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Structure of gaseous detonation. IV. Induction zone studies in H2-O2 and CO-O2 mixtures
Tenth Symposium (International) on Combustion,
pp. 785--795,
The Combtmtion Institute, 1965
STRUCTURE OF GASEOUS DETONATION. IV. INDUCTION ZONE STUDIES IN H2-O2 AND CO-O~ MIXTURES I)ONALD R. WHITE AND GEORGE E. MOORE General Electric Research Laboratory, Schenectady, New York
The density structure of the flow behind shock waves in H:-02 and in CO-O~ mixtures has been examined interferometrically. In the former case it is shown that the oxygen is vibrationally excited before observable exothermic reaction. At least for very rich mixtures and probably for all mixtures, the hydrogen is also, since the vibrational relaxation time for H2 (as well as for D.~) is found to be less than 2 X 10-e arm see at 1400~ The induction time for exothermic reaction has been measured for 0.0075 G [-]I.,]/[02] < 100 and the data may be fit to better than a factor of two for 2200 :> T :> 1100~ by log~0 ([O2][H2])89 = 3100/T 9.8, where concentrations are in moles/liter and time in seconds. Induction times in 2 H2 -{- 5 Air are also found to be represented by this equation. The observed density profiles in the region of rapid exothermic reaction have been analyzed for a number of very rich and very lean mixtures, assuming heat evolution to be due to threebody recombination processes, and termolecular rate constants of reasonable magnitude have been deduced. In 8 CO -~- O2, it is shown that both reactants become vibrationally equilibrated prior to reaction, and that the vibrational relaxation time is significantly less than for pure CO, implying that vibrational exchange with excited O~ is an important process in excitation of the CO. Addition of up to 1% H~ is shown to reduce the relaxation time and accelerate the reaction, but not to affect the maximum density. With the thinner reaction zone due to added I[2, the detonation is observed to develop spin and to acquire the characteristic "turbulent" appearance due to the transversely propagating shocks behind the main shock front and the consequent shear layers in the flow.
Introduction The density structure of the flcJw behind shock wave in an exothermally reactive medium is found to consist, in general, of at least three regions. Immediately behind the translationrotation shock front, the density increases as energy is transferred into internal degrees of freedom, specifically vibration. Next, in the case of 112-02 mixtures at least, there is an extended nearly-constant-density induction zone at this maximum density (the von-Neuman "spike"), and then the density decreases as heat is released. This paper presents observations of this structure in hydrogen~)xygen and carbon monoxideoxygen mixtures. These experiments were done in an 8.25-cmsquarc shock tube with the observing station 8 m from the diaphragm. The primary observational technique was optical interferometry. Tile equipment and procedures were essentially the same as described in preceding and referenced papers, and any significant departure will be pointed out at tile appropriate point. Since smooth shock waves
followed by laminar induction zones are not in general observed to exist in detonable mixtures, ~ many of these data have been obtained using a converging~liverging section in the shock tube." It has been observed that the flow behind a cylindrically expanding shock wave in a detonable mixture initially has a laminar structure under certain conditions and is therefore amenable to quantitative optical analysis.
Hydrogen-Oxygen Mixtures Vibrational Equilibration
The rate of vibrational excitation relative to that of chemical reaction behind a shock wave has been the subject of a number of investigations in the past. 3'4 Since the former causes an increase in density and the latter a decrease, this question may be studied by comparing the maximum postshock density pb with that calculated assuming vibrational cquilibration but no chemical reaction. To the extent that these values agrce, we may conclude that cxothermic reaction occurs
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(b) FzG. 1. Maximum induction zone density ratio vs shock M a c h Number. (a) D a t a for the three leanest mixtures, obtained in the constant area shock tube, where a nearly constant velocity shock is observed to be followed b y a one-dimensional flow. (b) D a t a obtained in a two-dimensional nozzle where the attenuating shock front is followed b y a n expansion and, hence, measurement errors are relatively large. 786
STRUCTURE
OF GASEOUS
subsequent to the completion of vibrational relaxation. In Fig. 1 are shown observed values of the maximum density in mixtures in which 0.0075 _< ]-H2~/]-02~ ~ 24 and which contain no inert diluent. Mixtures containing 3% H2 or less were studied in the constant-area shock tube; in the others the two-dimensional nozzle technique was employed, using in most cases a 10.8-degree expansion from a 0.36-cm-high throat. Solid lines show the calculated density ratios for pure oxygen ([-H2~/[-O2~ = 0) and pure hydrogen ([-H2J/[-02] = ~ ). The location of two intermediate mixtures is indicated. The leanest mixtures are seen to agree very well with the pureoxygen calculation, confirming and extending earlier work ~ showing that oxygen vibrational excitation precedes reaction. The scatter is sufficiently great for the richest mixtures that the state of excitation of the hydrogen is not clear from these data. Further experiments therefore were done with still richer mixtures, [-H2~/FO2~ = 50 and 100, where a laminar structure can again be obtained in the constant-area tube. Here argon was used as a diluent to facilitate generation of sufficiently strong shock waves. The data are compared in Fig. 2 with Hugoniot calculations assuming hydrogen vibration unexcited (lower curve) and excited, t t is clear that in these mixtures vibrational excitation of the hydrogen precedes reaction. Vibrational Relaxation T i m e
The vibrational relaxation time for 02 at combustion temperatures has been determined both pure e and in mixture with H2. ~ I t may be calculated for any given mixture using pro, = 1.49 X 10-1~ exp(133T-t), pro~-H2 = 10- s exp(36T-t), T -1 = ( 0 / T 0 2 ) +
[(1 -- r
(1) (2)
DETONATION
787
r for 02 in a mixture where its mole fraction is r p is in atm, and T is the average relaxation zone temperature in ~ The relaxation time for O2 is always less than the observed induction time for exothermic reaction for temperatures below 2000~ In the experiments reported in Fig. 2 in the constant-area tube, where the maximum density shows the H2 to be vibrationally equilibrated, this density was measured within a millimeter of the translational shock front for initial pressures from 0.04 to 0.1 arm. The vibrational relaxation zone was not discernable in any of these experiments, including those with no oxygen. Therefore, considering only H2-H2 collisions, the relaxation time at 1400~ must be less than about 2 X 10-6 arm sec, an upper limit consistent with the earlier estimate by Gaydon and Hurle. s This relaxation rate is faster than would have been expected on the basis of a correlation of relaxation times in other simple systems. 9 The vibrational relaxation time of deuterium was also sought at about 1500~ and 63% of the density change expected to result from vibrational relaxation was observed to occur within 2 X 10-8 atm sec. Other features, however, suggest a more complex relaxation process. Using this upper limit, the vibrational relaxation time of H~ due to only H2-H2 collisions in, for example, H~ + 3 02 is comparable to the induction time, so we cannot as yet state for H2: as we can for O2, that vibrational excitation always precedes reaction. Considering, however, that the relaxation time may be much less than this upper limit, and that in leaner mixtures vibrational excitation of H2 by exchange with excited O2 is expected to become an important process, and that 02 and other diluent molecules will be nearly as effective as another H~ as a collision partner, it appears highly probable that the relaxation time for H2 is, in general, less than the induction time, and may be much less.
