1、NASA TECHNICAL NOTE NASA TN D-8351 ;n M f NOISE RESPONSE OF CAVITIES OF VARYING DIMENSIONS AT SUBSONIC SPEEDS Patricia J. W. Block Langley Research Center kmpton, Va. 23665 Y I I IATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. DECEMBER 1976 Provided by IHSNot for ResaleNo reproductio
2、n or networking permitted without license from IHS-,-,-NOISE RESPONSE OF CAVITIES OF VARYING DIMENSIONS AT SUBSONIC SPEEDS Patricia J. W. Block Langley Research Center SUMMARY An expression including the effect of the length-to-depth ratio is obtained to predict the resonant frequencies of a flow-ex
3、cited cavity and is shown to be in good agreement with experimental results. Interaction between the lengthwise vortical-acoustic modes and the depthwise standing-wave modes is shown to occur at Mach numbers between 0.1 and 0.5. A simple expression for the Mach number at which maximum-amplitude resp
4、onse occurs is derived on the basis of the interaction, and the onset Mach number is found to be slightly lower. The effect of the cavity dimensions on the type of noise spectra produced by the cavity is investigated. A circular-faced and a square cavity are compared as noise generators in a flow. I
5、NTRODUCTION In view of possible future reduction in certification levels for overall aircraft noise and of the recent advances in propulsive noise suppression, airframe noise reduction has become an important research objective. This objective has engendered the study of non- propulsive flow-surface
6、 interaction noise sources found on the airframe. One such noise source, the flow-excited cavity, can be used to model several structures on the airframe, in particular the landing gear wells. The literature contains many papers on large-amplitude internal pressure oscilla- tions found inside a flow
7、-excited cavity. A review of this literature may be found in ref- erence 1. There is very little information, however, concerning the sound generated by such an arrangement. It was shown in reference 1, where external or farfield sound mea- surements of a flow-excited cavity were made, that most but
8、 not all of the modes of the internal pressure fluctuations radiate as sound. Analytical models and flow visualizations contained in the work on internal pressure oscillations are helpful, therefore, in assessing the important parameters of noise generation. The prediction of the lengthwise internal
9、 oscillation frequencies reported in refer - ence 2 provides a semiempirical relationship for the Strouhal number; or nondimensional frequency, based on the cavity streamwise length. However, the dependence of Strouhal Provided by IHSNot for ResaleNo reproduction or networking permitted without lice
10、nse from IHS-,-,-number on cavity length-to-depth ratio from this relationship proved to be contrary to the experimental results of the present study. The analysis of reference 3 gives physical significance to the empirical constants in the Strouhal relationship of reference 2; how- ever, no depende
11、nce on length-to-depth ratio was obtained in the final result. This paper extends the work of reference 3 to include the effect of length-to-depth ratio on Strouhal number. Other investigators (refs. 4 and 5) have studied the depthwise modes that occur in cavities whose length-to-depth ratio is less
12、 than about 2. In this paper these results are written in the form of a Strouhal number also based on length for purposes of comparison with the Strouhal number of the lengthwise oscillation. On the basis of this comparison, a quantitative explanation is given for the interaction or coupling between
13、 lengthwise and depthwise modes observed in reference 1. Also a simple expression for the approximate Mach number at which oscillations begin in a cavity is obtained. An additional purpose of this paper is to gain insight regarding the important param eters of sound generation by a cavity in a flow.
