Stabilization and Combustion Processes of Turbulent Premixed Lifted

Energy & Fuels 2008, 22, 925–934

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Stabilization and Combustion Processes of Turbulent Premixed Lifted Methane-Air Flames on Low-Swirl Burners Sungmo Kang, Hoojoong Kim, Jeongwon Lee, and Yongmo Kim* Department of Mechanical Engineering, Hanyang UniVersity, Seoul 133-791, South Korea

Jae-Hwa Chung and Dal-Hong Ahn Korea Electric Power Research Institute, Daejeon 305-333, South Korea ReceiVed July 31, 2007. ReVised Manuscript ReceiVed NoVember 15, 2007

This study has numerically modeled the stabilization and combustion processes of turbulent lifted methane-air premixed flames on low-swirl burners (LSB). In these turbulent swirling premixed flames, tangentially injected air jets induce a turbulent swirling flow which plays a crucial role in stabilizing the lifted turbulent flames. In the present approach, the turbulence-chemistry interaction is represented by the level-set-based flamelet model. Two- and three-dimensional computations have been made for various swirl numbers and nozzle lengths. In terms of the center line axial velocity, mean progress variable, rms axial velocity fluctuations, and local equivalence ratios, numerical results are compared with experimental data. The three-dimensional approach, compared to the two-dimensional approach, yields a much better conformity with measurements without any analytic assumptions on the inlet swirl profiles. Numerical results indicate clearly that the present level-setbased flamelet approach has realistically simulated the structure and stabilization mechanism of the lifted turbulent stoichiometric and lean methane-air premixed flames on the low-swirl burner.

1. Introduction Economical and environmental problems are strongly related to the fact that most (∼90%) of the worldwide energy supply is provided by combustion processes of fossil fuels which are inevitably followed by the emission of unwanted pollutants. Particularly, the intensified use of energy has rapidly increased the global NOx emission from combustion devices. Thus, the regulations on the allowable pollutant emission have been increasingly more stringent and have led to the strong demand for development of advanced clean combustion systems which fulfill simultaneously lower emissions of pollutants and higher efficiency of fuel consumption. Lean premixed combustion is one of the most promising technologies to reduce NOx emission from gas-turbine combustors. Thus, in order to meet increasingly strict NOx emission regulations, most of the low-NOx power-generation gas turbines operate in the lean premixed mode because this operation mode reduces the flame temperature and substantially decreases the amount of pollutants (CO and NO) formed at the flame front. To ensure flame stabilization, the premixed dry low emission (DLE) combustors usually utilize high-swirl injectors. Especially in lean premixed combustion conditions, flame stabilization is relatively sensitive to the strength of swirl which is needed to achieve the high turbulent flame speed and the flow reversal. Thus, a large portion of air is swirled to stabilize the lean premixed combustion processes. In the swirl-induced recirculation zone, the flame-holding process is achieved by continuously providing the ignition source through the mixing of the hot combustion products with the incoming unburned mixture. This * Corresponding author: e-mail [email protected]; phone +82-22220-0428; Fax +82-2-2297-3432.

flame stabilization process utilizes flow recirculation to create a low fluid-particle velocity region together with a sufficiently long residence time and high turbulence intensities. These are essentially needed for flame anchoring in the turbulent reacting flow processes of gas turbine combustors. However, to comply with the increasingly strict NOx emission regulations, the equivalence ratio needs to be decreased toward the lean flammability limit. As a result, the corresponding ultralean premixed combustion processes become susceptible to the combustion-driven oscillations. There has been substantial research effort1–4 to investigate the mechanisms driving combustion instabilities and their control. Also, there are other research efforts on clean combustion technologies including catalytic combustors5 and the use of alternate fuel.6,7 However, in view (1) Candel, S. Combustion dynamics and control: progress and challenges. Proc. Combust. Inst. 2002, 29, 1–28. (2) Lieuwen, T.; Zinn, B. T. The role of equivalence ratio oscillations in driving combustion instabilities in low NOx gas turbines. Proc. Combust. Inst. 1998, 27, 1809–1816. (3) Richards, G. A.; Gemmen, R. S.; Yip, M. J. A Test Device for Gas Turbine Combustion Oscillations. ASME J. Eng. Gas Turbines Power 1997, 119, 776–782. (4) Lee, S.-Y.; Seo, S.; Broda, J. C.; Pal, S.; Santoro, R. J. An experimental estimation of mean reaction rate and flame structure during combustion instability in a lean premixed gas turbine combustor. Proc. Combust. Inst. 2000, 28, 775–782. (5) Etemad, S.; Pfefferle, W. C.; Smith, L.; Karim, H.; Castakli, M.; Boors, S.; Lyubousky, M. Catalytic combustion enabling technologies developing program for industrial gas turbine systems. DOE/CH/10939, Final Report, Jan 2002. (6) Schefer, R. W.; Wicksall, D. M.; Agrawal, A. K. Combustion of hydrogen-enriched methane in a lean premixed swirl-stabilized burner. Proc. Combust. Inst. 2002, 29, 843–851. (7) Basu, A.; Gradassi, M.; Sillis, R. ; Fleisch, T.; Puri, R. Use of DME as a Gas Turbine Fuel; ASME paper 2001-GT-0003, ASME Turbo Expo, 2001.