(3) Induction Time
where vo~ is the relaxation time in seconds for pure 02, rO~-H2 for 02 infinitely dilute in H2, and
0 ~ A , + w [0.9eHz§
0 z)
In these mixtures, the induction zone is terminated by a relatively abrupt decrease in density, and this induction distance d~ is converted to an induction time for exothermic reaction ti by ti = ( d i / V , ) ( p b / p l ) ,
-o l , , , i
s,
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Pb
Pj 4
5 6 SHOCK MACH NUMSER
FIG. 2. Maximum induction-zone density ratio for very rich mixtures studied in the constant-area tube,
where V, is the shock velocity. Data are plotted in Fig. 3 as I-0:Jt~ versus the reciprocal vibrationally relaxed temperature. They are separated into two groups for clarity and may be compared with the solid line reproduced from the work of Schott and Kinsey3 ~ I t is seen that, although the slopes are comparable, the various mixtures do separate using the molecular oxygen concentration as a scaling factor for the induction time.
788
DETONATIONS
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FIG. 3. Induction time for exothermic reaction as a function of vibrationally equilibrated temperature. The three leanest and two richest mixtures were studied in the constant-az~a tube. The scale is shifted for the richer mixtures for clarity in presentation. The solid line is reproduced from Schott and Kinsey (Ref. 10). In Fig. 4 these same data are replotted using now ([-O2-]EH2~89 and it is seen that the separation between even extreme mixture groups becomes comparable with the scatter within each group. The low-temperature divergent-nozzle data for intermediate mixtures are less reliable because the reaction zone becomes relatively thick and the velocity history of the shock is not known sufficiently well to apply the necessary temperature correction. Between about 1100 ~ and 2100~ this induction time may be represented to better than a factor of 2 for all mixtures by the relation logl0{(EOs-][-H2~)89 = 3 1 0 0 / T - - 9.8,
(4)
where concentrations are in moles per liter, and time in seconds and T is the vibrationally relaxed temperature in ~ Belles and Lauver 11 point out that this concentration dependence of the induction time is to be expected for lean mixtures, but the situation is not clear for other mixtures. For comparison, the calculated vibrational relaxation time for the 02 is also plotted on Fig. 4 for several mixtures. In the leanest mixtures, the relaxation time can become a significant fraction of the induction time. This is more noteworthy when one remembers that the relaxation time is a "l/eth" time, whereas the induction time is not. In records at the higher temperatures, of which Fig. 5 is an example, the constant-
789
STRUCTURE OF GASEOUS DETONATION 10-6 - -
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IO00/Tb FIG. 4. Induction time for exothermic reaction using ([O2][H,])i as the scaling factor.
FIG. 5. Interferogram of a rightward propagating Mach 4.91 shock wave in 0.0075 H2 -4- 0.9925 02 at pl = 0.12 a t 9 Vertical height of the region shown is 1.2 cm and the density decrease following a t t a i n m e n t of the density maximum is a b o u t 4 % of the maximum density.
790
DETONATIONS
density induction zone becomes of vanishingly short duration. After a still-approximatelyexponential approach, the attainment of the vibrationally relaxed density is followed immediately by the decrease in density signalling exothermie reaction. Induction time data have also been obtained for 2 H2 ~ 5 Air using both the incident shockdivergent nozzle technique and reflected-shock ignition in the constant-area tube. These results ~ also are consistent with Eq. (4). It should be noted here that the presently defined induction time--to the onset of observable cxothermic reaction--is not expected to coincide with the time derived from observations of the growth of [-OH-]. The [-OII3 should attain its maximum through the bimolecular chainbranching reactions at conditions approximating the partial equilibrium state (PES), is and the induction time measured by Schott and Kinsey z~ was defined by a minimum detectable value of [-OI-]3 less than the maximum and occurring prior to the maximum. The two experimental criteria arc probably equivalent within data scatter for most mixtures and for moderate temperatures since the PES is generally exothermic and therefore the density will begin to fall prior to attainment of the PES. For a large excess of 02, and for the higher temperatures, however, the PES is endothermie; and consequently the density decrease must be due solely to the recombination reactions and will first be observed subsequent to attainment of the PES. Therefore, under these conditions the interferometrically observed induction time will be longer than the [-OH-] time.
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A striking and common feature of most experiments (see, for example, records of Ref. 5) is that the induction zone is terminated by a narrow region in which the density decreases abruptly, and then, still well above the density calculated for chemical equilibrium, tends to level off and continue to decrease more slowly. Since the reactions in the induction zone are predominantly the bimolecular chain-branching reactions, and the exothermic reactions the termolecular recombination reactions, it was considered that the abrupt density decrease might be due to the approach to an exothermic partial equilibrium state (PES) via bimoleeular kinetics. To assist in a test of this hypothesis, G. L. Schott calculated the composition and thermodynamic parameters of the PES for three mixtures, 2 H2 -F 02 -b 2 CO, 7 H2 -{- 02, and H2 -F 3 02. From the composition, the specific refractivity was calculated and found to be, respectively, 3%, 4.7%, and 0.5% greater than the unreacted mixture, this increase in refractivity being due to the large hydrogen-
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(el FIG. 6. Measurements of the rapid density decrease following the induction zone. The circle is the density value at the point where it is decreasing most rapidly. The ends of the vertical bars are an an estimate of the upper and lower "knees" in the density profile.
STRUCTURE
OF GASEOUS DETONATION
atom concentration ~4 in the PES. Using this corrected refractivity, the density was found at three locations in this region of rapid decrease; the "upper knee", the inflection point of maximum slope, and the lower knee. The results are shown in Fig. 6, where the inflection-point density is represented by the circle, and the other values are shown by the length of the vertical bar. Two features should be noted. First, the entire density change in the region cannot be attributed to the bimolecular reactions. Second, in the He + 3 O.~ the PES state is less exothermic, and for the stronger shocks becomes slightly endothermic. In this mixture the inflection point is reached more rapidly, as shown by the proximity of the circle to the top of the vertical bar. This suggests that the concave downward portion of the density (the "upper knee") may be the combined result of the approach to the PES and the beginning of the recombination reactions, and the concave upward portion is predominantly the latter. Attempts were made to estimate a recombination rate constant in each of thirteen interferograms, utilizing the observation that the steepest slope in the density profile can be simply related to the assumed three-body recombination process starting from the PES. Later parts of the profile could also be used in some cases, but with more difficulty or less accuracy. Three records from 7 He + Oe mixtures were thus analyzed, for which the PES composition had been computed and from which the principal radical to be recombined is H (mole fraction 0.24), with only minor amounts of OH and O. Assuming the main process to be H + H + M--* He + M, these records yielded (3.5 2= 0.3) X 109 (liter/ mole) e sec-1 at 1600~176 which appears to be somewhat higher than most previous estimates of this termolecular constant, among third bodies in this case would be a considerable amount of water (mole fraction 0.24). Similar measurements were made on two interferograms obtained from experiments in 0.333 Ar + 0.667 (0.98 He + 0.02 Oe), for which the mole fraction of H (and HeO) in the PES is about 0.026, with very small amounts of other radicals. Again assuming the main process to be H + H + M ---* He + M (where in this case M is Ar or, more likely, He), analysis of the profiles yielded the termolecular constant: (0.95 2= 0.1) X 109 (liter/mole) e sec-1 at about 1600~ A third rich composition (8 He + Oe + 91 At, the same as mixture R-3 studied by Sehott and Bird ~5) gave three interferograms from which the three-body constant (1.4 + 0.2) X 109 (liter/mole) e see-1 was computed, in fair agreement with the estimate from the second mixture and substantially lower than that from the first, possibly reflecting differences in third-body
791
efficieneies. It is, however, about a factor of 2 higher than that obtained by Schott 15 for this composition. Five records were obtained with very lean mixtures, 0.75% and 1.5% H~ in Oe, in which the PES should consist of 0 and H20 in mole fractions roughly equal to each other and to that of the initial He, with minor amounts of H and OH. Assuming the recombination process to be 0 + O + M--~ Oe + M (where iV[ is predominantly Oe), the termolecular constant so obtained is (8 2= 3) X 109 (liter/mole) e sec-1 at about 1400~ This constant is somewhat larger than previous estimates, ~s but here it is possible that recombination may also be occurring by a mechanism involving H + O~ + M--+ HOe + M for which the termolecular constant is probably larger 1~ and which cannot be excluded, since I-HI rOe-] is comparable with or larger than [-0] e in the PES, even though I-HI is small. In any event, this portion of the density profile appears clearly to be identified with three-body recombination; the variation of the slope with density and atom mole fraction appears to be consistent with a termolecular process. In view of the uncertainties in obtaining the slopes and simplifying assumptions in reducing the data, the constants deduced are fairly reproducible and not unreasonable for such processes. It is anticipated that continuing efforts to analyze the whole profile in this region by machine computation will yield better data which can be more closely identified with specific reactions.
