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Brightness temperature of detonation wave in liquid explosives
A c t a Astronautica.
Vol. 3, pp. 555-566. Pergamon Press 1976. Printed in the U.S.A.
Brightness temperature o[ detonation wave in liquid expiosivest~ P. A. U R T I E W Lawrence Livermore Laboratory, University of California, Livermore, CA 94550, U.S.A. (Received 5 September 1975; revised 18 November 1975) Abstract--An optical technique for measuring thermal radiation off hot surfaces has been used to measure the brightness temperatures of the detonation waves in some liquid explosives. Nitromethane, tetranitromethane, and hydrazine--hydrazine-nitrate solutions have been used as the testing liquids. Comparison of our nitromethane data with data reported in the literature reveals good agreement. This good agreement leads us to the conclusion that this technique may be applicable to other, more sophisticated, explosives for which experimental data are not available. The possible effect of the nonuniform structure of the wave is discussed, and an estimate is made of the error that may result from the nonuniform distribution of temperature. Introduction
IN ORDER TO understand fully the p h e n o m e n o n of detonative combustion in condensed high explosives, it is important to k n o w both the pressure and the temperature under which such a detonative process takes place. The temperature m a y be of even greater importance in describing the chemistry associated with the combustion in which a fully developed detonation wave occupies a very narrow region. Yet, the temperature is the only parameter that does not yield itself readily to an experimental measurement. The detonation temperatures of condensed explosives are calculated values obtained by various equation of state schemes.§ Experimental values are very scarce and, for most explosives, nonexistent. Initial attempts to measure the temperature of detonation in high explosives are made by Gibson et al. in 1958, followed by a group of Russian investigators in 1960 (Voskoboinikov and Apin, 1960). Although unpublished but referenced by Mader in 1961, Davis has measured the brightness temperature of several liquid explosives. Burton and Hicks in 1964 made an attempt to resolve the true temperature of some liquid explosives by taking into account the emissivity of the detonation front. The emissive spectrum of detonation in nitromethane (NM) was also investigated by Dremin and Savrov in 1965 and again by Trofimov and T r o y a n in 1969. Persson and Sj61in (1972) investigated the onset of detonation in N M and measured the temperature of the wave while still in the precompressed region behind the shock. They also measured the temperature of the overdriven state as it emerged from behind the initial shock. Their measurements were made relative to the steady state values for which they accepted those of Gibson et al. tPaper presented at the Fifth Colloquium on Gasdynamics of Explosions and Reactive Systems, Bourges, France, 8--11 September 1975. :~Work performed under the auspices of the U.S. Energy Research and Development Administration. §see Mader (1963), Cheret (1971) and Hardesty and Lysne (1974). 555
556
P, A. Urtiew
Most m e a s u r e m e n t s of t e m p e r a t u r e have been made with NM as the liquid explosive. The values r e c o r d e d in the literature f r o m both theoretical calculations and experimental m e a s u r e m e n t s v a r y b y as m u c h as 900 K, varying b e t w e e n 2960 and 3800 K. It is felt that additional m e a s u r e m e n t s are needed to resolve the p r o b l e m and to s u p p l e m e n t the available information by a different technique. The p u r p o s e of this p a p e r is to present such a s u p p l e m e n t a r y information on N M and provide new information on certain other liquid explosives and to describe the technique, which in some respects is less c o m p l e x than the techniques used b y others. The simplification should allow adaptalion to e x p e r i m e n t s on a m o r e general class of explosives.
Experiment M e a s u r e m e n t of t e m p e r a t u r e in dynamic processes, such as shock or detonation, is hindered b y the e x t r e m e l y fast rates and high pressure amplitudes. Consequently, any "in c o n t a c t " measuring techniques can be rejected because of their r e s p o n s e and inability to withstand the high pressure of their surroundings. A logical alternative to an "in c o n t a c t " technique is the optical technique where one m e a s u r e s the a m o u n t of thermal radiation that is emitted f r o m the radiating surface. The surface m a y be that of a shock heated b o d y or the detonation front, itself. This technique represents a modification of a previously d e v e l o p e d s y s t e m described elsewhere (Urtiew and G r o v e r , 1973). The technique was used to m e a s u r e the brightness t e m p e r a t u r e of shock heated solids. The main features of the present e x p e r i m e n t are illustrated in Fig. 1. The container for the explosive under investigation consists of a stainless steel tube divided into two parts b y a 25 ~m-thick aluminized Mylar film.t The film is used to p r e v e n t the light sensitive element f r o m detecting detonation front radiation b e f o r e the detonation w a v e enters the u p p e r chamber. The liquid is poured into the container through the filler tube, and a small b y p a s s and vent assure that both lower and u p p e r c h a m b e r s are filled without air p o c k e t s or bubbles forming. A conventional d e t o n a t o r - H E l e n s - b o o s t e r a s s e m b l y initiates detonation of the liquid explosive. A 0.254 m m thick stainless steel foil separates the liquid explosive f r o m the T N T booster. The total length of the lower c h a m b e r is a p p r o x i m a t e l y 15 cm, which is sufficient for the detonation w a v e to b e c o m e well-established and to r e a c h its steady state velocity. The upper c h a m b e r contains a p h o t o d e t e c t o r (a simple silicon diffused photodiode); a n a r r o w - b a n d interference filter; an aperture of particular size; and a quartz window, which not only serves as a protective shield for the other c o m p o n e n t s of the gauge but also as an additional diagnostic for the w a v e velocity. It provides an interface at which the light signal suffers a slight change, yielding an accurate record of the transit time of the w a v e through the u p p e r chamber. The velocity of the w a v e just prior to its impact upon the Mylar film is m e a s u r e d b y a set of time-of-arrival pins
tReference to a company or product name does not imply approval or recommendation of the product by the University of California or the U.S. Energy Research and Development Administration to the exclusion of others that may be suitable.
