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Analysis of blow-out mechanisms of turbulent swirl-stabilized non-premixed

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11th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute

March 24–27, 2019 Pasadena, California

Analysis of blow-out mechanisms of turbulent swirl-stabilized

non-premixed flames

Dong Li 1, Thomas Jaravel1, Matthias Ihme1,*

1Center for Turbulence Research, Stanford University, Stanford, CA 94305, United States *Corresponding Author Email: mihme@stanford.edu

Abstract: The understanding of flame blow-out is of fundamental importance for practical appli-cations. In particular, the reliable prediction of blow-out limits is of direct relevance for the design of gas turbine combustors that operate under fuel-lean conditions. The objective of this work is to investigate the physical mechanisms and parameters that control the transient blow-out dynamics of turbulent swirl-stabilized non-premixed flames using a large-eddy simulation database. To this end, three-dimensional Lagrangian flamelet structures are extracted and the temporal evolution of the mixture fraction conditioned profiles of temperature, heat release rate and scalar dissipation rate during the blow-out sequence are analyzed in detail. It is observed that the increase in the sca-lar dissipation rate at fuel-lean conditions is causal for the flame lift-off and subsequent blow-out. Keywords: Lagrangian flamelet structures, lean blow-out, swirl-stabilized non-premixed flame, large-eddy simulation

1. Introduction The understanding of flame blow-out is of fundamental importance for practical applications. With advances in diagnostic techniques and turbulent combustion models, the investigation of the mechanisms responsible for blow-out has become possible using physical experiments and numerical simulations. Early studies of blow-out dynamics primarily focused on bluff-body stabilized flames and semi-empirical correlations were proposed to predict blow-out limits [1-4]. Stöhr et al. [5] inves-tigated the blow-out mechanism of a partially premixed swirl-stabilized flame in a gas turbine model combustor using chemiluminescence imaging and simultaneous stereo-PIV and OH-PLIF measurements. The blow-out process was found to occur when the extinction of the flame root persisted over a period of the precessing vortex core (PVC) oscillation. Sutton and Driscoll [6] simultaneously measured the mixture fraction, scalar dissipation rate, temperature and fuel con-sumption rate in a turbulent non-premixed jet flame. It was observed that the strong instantane-ous scalar dissipation rate at the stoichiometric contour may lead to local flame extinction. Re-cently, Cavaliere et al. [7] examined the behavior of swirling premixed, non-premixed and spray flames close to blow-off limit and during blow-out transient. Computational studies on local and global extinction have been carried out with various com-bustion models, such as the Probability Density Function (PDF) model [8,9], Flamelet/Progress Variable (FPV) model [10, 11] and Conditional Moment Closure (CMC) model [12, 13]. Zhang and Mastorakos [14] performed large-eddy simulations (LES) of a swirling non-premixed me-thane flame to assess the capability and accuracy of the LES-CMC model to predict the blow-off condition. The blow-off air velocity obtained from the simulations were found to be larger than