Carbon Monoxide-Oxygen Two sets of experiments have been run in CO-O2 mixtures. In the first, mixtures of C O + O2, 8 CO + 02, and 4 CO + 02 were prepared from cylinders of Matheson "CP" CO and Matheson "extra dry" 02, with no effort made to remove any trace quantities of H2, estimated by vibrational fluorescence measurements is to be 5 ppm for the CO and very small but not quantitatively known for the 02. The gases were passed through a dry ice-acetone cold trap both in loading the mixing chamber and later in transferring the gas to the shock tube. In the second series, a tank of 8 CO + Oe was prepared which contained also 1% H2. After the desired experiments were run, the pressure was reduced to 31.6% of the initial charging pressure, and then CO and Oe added in the ratio of 8:1 to bring the total pressure back to its initial value. Repeating this procedure gave mixtures of 8 CO -+- Oe containing 1%, 0.316%, 0.1%, 0.0316%, and 0.01% He, plus, of course, any He level present in the CO and Oe. In this second series of experiments, the radiation from the shocked gas was monitored by a photomultiplier through a 4358A interference filter.
792
DETONATIONS
8 CO + 0~,
VIBRATIONAL~' ' ' ' ~
Pb/P, 5 5
v 0.10 A 0.32 0 1.0 I
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l
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6 7 SHOCK MACH NUMBER-Ms
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FIG. 7. Maximum density found behind shock waves in 8 CO ~- O2. Data with added H~ could be obtained in the constant-area tube for relatively strong shocks only, because of the aplanarity of moderate-strength shocks (see Fig. 10). Previous work 1 has shown that for 2 He ~ 02 ~- 2 CO, the intensity is proportional to the concentration product [-CO] [-07, and this same relation would be expected to hold in other nitrogen-free gas mixtures. In all experiments with less than 0.1% H2 added, the shock tube was evacuated to below 0.2 X 10-6 atm before loading. For other experiments a pressure below 0.5 X 10-6 atm was achieved, initial pressures of the test gas ranged from about 0.02 to 0.2 atm.
excitation of N2 in air below 3000~ has been noted, ~ and a study of the vibrational relaxation in a number of N2-O~ mixtures has determined the rate constant for this vibrational exchange reaction between 1000 ~ and 3500~ Since the difference in the size of the vibrational quantum is less in CO-02 mixtures than in N2-O2, we would expect the V-V process to be relatively more important. Verification of this requires a comparison b e t w ~ n the observed relaxation rate and that calculated for the given mixture assuming only the T - V process operative. Since the T - V excitation of CO is partially by collisions with O~., and vice-versa, the probability for this process must be determined. From a correlation of data on the relaxation times of many diatomic molecules in collision with a wide range of collision partners, 9 we conclude that for the T - V process the relaxation time of the CO and the 02 in these mixtures should each be very nearly the same as in the pure gas. In previous interferometric studies of vibration relaxation, the analysis due to Blackman ~ and Blythe ~ has been employed, and the density approach to equilibrium has been found to be well represented by an exponential in simple systems or, in Nr-Oe mixtures, by a sum of exponentials. A semi-log plot, such as Fig. 8, of the difference between the observed and relaxed densities versus distance behind the shock front is found to be.
Vibrational Equilibration The first question to determine is whether or not one or both components are vibrationally equilibrated before reaction. Since the CO vibration is expected to be the slower to excite and since its heat capacity at a given temperature is less than O.% a mixture rich in CO was chosen for examination. The maximum density found in 8 CO ~ O~ is plotted in Fig. 7. Also included here are data points from mixtures containing small amounts of H~. We conclude that vibrational equilibration of both reactants precedes exothermic reaction. Similar observations have been made for 4 CO -~ 02 and CO -~ O~ with somewhat more scatter in fewer data points.
Vibrational Relaxation Time The vibrational relaxation time has been determined for pure CO, zg-2z and for pure O2. 6 In a mixture of diatomic gascs, that species with the longer relaxation time (CO in this case) is excited through two parallel processes, by a simple collisional conversion of trans]ational to vibrational energy ( T - V process), and by the exchange of a vibrational quantum from the more easily excited species (V-V process) with only the quantum difference being taken from translation. The predominant effect of the V-V process in the
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FIo. 8. Increase of the density during vibrational relaxation versus distance behind the translationshock front.
S T R U C T U R E
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G A S E O U S
Exothermic Reaction Zone
PURE Prv otto. sec A 0
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Fro. 9. Vibrational relaxation time based on the initial rate of change of density behind shock waves in CO-O2 mixtures. This time is not adequate to characterize the relaxation since the approach to equilibrium is not exponential in the density. linear in simple systems, but to be concave downward in C 0 - 0 2 mixtures. Since the early portion appears to be at least approximately linear, however, a time constant based on this initial slope has been calculated. (The actual approach to equilibrium will be more rapid than if it were
~!!~i~ii i:i ~ii~ iii! !i~i~ :~i~!~!!i~ii!ii~i~i ~
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793
IV
exponential with this "relaxation time".) D a t a for "H~-free" mixtures are plotted in Fig. 9. The CO clearly relaxes at a more rapid rate when O2 is present. Studies aimed at determining the rate of the V-V exchange reaction as a function of temperature are continuing.
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D E T O N A T I O N .
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In C 0 - 0 2 mixtures the attainment of maximum density is followed immediately by a decrease in density due to reaction, so in the sense that there is no high-density plateau, there may be said to be no induction zone. The addition of H2 in small quantities is found to produce marked changes in the structure. The known effectiveness of H2 as a collision partner greatly speeds the vibrational excitation process. Furthermore, the participation of H2 in the reaction accelerates the rate of heat release, producing a much thinner reaction zone although only a small change in the over-all exothermicity. The not-surprising result is that the front becomes aplanar and acquires the "turbulent" appearance characteristically observed for detonation. The sequence of interferograms in Fig. 10 illustrates the effect of H2 on Much 5.4 shock waves into 0.1 atm of 8 CO + 02. The highly turbulent appearance with the addition of 1% H2 is due to the existence of a number of transverse shocks (multiheaded spin), and with less H2 the appearance of a single cusp in the front indicates singleheaded spin. With a minimum amount of H2, the heatrelease rate becomes sufficiently small that the shock front is plane and the reaction zone relatively well behaved. By producing still stronger shock waves it is possible to maintain a laminar structure even with 1% H2, and the density structure from three such records is shown in Fig. 11. In these
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FIG. 10. The structure of detonation in 8 CO -I- 02 at p~ = 0.1 arm with added small amounts of H2. M , ~ 5.4. The horizontal bars are reinforcements over the 8.2~-cm-ldgh windows. Note the cusp in the primary shock front for intermediate amounts of H2. The right-hand record contains no deliberately added
H2, only residual impurities. An increase in density displaces the fringes upward.
