Donald R. White

Systematics of Vibrational Relaxation

A large number of data points for the vibrational relaxation time (pτv in atm sec) of simple systems have been logarithmically plotted vs (T°K)—⅓. It appears that each system is well represented by a straight line, and that most of these straight lines when extended to higher temperatures intersect near the point [pτv=10—8 atm sec, (T°K)—⅓=0.03]. Systems with a small reduced mass μ are exceptions to such a simple convergence, and in an improved scheme, the location of the convergence point is dependent on the reduced mass. Such a presentation has lead to an empirical equation correlating available measurements of vibrational relaxation times: log10(pτv)=(5.0×10−4)μ12θ43[T−13−0.015μ14]−8.00, where θ is the characteristic temperature of the oscillator in K deg. This equation reproduces the measured times within 50% for systems as diverse as N2, I2, and O2–H2. In the worst case thus far, O2–Ar near 1000°K, it is off by a factor of 5.

Optical Refractivity of High‐Temperature Gases. II. Effects Resulting from Ionization of Monatomic Gases

This paper describes shock‐tube studies of the optical index of refraction of ionized argon in which observed optical effects have been related to the ionization of the shocked argon. The plasma dispersion formula has been applied to the measured refractivities to determine values of equilibrium electron concentrations on the order of 1017 cm−3. Good agreement is found between experimental and calculated values of the degree of ionization. The ionization relaxation process is strikingly portrayed in the interferograms and may be studied in some detail. Some questions concerning proposed kinetics for the relaxation behind strong shock waves in monatomic gases are discussed.

Turbulent Structure of Gaseous Detonation

Self‐sustaining and overdriven detonations in 2H2 + O2 + 2CO have been studied in a shock tube at initial pressures from 0.01 to 1.4 atm. Measurements have included pressure, density obtained interferometrically, and luminosity whose intensity is shown to be proportional to [CO][O]. Strongly overdriven waves are one dimensional and are followed by the calculated equilibrium state. Self‐sustaining detonations are followed by a state in which the pressure and density are lower than calculated according to the usual C‐J hypothesis, and in which the flow is supersonic with respect to the wave front. Furthermore, the flow in and behind the reaction zone invariably appears to be turbulent. In an examination of the implications of this turbulence, a Chapman‐Jouguet detonation is considered to be one with the minimum velocity of propagation which will satisfy the conservation relations for turbulent flow at the rear of reaction zone. It is shown that this minimum (C‐J) velocity is slightly greater than that calcu...

Vibrational Energy Exchange between N2 and CO. The Vibrational Relaxation of Nitrogen

The vibrational energy exchange N2(v=1)+CO(v=0)=N2(v=0)+CO(v=1) should be fast, due to near resonance of the energy levels. We have studied the rate of this exchange relative to the rate of energy transfer from translational to vibrational degrees of freedom in a shock‐heated mixture of 1% CO—99% N2. Vibrational relaxation of the CO is observed by its infrared emission near 2000 cm—1. The density change behind the incident shock is simultaneously observed with an interferometer and gives a measurement of the N2 relaxation time. In the 3200°—4200°K range both methods are applicable; they yield identical relaxation times within the data scatter of ±20%. In contrast, at 3600°K, the vibrational relaxation time of pure N2 is four times that of pure CO. The exchange reaction thus appears fast enough to make the vibrational temperatures of the N2 and CO equal during the vibrational relaxation of the mixture. In the 1900° to 5400°K range, our study gives vibrational relaxation times in seconds for pure N2 (p=1 at...

Influence of diaphragm opening time on shock-tube flows

Shock waves generated in a shock tube by use of hydrogen or helium as a driver gas and air, nitrogen, oxygen or argon as a driven gas have higher velocities than predicted by simple theory when sufficiently large diaphragm pressure ratios are used. Expected shock-tube performance curves have been constructed using the equilibrium Hugoniot for the driven gas, both for the usual model of shock tube flow, which assumes instantaneous diaphragm removal, and for a suggested model based on a finite rupture time for the diaphragm. Agreement between experiment and the latter model is in general good, and the differences are qualitatively accounted for by the pressure waves expected to result from mixing between driver and driven gases at the contact surface. These waves may be either compression or expansion waves, depending on the relative heat capacities of the two gases. The maximum shock strength observed as a shock goes down the tube was found to occur at a distance from the diaphragm which increases with the shock strength, and the strongest shocks were found to be still accelerating at the end of a 42 ft. long shock tube of 3 1/2 in. square cross-section. Diaphragm breaking time has been measured and found to be consistent with the observations on the shock formation distance.

