Direct shock tube measurements of oxygen-atom recombination rates

DIRECT SHOCK OXYGEN-ATOM

TUBE MEASUREMENTS OF RECOMBINATION RATES R. I. SOLOUKHIN

University of Novosibirsk, U.S.S.R. Oxygen-atom rccombi,'ation rates ha~'e been measured c,~cr the temperature range 3000 to 3800 K usinga method which affords direct control over the recombination process stimulated in a rapidly expanded s':nple of ~ in a shock tube. A knife edge "trap' ~as placed in the shock tub.- channel in order to provide partial reflection o~ incident shock wa,,,cs. Density variations in the expanded gas region were measured with a quantitative interferometric chronometer b~ using the hdium ncoa laser as a light source. Simultaneous pressure measllrements enable the relaxation eff~t to be detected from a comparison of the local change of pressure with the density variatio,-:.-'- A strong temperature dependence for the recombination rate coelticients wit~, the oxygen molecule as the dominant catalyst was obtained in the limits 129 to 0.41 x i0 ts ¢ m 6 mole -z sec-t at ~,00ff to 380ffK respectivdy. The data agree well with recombination rates evaluated from dissociation rate measur,-m~nts, home. gas dynamic applications of the results to quasi-stationary expanded shock tube flow analysis ate discussed. MeasutB-t decay distances of the recombination relaxation in rarefaction waves generated in non-equilibrium flows around a comer ate in accordance with the recombination rate data.

Introduction EXi'|~R|Mt~NI"At,data on absolute values of the rates for oxygen-alom recombination have become important in the analysis of combustion systems as well as in high temperature gas dynamics. Over a wide teml~rature range, shock tube dissociation, experiments provide measurements of recombination rates determined as a ratio of dissociation rates and equilibrium constants, but this method should be verified independently to exclude some possible uncertainties in dissociation kinetics, especially as a discrepancy has been found in data obtained by different investigators (see comparisons in refs, 1 and 2, and an attempt at direct measurements described in ref, 3). The work to be described in this paper concerns direct measurements of recombination rates for shock-dissociated pure oxygen at temperatures above 3000°K. It appears that the method devdoped may be widelyused in studies of rapidly cooled reacting systems under shock •tube conditions. A quasi-stationary flow of dissociated gas around a corner 4' 5 is a convincing example of 489

the coupling between recombination relaxation effects and the supersonic flow structure. According to theoretical predictions''4 recombination relaxation phenomena in oxygen readily occur in quasi-stationary shock tube expansion flows. While no systematic experiments have been performed before, and only a short remark on the frozen sound velocity observations in an expanded wave flow has been reported s, an examination of two-dimensional rarefaction wave structure in dissociated gas flows would seem to be a reasonable area for the application of the measured recombination rate data, The detailed structure of the density field for air and oxygen in the vicinity ofthe corner point is studied in the present work using interferemetric observations, It is shown that the results of these experiments may be explained on the basis of the measured recombination rate data.

F,x 0) Shock tube,s and apparatus A rectangular brass shock tube 3 an x 1.5 em in cross section and 2 m long ¢ompl¢~ with tl~ observation section was used in the tint part of

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the experiments. Figure 1 shows some details of the instrumentation. In order to providea partial reflection of the shock wave a 'trap'-type sharp edge insertion I cm x 1.2 cm was placed in the tube channel, The gas pressure profile of the process was recorded al the central part o[ the trap with a barium titanate transducer whid~ has a spatial resolution o1'1 mm. Density-variation measurements were conducted simultaneously. A Michelson-type interferometer was employed in a chronographic manner using a helium-neon laser light source, The interferometer fringe displacements were detected by a photomultiplier system through an orifice of 2 mm 2 which isolated a small region of the fringe field in the vicinity of the pressure transducer. Typical pressure and density records of the process are shown in Figure 2. The same process may be recorded by streak camera photographs obtained by using a slit oriented along the direction of the shock front.