794
DETONATIONS
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Fro. 11. Density porfiles behind Maeh 7 shock waves in 8 CO ~ O: at 0.04 atm with various amounts of H2 added. experiments, as a small amount of He is added, the blue luminosity is seen to rise much more rapidly to a higher peak, and then decrease slowly toward a steady state, consistent with the expectation that a small amount of He will rapidly produce a higher-than-equilibrium oxygen-atom concentration via the bimolecular chain-branching reactions. Discussion
In these experiments we have explored the density structure of the flow behind shock waves in H2-O2 and C 0 - 0 2 mixtures. From measurements of the maximum density it appears that vibrational excitation precedes reaction in both systems. The induction time for exothermic reaction in H2-Oe mixtures has been measured in experiments in which r H 2 ] / FOe-] has been varied by a factor of 1.3 X 104 and it is observed that ([-OeJ[-tIeJ)~'t~ is more nearly independent of the mixture at a given temperature than is I-Oe-]ti. It has been verified that the density decrease terminating the measured induction zone is primarily due to recombination reactions. The observed instability of a one-dimensional flow through a shock-induced exothermic reaction tion zone is a subject of current investigation.~ The detailed analysis of the mechanism b y which a weak shock stably propagates transversely through the reacting medium must in time require a knowledge of the structure of this reaction zone ahead of the disturbance. I t is hoped that these studies will provide additional input for such analyses.
A fundamental problem in the chemistry of fast reactions is the extent to which the rate of a given reaction depends upon the state of vibrational excitation of the reactants. For the systems and conditions examined here, it appears that vibrational excitation precedes chemical reaction, but we cannot as yet conclude that this is a general result or that the reaction rates have been demonstrably influenced by the state of vibrational excitation. One of the experimental problems in such studies lies in the enormous effectiveness of He in producing vibrational excitation--it is difficult to modify this excitation rate in the H2-O2 reaction. One of the next possibilities to explore is the D2-0e system, where He should be of comparable effectiveness to De in the excitation of 0e, and where comparison of experiments first with tie and then with Ar as a diluent should provide information on the extent to which the more rapid vibrational excitation in the former case affects the initial or subsequent course of the reaction. The CO-02 system seems particularly inviting for further study for several reasons. The vibrational relaxation time is sufficiently long that comparison of experiments first with helium and then with argon as a diluent should enable even greater control over the rate of vibrational excitation, still without modification of the kinetics. Measurements of the heat release (through the density) and the atomic oxygen concentration (from the blue luminosity) should permit comparison with proposed kinetic systems, and ability to control the rate of heat release through added He should elucidate the relation between the reaction-zone thickness and the transverse structure (multiheaded spin) of the detonation, e6 The results in this paper form a basis for such future studies. ACKNOWLEDGMENT
I t is a pleasure to acknowledge the assistance received from discussion of these problems with Roger Millikan, Garry Schott, and Charles Fenimore, and the experimental assistance of K. H. Cary. This work was supported in part by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force. REFERENCES
1. WroTE, D. R.: Phys. Fluids 4, 465 (1961). 2. WHITE, D. R. A N D C A R Y , K. H.: Phys. Fluids 6, 749 (1963). 3. PATCH, R. W.: ARS J. 31, 46 (1961). 4. NICHOLLS, J. A., ADAMSON,T. C., JR., A~'D MORRmON, R. B.: AIAA J. 1, 2253 (1963). 5. WHITE, D. R.: Phys. Fluids 6, 1011 (1963).
STRUCTURE OF GASEOUS DETONATION 6. 7. 8.
9.
10. 11.
12.
13. 14. 15.
WHITE,D.
R. AND MILLIKAN, R. C.: J. Chem. Phys. 89, 1803 (1963). WHITE, D. R. AND MILLIKAN, R. C.: J. Chem. Phys. 39, 2107 (1963). GAYDON, A. G. AND HURLE, J.: Eighth Symposium (International) on Combustion, p. 309, Williams and Wilkins, 1962. MILLIKAN, R. C. AND WHITE, D. R.: J. Chem. Phys. 39, 3209 (1963). SCHOTT, G. L. AND KINNEY, J. L.: J. Chem. Phys. 29, 1177 (1958). BELLES, F. E. AND LAUVER, M. R.: Tenth Symposium (International) on Combustion, p. 285, The Combustion Institute, Pittsburgh, Pa., 1965. SCHELLER, K. AND WHITE, D. R.: to be published as an Aerospace Research Laboratory Report, OAR, Wright-Patterson Air Force Base, Ohio. SCHOTT,G. L.: J. Chem. Phys. 82, 710 (1960). WHITE, D. R.: Phys. Fluids 4, 40 (1961). SCHOTT,G. L. AND BIRD, P. F.: Paper presented
16. 17.
18. 19. 20. 21.
22. 23. 24. 25. 26.
795
before the ACS Div. of Fuel Chemistry, Philadelphia, April 9, 1964. DUFF, R. E.: J. Chem. Phys. 28, 1193 (1958). FENIMORE, C. P. AND JONES, G. W.: Tenth Symposium (International) on Combustion, p. 489, The Combustion Institute, Pittsburgh, Pa., 1965. MILLIKAN,R. C. :J. Chem. Phys. 38, 2855 (1963.) MATTHEWS, D. L.: J. Chem. Phys. 34, 639 (1961). HOOKEn, W. J. AND MILLIKAN, R. C.; J. Chem. Phys. 38, 214 (1963). WINDSOR, M. W.~ DAVIDSON,H., AND TAYLOR, R. L.: Seventh Symposium (Internalional) on Combustion, p. 80, Butterworths, 1959. WHITE, D. R. AND MILLIKAN, R. C.: AIAA J. 2, 1844 (1964). BLACKMAN,V.: J. Fluid Mech. I, 61 (1956). BLYTHE, P. A.: J. Fluid Mech. 10, 33 (1961). ERPENBECK, J. J.: Phys. Fluids 7, 684 (1964). DOVE, J. E. AND WAGNER, H. (~G.: Eighth Symposium (International) on Combustion, p. 589, Williams and Wilkins, 1962.
COMMENTS Mr. F. E. Belle~ (NASA Lewis Research Center): Wagner has asked whether the effect of approaching the limit could be seen in the shock-tube measurements of induction time. Dr. Gordon Skinner of Monsanto Research has observed such effects: i.e., a plot of hi (t~[-O2]) versus reciprocal temperature bends sharply upwards at about 900~176 shocked gas temperature. Dr. D. R. White: At the lower temperature experiments reported here, the density decrease, signaling
the termination of the induction zone, becomes more gradual and, hence, less-clearly defined. Attempts were made to extend the data to lower temperatures in reflected-shock experiments, by measuring the heat transfer to the reflecting surface; but, again, the abrupt increase in heat-transfer rate, seen at the end of the induction time at higher temperatures, became smoothed as one approached 1000~ Lacking an adequate experimental definition of the induction time, we did not continue work at lower temperature.
