A DNS study on the stabilization mechanism of a turbulent lifted ethylene jet flame in highly-heated coflow

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Proceedings of the Combustion Institute 33 (2011) 1619–1627

Combustion Institute www.elsevier.com/locate/proci

A DNS study on the stabilization mechanism of a turbulent lifted ethylene jet flame in highly-heated coflow Chun Sang Yoo a,⇑, Edward S. Richardson b, Ramanan Sankaran c, Jacqueline H. Chen b a

School of Mechanical and Advanced Materials Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Republic of Korea b Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969, USA c National Center for Computational Sciences, Oak Ridge National Laboratories, Oak Ridge, TN 37831-06008, USA

Abstract Direct numerical simulation (DNS) of the near-field of a three-dimensional spatially-developing turbulent ethylene jet flame in highly-heated coflow is performed with a reduced mechanism to determine the stabilization mechanism. The DNS was performed at a jet Reynolds number of 10,000 with over 1.29 billion grid points. The results show that auto-ignition in a fuel-lean mixture at the flame base is the main source of stabilization of the lifted jet flame. The Damko¨hler number and chemical explosive mode (CEM) analysis also verify that auto-ignition occurs at the flame base. In addition to auto-ignition, Lagrangian tracking of the flame base reveals the passage of large-scale flow structures and their correlation with the fluctuations of the flame base similar to a previous study (Yoo et al., J. Fluid Mech. 640 (2009) 453–481) with hydrogen/air jet flames. It is also observed that the present lifted flame base exhibits a cyclic ‘saw-tooth’ shaped movement marked by rapid movement upstream and slower movement downstream. This is a consequence of the lifted flame being stabilized by a balance between consecutive auto-ignition events in hot fuel-lean mixtures and convection induced by the high-speed jet and coflow velocities. This is confirmed by Lagrangian tracking of key variables including the flame-normal velocity, displacement speed, scalar dissipation rate, and mixture fraction at the stabilization point. Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Direct numerical simulation (DNS); Auto-ignition; Turbulent lifted flame; Ethylene; Reduced mechanism

1. Introduction The stabilization mechanism of turbulent lifted jet flames in a heated environment is of practical ⇑ Corresponding author. Fax: +82 52 217 2309.

E-mail address: [email protected] (C.S. Yoo).

importance as lifted flames exist in the near-field of fuel jets in diesel engines and gas turbines for power generation [1–6]. Therefore, numerous experimental and numerical studies have been conducted and various theories have been also proposed to explain the stabilization mechanisms of turbulent lifted jet flames. The theories can be categorized based on the premixedness of the

1540-7489/$ - see front matter Ó 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.proci.2010.06.147

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mixture upstream of the flame base: premixed flame theory, non-premixed flamelet theory, and edge flame theory. Based on the effect of local turbulence structure, stabilization can be described by turbulence intensity theory and large eddy theory. The readers are referred to comprehensive reviews by Lyons [5] and Pitts [6] for details of the theories. Auto-ignition was found to be another relevant stabilization mechanism in a heated environment [2,3,7]. From a previous DNS study [7], the stabilization mechanism of a turbulent lifted hydrogen jet flame in a hot coflow was found to be due to the auto-ignition of fuel-lean mixtures supported by the hot coflow temperature exceeding the auto-ignition limit. It was also found that the lifted flame base exhibits a cyclic movement by the competition between auto-ignition in the fuel-lean mixtures and the passage of large-scale flow structures [7]. Recently, Pickett et al. [8] experimentally investigated the lift-off stabilization of a high-speed diesel jet in a hot environment and at high pressure in a constant pressure spherical bomb. The results show that the lift-off height exhibits a saw-tooth shaped movement due to consecutive auto-ignition events as shown in Fig. 1. However, the interaction between auto-ignition and the local flow field was not fully appreciated due to the dearth of simultaneous experimental measurements of key species and velocity fields. In the present study, in order to understand the stabilization mechanism of a high-speed fuel jet in a hot environment, three-dimensional direct numerical simulation (DNS) of a turbulent lifted ethylene jet flame in a hot coflow was performed using a reduced ethylene–air reaction mechanism. To mimic the hot environment, the coflow temperature is specified sufficiently high such that auto-ignition can readily occur, even in the presence of thermal dissipation due to turbulent mixing. However, the speeds of the fuel jet and the coflow are also specified high enough to lift the flame from the fuel jet nozzle. Ethylene was adopted as the fuel because it is a relatively simple hydrocarbon and its reaction mechanism is well-known. Moreover, the recent development of novel mechanism reduction methods [9] such as the direct relation graph (DRG)

