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Variation of **flame** front geometry in conical **turbulent** **premixed** methane/air flames
Smallwood, G. J.; Deschamps, B. M.; Gulder, O. L.; Snelling, D. R.

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Gulder, O. L.; Smallwood, Gregory J.; Wong, R.; Snelling, D.R.; Smith, R.; Deschamps, B. M.; Sautet, J. -C.

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Wong, R.; Sautet, J. C.; Snelling, David; Smallwood, Gregory; Gulder, O. L.

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P /¼0:65 ¼ 0:97.
The ORZ space-averaged **flame** intensity is plotted over time in Fig. 15 for / ¼ 0:60; / ¼ 0:63; / ¼ 0:66 along with its discrete
Fourier transform using the fast Fourier transform (FFT) algo- rithm. The spectral analysis shows the presence of low frequency events in the range (1 Hz–10 Hz) and a clear tone occurring around 28 Hz. The Strouhal number associated with this peak at 28 Hz, based on the inlet diameter and the inlet bulk velocity, is St 0:12. From the temporal variation of the signal, we see that the low frequency events correspond to the re-appearance of the **flame** in the ORZ. In some of these appearance instances, the **flame** reaching the ORZ is quickly extinguished. In other instances, the **flame** is advected along the outer recirculation vortex ring, sur- vives and rotates around the combustor’s centerline as it propa- gates. This rotation motion was highlighted in our previous work and associated with the 28 Hz frequency peak. It was also found to be dominated by hydrodynamics and not fuel dependent [ 24 ]. The two frequency bands observed here using **flame** chemilumi- nescence data were also confirmed based on the velocity field: we performed a dynamic mode decomposition (DMD) of the instanta- neous PIV measurements [ 25 ] to extract dominant dynamics of the reacting flow for the different **flame** macrostructures. This approach showed that the transition from configuration III to IV is associated with these frequency bands, as well. In addition, the low frequency band was also linked to changes in the IRZ struc- ture [ 25 ]. Low frequency motion of the IRZ has been previously highlighted in the bubble-type vortex breakdown [ 14 ]. Most prob- ably, this low frequency motion is related to the cyclic filling and emptying of the vortex breakdown bubble volume that has been previously reported by Brucker and Althaus [ 26 ] as well as Billant et al. [ 27 ]. During this motion, the incoming fluid through the an- nular jet around the bubble is entrained inside the bubble from the downstream part of the bubble then ejected from it from the upstream part. Billant et al. [ 27 ] proposed an approximation for the frequency of this filling and emptying cycle based on a simple scaling analysis: f / V= _ Q with V being the volume of the inner recirculation bubble and _ Q being the volumetric flow rate into the bubble. In the case of the swirling flow setup studied in this paper,

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The paper is organized as follows: Section 2.1 presents the target conﬁguration followed by its acoustic characterization in Section 2.2. To do so, a 3D Helmholtz solver is used to provide all modes of the set-up before performing LES. After the presentation of the LES solver (Section 3), the simulation is validated against experimental data for both **non**-reacting and reacting ﬂows (Section 4). Sections 5 and 6 compare LES and experimental observations of self-excited longitu- dinal and transverse modes, respectively. The resulting pressure am- plitudes and phases are also compared to the Helmholtz solver pre- dictions to identify the mode natures.

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This article describes recent progress on **premixed** **flame** dynamics interacting with acoustic waves. Expressions are derived to determine the stability of combustors with respect to thermoacoustic oscillations. The validity of these expressions is general, but they are illustrated in laminar systems. Laminar burners are commonly used to elucidate the response of **premixed** flames to incoming flow perturbations, highlight the role of acoustic radiation in their stability, identify modes associated with thermoacoustic intrinsic instabilities and decipher the leading mechanisms in annular systems with multiple injectors. Many industrial devices also operate in a laminar **premixed** mode as, for example, domestic gas boilers and heaters equipped with matrix burners for material processing in which unconfined flames are stabilized at one extremity of the system. This article proposes a systematic approach to determine the stability of all these systems with respect to thermo-acoustic oscillations by highlighting the key role of the burner impedance and the **flame** transfer function (FTF). This transfer function links in frequency space incoming flow perturbations to heat release rate disturbances. This concept can be used in the **turbulent** **flame** case as well. Weakly nonlinear stability analysis can also easily be conducted by replacing the FTF by a **Flame** Describing Function (FDF) in the expressions derived in this work. The response of **premixed** flames to harmonic mixture compositions and flowrate perturbations is then revisited and the main parameters controlling the FTF are described. A theoretical framework is finally developed to reduce the system thermoacoustic sensitivity by tailoring the FTF.

