Direct Numerical Simulation Study of an Experimental Lifted H2

Sep 24, 2012 - ABSTRACT: Direct numerical simulation (DNS) is used to investigate an experimental lifted turbulent H2/N2 flame in a co- flow of hot pr...
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Direct Numerical Simulation Study of an Experimental Lifted H2/N2 Flame. Part 1: Validation and Flame Structure Kun Luo, Haiou Wang, Fuxing Yi, and Jianren Fan* State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, People’s Republic of China ABSTRACT: Direct numerical simulation (DNS) is used to investigate 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 fourthorder 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 combustion is employed. The inflow turbulence is considered by adding a random velocity field to the mean flow. The Reynolds number based on the exit diameter and jet velocity is 23 600. In total, more than 285 million grids are used, and the grid spacing is sufficient to resolve all of the turbulence scales and the flame structure. The comparison of the DNS results and the measurements is carried out for various scalars, including the mixture fraction, temperature, and mass fractions of H2, O2, H2O, and OH. Good agreements are observed for the Favre mean and fluctuating components, which validate the present approach and code. The overall flame structure is also outlined. Two combustion modes are identified in the lifted flame, and the non-premixed combustion dominates. the premixed turbulent low-swirl laboratory flames. They compared the numerical results to the measurements and then used the DNS data to further probe the time-dependent threedimensional (3D) structure of the flames in the turbulent flows. In the present study, a fully compressible 3D solver for reacting flows has been developed and applied to investigate the lifted turbulent flame from Cabra et al.1 by means of DNS to verify whether this code could reproduce the experimental flame as well as to analyze the flame stabilization mechanism. The burner designed by Cabra et al.1 has a simple and well-defined configuration, and comprehensive data are available. The flame is a lifted turbulent H2/N2 jet flame issuing into a co-flow of lean combustion products. It is the target flame for many numerical investigations. Myhrvold et al.10 used the eddy dissipation concept (EDC) combustion model and four different turbulence models to study the flame. Patwardhan et al.11 employed the conditional moment closure (CMC) method to investigate the lifted turbulent jet flame in a 2D axisymmetric configuration. The predicted flow and scalar fields agreed well with experimental data. Masri et al.12,13 employed the composition probability density function (PDF) and joint PDF approaches to study the flame. They found that the joint PDF calculations generally gave better agreement with the measurements than the composition PDF calculations. Various combustion models have also been coupled with LES to investigate the Cabra burner. Jones and Navarro-Martinez14 used a subgrid PDF method to study the stabilization mechanism. They suggested that the stabilization is associated mainly with the chemistry. Navarro-Martinez and Rigopoulos15 employed CMC to simulate the methane flame using the same burner. Presumed filtered density function (FDF) and monotonically integrated LES (MILES) were adopted to study the flame by Duwig and Fuchs.16 The flame lift-off was

1. INTRODUCTION Turbulent combustion is critical in energy conversion processes. The prediction of turbulent combustion is of prime importance in some industrial combustors, such as aircraft engines and coalfired boilers, to which experimental measurements are not accessible. Generally speaking, there are three ways to predict turbulent combustion, namely, Reynolds-averaged Navier− Stokes (RANS), large-eddy simulation (LES), and direct numerical simulation (DNS). The first two approaches have been used extensively for industrial and laboratory combustors. However, it should be emphasized that both of them cannot provide sufficient information to understand turbulent flames as physical assumptions and submodels are employed. Meanwhile, DNS is considered to be the most precise approach and can reproduce real flames because all of the relevant turbulence and flame scales are resolved. In addition, DNS can be used to reveal the underlying mechanisms of turbulent combustion and validate and improve the RANS and LES submodels. The major limitation of using DNS to study turbulent combustion lies in its expensive computation. Recently, with the development of computer technology, many researchers have used DNS to study laboratory-scale flames.2−8 As a pioneering attempt, Mizobuchi et al.2 simulated an experimental turbulent hydrogen-lifted jet flame with a Reynolds number of 13 600. More than 22 million grid points were used. DNS results showed that the lifted flame structure was very complicated and premixed and diffusion combustion could coexist in the flame zone. Very few studies have made statistical comparisons between DNS and experimental results, because such comparisons are usually very computationally costly. Moureau et al.5 applied DNS to simulate a laboratory-scale swirl burner measured by Meier et al.9 The DNS had a resolution of less than 100 μm with an unstructured mesh of 2.6 billion cells. A comparison of the DNS to the experimental results was made, and a new subgrid scale closure for premixed turbulent combustion was proposed. More recently, Day et al.6 presented a combined computational and experimental study to investigate © 2012 American Chemical Society

