Airfoil Self - Noise and Prediction

NASA Reference Publication 1218 July 1989 Airfoil Self-Noise and Prediction Thomas F. Brooks, D. Stuart Pope, and Michael A. Marcolini I-/1/71 Uncla 01£77 s 17 I NASA Reference Publication 1218 1989 Airfoil Self-Noise and Prediction Thomas Langley Hampton, F. Brooks Research Center Virginia D. Stuart Pope PRC Kentron, Inc. Aerospace Hampton, Michael Langley Hampton, National Aeronautics and Space Administration Office of Management Scientific and Technical Information Division Technologies Virginia A. Marcolini Research Virginia Center Division Contents Suminary .................................. 1. Introduction 1.1. ................................ Noise Sources and Background 1.1.2. Separation-Stall 1.1.3. Laminar-Boundary-Layer-Vortex-Shedding 1.1.4. Tip Vortex 1.1.5. Trailing-Edge-Bluntness Overview and 2.2. Instrumentation 2.3. Test Conditions 2.4. Wind Tunnel 3.1. Scaled 3.2. Calculation Acoustic 4.2. Correlation 4.3. Self-Noise 5.1. Noise Corrections Procedures ............. 4 5 5 5 Trailing 5 Edge ................ 9 9 ......................... 9 .......................... Editing Spectra 15 ......................... and Spectral 15 Determination ............. 15 ........................... 17 ............................. Data 51 Noise Data 5.2.2. Calculation 5.2.3. Comparison With ...................... Formation 5.3.1. Calculation 5.3.2. Comparison Noise Procedures With Noise FILMED 66 ...................... 71 ...................... 71 71 ...................... 73 Noise ............................ NOT 62 63 Trailing-Edge-Bluntness-Vortex-Shedding Experiment ............. ....................... Data 51 62 ....................... Data . 59 ........................... Procedures Noise 51 54 ....................... Data Flow 51 Laminar-Boundary-Layer-Vortex-Shedding Scaled Separated ......................... ........................ With 5.2.1. and ........................... Comparison BLANK Noise .............................. 5.1.3. P/_GE 4 4 .............. 73 73 111 PRECEDING 3 5 at the Procedures 5.4.1. ....... ........................ Parameters Scaling Vortex Noise ............................. Calculation Tip VS) ........................... 5.1.2. 5.3. (LBL ......................... Zero angle of attack Nonzero angle of attack 5.2. 3 Vortex-Shedding Identification Scaled 2 ..................... Turbulent-Boundary-Layer-Trailing-Edge 5.1.1. ........ ........................... Measurements Source Noise ............................ Data 4.1. Spectral Formation Facility 3. Boundary-Layer (TBL-TE) ........................ of Experiments Models 2 Trailing-Edge Noise of Report 2.1. 5.4. ...................... Turbulent-Boundary-Layer 2. Description . 2 1.1.1. 1.2. . 1 6. 5.4.2. Scaled 5.4.3. Calculation Procedures 5.4.4. Comparison With Comparison 6.1. Study Data ........................... of Schlinker 6.1.1. Boundary-Layer 6.1.2. Trailing-Edge Study of Schlinker 6.3. Study of Fink, 7. Conclusions With and ...................... Published 81 Results .............. 83 Amiet ..................... 83 ..................... 83 Measurements and Predictions .......... 83 .......................... Schlinker, and 88 Amiet ................... 88 ............................... Appendix A--Data Processing Appendix B-I-Noise Directivity Appendix C Appendix D--Prediction Tables 78 Definition Noise 6.2. References Data of Predictions 74 ....................... Application 99 and Spectral ............ 100 ........................ of Predictions Code Determination 105 to a Rotor ........................ Broadband Noise Test ..... 108 112 ................................. 133 ................................... 134 iv £ Symbols A a, M parameters of shape function A, eqs. (37) and (38) B b, b0 c chord Co medium Dh directivity length, of sound, function F(St) m/s Rij(r) cross-correlation St, Stl, limit), Stl, St2 Mi and from observer, m spectrum of self-noise, M j, Pa 2 source numbers to Pa2/Hz defined St l, St_ universal function, St" Strouhal numbers for LBL-VS section 5.2. shape Strouhal number defined tip vortex formation section 5.3. spectral shape function for LBL VS noise, eq. (57) G2 Rc-dependence for LBL VS noise peak amplitude, eq. (58) t time, U free-stream G3 angle dependence function, eq. (60) u_ convection velocity, x streamwise axis, G4 peak Y lateral z vertical C_TIP angle of attack of airfoil oncoming flow, deg aTIP corrected angle of attack airfoil tip, eq. (66), deg g_t airfoil enced Hz St m level for G2 function tunnel h TE between Mi and M j, height, thickness bluntness), m K2 constants, (47), (48), L span, LI sectional unit defined for vortex-shedding 5.4. s velocity, m/s m/s see fig. B3, m (degree of axis, axis, axis, m m tip to of angle of attack referto tunnel streamwise deg m Og, K, K1, AK1, number for G5, shape function for TE noise, eqs. (75)-(82) cross-spectrum microphone pa2/Hz Strouhal TE-bluntness noise, section eq. (74) H for noise, G1 c_j(f) noise scaling, frequency, spectral bluntness for defined noise f G5 on between distance Strouhal in tip TBL--TE and separation scaling, section 5.1. directivity function for translating dipole (low-frequency limit), eq. (B2) spectral eq. (18) number region Reynolds number based chord length, cU/u s(f) m U/co microphones for TE noise (high-frequency eq. (B1) number, Rc m speed scale, of tip vortex maximum Mach vortex formation (42) parameters of shape function B, eqs. (43) and (44) D_ Mach Mmax spectral shape function for separation noise, eqs. (41) and correlation spanwise extent at TE, m spectral shape function for TBL-TE noise, eqs. (35) and (36) a0 turbulence defined by eqs. and (49) (18), m lift of blade, 6* lift per span v effective aerodynamic of attack, corrected wind tunnel effects, angle for open deg boundary-layer thickness, boundary-layer thickness, m displacement m F tip vortex O angle axis deg from strength, m2/s source streamwise x to observer, for b0, _, and 00 is for airfoil at zero angle of attack, reference value see fig. B3, 1/3 boundary-layer thickness, m kinematic time momentum Abbreviations: viscosity delay, angle from to observer, ¢ spectral presentation of medium, m2/s T 1/3-octave s source lateral axis see fig. B3, deg cross-spectral phase angle, angle parameter related face slope at TE, section deg y BL boundary LBL laminar boundary LE leading edge LHS left-hand Mi microphone layer to sur5.4, Subscripts: of airfoil number average e retarded coordinate OASPL overall dB RHS right-hand SPL sound sound pressure pressure level, turbulent TE trailing edge UTRC United Center Technologies shedding pressure 8 suction TIP tip of blade VS vortex TOT total 2D two-dimensional Ot angle 3D three-dimensional of airfoil dependent vi spectrum, Pa) boundary P side level, side TBL side of airfoil i for i -- 1 9, see fig. 4 dB (re 2 × 10 -5 avg blade side through deg layer of airfoil layer blade Research Summary An overall prediction method has been developed for the self-generated noise of an airfoil blade encountering smooth flow. Prediction methods for individual self-noise mechanisms are semiempirical and are based on previous theoretical studies and the most comprehensive self-noise data set available. The specially processed data set, most of which is newly presented in this report, is from a series of aerodynamic and acoustic tests of two- and three-dimensional airfoil blade sections conducted in an anechoic wind tunnel. Five self-noise mechanisms due to specific boundary-layer phenomena have been identified and mod- eled: boundary-layer turbulence passing the trailing edge, separated-boundarylayer and stalled-airfoil flow, vortex shedding due to laminar-boundary-layer instabilities, vortex shedding from blunt trailing edges, and the turbulent vortex flow existing near the tips of lifting blades. The data base, with which the predictions are matched, is from seven NACA 0012 airfoil blade sections of different sizes (chord lengths from 2.5 to 61 cm) tested at wind tunnel speeds up to Mach 0.21 (Reynolds number based on chord up to 3 x 106) and at angles of attack from 0 ° to 25.2 °. The predictions are compared successfully with published data from three self-noise studies of different airfoil shapes, which were tested up to Mach and Reynolds numbers of 0.5 and 4.6 x 106, respectively. An application of the prediction method is reported for a large-scale-model helicopter rotor and the predictions compared well with data from a broadband noise test of the rotor, conducted in a large anechoic wind tunnel. A computer code of the methods is given for the predictions of 1/3-octave formatted spectra. I. Introduction Airfoil _W self-noise is due to the interaction tween an airfoil blade and the turbulence produced in its own boundary layer and near wake. It is the total noise produced when an airfoil encounters smooth nonturbulent inflow. Over the last decade, research has been conducted at and supported by NASA Langley Research Center to develop fundamental understanding, as well as prediction capability, of the various self-noise mechanisms. The interest has been motivated by its importance to broadband helicopter rotor, wind turbine, and airframe noises. The present paper is the cumulative result of a series of aerodynamic and acoustic wind tunnel tests of airfoil sections, which has produced a comprehensive data base. A correspondingly extensive semiempirical scaling effort has produced predictive capability for five self-noise mechanisms. 1.1. Noise Previous broadband Sources and research efforts noise mechanisms ake Turbulent-boundary-layermtrailing-edge noise _Laminar r- Vortex undary layering waves Laminar-boundary-layer--vortex-shedding noise V Boundary-layer (prior to 1983) for the are reviewed in some Large-scale separation (deep stall) Separation-stall noase _Blunt \ trailing edge Trailing-edge-bluntness--vortex-shedding noise Turbulent-Boundary-Layer-Trailing-Edge TE) Noise Using measured surface pressures, Brooks and Hodgson (ref. 2) demonstrated that if sufficient information is known about the TBL convecting surface pressure field passing the TE, then TBL-TE noise can be accurately predicted. Schlinker and Amiet (ref. 3) employed a generalized empirical description of surface pressure to predict measured noise. However, the lack of agreement for many cases indicated 2 .. Background detail by Brooks and Schlinker (ref. 1). In figure 1, the subsonic flow conditions for five self-noise mechanisms of concern here are illustrated. At high Reynolds number Rc (based on chord length), turbulent boundary layers (TBL) develop over most of the airfoil. Noise is produced as this turbulence passes over the trailing edge (TE). At low Rc, largely laminar boundary layers (LBL) develop, whose instabilities result in vortex shedding (VS) and associated noise from the TE. For nonzero angles of attack, the flow can separate near the TE on the suction side of the airfoil to produce TE noise due to the shed turbulent vorticity. At very high angles of attack, the 'separated flow near the TE gives way to large-scale separation (deep stall) causing the airfoil to radiate low-frequency noise similar to t,hat of a bluff body in flow. Another noise source is vortex shedding occurring in the small separated flow region aft of a blunt TE. The remaining source considered here is due to the formation of the tip vortex, containing highly turbulent flow, occurring near the tips of lifting blades or wings. 1.1.1. (TBL Turbulent be- Tip vortex Tip vortex formation Figure 1. Flow conditions producing noise airfoil blade self-noise. a needfor a moreaccuratepressure descriptionthan wasavailable.Langleysupporteda researcheffort (ref.4) to modeltheturbulencewithinboundarylayersasa sumofdiscrete"hairpin"vortexelements.In a paralleland follow-upeffort, the presentauthors matchedmeasured and calculatedmeanboundarylayercharacteristics to prescribed distributionsofthe discretevortex elementsso that associatedsurface pressurecouldbedetermined.The useof the model to predictTBL TE noiseproveddisappointingbecauseof its inabilityto showcorrecttrendswith angleof attackor velocity.Theresultsshowedthat to successfully describethesurfacepressure, thehistory of the turbulencemustbe accountedfor in addition to the meanTBL characteristics. This levelof turbulencemodelinghasnot beenattemptedto date. A simplerapproachto the TBL TE noiseproblemis basedon the Ffowcs Williams and Hall (ref. 5) edge-scatter formulation. In reference 3, the noise data were normalized by employing the edge-scatter model with the mean TBL thickness 5 used as a required length scale. When 5 was unknown, simple flat plate theory was used to estimate 5. Spectral data initially differing by 40 dB collapsed to within 7 dB, consistent with the results of the approach discussed above using surface pressure models. The extent of agreement between data sets was largely due to the correct scaling of the velocity dependence, which is the most sensitive parameter in the scaling approach. The dependence of the overall sound pressure level on velocity to the fifth power had been verified in a number of studies. The extent to which the normalized data deviation was due to uncertainty in 5 was addressed by Brooks and Marcolini (ref. 6) in a forerunner to the present report. For large Rc and small angles of attack, which matched the conditions of reference 3, the use of measured TBL thicknesses 5, displacement thicknesses 5", or momentum thicknesses/_ in the normalization produced the same degree of deviation within the TBL TE noise data. Subsequently, normalizations based on boundary-layer maximum shear stress measurements and, alternately, profile shape factors were also examined. Of particular concern in reference 6 was that when an array of model sizes, rather than just large models, was tested at various angles of attack, the normalized spectrum deviations increased to 10 or even 20 dB. These large deviations indicate a lack of fidelity of the spectrum normalization and any subsequent prediction methods based on curve fits. They also reinforce the conclusion from the aforementioned surface pressure modeling effort that knowledge of the mean TBL characteristics alone is insufficient to define the turbulence structure. The conditions under which the turbulence evolves were found to be important. The normalized data appeared to be directly influenced by factors such as Reynolds number and angle of attack, which in previous analyses were assumed to be of pertinence only through their effect on TBL thickness 6 (refs. 3 and 7). Several prediction schemes for TBL TE noise have been used previously for helicopter rotor noise (refs. 3 and 8) and for wind turbines (refs. 9 and 10). These schemes have all evolved equations which were fitted to the of reference 3 and, thus, are limited cerns of generality discussed above. 1.1.2. Separation-Stall from scaling law normalized data by the same con- Noise Assessments of the separated flow noise mechanism for airfoils at moderate to high angles of attack have been very limited (ref. 1). The relative importance of airfoil stall noise was illustrated ill the data of Fink and Bailey (ref. 11) in an airframe noise study. At stall, noise increased by more than 10 dB relative to TBL TE noise, emitted at low angles of attack. Paterson et al. (ref. 12) found evidence through surface to far field cross-correlations that for mildly separated flow the dominant noise is emitted from the TE, whereas for deep stall the noise radiated from the chord as a whole. This finding is consistent with the conclusions of reference 11. No predictive methods are known to have been developed. A successful method would have to account for the gradual introduction of separated flow noise as airfoil angle of attack is increased. Beyond limiting angles, deep stall noise would be the only major contributing source. 1.1.3. Laminar-Boundary-Layer Shedding (LBL VS) Noise When a LBL exists over Vortex- most of at least one side of an airfoil, vortex shedding noise can occur. The vortex shedding is apparently coupled to acoustically excited aerodynamic feedback loops (refs. 13, 14, and 15). In references 14 and 15, the feedback loop is taken between the airfoil TE and an upstream "source" point on the surface, where Tollmien-Schlichting instability waves originate in the LBL. The resulting of quasi-tones related TE. The gross trend was found by Paterson Strouhal number basis noise spectrum is composed to the shedding rates at the of the frequency dependence et al. (ref. 16) by scaling on a with the LBL thickness at the TE being the relevant length scale. Simple fiat plate LBL theory was used to determine the boundarylayer thicknesses 5 in the frequency comparisons. The use of measured values of 5 in reference 6 verified the general Strouhal dependence. Additionally, 3 forzeroangleofattack,BrooksandMarcolini(ref.6) foundthat overalllevelsof LBL VS noisecouldbe normalized sothat thetransitionfromLBL VSnoise to TBL TE noiseis a uniquefunctionof Rc. There have been no LBL VS noise prediction methods proposed, because most studies have emphasized the examination of the rather erratic frequency dependence of the individual quasi-tones in attempts to explain the basic mechanism. However, the scaling successes described above in references 6 and 16 can offer initial scaling guidance for the development of predictions in spite of the general complexity of the mechanism. 1.1.3. Tip Vortex Formation Noise The tip noise source has been identified with the turbulence in the local separated flow associated with formation of the tip vortex (ref. 17). The flow over the blade tip consists of a vortex with a thick viscous turbulent core. The mechanism for noise production is taken to be TE noise due to the passage of the turbulence over the TE of the tip region. George and Chou (ref. 8) proposed a prediction model based on spectral data from delta wing studies (assumed to approximate the tip vortex flow of interest), mean flow studies of several tip shapes, and TE noise analysis. Brooks and Marcolini (ref. 18) conducted an experimental study to isolate tip noise in a quantitative manner. The data were obtained by comparing sets of two- and three-dimensional test results for different model sizes, angles of attack, and tunnel flow velocities. From data scaling, a quantitative prediction method was proposed which had basic consistency with the method of reference 8. 1.1.5. Noise Trailing-Edge-Bluntness Vortex-Shedding Noise due to vortex shedding from blunt trailing edges was established by Brooks and Hodgson (ref. 2) to be an important airfoil self-noise source. Other studies of bluntness effects, as reviewed by Blake (ref. 19) and Brooks and Schlinker (ref. 1), were only aerodynamic in scope and dealt with TE thicknesses that were large compared with the boundary-layer displacement thicknesses. For rotor blade designs, the bluntness is likely to be small with boundary-layer thicknesses. and wing compared Grosveld (ref. 9) used the data of reference 2 to obtain a scaling law for TE bluntness noise. He found that the scaling model could explain the spectral behavior of high-frequency broadband noise of wind turbines. Chou and George (ref. 20) followed suit with an alternative scaling of the data of reference 2 to model the noise. For both modeling techniques neither the functional dependence of the noise on boundary-layer thickness (as compared with the TE bluntness) nor the specifics of the blunted TE shape were incorporated. A more general model is needed. 1.2. Overview of Report The purpose of this report is to document velopment of a self-noise prediction method the deand to verify its accuracy for a range of applications. The tests producing the data base for the scaling effort are described in section 2. In section 3, the measured boundary-layer thickness and integral parameter data, used to normalize airfoil noise data, are documented. The acoustic measurements are reported in section 4, where a special correlation editing procedure is used to extract clean self-noise spectra from data containing extraneous test rig noise. In section 5, the scaling laws are developed for the five selfnoise mechanisms. For each, the data are first normalized by fundamental techniques and then examined for dependences on parameters such as Reynolds number, Mach number, and geometry. The resulting prediction methods are delineated with specific calculation procedures and results are compared with the original data base. The predictions are compared in section 6 with self-noise data from three studies reported in the literature. In appendix A, the data processing technique is detailed; in appendix B, the noise directivity functions are defined; and in appendix C, an application of the prediction methods is reported for a helicopter rotor broadband noise study. In appendix D, a computer code of the prediction method is given. 2. Description The details of Experiments of the measurements and test facil- ity have been reported in reference 6 for the sharp TE two-dimensional (2D) airfoil model tests, in reference 18 for corresponding three-dimensional (3D) tests, and in reference 2 for the blunt TE 2D airfoil model report 2.1. test. Specific information is presented here. Models applicable to this The models were tested in the low-turbulence potential core of a free jet located in an anechoic chamber. The jet was provided by a vertically mounted nozzle with a rectangular exit with dimensions of 30.48 × 45.72 cm. The 2D sharp TE models are shown in figure 2. The models, all of 45.72-cm span, were NACA 0012 airfoils with chord lengths of 2.54, 5.08, 10.16, 15.24, 22.86, and 30.48 cm. The models were made with very sharp TE, less than 0.05 mm thick, without beveling the edge. The slope of the surface near the uncusped TE corresponded to the required 7 ° off the chord line. The sharp TE 3D models, shown in figure 3, all had spans of 30.48 cm and chord lengths that were the same as the five largest 2D models. The 3D models had rounded tips, defined by rotating the NACA 0012 shape about the chord line at 30.48-cm span. An NACA 0012 model of pertinence to the present paper, which is not shown here, is the blunt-TE airfoil of reference 2, with a chord length of 60.96 cm. Details of the blunt TE of this to the mod- els, provided support and flush-mounting on the side plates of the test rig. At a geometric tunnel angle of attack o_t of 0 °, the TE of all models was located 61.0 cm above the nozzle exit. The tunnel angle at is referenced to the undisturbed tunnel streamline direction. In figure 4, an acoustic test configuration for a 3D model is shown. A 3D setup is shown so that the model can be seen fitted to the side plate. The side plates (152.4 x 30.0 x 1 cm) were reinforced and flush mounted on the nozzle lips. For the 2D configurations, an additional side plate was used. 2.2. M7) and 30 ° aft (M5 and and processing approaches A. For the aerodynamic tests the the right in figure 4 were removed a large three-axis computer-controlled used to position hot-wire probes. probes included both figurations. In figure and Facility large model are given in section 5. The cylindrical hubs, shown attached 30 ° forward (M4 and The data acquisition described in appendix M8). are microphones to and replaced by traverse rig The miniature cross-wire and 5, a cross-wire single-wire conprobe is shown mounted on the variable-angle arm of the traverse Again, for clarity, a 3D airfoil model is shown. probes were used to survey the flow fields about rig. The the models, especially in the boundary-layer and nearwake region just downstream of the trailing edge. 2.3. Test The models Conditions were tested at free-stream velocities U up to 71.3 m/s, corresponding to Mach numbers up to 0.208 and Reynolds numbers, based oil a 30.48-cm-chord model, up to 1.5 x 106. The tunnel angles of attack c_t were 0 °, 5.4 °, 10.8 °, 14.4 °, 19.8 °, and 25.2 ° . The larger angles were not attempted for the larger models to avoid large uncorrectable tunnel flow deflections. For the 22.86-craand 30.48-cm-chord models, (_t was limited to 19.8 ° and 14.4 ° , respectively. For the untripped BL cases (natural BL development), the surfaces were smooth and clean. For the tripped BL cases, BL transition was achieved by a random distribution of grit in strips from the leading edge (LE) to 20 percent chord. This tripping is considered heavy because the chordwise extent of the strip produced thicker than normal BL thicknesses. It was used to establish TBL even for the smaller models a well-developed and at the same time retain geometric similarity. The commercial grit number was No. 60 (nominal particle diameter of 0.29 mm) with an application density of about 380 particles/cm 2. An exception was the 2.54-cm-chord airfoil which had a strip at 30 percent chord of No. 100 grit with a density of about 690 particles/era 2. 2.4. Wind Tunnel Corrections Instrumentation For all of the acoustic testing, eight 1.27-cmdiameter (1/2-in.) free-field-response microphones were mounted in the plane perpendicular to the 2D model midspan. One microphone was offset from this midspan plane. In figure 4, seven of these are shown with the identification numbers indicated. Microphones M1 and M2 were perpendicular to the chord line at the TE for at = 0 °. The other microphones shown were at radii of 122 cm from the TE, as with M1 and M2, but were positioned The testing of airfoil models in a finite-size open wind tunnel causes flow curvature and downwash deflection of the incident flow that do not occur in free air. This effectively reduces the angle of attack, more so for the larger models. Brooks, Marcolini, and Pope (ref. 21) used lifting surface theory to develop the 213 open wind tunnel corrections to angle of attack and camber. Of interest here is a corrected angle of attack _, representing the angle in free air required to give the same lift as at would give in the tunnel. One has from reference 21, upon ignoring 5 L-82-4573 Figure 2. Two-dimensional NACA 0012 airfoil blade models. L-82-4570 Figure 3. Three-dimensional NACA 0012 airfoil blade models. ORIGINAL BLACK 6 AND WHITE PAG1E PHOTOGRAPH Rt ,_ .... OR!_qTN_L" P_CE' .... ,C_ A;",O WHITE PHOTOCR/_,pH Microphone M2 L-89-42 Figure 4. Test setup for acoustic tests of a 3D model airfoil. Traverse Hot-wire arm probe Trailing 3D airfoil edge Side plate model L-89-43 Figure 5. Tip survey using hot-wire probe. small camber The effects, a, (1) --- _t/_ where = (1 + 2a) 2 + and a = (r2/48)(c/H) 8 2 term c is the airfoil chord and H is the tunnel height or vertical open jet dimension for a horizontally aligned airfoil. For the present 2D configurations, a./at equals 0.88, 0.78, 0.62, 0.50, 0.37, and 0.28 for the models with chord lengths of 2.54, 5.08, 10.16, 15.24, 22.86, and 30.48 cm, respectively. 3. Boundary-Layer Trailing Parameters at the as a function of Reynolds number based ou the chord Rc. As Rc increases, the thicknesses decrease for both the tripped and the untripped boundary layers. The tripped boundary layers are almost uniformly thicker than the corresponding untripped boundary layers. One should refer to reference 21 for details of the boundary-layer character for the cases of figure 6. In general, however, one can say that the tripped boundary layers are fully turbulent for even the lowest Rc. The untripped boundary layers are laminar or transitional at low Rc and become fully Edge The purpose of this section is to present measured boundary-layer thicknesses from reference 21 and to document corresponding curve fit scaling equations to be employed in the normalization of the airfoil self-noise data. The data presented are the result of hot-wire probe measurements made in the boundary-layer/ near-wake region of the sharp TE of the 2D airfoil models. The probes were traversed perpendicular to the model chord lines downstream of the TE. These measurements were made at 0.64 mm from the TE for the 2.54-cm-chord airfoil and at 1.3 mm for the other airfoils. The integral 99 percent of the potential values of 6 were chosen by carefully examining the respective turbulent velocity and Reynolds stress distributions as well as the mean profiles. For all cases, the estimated accuracy of 6 is within ±5 percent for the turbulent-boundarylayer (TBL) flow and +10 percent for the laminar and transitional flows, whereas the error range for the integral thicknesses 5* and 0 is less (ref. 21). 