1、,9.,.-! :. “ .*.,!. ,m,.!.”,:;,.,a, “, ,. ”,.,” :“; “.-,L.J.iIJ:,:! ,.,.“,- ,.4“1,a71. WashingtonJuly1937Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,.-31176013644928 _ .4“.,a71“-*.-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS-.-TECHNICAL NOTE NO
2、.-NOISE FROM PROPELLERS WITH605SYMMETRICALSECTIONS AT ZERO BLADE ANGLEBy A, F. DemingSUMMARYA theory has %een deduced for the iro$ationnoise!from a propeller tvithl)ladesof symmetrical section aboutthe chord line and set at zero blade angle. Owing to thelimitation of the theory, the equations give w
3、ithout ap-preciable error only the sound pressure for cases wherethe wave lengths are large compared with the blade lengthsWith the aid of experimental data o%tained from,atwo-%lade arrangement, an empirical Telation was intro-duced that permitted calculation of higher harmonics- Thegenerality of th
4、e final relation given is indicated bycomparison of measured and calculated sound pressure forthe fuildauental and second harmonic of a four-blade ar-rangement=INTRODUCTIONThe sulject of aircraft noitieis one u-fgreat com-plexity and may bedivided into many parts depending onthe various possille sou
5、nd sources involved. On the prac-tical,side the question-of reducing aircraft noise has,to date, teen largely one of insulation of ca%ins withlloundmrooflla%sor%ing materials. This remedy togetlierwith reduction of vi%ration has been very effective in re-ducing noise in aircraft cabins to levels now
6、 consideredtolera%le.The largest contributor to aircraft noises is thepropeller itself. The aircraft propeller is a very unusu-al type compared with ordinary sound generators. Compar -jatively little has been done toward analyzing the mechan+ism of the propeller as a source of sounds although a more
7、nearly complete analysis of propeller noise would be ofvalue, at lce,stfrom considerations of attempts to cur% orProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 N.A.C,A. Technical Note No. 605a71reduce the noise at the source rather than by its lat
8、erabsorption and reflection.Much of the published theoretical work on propellernoise is mentioned in a recent paper by Gutin (reference 2),which deals with the noise generfitedby a propeller owingto the creation of torque and thrust. !l!hepresent paperdeals with the effect of section or blade thickn
9、ess in re-gard to propeller noise and the theory is augmented hyexperimental data. It may be mentioned that the soundpressures calculated from Gutins relations did not checkthe values obtained %y measurements accomplished here ofpropellers operating under normal conditions of speed andthrust. Gutin!
10、s relation gives values for the fundamentalsound pressure of a two-blade propeller many times thosemeasured. His relation gives two comonents 180 out oftime phase with each other, whereas actually there existsanother component 90 tO either of these components.Eart (reference 2) presents some general
11、 considerationsand conceptions of the subject of noise from rotating ob-jeCtS. As Eartts paper does not include in any quanti-tative manner the consideration of thrust or torque, itmay perhaps le said tO apply rather closely to the subjectof the present discussion.Propeller noise may be classified i
12、nto the same twodivisions that hold for the noise generated by any revolv-ing object. This classification of IIvortexnoise?andIrrotati,onnoise!?was introduced in reference 3. Afterthis paper had been completed an artfcle on the same sub-ject appeared. (See reference 4.) Rotation noise for anormal pr
13、opeller is the more important of the two, underthe usual operating conditions of a propeller, because mostof the sound energy and odness (reference 5) is involvedin it, The vortex noise is due tO the shedding of vorticesfrom the propeller blades and manifests itself as a contin-uous acoustic spectru
14、m (on a timeeaverage basis). A StUiiyof vortex noise is given in reference 6. The rotationnoise is due to the revolving pressure field, or the waveenveopirlgthe blades, and is also possible of divisioninto two parts. one part is due to the production ofthrust: the other part-is duc to the thickness
15、of theblades displacing air in both directions perpendicular tothe path of the blades,The problem here is to evelop a solution for soundpressure of the fundamental and the first few harmonics Ofrotation noise at a distant point generated by a proeller.-.b.Provided by IHSNot for ResaleNo reproduction
16、 or networking permitted without license from IHS-,-,-M.A.C.A. Technical Note No. 605%. . . . -3b-b.with symmetrical-section, evenly spaced blades set atzero blade angle, and revolving at tip speeds below thatof sound. Such an arrangement will, of.course, produceno thrust since there is a symmetry a
17、bout the plane of ro-tation and no possibility of an angle of attack existingto produce a flow. The upper speed limit, as far as thispresentation is concerned, may be said to be determined %Ythe speed that produces local velocities equal to that ofsound aad it will, in general, bedetermined ly the t
18、hick-ness ratio and shape of the blade sectionsconsidered.This upper limit will, for most thickness ra,tiosand.streamline shapes used, be-about 0.7-0.8the velocity.ofsound.DERIVATION Ol?FoRMULASFigure 1 represents the.geometry of the pro%lem ofrotation noise generated by revolving symmetrical-sectio
19、nblades with zero blade angle. It is assumed in this paperthat the sound emanates from a narrow ring and that themovemeiltof the blades can be represented for purposes ofsound generation by an infinite number of ifinitesimalline pistons in this ring, each of which is given a phaseappropriate to its
20、position around the ring.“t=v-Iil figure 1, 0 is the center of the disk described IJYthe revolving blades. In plan view the axis of the %ladesis denoted %y the line All, the disk by COD; and theobservers position by P. In elevation view the axis isthrough O perpendicular to the paper: the disk is de
21、no-ed hy ACBD. The center of gravity of the elementarysources is descri%ed by the radius KR. The angle the ra-dius vector r (or 1) makes with the axis of rotation isP. It is seen that, as the angle Q is changed continu-ously, the distance from the observerat P changes peri-odically by the amount +x.
