H2F2 chain reaction rate investigation

Z Qcant. Spectrosc. Radiat. Transfer, Vol. 17, pp. 97-116. Pergamon Press 1977. Printed in Great Britain

H2-F2 CHAIN REACTION RATE INVESTIGATIONf JOaN C. CUMMINGS,~ J. EUGENE BROADWELL,WILLIAML. SHACKLEFORD, ARVEL B. WrrrE, JACK E. TROST and GEORGE EMANUEL§ TRW Defense and Space Systems, Redondo Beach, CA 90278, U.S.A. (Received 9 July 1976)

Abstract--Experimental performance of chemical lasers pumped by the He+F2 chain reaction has consist~tly fallen belowexpectations, althoughthe "hot", H + F2--, HF(v) + F, pumpingreaction produces greater vibrational excitation than the "cold", F + H2-* HF(v) + H, reaction used in most HF cw chemical lasers. The reasons for this discrepancyare examinedby measuringspatially-resolvedHF(v) numberdensity and the temperature profiles in a laminar, parallel flow, hydrogen-fluorinemixinglayer and comparingthe results with theoretical computations. By dissociating either the hydrogenor fluorine molecules with arc heaters, kinetics of the hot and cold reaction systems are separately investigated. From a comparisonof the experimental vibrationalpopulationsand the theoretical predictions, it is concludedthat: (1) previously-used pumping and deactivation rates associated with the cold reaction") are approximately correct, (2) the deactivation of high vibrational levels populated by the hot reaction is muchfaster than previouslystated in Ref. (1), and (3) the inclusion of multiquantum HF(v) V-T (or V-R) deactivationreactions, which sharply decreases the numberdensityof the upper vibrationallevels, greatlyimprovesthe agreementbetween theory and experiment. 1. INTRODUCTION THE OamC~VE of this work is to establish whether or not the currently available Hz-F2 chain reaction rate coefficients ") are approximately correct, and if not, to suggest a more accurate set. Our motivation is the large discrepancy between the theoretically predicted and the experimentally realized H F chain laser performance; the actual efficiency being lower by a factor between 5 and 30. (2) We compare the experimentally determined HF(v) profiles in a laminar mixing layer with those predicted theoretically in a computation that makes use of the rates in question. An attempt is then made to infer the necessary corrections, and the calculation is repeated. The experiments were carried out in the "Reactive Flow" facility described in Refs. (3) and (4). In this apparatus, the reaction between hydrogen and fluorine occurs in a laminar mixing layer between two supersonic streams. The H F ground and excited state profiles are measured spectroscopically at several axial locations. The theoretical predictions come from a boundary-layer program, (5) which has been modified to solve numerically the equations for a multicomponent reacting free shear layer (see Appendix A). The program allows arbitrary free-stream conditions, and, therefore, the influence of the nozzle-wall boundary layers is accounted for on the edge conditions of the mixing layer. A similar comparison of experimental and theoretical profiles for the "cold" reaction, H2 + F ~ HF(v) + H, is also described. In this case, where the theoretical and experimental laser performance results are in good agreement, the kinetic rates are reasonably well established. This agreement serves as a partial validation of the foregoing approach. The satisfactory state of the cold reaction kinetics implies that the difficulty with chain reaction operation lies with the "hot" reaction, H + F2-~ H F ( v ) + F, and/or the deactivation of high vibrational levels populated by this reaction. For this reason, it was decided to use the arc heaters to dissociate hydrogen, and to study first the hot reaction alone. For these experiments, the fluorine plus diluent stream is unheated while the hydrogen plus diluent stream is heated to a fWork supported by the AdvancedResearch Projects Agencyand the Air Force Weapons Laboratoryunder Contract F29601-73-A-0036-002. ~Present address: Sandia Laboratories, Albuquerque, NM 87115, U.S.A. §Present address: Los Alamos Scientific Laboratories, Los Alamos, NM $7545, U.S.A. 97

98

JOHNC. CUMMINGSet al.

temperature sufficient to produce in excess of 95% dissociation of hydrogen at chemical equilibrium. These experiments are followed by studies of the standard H2-F2 chain reaction mode: the hydrogen stream is unheated and the fluorine stream is raised to temperatures sufficient to provide various degrees of fluorine dissociation.

2. EXPERIMENTAL APPARATUS AND DIAGNOSTICS (aT A p p a r a t u s A schematic, Fig. 1, of the test facility shows the dual arc-driven, parallel nozzle flow arrangement. The arcs are operated to dissociate SF6 or F2 and provide a heated F/Nz mixture stream, ranging in stagnation temperature between about 500 and 2400K. The other stream provides HJN~ mixture at either 300 or about 3500K. A summary of test configurations for those tests analyzed is shown in Table 1. For most tests, the F-atom source is F2 and the diluent is N2. The two nozzles, RF-1 and RF-2, differ only in size, with the smaller RF-2 nozzle allowing operation at a higher exit pressure. The supply system consists of standard pressurized gas cylinders. Flow rate measurements of each gas are achieved by sonic control orifices. Two Thermal Dynamic model F-80~arc heaters, two control consoles, and six 40 kw d.c. power supplies provide the electrical energy. An O~