14、 This experimental study includes measur ments of noise produced by cavities (rectangular and circular faced) of varying dimensior in a subsonic flow. Special emphasis was given to the spectral shape of the noise for the purpose of delineating regions of broadband or narrowband sourcebehavior as a f
15、unction of the flow velocity and cavity shape. Noise measurements were made in a reverberant environment over a Mach number range from 0.1 to 0.5. The cavity length-to-depth ratic varied from 0.3 to 8.0 and the length-to-width ratio varied from 0.3 to 1.85. SYMBOLS A?B constants in equations (5), (6
16、), and (7) having empirical values of 0.65 and 0.7 respectively a speed of sound, m/sec C proportionality constant D cavity depth, cm f frequency, kHz H?h magnitude and phase, respectively, of summation of monopole sources in equation (B6) Hf Hankel function of first kind 2 Provided by IHSNot for Re
17、saleNo reproduction or networking permitted without license from IHS-,-,-h07hi L LP LW M m NSt n P P Q RA r S t r intercept and slope, respectively, of phase function h when plotted against wL/a (see eq. (B9) Bessel function of first kind ratio of average vortex convection velocity across cavity mou
18、th to free-stream velocity, taken to be 0.57 real and imaginary parts of complex wave vector in x-direction cavity length (streamwise direction), cm acoustic pressure level, dB (re 20 pPa) acoustic power level, dB (re 1 pw) free-stream Mach number mass of fluid Strouhal number mode or stage number o
19、f vortical-acoustic oscillation acoustic pressure rms acoustic pressure ratio of center frequency to bandwidth of response of an oscillator specific acoustic radiation resistance radial distance from acoustic source acoustic source strength time radial acoustic velocity 3 Provided by IHSNot for Resa
20、leNo reproduction or networking permitted without license from IHS-,-,-uce free-stream velocity, m/sec W cavity width (cross-stream direction), cm specific acoustic radiation reactance xA X,Y rectangular coordinates Bessel function of second kind a! empirical constant in equation (2) P phase differe
21、nce between source and shear layer displacement at trailing edge 77 displacement of shear layer in y-direction P fluid density lag of shear layer displacement behind forcing mechanism at leading edge of cavity 0 angular frequency, 2af Subscripts : d depthwise standing-wave oscillation 1 lengthwise v
22、ortical-acoustic oscillation Abbreviations : ANRL aircraft noise reduction laboratory MIC microphone rms root mean square rPm revolutions per minute 4 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TEST APPARATUS AND PROCEDURE This experiment was ca
23、rried out .in two different reverberant environments, each having subsonic flow capability. These facilities were the Langlgy 55-foot vacuum cylinder and the reverberation room of the Langley aircraft noise reduction laboratory (ML) * Langley 55 -Foot Vacuum Cylinder Facility.- The vacuum cylinder i
24、s 55 feet in diameter with a hemispherical top (fig. l(a) and a volume of 3794 m3. To obtain flow over the cavity, the cylinder is par- tially evacuated and the cylinder pressure read. The air is exhausted into the cylinder through a 6.35-cm by 25.4-cm rectangular nozzle (fig. l(b) with a pneumatica
25、lly con- trolled conical inlet port plug. The velocity of the air through the nozzle was computed according to the compressible flow tables from the difference between the atmospheric pressure and the cylinder pressure which was read continuously. This method provided an absolute velocity within 1 p
26、ercent of that obtained in previous calibrations using a pitot- static tube; however, during a run the pressure differential, thus the velocity, varied. The variation in velocity during a run amounted to 4 percent of the average velocity for a Mach number of 0.17 and less than i2 percent for a Mach
27、number of 0.5. Test setup.- The nozzle guided the flow parallel to a flat 1.2-m-square plate in which the cavity was located (fig. l(b). The cavities used in this facility had a fixed depth of 3.81 cm. The length (streamwise direction) and width were varied independently from 2.54 cm to 7.62 cm. A c
28、ircular-faced cavity with a diameter of 7.62 cm was also tested. The test conditions for this experiment are given in table I. Acoustic measurement.- Acoustically, the inside of the cylinder, where sound mea- surements were made, was highly reverberant with a mean reverberation time of 10 sec. Altho
29、ugh this facility was not designed as a reverberation chamber, previous acoustic cal- ibrations (ref. 6) demonstrated the suitability of this facility for acoustic research and also its reverberant characteristics at the measurement position. By using these calibra- tions, a single one-half-inch con
30、denser-type microphone was placed inside the chamber where the acoustic field was known to be reverberant. All rms pressure levels were con- verted to acoustic power levels as specified in the American National Standard S1.21-1972 (ref. 7) using the 1-kHz reverberation time. Since the reverberation
31、time changes with frequency, conversion of the data using a single reverberation time (viz, that of 1 kHz) leads to a small error in the power level across the spectrum. A correction for this error has not been applied to the data since comparisons of a qualitative nature only are pre- sented herein
32、. The corrections, however, are provided in appendix A for those interested in obtaining the true power levels across the entire frequency range. The barometric pressure change in the chamber from the highest velocity to the lowest amounted to a 5 Provided by IHSNot for ResaleNo reproduction or netw
33、orking permitted without license from IHS-,-,-correction to the acoustic power of less than 0.1 dB. This correction was less than the accuracy of the spectral amplitude estimates which were about 1 dB. The data were obtained on line by means of the microphone with a preamplifier, filter, amplifier,
34、Fourier analyzer, and X-Y plotter. Narrowband spectra from 0 to 5 kHz were obtained from the microphone for each test condition. The frequency resolution was 20 Hz for all spectra. Langley ANRL Reverberant Chamber Facility.- The ANRL reverberation room is shown in figure 2(a). The air is pro- vided
35、by a centrifugal compressor through a 30-cm by 60-cm rectangular nozzle. The velocity through the nozzle was calibrated with a Pitot-static probe and was controlled by setting the compressor rpm. The error in velocity with this method was less than 4 per- cent. In this facility, Mach numbers from 0.