3.1. Scaled 6" and 0 at st = 0 ° are given in figure 6 for both the artificially tripped and the untripped boundary-layer conditions. The The attack Calculation approximated boundary-layer boundary in the following section. stalls the airfoil. In reference 21, the data are discussed pared with flat plate experimental results from boundary-layer prediction codes. and comand results Procedures boundary-layer are are specified finally subscript 0 for the thicknesses indicates that the airfoil is at zero angle of attack. The parameters are normalized by the chord length c and are given 3.2. equations 6, the boundary-layer by curve fits whose ity of the adverse pressure gradient. The converse is true for the pressure side, where the pressure gradient becomes increasingly favorable. Also included in" figures 7 and 8 are curve fits to the data. For the pressure side of the airfoils, the curves are the same for the tripped and untripped cases. The suction side curves differ, reflecting differences in the angle dependence of where the TE boundary layer separates and Data The thicknesses 6 and integral properties at the TE of the sharp TE 2D airfoil models for high Rc. In figure data are approximated Angle-of-attack effects on the thickness parameters are given at free-stream velocities of 71.3 and 39.6 m/s for the untripped and tripped BL airfoils in figures 7 and 8. The parameters are normalized by those measured for the corresponding cases at zero angle of attack, given in figure 6. The data are plotted against the corrected angle (_, of equation (1). The collapse of the data is much improved over that when st is used (ref. 21). In general, the data show that for increasing c_, (or c_t) the thicknesses increase on the suction side because of the increasing sever- BL parameters-- displacement thickness 5' and momentum thickness 0 were calculated from mean velocity profiles with the BL/near-wake thickness 5 specified. The thickness 5 is that distance from the airfoil surface where the mean velocity reaches flow stream velocity. The turbulent thickness thickness thickness by the parameters curve at the fits 5, displacement to the thickness TE data of a symmetric of figure 5", and 6. momentum NACA The 0012 airfoil expressions thickness 0 are, zero angle of for the at curve fits for for the heavily tripped layer, 50/c = 1011.892-0.9045 0.0601Re log Re+0.0596(log R_) 2] (2) (Re < 0.3 x 106) 0"114 (3) 1013.411-1.5397 log nc+0.1059(log Re) 2] (Rc>O.3x 106 ) (Rc < 0.3 x 106) O0/c ---- 0.0723Rc .1765 log P,w+0.0404(log Re) 2] 1010.5578_0.7079 (4) (Rc > 0.3 x 106 ) 9 Boundary layer Tripped Untripped © Airfoil chord, cm • . • • • O [] 30.48 15.24 10.16 5.08 2.54 1 80/c -4 .01 J L I I I I I _ I t I I _ J i i n i i I i , J i I _ I r I ' ' ' ........ I 86/c .001 .02 .01 : ..... ' ' I _---_-_a_O • I O • _- .... -_. e0/c .001 .04 J I I Ill J 1 Reynolds Figure 6. untripped 10 Boundary-layer BL and I [ .1 thicknesses broken lines are at the for tripped trailing BL. edge number, of 2D J J J L l 1 ' 3 X 10 6 Rc airfoil models at angle of attack of zero. Solid lines are for iflll [ i I ' I.... t j[lll , j I I I I I[IIfTTI I L- 't _4 Ilr II "I 0 / jJILI IllJJ o u"XI I i J I i i t _ II I _ 0 I o 0 r ,,-- r o ..,4 "0 co I..O lllll r i [ I [ITI[ I Illlll l I I [ 111111 I 8 d_d_N o _r --_I i o 0 kt-.1 0@_ -=_0_ .__o i O_SOL_ k _ n d i = d • \ _.o ' Ct _,.+-- I II \ --_ II 0 o "_ _ I' I C \ \ IIl_l IIILI o Od L I J I 111 o r 0 r- } I I • If) 0 r -,'0 _o 0,I 0 • Cn, l I I o I o r- o 11 _ ' I...... i, I.... I I TTIIII -4 _ I IIIIII I I T IIIIIT ' I lo Od i° 4 ,.= LO"_ I \ \ \ ",.0 \ \ m o_ ,.\ \ \ A. \ \ <_ \ I I I III] 0 _ L J i ,, I° I I 0 l_llll i T . ]111 I I I 0 I Ili111 IIITII; I I IIII1[1 I I IHIIT 1 IITll f I I 1 oE _,-o_ 4 m I k \ \ I-- \_. m \ \ I 0 I Ill_li J 0 12 \ I T-- co _l_l_lt •,-- 0 _O I I 0 0 U3 ',,-- Cb 0 0 I I l 0 04 0 r,/) wherethe zerosubscriptsindicatezeroangleof attack,zerolift on thesesymmetricairfoils.Forthe untripped (natural The transition) boundary boundary-layer attack thicknesses for the pressure layers, 60/C = 1011.6569-0.9045 log Rc+0.0596(log Re) 2] (5) _/e = 10 [3'0187-1'5397 log Rc+0.1059(log Re) 2] (6) O0/e = 1010.2021-0.7079 log Rc+0.040a(log p_)2] (7) thicknesses and side, the for corrected for the angles both the tripped airfoils at nonzero o_,, are given and the untripped angle in figures boundary 6p _-- 10[_0.04175a,+0.00106o_,2 60 P suction attached, the suction side, separated side for the near the parametric the tripped trailing behavior of the edge, or separated boundary 6s in terms 8. The layers, of the expressions zero-angle-of- for the curve layers thicknesses ] (8) (9) ] (10) depends a sufficient fits are ---- 10[ -0'0432°_*+0"00113a.2] 0p = 10[_0.04508a,+0.000873a,2 00 For the of attack, 7 and on whether distance upstream the boundary to produce layers are stall. For (fig. 7), [ lO0"0311a* (0° -< or, _< 5 °) (11) _0 = / 0"3468(100"1231'_*) 5.718(100"0258a*) (50 < o_, < 12.5 °) (12.5 ° < o_, < 25 °) (0° < a, < 5o) 6__= 6_ 0.3s1(100.1516-,) { 100.0679c_, 14.296(100"0258a*) (5 ° <a, (12.5 ° < a, < 12.5 ° ) (12) < 25 ° ) (0° < _, < 5°) _00 100'0869a' ) Os = { 0.6984( 100"0559c_* 4.0846(10 °'°258a*) (5 °<a,<12.5 °) (13) (12.5 ° < o_, _< 25 °) 13 Forthe suction side for the untripped boundary layers (fig. 8), (0 ° < a, 5s = 60 0.0303(1002336_* 100.03114a, 12( I00"0258_" ) (7.5 ° < a, (12.5 ° < a, (0 ° < a, 6._ = 6_ 0.0162(100.3066c_, 100.0679a* 52.42(100"°258_* ) Oo 14 0.0633(100.2157_, 100.0559a* 14.977(10 °'°25s_* < 12.5 ° (12.5 ° < a, (14) < 25 ° < 7.5 ° (7.5 ° < c_, _< 12.5 ° (0 ° < a, Os = < 7.5 ° (15) < 25 ° _< 7.5 ° (7.5 ° < or, < 12.5 ° (12.5 ° < c_, < 25 ° (16) 4. Acoustic The termine Measurements aim of the acoustic spectra measurements for self-noise from airfoils was to deencoun- tering smooth airflow. This task is complicated by the unavoidable presence of extraneous tunnel test rig noise. In this section, cross-correlations between microphones are examined to identify the self-noise emitted from the TE in the presence of other sources. Then, the spectra of self-noise are determined by performing Fourier transforms of cross-correlation data which have been processed and edited to eliminate tile extraneous contributions. The results are presented as 1/3-octave spectra, which then form the data base from which the self-noise scaling prediction equations are developed. 4.1. Source Identification The upper curves in figure 9 are the crosscorrelations, R12(r) = (pl(t)p2(t + r)}, between the sound pressure signals Pl and P2 of microphones M1 and M2 identified in figure 4. Presented are crosscorrelations both with and without the tripped 30.48cm-chord airfoil mounted in the test rig. Because the microphones were on opposite sides of, and at equal distance from, the airfoil, a negative correlation peak occurs at a signal delay time T of 0. This correlation is consistent with a broadband noise source of dipole character, whose phase is reversed on opposing sides. When the airfoil is removed, the strong negative peak disappears leaving the contribution from the test rig alone. The most coherent parts of this noise are from the lips of the nozzle and are, as with the airfoil noise, of a dipole character. The microphone time delays predicted for these sources are indicated by arrows. The predictions account for the effect of refraction of sound by the free-jet shear layer (refs. 22 and 23), as well as the geometric relationship between the microphones and the hardware and the speed of sound. The lower curves in figure 9 are the crosscorrelations, R45(7-), between microphones M4 and M5. The predicted delay times again appear to correctly identify the correlation peaks associated with the noise emission locations. The peaks are positive for R45(T) because both microphones are on the same side of the dipoles' directional lobes. The noise field is dominated by TE noise. Any contribution to the noise field from the LE would appear where indicated in the figure. As is subsequently shown, there are contributions in many cases. For such cases the negative correlation peak for R12(r) would be the sum of the TE and LE correlation peaks brought together at _- = 0 and inverted in sign. In figure 10, the cross-correlations R45(T) are shown for tripped BL airfoils of various sizes. The TE noise correlation peaks are at TTE = --0.11 ms for all cases because at at = of all models is the same. The with chord size, as is indicated 0 °, the TE location LE location changes by the change in the predicted LE noise correlation peak delay times. For the larger airfoils in figure 10, the TE contribution dominates the noise field. As the chord length decreases, the LE noise peaks increase to become readily identifiable in the correlation. For the smallest chord the LE contribution is even somewhat more than that of the TE. Note the extraneous, but inconsequential, source of discrete low-frequency noise contributing to the 22.86-era-chord correlation, which can be readily edited in a spectral format. It is shown in reference 6 that the LE and TE sources are uncorrelated. The origin of LE noise appears to be inflow turbulence to the LE from the TBL of the test rig side plates. This should be the ease even though the spanwise extent of this TBL is small compared with the portion of the models that encounter uniform low-turbulence flow from the nozzle. Inflow turbulence can be a very efficient noise mechanism (ref. 24); however its fldl efficiency can be obtained only when the LE of the model is relatively sharp compared with the scale of the turbulence. The LE noise contributions diminish for the large chord because of the proportional in LE radius with chord. When this radius increase increases to a size that is large compared with the turbulent" scale in the side plate TBL, then the sectional lift fluctuations associated with inflow turbulence noise are not developed. 4.2. Correlation Determination Editing and Spectral The cross-spectrum between nficrophones M1 and M2, denoted G12(f), is the Fourier transform of R12(r). If the contributions from the LE, nozzle lips, and any other coherent extraneous source locations were removed, G12(f) would equal the autospectrum of the airfoil TE self-noise, S(f). Actually the relationship would be G12(f) = S(f)exp[i(21rfrTE =t=7r)], where i = v/-Z1 and TTE is the delay time of the TE correlation erence 2. peak. This approach is formalized in ref- In reference 6, the spectra were found from G12(f) determined with the models of the test rig after a point-by-point vectorial subtraction of Gl2(f) determined with the airfoil removed. This was equivalent to subtracting corresponding R12(T) results, such as those of figure 9, and then taking the Fourier transform. This resulted in "corrected" spectra which were devoid of at least a portion of the background test rig noise, primarily emitted from the nozzle lips. The spectra still were contaminated by the LE noise due to the inflow turbulence. 15 .005 .... i .... Nozzle i .... liP R12 ('c), I ' Nozzle _ ' ' lip I pa 2 ...... Test rig without .OO5 R45 airfoil TEl l A rfo I A - ,F%z,e%z,e 0 pa 2 -' 0052 Figure 9. Cross-correlations c = 30.48 cm; BL tripped; .... for -1_ .... 0I .... Delay time, "c,ms two microphone at = 0°; U = 71.3 m/s. pairs with Arrows 1I .... and indicate 2 without airfoil mounted predicted values of r. (From in test rig. ref. 6.) ' ' ' ' I ' ' ' ' i , , , , I ' ' ' "7 .005 Chord length, cm TE _ 22.86 1 t 4 LE 0 .005 - oi .005 0 TE l LE .005 0 TEj LE .005 0 .005 0 TE ILE 2.54 -.005 ..... -2 Figure 10. Arrows 16 Cross-correlations between indicate values predicted microphones of r. (From _ I .... i .... -1 0 Delay time,z, ms M4 and ref. 6.) M5 for tripped BL _ .... 1 airfoils of various chord sizes. U = 71.3 m/s. In the present were obtained by paper, taking most spectra presented the Fourier transform of microphone-pair cross-correlations which had been edited to eliminate LE noise (see details in appendix A). The microphone pairs used included M4 and M5, M4 and M8, and M4 and M2. These pairs produced correlations where the TE and LE noise peaks were generally separated and readily identifiable. Referring to figure 10 for R45(T), the approach was to employ only the left-hand side (LHS) of the TE noise peak. The LHS was "folded" about r at the peak (7TE) to produce a nearly symmetrical correlation. Care was taken in the processing to maintain the actual shapes near the very peak, to avoid to the extent possible the artificial introduction of high-frequency noise in the resulting spectra. Cross-spectra were then determined which were equated to the spectra of TE self-noise. The data processing was straightforward for the larger chord airfoils because the LE and TE peaks were sufficiently separated from one another that the influence of the LE did not significantly impact the TE noise correlation shapes. For many of the smaller airfoils, such as those with chord lengths of 2.54, 5.08, and 10.16 cm shown in figure 10, the closeness of the LE contribution distorted the TE noise correlation. A processing procedure "separate" the TE and tance from one another, was developed to effectively LE peaks to a sufficient diswithin the correlation pre- sentation, so that the correlation folding of the about rTE produced a more accurate presentation the TE noise correlation shape. The separation LHS of pro- cessing employed symmetry assumptions for the TE and LE noise correlations to allow manipulation of the correlation records. This processing represented a contamination removal method used for about one- quarter of the spectra presented for tile three smallest airfoil chord lengths. Each case was treated individually to determine whether correlation folding alone, folding after the separation processing, or not folding at all produced spectra containing the least apparent error. In appendix A, details of the editing and Fourier transform procedures, as well as the separation processing, are given. 4.3. Self-Noise Spectra The self-noise spectra airfoil models with sharp for the 2D NACA TE are presented 0012 in a 1/3-octave format in figures 11 to 74. Figures 11 to 43 are for airfoils where the boundary layers have been tripped and figures 44 to 74 are for smooth surface airfoils where the boundary layers are untripped (natural transition). Each figure contains spectra for a model at a specific angle of attack for various tunnel speeds. Note that the spectra are truncated at upper and lower frequencies. This editing of the spectra was done because, as described in appendix A, a review of the narrow-band amplitude and phase for all cases revealed regions where extraneous noise affected the spectra in a significant way (2 dB or more). These regions were removed from the 1/3-octave presentations. The spectra levels have been corrected for shear layer diffraction and TE noise directivity effects, as. detailed in appendix B. The noise should be that for an observer positioned perpendicular to, and 1.22 m from, the TE and the model midspan. In terms of the directivity definitions of appendix B, re = 1.22 m, Oe = 90 ° , and (be = 90 ° • In section 5 (beginning on p. 51), the character and parametric the self-noise, as well as the predictions compared with the data, are discussed. behavior which of are 17 80 70 _ 70 SPL_/_ , * o Data Total prediction TBL-TE suction TBL-TE pressure Seporotlon A side W o _r o O 50 _ I 0 40.2 1 Frequency, (o) 60 SPLI/_ dB , U = ' '''"1 ' 60-- 6O dB i side 10 1 . 50 "-_o o 40 -- ' '''"I , 1 Frequency, _'-o , , ,,,,,I 10 20 kHz (b) U = 55.5 m/s m/s ' _r. , ,,,,,I t .2 kHz 71.3 ' '''"1 o 30 20 ' ' ' '''"I ' '''"1 50 60 L 50 40 40 ' ' ' '''"1 i 0 30 -- - 30 0 0 I 20 I I I I III .2 I I 1 Frequency, (c) Figure 11. I I I III , ,, .,,.I 20 10 20 .2 39.6 m/s spectra for , 1 Frequency, kHz U = Self-noise I (d) 30.48-cm-chord airfoil with tripped U BL at III I = st , ,, ,,,,Y;. 10 20 kHz 31.7 m/s = 0 ° (o, = 0°). 80 70 SPLI/_ , , i ,,;, I - , Data * Total prediction O TBL-TE suction -- i i ' ' press ;"/ o i TBL-TE " Separation re side 60 -- 50 side I I I -_ Q Q A __ A ,, , , ,,,,,i , 60 I I I I 1 I II1 I dB 8 50 i A 8 A A [] _ A ,,,I 40.2 1 Frequency, (o) Figure 18 12. Self-noise U = spectra , _ , , ,,,,I 10 -W 30 n] 20 20 .2 I Frequency, kHz 71.3 m/s for 30.48-cm-chord (b) airfoil with tripped BL at U = O0 _ o , , ,,_,,i 10 kHz 39.6 (_t = 5.4 ° ((_, m/s = 1.5°) • 2O 80 70 SPL,/_ -- ' '''"1 J * 0 Data Total prediction TBL-TE suction ' 70 ' TB/-TE ' '''"/press [] " ' ' '''"1 re side ' ' ' '''"1 Separation side 60 A , 50= A dB D [] [] D A O I 501 60 - 40 •2 A 40 n e ,,, 0 6o|, , '''"I , 30 10 0 1 Frequency, (o) U = 71.3 20 , , ,,,,I .2 kHz m/s ' ' ' '''"I ' , I Frequency, (b) U = 55.5 60 ' ' '''"1 8 8-- o A 8"] = 0 , 0 , t,,,,l 10 20 kHz m/s ' ' ' '''"1 50 50 _ SPL1/_ dB , 8 __ 401--,, a " _ O a",_. 40 -- Oo"_ _ o 30 _' 0 8 ,, 0 o 8"-" ! 30 0 0 _ A A _ -- 0 " 0 _[ -- 0 0 20 i I i i llll .2 , t 1 Frequency, (c) Figure 13. 80 U = Self-noise t I I]Jl 0 I 20 10 20 .2 1 Frequency, kHz 39.6 spectra ' ' ''"I t m/s for ' Data 'Jr Totol prediction 30.48-cm-chord airfoil ' ' ' ''"I o A TBL-TE pressure Seporotion with tripped 7° i' side BL (d) U = at cq = 10 20 kHz 31.7 m/s 10.8 ° (a, ''""I = 3.0°). ' ' ' '""I 60 70 SPL1/3 dB --_ , ooO° 50--, ° 40 _ o o - , o . i , i i ill .2 i 1 Frequency, (o) Figure 14. o k. Self-noise U = spectra ! 0 o_[ "" 0 , i i ' "_ 1- ,,tlO l 10 8 40 _. 20 30 T , i i i iiii .2 kHz 71.3 m/s for 30.48-cm-chord t 1 Frequency, U (b) airfoil with tripped BL at at = i i i i i 10 20 kHz 39.6 m/s = 14.4 ° (c_, = 4.0°). 19 80 ' ''"'t Dora _r Totol prediction o TBL-TE suction side 70 _ SPLII_ dB ' o' TBL-TE ' ''"'!,press-re | side "_ Seporotlon ' ' '''"1 • ,o , , °°t lit o_r ,,,,I I I i , I Illl 1 10 Frequency, kHz (o) U = 71.3 m/s 40.; 60 ' ' '''"I ' 20 , _ 40 i ' 50 -- 30 -- i i iiii i I i 1 Frequency, kHz (b) U = 55.5 m/s ' '''"1 ' i I llil 10 2O ' ' '''"1 - . - o-lt 30 o . o 20 i I I I Jill .2 I i 1 Frequency, i O I i ilil 20 10 I 20 .2 airfoil with I I I IIII Figure 15. Self-noise kHz spectra for 22.86-cm-chord 80 , I I I I press Illil I re slde TBL-TE & Seporotion 5O i i i Jill = , = , ,,,,I I .e 50_ ' i o , , 10 i lili 0 '_ A z_ 20 30 o 0 A 0 I I I I I I I 10 2O = 0°). I I I I II I o *[] ,it ,, oft & A 0 .2 , , 4',,,,,I 1 Frequency, kHz (b) U = 55.5 m/s ' ' '''"1 ' ' 10 2O 10 20 ' '''"1 D 40 I_ o 8- 30 m A A o 0 A i Figure T* Ill _ a, .2 I , I,,,,I 6O I o _ 0 A -- 20 I _ o 30 I o 0 50 40' ._o 0 1 Frequency, kHz (a) U = 71.3 m/s 60 I ° % 40 40.2 I _r 6O 50 , I 131 60 o [] A , a , ,,,_l I BL at at = 0 ° (a, tripped 7O I I I I I I I - I Dora * Totol prediction 70 __ 0 TBL-TE suction side I 1 Frequency, kHz (d) U = 31.7 m/s (c) u = _9.6 m/s 2O _ 0 0 .2 60 ' ' '''"I 0 ::Ti O$ 50 SPLI/3 dB ' ' '''"1 o _r O o } SPLI/_ dB ' . 50r_ SPLI/3 dB 7O i i illil I i O I 1 Frequency, kHz (c) U = 39.6 m/s 16. Self-noise spectra I •, I Illl 10 for 22.86-cm-chord 20 airfoil 20 I I A t i i o , , ii,_ 1 Frequency, kHz (d) U = 31.7 m/s .2 with I ilill tripped BL at at -- 5.4 ° (a, ._ = 2.0°). 80 I - | 70 _ / SPLII3 dB ' ' Data '''''I ' _ Total prediction O TBL-TE suction side a ' " ' '''"I TBL-TE pressure side I 70 '''"I ' I ' ' '''"I ' Separation -- 60 - 50 , 6o_ 8 8 '°L: 40 1 ' , o o a , , ,,,,I .2 & , t I ,,lll ._ I O -- , _' ,,,,,I I --_ r , I 10 ,llJl 20 I ' A [] "--& a O ,o & , , ,,,,,I 30.2 , OOo , _' ,,,,,I 1 Frequency, kHz (b) U = 55.5 m/s I 60 ** I 40 - 1 Frequency, kHz (a) U = 71.3 m/s 60 50 - [] 50 - 30L. u [] I ' ''"I ' I0 20 ' ' ' ''"I __ A n 8 30 t & -- 0 t- 0 ,, O 20 J , J ,,,,I .2 _ I , Ill,l 1 Frequency, kHz (c) U = 39.6 m/s Figure 17. Self-noise 80 ' - SPLI/3 dB J spectra ' ' ''"I Data Total prediction 10 20 for 22.86-cm-chord ' 2o O airfoil ' ' ' ''"I I m TBL-TE pressure sidel " Separation I , , ,.,,,I .2 with mr o ° A I , , I I II_II 1 Frequency, kHz (d) U = 31.7 m/s tripped = 10 20 BL at at = 10-8 ° (c=, = 4.0°). I , ' ''''I 70- t 0 ' ' ' ' ''''I , °o, ooOoo oooo [] , . Io u I I A I I I II 40.2 I so?a _ I O I 1 I I I II B ? 10 0 1_" t I r 20 .=o_ *. o a [] 30 -_ .2 = 18. Self-noise spectra for 22.86-cm-chord airfoil with 0 & ,,,,,I , 0 "u tripped mr , , ,,°,_.,Imr. 1 Frequency, kHz (b) U = 39.6 m/s Frequency, kHz (o) U = 71.3 m/s Figure J ° BL at at = 14.4 ° (a, 10 20 = 5.3°). 21 90 ' ' ' ''"I ' ' ' ' ''"I DoLo o TBL-TE pressure sl '_ Total prediction & Se oration Conside I 80 SPLv3 dB I 70i_. 60 , 000 0 50 [] 5_ u.2 , i@,l 10 1 Frequency. kHz (o) U = 71.3 m/s 70 ' ' '''"1 ' ' ' '''"1 _ n o A° o [] o 40 -- °o_i._. "0 30 P .2 Figure 22 i "_ik o [] J ,IJll _ , 19. Self-noise spectra W 0 Z_ P, n J _ T bnnl / ott 1 10 Frequency, kHz (b) U = 55.5 m/s = _ _ J Innl .2 u , u , ,uu I ' ' 2O i ' ' 'U'l I 40 30-- t _r 11, , , 9,,,nl =. 1 Frequency, kHz (c) U = 39.6 m/s O i 80002, 50 40 60 60 SPLI/_ , dB 20 [] a -- 10 for 22.86-cm-chord 20 , 20 .2 airfoil with i tripped I Ilinl J i t 1 Frequency, kHz (d) U = 31.7 m/s BL at at = 19.8 ° (a, J itll? = 7.3°). lO 2O 70, 80 _ 70 SPLI/3 dB , * 0 I I 1 I I I [ I Dote Totolpred[ction TBL-TE suction I I I I I II1!1 [] TBL-TE press_re A Seporotion side side 60 I I W 0 I I III I IIIII I I i I I I ill I i I I Illll i I t-- 501 60 W o w o _r o "_" o o OI i i IItJl 50 40,_o I 40.2 i _ ,,,,,I 1 Frequency, (o) 60 , , , ,,,l ' 20 10 U = I 3O I 1 Frequency, .2 kHz 71.3 I (b) m/s , , , i ,,_, 60 I ' U = 20 kHz 55.5 ' ' ''"1 I 10 ' m/s ' ' '''"1 50 50 SPLII3 -- w _ , 40 dB 40 _r o o 30 * o q o WO o_ 0 _ TM 0 30 o o . o t t IIII t 1 Frequency, (c) Figure 80 w __ 0 70 SPLI/3 dB , 20. ; U Self-noise = I t t ,,,I ' 10 39.6 ' ' ''"1 ' for ' 15.24-cm-chord ' ' ''"1 o TBL-TE pressure z_ Seporotion airfoil . s,de P , I Figure 21. , 1 Frequency, (o) Self-noise U 60 tripped BL U at = at ' ' ' ''"I I I I I Ill? 'A" 10 20 kHz 31.7 m/s = 0 ° (a, ' = 0°). ' ' ' ''"I side 5O 40.2 with I 1 Frequency, (d) - oO .2 20 Z "_, .... l l llll m/s 60 . 20 i kHz spectra Dote Totol prediction TBL-TE suction I I = , \, _,,,,I 50-- 30 --o 20 10 20 , .2 kHz 71.3 spectra m/s for & 0 A 15.24-cm-chord airfoil with 0 , i , ,ill I I Frequency, (b) U = 39.6 tripped BL at at I t , I ,Ill 10 20 kHz m/s = 5.4 ° (a, = 2.7°). 23 9O 80 I 80 -SPLI/5 dB I I I ! II ' ' '''"1 I - u Data u u u u I II v o TBL-TE pressure side * Total prediction A Separation O TBL-TE suction side , go 70-- 70 -- 60 -- 50 __e ' ' o ° ° ° ° Oo--2 o a SPLt/3 dB ' 50.2 i 7o ' ' '''"1 ' ' 2O .2 ' 5O _ ° o A - [] I .2 P o, ,.,.I , A 0 --',B O , , . °i 90 80 _ 22. Self-noise spectra ' '''"1 ' ' ' '''"1 o I 10 20 10 20 -- - t iII "it" _r 10 for 15.24-cm-chord z_ '=' . 20 airfoil i i t i ill I i u i i i lit| Doto n TBL-TE press,',re sFde * Totol prediction A Seporotlon O TBL-TE suction side 70 60 __ _+ 4O t 1 Frequency, kHz (c) U = ,.39.6 m/s Figure 0 1 Frequency. kHz (b) U = 55.5 m/s 70 ' '''"I _ 40 50 30 o o , ,®,=,,,I 30 .2 with 0 " I I ,. 1 Frequency. kHz (d) U = 31.7 m/s tripped BL at at = 10.8 ° (o, I ' '''''I 70 I Itll = 5.4°). ' ' ' '''''I i I 50 +, 50.2 Figure 24 , , cp b,?,_ 10 1 _. Frequency, kHz (o) U = 71.3 m/s 60 A . , ,_,,I 60-- 40 SPL1/_ dB , ' '''"1 -o 40 ....... , o ° I Frequency, kHz (o) U = 71.3 m/s 23. Self-noise spectra 30 10 for 15.24-cm-chord 20 I .2 iiillilil 1 Frequency, 0 ,<h,,,ll with tripped = 10 kHz (b) u = 39.6 m/s airfoil t BL at at = 14.4 ° (a, = 7.2°). t 2O 90 f SPLva dB , m 80 I I _11 I I 701 o A I I I I I 80 I TBL-TE presslure Separation side side ' ' '''"1 I I , ' ' '''"1 I I I 60 , , ,,,,I , , , , ,,,,+ 1 10 2O 40 I I I Itl .2 1 Frequency. Frequency, kHz (o) U = 71.3 m/s SPL1/_ dB ' 50 50.2"-'-- 70 ' 70 x.Z . - 60 I I Data _r Total prediction 0 TBL--TE suct;on i i I IIII I I I I I I lit i 10 20 10 20 kHz (b) U = 55.5 m/s ! 70 I I IIIJ 60' 60 50 50 40 I I ' ''"1 ' ' ' '''"1 ,,,,,I , , 40 t_ _r ,, 3o ,,,,,I .2 , ,, 1 Frequency, (c) Figure 24. U Self-noise = ,,,,,,I, ,, 30 10 20 .2 1 Frequency, kHz 39.6 spectra m/s for 15.24-cm-chord airfoil 9O with tripped (d) U at a_ = BL -- ,I',,,,I kHz ..31.7 m/s 19.8 ° (a, = 9.9°). 70 I I I I III I I Data * Total prediction 8O -- O_T__-_TE suction I o & I 1 I I I I I I TBL-TE pressure Separation side side 60 i I I I 1 II I i I I I I I II 1 J _ I , e,,,I _ ill _r SPL1/s , 70 50 6O 40 dB _k , , ,,,,I 50.2 1 Frequency, (o) Figure , 25. Self-noise U = spectra , , , ,,=,_ 10 , 3O 20 , ,,llll .2 1 Frequency, (b) U = 39.6 kHz 71.3 for m/s 15.24-cm-chord airfoil with tripped BL at at 10 20 kHz m/s = 25.2 ° (a, = 12.6°). 25 8O 70 70 _ 60 -- 50 I I I III I - I Data * Total prediction 0 TBL-TE suct;on -- 60 6O I -- 40 -- '''"1 i , U = i , o 0 ' 30 I I iiiii 1 Frequency, 60 ' '''"1 i o r .2 50-- w o i i i i illl i i I Frequency, I , , i,,l ! 20 10 W 0 20 '''"1 i i1111 i 10 2O kHz ' ' ' '''"1 owx 0 .o o I _" ' I I I III .2 26. ' kHz _ 60 -- spectra ' ' ''''I Data Total prediction TBL-TE suction * o 70 Self-noise for ' (d) lO.16-cm-chord airfoil with tripped 70 ' ' ' ''''I TBL-TE pressure Separation o " BL 60 50-- _ [] [] 1,1 @ o @ 00_ A 40 0 I mlllll I l I , I o Frequency, (o) 70 U = ' ' ''"1 , _,,,I 10 2O A [] @ -- o iP 40.2 zL- I 30 ' 60 ' '''"1 31.7 = 0 ° (c_, 2O m/s ' , 60 -- 50-- 50 -- 40 1,1 = 0°). ' ' '''"I ,-, A , o o A I 1 Frequency, (b) U = 55.5 .2 m/s ' at o Q A i I , , , Ill kHz 71.3 10 oe@_ • o I IIl(r'_ kHz = at 1 I -- 50-- ° I U ' ' ' ''"I side side - I 1 Frequency, dB ,,,,,, I i I , , Itl 10 2o kHz m/s , I t --! o , , ,,,,,, I o -- o 40 -- o @ 3O •' o o I 27. i 20 1 Frequency, (c) Figure o Q -- 30 .2 26 i 40-- w o 80 , I (b) u = 55.5 m/s _o Figure SPL1/_ dB i .2 (c) u = ._9.6 m/s , w 0.4 ( i m/s ' o "JO ,A.o _rO kHz , ' ''"1 ' '''"1 o 2O 10 71.,3 ' 0 , ,,,1 o SPL1/_ ' 50-- 30-- 20 i -- 40-- 0 1 Frequency, 50 _ side side W 0 * 0 0 i i ii111 (o) , I I I press-re II|!j " I TBL-TE A Seporotlon 50 40.2 SPL1/3 dB I Self-noise U = spectra 10 20 I Illll for m/s ]0.16-cm-chord 1 1 Frequency, .2 kHz .39.6 (d) airfoil with tripped 'if o BL at U at = t I I IIItl "I 10 kHz .31.7 = 5.4 ° (a, m/s = 3.3°). 20 90 ' ' ''"I ' ' ' ' ''"I Data : TBL-TE pressure side * Total prediction Separation 8O _ o TBL-TE suction side SPLII 5 ' dB ' .*_°°Oo:,\ - e _ . ., , A ,,,,,t :,= o ,,_,__. ' ' '''"1 ' 10 20 ' ' '''"1 A Av* -u A Q D , , ,,,_,I 50 .2 o A o , , t t 28. Self-noise spectra I I II_ .2 ° I 1 Frequency. t p , , o ,,I " 10 20 kHz (b) u = 55.5 m/s , , ,,,,, I , , , ,,,,,, I ' ' 50 --• 40 " ,m,,,,l"° 30 10 ' ' ''"I 20 airfoil I o TSL-TE pressure slde A Seporotion A, ll\ t\ 0o " -oo0 5o2, ,,; ' I .2 with tripped 80 70 80 _eide _ * _. _ ._5°°o_ Self-noise spectra 0"_ o* I o = o t b' i illil" j_ a' I Frequency, kHz (d) U = 31.7 m/s t t i J ,*Jl 10 BL at c_t = 10.8 ° (a, = 6.7°). i i i I illi I I I i ilil I i I I ilii 2O I -- t 50 ..... ,o 40 2O .2 Frequency, kHz (o) U = 71.3 m/s 29. " t for 10.16-cm-chord 9O ' '''''I - ' Data * Total predictron -- o 1 Frequency, kHz (c) U -- .39.6 m/s Figure Figure I t 60-- 50 --e 70 - / O I 40 7O 60 -- , ' ' '''"1 50 08* 1 Frequency, kHz (o) U = 71.3 m/s 70 SPLIIm dB ' 60 50.2 40 ' ' '''"1 70 70 60 SPLII3 , dB 8O for 10.16-cm-chord airfoil with tripped i l I"l"ilil, 1 Frequency, kHz (b) U = 39.6 m/s BL at at = 14.4 ° (a, l 10 I 2O = 8.9°). 