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Stabilization mechanism of lifted jet diffusion flames
Twenty-Fifth Symposium (International) on Combustion/The Combustion Institute, 1994/pp. 1183-1189
STABILIZATION MECHANISM OF LIFTED JET D I F F U S I O N FLAMES CAROLYN R. KAPLAN* AND ELAINE S. ORAN**
*Chemistry Division, **Laboratoryfor Computational Physics and Fluid Dynamics Naval Research Laboratory Washington, D.C. 20375, USA AND
SEUNG W. BAEK
Department of Aerospace Engineering Korea Advanced Institute of Science and Technology Taejon, Korea Flame lift and stabilization are studied using numerical simulations of diffusion flames resulting from a methane jet injected into an air background. The numerical model solves the time-dependent, axisymmetric, multidimensional Navier-Stokes equations coupled to submodels for chemical reaction and heat release, soot formation and radiation transport. Simulations are conducted for an undiluted methane jet and for two nitrogen-diluted jets (CH4: N2/3:1 and CH4:NJ1 : 1). The jet exit velocities range from 20 to 50 m/s through a 1-cm-diameter nozzle, coflowing into a 30-cm/s air stream. The flame liftoff height increases linearly with jet exit velocity and the stabilization height increases as the nitrogen dilution of the jet increases. The computations show that the flame is stabilized on a vortical structure in the inner shear layer, which is on the stoichiometric surface at a height where the local axial velocity is approximately equal to the turbulent burning velocity. There is no appreciable chemical heat release in the region below the stabilization point, although a stoichiometric surface exists in that region. The flame base moves upward with the vortical structure to which it is attached, and then quickly jumps down to attach to a new, lower vortex, resulting in an oscillating (1-2 cm) flame liftoff height. The results corroborate parts of both the premixedness and extinction stabilization theories, and suggest that the liftoff mechanism is a result of complex fluid-chemical interactions, parts of which are incorporated in the simplified theories.
Introduction Although a great deal of research has been devoted to the study of liftoff and blowout of turbulent jet diffusion flames, the physical mechanisms responsible for flame stabilization are still controversial. A recent review by Pitts [i] summarized published experimental and theoretical results and has concluded that none of the theories currently avaitabIe is totally satisfactory. Pitts [1] further concludes that the current experimental characterization of flame stabilization is insufficient to determine the actual physical processes that determine liftoff and blowout. The phenomenon of liftoff has been experimentally investigated for many decades through flow visualization studies. Vanquickenborne and van Tiggelen [2] provided extensive experimental measurements of nonreaeting and reacting turbulent jets of methane over a broad range of jet exit diameters and velocities. Their findings [2] show that lifted flames are stabilized in a turbulent region of the jet near the radial position where the time-averaged fuel mass fraction equals that required for stoichiometric
burning. Other measurements of jets of mixtures of natural gas and hydrogen [3,4] showed that the most likely radial position for combustion to occur is along the mass-fraction contour where the laminar flame speed is maximum. Extensive experimental studies by Kalghatgi [51 for a variety of fuels and a wide range of jet diameters and velocities have resulted in empirical correlations between liftoff height, jet velocit3,, and maximum laminar flame speed. Observations for lifted natural-gas flames have been reported by Eickhoff et al. [6] and Sobiesiak and Brzustowsld [7] and for propane flames by Savas and Gollahalli [8]. Analysis of the experimental studies has resulted in the development of theoretical treatments of flame stabilization. Vanquickenborne and van Tiggelen [2] suggested that the stabilization of lifted turbulent jet diffusion flames can be understood by assuming that the fuel-air mixture is fully premixed at the base of the lifted flame. They then define a local flame speed, which is determined by the local turbulence structure. The flame is stabilized at a position where the local time-averaged axial velocity along the stoichiometric mass fraction contour equals the local flame
1183
1184
TURBULENT FLAMES
speed. Results of other experiments [3-7] have supported this premixedness model. Several more recent theories challenge this by proposing that the stabilization of lifted flames results from flame extinction processes that occur in turbulent structures of the nearby unignited flow, Many different types of extinction processes have been suggested [9-14]. Peters and Williams [9] analyzed the problem in terms of the laminar flamelet model, in which flamelets are extinguished when the local turbulence-induced concentration gradients are sufficient to quench combustion. Flame stabilization occurs at the point where combustion extinction and propagation are balanced. Janicka and Peters [10] considered the effects of assumptions concerning the scalar dissipation on calculated values of liftoff height. Donnerhack and Peters [11] tested a local quenching theory, in which they state that extinction occurs when the rate of heat conduction to the sides of the flame exceeds the rate of heat production due to chemical reaction. Byggstoyl and Magnussen [13] suggest that the extinction occurs in the smallest vortices of the flow, while Broadwell et al. [14] suggest that lifted flames result from flame extinction in large-scale turbulent structures. In this paper, we describe results from a time-dependent numerical model used to study the unsteady behavior of an axisymmetric coflowing methane-air jet diffusion flame. First, we use a series of calculations with increasing jet exit velocities to demonstrate that the numerical model can, in fact, simulate the phenomenon of flame lift and that the results are consistent with the correct physical behavior. Then we analyze these flames to determine trends in liftoff behavior and make comparisons with some of the current theories of flame stabilization. Numerical Method The numerical model solves the time-dependent equations for conservation of mass density, momentum, energy, individual species number densities, soot number density, and soot volume fraction [15]. The solution to the conservation equations includes both radial and axial components of molecular diffusion, thermal conduction, viscosity, radiation transport, and convection; that is, we do not make boundary-layer approximations and do not restrict the Lewis number to unity. These equations are rewritten in terms of finite-volume approximations on an Eulefian mesh and solved numerically for specified boundary and initial conditions. The model consists of separate algorithms for each of the individual processes, which are then coupled together by the method of timestep splitting [15-19]. The different algorithms and how they are applied to solve for the convective [20], diffusive, and radiation transport processes have already been de-
