1、ontrac/N-y iZ /olse o! .pe;-24222(NASA-CR-4499) THEORY FOR NOISE OFPROPELLERS IN ANGULAR INFLOW WITHPARAMETRIC STUDIES AND EXPERIMENTALV_RIFICATION Final Report (UnitedTechnologies Corp.) 111 pUncl asHI/71 0158469Provided by IHSNot for ResaleNo reproduction or networking permitted without license fr
2、om IHS-,-,-T. _- _-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NASA Contractor Report 4499Theory for Noise of Propellersin Angular Inflow WithParametric Studies andExperimental VerificationDonald B. Hanson and David J. ParzychHamilton Standard Di
3、visionUnited Technologies CorporationWindsor Locks, ConnecticutPrepared forLewis Research Centerunder Contract NAS3-24222National Aeronautics andSpace AdministrationOffice of ManagementScientific and TechnicalInformation Program1993Provided by IHSNot for ResaleNo reproduction or networking permitted
4、 without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TABLE OF CONTENTSSectionsSummary .1 Introduction 22 Background 3Theory Derivation 4Theoretical Foundation - Goldsteins Acoustic Analogy . 4Derivation of General Noise Radia
5、tions Equations 5Coordinate Systems and the Greens Function 5Thickness Noise . 6Loading Noise 9Quadrupole Noise 10Discretization of Area Elements and Equations for Near Field . 12Derivation of Far Field Radiation Formulas 13Thickness Noise . 13Loading Noise 154 Numerical Precision and Mesh Sizes 175
6、 Parametric Studies and Theoretical Trends . 19Precision of Source Placement 19Source Strength Effects 19Angular Inflow Effects . 206 Experimental Verification of Angular Inflow Theory . 22Propeller Data Comparisons . 22SR7A Prop-Fan Data Comparison 22SR7L Prop-Fan Test Assessment (PTA) Flight Data
7、Comparison . 237 Concluding Remarks 268 References 27AppendicesA Propeller Coordinates, the Greens Function, and its Derivatives . 29B Computation of Source Terms for Radiation Integrals 33C Blade Geometry for Mean Surface Representation 40D Observer Coordinate Systems . 42E Far Field Greens Functio
8、n 46F List of Symbols . 50G Users Manual for Computer Program . 53Figures 74Page,.111PREEDING PAGE BLANK NO1“ FILMEDProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-iProvided by IHSNot for ResaleNo reproduction or networking permitted without license
9、from IHS-,-,-SUMMARYThis report presents the derivation of a frequency domain theory and working equations forradiation of propeller harmonic noise in the presence of angular inflow. The theory is based onthe acoustic analogy generalized for a moving medium by M. E. Goldstein of NASA-Lewis.In applyi
10、ng the acoustic analogy, integration over the tangential coordinate of the source regionis performed numerically, permitting the equations to be solved without approximation for anydegree of angular inflow. All source terms are included. The thickness source is representedby a monopole distribution
11、that is unsteady by virtue of varying blade section relative speed.Loading, represented by dipole distributions, may be unsteady and includes radial, tangential,and axial components. The quadrupole term includes all nine components and also may beunsteady. General equations are written for sources o
12、n the actual blade surfaces; these give thesound field exactly, assuming that the source terms are known and that there are no surfacespresent other than the blades. However, for most purposes, a mean surface approximation willbe adequate. In this case, the sources may be placed on the camber surfac
13、e (or the chord line).For far field calculations, special forms of the equations are given to reduce computer runningtime. Angle of the propeller inflow is specified in terms of yaw, pitch, and roll angles of theaircraft. Since these can be arbitrarily large, the analysis applies with equal accuracy
14、 topropellers and helicopter rotors.The quadrupole derivation has been carried only far enough to show feasibility of thenumerical approach. However, for thickness and loading, the derivation is given in completedetail with working equations for near and far field. Explicit formulas are presented fo
15、rcomputation of source elements, evaluation of Greens functions, and location of observer pointsin various visual and retarded coordinate systems. The resulting computer program, calledWOBBLE, has been written in FORTRAN and follows the notation of this report very closely.Only about 60 lines of cod
16、e are required to compute the linear radiation terms exactly.The new theory was explored to establish the effects of varying inflow angle on axial andcircumferential directivity. Also, parametric studies were performed to evaluate variousphenomena outside the capabilities of earlier theories, such a
17、s an unsteady thickness effect.Validity of the theory was established by comparison with test data from conventional propellersand Prop-Fans under a variety of operating conditions and inflow angles. Agreement with thepropeller data is excellent and provides a satisfying verification of the theory.
