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Direct Numerical Simulation Study of an Experimental Lifted H2/N2 Flame. Part 2: Flame Stabilization Haiou Wang, Kun Luo, Fuxing Yi, and Jianren Fan* State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, People’s Republic of China ABSTRACT: The stabilization of an experimental lifted turbulent flame is studied using direct numerical simulation. An eighthorder central spatial difference scheme and a fourth-order explicit Runge−Kutta time integration method are employed to solve the fully compressible N−S equations. A 9-species and 19-step mechanism for hydrogen/air combustion is used. The interactions between the flame islands and large eddies are examined. Two modes of the interactions are identified. On the one hand, large eddies may exert extensive strains and high dissipation rates on the flame, resulting in local extinction. On the other hand, large eddies may modify the flow field to connect the flame islands with the flame base. The flame base and ignition kernels are found on the lean-fuel side and in locations with low scalar dissipation rate. A new coordinate conditioned on the stabilization point is adopted to perform averaging. The averaged quantities obtained under the new coordinate reflect the characteristics in the vicinity of the flame base. Finally, statistics of the stabilization point are analyzed in terms of time evolution and probability density function. It is speculated that the flame is stabilized by a competition of autoignition and large-scale structures.

1. INTRODUCTION Lifted flames have been extensively studied since the 1960s, because they include fundamental mechanisms as well as practical interest. Lifted flames are found in practical combustors to reduce damage to the burner and intensify heat release. They exhibit many characteristics, among which flame stabilization is of prime importance. A good understanding of these characteristics could help to design combustion devices with reduced pollutant emissions, and enhanced thermal efficiency and overall flame stability. It is well-known that lifted laminar flames are stabilized in virtue of the so-called triple-flame.1 However, the stabilization mechanism for lifted turbulent flames is not clearly understood. Different but sometimes overlapping theories of flame stabilization have been presented. Vanquickenborne and van Tiggelen2 proposed the premixed flame stabilization theory. They studied lifted diffusion methane flames and found that the flame stabilized at a region where a stoichiometric mixture was formed. An experimental relation between the turbulent burning velocity and turbulent intensity was obtained under the assumption of the balance between gas flow velocity and turbulent burning velocity. Peters and Williams3 conducted a theoretical analysis of turbulent jet diffusion flame. They regarded the flame as an ensemble of laminar diffusion flamelets, and local quenching events for flamelets were attributed to excessive flame stretch. Experiments in counter-flow diffusion flames supported this point of view. However, it ignored the mixing of the fuel and oxidizer upstream the stabilization point. Buckmaster and Weber4,5 proposed the edge-flame concept. It assumed that the flame leading edge was partially premixed and could propagate upstream to counter the local flow field. Aside from the three categories above, there are two categories based on the local turbulence effect. One is the turbulent intensity theory6 and the other one is the large eddy concept.7 In a review paper, Pitts8 discussed the weakness of each theory and concluded that no satisfactory models existed. He suggested that the premixed flame theory could be improved by © 2012 American Chemical Society

Figure 1. Instantaneous iso-surfaces at temperature 1100 K (yellow) and hydroperoxyl (HO2) mass fraction of 0.0001 (blue) near the flame base of the lifted turbulent flame.

incorporating the large eddy concept. Lawn9 classified the lifted flame stabilization mechanisms into three categories by including the turbulent intensity theory and the large eddy concept in the premixed flame theory. Most research on lifted turbulent flame stabilization was conducted on fuel jets in cool air. It is worth noting that in a heated air coflow or vitiated coflow consisting of hot combustion Received: May 6, 2012 Revised: July 9, 2012 Published: July 12, 2012 4830

dx.doi.org/10.1021/ef3007728 | Energy Fuels 2012, 26, 4830−4839

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Figure 2. Sequential images of YHO2 at t = 10.66τj in a typical x−r plane, where τj is the flow-through time. The white solid line denotes the YOH = 0.00034 iso-line.