method enables full three-dimensional DNS of simple hydrocarbon fuel jets with the help of fast-growing supercomputing resources [10]. Following the methods developed in the previous study of a lifted hydrogen jet flame [7], the objective of the present DNS study is to determine the role of auto-ignition in the stabilization of a lifted ethylene flame by examining in detail the instantaneous and time-averaged flame/flow characteristics near the flame base. In addition, the role of the near-field, large-scale fluid motion in the stabilization mechanism is elucidated by Lagrangian tracking of the flame base together with relevant scalar and velocity fields. 2. Problem configuration Similar to the previous DNS study of turbulent lifted hydrogen jet flame [7], the DNS of a turbulent lifted ethylene jet flame was performed in a three-dimensional slot-burner configuration. Fuel issues from a central jet composed of 18% ethylene ðC2 H4 Þ and 82% nitrogen by volume at an inlet temperature of T j ¼ 550 K. The central jet is surrounded on either side by co-flowing heated air streams at T c ¼ 1550 K and at atmospheric pressure. The temperature is high enough for the mixtures upstream of the flame base to auto-ignite rapidly. The mixture composition was selected such that the stoichiometric mixture fraction, nst ¼ 0:27, based on Bilger’s definition [11], resides in a region of high shear in the developing jet. The mean inlet axial velocity, U in , is given by:    Uj  Uc y þ H =2 U in ¼ U c þ tanh 2d 2   y  H =2  tanh ; ð1Þ 2d where U c ð¼ 20 m=sÞ and U j ð¼ 204 m=sÞ denote the mean coflow and mean inlet jet velocities, respectively. H is the jet width at the inlet and d is specified as d ¼ 0:05H . Note that the coflow velocity is specified such that the turbulent flame is lifted in spite of the high coflow and fuel jet

Normalized value

Lift-off height (mm)

1.0 55 50 45

(Uin-Uc)/(Uj-Uc), ξ (Tin-Tc)/(Tj-Tc)

H

0.5

40 0

2

4

6

Time (ms)

8

10

12

0.0

-1.0

-0.5

0.0

0.5

y/H Fig. 1. Temporal evolution of the lift-off height of a diesel jet (private communication, L. Pickett, 2009).

Fig. 2. Mean profiles at the inlet boundary.

1.0

C.S. Yoo et al. / Proceedings of the Combustion Institute 33 (2011) 1619–1627 Table 1 Numerical and physical parameters of the DNS. Parameter Jet width ðH Þ Domain ðLx  Ly  Lz Þ Grids ðN x  N y  N z Þ Mean inlet jet velocity ðU j Þ Laminar coflow velocity ðU c Þ Jet temperature ðT j Þ Coflow temperature ðT c Þ Rej ¼ U j H =m Velocity fluctuation ðu0 =U j Þ

