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A numerical analysis of the structure of a turbulent hydrogen jet lifted flame
Proceedings of the Combustion Institute, Volume 29, 2002/pp. 2009–2015
A NUMERICAL ANALYSIS OF THE STRUCTURE OF A TURBULENT HYDROGEN JET LIFTED FLAME YASUHIRO MIZOBUCHI,1 SHIGERU TACHIBANA,1 JUNJI SHINIO,1 SATORU OGAWA1 and TADAO TAKENO2 1 CFD Technology Center National Aerospace Laboratory of Japan 7-44-1 Jindaij-Higashimachi, Chofu Tokyo 182-8522, Japan 2 Department of Mechanical Engineering Meijo University 1-501 Shiogamaguchi, Tempaku-ku Nagoya 468-8502, Japan
This paper presents a direct numerical simulation (DNS) study of the flame structure of a turbulent hydrogen jet lifted flame. The diameter of the hydrogen injector is 2 mm, and the injection velocity is 680 m/s. The time-dependent three-dimensional simulation was made with full chemical kinetics and rigorous transport properties. More than 22 million grid points were used. The numerical analysis, in terms of the normalized flame index, has made clear that the lifted flame is not a single flame, but a complex flame consisting of three flame elements: (1) a stable laminar leading-edge flame, (2) a conical inner vigorous turbulent premixed flame, and (3) a number of floating diffusion flame islands, surrounding the inner premixed flame. The stable laminar leading-edge flame of ring shape is stabilized outside the turbulent jet and has a triple flamelike structure with the normalized flame index around unity, indicating that the incoming flow almost balances with the laminar burning velocity. The floating flame islands are produced by turbulent behavior and local extinction of the inner premixed flame. The detached gas volume flows downstream, continuing to burn by the molecular diffusion of oxidizers. The inner rich premixed flame is strongly turbulent by the instability of the hydrogen jet at the tip. The flame is strongly stabilized by the leading-edge flame, and the heat release layer of the flame is deviated from the hydrogen consumption layer, indicating that the turbulence modifies the inner flame structure. The respective flame elements have their own complicated three-dimensional structure, and further studies are required to understand in detail the structure and stability of the lifted flame. The present study has revealed that this kind of DNS study is very useful to investigate various very complicated flame structures, such as the lifted flame.
Introduction The lifted flame is one of the most important and interesting flame configurations from the viewpoint of fundamental and practical research. In particular, the structure and the stabilization of lifted flames have been investigated enthusiastically, from the viewpoints of flamelet extinction [1] and triple flame structure [2–5]. Most of the former works, however, are based on two-dimensional theories and simulations, and therefore the details of the flame structure and the stabilization mechanism have not been revealed yet, especially for three-dimensional and turbulent lifted flames. The authors have been simulating a hydrogen/air turbulent jet flame by the direct numerical simulation (DNS) approach and succeeded in capturing the lifted flame solution [6]. The time-dependent three-dimensional simulations have been made with
full chemical kinetics and rigorous transport properties. The computation, with more than 22 million grid points, has been conducted using the vector parallel computer numerical wind tunnel at the National Aerospace Laboratory of Japan. From observations of simulated complicated combustion flowfields and short-term (⯝0.1 ms) unsteady flame behavior, important and interesting aspects of the lifted flame have been revealed. In this paper, the structure of the lifted flame is investigated first, and three flame elements are introduced. Then various phenomena related to the respective flame elements is discussed.
Flame Configurations The flame configuration followed the experiment by Cheng et al. [7]. A hydrogen jet is injected into
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TURBULENT COMBUSTION—Large Eddy and Direct Numerical Simulations
