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On the structure, stabilization, and dual response of flat-burner flames
On the Structure, Stabilization, and Dual Response of Flat-Burner Flames J. A. ENG, D. L. ZHU, and C. K. LAW Depatiment of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544
A comprehensive computational and experimental study has been conducted on the structure and stabilization dynamics of the classical planar flame over a flat, porous burner. The specific issue addressed is the apparent dual response nature of the flat-burner flames in that previous studies have shown the existence of two flame speeds for either a given heat loss rate or a given flame standoff distance. The present study demonstrates that the flame response is actually unique when the flame burning rate is considered to be the independent variable, that the turning point behavior of the flame response is a manifestation of system nonmonotonicity rather than extinction, and that the flat-burner flame does not appear to possess distinct extinction states. Results obtained from computational simulation of the flame structure with detailed transport and chemistry agree well with the experimental temperature and major species profiles determined through laser Raman spectroscopy.
NOMENCLATURE specific heat mass flux from the burner f qF
f/f”
heat of combustion per unit mass of fuel @L.nondimensional heat loss rate to the burner, defined in Eq. la T temperature T, activation temperature
i:
c,T/(qFy,)
X
distance from burner surface
.i
[f “/(W,>Ix
Y,
reactant mass fraction in freestream thermal conductivity
A
Subscripts f i S U
flame species burner surface freestream
Superscripts 0
w
adiabatic state nondimensional
quantity
INTRODUCTION Although the propagation of the adiabatic, steady, one-dimensional planar premixed flame COMBUSTIONAND
FLAME
100: 645-652
in the doubly infinite domain has formed the backbone in studies of both laminar and turbulent premixed flames, corresponding experimental studies of the associated flame structure have not been successful because of the substantial difficulty in establishing such a flame in the laboratory. Instead, most investigations of planar flames have been conducted by using the flat-burner flame, in which a planar flame is stabilized through heat loss to the porous surface of a flat burner, from which the combustible mixture is introduced. Using such a technique, worthwhile information has been obtained on the chemical kinetics of premixtures in general, and the dynamics and structure of premixed flames in particular. Notable examples are Spalding’s technique [l] for the determination of the laminar flame speeds of combustible mixtures by linearly extrapolating experimental flame speeds with various heat loss rates to the state of zero heat loss, and the detailed quantification of the species concentration profiles across the flame, from which fundamental information on reactions of interest can be determined. In the seminA analysis of Spalding [2] for the freely propagating planar flame with volumetric heat loss, the flame response exhibits the characteristic extinction turning point behavior, indicating the existence of dual flame speeds for a given heat loss rate when it is smaller than a critical value, and no solution
(1995)
Copyright 0 1995 by The Combustion Institute Published by Elsevier Science Inc.
OOlO-2180/95/$9.50 SSDI OOlO-218Ot94)00102-X
646 when such a value is exceeded. A companion stability analysis further demonstrates that solutions on the slower branch are unstable, implying that the solution is unique for a subcritical heat loss rate, and that the critical state can be identified as that of extinction. While the theoretical results of Spalding appear to be unambiguous, a subsequent experimental study by Spalding and Yumlu [3], using the flat-burner flame, reveals a dual response behavior. That is, with increasing heat loss rate to the burner, the flame response consists of an upper branch as well as a lower branch which merges at a turning point. Thus, for a certain range of the heat loss rate around the turning point, there are two possible values for the flame speed. Subsequently, Ferguson and Keck 141 also observed such a dual response behavior for the flat-burner flame, in that there are two possible values for the flame speed and the flame temperature for a given flame standoff distance. It was further indicated that since the turning point for such a plot corresponds to the minimum distance the flame can approach the burner surface, this distance can be identified as the quenching distance of the flame. Such simultaneous dual responses were also reported by Yamazaki and Ikai [5] through experimental and thermal-based theoretical investigations. Recently Chao and Law [61 analyzed the flat-burner flame using activation energy asymptotics. Some preliminary observations were made regarding the flame response including its nonmonotonic behavior. The system response, however, turns out to be richer than originally recognized. Thus the first objective of the present study is to provide a comprehensive discussion of the possible flame responses, especially with regard to the issue of the experimentally observed dual behavior. Our second objective is to perform a careful and comprehensive experimental investigation of the “non-monotonic” behavior of the global properties of burner-stabilized flames. Such an investigation is needed because the study by Spalding and Yumlu [3] was concerned only with the response of the flame speed to variations in the heat loss rate, while that by Ferguson and Keck [4] only with the response of the