Flow in shock tubes with area change at the diaphragm section

This paper describes theoretical and experimental studies of the effects on shock tube flows of a monotonic convergence at the diaphragm section. Systematic flow equations are developed for tubes of uniform bore and tubes having either a monotonic convergence or a convergence-divergence in the diaphragm section. Except across the shock front itself, isentropic processes and ideal-gas behaviour have been assumed. Simplified procedures are presented for predicting the ideal-flow parameters over a wide range of operating conditions, as well as for comparing straight and convergent tubes. Such comparisons made by other investigators are found to be incomplete or in error. The experiments described utilize a very simple device for altering the diaphragm section convergence and a multi-station measurement of shock velocity. The expected effect of convergence is verified over a wide range of Mach numbers. Even at Mach numbers where the processes of shock formation can no longer be ignored, it is found that the relative performance between a uniform and convergent tube is preserved.

Vibrational Relaxation of Oxygen

The vibrational relaxation of oxygen has been studied by shock‐tube interferometry from 600° to 2600°K with the result that at 1 atm pressure the relaxation time τv in seconds is found to be τv=1.49×10—10 exp (133T—½). The presence of up to 2% CO has no observable effect on this time. The previous experimental work of Blackman was probably influenced by impurities at the lower temperatures but the present results are in accord with his at the higher temperatures. Comparison is made with various theoretical calculations and the primary temperature dependence of T—½ is confirmed. It is further noted that Schwartzs Method A of matching the exponential interaction is in better accord with observations than Method B.

Oxygen Vibrational Relaxation in O2–He and O2–Ar Mixtures

The vibrational relaxation time of oxygen in several mixtures of O2+He and O2+Ar has been determined by shock‐tube interferometry. Using the previously determined data for O2–O2 collisions, the vibrational relaxation time for O2–He and O2–Ar collisions has been found. The latter is in agreement with Camacs determination and extends to somewhat lower temperatures. For oxygen infinitely dilute in helium, the vibrational relaxation time in atm·sec is given by pτv=5.3×10—9 exp(60T—½) from 400° to 1600°K.

Density induction times in very lean mixtures of D2, H2, C2H2 and C2H4, with O2

The induction time for shock-wave-induced exothermic reaction in lean O 2 -D 2 , O 2 -H 2 , O 2 −C 2 H 2 , and O 2 −C 2 H 4 mixtures has been measured in the constant-area shock tube using optical interferometry. For fuel/oxygen ratios of a few per cent and for 1100 T 10 ([O 2 ] 1/3 [H 2 ] 2/3 t i )=−10.44+17,200/4.58 T , log 10 ([O 2 ] 1/3 [C 2 H 2 ] 2/3 t i )=−10.81+17,300/4.58 T , and log 10 ([O 2 ] 1/3 [C 2 H 4 ] 2/3 t i )=−11.00+17,900/4.58 T . Essentially the same activation energy (∼17.3 kcal/mole) is shown by H 2 , C 2 H 2 , and C 2 H 4 , but that of D 2 appears to be slightly less. With respect to H 2 , the induction times for D 2 , C 2 H 2 , and C 2 H 4 are about 1.5, 0.5, and 0.4, respectively. The more nearly stoichiometric mixtures show induction times inversely proportional to the geometric mean reactant concentration, and the dependence on the fuel concentration increases with decreasing fuel/O 2 ratio, dependence on [O 2 ] vanishing for the leanest O 2 −C 2 H 4 mixtures. The vibrationally relaxed but unreacted density is always attained prior to exothermic reaction, and changing the relaxation time with respect to the induction time has no effect on the latter within the data scatter.

Vibrational Relaxation of Oxygen by Methane, Acetylene, and Ethylene

The vibrational relaxation of oxygen containing from ¼% to 2% of CH4, C2H2, and C2H4 has been studied by shock‐tube interferometry. From about 450° to 1300°K the vibrational relaxation zone is not affected by chemical reaction, and the observed oxygen relaxation in mixtures containing only small amounts of hydrocarbon may be accounted for by using the standard formula for a binary mixture and assuming the relaxation time in seconds of oxygen dilute in 1 atm of the hydrocarbon to be given by log10τO2–CH4 = 18T—⅓−8.7, log10τO2–C2H2 = 7.5T—⅓−7.3, and log10τO2–C2H4 = −6.92. For higher temperatures, the exothermic reaction may result in a nonlaminar flow behind an aplanar shock, and the relaxation zone then cannot be resolved interferometrically. For still higher temperatures the relaxation zone is again laminar, but the vibrational excitation of O2 is accelerated by concurrent chemical reactions in the induction zone. From the observation at lower temperatures that τO2–CH4