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the colormap shows the light intensity recorded by the camera
0 and 1 in the unburned and burned gas respectively. This binarization procedure leads irremediably to a digitization noise (pixelization) which, in the present case, is smoothed using a low-pass Gaussian filter, with filter size equal to 3 times the spatial resolu- tion. It was checked that doubling filter size did not yield observable changes on the properties of interest (namely the **flame** wrinkling distribution § III ). This indicates that the present measurements are well re- solved and that the filter size that is used here is much smaller than that of the smallest **flame** wrin- kling characteristic length-scale. An example of **flame** contour detection, superimposed on the original im- age is presented as an illustration in Fig. 2 . For the present case, we made the choice of focusing only on the longest contour representing the largest topolog- ically connected object, whereas holes and pockets are not taken into account. The contribution of these missing **flame** holes and pockets to e.g. the **flame** surface density was rather limited notwithstanding the relatively low turbulence intensity of our experi- ments. Future work is however needed to incorporate these disconnected objects into a more self-consistent description. The axis coordinate system is the fol- lowing, the streamwise distance x coincides with the direction of the bulk flow whereas the transverse dis- tance is noted y (Fig. 2 ).

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at (or close to) the leading edge is not substantially influenced by the heat release, contrary to the reaction zone where the increase in e.g. fluid viscosity is important and strongly alters the turbulence statistical characteristics. In other words, modelling strategies will be simplified as there is no need to account for the effect of temperature increase on the dynamical straining. The third reason is that there is a long tradition of theoretical work (see e.g. the review paper by Lipatnikov & Chomiak ( 2005 )) revealing the importance of concept of **flame** leading points, whose positions depend obviously on the leading edge displacement speed. A recent study presented at the last symposium (Kim 2017 ) highlights that this concept remains very attractive and has strong potential for modelling **turbulent** **premixed** flames. A better understanding of the kinematic features of the leading edge and its dependence to curvature and hydrodynamic straining is thus of capital importance in this context. The fact that the particular isotherm which is tracked here is not accurately known appears as problematic only in an experimental perspective. It does not preclude using hS u

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This study focuses on the response of **premixed** flames to a transient hydrodynamic perturbation in an intermediate situation between laminar stretched flames and **turbulent** flames: an axisymmetric vortex interacting with a **flame**. The reasons motivating this choice are discussed in the framework of **turbulent** combustion models and **flame** response to the stretch rate. We experimentally quantify the dependence of the **flame** kinematic properties (displacement and consumption speeds) to geometrical scalars (stretch rate and curvature) in flames characterized by different effective Lewis numbers. Whilst the displacement speed can be readily measured using particle image velocimetry and tomographic diagnostics, providing a reliable estimate of the consumption speed from experiments remains particularly challenging. In the present work, a method based on a budget of fuel on a well chosen domain is proposed and validated both experimentally and numerically using two-dimensional direct numerical simulations of **flame**/vortex interactions. It is demonstrated that the Lewis number impact neither the geometrical nor the kinematic features of the flames, these quantities being much more influenced by the vortex intensity. While interacting with the vortex, the **flame** displacement (at an isotherm close to the leading edge) and consumption speeds are found to increase almost independently of the type of fuel. We show that the total stretch rate is not the only scalar quantity impacting the **flame** displacement and consumption speeds and that curvature has a significant influence. Experimental data are interpreted in the light of asymptotic theories revealing the existence of two distinct Markstein numbers, one characterizing the dependence of **flame** speed to curvature, the other to the total stretch rate. This theory appears to be well suited for representing the evolution of the displacement speed with respect to either the total stretch rate, curvature or strain rate. It also explains the limited dependence of the **flame** displacement speed to Lewis number and the strong correlation with curvature observed in the experiments. An explicit relationship between displacement and consumption speeds is also given, indicating that the fuel consumption rate is likely to be altered by both the total stretch rate and curvature.

