Study of shock waves from high explosives

379

SHOCK WAVES FROM HIGH EXPLOSIVES

V. O t h e r Characteristics Calculated values of temperature, T, and pressure, P, are shown in :Figures 6 and 7 although these values cannot be considered accurate for

J-o

xlO~bo.j l,~

(,)-

TitT

(.)--

3~ 2o

,

'"~'°"{~ 1: {:7~.ua

REFERENCES

~ttrate (a}

]

1. JOUGUET, E. : Mechanique des Exp~osifs. Paris, Doin et Fils, 1917. 2. SCHMIDT, A.: Z. ges. Schiess-u. Sprengstoff., 30, 364 (1935); 31,220, 243 (1936). 3. CooK, M. A.: J. Chem. Phys., 15, 518 (1947); 16, 1081 (1948). 4. JONES, H., AND MILLER, A. R.: Proc. Roy. Soc., London, A194, 480 (1948). 5. BRINKLEY, S. R., AND WILSON, E. B.: OSRD Rept. No. 1231 (PB-18859) (1954). 6. COTTRELL, T. L., AND PATERSON, S.: Proc. Roy. Soc., London, A213, 214, 1952. 7. JONES, H.: Third Symposium on Combustion, Flames and Explosion Phenomena, p. 590. Baltimore, The Williams & Wilkins Co., 1949. 8. PATERSON,S.: Research, 1, 221 (1948). 9. KIHARA, W., AND HIKITA, T.: Fourth Symposium (International) on Combustion, p. 458. Baltimore, The Williams & Wilkins Co., 1953. 10. ROSSINI, F. D.: Thermodynamics and Physics of Matter, p. 307. Princeton, Princeton University Press, 1955.

Z

//,4

g/Ill/ 7/ ////~ V

A /:

i

i/

I

I

gives higher detonation velocities than the real ones, especially for high density explosives. To find the true cause of this discrepancy, further theoretical and experimental investigations are needed. At the present time we are inclined to think that the problem may exceed the scope of the hydro-thermodynamic theory of detonation, and that it must be supplemented by some chemico-kinetical considerations. The fact that the sensitivity of explosives usually drops as the initial density increases may support this view.

j

I?~Z

FIG. 7. Ideal detonation pressures. high density explosives. Curves a are for the assumption of homogeneity and b for that of thermal equilibrium.

VI. Conclusion In conclusion the absolute calculation of detonation characteristics on the basis of molecular constants derived from the compressibility data

48

STUDY OF SHOCK WAVES FROM HIGH EXPLOSIVES By TSUTOMU HIKITA, TETSURO ASABA AND K U N I A K I YONEDA The study of luminous phenomena that accompany the detonation of condensed explosives is of interest in connection with both detonation and shock mechanisms. In recent years, photographic studies by Muraour' have shown that the luminosity associated with detonation is emitted mainly by the shock wave produced in the am-

blent gas. In particular, a shock wave confined in a tube is less attenuated and generally highly luminous over a rather long distance, whereas the light due to detonation gases is comparatively weak except in the case of a secondary combustion or recompression during the expansion of the detonation gases.

380

HIGH SPEED REACTIONS

The present paper describes investigations of the luminous phenomena produced by detonation of an explosive charged in a glass or other transparent tube. This includes: (1) measurement and calculation of the initial propagation velocities of explosive-produced shock waves in various gases; (2) study of the dark zone that exists directly above the charge surface and which is to be associated with the shock formation length and with the detonation wave structure; (3) spectroscopic study of temperature measurement for explosive-produced shock waves. S h o c k Wave Velocity, Its M e a s u r e m e n t and Calculation

Figure 1 illustrates the experimental arrangement used to measure shock wave velocities. A glass tube, 13 mm in inner diameter and 1 m long,