Received: May 6, 2012 Revised: September 17, 2012 Published: September 24, 2012 6118

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found to be very sensitive to small changes in the co-flow temperature but weakly sensitive to the combustion model or the grid resolution. This paper provides the first part of the two investigations. The validation of the DNS results against experimental data is performed, and the flame structure is discussed. The second part (10.1021/ef3007728)17 mainly focuses on the flame stabilization. To the authors’ knowledge, this is the first attempt to study the Cabra burner using DNS. The remainder of the paper is organized as follows. Section 2 introduces the details of the simulation, including the experimental configuration, governing equations, boundary conditions, and grid system. Section 3 presents the comparison of the DNS results and the measurements and outlines the flame structure. Finally, some conclusions are made in section 4.

ω̇ ′T = − ∑ hαωα̇

(7)

α=1

2. NUMERICAL APPROACH

where hα is the enthalpy of species α. The above fully compressible Navier−Stokes equation system is solved using a DNS code developed in our group.19 A fourth-order explicit Runge−Kutta method for time integration and an eighth-order central scheme for spatial differencing are used with an eighth-order filter for removing spurious high-frequency fluctuations in the solutions.20 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.21 is adopted. Reverse rate constants are computed from the forward rate constants and the equilibrium constants. CHEMKIN software libraries are linked to the current code to evaluate the reaction rate, thermodynamic, and transport properties.22,23 The Reynolds number based on the exit diameter and jet velocity is 23 600. The inflow turbulence is fully developed, and hence, we use the 1 /7 law to depict the inflow axial velocity profile, which is expressed as

The burner was designed by Cabra et al.,1 who carefully measured Favreaveraged and root-mean-square (rms) statistics of scalar variables, such as temperature and species mass fractions. The burner consists of a fuel jet (25% H2 and 75% N2 in molar fraction) with a coaxial flow of hot combustion products from a lean premixed H2/air flame. The central jet has an inner diameter of 4.57 mm and a wall thickness of 0.89 mm and locates at the center of a perforated disk with a diameter of 210 mm. The disk has 2200 holes of 1.58 mm diameter. The overall blockage of the perforated disk is 87%. The central fuel jet extends 70 mm downstream of the surface of the perforated plate, so that the fuel mixture exits in a uniform composition for the co-flow. The numerical approach is based on the solution of the compressible Navier−Stokes equation for a reactive system18

where R is the radius of the central jet. The corresponding mean inflow axial velocity profile for the burner exit is shown in Figure 1. It is shown that the computed velocity is in good accordance with the measured velocity.26

∂(ρuj) ∂ρ + =0 ∂t ∂xj

(1)

∂(ρYα) ∂ ∂ + (ρYαuj) + (ρYα(Vαj + V jc)) = ωα̇ ∂xj ∂t ∂xj

(2)

N ∂τij ∂(ρui) ∂p ∂ + (ρuiuj) = − + + ρ ∑ Yαfα , i ∂t ∂xj ∂xj ∂xj α=1

(3)