scribed in detail [15-17], and are not discussed here. However, the algorithms for chemical reaction and soot formation are different than those used previously [15,16], and therefore are described below. We represent the chemical reaction and energy-release process phenomenologically using a finite-rate, single-step, quasi-global Arrhenius expression [21] d[CH4] dt
2.3 • 107 9e x p [ ~ ] [ C H 4 ] - ~
L3
(1) where T is temperature and R is the universal gas constant. Equation (1) is used to calculate the rate of depletion of CH,. In order to prevent an infinite reaction rate when the CH4 is fully depleted, we assume a zero reaction rate when the CH4 concentration falls below 1.0 • 10 -20 moles/cma. The concentrations of 02, CO2, HzO, and N2 are then calculated based on their respective stoichiometric coefficients. The chemical heat release rate is then determined from d[CH4] Q =
- AHc
dt
(2)
where 2H c is the heat of combustion for CH 4 oxidation. The evolution of soot number density and soot volume fraction is represented by two coupled ordinary differential equations derived by Syed et al. [22] based on their experimental measurements in methane-air diffusion flames, and include terms for soot nucleation, surface growth, and coagulation on the soot formation rate. dnd
-dt
= No C ~p ZT1/2Xfu~l e - T~/T
1 No C # T j/z n~ df~
dt
-
1 --
(3)
[C nl/a(ot ~ s o o.t jf~z/3oT1/2X, .e -T#T L ? a v/ tfuel
Psoot
+ C~C~p2T1/2Xf, ele-Ta/T ]
(4)
where nd is the soot number density, No is Avogadro's number, p is the fluid density, Xr,el is the fuel mole fraction, andfv is the soot volume fraction. The constants, Ca, Cp, Cy, C~, T~, Tr are taken from Ref. 22, and Psoot,the density of a soot particle, is assumed to be 1.8 g/cm3. The soot volume fraction and number densities, as calculated in Eqs. (3) and (4), are further reduced by a soot oxidation algorithm [15].
STABILIZATIONMECHANISM OF LIFTED JET DIFFUSION FLAMES Fuel Mole Temperature Soot Volume Fraction Fraction
OU~OW
10
C~
0 Fuel Air coflow
r (cm)
FIG. 1. Initial conditions and computed contours for a laminar methane-air diffusion flame.
Results Steady Methane-Air Diffusion Flame:
Simulations were first conducted for a steadystate, laminar methane-air diffusion flame for which the experimental data of Mitchell et al. [23] are available. Figure 1 shows a schematic of the computational conditions and results from a simulation in which undiluted methane flows at 5 cm/s through a 1.2-cm-diameter tube, while air flows at 10 cm/s through the outer annular region. The full computational grid is 10 • 20 cm and consists of 128 • 152 cells. Cells of approximately 0.02 • 0.02 cm are concentrated around the jet exit; the grid spacing is then gradually stretched in both the radial and axial directions [15-17]. This time-dependent calculation
=
2000
~"
1185
showed that the flame reached the steady state shown by 12,000 timesteps (0.12 s). The contours of fuel mole fraction, temperature, and soot volume fraction predict that the flame height is approximately 8 cm, based on the height of the sooting layer. The maximum soot volume fraction is 3.6 • 10 -7, and is located on the fuel-rich side of the high-temperature region. Figure 2 compares experimental and computed radial profiles of temperature at selected heights above the burner for which experimental data were presented [23]. The dashed line is the curve drawn by Mitchell et al. [23] through their experimental data points (error bars are not included with the experimental results). In general, the agreement is quite reasonable, although there is a tendency for the simulations to predict a flame sheet thickness that is wider than those observed experimentally at lower heights in the flame. Unsteady Lifted Methane-Air Diffusion Flame:
Simulations of lifted flames were then conducted for cases in which the fuel mixture flows at a high velocity through a 1.0-cm-diameter jet into a lowvelocity (30 cm/s) coflowing air stream. The fuel streams considered included undiluted methane and also nitrogen-diluted (CH4:N2/3 : 1 and CH4 : N2/1 : 1) fuel mixtures. Figure 3 shows contours of temperature, chemical heat release rate, and radial velocity for cases in which the undiluted methane fuel jet velocity varies from 20 to 50 m/s. The location of the stoichiometric surface is shown by the solid line with black circles superimposed. The radial velocity contours show the Kelvin-Helmholtz instabilities, which form in the shear layer between the highand low-velocity streams. The dashed lines in the radial velocity contours correspond to counterclockwise rotating structures, while the solid lines correspond to clockwise-rotating structures. As shown in
=
I
! 5.0 cm =height' sire.
1500 "-I
1000 i~
500 0 0
1
r (cm)
2
3
0
1
2
r (cm)
3 0
1
2
3
r (cm)
FIG. 2. Comparisonbetween simulation and experimental results [23] for laminar methane-air flame. The dashed line is the curve drawn by Mitchell et al. [23] through their experimental data.
1186
TURBULENT FLAMES 20 m/s
30 m/s
7.2 c m >
__
:a) i ~
~b~
50 m/s
40 ra/s 12.5 cm
FIC. 3. (a) Temperature (K), (b) chemical heat release rate (ergs/cm~s), and (c) radial velocity(cm/s) contours for undiluted methane fuel jet; jet inflow velocities 20-50 m/s. Heavy solid line with solid circular symbols corresponds to the location of the stoichiometric surface. Arrow points to liftoff height.
