l
LEON LAPIDUS, J. B. ROSE",
and R. H. WILHELM
Princeton University, Princeton, N. J.
Flame Propagation Rates Chemical N a t u r e of Attachment Surface A novel approach to the, basic phenomenon of flame propagation presents a self-consistent theoretical model which leads to quantitative values of surface recombination coefficients relative to platinum surfaces
~ R E V I O U S experimental studies (3, 4, 9) indicated, with one exception, an apparently negligible effect of the chemical nature of coated surfaces on flame properties, notably, stability limits and quenching distances. The exception, by Laffitte, Elston, and Pannetier (5, 6), showed that the flammability limits of combustible mixtures in narrow propagation tubes were changed by the water vapor adsorbed on the surface and by the treatment given the tubes prior to ignition. Theoretical studies by Simon and Belles f72) of quenching data have led these authors to propose radical destruction at the surface as an important step. Present studies of methane-air flames were initiated on the hypothesis that free radical destruction at the surface may be significant and that adsorbed water vapor, which is known to retard radical recombination ( 7 7 ) , will, under most combustion circumstances, cause widely dissimilar substrate materiaIs to appear alike. Dried surfaces might, on this basis, reveal interesting properties. Experiments were designed for rate measurements through use of a slot burner. Premixed gases rose vertically from the burner, the combustible mixture being ignited at one end of the burner and propagating horizontally
Present address, Shell Development Co., Emeryville, Calif.
along the top to the other end of the burner. The velocity of flame propagation was measured photographically. The slot tip was carefully controlled in regard to temperature and moisture content prior to each propagation experiment. Surfaces were platinum plated, brass, and magnesium oxide coated. The fuel was dry premixed methane and air.
Theory Burning velocity is, in general, a complicated function of composition, pressure, temperature, and heat and radical loss to surfaces. Variations in any of these quantities will alter the burning velocity, which is a measure of the overall reaction rate. An important factor in determining the reaction rate appears to be the free radical concentration (2, 70, 73, 74). In particular, if all other quantities are held constant, the burning velocity is proportional to the square root of an average free radical concentration, The theory presented here is valid to the extent that this square root law of burning velocity holds. I t appears that changes in burning velocity which result solely from a change in the chemical nature of an adjacent surface are due to a corresponding change in the average free radical concentration in the localized zone. The
change in free radical concentration due to a change in the surface is caused by an increase or decrease in the efficiency of surface recombination of free radicals. A surface which is very efficient in removing free radicals will cause a lowering of the free radical concentration before an advancing flame front with a consequent lowering of the burning velocity. The relative change in velocity when all conditions are held constant except the chemical nature of the surface therefore gives a quantitative measure of the change in the surface recombination efficiency. T o obtain a relation between the change in surface efficiency and the corresponding change in burning velocity, i t is necessary to obtain a quantitative expression for the free radical concentration as a function of surface efficiency, and to have in hand a relation between burning velocity and free radical concentration, here taken to be the square root law. The square root law is written as:
where V, = burning velocity, j = average free radical concentration, and K1 is a constant which depends on temperature, pressure, and the kinetic scheme. XI is assumed to be fixed for a given set of data. In particular, for a given combustible mixture (say methanehair) K1 is VOL. 49, NO. 7
JULY 1957
1 18 1
assumed to be independent of composition. The change in velocity with composition will therefore result only from a corresponding change in j . A value of j i is secured by considering a simplified one-dimensional model of a flame as indicated in the diagram. The effective gas flow velocity, V,, is normal to the surface, as shown. The temperature of the combustible gas mixture has the value To at the surface ( x = 0) and rises to its final value, T,, as x -c m . At a certain distance: 1, the concentration of product becomes appreciable and increases rapidly to its final value. Y,, releasing the heat of combustion. Radicals are produced in the hot zone ( x > a) and diffuse back into the cold zone (0 < x < a). For large x the radical concentration approaches its equilibrium value y,. while its value yo at the surface depends on the surface conditions. The value ofy at x = 3 is taken to be the effective value in Equation 1 for determining the burning velocity. In the cold region the rate of production of radicals is zero and the equation of continuity for y gives
velocity, V, is the photographically measured flame velocity parallel to the slot burner surface and at right angles to the flow velocity. A useful relation is obtained from Equation 5. Consider two surface conditions with coefficients y1 and yz, with corresponding a1 and a2. If all other conditions except composition are constant. it follows from Equation 5 and the expression for VBathat the corresponding velocities, as measured, are related by VI2 - V22 =
VB;
-
If two surface conditions can be obtained such that a1 and a2 are known, then constant K is determined by Equation 6. The value ~3 corresponding to a third surface coefficient, 7 3 , is then given in terms of the measured velocity difference by fl3
8-1
-
VI2
-
vas
K
> 10,
VB? =
For a given mixture the right side of this expression is independent of composition and constant, depending in its value only on the two surface coefficients, y1 and yz. Velocities V I and Vz, of course, depend on composition, but will be such that the difference of their squares is a constant.