gases using two-dimensional DNS with single-step chemistry and unit Lewis number assumptions. They found that the unsteady wrinkled triple-flame propagated at a relatively slower speed than the mean inflow imposed, and was driven downstream continuously. Occasional reignition events were responsible for the stabilization of the flames, which was triggered by hot gas convected by recirculation. More recently, Yoo et al.16,17 used three-dimensional DNS to investigate the stabilization mechanism of a high speed jet in a hot coflow with detailed chemistry, thermodynamics, and transport. Hydrogen and ethylene were chosen as the fuels. Both of the two flames with different fuels revealed that the flame stabilization was a consequence of the balance between consecutive autoignition events in hot fuel-lean mixtures and convection induced by the high-speed jet and coflow velocities. The relative position of the flame base and the coherent flow structure induced a cyclic motion of the flame base. In the present study, three-dimensional DNS with detailed chemistry is applied to investigate the stabilization of the experimental lifted turbulent flame of Cabra et al.11 This is the

products at temperature exceeding the ignition limit, autoignition plays an important role in the flame stabilization.10 Cabra et al.11 designed a burner with a simple and well-defined configuration. The flame was a lifted turbulent H2/N2 jet flame issuing into a coflow of lean combustion products, which admitted the possibility of autoignition of the mixed fluid. Gordon et al.12 investigated the stabilization of lifted turbulent methane flames with a quantitative joint temperature, OH, and CH2O measurement method using the same burner as Cabra et al.11 They further confirmed that autoignition was the main stabilization mechanism in this lifted flame. Oldenhof et al.13 and Medwell14 studied lifted turbulent flames in a hot and diluted coflow, respectively. Oldenhof et al.13 found that the flame base behaved fundamentally differently from that of a conventional lifted jet flame in a cold air coflow. Ignition kernels were continuously being formed in the flames, growing in size while being convected downstream. Very few direct numerical simulations (DNS) of lifted turbulent flames in a hot coflow have been performed. Jiménez and Cuenot15 investigated turbulent flames stabilized by hot 4831


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Figure 3. Sequential images of YHO2 at t = 10.85 τj in a typical x−r plane, where τj is the flow-through time. The white solid line denotes the YOH = 0.00034 iso-line.

The governing equations were described in the first part18 of our investigations. The spatial derivatives at interior points are evaluated using an eighth-order central difference scheme, and the order of differentiation falls gradually to a third-order onesided scheme at the boundaries. The resultant accuracy of the difference scheme is fourth-order. An explicit 10th-order filter is adopted to remove spurious high frequency fluctuations in the solutions. The time integration is carried out using a classical fourth-order explicit Runge−Kutta method.19 A 9-species (H2, O2, OH, H2O, H, O, H2O2, HO2, and N2) and 19-step mechanism for hydrogen/air combustion by Li et al.20 is adopted. Thermodynamic and transport properties are evaluated using the CHEMKIN software libraries.21,22 The boundaries in all three directions are taken to be nonreflecting, and treated using the improved Navier−Stokes Characteristic Boundary Conditions (NSCBC) formulations.23,24 The target flame of the present study is designed by Cabra et al.11 The burner consists of a fuel jet (25% H2 and 75% N2 in molar fraction) with a coaxial flow of hot combustion products

second part of the two investigations. In the first part,18 the comparison of the DNS results and measurements was carried out for various scalars, including the mixture fraction, temperature, and mass fractions of H2, O2, H2O, and OH. Excellent agreements were achieved for the Favre mean and fluctuating components. The validity of the DNS results and the importance of flame stabilization motivate the authors to further explore the flame stabilization using the DNS database. The remainder of this Article is organized as follows. First, the numerical method is briefly outlined in section 2. The dynamics of the flame base and stabilization point are analyzed in detail in section 3. The instantaneous flame base as well as the conditional averaged flame base are presented. Probability density functions (pdf’s) of different variables at the flame base are presented. Finally, some conclusions are given.

