PULSATION AND VIBRATION distribution behind the shock wave (assuming the index of refraction of the gases do 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 to 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 to 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 that 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 that a potential wave, due to partial unmixing, should exist if an 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. The 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 that 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 to 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, the 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 an undamped wave. This is to 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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1183
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT amplified by the combustion process, having a frequency equal t o a resonant frequency of the gas in the burner. A program was carried out in the General Electric Co. by the authors to investigate the combustion instability phenomenon commonly known as screech. Tests were performed using burners ranging from 6 to 18 inches in diameter, as well as burners of square and rectangular cross section. Preheated air entered the burner a t temperatures between 400" and 1600" F. and velocities between 100 and 450 feet per second. Many different burner lengths and flame holder configurations were employed. Excellent correlation was found between the measured screech frequencies and the theoretically predicted transverse resonant frequencies of the gas in the burner. The occurreiice of screech depends on burner configuration, flow parameters upstream from the combustion zone, and combustion properties of the gas. An oscillation of the flame front accompanied screech; the measured frequency of this osciIIation was equal to the measured screech frequency.
ORGAN-PIPE OSCILLATIONS IN DEEP-PORTED BURNER ABBOTT A. PUTNAM AND WILLIAM R. DENNIS Baffelle Memorial Insfifufe, Columbus,
D
Ohio
ATA are presented on acoustic oscillations produced by a burner using a hexagonal bank of hypodermic tubes as deep ports. Most of the tests were made with ethane as the fuel, but some tests were run with methane and propane, for comparison purposes. Both the diameter and length of the combustion chamber were varied during the tests. The combustion chamber could be considered as a driver which forced the slugs of gas in the ports to oscillate. Burning of the incremental pulses of combustible mixture periodically issuing from the ports furnished energy to drive the oscillations when the pulses burned in phase with the oscillating component of the pressure in the chamber. The phasing depended on a time-lag factor which was a function of the velocity of the gases through a space, similar t o dark space, between the burner ports and the mean flame surface, and the width of the space itself. The oscillations not only ceased when there was a failure to satisfy the timing criterion, but also ceased when the air/fuel ratio approached either rich or lean blowoff limits of the conventional type. This latter cessation apparently was connected with the
fact that the flame burned from fewer and fewer ports as the limits were approached, and thus less driving energy was available.
INACCURACIES IN HIGH-SPEED OSCILLATORY PRESSURE MEASUREMENTS *
R. 8. LAWHEAD
Norfh American Aviafion, Inc., Propulsion Field laboratory, Chafsworth, Calif.
P
ICKUP calibration, sensitivity to mechanical vibration, and probe effects are some of the problems encountered in the measurement of oscillatory pressures. A dynamic calibration of a condenser-type pressure pickup may be made b y using a small cylinder chamber excited by a n acoustic driver unit giving root mean square prepsure amplitudes t o 0.05 pounds per square inch. By alternately measuring t h e pressure variations a t the end wall of the chamber with the test pickup and a calibrated microphone and comparing the results, it is possible to obtain a frequency response-calibration a t frequencies to 4000 cycles per second. I n some applications, particularly those involving combustioni.e., rocket engines-the pressure pickups may be subjected t o severe mechani cal oscillations t h a t can cause spurious output signals. The existence of such mechanical effects can not always be detected from ordinary laboratory shake table tests. Therefore, actual environmental testing, with the pickup mounted alternately in a normal and blind pressure tap, is recommended. Occasionally it is necessary to use some sort of pressure t a p i n which the pickup diaphragm is not flush with the chamber wall for the measurement of high-amplitude, high-frequency oscillating pressures. This may introduce large changes in amplitude and phase which must be accounted for in interpreting such data. For small amplitude oscillations, equations analogous t o those of electrical transmission lines give an adequate approximation. However, a t large amplitudes these equations no longer apply. Experimental data have been obtained t o show:
1. The effect of probe length and volume on the amplitude and phase of the indicated pressure 2. The introduction of spurious resonances by pressure probes 3. The attenuating effect of undegassed liquid trapped in the pressure probes This work was conducted as p a r t of 4ir Force Contract A F 33(038)-19430.
Reprints .of this symposium may be purchased ;for F$1.25 -each from-the Reprint Department, American Chemical Society, 1 155 Sixteenth-St., N.W., Washington 6, D. C.
E N D OF S Y M P O S I U M AND E N D OF E N G I N E E R I N G , DESIGN, AND PROCESS D E V E L O P M E N T - S E C T I O N
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 41, No. 6