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of practical application, these new technologies must resolve many technical issues in terms of system integration, control, durability, maintenance, and cost. On the other hand, Cheng and his colleagues8–14 at Lawrence Berkeley National Laboratory (LBNL) have made impressive progress in the development of an innovative lean premixed low-swirl burner which ensures ultralow emission and combustion stability. This low-swirl burner (LSB) generates the turbulent lean premixed flame which is stabilized in the divergent flows generated by the low swirl. This LSB yields a stable flame field which is nearly oscillation-free and therefore less vulnerable to blow-off. Unlike conventional high-swirl burners, the low-swirl burner for a wide range of operating conditions does not lead to vortex breakdown which generates flow recirculation. In the LSB, the flow stream diverges and slows down due to swirl. The velocity decay of this divergent flow creates the flame stabilization zone where the local flow velocity is equal to the flame speed. However, at a certain condition, an LSB possibly yields a weak recirculation zone at a location further downstream from the flame anchoring upstream site. Moreover, the flame in the LSB does not yield flashback and blowout because the flow velocity at the burner exit is much higher than the flame speed and the velocity at the downstream flame zone is much lower than the flame speed. Even if the LSB was originally developed for fundamental turbulent premixed combustion research for the determination of turbulent burning velocity as well as the evaluation of regime diagram for turbulent premixed flames,8–10 it has been recognized that combustion technology utilizing this LSB has the great potential in clean combustion applications owing to its robust stability over wide a range of operating conditions.11–14 This low-emission lean premixed combustion technology was successfully demonstrated for industrial heating systems11–13 and ongoing research14 is currently underway for further development of gas turbine applications. Recently, Tachibana and Zimmer15,16 investigated the effect of swirl intensity, equivalence ratio, and nozzle length on the structure and stabilization of the turbulent lean premixed lifted flame over the LSB. They also studied the effects of global flame bouncing on the flame stability as well as the effects of swirl on flame properties. By (8) Chan, C. K.; Lau, K. S.; Chin, W. K.; Cheng, R. K. Freely propagating open premixed turbulent flames stabilized by swirl. 24th (Int.) Symp. Combust. 1992, 511–518. (9) Cheng, R. K. Velocity and scalar characteristics of premixed turbulent flames stabilized by weak swirl. Combust. Flame 1995, 101, 1–14. (10) Plessing, T.; Kortschik, C.; Peters, N.; Mansour, M. S.; Cheng, R. K. Measurements of the turbulent burning velocity and the structure of premixed flames on a low-swirl burner. Proc. Combust. Inst. 2000, 28, 359– 366. (11) Yegian, D. T.; Cheng, R. K. Development of a lean premixed lowswirl burner for low NOx practical applications. Combust. Sci. Technol. 1998, 139, 207–227. (12) Cheng, R. K.; Yegian, D. T.; Miyasato, M. M.; Samuelsen, G. S.; Benson, C. E.; Pellizzari, R.; Loftus, P. Scaling and development of lowswirl burners for low-emission furnaces and boilers. Proc. Combust. Inst. 2000, 28, 1305–1313. (13) Littlejohn, D.; Majeski, A. J.; Tonse, S.; Castaldini, C.; Cheng, R. K. Laboratory investigation of an ultralow NOx premixed combustion concept for industrial boilers. Proc. Combust. Inst. 2002, 29, 1115–1121. (14) Johnson, M. R.; Littlejohn, D.; Nazeer, W. A.; Smith, K. O.; Cheng, R. K. A comparison of the flowfields and emissions of high-swirl injectors and low-swirl injectors for lean premixed gas turbines. Proc. Combust. Inst. 2005, 30, 2867–2874. (15) Tachibana, S.; Zimmer, L.; Suzuki, K. Flame front detection and dynamics using PIV in a turbulent premixed flame. 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 2004. (16) Tachibana, S.; Zimmer, L. Effect of swirl on the stability of a lifted flame sustained by a low-swirl burner. Proceedings of 20th Int. Colloquium on the Dynamics of Explosions and ReactiVe Systems, McGill University, Montreal, Canada, July 31-Aug 5, 2005.

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using the Mie scattering and PLIF image of some representative chemical species, Tachibana and Zimmer15,16 have attempted to detect the flame front boundary to find many physical aspects such as flame-vortex interaction, flame wrinkling and its relation to the turbulence levels, and flame holding mechanism. The data obtained in their measurements15,16 were also used to analyze the conditional mean velocity analysis as well as the global flame bouncing motion. In this aspect, it is worthwhile to systematically understand the turbulent mixing, combustion, and flame stabilization processes in the lifted turbulent premixed flames of the LSB. This study has numerically modeled the combustion processes of the lifted turbulent swirling methane-air premixed flames on the LSB. In these turbulent swirling premixed flames, tangentially injected air jets induce a turbulent swirling flow which plays a crucial role in stabilizing the lifted turbulent flames. In the present approach, the turbulence-chemistry interaction is represented by the level-set-based flamelet model. In order to maintain reasonable computational accuracy, geometric flexibility, and the proper turnaround time of 3-D calculations using detailed chemistry, the present approach has been implemented in the context of an unstructured-grid finitevolume method. Two- and three-dimensional computations have been performed for one turbulent stoichiometric-premixed methane-air flame8 and six lean-premixed15 methane-air flames stabilized by different low-swirl burners of different swirl numbers and nozzle lengths. In terms of the center line velocity profiles and flame liftoff heights, numerical results are compared with the experimental data. On the basis of numerical results obtained in this study, a detailed discussion has been made about the effects of swirl intensity and nozzle length on the flame stabilization and the structure of turbulent lean-premixed lifted flames in the LSB. The numerical results clearly indicate that the present level-set-based flamelet approach has realistically simulated the structure and the stabilization mechanism of lifted turbulent swirling stoichiometric and lean premixed flames on low-swirl burners. 2. Physical and Numerical Models 2.1. Governing Equations. The density-weighted Navier–Stokes equation, the energy equation, the k- turbulence model equations, and the mean and variance of mixture fraction equations are employed to predict the turbulent reacting flows and are represented by the following form: ˜ ∂ ˜ ∂ ˜) ) ∂ (Γ ∂φ ) + S (Fφ) + (Fu ˜jφ φ φ ∂t ∂xj ∂xj ∂xj