2. NUMERICAL METHOD The DNS database is generated using a DNS code developed in our group solving the fully compressible N−S equations. 4832


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Figure 4. Sequential images of the normalized flame index. The white solid line denotes the YOH = 0.00034 iso-line.

the lifted turbulent flame. In numerical investigations, HO2 is usually used to track ignition kenels.28,29 It is seen that there are ignition kernels in the upstream of the flame base, followed by intense reactions and heat release. These ignition kernels are important for the flame stabilization, which will be discussed in more detail later. 3.1. Instantaneous Flame Base. Many theories for the lifted turbulent flame stabilization have been proposed.2−7 Autoignition was confirmed as a major stabilization mechanism of the lifted turbulent flames in hot coflow.11,16 In the following, the roles of autoignition, large-scale structures, and premixedness will be examined, while the characteristics of the flame base will be delineated. The stabilization point is defined at the most upstream location with the mass fraction of hydroxyl (OH) above a certain threshold. After a few tests, we find that YOH = 0.00034 gives the best result. It should be noted that this value corresponds to about 10% of the maximum mass fraction of hydroxyl in the domain, a little higher than those in the literature.16,17

from a lean premixed H2/air flame. The central jet has an inner diameter D = 4.57 mm and extends 70 mm downstream of the surface of the perforated plate, so that the fuel mixture exits in a uniform composition for the coflow. The boundary conditions of the central jet and coflow for the simulation are listed in Table 1 of ref 18. A random velocity disturbance proposed by Bogey and Bailly25 is superimposed on the mean flow to facilitate the transition to turbulence. The computational domain is 26D × 16D × 16D in the streamwise x, transverse y, and spanwise z directions, and is discretized using a grid number of 1088 × 512 × 512 with the grid spacing of the same order of the Kolmogorov scale,11 ensuring that the turbulence scales as well as the flame structures are well resolved. The computation advances for 14 flow-through times, which are sufficient to provide stationary statistics.

3. RESULTS AND DISCUSSION Figure 1 shows the instantaneous iso-surfaces of temperature and hydroperoxyl (HO2) mass fraction near the flame base of 4833


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Figure 5. Sequential images of the scalar dissipation rate. The YOH = 0.00034 (white) and stoichiometric mixture fraction fst (black) iso-lines are superimposed.

Figures 2 and 3 show the sequential images of YHO2 at two representative timings. The time interval between the images is about 0.02τj. Instantaneous images are extracted from a typical x−r plane. Generally, there are two stabilization points in each image, but without loss of generality only one-half of the image is analyzed. The white solid line denotes the YOH = 0.00034 isoline. It is observed that there are pockets in the upstream of the flame base where the HO2 accumulates, eventually leading to the formation of other radicals to initiate the combustion, which implies that autoignition plays an important role in the flame stabilization. Important interactions between the flame base and turbulent eddies are also revealed in these figures. As shown in Figure 2a, the instantaneous flame is stabilized at about five-diameter downstream from the burner exit. The flame base looks very slim and wrinkled. As time advances, the flame base interacts with the turbulent structures. Large eddies may exert extensive strains and high dissipation rates on the flame, resulting in local extinction. After a short time, the stabilization point is separated from the flame base because of

Figure 6. Sketch map of the flame base. 4834


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Figure 7. Contours of the conditional averaged (a) axial velocity, (b) temperature, and mass fractions of (c) OH and (d) HO2. The white dot represents the stabilization point.

local extinction, and an isolated flame island is formed (Figure 2b). The flame island tends to decrease in size, partly due to a lack of radicals. Finally, the flame island disappears, while the flame base is convected downstream as shown in Figure 2d. Figure 3 exhibits another mode of interactions between the flame base and turbulent eddies. At first, a flame island is formed near the flame base (Figure 3a). The flame island tends to connect with the flame base, developing into a more stable flame base (Figure 3d). This connection may result from the different convection velocities of the flame base and the flame island. Thus, one of the effects of turbulent eddies is to modify the flow field to connect the flame island with the flame base. From Figure 3, it is also seen that the flame island grows with time. The flame index is often used to distinguish premixed flames from nonpremixed flames. To characterize the combustion modes in the flame, a normalized flame index FI is defined as:27 FI =