Apparatus The slot burner shown in Figure 1 was constructed so that tips could be readily interchanged and surface temperature carefully controlled and measured. The body of the burner was made of two solid brass pieces, 24 inches long, 6
LUMINOUS ZONE
3
"F
GAS FLOW T=Ta Y = Yco
VT
,-fro
where V , is the thermal velocity of the radicals. Equations 2 and 3 are readily solved if Vp and D are assumed constant. The solution is
TO
Combining Equations 1 and 4 and letting K = KlKz, the final burning velocity expression is obtained:
YO In reducing experimental data with Equation 5 it must be kept in mind that the burning velocity, VB, so determined is actually the resultant vector velocity of V, and V-i.e.. VBz = VFz V 2 . The
+
1 182
a2
with an error of less than 10%.
where D is the diffusion coefficient and js is the flux of radicals into the surface. Following Shuler and Laidler ( 7 7) a surface recombination coefficient, ?, is defined as the fraction of radicals striking the surface which recombine. The magnitude of y depends on the chemical nature of the surface, the particular radicals being considered, and the temperature of the surface. It is possible that the value of y may also depend on the concentration of radicals at the surface, yo. However, the assumption is made here that y does not depend on yo, so that the flux is given by the linear relationship in yo (7 7) =
u1
+a1
In particular, if a1 < 0.1 and then ET = VI2 - V,z and
SURFACE
fs
+-1
INDUSTRIAL A N D ENGINEERING CHEMISTRY
x =o
-X
X-
Schematic diagram of one-dimensional flame
r.
Y,
y.
X.
Temperature Product concentration Radical concentralion Surface recombination coefficient
FLAME P R O P A G A T I O N RATES
GAS METERING and MIXING PATH NEEDLE VALVES
C"4
A1203 DRYER
AIR
ROTOM ETERS
Ah03 DRYER
v
v
MCKED BED MIXING CHAMBER
I TC) SLOT BURNER
BURNER
J Y LE BRASS TIPS I @ @ 0 1
10
Hi0 out
E ACH
COhlSTANT TEMPERATURE CIRCULATING WATER JACKET
HO :
In
1-
PREMIXED GAS INLET AT THREE POINTS
24-
f
Figure 1. Metering and mixing path for combustion gases and schematic of slot burner
inches high, and '/z inch thick, spaced l / ~ ,inch apart. Ends and bottom were closed with thin brass sheet and the brass tips were attached on top of the unit. Sections were machined from near the top section, through which water from a constant-temperature bath was circulated. A further segment was removed from the bottom of one of the brass pieces and used to distribute the gas mixture to the burner. The gas was led into the chamber by three connecting tubes and then passed through a sheet of porous metal placed at the innermost side of the chamber. The porous metal distributed the gas mixture over the length of the burner. Air and technical methane were individually passed through alumina desiccant columns to remove water vapor to a low value. Fischer and Porter rotometers were used as metering devices. The two gases were mixed by injecting one stream into the other and allowing the resultant mixture to pass through a column packed with spheres. To measure surface temperature, five iron-constantan thermocouples were spaced along the burner length. These couples were inserted horizontally into the tips and then vertically until they were within '/a2 inch of the surface on
Figure 2.