27 90 I O0 I 9O _ SPLII dB _ ' I I I III I I Data _r Total prediction o TBL-TE suction I I I I I I I / [] TBL-TE pressure A Separation side ' _-i 7 si 80 ' '''"1 ' ' ' '''"1 P- t 70 80 I 60 7O 50 60.2 1 10 Frequency, (o) U = 71.3 7O I '''"1 I 20 * I Frequency, ' (b) U = I0 70_60 55.5 m/s I I I i i II I I i i I I III I t 50 40 4O _r I 30 I .2 1 Frequency, (c) Figure 1001 90 SPL1/3 , 30. Self-noise = 10 i,,l .2 20 1 Frequency. kHz 59.6 spectra ' ' '''"I Data "Jr Total prediction O TBL-TE suction t -- U 2O kHz ' ' '''"1 60' SPL1/3 dB .2 kHz m/s (d) m/s for 10.16-cm-chord ' o' airfoil ' '''"I TBL-TE pressure Separation A side , side with tripped BL at U at 10 = = 31.7 m/s 19.8 ° (a, ' ' ' ''"1 70 2O kHz ' = ' 12.3°). ' '''"1 60 dB 70 80_ 40 50 , 60.'..._ ' ' ' ' ' _ =' , Frequency, (o) U = 71.3 Figure 28 31. Self-noise spectra , , ,,I r for __ , , , ,,,,I 50 10 20 _ ill- .2 10.16-cm-chord (b) airfoil with , 1 Frequency, kHz m/s tripped BL at U at _ = = , , _, ,Ill 10 kHz 39.6 25.2 ° (a, m/s = 15.6°). 2O 80 70 -- 70 $PLI/_ dB , Data TBL-TE o_ Total predictTon TBL-TE euctTon t, side pressure i s;de Separation i i lilj i I lilj •1_-o o 40 i -- 1 Frequency, (o) 60 , I 50 -- 40 -- I U = 10 71.3 '''"1 20 ' ' (b) ' '''"1 "°f 30 o .2 1 Frequency, U -- (c) Figure 80 ' - 70 , 1 32. Self-noise °o m/s spectra for ' suct;on I IllJ ' o i 20 I 5.08-cm-chord a ' ' ''"1 TBL-TE pressure A Separation with I sideJ 60 J 50 -- 40 -- tripped BL U at = 20 m/s ' ' ' '''"1 I I I 1 I IlllI 10 20 kHz 31.7 m/s (xt = 0 ° ((_, ' ' '''"I ' = 0°). I ' ' ' ';"I 1 =- " [] [] & O 8 o till 10 1 Frequency, .2 airfoil side w W - , o (d) o o@ 50 I o 20 10 pred;ct;on TBL-TE I I kHz 55.5 _ ,,lOII kHz 39.6 ' ' ''"1 Data °_ Total I = , -w o-- , U ' '''"1 0 'k 0 , Wrl Ill i 1 Frequency, .2 60 o I 0 ,ff 0 II,l , m/s 30-- I , kHz o 20 , 30 40.2 O,A- srO 0 _r o dB I 50_ I SPLI/3 , 60-- 60-- 50-- SPL1/_ dB t n • 30 °_ o 0 [] "_,_ 0 11. 0 -@ z: o [] o, 40. , , n nJ _ u "I I I I I Ill 1 10 Frequency, (a ) Figure I 33. Self-noise ol U = 20 I 20 I n I llll kHz 71.3 spectra m/s for 5.08-cm-chord (b) airfoil with I 1 Frequency, .2 tripped BL at U = i I I i]lln lO 20 kHz 39.6 c_t = 5.4 ° (_, m/s = 4.2°). 29 90 SPLv3 dB , ' 80 _ 70 - 60 -- ' ' ''"1 ' Dote o* Totol prediction TBL-TE suction ' : 80 ' ' ''"1 TBL-TE pressure Seporotion side 70 0 • 0 -A 50 .2 , , 1 Frequency, (o) 70 ' '''"1 ' ' ' '''"1 _['_ -- 60-- _ I 50-- A I_ , , ,,,,I ' ' side U _. l, , 5/_,,,,= 10 2O 40 .2 1 Frequency, kHz = 71.3 ' ' ''"1 m/s ' ' (b) 60 ' '''"1 I" st I ' -- 50 50: -- 40 40 -- 30_ = 55.5 ' '''"1 tit 60 U 10 m/s ' tili 20 kHz ' ' '''"1 il r - / "%. _ i ,,,,,I , 30 .2 I (c) Figure 34. 1 O0 90 SPL1/_ , _ I 1 Frequency, 0 ' U Self-noise .... I IIIII J 2O 10 20 , ,,,,,I I .2 1 Frequency, kHz = 59.6 spectra "1 Doto Totol prediction TBL-TE suction I m/s for ' ' o A (d) 5.08-cm-chord airfoil with tripped BL at U at = = I I I I II1? I 10 20 kHz 51.7 m/s 10.8 ° (a, = 8.4°). 70 ' ' ''"1 TBL-TE pressure Seporotion I side side I III I 6O 80 50 dB ii 70' 60.2 - I ....... ' 1 Frequency, (o) Figure 3O 35. Self-noise U = spectra ' ' '''T'+ 10 20 40 -- 3o , , , ,,,,I .2 kHz 71.3 m/s for 5.08-cm-chord (b) airfoil with , 1 Frequency. tripped BL at U at = = , , , ,,,,+ 10 kHz 39.6 14.4 ° (a, m/s = 11.2°). 20 90 ' ' ' ''"I -- 80 SPLII dB 3 ' ' Data Total prediction TBL-TE suction ' : ' ..... 8o I TBL-TE pressure Separation side ' ' ' ''"l ' ' ' '''"1 side 7o: 701 6O 50 60 *mr \ -- e III mr i , I i Jill 50.2 I ! , , t ,ill 1 Frequency, (o) 70 I i I IIII 40 _ 10 U = 2O , , ,,,,,i , .2 kHz 71.3 I (b) m/s i ! ! I I III 60 i , 1 Frequency, I U = 10 2O kHz 55.5 , ' ''"I j ,,,",,1, m/s I i i I J,,, I 6O mr SPLtl dB 3 ' 40 50 mr 40 30 -- -- mr mr i _o , , , ,,,,I .2 I I 1 Frequency, (C) Figure 36. Self-noise U = -- 2O 10 39.6 spectra .2 5.08-cm-chord Data _r Total predictTon 0 TBL-TE suction side TBL-TE pressure A Separation i , 1 Frequency, , , ,,i,l 10 20 kHz (d) U = 31.;, m/s m/s for i i , ,i,,l kHz 9Ol , o, 80 , 20 , ?,,,,I airfoil with tripped BL at at = 17o ' s_ = 19.8 ° (a, ' '''"I ' ' 15.4°). ' '''"I 60 5O 60 mr 40 mr , 50.L3/ i i i i i Iil1 I Frequency, (o) U = 71.3 Figure 37. Self-noise spectra I _1'_- .... 110 20 i i i llll .2 1 Frequency, kHz mls for 5.08-cm-chord (b) airfoil I ! ? I I llll 30 with tripped BL at U at = = 10 2O kHz 39.6 25.2 ° (a, m/s = 19.7°). 31 80 -' 70 SPLII,_ , dB -- ' ' ''''1 Data Total prediction TBL-TE suction ' ' a & side i i iii I i I I I , ,,,,,,I iii I I 50 .o o w I I 40.2 I 50 , ,,,,I I , o, '''"1 ' _r 40 ' , ,,,,I 1 Frequency, kHz (o) U = 71.3 m/s 60 , I 60 60-- 50-- SPLI/_ dB 70 ' ' ''"1 TBL-TE pressure side Separation 10 30 2O 0 11r ,,,,,I .2 60 ' ' '''"1 -- 40-- 9 1 Frequency, kHz (b) U = 55.5 m/s ' ''"1 50 -- 40 -- 30 -- ' 10 20 ' ' '''"1 o t 0 30-- o _r o _t I 20 I I .2 I 0 I I llJ Figure 80 ' 38. Self-noise , I spectra ' ' ''"1 Data * Total prediction 70 -- o TBL-TE suction side SPLI/._ dB 1 I I l llll 1 Frequency, kHz (c) U = .39.6 m/s ' 10 for 2.54-cm-chord ' airfoil 70 ' ' ''"1 o ?o %, . & • ' ' illll I A [] I , () 20 10 ' 60 ' ' '''"i -- 40 30 -- D 0 i J i i ,III .2 A I [] i Self-noise spectra O A 30 _ i it _Jll 1 Frequency, kHz (C) U = .39.6 m/s 39. I ! I Ill I I I I I I I il I 10 for 2.54-cm-ehord [] t i t IIII -- / 20 airfoil , , ,,,,I 2O .2 with I I ' I I Ill 10 2O ,.,z o & L Q , e , , i,,,l I Frequency, kHz (d) U = 31.7 m/s tripped 0 ' ' '''"1 @ o I I Frequency, kHz (b) U = 55.5 m/s ' ' '''"1 40 0 32 30 ' .2 50-- Figure I 20 BL at at = 0° (o_, = 0°). 40 _-- -- 2O tripped 10 -- 50 0 , , ,,i,,I [] 60 SPLII3 dB ,,,I o, O i ?,,_Jl 1 Frequency, kHz (o) U = 71.3 m/s ' ' '''"l I I 60 -- . ' I 1 Frequency, kHz (d) U = 31.7 m/s with 50 - 40.2 I .2 o TBL-TE pressure side " Separation 60 -- 50 20 20 BL at at = 5.4 ° (a, = 4.8°). o 10 2O 80 90 I i , i , i1 Data _r Total prediction __ 0 TBL-TE suction 80 70 I _ a * ! I I I I II TBL-TE pressure Separation side side - o 60-- o • w 6 " 70 -- 60 -- 50 --_ I I I 1 ill i I I , , Jl,I i i i ii iii I I [ I , ,,;I I r 40 50, 1 10 Frequency. (o) SPL1/3 dB , U = 20 kHz 71.3 (b) m/s 70 60 60 50-- 30 30 I r .2 I I = IIII I Figure 40. go , J i 80 I-- I 1 Frequency, (c) . = U * 0 U Self-noise = I I I Illi = 55.5 '''"1 ' m/s ' ' '''"1 I--_ I I I I Illi I .2 20 1 Frequency. kHz 39.6 m/s spectra , ' ' ''' Data " Total prediction TBL-TE suctior_sil_e for ' (d) 2.54-cm-chord airfoil _ ' ' ' '''1 TBL-TE pressOre Separation a " 70p. % I slde I | _1 -1 20 kHz i 20 10 * 10 ,o _ 50 40 SPL1/_ dB 1 Frequency. .2 with tripped 70 BL at U = cq = ' ' ' ''"I I I I IIIII 10 20 kHz 31.7 m/s 10.8 ° (a, ' = 9.5°). ' ' '''"I 50 40 -i _ni , , _.2 , , ,ill 1 (o) Figure I 1 Frequency, 41. Self-noise U = spectra I i '1 i,,,I 10 .2 20 1 Frequency. (b) U = 39.6 kHz 71.,.3 for m/s 2.54-cm-chord airfoil with tripped BL at at = 10 20 kHz m/s 14.4 ° (a, = 12.7°). 33 9O I SPLII5 , 80 -- 70 1 I I I Doto III I I O_ Total prediction TBL-TE suction _ I I I I I| I a TBL-TE pressure A Seporofion 80 ' ' '''"I side side ' ' ' '''"I 70-- . dB 6O 5O i i J i m,,I I 50.2 i i i 1 Frequency, i =_._1 10 _ 40 , 2O i ' llllJ 60 SPLI/3 dB , 50 (b) _, i 1 Frequency, (o) U = 71.3 m/s 70 I .2 kHz 70 U = Pii,l i 10 2O kHz 55.5 ' ' ''"I ' i m/s ' ' ' ' ''"I 5O 401 L_ _ 40 _ tr _4r I 30 I I I IIII .2 I 1 Frequency, (C) Figure 42. 100 90 SPLI/3 dB U Self-noise w o ,_, rill 30 2O , ,J]l!l for ' 2.54-cm-chord airfoil ' ' ' ''"I : TBL-TE pressure Separation side side with 80 i lw I I IIIll 1 Frequency. kHz (d) U = 31.7 mls m/s tripped ' BL at at = 19.8 ° (a, ' ' ''"I ' = ' I 10 2O 17.4°). I I , I II I I IIIII I 70_ , 70-80-- 5O ,I 60.2--- 1 (o) Figure 43. Self-noise U = spectra _ 40' 10 Frequency, 34 , .2 kHz -- 39.6 spectra Doto Totol predlct[on TBL-TE suction i lO ' ' ' ''"I -- i 2O , I ' I IIII .2 kHz 71.3 for m/s 2.54-cm-chord I (b) airfoil with ll', 1 Frequency. tripped BL at at U = 10 kHz 39.6 = 25.2 ° (a, m//s = 22.2°). 20 80 ' ' ''''I - 70 SPLv3 dB ' Data * Totolpredlct[on -- 0 TBL-TE suction side ' ' ' ''''I a TBL-TE " 0 Separation LBL-VS pressure side 60--70 I I , ; Ill I ' . , 60 -- ****_ 50- * _ . ; oo i , t , _,_,1 1 10 Frequency, kHz (o) U = 71.,3 m/s i i r ,ill * = I =;I I ---i ** / -- , ,,,,I 60 I v °o%_, 40--. 0 40. 2 i I i i i i mill 20 I ;o rO 30 i I I .2 / 60 _ 50 ' ' I I I I11 . O I I 1 . Frequency. kHz (b) U = 55.5 rn/s I , ,Ill ' ''"l ''°"1 ' ' ' | 10 20 5O SPLI/_ dB ' 40 * 30 o 0 _ 30 -o; h. 0 m 0 20 J i i fJJl1' .2 I _l 1 Frequency, I t lllll 20 10 20 .2 1 Frequency, kHz (c) u = 39.6 m/s Figure 44. Self-noise spectra (_, = oo). 80 70 SPLI/a dB , -- _r 0 ' ' ' ''"1 Data Total prediction TBL-TE suction side 60-- a & <> ' ' airfoil ' ''"1 TBL-TE pressure Separation LBL-VS sl with .,_1 untripped BL (natural 7°I ' '''"'1 transition) ' at at = ' '''"'1 / 60 k-- I j 50 I-- 88_'8-°0!"_o_>A°888__ 8 40.2 _ _ Figure 45. =- , _,,,,1" a , Self-noise spectra ux= , .7-,.,I A I Frequency, kHz (o) U = 71.3 m/s x_'.[]-"-° 08 40_ ,_ T 10 for 30.48-cm-chord 0° I ._r. 5o- 20 (d) u = 31.7 m/s for 30.48-cm-chord ' 10 kHz 20 airfoil 30- / _J i .2 with "o.:..'_. 1 Frequency, kHz (b) U = 39.6 m/s untripped BL at at = 5.4 ° (a, 10 v 20 = 1.5°). 35 go ' ' ' ''''I ' a' ' ' ''"I Data I'BL-TE pressure side * Totolpred[ct[on z_ Separation -- 0 TBL-TE suction side 0 LBL-VS -- 80 SPLI/3 dB ' 80 ' '''"1 ' ' ' '''"1 70 , 60 70 __oelo_ 0 50.2 , i _ ]_l 80 ' ' __-- I Frequency. kHz (a) U = 71.3 m/s ' ''"l i , I _rn 50 60 10 20 =po 40 80 i ,,,,j i .2 ' _. - 4.0 L _0 _ * ° -a_** i _>i_,tP I L i _, 1 Frequency, kHz (b) U = 55.5 m/s ' '''"1 ' ' \ i?IT _ 10 = 20 ' '''"1 .t 70 70 --_ SPLI/3 dB , 60 50 60 50 _ i 40 # .2 80 = i _' e • m_JN._ 1 Frequency, kHz (c) U = 39.6 m/s Figure 90 T m H,,,T 46. Self-noise spectra ' - ' ' ''''1 Data Total predictTon --0 TBL-TE 10 20 for 30.48-cm-chord ' airfoil ' ' ' .... I a TBL-TE pressure side & ,_eporotion 4O I iltl .2 with 1 Frequency, kHz (d) U = .31.7 m/s untripped , * , 36 ' ' ' ''"l e ' ' ' ' ''"l 60 60 Figure BL at at = 10.8 ° (c_, = 3.0°). 70 70 50.2 20 80 _ SPLI/3 dB 10 @ , eY, A,I o , [] p , ; p,_,_. 1 Frequency, kHz (o) U = 71.3 m/s 47. Self-noise spectra 5O - for 30.48-cm-chord 10 \ 20 airfoil 40 with ,± .2 1 Frequency. kHz (b) U = 39.6 m/s untripped BL at c_t = 14.4 ° (a, = 4.0°). 10 20 80 -- 70 SPL1/_ dB , * 0 ' ' ' ''"1 ' Data Tolalpred;cfion TBL-TE suction a " O side 60-- ' ' ' ''"1 TBL-TE pressure Separation LBL-VS W side -4 60-- "A" 50-- 40 * o I I _o , _'_*,o ,,ll 40.2 I I 1 Frequency, (a) 60 U = , I I,_,l 20 I ' ' '''"1 ' oo ] III .2 I (b) U "o__ I 1 Frequency, m/s '_ , , Illl I 10 20 kHz = 55.5 m/s ' ' '''"1 50 ._t_w , 0 " kHz 71.,:3 5O SPLt/_ dB • rt%l 30 10 ._o _ 8 _r 40 -- _t_ro ° _ro _r 0 30 0 0 0 _0 0 o 0 I 2O I I I1_11 .2 I Figure 48. U Self-noise = I _ 0 I I I I _,1111[ 10 30 **g°o 2o , ,?J,,,I o° 20 o o , .2 39.6 m/s spectra I I I l Data Total predict;on TBL-TE suction side for ' (d) 22.86-em-chord airfoil ' ' ' ''"I Seporotlonpressure LBL-VS T_L-TE I with untripped 80 ' U BL = at at ' '''"1 _ _'_ ...-I ° "x,; , ?,,,,,I 1 Frequency, kHz 80 70 I 1 Frequency, (c) 0 "T 10 20 kHz 31.7 m/s = 0 ° (a, ' ' = 0°). ' '''"1 s; 70 _t SPLI/3 dB , 60-- 50 60-- -- 50-- 40.2 1 Frequency. (o) 8°L' SPLI/3 dB U = ' '''"1 10 20 _o 40 .2 1 Frequency, kHz 71.3 m/s _ (b) ' ' '''"1 8° I '' 70 70 O___ 50 60 _ 50 60 U = 10 20 10 20 kHz 55.5 m/s '''"1''' '''"1 • eO , 40 40 .2 1 Frequency, (C) Figure 49. Self-noise U = spectra 10 20 iiI .2 1 Frequency, kHz 39.6 m/s for 22.86-cm-chord (d) airfoil with untripped BL U at = at kHz 31.7 = m/s 5.4 ° (a, = 2.0°). 37 I 9O SPLM_ dB - I I | I I I I Data Total pred;ction I I I I I I I I I a TBL-TE pressure s;de A _eporotlon , '° 50.2 1 10 20 90 ' 80 -- 70 -- 60 -- 50 ' '''"1 i I IIJl I ._' . i llll 1 Frequency. 8O I I ' U = '''"1 7O , 6O 6O 5O 50 -- _ o .2 (c) Figure 38 *88 ° 1 Frequency, . 50. Self-noise U = 39.6 spectra 10 20 ' ' I Frequency, (d) U = with ''"'1 o _ , , .,®._68__ .2 m/s airfoil m/s • kHz for 22.86-cm-chord 55.5 - 40 4O untripped 2O • • SPLM_ dB 10 kHz ' o 7O ' '''"1 . ,, .,_,__ _.o__.,, ,,,% .2 (b) I ' to Frequency, kHz (o) U = 71.3 m/s 8O ' 31.7 ,_,,,I 10 kHz m/s BL at (_t = 10.8 ° (c_, = 4.0°). 2O SPLI/_, 90 -' ooto' ' '"'l 80 o ' o'_L-TE' ' ''"lpr.ssu,e s,d." I 801 ' ' ' ' '''1 Toto.., r.,.ct,on __ ." . ' ' ' ' '''1 * ._L-,_.o.,o0.,0. O/L%? -I _o 7o _;,o ' ' * #'t'l so. u__ _ i .;o_ _- -°8 ' ' = _"_"10 _12040.2 *_?_,J,I1 I ' Frequency, (o) Figure 90 ' I 80 51. 0 ' Self-noise U = spectra Frequency, m/s (b) for 22.86-cm-chord Date ' '''"I Totol TBL-_ kHz 71.3 o TBL-TE ' ' redact|on suction side ' '''" airfoil pressure sldel A Se orotion o ,B_-VS I J (o) Figure 52. Self-noise U = spectra untripped 701 ' ' '""I I 3o I , .2 kHz 71.3 m/s for 22.86-cm-chord -, , m,,l _, 1 with untripped m/s ' = 5.3°). ' '""I ' . _" ._ , j_,,,,l °o _* _o°O10 Frequency, (b) airfoil kHz .39.6 BL at at = 14.4 ° (_, 60 _ _ ,o_ , *,":,-,+_ , , .o;,o,_..j 1 10 20 Frequency, with U = ® \ _. / _)m_%kl_l_rlO 2O -- 20 kHz U = 39.6 BL at at = 19.8 ° (a, m/s = 7.3°). 39 70, 70 -l l = = , , Ii Data O* TBL-TE Total prediction suct;on 6O -- SPLI/_ , 50 -- 40 -- I : a A 0 side I ! TSL-TE I I I| i pressure s_de Separation LBL-VS ' 60 ' '''"1 ' ' ' '''"1 / -fl -- 50 dB 40 _o t¢o I I lliJ 302"m. (o) SPLt/a dB , I l U = , i i ,,,_ _,o,,,,i 30 10 20 kHz m/s 71.,3 '''"1 ' ' (b) ' '''"1 50-- 40-- 4O P-- I 1 Frequency, kHz (c) U = .39.6 m/s .2 Figure 90 L 53. Self-noise spectra ' _ ' _'"I Data • " Total predict;on for ' O I I I II+II 10 15.24-cm-chord 30 20 airfoil ' ' ' ''"I [] TBL-TE pressure A Sepadbtion o ' ' '''"1 I I m/s with ' ' '''"1 , , , , o_ ,,T _ .\ 1 Frequency, kHz (d) U = .:31.7 m/s untripped 90 ' I BL at III I at = 0 ° (a, 10 = 0°). I I I I I I I 80 -- 70 -- 60-t : 1 10 20 I 50 54. Self-noise spectra for 15.24-cm-chord I i t° I I 1 Frequency, .2 Frequency, kHz (o) U = 71.3 m/s 4O IIII I ,t Q,_ t \'_ 0 Figure | TBL____ 502 , , 20 kHz 55.5 _ , ,e,T .2 side , 8070 -60 = I 10 70 50-- _r o I _r PlII_ U , ,,,?,1o , 1 Frequency, 60-- I ? .2 60-- 3O SPL1/_ dB o I I 1 Frequency, 70 -- o (b) airfoil with untripped BL U at at = i i I i I'_,l ,tlt t 10 kHz 39.6 m/s = 5.4 ° (a, = 2.7°). 20 90 SPLI/_ dB ' Data _t Totolpredictlon 80 70 0 TBL-TE a A suctlon s;de 2 TBLx_ pressure Se_rd_Lgn i/E-V side I I I I I I I I I I I _ 1 70 60 o 60 . A o o A _ 50 _ _ , , , ,-,_,_ 1 5o.2 , , , ,,9,_,10_ , Frequency, (o) .2 55. 90 8O _ , U = 71.3 * o Self-noise spectra ' J '_rll Data Total prediction TBL-TE suction _ a | 20 40.2 ; _' , _,,,,I m/s 10 ' side 20 .2 15.24-cm-chord airfoil ' ' ' ' '''I a TBL-TE pressure A Separation o LBL-VS with 1 Frequency, (d) U = 31.7 untripped i 70 side 70-- 60 -- 50 -- BL at c_t = ' ' ''"I o r _ ? I ,l÷,t 10 20 10 20 kHz (b) U = 55.5 kHz m/s for , 1 Frequency, kHz 1 Frequency, (c) U = 39.6 Figure SPL1/_ dB 80 I m/s kHz m/s 10.8 ° (c_, ' = 5.4°). ' ' '''"I _. 60-- _v W , _,,,T 50.2 ÷ , I_Q Frequency, Figure , , .,_*_, 1 (a) 56. Self-noise 40 o Ooo . U = spectra 20 -- o o ) 30 t .2 .o kHz 71.3 for m/s 15.24-em-ehord airfoil with untripped o v 1 Frequency, (b) U = 39.6 BL at at = °\.8. __ 10 20 kHz m/s 14.4 ° (a, = 7.2°). 41 Jr_ll 6O 8,0 50 '_ / Jr .... 5o_---__ 10 _ FrequencY, 20 .2 Frequency, kHZt_ (b) u = 39.6m/_ kHZ (o) u = 71.3 mls Figure 57. SeLf-noise spectra for 15.24-cm-chord airfoil with untripped BL at at = 19"8° (_* = 9'9°)" 6O 80 60 I 50 _ - .2 i - ..... Frequency, (a) Figure 42 58. Self-noise _.u, KHz U = 71.3 spectra 10 - 0 20 .2 Frequency, kHzp_ tb _, U = 39.6 m/_ _ " m/s for 15.24-cm-chord = airfoil with untripped BL at a_ = 25.2° (a, 12.6°)" 80 , , , i J ,, * 80 I ooto - ' Totolpred[cfion 6070° 50 " TBL-TE_ttsuction * , 40. , ' TBL-TE ' ' ''"1 pressure o Seporotion °*i i t Jl_ r 0 _- I 1 6070 50 o , , ,,,,I 1 I | | o0 o . o ' s,de 6 10 I 4.0 20 I I I I III .2 Frequency. kHz (o) U = 71.3 m/s 80 ' ' '''"1 ' ' I I I I I III J 10 20 10 20 70-- 60 -- 60-- 50 -- 50 -- , , ,',,,I • I 40 I I I .2 I Frequency, kHz (c) U = 39.6 m/s Figure 59. 1 O0 I I Self-noise I spectra I I I I 10 D I 40 20 .2 , o 1 Frequency, 0 kHz (d) u = 31.7 _/_ for 10.16-cm-chord I I Doto * Totol predlct[on I I I airfoil with 90 I I I " I TBL-TEpressure Seporot_n 0 LBL-V_• untripped BL at at = 0 ° (a, ' ' ''"1 . side 90 ' = 0°). ' ' °@ '''"1 80-__ 0 SPL1/_ dB I 8O ' '''"1 70 SPL1/3 . dB _ 1 Frequency, kHz (b) U = 55.5 ,',',/s TBL-TE suction side t _ , 80 / 70-- _ 60-- ,_ 60 . 2 , , , ,x,,, _r t Frequency, (o) U = 80 SPL,/3 dB , ' ' '''"1 ' ' _' ',,I 10 %_0 50 i .2 71.,:3m/s ' ' 70 ' '''"1 ' '''"1 60-- 50 -- 50-- 40 -- , . ,., Figure °°• , ,i 1 Frequency, kHz (c) U = ,:39.6 m/s 60. Self-noise spectra for 10.16-cm-chord 10 20 airfoil 30 with ^°eo_ R_ _ O I , \ ' TPIIII 1 Frequency. kHz (b) U = 55.5 m/s 60 -- .2 illl_r kHz 70-- 4O i ,- $o,,,I .2 ' ' ' '''"1 ,o I- , ,,,_,_,.e 1 Frequency. kHz (d) U = 31.7 m/s untripped 10 BL at at = 5.4 ° (a, 10 20 20 = 3.3°). 43 80 I 1 I I I I I I Data T[]t[]l prediction TBL-TE suction * I I I I I I I I I o TBL-TE pressure & Sepor[]tion ¢ LBL-VS side 70 _o SPLI/s I . sldeJ | _1 _$_ 70 60-- ' '''"1__.' | , _.' ' '''"1 t 50-- dB II 0 40-- & 0 O i O 40 2 . [] , , ,lllJ, 1 Frequency, (o) 60 i I i ilil U = IOI __91Ull,I 10 0 I Ot 30 20 I I lllil 1 Frequency, .2 i I U (b) m/s i l i,,l I I I 60 [] a a _n a !°l kHz 71.3 I 0 0 I 0 I lllll 0 10 20 kHz 55.5 = ' '''"I ' m/s ' ' '''"I 50-- SPLI/3 dB , 40 o 30-- _ oO- i 8 _ °= . o, , , ,,,#,1 i ,,,,,I 1 Frequency, (c) U = 39.6 .2 Figure 80 70 SPLI/3 dB , 61. ' * __ 0 Self-noise spectra 10 ' ' ''"l ' Dot[] o Total prediction "k _r TBL-TE suctiorl_side-; "A" 60 -- q 30 .k 20 20 10.16-cm-chord I ! I I III airfoil A / o8° I I 1 Frequency, untripped BL U = at at I I II _ 10 20 kHz 31.7 = t I m/s 10.8 ° (a, = 6.7°). 70 I TBL-TE pressure Separation LBL-VS I slde I I I III I 1 I I I IIII I 60 50: 4 o 'k o 8 o 50' _ , , ,,,,I .2 with a o (d) g_ @ A o kHz m/s for __ O ° o 20 - • -- _r 40 A A 90"_ I I I I iiii 40.2 ...... 1 Frequency, (a) Figure 44 62. Self-noise U = spectra Illlit I 10 0 i 30 20 i i i iiii .2 kHz 71.3 for m/s 10.16-cm-chord i 1 Frequency, (b) airfoil with untripped BL U at = c_t = i i i l iiiI 10 kHz 39.6 m/s 14.4 ° (a, = 8.9°). 2O SPLII_ , 90 , , l,,,, I 80, Data _t Total predictTon -_°_Tl_-'ttl'E_ suct;°n 70 7O I I m A O side I I I Ill | I TBL-TE pressure Separation LBL-VS i l j |i| I ! i i i i Ill I U i side 60 50 __ dB -- I I I I I ill 5°.2 I i (0) 90 I i III 63. I U Self-noise l l I = 20 71.3 lO.16-cm-chord I I I I I III airfoil TBL-TE pressure Separation 0 LBL-VS untripped 7O I = " with i side BL i i U = at (_t = i I II I , , , , ,*,I 10 2O kHz 39.6 m/s 19 .80 (c_, = 12.3°). i i i i ii i i , , * I 60 x_TE suction side 70 50 60 4O I ! , I I I I II 50.2 _ , , , _,,,] 1 10 (a) 64. Self-noise = 71.3 spectra for U 20 30 .2 1 Frequency, m/s 10.16-cm-chord (b) airfoil with I , , , ,,,,I kHz Frequency, Figure i 1 Frequency. (b) 80 , [ , I,,,I m/s for - Data 'JrTotal prediction SPL1/3 dB , .2 kHz spectra III m 30 1_ 10 Frequency, Figure I 1 40 untripped BL at U at = , ,L,,I I0 2O kHz 39.6 = 25 .20 m/s (c_, = 15.6°). 45 9O I 80 -- 0 SPLI/5 dB , I I I I I II I I I I I 90 I I II Data i Total pred;ctlon a TBL-TE pressure side a, Separation /a,\ TBL-TE suction side 0 LBL-VS t/-_l r l / I so.2 , .... ,N1_ 70 -- 60 -- oOOo _ , *, , ,_P,T,I t0 l I III ' 20 ' ' '''"1 ' ' SPLI/_ dB , .2 90 ' '''"1 __ 70-- 70 -- 60-- 60 -- 1 Frequency, 5 50.2 10 / dB SPL;/+ , , spectra , = , , ,, I Data Total prediction , for 5.08-cm-chord airfoil , _, , ,,, ! 1 side I TBL-TE pressure & Separation A / o with 70 80 50 90 * TB,.-r, .,.,o,,o..+d,, * LBL-VS_+ 0+_ 70 f 40 60.2 Figure 46 65. Self-noise - I III ' ' I 10 20 10 20 ' '''"1 1 Frequency, kHz (d) U = 31.7 m/s kHz (c) u = 39.6 m/s 100 / l I .2 Figure I +,* , ,,,.,+,+o ' '''"1 -- I I 1 80 5O I Frequency, kHz (b) U = 55.5 m/s • 80-- l ,,,,J,,i 50 Frequency, kHz (o) U = 71.3 m/s 90 I 80 - / \ 70 I ...... 66. IJ""T-_ ,_'_,,,_1 1 Frequency, kHz (o) U = 71.3 m/s Self-noise spectra for 5.08-cm-chord 10 untripped BL at at = 0° (_, ° _l''"l ' 60 __ou ' - = 0°). '_''_1 o -.+O' 9 0 0 I 30 20 airfoil .2 with _ _ , ,,,t& O ÷ _ • ,,,,,I 1 Frequency, kHz (b) U = 39.6 m//s untripped BL at et = 5.4 ° (e, = 4.2°). 10 o 20 80 _ 70 SPL1/_ , ' ' 0 TBL-TE suction side , , side - -- • 60-- 80 '''"I'BL-TE '"', pressure a /[ 70 -- 60 -- , , I,,, I , , , , ,,,, I I I I , dB 50-- ID W 0 , - , A A ,,,,I , 40.2 , (o) 70 , , ,,,,I ,, ' = 10 Frequency. SPLI/_ dB , 1 U = 50 -- ¢1 "Jro 40 20 I t I IIII I .2 1 Frequency, kHz 71.3 ' '''"1 ' I I II * 60 ' '''"1 ' '''"1 60 -- 50 50 -- 40m 40 -- kHz ' ' ' '''"1 m 111 ilk 30 -- r 1 I 30 2O I 1 Frequency, .2 (c) Figure 90 , 67. U = Self-noise 10 _114/ 20 1 Frequency, m/s for I (d) 5.08-cm-chord 1 a I I TBL-TE I I airfoil II / pressure A Seporotion o LBL-VS l_.,._ with untripped BL 70 ' ' '''"1 I , U at = at 10 20 I I, 10 20 kHz 31.7 m/s = 10.8 ° (a, = 8.4°). ' ' ' '''"1 , , , side GO 50 70_u- 60 I .2 kHz .:39.6 spectra ' ' ' ''"1 Dote • " Totol prediction 0 TBL-TF.=._ide 8O SPL1/3 dB 20 10 (b) u = 55.5 m/s m/s ' I ii -- lit , , _ ,ft,l t 50.2 , , (a) 68. Self-noise , ,,,,I 10 Frequency, Figure , 1 U = -- 20 40 30 , ,,,,I .2 1 Frequency, kHz 71.3 spectra (b) m/s for 5.08-cm-chord airfoil with untripped BL U at at = kHz 39.6 = , ,t m/s 14.4 ° (c_, = 11.2°). 47 1 O0 8O I *- I I I Ill i I I Data prediction Total I I I TBL-TE Separationpress re side O LBL-VS 90 , ' '''"1 ' ' ' '''"1 I_ i I I 70 TBL-TE --0 SPL1/_ dB ' I 1 IIU : _n side / 80 70 \ 60 -- i, _ _ _r 60.2 ,, I Figure 69. I •Ir I ,,,,I _ I I I I I I for I 20 I 4O I llllll .2 1 Frequency, (b) 5.08-cm-chord I o A . I 10 kHz m/s spectra Dote .,_ Totolzl_re_l_ct!on ¢r , ?_,,,,I 1 Frequency, (o) U = 71.3 Self-noise 50 _ 11 I I I I airfoil I I I TBL-TE pressure Seporotion with untripped BL I I I III I 70 I at side = U at 20 kHz 39.6 = I I II I l 10 m/s 19.8 ° (c_, = I I , 15.4°). I I ,III ! I I 60t_ SPL,/3 dB , 70 -_ 50 -- 60 - 4-0 -- , , J , ,,,,I 50.2 (a) Figure 48 _, 1 Frequency, 70. Self-noise U = spectra _ _r _'__ i ,,_,I 10 20 30' .2 for m/s 5.08-cm-chord (b) airfoil with I 1 Frequency, kHz 71.3 i J , , lJlll untripped BL at J , , ,Jill 10 kHz U = 39.6 m/s at = 25.2 ° (a, = 19.6°). 20 1O0 100 -I Data I I I I I I l Total prediction a I TBL-TE I I I press I I I _'i ,_ Separation L I I ji, , 70 1 1 II 10 90 -- 80 -- ' ' ' ''"I _ ' I I I IIIII I Q 20 6O I I I 1 @ I I1[ 1 _'reque ncy, kHz (b) U = 55.5 m/s .2 Frequency, kHz (o) U = 71.3 m/s gO I 70 -- - 60.2 I _1 90 SPL1/_ dB I i{ 8O ' ' ''"I ' ' ''''1 ' ' 10 ' 20 '''"1 70-- 70 -- @ 60-- -0 8,0 _ 60 -- __ ° --_i 50 , , , lililJ, .2 , T Frequency, L_ i , ,,,,I 40 Figure -I 70 _ 1 Frequency, kHz (d) U = 31.7 m/s 20 .2 airfoil with 10 kHz (c) u = 39.6 m/s 80 e --" 50-- 71. Self-noise Dotlol i i i spectra i i I I for 2.54-cm-chord 0 ITBL_TEI i ipressurel i i I sldell . * Total prediction & Separation / 0 TBL-TE suction side o LBL-VS --I untripped 70 I I I BL at (_t = 0° (_, I I I iI l 20 = 0°) • i 60 10 i i i i __._._ i i1 _[_ | / -'-_ / SPL1/3 dB , e 50 . . o @ 402 70 , , ,,,,,I ,o, , I Frequency, kHz (a) U = 71.3 m/s ' '''"1 ' ,,,,,1810 • 4o _ _ 20 30.2 , ' ' '''"1 I 50-- 40 -- 30 -- 40-I Figure I I I Ill I I ,", I spectra I Frequency, , I , , ,,,?,I 20I 10 kHz I '''"1 ' for 2.54-cm-chord 10 ' ' '''"1 [] • I I IqllT 1 Frequency, kHz (c) U = 39.6 m/s 72. Self-noise , ,,,,,I o 8 I _I (b) U = 55.5 m/_ 60 -- .2 =aT__ [] 50 30 o I 60-- @ _ . 20 airfoil 20 I I with ,J,,,l , , , ?,,,,I 1 Frequency, kHz (d) U = 31.7 m/s .2 untripped -- o o 10 20 BL at c_t = 5.4 ° ((_, = 4.8°). 49 9O 80 I 8O _ I I I III i Data • " Total predlct[on 0 TBL-TE suction I I side trt SPLI/a , I I I I I I o TBL-TE pressure & Separation o LBL-VS side I I i Inn I i I I t111 U U n _U I I I I nl_ I 70-- _t 70-- 60-- dB 60-- _ VO _ , _ , P_,_I 50._ (o) 70 SPL1/_ dB . , ' U = ' '''"1 9 , I I ll=l , 1 Frequency, 50-- it _ 40 10 2O i .2 1 Frequency, kHz 71.3 m/s ' ' U (b) = I iii I 10 55.5 m/s 80 ' '''"1 2O kHz I 6O 70 -- 50 60 -- 4O 50-- '_"1 J 30 I t llll I 1 Frequency, (C) U = 39.6 .2 Figure 1 O0 go SPLII3 dB , _ 73. Self-noise spectra I I I Itll It 2O .2 2.54-cm-chord airfoil ' ' ' ''"1 o TBL-TE pressure z_ Separation <> LBL-VS with , 1 Frequency, (o) Figure 74. Self-noise U = spectra , = I BL at I U I I 20 = 10.8 ° (a, II I .2 = 9.5°). I with untripped n I Frequency, (b) airfoil I n , , ,,,,n 40 m/s 2.54-cm-chord at i I I l II I i n n anJl -- kHz for 2O 70-- , n_,,,l 10 71.3 10 kHz 80 50 ,,,,I untripped side 7O , , ,,,,,,,I (d) U = 31.7 m/_ 60 , , 1 Frequency, kHz m/s 80 , , .",,,,,I 40 10 for ' ' ' ''"1 ' Data _r Total predictTon o TBL-TE suction side 60.2 5O I BL at U at = = 10 kHz 39.6 14.4 ° (c_, m/s = 12.7°). 20 5. Spectral Scaling As mentioned In this section, the scaling laws are for the five self-noise mechanisms. The developed spectra of figures 11 to 74 form the basis of the scaling for three of the mechanisms: turbulent-boundary-layertrailing-edge (TBL-TE) noise and separation noise were scaled from the tripped boundary-layer cases, and laminar-boundary-layer-vortex-shedding (LBLVS) noise was scaled from the untripped cases. For the tip vortex formation noise mechanism, both the data and the scaling approach are obtained from reference 18. Finally, for TE-bluntness vortex-shedding noise, spectral data from the study of reference 2, as well as previously unpublished data from that study, form the basis of scaling analysis. What has become traditional TE noise scaling is based on the analysis of Ffowcs Williams and Hall (ref. 5). For the problem of turbulence convecting at low subsonic velocity Uc above a large plate and past the trailing edge into the wake, the primary result is (P2) C(t'0 -_0 _ (17) D where (p2 / is the mean-square sound pressure at the observer located a distance r from the edge. The medium density is P0, vP2 is the mean-square turbulence velocity, cO is the speed of sound, L is the spanwise extent wetted by the flow, and/: is a characteristic turbulence correlation scale. The directivity factor D equals 1 for observers normal to the surface from the TE. The usual assumptions for boundarylayer flow are that v I cx Uc <x U and £ c( 6 or 5", where 5 and 5* are, respectively, the boundary-layer thickness and displacement thickness. Fink (ref. 25), when normalizing airframe noise data where TBLTE noise was believed to be dominant, assumed a universal spectrum shape F(St) for where St is the Strouhal number fS/U. F(St) depended only on the ratio - 10 log noise, shape of St to its peak value Stpeak. This gave the following form for the 1/3-octave sound pressure presentation: SPLu3 the The normalization level spectral 1-_ with SPL1/3 = OASPL + F(St) and where K is an empirical constant which was determined when the velocity U is given in units of knots. of the airfoil self- of the present report were form, in reference 6, and 1, some prenor- malized in the manner of equation (18) using measured values of/i. It was found that, contrary to what was previously assumed (e.g., refs. 25 and 3), the normalized levels, spectral shape, and Strouhal number were not independent of airfoil size, airfoil angle of attack, and free-stream velocity. However, the limited scope of the paper, as well as the uncertainty caused by the aforementioned extraneous noise contamination of the uncorrected spectra, prevented a clear definition of the functional dependences. The corrected spectra of the present report are used to determine the parametric dependences and to account for these in the spectral scaling. 