1、NASA Technical Memorandum 4363Measurements of FluctuatingPressure in a RectangularCavity in Transonic Flowat High Reynolds NumbersM. B. Tracy, E. B. Plentovich,and Julio ChuLangley Research CenterHampton, VirginiaNA. ANational Aeronautics andSpace AdministrationOffice of ManagementScientific and Tec
2、hnicalInformation Program1g92Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- 2 :=E2Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-AbstractAn experiment was performed in the Langley 0.3-Meter Transon
3、ic Cryo-genic Tunnel to study the internal acoustic field generated by rectangu-lar cavities in transonic and subsonic flows and to determine the effect ofReynolds number and angle of yaw on the field. The cavity in this study was11.25 in. long and 2.50 in. wide. The cavity depth was varied to obtai
4、n length-to-height (l/h) ratios of _._0, 6.70, 12.67, and 20.00. Data were obtainedfor a free-stream Mach number (M_c) range from 0.20 to 0.90, a Reynoldsnumber range from 2 x 106 to I00 x 106 per foot with a nearly constantboundary-layer thickness, and for two angles of yaw of 0 and 15 . Resultssho
5、w that Reynolds number has little effect on the acoustic field in rectangularcavities at an angle of yaw of 0 . Cavities with 1/h = _._0 and 6. 70 generatedtones at transonic speeds, whereas those with I/h = 20.00 did not. This trendagrees with data obtained previously at supersonic speeds. As _Ioc
6、decreased,the amplitude and bandwidth of the tones changed. No tones appeared forM_ = 0.20. For a cavity with l/h = 12.67, tones appeared at M_o = 0.60,indicating a possible change in flow-field type. Changes in acoustic spectrawith angle of yaw varied with Reynolds number, hiM, I/h ratios, and acou
7、sticmode number.IntroductionCarrying weapons internally provides aerody-namic advantages in flight; however, difficulties suchas large nose-up pitching moments or store structuralvibration can arise when a store is required to sep-arate from a cavity exposed to an external flow. Toensure safe separa
8、tion of a store exiting from a cav-ity, it is necessary to study the flow disturbances gen-erated when a rectangular cavity is introduced intouniform flow. In addition to changes in the meanpressure distribution in the cavity, an acoustic pres-sure field with high-intensity tones that radiate fromth
9、e cavity can occur as reported in references 1 i0.This paper addresses acoustic tone generation undertransonic and subsonic conditions.Four types of flow have been observed for cav-ities under supersonic conditions: closed, open,transitional-closed, and transitional-open. (See, forexample, refs. ll
10、and 12.) Closed cavity flow, inwhich the shear layer attaches to the floor of thecavity, is observed for cavities with length-to-height(l/h) ratios greater than 13 at supersonic speeds.Such flow produces an adverse static pressure gradi-ent in the cavity that causes a separating store to ex-perience
11、 large nose-up pitching moments. Open cav-ity flow, in which the shear layer bridges the cavity,is seen at supersonic speeds for cavities with I/h ra-tios less than 10. Although this type of flow pro-duces a more uniform static pressure distribution, itis this flow regime that can produce high-inten
12、sityacoustic tones. Transitional-closed and transitional-open flows are two distinct transitional flows forwhich the corresponding acoustic fields have not bccndetermined.The mechanism that produces the acoustic tonesis understood to be a reinforcement between insta-bilities in the shear layer that
13、bridges the cavityand pressure waves generated in the cavity whenthe shear layer impinges on the aft wall. Acoustictones occur at discrete frequencies that correspondto characteristic pressure patterns (standing waves ormodes) in the cavity. Although there is no satisfac-tory method to predict tone
14、amplitude (or whetherthey will occur), the frequencies at which the tonesmay occur can be predicted by a semiempirical equa-tion determined by Rossiter in reference 1 and mod-ified by Heller, Holmes, and Covert in reference 2.The modified Rossiter equation, which is describedlater, depends on cavity
15、 dimensions and flow speed.The purpose of this study was to determine iftones are generated at transonic speeds for the samegeometries (l/h ratios) as at supersonic speeds andto determine the effect of Reynolds numbcr (apartfrom boundary-layer thickness) and angle of cavityyaw on the internal acoust
16、ic fields.Symbols and AbbreviationsFPLffmhfluctuating pressure level, dB re qocfrequency, Hzfrequency of acoustic mode, Hzcavity height, in.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-k(M_)lA_mPpt,_cq_R_UocXYZa(l/h)empirical ratio of shear layer
17、andfree-stream velocitiescavity length (11.25 in.), in.free-stream Mach numberacoustic mode numbermeasured fluctuating pressure, psffree-stream total pressure, psifree-stream dynamic pressure, psffree-stream unit Reynolds numberper footfree-stream total temperature, Kfree-stream velocity, fpslongitu