(1)

where φ includes mean velocity vector, mean enthalpy, turbulent kinetic energy and dissipation rate, and the mean and variance of mixture fraction. Γφ and Sφ represent the diffusion coefficient and the source term of its equation, respectively. Diffusion coefficients and source terms can be found in our previous work.17 As an alternative to the local equivalence ratio, the mean mixture fraction is solved to account for changes in the local equivalence ratio due to entrainment of air and/or different equivalence ratios among the incoming mixtures. 2.2. Flamelet Model Based on Level-Set Approach. In the turbulent partially premixed flames, a formulation for both premixed and nonpremixed combustion has to be used. For this purpose, the flamelet model for nonpremixed combustion is (17) Kang, S.; Kim, Y. Parallel unstructured-grid finite-volume method for turbulent nonpremixed flames using the flamelet model. Numer. Heat Transfer, Part B 2003, 43, 525–547.

Turbulent Premixed Lifted Methane-Air Flames

Energy & Fuels, Vol. 22, No. 2, 2008 927

combined with the flamelet model for premixed combustion. The mixing of fuel and oxidizer in the turbulent flow field is described by the transport equation of the mean mixture fraction and its variance.19 In order to describe the premixed combustion, the level-set approach based on the G equation18 is introduced, where an isoscalar surface G(x,t) ) G0 defines the location of the instantaneous premixed flame front. Thus, this surface divides the flow field into the regions of burnt gas where G(x,t) > G0 and unburnt mixture where G(x,t) < G0. Since G is the nonreacting scalar, it avoids complications associated with countergradient diffusion, and there is no need for a source term closure. The equation for the mean location of the turbulent flame front is written as19 ˜) ∂(F G ˜) ) (Fs )|∇G ˜| - F D κ˜|∇G ˜| + ∇ · (Fu ˜G T t ∂t

(

κ˜ ) ∇ · n˜ ) ∇ · -

˜ ∇G ˜| |∇G

)

(2) (3)

where sT is the turbulent burning velocity, κ˜ the curvature of the mean flame front, n˜ the unit vector normal to the flame front, and Dt the turbulent diffusivity, which can be determined from the integral length scale l and the velocity fluctuation V′ as Dt ) a4lV ’ ,

l ) a1V’3 ⁄ ˜,

V ’ ) (k˜ ⁄ a2)1⁄2

(4)

where the constants are a1 ) 0.37, a2 ) 1.5, and a4 ) 0.78 derived from turbulence modeling. The equation for the variance ˜ is19 of G ˜″2) ∂(FG ˜″2) ) ∇ · (FD ∇ G ˜ 2 ˜2 + ∇ · (Fu ˜G t | ″ ) + 2 FDt(∇G) | ∂t ˜ ˜ 2 ″ (5) csF G ˜k where ∇| denotes differentiation only tangential to the mean flame front and cs is a modeling constant of 2.0. In order to model the turbulent burning velocity sT in eq 2, It is assumed that the partially premixed flame propagates through a stratified, locally premixed environment. For premixed turbulent combustion, sT can be determined from an algebraic expression:19 a4b32 sT - sL )Da + V’ 2b1

[(

)

]

2 a4b32 Da + a4b32Da 2b1

1⁄2

(6)

where sL is the laminar burning velocity of a plane flame, the Damköhler number is Da ) sLl/(V′lF), lF is the laminar flame thickness, and the constants are b1 ) 2.0 and b3 ) 1.0. In cases of variable local equivalence ratio a conditional turbulent Damköhler number Da(Z) as a function of the mixture fraction (Z) is introduced to determine the conditional turbulent burning velocity sT(Z) as sT(Z) ) sL(Z) + V ’ f{Da(Z)}

(7)

where f{ } represents the right-hand side of eq 6 and Da(Z) is defined as19 (18) Williams F. A. Turbulent Combustion. In The Mathematics of Combustion; Buckmaster, J. D., Ed.; Society for Industrial and Applied Mathematics: Philadelphia, PA, 1985; pp 197–1318. (19) Peters N. Turbulent Combustion; Cambridge University Press: Cambridge, 2000.

Da(Z) )

sL2(Z)l sL(Z)l ) V ’ lF(Z) V’D

(8)

In the second part of the above equation, the laminar flame thickness has been replaced by lF(Z) ) D/sL(Z) where D is the laminar diffusivity. 2.3. Flamelet Library Procedure. For species i, a laminar flamelet library can be denoted by Yi(G,φ). Here, φ˜ denotes the equivalence ratio and G the flamelet coordinate, whose origin G ) G0 is fixed at the inner layer. This study defines it at the peak of CH2O concentration. The flamelet library is preprocessed by solving flamelet equations prior to flow calculations. Assuming that the distance normal to the mean flame front is ˜ is the Favre mean in space, the mean mass ˜ (G(x) - G0) and G fraction of species i may be calculated as ˜ (x) ) Y i

∫ ∫ +∞

0

+∞

-∞

Yi((G - G0) ⁄ σ ˜, φ)P(G, φ;x) dG dφ (9)