Progressive changes in flame front as methane concentration increases
Surface temperature 31.5' C., 45' beveled tips. Reading from left top down and then from right top down, u/u, = 0.631,0.675,0.764,0.040,0.906,0.904, 1.05, 1.1 2, 1.1 0, 1.22
VOL. 49, NO. 7
JULY 1957
1 1 83
I3-
I2-
which the flame burned. A Leeds Cy: Northrup precision potentiometer was used to read the couples. Preliminary experiments indicated that with water circulating through the burner jackets each thermocouple indicated a surface temperature within 1’ C. of the water temperature. The circulating water could be maintained within 1 0 . 5 ’ C. limits.
vm = 85 2
cmy’sec um=l47 % CHq
I I-
X
IO0 9-
9,” 0 7-
Techniques and Procedures
0 6-
-4Bolex 16-mm. movie camera was used to photograph flame propagation along the burner top. The use of Super 04XX film and a 1.4 f lens allowed direct 0 I I I ! I ! I photographs of the flame to be taken. 0306 07 08 09 11 12 13 14 The camera was placed on a level with the top of the burner and focused so that the center 18 inches were included in the field of vision. The speed of the camera was determined to be 63 It 0.5 frames per second, and this value was checked continually against a stop watch. Figure 2 shows typical photographs. A traveling horizontal cathetometer was used to evaluate flame speed from the developed film. Two different velocities were calculated; “free flame velocity,” based on the front of the flame above the burner, and “surface flame velocity,” based upon the contact point between flame and burner (see Figure 2). The results of this study were found not to depend upon the mode of flame measurement. Therefore results are presented entirely in terms of surface flame velocity. Two sets of brass burner tips were used. In the first set the brass was beveled a t an ! I I I 1 --!-A angle of 45’, down and away from the 07 08 03 IO /I 1; 13 14 point of gas exit. From an end view of the burner these tips appear as triangles. Figure 4. Normalized methane-air flame velocity vs. normalized methane In the second set, the tips were rectancomposition on slot burner gular and presented a flat surface perPlatinized surface with flat tips pendicular to the vertical flow of gas. X wet surface (exp.) 0 dry surface (exp.) A dry surface (calcd.) Tips were platinized by plating in an I I -? electrolytic cell using Baker plating soluI V, = 860 crn/sec tion and a platinum foil electrode. A Um=143 1 ‘’ CHq magnesium oxide-covered surface was prepared by allowing the fumes from burning magnesium metal to condense on / the metal surface. Special precautions were taken to prevent deposition of oxide 10on the inside edges of the tips. Solid, compressed magnesium oxide bars (fab0 ricated through the generous cooperation h a : 08 of the Johns-Manville Corp., Manville, N. J.) in the precise shape of the metal rectangular tips also were constructed. However, the high temperatures required for drying the surface caused 5these bars to crack. Data secured with the magnesium oxide bars thus were 040 limited to humidified surfaces. @ 0 3Two procedures were used to place a surface film of adsorbed water on the I , I , metal tips. In one the metal was exposed to air until equilibrium conditions were attained. In the second, the tips were simply wiped with a damp cloth. Propagation velocities were independent 0 9-
5,
:::/
1 184
INDUSTRIAL AND ENGINEERING CHEMISTRY
FLAME P R O P A G A ' I I O N R A T E S
vm=82 2cm/sec
um=176% CH,
O9I OB
//
/ 0. .-
,
a7
I
08
",", I
09
I
I
IO
1.1
-..,
,
12
Figure 6. Normalized methane-air flame velocity vs. normalized methane composition on slot burner Brass surface with 45' wedge tips X wet surface 0 dry surface (exp.) A dry surface (calc.)
