- Email: [email protected]
Multiheaded structure of gaseous detonation
Multiheaded Structure of Gaseous Detonation R. I. SOLOUKHIN Institute of Hydrodynamics, U.S.S.R. Academy of Sciences (Siberian Division), Novosibirsk-90, U.S.S._~?. (Received May 1965)
The "multiheaded spin" structure of self-sustaining gaseous detonations in oxy-acetylene mixtures has b e e n s t u d i e d a t initial pressures /tom 0"03 to 0"2 arm. Density measurements have been made using an interterometer and quantitative schlieren techniques together with high speed photography and pressure and temperature records. To compare the non-equilibrium zone with the chemical kinetic data the ignition delay measurements were performed for oxy-acetylene mixtures at T = I 000" to 2 500*K using the reflected shock wave method. The kinetic data are described by --log (r [Oe]) mole sec l -~ = 11.56 + O"1 5 - - (25 000 + 2 200) / 4"58 T According to these data the observed shock-reaction zone thickness is more titan one order longer than the one-dimensional stationary one. Hydrodynamic explanations of this fact based on ihe transverse compression wave scheme are proposed. The diffraction of multiheaded detonat;on waves is described as an example of the influence of flow conditions on the structure of the detonation wave.
cording to our observations ~,' a well regulated system of transverse waves exists behind the shock detonation front. It seems to be very important to establish some of the general relations between the parameters for h ansverse waves and the structure of the entire detonation ~v ~ve. A flat channel has been chosen as a form of explosion vessel to simplify the conditions of wave propagation. The process seems to be volumetric, however, at high pressures and ~hc obsela'atiorL field is distorted by thn,~. dimensional effects i,~ the direction of the light path. Nevertheless the quite definite peculiarities of mulfiheaded waves could be clearly seen in both interferogram and pressure records" the detonation front Consists of periodically pulsating local shock fronts, most of the mixture being combusted directly at the incident shocks. Some portions of the compressed gIs are inflamed by transverse shock fronts after secondary compressions. This very ~econdary combustion may be considered as the source of an additional density increase behind the first shock transition. It should be pointed out that the whole length of the disturbed zone is thus determined by the characteristic size of the region of transverse waves and it may be significantly creater thatt the cbemieal reaction zone thickness.
Introduction IT IS obvious now that the one-dimensional 'classical' shock-reaction zone of gaseous detonation is not realized under ordinary conditions. According to D. F. HORNIG~, the real thickness of the shock transition in detonation waves differs from the one-dimensional one up to initial gas pressures of more than 20 atm. It is interesting therefore to perform a variety of experimental observations of detonation front structure for multiheaded waves, i.e. for the general case of the phenomena considered. The first work in this direction was done by D. R. WHITE 2, who considered in detail only the case of overdriven detonations which are very close to one-dimensional waves. Self-sustaining detonations with thetr complicated structure were analysed by him as turbtflent phenomena with a disorderly mixing combustion zone. Diffraction experiments reported here indicate the x'ery stable characfer of *.he multiheaded combustion mechanism under various flow conditions. Detonation fronts maintain their 'discrete' structure with a quite defiuite specific number of transverse waves after their re-establishment during diffraction. These experiments show once more that the 'discrete' structure is an ~nternal property of the front region itself and is independent of the external conditions. Ac51
52
R.I.
Soloukhin
Vol. 10
Figure I. Pressure (1) and density (2) records. Shock wave in argon, p i = 0 . 1 atm, shock Mach number M1=2"5. The second j u m p in the oscillogram (1) was registered by a separate gauge at the tube end. Time ma~'k~: 20 l,tsec apart
time resolution of the pressure measurements was less than 0-S psec. Shock velocities in these expe ".riments were dete,-mined b y schlieren streak photographs v~th an accuracy of about 0-5 per cent. The luminosity profile behind the detonation wave was observed with a prism spectrometer which could transmit two separate hydrogen lines (H a and H~) of width about 2 A. In addition to compari~ns of the pressure profiles the records of the line intensities were used for temperature measurements by the two-line method, transition probabilities being well known for the hydrogen lines. At T ~ 4 000 ° K the errors in temperature measurements were less than two per cent, i.e. + 8 0 ° . It m a y be noted that the applied method has some advantages in comparison with the reversal method. It is free from any errors arising in the background source temperature measurer ents occurring at high temperatures. Hy Jgen atoms exist in most real detonation proces. ; and their relaxation time is short enough tG avoid non-equilibrium effects. As the result:, show, self-absorption causes no perceptible effects under our conditions. Because. of the small density change effects in self-sustaining waves the most convenient thermodynamic parameters for the study of non-equilibrium processes in detonation waves are temperature and pressure. Density measurements are usually used for relaxation observations in inert media. We have an 'intermediate' case here; that is why the density measurements were used in combination with other methods. Two methods were used for the density measurements. A quantitative schlieren technique based on the refraction of a beam of parallel light when the shock front was crossed at an oblique angle was used :n inert gases ~. The scheme of this method is shown in F i g u r e 2. The photomultiplier signal is proportional to the light intensity change which in turn depends on the light divergence after refraction at the shock 6 ~-- (An :/n) tan a _~ K Ap t~tn a
combined with pressure records are 20 /.¢sec apart. The reflected shock signal was re~stered by a separate gauge at the end of the tube. The
The light source (slit) irnat.,e at the focal plane of the system is hidden pactial!y by the schlieren screen (knife), the extent of ~zilis closing being selected to provide the linear dependence
Experimental Methods
(1)
Instrumentation and
procedures
A square shock tube 5 cm x 5 cm and associated apparatus was used for the ignition and schlieren measurementsL To shorten the optical path of the interferometer a tube 3 cm x 1-5 cm was used in these experiments. Some of the pressure and luminosity measurements were performed with a 2-5 x 0-5 cm tube. Observation sections were located as far a s 40 to 7 0 l, from the ignition point, where ; is the largest cr~s-section dimension. Spirals in~rted into the ignition tube end were used in experiments on self-sustaining detonations. Pressures were measured using a barium titanate gauge ~ intended for recording impulses. The piezoelement, 1 m m in diameter, soldered with a long zinc rod having the same acoustic impedance, was inserted into the aluminium tube filled with wax to eliminate the influence of ,..t, .~,c vibrations. Gauges were calibrated using weak shocks in air and argon and the estimated error was less than three to five per cent. The amplitude of the gauge disturbances was of the same order of magnitude. Pressure records for i~cident and reflected shocks in argon ( p t - 0 . 1 atm) together with the density oscillograms (see below) are reproduced in F i g u r e 1. Time marks
Mai~ch 1966
Multiheaded structure of gaseous detonation
53
be made with hi.~h accuracy f.,r this purpose. Lastly, the space ~md time accuracy arc independent of the filming slit width and m a y be high enough. Monochromatic measurements
.
