I
JOSEPH GRUMER, JOSEPH M. SINGER, J. KENNETH RICHM0ND;and
JAMES R. OXENDINE]
Division of Explosives Technology, U. S. Bureau of Mines, Pittsburgh, Pa.
Photographic Studies of Turbulent Flame Structure Experiments showed that.. . ,The
turbulent flame brush is a zone of nonhomogeneous and partly discontinuous burning
,Flamelets within the brush are extinguished by turbulent mixing of burned and unburned gas, ignited by turbulent transport of enthalpy into transient zones of ignitable gas
b Ignition depends signiflcantiy on chemical considerations affecting ignition lag and ignition temperature
REGENT
STUDIES of turbulent burning have resulted in the concept that the turbulent flame brush is composed of a single fluctuating, wrinkled, essentially continuous, laminar combustion wave. This has been the basis of published theories of turbulent burning velocity (3-5, 7, 73), flame-generated turbulence (4, 5, 7, 70), and stability of turbulent flames ( 6 ) . Previously reported tests of these theories appear inconclusive. The concepts of turbulent burning via a continuous reaction zone (7, 72) and via flamelets ( 7 7) have been proposed but not proved. T o help resolve the uncertainties, new photographic tests have been made.
flame is obviously fluctuating in some manner. As temperature levels and density gradients from a fluctuating heat source build up and decay continuously, one cannot be certain of the relationship between particular density gradients causing schlieren and their generating sources. The schlieren could be caused by integrated density gradients resulting from present, neighboring, or departed heat emitters and from changes in composition. I n view of these uncertainties, an experimental study was made of the reliability of schlieren photography as a tool for elucidating the structure of the turbulent flame brush. Figure 2 shows the optical system that was utilized. The
object-image ratio was 2. The light source was a Western Union type 10watt flash tube which could be flashed for times varying from about 10 microseconds to 2 milliseconds. The duration of each flash was measured with an oscilloscope; values given in Figures 3, 4, and 8 are the durations of light above half peak intensity. These are approximately half of the durations of light above one tenth peak intensity, excep tfor flashes longer than 125 microseconds. The decay curves of the longer flashes were more gradual, reaching half peak intensity in one third to one fourth the time for decay to one tenth intensity. Figure 3 was obtained with this system by photographing a stoichio-
Experiments and Discussion
The main evidence offered in support of the fluctuating, laminar wave consists of very short duration schlieren and shadow (a few microseconds) and smoke photographs of the turbulent flame brush (4, 5, 7, 73). The similarity of schlieren and shadow photography makes it possible to evaluate both techniques by testing one, for the present purpose. Schlieren Photography
Figure 1 consists of a schlieren photograph and a direct time exposure of the turbulent flame brush. In the region of the flame brush as defined by the direct photograph, the schlieren seem to outline a continuous surface characterized by sharp edges directed toward the burned gas. However, no real evidence exists that the sharp outlines of the schlieren photograph of Figure 1 are a motionarrested view of the turbulent flame brush, as has frequently been suggested. A twoadimensional continuous schlieren (low temperature) outline, as in Figure 1, can result from a discontinuous threedimensional distribution of high temperature points. In addition, the turbulent Present address, Aerial Reconnaissance Laboratory, Wright-Patterson Air Force Base, Ohio.
Figure 1. Direct long exposure and schlieren few-microsecond exposure photographs of turbulent stoichiometric natural gas-air flame Reynolds No.
10,000. Tube diameter 3.1 6 cm. VOL. 49,
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Power supply and variable time-control circuits
- c,,nrhvnni7ar =“A
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\ i I Point
source 16 ’ mirror-,
I
I
Camera -J
Figure 2.
vy’
I\’
f 2.5
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\-Ilex No. 3 synchro shutter
Schlieren optical system
metric 10,000 Re (Reynolds number 10,000) and a 25:OOO Re natural gas-air flame on a 5.08-cm. tube. I n the two photographs of 10,000 Re flames, blurring is absent at 35 microseconds viewing time and barely perceptible a t 80 microseconds, From close inspection of the negatives it appears that a travel of 1 mm. in the flame would be discernible as blurring with the optical system employed. Thus the 80-microsecond duration for blurring corresponds to an apparent velocity of about 1200 cm. per second. At longer light durations (Figure 4) the shape of the schlieren changed materially, measurable streaks developing in the longer view photographs. The lengths of these streaks indicate apparent velocities of the density gradients approaching 3600 cm. per second. By contrast, the average approach flow velocity is 300 cm. per second. Despite the admitted uncertainty of the measurement method-whether flash duration to half peak intensity or duration to one tenth peak intensity should be used, for example-the apparent velocities of the density gradients are obviously too large to represent flame-front movements. Similar results were obtained with the second set of photos for a 23,000 Re flame (Figure 3).