of the method of moistening used. The first method was employed with magnesium oxide-coated brass. To secure a dry surface, a long hood of brass which contained a GE Calrod heater was fabricated. When this hood was placed on the burner, the heater was positioned approximately '/4 inch from the burner surface. Heat was applied over the entire burner length. A burner surface temperature of approximately 200' C. was reached in about 1 hour. Dry nitrogen gas was passed through the burner during the cooling, to minimize backdiffusion of water vapor from the air to the burner surface. This flow of inert gas plus a labyrinth path provided by the hood assured a dry surface until the prime propagation experiment was started. The constant-temperature bath was used to attain the final equilibrium temperature. The methane and air rates were adjusted to a predetermined value as the nitrogen was turned off and when the flow rate was steady the strip heater was lifted off and the gas mixture ignited at one end of the burner; the time in-, volved in this last sequence was approximately 5 seconds. Immediately before the flame was lighted, the camera was started and allowed to continue until the flame had reached the far end of the burner. The rate of flame propagation was uniform and independent of direction of propagation as well as method of ignition. Treatment of Data
As a matter of convenience in the comparison and treatment of data, the curves of measured surface propagation velocity us. composition were normalized. For each series of wet and dry runs it was assumed that the point of maximum measured velocity represented the same methane-air ratio. This point was taken
Figure 7. Normalized methane-air flame velocity vs. normalized methane composition on slot burner Platinized surface with 45' wedge tips X wet surface 0 dry surface (exp.) A dry surface (calc.)
to correspond to lOyo methane, the maximum velocity point for a methaneair mixture (8). The difference between the measured inlet composition and the assumed value is attributed to air entrainment, as discussed below. For each series of runs the maximum measured flame velocity, Vm, and corresponding per cent of methane, u,, are obtained. The normalized curves of V/Vm us. u/um are presented in Figures 3 to 7 . Curves are drawn through the experimental points as shown. Computed points are designated by triangles.
that for dry conditions. Brass surfaces show an intermediate effect. Air entrainment was evident through the fact that the lower experimental burning lirnit was approximately 8.5y0 methane and the maximum peak in the composition-velocity curve was 14 to 1870. These values are higher than the 5% lower limit and 10% stoichiometric composition for methane-air. Normalization was intended to correct for air entrainment in the interpretation of results.
Results
Table 1. Velocity
Data include the following conditions: two different geometrically shaped brass burner tips; surfaces of brass, magnesium oxide, and platinum; wet and dry surfaces. Surface temperature was held a t 3 2 O C. and the total volumetric flow rate at 1.44 cu. feet per minute. Figures 3 to 7 indicate two different types of burning. As composition i s increased, flame velocity rises to a maximum and then begins to decrease. A complete viscous-type burning curve envelope is not developed, however, because of the onset of turbulence at a com-, position on the rich side. Figure 2 shows the progressive change in flame front as composition is increased; the turbulent character of the flame is apparent at high fuel concentrations. Curves for the humidified surfaces are independent of the surface coatings, and the shape of burner tips. In dry experiments, by contrast, a marked dependency on the surface coating is noted. With magnesium oxide, which exhibits little chain breaking (7), the natures of dry and wet surfaces are not differentiated. With a platinum surface, the most potent chain breaker (7), the velocity under moist conditions is higher than
Determination of Average Squared Difference from Experimental Dd'ta
Platinum, 32', (VW)max
VW/
Brass, 3 2 O
MgO, 3 2 O
= 85 2
(Vw)rnax = 86.0