.
-,...
/ Figure 2. Apparatus Io; quantitative schlieren measurements with oblique angle lighting. (1) mirrors, (2) shock tube placed at angle o~ to the schliere~ ligh~ beam, (3) shock wave front, (4) ]lash lamp, (5) photo~nultiplier
between the optical refractivity gradient and the photomultiplier current (light intensity). The sensitivity of the method is determined by the foca! distance of the system t = 200 cm and by the slit width d = 0, 1-0, 3 mm. Calibrations bv weak shocks in argon and some theoretical evaluations ( / = 2 0 0 cm) lead to a quite acceptable sensitivity using this method (about two to five per cent). Of course the optical refractive index gradient appearing behind the shock front will make the analysis of the results obtained more complicated. At initial pressures above 0-15 atm the schiieren signals have a flat form like the ones that correspond to a shock wave in argon (see Figure I). We can thus measure the density jump, in these cases. To avoid the luminosity of tl'e detonation itself a flash lamp was used ab -he light source. Calibration oscillograms it: acetylene-oxygen mixtures (C2H.,+2.,~O.~) withoat ignition and with a typical detonati~m record are shown in Figures 3(a) and (b). Optical interftrometry was used as the secured method for density measurements. A Mictwlson's type interferometer was employed together with high-speed stre:~k cameras and spark photography. It was f~und that the 'compensation' method of photogral'hy based on the exact compensation of shock motion bv the m,,ti,m .,~ the film image in the same direction' is preferable to spark photography. The c~m,.pt'nsati~,~ method may be used with interferometers h a v i ~ a limited size of observation field fc.r makin~ observations on quite long objects. The narr,,w glass windows of the explosion ch;tmlwrs can
Figure 3. Oscillographic data of schlieren density measuremtnts with flash light: (at weak shock wave in (72I-t2+2".'3 02 without chemical reaction (calibration), (b) detonation wave in same mixture. Time marks 20 p.sec apart
were performed by using interference and cCJl::,ar t.,lass filters h = 5 100 to 5 700 A,. In Figure 4 monochromatic interferograms at the two initial press~,res of t1.1)4 and I).05 atm of a stoichi,~metric oxy-acetylene mixture are shown. Figure 4(a) corlespop.ds to a non-stationary case and c~msists of a long 'transition' zone. "rh~. second tree c(~rresponds to an ordinary stationary wave with an initial density jllnl I, cl,~s,, t,, th,~t ,~f the lirsl case (.O~ p, "'- 3.r31. T'w~ v i s u a l i z a t i , m meth,~ds v.'~.r(, us~.d t~,r tt~ ,°
(lii]racti~m .~tv.di~'s. Tlw '.~+til! pi,,,t~,~rap!~' ,.~ay: is the ~encralizati~m of ,-:~rt,m s~,,,t m~,th~d, the. ~:,fincidcnce p~ints ~t i~rin;arv and tral~vcrs,.
54
Vol. 10
R. I. Soloukhin
shocks are of very high luminosity and produce the trajectory trace image on the motionless film in a camera with an opened shutter. Time development ( ~ e ) i s provided here directiy
/,0 30
o-I~"
20 i0 0 4 3 2
/ I
,"k f-'7"-
r ~1~,
-
1 5000
o.
,\
g I
,,e.
4 500
_.., ....
4 000 I
Figure 4. Interlerograms of detonation in C ~ + 2"5 02." (a) pl=O'04 arm, weakened wave; (b) p:=o'05 arm, self-sustaining wave
by the detonation wave propagation. No independent motion of the film is required. Schlie:en techniques together with high-speed photography (0-56 x 106 frames per second) were used for the diffraction study of detonation in a flat channel. The same conditions were provided when comparing the film patterns with the 'still photograph' data. (2) Sel/-sustaining waves data In Figure 5 the variation in gaseous temperature, pressure, etc. behind the detonation front in C.,H~+ 2-50~ at p~ =0.09 arm are compared. Broken lines denote the equilibrium states. It should be borne in mind that the temperature recorded for the gas volume is the highest and not the average one. The correspondence between measured and equilibrium parar~eters is established only after four to six micr(,seconds behind the front. Zones close to the front consist of vibrations corresponding to the complicated structure of pulsating shock fronts, only the highest values of the gas parameters are of interest in ~ i s area. To compare the pressure and luminosity profiles at different initial pressures two serie~ of oscillograms are shown in Figure 6 for C2H2+2.5 02 and C~H2+O., mixtures. It is clear that the first
"-
0"5
\
----~
0 2 4 6 Time, psec
8
Figure 5. Pressure. density, temperature and light emission (Hp) data to same time scale. 5elf-sustaimng detonation in C2H~+2"5 02 at pz=o'09 arm
pressure peak (P2 ~ 20 to 25 p~) precedes the appearance of luminosity. At most pressures ( p 2 ~ 6 0 Pt) the luminosity maximum is o~erved. The pressures measured in the 'equilibrium' zone and also the highest pressmes are plotted in Figure 7 (Pt =0.2 arm) as a function of acetylene percentage. The solid lines axe the calculated equilibrium pressures for the onedimensional detonations [Figure 7(a)] and for shock waves having the same velocity as detonations [Figure 7(b)]. There is no agreement between measured and calculated pressures in the latter case because the physical scheme of the shock transitions differs sufficiently from the one-dimensional theory of waves ~fith a stationary chemical reaction zone. In Figure 8 temperalure measurements for the 'equilibrium' zone extrapolated to an initial pressure p , = l arm, are compared with the equilibrium state calculations. According to the data of Figure 5 high temperatures are observed in the 'transition' zone. Such t~mper-
March 1966
Muldheaded structure of gaseous detonation
(a)
f-., {b)
(c)
i
2
-~
55
(e)
(d)
:~1"'-'-'--
j
-~--
,
\
m
/-.