22、 It is assumed tha,t L islarge compared with R.For purpose of analysis let it %e assumed that thefundamental and first few harmonics of the rotation noiseemanate from a ring of mean radius KR. The area of thesources on one side of the disk would then bes =2Tr HKR2 (1)where H is a small quantity less
23、 than 1 and K, a quan-tity near to but less than 1. The quantity H may %eProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 N.A.C.A. Technical Note No. 605tfirmedthe lwidthllof the euivalent ring and is given asa fraction of the radius R.Since the bla
24、des are of symmetrical section about thechord, have zero blade angle, and operat in quiescentair, it is seen that a symmetry exists about the plane ofthe disk, It can therefore be assumed that only one-halfthe blade, or one side of the,chord, is operating and work-ing next to a wall of infinite exte
25、nt. T!hisfact allowsthe use of Rayleighls relation (reference 7) for the po-tential at a point due to a source in a wall of infiniteextent. . (If a thrust is exerted, a more general relationwould be usedgiving the potential due to a doulle sourceas well.) Rayleighs relation is(2)whereVIZ33. anr,ie t
26、he velocity potential at any point in ques-tion due to source dS a71velocity normal to planedistance frem the elementary source to the pointin questionf, freq-uen.cyA, wave lengthG, velocity of sounddS, area of elementary sourceFor the purposes of the pro%lem in hand, these rela-tions become-vhre Po
27、 is the mean density.(6)(7(9). .-,(8)since(lo) “8“.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,. .,.N.A.C,A. Technical Note No. 605On differentiating the exponent in M,7i(-l)qn qnw p H KR2 i(qnwt+qn”k )p qn._- Jqn(ml) !qn e (11)As the only conc
28、ern is with the sound-pressure ampli-tude, all phase f,actorscan be neglected. Then equation(11) l)ecomesH KRa Jqn (ml) !qnPqn = qnw p. - - t (12)Remembering thatvw=-Rthereforeand:m1 = k KR sin =qnKsiniqn = “i. Aqn= V qn x (function of mean sectionsize and shape over out-er portion, HR)= KV Aqn (as
29、first approximationu where a and b aremeasured at radius KR;a/l is small, about0.1)where a is 1/2 thicknessb, chordAnd, since equation (12) gives the maximum value insteadof the root mean square, the equation must be divided %yF 2. ,Finally,poqnaAPqn = -e- I?V JqnA bt (m,) (13)Provided by IHSNot for
30、 ResaleNo reproduction or networking permitted without license from IHS-,-,-N.A.C.A. Technical Note No. 605The sound.pressure of the fundamental and lower har-monics is thusolained in terms of the aerodynamic .veloc-ity head pJVV, the geometry “ofthe arrangement, andthe acoustic properties of the me
31、dium.EXPERIMENTAL CHECK ON ACCURACY OF THEORYBefore any calculations can be made, some of the Tcl-ues in equation (13) must be ascertained. All values ex-cept An, K, and E are directly known or can he foundwithout any intuitive considerations of the problem. Thevalues Aqn, and H wil1now be establish
32、ed.For rectangular excitation or rectangular wave formit can be shown that the Fourier coefficient is given %yFor small angles,(14)(15)where g is any radiu from O to R. This relation 170ulCihold Good, of course, only for values of the radius Gdescri%iigthe outer portions, which is the region con-cer
33、ned.Assigning values to the fractions H and K is anatter cf a little less defiiziteprocedure. If it he as-sumed that the effectfvenesof the radius in producingthe sound pressure of the fur-idan.entalat a distant pointvaries as the x pocr of the radius g, the radii de-scri.hiilgthe centers of gravity
34、 would be (x+l)/(x+2)R,As a result of measurenonts of the radiated soundpressures of the fundamntal frequency in th plane of ro-t.tion ( = 901 from tno identically equally spacedrotating blades rithsyr,netricalsocti.onsand zero bladallglet it was found that the sound yrcssurc p varies asthe fourth p
35、overof the tip spoe?.for tip speeds belowthat of soilnd. OIcmay from this result expect the conicr“.“. .,.“?“+Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.-. .,.I?.A.C.A. Technical Note No. 605 9,.of gravity of the sound sources in the disk of th