Here the flame surface area ratio is approximated as σ˜ ) sT/sL. The joint pdf P(G,φ) can be obtained in different ways such as measurements or a pdf-transport formulation20 but more often a presumed-shape pdf approach is used.19,21 Using Bayes’ theorem and assuming the stochastic random variables being statistically independent lead to P(G, φ) ) P(G) P(φ) (10) The joint pdf can be obtained if P(G) and P(φ) are modeled separately. Here a Gaussian shape is assumed for the marginal pdf P(G):19 ˜″2)-1⁄2 exp[-(G - G ˜(x))2 ⁄ (2G ˜″2)] P(G) ) (2πG (11) The delta function is used for P(φ) under the assumption that it can be a choice for the premixed flames which have a dominant premixed combustion mode and a relatively low gradient of mixture fraction in the main flame zone. The mean temperature is calculated from the mean enthalpy by using the local mean mass fractions, and then the density is determined from the equation of state. 2.4. Reinitialization. The level-set method is quite efficient and robust to track the motion of interface for the interested ˜ equation is object. In this turbulent flame calculation, the G used to determine the mean flame position because the turbulent burning velocity sT is only defined at the mean flame front. To ˜ outside G0 is calculated avoid numerical difficulties, the scalar G as a distance function. This distance function can be obtained using the so-called reinitialization procedure22 which satisfies ˜ | ) 1 outside the mean flame front. The present approach |∇G employs the method proposed by Sussman et al.,22 which is required to solve the following Hamilton-Jacobi equation: ∂θ ) sign(θ0)(1 - |∇θ|) ∂t

with ˜(x, t) - G θ(x, 0) ) θ0(x) ) G 0

(12)

or in discretized form: θn+1 ) θn - ∆t sign(θ0)(|∇θn| - 1)

(13)

where the superscript n is the pseudo-time-marching number, ∆t is a time-step size which is different from the flow time scale, (20) Pope, S. B. Pdf methods for turbulent reactive flows. Prog. Energy Combust. Sci. 1985, 11, 119–192. (21) Nilsson P. A Level-set Flamelet Library Model for Premixed Turbulent Combustion. Ph.D. Thesis, Lund Institute of Technology, Lund Sweden, 2001. (22) Sussman, M.; Fatemi, E. Level Set Redistancing Algorithm. SIAM J. Sci. Comput. 1999, 20, 1165–1191.


and sign(θ0) is a sign function. This evolution equation has characteristics that originate at the flame surface and propagate the unitary gradient information from there into the surrounding field. Since the zero level set represents a moving boundary interface, it must not move during reinitialization. However, this zero level set moves in actual computation, and numerical error deviated from the zero level set is introduced. In fact, the volume with the zero level set shrinks and is not conserved in the reinitialization process. In the present study the proper treatment suggested by Sussman et al.22 is used to conserve the volume during the reinitialization process. In the context of the unstructured-grid FVM, the interface gradient is calculated by distance-weighted averaging of the cell-centered gradients of two cells sharing the interface. 2.5. Pressure-Based Unstructured-Grid Finite-Volume Method and Parallel Strategy. To discretize the spatial domain in context with the unstructured-grid finite-volume method, the cell-centered, collocated scheme is employed here because the control volume can be represented by the numerical grid itself, and the coding structure including the imposition of boundary conditions can be further simplified. The cell types may include triangular and quadrilateral for 2-D problems and tetrahedral, prism, pyramid, and hexahedral for 3-D problems. The cell type in each problem can be single or mixed. All transport variables are stored at cell centers. At an interface between cells, the diffusion term can be approximated on the basis of secondorder finite difference scheme for the tangent vectors and metric tensors in a curvilinear system. Here the primary diffusion is treated implicitly while the cross-diffusion is handled explicitly. The second-order upwinding scheme is used for the convective flux terms. In this scheme, the face value is evaluated via the value at the upwind cell, and a linear reconstruction procedure is used to achieve second-order accuracy. For temporal integration, a general implicit-discretized time-marching scheme with a flux correction is employed for the system of linearized algebraic equations. In this integration procedure, various temporal schemes including the implicit Euler or Crank-Nicholson can be constructed simply by changing the time-marching control parameter. In this study, the pressure-velocity coupling in the chemically reacting flows is handled by the multiple pressure-correction method.23 In order to avoid the well-known checkerboard flow fields, according to the concept of Rhie and Chow24 developed for the structured-grid method, the pressure-damping term is introduced in context of the unstructured-grid procedure. The detailed formulations regarding the present pressure-based unstructured-grid finite-volume method are well described in our previous work.17,25 3. Results and Discussion In the present study, this level-set-based flamelet approach in conjunction with a parallel unstructured-grid finite-volume method has been applied to numerically investigate the stabilization characteristics and combustion processes of the turbulent lifted methane-air flames on low-swirl burners.8,15 The typical LSB consists of a central nozzle of fuel/air mixture and tangential air jets. Swirl is generated by the tangentially injected (23) Kim, Y. M.; Chen, C. P.; Ziebarth, J. P.; Chen, Y. S. Prediction of fast transient spray-combustion flows. Numer. Heat Transfer, Part A 1994, 25, 21–42. (24) Rhie, C. M.; Chow, W. L. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 1983, 21, 1525–1532. (25) Kang, S.; Kim, Y. M. Pressure-based unstructured-grid finitevolume method for simulating laminar reacting flows. Numer. Heat Transfer, Part B 2002, 41, 53–72.