557
Brightness temperature of detonation wave in liquid explosives
]I
Detailsof A- A
I
I I l e A l ~M
[
~
PF~rdetector
erture
~-----Quartzwindow l ~ A l u m i n i z e d mylarfilm
U Time - of arrival pins
"Temperature gauge"
Stainless steel tube Filler tube Booster~
~
P-40lens
Fig.1.Diagramof
,
o
~
experimental system, which consists of stainless steel tube filled with explosive liquid and "temperature gauge" on top of tube (details of temperature shown in insert).
gauge
(BaTiO3), which are located 1 and 6 mm below the film plane. These pins also provide the necessary trigger to the oscilloscopes. The theory for such an optical technique and the calibration of the gauge are described elsewhere (Urtiew, 1973). The experiments were performed with NM, tetranitromethane (TNM), and three hydrazine--hydrazine-nitrate compositions. Most of the tests were done using a near IR filter (0.9/~m). The photodetector has a maximum sensitivity in this region. All the investigated liquids are transparent in this range, and there should be no unforeseen absorption ahead of the detonation front.
558
P.A. Urtiew
Analysis
Typical oscilloscope records are shown in Fig. 2. The (a),(b), and (c) records represent, respectively, the intensity of radiation crnitted from the detonation front in N M , T N M , and a 21/79 hydrazine---hydrazine-nitratc solution ( H / H N L Although the records show variation of the response at the interfaces, as the detonation wave travels between the two boundaries of the upper chamber, the intensity actually remains nearly constant. The analysis is carried out on a time-space diagram where the history of the wave travel is determined through correlation of various times. Such a composite diagram is illustratedin Fig. 3. The geometry of the test chamber is shown to scale so that its ccnterline serves as the space axis for the plot. The time scale is plotted to the scale of the experimental record. Setting the origin of the plot at the firstpin below the Mylar film, wc can trace the history of the wave as it propagates through the system. The slope of the line in the time-space plane determines the velocity of the wave. In all cases investigated so far with N M , these values corresponded to the velocity of a fully developed detonation wave differingfrom its theoretical value by less than 2%. For the particular case shown in Fig. 3, the velocity of the wave
i
i
,
2
.... .......
(a)
L_L_a
[ ', .... (b)
"
i
i
r- ~- ~ =,,
-
~
"7
......t ~~
i
i
-
(c) Fig. 2. Typical oscilloscope records of intensity with same vertical scale of 1 V/cm and same horizontal scale of 0.5/~sec/cm.
Brightness temperature of detonation wave in liquid explosioes
559
todetector
'°I
z
~ 30
~ explosive I ~ ~AI-Mylar ! 10 Pin
2f~'~]
Pin l / ~
0
I (c)
2
3
4
Time - us
Fig. 3. Composite diagram showing typical results obtained with nitromethane: cross section of "temperature gauge" which corresponds to A-A in Fig. 1, time-space plot of detonation wave, time resolution of intensity in volts, and time resolution of temperature in K.
travelling through NM is 6.20 mm//~sec, as compared to 6.33 mm/~sec accepted to be the true C-J detonation velocity. The initial overshoot is of little significance for the purpose of measuring temperature. It may be a subject for further investigation of the wave interaction with the Mylar film. The rise time of the signal is of the order of 40 nsec as limited by the response of the electronic circuit following the detector. Based on the assumption that the radiating front is a blackbody, the transformation from the intensity record to brightness temperature is accom-
560
P . A . Urtiew
plished through a simple relation: T=~--
+ln~-lnh
(1)
where h is the experimental value of intensity in volts; A is the wavelength in/xm; c2 is the second radiation constant 14,387 ttmK; To is the temperature of the reference radiatior, in this case 3800 K, the temperature of the carbon arc light source; and ~ is the constant determined during the calibration of the gauge (Urtiew, 1973). The brightness temperature of the wave analyzed in Fig. 3 is also shown in that same figure below the intensity record. Since all the experiments were performed with a single interference filter (i.e. at one wavelength of the optical spectrum), the temperature that is deduced from such an experiment represents only the brightness temperature of the wave, and it may or may not correspond to the true temperature of the wave front. The obstacle here is the emissivity, which for most of the explosives is unknown. One of the reasons for making tests with NM, which has been tested many times by others, is the fact that some work has been reported on its emissivity. Although Dremin and Savrov (1965) have indicated that in the spectral range of their investigation (0.4 < )t <0.6), emissivity is not unity and is wavelengthdependent. Burton and Hicks (1964), as well as Trofimov and Troyan (1969), operating in almost the same spectral range, came to the conclusion that radiation emanating from the detonation front is very nearly the same as that from a blackbody. However, if one were to extrapolate Dremin's results into the near IR, where our investigation was carried out, they too seem to support the assumption of the blackbody radiation. To observe the spectral effect on the detonation temperature of NM, several experiments were performed with ?t = 0.6, 0.7, 0.8, and 0.9/zm. The results are shown in Fig. 4 where the brightness temperature is plotted vs the wavelength. Arrows on the right indicate the results of other investigators without reference to any particular wavelength. It is quite evident from this figure that the brightness temperature is somewhat wavelength-dependent, and at shorter wavelengths it is higher. If we are to take emissivity into account, the temperature would be still higher. Disregarding the visible part of the spectrum, however, and taking only the near IR where all indications are that emissivity is close to unity, the results seem to agree quite well with those of Mader (1961) and Burton and Hicks (1964). Theoretical calculations differ immensely depending on the equation-of-state scheme used for that purpose. As illustrated by Lee (1975), the LJD and BKW schemes offer the two extremes, while the JCZ3 yields a result closer to the experimental values. Included in Fig. 4 are other theoretical values which fall below, and above those determined experimentally. The results of TNM and hydrazine---hydrazine-nitrate solutions together with NM are given in Table 1. Also included are the detonation velocities and comparable values from other sources. Measurements were made with only one interference filter of 0.9 ttm. No data are available on the emissivity of these explosives; therefore, no estimate of deviation from the true temperature could be
Brightness temperature of detonation wave in liquid explosives
l
I
I
l
References Gibson et a l . , 1958 (F) Lee ( L J D - ~ ,1975 (T) Hardesty and Lysne, 1974 (T) Trofimov and ~Troyan, 1969 (E) Hardesty and ~Lysne, 1974 (T) Lee (JCZ3), 1975 (T) Mader, ]961; Burton and Hicks, 1964 (E)
3.5
l
÷
o
561
÷
--m m
3.0
Cheret, 1971 (T) \Voskoboinikov and Apin, 1960 (E) Mader, 1961 (T) Lee (BKW), 1975 (T)
0.6
0.7
0.8 -
0.9
um
Fig. 4. Brightness temperatures of detonation wave in nitromethane as deduced from measurements at different parts of optical spectrum.