still air from a round nozzle whose diameter D is 2 mm. The jet velocity is 680 m/s, the Mach number is 0.54, and the Reynolds number based on the diameter is 13,600. In the experiment, a lifted flame with a liftoff height of 7D was observed. Computational Model The nine-species (H2, O2, OH, H2O, H, O, H2O2, HO2, and N2) and 17-reaction model by Westbrook [8] is employed. The air is assumed to be composed of 22% O2 and 78% N2 in volume. The diffusion flux is evaluated using Fick’s law with binary diffusion coefficients. The transport coefficients of each chemical species, namely, viscosity ls, heat conductivity js, and binary diffusion coefficient Ds, are evaluated using the Lennard-Jones intermolecular potential model [9], and those of the gas mixture are calculated by Wilke’s empirical rule [10]. The enthalpy of each chemical species is derived from JANAF [11]. Governing Equations The governing equations are the compressible three-dimensional Navier-Stokes equations, the conservation equations of total energy and chemical species, and the equation of state. The equation of total mass conservation is solved additionally. They are written for a generalized curvilinear coordinate system as Q F F Ⳮ ni ⳱ vni Ⳮ Hc, s ni ni
(1)
with
冤冥 冤 冤 冥
q qu1 qu2 Q⳱ V qu3 E qzs
Fni ⳱
冥
nij quj nij qu1uj Ⳮ ni1 p nij qu2uj Ⳮ ni2 p nij qu3uj Ⳮ ni3 p nij(E Ⳮ p)uj nij qzsuj
0 nijs1j nijs2j Fvni ⳱ nijs3j nij(sjkuk Ⳮ qj) nij qDszs, j E ⳱ e Ⳮ 0.5q(u12 Ⳮ u22 Ⳮ u32) e ⳱ 兺 qzs(Hs Ⳮ DHfs) ⳮ p
s
Computational Method Discretization Method The governing equations are discretized in a finitevolume formulation. The convective terms are evaluated using an upwind total variation diminishing (TVD) numerical flux based on Roe’s approximate Riemann solver [12,13], considering the properties of the hyperbolic equations. The higher-order flux is constructed extrapolating the characteristics using two types of flux limiters [14]. The accuracy of the flux is third-order in smooth regions. A problem of ordinary TVD fluxes is that they fall into first order around the locations where the sign of the characteristics gradient changes. In such locations, this TVD numerical flux can be more dissipative than in smooth regions, but it remains second order and the order of the truncation error is still higher than the order of the viscous and diffusion terms. The viscous terms are evaluated with standard second-order difference formulae. The diffusion fluxes at the cell interfaces are modified so that the total mass is conserved [15]. The time integration method is the explicit Runge-Kutta multistage method. The second-order time integration is used. Boundary Conditions The surfaces of the nozzle tube are assumed to be slip walls. On the jet exit, the axial velocity is extrapolated, the total pressure and the total temperature are fixed to the values which realize a 1/7 power-law boundary layer when the exit pressure is the atmospheric pressure, and no artificial disturbance is imposed. At the outer boundaries, the non-reflection condition [16] is applied. At the initial state, the computational region is filled with still air. After the cold flowfield is established, heat is added for ignition. Grid System
s
sij ⳱ l(ui, j Ⳮ uj,i ⳮ 2/3dijum,m) q j ⳱ jTj Ⳮ 兺 qDshszs, j p ⳱ RuT
of species s. The Hs and DHfs are the enthalpy and the heat of formation per mole of species s, respectively, and Ru is the universal gas constant. Hc is the chemical source term vector. The (x1, x2, x3) (x, y, z) and (n1, n2, n3) (n, g, f) are Cartesian and curvilinear coordinate systems, respectively; ( ),i ( )/ xi, V is the cell volume, and nij is the cell-interface normal vector. Finally, ui, q, and p are the xi velocity, the density, and the static pressure, respectively.
兺s qzs
(2)
where zs is the mole number density per unit mass
The grid system is rectangular. In this paper, the y-direction is the jet axial direction, the x- and zdirections are normal to the y-direction, and the origin is the jet exit center. The computational region is ⳮ15D ⱕ x, z ⱕ 15D and ⳮ3D ⱕ y ⱕ 20D. The
STRUCTURE OF HYDROGEN JET LIFTED FLAME
2011
Structure of the Lifted Flame The flame structure is analyzed using the flame index (F.I.) [18]. The F.I. is defined as F.I. ⳱ YH2 • YO2
Fig. 1. Instantaneous isosurface of temperature at 1000 K with hydrogen mole density.
grid spacing is 0.05 mm in ⳮ1.25D ⱕ x, z ⱕ 1.25D, 0 ⱕ y ⱕ 8D. This size is 2.5 times as large as the Kolmogorov scale measured in the experiment around the ignition point and is about 1/10 of the heat release layer width of the laminar normal flame calculated by PREMIX [17]. The grid spacing is coarser as the distance from the above-mentioned region is increased. The grid number is about 22.8 million. Results and Discussion A stable lifted flame is obtained in the numerical simulation in the same way as in the experiment. The isosurface of temperature at 1000 K is shown in Fig. 1 with hydrogen mole density on the surface. The time-averaged liftoff height is around 11 mm. The lifted flame is stabilized for more than 3 ms around the averaged location with some fluctuations. The simulated liftoff height is slightly shorter than the experimental one, but this agreement is fair considering the difficulty of the problem. In the remainder of this paper, the structure and some interesting aspects of this simulated lifted flame are investigated.
