Flame Stability in Body Recirculation Zones JOHN P. LONGWELL, EDWARD E. FROST, Standard Oil Development Ca., P.O. Box 727, linden,
MALCOLM A. WEISS
AND
N. 1.
T
*
particle in the recirculation zone was estimated at 0.008 second H E stabilization of a flame in the eddy region behind a bluff body in a high velocity gas stream is a process of practical a8 (for a 1.9-cm. V-gutter in a 6100 cpl. per second stream). However, the sodium vapor from entering particles appeared well as theoretical interest. (A bluff body consists of any to diffuse completely throughout the zone in about 0.0002 immersed object whose downstream shape is blunt enough to second. Thus the ratio of mixing to residence time is about create a wake of eddies in the stream behind the object.) The practical interest arises because some high output combustors1 to 40. With this rapidity of mixing, one would expect a fair degree of e.g., for jet engines-anchor the flame in this manner. A flame homogeneity in the zone. This is confirmed by gas sampling so stabilized can be made to spread throughout the entire flamtraverses made throughout the zone with a water-cooled probe. mable mixture. Flame stabilization by small scale bluff bodies A typical set of oxygen consumption (as given by a meter measof various geometries has been studied by several recent investiuring the paramagnetic properties of the gas) traverses is shown gators, including the work of DeZubay ( 8 ) on disks, Haddock (6) and Scurlock (10) on normal cylinders, Longwell et al. (7) on in Figure 1. Although the results are necessarily time average values, they are supporting evidence for homogeneity. parallel cylinders, gutters, and cones, and Weir et al. (11) on spheres. Each of these investigators proposed an empirical corThe stability of a bluff body depends in some way on the resirelation for his own data. However, none of these correlations dence time of gases in the recirculation zone. (Stability is deis of wide applicability and there is not yet available a general fined as the range of equivalence ratios over which a flame can theorv of flame stabilization behind bluff bodies. be maintained, other conditions constant; the equivalence ratio Any general theory of stabilization is the ratio of the fuel present t o the must account for several features that amount of fuel required in a stoichioare always observed experimentally. metric mixture.) There is much eviFirst, the region behind a baffle is a dence for this conclusion in the work % o CONSUM , zone of intense eddy recirculation. of all the investigators Dreviouslv cited. There are masses of gas in this zone that have net upstream velocities. One can depends on the rate a t which mass env) demonstrate this very simply by a prob-N ters the zone divided by the zone ing technique. A sodium acetate-coated volume. One might reasonably assume ceramic rod, pointing upstream, is that the rate of mass entry depends moved axially so that its tip is located largely on the velocity past the bluff -$ near the downstream end of the recircuW body. I n addition, it is reasonable to -I lation zone, Adjacent locations will be believe that the zone size depends on U I& found such that sodium tracers will ap4: the size of the stabilizer. Thus, stability m -2 pear continually, sporadically, or never range would decrease as residence time U 0 decreases because of increased velocity, upstream of the tip. The location corresponding t o sporadic upstream tracers 3 or decreased stabilizer size. These recan logically be judged the limit of a zone a W -0 sults have been obtained invariably by Iof recirculation. Thus recirculation can all experimenters. It is also usually UJ 2 be demonstrated and the axial limit of found that when the stability limits the recirculation zone fixed by such a are crossed, blowout of the flame occurs a -In technique. at a distinct point; the flame is not ordiFlow in the recirculation zone is not narily gradually attenuated to extincsmooth and continuous. Vortexes and tion. eddies are formed and destroyed. -0 Finally, there is a static pressure Therefore, the zone is one of intense mixing andany small mass of gas entering the zone loses its identity quickly compared t o the average length of time it remains in the zone. This is illustrated in the high speed motion pictures of Nicholson and Field (9),who photo_ graphed the flame in the wake of various the stabilizer. Flow in the wake of two-dimensional 5.7-cm. baffles using sodium acetate tracer One can summarize the general char60' V-gutter. Heptane fuel, stoichiometric, powder in the stream. In one run, for entering a t 9150 cm. Der second; 1 atm.. acteristics outlined above. Evidently, example, the average residence time of a and 422' K. stabilization occurs in a zone with a high
J
~~~
z
1629
Vol. 45, No. 8
INDUSTRIAL AND ENGINEERING CHEMISTRY
1630
mixing intensity and approximately homogeneous composition. The stability range depends on the residence time in that zone, and furthermore, the range is inversely dependent on pressure at a
1.0
For the steady-state reactor of volume V,with an entering mass air flow rate of A and ratio of fuel to air mass of f / a , a material balance can be written as
Defining the efficiency, e, as the fraction of fuel consumed, the left term in Equation 1 is the difference in fuel carried by inlet and exit streams and the light term is the rate a t which fuel is consumed within the recirculation zone. The concentrations are related to inlet temperature and eoncentrations by
0.8
C r = Clj.,(l
-
e)Td2’
(2)
0.6
J 0
0.4
0.2
LOWERMOST SECTIONS OF CURVES
0
I
02
0.1
0.3
0.4
A/VP’
Figure 2.