5.1. I. 5.1. Turbulent-Boundary-Layer-Trailing-Edge Noise and Separated Flow Noise in section noise spectral data sented, in uncorrected Scaled Data Zero angle of spectra for four speeds, are scaled. figures 11, 20, 26, and the boundary the normalization Scaled SPL1/3 attack. In figure 75, 1/3-octave airfoil sizes, each at four tunnel The spectra are obtained from and 32. The angle of attack is zero layers are tripped. The form of is = SPLu3 - 10 log (M 5 5_L r-_) (19) where Mach number replaces the velocity in knots, 6_ replaces 5, and re replaces r. The retarded observer distance re equals here the measured value, 122 cm (see appendix B). For the right side of equation (19) to be accurately expressible by the form F(St)+ K of equation (18), the scaled spectra of figure 75 should be identical to one another for all cases. However, the peak Strouhal number, spectral shape, and scaled level vary significantly. For each spectrum in figure 75, a symbol indicates the approximate spectral peak location. The peak locations were based on gross spectral shapes and trends rather than specific peak maximums. The peak Strouhal number, Stpeak ---- (f S* /U)peak, and scaled levels corresponding to these peak locations are shown in figures 76 and 77, respectively, as a function of Reynolds number Rc. These data are also presented in table 1 (at the back of this report). Included in the figures are the other cases for tripped BL airfoils of different chord lengths. Also included are data at nonzero angle of attack for subsequent discussion. The displacement thicknesses for the suction side, 5_, are used for these normalizations. In figure 76, Stpeak for zero angle of attack (solid symbols) shows no clear Rc-dependence, but a Mach number dependence is apparent. The horizontal lines through the data correspond to the function 51 InlJlnnnFluunFItrnnlJn IFIllllllltttllttttltttt .o ._ ,_.; Y o f -_0 00 II .kO 0 ? II n _C./3 ¢',1 L_ o \,\b £ \,,;- e., 0 L_ JlnllJJllllll_lnJJlllll 0 LO 0 _ 0 0 CO 0 04 o C_C_ 0 _-- o o _ o _ o _ o _ oo 0 il d It lit il Ill It I uJ It lit tt II ut I_l 17 I][ [n lit UllJU i..¢") tn II m I_ LZ")C'_0 "3 !!l :It on ,/{ qO " m /, ,_" / /'./ e_ ._o _'0 sO II II 0 -o..,- 2 ° _ _ "-:. C/) '_.00 O0 ,...I d & CO :x,',\ \ \ \ I'.- 0 It 0 L_ IIla t _n 0 _1" I_n 0 CO 8P '8/l-ld G2 a n I _l 0 O,J al laJ 0 T- S peleOS L_ 0 It O0 0 o o L._ o '_- o co 8P '_/I'-IclS o o,.I o _'- pel_0S oo o ] i _ I w , , J ] z i I i i i i ] I f i I i i i J ] o_t' deg ,,+ • "&z& o 5.4 14.4 ++ .t g "" [] - -z-_--_ Z-Z St 1 ....... nohA'.6 oo 1 O O,00 [] .-. [] L-J IU I -- _ 1 • 1 212 .,k _... 9 + A_ _,.)A _ -- 10.8 0 U OV 9 •.A " .. -. 240464606 2 25.2 A _ _" _ U U,m/s .093 .116 31.7 39.6 _.163 \ .209 55.5 71.3 / - @ " 12 4 12 6 12 12 i _ 13_ .01' ! I [ I I 10 4 I | I I I I 76. inches Peak (for _ i I i 1[ 10 5 Strouhal brevity 1 50 number of notation). , , for TBL TE , , , I ''I J J L _ _ _ i J 10 6 Reynolds Figure I noise versus number, Reynolds ' Rc number. ' ' 10 7 ' Numbers aligned ' ' ''1 with data ' ' are chord I ' I sizes l I in I oct' deg 5.4 m 140 "O 'C'_'_ K1 10 z_ 4 A_> 10"8 14.4 19.8 + 25.2 1 1 2 4 .._, z,,,2 : .,,_ <>-^.9 _,. [] _57_,1_4Lj4_7,_, g_ _1 13_ co "O 130 6_612612 9 + a. 120 110 I , , , L nnnl 10 4 I I 77. Peak , _ i innl 10 5 scaled level for TBL TE noise versus I I I , _ ''_ 10 6 Reynolds Figure 12 12 Reynolds number, number. Numbers 10 7 Rc aligned with data are chord sizes in inches. 53 St1 = 0.02M -°'6 for the presented number and is taken to approximate values of Mach the behavior of Stpeak. For the scaled levels in figure 77, a continuous function, designated as K1, that is comprised of Rc-dependent segmented lines is drawn to approximate the zero-angle-of-attack data. Other choices for a function to approximate these data are possible but the one shown, which is chosen to be constant for high Rc, was found to be compatible with higher Reynolds number data obtained from other studies, as is shown subsequently. Note that the behavior of K1 at very low Rc is at most academic because of the lack of importance of this TBL-TE noise mechanism in this range. In figure 78(a), a shape function denoted by A is proposed as representative of the 1/3-octave spectral shape of the TBL TE noise mechanism. (Fig. 78(b) presents a corresponding shape function for separated flow noise.) The spectrum A is a function of the ratio St/Stpeak that is symmetric about St/Stpeak -1.0. The spectral width or broadness depends on Rc. Two extremes in A are shown corresponding to socalled maximum and minimum Reynolds numbers. Intermediate values of Rc require interpolation. As seen in figure 75, the larger chords have the broadest TBL-TE spectra. The spectrum A was matched to these and the other chord lengths. The specific details of A and the other functions are given in the calculation procedures section (5.1.2.). One of the key results of reference 2 is that each side of an airfoil with well-developed boundary layers produces TBL-TE noise independently of the other side. This is not in conflict with our scaling approach for the symmetric airfoil at zero angle of attack. Consistency of this with equation (19) merely requires a level adjustment (-3 dB) of the scaling equations to account for the equal contributions of the two sides to the total spectrum. For the pressure and suction sides, i = p or s, Scaled SPLi = SPLi = A \Stl - 10log + (K1 - 3) where Sti = (f6_/U). The total zero angle of attack then is SPLTBL where a understood. (M 56_L_ TBL-TE (20) noise TE ----10log (10 SPL_/10 + 10 SPLp/10) 1/3-octave presentation for spectra for (21) is Nonzero angle of attack. In figure 79, scaled noise spectra are presented for the same tripped BL airfoil 54 models as in figure 75, but here the angle of attack is varied while holding tunnel velocity constant at U = 71.3 m/s. The tunnel angles of attack cq are given along with the effective angles a,. The level normalization approach and Strouhal scaling are the same as in figure 75 except that here the displacement thickness of the suction side of the airfoil 5" is used. For increasing c_, the peak Strouhal number and level increase and the spectra become sharper at the peaks. Beyond limiting values of a,, roughly corresponding to stall, substantial changes occur to the scaled spectra. If equations (20) and (21) were used to predict the spectra in figure 79 and the predictions scaled accordingly, one would find for increasing angle of attack that peak Strouhal number would remain constant, peak level would decrease, and the spectral shape would become broader at the peak. This is because the suction side contribution would remain dominant and that of the pressure side would shift to higher frequencies at reduced levels. These trends, of course, are virtually opposite to those observed. The approach that is now taken is to postulate at nonzero angles of attack an additional contribution to the spectrum that controls the spectral peak. To justify this, one could hypothesize that the spectrum is the total from attached TBL contributions, as formulated in equations (20) and (21), and a contribution from a separated portion of the TBL on the suction side. The modeling approach, however, is not without conflict at the low Reynolds numbers, as is discussed subsequently. Model details are developed below, after establishing the Strouhal and level scaling behavior for the angle cases. In figure 79, for each spectrum, symbols indicate the approximate peak Strouhal locations. As in figure 75, the locations of the peaks were based on gross trends and shapes of the spectra rather than precise peaks. These values of Stpeak are included in figure 76 for the various chords, speeds, and angles of attack, along with the zero angle values previonsly discussed. Again little direct Rc-dependence is noted for Stpeak. The basic trends observed can be explained by velocity and angle dependence. The values of Stpeak are plotted versus corrected angle of attack a. in figure 80. For reference, the chord lengths (in units of inches for presentation convenience) are given. Through the data are drawn data-fit lines designated as St2, corresponding to two velocity values. At a. --- 0 °, St 2 becomes the function Stl of figure 76. In the hand-fitting procedure to determine St2, some preference was given to the higher speed cases. This preference is discussed subsequently with regard to Strouhal peak level scaling. As for the substantial 0 I I I I I I I A max for large Rc m i Function A level, dB -10 A min for small R I -20 I I Illl I I 10 1 .1 Strouhal number (a) Function 0 A for TBL-TE noise, equations I ratio, St/St peak (35) to (40). I I I I I i I I I B max for large Rc Function B level, dB -10 B min for small Rc -2O .1 1 Strouhal (b) Function Figure 78. One-third-octave B for separated spectral 10 number ratio, St/St 2 flow noise, equations shapes as functions (41) to (46). of Strouhal and Reynolds numbers. 55 o "-' o o o o o o OJ "_"CXI "_"_.0 0 0 0 0 0 _- 00',_- _00,I I I [ I I I I [ I I kO I I o_c_,_c_ •,-',-',-OJ , i I i i / i i i i / ,, ' , / ', II I I /" /"" o []<]0-4 _, ....'" .S ,_ . o =) / o ..s: ._(,0 _0 {"'..<'" II o II ,-:._ 'V,/" \ " "z. r./) ¢.-, -,.f oo o LO II '\: 0 0 0 _ ii li 0 _ I_l JI o 0 _ lii If 0 _ I il il O0 0 Ill 0 IF 0 '_- 0 CO _ _ n nol$%U_J o - * b _'°° ,:c6_ o 6u 0 04 0 _-- O0 0 " u u u I I I I n I ; u ; _ O')l"--_O, lqC) __ om_05ai_ , .." i .* /:. --oo_d_o_ _-_o_-_o_ _" S u-i d 4 •-- _.,-0,1 'l I!!l : II ',,I, /; on<]O ',: ',111:/ / /:' i on._Oz_, /,p" ./,//2" ,('" "_, ..' / i / .._..::J ti o It _.r/? ob ¢o \ k \ 0 0 0 0 1.0 0 _ 0 CO 8P '_/l-ldS 56 0 OJ Pel_oS 0 T- O0 0 " o o _ o O_ 8P '8/LldS o OJ peleoS o .,- oo 0 © e- ? data scatter of figure 80, some comments are warranted. It was found that if one used the actual measured values of 6_ (where available) in the Strouhal scaling, one would have a similar degree of scatter to that shown in figure 80, where scaled values of 6_ (eq. (12)) were used. Also if untripped BL airfoil results were plotted, for those limited number of cases where the LBL-VS shedding source is not apparent in the spectra, the scatter and trend would be about the same as those shown in figure 80. Other deviations of the data from the St2 lines occur at mid to high angles of attack, where the low-frequency parts of the spectra were limited by the experimental high-pass filtering and thus values of Stpeak were inaccurately large. The behavior of St2 seen in figure 80 at the higher angles of attack (where the horizontal lines are placed lower than the data) was chosen to approximately correct this bias. The scaled levels corresponding to spectral peaks chosen in figure 79 are shown in figure 77 with the other cases. The previously indicated conflict within the data base for the proposed modeling approach, which hypothesizes contributions from two attached TBL's and an angle-dependent separationrelated portion, is seen in figure 77. Peak levels for the two smallest chord lengths, except at the highest speeds, significantly decrease as the angle of attack increases from zero. This is incompatible with the modeling approach. A choice is made to ignore the conflicting low Reynolds number data in the model development. While admitting that the inclusion of the low Reynolds number behavior would conceptually be desirable for completeness of the modeling, the exclusion is believed justifiable because of the greater interest in higher Reynolds number conditions. The TBL-TE noise mechanism is not considered if this important were not for low Reynolds the case, it is not numbers. Even certain that the present test flow conditions with heavy leading-edge tripping for airfoils at nonzero angles of attack properly represent the mechanism, especially for higher angles where relaminarization of the pressure-side boundary layer is possible. Regardless, the results of the scaling are compared subsequently with the spectra of all the data to allow a direct assessment of the effect of modeling choices. The scaled levels of figure 77 for chord lengths of 10.16, 15.24, 22.86, and 30.48 cm are plotted in figure 81 versus a,. If the portion of these levels that cannot be accounted for by the modeling of equations (20) and (21) can be extracted, this portion would be designated as the separated flow noise contribution. Calculations were performed by taking into account that the Strouhal dependence of A in equation (20) would follow St1 of figure 76 rather than St2 of figure 80, which applies to that portion extracted. The extracted levels are given in figure 82. These extracted levels are normalized by subtracting the zero-angle-of-attack function of figure 77 (K1) for the particular chord lengths and speeds. Although substantial scatter is present, a basic trend of increasing importance for increasing angle and speed is seen. Drawn through the data is a function designated as K 2 - KI which represents a partially observed, partially postulated dependence on velocity and angle of attack. The assigned spectral shape for this additive source is function B, which is given in figure 78(b) and is defined in a manner similar to function which is dependent The dependent A of figure 78(a) to have a width on chord Reynolds number. resulting scaling noise SPLa is Scaled SPLa model = SPLa - for / 10 log/m5 t, the __*L\ "-/ (St_'_ = B t, St_2/ + K2 where this represents the separated-boundary-layer noise contribution to the total noise. The total TE and separation SPLTo noise T = lOlog angle- ) (22) TBL- is then (10 sPL"/IO + IoSPLp/10) + 10 SPL'/I° (23) During development of the scaling procedures, equations (20), (22), and (23) were compared with spectra for all tripped BL airfoils and with spectra for the untripped BL airfoils for which TBL-TE noise appeared to significantly contribute. Analyses of comparisons resulted in optimization of curves A and B, as well as development of the specific calculation procedures. The analysis found that better results are obtained when the Strouhal dependency of the suction-side spectrum SPLs is (St 1 + St2)/2 rather than Stl. It was found that for better SPL agreement, one should make an adjustment in pressureside level SPLp (defined as AK1 in the following section) as a function of angle of attack and Reynolds number based on the displacement thickness 6_. This adjustment diminishes the pressure-side contribution for increasing angle and decreasing velocity. Also it was found that the drastic spectral shape changes that occur at sufficiently high angles of attack, near stall, are roughly simulated by a calculation procedure change. At the value of a, corresponding to the peak of the appropriate /(2 curve, the spectral 57 . _ i i I I i i 'i I I , I i i 4 6 ' 12' 0 [] 5 2 1 /- St2f°rM= .093 / ' 1 - [] O.. 03 _- 4 St 2 for M = .209 E E t:} £ 12 12 0 [] <_ ,_ 03 13_ .01 , , , , I 5 0 , , , , 1 10 , i i , Angle of attack, Figure 80. Peak Strouhal chord sizes in inches. number for TBL-TE noise versus angle U, m/s 31.7 39.6 55.5 71.3 1 15 (z,, of attack. , M .093 .116 .163 .209 j l , I 20 _ , , , 25 deg Data from figure 76. Numbers aligned with data are 150 U, m/s 140 - 4 4 4 A O n 10 31.7 39.6 © 55.5 Z_ 71.3 4 A o 130' © O 13 120 13 6 110 L 0 , l _ , I 5 , , , _ I 10 _ , , Angle of attack, Figure 81. in inches. 58 Peak scaled level for TBL-TE versus angle of attack. Data from _ I 15 , , _ , I 20 , j _ , 25 o_., deg figure 77. Numbers aligned with data are chord sizes contributionsSPLsand SPLpin equation(23) are eliminatedandthe B curve of equation (22) is re- The calculation procedures are specified in the next section followed by comparison with the spectral data base. placed by an A curve corresponding to a value of Rc which is three times the actual value. 2O ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' m 20 I ' ' U, m/s 31.7 .093 [] A 39.6 .116 4 A \/" 55.5 .163 71.3 .209 10 c 6A r: .. 9 46 A vIL_A__ - ' M O ZX ,,i ' o- . K 2 -K 1 .16 _20| , o , , I , , , , I 5 , 82. with data 5.1.2. Angle-dependent are scaled chord sizes Calculation in , , t 10 noise levels as . , , 9 i I of attack, referenced to zero angle a., of TE noise I I I I 20 15 Angle Figure , 13 t 25 deg attack, TBL model. Numbers aligned inches. Procedures The total TBL-TE and separation SPLTo noise spectrum T = 10 log (10 in a 1/3-octave SPLc'/10 4- 10 SPLs/10 presentation is predicted by (24) 4- 10 SPLp/10) where SPLp = 10 log (5_MSL-Dh_ \ re / SPL, = 10log (6*_Dh5 \ re / + A (Stp'_ + (K] - 3) + AK1 (25) 4-A (St,_ \Stl] 4- (K1 - 3) (26) k_] and SPLe= \ for angles of attack up to (e,)0, 4- B(Sts_ lOlog(_f;iSL-Dhl re an angle to be defined ] later \St2] (27) + in this section. K2 At angles above (a,)0, SPLp = -oo (28) SPLs = -oo (29) 59 and SPLa= where A' is the curve A but De are given D h and The Strouhal lO log ( 5* M_L-Dt for a value in appendix definitions are of Rc which B by equations (see figs. \St2] is three (B1) 76 and 80) Stp- f6pu times and (B2), Sts St1 = 0.02M S--tt - +A,(sts5 _ the + K2 actual (30) value. The directivity functions respectively. -- _f6* (31) -°6 (32) St1 + St2 2 (33) and 1 100'0054(a*-1"33)2 (a, < 1.33 °) (1.33 ° < a, _< 12.5 °) (34) St 2 = St I x { 4.72 For the spectral shape function the function A for a particular Ami n corresponding to chosen Amin(a) (12.5 ° < a,) definitions, we first consider the function A of figure 78(a). Reynolds number Rc is obtained from an interpolation of the values, (Re)max and (Rc)min. The two curves are defined as ,/67.552 - 886.788a -32.665a + 3.981 2 - 8.219 As discussed, curves A,nax and (a < 0.204) (0.204 (35) < a < 0.244) = { -142.795a 3 + 103.656a 2 - 57.757a + 6.006 (0.244 < a) and Amax(a) x/67.552 - 886.788a -15.901a + 1.098 a is the Strouhal absolute number, value Stpeak (a < 0.13) (0.13 (36) < a < 0.321) ={ -4.669a where 2 - 8.219 ----Stl, of the Stl, 3 + 3.491a 2 - 16.699a logarithm of the ratio + 1.149 (0.321 of Strouhal number, St < a) = Stp or Sts, to the (37) a = I log(St/Stpeak)t The absolute The This 6O -20 value interpolative is used because procedure dB corresponds peak or St2: the includes to a horizontal spectral defining axis shape is modeled a value, intercept a0(Rc), in figure to be symmetric at which 78(a) about the spectrum for an interpolated a = 0. has a value curve. of -20 The dB. function ao(Rc) is given by ao(Rc) An interpolation = (-9.57 0.57 1.13 factor x 10-13)(Rc - 8.57 x 105) 2 + 1.13 AR(aO) is determined where Amin(a0) and Amax(a0) be evaluated for any frequency The The function B A above. result two Brain(b) (27) curves = = Amin(a and Bmax (38) x l05 < Rc) - Amin(aO) = Amax(ao) for use in equations in equation The x 105 ) (39) - Amin(ao) are the Amax and Ami n spectra evaluated at a 0. The spectrum by computing the Strouhal number St and the corresponding A(a) function x 104 _< Rc <_ 8.57 from AR(aO) factor. x 104 ) (8.57 -20 interpolation (9.52 (Rc < 9.52 (26), and ) + AR(ao)[Amax(a) shown and (25), plotted Brain, is (4o) - Amin(a)] in figure through (30) shape A can now a and using the which -83.607b + 8.138 V'16.888 - 886.788b 2 - 4.109 -817.810b 3 + 355.210b 2 - 135.024b 78(b) is calculated B is obtained from (0.13 + 10.619 in a manner similar interpolation, are < b < 0.145) (b < 0.13) (0.145 < b) to (41) and Bmax(b) x/16.888 - 886.788b -31.330b + 1.854 2 - 4.109 (b < 0.10) (0.10 (42) < b < 0.187) = { -80.541b 3 + 44.174b 2 - 39.381b + 2.344 (0.187 < b) where b = I log(Sts/St2)l The spectral shape for values of b of bo(Rc) The interpolation B for intermediate = (-4.48 0.30 0.56 factor BR(bo) values x 10-13)(Rc of Rc have - 8.57 x 105) 2 + 0.56 is defined the result axis (9.52 intercepts at -20 for use in equation B(b) (27) dB in figure (Rc < 9.52 x 104) x 104 < Rc <_ 8.57 x 105) 78(b) (44) x 105 < Rc) as -20 thus horizontal (8.57 BR(bo) and (43) = Bmax(b0) - Bmin(b0) - Bmin(b0) (45) is = Brain(b) + BR(bo)[Bmax(b) - Brain(b)] (46) 61 TheamplitudefunctionK1 in equations (25) and (26) is plotted in figure 77 and (Rc < 2.47 K1 = -9.01og(Rc) + 181.6 -4.31 log(Rc) + 156.3 128.5 (2.47× The level adjustment previously mentioned for the appears as AK1 in equation (25). This is given by _-- _ c_, RS_ is the Reynolds The amplitude given as number function/{2 based (47) x 105 < Re) for nonzero angles of attack (R_; < 5000) (48) [0 where 105 ) contribution [, ( AK1 pressure-side by × 105) 105_<Rc<8.0× (8.0 is given (5000 < R_;) on pressure-side of equations (27) and displacement (30) thickness. is plotted for some -1000 V//32_ (/3/_)2(a, _ .y0)2+/3o ('_0 -'_ values of M (a, < "_0 - "_) -< a, <_ "Y0 + "/) in figure 82 and is (49) K2 = K1 + { -12 (_0 + "Y< _,) where -), = 27.094M /3 = 72.65M The above angle is valid definitions the use of equations supposedly stalled be equal is first. to the peak 5.1.3. above for all values (25), are of a,, (26), and flow condition. Comparison of the With + 3.31 + 10.74 in units even "_0 = 23.43M when fl0 = -34.19M- of degrees the K2 function defined where are the switch Data tion 3 and the directivity functions from appendix B (where re = 1.22 m, Oe = 90 °, and (I)e = 90°). The total self-noise is given as well as the individual noise components of TBL TE noise from the suction and pressure sides and separation noise. The predictions follow the shapes and levels of the data, especially for the larger airfoils and the lower angles of attack where the scaling accuracy was most emphasized. Predictions of TBL TE and separation noise are also shown for the untripped BL airfoils in figures 44 to 74. noise in sign. in equation flow to equations occurs, by "Y0 in equation (50) f as positive total TBL / 13.82 taken of the attached The scaling predictions of TBL-TE and separation noise are compared with the noise data in figures 11 to 43 for the tripped BL airfoils. The calculations used the appropriate values of 6" from sec- 62 and calculation (27) for assumed The angle +4.651 specified previously (50) or whenever For the many (28), a, The K2 (24) switches from and for a (29), definition as (a,)0, (30) exceeds untripped is taken to 12.5 °, whichever cases where these sources are predicted to be dominant, the agreement is generally good. Even where the LBL VS noise dominates, the TBL TE and separation contributions help with the overall spectral agreement. 5.2. Laminar-Boundary-Layer-VortexShedding Noise As previously described in section boundary-layer instabilities couple feedback to produce quasi-tonal noise. TBL-TE methods erratic band noise, there are no LBL established in the literature behavior spectra of the multiple and the general 1, laminar- with acoustic In contrast to VS noise because tones in the complexity scaling of the narrowof the mechanism. Two key results from the literature which provide initial scaling guidance are (1) that the gross trend of the frequency dependence was found to scale on a Strouhal basis, with the relevant length scale being the laminar-boundary-layer thickness at the airfoil trailing edge (ref. 16), and (2) that on the basis of the limited data from the data base of the vicinity speeds (ref. established. all TBL TE chord airfoil, the present paper as reported in reference (6), overall levels tended to coalesce to a unique function of Rc when normalized in the fashion of TBL-TE noise. velocity. Although the boundary layer is the trailing edge at all velocities shown, exists over larger portions of the airfoil velocities. As mentioned for the LBL-VS that The scaling approach taken for TBL TE that a dency eters, number. narrow broad spacing taken herein is similar noise in the last section to in universal spectral shape and Strouhal depenis modeled in terms of boundary-layer paramMach number, angle of attack, and Reynolds The use of 1/3-octave spectra, rather than band, permits such an approach because the spectral bands overlap the tonal frequency to give smoother and generally single-peaked spectra. 5.2.1. Scaled Scaled four airfoil presented The angle layers are Scaled for level scaling by the addition of a peak when the flow velocity is diminished. The peak levels increase with decreasing anism, any spectral tonal contributions peaks containing should scale with turbulent at laminar flow at the lower noise mech- a number of Strouhal num- bers based on boundary-layer thickness. This is the case in figure 83(b) with St r _ 0.27. For the shorter 10.16-cm-chord airfoil, in figure 83(c), the LBL VS noise peaks become even more dominant for decreasing velocity. Note also the changing Strouhal dependence, not noted in previous studies. The shorter 5.08-cm-chord airfoil, in figure 83(d), has even more pronounced level and Strouhal dependence with velocity variations. Data 1/3-octave sound pressure level spectra for sizes, each at four tunnel speeds, are in figure 83 from figures 44, 53, 59, and 65. of attack for all is zero and the boundary untripped. The normalization employs SPL1/3 of the trailing edge at all four tunnel 21), so no laminar vortex shedding is The noise produced is assumed to be noise. In figure 83(b) for the 15.24-cmthe broad spectral shapes are changed = SPL1/3 - 10log (M 55pL'_ rl ) (51) and st'- lip (52) U for Strouhal frequency scaling. For the symmetric airfoils at zero angle of attack, 5p = 6s = 50. The scaling approach differs from the TBL TE noise scaling because of the use of 6p, the boundary-layer thickness on the pressure side of the airfoil, rather than 5", the boundary-layer displacement thickness on the suction side. The use of 5p as the pertinent length scale follows from reference 16 and was found to give seemingly better results in initial scaling of the present data base than 5_ and by far better than c, 6s, or 6_ for angles of attack other than zero. In figure 83(a) for the large 30.48-cm-chord airfoil, the spectra appear to be of smooth broad hump shapes. There is no apparent contribution to the spectra from LBL-VS noise which is peaked in character. The boundary layers are fully turbulent in Whereas figure 83 shows the dependence of LBL VS noise on velocity for the various airfoil sizes at zero angle of attack, figure 84 shows the effect of angle of attack a, of the airfoils at a velocity of 71.3 m/s. The spectra for the 30.48-cm-chord airfoil, shown in figure 84(a), change from being dominated by TBL TE noise, for c_, = 0 °, to being dominated by LBL VS noise, for c_, = 4.0 ° . So even with a large Reynolds number (Rc = 1.52 × 106), LBL-VS noise occurs. With increasing a,, the boundary layer on the pressure side becomes more sufficiently large portion of the chord creased shedding and corresponding 15.24-cm-chord airfoil (Rc = 7.58 × figure 84(b), til a certain laminar over a to result in innoise. For the 105), shown in the LBL-VS noise increases with c_, unvalue is reached where it diminishes. At a, = 7.2 °, no apparent shedding noise is shown. o_, = 9.9 °, the noise changes appreciably to that stalled flow as discussed in the last section. The At for use of 5p as the characteristic length scale apparently results in-a proper Strouhal scaling for the shedding noise peaks; but, as expected, the spectra for a, = 0 °, 7.2 °, and 9.9 °, which are dominated by TBLTE and separated flow noise, diverge in this normalized format. A similar angle-dependent behavior where spectra do not coalesce is seen for the 10.16-cm-chord airfoil, in figure 84(c), where LBL VS noise is apparent at c_, = 0 ° and 3.3 ° but not at the higher angles. For the 5.08-cm-chord model, figure 84(d) shows large-amplitude LBL VS noise at a, =0 ° and 4.2 ° . 63 1 lllifftJllillltrtltll iiilllll[lil i it il iii li I._ / / / I..0 .J // I .// ,- &,," {' _._ r../3 ;> .i' ::3 <] 0 "-4 I:£ •.J:: o &. 0 II ? '_. r..f) c"q k\, ui 0o ", \ \\,_, \ , o 00 0 :J 11 C) LC) ,r- Ill II 0 _ .r-- Ill Jl 0 CO _-- I :j :j IIjj C) 04 .r--- LO 0 E:) OC) C_ 0 --.r'- II 0 C:) O0 " (Z:) I_ 0 _ CZ) _ 0 O0 03 II ' IlillllirfilJtlllJill // /4 °- S 4";" E .--_ o'_,- # 14 I'! !jr ' / /,/,'_ I //,V oDqO ,.2o .....<_-.--m3 [ o ,.£ _. 0 uO X,,\ II o .J:::: o \ ' _ 0o _2 0 tt 0 IJllt tliltlllitllJltt 0 _1" 0 03 8P 'E;/L-iclS 64 LO 0 I 0 OJ 0 ,,-- Pale0 S 0 O0 0 _ " 0 £0 _1_ _ 0 I_i 0 gp U") 0 _ljl_ 0 E:) 'E;/Lqd S Pele0S O0 "_ ¢,p It II lit Illlllllllllllll o o o o l, ,' !III ' I I o []<ION ..= 0 0 _O 0 [] ,-t.-. II II Y .,?, v II o II o I o OO o _D ,r- I IIIII IIIIt o IJlll II1,1 LO II I I I , I , , , , II , _"_ I i, , i I l, i 0 0 0 0 0 O0 LO _" O_ O_ " u_ I IOI o 4, I011011 I 0 I I I I I l 11 I I I I eO I_ (3_(_I o o _0_ .