J. A. ENG ET AL. flame speed and temperature to the flame location. Since all parameters are interdependent in this problem, a complete experimental verification of the system behavior requires the simultaneous specification and characterization of the flame speed, flame temperature, flame standoff distance, and the heat loss rate for a given situation. Furthermore, a closer examination of the data of Ref. 3 reveals some unquantifiable, but possibly quite serious, inaccuracies. For example, the reported flame speeds of acetylene/air mixtures appear to be too low to be possible. We have found in the present study that determination of the heat loss rate through measurement of the average change in the coolant temperature can be quite inaccurate. Our third objective is to explore and possibly verify the quantitative predictability of the flat-burner flame through computational simulation. In order to achieve this goal, we shall first obtain quantitatively accurate data on the flame structure using laser diagnostics. Specifically, we shall determine the temperature and major species profiles using Raman spectroscopy. These data will then be compared with the computed results using detailed chemistry and transport. The present state of flame diagnostics and simulation demands a reasonable degree of agreement between the measured and computed results, if the process is described well and the experiment and computation conducted accurately. A quantitative and comparative study of the present nature has not been conducted for this important bumerstabilized flame. In the following sections we shall sequentially present discussions of the qualitative flame dynamics, the experimental and computational methodologies, and comparison of the results. QUALITATIVE FLAME DYNAMICS Straightforward activation energy asymptotics yields the following relations between the mass burning rate of the flame f, the flame standoff distance 2, relative to the burner surface 2, = 0, the flame temperature Tf, the burner surface temperature T,, and the heat loss rate to
FLAT-BURNER
647
FLAMES
the burner &:
008
r
cjL=(g)o=f[l-(ff-fs)], (la) 0.02 t
where fu is the freestream tempezature of the unburned mixture, f; = 1 + ?,,, T, the activation temperature, and the superscripts “0” and “ N ” respectively designate the adiabatic state and a nondimensional quantity defined in the Nomenclature section. Furthermore, we shall use fa = 6 and fu = 0.12 in all of the_follo$ng calculations. Thus by further fixing T, = T, = 0.12, and with either &_ or Zf as the independent variable, the behavior of the other three system parameters can be plotted, as in Figs. 1 and 2, respectively. The behavior is clearly nonmonotonic. Specifically, Fig. 1 reproduces the observation of Spalding and Yumlu [3] that there are two flame speeds for a given heat loss rate, while Fig. 2 reproduces the observation of Ferguson and Keck 141 that there are two flame speeds and flame temperatures for a given flame standoff distance.
%. Fig. 1: Representative analytical solutions for the burning rate f, flame standoff distance fr, and flame temperature T{ as functions of the heat loss rate to the burner & with a fixed burner surface temperature f3, demonstrating the multiplicity of the flame responses in such a plot.
Fig. 2. Representative analytical solutions for the burning rate f, flame temperature Y$ and heat loss rate to the burner & as functions of the flame standoff distance .Ef with a fixed burner surface temperature fS, demonstrating the multiplicity of the flame responses in such a plot.
However, as first recognized in Ref. 6, concerns about the dual solutions are actually unwarranted because of the fundamentally different nature of the freely propagating flame and the burner-stabilized flame. That is, unlike the nonadiabatic freely propagating planar flame model of Spalding [2] for which the heat loss intensity can be independently specified, for the flat-burner flame, with fixed burner surface temperature, the heat loss rate is frequently a response of the system and therefore cannot be easily manipulated to bring about flame extinction during experimentation. The same observation applies to the flame standoff distance and flame temperature being responses of the system. Indeed, the parameter which is the most natural independent variable for the flat-burner flame is actually the flow rate and thereby the (nonadiabatic) flame speed. Consequently, with f being the independent parameter, for c = f,,;,, Fig. 3 shows that all flame characteristics including the flame standoff distance and the heat loss rate respond uniquely. As such, it is possible that the observed “turning points” are simply the states at which the flame exhibits a nonmonotonic behavior, and therefore are not the states of extinction. To further substantiate the above possibility, we note that in Figs. l-3 the burner surface temperature p$ is fixed while the heat loss rate gL is varied. An alternate experimental approach is to hold gL fixed and vary T, for each
648
J. A. ENG ET
0.08
0.06
004 ‘i,
0.02
0.00 0.0
0.2
0.4
0.6
0.8
10
i
Fig. 3. Representative analytical solution_s for the flame standoff distance ff, flame temperature Tf, and heat loss rate to the burner t& as functions of the burning rate f with a fixed burner surface temperature T,, demonstrating the uniqueness of the flame responses in such a plot.
value of f, as shown in Fig. 4 for &, = 0.065. It is seen that the flame responses are again unique with varying f: Another possible_experimental procedure is to fix the flow rate f and independently change the cooling rate of the burner, which will yield the corresponding & and T,. Figure 5 shows such a plot, for 0.7, which further demonstrates the uniqueness of the flame response. The monotonicity of the flame response with f fixed is also worth noting. It is therefore quite clear that, depending on the specific parameters used as the dependent and independent variables, the flame response can be either monotonic, nonmonotonic, or dual valued. The important point to recognize
fr=
02
R 2.0 1.0 ii\
i 0.1
-------
0.0’0.1* 0.0
0.32
0.2
0.4
0.6
0.8
I.0
Lo
T Fig. 4. Representative analytical solutions for the flame standoff distance .Cf, flame temperature F!, and burner_ surface temperature FS as functions of the burning rate f with a fixed heat loss rate to the burner &, demonstrating the uniqueness of the flame responses in such a plot.
Fig. 5. Representative analytical solutions for the flame standoff distance .Zf, flame temperature $, and burner surface temperature fS as functions of the heat loss rate to the burner &, with a fixed burning rate f, demonstrating the uniqueness of the flame responses in such a plot.
is that, when dual responses occur, solutions on both the upper and lower branches are potentially physically realizable, and the “tuming point” does not designate the state of extinction. Indeed, the relevant critical phenomenon for the flat-burner flame does not appear to be extinction through heat loss. Rather, it is the blowoff of the flame when the flow velocity exceeds the adiabatic flame speed. In realistic situations it is well known that the flame becomes wrinkled in order to accommodate the increased mass flow rate.