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Test

Reaction

Source Diluent

50

cold

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N2

yes

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Mixin~ Re~!on

Nozzle

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N2

Heated

Configuration

Coating

no

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no

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Reentrant Windows no

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Reference

7

67

cold

SF6

N2

yes

N2

no

RF-2

no

no

no

IR mapping

3

147

hot

F2

N2

no

N2

yes

RF-2

no

no

yes

[R emission

8 8

152

chain

F2

N2

yes

N2

no

RF-2

no

yes

yes

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153

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F2

N2

yes

N2

no

RF-2

no

yes

yes

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8

156

hot

F2

N2

no

N2

yes

RF-2

yes

yes

yes

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161

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yes

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8

H2-F2chainreactionrateinvestigation

99

molar flow rate equal to that for SF+ is injected to form SO2 to avoid deposition of sulphur on the walls of the apparatus. To achieve a simple mixing configuration the two nozzles are designed to produce a uniform constant pressure flow in the inviscid core at the nozzle exit. A Mach 4 nozzle with uniform parallel exit flow and minimum length was designed using a technique based upon the method of characteristics, and then corrected for the boundary layer displacement. Both hydrogen and fluorine nozzles have identical contours and are separated by a 1.5 mm divider at the exit plane. Each nozzle has four static pressure taps along its internal contour, and verify that no anomalies, such as shock waves, are present. Gas total temperature is deduced by a sonic flow calculation. Arc power, heat loss and operating pressures are monitored during the tests. The chamber into which the nozzle assembly protrudes consists of a rectangular box with nominal dimensions of 35 x 35 x 16 cm. One side plate contains a Pitot probe assembly, while the top and bottom plates contain quartz windows for spectroscopic measurements. Figure 2 provides a general picture of the supersonic flowfield in plane view. For a given diluent, used in both streams, the primary variables are the pressure level, the stagnation temperature and stoichiometry. In all runs, the nozzle exit pressures are equalized and then the cavity pressure is matched to this pressure. Under these conditions, the Pitot probe surveys indicated that the nozzle exit flows are free of shock waves of any appreciable strength. As shown in Table 1, shrouds are used on both sides of the jet (Fig. 2) on the later tests to assist in reducing jet oscillations. (b) Diagnostics The diagnostic techniques include spectral emission measurements in the 2 to 4/~m region, absorption (or gain) measurements, i.r. mapping of HF emission in the 2-3 ~m region, and Pitot pressure surveys. Figure 3 is a schematic layout of the emission and absorption measurement apparatus. Emission spectra of 2-4/~m yield HF line intensities for various fundamental radiative transitions. The optical observations are made along a line of sight parallel to the nozzle divider to take advantage of the two-dimensionality of the flow. Emission data is recorded on digital tape and reduced by a computer code,(+~which converts the data to intensity vs wavelength, identifies all spectral lines and computes the species concentration, rotational temperature and associated standard deviations using a least-square algorithm. Absorption/gain measurements are carried out in conjunction with the emission measurements using selected v = 0 ~ 1 lines, thus providing a method for determining the HF(0) concentration. The apparatus and analytical methods are identical to those described in Ref. (7). The probing light source is a low pressure H~F2 burner. Analysis of the data requires a knowledge of the spectral line profiles of the probing source and of the probed medium, and these are assumed to correspond to Doppler broadening at the appropriate measured spectroscopic rotational temperatures. The analysis of absorption data is performed with a computer program where the input parameters are the measured spectral line transmittance, the source and mixing layer temperatures, estimated measurement errors, and spectroscopic constants. TYPICAL VELOCITY PROEILE

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100

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Fig. 3. Schematicof the experimentalconfigurationusedfor emissionand absorptionspectroscopy. In conjunction with the hot reaction investigation, an electron beam excitation technique is used in an attempt to determine the degree of dissociation in the heated hydrogen jet. Energetic ( - 30--50 kv) electrons excite H2 to the B IX+ upper state, followed by rapid decay with emission of the vacuum ultraviolet Lyman bands. Ideally, a measurement of the intensity of a selected band of the H: Lyman system should provide a measurement of the H2 concentration. The technique is only partially successful in yielding quantitative H2 concentrations because of problems attributed to the presence of bands of impurity species and variations in the spectral character of the Lyman bands when the hydrogen stream is heated. 3. RESULTS AND DISCUSSION (A) The cold reaction Conditions for the laminar mixing layer calculations are summarized in Table 2, where cases I and II correspond to runs 50 and 67, respectively, of the Reactive Flow facility.(7) In these cases, the cavity pressure, the freestream chemical concentrations, velocities and temperatures, as well as the initial boundary layer profiles (assuming no F-atom wall recombination), were all matched to the experimental values. For case I (Fig. 4), there is agreement for the vibrational number densities between experiment and theory that a total inversion, which appears early in the mixing layer, has disappeared at about x = 4.55 cm. There is good quantitative agreement between the measured and predicted peak concentrations for vibrational levels 1, 2 and 3. For instance at x = 4 cm, the maximum experimental HF(1) and HF(2) concentrations are 5.5 x 10`4 and 4.0 x 10'4 mol/cm 3, respectively, compared to a computed value of 9.3 x 1014and 3.5 x 10'4 mol/cm3 (at 4.55 cm). This comparison appears in Fig. 4 and a similar one at 7 cm in Fig. 5. The estimated accuracy of the HF(V-> 1) population measurement is -+25%. There is a larger discrepancy in the ground state values, the measured concentration being about a factor of three smaller. As is pointed out in Ref. Table2. Initialcoreconditionsfor cold-reactionmixing-layercalculationswithN2diluent Case

PressureTorr

Velocity km/sec

Fluorine Streams Temp. Fluorine K Mass Fraction

Velocity km/sec

Hydrogen Strlmu Temp. Hydrogen K Mass Fraction

I

5.2

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500

0.0772

0.7355

71.0

'0.0109

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3.4

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498

0.0959

0.7154

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H2-F2 chain reaction rate investigation

101

EXPERIMENTAL DATA POINTS

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Fig. 4. Comparison of theoretical and experimental HF profiles (case I). Theory at x = 4.55 cm, experiment at 4 cm, pressure = 5.3 torr. See Table I for the experimental configuration.

EXPERIMENTAL DATA POINTS

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Fig. 5. Comparison of theoretical and experimental HF profiles (case I). Theory at 7.0 cm, experiment at

8 cm, pressure= 5.3 torr. (7), the ground state measurements are influenced by absorption occurring in the recirculating product gases that contain HF(0). The effect reduces the accuracy of the ground state measurement to approximately a factor of two. As shown in Table 1, reentrant windows, placed close to the jet (Fig. 3), are used in subsequent tests to minimize this difficulty. The comparison for case II is shown in Figs. 6 and 7. It is similar to case I, i.e. the computed maximum ground state concentration exceeds the measured value by a factor of four or five, and the excited state values are about twice their experimental counterpart. In both cases, the mixing layer width is greater in the experiment by about a factor of two. The recirculating HF(0) has already been identified as a source of error in the HF(0) measurements. A plausible explanation of the excited state concentration and width discrepancies is the unsteadiness of the jet and hence of the mixing layer. Such jet motion, not unusual for free jets, has sometimes been observed in the Reactive Flow facility. Because the concentration distributions are sharply peaked, jet oscillation would reduce the measured maximum value and, of course, increase the

102

JOHNC. CUMMINGSet al.

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apparent width. Note that the larger experimental widths and smaller concentrations mean that there is good agreement between theory and experiment for the integrated excited state flux. It should be recognized that although we desire to improve the comparison between the mixing calculations and the measurements, the factor of two discrepancy is actually encouraging. (Recall that the discrepancy with the chain is an order of magnitude.) Considering the extensive chemical kinetic model involved, the multi-component diffusion of the species and the presence of initial boundary layers, the agreement obtained is, in fact, good. Experimental mixing layer temperatures were typically 800 K, in good agreement with the theoretical calculations. (b) The hot reaction For the hot reaction investigation, it is desirable that the hydrogen ente.ring the mixing layer be fully dissociated. Even when the arc plenum is operated at ( - 3500 K) temperatures sufficient to completely dissociate the hydrogen (at chemical equilibrium), some atomic recombination

H2-F2chainreacfionrateinvesfigafion

103

might occur on the cold copper nozzle walls. Since the nozzle boundary layers are thick, this suggests the presence of a thick layer of recombined H2 leaving the nozzle and entering the mixing layer. The H-atom concentration is expected nearly to vanish at the wall if the probability of hydrogen recombination in a single wall collision, 7, exceeds 1/8, the (mean free path)/(boundary layer width) ratio. In the experiment this ratio is about 3 x 10-3. A typical value of 7 for H-atom recombination on metallic surfaces is 10-', °) thus the wall is fully catalytic. The reduction of atom concentration entering the mixing layer would reduce the rate of HF production. Since the HF concentrations measured in the first tests are significantly lower than predicted, the possibility of wall recombination must be considered. A new nozzle was therefore coated with Teflon, a substance with a recombination probability less than 10-4. Tl~e effect of the coating is discussed later. The experimental excited state profiles and temperature for the hot reaction with nitrogen diluent (test 147) are given in Fig. 8 for an axial station 5.08 cm from the nozzle exit plane. Computational results for this experimental condition (at 4.32 cm) appears in Figs. 9-11. A comparison of Figs. 8 and 9 shows major discrepancies. First, the theory predicts rotal inversion while none is observed in the experiment. Second, the total HF concentration in the experiment is an order of magnitude lower than the theory. Before these differences could be attributed to errors in the hot reaction kinetic rates, it is necessary to assess the effect of wall catalyticity and of the possibility that the arc was not fully dissociating the hydrogen. At the time of these experiments, the Teflon-coated nozzles were not

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Fig. 8. Results of test No. 147D, x = 5.08 cm past exit. See Table 1 for the experimental configuration.