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Figure 6 **Flame** Surface Density of OH for **premixed** and stratified flames
Although the bias of the FSD profiles did not vary among conditions, comparing the homogeneous and stratified profiles reveals a **non**-linear increase in FSD with increasing gradient. The effect is strongest for the weaker gradients but levels off as stratification increases. This was expected based on the qualitative visual inspection of individual fluorescence images, in which stronger mixture gradients were associated with increased wrinkling and corrugation of the **flame** front, ultimately leading to the appearance of local extinctions along the stratified front. The appearance of extinctions explains the levelling off of FSD for the largest mixture gradients. Although the measured **flame** brush thickness (defined as the perpendicular distance between 〈c〉=0.1 and 〈c〉=0.9 contours) was consistently greater with stratification (~10.5 mm compared to 9.5 mm for the homogeneous **flame** at the same axial position x = 45 mm above the exit of the burner), it did not change significantly as the gradient was increased. This suggests that the dominant effect of large scale mixture gradients may be to enhance both the number and intensity of wrinkles, similar to the reported effects of small scale inhomogeneities in equivalence ratio [6,7].

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Due to their negative impacts on environment and human health, future reg- ulations on soot emissions are expected to become stricter, in particular by controlling the size of the emitted particles. Therefore, the development of pre- cise and sophisticated models describing the soot production, such as sectional methods, is an urgent scientific and industrial challenge. In this context, the first objective of this work is to use for the first time a sectional model to per- form an LES of a sooting **turbulent** flames in order to demonstrate its capacities. For this, the whole LES formalism for this approach is developed. It includes state-of-art models for the description of the gaseous phase and an extension of a soot subgrid intermittency model to the sectional approach, originally pro- posed for the hybrid method of moments. Then, the LES is used to analyze a **turbulent** **non**-**premixed** ethylene-air jet diffusion **flame** and results are validated by available experimental data. The quality of results for the gaseous phase is satisfactory and results for the solid phase show a reasonable agreement with the experimental results in terms of localization, intermittency and soot volume fraction magnitude. Once the coupled LES-sectional approach validated, having access to the full information on the spatial and temporal evolution of the soot Particle Size Distribution (PSD), the second objective of this work is to provide

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Another issue with **turbulent** flames is that the instantaneous **flame** surface area is generally not known. It is then difficult to compare, quantitatively, the measured chemiluminescence inten- sities to numerical results from 1-D FPF simulations, where the chemiluminescence intensities are computed per unit of **flame** sur- face area. This problem can however be circumvented by examin- ing chemiluminescence intensity ratios between different couples of excited radicals. This method allows removing the contribution of the **flame** surface area [11,14,16,18–20] . In this case, species con- centrations cannot however be compared directly.

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Keywords: **Premixed** **Turbulent** Combustion, **Flame** Brush, **Flame** wrinkling
1. Introduction
Turbulence gives rise to a large and continuous range of scales. The largest eddies reflect the way kinetic energy is injected in the system and therefore depend on the type of flow. These large-scales are sometimes referred to as coherent structures whose topology and dynamic are strongly affected by initial and boundary conditions. In contrast, one frequently asserts that the anisotropic and **non**- universal influence of the largest scales diminishes during the first **non**-linear local interactions and is thus expected to decline at the smallest scales. Consequently, it is still often postulated that the smallest scales have the best prospect of being universal or quasi-universal [1]. Since, in **premixed** combustion, the corrugation of the **flame** front results mainly from the interaction with turbulence, it may be argued that such a statement holds also for the statistics of the **flame** front wrinkles at a given scale. This intuitive conjecture encourages us in exploring the multi-scale nature of **turbulent**

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1. Introduction
The instabilities of swirled **turbulent** flows have been the subject of intense research in the last ten years. One important is- sue has been to identify the possibilities offered by simulation and especially Large Eddy Simulation (LES) to predict self-excited com- bustion oscillations. The specific example of swirled combustors where flames couple with acoustic modes has received significant attention [1–4] because such oscillations are often found in real gas turbines [5,6] . An important question in swirled unstable flames is the effect of mixing on stability. In most real systems, combustion is not fully **premixed** and even in laboratories, very few swirled flames are truly fully **premixed**. The effects of equivalence ratio fluctuations on **flame** stability in combustors have been known for a long time [7,8] : changes in air inlet velocity induce variations of the flow rate through the **flame** but may also induce mixing fluc- tuations and the introduction into the combustion zone of **non**- constant equivalence ratio pockets. These pockets create unsteady combustion and can generate instabilities.