£ o o o '_- O0 _" O0 s I' i,! ' III ' I " II /S I I o []<]ON 6 / / ff li f " / I I .-" ::D 0 CL i I ,-i--. I tl \ 0 © II Y F; Y I, \\ \ oO _0 I.-, b,O E, o. 0 / 0 L_ liiiliillliililll 0 _- illll 0 _ 8P '_/l'-IdS 0 (Xl iI 0 _- Pele0S O0 0 LO 0 i I o " I I I I I i i i I i_ 0 0 I.i"l \ 1 _- i I I I , i i I I , i i/ 0 _ 0 CO i'O 0 O0 _ ' 8P 'O/LGclS PeleoS 65 The LBL-VS noise portions of the spectra (figs. 83 and 84) are rather invariant with respect to spectral shape. Based on this observation, a function G1 (shown in fig. 85) was chosen as a shape to represent the LBL-VS contribution to the self-noise 1/3-octave spectra for all cases. The level of G1 at St I -- Stpeak has a value of -3.5 dB. The reference level of 0 dB is the integrated total of G1. To permit an orderly study of the Reynolds number and angle dependences of the spectral data, the shape G1 was matched to the individual spectra to obtain reference overall peak levels and Strouhal numbers. Emphasis was placed on matching the global spectral shape of G1 to the data rather than matching 1/3-octave band peak or overall levels. Reference peak locations are indicated by the symbols in figures 83 and 84. ! In figure 86, the chosen values of Stpeak are plotted versus the Reynolds number Rc for the 42 cases where LBL-VS noise is prominent. The values are also given in table 2 (at the back of this report) along with the effective angles of attack a, corresponding constant range to cq. For a, -- 0, Stpeak is approximately at low Rc and increases with Rc in the mid- of Rc shown. The values of Stpeak are lower for nonzero angles of attack. A function St_ is drawn to approximate the data of zero angle of attack. A constant value for St_ is chosen for high Rc, where no zero-angle-of-attack data are present, because the value permits a simple angle dependence definition J I for Stpeak. In figure 87, Stpeak is normalized by St_ and plotted versus a,. For each of the six airfoils, the line described by 10 -0.040* approximates the angle dependence. 5.2.2. The Calculation LBL VS noise Strouhal definitions crease as Rc increases. For the larger angles of attack, the peak levels are lower and the corresponding values of Rc are larger. Superimposed on the data are curves of identical shape, called here "level shape curves," which are positioned in a monotonically decreasing fashion to approximately correspond to the data trends with angle variation. The angles indicated for each curve position should not necessarily match the angle values listed for the data because the data values are rounded off in the figure, as mentioned. The intent is to use the curves, with their functional relationship to (_, and Rc shown in figure 88, to represent the amplitude definition of LBL VS noise. In the following calculation procedures section, a function G2 specifies the curve shape, G3 is the angle dependence for the level of the G2 curve, and a reference (Rc)o value is defined as a function of angle to specify the Reynolds number dependence. The success of the functions in normalizing the data is shown in figure 89 where peak scaled 1/3-octave level minus G3 is compared with the function G2. In this format the individual angle numbers should ideally match the G2 curve. Although the agreement shown is certainly not complete, it is regarded here as acceptable. Note that much better curve fits to the data would be possible if a requirement for monotonic functional behavior had not been imposed on G3 and (Rc)o. Procedures spectrum SPLLBL The The reference peak scaled levels which correspond t to Stpeak in figure 86 are plotted versus Rc in figure 88. To show general trends more clearly, the symbols are replaced by the value of (_,, rounded off to the nearest whole degree (see table 2 for more exact values). In this format it is seen that for each c_, the scaled levels tend to increase, peak, and de- in a 1/3-octave VS = 10log are (see presentation r2 figs. 86 and is predicted + G1 _Stpeak] by + G2 (---R_c)0 + G3((_,) (53) 87) (54) (Rc_< St_ = 66 0.001756Rc 0.18 0.28 0"3931 (1.3× 105 <Rc_<4.0x 1.3× 105 ) 105 ) (4.0 x 105 < Rc) (55) ! I I I | w I I i_ ! i s • . i • . -10 Function G1 level, dB -20 ce -3O i ___ __ i I I t 5 i I0 1 Strouhal Figure 85. One-third-octave spectral shape number function ratio, St'/Stpeak G1 for LBL VS noise, equation (57). ; _ 4 94 -4 _('5_ _ 12 Srpeak 1 I I I ! St'l / 6 I 9 .1 o_t' deg © [] 0 5.4 <> 1o.8 ,_ .01 i i ' , 10 4 i J l,l l Peak Strouhal , , number for LBL VS noise I , , ,ll 10 5 I I I i i versus Reynolds number, number. I i 10 7 10 6 Reynolds Figure 86. inches. , 14.4 Rc Numbers aligned with data are chord sizes in 67 U_ m/s 0 31.7 13 39.6 <_ 55.5 71.3 (_ 2.54 cm chord 15.24 cm chord 22.86 cm chord 30.84 cm chord Stpeak St "1 .5 2 5.08 cm chord I Stpeak St "1 .5 2 F 10.16 | cm chord / Stpeak .5 0 5 0 5 oc,, deg Figure 68 87. Peak Strouhal number o_ ,, deg for LBL VS noise versus angle of attack. Data from figure 86. 0 170 _ Level shape f13 -O 160 (1) > a) "ID 150 09 140 [3_ "7./. 130 04 , 10 5 Reynolds Figure 88. Peak scaled levels for LBL VS noise versus * L _ L] 10 7 10 6 number, Reynolds number. Rc Data symbols are values of a, rounded off to nearest degree. 0 rn "(5 (3 -10 _o ¢- E -2O > "O o ¢o -3O [3_ -4O .1 1 Reynolds Figure Data 89. Normalization from figure of LBL 88. Data VS symbols noise peak are values scaled of a. 10 number levels rounded by 100 ratio, R c/(R c)0 functions off to nearest G2, equations (58) and (59), and G3, equation (60). degree. 69 and Stpeak (56) = St_ × 10 -O'04a" m The directivity shape, in terms function of the D h is given ratio by equation of Strouhal number 39.8 log(e) 98.409 Gl(e) = -39.8 where e = Stl/Stpeak (see figs. 88 and 89) . The peak a2(d) where d = Rc/(Rc)o and the log(e) log(e) scaled = angle-dependent level for the - 506.25[log(e)] level shape curve G2 depends + 9.125 - 114.052[log(d)] spectral 2 + 9.125 -77.852log(d) + 15.328 number (57) < e _< 1.674) on Reynolds < e) number and angle and is (d < 0.3237) -65.188log(d) (0.3237 < d < 0.5689) (0.5689 < d _ 1.7579) (1.7579 < d < 3.0889) (3.0889 (58) < d) is (59) 100.215a,+4.978 100"120a*+5"263 curve the < e _< 1.17) (1.674 65.18Slog(d) Reynolds G1 defines < e < 0.8545) (0.8545 (1.17 + 15.328 shape 2 + 2.0 G3(a,) 70 (0.5974 - 11.12 (Rc)O = The function (e < 0.5974) 77.852log(d) reference B. The as (see fig. 85) + 2.0 + V/2.484 -98.409 in appendix - 11.12 log(e) -5.076 (B1) to its peak, is = 171.04 - 3.03a, (60) 5.2.3. Comparison With airfoil models shown in figures 2 and 3, respectively. The premise of the tip noise determination method was that 3D models produce both tip noise and TBLTE noise, while the 2D models produce only the latter. The study produced a prediction method in gen- Data The spectral predictions from the above equations are compared with the untripped BL airfoil noise data in figures 44 to 74. The great sensitivity of this mechanism to angle and velocity change can be clearly seen. In many respects the prediction agreement in shape, level, and actual occurrence of LBL-VS noise is good. Also as indicated in the last section, the combined contributions of LBL VS, TBL TE, and separation noise are important to the total predictions for this untripped BL airfoil data. 5.3. Tip Vortex Formation eral agreement with anism first proposed The Calculation tip vortex model of the mechNajjar, and Kim (ref. 17). The noise is associated with the turbulence in the locally separated flow region at the tip of a lifting blade, where the tip vortex is formed. The flow field is illustrated in figure 90 for an airfoil blade tip U. Noise at an angle of attack O_TiP to the flow of velocity The flow over the blade tip consists of a vortex of strength wise extent The prediction method proposed in this section for tip vortex formation noise is that developed by Brooks and Marcolini (ref. 18). The study isolated this high-frequency broadband self-noise by comparing aerodynamic and acoustic test results of both two-dimensional (2D) and three-dimensional (3D) 5.3.1. the physical by George, F with at the a thick viscous TE is g. The core whose recirculating spanflow within the core is highly turbulent . The mechanism of noise production is taken to be TE noise due to • the passage the wake. of this turbulence over the edge and into Procedures formation noise spectrum in a 1/3-octave presentation is predicted by \ SPLTI p = 10log The Strouhal number ( M2M3ax_2-_h re2 I] - 30.5(log (61) St r_ + 0.3) 2 + 126 is J'/ Stll = _]max The directivity equation The function (61), spanwise which Oh gives extent at the is given the by equation frequency TE (B1) dependence, of the separation (62) in appendix is a parabolic due to the tip e/c _ 0.008_TI where c is the oncoming the chord flow. trailing length The edge and maximum C_TiP (see Mach discussion number Mmax M Mmax is is the fit about vortex term a peak is, for the on the Strouhal tested right side number rounded of 0.5. (63) is the angle flow within of attack or about the of the tip separated region to the flow region Mach number of the oncoming ,_ (1 + 0.036C_TiP) Note that actual aspect ratio in reference rotor and _TIP is in the angle use of equations of attack of the (63) tip to the (large span), is untwisted, 18. When the tip loading propeller at flow to the airfoil (64) tip region. The velocity corresponding to Umax = coMmax the of tip, P below) of the second is Mmax/M where B. The blades, and (64) oncoming to determine flow be redefined Ot_FIP = (0_ref _ and when and encounters uniform characteristics differ from C_TiP must (65) according the Mmax,OtTIP blade under is correctly consideration regarded has as a large flow over its span. This is the reference case those for the reference case, such as for some to computed ,] y_TIPJ sectional loading. The redefined C_TIP 71 Z Noise ._ Observer Figure 90. Formation of tip vortex. 9O u 8O u I , I I I I Data (ref. 18): -- --- u Predictions" 2D 3D o A o 70 Tip Total Total I I I , I I uI with tip without tip SPL 1/3, O dB ¢1 O 60 O _ 50 O I 40 I I l llll .2 o j have 72 91. Noise been spectra adjusted of a 3D 15.24-cm-chord to match I the same span. airfoil with U = 71.3 m/s, Z% -_,, , _, ,,,I 1 v._ 10 Frequency, Figure o o o o A a span of 30.48 (_t = 10.8 °. 20 kHz cm, and that of a 2D airfoil section where levels where O_TiP is the lift slope tip loading OL_/Oy the tip and is taken to be high, as tunnel tip noise (square-off employing angle the L _ is the to be testing prediction or cut-off) limited unit tip noise span at to the tip levels tips the definition proposed present by prediction are based which measurements of _ in equation 8. on data reference reported This 5.3.2. definition (63). The For consistency, strength The use y. The F (of fig. of _TIP sectional 90). rather When than _TIP from airfoils in the literature. measurements the with 8 considered, following rounded along with The different blade tips. rounded tip tips, Of interest geometries required the prediction equations of the present of reference 8. The constants in equation did not confirm definition the definition for 8. is proposed is a in calculations a paper (61) of f for rounded for fiat tips for the equations: f/c equation vortex position effects. equations reference spanwise increase. different definition of the separated flow region size/?. In applying for flat tips, it does not appear appropriate to use the definition reflect the solution for arbitrary aspect ratios, blade twist, and spanwise flow which provide guidance in the evaluation of equation (66) for aspect tip geometry tip flow lift per proportional predicted (63) and (64) generalizes the Reference 18 contains examples as well The flat near is found in equations variations. ratio, geometric = of _ approximately (63) for rounded Comparison tips. With There 0.0230 0.0378 accounts + 0.0169o_I P + 0.0095o_?ip for differences is at present between no experimental Data Noise data from reference 18 (fig. 7) are presented in figure 91 along with predictions of tip noise and the combined contributions of TBL TE and separation noise. The rounded tip 3D model has a chord of 15.24 cm and a span of 30.5 cm. The corresponding 2D model has a span of 45.7 cm so its noise spectrum levels in the figure were adjusted downward by 1.8 dB (based on a 10 log(L) dependency) to obtain that expected for a 30.5-cm span. The difference between the 2D and 3D spectra should be that due to tip noise. The predictions in figure 91 for TBLTE and separation noise, which employed the angle _, = 0.5(10.8 °) to account for the wind tunnel correction, should ideally match the 2D model spectrum. The tip noise prediction adds to the prediction to obtain a total which should match the 3D model spectrum. The tip noise prediction involved the use of equation (66) because of the finite extent of the span as well as open wind tunnel influences. Based on the lift distributions presented in reference 18, the tip angle becomes o_i P -- 0.71(10.8°). While a slight overprediction at higher frequencies is seen in figure 91 for this particular example, the differences between levels with and without tip noise are the same for both data and prediction. The comparison shows consistency and compatibility not only with the data but also between the self-noise prediction methods. (67) (0 ° < oz_i p _< 2 ° ) (2 ° < c_?ip) the definition confirmation of reference of equation 8 and that of (67). 5.4. Trailing-Edge-Bluntness-VortexShedding Noise In this section, the experiment of reference 2 is briefly described, published and previously unpublished TE bluntness noise data from the study are presented, 5.4.1. and a prediction method is developed. Experiment The Brooks-Hodgson experiment (ref. 2) employed an experimental arrangement similar to that reported in section 2 of the present paper with respect to hardware and acoustic measurement. However, in reference 2, the model airfoil tested was large with a 60.96-cm chord length. When BL tripping was used, 2.0-cm-wide strips of No. 40 grit were applied at 15 percent of the chord. Rather than the TE being sharp, the model TE thickness, or bluntness, was h = 2.5 mm. Figure 92 shows the TE region of the airfoil. The TE geometry was rounded at the two edges and fiat between the rounded edge portions, which each comprised about one-third of the 2.5-mm thickness. The thickness h was varied, with edges of similar geometry, by alternately attaching extensions on the edge, as illustrated in figure 92(a). Also tested were sharp-edge (h = 0) plate extensions 15.24 and 30.48 cm long, as shown in figure 92(b). Another sharp-edge extension (not shown) was a 2.54-cm-long "flap" extension placed at 17.5 ° off the chord mean axis at the trailing edge. In addition, blunt plate extensions were tested which were 15.24 cm long with 73 h = 2.5 and 4.8 mm and 4.8 mm. These extensions are shown in figure 92(c). used to provide a smooth airfoil to the extensions. 30.48 cm long with h = with rounded TE corners Tape, surface 0.08 mm transition thick, was from the Presented in figure 93, from reference 2, are power spectral noise data of the airfoil at four flow velocities. The airfoil is at zero angle of attack and the boundary layers are tripped. The microphone observer position is re = 1.22 m and Oe = 90 ° with respect to the model trailing edge. For two speeds, the spectra are given for the four TE thicknesses of figure 92(a). The spectral results for the sharp, h = 0, TE cases should be all due to TBL-TE noise. The bluntness contributes additively at high frequencies to the spectrum levels. The values given for h/5* in figure 93 differ slightly from those specified in reference 2 because 6' here is calculated from the BL thickness scaling equations of the present paper. Data are presented in reference 2 for the sharp geometries of figure 92(b), as well as the mentioned 17.5 ° sharp flap extension. These geometries give essentially the same spectra as the sharp extension of figure 92(a). This demonstrates that TBL-TE noise is rather invariant with regard to geometry changes in the edge region, as long as the TE is sharp and the boundary layers are substantially the same. Trailing-edge bluntness noise spectra in a smoothed 1/3-octave format are presented in figure 94 for the edge geometries of figures 92(a) and 92(c). These spectra are the result of a spectral subtraction process between the total spectra and the corresponding sharp TE spectra and should thus represent the bluntness contribution only. With the exception of the eight spectra also represented in figure 93, the data have not been previously published. The indicated values of h/_* for the extensions are based on calculations of _f* for the TE of the airfoil without the extensions. This is justified by indications that the boundary layers did not substantially change over the zero pressure gradient extension plates due to the influence of the upstream adverse pressure gradient (ref. 2). The spectrum for the airfoil with h = 2.5 mm and h/_* = 1.15 in figure 94 is for naturally transitional boundary layers; all others are for tripped boundary layers. 5.4.2. Scaled spectral Strouhal humps as the reference. number, defined as Sdtt _peak The peak fpeakh U (68) plate extensions of figure 92(c) are uniformly higher, for the same thickness ratios, than for the edge extensions of figure 92(a). Also shown are two results • obtained from Blake (ref. 19). Blake presents surface pressure data for a large array of plate edge geometries all for very large values of h/6* (with the exception of the ref. 2 data reported and the one case shown in fig. 95 at h/6* = 5.19). Blake, for most data, employed Strouhal relationships which depend on special wake stream thicknesses, and convection velocities not available without measurements. From Blake, however, it is obvious that different TE geometries have different frequency dependences, consistent with the result of figure 95 that Strouhal numbers for the flat plate extension and the airfoil TE geometries differ. The primary difference between the geometries is that the NACA 0012 airfoil has a beveled or sloping surface upstream of the trailing edge with a solid angle • of 14 ° and the flat plate has q2 = 0 °. The result shown from Blake in figure 95 at hi6* = 5.19 is for a plate with ko = 12.5 ° and nonrounded TE corners. In figure 95, parallel curves are fitted to the data. The curves, designated with values of _, are defined on the basis of a match point at h/6* = 20 for ko = 0 °. From Blake's scaling for a thick flat plate (h/6* large) with nonrounded TE corners, one can determine that fh/U = 0.21 at hi6* = 20. The curve for kO = 14 ° intercepts Blake's k0 = 12.5 ° result, but this is deemed an acceptable deviation from the curve fit. For scaling purposes, values of q,Ht '-'_peak for • values other than 0 ° and 14 ° could be determined as described in the calculation follow. by linear interpolation procedure section For amplitude scaling, the peak values of the octave spectra of figure 94 were normalized as Scaled peak SPL1/3 = Peak SPLl/_ - 10 log \ 74 of is plotted versus the thickness ratio h/6* in figure 95. The Strouhal numbers increase with increases in thickness ratio. The Strouhal numbers for the Data The spectra of figure 94, as well as limited frequency data of Blake (ref. 19), form the foundation of the scaling approach. As with the scaling approach for TBL-TE and LBL-VS noise, the level, frequency, and spectral shape are modeled as functions of flow and geometric parameters. For the level and frequency definition, we chose the peak of the value to 1/3- M55hL re_ ] (69) The 5.5 power for Mach number dependence was determined to give better overall scaling success than either a 5 or 6 power. Figure 96 shows the scaled levels plotted versus the thickness ratio h/5*. As in figure 95 for the Strouhal dependency, the scaled levels are uniformly higher for the plates than for the h = 2.5 mm /h = 1.9 mm .._L | h = 1.1 mm 60.96-cm-chord NACA 0012 airfoil __,_ / (a) TE Extensions, Which h = 0 (sharp trailing edge) _ _- Trailing-edge are Alternately extensions Attached Length Airfoil (b) Sharp Edge Plates P---- Length ---4 / Airfoil Surface transition (c) Figure 92. Illustration Blunt Edge Plates of trailing-edge extensions and plates. Smooth surface transition is provided for all geometries. Shard TE (h = 0) Blunt TE (h = 2.5 mm) Blunt TE (h = 1.9 mm) Blunt TE (h = 1.1 mm) ..... m ....... 50,,__h/5* = 0 4O /1-_, 0.62 ,_,,,,.,_,x.v.....- 0.46 ,,\ 30 (S(f) 101og \p_ o-, "_" "" _...%.,...... _" U -- 69.5 m/s ) 2O Vv 10 .3 • 30.9 m/s 1 10 Frequency, kHz Figure 93. Spectral density for TE noise for 60.96-cm-chord airfoil with various degrees of TE bluntness. Oe = 90 °. Level referenced to 1-Hz bandwidth. Data from reference 2. Tripped BL; at = 0% 75 100 I I I I I I I I I / I I I I I I Plate with h = 4.76 mm Length = 30.48 cm, M = .206, h/5* = 1.16 90 Plate with h = 4.76 mm Length = 15.24 cm, M = .206, h/5* = 1.16 80 _ Airfoil 70 -- M = .203 .203 SPL1/3, dB I with /", h = 2.54 mm: i I I : .62 I ,, .60 . 158 .56 •135 .55 Airfoil: I , 60 -- M = .206= 15.24cm Length h/5* = .62 _ h/5* = 1.15 m •181 Plate with h = 2.54 mm I h = 1.g mm M = .203 h/,5* = .46 "'_h=1.1 mm M = .203 % • h/5" = .27 h = 1.9 mm, M = . 113, h/5" 50 _ ! = .40 "-- 40 30 .2 1 10 Frequency, Figure 94. TE-bluntness extensions (fig. 92(c)) 76 vortex-shedding attached. noise extracted from data 20 kHz of figure 93, data for untripped BL, and data with plate .3 I I I I I I I ] I I I i I i I I Limiting value,"4 .2 _ _ ref. 19 -_ Equation (72) "Q.. 03 Plate, ref. 19 J_ E : "1 c- t"I £ _ D _=14 .1 _ions 03 13_ I I I I I I I 1 ° [] A /1 "z"'--_ Airfoil TE extensions h = 2.54 cm h = 1.9 cm h= 1.1cm O V /"] Plate extensions h = 4.76 cm, 30.48 cm long h = 4.76 cm, 15.24 cm long h = 2.54 cm, 15.24 cm long I I I 1 = 12.5° I I I I 1 Thickness Figure 95. Peak Strouhal number for bluntness ratio, h/5* noise versus thickness ratio h/tf* determined from figure 94 and Blake (ref. 19). 180 170 m 160 "O _ 150 D_ O3 140 El. o 03 130 Key as per figure 95 120 110 [ _ _ _ 0 Figure 96. Peak scaled levels for bluntness I .5 _ _I _ J J 1 h/5* noise versus thickness ratio hi6* determined I 5 _ _ 0 from figure 94. 77 edgeextensionsfor the samethicknessratios. The levelsincreasewith increasingthicknessratios. The edgeextensiondata for the two smallerthicknesses of h = 1.1 and 1.9 mm at M -- 0.113 deviate most wings should be in the range where and scaling confidence is greatest. The Calculation TE are III for the plate extensions, _ = 0 °, in figures 97(b), respectively. The shapes reflect the tions that the spectra are sharper for the the same hi5*, and the spectra widen in frequencies for decreased h/5* values for plates and the edge extensions. The spectral 97(a) and observaplates for the lower both the curve fit is specified as the function G5(h/5*, _) whose peak level is 0 dB and whose shape is defined in terms of St m /S t m peak" The specification of G5 for in-between values of ko would be an interpolation between the limiting cases shown in figures 97(a) and 97(b). Procedures bluntness noise spectrum in a 1/3-octave presentation is predicted by ., (70) Stm ) Stpeak The directivity present Given the specification of the functions Stpeak and G4, a definition of the spectral shape completes the scaling. Spectral curve fits for the data of figure 94 are shown for the airfoil TE extensions, ko = 14 °, and from a straight line trend. Because of signal-tonoise concerns in the specification of these points, these data have the least confidence in the figure and are thus ignored in the specification of a curve fit. However, the accuracy of the resultant scaling equations in predicting these data is subsequently examined. The curve fits, designated as G4(h/5*, _), shown for the data are straight lines which are chosen to level off at h/_* = 5. The curve fit behavior at high h/6* is admittedly rather arbitrary, but there are no noise data available for guidance, unlike in the above Strouhal scaling where some frequency data from Blake are used. Fortunately, in practice, the likely values of h/_* to be found for rotor blades and 5.3.3. data function D h is given by equation (B1) in appendix Stm= B. The Strouhal definitions are (see fig. 95) f__hh U (71) and -1 ¢,m _peak 1 + -- 0.235 ( 0.1(h/6*vg The h/6avg thickness term is the ratio -2 h/5_vg 0.212)- ) + 0.095 of TE thickness - 0.0132 0.0045k0 h/f_vg ( (72) ) (0.2 - 0.00243k0 (degree < h/fiavg ) (h/6*vg of bluntness) h to the average < 0.2) boundary-layer displacement 6avg, where (73) _avg -- _ + _; 2 The angle k0 is the solid angle, in degrees, edge on a flat plate ko = 0 °, whereas for other TE geometries is discussed The peak level of the spectrum is determined = The shape of the procedure involves the 17.51og 169.7- from (,fv,st., ' _, sloping _ Stpeak ) the surfaces function + 157.5 upstream The = (C5)_v=oo of the - 1.114kO edge. for this For an parameter [(Gs)g=14o (74) (h/6avg < 5) (5 < h/_avg ) G5 (see figs. 97(a) and 97(b)) for k0 = 0 ° and 14 ° as follows: + 0.0714k0 trailing determination G4 (see fig. 96) where 1.114k0 spectrum is defined by the function an interpolation between the spectra G5 78 between ko = 14 ° for an NACA 0012 airfoil. in section 6 and appendix C. - (G5)_=o where o] the calculation (75) I 10 I 0 ' ' ' ' ' ''1 I ! I t I I l i t | ' I = (G5)_ ' I • = 14 o-10 dB -20 I ! -30.1 Strouhal (a) 10 (G5),_ = 0o I 0 1 I I I I ratio, St"'/St'p_ak • = 14 °. I I I I I I I I I I I I | i i I I I I -10 dB -20 - h /, , /, ,_ I -30.1 Strouhal I 10 1 ratio, St'"/St'l_ak (b) • = 0°. Figure 97. Spectral shape functions for TE bluntness noise. 79 where (7 < 70) 2.5k//1 - (rl/#) v/1.5625k I mTl+ - (G5)¢=14o 1194.997/2 -155.543_? (70 5 v < o) 2 - 2.5 (76) - 1.25 (0 < y < 0.03616) + 4.375 (0.03616 ttt 7/= < 7) Ill log(St /Stpeak (77) ) 0.1221 (h/6avg < 0.25) -0.2175(h/6_vg ) + 0.1755 (0.25 < h/6avg < 0.62) -0.0308(h/6_vg ) + 0.0596 (0.62 _< h/6avg < 1.15) (78) 0.0242 (1.15 < h/5*vg ) (h/6_vg < 0.02) 1.35 (0.02 < h/5_vg < 0.5) 308.475(h/6_vg ) - 121.23 (0.5 < h/6_vg < 0.62) 224.811(h/6_vg ) - 69.35 1583.28(h/5_vg ) - 1631.59 68.724(h/6_vg ) - (79) m (0.62 < h/6_vg < 1.15) (1.15 < h/5_vg < 1.2) 268.344 (1.2 < h/6:vg ) r/0 =-- _/ 6.25+m2# m2#4 2 (80) -2.5-mr/0 (81) and k=2.5 The spectrum but replacing (Gs)_=0o (h/6avg) is obtained by (h/Savg) equations (76) through (81), as one would for (G5)_=14 o, I where h 8O by computing 1- = 6.724 6aX-_g - 4.019 + 1.107 (82) 5.4.4. Comparison With Data and 99(a), there is no bluntness contribution. Overprediction is seen for the TBL TE noise at the lowest frequencies and some underprediction is appar- Noise spectra for the airfoil with different TE thicknesses (geometry of fig. 92(a)) are presented for the flow Mach numbers of M = 0.21 and 0.12 in ent in the higher frequencies speed. For the nonzero TE figures tained verting curves ness noise contributes to the total spectra at high frequencies and renders good comparisons with the data. Good agreement is found even for the aforementioned smaller thickness cases at low Mach num- noise 98 and 99, respectively. The data were obby digitizing the spectra of figure 93 and conthese to 1/3-octave levels. The prediction shown are those of TBL TE and bluntness sources. For the sharp TE of figures 98(a) ber (figs. 99(c) and for the thicknesses highest flow the blunt- 99(d)). 81 8O I -- 70 SPLv_ dB , I t I I 11 I I Data _r Totolpred[ction o TBL-TE suction I I I I I 80 I I| o TBL-TE pressure A Sel_oration ¢_ Bluntness side w o _*o o _ v ° ;'It o I I IIIJ I 40.2 1 Frequency, (o) 80 h = I I I I _0 II 20 m 5O d, I i Illll (c) One-third-octave I h = presentation I I I Data I III i J I llz -- 50 ;-__o -,i. o ; , 1.9 I of figure i 20 93 at I I I I III U = 40 2. side 69.5 ?