~~

"~

safety glass widow

slit

FIG. 1. Experimental arrangement. in the lower part of which 15 g of pentaerythritoltetranitrate (PETN) is charged at the density of ~ 1 . 0 g/cc (after evacuation, the tube space is filled with a gas) has been used as a high-explosive shock tube. The reaction is initiated by 4 g of P E T N (density ~-~0.8 g/cc) used as a booster charge which, in turn, is detonated by an electric blasting cap. A high-speed rotating-drum camera is used for measuring time-distance relation of the luminous phenomena traveling down the shock tube. The camera consists essentially of a drum that has a slot on its inner periphery of 54.3 cm to hold a 35-mm film; the drum is directly connected to a universal motor giving a maximum film speed of 160 m per second. The rotating speed of the drum is fixed through the measurement of the frequency of the alternating current induced in a pick-up by a magnet mounted on the shaft of the motor. The camera set is operated under a reduced pressure of about 20 mm Hg. In this experiment the tube axis is directed perpendicularly to the motion of the film.

PETN-produced shock waves are generally highly luminous except in a light gas like hydrogen or in a polyatomic gas like butane. Even in such gases the time when the shock wave arrives at the top end of the tube is clearly indicated by a bright luminosity, due to the collision with the solid wall; knowing this, we can estimate the mean shock velocities. As a preliminary test, the interference effects of glass cracks and of "boundary disturbances" (recently found by Shreffier and Christian 2) on the shock traces have been investigated. In this experiment the internal reflection from glass cracks whose propagation velocity may exceed 5300 m/sec 3 was found to give no interference (Fig. 7). While the boundary disturbances were certainly observed for argon or chlorine shocks, at least in the initial period of shock formation the masking action of the boundary disturbances was considered negligible. Thus the shock velocities can be obtained from the slopes measured along the image-fronts in the streak photographs. Reproducibility of the measurement is satisfactory, the deviations from mean values being within 5 per cent. Sample photographs are shown in Figure 2, and the observed velocities are summarized in Table 1, together with the approximate values of the attenuation constant K in the following equation 4 1

1

= b~ + K x

where D is the observed shock velocity at a distance x from the charge surface and Do the value of D forx = 2 ~ 4 cm, the values for x = 0 being uncertain. CALCULATION OF SHOCK WAVE PARAMETERS

The initial velocity and other characteristics of an explosive-produced shock wave have been calculated theoretically by means of the so-called "matching technique, ''5 where it is assumed that across the boundary between the explosive and the air the pressure as well as the material velocities remain constant in both the shock wave emitted into air and the rarefaction wave reflected back in detonation gases. Moreover, it is assumed that the lateral and forward-moving rarefactions which inevitably follow the real detonation wave can be neglected. We assume implicitly that the shock formation occurs instantaneously, and the detonation wave can be represented by ChapmanJouguet variables, the existence of a reaction zone being ignored.

SHOCK WAVES FROM HIGH EXPLOSIVES

381

In order to find the pressure P and the material velocity U in an explosive-produced shock wave, we must know two possible relations between P and U in both shock and rarefaction waves: a common value of P or U to both waves is what we want. P-U relation in shock waves in air or any other gas has been derived from the Rankine-Hugoniot shock equations on the assumption that the gas is perfect, and that only the translational and rotational freedoms of the gas molecules are excited during shock formation; naturally some ionization or dissociation occurs, but in so far as the P-U relation is concerned the error due to this last assumption may not be serious--although temperature values must be corrected. The P-U relation in the rarefaction wave has been obtained by the numerical integration of the Riemann function

as the material velocity is U= W-,,where W is the material velocity in the detonation wave. In calculating the above equations, the KiharaHikita equation of state for high temperature gases was applied with satisfactory results. G' 7 Calculated P-U relations in rarefaction waves in detonation products of P E T N of densities 0.8, 1.0, 1.2 and 1.6 g/cc are shown in Figure 3, together with the calculated results of P-U relations in shock waves in hydrogen, methane, butane, chlorine, and argon gas at 1 atmos, and in air at various pressures. Table 1 summarizes the calculated values of characteristics of shock waves produced in various gases from P E T N of density 1.0 g/cc. It will be seen (Table 1) that in less resistant hydrogen gas the shock wave travels at a high velocity and with little attenuation, the situation being similar to that in air at a reduced pressure of 50 mm Hg. In argon gas, a strong shock with high temperature and pressure is formed but is followed by rapid attenuation. In spite of the many simplifications involved in the calculation, the agreement of the initial shock velocities with the observed values is good if we consider that the observed data are for shock waves at a distance of 2 ~ 4 cm from the charge surface---those for a distance of 0,-.2 cm being higher but rather uncertain.