18、Agreement withthe Prop-Fan data is not as good. Since the acoustic equations are exact, the difficulty must bein estimating the aerodynamic blade loading and not with the acoustic radiation equations. ForProp-Fans, tip flow is influenced by vortex loading which can dominate the noise at subsonictip
19、speeds but is of secondary importance for aerodynamic performance.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SECTION 1INTRODUCTIONIt has been known for some time that propeller noise can be strongly affected by any inflowthat leads to unsteady b
20、lade loading. Experimental and theoretical research in this areaintensified in the 1980s primarily as a result of the advaficed turboprop_ogram_atIq_._SA, itwas believed that noise due to angular inflow could be predicted accurately by computing theblade loading from an unsteady aerodynamic analysis
21、 and then using an axi_ flow=mqd.e! for thenoise radiation. However, in 1990 Mani (Ref. 1) showed v_ _.-flrs(0rder anaiysi_ tfiatfi_eCrossflow Mach number could have a more important impact on the noise than would the unsteadyloading. Krejsa (Ref. 2) extended Manis work to all orders and showed an-i
22、n_pressiveagreement with test results. The work at Hamilton Standard grew out of discussions with thenoise group at NASA Lewis and with Mani. The first contribution from Hamilton Standardwas a paper by Hanson (Ref. 3) which showed that noise-in tlae far field could be_described_interms of “wobbling
23、modes“ whose simple form clarified the physics of the noise generationprocess. The noise increase above the levels predicted with unsteady loading but axial inflowwas traced directly to the increase in the Mach number of the blade sources with respect to theobserver. The second contribution from Ham
24、ilton Standard is the work reported herein.The objective of this work was to develop the noise theory for the near field via a directfrequency domain analysis valid when the propeller shaft is inclined at any angle to the-flightdirection, as suggested by Figure 1. Geometrical approximations of the p
25、revi0us _frequencydomain methods have been eliminated so that the radiation equations are exact for specifiedlinear sources. This report presents the derivation of the theory, results of exercising the theoryin parametric studies, and a validation of the theory by comparison with test data. Note tha
26、t theanalysis applies strictly to pure angular inflow, not to distorte d !nfl0w. _:_ Unqikepreviotis“ works by Hanson which place sources on the propeller advance surface, thenew equations place sources on the blade surfaces assuming this source information (bladepressure distribution and geometry)
27、is available from a finite element aerodynamic solution.However, guidance is also given for use of the thickness and loading sources specified in termsof blade section thickness and lift distributions placed on a mean camber or chordal surface. Inthe near field formulation, loading variation may be
28、represented directly as a time history, ifdesired, eliminating summations over spinning modes. The far field formulation is an exactextension of the near field model and uses identical source input. Tangential integration isperformed analytically, leading to Bessel functions as in earlier far field
29、formulations andreproducing the “wobbling mode“ behavior first revealed in Ref. 3. However, the chordwiseintegration is left in numerical form to retain the exact nature of the solution. Although thederivation is somewhat complex, the working equations are simple and easy to interpret.The FORTRAN so
30、urce listing, compiled code for the IBM PC, and associated input andoutput data sets are available from the Contract Manager, Mr. Bruce Clark, at the NASA LewisResearch Center, 21000 Brookpark Road, Cleveland, Ohio 44135. Telephone number 216-433-3952.-2-Provided by IHSNot for ResaleNo reproduction
31、or networking permitted without license from IHS-,-,-SECTION 2BACKGROUNDFor simplicity, the earliest analyses of propeller noise (in the 1930s and 40s) modeled theblades as body forces in an infinite medium with no other surfaces and no mean flow. Forwardflight effects were added by Garrick and Watk
32、ins (ref. 4) in the 1950s. When applied topropellers in an ideal environment, predictions from these theories compared favorably with testdata. However, propellers of practical interest are installed on aircraft with reflecting surfacesand with inflow that generates unsteady loading. Under these con
33、ditions, agreement betweennoise theory and test data was often disappointing. Unsteady blade loading caused by non-idealinflow was believed to be the problem. Progress toward representing the true flow environmentwas slow. Noise analyses for unsteady blade loading without forward flight were studied
34、extensively in the 60s, most notably by Morse and Ingard (Ref. 5), Lowson (Ref. 6), andWright (Ref. 7). Forward flight was added to these models in the 70s and 80s by Hanson(Refs. 8, 9).In the 80s Farassat refined the modeling in his time domain methods for propellers andhelicopter rotors (WOPWOP, f
35、or example) by accounting for a general motion of the rotorincluding that where the rotor axis was tilted with respect to the flight direction. This aspectof his method was not explored extensively but it is documented in a paper by Padula and Block(Ref. 10). It wasnt until the late 1980s that the a
36、ngular inflow problem was given seriousconsideration. In 1988, R. Stuff published the first frequency domain theory for rotating pointloading sources with inflow at an angle to the axis of rotation (Ref. 11). Soon thereafter, workon angular inflow effects was sponsored by NASA-Lewis with Mani (Ref.