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the experimental value by 25%. In addition, it was observed that the conditionally filtered stoi-chiometric scalar dissipation rate showed high-frequency and high-magnitude fluctuations as blow-off was approached. More recently, Ma et al. [15] investigated the flame structure and tran-sient blow-out dynamics in a swirl-stabilized combustor using two different combustion models, namely the FPV model and a thickened flame (TFLES) approach with finite rate chemistry. The comparison of the two models indicated quantitative difference in the prediction of the transient blow-out dynamics, and an early warning criterion was employed to identify precursors that trig-ger blow-out. Despite the recent progress, the numerical simulations of flame blow-out in turbu-lent swirl-stabilized combustors are comparatively limited. In particular, the blow-out mecha-nisms of swirl-stabilized non-premixed flames remain only incompletely understood due to the complex interactions between turbulence, chemistry, and combustor geometry. The objective of this study is to investigate the underlying physical mechanisms and parame-ters that control the transient blow-out dynamics of turbulent swirl-stabilized non-premixed flames using a LES database [15]. To this end, three-dimensional Lagrangian flamelet structures are extracted from instantaneous mixture fraction field and the temporal evolution of the mixture fraction conditioned profiles of temperature, heat release rate and scalar dissipation rate during the transient blow-out sequence are analyzed in detail. The remainder of this paper structured is as follows. The non-premixed flame configuration and LES-database considered in this work are summarized in Section 2. The flamelet extraction method is described in Section 3. The numeri-cal results and discussion are reported in Section 4. Finally, conclusions are drawn in Section 5. 2. Swirl-stabilized non-premixed flame configuration The swirl-stabilized non-premixed flame configuration considered in this study was designed at the University of Cambridge [7] to experimentally investigate the dynamics of blow-out for different flame configurations. The size of the rectangular combustion chamber is 95×95×150 mm3. Swirling air is provided by an annulus and the flame is initially stabilized by a bluff body with a diameter of 25 mm. Methane is injected into the combustor through a central pipe of di-ameter 4 mm with a constant velocity of 29.2 m/s. The air velocity is 15.3 m/s under stable con-ditions, while blow-out is induced by a sudden increase in the air velocity to 30 m/s. The inlet temperatures for both fuel and air are 298 K. LES of the turbulent swirl-stabilized methane/air flame has also been carried out by Ma et al. [15] at stable and blow-out operating conditions using FPV and TFLES models. Only the data-base obtained using TFLES-calculations are considered in this study. The reaction chemistry is represented by a reduced methane-air combustion mechanism derived by removing unimportant species and reactions from the detailed GRI 3.0 mechanism [16]. A more detailed description of the LES configuration can be found in Ref. [15]. 3. Flamelet extraction method In order to investigate the physical mechanisms that lead to blow-out in a swirl-stabilized combustor, instantaneous Lagrangian flamelets are extracted from the three-dimensional flow field. Similar to the methodology proposed by Chan et al. [17], the three-dimensional Lagrangian flamelet structures can be obtained by integrating the following equation:

(1)

where represents the vector of spatial coordinates, is the mixture fraction, is the normal vector of the mixture fraction isosurface. A schematic illustration of the flamelet extraction

dx = n dZ∇Z

,

x Z n

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method is shown in Figure 1. The instantaneous stoichiometric mixture fraction isosurface is shown in gray. The Lagrangian flamelet coordinate is constructed along the mixture fraction gra-dient direction n, with the starting point located on the stoichiometric isosurface. For each stoi-chiometric location, one instantaneous flame element can then be extracted by integrating Eq. (1) along the flamelet-aligned direction . As shown in Figure 1, the local flamelet structure col-ored by instantaneous temperature is quasi one-dimensional. It should be pointed out that the di-rection of the integration path includes both the fuel-lean and fuel-rich directions. Integration is terminated when a stationary point is reached in the mixture fraction field. Once the extraction has been performed, the mixture fraction conditioned profiles of quantities of interest, such as temperature, heat release rate and scalar dissipation rate, can be obtained through the interpola-tion onto each flamelet. The one-dimensional conditional temperature profiles of the flamelet satisfy the classical flamelet equations [18,19].

Figure 1: Schematic illustration of the flamelet extraction method on an instantaneous stoichio-metric mixture fraction isosurface (gray). Flamelet structure is colored by instantaneous tempera-ture and black arrows represent velocity vectors of the flamelet (scaled relatively by magnitude).

To describe the chemical reactions that occur in the vicinity of the stoichiometric mixture frac-tion isosurface, a large number of flamelets are extracted to obtain conditionally-averaged quan-tities, assuming axis-symmetric flow conditions. As an example, the mixture fraction conditioned temperature profiles as well as the corresponding conditional mean temperature profile are pre-sented in Figure 2. Unless otherwise stated, multiple flamelet structures considered in this study are extracted near the flame root region at the axial location x = 2 mm, which is very close to the nozzle exit, as shown in Figure 3. This location was selected to examine regions of high strain rates and to examine their importance in controlling the local extinction of turbulent swirl-stabilized flames [5].

n

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Figure 2: Conditional temperature profiles as a function of mixture fraction for the flamelets ex-tracted at the axial location x = 2 mm. Red line denotes the conditional mean temperature profile.