J
0
2 r (cm)
Fig. 3, the liftoff heights are 4.6, 7.2, 9.4, and 12.5 cm for the 20, 30, 40, and 50 m/s cases, respectively. For all of the cases shown, the base of the lifted flame is situated on the stoichiometric surface, and is attached to a Kelvin-Helmholtz structure; that is, the stoichiometric contour passes through the vortical structure at the flame stabilization location. Figure 4 shows that there is reasonable agreement between the simulation results and the experimental data of Kalghatgi [5]. Both show a linear relationship between flame liftoff height and jet exit velocity. Figure 4 also shows results from a simulation in which the fuel jet is diluted with nitrogen (CH4:N2/I:I). As expected, the liftoff height is greater for a given jet inflow velocity for the nitrogen-diluted case, as the residence time (chemical time) is longer when the fuel stream is diluted. For the nitrogen-diluted case, the liftoff height is again a linear function of the jet exit velocity, but the slope of this line is greater than that for the undiluted case. This phenomenon of a steeper slope with increasing nitrogen dilution has also been shown experimentally [11,24] in studies of the effect of jet dilution on liftoffheight. The liftoff heights presented in Fig. 4 were taken from instantaneous temperature images at one particular timestep (15,000 timesteps). However, animations of this unsteady flame show that the liftoff height fluctuates. That is, the base of the flame moves up with the vortical structure to which it is attached,
25 20
'. 'im. o
E x p [5] (undiluted)
"
Sim. (50% diluted)
15 A 0
11 o
0
9
0
c~
0
0
O0 0
O!
~
i
I
20
30
40
"
I
50
u o (m/s)
FIG. 4. Liftoffheight as a function of jet exit velocityfor simulations (undiluted fuel jet and 50% diluted fuel jet) and experimental measurements (undiluted fuel jet).
STABILIZATIONMECHANISM OF LIFTED JET DIFFUSION FLAMES
1187
TABLE 1 Comparison of turbulent burning velocity (S,) to fluid axial velocity (from the simulations) at the liftoff height. Method used to calculate St is outlined at bottom.
Jet velocity (m/s)
Liftoff height (cm)
Rz at liftoff heighta (approx.)
20 30 40 50
4.6 7.2 9.4 12.5
38 50 87 144
S,/S~ b
S t (approx.) at liftoff height ~ (em/s)
Axial velocity at liftoff height, from simulations (cm/s)
1.7-2.6 1.9-3.0 2.6-4.0 3.3-5.1
70-105 75--120 105-160 130-205
60-100 80-110 110-170 140-220
aFrom Eq. (6). bFrom Eq. (5), and experimental results [5,25]. ~Based on Su = 40 cm/s, and Sr from previous column.
and then quickly jumps down to attach to a new, lower vortex, resulting in an oscillating flame height. The fluctuation in liftoff height due to this movement is approximately 1 to 2 cm. Tests o f Flame Stabilization Theory:
The computations have shown that the numerical model does indeed simulate the phenomenon of flame liftoff, and the results are consistent with published experimental data. Now, we compare the simulation results with some of the current theories of flame lift~ One of the important hypotheses from the premixedness theory of Vanquickenborne and van Tiggelen [2] is that the base of the flame stabilizes on the stoichiometric surface at the height where the local axial velocity is equal to the turbulent burning velocity. In order to evaluate this hypothesis, we calculated the ratio of the turbulent burning velocity to the maximum laminar burning velocity (St/Su) at the liftoff height based on a correlation by Kalghatgi [5]
s! = S~
Rz.f~(W~,~). K
(5)
wheref4 and K are constants taken from Ref. 5 (f4 = 0.138, K ranges from 0.56 to 1.3). The term R l is the turbulent Reynolds number, given by u'l nz
=
--
Vs
(6)
where u' is the root mean square (rms) fluctuation velocity, I is the turbulent integral length scale in the jet mixing layer, and vs is the kinematic viscosity at the base of the flame. In Ref. 5, the values of St/Su as a function ofRy 2 from Eq. (5) are favorably compared with an experimentally determined ratio of
turbulent burning velocity to laminar burning velocity as a function of Ry 2 by Smith and Gouldin [25]. That is, the experimental data points of Smith and Gouldin [25] fall within the range of values of St~S, for a given R l from Eq. (5). Therefore, using values o f u ' = 2 rn/s (simulation results show rms velocity fluctuations on the order of i t o 2 m/s), and calculating I based on correlations from Abramovich [26] and Davies et al. [27], l = Cz
(7)
(where C is a constant, and z is the axial height), we calculated values of R l at the flame lift height from Eq. (6), and used that value to calculate a range of St/Su from Eq. (5). Table 1 lists the values of these quantities for the four cases in which the jet is undiluted. Based on a maximum laminar burning velocity Su = 40 cm/s for methane-air flames, we calculated the range of turbulent burning velocities, St, at the liftoff height, as shown in Table 1. We then compared these calculated values of St with the axial velocity at the liftoff height based on the simulation results. The axial velocity fluctuates considerably (varies from negative to positive values) within the rotating vortical structures to which it is attached. However, the axial velocity is always positive (flowing upwards) in the region immediately below the vortical structure to which the flame is attached. For each of the jet velocities considered, Table 1 shows the range of axial velocity values in the region immediately below the vortical structure to which the flame is attached. As shown, this range of axial velocities based on the simulations is approximately the same as the range of calculated [from Eqs. (5) and (6)] turbulent burning velocities at the liftoff height. Although the results above show that the simula-
1188
TURBULENT FLAMES
tions do, in fact, corroborate some parts of the premixedness theory [2], this does not imply that the simulations conflict with some of the proposed extinction mechanisms [9-14]. In fact, the computations show that although a stoichiometric surface exists in the region below the stabilization point (as shown in Fig. 3), there is no appreciable chemical heat release or formation of products in that region. This lack of heat release may be due to a local quenching process within the turbulent structures of the jet. The simulation results show that strain rates in the highly turbulent structures near the jet exit are approximately 1000-1400 s -1, then decrease to values of approximately 300--500 s 1 at the stabilization point, and continue to decrease with increasing height. Further analysis is planned to fully investigate the strain rates and scalar dissipation in the turbulent structures of the jet.