N.j~
4
I
._/-,_ 1
_j
f
fIN
~ (f) -~
0~
2 \ 4 6
0
4
(\:")
-~
j
/ \~(o
/ \.(j)
\
\./~2
j
--q 6
0
2
4
6
0
2
4
6
0
2
4
6
\:._ 0
2
4
6
Tracings o] photomultiplier (Ha) and pressure records /or detonations in C9He+2"50~ (upper series) and in C.oH2+O~ (lower series), pl= (a, I) 0"06; (b, g) 0.08; (c, h) 0"09; (d, i) 0"11; (e, j) 0"14 atm respectively
Figure 0.
(a) a
40
........~
3o
-~. . . . . . . . . . .
1
~0
40
Oo -
% C2H2
ature peaks (up to T ~ 5000°K) exist for mixtures of different compositions. Density measurements for C,.,H.,+ 2.5 O., mixtures are shown in Figure 9 as a function of initial pressure. Density increase, registered by the schlieren method, is obsel~ced beginning from p~ ~ 100 mm of mercury where the size of shock roughnesses is of the order of 1 r n m The interferometer data for the 'equilibrium' zone (4 to 6 psec) begin to be unstable only at p~ ~-~ 50 mm of mercury. It should be pointed out that some difficulties may arise du,.~ to uncertainty in the value of high temperattare gas 4 600
80 7O
4 400
-
t
40 3o
,--,
t {
l
-
4 200
t I I
40
~o
6o
"/, C 2H 2
Figu~,; 7. Shocked gas pressure behind sell-sustaining detonation waves in x C,.,l-Io.+Oo. as a ]unction of acetylene concentration: (a) "equilibrium" data (I calcd, 2 obsd), (b) pressure "peak" data compared with ,hemical reaction "peak" in one-dimensional detonations
4 00(2[
J 30
4'0 %
5'0
60
C2H2
Figure 8. Calculated (brohen iine) and measured (extrapolated to pl--I atm) temperature.~ as a /unction of acetylene percentage ('equilibrium" zoncl
56
R.I.
t
Soloukhin
Vol. 10
tween these dzta is good in spite of the differences in methods and shock wave conditions.
0,
The activation energy, however, seems to be determined here more exactly than in ref. 7 insofar as the temperature interval is wider in these experiments (1 000 ° < T < o 500 oK).
e- 2 ,,.t
The data shown in Ftgure tO may be described by - l o g {~'[ 02] } mole sec 1-~ = 11.56 _+0-15 - (25 000 +_2 200) / 4- 58 T
1 .Z,
1-6
2-0
1-8
2-2
log p|[mm Hg]
Figure 9. "E~tuilibrium" density data on self-sustaining detonations in C~H2+2-50.~: (1) schlieren method; (2) inter]erometer data
The data considered cover all the temperatu,'es that are of interest for detonation processes. The highest shock temperatures corresponding to the stationary wave zone ( D = 2 300 t o 2 500 m / s e c in C2H~+2-5 02) are 2 100 ° to 2 390°K respectively.
refractivity. Experimentally determined specific refracti~dties for OH and other species were used ~. (3) Ignition delay measurements The ignition delay data determined by the usual reflected shock method', in C~H~+ 2-5 O.. + x Ar mixtures, axe plotted in Figure tO. The ultraviolet radiation delay data in the oxy-acetylene reactions: are also shown. The agreement be-
9
.-1 o-2
L "::\ ~-08
,o1
0 0 I
Figure I t . "Still" photographs o[ detonation diffractions in ('2I~z+2-50~: (a) detonation destroyed, only the transverse waves remain in the central area of the diverging wave until the rare[action waves arrive; (bj d~,tomttion i.~ r~-established in th,' centre alter s,,utt, lran.svcrse 1uaz'e collisit,ns
7
1
04
0"6
c3/r, [oK-,]
I
0-8
I
°i 10
Figure i0. Dependence of duration of induction period in oxy-acetylene reaction on temperature: (I) K i s t i a k o w s k y and Richards's data 7, (2) reflected shock measurements. Solid hne corresponds to activation energy 25 fecal/mole
(4) Diffraction o/detonations Diffraction experiments were perfi)rmed ill ltat channels 5 mm d.:ep. Figures ! ! (a)md (b) s;,,'Jw two still photographic re.co,his fl,r (a) the fully (lestroy,.d and (b) the re-0stablished detonation,. It is clearly seen fr,,m tlwsc eXlW3iments tt~at
March 1966
Multiheaded structure of gaseous detonation
the lateral areas of the shock front cannot ensure gas ignition. As there are no collisions, transverse waves are weakened gradually (case a). If in the central parts of shock fronts, some transverse waves of opposite direction remain, the detonation r6gime maintains itself due to wave collisions in these areas (case b), and the detonation waves are re-established as a whole.