(3)
where Ys is the mass fraction of chemical species s. The flame is a premixed flame when the F.I. is positive and a diffusion flame when the F.I. is negative. The F.I. is normalized into normalized flame index (N.F.I.) in the following manner: the positive F.I. is normalized by the F.I. of the one-dimensional laminar premixed flame which corresponds to the local mixture fraction, and the negative F.I. is normalized by the F.I. at the extinction limit of the one-dimensional counterflow diffusion flame. The F.I. used for normalization is, for example, 1.03 ⳯ 105 mⳮ2 for stoichiometric premixed flames and 3.28 ⳯ 106 mⳮ2 for diffusion flames. By this normalization, the N.F.I. can be an indicator of the local burning velocity for premixed flames and of the local extinction for diffusion flames. Figure 2 shows the instantaneous isosurfaces of the N.F.I., where the isosurfaces at 1.0 and ⳮ0.0002 are painted yellow and green, respectively. The N.F.I. is set to zero where the temperature is less than 600 K for better observation. A complicated three-dimensional structure is observed. On the inner side of the lifted flame, a Bunsen-flame-like conical premixed flame is formed, and a number of diffusion flames surrounding the inner premixed flame are observed, which look like floating islands. The instantaneous N.F.I. distribution in the x-y plane is presented in Fig 3, and the close-up view around the leading edge is also shown. The positive isolevels are drawn with solid lines from 0.4 to 10.0 by 0.4, and the negative contours are drawn with dashed lines from ⳮ0.0002 to ⳮ0.001 by 0.0002. The stoichiometric mixture fraction (⳱0.02957) lines are drawn with thick black lines. The inner premixed flame is rich and vigorously turbulent, and the outer diffusion flame islands are aligned along the stoichiometric lines. The leading-edge flame is composed of a rich premixed flame, a diffusion flame, and a lean premixed flame. The flame is located around the stoichiometric line, indicating that the flame is located outside the turbulent jet, where the flow is stable and almost laminar, as shown later. Above observation shows that the lifted flame is not a single flame, but a complex flame consisting of following three flame elements: (1) a stable laminar leading-edge flame, (2) a vigorously turbulent inner premixed flame, and (3) floating diffusion flame islands. In the following, the structure of the respective flame elements will be discussed. Stable Laminar Leading-Edge Flame The lifted flame is stable during the observation, because the leading-edge flame is stable. As shown
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TURBULENT COMBUSTION—Large Eddy and Direct Numerical Simulations
Fig. 3. Instantaneous distribution of the N.F.I. in the x-y plane. Positive isolines are drawn with solid lines, negative with dashed lines, and stoichiometric mixture fraction isolines with thick lines.
Axial velocity (m/sec)
a)
3
b)
: Location A : Location B
10.0
9
in Fig. 3, the leading-edge flame has a triple flamelike structure and is located around the stoichiometric line, that is, outside the turbulent jet, and therefore the velocity is small and the flow is almost laminar. The time traces of the axial velocity and heat release rate at location A in Fig. 3 are shown in Fig. 4a and b, respectively. The location A is on the lean side, and it is the most stable location during the observation, where the flowfield is very calm and laminar and the heat release is very stable. The strong stability of the leading-edge flame is produced by such lean premixed flames at the flame bottom, and no significant movement of the leading-edge flame is observed during this observation. The N.F.I. is about unity around location A, which indicates that the incoming flow almost balances with the laminar burning velocity. This is because the flame index is proportional to the laminar burning velocity. In fact, the averaged axial velocity at location A is about 3 m/s, while the laminar burning velocity corresponding to the local mixture fraction is calculated to be about 2 m/s. However, as shown in Fig. 5, the leading-edge flame of ring shape has a
0.0
(10 J/m /sec)
Fig. 2. Instantaneous isosurface of N.F.I.: yellow, N.F.I. ⳱ 1.0; green, N.F.I. ⳱ ⳮ0.0002.
Heat release rate
100.0
0.0 0.0
50.0
100.0
–6
Time (10 sec)
Fig. 4. Time trace of (a) axial velocity and (b) heat release rate at locations A and B in Fig. 3.
complicated three-dimensional structure in the circumferential direction, and it is unsteady with long timescales. Further studies based on three-dimensional and unsteady observations are required to understand the detailed stabilization mechanism. Floating Diffusion Flame Islands The outer floating diffusion flame islands are not stabilized at the fixed positions, but flow slowly
STRUCTURE OF HYDROGEN JET LIFTED FLAME
Fig. 5. Three-dimensional view from below of the leading-edge flame. Hydrogen consumption rate isosurfaces at 104mol/m3/s are drawn with distribution of the N.F.I. on the surfaces. The light blue region is a premixed flame, and the region from green to red is a diffusion flame.
downstream along the stoichiometric plane. Fig. 6 shows the hydrogen consumption rate isosurfaces at 104 mol/m3/s with the N.F.I. distribution on the surfaces at sequential time stages (Dt ⳱ 30 ms). The light blue regions correspond to positive N.F.I., that is, to the premixed flame, and the regions from green
2013
to red correspond to the diffusion flame. Due to the turbulent behavior of the flame, the rich mixture of the inner premixed flame reaches the stoichiometric plane at some locations. Then a diffusion flame which is attached to the inner premixed flame is formed, as shown in Fig. 6a. After that, local extinction occurs in the inner premixed flame because the oxygen is consumed, and then diffusion flame islands are detached from the inner premixed flames as shown in Fig. 6b, c. The detached flame islands flow downstream, continuing to burn by the molecular diffusion of oxidizers. Fig. 7 shows the relation between the size of the flame island and the maximum hydrogen consumption rate in the flame island for two flame islands at various time stages. The thickness is defined as the thickness of the iso-surface at one-fifth of the maximum value for each flame island. The hydrogen consumption rate is almost proportional to (flame island thickness)ⳮ2, which indicates that combustion in the flame islands is governed by molecular diffusion. Vigorous Turbulent Inner Premixed Flame The inner premixed flame is strongly turbulent. Vigorous fluctuations at location B in Fig. 3 are shown in Fig. 4a and b. The vigorous turbulence in the turbulent premixed flame originates from the high-frequency instability of the hydrogen jet at the tip. In many locations in the turbulent premixed flames, a very large N.F.I. is observed. In such locations, the flame is going toward extinction due to excess gas supply by diffusion. This very unstable turbulent premixed flame is strongly stabilized by
Fig. 6. Production of diffusion flame islands. Hydrogen consumption rate isosurfaces at 104 mol/m3/s are drawn with distribution of the N.F.I. on the surfaces at sequential time stages in (a), (b) and (c), with a time interval of 30 ls.