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Figure 1. Flame regimes estimated along the center line of premixed methane/air flames in two different low-swirl burners. φ ) 0.63 corresponds to the case of S ) 1.32 with L ) 90 mm.

air jets and induces a flow divergence above the burner exit. As a turbulence generator, a turbulence grid or a perforated plate is placed upstream of the tangential jets. A geometric swirl number8,15,26 is given by S)

πRjRQj2 cos R Aj(Qj + Qm)2

(14a)

or S)

πR2Qj2 cos R Aj(Qj + Qm)2

(14b)

Here, Rj and R are the radii of the air jets and the main nozzle, respectively, Aj is the total area of air jets, Qj and Qm are the total mass flow rate of the air jets and the mixture, respectively, and R is the inclined angle of the air jets. For a given swirl number, the swirl velocity components can be determined on the basis of a mass flow rate of air jets obtained from eq 14. An air entrainment in the open flame system and the tangentially injected air jets lead to a change in the local equivalence ratio. To account for the effects of this mixture stratification, the flamelet library has been generated for the wide range of equivalence ratios. The GRI-Mech 3.0 chemical mechanism involving 53 species and 325-elementary reactions27 is used in all computations. In the flow calculations, the entrainment of fluid is modeled by a free stream. The computational domain was discretized into about 12 000 triangles and 140 000 hexahedrons in 2-D and 3-D space, respectively, where typical grid size across a flame front is kept to about 2–4 mm. Cold flow calculations begin first, and then an ignition of mixture follows through an initial G field with a 30 mm radius ignition core r0 at x0 ) 50 mm downstream of the burner exit, given as G ) r0 - |x - x0| (see Figure 2a). This ignition core resembles the small blunt body used as a lighting source in the experiment. After ignition, the flame front propagated until it finally reached a stationary condition. Computations have been performed for a stoichiometricpremixed flame8 and six lean-premixed15 flames stabilized above different low-swirl burners for different swirl numbers and nozzle lengths. It is worthy to compare the flame regimes of the premixed combustion in both low-swirl burners. On the basis of estimated characteristic velocity and length scales along the (26) Johnson, M. R.; Cheng, R. K. Dynamics of flame flowfields in a low-swirl burner. Proceedings of the 19th International Colloquium on the Dynamics of Explosions and ReactiVe Systems, Hakone, Japan, 2003. (27) Smith, G. P.; Golden, D. M.; Frenklach, M.; Moriarty, N. W.; Eiteneer, B.; Goldenberg, M.; Bowman, C. T.; Hanson, R. K.; Song, S.; Gardiner, Jr., W. C.; Lissianski, V. V.; Qin, Z. Gri-mech 3.0, University of California Berkeley, 1999; http://www.me.berkeley.edu/gri_mech/.



Figure 2. Problem configuration for a turbulent stoichiometric-premixed methane/air flame (Um ) 5 m/s, d ) 50 mm, dj ) 6.1 mm): (a) surface grid, inlet boundary conditions, and initial isosurface of G ) 0; (b) secondary flow vectors at the cross section containing air jets; (c) blowup of burner.

Figure 3. Mean flame field calculated at the center plane of z ) 0: (a) velocity vectors, (b) scalar G, and (c) temperature.

center line, the flame regimes are plotted in Figure 1 in terms of V′/sL and l/lF. The reaction zones for the turbulent stoichiomeric-premixed CH4/air lifted swirling flame8 are mostly placed in the corrugated flamelets regime. On the other hand, the reaction zones for the turbulent lean-premixed CH4/air lifted swirling flame15 are located in the thin reaction regime or the edge between the corrugated flamelets regime and the thin reaction regime. The results indicate that the decreased equivalence ratio corresponds to an increased Karlovitz number of Ka ) (V′/sL)3/2/(l/lF)1/2. 3.1. Turbulent Stoichiometric-Premixed CH4/Air Lifted Flame on LSBs. The turbulent stoichiometric-premixed flame8 in an LSB has been chosen as the first validation case. The burner consists of a central nozzle of 50 mm diameter surrounded by an annular coflow air of 114 mm diameter and two tangential air jets of 6.1 mm diameter. Experiments were carried out for different equivalence ratios of φ ) 0.65–1.0 and turbulence intensities. Typical conditions are a bulk mean velocity of both mixture and annular coflow, Um of 5 m/s, and a swirl number of S ) 0.07 given by eq 14a. The measurements include the mean and the rms velocities. Among the experimented flames, a stoichiometric-premixed CH4/air flame called SWF48 has been chosen as a test case. Using the total mass flow rate of both mixture and coflow air, Qm of 0.0595 kg s-1, the swirl number of 0.07 corresponds to the total mass flow rate of the air jets, Qj, of 0.005 64 kg s-1. This leads to a tangential velocity of 82.37 m/s based on an air density of 1.172 kg m-3. In the case of an axisymmetric model, the swirl is modeled