SlllTllTlary A solution of the time-dependent multidimensional reactive flow Navier-Stokes equations has been obtained to study the stabilization mechanism of lifted jet diffusion flames. Although this computation is based on axisymmetric geometry, and hence neglects nonsymmetric turbulence behavior, it is able to capture the fluid-chemical interactions that are important in turbulent flows and contribute to flame lift. The liftoff heights are in reasonable agreement with published experiments; the results show a linear relationship between liftoff height and jet exit velocity, and the liftoff height increases with increasing fuel dilution due to longer residence times. The computations are compared with some of the current theories of flame stabilization, and show that the flame is stabilized on an inner shear layer vortical structure, which is on the stoichiometric surface at a height where the local axial velocity is approximately equal to the turbulent burning velocity. In the region below the stabilization point, strain rates are very high and there is no appreciable chemical heat release, even though a stoichiometric surface exists there. The simulation results corroborate parts of both the premixedness and extinction stabilization theories, and suggest that the liftoff mechanism is a result of complex fluid-chemical interactions, parts of which are incorporated in the simplit~ed theories. Future work includes further investigation of the strain rates and extinction in the turbulent jet region and possible development of a three-dimensional model to fully characterize the effects of nonsymmetric turbulence behavior. Acknowledgments This work was sponsored by the Naval Research Laboratory through the Office of Naval Research. Computing time was provided by Numerical Aerodynamic Simulator
(NAS), the Pittsburgh Supercomputing Center, and the Naval Research Laboratory. The authors acknowledge Drs. F. Williams, P. Tatem, and J. Boris for providing the necessary resources and environment for the accomplishment of this work.
REFERENCES 1. Pitts, W. M., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 809-816. 2. Vanquickenborne, L., and van Tiggelen, A., Combust. Flame 10:59-69 (1966). 3. Hall, L, Horch, K., and Gunther, R., Brennst.Warme-Kraft 32:27-31 (1980). 4. Gunther, R., Horch, K. and Lenze, B., First Specialist Meeting (International) of the Combustion Institute, The Combustion Institute, Pittsburgh, 1981, p. 117. 5. Kalghatgi, G. T., Combust. Sci. Technol. 41:17-29 (1984). 6. Eickhoff, H., Lenze, B., and Leuckel, W., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1985, pp. 311-318. 7. Sobiesiak, A., and Brzustowski, T. A., "Some Characteristics of the Stabilization Region of Lifted Turbulent Jet Diffusion Flames," abstract for paper presented at the 1984 Fall Technical Meeting, Eastern Section, The Combustion Institute, Clearwater Beach, FL, December 1984. 8. Savas, O., and Gollahalli, S. R., AIAAJ. 24:1137-1140 (1986). 9. Peters, N., and Williams, F. A., AIAA J. 21:423~t29 (1983). 10. Janicka, J., and Peters, N., Nineteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1982, pp. 367-374. 11. Donnerhack, S., and Peters, S., Combust. Sci. Technol. 41:101-108 (1984). 12. Peters, N., Combust. Sci. Technol. 30:1-17 (1983). 13. Byggstoyl, S., and Magnussen, B. F., in Turbulent Shear Flows 4 (L. J. S. Bradbury et al., Eds.), Springer, New York, 1985, p. 381. 14. Broadwell, J. E., Dahm, W. J. A., and Mungal, M. G., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1984, pp. 303310. 15. Kaplan, C. R., Baek, S. W., Oran, E. S., and Ellzey, J. L., Combust. Flame 96:1-21 (1994). 16. Kaplan, C. R., Baek, S. W., and Oran, E. S., AIAA Paper 93-0109, American Institute of Aeronautics and Astronautics, Washington, D.C., 1993. 17. Ellzey, J. L., Laskey, K. J., and Oran, E. S., Combust. Flame 84:249-264 (1991). 18. Ellzey, J. L., and Oran, E. S., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 1635-1640. 19. Oran, E. S., and Boris, J. P., Numerical Simulation of Reactive Flow, Elsevier, New York, 1987.
STABILIZATION MECHANISM OF LIFTED JET DIFFUSION FLAMES 20. Patnaik, G., Guirgnis, R. H., Boris, J. P., and Oran, E. S.,J. Comput. Phys. 71:1-20 (1987). 21. Westbrook, C. K., and Dryer, F. L., Combust. Sci. Technol 27:31~t3 (1981). 22. Syed, K. J., Stewart, c. D., and Moss, J. B., Twenty-
Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 15331541. 23. Mitchell, R. E., Sarofim, A. F., and Clomburg, L. A., Combust. Flame 37:227-244 (1980).
1189
24. Miake-Lye, R. C., and Hammer, J. A., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 817-824. 25. Smith, K. O., and Gouldin, F. C., AIAA J. 17:12431250 (1979). 26. Abramovich, G. N., The Theory of Turbulent Jets, The M.I.T. Press, Cambridge, MA, 1963. 27. Davies, P. O. A. L., Fisher, M. J., and Barrat, M. J., j. Fluid Mech. 15:337 (1963).
COMMENTS Yei-Chin Chao, National Cheng Kung University, Taiwan, ROC. The lifted flame at the present conditions usually stabilizes downstream of the end of the potential cone where the near-field large coherent structures start to cascade into small eddies and the helical stability modes step in, or dominate the flow. What is the computational grid size at the flame base and how does it compare with the small-eddy scale? How do you take the helical mode into consideration in your computation? The lift-offheight fluctuation in your animation indicates the jump of flame base from a vertical structure to another. Did you find "braids" (Ref. 1) formed between vortices before flame jumping?
REFERENCE 1. Chao, Y. C., and Jeng, M. S~, Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 333-340.
Author's Reply. Computational cells are 0.02 • 0.02 cm near the jet exit, and then are slowly stretched in both the radial and axial directions. At the flame stabilization locations, the cell size is 0.02 cm in the radial direction and varies in the axial direction according to the problem modeled. For the 20 m/s jet, stabilized at z = 4.6 cm, zlz = 0.07 cm, while for the 50 m/s case, stabilized at z = 12.5 cm, Az = 0.15 cm. These computational cell sizes are substantially smaller than the small-eddy scale, which is about ~0.4 cm. This computation is a direct numerical simulation that solves the multidimensional, axisflnmetric, time-dependent, reactive-flow Navier-Stokes equations. Because it is basically two-dimensional, we cannot see a three-dimensional helical mode. Contours of fuel mole fraction, temperature, and the stoichiometric surface show significant deformation and stretching as the flame base moves from one vortical structure to another. This stretching is very similar to the "braiding" phenomenon shown in Fig. 4 of the referenced paper.