Fmure 2, Oscillogram sho~ing the pressure profile {upper trace~ and tile density record (bottom trace) ,,ersus time. Shock wa~e in c,xygen: initial pressure 0.12 aim, M, = 6.9, 1" = 3 3511 K. S~cep duration 21~ microseconds

The corresponding time-resolved interferogram for both parts of the shock tube flow field is shown in Figure 3. Photomultiplier densitychange records, however, provide mote distinct recordings due to the high conirasl of the

December 1967 DIRI!CI SttOCK I (;BE MliASIRI!MI!NIS O F

laser-lit fringes. In their assessment, small deviations in the effective refractive index value due to gas dissociation were taken into account in accordance with the shock tube data presented in ref. 7. A square brass shock tube 5 c m x 5 cm and 3"5 m long was operated with a high speed camera for the density field photography in the corner flow experiments. A rotating-mirror camera having a frame frequency of 2 to 5 x l0 s sec-' was synchronized electronically with a combustion driver-section. Oxygen hydrogen stoichiometric mixtures at initial pressures between 2 and 3 atm were used as the driver-gas to provide shock Math numbers in the range from 8 to 13 a~I initial pressures varying from

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The gas temperature was not monitored in the recombiqation rate measurements. Reaction times were referred to.the reflected shock wave temperatures obtained from equilibrium gas dynamic calculations. The extent of the accuracy in such an approximation is determined by shock-to-boundary layer interaction effects {see Figure 3), and it may be evaluated from the independent pressure and density measure100~s

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5 to 20 mm of mercury. Shock wave vdocities were determined by three shock-front piezogauge detectors, with I mm space resolution. and at signal from the last of these mw be seen in the pressure trace in Figure 2.

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ments. The measured values of reftect~ wave pressures and densities are seen from Figure 4 to be about 15 to 20 per cent greater than the calculated ones. But the temperature deviations due to these effects should not be greater than + IY0deg.K, These data also confirm that the dissociation equilibration is established within 5 to 10 microseconds (!'R = 4 to 9 atm} after the wave reflection, and this observation agrees well with dissociation kinetic measurements for oxy,,en A comparison of tM pressure and density time variations in the expanded arm, expre~,ed in terms of the effective isentropic index ~,(t} = d log t,/d log#, serves to extmcf rdaxation time data from the osdIIograms. The tnanner of data reduction is shown in Figure 5.

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A lag in the recombination heat release leads to quite a sudden drop in ;.,, According to the simplest ideal gas approximation, d log p 1 dq d log i' = 7i,l + c,,7
,~hmvn in Figure 6, If it is assumed that thc pholonmltiplier output is proportional to tllc atomic oxygen concentration, the observed lurninostly profiles are seen to be in reasonable accord with the interpretations of the relaxation phenomena (see Figure 5). Thus, alier ,t stage of sims change of emission intensity, a sudden fall of the light oulput is observed after a time interval similar to tMi which Ms been determined to be the relaxation time by the other above method. Figure 7 shows a plot of experin~ental valt|cs of atornic oxygen recombination rates obtained at various teml'~eratures with nmlecuku" ox)gen as the third body, Tlus choice of nMecuku oxygen as the catalyst seems to be a reasonable one since the degree of dissociation xaries onb; from 0.04 to 0.15 in the experiments. 2,0

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(3) Non-eq~fflibri~m: expansion ware structure Typical interkrograms of the expansion flow fields of dissociated oxygen are shown in Figure 8. The first photograph represents a number of successive frame~ of the expansion process, whereas the later interferograms are single frames of the corresponding series, It appears that a special choice of frames for examination is required since the real duration of the steady state flow pattern isshorten¢
precisely frozen sound velocities are observed at the beginning of the expansion gas flows. The point of appearance of the change in slope of the wave head at higher initial pressures leads to the evaluation of the relaxation zone length. Some typical parameters of the process and measured relaxation zone lengths for air and oxygen are listed in Table 1. Discussion In order to compare the two types of recombination relaxation data obtained by the independent techniques the non-equilibrium zone length evaluations should be assessed on the basis of the recombination-rate data shown ir Figure 7. Corresponding calculations were carricd out by using the method described in ref, 4, The decay distances of the frozen wave head (in cm) are shown in Figure 10 on a logarithmic scale as a function of the incident wave Math numbers at various initial gas pressures, The total gas density was used to obtain the third body concentration ill these evaluations. The dashed line illustrates corrections which should he done if it is assumed that only the oxygen molecule is taken as the dominant catalyst.