in the same way as in the recent work by Chao et al.28 where the air jets are modeled on a 5 mm wide annulus, leading to a radial velocity of 2.7 m/s and a tangential velocity of 76.3 m/s. Figure 2 shows the configuration for the LSB through a threedimensional computational grid consisting of 139 520 hexahedrons. The computational domain extends to x ) 0.9 m downstream of the nozzle exit and r ) 0.65 m in the radial direction. Corresponding to the turbulence grid position in the experiment, the mixture is located at 25 mm upstream of the tangential jets. Assuming a turbulence intensity of 5% of the mean velocity, the turbulent kinetic energy is prescribed at the inlet. Figure 3 shows the predicted mean fields of velocity vectors, scalar G, and temperature at z ) 0. These three-dimensional numerical results well reproduce the essential flame pattern of the lifted turbulent premixed weak swirling flame such as a curved thick flame brush observed in the experiment. In this LSB, the turbulent premixed lifted flame is characterized by the freely propagating premixed flame,8 and it is stabilized in the divergent flow generated by the weakly swirling flow. The predicted results shown in Figure 3 well reproduce the measured flame characteristics.8 Figure 4 presents the measured and predicted center line profiles of mean axial velocity in this lifted turbulent premixed flame stabilized over the LSB. Even if slight deviations exist, (28) Zhao, Q. W.; Chan, C. K.; Zhao, H. F. Numerical simulation of open swirl-stabilized premixed combustion. Fuel 2004, 83, 1615–1623.


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Figure 4. Centerline profiles of calculated and measured mean axial velocity.

the predicted center line velocity profile of the three-dimensional model is reasonably well agreed with the experimental data. These results imply that the level-set-based flamelet approach employed in the present study is capable of correctly predicting the turbulent flame speed and the flame brush thickness which strongly influences the mean flow fields of turbulent premixed flames. However, when the two-dimensional model is applied, the mean axial velocity along the center line is substantially overestimated before the flame front and remarkably underestimated behind the flame front. This trend was also observed in the previous two-dimensional simulation performed by Chao et al.28 This discrepancy is mainly attributed to the asymmetry of the tangentially injected jet-induced swirling flow field which is clearly displayed at the secondary-flow vectors in Figure 2b. This result suggests that the two-dimensional axisymmetric model is unable to correctly reproduce the mixing characteristics and the structure of turbulent lifted premixed low swirling flames induced by two tangentially injected air jets. 3.2. Turbulent Lean-Premixed CH4/Air Lifted Flames on LSBs. Tachibana and Zimmer15 investigated experimentally turbulent premixed flames in an LSB and reported detailed discussions on ways of flame front detection. In their measurements,15 the burner consists of a main nozzle of 53 mm diameter and four tangential air jets of 2 mm diameter with an inclined angle of 20°. Compared to the LSB8 discussed in the previous section, the diameter of the air jets is much reduced with the absence of the annular coflow air. Typical conditions are a CH4/ air mixture of φ ) 0.63, a bulk mean velocity of mixture, Um of 5 m/s, a blockage of punching plate of 64%, and swirl numbers of S ) 0.97–1.51 with nozzle lengths of L ) 30–150 mm. The experimental data included unconditional mean velocities and velocity fluctuations, unburnt and burnt conditional velocities, and the Reynolds mean progress variable. The swirl number is given by eq 14b, and here the Reynolds mean progress variable is calculated from following relations: c (x) )

˜c 1 - γ(1 - ˜c)

with γ )

F (x) 1-γ ) Fu 1 - γ(1 - ˜c)

Fu - Fb Fu

(15) (16)

where c˜ is the Favre mean progress variable and the unburnt and the burnt densities are given respectively by Fu ) 1.154 and Fb ) 0.19 kg m-3, leading to a gas expansion parameter of γ ) 0.835. Among the experimental conditions, this study selected six flames of S ) 1.14, 1.32, and 1.51 with L ) 90 and 150 mm as test cases. Using a mass flow rate of mixture, Qm of 0.012 72 kg s-1 based on the unburnt density of 1.154 kg m-3, swirl numbers of 1.14, 1.32, and 1.51 correspond to the total mass flow rates of air jets, Qj, of 0.001 153, 0.001 25, and 0.001 346 kg s-1, respectively. For example with S ) 1.32,

the corresponding mass flow rate Qj of 0.001 25 kg s-1 results in an axial velocity of 29.043 m/s and a tangential velocity of 79.795 m/s. For an axisymmetric flow configuration of S ) 1.32, the swirl inlet by air jets is modeled by a 1.64 mm wide annulus, leading to a radial velocity of 3.907 m/s, a tangential velocity of 40.8 m/s, and an axial velocity of 1.16 m/s. Figure 5 shows the configuration of the LSB and threedimensional computational grid arrangement with 120 512 hexahedrons. The computational domain extends axially to x ) 0.35 m downstream of the nozzle exit and radially to r ) 0.25 m. Because of the uncertainty of the turbulence-grid position and the turbulence intensity at inlet in the experiment,15 the mixture is injected at 10 mm upstream of the tangential jets. The turbulence intensity at the inlet is assumed as 5% of the mean velocity. Figure 6 shows the predicted mean fields of velocity vectors, scalar G, and temperature for S ) 1.32 with L ) 90 mm at z ) 0. The predicted flame patterns of this lifted turbulent premixed low swirling flame reasonably well reproduce those visualized in the experiment.15 The measured and predicted center line profiles of the mean axial velocity and the Reynolds mean progress variable are compared in Figure 7. The agreement between the experimental data15 and the three-dimensional computation results is quite favorable. Again, this result confirms that the level-set-based flamelet approach employed here has the capability to realistically simulate the turbulent flame speed and the flame brush thickness even for a much leaner premixed flame (φ ) 0.63) where the Karlovitz number is relatively high compared to the stoichiometric premixed flame8 discussed above. In terms of the mean axial velocity along the center line, the 2-D model underestimates before the flame front and overestimates far downstream of the flame front. However, compared to that of the stoichiometric premixed flame discussed in the previous section, slight deviations exist with both measurements and 3-D results. These deviations are also mainly caused by the axisymmetric modeling for the tangentially injected jetinduced swirling flow. Since this turbulent lifted premixed swirling flame induced by four tangentially injected air jets has a relatively small departure from the axisymmetric assumption, the two-dimensional model yields a relatively low deviation from the three-dimensional results or experimental data. In order to check the predicative capability for the dilution characteristics in the mixing layer of the low-swirl burner, additional calculations are made for measurements29 of the LSB with a nozzle length (L ) 90 mm) and the equivalence ratio of φ ) 0.6. In general, the dilution process in the LSB is influenced by the turbulent mixing process between the tangentially injected swirling air jets and the centrally injected premixture inside the nozzle, the swirl-induced flow divergence, the flow redirection due to the lifted flame, and an air entrainment into the mixing layer. First, to identify the effects of swirl-induced flow divergence and the flow redirection due to the lifted flame on the dilution process, comparison between the nonreacting fields and the lifted flame fields (S ) 1.4, 1.6) has been made. At the radial location (r > 24 mm), the higher swirl case yields the much higher local equivalence ratio due to the much stronger flow divergence effect. Numerical results also indicate that, compared to the nonreacting case, the reacting case yields the (29) Zimmer, L.; Tachibana, S. Laser Induced Plasma Spectroscopy for Local Composition Measurements Inside a Low Swirl Burner. Proceedings of 20th International Colloquium on the Dynamics of Explosions and ReactiVe Systems, McGill University, Montreal, Canada, July 31-Aug 5, 2005.