Coaxial surrounding air
for studies of turbulent flames
The downstream velocities of flame brush fluctuations in flames filled with ammonium chloride smoke were measured from high-speed movies; the average values obtained, 680 and 950 cm. per second for 10,000 and 25,000 Re flames, are also high but closer to the approach flow velocities. Schlieren photographs of turbuIent flames are usually taken with a vertical knife-edge: which accentuates the vertical components of the density gradients. The result of rotating the knife-edge through a 90’ angle is shown in Figure 5. I t seems unlikely that an instantaneous continuous combustion wave can have all the wrinkles revealed by the vertical and horizontal orientations of the knifeedge. On the other hand, if the revealed density gradients are not held to be identical in shape and position with flame surfaces, the observed knife-edge effect is understandable. The schlieren photos of Figure 6 are different for a given turbulent flame, depending upon whether the flame is piloted by a laminar hydrogen flame or by heating the port rim electrically. This is shown by the four photos to the right. The four left photos of Figure 6 show that schlieren are not eliminated by turning the turbulent flame off. leaving the pilot on, and the main air
flowing. The same effect may be seen in Figure 7 , where the schlieren remain when a flame is disrupted by making the mixture progressively more lean. Figure 8 shows that the schlieren observed in a turbulent flame brush may be attributable, at least in part, to the pilot flame and are influenced by the orientation of the schlieren knife-edge. The abundance of schlieren in photos of a heated turbulent nonburning stream is particularly significant, as these demonstrate the inability of the technique to distinguish the presence or fullness of a turbulent flame. Further evidence of confusion of turbulent flame schlieren is given in Figure 9. which compares direct photographs of a slowly fluctuating, very rich turbulent flame with a schlieren photograph of the same flame. The involved “hash” of the schlieren obliterates the shape of the flame, although the fluctuations were slow enough to make the shape obvious to the eye and to the direct view camera. In another experiment the turbulence level in a 10,000 R e flame was increased by grids. The schlieren photograph of this flame no longer showed a continuous surface, such as in Figure 1. Other investigators have observed that schlieren photography is unsatisfactory for analyzing low-pressure flames with grid-induced turbulence ( 8 ) . It seems likely that the schlieren shown in the preceding figures result from density gradients that are composites of the interaction of the approach flow with heat from the flame holder and from the turbulent flame brush, if the last is present. These yield density gradients whose shapes and positions need not conform to the shape and position of the instantaneous turbulent flame. Hence, from these figures it is concluded that schlieren photography as it has been used is not a reliable method of analyzing the structure of the turbulent flame brush.
D
L
Figure 3. gradients
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Schlieren photographs of turbulent stoichiometric natural gas-air flames, showing apparent velocity of density Tube diameter 5.08 cm.
Reynolds No. Viewing time, psec. Estimated turbulence intensity, cm./sec. Av. flow velocity, cm./sec. Apparent velocity of density gradients, cm./sec.
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A
a
10,000
10,000
C 25,000
80
35 15 300
80 38 750
750
About 1200
About 2900
About 2900
15 300 About 1200
D
25,000 35 38
A
C
B
E F Schlieren photographs of turbulent stoichiometric natural gas-air flames, showing effect of viewing time D
Figure 4.
Reynolds No. 10,000.
A.
2.6 milliseconds 8.
500 microseconds
Smoke Photography Photographs were also taken of turbulent flames containing ammonium chloride ( 5 ) and zinc oxide smoke. Ammonium chloride smoke was prepared by metering anhydrous ammonia and hydrogen chloride gas into the
C.
250 microseconds
Tube diameter 5.08 cm.
D. 125
microseconds
main flow; zinc oxide smoke was prepared by arcing two zinc rods in the input air stream. These smokes were illuminated by a calibrated G.E. FT.220 flash tube, powered by either a 4or a 16-pfd. condenser. The 16-yfd. gave approximately four times the light intensity of the smaller condenser with
E.