made. Of interest here is that the experiments with hydrazine-hydrazine-nitrate solutions yielded a higher detonation temperature than originally predicted, h o w e v e r , no explanations of these results can be offered at this time. Effect of wave structure While there is a definite concern over the emissivity of the w a v e front, an error m a y also result from a nonuniform distribution of temperature across the w a v e front due to its structural peculiarities that have been s h o w n to exist in N M detonations (Urtiew and K u s u b o v , 1972). T h e s e structural peculiarities are believed to be the unique feature of all liquid detonations (Urtiew, 1975). Since the temperature is deduced from the e m i s s i v e p o w e r of radiation, the average temperature will depend on the spectral range in which this observation is made. If the p o w e r distribution across the w a v e front is expressed as P ( x ) , the average p o w e r deduced from the experiment is the integral of such distribution taken over the w h o l e area. The e m i s s i v e p o w e r of radiation is expressed by Planck's radiation law: C2
--1
(2) and is dependent on both wavelength and temperature. H o w e v e r , w h e n narrow-band interference filters are within the range where exp (cdAT)>> 1, the e m i s s i v e p o w e r at an u n k n o w n temperature can be normalized by that o f a k n o w n
100
100
100
NM
NM
NM
E--Experimental. T--Theoretical.
100 100 100 100 100 100
NM NM NM NM NM NM
5.9/70/24.1
70/30
H/HN
H/HN/H20
100 100 100 21/79
Composition (%)
TNM TNM TNM H/HN
Explosive liquid
1.13
1.13
1.13
1.13 1.13 1.13 1.13 1.13 1.13
1.384
1.135
1.64 1.64 1.64 1.421
6.20
6.20
6.20
6.20 6.20 6.20 6.20 6.20 6,20
7.775
8.025
6.36 6.36 6.36 8.600
Density(g/cc) Present
--
--
6.4
6.36 5.741 6.055 8.82 8.58 8.89 7.87 8.14 7.48 6.29 6.87 6.353 -6.29 --
Other
--
Voskoboinikov and Apin, 1960 (E) --
Mader, 1963 (E) Mader, 1963 (T) Fickett, 1962 (T) Lee, 1975 (T) Finger, 1974 (E) Lee, 1975 (T) Finger, 1974 (E) Lee, 1975 (T) Finger, 1974 (E) Mader, 1961 (E) Mader, 1961 (T) Fickett, 1962 (T) -Cheret, 1971 (T) --
Reference
Detonation velocity (mm/p.sec)
3300
3300
3300
3300 3300 3300 3300 3300 3300
4000
2180
2840 2840 2840 2900
Mader, 1963 (E) Mader, 1963 (T) Fickett, 1962 (T) Lee, 1975 (T)
Reference
Mader, 1961 (T) Mader, 1961 (T) Fickett, 1962 (T) Gibson et al. 1958 (E) Cheret, 1971 (T) Hardesty and Lysne, 1974 (T) Voskoboinikov and Apin, 1960 (E) 3380 Burton and Hicks 1964 (E) 3600 Trofimov and Troyan, 1969 (E)
3380 2960 3803 3800 3136 3544 3700 3100
1123 Lee, 1975 (T)
1863 Lee, 1975 (T)
2800 1621 2442 1681
Present Other
Detonation temperature (K)
Table 1. Temperatures and velocities of detonation wave in nitromethane, tetranitromethane and hydrazine__hydrazine_ nitrate solutions
>
Brightnesstemperatureo/ detonationwavein liquidexplosives
563
o n e to obtain: P~T
[~2
1
1
T h e e x p r e s s i o n for the average p o w e r o f radiation can be written in the f o l l o w i n g integral form: a,v = ~
a (x) dx,
(4)
w h e r e L stands for a fixed length o f a half c y c l e o f temperature distribution. Substituting for oe its equivalent f o r m o f eqn (3), w e obtain: ,
or further simplified,
T.__~_To AT°ln{l foLexp[-)t;ix)Jdx} [
r
I
I
I
(5)
I
[
Tmi n : 2000 K
2.0
~
Tmi n : 3000 K
.} 0.6 1.5
:I
E
o.5
b--
0.3 0.2 1.0 6
Tmax - Tmi n T max
;7
I 0.4
0.5
I
1
I
I
I
0.6
0.7
0.8
O.g
1.0
~.
-
I l.l
~m
Fig. 5. Effective spectral temperatures as obtained from nonuniform radiation; results of integration of eqn (6) with temperature distribution of eqn (5).