More or less partially premixed reaction zones develop for FI ranging from −1 to 1. The sequential images of the normalized flame index are shown in Figure 4. The YOH = 0.00034 iso-line is also superimposed. To exclude the areas where chemical reactions are not evident, a threshold for the normalized flame index is defined. When the local heat release rate is lower than 104 J/m3·s, the normalized flame index is set to zero. It is shown that premixed combustion and nonpremixed combustion coexist at the flame base. However, nonpremixed combustion dominates. Figure 4a demonstrates that a pocket of premixed mixtures locates between the flame base and the flame island. After the connection process discussed earlier, this pocket is convected downstream and enveloped by the flame base (Figure 4d). Although premixed mixture is found at the flame base in the present lifted turbulent flame, there is no evidence of propagating premixed flame as the stabilization mechanism. Important characteristics of the lifted turbulent flame are outlined in Figure 5, where sequential images of the scalar dissipation rate are presented. The scalar dissipation rate N is defined as N = 2D|▽f |2, where D is the diffusion coefficient and f is the mixture fraction. The YOH = 0.00034 (white) and stoichiometric mixture fraction fst (black) iso-lines are also superimposed. Several distinct properties could be pointed out. First, the flame base is on the lean side of the stoichiometric

∇YH2·∇YO2 |∇YH2·∇YO2|

(1)

According to the definition, the normalized flame index measures the cosine of the angle of the fuel and oxidizer gradients. When FI is close to 1, premixed combustion dominates, while nonpremixed combustion is dominant when FI is close to −1. 4835


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Figure 8. Contours of the conditional averaged (a) mixture fraction, (b) scalar dissipation rate, and (c) normalized flame index. The white dot represents the stabilization point.

Other experiments and simulations also supported this point of view.11,16 Second, the flame base and ignition kernels are found in locations with low scalar dissipation rate. The scalar dissipation rate characterizes the stiffness of the mixture fraction and the intensity of the local diffusive transfer. Higher scalar dissipation rates imply stiffer mixture fraction distributions and thus larger heat losses, so that ignition always occurs in low scalar dissipation rate regions. Finally, it is seen that the stoichiometric mixture fraction iso-line corresponds to regions with high scalar dissipation rate, implying the gradient of the mixture fraction is significant along the stoichiometric mixture fraction iso-line. 3.2. Conditional Averaged Flame Base. The stabilization point moves randomly under the effect of turbulence and autoignition. To further explore the dynamics of the flame base, averaged quantities are studied. When averaging is conducted in the laboratory coordinate, many characteristics of the flame base are lost. Thus, a new coordinate to perform averaging around the stabilization point is adopted. To account for the movement of the stabilization point, the origin of the new coordinate is fixed to its instantaneous location. The instantaneous quantities in the laboratory coordinate are transformed into the new coordinate using a first-order interpolating method. More than 2000 instantaneous images with about four flowthrough times are used to obtain averaged values. Figure 6 shows the sketch map of the flame base and reveals the relation of the

Figure 9. Time evolutions of the axial (a) position and (b) velocity at the stabilization point. The vertical solid and dash lines outline two different timings.

mixture fraction iso-line. Tacke et al.26 performed a detailed study of hydrogen lifted flames utilizing Raman/Rayleigh/LIF. They found that the stabilization zone was in lean mixtures. 4836


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Figure 10. The pdf’s of the (a) mixture fraction, (b) normalized flame index, (c) heat release rate, and (d) temperature at the stabilization point.

stabilization point. The evolutions exhibit sawtooth shapes. From Figure 9a, it is seen that the stabilization point is continuously convected downstream, and then quickly moves upstream, which is caused by autoignition. The typical time scale of the fluctuation of the stabilization point is about one tenth of the flow-through time. The correlation of the axial position and velocity is revealed in Figure 9, where two vertical lines outline two representative timings. It is seen that when autoignition occurs, the stabilization point moves upstream while the local axial velocity increases. The evolution of the axial velocity at the stabilization point is more complicated. Just ahead of the dash vertical line, the local axial velocity experiences a strong fluctuation, which is attributed to the large-scale structures in the shear layer. The mean axial velocity at the stabilization point is 22.78 m/s, about an order of magnitude higher than the laminar flame velocity of hydrogen combustion; thus premixed flame propagation is not able to stabilize the lifted turbulent flame. From the analyses in section 3.1, it is shown that autoignition and the large-scale structures are responsible for the flame stabilization, which is consistent with the studies of Yoo et al.16,17 The pdf’s of different scalars at the stabilization point are investigated. Shown in Figure 10a is the pdf of the mixture fraction. It is seen that the mixture fraction is well below the stoichiometry value of 0.474, which confirms that the stabilization zone is in lean mixtures. By examining the normalized flame index at the stabilization point, we find that most points are close to −1, which means that at the stabilization point most combustion takes place in a nonpremixed mode. However, there is probability that premixed combustion occurs. The mean heat