pp. 785--795,
The Combtmtion Institute, 1965
STRUCTURE OF GASEOUS DETONATION. IV. INDUCTION ZONE STUDIES IN H2-O2 AND CO-O~ MIXTURES I)ONALD R. WHITE AND GEORGE E. MOORE General Electric Research Laboratory, Schenectady, New York
The density structure of the flow behind shock waves in H:-02 and in CO-O~ mixtures has been examined interferometrically. In the former case it is shown that the oxygen is vibrationally excited before observable exothermic reaction. At least for very rich mixtures and probably for all mixtures, the hydrogen is also, since the vibrational relaxation time for H2 (as well as for D.~) is found to be less than 2 X 10-e arm see at 1400~ The induction time for exothermic reaction has been measured for 0.0075 G [-]I.,]/[02] < 100 and the data may be fit to better than a factor of two for 2200 :> T :> 1100~ by log~0 ([O2][H2])89 = 3100/T 9.8, where concentrations are in moles/liter and time in seconds. Induction times in 2 H2 -{- 5 Air are also found to be represented by this equation. The observed density profiles in the region of rapid exothermic reaction have been analyzed for a number of very rich and very lean mixtures, assuming heat evolution to be due to threebody recombination processes, and termolecular rate constants of reasonable magnitude have been deduced. In 8 CO -~- O2, it is shown that both reactants become vibrationally equilibrated prior to reaction, and that the vibrational relaxation time is significantly less than for pure CO, implying that vibrational exchange with excited O~ is an important process in excitation of the CO. Addition of up to 1% H~ is shown to reduce the relaxation time and accelerate the reaction, but not to affect the maximum density. With the thinner reaction zone due to added I[2, the detonation is observed to develop spin and to acquire the characteristic "turbulent" appearance due to the transversely propagating shocks behind the main shock front and the consequent shear layers in the flow.
Introduction The density structure of the flcJw behind shock wave in an exothermally reactive medium is found to consist, in general, of at least three regions. Immediately behind the translationrotation shock front, the density increases as energy is transferred into internal degrees of freedom, specifically vibration. Next, in the case of 112-02 mixtures at least, there is an extended nearly-constant-density induction zone at this maximum density (the von-Neuman "spike"), and then the density decreases as heat is released. This paper presents observations of this structure in hydrogen~)xygen and carbon monoxideoxygen mixtures. These experiments were done in an 8.25-cmsquarc shock tube with the observing station 8 m from the diaphragm. The primary observational technique was optical interferometry. Tile equipment and procedures were essentially the same as described in preceding and referenced papers, and any significant departure will be pointed out at tile appropriate point. Since smooth shock waves
followed by laminar induction zones are not in general observed to exist in detonable mixtures, ~ many of these data have been obtained using a converging~liverging section in the shock tube." It has been observed that the flow behind a cylindrically expanding shock wave in a detonable mixture initially has a laminar structure under certain conditions and is therefore amenable to quantitative optical analysis.
Hydrogen-Oxygen Mixtures Vibrational Equilibration
The rate of vibrational excitation relative to that of chemical reaction behind a shock wave has been the subject of a number of investigations in the past. 3'4 Since the former causes an increase in density and the latter a decrease, this question may be studied by comparing the maximum postshock density pb with that calculated assuming vibrational cquilibration but no chemical reaction. To the extent that these values agrce, we may conclude that cxothermic reaction occurs
785
.
/ 0
[H,]lb,]
/0.33
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.I 7 J(:O
DENSITY RATIO
Pb
P, NO EXCITATION OF VIBRATION
5.(3
()r
= )'z
5.0 SHOCK MACH NUMBER- Ms
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6.0
(a) I
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9 0.064
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9 0.10
DENSITY RATIO
o 0.33
k
A7
012 V 24
Pb
7 r
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o 9
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NO EXCITATION Of
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VIBRATION
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5.0 SHOCK MACH NUMBER- Ms
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(b) FzG. 1. Maximum induction zone density ratio vs shock M a c h Number. (a) D a t a for the three leanest mixtures, obtained in the constant area shock tube, where a nearly constant velocity shock is observed to be followed b y a one-dimensional flow. (b) D a t a obtained in a two-dimensional nozzle where the attenuating shock front is followed b y a n expansion and, hence, measurement errors are relatively large. 786
STRUCTURE
OF GASEOUS
subsequent to the completion of vibrational relaxation. In Fig. 1 are shown observed values of the maximum density in mixtures in which 0.0075 _< ]-H2~/]-02~ ~ 24 and which contain no inert diluent. Mixtures containing 3% H2 or less were studied in the constant-area shock tube; in the others the two-dimensional nozzle technique was employed, using in most cases a 10.8-degree expansion from a 0.36-cm-high throat. Solid lines show the calculated density ratios for pure oxygen ([-H2~/[-O2~ = 0) and pure hydrogen ([-H2J/[-02] = ~ ). The location of two intermediate mixtures is indicated. The leanest mixtures are seen to agree very well with the pureoxygen calculation, confirming and extending earlier work ~ showing that oxygen vibrational excitation precedes reaction. The scatter is sufficiently great for the richest mixtures that the state of excitation of the hydrogen is not clear from these data. Further experiments therefore were done with still richer mixtures, [-H2~/FO2~ = 50 and 100, where a laminar structure can again be obtained in the constant-area tube. Here argon was used as a diluent to facilitate generation of sufficiently strong shock waves. The data are compared in Fig. 2 with Hugoniot calculations assuming hydrogen vibration unexcited (lower curve) and excited, t t is clear that in these mixtures vibrational excitation of the hydrogen precedes reaction. Vibrational Relaxation T i m e
The vibrational relaxation time for 02 at combustion temperatures has been determined both pure e and in mixture with H2. ~ I t may be calculated for any given mixture using pro, = 1.49 X 10-1~ exp(133T-t), pro~-H2 = 10- s exp(36T-t), T -1 = ( 0 / T 0 2 ) +
[(1 -- r
(1) (2)
DETONATION
787
r for 02 in a mixture where its mole fraction is r p is in atm, and T is the average relaxation zone temperature in ~ The relaxation time for O2 is always less than the observed induction time for exothermic reaction for temperatures below 2000~ In the experiments reported in Fig. 2 in the constant-area tube, where the maximum density shows the H2 to be vibrationally equilibrated, this density was measured within a millimeter of the translational shock front for initial pressures from 0.04 to 0.1 arm. The vibrational relaxation zone was not discernable in any of these experiments, including those with no oxygen. Therefore, considering only H2-H2 collisions, the relaxation time at 1400~ must be less than about 2 X 10-6 arm sec, an upper limit consistent with the earlier estimate by Gaydon and Hurle. s This relaxation rate is faster than would have been expected on the basis of a correlation of relaxation times in other simple systems. 9 The vibrational relaxation time of deuterium was also sought at about 1500~ and 63% of the density change expected to result from vibrational relaxation was observed to occur within 2 X 10-8 atm sec. Other features, however, suggest a more complex relaxation process. Using this upper limit, the vibrational relaxation time of H~ due to only H2-H2 collisions in, for example, H~ + 3 02 is comparable to the induction time, so we cannot as yet state for H2: as we can for O2, that vibrational excitation always precedes reaction. Considering, however, that the relaxation time may be much less than this upper limit, and that in leaner mixtures vibrational excitation of H2 by exchange with excited O2 is expected to become an important process, and that 02 and other diluent molecules will be nearly as effective as another H~ as a collision partner, it appears highly probable that the relaxation time for H2 is, in general, less than the induction time, and may be much less.