EXPERIMENTAL AND COMPUTATIONAL METHODOLOGIES The burner used for the present experiments was made of porous sintered bronze with a 20-pm pore size. A schematic of the burner cross section is shown in Fig. 6. The porous plug has a diameter of 5.08 cm and thickness of 1.27 cm. Cooling was accomplished by passing water at a controlled rate through cooling coils imbedded in the burner, based on the recommendations of Pagni et al. [7], with the coils positioned at least 3 coil diameters away from the burner surface in order to minimize their perturbing effects on the flow. A circular porous ring was placed around the main burner to provide a uniform coflow of the inert gas to shield the flame from the environment. Five thermocouples were inserted at several distances from the burner surface to measure
FLAT-BURNER
Fig. 6. Schematic setup.
649
FLAMES
of the flat-burner
and experimental
temperatures within the burner and hence determine the corresponding heat loss rate. Experimental observation of the non-monotonic response behavior requires measurement of both the flame standoff distance and the burner heat loss rate. The leading and trailing edges of the luminous zone were visually measured by a microscope, and the flame location was taken to be the mid-point between them. The final flame temperature was measured with a thermocouple for additional comparison with the numerical and laser diagnostic results to be discussed subsequently. A Platinum-13% Rhodium/Platinum thermocouple was used with radiation correction [81, with an estimated measurement error of roughly +50 K. The heat loss rate was calculated from Fourier’s law, using the measured value of the conductivity of the porous material and the temperature gradient at the burner surface from the thermocouples in the burner. To measure the conductivity of the porous material, a cylindrical disk of the material was positioned between two cylinders of a reference material with known conductivity. By placing a temperature
difference across the system, and measuring the temperature gradient in both the porous and reference materials, the conductivity of the porous material was determined by continuity of the heat flow. Detailed profiles of the temperature and the major species of 0, and CO, were measured across the flame by using spontaneous Raman spectroscopy. Here a pulsed Nd-Yag laser operating at 532 nm and 20 Hz was focused above the burner surface with a plano-convex lens, and the scattered Raman signal was passed through a monochrometer with a 2400groove/mm grating and detected with a photodiode array. The temperature was determined from the vibrational Stokes Raman scattering of N, using a modified version of a program developed at Sandia for CARS measurements. The program generates a library data base of theoretical spectra at temperatures of 50-K increments, and performs a least squares fit to interpolate between the library spectra to obtain the temperature for a given spectra. Details of the experimentation can be found in Ref. 9. The numerical simulation was conducted by using a version of the one-dimensional premixed flame code of Kee et al. [lo]. The program uses finite differences to solve the governing equations of mass, species, and energy conservation with detailed kinetics and species diffusion. Two free-standing programs [ll, 121 are used to evaluate the chemical reaction rates, thermodynamic data and transport data. For the, burner-stabilized flame, the burning rate f is specified. At the burner surface the temperature and mass flux fractions of the ith species, fi, are also given. Note that an implicit assumption here is that the burner surface is inert to all chemical reactions. The mass fluxes for the individual reactant species are known from the unreacted mixture ratio, and are zero for intermediate species and product species. At the burned hot boundary, the conditions imposed are vanishing of the temperature and species gradients. RESULTS
AND DISCUSSIONS
The overall response of a methane/air flame at atmospheric pressure and an equivalence
J. A. ENG ET AL.
650 ratio of 0.7 was studied as a function of the mass flow rate f. The burner surface temperature was 332 K, and was held constant throughout the experiments by varying the water flow rate through the burner. The adiabatic flame temperature for this unburned mixture temperature is Tf” = 1940 K, and the adiabatic mass burning rate is f” = 0.026 gm/cm*-s. Nitrogen was used for the inert coflow, and its flow rate was adjusted so that the edge of the flame was flat. The flame responses measured are the flame temperature, the heat loss rate to the burner, and the boundaries of the luminous zone of the flame. The experimental flame location is then taken as the center of the luminous zone. Furthermore, since the luminosity for lean flames is mainly due to the CH radical 1131,the definition of the flame location used for the numerical work is the position of maximum CH concentration in the flame. Figure 7 compares the measured and computed flame temperatures as a function of the mass flow rate. It is seen that they increase monotonically with the burning rate, in agreement with the analytical result. Furthermore, they can also be considered to agree well with each other within the accuracy of the experimentation. Figures 8 and 9, respectively, compare the measured and computed heat loss rate and flame standoff distance as functions of the mass flow rate, with the experimental flame dimension also marked off. The agreement is generally satisfactory and the flame responses are as predicted from the analysis and computation. The computed heat loss rates are slightly
3.5 8
3.0.
r? g b
2.5 -
B 2.0 OS I 2 1.5. 3 z
-
Computation Experiment
0 1.0.
”
0.5’ 0.000
” ”
’
0.005 0.010 0.015 0.020 Mass Flow Rate, gm/cm*-see
0.025
Fig. 8. Computed and measured heat loss rate as a function of the mass flow rate.
higher than the measured values, possibly caused by the radiative heat loss from the flame which is not included in the computation. It is, however, also significant to note that the experimental flame location does not exhibit a clear minimum in that it does not unambiguously show the ascending portion as predicted by the theory. Experimentally, as the flame location was reduced to its minimum value as represented by the nearly flat portion of the data, further increases in the mass flow rate caused the flame to become wrinkled. This same phenomenon was also reported by Ferguson and Keck [4]. Physically, since the heat loss rates at such states are very small because of the high mass flow rate (see Fig. 81, the flame tends to resemble the adiabatic flame which is however intrinsically unstable for flows generated by the porous burner, as shown by 2.0 __
-
computation
I Experiment looOL 0.000
Computation
0.005 0.010 0.015 0.020 Mass Flow Rate, gm/cm*-set
Fig. 7. Computed and measured flame temperature function of the mass flow rate.