TURBULENT COMBUSTION—Large Eddy and Direct Numerical Simulations
3
Maximum hydrogen consumption rate (mol/m /sec)
2014
12000.0
10000.0
8000.0
6000.0
2.0
4.0 Flame island thickness
6.0 –2
–2
(mm )
Fig. 7. Relation between hydrogen consumption rate and diffusion flame island thickness.
the stable leading-edge flame. The reaction layers are continuous between the leading-edge flame and the turbulent premixed flame (see Fig. 8). The stabilization is achieved via continuous reaction layers. Fig. 8 shows the close-up views of the hydrogen consumption rate distribution (Fig. 8a) and the heat release rate distribution (Fig. 8b). The hydrogen consumption layers are rather continuous. On the other hand, the succeeding heat release layers are rather disrupted and deviated from the hydrogen consumption layers. In the laminar normal flame, these two layers are displaced in parallel because the major reactions for hydrogen consumption and for
heat release are different. But in the turbulent premixed flames, the displacement is strongly distributed and modified. This is the effect of the vigorous turbulence in the flames. As observed in Fig. 4a, in the turbulent premixed flames, the timescale of turbulent fluid motion sf is quite small and the Fourier analysis shows sf is from 0.02 to 0.05 ms. The reaction timescale can be defined as sr ⳱ Dx/SL, where Dx is the distance between the peak locations of hydrogen consumption rate and heat release rate in the laminar premixed flame and SL is the corresponding laminar flame speed. This timescale can be estimated as a function of the mixture fraction in the premixed flame from one-dimensional premixed flame computation. In the regions where the deviation is remarkable, the mixture is rich and the mixture fraction is from 0.08 to 0.12, which corresponds to sr from 0.05 to 0.15 ms. The two timescales are of the same order, and sf is smaller than sr. Hence, the kinetics in the reaction layers are easily disturbed by turbulence and the deviation is produced. The combustion configuration in those regions is not in the flamelet regime, but can be classified into the broken reaction zones in the regime diagram for premixed turbulent combustion [19].
Conclusions The following conclusions are obtained from the analysis of DNS data of a turbulent hydrogen jet lifted flame. 1. The lifted flame structure is strongly three dimensional and is not a single flame, but a complex
Fig. 8. Deviation of heat release layer from hydrogen consumption layer; (a) hydrogen consumption rate, (b) heat release rate.
STRUCTURE OF HYDROGEN JET LIFTED FLAME
2.
3.
4.
5.
flame consisting of three flame elements: a stable laminar leading-edge flame, a vigorously turbulent inner premixed flame, and a number of floating diffusion flame islands. The leading-edge flame is stabilized outside the turbulent jet, where the N.F.I. is about unity, and it has a triple flamelike structure. The incoming flow almost balances with the laminar burning velocity. The floating diffusion flame islands are produced by turbulent behavior and local extinction of the inner turbulent rich premixed flame, and they flow downstream, continuing to burn by the molecular diffusion of oxidizers. The inner turbulent premixed flame is stabilized by the stable leading-edge flame. In this turbulent premixed flame, the reaction layers are disturbed by turbulence and the heat release layers are deviated from the hydrogen consumption layers. The combustion in such regions can be classified into the broken reaction zones in the Borghi regime diagram. This kind of DNS study is very useful for studying various very complicated flame structures, such as the lifted flame.
The respective flame elements have their own complicated three-dimensional and unsteady structure, and further studies based on three-dimensional and long-term observations are required. Acknowledgments This research was carried out as a research activity at the Center for Smart Control of Turbulence funded by MEXT (Ministry of Education, Culture, Sports, Science and Technology) of Japan.