36、e rotating blades to be at a ra the fundamental will, ofcourse, be-considered first. The values substituted are:P = 112 x 10-3 grams/cm3$ air densityq 1$= order of harmonicn= 2, number of bladesa= 0.39 x 2.54 cm, 1/2 blade thickness% = 3*9O x 2.54 cm, blade chordR = 4,0 x 12 x 2.54 cm, blade length
37、(radius tollade tip)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 N.A.,C.A.Technical Note No, 605K= 0.80, fraction of R to center of gravity of. sourcesv= ,tip speed iq cm/sec.1 = 80 X 12 X-254cm, distance of microphone tocenter of revolving bla
38、desml = qn sin KV/C (sin = 1.0)c = 1100 x 12 x 2.54 cM/see, velocity of sound!3= 0.40, fractional width of equivalent ring!lheresults are shown in the following table:I Calculated plxaKV/C I Obserred.pzxaqn = 1 X 2 (bar) (bar)r-._I-0.603 0.72 0.82.541 .47 . ,51.380 .103 ,11The comparison is quite fa
39、vorable for the fundamentalsound pressure but, when checking the theory with experi-mental.data for higher harmonics, it was found that appreciahle differences occurred This difference, however,only gradually lecame larger as higher and higher orderharmonics were considered; the error for the second
40、 hardmonic, for instance,was not unduly large.*Although the relation qn = KV Aqn gives a correctresult, the factor a/b should %e nearer 2a/b. Apparent-ly, errors in othr factors are compensating. No claimsare made relative to the favrablc check here between thetheory and experimental results; othor
41、than for yurpose ofsoufidcalculations, the results are fairly good. The fac-tors K and II, for instance, could hardly be said to bcrigorously obtained; strictly speaking, the integrationshould te carried.out over the entire,disk-. . .*Provided by IHSNot for ResaleNo reproduction or networking permit
42、ted without license from IHS-,-,-,. .N.A.C.A, Technical Note No. 605 11ApparatusThe lfull-scalelfblades used in this work were rotatedby a 200-horsepower, 3,600 r.p.m., slip-ring motor caPa-ble of being set at any angle in the azimuth circle. Thismotor was specially built by the General Electric Com
43、panyfor the N.A.C.A. for propeller-noise and other research.Figure 2 shows a propeller mounted on this motor. Thismotor is located on a beach 235 feet from the nearestbuilng, within which the motor control and the sound re-cording apparatus are situated. The microphone is placed80 feet from the moto
44、r.The microphones used are the Western Electric No.618-A electrodynamics type and are connected to the sound-recording apparatus by shielded ca%le. The recording andmeasuriilg equipment used in this work includes amplifiers,filters? attenuators, and an autom.atic-recording soundanalyzer. A schematic
45、 sketch of the hook-up of this equip-ment is given in figure 3 and a photograph of the appara-tus in figure 4. The principle of operation of this ana-lyzer is given in reference 8, but the analyzer has subse-quently been much improved.The data to follow giving sound pressure againstK v/c were obtain
46、ed from sound-analyzer records whichwere corrected for errors due to the over-all frequencycharacteristics. Over-all calibrations from microphoneto analyzer tveremade before and after each series of runsand the variations in over-all amplificationwere nevermore than a few percent, The calibrating un
47、itused wasaWestern Electric AME-29 unit built to accommodate 618-microphones,The accuracy of the sound pressures given in thispaper is comparable with the accuracy of the output of theAME-29 calibrating unit oxcep for errors in measuring theanalyzer records. The error involved in measuring thesereco
48、rds is not over 5 percent. It will be noticed thatthe analyzer records (fig. 5) give a fairly definite pat-tern for the fundamental and harmonics and, by systematicmeasurement, errors of”only a few percent are involved.Thecalibration was always taken at 500 cYcles with0.29 volt impressed across the calibrating unit, which atthat frequency,.giv a soundmressure with the dynamicmicrophone of 1 %ar. The volage across the calibratingunit w