(3) Induction Time
where vo~ is the relaxation time in seconds for pure 02, rO~-H2 for 02 infinitely dilute in H2, and
0 ~ A , + w [0.9eHz§
0 z)
In these mixtures, the induction zone is terminated by a relatively abrupt decrease in density, and this induction distance d~ is converted to an induction time for exothermic reaction ti by ti = ( d i / V , ) ( p b / p l ) ,
-o l , , , i
s,
oO
Pb
Pj 4
5 6 SHOCK MACH NUMSER
FIG. 2. Maximum induction-zone density ratio for very rich mixtures studied in the constant-area tube,
where V, is the shock velocity. Data are plotted in Fig. 3 as I-0:Jt~ versus the reciprocal vibrationally relaxed temperature. They are separated into two groups for clarity and may be compared with the solid line reproduced from the work of Schott and Kinsey3 ~ I t is seen that, although the slopes are comparable, the various mixtures do separate using the molecular oxygen concentration as a scaling factor for the induction time.
788
DETONATIONS
10-5
I
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v 24 v I
I 0.8 IO00/T b
I
+ 50 x I00 l 1.0
10-9
FIG. 3. Induction time for exothermic reaction as a function of vibrationally equilibrated temperature. The three leanest and two richest mixtures were studied in the constant-az~a tube. The scale is shifted for the richer mixtures for clarity in presentation. The solid line is reproduced from Schott and Kinsey (Ref. 10). In Fig. 4 these same data are replotted using now ([-O2-]EH2~89 and it is seen that the separation between even extreme mixture groups becomes comparable with the scatter within each group. The low-temperature divergent-nozzle data for intermediate mixtures are less reliable because the reaction zone becomes relatively thick and the velocity history of the shock is not known sufficiently well to apply the necessary temperature correction. Between about 1100 ~ and 2100~ this induction time may be represented to better than a factor of 2 for all mixtures by the relation logl0{(EOs-][-H2~)89 = 3 1 0 0 / T - - 9.8,
(4)
where concentrations are in moles per liter, and time in seconds and T is the vibrationally relaxed temperature in ~ Belles and Lauver 11 point out that this concentration dependence of the induction time is to be expected for lean mixtures, but the situation is not clear for other mixtures. For comparison, the calculated vibrational relaxation time for the 02 is also plotted on Fig. 4 for several mixtures. In the leanest mixtures, the relaxation time can become a significant fraction of the induction time. This is more noteworthy when one remembers that the relaxation time is a "l/eth" time, whereas the induction time is not. In records at the higher temperatures, of which Fig. 5 is an example, the constant-
789
STRUCTURE OF GASEOUS DETONATION 10-6 - -
l
I
1
1
,.
1
[,,]/[o,]
A
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//'VIBRATIONAL RELAXATION OF THE 02 f17
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0.8
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IO00/Tb FIG. 4. Induction time for exothermic reaction using ([O2][H,])i as the scaling factor.
FIG. 5. Interferogram of a rightward propagating Mach 4.91 shock wave in 0.0075 H2 -4- 0.9925 02 at pl = 0.12 a t 9 Vertical height of the region shown is 1.2 cm and the density decrease following a t t a i n m e n t of the density maximum is a b o u t 4 % of the maximum density.
790
DETONATIONS
density induction zone becomes of vanishingly short duration. After a still-approximatelyexponential approach, the attainment of the vibrationally relaxed density is followed immediately by the decrease in density signalling exothermie reaction. Induction time data have also been obtained for 2 H2 ~ 5 Air using both the incident shockdivergent nozzle technique and reflected-shock ignition in the constant-area tube. These results ~ also are consistent with Eq. (4). It should be noted here that the presently defined induction time--to the onset of observable cxothermic reaction--is not expected to coincide with the time derived from observations of the growth of [-OH-]. The [-OII3 should attain its maximum through the bimolecular chainbranching reactions at conditions approximating the partial equilibrium state (PES), is and the induction time measured by Schott and Kinsey z~ was defined by a minimum detectable value of [-OI-]3 less than the maximum and occurring prior to the maximum. The two experimental criteria arc probably equivalent within data scatter for most mixtures and for moderate temperatures since the PES is generally exothermic and therefore the density will begin to fall prior to attainment of the PES. For a large excess of 02, and for the higher temperatures, however, the PES is endothermie; and consequently the density decrease must be due solely to the recombination reactions and will first be observed subsequent to attainment of the PES. Therefore, under these conditions the interferometrically observed induction time will be longer than the [-OH-] time.
OENS,'Y2H..0..2C0 RAT'~ 4
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SHOCKMACHNUMBER
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Exothermic Reaction Zone
A striking and common feature of most experiments (see, for example, records of Ref. 5) is that the induction zone is terminated by a narrow region in which the density decreases abruptly, and then, still well above the density calculated for chemical equilibrium, tends to level off and continue to decrease more slowly. Since the reactions in the induction zone are predominantly the bimolecular chain-branching reactions, and the exothermic reactions the termolecular recombination reactions, it was considered that the abrupt density decrease might be due to the approach to an exothermic partial equilibrium state (PES) via bimoleeular kinetics. To assist in a test of this hypothesis, G. L. Schott calculated the composition and thermodynamic parameters of the PES for three mixtures, 2 H2 -F 02 -b 2 CO, 7 H2 -{- 02, and H2 -F 3 02. From the composition, the specific refractivity was calculated and found to be, respectively, 3%, 4.7%, and 0.5% greater than the unreacted mixture, this increase in refractivity being due to the large hydrogen-
EOUILIBRIUM ST:TE I
Hz+
30 z
~
,
.
.
~
DENSITY RATIO
PARTIAL
~s
P
r, gOUILIBRIUM
3
I"
I
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4 5 SHOCKMACHNUMBER
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I
6
(el FIG. 6. Measurements of the rapid density decrease following the induction zone. The circle is the density value at the point where it is decreasing most rapidly. The ends of the vertical bars are an an estimate of the upper and lower "knees" in the density profile.
STRUCTURE
OF GASEOUS DETONATION
atom concentration ~4 in the PES. Using this corrected refractivity, the density was found at three locations in this region of rapid decrease; the "upper knee", the inflection point of maximum slope, and the lower knee. The results are shown in Fig. 6, where the inflection-point density is represented by the circle, and the other values are shown by the length of the vertical bar. Two features should be noted. First, the entire density change in the region cannot be attributed to the bimolecular reactions. Second, in the He + 3 O.~ the PES state is less exothermic, and for the stronger shocks becomes slightly endothermic. In this mixture the inflection point is reached more rapidly, as shown by the proximity of the circle to the top of the vertical bar. This suggests that the concave downward portion of the density (the "upper knee") may be the combined result of the approach to the PES and the beginning of the recombination reactions, and the concave upward portion is predominantly the latter. Attempts were made to estimate a recombination rate constant in each of thirteen interferograms, utilizing the observation that the steepest slope in the density profile can be simply related to the assumed three-body recombination process starting from the PES. Later parts of the profile could also be used in some cases, but with more difficulty or less accuracy. Three records from 7 He + Oe mixtures were thus analyzed, for which the PES composition had been computed and from which the principal radical to be recombined is H (mole fraction 0.24), with only minor amounts of OH and O. Assuming the main process to be H + H + M--* He + M, these records yielded (3.5 2= 0.3) X 109 (liter/ mole) e sec-1 at 1600~176 which appears to be somewhat higher than most previous estimates of this termolecular constant, among third bodies in this case would be a considerable amount of water (mole fraction 0.24). Similar measurements were made on two interferograms obtained from experiments in 0.333 Ar + 0.667 (0.98 He + 0.02 Oe), for which the mole fraction of H (and HeO) in the PES is about 0.026, with very small amounts of other radicals. Again assuming the main process to be H + H + M ---* He + M (where in this case M is Ar or, more likely, He), analysis of the profiles yielded the termolecular constant: (0.95 2= 0.1) X 109 (liter/mole) e sec-1 at about 1600~ A third rich composition (8 He + Oe + 91 At, the same as mixture R-3 studied by Sehott and Bird ~5) gave three interferograms from which the three-body constant (1.4 + 0.2) X 109 (liter/mole) e see-1 was computed, in fair agreement with the estimate from the second mixture and substantially lower than that from the first, possibly reflecting differences in third-body
791
efficieneies. It is, however, about a factor of 2 higher than that obtained by Schott 15 for this composition. Five records were obtained with very lean mixtures, 0.75% and 1.5% H~ in Oe, in which the PES should consist of 0 and H20 in mole fractions roughly equal to each other and to that of the initial He, with minor amounts of H and OH. Assuming the recombination process to be 0 + O + M--~ Oe + M (where iV[ is predominantly Oe), the termolecular constant so obtained is (8 2= 3) X 109 (liter/mole) e sec-1 at about 1400~ This constant is somewhat larger than previous estimates, ~s but here it is possible that recombination may also be occurring by a mechanism involving H + O~ + M--+ HOe + M for which the termolecular constant is probably larger 1~ and which cannot be excluded, since I-HI rOe-] is comparable with or larger than [-0] e in the PES, even though I-HI is small. In any event, this portion of the density profile appears clearly to be identified with three-body recombination; the variation of the slope with density and atom mole fraction appears to be consistent with a termolecular process. In view of the uncertainties in obtaining the slopes and simplifying assumptions in reducing the data, the constants deduced are fairly reproducible and not unreasonable for such processes. It is anticipated that continuing efforts to analyze the whole profile in this region by machine computation will yield better data which can be more closely identified with specific reactions.