104

JOHN C. CUMMINGS et al. 1.8

HF (v), V : 0-7 SPECIES PROFILES 1.6

HF CHAIN - 1 RATES X : 4.32 CM NONCATALYTIC WALL 100% H2 DISSOCIATION

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available, nor was there any direct method of measuring the H/H2 ratio. To assist in the assessment, two additional calculations were performed. In the first, the hydrogen concentration profile leaving the nozzle was modified to approximate that of a fully-catalytic wall, i.e. the H-atom concentration was set equal to zero on the wall. The HF(v) profiles for this case are shown in Fig. 10. In comparison with Fig. 9, we conclude that the effect of wall recombination on either total HF production or on relative concentrations of the vibrational levels is less than 30%. Another hypothesized reason for the low experimental HF(v) concentrations is that the arc-heated nitrogen temperature is insufficient to fully dissociate the hydrogen. A run with only 10% hydrogen dissociation produced the HF(v) profiles shown in Fig. 11. The total HF produced is reduced by a factor of about 6, resulting in better agreement with the theoretical total HF predictions, but the discrepancy in the relative vibrational level concentrations remains. Experimental conditions corresponding to those for Fig. 8 were then rerun with the Teflon-coated nozzles. The total amount of excited HF observed (test 156) was approximately twice as high as in the uncoated nozzle case (test 147). The differences are largest in the higher vibrational levels, e.g. HF(4) has four to six times the concentration of the earlier tests. This observation is explained by the higher H-atom concentration in the boundary layer and the consequent higher hot reaction pumping rate in the mixing layer. The reduction in the H2 concentration would also have a favorable effect, since this molecule is a deactivator. It is evident that the reduction in wall catalysis did change the relative ratio of the vibrational levels, but again, the change is slight in comparison with predicted results.

H2-F2 chain reaction rateinvestigation

105

1.8

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HF (v), V = 0-7 SPECIES PROFILES X = 4.32 CM CATALYTIC WALL 100% H2 DISSOCIATION HF CHAIN - 1 RATES

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Fig. 10. Mixing-layer calculations of HF(v) concentrations as a function of y at x = 4.32 cm (HF chain-I rates). 1.2

u

1.0 HF (v), V = 0-7 SPECIES PROFILES X = 4.32 CM CATALYTIC WALL 10% H2 DISSOCIATION HF CHAIN - I RATES

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0.5

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Fig. 11. Mixing-layer calculation of HF(v) concentrations as a function of y at x = 4.32 cm (HF chain-I rates).

106

JOHNC. CU~ImNGSet

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Fig. 12. ResultsoftestNo. 161A,x =5.08cmpastexit.SeeTablelforexpcrimenmlconfig~ation. With N, as diluent, there is the possibility on the F, side, when heated sufficiently, for the formation of NF~. Similarly, on the heated Nz-H2 side there is the possibility of NH3 as well as N atom formation, although equilibrium calculations indicated both possibilities to be negligible. Test 161 eliminated these considerations by substituting argon for the diluent. Figure 12 shows the results for this test, where the H2 and F2 flow rates are the same as those in tests 147 and 156. This diluent change decreases the core temperature of each stream by about 60% and slightly reduces the velocity. The HF(v) distribution is more uniform with argon diluent particularly at x = 5.08 cm (compare with Fig. 8). The populations of v = 1 and v = 2 are about equal, with v = 3 only about 30% less. The populations of v = 4, v = 5 and v = 6 are nearly equal to each other and are about two thirds of the v = 3 population at x = 5.08 cm, and one third of the v = 3 population at x = 10.16 cm. The total excited population is about the same as had been obtained with N2 diluent. While the differences in the degree of vibrational excitation with argon substituted for N2 are significant, this again is not an order-of-magnitude effect. The population of v = 5, for example, is increased by a factor of 2 with the argon diluent, with lower v levels affected correspondingly less and v = 6 somewhat more. The general conclusion is that there is a major discrepancy between the experimental HF(v) profiles and the computer predictions using the chemical rates based on COnEN'S('°} compendium. At this point, a new set of rates (HF chain-II) were developed that are discussed in Appendix B. The principal difference between the new and the old rates is the inclusion of multiquantum HF(v) transitions that deactivate the upper levels at a rapid rate. To compare the two rate packages, the N2 diluent, 100% H2 dissociation, noncatalytic wall case (Fig. 9) was recomputed. The results (Fig. 13) indicate the width of the reaction zone and the total HF produced are not significantly changed, but the HF(v) distribution is drastically modified. In particular, the new rates favor the v = 0 and 1 levels at the expense of the higher levels. Some additional rate changes were then made (see HF Chain-III rates in Appendix B) and both argon and nitrogen diluent cases were computed. This last change in the rate package caused only minor changes in the relative HF(v) ratios from the results with the modified rates for the above nitrogen case. In approximate accord with the experimental situation, there is little

Hz--Fzchainreactionrateinvestigation

107

=0

1.4

I

HF (v), V = 0-7 SPECIES PROFILES

1.2

HF C H A I N - 2 RATES X = 4.32 CM NONCATALYTIC WALL

0 1.0

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0 o Io

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z Z 0 u

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Fig. 13. Mixing-layercalculationof HF(v) concentrationsas a functionof y at x = 4.32cm (HF chain-II rates). difference in these ratios between the nitrogen and argon cases. The calculations show that the mixing zone is thinner when argon is the diluent, presumably because of the reduced diffusion coefficient and lower temperatures in this case. This trend is noted in the experimental results at 10.16 cm, but not at 5.08 cm. To resolve the discrepancy concerning the rate of HF production, it would be necessary to assume that the product of the rate coefficient of the H + F2 ~ HF + F reaction and the degree of hydrogen dissociation is an order of magnitude less than one would infer by assuming 100% H2 dissociation and the hot reaction rate coefficient in Appendix B. [The total "hot" reaction rate of Appendix B is taken from discharge flow tube measurements of Ref. (11), which may be too fast."~q When catalytic wall recombination and the larger width of the experimentally observed mixing layer are taken into consideration, a discrepancy of about a factor of five still remains. At this time, the electron beam diagnostic was used in an effort to determine the degree of dissociation of the hydrogen jet. Although cold flow calibration tests demonstrated a linearity between H2 partial pressure and the intensity of the 1608A H2 Lyman (5,12) R-branch head, problems of impurity contamination and changing band shape prevented quantitative application of the technique with arc-heated HJN2 (1.7% H2) mixtures. When the measurements were repeated with 3.4% H2 molar ratio, decrease in H2 concentration with increasing arc plenum temperature was noted, giving confidence that the degree of H2 dissociation at 3500 K plenum temperature is 60_ 30%. If this degree of dissociation is obtained, the rate of the hot reaction would have to be reduced by a factor of two to five below the value of Ref. (11) (at - 6 0 0 K) in order to explain the experimental results. It is important to note that just on the basis of the results already discussed, it is justified to conclude that an error in the deactivation rates of high vibrational levels populated by the hot reaction explains the overly optimistic earlier chain laser performance predictions. "~ (c) The chain reaction In the chain reaction investigation the hydrogen stream was unheated while the fluorine containing stream was raised to various temperatures (Table 1) and, hence, to various levels of