564
P . A . Urtiew
This expression then represents the average temperature that we would get from a nonuniform distribution T(x) with a known temperature, To. For the purpose of illustration, let us assume an idealized temperature distribution:
T(x) = Tmi.(l - 8Lx ) -' ,
(6)
where: Train = To
and 8=
T m x - T~n Tm~x
The results of integrating eqn (5) with the chosen temperature distribution are shown in Fig. 5 where we can see the effect of 8, A, and T~o on the overall spectral temperature, T~. The most significant effect is seen to occur at shorter wavelength and with larger values of 8 that stand for larger peak temperatures. For a
L
T
2.0
F- ....... ~ . . . . . . 7
r
~- - - - -
Tmin = 2000 K --~
-~
min = 3000 K
= 0.9 ~m
/
/
/ 1.5
/
-
/
/
/ /
--
1.0
f
J ~,
7 I 0.I
I "0.2
I 0.3
t - 0.4
--
1
l
0.5
0.6
~_.J 0.7
Fig. 6. Effect of 8 on average t e m p e r a t u r e w h e n m e a s u r e d at A = 0.9/~m.
Brightness temperature of detonation wave in liquid explosives
565
particular wavelength, A = 0.9/xm, the effect of T~n and 8 is illustrated in Fig. 6. This distribution is chosen only for its mathematical simplicity, it is nevertheless a very realistic one considering the effects of a possible nonuniformity due to the cellular structure of the wave front. Of course, here we are dealing with the fully developed detonation whose cellular structure is so fine that it has not yet been observed experimentally. Such a fine structure suggests very fast changes within each individual cell that would tend to dampen the amplitudes of fluctuations in pressure and therefore in temperature, also. Thus, the temperature deduced from these records should represent an average of the spread of not more than 200 K; this spread leads to an uncertainty of less than 3%.
Summary As pointed out earlier, the temperature of detonation and other dynamic systems does not yield itself readily to an experimental measurement. The system just described is by no means perfect and b e y o n d question. The problem of emissivity remains unresolved although on the basis of investigations with NM we can stipulate that detonation waves emit blackbody radiation. The nonuniform heating also may be present, and if so it may have some effect on the results. H o w e v e r , comparison of results with those already available in the literature is encouraging. The technique is relatively simple and for that reason m a y be easily adapted to other liquid explosives that have not been investigated. Acknowledgements--The author wishes to thank E. L. Lee, M. Finger, and B. Hayes for many discussions on the subject; K. V. Fordyce for preparations of proper explosive solutions; and J. D. Longwith for his technical assistance in building shots and performing the experiments.
References Burton, J. T. A. and Hicks, J. A. (1964) Detonation emissivities and temperatures in some liquid explosives, Nature (Lond.) 202, 758-759. Cheret, R. (1971) Contribution a l'etude numerique des produits de detonation d'une substance explosive, Commissariat a L'Energie Atomique, Rapport CEA-R-4122, GIF-sur-YVETTE, France. Dremin, A. N. and Savrov, S. D. (1965) Emission spectrum of a detonation wave in nitromethane, Zh. prikl. Mekh. tekh. Fiz. 1, 103-105. Fickett, W. (1962) Detonation properties of condensed explosives calculated with an equation of state based on intermolecular potentials, Los Alamos Scientific Laboratory, Los Alamos, N. Mex., Report LA 2712. Finger, M. (1974) Lawrence Livermore Laboratory, Livermore, Calif., Private communication. Gibson, F. C., Bowser, M. L., Summers, C. R., Scott, F. H. and Mason, C. M. (1958) Use of an electro-optical method to determine detonation temperature in high explosives, J. appl. Phys. 29, 628-632. Hardesty, D. R. and Lysne, P. C. (1974) Shock initiation and detonation properties of homogeneous explosives, Sandia Laboratories, Alburquerque, N. Mex., Report SLA 74-0165. Lee, E. L. (1975) Lawrence Livermore Laboratory, Livermore, Calif., Private communication. Mader, C. L. (1961) Detonation performance calculations using the Kistiakowsky-Wilson equation of state, Los Alamos Scientific Laboratory, Los Alamos, N. Mex., Report LA-2613. Mader, C. L. (1963) Detonation properties of condensed explosives computed using the BeckerKistiakowsky-Wilson equation of state, Los Alamos Scientific Laboratory, Los Alamos, N. Mex., Report LA-2900.
566
P~ A. Urtiew
Persson, P. A. and Sj61in, T. (1972) Light emission during initiation of liquid explosives, in Fifth Symposium (International) on Detonation, pp. 153-168, ONR, Dept. of the Navy, Arlington, Va. Trofimov, V. S. and Troyan, A. V. (1969) Luminescence spectrum of nitromethane detonation, Fizika Gorenia i Vzryva 5(2), 280-282. Urtiew, P. A. (1973) Phenomenological survey of experimental determination of temperature of shock-heated solids, Lawrence Livermore Laboratory, Livermore, Calif., Report UCRL-51432. Urtiew, P. A. (1975) From cellular structure to failure waves in liquid detonations, Comb. and Flame 25(2), 241-245. Urtiew, P. A. and Kusubov, A. S. (1972) Wall traces of detonation in nitromethane-acetone mixtures, in Fifth Symposium (International) on Detonation, pp. 105-113, ONR, Dept. of the Navy, Arlington, Va. Urtiew, P. A. and Grover, R. (1973) Radiation temperature in solids under shock loading, in Fifth Symposium (International) on Temperature, pp. 677-684, National Bureau of Standards, Washington, D. C. Voskoboinikov, I. M. and Apin, A. Ya. (1960) The measurement of detonation front temperatures for explosives, Dokl. Akad. Nauk SSSR 130, 804-806.