Locus of Operation of Homogeneous Reactor
Computed from Equation 5 assuming E as 40,000 calories per mole, 6 ’ as 4 X 1 0l2cc. per gram second, heptane fuel, entering mixture at 366’ K.
given velocity. The stability range is well defined and, as one crosses its limits, a sharp blowout is usually obtained. The purpose of this paper is to show that these features of bluff body stabilization can be accounted for by considering combustion to be a second-order chemical reaction occurring at steady state in a homogeneous region. Discussion is confined to systems with premixed and homogeneous fuel-air entry, and to hydrocarbon fuels.
Stabilization Theory Considers Combustion Second-Order Reaction at Steady State
The recirculation zone behind a bluff body is assumed to be a definite volume in which a homogeneous chemical reaction occurs a t steady state, Unburned mass feeds into the zone a t constant rate and is instantaneously mixed with all the other material within the zone. Burned material leaves the zone at constant rate with a temperature and composition identical to that within the zone, Heat losses to the stabilizer or to the main stream are neglected. No error results from any part of these heat losses which cause heating of unburned material that eventually enters the recirculation zone. It is assumed that combustion within the recirculation zone occurs according to a second-order reaction rate equation. A second-order equation is required to amount for the observed effect of pressure. I n the kinetic equation we suppose a constant collision factor, B‘, and activation energy, E. The actual rate-limiting reactants are unknown, but their concentrations can be assumed proportional to air and fuel concencentrations, CA and CF, respectively. The “collision factor,” B’, thus lumps the frequency factor and the concentration proportionality constants.
In Equation 3, g is defined as the equivalence ratio for lean mixtures and 1for rich mixtures. The equation assumes that for inlet mixtures leaner than stoichiometric (equivalence ratios less than l . O ) , the fuel that burns always combines with air in stoichiometric proportions. For inlet mixtures richer than stoichiometric, the fuel and air combine in the same proportions as exist in the inlet mixture. I n Equations 1 t o 3 and below, fuel and air concentrations are expressed in mass (rather than moles) per unit volume. Mole concentrations of hydrocarbon fuels, which crack before actual combustion, are meaningless for a kinetic treatment. C p 0 can he written, from the perfect gas law, as (4) where P is the static pressure (atmospheresj and M the fuel molecular weight. Substituting Equations 2 t o 4 in 1 gives
Equation 5 describes the performance of a homogeneous reactor burning a fraction, E , of the entering fuel. The temperature, T , is the adiabatic flame temperature that results from burning fraction e of fuel for any particular entering equivalence ratio. If the reactor is not adiabatic, the T corresponding to a given E must be reduced accordingly. Equation 5 can be plotted for various equivalence ratios as illustrated in Figure 2, and several features of interest noted. First, the equation ie triple-valued in part. For any given air rate (below the critical blowout value), reactor volume, pressure, and equivalence ratio, there are three efficiencies a t which the reactor may operate. The lowest efficiency, almost indistinguishable from the z-axis, is of no practical significance. Here, no LLflame” is present and material passes through the reaction zone with an extremely low reaction rate, as predicted by extrapolation of the reaction rate equation to inlet temperatures. The intermediate efficiency (shown dotted) is believed to have no physical significance as decreasing residence time-Le., increasing A/VP2-should not result in an increased efficiency. Therefore, only one curve, the uppermost, is of practical interest. In this curve, as air rate is increased, efficiency slowly decreases until the maximum abscissa of the upper curve is reached. On further increase of mass flow, stable operation requires a sudden drop to the lowermost curve, resulting in the sharp blowout usually observed. Furthermore, for equivalence ratios leaner or richer than stoichiometric, this bloyout always OCCUI‘S a t progressively lower mass flows the farther one is removed from stoichiometric. These characteristics of Equation 5 are in accord with the observed behavior of flames stabilized behind bluff bodies.