108

JOHN C. CUMMINOS et aL

fluorine dissociation. Experiments were performed with uncoated and Teflon-coated walls and with nitrogen and argon as the diluent. In these tests, however, no effect of wall coating or diluent was apparent in the experimental results. The discussion is focused on Test Nos. 152 and 153, Table 3, which provides a total of six operating conditions at F2 arc-plenum temperatures from 500 to 1200K. As the F~ arc-plenum temperature is varied, the nozzle exit pressures are maintained at - 2.5 Torr, and the hydrogen nozzle flow conditions are unchanged. Spectroscopic measurements are made at locations 2.5, 6.9 and 10.7 cm past the nozzle exit. Side-wall shrouds (Fig. 2) are used to minimize recirculation. Table 3 lists values of the fluorine arc-plenum temperature T,~, the calculated equilibrium dissociation of fluorine a, the reaction-zone width at half-maximum intensity, the rotational temperatute at the center of the reaction zone, and the peak population of HF in vibrational levels 1 through 5. Rotational temperature is defined from a linear-regression Boltzmann fit for states where Y -< 8, since evidence of anomalously high populations of the higher Y levels are observed. Figure 14 illustrates this effect. This non-Boltzmann rotational distribution is not obsJrved in F + H2 cold reaction tests. It can be attributed to redistribution of vibrational energy from the upper levels into high rotational states, via V-R processes, and the relatively slow rate of rotational relaxation of high-J states. "3~ For the range of arc-plenum temperatures covered, the chemical equilibrium value of a varied between 2 × 10-5 and 0.86. The measured concentrations of excited HF in the reaction zone increased monotonically with the fluorine arc-planum temperature and predicted disociation, ultimately increasing by a factor of about 30. To compare with these data, a series of three cases with a =0.03, 0.10 and 0.30 were calculated at the corresponding experimental condition. These calculations assumed a non-catalytic fluorine nozzle wall and used the final rate package, HF chain-III. Since the comparison between the theoretical and experimental mixing layer widths are similar to the earlier runs, the discussion of the HF concentrations is restricted to a comparison of the maximum concentrations. Tables 4(a) and (b) show the maximum concentrations and temperatures from the mixing layer profiles, as well as experimental values from selected runs. Experimental errors are generally - 25% or -- 2 x 10-8 mol/cm ~, whichever is greater. We first note that the total of the excited state concentrations in the theory and the experiment vary with a in a similar way. Further, the absolute values of the total excited state concentrations Table 3. Summaryof spectroscopic measurements Test Condition X No. No. (cm) T(t~

152

152

152

153

153

153

-l 5'3 -I 4

6.9 6.9

920

-23 -24

6.9 6.9

1780

-23

10.7

-24

I0.7

-33 -33

2.5 6.9

-33

10.7

-I 3 -I 4

6.9 6.9

-I 3

10.7

-23 -23

6.9 I0.7

I170

-33

6.9

500

-33

I0.7

720

II000

~(I)

YF2(2)l ReactiOlzone T(6) FWHM (K)

Icm)

.18

.023

,007

,40

.86

.073

.073

• 074

• 043

,043

2 X 10-5 ~,043

.46

T , . = 300 K ; P , F = P , , = 2.5 ton';

YH2= 0.0~:z))

[HFy] ~ mole/cm3 x 1o 13 V-I

423 5 28 50.0~15.0

v

2

v

.45 5 .10

.33 .2B .30 .33

383 ~ 33 22.4~3.0

11.3 +- 2.9

4,4 + 1.6

.57

388 ~ 35 26.453.4

12.1~3.1

4.5 + 1.6

.36 • 38 .46

6.2~0.9 14.1~2.1 343 5 34 15.052.4

4.2~I.I 6.7~I.7 6.852.1

.43

448 5 32 4 2 . 5 5 4 . 4

• 62

470 5 44

.47 • 61

473 ~ 28 58.7~5.4 477 ~ 29 58.0~5.1

33.454.7 30.0~4.2

,38 ,53

354 ~ 54 425 ~ 66

1.72 ~ .35 2,02 ~ .53

.98 ~ .49 .98 ~.41

23.6~3.2

-+ *+ t

.30 .28 .30 .34

.50 -+ .I0

2.5 +- 1.9

.94 .71 .92 .89

1.3 ~ 0.5

.24 + .08

.08 5 .02

2.4 + 0.9 1.9 + 0.9

.43 + .14 .44 + .18

.10 + ,03 .12 5 ,02

23.7~4.3 8.O +- 2.1 2 . 0 0 5 .40 21.7~12.3 12.6 + 8.6 2.30 -+ .70 I0.152.3 2.7 -+ 0.9 0.70 t .20

. 6 0 5 .10

11.1 -+ 2.2 2.5o+- .4o 9.3 +- 1.8 2.1o -+ .3o .88 -+ .57 .51 -+ .28

-+ -+ t 5

.09 .10 .08 .II

.60 -+ ,20 .30 -* .10

.6or .lO .5o t .o8

.07 -+ .03 .04 + .02 .09 -+ .04 .013 +- .008

rff'l (I)

~ =T F T ~

(2) (3)

yH2 and yF2 are the mole fractions of H2 and F2 in t h e i r respective j e t s . 2.5 - 3.5 pm scan at moderate sensitivity (best f o r v = I , 2, 3, and temperature)

(4)

2.8 - 3.5 pm scan at high s e n s i t i v i t y (best f o r v = 4 and 5)

(5)

Data reduced by hand show anomalously high excitation f o r J ~ 8 Temperatures based upon b e s t - f i t with J ~ 9. Higher J-levels have anomalously high populations.

(6)

V-5

23.6 5 4.4 I0.7 -+ 2.7 2.10 -+ .50 15.9 + 8.1 8.4 -+ 5.1 1.90 + .60 (also v = 6: 0,19 + ,Q4)

.44

381 5 34 343 ~ 27

L

V 4

H2-F2 chain reaction rate investigation

109

103

ROTATIONAL OF EQUILIBRATED LEVELS(J' s 8 ) = 320 K

102

LEGEND O V'=I nl V ' = 2 A V'=3

0v':4 ~-

S

® V'=5

10

V

V'=6

I "TEMPERATURE"-~ 2000 K FOR 12 -~ J' -~ 16

+ +

0a. ~ >

/

100

10-1

v:5

0

~ v = 3 "~V= 4

10-2 /

l

I

I

I

I

1000

2000

3000

4000

5000

ER~UPPERLEVELROTATIONALENERGY~CM-I

Fig. 14. Semilogarithmic plot of HF~.,/(2J' + 1) vs rotational energy for test 152, condition 1.