Figure 12.
57
transverse shocks periodically collapse, coalesce and propagate, h s t e a d of the expected r~,,d '---' 0"2 X 10 -7 sec for the one-dimensional detonations ( p ~ , / - 1 atm) we have here ~" ~ 0-5' to 3 x 10 -~ see (Figure 5). The latter values agree well wilh the lmninosity-to-pressure delays (see Figure r') and with the delay data corresponding to the absolute pressure jumps
Schlieren p h o t o g r a p h series on detonation diffraction. The regular deformations of the shock ]rent due to m u l t i h e a d e d spin are visible
Figure 12 represents some schlieren records of detonatiol: diffraction obtained with frequency of 560 000 frames per second. Local distortions of the shock front are clearly visible in these photographs.
(p,, ~ 20 to 40 p~ compared with p., ~ 7S p~ for the one-dimensional case). According to the data shown in Figure 10 ignition delays are of order fi0 /.tsec when p,---, 20 Pl (To,--~ 980°K), i.e. waves (2) ,and (2') are not able to ignite the gas fast enough, their appearance on the pressure records like Figure 5(a), however, being more probable because of the relatively large size of (2.) and (2") front areas. Pressure gauge traject~,ries on the streak photographs (line,; p a r a l M t~) the tiine axis) will
Discussion The main features of the phenomena considered refer to the multiheadod structure of detonations as the only stable flow pattern. There is no 'classical' shock chemical reaction zone in pressure anti density records. A sketch of real
2 2r
2r i
,
"3" i i
1
~,
15 I"u4urc
I i
13.
lnl, r?r,,tut~on
i i
,
,,f a m u l t i h c a d t , d
~,',.tvc s t v u c t ' ~ r c :
\
(li
arras
of the
prZm.~ry [a.st tA,n,'tiun; (2j a~t~t (2') gradu,dlv i,,,al
sll~ck ct,nliguratuJlls is stioxvn 9 ir~ Figure 13. The /2as is c,mlinuously lmrnt in an.as (1) inimediately after the priniary ccmipression as well :is ili tlie tratlsvt.rse ~v:tves (3) after the sec~mdarv c,mipressions. The wave areas like (2) and t2'.~ a r e the grad,ially weakened r;hocks arisin~ fnm, the c~llisions of two waves (3). The areas (4) i,ctxv~.,.n t2') , n d the' |t:u:le trolit contain s~mac [)tlrti~tilS (if illibllrllt C ~ l l l l)Ic~%('d ~,ls \vht.r~.
int~.r.~ect the traces of the transveis~, ~:~nn])rcssi(,ll w:tx'cs in burnt gas:' without fail after a timt interval of the order of t - a e - . . - 1 0 ~' s,,c. where a i.-, a mezm distance, t)~.l~v,.cn tl~t~ t r a n s verse w:tves, and ~, denotes ~a,v,c v~h~cilv. An additional burnt gas c,~inpressi~m ttl~ls exists i~ these waves, troin p.. ~ 2tl p, t,, p : - - - 4 0 p~, .ace Fia, ure 5(ai and the corrt.st,,n(!in~ l:'il~l,,'r~',--
58
R. L Soloukhin
T;~---2 ~ × ~ 5 0 0 0 ° K in accordance with temperature measurements [Figure 5(c)]. As a result the temperature peaks usually observed in detonation fronts may be explained hydrodynamically and not as due to a chemical phenomenon. Flow patterns in diverging waves differ from those in the ordinary case, on account of the existence of additional pressure and temperature gradients. Some rough calculations9 show that, in a direction perpendicular to incident wave propagation, weak side waves exist. The Math numbers of these waves (M ~_~ 3-5; P2 ---~ 15 :~) may be evaluated by the arbitrary discontinuity break-up method. The product state behind ordinary detonations should be chosen as the high pressure gas conditions. Pressure decrease in the side areas of the detonation front leads to the attenuation of the t~nsverse w ryes. Having no collisions with oppositely directed waves transverse shocks cannot support the multiheaded mechanism of ignition and a destruction of the detonation as a whole may be observed [Figure I 1 (a) ]. It should be noted as an experimental fact that a 'critical' number of transverse one-directional waves related to the channel size or the tube diameter is about 10 or 13 in C2H2+O~ for flat channels and tubes respectively.
Vol. 10
Condusion R should be stated in conclusion that in the experiments a universai character of the stable multiheaded spin mechanism in gaseous detonations was established. Some general features of the parameter distributions in detonation waves as a, whole were considered although the complete theoretical scheme of this non-stationary process is still too complicated. It seems to be satisfactorily established that the ignition kinetic data presented are in good agreement with the hydrodynamic aspect of the flow patterns.
References x HOR~IG, D. F. 11epr. Frick Chem. Lab. Princeton Univ., X I I Solv. Congr., Brussels, 1962 WHITE, D. R. Physics of Fl~c~d~, 1961, 4, 465 3 SOLOUKHIN, R. I. Izvest. A~ad. Nauk S.S.S.R., Otdel. tekh. Nauk (Mechanika), 1959, 6, 145 4 SOLOUKHIN, R. I. Shock Waves and Detonation in Gases. Fizmatgiz: Moscow, 1963; see also: Soviet Phys. Usp. 1964, 6, 523 5 SOLOUKHL~, R. I. Combustion and Explosion Problems. Ed. Akad. Nauk S.S.S.R. (Sib. Div.), 1965, No. 1, 112 6 W H I T e , D. R. Physics of Fluids, 1961, 4, 40 7 KISTIAKOWSKY, G. W.
and
RICHARDS, L.
W.
J. chem. Phys. 1962, 36, 1707 s MXTROFA.~OV, V. V. Prikl. mech. tekh. Fiz. 1962, No. 4 100 9 MITRCDFANOV, V. V. and SOLOUKHIN~ R. I. Dokl.
