool through the mechanisms of flame siphoning and product-side flame annihilation. Flame siphoning is primarily driven by flame-scale vorticesinducingregionsoflargepositivecurvature. Product-sideflameannihilation is caused by vortices larger than the flame-scale warping the flame surface into an- nihilating with itself. Both of these mechanisms introduce intermediates, products, and thermal energy into the reactant pool. The accumulation of thermal energy in the reactant pool and mutual flame annihilation could skew the temperature gradients towards lower values, and this 72 could be incorrectly interpreted as flame broadening. Similarly, the accumulation of formaldehyde upstream of the flame could also lead to misinterpretation given that its concentration is used to mark the thickness of the preheat zone based on what is known for one-dimensional laminar flames. Regarding the effects of eddy scales on the flame, it was shown that eddies that are smaller than the laminar flame thickness have minimal measurable effects on the flame structure contrary to larger eddies that could modify the flame topology and local structure. The dissipation rates of sub-flame-scale vortices is rather high when computed with realistic values of viscosity, and as a result they do not survive long enough to enter the preheat zone and modify its structure. These results do not support the Damk¨ ohler second hypothesis and as a result, the general validity of arguments used to identify the thin reaction zone regime as well as its boundary with the corrugated flamelet regime in legacy turbulent premixed flame diagrams. An argument could be made though, that flame-turbulence interactions are no- tably more complex compared to the configuration considered in the present study, and thus it is conceivable that conditions allowing sub-flame-scale vortices to enter the flame do exist. However, such conditions could not be identified in the present study for highly energetic vortices. Nevertheless, if they exist the general validity of the Damk¨ ohler second hypothesis will still be in question given that such conditions may not correspond to a nominal flame structure (considered herein) that has been the basis for formulating scaling laws of turbulent combustion. 73 In closing, while the results of the present canonical study cannot reveal all intricacies associated with fully turbulent flows, the aim was to provide additional evidence/basis for guiding statistical analyses of complex reacting flows and the attendant physical interpretations. 74 Chapter 5: Future Work This work has demonstrated that two mechanisms are capable of pulling thermal energy, intermediates, and products into the reactants side of the flame without the existence of sub-flame-thickness scale eddies. While these VFI cases were a useful canonical configuration, it cannot replicate all of the aspects of turbulence interacting with the flame. Asanextstep, full3DDNSshouldbedoneandtheaforementionedmechanisms should be evaluated in this context. While 3D planar DNS is not a new aspect in combustion literature, searching for these two phenomenon in the context of re- evaluating regime diagrams is. Extension of this work to studying the broken reaction zone regime is also of interest. Whether that be through vortex flame interaction or DNS, investigating how reaction layers become distributed is an attractive research direction. Thisworkwasdoneusingleanconcentrationsofmethanewhichisnotsubjectto preferentialdiffusioninstabilities. Theuseofhydrogen,acarbonneutralfuelandre- newable energy alternative, as a reactant causes major thermo-diffusive instabilities 75 which could influence how it transitions between regimes of combustion. Specifi- cally, both mechanisms rely on the formation of curvature/peninsulas in the main flame surface to initiate. 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In: Zeitschrift Elektrochemie und angewandte physikalische Chemie 46.11 (1940), pp. 601–626. 82 Appendix A: Evaluating Numerical Dissipation In order to access the extent to which numerical diffusivity affects these solutions a non-reacting case was solved. The conditions of the smallest vortex case, L0.5, with a modified domain of D H = 9D V and W H = 9D V were used because this vortex is most affected by viscosity. The exact solution for the maximum speed of the vortex isgivenbyEq.A.1[29]. Theexactsolutionisplottedagainstthemaximumvelocity in the non-reacting simulation in Fig. A.1. There is a slight deviation between the simulated vortex speed and the exact speed in the first two milliseconds that slowly shrinks with time. Numerical diffusivity may slightly enhance the effective viscosity of the simulated solution, however it does not result in more than an 8% error in the maximum velocity. u max (t)=U θ D 2 V 8ν 3/2 t+ D 2 V 8ν − 3/2 (A.1) 83 Figure A.1: Exact solution of maximum speed of vortex compared to simulation. 84

Abstract (if available)

Abstract Classical turbulent flame regimes have long been used as the basis for understanding a turbulent flame's structure and developing turbulent flame models. These regimes are defined by qualitative scaling arguments regarding the role of turbulence in modifying the shape of the flame surface and the internal flame structure. One of these arguments, the Klimov-Williams criterion, states that when the smallest eddies in the turbulent flow, the Kolmogorov scale, are smaller than the flame thickness they can enter the preheat zone and cause mixing thereby increasing the flame thickness. Many experimental and numerical works show an increase in the flame thickness with increasing turbulence intensity. However, there is little direct evidence regarding the role of sub-flame-thickness scale eddies in broadening the flame structure.
The goal of this work is to evaluate the effect of small eddies on the flame structure and explore possible mechanisms that lead to a broadened preheat layer by simulating several cases of high-speed vortex-flame interaction. This configuration consists of a lean atmospheric pressure methane/air flame interacting with vortices ranging from five times to half of the laminar flame thickness. Vortices smaller than the flame thickness were found to have minimal impact on the flame before dissipating away. On the other hand, vortices on the scale of the flame or larger were able to transport thermal energy, intermediates, and products to the reactant side of the flame. Two separate mechanisms were responsible for this, flame siphoning induced by large curvature of the flame front, and product-side flame annihilation which is analogous to extinction in a symmetric counter-flow burner. These results raise questions about the validity of classical scaling arguments regarding broadened preheat zone flames.

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Creator Luna, Steven (author)

Core Title Re-assessing local structures of turbulent flames via vortex-flame interaction

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Degree Conferral Date 2022-12

Publication Date 12/15/2022

Defense Date 12/05/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag combustion,OAI-PMH Harvest,reacting flows,thermofluids,turbulent combustion,turbulent flame regimes,turbulent reacting flows

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Language English

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Advisor Egolfopoulos, Fokion (committee chair), Ronney, Paul (committee member), Tsotsis, Theodore (committee member)

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