PULSATION AND VIBRATION distribution behind the shock wave (assuming the index of refraction of the gases d o not change in the transition zone.) as the shock wave plus transition zone enter the light beam. By measuring these density distributions the way the gas or gases relax t o equilibrium after the enthalpy of the gas is increased suddenly a calculable amount by a shock wave can be determined. The theoretical aspects of the instrument and its predicted performance were verified experimentally by measuring vibrational heat capacity relaxation times behind shock waves in oarbor! dioxide containing water vapor. The instrument in these tests demonstrated a sensitivity sufficient t o record a change in atmospheric density of 0.5% over I-mm. distance and a space resolution of the density in the shock tube of 0.1 mm. corresponding t o times of the order of 0.1 microsecond. *
Literature Cited (1) Carrington, Tucker, and Davidson, Sorman, J . Phys. Chem., 57,
418 (1953).
(2) Smiley; E.
E”.,
Winkler, E. H., and Slawsky, Z. I., J . Chem. Phys., 20, No. 5, 923 (1952).
This research was partially supported by the United States Air Force through the Office of Scientific Research of the Air Research and Development
Command.
ULTRASONIC UNMlXlNG OF ISOTOPIC SOLUTIONS S. G. BANKOFF’ AND
R. N.
LYON
shown t h a t the steady-state composition gradient is, a t most, very small. Hence, for practically all types of ultrasonic waves, no appreciable steady-state separation can be achieved in the gaseous state. This statement applies specifically to isotopic mixtures and becomes less valid for mixtures of widely differing molecular weight. It is also possible that under conditions where the Chapman and Cowling assumptions of the continuity of the hydrodynamic medium break down, some separation might be achieved. Debye ( 2 ) showed t h a t a potential wave, due t o partial unmixing, should exist if a n electrolytic solution is irradiated with a traveling ultrasonic wave. This effect was confirmed experimentally ( 5 )with a standing wave. I n this paper the magnitude of the unmixing associated with the Debye effect is shown to tie only about mole fraction at 100 megacycles and 0.1 watt per sq. em. This is true also for nonionic solutions. T h e unmixing is about the same for a standing wave as for a traveling wave, although in the former case the potential wave is a standing wave 90” out of phase from the velocity wave. No treatment has been found in the literature of the separation to be expected on passing either asymmetrical or damped sine waves through a liquid mixture. However, as Debye points out, the frictional coefficients are far larger than the dynamical coefficients in liquid systems. Hence, it is not probable t h a t appreciable separations could be reached a t present ultrasonic frequencies with either distorted or damped waves. Despite the intense accelerative effects of ultrasonic radiation, it is shown that negligible steady-state separation can be expected by passing either symmetrical or distorted sound waves, standing waves or damped waves through gaseous, and probably also liquid mixtures of isotopic constituents.
Oak Ridge National laboratory, Oak Ridge, Tenn.
T
HE high local accelerations and the multiple stage nature of
ultrasonic radiation apparently make it attractive for separations based on small differences in mass. Despite this apparent attractiveness, several authors have reported negative results from theoretical and experimental investigations of this possibility. However, these analyses deal with the simpler cases; and some instances of relatively large unmixing have recently been reported (3, 4). It seemed advisable, therefore, to institute a more comprehensive analysis, with special reference t o isotopic separations. A generalized theory for gaseous isotope separation is developed, based on integrating the binary diffusion equation ( 1 ) over one period a t cyclical steady state. This yields
Literature Cited
Chapman, S., and Cowling, T. G., “Mathematical Theory of Non-Uniform Gases,” Macmillan, New York, 1939. Debye, P., J . Chem. Phys., 1, 13 (1933). Frei, H., and Schiffer, AT., Phys. Rev.,71, 555 (1947). (4) Passau, P., Ann. SOC.Sci. Bruzelles, 62, Ser. I, 40 (1948). (5) Yeager, E., Bugosh, J., Hovorka, F., and McCarthy, J., J. Chem. Phys., 17, 411 (1949).
COMBUSTION OSCILLATIONS IN DUCTED BURNERS JOHN C. TRUMAN Aeronautical Engineering Dept., USAF lnsfitute of Technology, Wright-Patterson Air Force Base, Ohio
ROGER T. NEWTON
x
Small Aircraft Engine Dept., General Electric Co., Lynn, Mass.
where y is the mole fraction, z the distance along the column, t the time, X the wave length, c the velocity of sound, m the mass, p the pressure, k~ the thermal diffusion ratio, and T the temperature. These terms represent, respectively, the driving forces for diffusion due to concentration, pressure, and temperature gradients. Assuming a perfect gas adiabat, the thermal diffusion term vanishes. For isotopic mixtures, t h e coefficient of the pressure gradient is very nearly constant, and hence the pressure gradient term vanishes, or nearly so. Hence, the steady-state concentration gradient is zero, irrespective of wave form, for a n undamped wave. This is t o be expected from thermodynamic considerations. The analysis is somewhat more difficult for damped traveling waves, but b y a method of approximate series solution, it is 1
Permanent address, Rose Polytechnic Institute, Terre Haute, Ind.
A
PROBLEM of increasing importance in t,he development of
modern aircraft propulsion systems is that of combustion oscillations or combustion instability. These terms refer to periodic, large amplitude variations in pressure which are maintained in some manner by the combustion process. Such variations usually occur in the audiofrequency range. Their effects include changes in the chemical and thermodynamic processes of combustion, and hence in burner performance, and structural damage to burner components resulting from high amplitude pressure oscillations and from locally increased heat transfer rates. Most cases of combustion instability which have been reported in the literature fall into one of three classes: ( 1 ) oscillations associated with failure of the flame to stabilize on a flame holder; (2) oscillations depending on the existence of a time lag between the injection of propellants into the burner, and their transformation to high temperature gases; and (3) oscillations, initiated or
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1955
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