FIG. 2. Examples of streak photographs of the luminous phenomena produced in the explosive shock tubes (glass). (A) PETN (A = 1.0 g/cc) -- Air (5 mm Hg) (B) PETN (A = 0.9 g/cc) - Air (1 atmos.)

~5

\ _a.

.~

3

fVt.-t~

if" /-

I

2,0OO 4;,ooo ~oo0 g.000 "~y'~ FIG. 3. Pressure-material velocity relations in rarefaction waves in PETN-gas and in shock waves in various gases.

HIGH SPEED REACTIONS

382

If shock formation were instantaneous, as assumed in the above calculation, a microshock wave similar to that in Figure 2 might form even in the air space among particles of granular explosives. Paterson 8 recently calculated the temperature of a shock front that precedes the detonation zone in a granular explosive, and obtained an enormous shock front temperature, far higher than those we have calculated for P E T N produced shock waves. A high air pocket temperature (hot spot) probably is an important factor for initiating the det-

shock wave in air and the weak luminosity due to the detonation wave in an explosive, a less luminous zone exists; in the following we shall call it the dark zone. Many fully-exposed still-photographs of the luminous phenomena produced in high-explosive shock tubes have been taken through a red filter (6000 to 6500 _~), which makes it easy to distinguish clearly the relative intensity of the light from each part of the tube. Glass mainly was used for the tube because it has the strength needed t(~ extinguish the external-shock luminosity. A1-

T A B L E 1. CHARACTERISTICS OF THE SHOCK W A V E PRODUCED IN A GAs BY THE DETONATION OF P E T N ( D E N S I T Y = 1 . 0 O/CC), WHOSE C H A P M A N - J o u G U E T CHARACTERISTICS ARE: DETONATION VELOCITY =

5550 M/sEe, PRESSVRE = 8 X 104 BAR, TEMPERATVRE = 4160°K, MATERIALVELOCITY 1400 M/SEC, DENSITY (1/V~) = 1.37 o/cc, ANn OBSERVEDDETONATIONVELOCITY= 5500 ± 100 M / S E e

=

Characteristics Calculated

Gas in Shock Tube

Temperature (transl. + rotat.) T (°K)

Material velocity U (m/sec)

Initial shock velocity Do (m/sec)

Initial shock velocity* Do (m/sec)

Attenuation constantt K X 10~ (sec/mD

55 85O 590 320 1000 1200 150 52

3100 63200 29000 14900 42000 56600 35800 383OO

7400 6170 6370 6670 6000 5920 7070 743O

9100 8220 7660 7810 7000 6700 8510 8900

83OO 7550 6900 7100 6300 62O0 8500 9500 12400

6.7 35.0 22.0 22.5 47.5 38.0

17300

8600

3660

4200

Pressure P (bar)

Hydrogen (1 atmos)... Argon (1 atmos) . . . . . . . . Air (1 atmos) . . . . . . . . . . Methane (1 atmos) . . . . i s o - B u t a n e (1 atmos).. Chlorine (1 atmos) . . . . Air (150 mm Hg) . . . . . . Air (50 mm Hg) . . . . . . . Air (1 mm Hg) . . . . . . . . Air (100 atmos) . . . . . . . .