Figure 3: Lagrangian flamelet structures extracted from instantaneous stoichiometric mixture

fraction isosurface at the axial location x = 2 mm: (a) three-dimensional flamelet structures; (b) projection of three-dimensional flamelet structures onto the y-z plane. Note that the flamelet

structures are colored by temperature.

4. Results and Discussion

By utilizing the flamelet extraction method described in Section 3, three-dimensional Lagran-gian flamelet structures are extracted from the time-resolved LES database to obtain time-dependent and mixture fraction conditioned results. The temporal evolution of conditionally-averaged quantities is analyzed in order to examine the physical mechanisms responsible for blow-out in a turbulent swirl-stabilized combustor. Figure 4 shows the temporal evolution of the mixture fraction conditioned temperature profiles averaged over 300 flamelets that are extracted at the same axial location x = 2 mm. Here t = 0 ms corresponds to the time instance at which the air velocity is increased from 15.3 m/s to 30 m/s, while the fuel inlet velocity remains constant during blow-out. Hence, the overall equivalence ratio is reduced from 0.39 to 0.2. At first instants (t = 0 - 5 ms), the conditionally-averaged tem-perature gradually decreases with time, which is in agreement with the scattered data of tempera-ture in mixture fraction space reported in Ma et al. [15]. Meanwhile, the peak location of the

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temperature profiles tends to shift toward the fuel-rich side in the first phase of the blow-out se-quence. This is mainly attributed to the strong flame lift-off as a result of the velocity impulse. Then, the conditional mean temperature remains nearly constant until about t = 8 ms (Figure 4b). After that the temperature profiles exhibit strong fluctuations, resulting in an initial increase in temperature and subsequent temperature reduction (t = 8 - 11 ms), as shown in Figure 4(c). After a transition period over which the temperature profiles remain almost unchanged (Figure 4d), strong temperature fluctuations reoccur (t = 14 - 17 ms). In fact, significant local extinction and reignition events take place during the second phase of the sequence. In other word, the condi-tional mean temperature profiles exhibit intermittent behavior before the onset of complete ex-tinction. This is probably due to the fact that the non-premixed flame intermittently lifts-off the circular bluff body during the transient blow-out, which is also captured in previous experiments using high-speed OH-PLIF imaging [7]. In the third phase (t = 21 - 25 ms), shown in Figure 4(f), the temperature is reduced and the flame gradually approaches global extinction. After t = 25 ms, the flame is completely extinguished.

Figure 4: Temporal evolution of mixture fraction conditioned temperature profiles averaged over

300 flamelets extracted at the same axial location x = 2 mm.

Figure 5 reports the time evolution of the conditional mean heat release rate during the transi-ent blow-out. The location of the stoichiometric mixture fraction, Zst = 0.054, is shown by a ver-tical dashed line. As seen in Figure 5(a), the mixture fraction conditioned heat release rate firstly exhibits significant resistance and its peak value is found to increase when blow-out is triggered. This is consistent with the numerical results of volume integrated heat release rate reported in previous studies [14]. After t = 1.5 ms, the peak magnitude of the heat release rate starts to de-crease progressively until t = 5 ms. In fact, the incoming fresh reactants are pushed toward the region far away from the nozzle exit at this instant due to the increase in the air inlet velocity, as shown in Figure 6(c). As time progresses (t = 6 - 20 ms), local extinction induces high-magnitude fluctuations of the conditionally-averaged heat release rate (Figure 5b). In the third phase of the blow-out sequence (t = 21 - 25 ms), the heat release rate gradually reduces and eventually approaches zero after t = 25 ms, indicating complete flame extinction.

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Figure 5: Temporal evolution of conditionally-averaged heat release rate with respect to mixture

fraction. The vertical dashed line represents the location of stoichiometric mixture fraction.

Figure 6: Time sequence of instantaneous heat release rate during the blow-out transient in a cen-

tral x-y plane. The stoichiometric contour is superposed, denoted by the solid red line.