2.0 mm 15H  20H  3H 2025  1600  400 204 m/s 20 m/s 550 K 1550 K 10,000 0.10

temperatures. The mean inlet scalar and velocity profiles are shown in Fig. 2. Velocity fluctuations, u0 , are imposed on the mean inlet velocity, obtained by generating an auxiliary homogeneous isotropic turbulence field based on a prescribed energy spectrum as in [10,12]. The numerical and physical parameters at the inlet are summarized in Table 1. The computational domain is 15H  20H  3H in the streamwise, x, transverse, y, and spanwise, z, directions. A uniform-grid spacing of 15 lm is used in the x- and z-directions, while an algebraically-stretched mesh is used in the transverse direction following [7,10]. The width of the uniform-grid region in the transverse direction was carefully chosen to ensure that the instantaneous jet flame and mixing zone always remained well within the fine-mesh region of the domain. The mildly stretched mesh outside of the uniform-grid region is intended to move the transverse boundary farther from the turbulent jet to avoid entrainment of fluid at the boundary into the domain without incurring prohibitive computational cost. Previous results [10] have demonstrated that the grid-stretching effect on the solution is negligible. The compressible Navier–Stokes, species continuity, and total energy equations were solved using the Sandia DNS code, S3D [13]. A fourthorder explicit Runge–Kutta method for time integration [14] and an eighth-order central differencing scheme for spatial discretization [15] were used with a tenth-order filter. A reduced ethylene–air kinetic mechanism, developed using the algorithms reviewed in [9], was adopted. The mechanism is comprised of 22 species ðH2 ; H; O;O2 ; OH;H2 O;HO2 ; H2 O2 ; CH4 ; CO;CO2 ; CH2 O;C2 H2 ; C2 H4 ; C2 H6 ; HCCO;CH2 CO;CH3 CHO;a  C3 H5 ; C3 H6 ; and N2 Þ and 18 global reaction steps [16]. CHEMKIN and TRANSPORT software libraries [17,18] were linked with S3D to evaluate reaction rates, thermodynamic and mixture-averaged transport properties. Navier–Stokes characteristic boundary conditions (NSCBC) were used to prescribe the boundary conditions [19]. Improved non-reflecting inflow and outflow boundary conditions [12,20,21]

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were used in the x- and y-directions, and periodic boundary conditions were applied in the z-direction. Based on the prescribed inlet jet velocity and the streamwise domain length, a flow-through time, sj ð¼ Lx =U j Þ, is approximately 0:147 ms. For computational expediency, the simulation was initially advanced with a coarse grid resolution of 40 lm until the flame attained statistical stationarity. The solution was then mapped onto a finer grid of 15 lm and was advanced at a constant time step of 5 ns through 6sj . The simulation was performed on the Cray XT4/XT5 at Oak Ridge National Laboratories and required 14 million CPU-hours running for 20 days on 30,000 processors. The simulation generated 250 TB of field data. The central ethylene/nitrogen jet was self-ignited by the highly-heated coflow within one flow-through time and the lifted jet flame base approached statistical stationarity and fluctuated about its steady stabilization lift-off height,  h, of approximately h=H ¼ 5:8. 3. Results – auto-ignition Figure 3 shows an instantaneous volume rendering of the mass fractions of hydroxyl (OH) and perhydroxyl ðHO2 Þ from the lifted ethylene/ air jet flame. Hydroxyl is often used as a marker of the lifted flame base or high temperature reaction region [4,7], and perhydroxyl is an important intermediate species in the auto-ignition of an ethylene–air mixture [22]. It is readily observed that the perhydroxyl radical starts to accumulate immediately downstream of the fuel jet inlet due to the high coflow temperature, but hydroxyl does not accumulate until much further downstream, at approximately two-fifths of the domain height where ignition occurs. Note also that distinct ignition kernels, demarcated by high OH concentrations, form upstream of the location where

Fig. 3. A typical image of mass fractions of OH and HO2 .