80 microseconds F.
35 microseconds
half peak duration of 219 and 175 microseconds, respectively. Some typical ammonium chloride smoke photographs are presented in Figure 10. The smoke outlines of the 50,000 Re flame are sharp, with a 175microsecond flash, and somewhat blurred during a 21 9-microsecond exposure
Figure 5. Effect of orientation of knife-edge on density gradients made visible by schlieren photography of stoichiometric natural gas-air flames Reynolds No. 25,000. Tube diameter 5.08 cm. left. Vertical knife-edge. Center. Horizontal.
Right.
Corner VOL. 49, NO. 2
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A
E
B
C
D
F
G
H
Figure 6. Comparison of microsecond schlieren photographs o f stoichiometric natural gas-air mixtures for various flows, pilots, and knife-edge orientations Tube diameter 5.08 cm.
C
D
E
25,000
25,000
25,000
25,000
50,000
50,000
25,000
Hot w a l l Horizon. Off
Hz-air Horizon.
Hot wall Horizon.
Off
On
Hp-air Horizon. On
Hot w a l l Vert. Off
Hot w a l l Vert. On
Hot w a l l Vert. On
A Reynolds No. Pilot Knife-edge Main flame
Figure 7.
B
F
G
H
25,000 Hz-air Vert. On
Schlieren photographs of
1 60,000 Reynolds No. flame-piloted natural gas-air flames, showing density gradients as flame i s extinguished b y leaning the mixture V'ewing time, 10 microseconds. 5.08 cm.
A. E. C.
Burner aiameter
Full stoichiometric flame Full lean flame Broken wide open very lean flame
B
A
A
C
B
C
D
E
Figure 8. Schlieren photographs of turbulent stoichiometric natural gas-air mixtures, showing density gradients attributable to pilot flame and orientation of schlieren knife-edge Reynolds No. 25,000.
Tube diameter 5.08 cm.
Pilot flame a n d flow o f main air on for all five tests
B
C
D
E
Off
On
Vertical
Vertical
Off Vertical
On Vertical
500
500
35
35
Off Horizontal 35
A Main Rarne Schlieren knife-edge Viewing time, psec.
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The 75,000 R e flame is sharply defined by the smoke during a 175-microsecond viewing time, but the 100,000 R e flame is not. A dependence of the smoke outline on viewing time and light intensity is indicated by these photographs. The ability of a 175-microsecond flash to stop the motion of a 75,000 Re flame disagrees sharply with the result in Figure 4, where an 80-microsecond exposure produced blurring in a schlieren photograph of a 10,000 Re flame. The apparent height of the smoke-filled outline has been observed to vary in repeated photographs of the same flame by as much as 30%. In disagreement, flame heights by schlieren photography fall within a range of 10%. Photographs were taken of turbulent flames filled with zinc oxide smoke, with the expectation that zinc oxide would sublime a t very close to the temperature of a stoichiometric flame and clearly show whether a continuous combustion wave was present in the turbulent flame brush. However, as shown in Figure 11, zinc oxide sublimes appreciably at about 1300' C. This is corroborated by Partington ( 9 ) . It was also observed that, as flame temperature was lowered to near the smoke vanishing temperature, the sublimation of the latter depended strongly on its concentration and probably its particle sizing, both of which are difficult to control when smoke is produced in an arc, The disappearance of smoke involves a rate process as well as a temperature level. Other conceivable complications are the roles of incident light and the amount and particle sizing of the smoke, the pickup of radiant heat, and possible chemical reaction between smoke and flame. The technique of smoke photography is not yet sufficiently
A
Schlieren view is single frame a t left
A.
Figure 10.
E.
0.01 second.
The luminosity of the turbulent flame was photographed directly using orthochromatic and panchromatic film. Sufficient sensitivity was obtained by using an f.2 lens with a focal plane shutter speed of 0.002 second to obtain the photographs in Figure 12. The shutter moved at right angles to the axis of flow, and the object-image ratio was
D
C.