2015
REFERENCES 1. Peters, N., and Williams, F. A., AIAA J. 21(3):423–429 (1983). 2. Kiori, P. N., Rogg, B., Bray, K. N. C., and Lin˜a´n, A., Combust. Flame 95:276–290 (1993). 3. Ruetsch G. R., and Vervisch, L., Phys. Fluids 7(6):1447–1454 (1995). 4. Favier, V., and Vervisch, L., Proc. Combust. Inst. 27:1239–1245 (1998). 5. Vervisch, L., and Poinsot, T., Annu. Rev. Fluid Mech. 30:655–691 (1998). 6. Mizobuch, Y., Tachibana, S., Shinjo, J., Ogawa, S., and Takaki, R., in IUTAM Symposium on Turbulent Mixing and Combustion, Kluwer Academic, Dordrecht, 2002, p. 337. 7. Cheng, T. S., Wehrmeyer, J. A., and Pitz, R. W., Combust. Flame 91:323–345 (1992). 8. Westbrook, C. K., Combust. Sci. Technol. 29:67–81 (1982). 9. Chapman, S., and Cowling, T. G., The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, 1970. 10. Wilke, C. R., J. Chem. Phys. 18(4):517–519 (1950). 11. JANAF Thermochemical Tables, Clearinghouse for Federal Scientific and Technical Information, Washington, DC, 1965. 12. Roe, P. L., J. Comput. Phys. 43:357–372 (1981). 13. Wada, Y., Ogawa, S., and Ishiguro, T., AIAA paper 890202. 14. Wada, Y., ‘‘Numerical Simulation of High-Temperature Gas Flows by Diagonalization of Gasdynamic Matrices,’’ Ph.D. thesis, University of Tokyo, 1995. 15. Mizobuchi, Y., and Ogawa, S., AIAA paper 2000-0184. 16. Thompson, K. W., J. Comput. Phys. 68:1–24 (1987). 17. Kee, R. J., Grcar, J. F., Smooke, M. D., and Miller, J. A., Sandia report SAND85-8240. 18. Yamashita, H., Shimada, M., and Takeno, T., Proc. Combust. Inst. 26:27–34 (1996). 19. Peters, N., J. Fluid Mech. 384:107–132 (1999).
A NUMERICAL ANALYSIS OF THE STRUCTURE OF A TURBULENT HYDROGEN JET LIFTED FLAME YASUHIRO MIZOBUCHI,1 SHIGERU TACHIBANA,1 JUNJI SHINIO,1 SATORU OGAWA1 and TADAO TAKENO2 1 CFD Technology Center National Aerospace Laboratory of Japan 7-44-1 Jindaij-Higashimachi, Chofu Tokyo 182-8522, Japan 2 Department of Mechanical Engineering Meijo University 1-501 Shiogamaguchi, Tempaku-ku Nagoya 468-8502, Japan
This paper presents a direct numerical simulation (DNS) study of the flame structure of a turbulent hydrogen jet lifted flame. The diameter of the hydrogen injector is 2 mm, and the injection velocity is 680 m/s. The time-dependent three-dimensional simulation was made with full chemical kinetics and rigorous transport properties. More than 22 million grid points were used. The numerical analysis, in terms of the normalized flame index, has made clear that the lifted flame is not a single flame, but a complex flame consisting of three flame elements: (1) a stable laminar leading-edge flame, (2) a conical inner vigorous turbulent premixed flame, and (3) a number of floating diffusion flame islands, surrounding the inner premixed flame. The stable laminar leading-edge flame of ring shape is stabilized outside the turbulent jet and has a triple flamelike structure with the normalized flame index around unity, indicating that the incoming flow almost balances with the laminar burning velocity. The floating flame islands are produced by turbulent behavior and local extinction of the inner premixed flame. The detached gas volume flows downstream, continuing to burn by the molecular diffusion of oxidizers. The inner rich premixed flame is strongly turbulent by the instability of the hydrogen jet at the tip. The flame is strongly stabilized by the leading-edge flame, and the heat release layer of the flame is deviated from the hydrogen consumption layer, indicating that the turbulence modifies the inner flame structure. The respective flame elements have their own complicated three-dimensional structure, and further studies are required to understand in detail the structure and stability of the lifted flame. The present study has revealed that this kind of DNS study is very useful to investigate various very complicated flame structures, such as the lifted flame.
Introduction The lifted flame is one of the most important and interesting flame configurations from the viewpoint of fundamental and practical research. In particular, the structure and the stabilization of lifted flames have been investigated enthusiastically, from the viewpoints of flamelet extinction [1] and triple flame structure [2–5]. Most of the former works, however, are based on two-dimensional theories and simulations, and therefore the details of the flame structure and the stabilization mechanism have not been revealed yet, especially for three-dimensional and turbulent lifted flames. The authors have been simulating a hydrogen/air turbulent jet flame by the direct numerical simulation (DNS) approach and succeeded in capturing the lifted flame solution [6]. The time-dependent three-dimensional simulations have been made with
full chemical kinetics and rigorous transport properties. The computation, with more than 22 million grid points, has been conducted using the vector parallel computer numerical wind tunnel at the National Aerospace Laboratory of Japan. From observations of simulated complicated combustion flowfields and short-term (⯝0.1 ms) unsteady flame behavior, important and interesting aspects of the lifted flame have been revealed. In this paper, the structure of the lifted flame is investigated first, and three flame elements are introduced. Then various phenomena related to the respective flame elements is discussed.