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vigorous flame reaction commences. These results imply that the fuel-rich reaction related to HO2 starts due to high temperature but the high temperature flame develops far downstream due to the fast fuel jet and coflow velocities. The ethylene lifted flame is examined using the chemical explosion mode (CEM) analysis (CEMA) [23], developed as a chemical diagnostic to delineate explosive regions from normal flames. A chemical mode is defined as the eigenmode of the Jacobian matrix of the chemical source terms in the species and temperature equations. By definition, the CEM is a chemical mode whose eigenvalue is positive, and hence, large eigenvalues of the CEM at a given location indicate that the corresponding mixture is highly explosive, which typically leads to ignition in a lossless homogeneous system [23]. In spatially non-homogeneous systems, CEM interacts with diffusion or other losses, and may not always result in ignition depending on the relative strength of the CEM compared with that of the loss, as roughly measured by a Damko¨hler number. Figure 4 shows the isocontours of eigenvalues of the CEM weighted by normalized Damko¨hler number, Dac . For the CEMA, Dac is defined as Dac ¼ kexp =v, where kexp is a positive chemical explosive mode, which represents a reciprocal time scale of the CEM. v is the scalar dissipation rate, defined as v ¼ 2Djrnj2 where D is the local thermal diffusivity. Note that v represents a reciprocal time scale of diffusion or loss in strained flames. A mixture with Dac  1 features a strong CEM and will likely result in ignition, otherwise ignition may be suppressed. The flame surface, defined as the locations where the eigenvalue of the CEM crosses zero, is also presented in the figure. Note that the flame surface

separates explosive regions from non-explosive, normal flame regions in the domain. The figure clearly reveals that the eigenvalues of the CEM weighted by Dac upstream of the flame base are much greater than unity, which implies that auto-ignition can occur in the corresponding mixtures. Moreover, there exist islands of auto-ignitive regions upstream of the flame base. It was confirmed by examining adjacent spanwise planes that the islands are not projections of reactive protrusions from neighboring spanwise locations. Therefore, CEM provides an unambiguous chemical diagnostic confirming that the present lifted jet flame is stabilized by ignition upstream of the flame base. For more complete results of CEMA of the present lifted flame, readers are referred to [16]. Global characteristics of the lifted flame are investigated by analyzing the Favre mean temper_ as q, ature, Te , and Favre mean heat release rate, e q_ starts shown in Fig. 5. It is readily observed that e to increase ahead of the mean lift-off height ðh=H ¼ 5:8Þ and approaches its maximum approximately at x=H ¼ 7. Past this vigorous q_ decreases significantly. Accordreaction region, e ingly, Te increases following e q_ and levels off beyond x=H ¼ 10. It is also observed that the q_ occurs at y ¼ 1:2d1=2 near the local peak of e flame base, and subsequently, slightly shifts towards the centerline as the flame develops downstream, where d1=2 is the local jet half-width [7]. These results imply that highly transient reactions associated with auto-ignition first occur slightly outside the shear region, followed by the development of a stable flame downstream.

(a)

1500

~

T (K)

15

2000

x/H = 3 x/H = 6 x/H = 7 x/H = 9 x/H = 12

1000 10

3 5 2

0

−6

−4

−2

0

2

4

6

0

y/H Fig. 4. Isocontours of logðk exp Þ  logðDac Þ= logðDac;max Þ. Solid line represents flame surface where the corresponding eigenvalues cross zero.

~.

1

(b) q (J/mm3s)

x/H

4

500 3.0

2.0

1.0

0.0 -3

-2

-1

0

1

2

3

y/δ1/2 Fig. 5. Favre means of (a) temperature and (b) heat release rate at different axial locations.

Conditional statistics of the auto-ignition process at the flame base are presented, which can be ultimately used for combustion model development and validation. The cross-stream conditional Favre mean, h/jgi, and variance, G// , of a variable, /, is defined as: RRR ðqðx; tÞ/ðx; tÞjn ¼ gÞ dy dz dt RRR h/jgi ¼ ; ð2Þ ðqðx; tÞjn ¼ gÞ dy dz dt

(a)

G// ¼ h/00 /00 jgi;

ð3Þ

(b)

where g is the sample space for n and /00 ¼ /  h/jgi is the fluctuation of the variable. Since conditional averages vary weakly in the cross-stream direction in this kind of flow [24], cross-stream averaging has been employed to increase the statistical sample size. Figure 6 shows the conditional Favre means of temperature, heat release rate, scalar dissipation rate, Damko¨hler number, Da, and the conditional Favre variance of v. Henceforth, Da is defined as the ratio of species reaction rate to diffusion such that it provides a measure of the local progress of ignition. A significant increase of heat and radicals due to ignition is manifested by large values of Da  Oð 1Þ. Da based on species k, is defined as [7,25]:

(J/mm3s)

1.0

(c)

10 4

<χ | η> (1/s)

C.S. Yoo et al. / Proceedings of the Combustion Institute 33 (2011) 1619–1627

10

x_ k Da ¼ ; j  r  ðqY k Vk Þj

(d)

(K)

1500 1000

.