December 1967

495

DIRECT SiIO('K it;liE MI~ASUREMENISOF OXYGEN-AIOM RECOMBINATION RATES

the partially reflected wave m e t h o d may be preferable for systematic recombination rate measurements. The strong temperature dependence of the recombination rate, which was also observed by other investigators in various gases t- 2.9 should be taken into account in gas d y n a m i c calculations. Thus, the recombination rate coefficient varies in the range (0.4 to 2) × lO ts cnl 6 mole -2 sec -~ between the temperatures 3000 ° a n d 3 8 0 f f K , whereas it was assumed constant at 0.67 x 10 - I s in calcuEtions '~ for the same temperature range,

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~ i l 11 12 13 it, Shock Mach Number Ftt;trRI! I0. Decay distance (cm) as a function of shock Math mzmber for oxygen at different initial pressures: I, p! = 7.6ram Hg. I', dashed line corresponds Io bc.lh atomic and molecular oxygen as third body concentratioz:,,: 2,pa = 14ram ttg: 3, Pt = 20ram Hg The measured values of the decay distances are seen from Table 1 to be in reasonahle agreement with evaluations based on the rec o m b i n a t i o n rate data obtained in the partially reflected wave experiments. This result seems to be a confirmation of the validity of both ~,he methods, but the stationary-wave technique is m o r e complicated both in the experimental procedure and in the data reduction. Therefore,

Referen¢~ t CLARKE. J. F. an'.l McCHEs.xEY, M,

The Dynamics~y-Reat

Gases, pp 191 and 364. Butterworth: London (1964} z WRAV, K. L. Tenth Symposium (International) on Combustion, pp 523-537. The Combustion Institute: Pittsburgh 11965) 3 WILSO,~,J. £fluht Mech. 15, 497 (1963) * GrAS& I. 1, and TAKA~O, A, Progress in Aeronautical Sciem'es, Vol. VI, pp 163--249, Pergamon: Oxford (1965) DREWRV,J. E. Annual Progress Report. Note (7.-15, p 33. Institute for Aerospace Studies, University of Toronto (l%5) JONES, N. R. and MCCtlESNEY,M. J. sci, lnstrum, 41, 682 (19(;4) ALmtER,R. A, and WHITe, D. R. Phrsics ~fFluids. 2, 153 (19591 8 WHITE,D, R. Physics efFluidL 4, 465 (1%1) HURUh I. R. Eleventh Symposium (International) ~l Combustion. Bezkeley, !%6. Paper No. 86

TABLE 1, Flow parameters in the recombination relaxation zone

Gas

1 2 3 4 5 6 7 8

Oxygen Oxygen Oxygen Oxygen Oxygen Oxygen Air Air

Shock Mach No.

lffl 10"3 11"03 11"6 12"13 12"4 11-2 12"8

Initial S h o c k Degree pressure, pressure, of dismm Hg ~u;:, saciation

temp. ~'K

AI,

3"3 2"45 2"84 3.12 3.42 2,07 2"9 2"13

3260 33~ 3485 3580 2660 3640 4200 5040

2.64 2"95 3"03 x.t3 3.21 3"41 2"76 2"71

14 14 14 14 7'6 14 7"6

04)75 I1 15 17 20 25 ---

Decay d/stare-e,

Gt~

Mf

2'45 2'69 2"79 2"83 2,~0 3-06 2"55 2-52

M ~p

2'41 2"65 2-77 2.8l 2,92 2.97 2"6t 2-53

Calcd

Exlnl

5 5"5 3"6 3-25 3-2 5,4

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