36、09 to 0.18 were achieved with this nozzle. Test setup.- The nozzle directed the flow over a flat plate in which the cavity was situated (fig. 2(b). This cavity had a fixed streamwise length of 4.05 cm and a width of 7.45 cm. The depth was varied from 0 to 13 cm. The test conditions in this facility
37、are listed in table II. Acoustic measurement. - The ANRL reverberation room is a rectangular chamber having splayed walls and a mean reverberation time of approximately 8 sec for frequencier above 250 Hz. Three one-half-inch condenser -type microphones were mounted inside the chamber and positioned
38、in the reverberant or diffuse field. This was done by suspending a calibrated broadband source in place of the cavity and positioning the microphones until all were recording the same spectra. Subsequent analysis of the cavity noise data from the three microphones showed agreement within 2 dB across
39、 the frequency range for all conditions. Narrowband spectra were obtained from all microphones from 0 to 10 kHz. Only the frequencies of the cavity oscillations are reported in this study, Consequently no spectral amplitude correction need be applied. Data were recorded on magnetic tape and analyzed
40、 by a digital computer. Outputs consisted of narrowband spectra with frequency resolution of 20 Hz. ANALYSIS Background Several investigators (refs. 1, 2, 4, 5, and 8 to 10) have recorded the frequencies of oscillation of flow-excited cavities. The Strouhal number, fL NSt = v, 6 Provided by IHSNot f
41、or ResaleNo reproduction or networking permitted without license from IHS-,-,-was observed to change slowly with Mach number. Rossiter (ref. 2) obtained the following empirical relationship for NSt 2 M E 0.4: (the Strouhal number for lengthwise oscillations) for fL- n-a (lis + NSt,2 = u, - Here, n i
42、s the stage or mode number, a is an empirical constant which increases as the length-to-depth ratio L/D increases, is the ratio of the vortex convection velocity across the cavity mouth to the free-stream velocity, and M is the Mach number. The value for a that is generally considered to produce the
43、 best fit is 0.25. Figure 3 shows Strouhal numbers obtained in several investigations plotted against Mach number. The value of L/D at each data point indicated by a test-point symbol is given in the key. The solid curves represent the first three modes of equation (2) where = 0.57 and a = 0.25. The
44、 data for values of M S 0.4 generally indicate that NstYl increases as L/D increases at a given Mach number. This implies that the Strouhal number is a function of L/D and that the dependence is inverse to that implied by equa- tion (2). These data include cases where the cavity depth was varied and
45、 where the streamwise length was varied to achieve the given L/D ratios. Also of note in figure 3 is the fact that for the Mach number range of interest (viz, 0.1 5 M C= 0.4), the L/D ratio of the cavities is less than about 4.0, although cavities of larger L/D were tested. Therefore, to improve the
46、 existing prediction methods for the middle and lower Mach number range, one should include the cavity depth by way of the L/D ratio and also consider other oscillatory phenomena common in cavities whose length-to-depth ratio is less than about 4.0. Other such phenomena include depthwise standing-wa
47、ve modes and the volume-dependent Helmholtz oscillation. Another motivation for considering these other oscillatory phenomena stems from observations (ref. 1) that coupling or interaction between the lengthwise, or vortical- acoustic, oscillations and the depthwise modes does occur in some situation
48、s. When the frequency of the lengthwise oscillation, which is not purely acoustic but depends on vortex shedding, approaches the frequency of the depthwise standing-wave modes, considerable amplification of the radiated sound occurs. In cavities whose ratio of volume to surface area is large, the He
49、lmholtz oscillation would be considered, but for the rectangular cav- ities tested herein, it is believed that the depthwise standing-wave oscillation is present. Resonant Frequency Prediction Lengthwise oscillations.- Several investigations (see ref. 1 for review) of cavity oscillation have concluded that a feedback mechanism, such as is found in edgetone pro- duction, is the cause