500 5.0

x/H = 3 x/H = 6 x/H = 7 x/H = 9 x/H = 12

4.0 3.0 2.0

0.0

χq

3

10 2 10

x/H = 3 x/H = 6 x/H = 7 x/H = 9 x/H = 12

1

10 0



where Vk and x_ k denote a diffusive velocity vector and a net production rate of species k, respectively. In this study, H2 O is adopted for the Damko¨hler number analysis. hT jgi first increases in a fuel-lean mixture and subsequently the peak shifts towards richer mixtures ðg  0:35Þ downstream of the mean flame _ base. Similarly, hqjgi initially increases upstream of the flame base and approaches its maximum approximately one and half jet-widths downstream of the flame base ðx=H  7:5Þ, similar to the conditional evolution in a hydrogen jet flame _ [7]. Further downstream, hqjgi attains its local peak in fuel-rich mixtures ðg  0:35Þ. It is also of interest to note from Fig. 6c that hvjgi is substantially lower than the corresponding extinction scalar dissipation rate, vq , from a onedimensional strained laminar non-premixed flame, even near the fuel jet nozzle, and becomes an order of magnitude smaller than vq near the flame base. Note that vqst  6000 s1 at nst . However, the variance of v shown in Fig. 6e is substantially larger than the conditional mean value, suggesting that locally v can exceed vq , and hence, local flame quenching or longer ignition delays can occur near the flame base [7,25]. Unlike the statistical characteristics of v, hDajgi exhibits large value ð 1Þ near and upstream of the flame base. In addition, the variance of Da (not shown) is considerably larger than the conditional mean value. Therefore, the local

x/H = 3 x/H = 6 x/H = 7 x/H = 9 x/H = 12

2000

x/H = 3 x/H = 6 x/H = 7 x/H = 9 x/H = 12

20 15 10 5

(e) Gχχ1/2 (1/s)

ð4Þ

1623

0 10 4 10 3 10 2 10

1

10

0

x/H = 3 x/H = 6 x/H = 7 x/H = 9 x/H = 12

0

0.2

0.4

0.6

Mixture fraction, η

0.8

1

Fig. 6. Conditional Favre means of (a) T, (b) q, _ (c) v, (d) Da, and (e) conditional Favre variance of v at different axial locations.

Da can be significantly larger than unity and hence, consistent with CEMA, auto-ignition is the main source of stabilization of the lifted flame. At x=H ¼ 9, the peak of hDajgi, which still remains greater than unity, shifts towards fuelrich mixtures, suggesting that auto-ignition also occurs there, whereas normal flames begin to develop near stoichiometric conditions. Further

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downstream where combustion occurs predominantly in flames, hDajgi and its conditional variance decrease across the full range of mixture fractions. This indicates a transition from autoignition to premixed or non-premixed flames where there is an intrinsic balance between reaction and diffusion. Together with the chemical explosive mode analysis, these flame characteristics clearly indicate that, due to the high coflow temperature, ignition occurs first under hot, fuel-lean conditions where ignition delays are shorter, consistent with previous DNS studies of auto-ignition [7,25]. 4. Results – flame base dynamics To understand the dynamics of the turbulent lifted flame, instantaneous snapshots of a twodimensional z-plane are extracted from the three-dimensional data. Figure 7 shows a typical temporal sequence of images of Y OH isocontours at the left leading edge of the lifted jet flame between t=sj ¼ 0:204 and 1.156 for the z = 0 plane. It is readily observed that, near the flame base, most of the OH radical is concentrated in a fuel-lean mixture ðn < nst Þ, and isolated ignition kernels develop at t=sj ¼ 0:272 and 0.748, which are immediately convected downstream by the high-speed jet flow. In the present study, we define the most upstream point of the Y OH ¼ 0:0004 isoline in a given z-plane as the location of the lifted flame base because the Y OH ¼ 0:0004 isoline effectively encompasses the thermal runaway region [7]. Henceforth, we refer to the most upstream point