August 1953
*
INDUSTRIAL AND ENGINEERING CHEMISTRY
1631
The familiar blowout curve for flame stabilizers is obtained by plotting the maxima of the curves of Figure 2. These points can be obtained directly by setting the derivative of Equation 5 equal to zero, giving
been observed, and this effect is accounted for in the kinetic treatment above. It was previously assumed that A = u. However, A is also proportional to the stream density-Le., static pressure. And finally, A depends in some manner on D. V depends almost entirely on some function of D. These terms can be combined, converting the A/VP2 group such that
Equation 6 , determined only by the fuel properties and equivalence ratio, is usually solved by trial. The values of E and T so obtained are substituted back in Equation 5 and the result then becomes the type of curve illustrated in Figure 3. The slope of both lean and rich blowout curves may be altered by adjusting only the activation energy, E, for a given fuel. The curve may be translated vertically by adjustment of E and/or the collision factor, B'. Figure 3 has the following properties, corresponding to the observed behavior of bluff body, stabilizers: Stability range widens as residence time increases (as A / V P decreases), owing to decreased velocity (chiefly through A / P ) past the stabilizer and/or increased stabilizer size (chiefly through V ) ; the range is inversely dependent on pressure for a given velocity past the stabilizer; the eddy zone is a region of high mixing intensity and approximately uniform composition in which burning occurs with a fairly high efficiency; and blowout occurs at a distinct point without gradual attenuation of the flame.
A uDc VP2 P
-
which is identical in form to the customary correlating group, uD*/P (since a S -1 according to DeZubay and Weir), if exponents b and c are equal. A further word is appropriate regarding these exponents. On examining the results of
0A
Elxn=rn
Application of Theory Depends on Experimental Data
The utility of Equations 5 and 6 in predicting the stability curve of a given stabilizer depends on knowledge of the kinetic constants, B' and E,and the values, A and V , associated with the fluid mechanics. Unfortunately there is virtually no knowledge of the kinetic constants of the combustion reaction a t usual combustion temperatures. Dugger (3) selected 38,000 calories per mole as the value of activation energy best representing the dependence of propane-air flame speeds on initial temperature. Extrapolation of low temperature (600' to 1000"C.) kinetic data on hydrocarbon oxidations gives values of 20,000 to 40,000. Other estimates (1) place B' as the order of 10'2 cc. per gram second. It is clear that these variables are not known with accuracy sufficient to be of quantitative use without other data. The volume, V, can be determined with fair accuracy by a probing technique. As discussed above, the axial limit is obtained with a sodium tracer probe. The transverse limits are obtained by a gas sampling technique, giving results of the type of Figure 1. Composition gradients a t the edge of the recirculation zone, determined by gas sampling, are sufficiently steep to fix the boundaries closely. The determination of A is much more difficult. An upper limit to A can be obtained by total head and gas sample traversing a t the downstream end of the recirculation zone. Although the mass burned a t this crosa section can thus be computed, it is impossible to tell how much of this mass actually burned in the recirculation zone and how much burning resulted from flame spreading of burned mass discharged from the recirculation zone upstream. Values so obtained indicate only the maximum order of magnitude to be expected. It is clear that if A and V were known throughout the range of operation of any given experimental system, a curve of the type of Figure 3 could be drawn. E and B' could then be determined empirically by matching the experimental data to the best-fitting curve given by Equations 5 and 6. Investigators who have studied the stability of bluff bodies have generally proposed a group of the type uPaDb as Correlating baffle performance with stability. Here D is the "characteristic" dimension of the stabilizer. This group compares with the A / V P z of Equation 5. Some effect of inlet temperature has also
EQUIVALENCE RATIO
Figure 3. Stability Curves for Three Activation Energies Cross plots of maxima of curves of type of Figure 2. Values of 6' arbitrarily adlusted to give same maximum ordinate for all E. 6 ' ~ 5.45 X lo'*, 6'40 = 4 X lo", 6'80 = 2.35 X 10". Heptane fuel, entering mixture at 366' K.