37、1) and Krejsa (Ref.2) as principal investigators. These and Hansons wobbling mode theory (Ref. 3) were far fieldmethods that revealed the importance of the cross flow Mach number but still included somegeometrical approximations. In the far field methods, the integration over the source in thetangen
38、tial direction was done analytically, leading to Bessel functions in the radiation equations.Meanwhile, Envia had been working on a near field method (Ref. 12) in which thecircumferential integration is done analytically as in the earlier Garrick and Watkins work (Ref.4). In order to explain near fi
39、eld observations on the Prop-Fan Test Assessment aircraft,Hanson and Farassat both generated near field methods capable of handling angular inflow.Hansons method (Ref. 13) was a simplified version of the present theory and Farassats (Ref.14) was a program in which he reinstated angular inflow capabi
40、lity in his time domain code.The present work returns to that same idea for the tangential integration but with the precisetreatment of blade geometry and inflow angle that was previously available only with the directtime domain methods of Farassat and others.-3-Provided by IHSNot for ResaleNo repr
41、oduction or networking permitted without license from IHS-,-,-SECTION 3THEORY DERIVATIONThe problem addressed in this section is noise of a propeller operating in a uniformlyflowing, unbounded medium containing no surfaces or bodies other than the propeller. Althoughthis is treated with complete gen
42、erality, there are limitations that should be explained. Inparticular, note that angular inflow does not imply distorted inflow. Thus, for example, noisecaused by wakes of an upstream wing could be calculated but the effect of refraction of thesound in the wake shear flow and reflection from the win
43、g would not be represented. Thissection starts with a review of Goldsteins version of the acoustic analogy (Ref. 15), which isthe starting point for development of the propeller noise theory. First, general equations arederived in the form of continuous integrals over the source. These are then disc
44、retized in a formdirectly applicable to computer coding with finite elements of blade area. Finally, special formsfor a faster running code are derived for the far field. Some of the details on coordinates,Greens functions, and source specification are relegated to Appendices A, B, C and E.Appendix
45、D gives a detailed treatment of observer coordinate systems to facilitate prediction atpoints specifed in visual or retarded coordinates and in systems aligned with the flight directionor aligned with the propeller axis. Finally, Appendix F provides a list of symbols.THEORETICAL FOUNDATION - GOLDSTE
46、iNS ACOUSTIC ANALOGYGoldstein extended Ffowcs-Williams at the end of thissubsection the other blades are accounted for by superposition. The pressure disturbance canbe written as the sum of the 3 terms in Equation 1:2 / =CoO = p(x,t) pr(x,t) +pL(x,t) +pQ(x,t) (7)so that the thickness noise isV DG dA
47、(y)d_“ (8)In this expression, VNdA is the volume displaced per unit time by the area element dA dueto the motion of the blade, if this is considered a source element, then the double integralsimply represents the summation over the surface and over source time of these elementsweighted by the Greens
48、 function derivative. The notation A(r) indicates that the blades aremoving. We prefer to do the surface integral in blade-fixed coordinates, which are defined inFigure 4. It can be seen that blade sections are defined by “cutting“ the blade with cylindrical-6-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-surfacesof radius ro=rs. The figure shows a typical section “unwrapped“ onto a plane in whichthe coordinates are xs and rs_bs. In this system, motion of the blade involves only the 4_ocoordinate. Thus, the area element i