⎛ ∂ρT ∂ρuiT ⎞ Dp ∂T + −ρ C p⎜ ⎟ = ω̇ ′T + ∂xi ⎠ ∂xi Dt ⎝ ∂t

⎧5 ⎛ ⎞1/7 ⎪ × 107 × ⎜1 − r ⎟ , r < R ⎝ R⎠ ⎪4 ⎪ ⎪ 0, R < r ≤ 1.4R U=⎨ ⎪ ⎛r ⎞ ⎪ 3.5 × ⎜⎝ − 1.4⎟⎠ /1.44, 1.4R < r ≤ 1.44R R ⎪ ⎪ 3.5, 1.44R < r ⎩

(8)

N

∑ YαVα , iCp, α α=1

∂u ∂ ⎛ ∂T ⎞ + ⎜λ ⎟ + Q̇ + τij i ∂xi ⎝ ∂xi ⎠ ∂xj N

+ ρ ∑ Yαfα , i Vα , i α=1

p=ρ

(4) Figure 1. Mean axial velocity profile at the burner exit.

Rc T W

(5)

where ρ is the density, u is the velocity, Y is the mass fraction, V is the diffusion velocity, Vc is the correction velocity, p is the pressure, T is the temperature, τij is the viscous stress tensor, f is the volume force, Q̇ is the heat source term, Rc is the perfect gas constant, and W is the mean molecular weight of the mixture. To ensure the compatibility of the species and mass conservation equations, only N − 1 species equations are directly solved. The mass fraction of N2 is computed as

The improved nonreflecting boundary conditions24 are used to deal with the inflow/outflow conditions. The inflow boundary conditions of the central jet and the co-flow for the present simulation are set according to the experiment as much as possible, as listed in Table 1. However, because the instantaneous velocity fluctuation information is not available from the measurements, we use a presumed profile to generate it following the previous study.25 The velocity fluctuation is obtained by superimposing disturbances on the mean flow. A random velocity field25 is calculated as follows:

N−1

YN2 = 1 −

∑ Yα α=1

ring ⎫ ⎧ m ⎧Ux ⎫ ⎧Ux ⎫ ⎪Ux ⎪ ⎨ ⎬ = ⎨ ⎬ + aU0 ∑ εi cos(iϕ + φi)⎨ ⎬ ⎪ ⎪ ring ⎩Uθ ⎭ ⎩Uθ ⎭ ⎩Uθ ⎭ i=n

(6)

ω̇ α is the reaction rate of species α and can be obtained from the detailed reaction mechanism. ω̇ ′T is the heat release rate defined as 6119

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

(9)

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Table 1. Inflow Boundary Conditions for DNS of the Lifted Turbulent Jet Flame in a Vitiated Co-flow central jet co-flow

temperature (K)

velocity (m/s)

YH2

Y O2

YH2O

YN2

305 1045

107 3.5

0.024 0.0

0.0 0.1709

0.0 0.0645

0.976 0.7464

ring ⎫ ⎧ ⎡ ⎪Ux ⎪ 2r Δ(x , r )2 ⎤⎧ r − r0 ⎫ ⎨ ⎬ = 0 exp⎢ − ln(2) ⎬ ⎥⎨ ⎪ ring ⎪ Δy 2 ⎦⎩ x0 − x ⎭ ⎣ ⎩Uθ ⎭ r Δy

processing units (CPUs) have been used for 3 months in the Shanghai Supercomputer Center. The flow-through time based on the maximum inlet jet velocity and the streamwise length is about 0.89 ms. A uniform time step of 61 ns is used to satisfy the Courant−Friedrichs−Lewy (CFL) condition as well as all of the time scales for hydrogen combustion. More than 0.2 million time steps are marched in the simulation, which equal 14 flow-through times and are sufficient to provide stationary statistics.