laboratory coordinate and the new coordinate. The averaged quantities obtained under the new coordinate are conditioned on the flame base and reflect the characteristics in the vicinity of the flame base. The contours of the conditional averaged axial velocity, temperature, and mass fractions of OH and HO2 are shown in Figure 7. The white dot presents the stabilization point. It is seen that downstream of the stabilization point, temperature starts to increase, which confirms that the YOH = 0.00034 isoline is a good marker of the stabilization point. The jet expands more quickly downstream of the stabilization point as shown in Figure 7b. The increase in the spreading rate is caused by the onset of intense heat release rate. It has been observed in Figures 2 and 3 that HO2 always accumulates at the periphery of the flame base, which is also illuminated in Figure 7d. The distribution of HO2 extends more upstream than other radicals, characterizing autoignition. Figure 8 displays the contours of the conditional averaged mixture fraction, scalar dissipation rate, and normalized flame index. It is seen that the mixture faction contour reproduces the axial velocity contour. The scalar dissipation rate is higher in the shear layer between the central jet and the hot coflow. The stabilization point is located next to the high dissipation rate region in the fuel-lean side. It is not surprising to observe that near the stabilization there exists a spot with the maximum scalar dissipation rate, which is consistent with the high mixture fraction gradient shown in Figure 8a. Figure 8c further confirms that at the flame base nonpremixed combustion is dominant. 3.3. Statistics of the Stabilization Point. Figure 9 shows the time evolutions of the axial position and velocity at the 4837


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Figure 11. The pdf’s of the mass fractions of (a) H2 and (b) O2 at the stabilization point.

flame is stabilized by a competition of autoignition and largescale structures.

release rate and temperature at the stabilization point are 4.1 × 108 J/m3·s and 1090 K, respectively. Figure 11 displays the pdf’s of the mass fractions of H2 and O2 at the stabilization point. The mean H2 mass fraction is 5% of that in the fuel jet, while the mean O2 mass fraction is 90% of that in the coflow, indicating that the fuel and oxidizer are partially premixed at the stabilization point. Mass fractions of radicals such as OH, O, and H start to increase at the flame base, where vigorous reactions are initiated.

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AUTHOR INFORMATION

Corresponding Author

*Tel./fax: 86-571-87951764. E-mail: [email protected]. Funding

This work is supported by the National Natural Science Foundation of China (No. 50976098) and the Fundamental Research Funds for the Central Universities.

4. CONCLUSIONS Direct numerical simulation is used to study the stabilization of an experimental lifted turbulent H2/N2 flame in a coflow of hot products of lean H2/air combustion. The DNS code solves the fully compressible Navier−Stokes equations. A fourth-order explicit Runge−Kutta method for time integration and an eighth-order central differencing scheme for spatial discretization are used. A detailed 9-species and 19-step mechanism for hydrogen/air combustion is employed. The boundary conditions of the central jet and coflow reproduce those in the experiment.11 The total grid number reaches 285 million. A detailed comparison between the DNS results and measurements is presented in the first part of the two investigations.18 The instantaneous flame base is studied, and important interactions between the flame base and turbulent eddies are revealed. Two modes of the interactions are identified. It is found that large eddies may exert extensive strains and high dissipation rates on the flame, resulting in local extinction. They may also modify the flow field to connect the flame island with the flame base. Other characteristics such as normalized flame index and scalar dissipation rate are investigated. Although premixed combustion is found at the flame base in the present lifted turbulent flame, there is no evidence of premixed flame propagation as the stabilization mechanism. To account for the movement of the stabilization point, a new coordinate whose origin is fixed to the instantaneous location of the stabilization point is adopted to perform averaging. It is seen that downstream of the stabilization point, temperature begins to increase. The jet expands more quickly downstream of the stabilization point due to the intense heat release rate. Statistics of the stabilization point are studies. The mean axial velocity at the stabilization point is about an order of magnitude higher than the laminar flame velocity of hydrogen combustion; thus premixed flame propagation is not able to stabilize the lifted turbulent flame. It is speculated that the

Notes

The authors declare no competing financial interest.

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REFERENCES

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