Table 4(a). HF(v)concentration and temperature at x - 6.9 cm; [HF(v)] x 10 '° mol/cm 3 "

I v'O J v=I J v-2 I v-3

I v=4 I v=S j v=6 J v-7 IT. K J ,HF, Experiment

0.007

2.34

1.11

0.40

0.07

0.02

. . . .

343

3.94

0.03

3.72

1.88

0.73

0.16

0.0S

. . . .

383

6.54

0.18

8.31

3.92

1.78

0.35

0.07

. . . .

423

14.43

0.40

7.06

3.94

1.33

0.33

0.10

. . . .

448

12.76

0.86

9.75

5.55

1.84

0.42

0.10

. . . .

473

17.66

4.65

Theory 0.03

0.54

1.16

1.33

0.82

0.45

0.40

0.33

0.11

432

0.I0

2.85

3.39

2.81

1.60

0.87

0.66

0.50

0.14

505

9.97

0.30

9,3,3

6.53

4.16

2.05

0.96

0,70

0.51

0.10

600

15.01

Table 4(b). HF(v) concentration and temperature at x - 10 cm; [HF(v)] x 10 '° mol/cm'

• I,-0 .

I vol I v-2 Iv.3 I vo4 Iv-5 I v-6 Iv.,

,,

IT. KI

E×periment

0.007

2.49

D.40 0.55

~--

1.13

0.32

0.07

0.02

. . . .

343

4.03

3.92

1.68

0.45

0.12

0.05

. . . .

470

6.22

9.63

4.98

1.54

0.35

0.08

. . . .

477

16.58

Theory 0.03

1.09

1.62

1.55

0.94

0.54

0.44

0.35

0.13

433

5.57

0.10

4.72

4.14

2.95

1.64

0.89

0.65

0.46

0.12

537

10.85

0.30

16.51

7.15

3.56

1.66

0.78

0,58

0.41

0.10

675

14.24

.

I10

JOHNC. CUMMINGSet al.

agree reasonably well, especially in view of the fact that a in the experiment must be inferred. Tentative conclusions from these two areas of agreement are: (1) a range of a was achieved in the experiment and (2) the pumping rates in the cold and hot reactions are approximately correct. Turning next to the distribution of excited states among the various levels, we observe that in the experiments the concentration drops monotonically with increasing v, at all a. In the theoretical results, this behavior is observed only for a = 0.30. There is, in fact, an absolute inversion at x = 6.9 cm between the theoretically predicted populations of levels 1 and 2 for tx = 0.03. Note also in Tables 4(a) and (b) the differences in behavior with axial distance between theory and experiment. Compare, for instance, the a = 0.40 result in the experiment to the a = 0.30 in the theory. At x = 6.9 cm the total excited state populations are approximately equal. At x = 10.7 cm the experimental value has dropped to approx. 1/2 of the theory, which has hardly changed. This indicates that in the experiment, deactivation has placed more molecules in the ground state. Referring next to the populations in vibrational levels 4 and above, we see that the experimental populations are lower by factors of 5-10 than those in the theory. Since the measurement can detect concentration as low as 0.02 × 10-~° mol/cm 3, this sets an upper bound to the concentration when no signal is seen. Consider level 6: the absence of signal implies that the observed values are over an order of magnitude below the theoretical prediction. All of these observations support the conclusion that the upper vibrational levels have been more rapidly depopulated than the last set of rate coefficients used in the theoretical calculations. 4. CONCLUSIONS The purpose of this investigation focused on the kinetic rates; in particular, (1) to determine if there are any gross errors in the chemical kinetic rate package that causes the discrepancy between the theoretical and measured chain reaction laser performance and, (2) if the rates appeared to be incorrect, to formulate a more accurate set. From a comparison between the experimental excited-state populations and those given by the mixing layer code, we conclude: (1) The cold reaction pumping and deactivation rates are approximately correct. (2) There is an error in the chemical rate associated with the deactivation of the high vibrational levels pumped by the hot reaction. (3) The inclusion of the multiquantum HF(v) transitions, which redistribute the vibrational energy in favor of the HF(0) and HF(1), greatly improves the agreement between theory and experiment. Even with these inclusions, however, the theoretical predictions of excited-state distribution are too optimistic. Subsidiary results from the experimental investigation are: (1) the application of a Teflon coating to the nozzle walls produced a minor change in the HF(v) disttributions, which is consistent with a reduction in wall catalyticity for H-atom recombination, (2) replacing the nitrogen diluent by argon resulted in more favorable (for lasing) HF(v) distributions but did not eliminate the large discrepancy between theory and experiment, and (3) the observed discrepancy between experimental and theoretically predicted HF formation due to the H + F2 reaction can be resolved if the rate of this reaction is two to five times slower than the currently assumed value, "°~ at 600 K. Acknowledgements--The authors gratefullyacknowledgethe assistance of M. KWOKand M. COHENof The AerospaceCorp. in kinetics; R. SORENSON,R. HILYARDand A. S. WHrrEMANfor experimental testing and diagnostics; D. HAFLINGERfor theoretical calculations, and M. BECKENHOLDTfor manuscript preparation. We also wish to thank the AFWL program monitors: L/C J. DOUOHTY,Capt. R. MrrCHAM,Capt. J. WAYI'A,Lt. M. DYER,and Capt. W. WATKXNSfor their technical contributions. Finally,the authorsexpresstheir gratitude to T. A. JAcoas,whoseknowledgeand specialinsightwere of crucial importance to the project.

REFERENCES 1. G. EMANUEL,N. COHENand T. A. JACOBS,JQSRT 13, 1365(1973). 2. TRW Final Report No. CSR-25691-4, prepared for Air Force Special Weapons Center under Contract No. F29601-74-C-0073,July 1974. 3. A. B. WrrrE, J. E. BROADWELL,W. L. SHACKLEFORD, J. C. CUMMINGS,J. E. TROST,A. S. WHITEMAN,F. E. MARBLE,D. R. CRAWFORDand T. A. JACOBS,TRW Report No. AFWL-TR-74-78,Feb. 1974. 4. W. L. SHACKLEFORD,A. B. WrrrE,J. E. BROADWELL,J. E. TROSTand T. A. JACOBS,AIAA J. 12, 1009(1974).(Synopticof AIAA Paper No. 73-640presented at Sixth Fluid and Plasma DynamicsConference,Palm Springs, CA., 16--18July, 1973.) 5. F. G. BLO'rl'NER,AIAA J. 8, 193 (1970).