(10)

The random velocity field is based on a combination of the jet azimuthal modes. εi is a random number in [−1, 1]. ϕi is a random number in [0, 2π]. U0 is the averaged velocity of the jet exit nozzle. a is the amplitude factor with a value of 0.0108. n and m determine the range of the fluctuating frequency and are chosen as 0 and 15, respectively. r is the distance to the central line. Δy is the minimum grid spacing in the transverse direction. Δ(x,r)2 = (x − x0)2 + (r − r0)2 is the square of the distance to the reference point (x0, r0). The random velocity field is updated in every time step. It should be noted that the random velocity field is generated in the shear layers between the central jet and the coflow. Bogey et al.25 demonstrated that this method was able to generate consistent turbulent statistics with experiments. The computational domain is 26d × 16d × 16d in the streamwise x, transverse y, and spanwise z directions. A uniform grid spacing of 108 μm is used in the x direction, and a stretched grid is used in both the y and z directions with a minimum grid spacing of 76 μm. The resultant grid number is 1088 × 512 × 512 = 285 212 672. The Kolmogorov scale estimated by Cabra et al.1 is between 50 and 500 μm in the stabilization region. It is also calculated to be about 30 μm using the DNS data, which is a little smaller than that of the measurement. Thus, the grid spacing and the Kolmogorov scale are of the same order, and the turbulent scales are well-resolved. As for the flame structure, it is known that a nonpremixed flame does not have a reference thickness. The thickness of stretched flames essentially depends upon stretch and can take a very wide range of values, which is very different from premixed flames, where a reference thickness may be introduced. Thus, we use the following method to verify the grid resolution for the flame. On one hand, the DNS results demonstrate that there are typically 6−15 points located within the thickness of the reaction zone of the lifted turbulent flame, as shown in Figure 2. Here, the reaction zone is defined as the area where

3. RESULTS AND DISCUSSION 3.1. Comparison to the Experiment. Figure 3 displays the computed axial profiles of the mean mixture fraction and

Figure 3. Comparison of the simulated and measured axial profiles of the Favre mean (a) mixture fraction and (b) temperature along the central line.

Figure 2. Grid distribution (white lines) across a typical reaction region (gray). The reaction region is defined as the area where the local heat release rate is higher than one-half of the maximum heat release rate in the global area of interest.

temperature along the central line compared to the measurements. The mixture fraction measures the local fuel/oxidizer ratio and is defined as

the local heat release rate is higher than one-half of the maximum heat release rate in the global area of interest, and the reaction zone thickness is defined as the local normal distance across the flame that is vertical to the local geometrical central line of the reaction zone. This definition is similar to the study by Law.29 One the other hand, as presented in the next section, the comparison between the DNS results and the experimental data indicates that the grid might not be adequate to describe the chemical reaction in the lift-off region but the general flame structure has been captured. To accomplish the DNS, 1024 central

f=

(1/2MH)(YH − YH,2) − (1/MO)(YO − YO,2) (1/2MH)(YH,1 − YH,2) − (1/MO)(YO,1 − YO,2) (11)

where M is the molecular weight and Y is the element mass fraction. The subscript 1 denotes the central jet, and the subscript 6120

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Figure 4. Comparisons of the simulated and measured radial profiles of the Favre mean and rms mixture fractions at three different axial locations: (a) mean, x/d = 1; (b) mean, x/d = 11; (c) mean, x/d = 14; (d) rms, x/d = 1; (e) rms, x/d = 11; and (f) rms, x/d = 14.

Figure 5. Comparisons of the simulated and measured radial profiles of the Favre mean and rms temperature at three different axial locations: (a) mean, x/d = 1; (b) mean, x/d = 11; (c) mean, x/d = 14; (d) rms, x/d = 1; (e) rms, x/d = 11; and (f) rms, x/d = 14.

2 denotes the co-flow. Figure 3a shows that the DNS results agree well with the measurements for the mixture fraction. In the

upstream region, the measured mixture fraction could be greater than 1, which may be attributed to the error of the experiment. 6121

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Figure 6. Comparisons of the simulated and measured radial profiles of the Favre mean and rms H2 mass fractions at three different axial locations: (a) mean, x/d = 1; (b) mean, x/d = 11; (c) mean, x/d = 14; (d) rms, x/d = 1; (e) rms, x/d = 11; and (f) rms, x/d = 14.