of this isoline as the ‘stabilization point’. This definition is necessary to characterize the evolution of key scalars and velocity in the vicinity of the lifted flame base. Note that Y OH ¼ 0:0004 represents approximately 5% of its maximum increase in the domain consistent with definitions used in previous studies [4,7]. The characteristics of the stabilization point movement are investigated by correlating with other key scalar quantities and velocity. The temporal evolution of the stabilization point along with flame-normal flow velocity ðu  nÞ, displacement speed ðS d Þ, mixture fraction ðnÞ, and scalar dissipation rate (v) at the z = 0 plane are presented in Fig. 8. All values are evaluated at the stabilization point. The displacement speed of species k, S d , is defined as: S d ¼ S Rd þ S Dd ¼

1 ðx_ k  r  ðqY k Vk ÞÞ; qjrY k j

ð5Þ

where S Rd and S Dd represent the reaction term and the diffusion components of S d , respectively. The hydroxyl iso-surface associated with the stabilization point, Y OH ¼ 0:0004, is used to evaluate the displacement speed [7,26]. It is observed in Fig. 8a that, in general, the stabilization point gradually moves downstream and transversely outward after a sudden jump upstream. This jump is associated with ignition of separate kernels of mixture upstream of the existing flame base. Ignition is manifested by a large value of S d as shown in Fig. 8b, which is mainly attributed to large values of S Rd (not shown) together with the vanishing scalar gradient at the point of ignition. In a sense, S d is unbounded at this singularity, but denoted by an

Fig. 7. Temporal evolution of OH mass fraction between t=sj ¼ 0:204 and 1.156. Solid lines and arrows denote nst and local velocity vectors, respectively.

C.S. Yoo et al. / Proceedings of the Combustion Institute 33 (2011) 1619–1627

x/H

-0.8

5.0

-1

y/H

4.0

Speed (m/s)

(b)

-0.6

6.0

-1.2

Sd

100

y/H

7.0

-u⋅n

50 0 -50

(c)

600

χ

ξ

0.1

ξ

400 0.05

0

200

0

0.5

1

1.5

2

2.5

3

χ (1/s)

x/H

(a)

1625

0

t/τj Fig. 8. Temporal evolution of (a) stabilization point ðx; yÞ, (b) u  n and S d , and (c) n and v between t=sj ¼ 0:0 and 3.0.

artificially large value numerically as in [7]. It is also observed in Fig. 8c that the stabilization point jumps to a location of lower scalar dissipation and higher mixture fraction (although still fuel-lean). The move to higher mixture fraction is associated with the transversely inward movement of the flame, and corresponds to higher mean axial velocities. Once the flame base has been established at a new upstream location, and the displacement speed has decayed below the local flow velocity, the kernel recedes downstream. While moving downstream, the reaction of the ignition kernel is retarded or quenched (see Fig. 7 at t=sj ¼ 0:748–0:884), or flame shortening occurs due to the jet entrainment structure (see Fig. 7 at t=sj ¼ 0:476–0:612). The corresponding displacement speed at the stabilization point decreases, and even becomes negative in some instances due to large negative S Dd (not shown). The downstream movement of the stabilization point is primarily attributed to large local convective velocity, and intermittently, negative displacement speed associated with quenching from locally high mixing rates (see Fig. 8b at t=sj ¼ 2:21 and 2.65). Eventually another ignition event causes the flame base to jump to a location upstream, forming a complete cycle. These ignition and flow characteristics result in a saw-tooth shaped behavior of the stabilization point, qualitatively similar to the diesel jet flame base movement shown in Fig. 1. From these results, we may conjecture that lifted diesel jet flame stabilization in a hot environment may be a result of a competition between consecutive ignition events causing the flame to