18、dinal distance from origin,in.lateral distance from origin, in.vertical distance from origin, in.empirical phase between instabilitiesin shear layer and pressure wavesratio of specific heat of test gasat constant pressure to that atconstant volume angle of yaw, degExperimental DescriptionTest Facili
19、tyThe experimental study was performed in the13- by 13-in. test section of the Langley 0.3-MeterTransonic Cryogenic Tunnel (0.3-m TCT) shown infigure 1. (Refs. 13 and 14 describe the facility andoperation in more detail.) The 0.3-m TCT is acontinuous-flow, fan-driven, cryogenic pressure tun-nel that
20、 uses nitrogen as a test gas. All tile wallsof the test section are solid. The sidewalls are rigid,whereas tile top and bottom walls are flexible andmovable. The latter are computer controlled, givenfeedback on wall position and pressure distribution,to achieve alignment with model streamlines. This
21、 isdone so that the flow in the vicinity of the model willbe the same as that obtained for the free-stream con-dition. Reference 15 gives a more detailed descriptionof the adaptive walls.The Mach number in the tunnel can be variedcontinuously from 0.20 through 0.95. The stag-nation pressure and temp
22、erature are variable from1.2 to 6.0 atm and 80 K to 320 K, respectively, which2permits unit Reynolds numbers up to 100 x 106 perfoot.ModelA rectangular cavity model was mounted on aturntable that was instMled in the sidewall of the0.3-m TCT. Figure 2 shows the cavity with dy-namic pressure instrumen
23、tation prior to installa-tion in the tunnel. The cavity was 11.25 in. longby 2.50 in. wide and the depth was variable to obtainl/h ratios of 4.40 (h = 2.56 in.), 6.70 (h = 1.68 in.),12.67 (h = 0.89 in.), and 20.00 (h = 0.56 in.). Theturntable could be rotated with respect to the flow toposition the
24、cavity with angles of yaw of 0 and 15 .InstrumentationThe model was instrumented with 18 dynamicpressure transducers (16 of which were along tilecentcrline and 1 each on the fore and aft walls athalf-depth) as shown schematically in figure 3. Theorigin of the coordinates used was the center top ofth
25、e forward cavity wall. The transducers were minia-ture, high-sensitivity, piezoresistive, differential dy-namic pressure transducers with a full-scale range of=t=10 psid and a resonant frequency of 130000 Hz.Transduccr 8 was sealed to determine the sensitiv-ity of the transducer to vibration, which
26、proved tobe negligible. The reference pressure was local staticprcssure. (Transducers 1 3 and 15-17 were mani-folded to a static pressure port identified as SR1 infigurc 3; transducers 4 11 were manifolded to SR2;and transducers 12-14, 18, and 19 Were manifoldedto SR3.) A 1000-Hz bench calibration v
27、erified thatthe tempcrature compensation maintained a sensitiv-ity that was within 10 percent of a reference sen-sitivity at 100 K. Analog data were recorded on two14-channel FM tape recorders using a medium bandformat at 30 in/see (0 10 kHz). A sine wave calibra-tion was applied to each pressure tr
28、ansducer severaltimes throughout the test.Test MatrixData were obtained for Moc = 0.20, 0.60, 0.80,and 0.90. The Reynolds number was varied from4 x 106 to 100 x 106 per foot at angles of yaw of 0and 15 .Boundary-Layer ThicknessBecause boundary-layer thickness is an impor-tant parameter in cavity flo
29、ws (refs. i6 and i7)and because it varies with Reynolds number, the ef-fect of Reynolds number was isolated from that ofboundary-layer thickness. For this experiment, aZim=uBmiZProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-nearly constant boundary-
30、layer thickness was main-tained for the range of test Reynolds numbers. Thethickness of the boundary layer at the leading edge ofthe cavity was determined with measurements madewith a total pressure rake by using a method de-scribed in reference 18. The boundary-layer thick-ness is defined as the di
31、stance from the surface atwhich the boundary-layer velocity equals 99 per-cent of the free-stream velocity. For -_loc = 0.60,the boundary-layer thickness was found to rangefrom 0.58 in. at R_ = 5 x 106 per foot to 0.47 in. atR_=85x 106per foot; and for Mcc=0.90, itranged from 0.51 in. at R_ = 13 106
32、 per footto 0.49 in. at R_ = 100 x l06 per foot. Measure-ments were made with the cavity floor positionedflush with the turntable (h = 0.00 in.).Data AnalysisAn antialiasing filter was applied at 5 kHz andthe analog data were sampled at 12.5 kHz. Thedigitized data were divided into 50 blocks (assume
33、dindependent) of 4096 points each. Each block wasFourier analyzed by using a Hanning window andthe resulting spectra were averaged. This processproduced spectra with a frequency resolution of 3 Hzand 95-percent confidence that the spectral estimatewas within 4-1 dB of the true spectra based on achi-