H2-F~ chain reaction rate investigation

111

6. J. T. LATIMORE,A. M. TAKEMOTO,R. A. ACKERMAN,W. L. SHACKLEFORDand G. EMANUEL,TRW report prepared for U.S. Army Missile Command AMSMI-RK, Contract No. DAAH01-73-C-0446, Redstone Arsenal, AL, Jan. 1974. 7. A. B. WrrrE, J. E, BROADWELL,W. L. SHACKLEFORD,J. E. TROSTand T. A. JACOBS,TRW Report No. AFWL-TR-72-247, June 1973. 8. A. B. WrrTE, J. E. BROADWELL,W. L. SHACKLEFORD,J. C. CUMMINGS,J. E. TROST,A. S. WHITEMAN,F. E. MARBLEand D. R. CgAWFORD,TRW Report No. AFWL-TR-75-266, Dec. 1975. 9. H. C. BERGand D. KLEPPNER,Rev. Sci. Instr. 33, 248 (1962). 10. N. COl/EN, Aerospace Report TR-0073 (3430)-9, Nov. 1972. 11. R.G. ALBRIGWr,A. F. DODONOV,G. K. LAVROVSKAYA,I. I. MOROSOVand V. L. TALROZE,J. Chem. Phys. 50, 3632 (1969). 12. N. COIlEN and J. F. Bola', Aerospace Report TR-0076 (6603)-2, April 1976. 13. J. C. POLANYIand K. B. WOODALL,J. Chem. Phys. 56, 1563 (1972). 14. M. KwoK, Private Communication. 15. P. S. GANGUHand M. KAUFMAN,Chem. Phys. Lett. 25, 221 (1974). 16. G. EMANUi~L,Simplified modeling of multi-quantum deactivation reactions, in press in AIAA J. (1976). 17. G. P. QUIGLEYand G. J. WOLG^, Paper No. MD-8, 4th Conf. on Chemical and Molecular Lasers, St. Louis, 1974. APPENDIX A

Mixing layer code A generalized laminar boundary layer calculation code with provisions for the inclusion of up to 70 chemical reactions, developed originally by Blottner,c5)has been modified to permit application to the mixing layers found in chemical lasers. The compressible boundary layer equations describing the mixing layer are solved, using the Levy-Lees transformed independent variables, by implicit finite-difference approximations which reduces the problem to that of solving algebraic equations for the dependent variables at each axial station. Basically, the boundary layer equations are first transformed into similarity form with new dependent and independent variables in order to obtain a set of equations appropriate for numerical solution. The governing partial differential equations are replaced by coupled finite difference equations which reduce to a set of tridiagonal matrices for each of the dependent variables across the layer. The equations are solved sequentially at each downstream station yielding profiles of velocity, temperature, density, and species concentration. The variables are determined with a resolution of up to 50 mesh points across the mixing layer, and the code has provisions for arbitrary initial conditions so that the effects of initial boundary layers can be taken into account. Transport properties are included using a simplified model which requires less computation time. The chemistry is treated in a general form, such that the chemical species involved, their thermodynamic and transport properties, and the chemical reactions and corresponding rate coefficients are all entered as data. The temperature dependence of each of the species viscosity and binary diffusion coefficients are given as inputs in the form In p,i ~ = A (In T) 2+ B In T + C, In PDii J which are curve fits to the theoretically or experimentally determined coefficients. For multicomponent diffusion, neglecting thermal diffusion, the mass flux for species i relative to the mass-average velocity,/'j, is

Oc~ Lei= 2 Ji -_ - - ~I~, L e,~y,

ci / ~

cj

where Lo = pd~D,~lk is the Lewis-Semenov number, p is the density, 6p is the mass averaged specific heat at constant pressure, k is the thermal conductivity (obtained from the viscosity using a modified Eucken expression),/z is the mixture viscosity, P, = iz~pIk is the Prandtl number, NI is the number of chemical species, M, is the molecular weight of species i and c, is the mass fraction of species i. The foregoing expression for ./, is exact for trace species and for constant Lewis-Semenov numbers. This approach is used to save computing time, since otherwise a complex, large-scale matrix inversion would be required at each point in the mixing layer. The molar enthalpy, specific heat, molecular weight, and heat of formation are stored as tabulated data, which are necessary to calculate the thermodynamic state at each point in the mixing layer. Finally, the forward and backward chemical reactiofi rate coefficients are used in the form

kk~} = ATBexp(-C/T).

APPENDIX B

HF kinetic rates As described in the text, three different chain reaction rate models are utilized. The first, given in Table B 1, is primarily based on Ref. I0, an early compendium by Cohen. This model contains the standard type of recombination, pumping, VV and VT (or VR) deactivation rates. Computer core size limitations restricted all rate models to 70 reactions; as a consequence, it was not possible to include deactivation rates for N2, At, He, or sulfur bearing compounds. Furthermore, in the first model this limitation prevented inclusion of multiquantum processes. Because of the large energy defect, the backward rate for VT reactions can be accurately approximated as zero. Since the code doesn't allow Do to be zero, a one or 10-6 is used instead (these are very small rate coefficient values). Special items of interest in the -I model include: (1) The F-atom three-body recombination rate is based on the measured dissociation rate plus the equilibrium constant. This recombination rate is unrealistically slow at room temperature. (2) For v ->4 the cold reaction proceeds in the reverse direction, thereby de-exciting HF(v), v ->4. (3) The important HF + HF and HF+ H VT processes assume Av = 1 and linear v scaling. (4) The forward rates for the process HF(v) + H2 ~ HF(v - 1) + He are the VV rate coefficients with H2 in ground state. The backward rate is taken as 0.1 of the forward rates. The actual HF + H2 VT rate is neglected, since it is slower than the VV rate. QSRT Vol. 17, No. 2~B

112

JOHN C. CUMMINGSet al. Table BI. HF chain-I rate model C2 e-1000C1/T k f = CO T

REACTION *

CO F2 F F F F F F F H

H H H H H H H HF1 HF2 HF3 HF4 HF5 HFb HF7 HF1 HF2 HF3 HF4 HF5

+R1 +H2 +HE ..,H 2 +M2 +HE +H2 *HZ +F2 +F2 eF2 +F2 +FZ eFZ +FZ +F2 +H2 +MZ eRE eH2 +HZ +N2 +R2 +F +F +F +F +F

-~F-6 ~+F HF7 HFI HF2 HF3 HF4 HF$ HF6 HF7 HF1 HF2 HF3 HF4 HF5 HF6 HF? HF1 i..HFZ HF3 HF4 MF5 HF6 HF1 _HF2 HF3 HF4 HF5 HFI HF2 HF3 HF4 HF1 HF2 HF3 HF1 HF2 HF3 HF4 HF5 HF6 HF7

+F +FZ +F2 ÷F2 +F2 +F2 +F2 +F2 9H +H ~H eH eH eH eH +HF1 ÷HF2 +HF3 eHF4 +HF5 +HF6 +HF2 ÷HF3 +HF¢ +HF5 +HF6 +HF3 +HF4 +HF5 +HF6 +HF4 ÷HF5 +HF6 +H2 +HE +HE +H2 eH2 +HE eHZ