* 0 II _r 2O kHz = 1.1 " J i,Jl I J m/s 70 I o TBL-TE pressure A Separation _ Bluntness O_.A i mm o i 1 Frequency, with ' side h ' ' .... ?*0 _ __ , ttj 10 -_ 20 kHz = predictions r_ 0 "A" 0 _r 0 "A" 0 _" 2.5 for I mm various ' ' degrees of bluntness. ' ' ''"1 60 _o " I I I I Ill I I I w ,j o I ' ' ' ''''I h I I:1 I tD i_r I 2O @ ' ' I Frequency, (b) h = 1.1 ' I I III I 60 50, 50 I I I I I i I I O_OW r, 30. 2 _ ' I I I ,o* I • , , , ,,il 1 presentation I'_" 10 Frequency, (C) h = 1.9 o 2O 30 P I 2 I I Illl (d) of figure 93 2O at U = 38.6 I 1 10 2O 1 1111 m/s with * o _" I 1 Frequency, kHz mm of spectra I _r o _r o _ o _ 0 r_ 40 0 W 0 _ I 10 kHz mm I i° r, " "_ Ib 70 i 60-- -- I 1 mm ' 0 ' lllt 30.2 kHz 0.0 0 _r 0 r, _r ow 10 = O__r 40 1 r. 82 I 10 r_ (d) o One-third-octave I _- _r 'R" 1_.. (o) 99. [ m mm I Frequency, Figure I )o I 40 I r, 50 30.,_ , h -- io w SPLva dB "A" 0 _r "A'_ kHz 40 70 I o ,A, W "R ,k SPL,/_ dB 0 0 0 ?*0,t_10 of spectra _) Total TBL-TEprediction suction 60 60 50 70 I 0 I lit o _r o_r 1 Frequency, - = II, 0 r_ .2 98. J (b) **oo J 0 80 ,k,l. 40 r, 1 Frequency, 70 --_ o I mm 0 Figure .= -- _I _ 40.2 kHz j 6O r, c= "k 70-- , ' ' ''"1 t_ r. 10 0.0 ' o 50 w o,k I ' .;;oO 60_ l ' ' ''"1 70 _o 60 5O SPLI/3 dB ' sid_ predictions h = kHz 2.5 for mm various degrees of bluntness. 6. Comparison of Predictions Published Results The scaling law predictions section with data from self-noise tions performed Center (UTRC). 6.1. Study at the United of Schlinker and With are compared in this studies of airfoil secTechnologies Research and Amiet span model is shown in figure 100. As in the present NASA Langley studies, the model was mounted on sidewalls and spanned the width of the open tunnel jet, so that the flow across the model was twodimensional. The nozzle providing the flow had a rectangular exit of dimensions of 29 cm × 53.3 cm. To isolate the TBL-TE noise from facility backnoise, a directional The experimental microphone configuration, system was illustrating the shear layer refraction effect on the TE noise received by the directional microphone, is shown in figure 101. The Mach numbers tested ranged from 0.1 to 0.5 and the tunnel angle of attack at varied from -0.4 ° (zero lift for this 6.1.1. Boundary-Layer Because only TBL desired, the boundary cambered airfoil) to 12 °. Definition TE noise measurements were layers were tripped by apply- ing thin serrated aluminum tape at the blade locations indicated in figure 100. The tape thickness was on the order of the BL displacement thickness at the points of application, providing minimum surface protrusion to avoid unnaturally large TBL thicknesses downstream. This "light" trip is in contrast to the present study where the trips were "heavy" for reasons discussed. Hot-wire measurements were made in the boundary-layer/near-wake region at the TE of the model. In figure 102, measured BL thicknesses are plotted versus Mach number for various tunnel angles of attack at. These data are from figure 17 of reference. 3. At zero lift, at = -0.4 °, in figure 102(a), the BL thicknesses 50 on the pressure and suction sides are approximately the same. This should be expected since they developed under approximately the same adverse pressure gradient. Included in figure 102(a) are corresponding values of BL displacement thicknesses, which were calculated by the present authors from velocity profiles presented in reference 3 (5" was not a quantity of interest in ref. 3). In figures 102(b) and 102(c), 8/c values are shown for at = 7.6 ° and 12 °, respectively. Comparing figures 102(a), 102(b), one can see that First, equations (2) and BL thickness ratio 8o/c ratio data Schlinker and Amiet (ref. 3) conducted tests in the UTRC Acoustic Research Tunnel to study TBLTE noise from a cambered helicopter blade section. The cross section of the 40.6-cm-chord and 53.3-cm- ground used. 102(c), as angle of attack in- creases, 6s increases and _p decreases. These measurements are compared with the thickness scaling equations of the present paper. _/c. To of figure (3) are used to calculate the and displacement thickness make the calculations 102(a), all calculated agree with the values of 6o/c and 6_/c were multiplied by a factor 0.6. This factor is taken to be the adjustment in equations (2) and (3) needed to make them appropriate for the "light" trip of reference 3. Next, the corrected angles of attack are determined by (1) adding 0.4 ° to at so that the tunnel angle is referenced to the zero-lift case and (2) using equation (1), with c = 40.6 cm and H = 79 cm, to obtain a. = 0 °, 3.9 ° , and 6.1 ° for at = -0.4 °, 7.6 °, and 12 °, respectively. These values of a. are now used in equations (8) and (11) to obtain t5p/8O and 8s/t5o, respectively. values of bs/c and 8p/c are compared in figures 102(b) and 102(c). 6.1.2. Trailing-Edge Predictions Noise The resultant with the data Measurements and Trailing-edge noise spectra in a 1/3-octave presentation are given in figure 103 for the airfoil at at = -0.4 ° with Mach number ranging from M = 0.1 to 0.5. The data were obtained by the directional microphone system at differing orientations to the airfoil. Shear layer corrections and directional microphone gain adjustments were made so that the data shown represent the noise radiated from a unit length of L = 0.3048 m of the TE span, at an observer distance of re = 3 m, and an observer angle be which is specified in the figure. Figures 104 and 105 contain spectra for the airfoil at at = 7.6 ° and 12 ° , respectively. The TBL-TE and separation noise spectra were predicted using the calculation procedures of the present paper. were calculated The values as described of a., in the 8_, and previous 6p used section. Because of the BL trips and the 2D flow, no LBL-VS or tip noise calculations were made. In performing the calculations for TE bluntness noise, one has to assign values of the TE thickness h and the TE flow angle parameter _. The thickness was indicated in reference 3 to be h = 0.38 mm but the shape of this small = 17 ° has gives reasonable TE region been used was not given. in the prediction prediction-data A value because of it comparisons. In figures 103 to 105, the predictions are compared with the measurements. As in the presentation of figures 11 to 74, the individual noise contributions are shown, along with the total summed spectra. The prediction-data comparisons are good, especially 83 Figure 100. Cross section of Sikorsky Open jet nozzle rotor blade (ref. 3). Span is 53.3 cm and chord length is 40.6 cm. Airfoil M=O f 4hear layer T acoustic rays -J_/ '_.._...__ Focal point microphone _- Directional microphone reflector Figure 101. UTRC experimental configuration directional microphone alignment. 84 of reference 3, showing the effect of tunnel flow and shear layer refraction on the .05 .04 0 Pressure [] Suction side 0.6 of that calculated equations _0 _0 c c side from of section 3 .03 '°'c .02 .01 5 0/c 0 (a) o_t= -0.4 ° (o_, = 0 °) .05 .04 i5s/C..._____ .03 C I1 _FL .02 © .01 I I I I (b) oct = 7.6 ° (o_, = 3.9 °) .05 5s/c [] [] 0 0 .04 6 .03 C .02 5p/C .01 o 0 I .1 0 C) I .2 Mach number, I I .3 .4 .5 M (c) oct= 12 ° (o_, = 6.1 °) Figure 102. equation Measured boundary-layer thickness at the TE of the Sikorsky airfoil (ref. 3). results of present paper, multiplied by 0.6 to account for light trip condition. Comparison is made with scaling 85 50 , - _,HIO Dot _r ToIol prediction 40 -- 0 TBL-TE suction side SPLI/_ , dB ' ' ' '""_ _o:*** ° __=7s4o 20 -- r. " I IIll 5 10 . 4 II_ I I I I ' ''"I ' ''''I ' ' ' ' ' '"I ,30 _ b t_ _" I _ _ i 40 20.4 ' 80 ' e e = 86.4 ° 60-- ' ' ee = 80.8 ° -_ I I -- _,. 13 - B 00_ -- r,, % "t I I _. 1 _' Frequency, kHz (0) U = 34.1 m/s 70 ' ''"I 4o-;*° _,, 10 ' .'.tL*. OW 1 ' *o*O_. ' 't IIll ' 50 -- 0 _ _. 0 r. I 60 a TBL- E pressure side & Seporotion " Bluntness i i ilil 10 Frequency, kHz (b) U = 68.1 m/s ' ''"I I i i ' ' ' ' ''"I 70 -- i i\i) 40 ' ' Oe = 93"8° -- __ _,o SPLII3 , 50,-_ 0 60 dB b 40 _ 0 -I I I ;o_ _r o,wb 0 SPLv3 , I I I I I I III I 1 A t, 40 I 4O 10 '''1 ' 70 '''' r, , , ,l,l .4 ,, _" u O0 0 -- , , " , a , ,,,l i 10 i 40 kHz (d) U = 146A m/s ' ¢r_ 50, , ,,J,l .4 1 " 1 Frequency, '''1 !| --t 8o f o.,, 0o o-.. dB C t_ 50 Frequency, kHz (c) U = 102.2 m/s 90|,' _ro0 o i III 30.4 o " o=o8.oo 1 • _ Pi,,l , P/ 10 40 Frequency, kHz (e) U = 170.3 m/s Figure 103. paper. 86 Noise spectra for Sikorsky airfoil at at = -0.4 ° (a, = 0°) from reference 3 compared with prediction of present 60 I I I I I - I I DotI _r Total prediction - ORT(_J_-TEsuction side 50 I 40 SPLI/5 , 30- I I I Ill E pressure I aI I TBLA Separation " Bluntness a _ ' 40 'L- [] ° [] o o o_ 30 40 10 Frequency. _. ,, b 20.4 ' A* A*. SPLI/3 , ' , , O _ 0 , -- o"%_ R, O O -'_[_ A , i,,,l c_ , o, 40 Frequency. kHz (b) U = 68.1 m/s ' ''"1 _ r_ _ 10 kHz ' ' "" 0 _B=_,_ 1 (o) U = 34.1 m/s ' ''''1 ' _ - ,,,,,I_, 1 6O ' ' '"1 Z_ . 70 ' A _ o o 20 .4 ' _ Oe = 75-4° n°° dB ' ''''1 side ee B0 I ' 70 = 86.4 ° ' ''''1 ' - ' ' ' ' '''1 _. ' ee=93.8 ' ° ;; o 5O _ -- dB o o[] oo_- D° 40 _ A ,, ,."_ o[]8 @ _ , Jl,II - _l -30.4 . ° ,, ,. o _ o:a ,,,ill 10 40 I .P 404 ' ' '''I ' ' ' , ,,..,I , o 10 40 Frequency. kHz (d) U = 146.4 m/s ' ' '"I 80 - 0 1 Frequency, kHz (c) U = 102.2 m/s 90 B- r, 0 , o p , ,_.,,I 1 50-0 ' ' ee = 98.0 ° - ."IF¢.. SPLv_ , 70 - ,, dB 601 o o °° o Lk 104. Noise o =:' __* o*_,_. Uo - O A so.4,°,,,,t Figure -- *goo_ _ , , , , _,_,,'i' 10 Frequency, kHz (e) U = 170.3 m/s 1 spectra ° _ for Sikorsky airfoil B B 0 ?,-,,= 40[ at a_ = 7.6 ° (_, = 3.9 °) from reference 3 compared with prediction of present paper. _o ,. '_:,L 60 ' ' ' '. '_,,'-'_,press're .'ide 80 • " Totolpredlctlon -- o TBL-TE suction side 70 SPLt/_ , 50 -8° 40 -- OOo ' ' ''"I ' ' ' ''"I ' I I ' A Separation " Bluntness o_** ee=80.8 ° -- _ /_ /_ t[ ee = 86.4° --_ / - dB A u O_,,_l_/_.__t O = =---_-_. [] a ° o ' , ,,,,I 3o.4 , ,, 1 ,,.,_,T^ 10 - _ 50-- [] 40 40 4 m Frequency. kHz (o) U = 68.1 m/s Figure 105. Noise spectra for Sikorsky airfoil at at = 12 ° (a, o , , ?.-_ - e __'- \1 , , ,;,,,,_ 1 _*_1 10 - 40 Frequency, kHz (b) U = 102.2 m/s = 6.1 °) from reference 3 compared with prediction of present paper. 87 considering that the predictions are based empirically on a different airfoil section and that the noise measurement methods were quite different. There does appear to be a mild overprediction of the TBL TE noise, although not consistently so. The extent of agreement in the spectra where the TE bluntness noise contributes is substantially due to the aforementioned choice of • = 17 ° (the previously used = 14 ° would result in a contribution about 3 dB higher 6.2. than that Study shown). of Schlinker The tests of Schlinker (ref. 26) were similar in design to that of reference 3, whose measurement configuration is shown in figure 101. The 2D airfoil model, however, was an NACA 0012 section (as in the present study) with a chord length of c = 22.9 cm. Again, the aim of the tests was to measure TBL TE and not LBL-VS noise. However, no BL trip was used at zero angle of attack because no LBL VS noise was identified (except for the lowest speed tested and those data were not presented). At (_t = 6 °, the LBLVS noise was pervasive so a trip was placed on the pressure side at 30 percent of the chord to eliminate the LBL VS noise. The TE noise spectra at various tunnel velocities are shown in figures 106 and 107 for the airfoil at at = 0 ° and 6 °, respectively. The data were processed so that the levels shown are for the full airfoil span of L = 53.3 cm and an omnidirectional observer positioned at re = 2.81 m and Oe = 90 °. For this airfoil, the corrected angles of attack, using equation (1) with c = 22.9 cm and H = 79 cm, are a, = 0 ° and 3.9 ° for at = 0 ° and 6 °, respectively. The predictions shown in figure 106 for zero angle of attack are for TBL-TE, LBL VS, and TE bluntness noise. The values of 50 and _ used in the predictions were obtained from equations (5) and (6), for an untripped BL airfoil. The predictions shown in figure 107 for cq = 6 ° are for only TBL TE, separation, and TE bluntness noise, since the LBL-VS noise was eliminated by the pressure side tripping. The required values of _ were calculated from equation (14), for an untripped BL. However, the values of _ were determined from equations (3) and (9), for a tripped BL and then multiplying the result by 0.6 (to reflect the "light" trip condition as discussed for the Schlinker and Amiet study). For the calculations for TE bluntness noise, there was no guidance from the paper for the specification of h and ko. A reasonable TE thickness of h -- 0.63 mm was assumed and the TE flow angle parameter was set at ko -- 23 °, because it gave good agreement for the high frequencies in figures 106 and 107. The overall agreement between the total predictions and the data appears good. 88 6.3. Study of Fink, Schlinker, and Amiet Fink, Schlinker, and Amiet (ref. 27) conducted tests in the UTRC tunnel to study LBL-VS noise from three airfoil geometries. The untripped BL airfoil models had an NACA 0012 planform and their geometries are shown in figure 108. The first had a constant-chord length of 11.4 cm across the span while the other two were spanwise tapered, having linearly varying chord lengths along the span. Of the tapered airfoils, the first had a taper ratio of 2 to 1 with chord length varying from 15.2 cm down to 7.6 cm. The other airfoil had a taper ratio of 4 to 1 with chord length varying from 18.3 cm to 4.6 cra. The span was L = 79 cm for all cases. Because the levels of the LBL-VS noise were sufficiently intense compared with the tunnel background noise, a directional microphone system was not used to measure the noise. Instead, far-field spectra were obtained with individual microphones placed on an arc of 2.25-m radius about the midspan of the models. The noise data from reference 27 which are presented in the present report are all from a microphone for which Oe ,-_ 90 °. Reference 27 presented most noise data in narrowband form at various bandwidths to allow exanfination of the tonal character of the LBL VS noise. To compare these data with the predictions of the present paper, the narrow-band data were digitized and converted to 1/3-octave presentations. As a check on this procedure, as well as a check on the consistency of the data presented in reference 27, overall sound pressure levels (OASPL) were computed from the digitized data and compared with overall levels reported from direct measurernent. The values generally agreed to within 1.0 dB. For the constant-chord octave spectra are shown airfoil at at = 4 °, 1/3in figure 109 for various tunnel velocities between U = 37 m/s and 116 m/s. The number of spectral bands, as well as the frequency range, presented for the spectra varies for the different speeds. This variation is due to the different narrow-band analysis ranges used in reference 27, as all available data were used to generate the 1/3octave band spectra. For U = 37 m/s, figure 109(a), the spectrum is fiat at the lower frequencies but is peaked between 1 and 3 kHz. From the narrow-band presentation of reference 27 (fig. 22), one finds that the fiat portion is dominated by broadband noise, which is characteristic of tunnel background contamination. It is noted again that these spectra are single microphone results from which the background noise has not been subtracted. The spectral peak region is due to the presence of three quasi-tones, representing the LBL-VS noise portion. At U = 52, 64, 60 60 I I I I I I I Dot • -" Totol 50 _" 0 I I I pred[ctlon TBL-TE suctlon side I I I I ' ''"1 " TBLE pressure Separation "0 LBL-VS Bluntness 5o-,k; _r oO 201 i ..4" 1 A " _llll r_ I I I I I IIII Frequency, U ' ' '"1 ' = I 40 ' , 50 dB ' . " o¢r O " 0 0 204 1 (b) m/s ' ' ' '"1 70 I ' 40 10 Frequency, ' ''"1 U = ' kHz 61.5 m/s ' ' ' ''"1 b b ' ' 60-- 60-- SPL1/3 0 kHz 44.3 ' ' _'"1 O 10 (o) 70 30"0 _O 0 ,_o O r_ "Or _ ' side 40 b _ ' I * - . *oO °: : 8o:' .koO_" _r ; _r 0 e 0 =, 40 , 3Q 0 r_ ,_ _ o_ O r. _,?II i i .'t" ' , ,,,I I .4 (c) 80 ' I i U ' '''1 i * * ,A0 -A" o _ 0 b = O ' ' 00_ _ 30 I I_l .4 40 lllll r_ [ I I (d) ' I IIII I I 10 Frequency, ' '''1 I 1 m/s ' 00# ,-, kHz 74.9 OO O_ro _, ( 10 Frequency, 4 o:- b _. /toO "A'O U : 40 kHz 91.9 m//s ' 70 SPLI/_ dB ' 60 50 -_. w o 404 , p,,,& 1 " . ,A, w'-o 0 , , , ,,,ill Frequency, (e) Figure 106. Noise spectra for NACA U = 0012 , 10 , ( 40 kHz 105.5 airfoil m/s at c_t = 0 ° (a, = 0 °) from reference 26 compared with prediction of present paper. 89 60 i i lwl / i I i - Dot •- Totol predlct_on 50 _ o TBL-TE suct;on side SPLI/3 , 40 -- I I I I I| o TBL-?E A Seporo|ion I pressure 60 I ' ' '_'1 ' ' ' ' ' '"1 ' ' side t_ Bluntness 50- 4o - _r dB o ° 30 --o _ "%0*" a • o._ . . ._,,s* 20.4_ I lllll o r , o A _-- ' ± ' ' _"'-_10 40 20.4 , ' ' '''l ' ' , dB 70, ' ' ' '''l 4o_ _ A o ° O , ,,,,I , o_" 10 '''''I ' 40 ' ' '''''I ' ' 5o _ It _r,,_ _ 0 [] _ 40_- ° i_ 30.4 _ _, ,,I , , , J la,10 l 1 . _ , Frequency, kHz 3o--' _' _'_ _ , ___ 40 ' ' '''I i ' ' ' ' '''I o b _, O g [] .4 ' , , ,,,,,t i l 1 O o o i 10 4O Frequency, kHz (d) U = 74.9 m/s (c) u = 61._ m/s ' 70 -SPL1/3 ; 60 5o- 80 _r 8* Frequency, kHz (b) U = 44..3 m/s 60 -SPL1/_ , 1 Frequency, kHz (o) U = 30.6 m/s 70 _ li , ,,_,_' i _ _ - 80 I m , ..... I ' ' ' ' .... I ' ' 70-- 60 60-- :oO dB m 50 o 0 [] , __,?,I 40.4 • ", , , i ,,,I 1 10 9 _ _W40 40 4 ,. P,_,, I = 90 Noise spectra for NACA 0012 airfoil at at = 6° (a, P, I I I r, _-*_,u_ O I I I 1 Frequency, kHz (e) U = 88.5 m/s Figure 107. paper. " !_ B III ^ 10 Frequency, I 0 [ 40 kHz (f) u = 105.5 m/s = 3.9 °) from reference 26 compared with prediction of present NACA 11.4-cm 0012 airfoils constant chord U 2:1 tapered _11.4 airfoil 5.2 7.6 4:1 tapered airfoil 4.6 8.3 I.. IFigure 79 108. Airfoil models of reference and 79 m/s, in figures 109(b), 109(c), and 109(d), the spectra are very peaked because of the dominating contributions from large numbers (10 to 15) of LBL-VS quasi-tones. At U = 98 and 116 m/s, in figures 109(e) and 109(f), the spectra are less peaked because of a somewhat decreased number of quasitones which become submerged within broadband background noise (which itself increases with speed). The strong velocity dependence seen clearly in figure 110 (from where the OASPL is plotted as a ity. The overall levels were directly noise between 200 Hz and 20 kHz, of the noise is fig. 25 of ref. 27) function of velocmeasured, for the rather than deter- mined by integrating measured spectra. The levels rise and then stabilize with increases in velocity. The resumed increase in levels at the highest speeds (approximately 100 m/s) is where the background noise appears to become dominant. Compared with the data in figures 109 and 110 are noise predictions of LBL-VS, TBL-TE, and separation noise. No consideration was given to bluntness noise because of the lack of information about the TE geometry as well as the fact that LBL VS noise dominates the predictions where comparative data are available. For the BL thickness determina- =- 27. All dimensions are in centimeters. tions, the equations of section 3 for ary layers were used. The corrected were calculated from equation (1), and H = 53 cm, which rendered for at = 0 ° and 4 °, respectively. ployed with the prediction equations at re = 2.25 m, Oe = 90 ° , and untripped boundangles of attack with c -- 11.4 cm a. = 0 ° and 1.9 ° These were emfor an observer (be = 90 ° . The predictions in figure 109 give good comparisons, except that the peak frequencies are lower than predicted. The previously described background noise contributions explain the differences for the lowest and highest speeds. For the predictions of OASPL in figure 110, the spectra for LBL VS, TBL-TE, and separation noise were summed. Predictions are presented for not only at = 4 ° but also at = 0 °, 2 °, and 6 ° . This is done to show the great sensitivity of the predictions to airfoil the data would most at _, 5 ° rather than angle of attack. It is seen that agree with predictions for about at = 4 °. This could be inter- preted to mean that possible experimental the agreement is on the order bias error in angle definition. of The tapered-chord airfoils were used in reference 27 to provide a continuous variation in expected vortex tone frequency to compare with an analogous rotating constant-chord blade. The tone variation 91 90 . . _ ,o__o,_ .'. _,ok o dB 60 ' __ 60 ,e 1 =0._ o .4 SPL41s . I \.. , t I ] 0 , _40 Frequency, .4 Frequency, k . (b_ U = 52.0 m/s "-' ,.u. ,u kHz 80 80 7 40 60_ .4 ° ,_ et 1 - _u 4 Frequency, ' 1 Frequency kHz, (,d) U - 79.0 m/s kHz (c) U = 64.0 m/s 100 s_,. o, _I00 _, _-' .... . ,oF __oo_ /. I I -_ _' ," _ / .1 -t ._ .__ 7°t- ". / i ,o FrequenCy, * " 60.4 1 Frequency, _o 40 _u4 I kHz (f) , °. "_ kHz 6.0 m/s U = 11 (e) U = 98.0 m/s 4° (a, Figure 109. Noise paper. 92 spectra for constant-chord airfoil at at = = 1'9°) from reference 27 compared with prediction of present 110 n 100 n i n I I II m m o 90 -- Data, 6o_ o_t = 4 --, h.ll_l__._... _ 40 -- 8O OASPL, dB 70 /' 60 Predictions / / ' / / 50 / / / 40 i J i i i i i 20 100 Velocity, Figure 110. of present Overall sound pressure level I versus velocity for constant-chord airfoil 200 m/s from reference 27 compared with predictions paper. 93 was found not to be continuous; however the tapered models did produce spectra containing a large number of peaks spread over a somewhat wider frequency range than those for the constant-chord airfoil at about the same velocities. In figure 111, 1/3octave spectra are shown for the 2-to-1 taper airfoil at at = 4 ° for tunnel velocities between U = 27 and 107 m/s. The data are similar to those for the constant-chord model, except that the peaks are generally less well defined. In figure 112, corresponding OASPL variations with tunnel velocity are shown for at = 4% Also in this figure, OASPL is shown for a range of velocities where at = 0 °. The predictions shown in figures 111 and 112 were obtained by dividing the models into 10 segments of constant chord (where actual chord length for each segment varied according to the blade taper), then making predictions for each segment, and summing on a pressure-squared basis the contributions of each. Angle-of-attack corrections for each segment were made by calculating the correction based on the mean chord (11.4 cm) across the span. This correction was then applied to the angle of attack for each of the blade segments. The corrected angles, therefore, 94 were the same as for the constant-chord model, that is, a, = 0 ° and 1.9 ° for at = 0 ° and 4 °, respectively. The comparisons between predictions and data for the 2-to-1 taper airfoil appear about as good as those for constant-chord comparisons. It appears that the predictions for OASPL at at = 4 ° (fig. 112) would best agree if at ,_ 3.5 ° had been used rather than 4% This again indicates that agreement is on the order of possible experimental angle definition error. The OASPL comparisons for zero angle of attack show the predicted trends to be quite good but the levels to be overpredicted by 5 to 7 dB. In figures 113 and 114 are the data and prediction comparisons for the 4-to-1 taper model at at = 0 °. The predictions are not as good as for the constantchord and the less tapered model, although the data still fall within a predictive range of at = 2 ° to 3% One should bear in mind that the flow behavior in the vicinity to deviate of the tapered models would be expected from the idealized 2D behavior assumed to be occurring over the small spanwise employed for the predictions. This makes to assess the meaning of the comparison for the tapered models. segments it difficult deviations 90 90 - 80 SPLI/5 Dat a pred|cUon -- O_ Total TBL-TE mucUon side '''"I ' A 0 5eporotlon LBL-VS I I I Ill I I I 80-- . 70-- dB 60 m m I 50.4 I I llll i 1 i 10 40 50.4 go , ,,, 'I ........ I I 90 I I I 10 4O ..... I ........ I I i 70 dB 60-- 60 i |) I I ' i@ll I0 kHz I i I I I I I Frequency, I I I Ill I u u i i mill I t ,,,,,, I 4O 50.4 , , , ,,,,,i I • I I I0 4O Frequency, kHz (d) U = 52.0 m/s (c) U = 40.0 m/s tO0 , i,,,,I 80 i 70-- 504 ' Frequency, kHz (b) U = 34.0 m/s 80-. ' m i i LI_I Frequency, kHz (o) U = 27.0 m/s SPLv5 ' TBL- E pressure side I i I I ! _! 90 lOo ' ''''I u u i i u iii I i i 90-t SPLI/5 . 7" 80-- 80-I dB _) 70-- • t I I fill 60.4 1 , , ,, ,,,i 70-- Q I I . m I i lO t 60.4 ' ''"I Frequency, kHz (e) U = 67.0 m/s 100 ''"'I I I I 1 f ill 100 I SPLI/3 , 90 I 90-- dB 1 i , _, i i i ill I , .... I 10 -- 7O 70 -- ,,,,,I ,. 8 ....... I 10 1 * , . m 40 Frequency, kHz (g) U : 88.0 elm 100 I kHz m/s 80 80-- Bo r,,,, 4O 10 Frequency, (f) U = 79.0 ' ''''1 i i i i lull 60.4 i iiii 1 , i I Frequency. kHz (h) U : 98.0 m/s I I I , , 90-- 80-SPLI/JdB ' $-_e 70-I 60.4 I , IIII F ? ® A,e, I lO 1 4o Frequency. kHz (1) U = 107.0 m/s Figure 111. Noise spectra present paper. for 2-to-1 tapered-chord airfoil at at = 4° (a, = 1.9 °) from reference 27 compared with prediction of 95 110 I i I I I I I I 100 o i f 9O 8O OASPL, dB / 7O o_t = 0 ° Predictions 6O °OOOoo =0 ° 5O 40 I 1 I I I I I 20 100 Velocity, Figure 112. predictions 96 Overall sound pressure of present paper. level I versus velocity for 2-to-1 tapered-chord 200 m/s airfoil from reference 27 compared with I 90 I I I I I / I I I I I II I 9o I [] TBL-'#E pressure side A Separation 0 LBL-VS Total prediction TBL-TE suction side 80 SPLI/s I °°, ' ''"I I I I I III I 80-- , 70-- dB 60-- 60 I I 50.4 1 10 4O I I IIII 50.4 1 90 , I I III I I I I I I 4O IO Frequency, kHz (b) U = 43.0 m/s Frequency. kHz (0) U = 30.0 m/s SPL1/3 I Ill 9o, '''"I I I 8O 80-- 70 70-- I I I I I I I I I I /2 ,e dB 60-- 60-- W_ "k I 50.4 90 SPL1/s , I I i i,,i,?. 10 Frequency, kHz (c) U = 55.0 m/s llll 1 I III I I _. I I I I I II 50 I 4O i,,,,l ,4 9o I 80 80-- 70 70-- dB '''"I I I I I I III I 60 -- 8 ,It I 50.4 go _r i I till 1 ' ''''I _" , II0,0,,I_ 10 Frequency. kHz (e) U = 70.0 m/s I I I I I I 40 Frequency, kHz (d) U = 61.0 rn/s I 60 10 I , I 40 50.4 I , _,t' IIII 0 IY#t.,TO.. 1 Y*, 10 40 Frequency, kHz (f) U = 79.0 m/s I I I 80-SPL1/s , 70-- dB * 60-_r _r*O000o I **n?,,,?,l I IIII 50.4 llr _r 1 08 10 ,, 40 Frequency, kHz (g) U = 88.0 m/s Figure 113. present Noise spectra for 4-to-1 tapered-chord airfoil at c_t = 0° (a, = 0 °) from reference 27 compared with prediction of paper. 