Vol. 3, pp. 555-566. Pergamon Press 1976. Printed in the U.S.A.
Brightness temperature o[ detonation wave in liquid expiosivest~ P. A. U R T I E W Lawrence Livermore Laboratory, University of California, Livermore, CA 94550, U.S.A. (Received 5 September 1975; revised 18 November 1975) Abstract--An optical technique for measuring thermal radiation off hot surfaces has been used to measure the brightness temperatures of the detonation waves in some liquid explosives. Nitromethane, tetranitromethane, and hydrazine--hydrazine-nitrate solutions have been used as the testing liquids. Comparison of our nitromethane data with data reported in the literature reveals good agreement. This good agreement leads us to the conclusion that this technique may be applicable to other, more sophisticated, explosives for which experimental data are not available. The possible effect of the nonuniform structure of the wave is discussed, and an estimate is made of the error that may result from the nonuniform distribution of temperature. Introduction
IN ORDER TO understand fully the p h e n o m e n o n of detonative combustion in condensed high explosives, it is important to k n o w both the pressure and the temperature under which such a detonative process takes place. The temperature m a y be of even greater importance in describing the chemistry associated with the combustion in which a fully developed detonation wave occupies a very narrow region. Yet, the temperature is the only parameter that does not yield itself readily to an experimental measurement. The detonation temperatures of condensed explosives are calculated values obtained by various equation of state schemes.§ Experimental values are very scarce and, for most explosives, nonexistent. Initial attempts to measure the temperature of detonation in high explosives are made by Gibson et al. in 1958, followed by a group of Russian investigators in 1960 (Voskoboinikov and Apin, 1960). Although unpublished but referenced by Mader in 1961, Davis has measured the brightness temperature of several liquid explosives. Burton and Hicks in 1964 made an attempt to resolve the true temperature of some liquid explosives by taking into account the emissivity of the detonation front. The emissive spectrum of detonation in nitromethane (NM) was also investigated by Dremin and Savrov in 1965 and again by Trofimov and T r o y a n in 1969. Persson and Sj61in (1972) investigated the onset of detonation in N M and measured the temperature of the wave while still in the precompressed region behind the shock. They also measured the temperature of the overdriven state as it emerged from behind the initial shock. Their measurements were made relative to the steady state values for which they accepted those of Gibson et al. tPaper presented at the Fifth Colloquium on Gasdynamics of Explosions and Reactive Systems, Bourges, France, 8--11 September 1975. :~Work performed under the auspices of the U.S. Energy Research and Development Administration. §see Mader (1963), Cheret (1971) and Hardesty and Lysne (1974). 555
556
P, A. Urtiew
Most m e a s u r e m e n t s of t e m p e r a t u r e have been made with NM as the liquid explosive. The values r e c o r d e d in the literature f r o m both theoretical calculations and experimental m e a s u r e m e n t s v a r y b y as m u c h as 900 K, varying b e t w e e n 2960 and 3800 K. It is felt that additional m e a s u r e m e n t s are needed to resolve the p r o b l e m and to s u p p l e m e n t the available information by a different technique. The p u r p o s e of this p a p e r is to present such a s u p p l e m e n t a r y information on N M and provide new information on certain other liquid explosives and to describe the technique, which in some respects is less c o m p l e x than the techniques used b y others. The simplification should allow adaptalion to e x p e r i m e n t s on a m o r e general class of explosives.
Experiment M e a s u r e m e n t of t e m p e r a t u r e in dynamic processes, such as shock or detonation, is hindered b y the e x t r e m e l y fast rates and high pressure amplitudes. Consequently, any "in c o n t a c t " measuring techniques can be rejected because of their r e s p o n s e and inability to withstand the high pressure of their surroundings. A logical alternative to an "in c o n t a c t " technique is the optical technique where one m e a s u r e s the a m o u n t of thermal radiation that is emitted f r o m the radiating surface. The surface m a y be that of a shock heated b o d y or the detonation front, itself. This technique represents a modification of a previously d e v e l o p e d s y s t e m described elsewhere (Urtiew and G r o v e r , 1973). The technique was used to m e a s u r e the brightness t e m p e r a t u r e of shock heated solids. The main features of the present e x p e r i m e n t are illustrated in Fig. 1. The container for the explosive under investigation consists of a stainless steel tube divided into two parts b y a 25 ~m-thick aluminized Mylar film.t The film is used to p r e v e n t the light sensitive element f r o m detecting detonation front radiation b e f o r e the detonation w a v e enters the u p p e r chamber. The liquid is poured into the container through the filler tube, and a small b y p a s s and vent assure that both lower and u p p e r c h a m b e r s are filled without air p o c k e t s or bubbles forming. A conventional d e t o n a t o r - H E l e n s - b o o s t e r a s s e m b l y initiates detonation of the liquid explosive. A 0.254 m m thick stainless steel foil separates the liquid explosive f r o m the T N T booster. The total length of the lower c h a m b e r is a p p r o x i m a t e l y 15 cm, which is sufficient for the detonation w a v e to b e c o m e well-established and to r e a c h its steady state velocity. The upper c h a m b e r contains a p h o t o d e t e c t o r (a simple silicon diffused photodiode); a n a r r o w - b a n d interference filter; an aperture of particular size; and a quartz window, which not only serves as a protective shield for the other c o m p o n e n t s of the gauge but also as an additional diagnostic for the w a v e velocity. It provides an interface at which the light signal suffers a slight change, yielding an accurate record of the transit time of the w a v e through the u p p e r chamber. The velocity of the w a v e just prior to its impact upon the Mylar film is m e a s u r e d b y a set of time-of-arrival pins
tReference to a company or product name does not imply approval or recommendation of the product by the University of California or the U.S. Energy Research and Development Administration to the exclusion of others that may be suitable.