0.025
as a
0.0 0.000 ”
”
”
”
”
”
”
”
”
”
”
0.020 0.010 0.015 0.005 Mass Flow Rate, @n/cm*-see
”
0.025
Fig. 9. Computed and measured flame standoff distance and luminous boundaries as functions of the mass flow rate.
FLAT-BURNER
FLAMES
651
McIntosh [14]. It may also be noted that flame wrinkling also occurs for the very small flow rates, which are less than 0.005 gm/cm’-s. Wrinkling for such situations is expected to be also affected by the relatively strong influence of buoyancy. Figures 10 and 11, respectively, compare the measured and computed temperature and CO, and 0, concentration profiles for a mass flow rate of 0.0097 gm/cm’-s. The overall agreement is good, although the calculated 0, mole fraction is about 25% higher than the measured results. Since the computation does not include surface reactions, the present level of agreement indicates that, even if these reactions were present, they would not affect the bulk flame properties to any significant extent. CONCLUDING REMARKS The comprehensive nature of the present study, and the qualitative and quantitative agreement obtained for the analytical, computational, and experimental results of the investigation, provide strong indication that our understanding of the structure and stabilization mechanism of the flat-burner flame is at a quite satisfactory state. Specifically, we now understand that the flame does not possess multiplicity of solutions in the sense of the characteristic ignition-extinction S-curve, that the flame response is unique when an appropriate parameter, such as the burner flow rate and hence the flame burning rate, is treated as the independent parameter of the system, and that the flame can freely adjust its standoff distance and hence
0
Computation Experiment
zoot~“‘~““~“““““““““.~““““‘i 0.0
0.5
1.0 1.5 2.0 2.5 3.0 Distance from Burner, mm
Fig. 10. Computed and measured temperature a mass flow rate of f = 0.0097 gm/cm’-s.
3.5
4.0
profiles for
__ Computation 0 70 Experiment
4 0.00
0.0
”
”
0.5
”
”
1.0
”
”
”
1.5
”
”
2.0
”
”
2.5
”
”
3.0
”
”
3.5
”
4.0
Distance from Burner, mm Fig. 11. Computed and measured CO, and 0, concentration profiles for a mass flow rate of f = 0.0097 gm/cm*-s.
the heat loss rate such that extinction is not the relevant critical phenomenon. Consequently, it is not appropriate to identify either the turning point of the heat loss curve as the state of flammability, or the minimum flame standoff distance as the quenching distance of the mixture. Within the framework of a steady and planar flame, the flame can only be blown off when the burner discharge velocity exceeds the adiabatic laminar flame speed. Realistically, flame wrinkling occurs before this state is reached. It is of interest to investigate the possible onset of intrinsic burner-induced instability 1141as the flame reaches the minimum standoff distance and starts to recede from the burner surface with increasing flow rate. This work has been sponsored by the Microgravity Combustion Program of NASA-Lewis, under the technical monitoring of Mr. Kurt Sacksteder. JAE also acknowledges the support by the Air Force Office of Scientific Research through an AFRAPT &Iir Force Research in Aero Propulsion Technology) traineeship. We thank Mr. J. B. Liu and Mr. C. J, Sung of Princeton University for their help in taking and ana&zing the jlame structure data, Professor Peck Cho of the Michigan Technological University for technical information, and a reviewer who brought Refi 5 to our attention.
REFERENCES 1. Botha, .I. P., and Spalding, D. B., Proc. R. Sm. Ser. A 2253-96 (1954).
J. A. ENG ET AL,. SpaIding, D. B., Proc. R. Sec. Ser. A 240:83-100 (1957). 3. Spalding, D. B., and Yumlu, V. S., Cornbust. Flame 3:553-556 (1959). 4. Ferguson, C. R., and Keck, J. C., Cornbust. Flame 3485-98 (1979). 5. Yamazaki, S., and Ikai, S., Trans. J. Sot. Me&. Eng., 37. 293:121-130 (1971). 6. Chao, B. H., and Law, C. K., Cornbust. Sci. Technol. 62:211-237 (1988). 7. Pagni, J. P., Ortega, A., and Toossi, R., Flat Flame Burner Analysis, Technical Meeting of the Western States Section of the Combustion Institute, Paper No. 79-47 (1979). 2.
R. C., and Iaurendeau, N. M., Cornbust. (1985). Sung, C. J., and Law, C. K., AIAA 31st Aerospace Sciences Meeting, Paper No. 93-0246 (1993). Kee, J. K., Grcar, J. F., Smooke, M. D., and Miller, J. A., Sandia Report SAND85-8240 (1985). Kee, J. K., Miller, J. A., and Jefferson, T. H., Sandia Report SAND80-8003 (1980). Kee, J. K., Wamatz, J., and Miller, J. A., Sandia Report SAND83-8209 (1983). Glassman, I., Combustion, Academic, 1987, p. 112. McIntosh, A. C., J. Fluid Mech. 161:43-75 (1985).