various investigators, one finds a remarkable lack of agreement. For example, DeZubay used flat disks oriented normal to the flow and found b to be -0.85. Scurlock and Haddock used two-dimensional cylinders normal to the flow and found b to be -0.45 and -0.5, respectively, fair agreement. Finally, Longwell (7) found b to be 1for cylinders, cones, and annuli with axes parallel to flow. Part of these discrepancies are no doubt due to differences in operating conditions. These are discussed in some detail by Longwell (6). However, it is clear that the proper exponent is a very complex function depending on the fluid mechanics of the system. This is equivalent to saying that the mass of air entering the recirculation zone, and to a lesser extent the volume of that zone, are not simply proportional to the obvious variables of the system. Much more detailed work in the immediate vicinity of the recirculation zone is required. For illustrating the application of Equations 5 and 6, the data of DeZubay can be used. This work was very carefully done and measured the stability of disks and washers (0.25 to 2.0 inches D ) in propane-air mixtures a t 3 to 17 pounds per square inch absolute. Equation 5 can thus be written as
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1632
DeZubay's exponent of P was 0.95, but the difference between this value and 1.0 can be neglected and still give a satisfactory correlation. C is the factor connecting A / V P t o DeZubay's correlating group. It is assumed to be constant throughout in the absence of contrary information. The term in brackets, for propane, is approximately 0.115 and varies only negligibly with
Vol. 45, No. 8
stoichiometric equivalence ratio. Taking a disk of diameter 5.7 cm., one can assume an equal recirculation zone volume per baffle area, and an equal mass flow per recirculation zone volume (for the same operating conditions). $]though this is not a precise method for computing A / V , i t is sufficiently accurate for the purpose here. The value of C so obtained is 2.3 x 10-6 and B' then becomes 4 X 1OI2 cc./gram second. Both B' and E have reasonable values when compared to those obtained through classical kinetic treatment as cited by Avery and Hart. The calculation above is obviously very approximate, but the order of magnitude is certainly clear. One would expect that B' for an ideal homogeneous reactor would be greater than the value approximated here. A bluff body recirculation zone is not perfectly mixed; there is also the very important fact that combustion is occurring in only part of the zone volume a t any instant-a result of the random shedding nature of the flow. This poor volume utilization tends to make the effective V smaller than the over-all V used here. Although the B' here may thus be lower than its true value, its utility is not thereby decreased. The value of 4 X 10l2 still represents a constant appropriate to many forms of practical combustion equipment.
2c
10
4
E
Heat liberation Rates Are of Importance in Assessing Performance
When the kinetic constants have been approximated, it becomes of interest to evaluate the heat liberation rate predicted by Equation 5. The maximum heat liberation rate (in calories per cubic centimeter per second) is of considerable importance in assessing the performance of any given combustion volume. Using an equivalence ratio of 1.0 and the constants arrived a t above, one finds the maximum value of AIVP2 to be equal to 0.36 gram per second per cc. atm.2 According to Equation 6, 72% of the fuel introduced with this air burns. Assuming a pressure of 1 atmosphere, the heat liberation rate is then 190 cal. per cc. second-equivalent to 77,000,000 B.t.u. per cubic foot per hour.
p 4
2 X
a
m
8n \
S
2
I
Figure 4.