Figure 7. Comparisons of the simulated and measured radial profiles of the Favre mean and rms O2 mass fractions at three different axial locations: (a) mean, x/d = 1; (b) mean, x/d = 11; (c) mean, x/d = 14; (d) rms, x/d = 1; (e) rms, x/d = 11; and (f) rms, x/d = 14.

The mixture fraction is kept unchanged in the jet core region. After about x/d = 6, it begins to decrease linearly. Minor discrepancies between the DNS results and the measurements are found in the downstream region. There are two explanations for the discrepancies. One is that there are uncertainties in the measurements. The other is that the inflow turbulence generated in the simulation is different from that in the experiment. The comparison of the temperature profiles between the DNS results and the measurements is shown in Figure 3b. The DNS results

are in excellent agreement with the measurements. It is obvious that after a distance of several nozzle diameters, the temperature increases linearly as the jet advances. Figures 4−9 show the comparisons of scalars at various axial locations between the DNS and the experiment. In each figure, Favre mean and rms properties of the scalar at three axial locations of x/d = 1, 11, and 14 are presented. Figure 4 shows the radial profiles of the Favre mean and rms mixture fractions at different axial locations. It can be seen that 6122

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Figure 8. Comparisons of the simulated and measured radial profiles of the Favre mean and rms H2O mass fractions at three different axial locations: (a) mean, x/d = 1; (b) mean, x/d = 11; (c) mean, x/d = 14; (d) rms, x/d = 1; (e) rms, x/d = 11; and (f) rms, x/d = 14.

Figure 9. Comparisons of the simulated and measured radial profiles of the Favre mean and rms OH mass fractions at three different axial locations: (a) mean, x/d = 1; (b) mean, x/d = 11; (c) mean, x/d = 14; (d) rms, x/d = 1; (e) rms, x/d = 11; and (f) rms, x/d = 14.

with the measured rms mixture fraction at x/d = 1, which results from the inconsistent inflow boundary conditions mentioned in section 2. Second, as the jet advances, the DNS results show good agreement with the measurements, which indicates that the inflow turbulence mainly influences the fluctuating components in the upstream region. At downstream locations, turbulence induced by instabilities, such as Kelvin−Helmholtz instability

the mean mixture fraction of the DNS results agrees well with that of the measurements. At x/d = 11 and 14, the computed mixture fraction near the axial line is slightly higher than the measured mixture fraction. From the mean mixture fraction profiles, it could also be seen that the half-width of the mixture fraction increases as the flame develops. The rms mixture fraction profiles are shown in panels d−f of Figure 4. Two points are evident. First, the computed rms mixture fraction does not agree 6123

