Contains reports on two research projects.U. S. Navy Office of Naval Research (Contract N00014-67-A-0204-0019

Ingard, K. Uno

Singhal, Vijay K.

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XI. PHYSICAL ACOUSTICSAcademic Research StaffProf. Uno IngardGraduate StudentsVijay K. SinghalA. REFLECTION OF SOUND FROM A SIDE-BRANCH CAVITYIN A DUCT IN THE PRESENCE OF FLOWU. S. Navy Office of Naval Research (Contract N00014-67-A-0204-0019)Uno Ingard, Vijay K. SinghalAs one problem in our study of the interaction of sound with flow in ducts, we areconsidering the absorption, reflection, and transmission of sound at a side-branch cavityin a duct with flow. In the experiments a sound pulse is produced in the duct from al -- - MM0.16M~0.16Fig. XI-1.The reflection coefficient as a func-tion of frequency. Cavity depth,3 in; cavity cross section, 3/4 X3/4 in; pipe cross section, 3/4 X3/4 in. For M - 0. 16, the uppercurve is obtained when the speakerand the microphones are upstreamof the cavity, and the lower curvewhen the speaker and the micro-phones are downstream of the cav-ity. The middle curve is for noflow.FREQUENCY( Hz)QPR No. 114(XI. PHYSICAL ACOUSTICS)sound source that can be either on the upstream or the downstream side of the cavity.In either case the incident and reflected sound from the cavity is measured by means ofmicrophones mounted in the side wall of the duct, and the frequency dependence of thepressure reflection coefficient is determined for different values of the flow Mach num-ber in the duct and for different values of the amplitude of the sound wave.The result at zero flow is shown in Fig. XI-1, which shows a typical resonancecurve, with the peak corresponding to a wavelength approximately equal to four timesthe depth of the side-branch cavity, as expected. The width of the curve is an expressionof the acoustic losses in the vicinity of the cavity. In the presence of flow the resultsdepend on whether the sound is reflected upstream or downstream. In the upstreamdirection the pressure reflection coefficient can be larger than unity, as indicated inFig. XI-1. Also, note that the peak of the curve is now shifted downward and the widthof the curve has decreased. The corresponding curve when the sound is reflected in thedownstream direction is also shown in Fig. XI-1.A detailed theoretical explanation for this behavior is still not available. Consideredqualitatively, the reason for the increased sharpness of the resonance curve is probablythat the cavity is excited into self-oscillation by the flow, in which case the total internalresistance is reduced. Similarly, the reason for a pressure reflection coefficient largerthan unity in the upstream direction is probably the same as that given in our previouspaper on upstream and downstream radiation into a duct with flow.1 A theoretical analy-sis of this problem is under way, which we hope to report in a subsequent quarterlyreport.References1. U. Ingard and V. K. Singhal, J. Acoust. Soc. Am. 54, 1343-1346 (1973).B. ACOUSTICALLY STIMULATED KARMAN VORTEXSHEDDING IN A TUBEU.S. Navy Office of Naval Research (Contract N00014-67-A-0204-0019)Uno Ingard, Vijay K. SinghalIn our continuing studies of sound propagation in ducts with flow, we are particularlyinterested in the interaction between sound and flow. One of the aspects of this interac-tion was discussed in Quarterly Progress Report No. 109 (pp. 39-47) which dealt withthe attenuation of sound resulting from turbulence. We now describe an experimentdealing with an acoustically induced instability resulting from the interaction betweenthe wake behind a cylinder and the first transverse acoustic mode in a pipe.Thus far, we have considered only a circular pipe containing a cylinder transverseQPR No. 114(XI. PHYSICAL ACOUSTICS)to the axis of the pipe. As the flow speed in the duct is increased to a value where theKarman vortex shedding frequency is coincident with the first transverse mode, strongcoupling between the wake and the sound field occurs, thereby resulting in self-sustainedscreech at a frequency equal to the cutoff frequency of the mode. This effect, which hasbeen observed earlier in a rectangular tube,l'2 is poorly understood. The purpose ofour studies is to determine the conditions under which screech is observed and to inves-tigate the aeroacoustic coupling mechanism quantitatively.1/4"12.5 Z10.07.55.02<2.5 ) 3'0.25 0.5ML" MD O "MLfD1,0N.911,Fig. XI-2. Acoustic coupling between the wake behind a cylinder in a ductand the first transverse acoustic mode of the duct.In Fig. XI-2 we have plotted the first cutoff frequency as a function of Mach number.We have presented two curves, one referring to the average Mach number in the ductand the other to the "local" Mach number in the vicinity of the cylinder. Also shown isthe velocity dependence of the Karman vortex frequency, based on a Strouhal numberof 0. 21. The observed screech frequencies are found to be close to the intersectionbetween the curves, that is, when the Karman vortex frequency coincides with theacoustic cutoff frequency. Actually, the observed data points lie somewhere betweenthe cutoff frequency based on the local Mach number and the duct Mach number. Similarresults have been obtained also for a cylinder 1/2 inch in diameter in a 1-inch pipe.QPR No. 1145/8"MEASUREDSCREECHFREQUENCYL = 1 1/4x L =9 1/2"0 L = 12 "fL1,00.75 1.0(XI. PHYSICAL ACOUSTICS)The pure tone that is produced is very intense. We have measured levels as high as115 dB outside the pipe, which is -30 dB larger than the overall flow noise. Included inour continued studies of this effect is a theoretical analysis of the problem, as well asfurther experiments not only with rigid but also with acoustically "soft" cylinders.References1. K. U. Ingard and W. M. Manheimer, "Sound Emission from Karman Vortices,"Quarterly Progress Report No. 70, Research Laboratory of Electronics, M. I. T. ,July 15, 1963, pp. 74-75.2. Flow Induced Vibrations in Heat Exchangers (American Society of Mechanical Engi-neers, December 1970), p. 46.QPR No. 114

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