Observed

7.5 5.5

* Values at the distance of 2 ~-~ 4 cm from charge surface. t values in 1/D = 1~Do 2 ? K x , x = 0 ~ 1 meter. onation reaction (Bowden-Yoffe9). However, in the narrow intergranular space, the hot spot may not grow enough to become an intense shock at a super-high temperature, because the hot spot loses its energy, in turn, for exciting the explosive particles. Knowledge concerning the shock formation length may be of help on this point.

Study of Dark Zone The discontinuous nature of the luminous phenomena that occur across the boundary between the surface of an explosive and a surrounding gas atmosphere has been observed in many photographic records of detonations, 1° but no proper explanation for the phenomenon has been given. Between the intense luminosity due to the

though cracks in glass often propagate with a speed comparable to that of air shocks in a tube, its real fracture is always delayed behind the passage of shocks, and a pattern of cracks is recorded on the still-photographs without disturbing the dark zone measurement. Sample photographs showing the dark zone are given in Figure 4. Approximate values of dark zone widths measured from photographic records for shock tube systems consisting of glass tube, argon gas, and various sorts of explosives are summarized in Table 2. The dark zone widths seem to depend upon the property of the shock-forming gas as well as the manner of detonation of shock-producing ex-

383

SHOCK WAVES FROM HIGH EXPLOSIVES

plosive; e.g., it seems that the dark zone is shortest with gases of high density and low specific heat, and with explosives of high detonation velocity and rapid completion of detonation reaction without solid particles entrained. The role of solid particles is to be emphasized; the dark zone widths for carbon-producing explosives ( T N T , tetryl, picric acid, nitroguanidine) or for explosives mixed with an inert m a t t e r ( P E T N + common salt or graphite) are rather longer than those for explosives that yield only gaseous prod-

charge surface; the full lines are for reaction paths in the detonation wave itself. The expanding delta zone will give rise to a compression wave in the outer atmosphere but not an instantaneous rise to a shock wave of high intensity owing to TABLE 2. DARK ZONE WIDTHS !V~[EASURED FROM STILL-PHOTOGRAPHIC RECORDS FOR SHOCK TUBE CONSISTING OF

GLASS TUBa (13-ram BORE), ARGON (OR HYDROGEN) GAS AND VARIOUS EXPLOSIVES. Explosive

Density g/cc

PETN

0.85

P E T N + NaC1 7:3

0.98 1.10

5:5

FIG. 4. Examples of still-photographs showing the dark zone phenomena for argon shocks in glass tube. (A) P E T N 70 + graphite 30 (/, = 0.98) (B) nitroguanidine (A = 0.72) (C) nitroguanidine (A = 0.55) (D) P E T N (A = 0.85) (E) picric acid (A = 0.85) (F) T N T (A = 0.95) ucts ( P E T N or nitroglycerine). The solid particle, whether reaction product or inert diluent or detonating particle, may retard shock formation by penetrating and disturbing the wave fi'ont which is on its way to shock formation. F r o m the above results, we take the dark zone as a measure of the shock formation length and draw a schematic diagram of time-distance relation of the wave phenomena in a high-explosive shock tube as shown in Figure 5. The dotted lines which form a delta zone (Fig. 5) represent the reaction paths of explosive particles that are thrown into the outer atmosphere after the arrival of the detonation front to the

P E T N + graphite 7:3 5:5 Nitroglycerine TNT T N T + NaC1 95:5 90:10 85:15 80:20 Nitroguanidine Tetryl Picric acid

0.98 0.95 1.6 0.95 0.98 1.0 1.1 1.15 0.72 0.85 0.85

Dark Zone Width mm

<0.5 ( ~ 4 mm in H~)

(~10 mm in H2) 3~6 (~13 mm in H~) 2~3 7N9 <0.5 3~6 4~--8 6 ~ 10 10 ~ 20 15 ,~ 30 6 ~ 10 2,~6 2~5

. ~~o~/~o Y/.Y ~

lum!nous zone I darkzo~le boundaryI

time "W

Ze FIG. 5. Schematic diagram for shock formation.