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and combustion instability, dominates, while the effect of inflow turbulence vanishes. The radial profiles of the Favre mean and rms temperature at the three axial locations are displayed in Figure 5. The predictions are in good agreement with the measurements for the Favre mean and rms temperature. However, the temperature at x/d = 11 is overpredicted. It is worth noting that the predicted lift-off height is lower than the measured lift-off height, so that chemical reactions are initiated earlier and the predicted temperature is higher than the measured temperature at the same axial location downstream of the stabilization region. The computed radial profiles of the mean and rms mass fractions of H2, O2, H2O, and OH are compared to the measurements and shown in Figures 6−9. It is seen from Figure 6 that the mean H2 mass fraction decreases along the central line as hydrogen is gradually consumed through chemical reactions. The computed profiles follow the trends of the experiment. At the axial location x/d = 11, the mean H2 mass fraction is slightly underpredicted in the shear layer, while the rms H2 mass fraction is overpredicted, as shown in Figure 6e. The fluctuating mass fraction is the highest at the axial location x/d = 14, where chemical reactions are very intensive. Thus, it is speculated that turbulence induced by the flame is significant in the present study. The predicted mean and rms O2 mass fractions are in good agreement with the measurements, as shown in Figure 7. However, the mean O2 mass fraction is slightly underpredicted at x/d = 11 and 14, and the rms O2 mass fraction is not wellpredicted in the co-flow region at the location of x/d = 1 because of the presumed inflow boundary condition adopted in the present study. Figure 8 delineates the mean and rms H2O mass fractions. In the upstream region, H2O only exists in the co-flow of products of lean hydrogen/air combustion. As the jet advances, reacting species diffuse to the flame front, where H2O is produced. At downstream locations, H2O may diffuse to the central line. The computed mean H2O mass fraction agrees well with the measured mean H2O mass fraction, although at some locations it is slightly overpredicted. Although the rms H2O mass fraction profiles are very complicated, the predictions are shown to be in accordance with the measurements. The comparison of the simulated and measured radial profiles of OH is shown in Figure 9. OH is an important radical in hydrogen/air combustion, which is usually used as a marker of the flame base. It is seen that, in the upstream region of x/d = 1, the OH mass fraction could be neglected because the chemical reaction has not yet been initiated there. At the location of x/d = 14, the simulated mean and rms OH mass fractions agree well with the measurements. However, overprediction is still observed at the location of x/d = 11, as shown in panels b and e of Figure 9. The reason is associated with the inconsistency of the lift-off height between the DNS and the experiment, as mentioned before. As a whole, the general agreement between the DNS results and those of the experimental measurements indicates that the present numerical approach applied in the DNS code is able to reasonably reproduce the laboratory flame. This gives us more confidence in studying the flame structure and the stabilization mechanism. 3.2. Flame Structure. For the lifted turbulent flame, it is interesting to examine the unsteady flame structure. The global structure of the lifted turbulent flame is delineated in Figure 10. The stoichiometric mixture fraction fst, which equals 0.474, is chosen to represent the flame front. The temperature is superimposed on the iso-surface of the stoichiometric mixture

Figure 10. Stoichiometric mixture fraction iso-surface colored by the temperature.

fraction. It is seen that the flame structure is rather complicated. At the inlet, the flow is laminar. As disturbances are added, the flow field begins to transit from laminar flow to turbulence. In the upstream region, hydrogen and oxygen diffuse to the stoichiometric mixture fraction iso-surface and mix sufficiently before chemical reactions take place. Because the co-flow consists of hot products of lean hydrogen/air combustion, the flame could be stabilized by autoignition in the shear layer, which will be explored in detail in the second part of the study (10.1021/ef3007728). Figure 10 indicates that, at downstream locations of the jet core region, chemical reactions are initiated and the temperature increases immediately. As the flow traverses downstream, the fine structures observed in the upstream region are dissipated, indicating that the effects of disturbances diminish. The lifted flame can be globally characterized by a lift-off height. In the present study, the predicted lift-off height is about 6.5d, which is lower than the experimental lift-off height of about 10d. However, it has been demonstrated that the lift-off height is very sensitive to the co-flow temperature. With almost the same conditions as those from Cabra et al.,1 Wu et al.26 measured a liftoff height of about 5.8d. They found that the co-flow temperature had significant effects on the lifted jet flame, especially for the cases of higher lift-off height, in which the lift-off height might decrease about 20 mm with the increase of 1 K of the co-flow temperature. Thus, it is acceptable to predict a different lift-off height from the measurement. The flame index has been used to distinguish premixed flames from non-premixed flames in various studies.7,27 To characterize the combustion modes in the present flame, a normalized flame index FI is defined as 6124

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Figure 11. Contours of the (a) heat release rate and (b) normalized flame index in a typical x−z plane.

FI =

∇YH2∇YO2 |∇YH2∇YO2|

Figure 12b indicates that there exist three combustion modes: a mixing mode, a fully burned mode, and an incomplete burned mode. In Figure 12c, the peak of the scatter plot shifts to the mixture fraction near the stoichiometric value and nearly all of the mixtures are fully burnt as the scatter points are close to the equilibrium line of the Burke and Schumann theory.28 It is worth noting that there are competing theories for the flame stabilization of the lifted turbulent flames. Cabra et al.1 found that, besides autoignition, the propagating partially premixed flame could also play an important role in the flame stabilization. The detailed investigation of the flame stabilization for the lifted turbulent flame is beyond the scope of the present study. It will be explored further in the second part of the investigations using the DNS database (10.1021/ef3007728).