*

•F eF =HF1 ÷H =HF2 +H =HF3 +H =HF4 +H =HF5 +H =NF6 +H mHF? *H =HF0 +F -HF1 +F "HF2 +F =HF3 +F =HF4 +F aHF5 +F =HF6 +F =HF? +F =NF0 ÷RE -HF1 +~2 =HFZ +R2 -HF3 +RE -HF4 +HE -HF5 +H2 =HF6 *ME eHF0 +F "HF1 +F -HF2 +F =HF3 +F 8HF4 +F uHF5 +F =HF6 eF =HF0 +FZ -HF1 ÷ F 2 eHF2 +FZ • HF3 +F2 =HF4 + F 2 eHF5 +F2 oHF6 +FZ mHF0 +H eHF1 +H oHF2 ~H oHF3 eH nNF4 +H =HF5 eH • HF6 +H =HF0 +HF2 =HF1 +HF3 -HF2 +HF4 mHF3 +HF5 mHF6 eHF6 =HF5 eHF7 -HF0 +HF3 mHF1 +HF~ aHF2 +HF5 =HF3 +HFb =HF4 +HF7 =HFO +HF4 =HF1 +HF5 =HF2 +HF6 =HF3 eHF7 uHFO +HF5 eHF1 eHF6 • HF2 +HF7 =HFO +H2 =HFI +H2 =HF2 +H2 mHF3 +H2 "HF6 +HE 8HF5 +HZ • HF6 +H2

+R1

S,0 7,8 2.64 1,32 1, 1, 1, 1. 1.1 2,5 3.5 3.6 1,6 3,6 4.8 5,5 1.0 2,0 3,0 4.0 5.0 6.0 7.0 1,5 .1,5 1.5 1.5 1.5 i,5 1,5 0,8 1.6 Z.4 3.2 4.0 4.8 5.6 1.8 3.6 5.4 7.2 g.o 1,08 1,Z6 1,5 1.5 1.5 1,5 1,5 1,5 7.5 7,5 7,5 7.5 7,5 3.75 3,75 3.75 3.75 1.875 1,875 1.875 9. 2,9 9. 2. Z, Z* 2.

C2 El3 El31 El4' El4 I

E1Z EI2 E12 E12 E13 El3 El3 EI2 El4 El4 El4 El4 El4 El4 El4 EIO El0 El0 El0 El0 ElO EIO E-3 E-3 E-3 E-3 E-3 E-3 E-3 El3 El3 El3 El5 El3 E14 El4 EIZ EI2 E12 EIZ E12 EIZ Ell Ell Ell

17.76 .8051 .8051 .8051 .2516 ,2566 .Z828 ,2828 1.208 1.208 1.208 1.208 1.208 1,208 1.208 1.208

,5~35 ,2516

-.8 -.8 -,8 -.8 -,8 -.8 -.8 1, 1. 1. 1. 1. 1, 1, 4. 4. 4. 4, 4. 4. 4,

,3522 .3522 .SSZZ .35ZZ ,3522 .35ZZ .$522 %5 ,5 .5 ,5 .5 ,5 .5 ,5 ,5 ,5 ,5 .5 ,5 .5 .5 .5 ,5 ,5

Ell Ell Ell Ell El1 Eli El1 Ell Ell Eli E12 E12 El3 E13 E13 El3

D2 e'lOOOD1/T kb = DO T

.28ze .5304 .7714 1.006 1.006 1,006 1,O06

The d e f | n t t t o n o f the H'$ ts gtven a f t e r T t b l e B2.

Ol

DO 5.42 1.0 1,0 1.0 7.4 1.1 1.9 1.9 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.

-.g97 .8051 .8051 ,8091 El; E13 E13 E13

1, 1. 1, 1. 1. 1, 1. 1. 1. 1. 1. .000001 .000001

O2, -,09

.Z5i6

.Z566 .2828 ,2828 1,208 1.208 1,208 1.208 1.206 1.208 1.208 1.208

.553~ .2516

,000001 .000001

.000001 .000001 .000001 1. 1. 1, be 1. 1. 1. 1,5 El2 1.5 S12 1,5 E12 1.5 El2 1.5 EI2 1.5 EI2 7.5 Ell 7.5 Ell 7,5 Ell 7,5 Ell 7.5 Ell 3.75 Ell 3.75 Ell 3.75 Eli 3.75 Ell 1.675 Ell 1,875 Eli 1.875 Ell 9, E10 2.9 Ell 9. Eli 2. E12 2. E12 2. E12 Z. EI2

.3522 ,35Z2 .35ZZ ,392Z .392Z .352Z .3522 .24?6 • 2410 • Z345 • 2300 • 2252 • 2219 • 4886 • 4?55 • 4645 • 4549 • 4468 • ?37g • 7055 • 6896 • 6768 • 9531 • 9304 • 9113 ,2828 .5304 .7714 1.006 1.006 1.006 1.006

,S .5 .5 .5 .5 .5 ,5 ,5 ,5 05 ,S .5 ,5 .5 .5 .5 .5 ,5

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114

JOHN C, CUMMINGSet al, M Values f o r HF C h a i n - I

Rates

M1 = 1.0 N2 + 1.0 H2 + 1.0 H + 2.4 F2 + 2.4 F + 1.0 HF(O) + 1.0 HF(1) + 1.0 HF(2) + 1.0 HE(3) + l . O HF(4) + 1.0 HF(5) + 1.0 HF(6) + 1.0 HF(7)

M2 = 1.0 HF(O) + 1.0 HF(1) + 1.0 HF(2) + 1.0 HF(3) + 1.0 HF(4) + 1.0 HF(5) + 1.0 HF(6) + 1.0 HF(7)

M Values f o r HF C h a i n - l l

Rates

M1 = 1.0 He + 1.0 N2 + 1.0 H2 + 3.0 H + 2.4 F2 + I 0 . 0 F + 1.0 HF(O) + 1.0 HF(1) + 1.0 HF(2) + 1.0 HF(3) + 1.0 HF(4) + 1.0 HF(5) + 1.0 HF(6) + 1.0 HF(7)

M2 = 1.0 He + 1.0 N2 + 1.0 H2 + 20.0 H + 1.0 F2 + 1.0 F + 1.0 HF(O) + 1.0 HF(1) + 1.0 HF(1) + 1.0 HF(2) + 1.0 HF(3) + l . O HF(4) + 1.0 HF(5) + 1.0 HF(6) + l . O HF(7)

M3 = l . O HF(O) + 1.0 HF(1) + 1.0 HF(2

+ 1.0 HF(3) + 1.0 HF(4) + 1.0 HE(5)

+ 1.0 HF(6) + 1.0 H E ( l )

M4 = l . O HE(1) + 2 . 0 HE(2) + 3.0 HF(3

+ 3.0 HF(4) + 1.0 HF(5) + 0.5 HF(6)

+ 0.25 HF(7)

M5 = 2.0 HE(2) + 3.0 HF(3) + 3.0 HE(4

+ 1.0 HF(5) + 0.5 HF(6) + 0.25 HF(7)

M6 = 3.0 HF(3) + 3.0 HF(4) + 1.0 HF(5

+ 0.5 HF(6) + 0.25 HF(7)

M7 = 3.0 HF(4) + 1.0 HF(5) + 0.5 HF(6

+ 0.25 HF(7)

M8 = 1.0 HF(5

+ 0.5 HF(6) + 0.25 HF(7)