Akad Nauk S.S.S.R. 1964, 159, 1~1o. 5, 1003
The "multiheaded spin" structure of self-sustaining gaseous detonations in oxy-acetylene mixtures has b e e n s t u d i e d a t initial pressures /tom 0"03 to 0"2 arm. Density measurements have been made using an interterometer and quantitative schlieren techniques together with high speed photography and pressure and temperature records. To compare the non-equilibrium zone with the chemical kinetic data the ignition delay measurements were performed for oxy-acetylene mixtures at T = I 000" to 2 500*K using the reflected shock wave method. The kinetic data are described by --log (r [Oe]) mole sec l -~ = 11.56 + O"1 5 - - (25 000 + 2 200) / 4"58 T According to these data the observed shock-reaction zone thickness is more titan one order longer than the one-dimensional stationary one. Hydrodynamic explanations of this fact based on ihe transverse compression wave scheme are proposed. The diffraction of multiheaded detonat;on waves is described as an example of the influence of flow conditions on the structure of the detonation wave.
cording to our observations ~,' a well regulated system of transverse waves exists behind the shock detonation front. It seems to be very important to establish some of the general relations between the parameters for h ansverse waves and the structure of the entire detonation ~v ~ve. A flat channel has been chosen as a form of explosion vessel to simplify the conditions of wave propagation. The process seems to be volumetric, however, at high pressures and ~hc obsela'atiorL field is distorted by thn,~. dimensional effects i,~ the direction of the light path. Nevertheless the quite definite peculiarities of mulfiheaded waves could be clearly seen in both interferogram and pressure records" the detonation front Consists of periodically pulsating local shock fronts, most of the mixture being combusted directly at the incident shocks. Some portions of the compressed gIs are inflamed by transverse shock fronts after secondary compressions. This very ~econdary combustion may be considered as the source of an additional density increase behind the first shock transition. It should be pointed out that the whole length of the disturbed zone is thus determined by the characteristic size of the region of transverse waves and it may be significantly creater thatt the cbemieal reaction zone thickness.
Introduction IT IS obvious now that the one-dimensional 'classical' shock-reaction zone of gaseous detonation is not realized under ordinary conditions. According to D. F. HORNIG~, the real thickness of the shock transition in detonation waves differs from the one-dimensional one up to initial gas pressures of more than 20 atm. It is interesting therefore to perform a variety of experimental observations of detonation front structure for multiheaded waves, i.e. for the general case of the phenomena considered. The first work in this direction was done by D. R. WHITE 2, who considered in detail only the case of overdriven detonations which are very close to one-dimensional waves. Self-sustaining detonations with thetr complicated structure were analysed by him as turbtflent phenomena with a disorderly mixing combustion zone. Diffraction experiments reported here indicate the x'ery stable characfer of *.he multiheaded combustion mechanism under various flow conditions. Detonation fronts maintain their 'discrete' structure with a quite defiuite specific number of transverse waves after their re-establishment during diffraction. These experiments show once more that the 'discrete' structure is an ~nternal property of the front region itself and is independent of the external conditions. Ac51
52
R.I.
Soloukhin
Vol. 10
Figure I. Pressure (1) and density (2) records. Shock wave in argon, p i = 0 . 1 atm, shock Mach number M1=2"5. The second j u m p in the oscillogram (1) was registered by a separate gauge at the tube end. Time ma~'k~: 20 l,tsec apart
time resolution of the pressure measurements was less than 0-S psec. Shock velocities in these expe ".riments were dete,-mined b y schlieren streak photographs v~th an accuracy of about 0-5 per cent. The luminosity profile behind the detonation wave was observed with a prism spectrometer which could transmit two separate hydrogen lines (H a and H~) of width about 2 A. In addition to compari~ns of the pressure profiles the records of the line intensities were used for temperature measurements by the two-line method, transition probabilities being well known for the hydrogen lines. At T ~ 4 000 ° K the errors in temperature measurements were less than two per cent, i.e. + 8 0 ° . It m a y be noted that the applied method has some advantages in comparison with the reversal method. It is free from any errors arising in the background source temperature measurer ents occurring at high temperatures. Hy Jgen atoms exist in most real detonation proces. ; and their relaxation time is short enough tG avoid non-equilibrium effects. As the result:, show, self-absorption causes no perceptible effects under our conditions. Because. of the small density change effects in self-sustaining waves the most convenient thermodynamic parameters for the study of non-equilibrium processes in detonation waves are temperature and pressure. Density measurements are usually used for relaxation observations in inert media. We have an 'intermediate' case here; that is why the density measurements were used in combination with other methods. Two methods were used for the density measurements. A quantitative schlieren technique based on the refraction of a beam of parallel light when the shock front was crossed at an oblique angle was used :n inert gases ~. The scheme of this method is shown in F i g u r e 2. The photomultiplier signal is proportional to the light intensity change which in turn depends on the light divergence after refraction at the shock 6 ~-- (An :/n) tan a _~ K Ap t~tn a
combined with pressure records are 20 /.¢sec apart. The reflected shock signal was re~stered by a separate gauge at the end of the tube. The
The light source (slit) irnat.,e at the focal plane of the system is hidden pactial!y by the schlieren screen (knife), the extent of ~zilis closing being selected to provide the linear dependence
Experimental Methods
(1)
Instrumentation and
procedures
A square shock tube 5 cm x 5 cm and associated apparatus was used for the ignition and schlieren measurementsL To shorten the optical path of the interferometer a tube 3 cm x 1-5 cm was used in these experiments. Some of the pressure and luminosity measurements were performed with a 2-5 x 0-5 cm tube. Observation sections were located as far a s 40 to 7 0 l, from the ignition point, where ; is the largest cr~s-section dimension. Spirals in~rted into the ignition tube end were used in experiments on self-sustaining detonations. Pressures were measured using a barium titanate gauge ~ intended for recording impulses. The piezoelement, 1 m m in diameter, soldered with a long zinc rod having the same acoustic impedance, was inserted into the aluminium tube filled with wax to eliminate the influence of ,..t, .~,c vibrations. Gauges were calibrated using weak shocks in air and argon and the estimated error was less than three to five per cent. The amplitude of the gauge disturbances was of the same order of magnitude. Pressure records for i~cident and reflected shocks in argon ( p t - 0 . 1 atm) together with the density oscillograms (see below) are reproduced in F i g u r e 1. Time marks
Mai~ch 1966
Multiheaded structure of gaseous detonation
53
be made with hi.~h accuracy f.,r this purpose. Lastly, the space ~md time accuracy arc independent of the filming slit width and m a y be high enough. Monochromatic measurements
.