(12)

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 unity, the two gradients are aligned and premixed combustion dominates, while when FI is negatively close to unity, the two gradients are opposed and non-premixed combustion dominates. The contours of the heat release rate and the normalized flame index in a typical x−z plane are shown in Figure 11. 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 smaller than 104 J m−3 s−1, the normalized flame index is set to 0. It is shown that the heat release rate is significant after the axial location x/d = 5 and most of the heat is produced in the region between x/d = 5 and 10. In the downstream region, the flame front interacts with the turbulent eddies and becomes quite wrinkled. The distribution of the normalized flame index is very complicated, as shown in Figure 11b. Premixed combustion and non-premixed combustion coexist in the lifted turbulent flame. However, by a close examination of Figure 11, it is found that regions where the heat release rate is higher share a negative normalized flame index, which means that most combustion occurs in the non-premixed mode. Figure 12 shows the scatter points of the temperature versus the mixture fraction at three different axial locations, e.g., x/d = 5, 7, and 10. In the upstream, all of the points are close to the mixing line, indicating that no reaction takes place in this region. The mixing line is important in ignition or quenching problems and more common to all flames that do not burn vigorously. It determines the extreme state of the flow, where mixing takes place without reaction. It is observed from Figure 12a that autoignition first occurs at the fuel-lean side with a mixture fraction of around 0.07. At the axial location x/d = 7, the peak of the scatter plot shifts to the mixture fraction of around 0.2, which is smaller than the stoichiometric mixture fraction of 0.474.

4. CONCLUSION A DNS study is carried out to investigate an experimental lifted turbulent H2/N2 flame in a co-flow of hot products of lean H2/air combustion by Cabra et al.1 The Reynolds number based on the exit diameter and jet velocity is 23 600. More than 285 million grid points are employed to resolve both turbulence scales and flame structure. A fourth-order explicit Runge−Kutta method for time integration and an eighth-order central differencing scheme for spatial discretization are used to solve the full compressible Navier−Stokes equation system. A detailed 9 species and 19-step mechanism for hydrogen combustion is adopted. The computation lasts over 14 flow-through times at a constant time step of 61 ns to provide stationary statistics. The computed axial profiles of the Favre mean mixture fraction and temperature are compared to the measurements, and good agreement is observed. The comparisons between the simulation and measurements of various scalars at three axial locations (x/d = 1, 11, and 14) are also conducted. It is shown that, although the computed rms components at the axial location x/d = 1 deviate from the measured rms components because of the inconsistent inflow turbulence, they are in good agreement at x/d = 11 and 14, which validates the present 6125

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approach and indicates that the inflow turbulence only affects the fluctuating components in the upstream region. The global structure of the lifted turbulent flame is also examined. At downstream locations of the jet core region, chemical reactions are initiated and temperature increases quickly. The fine structures in the upstream region are dissipated as the jet advances. The predicted lift-off height is lower than the measured lift-off height because the present flame is very sensitive to the co-flow temperature. The flame index indicates that most chemical reactions occur in the non-premixed mode. Furthermore, the scatter points of the temperature versus the mixture fraction at three different axial locations are plotted. All of the points are located between the mixing line and the equilibrium line.

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AUTHOR INFORMATION

Corresponding Author

*Telephone/Fax: 86-571-87951764. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (50976098 and 51176170) and partially supported by the Qianjiang Talents Project of Zhejiang Province of China (2011R10030).

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REFERENCES

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Figure 12. Scatter points of the temperature versus the mixture fraction at three different axial locations: (a) x/d = 5, (b) x/d = 7, and (c) x/d = 10. 6126

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