8. Peterson,
Flame 60:279-284
9. 10. 11. 12. 13. 14.
Received 27 May 1993; revised 20 April 1994
A comprehensive computational and experimental study has been conducted on the structure and stabilization dynamics of the classical planar flame over a flat, porous burner. The specific issue addressed is the apparent dual response nature of the flat-burner flames in that previous studies have shown the existence of two flame speeds for either a given heat loss rate or a given flame standoff distance. The present study demonstrates that the flame response is actually unique when the flame burning rate is considered to be the independent variable, that the turning point behavior of the flame response is a manifestation of system nonmonotonicity rather than extinction, and that the flat-burner flame does not appear to possess distinct extinction states. Results obtained from computational simulation of the flame structure with detailed transport and chemistry agree well with the experimental temperature and major species profiles determined through laser Raman spectroscopy.
NOMENCLATURE specific heat mass flux from the burner f qF
f/f”
heat of combustion per unit mass of fuel @L.nondimensional heat loss rate to the burner, defined in Eq. la T temperature T, activation temperature
i:
c,T/(qFy,)
X
distance from burner surface
.i
[f “/(W,>Ix
Y,
reactant mass fraction in freestream thermal conductivity
A
Subscripts f i S U
flame species burner surface freestream
Superscripts 0
w
adiabatic state nondimensional
quantity
INTRODUCTION Although the propagation of the adiabatic, steady, one-dimensional planar premixed flame COMBUSTIONAND
FLAME
100: 645-652
in the doubly infinite domain has formed the backbone in studies of both laminar and turbulent premixed flames, corresponding experimental studies of the associated flame structure have not been successful because of the substantial difficulty in establishing such a flame in the laboratory. Instead, most investigations of planar flames have been conducted by using the flat-burner flame, in which a planar flame is stabilized through heat loss to the porous surface of a flat burner, from which the combustible mixture is introduced. Using such a technique, worthwhile information has been obtained on the chemical kinetics of premixtures in general, and the dynamics and structure of premixed flames in particular. Notable examples are Spalding’s technique [l] for the determination of the laminar flame speeds of combustible mixtures by linearly extrapolating experimental flame speeds with various heat loss rates to the state of zero heat loss, and the detailed quantification of the species concentration profiles across the flame, from which fundamental information on reactions of interest can be determined. In the seminA analysis of Spalding [2] for the freely propagating planar flame with volumetric heat loss, the flame response exhibits the characteristic extinction turning point behavior, indicating the existence of dual flame speeds for a given heat loss rate when it is smaller than a critical value, and no solution
(1995)
Copyright 0 1995 by The Combustion Institute Published by Elsevier Science Inc.
OOlO-2180/95/$9.50 SSDI OOlO-218Ot94)00102-X
646 when such a value is exceeded. A companion stability analysis further demonstrates that solutions on the slower branch are unstable, implying that the solution is unique for a subcritical heat loss rate, and that the critical state can be identified as that of extinction. While the theoretical results of Spalding appear to be unambiguous, a subsequent experimental study by Spalding and Yumlu [3], using the flat-burner flame, reveals a dual response behavior. That is, with increasing heat loss rate to the burner, the flame response consists of an upper branch as well as a lower branch which merges at a turning point. Thus, for a certain range of the heat loss rate around the turning point, there are two possible values for the flame speed. Subsequently, Ferguson and Keck 141 also observed such a dual response behavior for the flat-burner flame, in that there are two possible values for the flame speed and the flame temperature for a given flame standoff distance. It was further indicated that since the turning point for such a plot corresponds to the minimum distance the flame can approach the burner surface, this distance can be identified as the quenching distance of the flame. Such simultaneous dual responses were also reported by Yamazaki and Ikai [5] through experimental and thermal-based theoretical investigations. Recently Chao and Law [61 analyzed the flat-burner flame using activation energy asymptotics. Some preliminary observations were made regarding the flame response including its nonmonotonic behavior. The system response, however, turns out to be richer than originally recognized. Thus the first objective of the present study is to provide a comprehensive discussion of the possible flame responses, especially with regard to the issue of the experimentally observed dual behavior. Our second objective is to perform a careful and comprehensive experimental investigation of the “non-monotonic” behavior of the global properties of burner-stabilized flames. Such an investigation is needed because the study by Spalding and Yumlu [3] was concerned only with the response of the flame speed to variations in the heat loss rate, while that by Ferguson and Keck [4] only with the response of the
J. A. ENG ET AL. flame speed and temperature to the flame location. Since all parameters are interdependent in this problem, a complete experimental verification of the system behavior requires the simultaneous specification and characterization of the flame speed, flame temperature, flame standoff distance, and the heat loss rate for a given situation. Furthermore, a closer examination of the data of Ref. 3 reveals some unquantifiable, but possibly quite serious, inaccuracies. For example, the reported flame speeds of acetylene/air mixtures appear to be too low to be possible. We have found in the present study that determination of the heat loss rate through measurement of the average change in the coolant temperature can be quite inaccurate. Our third objective is to explore and possibly verify the quantitative predictability of the flat-burner flame through computational simulation. In order to achieve this goal, we shall first obtain quantitatively accurate data on the flame structure using laser diagnostics. Specifically, we shall determine the temperature and major species profiles using Raman spectroscopy. These data will then be compared with the computed results using detailed chemistry and transport. The present state of flame diagnostics and simulation demands a reasonable degree of agreement between the measured and computed results, if the process is described well and the experiment and computation conducted accurately. A quantitative and comparative study of the present nature has not been conducted for this important bumerstabilized flame. In the following sections we shall sequentially present discussions of the qualitative flame dynamics, the experimental and computational methodologies, and comparison of the results. QUALITATIVE FLAME DYNAMICS Straightforward activation energy asymptotics yields the following relations between the mass burning rate of the flame f, the flame standoff distance 2, relative to the burner surface 2, = 0, the flame temperature Tf, the burner surface temperature T,, and the heat loss rate to
FLAT-BURNER
647
FLAMES
the burner &:
008
r
cjL=(g)o=f[l-(ff-fs)], (la) 0.02 t
where fu is the freestream tempezature of the unburned mixture, f; = 1 + ?,,, T, the activation temperature, and the superscripts “0” and “ N ” respectively designate the adiabatic state and a nondimensional quantity defined in the Nomenclature section. Furthermore, we shall use fa = 6 and fu = 0.12 in all of the_follo$ng calculations. Thus by further fixing T, = T, = 0.12, and with either &_ or Zf as the independent variable, the behavior of the other three system parameters can be plotted, as in Figs. 1 and 2, respectively. The behavior is clearly nonmonotonic. Specifically, Fig. 1 reproduces the observation of Spalding and Yumlu [3] that there are two flame speeds for a given heat loss rate, while Fig. 2 reproduces the observation of Ferguson and Keck 141 that there are two flame speeds and flame temperatures for a given flame standoff distance.