Carbon Monoxide-Oxygen Two sets of experiments have been run in CO-O2 mixtures. In the first, mixtures of C O + O2, 8 CO + 02, and 4 CO + 02 were prepared from cylinders of Matheson "CP" CO and Matheson "extra dry" 02, with no effort made to remove any trace quantities of H2, estimated by vibrational fluorescence measurements is to be 5 ppm for the CO and very small but not quantitatively known for the 02. The gases were passed through a dry ice-acetone cold trap both in loading the mixing chamber and later in transferring the gas to the shock tube. In the second series, a tank of 8 CO + Oe was prepared which contained also 1% H2. After the desired experiments were run, the pressure was reduced to 31.6% of the initial charging pressure, and then CO and Oe added in the ratio of 8:1 to bring the total pressure back to its initial value. Repeating this procedure gave mixtures of 8 CO -+- Oe containing 1%, 0.316%, 0.1%, 0.0316%, and 0.01% He, plus, of course, any He level present in the CO and Oe. In this second series of experiments, the radiation from the shocked gas was monitored by a photomultiplier through a 4358A interference filter.
792
DETONATIONS
8 CO + 0~,
VIBRATIONAL~' ' ' ' ~
Pb/P, 5 5
v 0.10 A 0.32 0 1.0 I
I
l
l
I
6 7 SHOCK MACH NUMBER-Ms
I
8
FIG. 7. Maximum density found behind shock waves in 8 CO ~- O2. Data with added H~ could be obtained in the constant-area tube for relatively strong shocks only, because of the aplanarity of moderate-strength shocks (see Fig. 10). Previous work 1 has shown that for 2 He ~ 02 ~- 2 CO, the intensity is proportional to the concentration product [-CO] [-07, and this same relation would be expected to hold in other nitrogen-free gas mixtures. In all experiments with less than 0.1% H2 added, the shock tube was evacuated to below 0.2 X 10-6 atm before loading. For other experiments a pressure below 0.5 X 10-6 atm was achieved, initial pressures of the test gas ranged from about 0.02 to 0.2 atm.
excitation of N2 in air below 3000~ has been noted, ~ and a study of the vibrational relaxation in a number of N2-O~ mixtures has determined the rate constant for this vibrational exchange reaction between 1000 ~ and 3500~ Since the difference in the size of the vibrational quantum is less in CO-02 mixtures than in N2-O2, we would expect the V-V process to be relatively more important. Verification of this requires a comparison b e t w ~ n the observed relaxation rate and that calculated for the given mixture assuming only the T - V process operative. Since the T - V excitation of CO is partially by collisions with O~., and vice-versa, the probability for this process must be determined. From a correlation of data on the relaxation times of many diatomic molecules in collision with a wide range of collision partners, 9 we conclude that for the T - V process the relaxation time of the CO and the 02 in these mixtures should each be very nearly the same as in the pure gas. In previous interferometric studies of vibration relaxation, the analysis due to Blackman ~ and Blythe ~ has been employed, and the density approach to equilibrium has been found to be well represented by an exponential in simple systems or, in Nr-Oe mixtures, by a sum of exponentials. A semi-log plot, such as Fig. 8, of the difference between the observed and relaxed densities versus distance behind the shock front is found to be.
Vibrational Equilibration The first question to determine is whether or not one or both components are vibrationally equilibrated before reaction. Since the CO vibration is expected to be the slower to excite and since its heat capacity at a given temperature is less than O.% a mixture rich in CO was chosen for examination. The maximum density found in 8 CO ~ O~ is plotted in Fig. 7. Also included here are data points from mixtures containing small amounts of H~. We conclude that vibrational equilibration of both reactants precedes exothermic reaction. Similar observations have been made for 4 CO -~ 02 and CO -~ O~ with somewhat more scatter in fewer data points.
Vibrational Relaxation Time The vibrational relaxation time has been determined for pure CO, zg-2z and for pure O2. 6 In a mixture of diatomic gascs, that species with the longer relaxation time (CO in this case) is excited through two parallel processes, by a simple collisional conversion of trans]ational to vibrational energy ( T - V process), and by the exchange of a vibrational quantum from the more easily excited species (V-V process) with only the quantum difference being taken from translation. The predominant effect of the V-V process in the
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Fro. 9. Vibrational relaxation time based on the initial rate of change of density behind shock waves in CO-O2 mixtures. This time is not adequate to characterize the relaxation since the approach to equilibrium is not exponential in the density. linear in simple systems, but to be concave downward in C 0 - 0 2 mixtures. Since the early portion appears to be at least approximately linear, however, a time constant based on this initial slope has been calculated. (The actual approach to equilibrium will be more rapid than if it were
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exponential with this "relaxation time".) D a t a for "H~-free" mixtures are plotted in Fig. 9. The CO clearly relaxes at a more rapid rate when O2 is present. Studies aimed at determining the rate of the V-V exchange reaction as a function of temperature are continuing.
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In C 0 - 0 2 mixtures the attainment of maximum density is followed immediately by a decrease in density due to reaction, so in the sense that there is no high-density plateau, there may be said to be no induction zone. The addition of H2 in small quantities is found to produce marked changes in the structure. The known effectiveness of H2 as a collision partner greatly speeds the vibrational excitation process. Furthermore, the participation of H2 in the reaction accelerates the rate of heat release, producing a much thinner reaction zone although only a small change in the over-all exothermicity. The not-surprising result is that the front becomes aplanar and acquires the "turbulent" appearance characteristically observed for detonation. The sequence of interferograms in Fig. 10 illustrates the effect of H2 on Much 5.4 shock waves into 0.1 atm of 8 CO + 02. The highly turbulent appearance with the addition of 1% H2 is due to the existence of a number of transverse shocks (multiheaded spin), and with less H2 the appearance of a single cusp in the front indicates singleheaded spin. With a minimum amount of H2, the heatrelease rate becomes sufficiently small that the shock front is plane and the reaction zone relatively well behaved. By producing still stronger shock waves it is possible to maintain a laminar structure even with 1% H2, and the density structure from three such records is shown in Fig. 11. In these
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FIG. 10. The structure of detonation in 8 CO -I- 02 at p~ = 0.1 arm with added small amounts of H2. M , ~ 5.4. The horizontal bars are reinforcements over the 8.2~-cm-ldgh windows. Note the cusp in the primary shock front for intermediate amounts of H2. The right-hand record contains no deliberately added
H2, only residual impurities. An increase in density displaces the fringes upward.