97 110 I I I I J I II 100 9O 8O OASPL, ata, o_t = 0 ° dB a t = 0° 7O Predictions 60 5O 40 J I i l I iiI 20 100 Velocity, Figure 114. predictions 98 Overall sound pressure of present paper. level versus velocity for 4-to-1 tapered-chord 200 m/s airfoil from reference 27 compared with 7. Conclusions This paper documents the development of an overall prediction method for airfoil self-noise. The approach is semiempirical and is based on previous theoretical studies and data from a series of aerodynamic and acoustic tests of isolated airfoil sections. The acoustic data processing employed a correlation editing procedure to obtain self-noise spectra uncontaminated by extraneous noise. Five self-noise mechanisms, each related to specific boundary-layer phenomena, are identified in the data and modeled. For each mechanism, the data are first normalized by fundamental techniques using scaled aerodynamic parameters. The spectral shape, level, and frequencies are then examined and modeled for dependences on parameters such as Reynolds number, Mach number, and geometry. The modeling accuracy of the resulting self-noise prediction methods is established by comparing predictions with the complete data base. The methods are shown to have general applicability by comparing predictions with airfoil self-noise data reported in the literature from three studies. A successful application model cific of the methods helicopter rotor Conclusions self-noise is reported broadband can be drawn mechanisms. for a large-scalenoise test. regarding For the the speturbulent- boundary-layer trailing-edge noise and separation noise sources, an accurate and generally applicable predictive capability is demonstrated, especially for the important conditions of high Reynolds number and low to moderate angle of attack. The mechanism which can dominate the spectra for low Reynolds number, laminar-boundary-layer-vortexshedding noise, is also demonstrated to have good predictive capability. For this quasi-tonal noise mechanism, there are some issues, not fully addressed herein, about how to apply the formulations in the most appropriate way to different airfoil geometries. The tip vortex formation noise source appears to be well predicted, although its relative lack of importance compared with the other self-noise sources prevents a full assessment of accuracy. The trailing-edge-bluntness-vortex-shedding noise source is shown to be very important and predictable by the method developed. For this source, there is an associated "flow angle" parameter which is found to be constant for any given trailing-edge geometry, but is difficult to determine a priori. However, for application of the bluntness noise prediction method, reasonable estimates for this parameter can be made based on the examples in this report. The unique prediction capability presented should prove useful for the determination of broadband noise for helicopter rotors, wind turbines, airframe noise, and other cases where airfoil shapes encounter lowto moderate-speed flow. For modern propeller designs, the present equations should be applied with some caution because the high-speed, high-loading, and skewed-flow conditions existing about propeller blades do not match the low- to moderate-speed and generally 2D flow conditions of the present data base. The computer codes given herein can be readily incorporated into existing or future noise prediction codes. The documentation provided in this report should provide the means to evaluate where and how any needed future refinements can be made in the prediction codes for particular applications. NASA Langley Research Center Hampton, VA 23665-5225 April 19, 1989 99 Appendix A Data Processing Determination In section to determine models A.1. and Spectral 4, the special the self-noise was summarized. Data processing approach used spectra for the 2D airfoil Details Acquisition are given and Initial here. Processing Signals from the microphones shown in figure 4 were recorded during the test on a 14-channel FM analog tape recorder, operated to provide a fiat frequency response up to 40 kHz. Individual amplifiers were used to optimize signal-to-noise ratio for each microphone channel, and pure-tone and white-noise insertions were used to calibrate amplitude and phase response, respectively. conditioning techniques These calibrations were the same and signalas in refer- ence 2, where additional details are given. The data were reduced from tape on a spectrum analyzer interfaced with a minicomputer. Pairs of microphones were used to obtain 1024-point cross-correlations at an analysis range of +4.167 milliseconds. A.2. Correlation show how the folding was accomplished. The discrete center is at VTE, whereas the effective center is to the left. The correlation values at TTE + Av and rTE + 2 AT must not be changed to avoid modifying the shape near the very peak. The correlation value at rTE + 2 AT is projected to the LHS to intercept a line connecting TTE -- 3 Av and 7TE -- 2 AT. This defines the constants _ and b which are shown. These constants then are used to interpolate points on the LHS to determine on the RHS, that is R (r_rE + NAt) between values =b--_---R Ar (rTE-- at the NAt) + _--_rR (TTE -- (N+ for N > 2. folded about interpolation The entire LHS the effective scheme. Effective center the points of the peak 1)AT) (A1) correlation center using is this peak Editing center The correlation records are modified to eliminate contributions from extraneous noise sources prior to taking the Fourier transforms to obtain the spectra. The first step is to remove, to the extent possible, the noise from the test hardware by subtracting the correlation R45(r) without the airfoil in place (the background noise) from R45(T) with the airfoil in place. (See fig. 9.) The resulting record should then be comprised of correlation peaks from the desired TE noise, LE noise, and other extraneous noise related to interaction between the model and test rig not accounted for in the subtraction. The TE and LE noise peaks in the cross-correlation are assumed to represent the autocorrelation of the TE and LE noise, respectively. To eliminate the LE contribution, the correlation record on the right-hand-side (RHS) of 7"TE is discarded and replaced by the mirror image of the lefthand-side (LHS). However, for this folding process, it was found that it is important to preserve the basic shape of the TE peak to more accurately represent the spectra at higher frequencies. Because this is a digital correlation, made up of discrete points which are AT apart, it is likely that the true TE noise peak falls somewhere between two discrete values of T. Folding about a discrete point instead of the actual effective peak center would introduce error by distorting the peak shape. In figure A1, the discrete points of the TE correlation peak are illustrated to 100 TTE+2AT interpolation FoldedfromPOints /_ Or ig"ml a in points_ correlation _ _ Figure A1. Sample correlation A.3. tion and Separation of TE and _, / i peak. LE Peaks As indicated in section 4, for some of the correladata for the three smaller chord lengths, the LE TE peaks are so close that the LE contribution overlaps and distorts the TE peak shape. For many suchcasesa procedurewasfoundto successfully removethe distortionprior to implementingthe TE peakfoldingprocess described above.Thisprocedure is explainedby wayofexampleforthe 5.08-cm-chord airfoil shownin the bottom traceof figureA2. The predictedlocationsof the TE andLE noisepeaksin the correlations areindicatedandagreewellwith the peaksin the actualtrace.Notethe proximityof the two peaks. The procedureto separatethesetwo peaksinvolvescombiningthe originalR45(r) at the bottom of figure A2 with time-shifted versions of itself, so that the peaks are separated by larger time delays. The procedure depends on the implied symmetry of the LE and TE peaks, inherent in the assumption that they represent the autocorrelations for the LE and TE noise, respectively. The first step is to invert R45(7) in sign, and reverse it in time, by "flipping" the correlation about "rLE. The result of combining these two curves is seen in the second trace from the bottom of figure A2, denoted R_5(T ). The two peaks seen here are the original TE noise peak, and an inverted TE noise peak at 2"rLE - "rTE. There is some increase in level and some distortion in the correlation record away from the peaks, as should be expected. The LE noise peak has been removed, but the inverted TE noise peak still affects the original peak at rTE. To remove the inverted peak, the initial R45(v) must be shifted by 2(TLErTE ) and summed with the previous result. This produces the third t! curve from the bottom in figure A2, denoted R45(v ). The TE noise peak has remained at rTE , while the LE noise peak is now at 3rLE - 2TTE. The peaks are now separated in time so that details of each peak can be seen. Note that as the peaks no longer affect one another's shape, their basic symmetry is evident. This helps to validate the initial assumption that the peaks represent the autocorrelations of TE and LE noise. If the peaks must be further separated, this procedure can be successively repeated, with the results of the next two iterations seen in the top two Ill llll traces of figure A2, R45(r) and R45(r ). It should be noted that only the inner portion of the correlation is shown (the correlation was performed for ±4.067 ms). Because of the data record manipulations, much of the outer portions of the correlations did not overlap and were thus zeroed out. A.4. Once Determination the correlation of Spectra records, or their modified forms after the separation processing, are folded about the effective peak center, the resulting TE noise correlations are transformed into spectra of the noise. Because the correlation record lengths are reduced by varying amounts (typically 20 per- cent) because of the editing described above, the use of fast Fourier transform techniques is not convenient. Instead, regular Fourier transform techniques are used in an approach based on chapter 9 of reference 28. In summary, a data window is applied to the correlation (eq. 9.116, ref. 28) and is used to provide the real and imaginary portions of the spectrum (eqs. 9.167-9.168, ref. 28). The resulting crossspectra (eqs. 9.172 9.174, ref. 28) are presented in terms of magnitude and phase. With the cross-spectra produced, amplitude corrections are applied to account for shear layer effects, using the technique of Amiet (ref. 22), as well as selfnoise directivity effects, which are described in appendix B. The spectrum for each microphone pair was corrected to an effective position of 90 ° with respect to the airfoil chord line. The combined effec_ of both of these corrections tended to be small, with the corrections for many test conditions being less than 1 dB. Since cross-spectra were obtained, the corrections for each of the two microphones involved were averaged to correct the cross-spectral magnitude. The results obtained from this method are given in figure A3 for the example correlation records of figure A2. Figure A3(a) shows the cross-spectrum obtained from the correlation of the original R45(_-) record, which is the bottom curve of figure A2, while figure A3(b) shows the cross-spectrum obtained after folding the R45(T) record about the TE noise peak. Note that the cross-spectral phase ¢ is a partial indicator of how well the cross-spectrum represents the total TE self-noise. Ideally the phase should vary linearly with frequency, ¢ = 360°fTTn . The breaks seen in this phase line and the corresponding spectral peculiarities indicate regions adversely affected by contamination, which was not removed by the background subtraction and, in the case of figure A3(b), the folding process. The contamination from the LE is seen to primarily affect the cross-spectrum of figure A3(a) below around 4 kHz. Folding the correlation removes most of this, leaving a dip in the spectrum of figure A3(b) at about 1.5 kHz. Figure A3(c) shows the spectrum for the third curve from the hott? tom in figure A2, R45(r), which is the modified correlation after two manipulations have separated the TE and LE noise peaks. The phase difficulty and spectral dip at about 1.5 kHz in figure A3(b) are eliminated in figure A3(c). Figure A3(d) shows the spectrum llll for the top curve of figure A2, R45(T), which is for four manipulations. This spectrum is similar to that of figure A3(c) except for some apparent increase in contamination at the low- and high-frequency ends. For the airfoil presented here, a choice was made to use the spectrum of figure A3(c), based on two 101 .010 0 .010 .010 R45 ('r) 0 .010 R45 ('c) .010 Predicted , -.010 -2 I -1 , I:TE 1 f A 10 R45 ('t) Predicted R45 (2'tLE "c) I:LE , 0 1 , 1 2 ms Figure A2. Separation of TE and LE peaks in a cross-correlation. Example for the 5.08-cm-chord airfoil with tripped BL. a, = 0°, U = 71.3 m/s. 102 is cross-correlation between microphones M4 and M5 103 separation manipulations, to represent the self-noise. The lower and upper limits to which the spectrum is believed to be accurate are from about 0.8 to 13 kHz. nipulations was advantageous for about a quarter of the cases. The table shows that a substantial number of correlations were not folded. For airfoils at For the other airfoils of this paper, similar of the limits were made and the spectra beyond these limits in their presentation, in section 4. sufficiently high angles of attack, low frequencies can dominate the noise. This results in large correlation humps, rather than the relatively sharp peaks which are needed in the folding process. For these cases, the raw cross-correlations are transformed, with only the background subtraction being performed. Also the correlations were not folded in the presence of strong LBL-VS noise. This noise can dominate all other To increase confidence, all the evaluations are cut off as indicated 2D airfoil spectra presented in figures 11 to 74 were found by averaging independently determined spectra from two microphone pairs. After the shear layer and directivity corrections were applied, the spectra from the two microphone pairs generally agreed to within 1 dB. In tables 1 and 2, the data processing and manipulations, and whether the correlations were folded or not prior to taking the spectra, are specified for each test case. It is seen that for the three larger airfoils, no correlation manipulations were needed to separate the LE and TE correlation peaks. For the three smaller airfoils, performing two separation ma- 104 self-noise sources, as well as the LE noise contamination, negating the need for the correlation editing. This correlation editing would have proved difficult, in any case, since vortex shedding produces noise at small bands of frequencies, appearing as damped sinusoidals in the correlation, which tended to mask other peaks. The effect of folding such cases was examined, however, little effect on the spectra. the correlation in and found to have Appendix Noise plate B Directivity The purpose of this appendix is directivity functions D h and De, which in the tunnel noise data processing for use in the prediction equations for sources. B.I. Retarded to define the are employed and proposed the self-noise Coordinates The retarded coordinate system is explained by first referring to figure B1 where the airfoil is at zero angle of attack to the tunnel flow. If the velocity were zero everywhere, sound from the model which reaches the microphones (M2 is shown) would follow the ray path defined by the measured distance rm and angle Ore. But with the velocity in the free jet equal to U, the ray which reaches the microphones follows first the radiation angle ®c until it encounters the shear layer where it is refracted. It emerges at angle Ot with an amplitude change and travels to the microphone. The theoretical treatment employed in this study for the angle and amplitude corrections is that due to Amiet (refs. 22 and 23). A convenient reference for the corrected microphone measurements is a retarded coordinate system where the source and the observer are at corrected positions. The angle Oe is referenced to a retarded source position and a corrected observer position where the distance between the positions is re = rm. As defined, if there were no shear layer present with flow extending to infinity, the center of the wave front emitted from the source would be at the retarded source position when the wave front reaches the corrected observer position. The retarded coordinates are equivalent to the emission time coordinates employed in the literature, for example, see reference 29, for moving sources and stationary observers. Figure B2 shows a source flyover geometry corresponding to the open jet wind tunnel geometry of figure B1. Physical equivalence between the cases is attained by accounting for the Doppler-related frequency shifts due to the relative motion between the source and observer in one instance and no relative motion in the other. There are no Doppler-related corrections required between the flyover tunnel cases as the effect of the flow on definition is already environment. B.2. Directivity included in the amplitude and wind the source wind tunnel Functions In figure B3, a 3D retarded coordinate system is defined where the origin is located at the trailing edge of a thin flat plate, representing an airfoil. The flat is in rectilinear motion of velocity U in direction of the negative xe axis. The observer is stationary. Trailing-edge noise is produced when boundary-layer turbulence and its associated surface pressure pattern convect downstream (with respect to the plate) at a velocity Uc (Mach number Mc) past the trailing edge. If the noise-producing turbulence eddies are sufficiently small and the convection velocities are sufficiently large to produce acoustic wavelengths much shorter than the chord length, the directivity can and be shown to be Anfiet, ref. 3) -Dh(Oe'cbe) where the (based oil analysis of Schlinker 2 sin2(O_/2) sin2 ¢_ (B1) "_ (1 + McosOe)[1 + (M - M_) cos O,,] 2 h subscript indicates the high-frequency (or large-chord) limit for D. The overbar on indicates that it is normalized by the TE noise diated in the Oe = 90 ° and Be = 90 ° direction, Dh raso Dh(90 °, 90 °) = 1. For the flyover plane (Be = 90°), equation (B1) is the same as equation (32a) of reference 3. In reference 3, the equation was compared favorably with measured airfoil TE noise results, for limited M and Oe ranges, as well as with previous theoretical results. The directivity expression used in reference 2 was found to give virtually identical results for low Mach numbers. Although developed for when the velocity U is parallel to the plate along the xe axis, equation (B1) can be applied when the plate or airfoil is at an angle of attack a to the flow. In application (refer to fig. B3), one should define the angles with respect to a coordinate system that is fixed with respect to the airfoil with the xe axis fixed along the chord line, rather than one where the Xe axis is fixed along the direction of motion. Note, however, that any analysis of Doppler frequency shifts (not treated in this paper) should reference angles with respect to the direction of motion. Applications of equation (B1) at angles of attack should result in little additional error to that already built into the relation. Because it was derived with the plate assumed to be semi-infinite Dh becomes inaccurate at shallow upstream angles (Oe ---* 180°), when applied to finite airfoils even for high frequencies. As frequency is lowered, the wavelengths become larger with respect to the chord and the directivity becomes increasingly in error. However, D h should be of sufficient accuracy to define the directivity of all the self-noise sources discussed because of their high-frequency character. The one exception to this is the stalled-airfoil noise. When the angle of attack of the airfoil is increased sufficiently, the attached or mildly separated TBL flow on the suction side gives way to large-scale 105 Ray Path 5_ / _.. I vRetarded Source \_ Positiort \ r "_ \__E)., / _ / !@ -'_.__ Ray Path Position _y.,_Path 2 I 1_ V Ray Corrected Observer -Shear tltff Pat I Layer u:o u=u I Figure Position B1. Sketch of shear layer refraction of Source at Reception of acoustic Position Time _7 F ° U(t-T*) paths. of Source at Emission -- transmission Time 1"* - Path 4_ Moving _r Observer Reception 106 B2. Emission from a source moving with by Source e = C o (t-T*) _ Figure Taken a constant velocity. at Time t /%. / %. %. / \ / / %. / )l / I "_ / Ze / / t / Plate moves at velocity U \ ,I I / / / / Stationary observer / / f / / I t / Ye /_We Figure B3. Flat plate in rectilinear separation. The turbulence eddies are then comparable in size to the airfoil chord length and the eddie convection speeds are low. The directivity for this low-frequency noise is more properly defined as that of a translating dipole, which is sin 2 Oe sin 2 (I)e Dt(0e' J)e)_ (1 + M cos ee) 4 (B2) where the _ subscript indicates a low-frequency limit. The coordinate system and comments about angle definitions in equation (B1) apply also in equation (B2). Equation (B2) is employed for the directivity in the expression for stalled flow noise (eq. (30)). For the motion. noise data reduction in the present study, equation (B1) was used in the determination of the self-noise spectral levels for the reference observer position, at re = 122 cm and Oe = 90 ° • First, shear layer refraction corrections were calculated to determine the spectral level adjustments, to add to measured values, and a resultant source-observer location at re and (_e. This was done while keeping track of the actual physical coordinates of the trailing edge which varied with airfoil angle of attack. Finally, equation (B1), with (I) = 90 ° and an assumed convection Math number of Mc _ 0.8M, was used to determine final level adjustments required to match results to the Oe = 90 ° location. 107 Appendix C Application of Predictions Broadband An BO-105 Noise acoustics helicopter to a Rotor Test test of a 40-percent scale main rotor was conducted model in the German-Dutch Wind Tunnel (DNW). Figure C1 shows an overview of the test setup in the large open anechoic test section. The 4-meter-diameter rotor is shown positioned in the flow between the nozzle on the right and the flow collector on the left. A key aim of the test was to produce a large benchmark aeroacoustic data base to aid and verify rotor broadband noise prediction. compared data In reference 30, the present authors with predictions of rotor broadband self-noise for a number of rotor operating conditions. The predictions employed the self-noise prediction methods, which are documented in section 5 of the present paper, and the NASA ROTONET program (ref. 31) to define rotor performance and to sum contributions In this of noise from individual appendix, the experiment blade segments. is not reviewed in detail nor are data-prediction comparisons presented, as reference 30 is complete in this regard. Rather, reference 30 is complemented by specifying how the self-noise prediction methods of the present paper were applied. Given below is a summary of the rotor prediction method, a definition of the rotor blade geometry and test modifications and a specification of input parameters for the individual source predictions. The degrees of success of data-prediction comparisons in reference 30 are discussed along with recommended refinements to the prediction methods. To produce a rotor prediction, the rotor geometry definition and flight conditions, specified as thrust, rotor angle, rotor speed, flight velocity, and trim condition, are provided as inputs to the ROTONET rotor performance module. The particular module used assumes a fully articulated rotor with rigid blades and a simple uniform inflow model. The module determines local blade segment velocities and angles of attack for a number of radial and azimuthal positions. Ten radial segments were considered at 16 azimuthal positions. The BL thicknesses and other parameters needed are calculated. The noise due to each source is predicted the ROTONET noise sum contributions after accounting number of blades, for each radiation blade segment, and module is used to from all blade segments to obtain, for Doppler shifts and the actual the noise spectrum at the observer. As indicated in reference 30, the accuracy of predictions depends on a number of factors including the accuracy of the performance module used. One may question the quasi-steady assumptions used in 108 defining the local BL characteristics, which ignore unsteadiness and resultant hysteresis effects. Likely more important is how well the aeroacoustic scaling determined from low-speed data extends to higher speed. The Mach number at the tip of the blades is 0.64 for rotor hover, whereas the 2D airfoil model tests were limited to Mach 0.21. Also there are questions on how to apply scaling obtained symmetrical NACA 0012 sections with particular geometries to the cambered NACA 23012 rotor with different TE geometries. The model rotor is a 40-percent-scale, bladed, hingeless 4.0 m and a chord BO-105 of 0.121 rotor, with m. A blade from TE blade four- a diameter of and its details are shown in figure C2. The blades have -8 ° linear twist and a 20-percent cutout from the hub center. The effects of several blade modifications were examined, including (1) application from the blade leading edge match the BL trip condition of Carborundum grit to 20 percent chord to for the 2D blade sec- tions described in section 2 of the present (2) taping of the TE with 0.064-mm-thick paper, plastic tape to modify the "step tab" geometry, and (3) attachment of a rounded tip to each blade (the standard blades C.I. have a squared-off Boundary-Layer tip). Definition With the local blade segment mean velocities and angles of attack determined by the rotor performance module, the equations of section 3 were directly applied to determine the BL thicknesses required in the noise predictions. Most noise comparisons in reference 30 are for the blades with untripped BL. For the tripped BL, the fact that the BL trip conditions for the rotor blades matched the 2D test models assured the appropriateness of using the equations for a heavy trip rather than modifying the equations as required for the UTRC comparisons reported in section 6. For all BL thickness calculations, the aerodynamic angles of attack were used in the equations. The aerodynamic angle is referenced to the zero lift angle, which is -1.4 ° from the geometric angle for the NACA 23012 airfoil. C.2. TBL-TE Prediction and Separation Noise Given the definitions of segment chord length, span width, velocity, aerodynamic angle of attack, and BL thicknesses, the calculation of TBL-TE and separation noise is straightforward section 5. From the data-prediction reference 30, it is concluded that as specified comparisons the TBL-TE in of and separation noise calculations demonstrated a good predictive capability for these mechanisms. The rotor was tested from hover to moderately high flight am_ L-89-44 m DNW Figure C1. Test for helicopter main rotor broadband noise study reported in reference 30. setup FLAPPING SENSORS LAGGING SENSORS -,_ ] X__I - TORSION f \ ,40"0 TIP ROUNDING MOD7 -_:J" '_ :-7_'"'%"_o_ '_''" = ------- NACA 121mm SENSOR _._ , 2000 23012 CHORD C TRAILING Figure C2. Model BO-105 blade details• EDGE All dimensions MOD in mm. 109 speeds for various climb and descent rates at different thrust settings. Diagnostics included 1/2 rotor speed tests and the BL tripping tests. It is noted that the TBL TE and separation noise predictions for a number of rotor conditions fell below contributions of LBL-VS, especially at the 1/2 rotor speed, and of TE bluntness noise. This represents a limitation of the comparisons which prevents sweeping statements regarding predictive accuracy of TBL-TE and separation noise sources. Still the agreements were quite good except when the rotor operated at full speed (tip speed of M = 0.64) and the boundary layers were tripped. Then the noise was underpredicted by about 6 dB. It is believed that for this high speed the heavy trip disturbed the flow substantially, made it dissimilar to the 2D model cases, where the speed was limited to M = 0.21, and perhaps changed the controlling noise mechanisms. Comparisons for the tripped BL rotor at 1/2 speed and the untripped BL blades at full and 1/2 speed produced good results. C.3. LBL-VS Noise Prediction The comparisons for LBL-VS noise in reference 30 showed, for a broad range of rotor conditions, very good predictions. As with the TBL-TE and separation noise predictions, the calculation of LBL VS noise is straightforward given the specification of local flow conditions at the blade segments. A special note should be made for one key parameter involved in the calculations. The angle of attack c_, employed in the LBL VS noise prediction (eqs. (53) to (60)) was the geometric angle rather than the aerodynamic angle for the NACA 