Flame Configurations The flame configuration followed the experiment by Cheng et al. [7]. A hydrogen jet is injected into
2009
2010
TURBULENT COMBUSTION—Large Eddy and Direct Numerical Simulations
still air from a round nozzle whose diameter D is 2 mm. The jet velocity is 680 m/s, the Mach number is 0.54, and the Reynolds number based on the diameter is 13,600. In the experiment, a lifted flame with a liftoff height of 7D was observed. Computational Model The nine-species (H2, O2, OH, H2O, H, O, H2O2, HO2, and N2) and 17-reaction model by Westbrook [8] is employed. The air is assumed to be composed of 22% O2 and 78% N2 in volume. The diffusion flux is evaluated using Fick’s law with binary diffusion coefficients. The transport coefficients of each chemical species, namely, viscosity ls, heat conductivity js, and binary diffusion coefficient Ds, are evaluated using the Lennard-Jones intermolecular potential model [9], and those of the gas mixture are calculated by Wilke’s empirical rule [10]. The enthalpy of each chemical species is derived from JANAF [11]. Governing Equations The governing equations are the compressible three-dimensional Navier-Stokes equations, the conservation equations of total energy and chemical species, and the equation of state. The equation of total mass conservation is solved additionally. They are written for a generalized curvilinear coordinate system as Q F F Ⳮ ni ⳱ vni Ⳮ Hc, s ni ni
(1)
with
冤冥 冤 冤 冥
q qu1 qu2 Q⳱ V qu3 E qzs
Fni ⳱
冥
nij quj nij qu1uj Ⳮ ni1 p nij qu2uj Ⳮ ni2 p nij qu3uj Ⳮ ni3 p nij(E Ⳮ p)uj nij qzsuj
0 nijs1j nijs2j Fvni ⳱ nijs3j nij(sjkuk Ⳮ qj) nij qDszs, j E ⳱ e Ⳮ 0.5q(u12 Ⳮ u22 Ⳮ u32) e ⳱ 兺 qzs(Hs Ⳮ DHfs) ⳮ p
s
Computational Method Discretization Method The governing equations are discretized in a finitevolume formulation. The convective terms are evaluated using an upwind total variation diminishing (TVD) numerical flux based on Roe’s approximate Riemann solver [12,13], considering the properties of the hyperbolic equations. The higher-order flux is constructed extrapolating the characteristics using two types of flux limiters [14]. The accuracy of the flux is third-order in smooth regions. A problem of ordinary TVD fluxes is that they fall into first order around the locations where the sign of the characteristics gradient changes. In such locations, this TVD numerical flux can be more dissipative than in smooth regions, but it remains second order and the order of the truncation error is still higher than the order of the viscous and diffusion terms. The viscous terms are evaluated with standard second-order difference formulae. The diffusion fluxes at the cell interfaces are modified so that the total mass is conserved [15]. The time integration method is the explicit Runge-Kutta multistage method. The second-order time integration is used. Boundary Conditions The surfaces of the nozzle tube are assumed to be slip walls. On the jet exit, the axial velocity is extrapolated, the total pressure and the total temperature are fixed to the values which realize a 1/7 power-law boundary layer when the exit pressure is the atmospheric pressure, and no artificial disturbance is imposed. At the outer boundaries, the non-reflection condition [16] is applied. At the initial state, the computational region is filled with still air. After the cold flowfield is established, heat is added for ignition. Grid System
s
sij ⳱ l(ui, j Ⳮ uj,i ⳮ 2/3dijum,m) q j ⳱ jTj Ⳮ 兺 qDshszs, j p ⳱ RuT
of species s. The Hs and DHfs are the enthalpy and the heat of formation per mole of species s, respectively, and Ru is the universal gas constant. Hc is the chemical source term vector. The (x1, x2, x3) (x, y, z) and (n1, n2, n3) (n, g, f) are Cartesian and curvilinear coordinate systems, respectively; ( ),i ( )/ xi, V is the cell volume, and nij is the cell-interface normal vector. Finally, ui, q, and p are the xi velocity, the density, and the static pressure, respectively.
兺s qzs
(2)
where zs is the mole number density per unit mass
The grid system is rectangular. In this paper, the y-direction is the jet axial direction, the x- and zdirections are normal to the y-direction, and the origin is the jet exit center. The computational region is ⳮ15D ⱕ x, z ⱕ 15D and ⳮ3D ⱕ y ⱕ 20D. The
STRUCTURE OF HYDROGEN JET LIFTED FLAME
2011
Structure of the Lifted Flame The flame structure is analyzed using the flame index (F.I.) [18]. The F.I. is defined as F.I. ⳱ YH2 • YO2
Fig. 1. Instantaneous isosurface of temperature at 1000 K with hydrogen mole density.
grid spacing is 0.05 mm in ⳮ1.25D ⱕ x, z ⱕ 1.25D, 0 ⱕ y ⱕ 8D. This size is 2.5 times as large as the Kolmogorov scale measured in the experiment around the ignition point and is about 1/10 of the heat release layer width of the laminar normal flame calculated by PREMIX [17]. The grid spacing is coarser as the distance from the above-mentioned region is increased. The grid number is about 22.8 million. Results and Discussion A stable lifted flame is obtained in the numerical simulation in the same way as in the experiment. The isosurface of temperature at 1000 K is shown in Fig. 1 with hydrogen mole density on the surface. The time-averaged liftoff height is around 11 mm. The lifted flame is stabilized for more than 3 ms around the averaged location with some fluctuations. The simulated liftoff height is slightly shorter than the experimental one, but this agreement is fair considering the difficulty of the problem. In the remainder of this paper, the structure and some interesting aspects of this simulated lifted flame are investigated.