To further analyze the blow-out mechanisms, the contours of instantaneous heat release rate during the blow-out event are plotted in Figure 6. For the stable case (t = 0 ms), combustion mainly occurs in the shear layer between the swirling air flow and inner recirculation zone. Con-sistent with the quantitative results of Figure 5, pronounced localized extinction is present during the second phase of the blow-out event. Furthermore, the flame reignition behavior is clearly vis-ible in Figure 6(d-f), characterized by localized pockets of high heat-release in regions close to the nozzle exit. As the flame gradually approaches the global extinction, it is interesting to ob-serve that the area of the instantaneous stoichiometric mixture fraction iso-contour tends to de-crease, leading to a significant change in the scalar dissipation rate, which will be discussed be-low. In addition, the stoichiometric iso-contour is found to become corrugated and fragmented at conditions close to blow-off. The time evolution of the conditionally-averaged scalar dissipation rate is presented in Figure 7. In general, the peak value of the scalar dissipation rate increases gradually during the initial phase of the blow-out event, as shown in Figure 7(a). This is probably due to the fact that the strain rate is obviously enhanced under blow-out conditions because of the increase in the air bulk velocity. The peak location of the scalar dissipation rate occurs in the region of highest

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shear. It is apparent that the peak location shifts toward the fuel-rich side, which is in agreement with previous results in a turbulent reacting jet-in-cross-flow [17]. Subsequently, significant lo-cal extinction events occur that are accompanied by strong fluctuations of the conditional mean scalar dissipation rate in the second phase of the blow-out sequence (t = 6 - 20 ms). However, it can be seen from Figure 7(c) that the high scalar dissipation rate continues to appear during the third phase (t = 21 - 25 ms), which is a direct indicator for flames approaching complete extinc-tion.

Figure 7: Temporal evolution of conditionally-averaged scalar dissipation rate.

Figure 8: Scatter plots of temperature as a function of scalar dissipation rate at stoichiometric condition. The scatter data are extracted from stoichiometric mixture fraction isosurface at the same axial location x = 20 mm. Red line denotes the steady-state S-curve obtained from the

steady flamelet equation with unity Lewis number assumption.

In order to further investigate the impact of scalar dissipation rate on blow-out, Figure 8 plots the temporal evolution of the scatter data of temperature as a function of stoichiometric scalar dissipation rate during the blow-out transient. For reference, the S-shaped curve obtained from the steady flamelet solution is shown by the solid red line. At stable operating conditions, these scatter data, which are extracted from stoichiometric mixture fraction isosurface at the same axial location x = 20 mm, follow the upper stable branch of the S-shaped curve, as shown in Figure 8 (a). With the change in the air inflow conditions, the flame tends to distribute in regions away from the upper branch, indicating the occurrence of local flame extinction. In particular, the local extinction phenomenon is more prominent in the second phase of the blow-out sequence (Figure 8d-f), featuring several clusters below the middle branch of the S-shaped curve. After t = 25 ms, nearly all scatter points are concentrated in the regions with low stoichiometric temperature and the flame blow-off takes place. In fact, the succession of strong fluctuations of the scalar dissipa-