%. Fig. 1: Representative analytical solutions for the burning rate f, flame standoff distance fr, and flame temperature T{ as functions of the heat loss rate to the burner & with a fixed burner surface temperature f3, demonstrating the multiplicity of the flame responses in such a plot.
Fig. 2. Representative analytical solutions for the burning rate f, flame temperature Y$ and heat loss rate to the burner & as functions of the flame standoff distance .Ef with a fixed burner surface temperature fS, demonstrating the multiplicity of the flame responses in such a plot.
However, as first recognized in Ref. 6, concerns about the dual solutions are actually unwarranted because of the fundamentally different nature of the freely propagating flame and the burner-stabilized flame. That is, unlike the nonadiabatic freely propagating planar flame model of Spalding [2] for which the heat loss intensity can be independently specified, for the flat-burner flame, with fixed burner surface temperature, the heat loss rate is frequently a response of the system and therefore cannot be easily manipulated to bring about flame extinction during experimentation. The same observation applies to the flame standoff distance and flame temperature being responses of the system. Indeed, the parameter which is the most natural independent variable for the flat-burner flame is actually the flow rate and thereby the (nonadiabatic) flame speed. Consequently, with f being the independent parameter, for c = f,,;,, Fig. 3 shows that all flame characteristics including the flame standoff distance and the heat loss rate respond uniquely. As such, it is possible that the observed “turning points” are simply the states at which the flame exhibits a nonmonotonic behavior, and therefore are not the states of extinction. To further substantiate the above possibility, we note that in Figs. l-3 the burner surface temperature p$ is fixed while the heat loss rate gL is varied. An alternate experimental approach is to hold gL fixed and vary T, for each
648
J. A. ENG ET
0.08
0.06
004 ‘i,
0.02
0.00 0.0
0.2
0.4
0.6
0.8
10
i
Fig. 3. Representative analytical solution_s for the flame standoff distance ff, flame temperature Tf, and heat loss rate to the burner t& as functions of the burning rate f with a fixed burner surface temperature T,, demonstrating the uniqueness of the flame responses in such a plot.
value of f, as shown in Fig. 4 for &, = 0.065. It is seen that the flame responses are again unique with varying f: Another possible_experimental procedure is to fix the flow rate f and independently change the cooling rate of the burner, which will yield the corresponding & and T,. Figure 5 shows such a plot, for 0.7, which further demonstrates the uniqueness of the flame response. The monotonicity of the flame response with f fixed is also worth noting. It is therefore quite clear that, depending on the specific parameters used as the dependent and independent variables, the flame response can be either monotonic, nonmonotonic, or dual valued. The important point to recognize
fr=
02
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0.32
0.2
0.4
0.6
0.8
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Lo
T Fig. 4. Representative analytical solutions for the flame standoff distance .Cf, flame temperature F!, and burner_ surface temperature FS as functions of the burning rate f with a fixed heat loss rate to the burner &, demonstrating the uniqueness of the flame responses in such a plot.
Fig. 5. Representative analytical solutions for the flame standoff distance .Zf, flame temperature $, and burner surface temperature fS as functions of the heat loss rate to the burner &, with a fixed burning rate f, demonstrating the uniqueness of the flame responses in such a plot.
is that, when dual responses occur, solutions on both the upper and lower branches are potentially physically realizable, and the “tuming point” does not designate the state of extinction. Indeed, the relevant critical phenomenon for the flat-burner flame does not appear to be extinction through heat loss. Rather, it is the blowoff of the flame when the flow velocity exceeds the adiabatic flame speed. In realistic situations it is well known that the flame becomes wrinkled in order to accommodate the increased mass flow rate.