384

HIGH SPEED REACTIONS

its rapid attenuation and, in addition, probably to the disturbing effect of flying explosive particles; for the compression wave to grow into a substantial form of shock wave, it will need some distance--that is to say, a shock formation length or a dark zone--which may be terminated near the point of completion of the reaction. For high explosives yielding only gaseous products, this distance of dark zone is very short (less than

main luminosity, probably due to shock waves, lasts only for 4 ~ 6 ~sec.) As in the case of shock formation in the outer atmosphere, a dark zone phenomenon has been found in the contact transmission of a detonation wave from one explosive to another less sensitive one. Thus, in Figure 6, a dark zone exists in the initial period of the T N T or nitroguanidine detonation which is transmitted from P E T N ,

FIG. 6. Streak photograph of detonation %ransmission from PETN to TNT.

FIG. 7. Streak photograph of a zebra charge in glass tube (celluloid tube gives a similar image).

0.5 mm) ; in the case of solid-producing explosives the solid particles outrunning the delta zone and weakening the growing shock prolong the distance of dark zone greatly. Thus the real process of shock formation may be too complicated to fo~znulate strictly but, at least for explosives with a short shock formation length, like PETN, we can apply the ordinary method of calculation approximately--as we have done in the preceding section. Streak photographs taken through the red filter for similar samples show the same dark zone phenomena as in Figure 6. (They show that the

whereas the P E T N detonation transmitted from T N T or nitroguanidine shows no appreciable dark zone. Furthermore, similar dark zones can be seen in the detonation of a "zebra" charge, where granular common salt of 5-ram width is placed in alternate layers with PETN. Figure 7 shows that the salt zone temporarily interrupts the progress of the detonation wave and delays the initiation of the adjacent P E T N layer for 3.4 ~sec, and that the first part of the salt zone emits a bright light due to the collision with the detonation wave, n but thereafter a dark

385

SHOCK WAVES FROM HIGH EXPLOSIVES

zone follows. The same phenomena are clearly observed in a still-photograph of the same zebra charge. The situation is similar when naphthalene, graphite or a sheet of paper is used in place of common salt in the charge, although the luminous part is shorter than that for common salt. From the above observations we conclude that: (1) The dark zone appearing just above the charge surface is a measure of shock formation length, which is determined by the nature of both surrounding atmosphere and detonation wave; in particular, solid particles entrained play an iraportant role. (2) The pure shock front preceding the detonation wave in a granular explosive

obtained the color temperatures, assuming blackbody radiation for the luminosities from the detonation. Recently, Kantrovitz et al25 measured the temperatures of argon shocks by means of Uns61d's or Baranger's theory. However, these methods cannot be applied to the temperature measurement of an air shock from a P E T N detonation, because its spectrum contains numerous metallic lines due to impurites and CN bands superimposed on the background of weak continuum, the oxygen or nitrogen lines being obscure. Therefore, in this experiment, we adopted the two-line method developed by Ornstein and his group I~ and, for reference, the method of Spier

:FIG. 8. Spectrum of PETN-produced air shock, Method (b). (a) Shows the method of having copper particles suspended in air. emits a light of moderate intensity by producing microshocks in the air space between granules, the energy of the micro-shocks being used to initiate an endothermal decomposition of the explosive. (The formation of microshocks may depend upon factors similar to those mentioned by Muraour. I (3) When a detonation wave collides against an inert or less reactive solid it is temporarily dammed up and raised to a higher temperature but, owing to the event, the steady form of the detonation wave being destroyed, a decayed shock front precedes the detonation zone and a dark zone forms which persists until the detonation wave recovers its steady form in the next explosive layers.