Figure 5. Problem configuration for turbulent lean-premixed methane/air flames (φ ) 0.63, Um ) 5 m/s, d ) 53 mm, dj ) 2 mm): (a) surface grid, inlet boundary conditions, and an isosurface of G ) 0; (b) secondary flow vectors at the cross section containing air jets; (c) blowup of burner.

Figure 6. Mean flame field calculated at the center plane of z ) 0 for S ) 1.32 with L ) 90 mm: (a) velocity vectors, (b) scalar G, (c) temperature.

Figure 7. Calculated and measured profiles of the mean axial velocity and mean progress variable along the center line for S ) 1.32 with L ) 90 mm.

much higher local equivalence ratio at r > 24 mm due to the flow redirection effects in the lifted flame. Figure 8 presents the predicted and measured29 radial profiles of local equivalence ratio at 10 mm above the burner exit. At the inner nearly intact core region (r < 12 mm), the predicted profiles are well agreed with experimental data for two swirl cases (S ) 1.4, 1.6). However, at the radial locations (12 mm < r < 24 mm), the present approach noticeably underestimates the equivalence ratio and overestimates the dilution. These deviated dilution characteristics are mostly originated from the incorrect turbulent mixing process between the tangentially

Figure 8. Comparison of radial profiles of local equivalence ratio along d45 line at 10 mm above the burner exit for S ) 1.4/1.6 with L ) 90 mm at φ ) 0.6. (d ) 53 mm, dj ) 2 mm, Um ) 5 m/s, Uj ) 88.992/ 95.785 m/s, u′m/u′j ) 5% of the bulk).

injected swirling air jet and the centrally injected premixture inside the nozzle. This discrepancy could be mainly responsible for the shortcomings of the k-e turbulence model based on the isotropic assumption especially in dealing with the complex swirling developing turbulent inside-nozzle flow with a strong anisotropic characteristics. At the outer radial locations (r > 24 mm) where the distribution of the local equivalence ratio is dominantly influenced by the swirl-induced flow divergence, the flow redirection due to the lifted flame, and an air


Kang et al.

Figure 9. (a) Mean velocity vectors and (b) contours of turbulent kinetic energy (m2 s-2) for S ) 1.32 with L ) 90 mm (d ) 53 mm, dj ) 2 mm, Um ) 5 m/s, Uj ) 84.916 m/s).

Figure 10. Calculated and measured profiles of the rms axial velocity fluctuations and mean progress variable along the center line for S ) 1.32 with L ) 90 mm.

entrainment, numerical results are in reasonably well agreement with experimental data. Figure 9 shows the predicted contours of turbulent kinetic energy and the velocity vectors for S ) 1.32. It can be clearly seen that the recirculation zone with the weak flow reversal is created at the far downstream region of the flame base. Numerical results also reveal that, along the center line, the turbulent kinetic energy gradually increases up to the edge of the weak recirculation zone formed and maintains the nearly same level within the recirculation zone. Figure 10 presents the predicted and measured center line profiles of the axial rms velocity fluctuations for S ) 1.32. Numerical results indicate that the rms velocity fluctuations

gradually increases along the axial coordinate, and this profile of rms velocity fluctuations is directly tied with that of turbulent kinetic energy discussed above. At upstream and downstream of the reaction front in the lifted flame, the predicted level of axial rms velocity fluctuations is in reasonably well agreement with experimental data. However, in the proximity of the reaction front, measurements15 indicate that the axial rms velocity fluctuation has the peak value which is nearly 1.7 times higher than the rms velocity fluctuations at the upstream and downstream of the reaction front. The present approach could not capture the abrupt change of the measured axial rms velocity fluctuation15 at the proximity of the reaction front. These discrepancies could be attributed to the defects of the RANSbased k-e turbulence model to deal with the strong anisotropic turbulence encountered in the reaction front. To improve the predicative capability of the present turbulent combustion model for the turbulent lifted flame fields of the low swirl burner, the future works must be systematically performed by utilizing the advanced turbulence model such as the LES (large-eddy simulation) model. Figure 11 shows the predicted contours of the CH mass fraction for three swirl numbers (S ) 1.14, 1.32, and 1.51) and two nozzle lengths (L ) 90 and 150 mm), respectively. According to measurements,15 the predicted liftoff height is defined as the position at half of the peak CH level along the center line. As displayed in Figure 11, the flame liftoff height decreases with increasing the swirl number. Around the flame stabilization region, the elevated swirl strength leads to a decrease of axial velocity due to the enhanced flow-divergence effect and an increase of the turbulent flame speed corresponding