move upstream and turbulent convection induced by the high axial jet velocity causing the flame to move downstream. From these observations, we postulate a stabilization mechanism for a turbulent lifted jet flame in a highly-heated coflow, incorporating the concept of large-scale flow structure [27] and ignition by hot coflow [7], such that the flame base fluctuates with the passage of a series of large-scale flow mixing structures and intermittent auto-ignition events occurring in fuel–lean mixtures. As illustrated in the cartoon in Fig. 9 depicting the sequence of ignition/coherent mixing events, the stabilization point quickly moves upstream due to auto-ignition in fuel–lean mixtures with low v. Following ignition, the stabilization point is not able to propagate upstream due to the low

Fig. 9. Schematic of the flame base movement: (a) ignition occurs in lean mixtures with low scalar dissipation rate; (b) the stabilization point is advected downstream by high axial velocity; and (c) ignition occurs in another large flow structure. The grey dot represents the stabilization point, and the dashed line denotes autoignition limit due to low temperature.

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flame speed compared to high oncoming axial jet velocity. Therefore, the stabilization point is convected downstream as it encounters another largescale flow structure with high axial jet velocity and scalar dissipation rate. Finally, ignition occurs in the large-scale flow structure, thus completing a full cycle. Examination of Figs. 7 and 8 readily shows one cycle of the flame base movement, consistent with this hypothesis. A comparison of the stabilization mechanisms of the turbulent lifted hydrogen jet flame [7] and the present lifted jet flame reveals that the present lifted jet flame does not exhibit an upstream propagation stage due to the low flame speed relative to the high local velocity associated with both the high-speed axial fuel jet and coflow. Rather, stabilization is achieved solely by consecutive auto-ignition events occurring in the hot, fuel-lean mixture. It is of interest to note that a simple estimate of the lift-off height based on the product of homogeneous ignition delay and mean convection velocity underpredicts the lift-off height since dissipation losses from the ignition kernel are not accounted for. The lift-off height from this homogeneous approximation is found to be approximately 1:5H . However, the actual lift-off height varies between 4:0H and 7:0H . Therefore, the ignition of this ethylene jet is delayed by 2.5–4.5 times, compared to the homogeneous ignition, similar to previous results obtained in ignition of a hydrogen/air mixture in homogeneous turbulence [25]. 5. Conclusions Three-dimensional direct numerical simulation of a turbulent lifted ethylene/nitrogen slot-burner jet flame in a highly-heated air coflow was performed using reduced chemistry and mixtureaveraged transport properties. The results show that, given a high coflow temperature, auto-ignition is the key mechanism responsible for flame stabilization. Typically, auto-ignition is found to occur in hot, fuel–lean regions with low scalar dissipation rate. Several independent diagnostics – Damko¨hler number, chemical explosive mode, and displacement speed analyses – show the presence of auto-ignition at the flame base. The conditional mean of the scalar dissipation rate is found to be an order of magnitude smaller than the laminar extinction scalar dissipation rate at the flame base. However, fluctuations of scalar dissipation rate are even larger than its mean value. Therefore, local flame quenching or longer ignition delays can occur near the flame base. It is also found that the stabilization points form a cycle with the passage of large-scale flow structures, and flame stabilization is determined by a balance between the local axial velocity

and consecutive auto-ignition events which favors hot environments with low scalar dissipation rate.

Acknowledgement The work at Ulsan National Institute of Science and Technology (UNIST) was supported by the 2009 Research Fund of UNIST. The work at Sandia National Laboratories (SNL) was supported by the US Department of Energy, the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, and Office of Advanced Scientific Computing Research. JHC was supported as part of the Combustion Energy Frontier Research Center, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001198. Figures 1, 3 and 4 were provided by Dr. L. Pickett, Dr. H. Yu at SNL, and Prof. T. Lu at the University of Connecticut, respectively.

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