Spectroscopic Measurement of Shock Wave Temperature Some spectroscopic measurements of detonation or shock temperatures have been performed by Muraour, 12Alentzev,13Fox 14and others. They

and Smit-MiessenI7 who used the unresolved CN bands. For a Boltzmann radiator, the next formula applies and gives the relative intensities of two atomic or ionic lines with different initial levels

I' I

A'g'v' exp ( - E ' / k T ) Agv exp (--E/kT)

where A is the transition probability, g is the statistical weight of the excited level with energy E which gives rise to the line with frequency v, T is the absolute temperature of the radiator and k is the Boltzmann constant. If the excited atoms in the air shock are in thermal equilibrium, the temperature of the air shock can be obtained by comparing the intensities of two metallic lines, but the spectrum of the air shock from P E T N has no lines suitable for that purpose. Accordingly, we have tried to insert intentionally the copper lines of 5106, 5153 and

386

HIGH SPEED REACTIONS

5220 (+5218) A, because they are not disturbed by lines or bands of other elements in the shocks and, in addition, they exist in a narrow wave length range (this is desirable from the standpoint of both film sensitivity for different wave lengths and deviations from the reciprocity law). Copper lines have been introduced (a) by mixing a small quantity (1 per cent) of fine copper powder with P E T N or (b) by suspending the copper particles in air through the electric spark between copper electrodes in which a small quantity of granular copper chloride is held, as shown in Figure 8(a).

/~o0~

o~ o

D

o

FIG. 9. Observed values of air shock temperatures. Q from the two lines of copper suspended in air by spark; © from the two lines of copper mixed in explosive; • from unresolved CN-bands. The experimental arrangement is similar to the previous one (Fig. 1). A Hilger-type quartz spectrograph with Kodak tri-X film replaces the rotating-drum camera. A glass tube of 18-ram bore and P E T N of 0.8 ~ 0.9 g/cc density are used. Together with the shock spectrum, the standardized tungsten lamp is spectrographed through a rotating sector which enables us to express the spectrum densities by corresponding intensities; the "intensity-area" of a line, i.e., area of the intensity-wave length diagram, is found by subtracting the part of the background continuum. Furthermore, we corrected the selfabsorption effect by comparing the intensities of two lines which have the same excitation level (copper lines of 5153 and 5220 A) by use of the equation expressing the weakening by self-absorption

1 (resultant) ~(Planek)

I =

1 -

e x p ~_

I(initial) 7 ~

j

where I(resultant) is the intensity actually observed I(initial) the intensity before self-absorption, and I(Planck) the intensity in radiation equilibrium. Transition probabilities of copper were found from the data of van Lingen. zs Figure 8(a) is an example of the spectrum of PETN-produced air shock. Figure 9 summarizes the values of air shock temperatures obtained by applying the two-line method for the spectra which were obtained according to methods (a) and (b) mentioned above. The values determined through the analysis of unresolved CN bands of (0-0) and (1-1) also were received. In method (a), where copper was mixed with P E T N , the temperature values were found to be relatively low (of the same order as the temperature values of CN radicals) and to remain almost constant along the shock path; in method (b), where copper was suspended in air, the highest temperature was obtained near the origin of the shock formation (in the dark zone, lines and bands are very weak) and the temperature values decreased along the shock path. I t is to be noted that the temperature value obtained here is either an effective excitational temperature of copper atoms entrained in the shock wave and in the detonation gases, or an effective vibrational temperature of CN radicals produced in the shock or detonation gases and not the temperature of the air itself which forms the shock wave. The problem is whether or not the copper atoms are in thermal equilibrium in the shock wave; in this respect method (b) seems preferable to others, although its accuracy is not so clear Acknowledgment

The authors are indebted to Mr. S. Kitaoka for his assistance in the experimental work. REFERENCES 1. MURAOUR, H.: 1Vfemor. Artil. Fr., 23, 867 (1949). 2. SHREFFLER, R. G., AND CHRISTIAN, R. H.: J. Appl. Phys., 25, 324 (1954). 3. TAYLOR,J.: Detonation in Condensed Explosives, p. 31. New York, Oxford Univ. Press, 1952. 4. SAVITT, J., AND STRESAU,R. Ho F.: J. Appl. Phys., 25, 89 (1954). 5. KISTIAKOWSKY, G. B., AND WILSON, E. B., JR.: OSRD Rept. 114 (1941).