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Fig. 6. Longitudinal cuts of the mesh passing through the middle of the combustion chamber for configuration BBBS SS. (a) Combustion chamber. (b) Zoom around the third baffle plate and the central obstacle. (c) Global view of the computational domain including the plenum which mimics the atmosphere. All dimensions are in mm.
The computational domain includes the venting chamber and a plenum, located at its outlet, which mimics the atmosphere. For all configurations, meshes are made of tetrahedral elements. The number of elements is constant for all LES configurations at all scales, around 20 million. Figure 6 shows a typical mesh for con- figuration BBBS SS. In the first two thirds of the combustion cham- ber ( x < 160 mm), the mesh resolution 1x (calculated from the nodal volume) is about 0.5, 3 and 12.2 mm respectively for the SS, MS and LS experiments. This mesh density has been chosen in order to ensure that the **flame**, even thickened, remains thinner than the distance between the bars of a baffle plate. As an exam- ple, for C 3 H 8 –air LES, the resulting maximum thickening factors F are of the order of 7.3 at SS, 44 at MS and 179 at LS (the **flame** is resolved on 5 grid points). The mesh is progressively coars- ened in the last third of the chamber, well after the central obsta- cle. The resolution at the exit of the combustion chamber reaches 1.5, 9 and 37 mm respectively for the SS, MS and LS configura- tions. The whole domain is initialized at rest. The venting chamber is initialized with a perfectly **premixed** mixture ( 8 = 1.0 for cases with CH 4 –air or C 3 H 8 –air mixtures, 8 = 0.7 for H 2 –air mixtures) at atmospheric pressure and temperature. The plenum is filled with air only. The walls of the venting chamber and the obstacles are modeled as **non**-slip walls. Navier–Stokes Characteristic Bound- ary Conditions (NSCBC) [67,68] are used on the borders of the plenum.

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The previous section has shown the dependence of the results on the **turbulent** combustion model. At this point, an important question is mesh dependency [73,74] . This issue is all the more important for the following since the grid resolutions used in the SS configuration and in the MS and LS configurations differ sig- nificantly (0.5, 3 and 12.2 mm respectively in the refined region). In order to assess the quality of the LES and in particular its de- pendency to the grid resolution, a VRLES was performed and com- pared to the LES presented in the last section. Configuration OOBS is considered here. This configuration induces a weakly **turbulent** flow for which the requirements in terms of mesh resolution are expected to be much lower than for the base case BBBS for in- stance. The efficiency function of Colin et al. is used in both cases. The key features of this VRLES are summarized in Table 5 in terms of number of cells and characteristic length scales: on this very fine grid, the level of description of the simulation corresponds to a Quasi-Direct Numerical Simulation (QDNS) of the **flame**. The LES models described above are always activated during the simula- tion. They naturally degenerate towards DNS if the mesh resolu- tion is high enough. Verifying that their contribution in this QDNS case remains very low is a good way to estimate the quality of the simulation. The objectives of this comparison are thus manifold:

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This article describes recent progress on **premixed** **flame** dynamics interacting with acoustic waves. Expressions are derived to determine the stability of combustors with respect to thermoacoustic oscillations. The validity of these expressions is general, but they are illustrated in laminar systems. Laminar burners are commonly used to elucidate the response of **premixed** flames to incoming flow perturbations, highlight the role of acoustic radiation in their stability, identify modes associated with thermoacoustic intrinsic instabilities and decipher the leading mechanisms in annular systems with multiple injectors. Many industrial devices also operate in a laminar **premixed** mode as, for example, domestic gas boilers and heaters equipped with matrix burners for material processing in which unconfined flames are stabilized at one extremity of the system. This article proposes a systematic approach to determine the stability of all these systems with respect to thermo-acoustic oscillations by highlighting the key role of the burner impedance and the **flame** transfer function (FTF). This transfer function links in frequency space incoming flow perturbations to heat release rate disturbances. This concept can be used in the **turbulent** **flame** case as well. Weakly nonlinear stability analysis can also easily be conducted by replacing the FTF by a **Flame** Describing Function (FDF) in the expressions derived in this work. The response of **premixed** flames to harmonic mixture compositions and flowrate perturbations is then revisited and the main parameters controlling the FTF are described. A theoretical framework is finally developed to reduce the system thermoacoustic sensitivity by tailoring the FTF.

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Possibility of performing tomography to detect **flame** contour.
PIV performed ZOOMED and UNZOOMED.
Next future steps
• Validate the NOSE measurements by testing experimental points in common with the sphere in **turbulent** and laminar case.