EXPERIMENTAL AND COMPUTATIONAL METHODOLOGIES The burner used for the present experiments was made of porous sintered bronze with a 20-pm pore size. A schematic of the burner cross section is shown in Fig. 6. The porous plug has a diameter of 5.08 cm and thickness of 1.27 cm. Cooling was accomplished by passing water at a controlled rate through cooling coils imbedded in the burner, based on the recommendations of Pagni et al. [7], with the coils positioned at least 3 coil diameters away from the burner surface in order to minimize their perturbing effects on the flow. A circular porous ring was placed around the main burner to provide a uniform coflow of the inert gas to shield the flame from the environment. Five thermocouples were inserted at several distances from the burner surface to measure
FLAT-BURNER
Fig. 6. Schematic setup.
649
FLAMES
of the flat-burner
and experimental
temperatures within the burner and hence determine the corresponding heat loss rate. Experimental observation of the non-monotonic response behavior requires measurement of both the flame standoff distance and the burner heat loss rate. The leading and trailing edges of the luminous zone were visually measured by a microscope, and the flame location was taken to be the mid-point between them. The final flame temperature was measured with a thermocouple for additional comparison with the numerical and laser diagnostic results to be discussed subsequently. A Platinum-13% Rhodium/Platinum thermocouple was used with radiation correction [81, with an estimated measurement error of roughly +50 K. The heat loss rate was calculated from Fourier’s law, using the measured value of the conductivity of the porous material and the temperature gradient at the burner surface from the thermocouples in the burner. To measure the conductivity of the porous material, a cylindrical disk of the material was positioned between two cylinders of a reference material with known conductivity. By placing a temperature
difference across the system, and measuring the temperature gradient in both the porous and reference materials, the conductivity of the porous material was determined by continuity of the heat flow. Detailed profiles of the temperature and the major species of 0, and CO, were measured across the flame by using spontaneous Raman spectroscopy. Here a pulsed Nd-Yag laser operating at 532 nm and 20 Hz was focused above the burner surface with a plano-convex lens, and the scattered Raman signal was passed through a monochrometer with a 2400groove/mm grating and detected with a photodiode array. The temperature was determined from the vibrational Stokes Raman scattering of N, using a modified version of a program developed at Sandia for CARS measurements. The program generates a library data base of theoretical spectra at temperatures of 50-K increments, and performs a least squares fit to interpolate between the library spectra to obtain the temperature for a given spectra. Details of the experimentation can be found in Ref. 9. The numerical simulation was conducted by using a version of the one-dimensional premixed flame code of Kee et al. [lo]. The program uses finite differences to solve the governing equations of mass, species, and energy conservation with detailed kinetics and species diffusion. Two free-standing programs [ll, 121 are used to evaluate the chemical reaction rates, thermodynamic data and transport data. For the, burner-stabilized flame, the burning rate f is specified. At the burner surface the temperature and mass flux fractions of the ith species, fi, are also given. Note that an implicit assumption here is that the burner surface is inert to all chemical reactions. The mass fluxes for the individual reactant species are known from the unreacted mixture ratio, and are zero for intermediate species and product species. At the burned hot boundary, the conditions imposed are vanishing of the temperature and species gradients. RESULTS
AND DISCUSSIONS
The overall response of a methane/air flame at atmospheric pressure and an equivalence
J. A. ENG ET AL.
650 ratio of 0.7 was studied as a function of the mass flow rate f. The burner surface temperature was 332 K, and was held constant throughout the experiments by varying the water flow rate through the burner. The adiabatic flame temperature for this unburned mixture temperature is Tf” = 1940 K, and the adiabatic mass burning rate is f” = 0.026 gm/cm*-s. Nitrogen was used for the inert coflow, and its flow rate was adjusted so that the edge of the flame was flat. The flame responses measured are the flame temperature, the heat loss rate to the burner, and the boundaries of the luminous zone of the flame. The experimental flame location is then taken as the center of the luminous zone. Furthermore, since the luminosity for lean flames is mainly due to the CH radical 1131,the definition of the flame location used for the numerical work is the position of maximum CH concentration in the flame. Figure 7 compares the measured and computed flame temperatures as a function of the mass flow rate. It is seen that they increase monotonically with the burning rate, in agreement with the analytical result. Furthermore, they can also be considered to agree well with each other within the accuracy of the experimentation. Figures 8 and 9, respectively, compare the measured and computed heat loss rate and flame standoff distance as functions of the mass flow rate, with the experimental flame dimension also marked off. The agreement is generally satisfactory and the flame responses are as predicted from the analysis and computation. The computed heat loss rates are slightly
3.5 8
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r? g b
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B 2.0 OS I 2 1.5. 3 z
-
Computation Experiment
0 1.0.
”
0.5’ 0.000
” ”
’
0.005 0.010 0.015 0.020 Mass Flow Rate, gm/cm*-see
0.025
Fig. 8. Computed and measured heat loss rate as a function of the mass flow rate.
higher than the measured values, possibly caused by the radiative heat loss from the flame which is not included in the computation. It is, however, also significant to note that the experimental flame location does not exhibit a clear minimum in that it does not unambiguously show the ascending portion as predicted by the theory. Experimentally, as the flame location was reduced to its minimum value as represented by the nearly flat portion of the data, further increases in the mass flow rate caused the flame to become wrinkled. This same phenomenon was also reported by Ferguson and Keck [4]. Physically, since the heat loss rates at such states are very small because of the high mass flow rate (see Fig. 81, the flame tends to resemble the adiabatic flame which is however intrinsically unstable for flows generated by the porous burner, as shown by 2.0 __
-
computation
I Experiment looOL 0.000
Computation
0.005 0.010 0.015 0.020 Mass Flow Rate, gm/cm*-set
Fig. 7. Computed and measured flame temperature function of the mass flow rate.