STABILIZATION MECHANISM OF LIFTED JET D I F F U S I O N FLAMES CAROLYN R. KAPLAN* AND ELAINE S. ORAN**
*Chemistry Division, **Laboratoryfor Computational Physics and Fluid Dynamics Naval Research Laboratory Washington, D.C. 20375, USA AND
SEUNG W. BAEK
Department of Aerospace Engineering Korea Advanced Institute of Science and Technology Taejon, Korea Flame lift and stabilization are studied using numerical simulations of diffusion flames resulting from a methane jet injected into an air background. The numerical model solves the time-dependent, axisymmetric, multidimensional Navier-Stokes equations coupled to submodels for chemical reaction and heat release, soot formation and radiation transport. Simulations are conducted for an undiluted methane jet and for two nitrogen-diluted jets (CH4: N2/3:1 and CH4:NJ1 : 1). The jet exit velocities range from 20 to 50 m/s through a 1-cm-diameter nozzle, coflowing into a 30-cm/s air stream. The flame liftoff height increases linearly with jet exit velocity and the stabilization height increases as the nitrogen dilution of the jet increases. The computations show that the flame is stabilized on a vortical structure in the inner shear layer, which is on the stoichiometric surface at a height where the local axial velocity is approximately equal to the turbulent burning velocity. There is no appreciable chemical heat release in the region below the stabilization point, although a stoichiometric surface exists in that region. The flame base moves upward with the vortical structure to which it is attached, and then quickly jumps down to attach to a new, lower vortex, resulting in an oscillating (1-2 cm) flame liftoff height. The results corroborate parts of both the premixedness and extinction stabilization theories, and suggest that the liftoff mechanism is a result of complex fluid-chemical interactions, parts of which are incorporated in the simplified theories.
Introduction Although a great deal of research has been devoted to the study of liftoff and blowout of turbulent jet diffusion flames, the physical mechanisms responsible for flame stabilization are still controversial. A recent review by Pitts [i] summarized published experimental and theoretical results and has concluded that none of the theories currently avaitabIe is totally satisfactory. Pitts [1] further concludes that the current experimental characterization of flame stabilization is insufficient to determine the actual physical processes that determine liftoff and blowout. The phenomenon of liftoff has been experimentally investigated for many decades through flow visualization studies. Vanquickenborne and van Tiggelen [2] provided extensive experimental measurements of nonreaeting and reacting turbulent jets of methane over a broad range of jet exit diameters and velocities. Their findings [2] show that lifted flames are stabilized in a turbulent region of the jet near the radial position where the time-averaged fuel mass fraction equals that required for stoichiometric
burning. Other measurements of jets of mixtures of natural gas and hydrogen [3,4] showed that the most likely radial position for combustion to occur is along the mass-fraction contour where the laminar flame speed is maximum. Extensive experimental studies by Kalghatgi [51 for a variety of fuels and a wide range of jet diameters and velocities have resulted in empirical correlations between liftoff height, jet velocit3,, and maximum laminar flame speed. Observations for lifted natural-gas flames have been reported by Eickhoff et al. [6] and Sobiesiak and Brzustowsld [7] and for propane flames by Savas and Gollahalli [8]. Analysis of the experimental studies has resulted in the development of theoretical treatments of flame stabilization. Vanquickenborne and van Tiggelen [2] suggested that the stabilization of lifted turbulent jet diffusion flames can be understood by assuming that the fuel-air mixture is fully premixed at the base of the lifted flame. They then define a local flame speed, which is determined by the local turbulence structure. The flame is stabilized at a position where the local time-averaged axial velocity along the stoichiometric mass fraction contour equals the local flame
1183
1184
TURBULENT FLAMES
speed. Results of other experiments [3-7] have supported this premixedness model. Several more recent theories challenge this by proposing that the stabilization of lifted flames results from flame extinction processes that occur in turbulent structures of the nearby unignited flow, Many different types of extinction processes have been suggested [9-14]. Peters and Williams [9] analyzed the problem in terms of the laminar flamelet model, in which flamelets are extinguished when the local turbulence-induced concentration gradients are sufficient to quench combustion. Flame stabilization occurs at the point where combustion extinction and propagation are balanced. Janicka and Peters [10] considered the effects of assumptions concerning the scalar dissipation on calculated values of liftoff height. Donnerhack and Peters [11] tested a local quenching theory, in which they state that extinction occurs when the rate of heat conduction to the sides of the flame exceeds the rate of heat production due to chemical reaction. Byggstoyl and Magnussen [13] suggest that the extinction occurs in the smallest vortices of the flow, while Broadwell et al. [14] suggest that lifted flames result from flame extinction in large-scale turbulent structures. In this paper, we describe results from a time-dependent numerical model used to study the unsteady behavior of an axisymmetric coflowing methane-air jet diffusion flame. First, we use a series of calculations with increasing jet exit velocities to demonstrate that the numerical model can, in fact, simulate the phenomenon of flame lift and that the results are consistent with the correct physical behavior. Then we analyze these flames to determine trends in liftoff behavior and make comparisons with some of the current theories of flame stabilization. Numerical Method The numerical model solves the time-dependent equations for conservation of mass density, momentum, energy, individual species number densities, soot number density, and soot volume fraction [15]. The solution to the conservation equations includes both radial and axial components of molecular diffusion, thermal conduction, viscosity, radiation transport, and convection; that is, we do not make boundary-layer approximations and do not restrict the Lewis number to unity. These equations are rewritten in terms of finite-volume approximations on an Eulefian mesh and solved numerically for specified boundary and initial conditions. The model consists of separate algorithms for each of the individual processes, which are then coupled together by the method of timestep splitting [15-19]. The different algorithms and how they are applied to solve for the convective [20], diffusive, and radiation transport processes have already been de-
scribed in detail [15-17], and are not discussed here. However, the algorithms for chemical reaction and soot formation are different than those used previously [15,16], and therefore are described below. We represent the chemical reaction and energy-release process phenomenologically using a finite-rate, single-step, quasi-global Arrhenius expression [21] d[CH4] dt
2.3 • 107 9e x p [ ~ ] [ C H 4 ] - ~
L3
(1) where T is temperature and R is the universal gas constant. Equation (1) is used to calculate the rate of depletion of CH,. In order to prevent an infinite reaction rate when the CH4 is fully depleted, we assume a zero reaction rate when the CH4 concentration falls below 1.0 • 10 -20 moles/cma. The concentrations of 02, CO2, HzO, and N2 are then calculated based on their respective stoichiometric coefficients. The chemical heat release rate is then determined from d[CH4] Q =
- AHc
dt
(2)
where 2H c is the heat of combustion for CH 4 oxidation. The evolution of soot number density and soot volume fraction is represented by two coupled ordinary differential equations derived by Syed et al. [22] based on their experimental measurements in methane-air diffusion flames, and include terms for soot nucleation, surface growth, and coagulation on the soot formation rate. dnd
-dt
= No C ~p ZT1/2Xfu~l e - T~/T
1 No C # T j/z n~ df~
dt
-
1 --
(3)
[C nl/a(ot ~ s o o.t jf~z/3oT1/2X, .e -T#T L ? a v/ tfuel
Psoot
+ C~C~p2T1/2Xf, ele-Ta/T ]
(4)
where nd is the soot number density, No is Avogadro's number, p is the fluid density, Xr,el is the fuel mole fraction, andfv is the soot volume fraction. The constants, Ca, Cp, Cy, C~, T~, Tr are taken from Ref. 22, and Psoot,the density of a soot particle, is assumed to be 1.8 g/cm3. The soot volume fraction and number densities, as calculated in Eqs. (3) and (4), are further reduced by a soot oxidation algorithm [15].