557
Brightness temperature of detonation wave in liquid explosives
]I
Detailsof A- A
I
I I l e A l ~M
[
~
PF~rdetector
erture
~-----Quartzwindow l ~ A l u m i n i z e d mylarfilm
U Time - of arrival pins
"Temperature gauge"
Stainless steel tube Filler tube Booster~
~
P-40lens
Fig.1.Diagramof
,
o
~
experimental system, which consists of stainless steel tube filled with explosive liquid and "temperature gauge" on top of tube (details of temperature shown in insert).
gauge
(BaTiO3), which are located 1 and 6 mm below the film plane. These pins also provide the necessary trigger to the oscilloscopes. The theory for such an optical technique and the calibration of the gauge are described elsewhere (Urtiew, 1973). The experiments were performed with NM, tetranitromethane (TNM), and three hydrazine--hydrazine-nitrate compositions. Most of the tests were done using a near IR filter (0.9/~m). The photodetector has a maximum sensitivity in this region. All the investigated liquids are transparent in this range, and there should be no unforeseen absorption ahead of the detonation front.
558
P.A. Urtiew
Analysis
Typical oscilloscope records are shown in Fig. 2. The (a),(b), and (c) records represent, respectively, the intensity of radiation crnitted from the detonation front in N M , T N M , and a 21/79 hydrazine---hydrazine-nitratc solution ( H / H N L Although the records show variation of the response at the interfaces, as the detonation wave travels between the two boundaries of the upper chamber, the intensity actually remains nearly constant. The analysis is carried out on a time-space diagram where the history of the wave travel is determined through correlation of various times. Such a composite diagram is illustratedin Fig. 3. The geometry of the test chamber is shown to scale so that its ccnterline serves as the space axis for the plot. The time scale is plotted to the scale of the experimental record. Setting the origin of the plot at the firstpin below the Mylar film, wc can trace the history of the wave as it propagates through the system. The slope of the line in the time-space plane determines the velocity of the wave. In all cases investigated so far with N M , these values corresponded to the velocity of a fully developed detonation wave differingfrom its theoretical value by less than 2%. For the particular case shown in Fig. 3, the velocity of the wave
i
i
,
2
.... .......
(a)
L_L_a
[ ', .... (b)
"
i
i
r- ~- ~ =,,
-
~
"7
......t ~~
i
i
-
(c) Fig. 2. Typical oscilloscope records of intensity with same vertical scale of 1 V/cm and same horizontal scale of 0.5/~sec/cm.
Brightness temperature of detonation wave in liquid explosioes
559
todetector
'°I
z
~ 30
~ explosive I ~ ~AI-Mylar ! 10 Pin
2f~'~]
Pin l / ~
0
I (c)
2
3
4
Time - us
Fig. 3. Composite diagram showing typical results obtained with nitromethane: cross section of "temperature gauge" which corresponds to A-A in Fig. 1, time-space plot of detonation wave, time resolution of intensity in volts, and time resolution of temperature in K.
travelling through NM is 6.20 mm//~sec, as compared to 6.33 mm/~sec accepted to be the true C-J detonation velocity. The initial overshoot is of little significance for the purpose of measuring temperature. It may be a subject for further investigation of the wave interaction with the Mylar film. The rise time of the signal is of the order of 40 nsec as limited by the response of the electronic circuit following the detector. Based on the assumption that the radiating front is a blackbody, the transformation from the intensity record to brightness temperature is accom-
560
P . A . Urtiew
plished through a simple relation: T=~--
+ln~-lnh
(1)
where h is the experimental value of intensity in volts; A is the wavelength in/xm; c2 is the second radiation constant 14,387 ttmK; To is the temperature of the reference radiatior, in this case 3800 K, the temperature of the carbon arc light source; and ~ is the constant determined during the calibration of the gauge (Urtiew, 1973). The brightness temperature of the wave analyzed in Fig. 3 is also shown in that same figure below the intensity record. Since all the experiments were performed with a single interference filter (i.e. at one wavelength of the optical spectrum), the temperature that is deduced from such an experiment represents only the brightness temperature of the wave, and it may or may not correspond to the true temperature of the wave front. The obstacle here is the emissivity, which for most of the explosives is unknown. One of the reasons for making tests with NM, which has been tested many times by others, is the fact that some work has been reported on its emissivity. Although Dremin and Savrov (1965) have indicated that in the spectral range of their investigation (0.4 < )t <0.6), emissivity is not unity and is wavelengthdependent. Burton and Hicks (1964), as well as Trofimov and Troyan (1969), operating in almost the same spectral range, came to the conclusion that radiation emanating from the detonation front is very nearly the same as that from a blackbody. However, if one were to extrapolate Dremin's results into the near IR, where our investigation was carried out, they too seem to support the assumption of the blackbody radiation. To observe the spectral effect on the detonation temperature of NM, several experiments were performed with ?t = 0.6, 0.7, 0.8, and 0.9/zm. The results are shown in Fig. 4 where the brightness temperature is plotted vs the wavelength. Arrows on the right indicate the results of other investigators without reference to any particular wavelength. It is quite evident from this figure that the brightness temperature is somewhat wavelength-dependent, and at shorter wavelengths it is higher. If we are to take emissivity into account, the temperature would be still higher. Disregarding the visible part of the spectrum, however, and taking only the near IR where all indications are that emissivity is close to unity, the results seem to agree quite well with those of Mader (1961) and Burton and Hicks (1964). Theoretical calculations differ immensely depending on the equation-of-state scheme used for that purpose. As illustrated by Lee (1975), the LJD and BKW schemes offer the two extremes, while the JCZ3 yields a result closer to the experimental values. Included in Fig. 4 are other theoretical values which fall below, and above those determined experimentally. The results of TNM and hydrazine---hydrazine-nitrate solutions together with NM are given in Table 1. Also included are the detonation velocities and comparable values from other sources. Measurements were made with only one interference filter of 0.9 ttm. No data are available on the emissivity of these explosives; therefore, no estimate of deviation from the true temperature could be
Brightness temperature of detonation wave in liquid explosives
l
I
I
l
References Gibson et a l . , 1958 (F) Lee ( L J D - ~ ,1975 (T) Hardesty and Lysne, 1974 (T) Trofimov and ~Troyan, 1969 (E) Hardesty and ~Lysne, 1974 (T) Lee (JCZ3), 1975 (T) Mader, ]961; Burton and Hicks, 1964 (E)
3.5
l
÷
o
561
÷
--m m
3.0
Cheret, 1971 (T) \Voskoboinikov and Apin, 1960 (E) Mader, 1961 (T) Lee (BKW), 1975 (T)
0.6
0.7
0.8 -
0.9
um
Fig. 4. Brightness temperatures of detonation wave in nitromethane as deduced from measurements at different parts of optical spectrum.