(3)
where Ys is the mass fraction of chemical species s. The flame is a premixed flame when the F.I. is positive and a diffusion flame when the F.I. is negative. The F.I. is normalized into normalized flame index (N.F.I.) in the following manner: the positive F.I. is normalized by the F.I. of the one-dimensional laminar premixed flame which corresponds to the local mixture fraction, and the negative F.I. is normalized by the F.I. at the extinction limit of the one-dimensional counterflow diffusion flame. The F.I. used for normalization is, for example, 1.03 ⳯ 105 mⳮ2 for stoichiometric premixed flames and 3.28 ⳯ 106 mⳮ2 for diffusion flames. By this normalization, the N.F.I. can be an indicator of the local burning velocity for premixed flames and of the local extinction for diffusion flames. Figure 2 shows the instantaneous isosurfaces of the N.F.I., where the isosurfaces at 1.0 and ⳮ0.0002 are painted yellow and green, respectively. The N.F.I. is set to zero where the temperature is less than 600 K for better observation. A complicated three-dimensional structure is observed. On the inner side of the lifted flame, a Bunsen-flame-like conical premixed flame is formed, and a number of diffusion flames surrounding the inner premixed flame are observed, which look like floating islands. The instantaneous N.F.I. distribution in the x-y plane is presented in Fig 3, and the close-up view around the leading edge is also shown. The positive isolevels are drawn with solid lines from 0.4 to 10.0 by 0.4, and the negative contours are drawn with dashed lines from ⳮ0.0002 to ⳮ0.001 by 0.0002. The stoichiometric mixture fraction (⳱0.02957) lines are drawn with thick black lines. The inner premixed flame is rich and vigorously turbulent, and the outer diffusion flame islands are aligned along the stoichiometric lines. The leading-edge flame is composed of a rich premixed flame, a diffusion flame, and a lean premixed flame. The flame is located around the stoichiometric line, indicating that the flame is located outside the turbulent jet, where the flow is stable and almost laminar, as shown later. Above observation shows that the lifted flame is not a single flame, but a complex flame consisting of following three flame elements: (1) a stable laminar leading-edge flame, (2) a vigorously turbulent inner premixed flame, and (3) floating diffusion flame islands. In the following, the structure of the respective flame elements will be discussed. Stable Laminar Leading-Edge Flame The lifted flame is stable during the observation, because the leading-edge flame is stable. As shown
2012
TURBULENT COMBUSTION—Large Eddy and Direct Numerical Simulations
Fig. 3. Instantaneous distribution of the N.F.I. in the x-y plane. Positive isolines are drawn with solid lines, negative with dashed lines, and stoichiometric mixture fraction isolines with thick lines.
Axial velocity (m/sec)
a)
3
b)
: Location A : Location B
10.0
9
in Fig. 3, the leading-edge flame has a triple flamelike structure and is located around the stoichiometric line, that is, outside the turbulent jet, and therefore the velocity is small and the flow is almost laminar. The time traces of the axial velocity and heat release rate at location A in Fig. 3 are shown in Fig. 4a and b, respectively. The location A is on the lean side, and it is the most stable location during the observation, where the flowfield is very calm and laminar and the heat release is very stable. The strong stability of the leading-edge flame is produced by such lean premixed flames at the flame bottom, and no significant movement of the leading-edge flame is observed during this observation. The N.F.I. is about unity around location A, which indicates that the incoming flow almost balances with the laminar burning velocity. This is because the flame index is proportional to the laminar burning velocity. In fact, the averaged axial velocity at location A is about 3 m/s, while the laminar burning velocity corresponding to the local mixture fraction is calculated to be about 2 m/s. However, as shown in Fig. 5, the leading-edge flame of ring shape has a
0.0
(10 J/m /sec)
Fig. 2. Instantaneous isosurface of N.F.I.: yellow, N.F.I. ⳱ 1.0; green, N.F.I. ⳱ ⳮ0.0002.
Heat release rate
100.0
0.0 0.0
50.0
100.0
–6
Time (10 sec)
Fig. 4. Time trace of (a) axial velocity and (b) heat release rate at locations A and B in Fig. 3.
complicated three-dimensional structure in the circumferential direction, and it is unsteady with long timescales. Further studies based on three-dimensional and unsteady observations are required to understand the detailed stabilization mechanism. Floating Diffusion Flame Islands The outer floating diffusion flame islands are not stabilized at the fixed positions, but flow slowly
STRUCTURE OF HYDROGEN JET LIFTED FLAME
Fig. 5. Three-dimensional view from below of the leading-edge flame. Hydrogen consumption rate isosurfaces at 104mol/m3/s are drawn with distribution of the N.F.I. on the surfaces. The light blue region is a premixed flame, and the region from green to red is a diffusion flame.