.
-,...
/ Figure 2. Apparatus Io; quantitative schlieren measurements with oblique angle lighting. (1) mirrors, (2) shock tube placed at angle o~ to the schliere~ ligh~ beam, (3) shock wave front, (4) ]lash lamp, (5) photo~nultiplier
between the optical refractivity gradient and the photomultiplier current (light intensity). The sensitivity of the method is determined by the foca! distance of the system t = 200 cm and by the slit width d = 0, 1-0, 3 mm. Calibrations bv weak shocks in argon and some theoretical evaluations ( / = 2 0 0 cm) lead to a quite acceptable sensitivity using this method (about two to five per cent). Of course the optical refractive index gradient appearing behind the shock front will make the analysis of the results obtained more complicated. At initial pressures above 0-15 atm the schiieren signals have a flat form like the ones that correspond to a shock wave in argon (see Figure I). We can thus measure the density jump, in these cases. To avoid the luminosity of tl'e detonation itself a flash lamp was used ab -he light source. Calibration oscillograms it: acetylene-oxygen mixtures (C2H.,+2.,~O.~) withoat ignition and with a typical detonati~m record are shown in Figures 3(a) and (b). Optical interftrometry was used as the secured method for density measurements. A Mictwlson's type interferometer was employed together with high-speed stre:~k cameras and spark photography. It was f~und that the 'compensation' method of photogral'hy based on the exact compensation of shock motion bv the m,,ti,m .,~ the film image in the same direction' is preferable to spark photography. The c~m,.pt'nsati~,~ method may be used with interferometers h a v i ~ a limited size of observation field fc.r makin~ observations on quite long objects. The narr,,w glass windows of the explosion ch;tmlwrs can
Figure 3. Oscillographic data of schlieren density measuremtnts with flash light: (at weak shock wave in (72I-t2+2".'3 02 without chemical reaction (calibration), (b) detonation wave in same mixture. Time marks 20 p.sec apart
were performed by using interference and cCJl::,ar t.,lass filters h = 5 100 to 5 700 A,. In Figure 4 monochromatic interferograms at the two initial press~,res of t1.1)4 and I).05 atm of a stoichi,~metric oxy-acetylene mixture are shown. Figure 4(a) corlespop.ds to a non-stationary case and c~msists of a long 'transition' zone. "rh~. second tree c(~rresponds to an ordinary stationary wave with an initial density jllnl I, cl,~s,, t,, th,~t ,~f the lirsl case (.O~ p, "'- 3.r31. T'w~ v i s u a l i z a t i , m meth,~ds v.'~.r(, us~.d t~,r tt~ ,°
(lii]racti~m .~tv.di~'s. Tlw '.~+til! pi,,,t~,~rap!~' ,.~ay: is the ~encralizati~m of ,-:~rt,m s~,,,t m~,th~d, the. ~:,fincidcnce p~ints ~t i~rin;arv and tral~vcrs,.
54
Vol. 10
R. I. Soloukhin
shocks are of very high luminosity and produce the trajectory trace image on the motionless film in a camera with an opened shutter. Time development ( ~ e ) i s provided here directiy
/,0 30
o-I~"
20 i0 0 4 3 2
/ I
,"k f-'7"-
r ~1~,
-
1 5000
o.
,\
g I
,,e.
4 500
_.., ....
4 000 I
Figure 4. Interlerograms of detonation in C ~ + 2"5 02." (a) pl=O'04 arm, weakened wave; (b) p:=o'05 arm, self-sustaining wave
by the detonation wave propagation. No independent motion of the film is required. Schlie:en techniques together with high-speed photography (0-56 x 106 frames per second) were used for the diffraction study of detonation in a flat channel. The same conditions were provided when comparing the film patterns with the 'still photograph' data. (2) Sel/-sustaining waves data In Figure 5 the variation in gaseous temperature, pressure, etc. behind the detonation front in C.,H~+ 2-50~ at p~ =0.09 arm are compared. Broken lines denote the equilibrium states. It should be borne in mind that the temperature recorded for the gas volume is the highest and not the average one. The correspondence between measured and equilibrium parar~eters is established only after four to six micr(,seconds behind the front. Zones close to the front consist of vibrations corresponding to the complicated structure of pulsating shock fronts, only the highest values of the gas parameters are of interest in ~ i s area. To compare the pressure and luminosity profiles at different initial pressures two serie~ of oscillograms are shown in Figure 6 for C2H2+2.5 02 and C~H2+O., mixtures. It is clear that the first
"-
0"5
\
----~
0 2 4 6 Time, psec
8
Figure 5. Pressure. density, temperature and light emission (Hp) data to same time scale. 5elf-sustaimng detonation in C2H~+2"5 02 at pz=o'09 arm
pressure peak (P2 ~ 20 to 25 p~) precedes the appearance of luminosity. At most pressures ( p 2 ~ 6 0 Pt) the luminosity maximum is o~erved. The pressures measured in the 'equilibrium' zone and also the highest pressmes are plotted in Figure 7 (Pt =0.2 arm) as a function of acetylene percentage. The solid lines axe the calculated equilibrium pressures for the onedimensional detonations [Figure 7(a)] and for shock waves having the same velocity as detonations [Figure 7(b)]. There is no agreement between measured and calculated pressures in the latter case because the physical scheme of the shock transitions differs sufficiently from the one-dimensional theory of waves ~fith a stationary chemical reaction zone. In Figure 8 temperalure measurements for the 'equilibrium' zone extrapolated to an initial pressure p , = l arm, are compared with the equilibrium state calculations. According to the data of Figure 5 high temperatures are observed in the 'transition' zone. Such t~mper-
March 1966
Muldheaded structure of gaseous detonation
(a)
f-., {b)
(c)
i
2
-~
55
(e)
(d)
:~1"'-'-'--
j
-~--
,
\
m
/-.