SHOCK-TUBE STUDY OF FLAME FRONT-PRESSUREWAVE INTERACTION 6. KIHARA, T., AND HIKITA, T.: Fourth Symposium on Combustion, p. 458. Baltimore, The Williams & Wilkins Co., 1953. 7. HIKITA, W., AND YONEDA, K. : Pron. Japan. Fifth Natl. Cong. for Appl. Mechanics, 367, (1955). 8. PATERSON, S. : Fifth Symposium on Combustion, p. 672. New York, Reinhold Publ. Corp., 1955. 9. BOWDEN,F., ANDYOFFE, A. D. : The Initiation and Growth of Explosions in Liquid and Solid. New York, Cambridge Univ. Press, 1952.

10. 11. 12. 13. 14. 15. 16. 17. 18.

387

PARISOT,A. : Memor. Artil. Fr., 18, 499 (1939). PATERSON, S.: Nature, 167, 479 (1941). MURAOV~, H.: Chim. et Ind., 47, 3 (1942). ALENTZEV,M., ET AL.: Exptl. Theoret. Phys. U.S.S.R., 16, 990 (1946). Fox, J. C.: PB Rept. 36957 (1945). KANTROVITZ,A., ET AL. : J. Appl. Phys., 26, 83 (1955). ORNSTEIN,L. S., AND BRINKMAN, H. : Physica, 1,797 (1934). SPIES, J. L., AND SMIT-MIESSEN, M. M.: Physica, 9, 193, 922 (1942). VAN LINGEN: Physica, 1, 797 (1934).

49 A S H O C K - T U B E STUDY O F FLAME FRONT-PRESSURE W A V E

I N T E R A C T I O N ~'

By G. H. MARKSTEIN Introduction

Many applications of combustion in a gaseous medium, and particularly those in jet and rocket propulsion, require burning rates far in excess of those corresponding to laminar flame propagation. I t is generally recognized that these rates are achieved by the interaction of the flame with more or less random flow disturbances that are often somewhat loosely called "turbulence." Apparently because of this terminology, recent studies have concentrated on interactions of pipe flow or grid-generated turbulence with open or enclosed flames while, in comparison, the study of interactions with other kinds of flow disturbanee has been neglected. Linearized perturbation analysis: has shown that in a flow devoid of rapid changes of average variables any random disturbance can be decomposed into three modes that are in first-order approximation independent of each other: namely, a vorticity mode (eddy turbulence), a pressure mode (random sound), and entropy spottiness. Whenever the average flow variables are subject to rapid changes, however, such as occur during passage through grids, shock waves, flame fronts, a This research was conducted under the auspices of Project SQUID, jointly sponsored by the Offiee of Naval Research, Department of the Navy, Office of Scientific Research, Department of the Air Force, and Office of 0rdnanee Research, Depart, merit of the Army.

or changes of cross section of a duct, the three modes become strongly coupled in first order. Thus, in a turbulent flame all three disturbance modes must be present. This may be of minor importance with open flames, since the pressure mode will be dissipated by sound radiating from the flame, and the entropy mode will appear only in the burned gases in the form of temperature and density fluctuations. I n the case of flames enclosed in a duct, however, the pressure disturbances may become as significant as eddy turbulence, for the energy contained in pressure waves will in general become trapped in the various resonance modes of the duct. The combustion process in ducts is therefore generally accompanied by intense sound waves that may include random noise as well as resonance oscillations. Undoubtedly these pressure waves must affect the flame in various ways, but the nature of these interactions is at present ill understood. The large majority of previous studies of pressure wave-flame front interactions was concerned with spontaneous generation of sound and vibrations by flames. A complete bibliography and adequate discussion of the numerous investigations in this field would be beyond the scope of this paper. Among their results, the following are of particular significance in relation to the present work: (1) The rate of flame propagation in tubes during "vibratory movement" exceeds that during