Figure 11. Distributions of CH mass fraction calculated for different swirl numbers and nozzle lengths at z ) 0: (a-c) S ) 1.14, 1.32, and 1.51 with L ) 90 mm; (d-f) S ) 1.14, 1.32, and 1.51 with L ) 150 mm.

Figure 12. Calculated flame liftoff heights for different swirl numbers and nozzle lengths.

to the increased turbulence intensity. Consequently, at the axial location much closer to the burner exit, the decreased axial velocity is balanced with the increased turbulent flame speed. Thus, these two effects mainly control the flame stabilization and the liftoff height of the turbulent lifted premixed low swirling flames. In terms of the flame liftoff heights for different swirl numbers and nozzle lengths, the quantitative comparison between prediction and measurement has not been made in this study because the measured line-of-sight integrated data are not quantitatively useful. Figure 12 shows the predicted flame liftoff heights for different swirl numbers and nozzle lengths. It can be clearly seen that the flame liftoff height increases with increasing the nozzle length. This is directly tied to the decay of turbulence intensity downstream of the nozzle. Since the reduced turbulence intensity results in the decreased turbulent flame speed, the flame with the much longer nozzle length could be stabilized at a region further downstream where the fluid particle velocity is balanced with the turbulent burning velocity. These predicted flame liftoff heights are qualitatively well agreed with the experimental data15 based on measured CH* chemiluminescence measurements. 4. Conclusions The level-set-based flamelet model has been applied to simulate the structure and the flame stabilization mechanism of the turbulent lifted stoichiometric and lean premixed flames stabilized above the low-swirl burner (LSB). In the case of the turbulent lifted lean premixed swirling flames induced by four tangentially injected air jets, computations are made for various

swirl numbers and nozzle lengths. On the basis of numerical results, the following conclusions can be drawn: (1) The present level-set-based flamelet approach well reproduces the essential flame pattern of the lifted turbulent stoichiometric and lean premixed swirling flames induced by tangentially injected air jets. In terms of the center line profiles of mean axial velocity and progress variable, the threedimensional approach, compared to the two-dimensional approach, yields a much better conformity with measurements without any analytic assumptions on the inlet swirl profiles. Numerical results suggest that the present level-set-based flamelet approach is capable of realistically simulating the turbulent flame speed and the flame brush thickness in the turbulent lifted premixed swirling flames with the corrugated or thin reaction regime. (2) In case of the lifted turbulent stoichiometric premixed swirling flame induced by two tangentially injected air jets, when the two-dimensional model has been applied, the mean axial velocity along the center line is substantially overestimated before the flame front and remarkably underestimated behind the flame front. This discrepancy is mainly attributed to the asymmetry of the tangentially injected jet-induced swirling flow field. This result suggests that the two-dimensional axisymmetric model is unable to correctly reproduce the mixing characteristics and the structure of turbulent lifted premixed low swirling flames induced by two tangentially injected air jets. (3) The flame liftoff height decreases with increasing the swirl number, and it increases with increasing the nozzle length. Around the flame stabilization region, the elevated swirl strength leads to a decrease of axial velocity due to the enhanced flowdivergence effect and an increase of the turbulent flame speed corresponding to the increased turbulence intensity. Consequently, at the axial location much closer to the burner exit, the decreased axial velocity is balanced with the increased turbulent flame speed. (4) The flame liftoff height increases with increasing the nozzle length. Since reduced turbulence intensity results in decreased turbulent flame speed, the flame with the much longer nozzle length could be stabilized at a region further downstream where the fluid particle velocity is balanced with the turbulent burning velocity. (5) Numerical results indicate that, compared to the nonreacting case, the reacting case yields the much higher local equivalence ratio at r > 24 mm due to the flow redirection effects in the lifted flame. At the radial locations (12 mm < r


< 24 mm), the present approach noticeably underestimates the equivalence ratio and overestimates the dilution. This discrepancy could be mainly responsible for the shortcomings of the k-e turbulence model based on the isotropic assumption especially in dealing with the complex swirling developing turbulentinside-nozzleflowwithastronganisotropiccharacteristics. (6) At upstream and downstream of the reaction front in the lifted flame, the predicted level of axial rms velocity fluctuations is reasonably well agreed with experimental data. The present approach could not capture the abrupt change of the measured axial rms velocity fluctuations at the proximity of the reaction front. These discrepancies could be attributed to the defects of

Kang et al.

the RANS-based k-e turbulence model to deal with the strong anisotropic turbulence encountered in the reaction front. To improve the predicative capability of the present turbulent combustion model for the turbulent lifted flame fields of the low swirl burner, the future works must be systematically performed by utilizing the advanced turbulence model such as the LES (large-eddy simulation) model. Acknowledgment. This work was supported by New & Renewable Energy R&D program (2006-N-CO12-P-03-3-020-2006) under the Korea Ministry of Commerce, Industry and Energy (MOCIE). EF700458U

Stabilization and Combustion Processes of Turbulent Premixed Lifted

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