made. Of interest here is that the experiments with hydrazine-hydrazine-nitrate solutions yielded a higher detonation temperature than originally predicted, h o w e v e r , no explanations of these results can be offered at this time. Effect of wave structure While there is a definite concern over the emissivity of the w a v e front, an error m a y also result from a nonuniform distribution of temperature across the w a v e front due to its structural peculiarities that have been s h o w n to exist in N M detonations (Urtiew and K u s u b o v , 1972). T h e s e structural peculiarities are believed to be the unique feature of all liquid detonations (Urtiew, 1975). Since the temperature is deduced from the e m i s s i v e p o w e r of radiation, the average temperature will depend on the spectral range in which this observation is made. If the p o w e r distribution across the w a v e front is expressed as P ( x ) , the average p o w e r deduced from the experiment is the integral of such distribution taken over the w h o l e area. The e m i s s i v e p o w e r of radiation is expressed by Planck's radiation law: C2
--1
(2) and is dependent on both wavelength and temperature. H o w e v e r , w h e n narrow-band interference filters are within the range where exp (cdAT)>> 1, the e m i s s i v e p o w e r at an u n k n o w n temperature can be normalized by that o f a k n o w n
100
100
100
NM
NM
NM
E--Experimental. T--Theoretical.
100 100 100 100 100 100
NM NM NM NM NM NM
5.9/70/24.1
70/30
H/HN
H/HN/H20
100 100 100 21/79
Composition (%)
TNM TNM TNM H/HN
Explosive liquid
1.13
1.13
1.13
1.13 1.13 1.13 1.13 1.13 1.13
1.384
1.135
1.64 1.64 1.64 1.421
6.20
6.20
6.20
6.20 6.20 6.20 6.20 6.20 6,20
7.775
8.025
6.36 6.36 6.36 8.600
Density(g/cc) Present
--
--
6.4
6.36 5.741 6.055 8.82 8.58 8.89 7.87 8.14 7.48 6.29 6.87 6.353 -6.29 --
Other
--
Voskoboinikov and Apin, 1960 (E) --
Mader, 1963 (E) Mader, 1963 (T) Fickett, 1962 (T) Lee, 1975 (T) Finger, 1974 (E) Lee, 1975 (T) Finger, 1974 (E) Lee, 1975 (T) Finger, 1974 (E) Mader, 1961 (E) Mader, 1961 (T) Fickett, 1962 (T) -Cheret, 1971 (T) --
Reference
Detonation velocity (mm/p.sec)
3300
3300
3300
3300 3300 3300 3300 3300 3300
4000
2180
2840 2840 2840 2900
Mader, 1963 (E) Mader, 1963 (T) Fickett, 1962 (T) Lee, 1975 (T)
Reference
Mader, 1961 (T) Mader, 1961 (T) Fickett, 1962 (T) Gibson et al. 1958 (E) Cheret, 1971 (T) Hardesty and Lysne, 1974 (T) Voskoboinikov and Apin, 1960 (E) 3380 Burton and Hicks 1964 (E) 3600 Trofimov and Troyan, 1969 (E)
3380 2960 3803 3800 3136 3544 3700 3100
1123 Lee, 1975 (T)
1863 Lee, 1975 (T)
2800 1621 2442 1681
Present Other
Detonation temperature (K)
Table 1. Temperatures and velocities of detonation wave in nitromethane, tetranitromethane and hydrazine__hydrazine_ nitrate solutions
>
Brightnesstemperatureo/ detonationwavein liquidexplosives
563
o n e to obtain: P~T
[~2
1
1
T h e e x p r e s s i o n for the average p o w e r o f radiation can be written in the f o l l o w i n g integral form: a,v = ~
a (x) dx,
(4)
w h e r e L stands for a fixed length o f a half c y c l e o f temperature distribution. Substituting for oe its equivalent f o r m o f eqn (3), w e obtain: ,
or further simplified,
T.__~_To AT°ln{l foLexp[-)t;ix)Jdx} [
r
I
I
I
(5)
I
[
Tmi n : 2000 K
2.0
~
Tmi n : 3000 K
.} 0.6 1.5
:I
E
o.5
b--
0.3 0.2 1.0 6
Tmax - Tmi n T max
;7
I 0.4
0.5
I
1
I
I
I
0.6
0.7
0.8
O.g
1.0
~.
-
I l.l
~m
Fig. 5. Effective spectral temperatures as obtained from nonuniform radiation; results of integration of eqn (6) with temperature distribution of eqn (5).