1/80
second
approximately 10. These photographs strongly indicate that the turbulent flame brush is made up of streaks of luminosity of varying intensity, suggesting flamelets. Many of these flamelets are inclined nearly parallel to the direction of flow. Photographs in Figure 13 taken with an f.1 lens and 0.001 as well as 0.002 second bear out the preceding set of experiments. For Figure 13 the focal plane shutter traveled with the direction of flow in the image. The slot size of the shutter was 0.317 cm. and its velocity was about 300 cm. per second a t 0.001-second exposure. Object-image ratio for the optical system for Figures 13 and 14 was 4. I n addition, Figure 15 contains direct photographs of 10,000 Reynolds No. kerosine-air flames, taken as for Figure 13, but a t 0.00077 second. The multiple separate flame surfaces in the brush of fire are more distinct than in Figures
Direct Photography
F
E
G
Ammonium chloride smoke photographs of stoichiometric natural gas-air flames
Varying light intensity, light duration, and flow. Reynolds No. Mlcroseconds
Few microseconds.
clear-cut to be employed in resolving the structure of the turbulent flame brush. In viey of the above considerations, it is judged that schlieren (and shadow) and smoke photography do not provide convincing evidence that the turbulent flame brush is composed essentially of a fluctuating, wrinkled, laminar wave, leaving this theory without experimental substantiation by photographic means.
B
A
C
B
Figure 9 . Comparison of schlieren and direct views of rich natural gas-air turbulent flame Reynolds No. 8000. Tube diameter 5.08 cm., 1.9 stoichiometric
A
B
50,000 175 FT. 220-4 p f .
75,000 175 FT. 220-4 pf.
Burner diameter 5.08 cm. FT. 220-1 6 pf. has fourfold light intensity of FT. 220-4 pf.
C
100,000 175 FT. 220-4 pf.
D 50,000 219 FT. 220-1 6 Mf.
E
G
F
75,000 219 FT. 220-1 6 pf. VOL. 49,
100,000 219 FT. 220-1 6 pf.
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125,000 219 FT. 220-1 6 p f .
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Figure 1 1 , Instantaneous zinc oxide smoke photographs of 2000 Reynolds No. natural gas-air flames, indicating that zinc oxide sublimes significantly at about 1550" K., rather than 2 100" K. A Mixture composition, fraction of stoichiometric Adiabatic flame temp., K.
0.6
1550
B 0.65
1730
D
C 0.7
0.75
1840
E Pilot flame only, no main flame
1930
v Figure 13. Direct short-exposure photographs of turbulent stoichiometric natural gas-air flames Reynolds No. 10,000.
Figure 1 2. Direct short-exposure photographs of turbulent flame, stoichiometric natural gas-air mixture Reynolds No. 10,000
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INDUSTRIAL A N D ENGINEERING CHEMISTRY
Tube diameter 5.08 cm.
B
A
C
A B Figure 15. Direct short-exposure photographs second) of turbulent kerosine-air flames Reynolds No. 10,000. Tube diameter 5.08 cm. A.
5. C.
D
lean Stoichiometric Rich
E
Figure 14. Direct photographs of 10,000 Reynolds No. natural gas-air flames Camera orientation varied Seconds Angle between direction of gas flow and shutter motion
A
B
0.001 0
0.001
C 0.001
0.002
90
150
0
D
E 0.002 90
(1/1300
F 0.002 180
tained with the camera in this position, even of completely stationary objects. Focusing was satisfactory for the 0 ' and 90' views. Table I is also of interest in regard to the possibility of shutter-produced distortions in the photographs of Figures 13 and 14. A range of relative velocities with reference to the size and velocity of the focal plane shutter slot is assumed for light emitters in the flame. Corresponding track lengths on the film and real velocities of the light emitters are calculated. All views in Figures 13 and 14 are of the same flame and taken with the same camera. The approach flow velocity was approximately 300 cm. per second. With reference to v
12 to 14. These photographs could not result from a single folded laminar cone of flame in the brush. Two items are prerequisite to consideration of these photographs: the sensitivity of the optical system and conceivable deformations that may be the consequence of the motion of the focal plane shutter and motion of possible surfaces within the turbulent flame brush. With reference to the first, the optical system for Figures 1 3 and 14 was capable of darkening a negative over the entire cross section of a laminar flame of natural gas-air. Densitometer measurements showed that the center of the negative was about half as dark as the outlines of the cone. Therefore photographic sensitivity was more than sufficient to detect two thicknesses of a laminar combustion wave. Some details of a turbulent flame brush were detected at 0.001 second, even a t f.2.8, indicating that the optical system had more than adequate sensitivity. Comparison of the lengths and inclination of streaks in Figures 13 and 14 rules out the possibility that these streaks result from the motion of the focal plane shutter and moving points of light or of the spotty extension of a moving curved thin surface of the flame comparable to the schlieren photograph in Figure 1. Figure 14 particularly reveals the influence of shutter orienta-
tion on the resultant photograph. The views labeled 180' are submitted for the record but discounted because, for some undetermined reason, clearly focused photographs could not be ob-
Effect of Travel of Focal Plane Shutter on Moving Emitters of Light (Shutter slot, 0.317 om. Shutter speed, 317 cm./sec.) Relative Speed of Emitters and 0,317-Cm. Real Speed of Slot Shutter, Length of Track Light-Emitting Cm./Sec. on Film, Cm. Object
Table I.