34、square distribution.Results and DiscussionSince the data were obtained for a wide range oftemperatures and dynamic pressures, the data werenondimensionalized by using free-stream parameters.The fluctuating pressure is presented in decibels(dB) as is customary for acoustic data and is non-dimensional
35、ized with free-stream dynamic pressureas is customary for aerodynamic data. The fluctuat-ing pressure level is defined as follows:FPL = 20 log pqocChart AFrequency is nondimensionalized by using the cavitylength l and the free-stream flow speed U_.The acoustic tones that radiated from the cav-ity co
36、rresponded to characteristic pressure patterns(standing waves or acoustic modes) in the cavity.An illustration of an acoustic mode shape in thecavity can be obtained by plotting the amplitudeof a tone, at a given frequency, as a function ofposition along the length of the cavity. Figure 4presents th
37、ree different mode shapes (correspond-ing to fl/Uoo _ 0.7, 1.1, and 1.5) in a cavity withI/h = 6.70, Mac = 0.80, _b = 0, and Rat = 99 x 106per foot. The acoustic mode shapes were similar tothose observed in organ pipes but were somewhatelongated, as if the downstream wall was soft. Sub-sequent data
38、are presented as acoustic spectra. Datafrom transducer 1 (see fig. 3) are used in this report asthey are representative of data obtained throughoutthe cavity but contained the least amount of broad-band noise (tones appeared higher against the back-ground in the spectra). Except where indicated, all
39、data are presented for an angle of yaw of 0 . Forreference, a set of nondimensional modal frequen-cies predicted by the modified Rossiter equation (seerefs. 1 and 2), which is given here asl m - c_ (l/h)fm u_are given in chart A where, from reference 1,“7= 1.4_(I/h) = 0.25k(M_) = 0.57(l/h = 4.o0)(M_
40、 = 0.40-1.20)Nondimensional modal frequencies at a Mach number of-Mode 0.20 0.60 0.80 0.900.38.901.411.922.442.953.460.32.751.181.612.042.472.900.30.701.101.501.902.302.700.29.681.061.451.842.222.613Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-The
41、coefficientsct and k used in the equation werepublished values (rcf. 1) obtained for I/h = 4.00 andM_c = 0.40 through 1.20, respectively. A summaryof the test points for which tones were observed isincluded in tile nominal test matrix given in table 1.Effect of I/hOne of the main objectives of this
42、study was todetermine if the tones that correspond to the pre-dicted Rossitcr frequencies arc generated by cavitieswith the same I/h ratios at transonic speeds as theyare at supersonic speeds. Figure 5 presents plotscomparing FPL spectra for the four I/h configura-tions at Moc = 0.60, 0.80, and 0.90
43、 and for the high-cst Reynolds number obtained (85 x 106, 100 x 106,and 100 x 106 per foot, respectively). The modalfrequencies predicted by the modified Rossiter equa-tion (for l/h = 4.00 and M_c = 0.40 1.20) are in-dicated by bold tick marks on the abscissa. Asdiscussed in reference 19, the modifi
44、ed Rossiter equa-tion is a semiempirical equation that was determinedfor a limited parameter range. These limitations mayaccount for the disagreement between the predictedmodal frequencies and those observed in this test.Figure 5 illustrates that the deeper the cavity(or greater the volume), the gre
45、ater the acousticpressures. Tones were observed for cavities withI/h = 4.40 and 6.70 but not 20.00, which agrees withdata obtained previously under supersonic condi-tions (ref. 20). The tones that appear in fig-ure 5 for I/h = 20.00 coincide with the tunnelfan blade passing frequency and first harmo
46、nic;fl/Ucc = 1.21 and 2.42, for Moc = 0.60; fl/U_c =1.13 and 2.26 for Mc_ = 0.80; and fl/Uoc = 1.07 and2.14 for Moc = 0.90. An unanticipated result was thepresence of tones for I/h = 12.67 at M_c = 0.60 butnot at ,/_c = 0.80 or 0.90, which indicated a possiblechange in flow field.Data for M_c = 0.20
47、 were available only forl/h = 4.40 and 6.70. There were no tones apparentand no notable differences between the spectra.Effect of Reynolds NumberAs indicated before, a nearly constant boundary-layer thickness was maintained for the test range ofReynolds numbers. Figures 6, 7, and 8 illustratethe eff
48、ect of Reynolds number on the cavity FPL foreach I/h configuration at Moo = 0.60, 0.80, and.0.90,respectively. Little change occurred with changingReynolds number. The tones, the significant fea-tures in the spectra, did not change in amplitude,bandwidth, or center frequency (modal frequency) asthe
49、Reynolds nmnber changed. Data for Moc = 0.20were available only for low Reynolds numbers (lessthan 30 x 106 per foot) and are not presented.Effect of Mach NumberMode amplitude and bandwidth changed withMach number. Different tones dominated the spectrafor different Mach numbers. Figure 9 gives thespectra and compares the cavity FPL with the Machnumber range for each 1/h configuration at = 0and R_c = 30 x 106 per foot.For cavities