Correlation of DeZubay's Disk Blowout Data
Equation 7 with E =
40,000 calories per
mole
air-fuel (or equivalence) ratio. I n Figure 4,DeZubay's data are plotted en masse. Various values of E are tried in Equations 5 and 6 and the one is chosen that gives a curve with a slope best fitting the slope of the data. The curves should be translated vertically as to fit, in effect ignoring the actual values of B' and C. For this particular case, E was found to be 40,000 calories per mole. The best fitting curve results in a value of U / D ~ - *of~1.55 P X lo4 a t an equivalence ratio of 1.0. Substituting these results and E in Equation 7 , one finds that B'/C = 1.73 X 10'7. B' and C can be separated approximately as follows. From Equation 7 , A/VP2 = Cu/DO.86P. For a given disk diameter, velocity, and pressure, one must know A and V in order to obtain C. These values can be estimated from the data of Figure 1. For this two-dimensional baffle, 5.7 cm. in width, the recirculation zone volume was found to be 27.4 cc. per sq. cm. of baffle cross-sectional area. Furthermore, after traversing just downstream of the recirculation zone, the mass rate entering the zone was estimated a t 0.047 gram per second per cubic centimeter of zone volume. These results were in a 9150 cm. per second air stream a t atmospheric pressure and a
DISTANCE NORMAL TO FLAME FRONTS
Figure
5.
Assumed Cube Temperature Profile, Normal to Flame Fronts
Although this is an extremely high rate of heat release, it has been approximately realized directly in experimental work. Mullen (8), in his investigation of flame spreading downstream of a bluff body in a cylindrical duct, found over-all heat liberation rates of about 90 for similar conditions. These rates were computed from the combustion efficiency a given distance downstream of the flame holder. However, the rate of heat release just downstream of the stabilizer is rather low. Although the average over-all rate is about 90, it is probable that local rates existed which were close to the 190 computed here. The magnitude of these heat liberation rates is so high that i t becomes difficult to account for them by a mechanism other than
August 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
approximately homogeneous combustion. in the following manner:
This can be illustrated
Assume that in a given volume (a cube of unit dimensions) combustion is occurring a t steady state. The mechanism of combustion can be chosen as one of the current turbulent flame concepts-that is, combustion proceeds through the unburned mixture with the laminar flame velocity, S, and the flame front is an area, A,, whose surface is greatly increased owing to turbulence effects. The volumetric rate of burning of cold gases, V,, is then
V,
=
AIS
(8)
If C1 is the heat release on burning a unit volume of cold gases, and Q is the total rate of heat release in the combustion volume, it follows that A,
=
-!?-
CIS
In the cube of unit volume, assume that the flame fronts are parallel planes oriented parallel to a face of the cube. If the cube size is large compared to the flame front spacing, one cannot arrange the flame fronts (for a given spacing) so a8 to obtain appreciably more flame front area than assumed here. The temperature profile, traversing normal to the flame fronts, would appear as in Figure 5 . The thickness of flame front is d, and the thickness of the layer of burned gases is 2dc. If the total fraction of fuel consumed in the cube is e, then
Acknowledgment
Acknowledgment is due W. H. Avery of the Applied Physics Laboratory, Johns Hopkins University, who originally suggested that under certain conditions combustion might be occurring approximately as a homogeneous chemical reaction. This study was carried out for the Bureau of Ordnance as part of Contract NOrd-9233. The authors are indebted to the Bureau of Ordnance and to the Standard Oil Development Co. for permission to publish the work. Nomenclature
A = mass flow rate of air, grams per second A! = flame front area, sq. cm. a, b, c = empirical exponents, dimensionleas = mass ratio of air to fuel = collision factor, cc./gram second C = connecting factor, see Equation 7 C1 = heat release on burning unit volume of cold gas, calories per cc. C A = concentration of air, grams per cc. = concentration of fuel, grams per cc. CF Cp, = inlet concentration of fuel, grams per cc. D = characteristic stabilizer dunension-e.g., diametercm. d = flame front thickness, cm. = semithickness of burned gas layer, om. d, E = activation energy, calories per mole E = fraction of fuel consumed
%f
= (a/f)-1
5
where T o and T F are absolute temperatures of unburned and burned gases, respectively. The number of flame fronts is d ) and the area of each flame front plane is unity. The I/(& total flame front area is thus given by
+
A,
=
+
--Ad
dc
Combining Equations 10 and 11 by eliminating d, and substituting in 9 gives the result (12)
1633
= mo ecular weight of fuel = static pressur; atmospheres =
rate of heat release, calories per second
R = universal gas constant 8 = laminar flame velocity, cm. per second T, T F , T o = absolute temperature (in reactor
in a F b a t i c flame, and in inlet stream, respectively), K. u = velocity of stream past stabilizer, cm. per second V = reactor volume, cc. V v = rate of burning (volumetric) of cold gas, cc. per second y =+for+$l; Ifor+zl 4 = equivalence ratio Literature Cited
Avery, W. H., and Hart, R. W., IND.ENG.CHEW,45, 1634 (1953).