10 100 200 300 317 350 400 600
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At 0.001-Second E x p o s u r e 10.4 019.73 1.32 0.69 0.83 0.19 0.68 0.019 0.63 0.000 0.61 0.021 0.56 0.066 0.48 0.15
1308 or 1228 868 1668 468 2068 2468 68 2536 0 2668 - 92 2868 - 332 3668 -1132
At 0.002-Second Exposure 1.33 0.69 83 6 436 0.82 0.19 1036 236 0.63 0.00 1272 0 0.42 0.20 2436 -1164 If shutter moves at right angles to travel of a point of light, length of track is equal to exposure time (0.001 sec.) X speed of light image on film. For example, 0.001 sec. X 300 cm./sec. X 1/4 = 0.076 om. Moving lines of light parallel to the axis are lengthened by the equivalent of the end of the line of light moving as a point. A series of moving parallel lines will be displaced with respect to one another along their line of travel by a shutter moving at right angles to travel of line. 50 100 159 450
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Figure 13, if points of light in the flame were moving with the approach velocity, in 0.001 second, these would produce a streak less than 2 mm. in length; in 0.002 second, a streak nearly 4 mm. in length. The observed streaks are much longer, as can be judged by noting that the base of each photograph represents 5 cm. Similarly, if points of light were moving in the flame with the approach velocity, these would produce tracks in the views labeled 90’ in Figure 14 of 0.75-mm. length (0.001 second) and 1.5-mm. (0.002 second). Accordingly, most of the lengths of the streaks in Figures 1 2 to 14 seem attributable to real dimensions of emitting surfaces within the flame brush. I t is concluded that the structure shown in the direct photographs of turbulent flame brush is not produced by lack of photographic sensitivity or shutter-produced distortions. These photographs have double bearing-they do not suggest in any way that the turbulent flame is made u p of a laminar wave fluctuating with the turbulence intensity, or that the turbulent flame brush is a continuous reaction zone. A few additional observations may be briefly listed. Stereoscopic direct photographs showed the flame streaks to be distributed in space around the port. The observed streaks did not appear to be solely the consequence of favorable orientation of the flame surface to the optical path. Reynolds number was increased to 25,000; the streaks appeared somewhat longer and more numerous. Fastax movies taken at 10,000 Re (about 2000 frames per second) gave the impression that the flame surfaces were traveling downstream from the burner rim and in toward the axis. However, the photographic quality of the stereo stills and of the Fastax movie was poor. These observations are accordingly reported with reservations. Additional Considerations
Any picture of turbulent flame structure that is derived from photography must of course be supplemented by any available evidence from other techniques. Contributions of this sort are rather meager. There was some hope that burning-velocity measurements might clarify the problem of structure by comparison of measured values with those predicted from theories based on the continuous wave model. However, available data do not seem to be sufficiently precise for this purpose; moreover, it is doubted that a discontinuous flame model would yield very much different predictions of burning velocity than the continuous wave when burning velocity is based on a hypothetical average surface within the brush (the device of defining an imaginary average surface to represent the turbulent flame
3 12
can be very useful and is not under objection here). The findings of the electronic probe method should be considered. At Reynolds numbers comparable to those studied herein, the probe indicates a continuous enveloping sheath of highdensity ionization. Therefore the flamelets must be closely packed with gaps obscured by the lifetime of ionization. This finding of the probe does not discriminate between models; but a t higher flow rates or with grid-induced turbulence, instantaneous discontinuities develop in the ionization sheath and only a discontinuous flame structure could apply. The probe has also been used to show a random distribution of “pockets” of ionization along the radial direction in the flame brush. This