794
DETONATIONS
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Fro. 11. Density porfiles behind Maeh 7 shock waves in 8 CO ~ O: at 0.04 atm with various amounts of H2 added. experiments, as a small amount of He is added, the blue luminosity is seen to rise much more rapidly to a higher peak, and then decrease slowly toward a steady state, consistent with the expectation that a small amount of He will rapidly produce a higher-than-equilibrium oxygen-atom concentration via the bimolecular chain-branching reactions. Discussion
In these experiments we have explored the density structure of the flow behind shock waves in H2-O2 and C 0 - 0 2 mixtures. From measurements of the maximum density it appears that vibrational excitation precedes reaction in both systems. The induction time for exothermic reaction in H2-Oe mixtures has been measured in experiments in which r H 2 ] / FOe-] has been varied by a factor of 1.3 X 104 and it is observed that ([-OeJ[-tIeJ)~'t~ is more nearly independent of the mixture at a given temperature than is I-Oe-]ti. It has been verified that the density decrease terminating the measured induction zone is primarily due to recombination reactions. The observed instability of a one-dimensional flow through a shock-induced exothermic reaction tion zone is a subject of current investigation.~ The detailed analysis of the mechanism b y which a weak shock stably propagates transversely through the reacting medium must in time require a knowledge of the structure of this reaction zone ahead of the disturbance. I t is hoped that these studies will provide additional input for such analyses.
A fundamental problem in the chemistry of fast reactions is the extent to which the rate of a given reaction depends upon the state of vibrational excitation of the reactants. For the systems and conditions examined here, it appears that vibrational excitation precedes chemical reaction, but we cannot as yet conclude that this is a general result or that the reaction rates have been demonstrably influenced by the state of vibrational excitation. One of the experimental problems in such studies lies in the enormous effectiveness of He in producing vibrational excitation--it is difficult to modify this excitation rate in the H2-O2 reaction. One of the next possibilities to explore is the D2-0e system, where He should be of comparable effectiveness to De in the excitation of 0e, and where comparison of experiments first with tie and then with Ar as a diluent should provide information on the extent to which the more rapid vibrational excitation in the former case affects the initial or subsequent course of the reaction. The CO-02 system seems particularly inviting for further study for several reasons. The vibrational relaxation time is sufficiently long that comparison of experiments first with helium and then with argon as a diluent should enable even greater control over the rate of vibrational excitation, still without modification of the kinetics. Measurements of the heat release (through the density) and the atomic oxygen concentration (from the blue luminosity) should permit comparison with proposed kinetic systems, and ability to control the rate of heat release through added He should elucidate the relation between the reaction-zone thickness and the transverse structure (multiheaded spin) of the detonation, e6 The results in this paper form a basis for such future studies. ACKNOWLEDGMENT
I t is a pleasure to acknowledge the assistance received from discussion of these problems with Roger Millikan, Garry Schott, and Charles Fenimore, and the experimental assistance of K. H. Cary. This work was supported in part by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force. REFERENCES
1. WroTE, D. R.: Phys. Fluids 4, 465 (1961). 2. WHITE, D. R. A N D C A R Y , K. H.: Phys. Fluids 6, 749 (1963). 3. PATCH, R. W.: ARS J. 31, 46 (1961). 4. NICHOLLS, J. A., ADAMSON,T. C., JR., A~'D MORRmON, R. B.: AIAA J. 1, 2253 (1963). 5. WHITE, D. R.: Phys. Fluids 6, 1011 (1963).
STRUCTURE OF GASEOUS DETONATION 6. 7. 8.
9.
10. 11.
12.
13. 14. 15.
WHITE,D.
R. AND MILLIKAN, R. C.: J. Chem. Phys. 89, 1803 (1963). WHITE, D. R. AND MILLIKAN, R. C.: J. Chem. Phys. 39, 2107 (1963). GAYDON, A. G. AND HURLE, J.: Eighth Symposium (International) on Combustion, p. 309, Williams and Wilkins, 1962. MILLIKAN, R. C. AND WHITE, D. R.: J. Chem. Phys. 39, 3209 (1963). SCHOTT, G. L. AND KINNEY, J. L.: J. Chem. Phys. 29, 1177 (1958). BELLES, F. E. AND LAUVER, M. R.: Tenth Symposium (International) on Combustion, p. 285, The Combustion Institute, Pittsburgh, Pa., 1965. SCHELLER, K. AND WHITE, D. R.: to be published as an Aerospace Research Laboratory Report, OAR, Wright-Patterson Air Force Base, Ohio. SCHOTT,G. L.: J. Chem. Phys. 82, 710 (1960). WHITE, D. R.: Phys. Fluids 4, 40 (1961). SCHOTT,G. L. AND BIRD, P. F.: Paper presented
16. 17.
18. 19. 20. 21.
22. 23. 24. 25. 26.
795
before the ACS Div. of Fuel Chemistry, Philadelphia, April 9, 1964. DUFF, R. E.: J. Chem. Phys. 28, 1193 (1958). FENIMORE, C. P. AND JONES, G. W.: Tenth Symposium (International) on Combustion, p. 489, The Combustion Institute, Pittsburgh, Pa., 1965. MILLIKAN,R. C. :J. Chem. Phys. 38, 2855 (1963.) MATTHEWS, D. L.: J. Chem. Phys. 34, 639 (1961). HOOKEn, W. J. AND MILLIKAN, R. C.; J. Chem. Phys. 38, 214 (1963). WINDSOR, M. W.~ DAVIDSON,H., AND TAYLOR, R. L.: Seventh Symposium (Internalional) on Combustion, p. 80, Butterworths, 1959. WHITE, D. R. AND MILLIKAN, R. C.: AIAA J. 2, 1844 (1964). BLACKMAN,V.: J. Fluid Mech. I, 61 (1956). BLYTHE, P. A.: J. Fluid Mech. 10, 33 (1961). ERPENBECK, J. J.: Phys. Fluids 7, 684 (1964). DOVE, J. E. AND WAGNER, H. (~G.: Eighth Symposium (International) on Combustion, p. 589, Williams and Wilkins, 1962.
COMMENTS Mr. F. E. Belle~ (NASA Lewis Research Center): Wagner has asked whether the effect of approaching the limit could be seen in the shock-tube measurements of induction time. Dr. Gordon Skinner of Monsanto Research has observed such effects: i.e., a plot of hi (t~[-O2]) versus reciprocal temperature bends sharply upwards at about 900~176 shocked gas temperature. Dr. D. R. White: At the lower temperature experiments reported here, the density decrease, signaling
the termination of the induction zone, becomes more gradual and, hence, less-clearly defined. Attempts were made to extend the data to lower temperatures in reflected-shock experiments, by measuring the heat transfer to the reflecting surface; but, again, the abrupt increase in heat-transfer rate, seen at the end of the induction time at higher temperatures, became smoothed as one approached 1000~ Lacking an adequate experimental definition of the induction time, we did not continue work at lower temperature.