STABILIZATIONMECHANISM OF LIFTED JET DIFFUSION FLAMES Fuel Mole Temperature Soot Volume Fraction Fraction
OU~OW
10
C~
0 Fuel Air coflow
r (cm)
FIG. 1. Initial conditions and computed contours for a laminar methane-air diffusion flame.
Results Steady Methane-Air Diffusion Flame:
Simulations were first conducted for a steadystate, laminar methane-air diffusion flame for which the experimental data of Mitchell et al. [23] are available. Figure 1 shows a schematic of the computational conditions and results from a simulation in which undiluted methane flows at 5 cm/s through a 1.2-cm-diameter tube, while air flows at 10 cm/s through the outer annular region. The full computational grid is 10 • 20 cm and consists of 128 • 152 cells. Cells of approximately 0.02 • 0.02 cm are concentrated around the jet exit; the grid spacing is then gradually stretched in both the radial and axial directions [15-17]. This time-dependent calculation
=
2000
~"
1185
showed that the flame reached the steady state shown by 12,000 timesteps (0.12 s). The contours of fuel mole fraction, temperature, and soot volume fraction predict that the flame height is approximately 8 cm, based on the height of the sooting layer. The maximum soot volume fraction is 3.6 • 10 -7, and is located on the fuel-rich side of the high-temperature region. Figure 2 compares experimental and computed radial profiles of temperature at selected heights above the burner for which experimental data were presented [23]. The dashed line is the curve drawn by Mitchell et al. [23] through their experimental data points (error bars are not included with the experimental results). In general, the agreement is quite reasonable, although there is a tendency for the simulations to predict a flame sheet thickness that is wider than those observed experimentally at lower heights in the flame. Unsteady Lifted Methane-Air Diffusion Flame:
Simulations of lifted flames were then conducted for cases in which the fuel mixture flows at a high velocity through a 1.0-cm-diameter jet into a lowvelocity (30 cm/s) coflowing air stream. The fuel streams considered included undiluted methane and also nitrogen-diluted (CH4:N2/3 : 1 and CH4 : N2/1 : 1) fuel mixtures. Figure 3 shows contours of temperature, chemical heat release rate, and radial velocity for cases in which the undiluted methane fuel jet velocity varies from 20 to 50 m/s. The location of the stoichiometric surface is shown by the solid line with black circles superimposed. The radial velocity contours show the Kelvin-Helmholtz instabilities, which form in the shear layer between the highand low-velocity streams. The dashed lines in the radial velocity contours correspond to counterclockwise rotating structures, while the solid lines correspond to clockwise-rotating structures. As shown in
=
I
! 5.0 cm =height' sire.
1500 "-I
1000 i~
500 0 0
1
r (cm)
2
3
0
1
2
r (cm)
3 0
1
2
3
r (cm)
FIG. 2. Comparisonbetween simulation and experimental results [23] for laminar methane-air flame. The dashed line is the curve drawn by Mitchell et al. [23] through their experimental data.
1186
TURBULENT FLAMES 20 m/s
30 m/s
7.2 c m >
__
:a) i ~
~b~
50 m/s
40 ra/s 12.5 cm
FIC. 3. (a) Temperature (K), (b) chemical heat release rate (ergs/cm~s), and (c) radial velocity(cm/s) contours for undiluted methane fuel jet; jet inflow velocities 20-50 m/s. Heavy solid line with solid circular symbols corresponds to the location of the stoichiometric surface. Arrow points to liftoff height.
J
0
2 r (cm)
Fig. 3, the liftoff heights are 4.6, 7.2, 9.4, and 12.5 cm for the 20, 30, 40, and 50 m/s cases, respectively. For all of the cases shown, the base of the lifted flame is situated on the stoichiometric surface, and is attached to a Kelvin-Helmholtz structure; that is, the stoichiometric contour passes through the vortical structure at the flame stabilization location. Figure 4 shows that there is reasonable agreement between the simulation results and the experimental data of Kalghatgi [5]. Both show a linear relationship between flame liftoff height and jet exit velocity. Figure 4 also shows results from a simulation in which the fuel jet is diluted with nitrogen (CH4:N2/I:I). As expected, the liftoff height is greater for a given jet inflow velocity for the nitrogen-diluted case, as the residence time (chemical time) is longer when the fuel stream is diluted. For the nitrogen-diluted case, the liftoff height is again a linear function of the jet exit velocity, but the slope of this line is greater than that for the undiluted case. This phenomenon of a steeper slope with increasing nitrogen dilution has also been shown experimentally [11,24] in studies of the effect of jet dilution on liftoffheight. The liftoff heights presented in Fig. 4 were taken from instantaneous temperature images at one particular timestep (15,000 timesteps). However, animations of this unsteady flame show that the liftoff height fluctuates. That is, the base of the flame moves up with the vortical structure to which it is attached,
25 20
'. 'im. o
E x p [5] (undiluted)
"
Sim. (50% diluted)
15 A 0
11 o
0
9
0
c~
0
0
O0 0
O!