downstream along the stoichiometric plane. Fig. 6 shows the hydrogen consumption rate isosurfaces at 104 mol/m3/s with the N.F.I. distribution on the surfaces at sequential time stages (Dt ⳱ 30 ms). The light blue regions correspond to positive N.F.I., that is, to the premixed flame, and the regions from green
2013
to red correspond to the diffusion flame. Due to the turbulent behavior of the flame, the rich mixture of the inner premixed flame reaches the stoichiometric plane at some locations. Then a diffusion flame which is attached to the inner premixed flame is formed, as shown in Fig. 6a. After that, local extinction occurs in the inner premixed flame because the oxygen is consumed, and then diffusion flame islands are detached from the inner premixed flames as shown in Fig. 6b, c. The detached flame islands flow downstream, continuing to burn by the molecular diffusion of oxidizers. Fig. 7 shows the relation between the size of the flame island and the maximum hydrogen consumption rate in the flame island for two flame islands at various time stages. The thickness is defined as the thickness of the iso-surface at one-fifth of the maximum value for each flame island. The hydrogen consumption rate is almost proportional to (flame island thickness)ⳮ2, which indicates that combustion in the flame islands is governed by molecular diffusion. Vigorous Turbulent Inner Premixed Flame The inner premixed flame is strongly turbulent. Vigorous fluctuations at location B in Fig. 3 are shown in Fig. 4a and b. The vigorous turbulence in the turbulent premixed flame originates from the high-frequency instability of the hydrogen jet at the tip. In many locations in the turbulent premixed flames, a very large N.F.I. is observed. In such locations, the flame is going toward extinction due to excess gas supply by diffusion. This very unstable turbulent premixed flame is strongly stabilized by
Fig. 6. Production of diffusion flame islands. Hydrogen consumption rate isosurfaces at 104 mol/m3/s are drawn with distribution of the N.F.I. on the surfaces at sequential time stages in (a), (b) and (c), with a time interval of 30 ls.
TURBULENT COMBUSTION—Large Eddy and Direct Numerical Simulations
3
Maximum hydrogen consumption rate (mol/m /sec)
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12000.0
10000.0
8000.0
6000.0
2.0
4.0 Flame island thickness
6.0 –2
–2
(mm )
Fig. 7. Relation between hydrogen consumption rate and diffusion flame island thickness.
the stable leading-edge flame. The reaction layers are continuous between the leading-edge flame and the turbulent premixed flame (see Fig. 8). The stabilization is achieved via continuous reaction layers. Fig. 8 shows the close-up views of the hydrogen consumption rate distribution (Fig. 8a) and the heat release rate distribution (Fig. 8b). The hydrogen consumption layers are rather continuous. On the other hand, the succeeding heat release layers are rather disrupted and deviated from the hydrogen consumption layers. In the laminar normal flame, these two layers are displaced in parallel because the major reactions for hydrogen consumption and for
heat release are different. But in the turbulent premixed flames, the displacement is strongly distributed and modified. This is the effect of the vigorous turbulence in the flames. As observed in Fig. 4a, in the turbulent premixed flames, the timescale of turbulent fluid motion sf is quite small and the Fourier analysis shows sf is from 0.02 to 0.05 ms. The reaction timescale can be defined as sr ⳱ Dx/SL, where Dx is the distance between the peak locations of hydrogen consumption rate and heat release rate in the laminar premixed flame and SL is the corresponding laminar flame speed. This timescale can be estimated as a function of the mixture fraction in the premixed flame from one-dimensional premixed flame computation. In the regions where the deviation is remarkable, the mixture is rich and the mixture fraction is from 0.08 to 0.12, which corresponds to sr from 0.05 to 0.15 ms. The two timescales are of the same order, and sf is smaller than sr. Hence, the kinetics in the reaction layers are easily disturbed by turbulence and the deviation is produced. The combustion configuration in those regions is not in the flamelet regime, but can be classified into the broken reaction zones in the regime diagram for premixed turbulent combustion [19].
Conclusions The following conclusions are obtained from the analysis of DNS data of a turbulent hydrogen jet lifted flame. 1. The lifted flame structure is strongly three dimensional and is not a single flame, but a complex
Fig. 8. Deviation of heat release layer from hydrogen consumption layer; (a) hydrogen consumption rate, (b) heat release rate.
STRUCTURE OF HYDROGEN JET LIFTED FLAME
2.
3.
4.
5.
flame consisting of three flame elements: a stable laminar leading-edge flame, a vigorously turbulent inner premixed flame, and a number of floating diffusion flame islands. The leading-edge flame is stabilized outside the turbulent jet, where the N.F.I. is about unity, and it has a triple flamelike structure. The incoming flow almost balances with the laminar burning velocity. The floating diffusion flame islands are produced by turbulent behavior and local extinction of the inner turbulent rich premixed flame, and they flow downstream, continuing to burn by the molecular diffusion of oxidizers. The inner turbulent premixed flame is stabilized by the stable leading-edge flame. In this turbulent premixed flame, the reaction layers are disturbed by turbulence and the heat release layers are deviated from the hydrogen consumption layers. The combustion in such regions can be classified into the broken reaction zones in the Borghi regime diagram. This kind of DNS study is very useful for studying various very complicated flame structures, such as the lifted flame.
The respective flame elements have their own complicated three-dimensional and unsteady structure, and further studies based on three-dimensional and long-term observations are required. Acknowledgments This research was carried out as a research activity at the Center for Smart Control of Turbulence funded by MEXT (Ministry of Education, Culture, Sports, Science and Technology) of Japan.
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