0.025
as a
0.0 0.000 ”
”
”
”
”
”
”
”
”
”
”
0.020 0.010 0.015 0.005 Mass Flow Rate, @n/cm*-see
”
0.025
Fig. 9. Computed and measured flame standoff distance and luminous boundaries as functions of the mass flow rate.
FLAT-BURNER
FLAMES
651
McIntosh [14]. It may also be noted that flame wrinkling also occurs for the very small flow rates, which are less than 0.005 gm/cm’-s. Wrinkling for such situations is expected to be also affected by the relatively strong influence of buoyancy. Figures 10 and 11, respectively, compare the measured and computed temperature and CO, and 0, concentration profiles for a mass flow rate of 0.0097 gm/cm’-s. The overall agreement is good, although the calculated 0, mole fraction is about 25% higher than the measured results. Since the computation does not include surface reactions, the present level of agreement indicates that, even if these reactions were present, they would not affect the bulk flame properties to any significant extent. CONCLUDING REMARKS The comprehensive nature of the present study, and the qualitative and quantitative agreement obtained for the analytical, computational, and experimental results of the investigation, provide strong indication that our understanding of the structure and stabilization mechanism of the flat-burner flame is at a quite satisfactory state. Specifically, we now understand that the flame does not possess multiplicity of solutions in the sense of the characteristic ignition-extinction S-curve, that the flame response is unique when an appropriate parameter, such as the burner flow rate and hence the flame burning rate, is treated as the independent parameter of the system, and that the flame can freely adjust its standoff distance and hence
0
Computation Experiment
zoot~“‘~““~“““““““““.~““““‘i 0.0
0.5
1.0 1.5 2.0 2.5 3.0 Distance from Burner, mm
Fig. 10. Computed and measured temperature a mass flow rate of f = 0.0097 gm/cm’-s.
3.5
4.0
profiles for
__ Computation 0 70 Experiment
4 0.00
0.0
”
”
0.5
”
”
1.0
”
”
”
1.5
”
”
2.0
”
”
2.5
”
”
3.0
”
”
3.5
”
4.0
Distance from Burner, mm Fig. 11. Computed and measured CO, and 0, concentration profiles for a mass flow rate of f = 0.0097 gm/cm*-s.
the heat loss rate such that extinction is not the relevant critical phenomenon. Consequently, it is not appropriate to identify either the turning point of the heat loss curve as the state of flammability, or the minimum flame standoff distance as the quenching distance of the mixture. Within the framework of a steady and planar flame, the flame can only be blown off when the burner discharge velocity exceeds the adiabatic laminar flame speed. Realistically, flame wrinkling occurs before this state is reached. It is of interest to investigate the possible onset of intrinsic burner-induced instability 1141as the flame reaches the minimum standoff distance and starts to recede from the burner surface with increasing flow rate. This work has been sponsored by the Microgravity Combustion Program of NASA-Lewis, under the technical monitoring of Mr. Kurt Sacksteder. JAE also acknowledges the support by the Air Force Office of Scientific Research through an AFRAPT &Iir Force Research in Aero Propulsion Technology) traineeship. We thank Mr. J. B. Liu and Mr. C. J, Sung of Princeton University for their help in taking and ana&zing the jlame structure data, Professor Peck Cho of the Michigan Technological University for technical information, and a reviewer who brought Refi 5 to our attention.
REFERENCES 1. Botha, .I. P., and Spalding, D. B., Proc. R. Sm. Ser. A 2253-96 (1954).
J. A. ENG ET AL,. SpaIding, D. B., Proc. R. Sec. Ser. A 240:83-100 (1957). 3. Spalding, D. B., and Yumlu, V. S., Cornbust. Flame 3:553-556 (1959). 4. Ferguson, C. R., and Keck, J. C., Cornbust. Flame 3485-98 (1979). 5. Yamazaki, S., and Ikai, S., Trans. J. Sot. Me&. Eng., 37. 293:121-130 (1971). 6. Chao, B. H., and Law, C. K., Cornbust. Sci. Technol. 62:211-237 (1988). 7. Pagni, J. P., Ortega, A., and Toossi, R., Flat Flame Burner Analysis, Technical Meeting of the Western States Section of the Combustion Institute, Paper No. 79-47 (1979). 2.
R. C., and Iaurendeau, N. M., Cornbust. (1985). Sung, C. J., and Law, C. K., AIAA 31st Aerospace Sciences Meeting, Paper No. 93-0246 (1993). Kee, J. K., Grcar, J. F., Smooke, M. D., and Miller, J. A., Sandia Report SAND85-8240 (1985). Kee, J. K., Miller, J. A., and Jefferson, T. H., Sandia Report SAND80-8003 (1980). Kee, J. K., Wamatz, J., and Miller, J. A., Sandia Report SAND83-8209 (1983). Glassman, I., Combustion, Academic, 1987, p. 112. McIntosh, A. C., J. Fluid Mech. 161:43-75 (1985).
8. Peterson,
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9. 10. 11. 12. 13. 14.
Received 27 May 1993; revised 20 April 1994