~
i
I
20
30
40
"
I
50
u o (m/s)
FIG. 4. Liftoffheight as a function of jet exit velocityfor simulations (undiluted fuel jet and 50% diluted fuel jet) and experimental measurements (undiluted fuel jet).
STABILIZATIONMECHANISM OF LIFTED JET DIFFUSION FLAMES
1187
TABLE 1 Comparison of turbulent burning velocity (S,) to fluid axial velocity (from the simulations) at the liftoff height. Method used to calculate St is outlined at bottom.
Jet velocity (m/s)
Liftoff height (cm)
Rz at liftoff heighta (approx.)
20 30 40 50
4.6 7.2 9.4 12.5
38 50 87 144
S,/S~ b
S t (approx.) at liftoff height ~ (em/s)
Axial velocity at liftoff height, from simulations (cm/s)
1.7-2.6 1.9-3.0 2.6-4.0 3.3-5.1
70-105 75--120 105-160 130-205
60-100 80-110 110-170 140-220
aFrom Eq. (6). bFrom Eq. (5), and experimental results [5,25]. ~Based on Su = 40 cm/s, and Sr from previous column.
and then quickly jumps down to attach to a new, lower vortex, resulting in an oscillating flame height. The fluctuation in liftoff height due to this movement is approximately 1 to 2 cm. Tests o f Flame Stabilization Theory:
The computations have shown that the numerical model does indeed simulate the phenomenon of flame liftoff, and the results are consistent with published experimental data. Now, we compare the simulation results with some of the current theories of flame lift~ One of the important hypotheses from the premixedness theory of Vanquickenborne and van Tiggelen [2] is that the base of the flame stabilizes on the stoichiometric surface at the height where the local axial velocity is equal to the turbulent burning velocity. In order to evaluate this hypothesis, we calculated the ratio of the turbulent burning velocity to the maximum laminar burning velocity (St/Su) at the liftoff height based on a correlation by Kalghatgi [5]
s! = S~
Rz.f~(W~,~). K
(5)
wheref4 and K are constants taken from Ref. 5 (f4 = 0.138, K ranges from 0.56 to 1.3). The term R l is the turbulent Reynolds number, given by u'l nz
=
--
Vs
(6)
where u' is the root mean square (rms) fluctuation velocity, I is the turbulent integral length scale in the jet mixing layer, and vs is the kinematic viscosity at the base of the flame. In Ref. 5, the values of St/Su as a function ofRy 2 from Eq. (5) are favorably compared with an experimentally determined ratio of
turbulent burning velocity to laminar burning velocity as a function of Ry 2 by Smith and Gouldin [25]. That is, the experimental data points of Smith and Gouldin [25] fall within the range of values of St~S, for a given R l from Eq. (5). Therefore, using values o f u ' = 2 rn/s (simulation results show rms velocity fluctuations on the order of i t o 2 m/s), and calculating I based on correlations from Abramovich [26] and Davies et al. [27], l = Cz
(7)
(where C is a constant, and z is the axial height), we calculated values of R l at the flame lift height from Eq. (6), and used that value to calculate a range of St/Su from Eq. (5). Table 1 lists the values of these quantities for the four cases in which the jet is undiluted. Based on a maximum laminar burning velocity Su = 40 cm/s for methane-air flames, we calculated the range of turbulent burning velocities, St, at the liftoff height, as shown in Table 1. We then compared these calculated values of St with the axial velocity at the liftoff height based on the simulation results. The axial velocity fluctuates considerably (varies from negative to positive values) within the rotating vortical structures to which it is attached. However, the axial velocity is always positive (flowing upwards) in the region immediately below the vortical structure to which the flame is attached. For each of the jet velocities considered, Table 1 shows the range of axial velocity values in the region immediately below the vortical structure to which the flame is attached. As shown, this range of axial velocities based on the simulations is approximately the same as the range of calculated [from Eqs. (5) and (6)] turbulent burning velocities at the liftoff height. Although the results above show that the simula-
1188
TURBULENT FLAMES
tions do, in fact, corroborate some parts of the premixedness theory [2], this does not imply that the simulations conflict with some of the proposed extinction mechanisms [9-14]. In fact, the computations show that although a stoichiometric surface exists in the region below the stabilization point (as shown in Fig. 3), there is no appreciable chemical heat release or formation of products in that region. This lack of heat release may be due to a local quenching process within the turbulent structures of the jet. The simulation results show that strain rates in the highly turbulent structures near the jet exit are approximately 1000-1400 s -1, then decrease to values of approximately 300--500 s 1 at the stabilization point, and continue to decrease with increasing height. Further analysis is planned to fully investigate the strain rates and scalar dissipation in the turbulent structures of the jet.