=E (VW)rnax
( V ~ ) m a x A(V') A(V2) Flat Tips on Burner
A( V')
0.6
0.7 0.8 0.9 1.0
A(Vz) K an
1
+ an
750 875 840 790
420" 470 450 360
814 814 1.00
425 814 0.52
Platinum, 32' ( V ~ ) r n a x ~-81.0
Vwl (V~)max
A(V2)
0.7 0.8 0.9 1.0
A(V2)
K
aD
1
+
0 814 0.1
320,
( v W ) ~ ~ ~ = 82.2 A(V2) MgO, 32'
45O W e d g e Tips on 0.6
0 0 0 0
Burner
760 a00 710 640
256 340 304 318 270
728 '728 1.00
298 728 0.41
No data
aD
VOL. 49, NO. 7
JULY 1957
1 1 85
faces are then obtained from
Discussion
D
Experimental results are interpreted by comparing the propagating velocities for a wet and dry metal surface. Denoting these two conditions by the subscripts W and D , the validity of Equation 6 is tested by calculating A(P) =
vw2 -
"D'
or several values of composition for each series of wet and dry runs (Table I). A( V2)is reasonably constant for each run, considering that it represents the difference of two squares and thus an averis also given. Equaage value, ,A( tion 6 can now be applied to the data in the form
T o determine K i t is necessary to assign a value to yrp and yD for one wet and dry run on the platinum surface. In their study of the recombination of hydrogen atoms on surfaces (77), Shuler and Laidler use a value of y = 2 X 10-5 for a water vapor-poisoned glass surface, and 0.03 for a clean glass surface, both at 300' K. A value of y 2 1.0 for hydrogen atoms on platinum at 600' K. has also been obtained (7). In view of these results it appears reasonable to assume that y w < lo-* for any water vaporpoisoned surface and yo > 0.1 for a clean dry platinum surface at ambient temperature. Based on the total flow rate, the burner slot dimensions, and a Poiseuille flow velocity distribution, the best value of VF,the effective flow velocity, is 20 cm. per second. Taking a mean thermal velocity for the radicals of 6 X lo4 cm. per second gives av < 0.075 for any wet surface and aD > 75 for the dry platinum surface. Since a w
< 0.075, 1
+ aw = 0
within the accuracy of the data. Also to the same accuracy for dry platinum an iT z =1 so that
All other values of an for the dry sur-
corresponding to Equation 7. Results are listed in Table 11. The values of the recombination coefficients as calculated for brass and magnesium oxide surfaces are based upon assumed values for the platinum surface (Equation 10). Intermediate values are obtained for the dry brass coefficients, while the dry magnesium oxide coefficient is no larger than that for a wet surface. Because of a D ) ,defithe behavior of the term ( a D / l nite values for aD, within the accuracy of the data, can be obtained only in the range 0.1 < U D < 10. The present development may be viewed as a model that is reasonable and compatible with the data, but at this stage of development does not exclude other models.
+
Summary and Conclusions
The activity of dry surfaces in affecting the rate of methane-air flame propagation has been investigated with a slot rate burner. An increase in activity in the order magnesium oxide, brass, and platinum, was observed. By contrast, flame propagation rates for all humidified surfaces and for dry magnesium oxide were identical. Between brass and platinum surfaces there were increasing differences in propagation rates for dry and moist specimens. The effects of methane-air composition ratio on propagation rates were generally similar to the characteristic curves obtained with free laminar flames, with a maximum at the stoichiometric ratio. At high methane-air ratios somewhat beyond the stoichiometric, the flames became turbulent, resulting in a sharp increase in propagation rate. Simultaneously, all differences between surfaces in regard to substrate or moisture condition disappeared. A theoretical analysis relates the rate of free radical surface recombination to the flame propagation rate. Surface recombination coefficients compare favorably with independent measurements in the literature on the recombination of hydrogen atoms on differently conditioned surfaces.
Table II.
Calculated Values of Recombination Coefficient Y D for Dry Surface (Assumed value for wet surface, yrn lo-*) an Surface Y," Geometry 1 an an