M9 = 0.5 HF(6

+ 0.25 HF(7)

MIO

=

1.0 F2

MII = 1.0 HF(I

+ I 0 . 0 HF(2) + I 0 . 0 HF(3) + I 0 . 0 HF(4) + I 0 . 0 HF(5)

+ lO.O HF(6) + I 0 . 0 HF(7)

MI2 = I 0 . 0 HF(2) + I 0 . 0 HF(3) + I 0 . 0 HF(4) + I 0 . 0 HF(5) + I 0 . 0 HF(6) + I 0 . 0 HF(7)

MI3 = I 0 . 0 HF(3) + I 0 . 0 HF(4) + I 0 . 0 HF(5) + I 0 . 0 HF(6) + I 0 , 0 HF(7)

MI4 = I 0 . 0 HF(4) + I 0 . 0 HF(5) + I 0 . 0 HF(6) + I 0 . 0 HF(7)

Ml5 = I 0 . 0 HF(5) + I 0 . 0 HF(6) + I 0 . 0 HF(7)

MI6 = I 0 . 0 HE(6) + I 0 . 0 HF(7)

115

H2-F2 chain reaction rate investigation

The -II rate model was compiled early in 1975 with the assistance of M. Kwok and N. Cohen of The Aerospace Corporation. COheN and Borr "~) have recently published a new compilation of the HF kinetics, and, as might be expected, the -II rates are in good accord with their recommendations. There are two notable differences: In their treatment of the HF+ H~ VV rate, Ref. (12) suggests a multiquantum process, whereas the -II model still uses the older values from Ref. (10). Multiquantum rates for HF + H2 where unknown at the time this work was performed. Furthermore, the scaling with v is faster than linear in the -II model, as compared with linear scaling in Ref. (12), thus the difference is not as significant as first appears. The second difference is for the HF + HF VT rate where Ref. (12) uses Av = i, but increases the rate rapidly with v, whereas the -If model uses results from the flow tube experiments of KwoK°4) with a multiquantum assumption. The F-atom recombination rate coefficient, the first reaction in Table B2, is based on Ref. (15). The H-atom recombination rate coefficient is given in Ref. (12), while H + F recombination was evaluated and found to be much slower than the preceding processes and therefore is not included. Normally, recombination is not important in cw chemical lasers. This, however, is not necessarily the case when chain reaction is occurring and the fluorine plenum temperature is as low as 500 K. The edge temperature on the fluorine side of the mixing layer then is very low and, consequently, three body recombination has a large rate coefficient. In cases where the fluorine is partially dissociated in the plenum and high temperatures (~ 1000 K) are achieved in the mixing layers, the thermal dissociation in the jet of F2, given by the forward direction of reaction 1, can become important. Thus, for the experiments involved, both the forward and backward directions for reaction 1, on occasion, can be significant. In view of this, measured rates are used for both directions; their ratio does not equal the equilibrium constant. The rates for the hot and cold pumping reactions are the same as in Ref. (12). Two VT processes, HF + HF and HF + H, are treated by a new multiquantum method."a) This method enables these processes to be considered despite the 70 reaction limitation. The reactions appear in the table with M~ through M7 and with M , through M~6, respectively. For HF+ HF VT, the v dependence is from KwoK,('4> while the T dependence stems from Ref. (12). The latter is given as 3 x 10~'T -' + 3.5 x 10"TT M

(BI)

and is reformulated in terms of the Arrhenius-type expression shown in the table. This expression is based on a least-square fit to item (B1), and a~'ees to -+12% in the temperature range of 100 to 1100 K. The HF+ H rates are based on those given in Ref. (12). For the HF(v) + F VT rate, Ref. (17) is used for v = 1 at 300 K. This rate is scaled linearly "2) with v and the T dependence is taken from Ref. (12). The coefficient Co, however, was incorrectly calculated by a factor of 3. The error is corrected in the -III rate model. Reference (12) is used for the HF(v)+Fz VT rate. Because the HF(v) + H2 VT rate is much slower than the HF(v) + He VV rate, the VT rate is again not included. The VV rate is used with the process modeled as a VT one, since core size limitations preclude inclusion of the H2(v) kinetics. The rates used are based on Ref. (12). The HF + HF VV rate coefficients are modeled as: HF(v) + HF(v' + Av) ~

HF(v - 1) + HF(v' + Av + 1),

k(v, v, Av) = v(v' + Av + l)T-'k(1, 1, Av),

with v - 1, v' -> 0. The v(v' + Av + I)T-' coefficient stems from Ref. (12), while the values of k(l, I, Av) are from Ref. (10). Finally, VV deactivation of HF(I) and HF(2) by N2 is included as a VT process, where the rate is based on Ref. (12). The changes introduced into the -II rates, to yield the -III rates, are shown in Table B3. They encompass a faster VT deactivation rate for HF(v >-4) + HF, faster deactivation of HF(v) by F, deletion of the slow HF(v) + F= process in favor of

Table B3. Changes introduced into -II rates for HF chain-III rates Reaction

Chanqes

HF(4) + M3 = !.13 + H8

Co = 3.2 x 1013

HF(5) ÷ H3 = H3 + /49

CO = 5.0 x 1013

IfF(6) + M3 = M3 ~- MIO

Co = 7.2 x 1013, Do = 1.4 x 1013 Co = 9.8 x 1013 7 M3+i = ~

v HF(v), i = I , . . . , 6

v=i 'HF(v+I) + F e HF(v) + F HF(v+I) + MIO = HF(v) + MIO lIF(v÷1) + H2 = Hr(v) + H2

Co = 1.6 x I 0 1 3 ( v ~ I ) , v = O, " . ,

6

(/410 = F2) delete

Co(~=l) = 1.2 x 1012, Co(V=2) = 2.4 x 1012, Co(V=3) = 3.2 x 1012, Co(V=4) = 4.0 x 1012, Co(V=5) = 2.0 x 1012, Co(V=6) = 1.0 x 1012

HF(v+I) + N2 = HF(v) + N2

This reaction is added ivith kf = 0.43 v T3"35 e2075/P'To kb = I . The Idst tlvo rePctions ar~ dc]eted in Table [;Z

116

JOHN C. CUMMINGSet al.

HF(v) + N2 VV, and a different v dependence for the HF(v ~ 2)+ H2 process. The temperature dependence of/9 for the HF(v) + N2 V V reaction is based on a least-square Arrhenius fit to that given by COHEN.~'°' The change in the HF + HF VT upper-v rate coefficients is based on Kwok's data.°'~ The HF + F rate is a correction as noted earlier. The change in the HF + H2 VV rate is from KwoK~1"~and represents a significant slowing down of the deactivation of the upper vibrational levels, with the rate coefficient now peaking at v = 4. This change should not affect the hot reaction experiment model comparison providing all, or most, of the H2 is dissociated. In retrospect, this rate change may be in the wrong direction in view of the much smaller HF(v -> 4) populations observed in the experiment. Indeed, if this process also involves multiquantum transitions,~'2~then the upper level deactivation rates may be significantly underestimated. This type of transition might also produce relatively large H2(v -> 2) populations. Recently, KWOK~14~has used such transitions to model his flow tube experiments.