SlllTllTlary A solution of the time-dependent multidimensional reactive flow Navier-Stokes equations has been obtained to study the stabilization mechanism of lifted jet diffusion flames. Although this computation is based on axisymmetric geometry, and hence neglects nonsymmetric turbulence behavior, it is able to capture the fluid-chemical interactions that are important in turbulent flows and contribute to flame lift. The liftoff heights are in reasonable agreement with published experiments; the results show a linear relationship between liftoff height and jet exit velocity, and the liftoff height increases with increasing fuel dilution due to longer residence times. The computations are compared with some of the current theories of flame stabilization, and show that the flame is stabilized on an inner shear layer vortical structure, which is on the stoichiometric surface at a height where the local axial velocity is approximately equal to the turbulent burning velocity. In the region below the stabilization point, strain rates are very high and there is no appreciable chemical heat release, even though a stoichiometric surface exists there. The simulation results corroborate parts of both the premixedness and extinction stabilization theories, and suggest that the liftoff mechanism is a result of complex fluid-chemical interactions, parts of which are incorporated in the simplit~ed theories. Future work includes further investigation of the strain rates and extinction in the turbulent jet region and possible development of a three-dimensional model to fully characterize the effects of nonsymmetric turbulence behavior. Acknowledgments This work was sponsored by the Naval Research Laboratory through the Office of Naval Research. Computing time was provided by Numerical Aerodynamic Simulator
(NAS), the Pittsburgh Supercomputing Center, and the Naval Research Laboratory. The authors acknowledge Drs. F. Williams, P. Tatem, and J. Boris for providing the necessary resources and environment for the accomplishment of this work.
REFERENCES 1. Pitts, W. M., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 809-816. 2. Vanquickenborne, L., and van Tiggelen, A., Combust. Flame 10:59-69 (1966). 3. Hall, L, Horch, K., and Gunther, R., Brennst.Warme-Kraft 32:27-31 (1980). 4. Gunther, R., Horch, K. and Lenze, B., First Specialist Meeting (International) of the Combustion Institute, The Combustion Institute, Pittsburgh, 1981, p. 117. 5. Kalghatgi, G. T., Combust. Sci. Technol. 41:17-29 (1984). 6. Eickhoff, H., Lenze, B., and Leuckel, W., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1985, pp. 311-318. 7. Sobiesiak, A., and Brzustowski, T. A., "Some Characteristics of the Stabilization Region of Lifted Turbulent Jet Diffusion Flames," abstract for paper presented at the 1984 Fall Technical Meeting, Eastern Section, The Combustion Institute, Clearwater Beach, FL, December 1984. 8. Savas, O., and Gollahalli, S. R., AIAAJ. 24:1137-1140 (1986). 9. Peters, N., and Williams, F. A., AIAA J. 21:423~t29 (1983). 10. Janicka, J., and Peters, N., Nineteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1982, pp. 367-374. 11. Donnerhack, S., and Peters, S., Combust. Sci. Technol. 41:101-108 (1984). 12. Peters, N., Combust. Sci. Technol. 30:1-17 (1983). 13. Byggstoyl, S., and Magnussen, B. F., in Turbulent Shear Flows 4 (L. J. S. Bradbury et al., Eds.), Springer, New York, 1985, p. 381. 14. Broadwell, J. E., Dahm, W. J. A., and Mungal, M. G., Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1984, pp. 303310. 15. Kaplan, C. R., Baek, S. W., Oran, E. S., and Ellzey, J. L., Combust. Flame 96:1-21 (1994). 16. Kaplan, C. R., Baek, S. W., and Oran, E. S., AIAA Paper 93-0109, American Institute of Aeronautics and Astronautics, Washington, D.C., 1993. 17. Ellzey, J. L., Laskey, K. J., and Oran, E. S., Combust. Flame 84:249-264 (1991). 18. Ellzey, J. L., and Oran, E. S., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 1635-1640. 19. Oran, E. S., and Boris, J. P., Numerical Simulation of Reactive Flow, Elsevier, New York, 1987.
STABILIZATION MECHANISM OF LIFTED JET DIFFUSION FLAMES 20. Patnaik, G., Guirgnis, R. H., Boris, J. P., and Oran, E. S.,J. Comput. Phys. 71:1-20 (1987). 21. Westbrook, C. K., and Dryer, F. L., Combust. Sci. Technol 27:31~t3 (1981). 22. Syed, K. J., Stewart, c. D., and Moss, J. B., Twenty-
Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 15331541. 23. Mitchell, R. E., Sarofim, A. F., and Clomburg, L. A., Combust. Flame 37:227-244 (1980).
1189
24. Miake-Lye, R. C., and Hammer, J. A., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 817-824. 25. Smith, K. O., and Gouldin, F. C., AIAA J. 17:12431250 (1979). 26. Abramovich, G. N., The Theory of Turbulent Jets, The M.I.T. Press, Cambridge, MA, 1963. 27. Davies, P. O. A. L., Fisher, M. J., and Barrat, M. J., j. Fluid Mech. 15:337 (1963).
COMMENTS Yei-Chin Chao, National Cheng Kung University, Taiwan, ROC. The lifted flame at the present conditions usually stabilizes downstream of the end of the potential cone where the near-field large coherent structures start to cascade into small eddies and the helical stability modes step in, or dominate the flow. What is the computational grid size at the flame base and how does it compare with the small-eddy scale? How do you take the helical mode into consideration in your computation? The lift-offheight fluctuation in your animation indicates the jump of flame base from a vertical structure to another. Did you find "braids" (Ref. 1) formed between vortices before flame jumping?
REFERENCE 1. Chao, Y. C., and Jeng, M. S~, Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1992, pp. 333-340.
Author's Reply. Computational cells are 0.02 • 0.02 cm near the jet exit, and then are slowly stretched in both the radial and axial directions. At the flame stabilization locations, the cell size is 0.02 cm in the radial direction and varies in the axial direction according to the problem modeled. For the 20 m/s jet, stabilized at z = 4.6 cm, zlz = 0.07 cm, while for the 50 m/s case, stabilized at z = 12.5 cm, Az = 0.15 cm. These computational cell sizes are substantially smaller than the small-eddy scale, which is about ~0.4 cm. This computation is a direct numerical simulation that solves the multidimensional, axisflnmetric, time-dependent, reactive-flow Navier-Stokes equations. Because it is basically two-dimensional, we cannot see a three-dimensional helical mode. Contours of fuel mole fraction, temperature, and the stoichiometric surface show significant deformation and stretching as the flame base moves from one vortical structure to another. This stretching is very similar to the "braiding" phenomenon shown in Fig. 4 of the referenced paper.