N.j~
4
I
._/-,_ 1
_j
f
fIN
~ (f) -~
0~
2 \ 4 6
0
4
(\:")
-~
j
/ \~(o
/ \.(j)
\
\./~2
j
--q 6
0
2
4
6
0
2
4
6
0
2
4
6
\:._ 0
2
4
6
Tracings o] photomultiplier (Ha) and pressure records /or detonations in C9He+2"50~ (upper series) and in C.oH2+O~ (lower series), pl= (a, I) 0"06; (b, g) 0.08; (c, h) 0"09; (d, i) 0"11; (e, j) 0"14 atm respectively
Figure 0.
(a) a
40
........~
3o
-~. . . . . . . . . . .
1
~0
40
Oo -
% C2H2
ature peaks (up to T ~ 5000°K) exist for mixtures of different compositions. Density measurements for C,.,H.,+ 2.5 O., mixtures are shown in Figure 9 as a function of initial pressure. Density increase, registered by the schlieren method, is obsel~ced beginning from p~ ~ 100 mm of mercury where the size of shock roughnesses is of the order of 1 r n m The interferometer data for the 'equilibrium' zone (4 to 6 psec) begin to be unstable only at p~ ~-~ 50 mm of mercury. It should be pointed out that some difficulties may arise du,.~ to uncertainty in the value of high temperattare gas 4 600
80 7O
4 400
-
t
40 3o
,--,
t {
l
-
4 200
t I I
40
~o
6o
"/, C 2H 2
Figu~,; 7. Shocked gas pressure behind sell-sustaining detonation waves in x C,.,l-Io.+Oo. as a ]unction of acetylene concentration: (a) "equilibrium" data (I calcd, 2 obsd), (b) pressure "peak" data compared with ,hemical reaction "peak" in one-dimensional detonations
4 00(2[
J 30
4'0 %
5'0
60
C2H2
Figure 8. Calculated (brohen iine) and measured (extrapolated to pl--I atm) temperature.~ as a /unction of acetylene percentage ('equilibrium" zoncl
56
R.I.
t
Soloukhin
Vol. 10
tween these dzta is good in spite of the differences in methods and shock wave conditions.
0,
The activation energy, however, seems to be determined here more exactly than in ref. 7 insofar as the temperature interval is wider in these experiments (1 000 ° < T < o 500 oK).
e- 2 ,,.t
The data shown in Ftgure tO may be described by - l o g {~'[ 02] } mole sec 1-~ = 11.56 _+0-15 - (25 000 +_2 200) / 4- 58 T
1 .Z,
1-6
2-0
1-8
2-2
log p|[mm Hg]
Figure 9. "E~tuilibrium" density data on self-sustaining detonations in C~H2+2-50.~: (1) schlieren method; (2) inter]erometer data
The data considered cover all the temperatu,'es that are of interest for detonation processes. The highest shock temperatures corresponding to the stationary wave zone ( D = 2 300 t o 2 500 m / s e c in C2H~+2-5 02) are 2 100 ° to 2 390°K respectively.
refractivity. Experimentally determined specific refracti~dties for OH and other species were used ~. (3) Ignition delay measurements The ignition delay data determined by the usual reflected shock method', in C~H~+ 2-5 O.. + x Ar mixtures, axe plotted in Figure tO. The ultraviolet radiation delay data in the oxy-acetylene reactions: are also shown. The agreement be-
9
.-1 o-2
L "::\ ~-08
,o1
0 0 I
Figure I t . "Still" photographs o[ detonation diffractions in ('2I~z+2-50~: (a) detonation destroyed, only the transverse waves remain in the central area of the diverging wave until the rare[action waves arrive; (bj d~,tomttion i.~ r~-established in th,' centre alter s,,utt, lran.svcrse 1uaz'e collisit,ns
7
1
04
0"6
c3/r, [oK-,]
I
0-8
I
°i 10
Figure i0. Dependence of duration of induction period in oxy-acetylene reaction on temperature: (I) K i s t i a k o w s k y and Richards's data 7, (2) reflected shock measurements. Solid hne corresponds to activation energy 25 fecal/mole
(4) Diffraction o/detonations Diffraction experiments were perfi)rmed ill ltat channels 5 mm d.:ep. Figures ! ! (a)md (b) s;,,'Jw two still photographic re.co,his fl,r (a) the fully (lestroy,.d and (b) the re-0stablished detonation,. It is clearly seen fr,,m tlwsc eXlW3iments tt~at
March 1966
Multiheaded structure of gaseous detonation
the lateral areas of the shock front cannot ensure gas ignition. As there are no collisions, transverse waves are weakened gradually (case a). If in the central parts of shock fronts, some transverse waves of opposite direction remain, the detonation r6gime maintains itself due to wave collisions in these areas (case b), and the detonation waves are re-established as a whole.
Figure 12.