One can substitute the following values in Equation 12 for stoichiometric propane and air, assuming an E of, say, 0.5: C1 = 0.64,S = 46, T F / T , = 6, Q = 190. The value of d so computed from Equation 12 is 0.022 cm. However, according t o the data of Fristrom ( 4 ) the flame front thickness of a propane flame is of the order of 0.05 cm. Thus in order to satisfy the heat release conditions, the flame fronts must overlap and cannot be discrete regions. But, if overlapping bccurs, the combustion volume begins to approach a zone of homogeneitywith composition and temperature not varying greatly from point to point. Conclusions
Under certain conditions, combustion appears to proceed homogeneously as a second-order chemical reaction, Such a hypothesis serves to explain all the gross features associated with flame stabilization behind bluff objects in high velocity air streams. Furthermore, this concept leads to the prediction of heat release rates which, though approximated experimentally, cannot be obtaiped by the assumption of discrete flame fronts and laminar burning velocities. The kinetic constants obtained in such a treatment are reasonable values when compared to similar constants extrapolated from classical kinetic measurements.
DeZubay, E. A,, Aero Digest, 61, 54 (1950). Dugger, G . L., J. Am. Chem. SOC.,72, 5271 (1950). Fristrom, R. M., et al., “Temperature Profiles in Propane-Air Flame Fronts,” Fourth Symposium on Combustion, Flame, and Explosion Phenomena, Baltimore, Williams & Wilkins, 1953. Haddock, G . H., “Flame Blowoff Studies of Cylindrical Flame Holders in Channeled Flow,” Calif. Inst. of Technol., J . P. L. Rept. 3-24 (1951).
Longwell, J. P., “Flame Stabilization by Bluff Bodies and Turbulent Flames in Ducts,” Fourth Symposium on Combustion, Flame, and Explosion Phenomena, Baltimore, Williams & Wilkins, 1953. Longwell, J. P., et al., “Flame Stabilization by Baffles in a High Velocity Air Stream,” Third Symposium on Combustion, Flame, and Explosion Phenomena, Baltimore, Williams & Wilkins, 1949. Mullen, J. W., 11, et al., IND.ENG.CHEM.,43, 195 (1951). Nicholson, H. M., and Field, J. P., “Some Experimental Techniques for the Investigation of the Mechanism of Flame Stabilization in the Wakes of Bluff Bodies,” Third Symposium on Combustion, Flame, and Explosion Phenomena, Baltimore, Williams & Wilkins, 1949. Scurlock, A. C., “Flame Stabilization and Propagation in High Velocity Gas Streams,” Massachusetts Institute of Technology, Meteor Rept. 19 (1948). Weir, A,, Jr., et al., “Blowoff Velocities of Spherical Flameholders,” University of Michigan, Re@. UMM-74 (1950). RECEIVED for review December 24, 1952.
ACCEPTED May 28, 1953.