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tion rate in Figure 7 increases the fraction of local flame extinction on the stoichiometric mixture fraction isosurface, eventually leading to complete extinction. 5. Conclusions In this work, physical mechanisms responsible for blow-out were investigated by analyzing a LES database of a turbulent swirl-stabilized non-premixed methane/air flame. For this, three-dimensional Lagrangian flamelet structures were extracted from instantaneous stoichiometric mixture fraction isosurfaces to obtain time-dependent and mixture-fraction conditioned numeri-cal results. The temporal evolution of conditionally-averaged profiles of temperature, heat re-lease rate and scalar dissipation rate during the transient blow-out sequence was analyzed. It is found that the local flame extinction and reignition events are closely related to large-magnitude fluctuations of these conditionally-averaged quantities. Conditional mean temperature profiles exhibit intermittent behavior before the onset of complete extinction. More importantly, this analysis indicates that the scalar dissipation rate plays an important role in the flame blow-out dynamics. A prominent source-mechanism triggering blow-out is the appearance of relatively high conditionally-averaged scalar dissipation rate. Successive strong fluctuations of the condi-tional mean scalar dissipation rate increase the extinguished fraction on the stoichiometric mix-ture fraction isosurface, eventually leading to complete extinction. 6. Acknowledgements Financial support through NASA Transformational Tools and Technologies Project with Award #NNX15AV04A and through Air Force Office of Scientific Research with Award #FA8650-17-C2036 is gratefully acknowledged. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercompu-ting (NAS) Division at Ames Research Center. 7. References [1] E. DeZubay, Characteristics of disk-controlled flames, Aero Digest 61 (1950) 54-56. [2] H.C. Hottel, G.C. Williams, W.P. Jensen, A.C. Tobey, P.M.R. Burrage, Modeling studies of baffle-type combustors, Symp. (Int.) Combust. 9 (1963) 923-935. [3] S.L. Plee, A.M. Mellor, Characteristic time correlation for lean blowoff of bluff-body-stabilized flames, Combust. Flame 35 (1979) 61-80. [4] K. Radhakrishnan, J.B. Heywood, R.J. Tabaczynski, Premixed turbulent flame blowoff velocity correlation based on coherent structures in turbulent flows, Combust. Flame 42 (1981) 19-33. [5] M. Stöhr, I. Boxx, C. Carter, W. Meier, Dynamics of lean blowout of a swirl-stabilized flame in a gas turbine model combustor, Proc. Combust. Inst. 33 (2011) 2953-2960. [6] J.A. Sutton, J.F. Driscoll, Imaging of local flame extinction due to the interaction of scalar dissipation layers and the stoichiometric contour in turbulent non-premixed flames, Proc. Combust. Inst. 31 (2007) 1487-1495. [7] D.E. Cavaliere, J. Kariuki, E. Mastorakos, A Comparison of the Blow-Off Behaviour of Swirl-Stabilized Premixed, Non-Premixed and Spray Flames, Flow Turbul. Combust. 91 (2013) 347-372. [8] J. Xu, S.B. Pope, PDF calculations of turbulent nonpremixed flames with local extinction, Combust. Flame 123 (2000) 281-307. [9] W.P. Jones, V.N. Prasad, Large Eddy Simulation of the Sandia Flame Series (D–F) using the Eulerian stochastic field method, Combust. Flame 157 (2010) 1621-1636.

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[10] M. Ihme, C.M. Cha, H. Pitsch, Prediction of local extinction and re-ignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach, Proc. Combust. Inst. 30 (2005) 793-800. [11] M. Ihme, H. Pitsch, Prediction of extinction and reignition in nonpremixed turbulent flames using a flamelet/progress variable model, Combust. Flame 155 (2008) 70-89. [12] A. Garmory, E. Mastorakos, Capturing localised extinction in Sandia Flame F with LES–CMC, Proc. Combust. Inst. 33 (2011) 1673-1680. [13] H. Zhang, A. Garmory, D.E. Cavaliere, E. Mastorakos, Large Eddy Simulation/Conditional Moment Closure modeling of swirl-stabilized non-premixed flames with local extinction, Proc. Combust. Inst. 35 (2015) 1167-1174. [14] H. Zhang, E. Mastorakos, Prediction of Global Extinction Conditions and Dynamics in Swirling Non-premixed Flames Using LES/CMC Modelling, Flow Turbul. Combust. 96 (2015) 863-889. [15] P.C. Ma, H. Wu, J.W. Labahn, T. Jaravel, M. Ihme, Analysis of transient blow-out dynamics in a swirl-stabilized combustor using large-eddy simulations, Proc. Combust. Inst., doi:10.1016/j.proci.2018.06.066(2018). [16] G.P. Smith, D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eiteneer, M. Goldenberg, C.T. Bowman, R.K. Hanson, S. Song, W.C. Gardiner, Jr., V.V. Lissianski, Z. Qin, GRI 3.0 Mechanism, 1999. [17] W.L. Chan, H. Kolla, J.H. Chen, M. Ihme, Assessment of model assumptions and budget terms of the unsteady flamelet equations for a turbulent reacting jet-in-cross-flow, Combust. Flame 161 (2014) 2601-2613. [18] N. Peters, Local quenching due to flame stretch and non-premixed turbulent combustion, Combust. Sci. Technol. 30 (1983) 1-17. [19] N. Peters, Laminar diffusion flamelet models in non-premixed turbulent combustion, Prog. Energy Combust. Sci. 10 (1984) 319-339.

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