564
P . A . Urtiew
This expression then represents the average temperature that we would get from a nonuniform distribution T(x) with a known temperature, To. For the purpose of illustration, let us assume an idealized temperature distribution:
T(x) = Tmi.(l - 8Lx ) -' ,
(6)
where: Train = To
and 8=
T m x - T~n Tm~x
The results of integrating eqn (5) with the chosen temperature distribution are shown in Fig. 5 where we can see the effect of 8, A, and T~o on the overall spectral temperature, T~. The most significant effect is seen to occur at shorter wavelength and with larger values of 8 that stand for larger peak temperatures. For a
L
T
2.0
F- ....... ~ . . . . . . 7
r
~- - - - -
Tmin = 2000 K --~
-~
min = 3000 K
= 0.9 ~m
/
/
/ 1.5
/
-
/
/
/ /
--
1.0
f
J ~,
7 I 0.I
I "0.2
I 0.3
t - 0.4
--
1
l
0.5
0.6
~_.J 0.7
Fig. 6. Effect of 8 on average t e m p e r a t u r e w h e n m e a s u r e d at A = 0.9/~m.
Brightness temperature of detonation wave in liquid explosives
565
particular wavelength, A = 0.9/xm, the effect of T~n and 8 is illustrated in Fig. 6. This distribution is chosen only for its mathematical simplicity, it is nevertheless a very realistic one considering the effects of a possible nonuniformity due to the cellular structure of the wave front. Of course, here we are dealing with the fully developed detonation whose cellular structure is so fine that it has not yet been observed experimentally. Such a fine structure suggests very fast changes within each individual cell that would tend to dampen the amplitudes of fluctuations in pressure and therefore in temperature, also. Thus, the temperature deduced from these records should represent an average of the spread of not more than 200 K; this spread leads to an uncertainty of less than 3%.
Summary As pointed out earlier, the temperature of detonation and other dynamic systems does not yield itself readily to an experimental measurement. The system just described is by no means perfect and b e y o n d question. The problem of emissivity remains unresolved although on the basis of investigations with NM we can stipulate that detonation waves emit blackbody radiation. The nonuniform heating also may be present, and if so it may have some effect on the results. H o w e v e r , comparison of results with those already available in the literature is encouraging. The technique is relatively simple and for that reason m a y be easily adapted to other liquid explosives that have not been investigated. Acknowledgements--The author wishes to thank E. L. Lee, M. Finger, and B. Hayes for many discussions on the subject; K. V. Fordyce for preparations of proper explosive solutions; and J. D. Longwith for his technical assistance in building shots and performing the experiments.
References Burton, J. T. A. and Hicks, J. A. (1964) Detonation emissivities and temperatures in some liquid explosives, Nature (Lond.) 202, 758-759. Cheret, R. (1971) Contribution a l'etude numerique des produits de detonation d'une substance explosive, Commissariat a L'Energie Atomique, Rapport CEA-R-4122, GIF-sur-YVETTE, France. Dremin, A. N. and Savrov, S. D. (1965) Emission spectrum of a detonation wave in nitromethane, Zh. prikl. Mekh. tekh. Fiz. 1, 103-105. Fickett, W. (1962) Detonation properties of condensed explosives calculated with an equation of state based on intermolecular potentials, Los Alamos Scientific Laboratory, Los Alamos, N. Mex., Report LA 2712. Finger, M. (1974) Lawrence Livermore Laboratory, Livermore, Calif., Private communication. Gibson, F. C., Bowser, M. L., Summers, C. R., Scott, F. H. and Mason, C. M. (1958) Use of an electro-optical method to determine detonation temperature in high explosives, J. appl. Phys. 29, 628-632. Hardesty, D. R. and Lysne, P. C. (1974) Shock initiation and detonation properties of homogeneous explosives, Sandia Laboratories, Alburquerque, N. Mex., Report SLA 74-0165. Lee, E. L. (1975) Lawrence Livermore Laboratory, Livermore, Calif., Private communication. Mader, C. L. (1961) Detonation performance calculations using the Kistiakowsky-Wilson equation of state, Los Alamos Scientific Laboratory, Los Alamos, N. Mex., Report LA-2613. Mader, C. L. (1963) Detonation properties of condensed explosives computed using the BeckerKistiakowsky-Wilson equation of state, Los Alamos Scientific Laboratory, Los Alamos, N. Mex., Report LA-2900.
566
P~ A. Urtiew
Persson, P. A. and Sj61in, T. (1972) Light emission during initiation of liquid explosives, in Fifth Symposium (International) on Detonation, pp. 153-168, ONR, Dept. of the Navy, Arlington, Va. Trofimov, V. S. and Troyan, A. V. (1969) Luminescence spectrum of nitromethane detonation, Fizika Gorenia i Vzryva 5(2), 280-282. Urtiew, P. A. (1973) Phenomenological survey of experimental determination of temperature of shock-heated solids, Lawrence Livermore Laboratory, Livermore, Calif., Report UCRL-51432. Urtiew, P. A. (1975) From cellular structure to failure waves in liquid detonations, Comb. and Flame 25(2), 241-245. Urtiew, P. A. and Kusubov, A. S. (1972) Wall traces of detonation in nitromethane-acetone mixtures, in Fifth Symposium (International) on Detonation, pp. 105-113, ONR, Dept. of the Navy, Arlington, Va. Urtiew, P. A. and Grover, R. (1973) Radiation temperature in solids under shock loading, in Fifth Symposium (International) on Temperature, pp. 677-684, National Bureau of Standards, Washington, D. C. Voskoboinikov, I. M. and Apin, A. Ya. (1960) The measurement of detonation front temperatures for explosives, Dokl. Akad. Nauk SSSR 130, 804-806.