again could be consistent with a flamelet concept; it seems distinctly at odds with the unsymmetrical wave structure suggested by schlieren photographs, in which smooth surfaces are oriented toward the unburned gas and sharp edges toward the burned gas. In this regard the distribution of luminous emitters has been found photometrically to be random and to exhibit displacements from the average position comparable to the distribution of ions. In view of all the experiments discussed in this paper, it is hypothesized that the turbulent flame brush is a zone of nonhomogeneous and partly discontinuous burning; that flamelets within the brush are extinguished by turbulent mixing of burned and unburned gas, ignited by turbulent transport of enthalpy into transient zones of ignitable gas; and that ignition depends significantly on chemical considerations affecting ignition lag and ignition temperature. Fuel-oxidant mixtures may vary in their ignition lags and temperatures and correspondingly in the effect of approach flow turbulence on their combustion rates. Those with shorter ignition lags and lower ignition temperatures will show a greater susceptibility to a given level of turbulence. Perhaps a significant function of turbulence in burning processes as compared to laminar burning can be more advantageously visualized in terms of “early ignition” or “turbulence-induced early ignition” than by models of “flame-generated turbulence.” Conclusion
Schlieren, shadow, and smoke photography are inadequate tools for analyzing the structure of the turbulent flame brush. Fast direct photography, although of limited range, has been very informative. The above evidence is nonsupporting and contradictory to both the wrinkled, fluctuating laminar wave and continuous reaction zone concepts
INDUSTRIAL AND ENGINEERING CHEMISTRY
of turbulent burning, but it is compatible with one of discontinuous flamelets. Of course, for flames of high turbulence, a high concentration of such flamelets would be indistinguishable from a homogeneous reaction zone. By no means are these experiments sufficient to establish beyond doubt the structure of all turbulent flames-for example, flames with high turbulence have not been tested. Independent verification of the flamelets observed by direct photography is lacking. Acknowledgment
The authors wish to thank Robert W. Van Dolah and David S. Burgess of the Division of Explosives Technology for aid and encouragement received in the course of this study. Photographs in Figures 1 and 10 were obtained in this laboratory while under the supervision of BCla Karlovitz, at present with Combustion and Explosives Research, Inc., Pittsburgh, Pa. Literature Cited (1) Avery, W. H., Hart, R. W., IND. END.CHEM. 45, 1634 (1953). (2) Bollinger, C. M., Williams, D. T., Natl. Advisory Comm. Aeronaut., Tech. Note 1707 (1948). ( 3 ) Damkohler, G., Natl. -4dvisory Comm. Aeronaut., Tech. Memo. 1112 (1947). (4) Karlovitz, B., “Fourth Symposium (International) on Combustion,” p. 60, Williams & Wilkins, Baltimore, 19.53. (5) Karlovitz, B., “Selected Combustion Problems,” AGARD, p. 248, Butterworths Scientific Publications, London, 1934. ( 6 ) Karlovitz, B., Denniston, D. W., Jr., Knapschaefer, D. H., Wells, F. E., 16id.. a. 613. ( 7 ) KarloLT’iiz, B., Denniston, D. W., Jr., Wells, F. E., J . Chern. Phys. 19, 541 (1951). ( 8 ) Kleder, C. L., Weller, A. E., Putnam, A. A , , Battelle iMemorial Inst., Tech. Rept. 15035-4 (1955). ( 9 ) Partington, J. R., “Textbook of Inorganic Chemistry,” p. 844, Macmillan, London, 3 937, 10) Scurlock, A. C., Grover, J . H., “Fourth Symposium (International) on Combustion,” p. 645, Williams & Wilkins, Baltimore, 1953. 11 ) Shelkin, K. J., Natl. Advisory Comm. Aeronaut., Tech. Memo. 1110 (1947). (12) Summerfield, M., Reiter, S. H., Kebely, V., Mascolo, R. W., Jet Propulsion 24, 254 (July-August 1954). (13) Wohl, K., Shore, L., von Rosenberg, H., Weil, C. W., “Fourth Symposium (International)on Combustion,” p. 620, Williams & Wilkins, Baltimore, 1953.
RECEIVED for review March 5, 1956 ACCEPTED August 22, 1956 First Regional Meeting, Delaware Valley Sections, ACS, February 16, 1956. Research supported by the U. S . Air Force through the Air Force Office of Scientific Research, Air Research and Development Command.