57
transverse shocks periodically collapse, coalesce and propagate, h s t e a d of the expected r~,,d '---' 0"2 X 10 -7 sec for the one-dimensional detonations ( p ~ , / - 1 atm) we have here ~" ~ 0-5' to 3 x 10 -~ see (Figure 5). The latter values agree well wilh the lmninosity-to-pressure delays (see Figure r') and with the delay data corresponding to the absolute pressure jumps
Schlieren p h o t o g r a p h series on detonation diffraction. The regular deformations of the shock ]rent due to m u l t i h e a d e d spin are visible
Figure 12 represents some schlieren records of detonatiol: diffraction obtained with frequency of 560 000 frames per second. Local distortions of the shock front are clearly visible in these photographs.
(p,, ~ 20 to 40 p~ compared with p., ~ 7S p~ for the one-dimensional case). According to the data shown in Figure 10 ignition delays are of order fi0 /.tsec when p,---, 20 Pl (To,--~ 980°K), i.e. waves (2) ,and (2') are not able to ignite the gas fast enough, their appearance on the pressure records like Figure 5(a), however, being more probable because of the relatively large size of (2.) and (2") front areas. Pressure gauge traject~,ries on the streak photographs (line,; p a r a l M t~) the tiine axis) will
Discussion The main features of the phenomena considered refer to the multiheadod structure of detonations as the only stable flow pattern. There is no 'classical' shock chemical reaction zone in pressure anti density records. A sketch of real
2 2r
2r i
,
"3" i i
1
~,
15 I"u4urc
I i
13.
lnl, r?r,,tut~on
i i
,
,,f a m u l t i h c a d t , d
~,',.tvc s t v u c t ' ~ r c :
\
(li
arras
of the
prZm.~ry [a.st tA,n,'tiun; (2j a~t~t (2') gradu,dlv i,,,al
sll~ck ct,nliguratuJlls is stioxvn 9 ir~ Figure 13. The /2as is c,mlinuously lmrnt in an.as (1) inimediately after the priniary ccmipression as well :is ili tlie tratlsvt.rse ~v:tves (3) after the sec~mdarv c,mipressions. The wave areas like (2) and t2'.~ a r e the grad,ially weakened r;hocks arisin~ fnm, the c~llisions of two waves (3). The areas (4) i,ctxv~.,.n t2') , n d the' |t:u:le trolit contain s~mac [)tlrti~tilS (if illibllrllt C ~ l l l l)Ic~%('d ~,ls \vht.r~.
int~.r.~ect the traces of the transveis~, ~:~nn])rcssi(,ll w:tx'cs in burnt gas:' without fail after a timt interval of the order of t - a e - . . - 1 0 ~' s,,c. where a i.-, a mezm distance, t)~.l~v,.cn tl~t~ t r a n s verse w:tves, and ~, denotes ~a,v,c v~h~cilv. An additional burnt gas c,~inpressi~m ttl~ls exists i~ these waves, troin p.. ~ 2tl p, t,, p : - - - 4 0 p~, .ace Fia, ure 5(ai and the corrt.st,,n(!in~ l:'il~l,,'r~',--
58
R. L Soloukhin
T;~---2 ~ × ~ 5 0 0 0 ° K in accordance with temperature measurements [Figure 5(c)]. As a result the temperature peaks usually observed in detonation fronts may be explained hydrodynamically and not as due to a chemical phenomenon. Flow patterns in diverging waves differ from those in the ordinary case, on account of the existence of additional pressure and temperature gradients. Some rough calculations9 show that, in a direction perpendicular to incident wave propagation, weak side waves exist. The Math numbers of these waves (M ~_~ 3-5; P2 ---~ 15 :~) may be evaluated by the arbitrary discontinuity break-up method. The product state behind ordinary detonations should be chosen as the high pressure gas conditions. Pressure decrease in the side areas of the detonation front leads to the attenuation of the t~nsverse w ryes. Having no collisions with oppositely directed waves transverse shocks cannot support the multiheaded mechanism of ignition and a destruction of the detonation as a whole may be observed [Figure I 1 (a) ]. It should be noted as an experimental fact that a 'critical' number of transverse one-directional waves related to the channel size or the tube diameter is about 10 or 13 in C2H2+O~ for flat channels and tubes respectively.
Vol. 10
Condusion R should be stated in conclusion that in the experiments a universai character of the stable multiheaded spin mechanism in gaseous detonations was established. Some general features of the parameter distributions in detonation waves as a, whole were considered although the complete theoretical scheme of this non-stationary process is still too complicated. It seems to be satisfactorily established that the ignition kinetic data presented are in good agreement with the hydrodynamic aspect of the flow patterns.
References x HOR~IG, D. F. 11epr. Frick Chem. Lab. Princeton Univ., X I I Solv. Congr., Brussels, 1962 WHITE, D. R. Physics of Fl~c~d~, 1961, 4, 465 3 SOLOUKHIN, R. I. Izvest. A~ad. Nauk S.S.S.R., Otdel. tekh. Nauk (Mechanika), 1959, 6, 145 4 SOLOUKHIN, R. I. Shock Waves and Detonation in Gases. Fizmatgiz: Moscow, 1963; see also: Soviet Phys. Usp. 1964, 6, 523 5 SOLOUKHL~, R. I. Combustion and Explosion Problems. Ed. Akad. Nauk S.S.S.R. (Sib. Div.), 1965, No. 1, 112 6 W H I T e , D. R. Physics of Fluids, 1961, 4, 40 7 KISTIAKOWSKY, G. W.
and
RICHARDS, L.
W.
J. chem. Phys. 1962, 36, 1707 s MXTROFA.~OV, V. V. Prikl. mech. tekh. Fiz. 1962, No. 4 100 9 MITRCDFANOV, V. V. and SOLOUKHIN~ R. I. Dokl.
Akad Nauk S.S.S.R. 1964, 159, 1~1o. 5, 1003