23012 airfoil section. The BL thickness calculations, however, used the aerodynamic angle, as previously stated. The use of the geometric angle for the noise calculation is justified by (1) the better rotor data-prediction comparisons found using the geometric rather than the aerodynamic angle and (2) the lack of guidance one has in applying the acoustic scaling laws which were based on symmetrical airfoil results, to airfoils that are cambered. Remember that the controlling mechanism of LBL VS noise is the presence of aeroacoustic feedback loops between the trailing edge and an upstream location on the airfoil surface where laminar instabilities occur. This geometric connection indicates that a purely aerodynamic angle definition for the LBL VS mechanism would not likely be correct. An alternate viewpoint of the angle definition problem would be that the aerodynamic angle should be used, which would increase the noise predicted over that measured, but that allowance should be made for the fact that the inflow to the rotor blade segments flow. The 110 is not the assumed smooth quasi-steady presence of sufficiently unsteady flow con- ditions over establishment portions of the of the rotor would LBL VS mechanism prevent the and related noise. Limiting LBL VS noise production measure of inflow turbulence offers promise finement to the self-noise prediction method. C.4. Tip Vortex Formation to some as a re- Noise The tip noise predictions were made for both the rounded and the squared-off blade tips tested. The performance module was used to determine the local flow velocities and angles for the tips at different azimuth locations. The _TIP used was the NACA 23012 aerodynamic angle. Because the tip loading characteristics for the rotor blades differed from the reference case of the tip noise model, which was an untwisted large-aspect-ratio blade with uniform flow over the span, the sectional lift term of equation (66) was evaluated. The sectional lift slopes for the rotor blades were analyzed by employing a lifting-surface model adapted from reference 18. The velocity and angle of attack were linearly varied over the span near the tip of the lifting surface blade. It was found that the tip loading is increased over the reference case by a small amount. For equation (66), the redefined _TIP angle was then given by ol_i P = 1.1O_Ti p. The predictions for tip noise in reference 30 were in all cases significantly below predictions for TBL TE noise. This makes it impossible to truly assess the accuracy of the tip noise modeling for the rotor. However, since the data comparisons with the total levels predicted were good for both low and normal rotor speeds, the tip noise is apparently well predicted. It is noted that a review of data for a number of rotor cases, not all given in reference 30, indicated no significant effect due to the blade tip modification. This is in line with prediction for this rotor. C.5. TE-Bluntness-Vortex-Shedding Noise Given the flow definition for the blade segments from the performance module, the bluntness predictions require the specification of thickness h and flow angle parameter ko. As with the UTRC test comparisons of section 6, it is not clear how to apply scaling laws obtained from an airfoil with a particular TE geometry to a rotor blade with a different TE. For the step tab TE geometry, shown in figure C2, h was specified as the actual 0.9 mm and ko was taken as 14 ° , which is actual solid angle of the surface at the TE of the NACA 23012 airfoil (same as the NACA 0012 airfoil). However, because of the 0.5-mm step 5 mm upstream of the TE, 0.5 mm was added to the calculated value of 5avg to approximately account for the anticipated step-caused BL flow deficit. For the TE tape modification case, bavg was taken as that calculated,becausethe stepwasremoved,but h was increased by four tape thicknesses. Had the tape remained fully attached to the TE surface (see fig. C2) during the test, two thicknesses would have been added. The flow angle if2 was taken as 18 °. The choice of this specific number was rather arbitrary, but is in line with that used for the UTRC comparisons (section 6) for rounded trailing edges. The tape rounded the TE bluntness which should reduce the persistence of and noise due to the separated flow in the near wake. The larger q angle value (18 ° compared with 14 ° ) results in less noise predicted. the ters The comparisons of reference 30 obtained using above "reasonable" choices for the TE paramegive good results for all 1/2 rotor speed cases. For the full rotor speed cases the levels were consistently overpredicted. This is believed to be due to a speed dependence for the bluntness mechanism that could not have been anticipated from the low speed airfoil data, from which the scaling laws were developed. Subsequent analysis indicates that nmch better agreement with data could have been obtained if the bluntness noise contribution was eliminated for blade segments exceeding Mach numbers of 0.45 or 0.5. This is in some conflict with comparisons in section 6 for the blade section noise of Schlinker and Amiet (ref. 3), which shows apparently strong bluntness noise at M = 0.43 and 0.5. However, based on the rotor results, an upper limit of 0.45 for the bluntness noise contribution is reconmmnded as a refinement to the prediction method. 111 Appendix D Prediction each noise mechanism followed by their total. The user selects which of the mechanisms to calculate. Code The airfoil self-noise prediction method is available as a computer code written in standard FORTRAN 5 specifically for the Digital Equipment Corp. VAX-11/780 series machine running under the VMS operating system. To the extent possible, the code has been made machine independent. There is one input file to the code and one output file. Input consists of user supplied NAMELIST parameters while output is a table of 1/3-octave centered frequencies with corresponding sound pressure levels for Table FORTRAN name D1. Segment Characteristics The airfoil section for which a prediction is desired is assumed to be composed of a number of segments, each having its own chord, span, angle of attack, freestream velocity, trailing-edge bluntness, and angle parameter, as well as observer directivity angles and distance. This permits a variety of configurations such as taper, twist, spanwise-varying free-stream velocity (for rotor blades), etc. The user may specify as many or few segments as desired depending on the complexity of the geometry. Characteristics for each segment are specified in the input file, which contains the FORTRAN variables given in table D1. Specified in Input File Symbol NSEG Description Number of segments C c Chord L L Span, R re Observer distance, THETA Oe Observer angle from x-axis, deg PHI _e Observer angle from y-axis, deg ALPSTAR length, m m Aerodynamic angle of attack, ALPHTIP ! oTIP Tip H h Trailing-edge bluntness, PSI _P Trailing-edge angle, U U ITRIP flow ILAM velocity, untripped Use tripped BL lightly tripped 1 IBLUNT IROUND BL Compute LBL not compute Compute 0 Do 1 Compute 0 Do Kinematic CO Co Speed tip sound, noise TE TE noise noise noise TE bluntness noise noise tip noise rounded tip square tip viscosity, of TBL bluntness compute Use VS TBL compute not condition noise LBL TE not • TaUt. v BL VS compute • VALSE.--Use VISC condition condition turbulent not 1--Compute ITIP m/see Use 0--Do m deg 1 1 deg deg 0- 0--Do ITURB angle, Free-stream 2-Use 112 In m/sec m2/sec in tip in tip calculation calculation Thepredictionshownin figure45(a)wasobtained usingthefollowinginput: $INDATA NSEG = 1, C L R THETA PHI ALPSTAR U ITRIP ILAM ITURB SEND = = = = = = = = = = .3048, .4572, 1.22, 90., 90., 1.516, 71.3, 0, I, 1, ITRIP ILAM ITURB ITIP ROUND SEND This Note that all parameters need not be included in the input if their default values are desired (see program listing for default values). In this example, only the laminar and turbulent mechanisms are computed and the untripped boundary layer condition is used in both mechanisms. The airfoil consists of one segment of constant chord and the observer is 122 cm directly beneath the trailing edge at the midspan. The freestream velocity has a constant value of 71.3 m/sec across the span. For this example, the output file is given in table D2. Similarly, the prediction obtained using the following $INDATA NSEG C L = = = 10., I0.. 1524 10..0305 R THETA PHI ALPSTAR ALPHTIP U shown input: in figure 91, was = = = = = = 10. 10. 10. 10. 7.7, 10. = = = = = 1, O, i, I, .TRUE., is an example 1.22, 90., 90., 5.4, 71.3, of a multisegmented case where each segment has the same geometry and inflow conditions. Turbulent-boundary-layer noise and tip noise are calculated where the tip is rounded and at an effective angle of attack of 7.7 ° . All segments are summed to yield a total prediction for each mechanism as shown in table D3. For the VAX-11/780 machine running under VMS, the following commands will compile, link, and execute the code (assumed to reside on PREDICT.FOR), read input from a file EXAMPLE.IN, and write results to a file EXAMPLE. OUT: $ FOR PREDICT $ LINK PREDICT $ ASSIGN EXAMPLE.IN $ ASSIGN EXAMPLE.OUT $ RUN PREDICT FORO04 FORO05 The detailsof execution forother machines or operating systems may vary. A listingof the code follows. 113 TableD2. OutputFile FromPredictionCodefor TestCaseof Figure45(a) ONE-THIRD SOUND PRESSURE FREQUENCY{HZ) SUCTION SIDE TEL SIDE OCTAVE PRESSURE LEVELS SEPARATION TEL SIDE THL LAMINAR BLUNTNESS TIP TOTAL ................................................................................................................ I00.000 20.654 28.704 -i00.000 -17.142 0.000 0.000 29.336 125.000 24.461 31.965 -100.000 -13.285 0,000 0.000 32.676 160.000 28.291 35.244 -75.254 -%.018 0.000 0.000 36.042 200.000 31.437 37.937 -49.243 -5.161 0.000 0.000 38.815 250.000 34.309 40.400 -27.506 -1.304 0.000 0.000 41.356 315.000 37.023 42.736 39.577 44.949 41.761 46.859 17.532 10.677 0.000 0.000 48.034 630.000 43.845 48.706 26.603 14.671 0.000 0.000 49.954 800.000 45.839 50.503 33.718 18.801 0.000 0.000 i000.000 47.581 52.106 38.756 22.658 0.000 0.000 53.568 1250.000 49.233 53.664 42.692 26.515 0.000 0.000 55.255 1600.000 50.987 55.368 46.294 30.782 0.000 0.000 57.106 2000,000 52.533 56.907 49.334 37.725 0.000 0.000 58.817 2500.000 54.074 57.750 51.298 47.262 0.000 0.000 60.167 3150.000 55.570 57.500 50.766 48.959 0,000 0.000 60.496 4000.000 56.044 56.082 47.711 41.796 0.000 0.000 59.455 5000.000 55.399 54.541 44.617 0.000 0.000 58.208 6300.000 53.840 52.942 40.974 28.433 0.000 0.000 56.553 B000.000 52.190 51.253 36.227 24.304 0.000 0.000 54.821 i0000.000 50.638 49.614 30.419 20.447 0.000 0.000 53.192 12500.000 49.044 47.890 22.834 16.590 0.000 0.000 51.523 16000.000 47.202 45.851 11.842 12.323 0.000 0.000 49.591 20000.000 45,436 43.863 8,466 0.000 0.000 47.731 25000.000 43.549 41.710 -16.833 4.609 0.000 0.000 45.737 31500.000 41.440 39.279 -37.092 0.614 0.000 0.000 43.503 40000.000 39.065 36.522 -62.593 400.000 500.000 Table D3. -9.030 2.690 6.266 6.820 32.428 -0.924 Output File From -3.515 Prediction ONE-THIRD SOUND PRESSURE FREQUENCY{HZ) SIDE SUCTION THL SIDE .......................................... 0.000 0.000 for Test 43.768 46.057 51.849 0.000 Case of Figure 40.987 91 LEVELS SEPARATION THL SIDE TBL LAMINAR BLUNTNESS TIP TOTAL ...................................................................... 19.913 43.883 125.000 23.788 46.159 160.000 27.673 48.459 16.851 200.000 30.853 50.372 250.000 33.746 52.155 315.000 36.470 53.894 -19.803 0.000 0.000 -34.005 43.900 0.000 0.000 -24.312 46.184 0.000 0.000 -14.255 48.498 29.124 0.000 0.000 38.723 0.000 0.000 2.145 52.407 46.334 0.000 0.000 9.738 39.024 54.662 55.609 52.245 0.000 0.000 16.940 57.320 57.165 56.460 0.000 0.000 23.074 59.897 -0.396 -5.769 50.452 500.000 41.202 630.000 43.274 58.766 59,996 0.000 0.000 28.824 62.489 800.000 45.252 60.360 63,297 0.000 0.000 34.121 65.130 46.980 60.940 65.719 0.000 0.000 38,475 67.016 48.620 60,473 65.697 0.000 0.000 42,257 66.917 1600.000 50.364 58.874 62.909 0.000 0.000 45.774 64.582 2000.000 51.911 57.328 59.818 0.000 0.000 48,349 62.363 2500.000 53.456 55.775 56.383 0.000 0.000 50.351 60.580 3150.000 54.709 54.122 51.975 0.000 0.000 4000.000 54.799 52.336 45.974 0.000 0.000 5000.000 53.761 50.565 38.550 0.000 0.000 52.917 6300.000 52.162 48.597 28.510 0.000 0.000 52.544 8000.000 50.507 46.387 15.081 0.000 0.000 51.512 54.736 I0000.000 48.936 44.132 0.000 0.000 49.955 53.078 12500.000 47.311 41.665 0.000 0.000 47.826 51.110 16000.000 45.415 38.655 -46,603 0.000 0.000 44.802 48.594 20000.000 43.583 35.650 -75.275 0.000 0.000 41.466 46.075 25000.000 41.611 32.347 -90.000 0.000 0.000 37.557 43.405 31500.000 39.390 28.582 -90.000 0.000 0.000 32.904 40.555 40000.000 36.873 24.291 -90.000 0.000 0.000 27.449 37.552 I000.000 1250.000 114 0.000 0.000 OCTAVE PRESSURE I00.000 400.000 Code 0.000 -0.755 -20.241 51.821 52.694 59.364 58.443 57.439 56.204 0001 PROGRAM PREDICT 0002 0003 0004 0005 ***** 0006 ................................ VARIABLE DEFINITIONS ***** 0007 0008 VARIABLE NAME DEFINITION UNITS 0009 0010 0011 ALPHTIP TIP 0012 ALPSTAR SEGMENT ANGLE 0013 ALPRAT TIP 0014 C SEGMENT 0015 CO SPEED 0016 FRCEN 1/3 0017 H SEGMENT 0018 IBLUNT FLAG 0019 ILAM FLAG 0020 ITIP 0021 OF ATTACK ANGLE LIFT OF CURVE DEGREES ATTACK DEGREES SLOPE CHORDLENGTH OF METERS SOUND OCTAVE METERS/SEC CENTERED FREQUENCIES HERTZ TRAILING EDGE TO COMPUTE BLUNTNESS TO COMPUTE LBL NOISE --- FLAG TO COMPUTE TIP NOISE --- ITRIP FLAG TO TRIP 0022 ITURB FLAG TO COMPUTE 0023 L SEGMENT SPAN 0024 MAXFREQ MAXIMUM NUMBER OF FREQUENCIES --- 0025 MAXSEG MAXIMUM NUMBER OF SEGMENTS --- 0026 NFREQ NUMBER OF 1/3 0027 NSEG NUMBER OF SEGMENTS 0028 P1 PRESSURE 0029 NOISE TBLTE METERS OCTAVE FREQUENCIES NT/M2 P3 PRESSURE ASSOCIATED WITH P4 TBLTE PRESSURE PREDICTION ASSOCIATED WITH P5 TOTAL PRESSURE PREDICTION ASSOCIATED WITH P6 PRESSURE P7 PRESSURE 0042 PHI DIRECTIVITY 0043 PSI BLUNTNESS 0044 R SEGMENT 0045 ROUND LOGICAL 0046 SPL TOTAL SOUND 0047 SPLALPH SOUND PRESSURE SPLBLNT SOUND SPLLBL SOUND SPLP SOUND SPLS SOUND SPLTBL TOTAL SPLTIP SOUND 0061 ST STROUHAL 0062 THETA DIRECTIVITY 0063 U SEGMENT 0064 VISC KINEMATIC ASSOCIATED TBLTE 0033 0034 0035 0036 0037 0039 0041 TIP 0048 0050 0052 0054 0056 TO 0058 0060 NT/M2 ANGLE DEGREES DEGREES OBSERVER DISTANCE ROUNDED PRESSURE TBLTE LEVEL BLUNTNESS LBL DB DB ASSOCIATED DB ASSOCIATED PREDICTION DB LEVEL TBLTE ASSOCIATED PREDICTION PRESSURE LEVEL TBLTE DB ASSOCIATED PREDICTION PRESSURE LEVEL TBLTE DB ASSOCIATED PREDICTION PRESSURE LEVEL NOISE --- ASSOCIATED PREDICTION LEVEL PRESSURE TIP TIP PREDICTION PRESSURE WITH METERS LEVEL LEVEL PRESSURE WITH 0059 PREDICTION INDICATING WITH 0057 NT/M2 WITH ANGLE WITH 0055 NT/M2 WITH PREDICTION NOISE WITH 0053 NT/M2 ASSOCIATED WITH 0051 NT/M2 ASSOCIATED WITH 0049 NT/M2 PREDICTION BLUNTNESS 0040 WITH PREDICTION LBLVS 0038 --- WITH PREDICTION PRESSURE 0032 --- NOISE LENGTH P2 0031 METERS LAYER ASSOCIATED TBLTE 0030 BOUNDARY THICKNESS DB ASSOCIATED PREDICTION DB NUMBER -- ANGLE FREESTREAM DEGREES VELOCITY METERS/SEC VISCOSITY M2/SEC 0065 0066 0067 PARAMETER (MAXSEG = 20, MAXFREQ = 27) 0068 0069 0070 FRCEN(MAXFREQ) ,C(MAXSEG) L(MAXSEG) 0071 I DIMENSION ST(MAXFREQ) ,SPLLBL(MAXFREQ) SPLTBL(MAXFREQ) 0072 2 U(MAXSEG) ,SPLP(MAXFREQ) SPLS(MAXFREQ) 0073 3 SPLALPH(MAXFREQ) ,SPL(7,MAXFREQ) R(MAXSEG) 0074 5 SPLBLNT(MAXFREQ) ,PHI(MAXSEG) SPLTIP(MAXFREQ) 0075 7 THETA(MAXSEG) ,ALPSTAR(MAXSEG) PSI(MAXSEG) 115 0076 8 H(MAXSEG) ,PI(MAXFREQ) ,P2(MAXFREQ) 0077 9 P3(NAXFREQ) ,P4(MAXFREQ) ,P5(MAXFREQ) 0078 1 P6(MAXFREQ) ,P7(MAXFREQ) 0079 0080 0081 REAL L 0082 LOGICAL ROUND 0083 0084 DEFINE 0085 ....................................... DEFAULT VALUES FOR NAMELIST DATA 0086 0087 0088 DATA C / MAXSEG*I.0 0089 DATA L / MAXSEG*.I0 0090 DATA R / MAXSEG * 1. / 0091 DATA THETA / MAXSEG * 90. / 0092 DATA PHI / MAXSEG * 90. / 0093 DATA ALPSTAR / MAXSEG * 0.0 / 0094 DATA H / MAXSEG * .0005/ 0095 DATA PSI / MAXSEG * 14.0 / 0096 DATA U / MAXSEG * 100. / 0097 DATA ITRIP / 0 / 0098 DATA ILAM / 0 / 0099 DATA ITURB / 0 / 0100 DATA IBLUNT / 0 / 0101 DATA ITIP / 0 / 0102 DATA ALPHTIP / 0.0 / 0103 DATA NSEG / 0104 DATA VISC / 1.4529E-5 / 0105 DATA CO / 340.46 / 0106 DATA ALPRAT / 1.0 / 0107 DATA ROUND / DATA NFREQ / / / i0 / .FALSE. / 0108 0109 27 / 0110 0111 SET 0112 ................................................ UP VALUES OF 1/3 OCTAVE CENTERED FREQUENCIES 0113 0114 DATA FRCEN / 100 125. , 160. , 200. , 250. , 315 400. , 500. , 630. , 800. , 0115 1 0116 1 1000 1250. , 1600. , 2000. , 2500. , 0117 3 3150 4000. , 5000. , 6300. , 8000. , 0118 2 10000 12500. 0119 3 31500 40000. ,16000. ,20000. ,25000. / 0120 0121 0122 C ,L R 0123 1 THETA ,PHI ALPSTAR 0124 2 H ,PSI U 0125 1 ITRIP ,ILAM ITURB 0126 2 IBLUNT ,ITIP ROUND 0127 3 ALPHTIP ,NSEG C0 0128 4 VISC NAMELIST /INDATA / 0129 0130 0131 0132 READ 0133 ................................................... IN NAMELIST DATA AND ECHO INPUT TO OUTPUT 0134 0135 OPEN(UNIT=4, 0136 READ(4,INDATA) STATUS = 'OLD') STATUS = 'NEW') 0137 0138 OPEN(UNIT=5, 0139 WRITE(5,INDATA) 0140 0141 0142 INITIALIZE 0143 PRESSURE 0144 ............................................ ALL LEVELS 0145 0146 DO 6001 I=I,NFREQ 0147 PI(I) = 0.0 0148 P2(I) = 0.0 0149 P3(I) = 0.0 0150 P4(I) = 0.0 116 PREDICTED TO PRESSURES ZERO AND SOUND FILE , 0151 e5(i) = 0.0 0152 P6(i) = 0.0 0153 p7(i) = 0.0 0154 0155 DO 6002 0156 J=1,7 SPL(J,I) 0157 6002 0158 6001 = 0.0 CONTINUE CONTINUE 0159 0160 0161 C FOR 0162 C TO 0163 C THE 0164 C EACH BLADE THE SEGMENT, MECHANISMS LAST MAKE A SELECTED. SEGMENT NOISE TIP PREDICTION NOISE IS ACCORDING PREDICTED FOR ONLY. 0165 0166 DO 6000 III=I,NSEG 0167 0168 IF (ILAM .EQ. i) 0169 1 0170 2 THETA(III),PHI(III),L(III),R(III),NFREQ, 0171 3 VISC,C0) CALL LBLVS(ALPSTAR(III),C(III),U(III),FRCEN,SPLLBL, 0172 0173 IF (ITURB CALL .EQ. I} 0174 1 TBLTE(ALPSTAR(III),C(III),U(IIi),FRCEN,ITRIP,SPLP, 0175 1 SPLS,SPLALPH,SPLTBL,THETA(III),PHI(III),L(III),R(III], 0176 2 NFREQ,VISC,C0) 0177 0178 IF (IBLUNT .EQ. 1) 0179 1 0180 1 THETA(III),PHI(III),L(III),R(III),H(III),PSI(III), 0181 2 NFREQ,VISC,C0) CALL BLUNT(ALPSTAR(III),C(III),U(III) ,FRCEN,ITRIP,SPLBLNT, 0182 0183 IF 0184 1 0185 2 ((ITIP .EQ. CALL 1) .AND. (III .EQ. NSEG)) TIPNOIS(ALPHTIP,ALPRAT,C(III},U(III),FRCEN,SPLTIP, THETA,PHI,R(III),NFREQ,VISC,C0,ROUND) 0186 0187 0188 C ADD 0189 C PRESSURE IN 0190 C THIS SEGMENT'S CONTRIBUTION ON A MEAN-SQUARE BASIS 0191 0192 DO 989 I=I,NFREQ 0193 0194 IF 0195 (ILAM .EQ. P5(I) 0196 = P5(I) I) THEN + 10.**(SPLLBL(I)/10.) ENDIF 0197 0198 IF (ITURB .EQ. I) THEN 0199 PI(I) = PI(I) + 10.**(SPLP(I)/10. ) 0200 P2(I) = P2(I) + 10.**(SPLS(I)/10. ) 0201 P3(I) = P3(I) + 10.**(SPLALPH(I)/10.) = P6(I) = P7(I) 0202 ENDIF 0203 0204 IF 0205 (IBLUNT .EQ. P6(I) 0206 1) + THEN 10.**(SPLBLNT(I)/10.) ENDIF 0207 0208 IF 0209 ((ITIP .EQ. P7(I) 0210 i) + .AND. (III .EQ. NSEG)) THEN 10.**(SPLTIP(I)/10.) ENDIF 0211 0212 0213 C 0214 C COMPUTE TOTAL PRESSURE FOR THE SEGMENT FOR ALL MECHANISMS 0215 0216 P4(I) = PI(I) + P2(I) + P3(I) + P5(I) + P6(I) + P7(I) 0217 0218 989 0219 6000 CONTINUE CONTINUE 0220 0221 C CONTRIBUTIONS 0222 C COMPUTE SOUND 0223 C FOR TOTAL 0224 C THE FROM PRESSURE ALL SEGMENTS LEVELS ARE FOR NOW EACH ACCOUNTED MECHANISM FOR. AND 0225 117 0226 DO 6003 I=I,NFREQ .NE 0 SPL(I,I) = I0 *ALOGIO Pl(i) (P2(I .NE 0 SPL(2,I) = I0 *ALOG10 P2(I) IF (P3(I .NE 0 SPL(3,I) = I0 *ALOGIO P3(I) 0230 IF (P4(I .NE 0 SPL(4,I) = i0 *ALOG10 P4(I) 0231 IF {P5(I .NE 0 SPL(5,I) = I0 *ALOGI0 PS(I) 0232 IF (P6(I .NE 0 SPL(6,I) = I0 *ALOG10 P6(I) 0233 IF (P7{I .NE 0 SPL(7,I) = I0 *ALOGI0 P7(I) 0227 IF (PI(I 0228 IF 0229 0234 6003 CONTINUE 0235 0236 WRITE 0237 OUTPUT FILE 0238 0239 0240 WRITE(5,7000) 0241 DO 0242 6005 I=I,NFREQ 0243 WRITE(5,7100) 0244 (SpL(J,I),J=I,3), IF 6005 (SPL(J,I),J=5,7), SPL(4,I) 0246 0247 FRCEN(I), 1 0245 (MOD(I,5) .EQ. 0) WRITE(5,7200) CONTINUE 0248 0249 7000 FORMAT(IHI,52X, 'ONE-THIRD 0250 1 0251 2 0252 3 0253 4 ' 0254 0255 5 6 ' ' 0256 7 ,,, ' 5X,' SUCTION 0258 7100 FORMAT(8FI5.3) 0259 7200 FORMAT(' 0260 8000 FORMAT(I3) 0261 8002 FORMAT(4110) 0262 0263 0264 STOP 0265 END ') SIDE TBL LAMINAR TIP PRESSURE PRESSURE ',' FREQUENCY(BZ) /,5X,8( 0257 118 OCTAVE',/,50X,'SOUND ////,5x,' ', SEPARATION '/, ', ' SIDE TBL ', ', ' SIDE TBL ', ',' ',' ................ BLUNTNESS TOTAL ),/) i' , LEVELS' OO01 SUBROUTINE 0002 LBLVS(ALPSTAR,C,U 1 ,FRCEN,SPLLAM,THETA,PHI,L,R, NFREQ,VISC,C0) 0003 0004 PARAMETER (MAXFREQ = 27) 0005 0006 0007 0008 C 0009 C ***** 0010 C ................................ VARIABLE DEFINITIONS ***** 0011 0012 C 0013 C VARIABLE DEFINITION NAME UNITS 0014 0015 0016 C ALPSTAR 0017 C C CHORD ANGLE LENGTH OF ATTACK DEGREES 0018 C C0 SPEED OF 0019 C D REYNOLDS 0020 C DBARH HIGH 0021 C DELTAP PRESSURE 0022 C 0023 C DSTRP PRESSURE 0024 C 0025 C DSTRS SUCTION 0026 C 0027 C E STROUHAL 0028 C FRCEN 1/3 0029 C G1 SOUND 0030 C G2 OVERALL 0031 C 0032 C G3 OVERALL 0033 C 0034 C ITRIP FLAG 0035 C L SPAN 0036 C M MACH 0037 C NFREQ NUMBER 0038 C OASPL OVERALL 0039 C PHI DIRECTIVITY 0040 C R OBSERVER DISTANCE 0041 C RC REYNOLDS NUMBER 0042 C RC0 REFERENCE REYNOLDS 0043 C SCALE GEOMETRIC SCALING 0044 C SPLLAM SOUND 0045 C 0046 C 0047 C 0048 METERS SOUND METERS/SEC NUMBER RATIO FREQUENCY DIRECTIVITY --- SIDE BOUNDARY LAYER SIDE BOUNDARY LAYER THICKNESS METERS DISPLACEMENT THICKNESS SIDE BOUNDARY DISPLACEMENT METERS LAYER THICKNESS NUMBER OCTAVE METERS RATIO --- FREQUENCIES PRESSURE HERTZ LEVEL FUNCTION SOUND PRESSURE LEVEL SOUND PRESSURE LEVEL DB FUNCTION DB FUNCTION DB TO TRIP BOUNDARY LAYER METERS NUMBER OF FREQUENCIES SOUND PRESSURE DB DEGREES FROM BASED SEGMENT ON NUMBER --- LEVEL DUE TO MECHANISM STPRIM STROUHAL NUMBER C STIPRIM REFERENCE 0049 C STPKPRM PEAK 0050 C THETA DIRECTIVITY ANGLE 0051 C U FREESTREAM VELOCITY 0052 C VISC KINEMATIC BOUNDARY DB BASED ON LAYER THICKNESS STROUHAL STROUHAL METERS CHORD TERM PRESSURE LAMINAR SIDE LEVEL ANGLE PRESSURE NUMBER NUMBER DEGREES METERS/SEC VISCOSITY M2/SEC 0053 0054 0055 0056 DIMENSION STPRIM(MAXFREQ) REAL L ,SPLLAM(MAXFREQ) ,FRCEN(MAXFREQ) 0057 0058 ,M 0059 0060 0061 C COMPUTE 0062 C ....................................... REYNOLDS NUMBER AND MACH NUMBER 0063 0064 M = U / CO 0065 RC = U * C/VISC 0066 0067 0068 C COMPUTE 0069 C .................................. BOUNDARY LAYER THICKNESSES 0070 0071 CALL THICK(C,U ,ALPSTAR,ITRIP,DELTAP,DSTRS,DSTRP,C0,VISC) 0072 0073 0074 0075 C COMPUTE DIRECTIVITY FUNCTION 119 0076 0077 0078 CALL DIRECTH(M,THETA,PHI,DBARH) 0079 0080 0081 0082 COMPUTE 0083 ................................. REFERENCE STROUHAL NUMBER 0084 0085 IF 0086 0087 (RC .LE. 1.3E+05) IF((RC IF (RC .GT. .GT. 1.3E+05).AND-(RC.LE.4.0E+05))STIPRIM=.001756*RC**.3931 4.0E+05) STIPRIM = .28 STIPRIM = .18 0088 0089 STPKPRM = 10.**(-.04*ALPSTAR) * STIPRIM 0090 0091 0092 0093 COMPUTE 0094 ................................. REFERENCE REYNOLDS NUMBER 0095 0096 0097 IF (ALPSTAR .LE. 3.0} RC0=lO.**(.215*ALPSTAR+4.978} IF (ALPSTAR .GT. 3.0) RC0=10.**(.120*ALPSTAR+5.263} 0098 0099 0100 0101 0102 COMPUTE 0103 .................................. PEAK SCALED SPECTRUM LEVEL 0104 0105 D = RC / RC0 0106 0107 IF (D 0108 IF ( (D 0109 1 G2 0110 = IF 0111 1 IF = 1 0114 .GT. (D (D .LE. + .5689}.AND. -114.052 * .GT. = G2=77.852*ALOG10(D)+15.328 .3237).AND. 65.188*ALOG10(D) ((D G2 IF .3237) .GT. ( (D G2 0112 0113 .LE. .5689)) 9.125 (D .LE. 1.7579) ) ALOG10(D)**2. 1.7579}.AND. (D .LE. 3.0889)) -65.188*ALOG10(D)+9.125 .GT. 3.0889) G2 _-77.852*ALOG10(D)+15.328 0115 0116 0117 G3 = 171.04 SCALE = 10. - 3.03 * ALPSTAR 0118 0119 * ALOGI0(DELTAP*M**5*DBARH*L/R**2) 0120 0121 0122 0123 COMPUTE 0124 SCALED SOUND PRESSURE LEVELS FOR EACH STROUHAL ............................................................. 0125 0126 DO I00 I=I,NFREQ 0127 0120 STPRIM(I) = FRCEN(I) * = STPRIM(I) DELTAP / U 0129 0130 / STPKPRM 0131 0132 0133 IF (E IF ((E 0134 .LT. G1 0135 IF 0136 = ((E IF 0138 = ((E G1 0139 IF 98.409 * = .LE..8545)) ALOG10(E} + .8545).AND. (E 2.0 .LT. 1.17)) -5.076+SQRT(2.484-506.25*(ALOG10(E) .GE. (E GI=39.8*ALOG10(E)-I1.12 .5974).AND.(E .GE. G1 0137 .5974) .GE. 1.17).AND. -98.409 .GE. * 1.674) (E )*,2.) .LT. ALOG10(E) + 1.674)) 2.0 G1=-39.80*ALOG10(E)-11.12 0140 0141 SPLLAM(I) 0142 0143 I00 CONTINUE 0144 0145 RETURN 0146 END 120 = G1 + G2 + G3 + SCALE NUMBER 0001 0002 SUBROUTINE TBLTE(ALPSTAR,C,U 1 ,FRCEN,ITRIP,SPLP,SPLS, SPLALPH,SPLTBL,THETA,PHI,L,R,NFREQ,VISC,C0) 0003 0004 0005 0006 0007 ***** 0008 ................................ VARIABLE DEFINITIONS ***** 0009 0010 0011 0012 VARIABLE NAME DEFINITION UNITS 0013 0014 0015 A STROUHAL NUMBER 0016 A0 FUNCTION USED IN 'A' CALCULATION 0017 A02 FUNCTION USED IN 'A' CALCULATION 0018 AA 'A' SPECTRUM 0019 SHAPE STROUHAL 0020 ALPSTAR ANGLE 0021 AMAXA MAXIMUM 0022 RATIO EVALUATED NUMBER OF AT RATIO DB ATTACK 'A' DEGREES CURVE STROUHAL EVALUATED NUMBER AT RATIO DB 0023 AMAXA0 MAXIMUM 'A' CURVE EVALUATED AT A0 DB 0024 AMAXA02 MAXIMUM 'A' CURVE EVALUATED AT A02 DB 0025 AMAXB MAXIMUM 'A' CURVE EVALUATED AT B DB 0026 AMINA MINIMUM 'A' CURVE EVALUATED AT 0028 AMINA0 MINIMUM 'A' CURVE EVALUATED AT A0 DB 0029 AMINA02 MINIMUM 'A' CURVE EVALUATED AT A02 DB 0030 AMINB MINIMUM 'A' CURVE EVALUATED AT B 0031 ARA0 INTERPOLATION 0032 ARA02 INTERPOLATION 0033 B STROUHAL NUMBER 0034 B0 FUNCTION USED 0035 BB 'B' 0027 STROUHAL 0036 NUMBER RATIO DB FACTOR --- FACTOR --- RATIO IN SPECTRUM --- 'B' CALCULATION SHAPE STROUBAL DB EVALUATED NUMBER AT RATIO DB 0037 BETA USED IN 'B COMPUTATION 0038 BETA0 USED IN 'B COMPUTATION 0039 BMAXB MAXIMUM 'B EVALUATED AT B DB 0040 BMAXB0 MAXIMUM 'B EVALUATED AT B0 DB 0041 BMINB MINIMUM 'B EVALUATED AT B DB 0042 BMINB0 MINIMUM 'B EVALUATED AT B0 DB 0043 BRB0 INTERPOLATION 0044 C CHORD 0045 C0 SPEED 0046 DBARH HIGH 0047 DBARL LOW 0048 DELKI CORRECTION 0049 DELTAP PRESSURE 0050 DSTRP PRESSURE 0051 DSTRS SUCTION 0052 FRCEN ARRAY 0053 GAMMA USED IN 'B' COMPUTATION 0054 GAMMA0 USED IN 'B' COMPUTATION 0055 ITRIP TRIGGER 0056 K1 AMPLITUDE FUNCTION 0057 K2 AMPLITUDE FUNCTION 0058 L SPAN 0059 M MACH 0060 NFREQ NUMBER 0061 PHI DIRECTIVITY 0062 P1 PRESSURE 0063 P2 SUCTION 0064 P4 PRESSURE 0066 R CONTRIBUTION SOURCE TO 0067 RC REYNOLDS NUMBER BASED ON CHORD 0068 RDSTRP REYNOLDS NUMBER BASED ON PRESSURE RDSTRS REYNOLDS SPLALPH SOUND 0065 0069 0070 0072 0074 0075 OF SOUND METERS/SEC DIRECTIVITY FREQUENCY SOUND SIDE DIRECTIVITY TO AMPLITUDE SIDE SIDE OF DB LAYER THICKNESS DISPLACEMENT METERS THICKNESS DISPLACEMENT CENTERED TO FUNCTION BOUNDARY SIDE METERS THICKNESS METERS FREQUENCIES TRIP HERTZ ----- BOUNDARY LAYER DB DB METERS NUMBER OF --CENTERED FREQUENCIES --- ANGLE SIDE SIDE DEGREES PRESSURE NT/M2 PRESSURE FROM ANGLE OBSERVER ATTACK NT/M2 METERS BASED DISPLACEMENT --- ON SUCTION THICKNESS LEVEL DUE TO ANGLE DUE TO PRESSURE CONTRIBUTION PRESSURE OF AIRFOIL --- THICKNESS NUMBER PRESSURE NT/M2 OF DISTANCE DISPLACEMENT ATTACK SPLP METERS FREQUENCY SIDE 0073 DB LENGTH SIDE 0071 FACTOR LEVEL OF DB DB 121 0076 SPLS SOUND 0077 PRESSURE SIDE 0078 OF LEVEL TOTAL 0080 STP PRESSURE 0081 STS SUCTION 0082 ST1 PEAK STROUHAL NUMBER 0083 STIPRIM PEAK STROUHAL NUMBER 0084 ST2 PEAK STROUHAL NUMBER 0085 STPEAK PEAK STROUHAL 0086 SWITCH LOGICAL SOUND TBLTE 0087 SUCTION PRESSURE LEVEL DUE TO MECHANISM DB SIDE STROUHAL SIDE THETA DIRECTIVITY 0089 U VELOCITY 0090 VISC KINEMATIC 0091 XCHECK USED STROUHAL NUMBER COMPUTATION ATTACK 0088 NUMBER NUMBER FOR OF 0092 TO DB SPLTBL 0079 DUE AIRFOIL OF ANGLE CONTRIBUTION ANGLE DEGREES METERS/SEC VISCOSITY TO CHECK M2/SEC FOR ANGLE OF ATTACK CONTRIBUTION 0093 0094 0095 PARAMETER (MAXFREQ DIMENSION = 27) 0096 0097 0098 SPLTBL(MAXFREQ) ,SPLP(MAXFREQ) 0099 I SPLALPH(MAXFREQ) ,STP(MAXFREQ) 0100 1 STS(MAXFREQ) ,FRCEN(MAXFREQ) ,SPLS(MAXFREQ) 0101 0102 LOGICAL SWITCH 0103 REAL L,M,KI,K2 0104 0105 RC = U * C 0106 M = U / C0 / VISC 0107 0108 0109 COMPUTE 0110 .................................. BOUNDARY LAYER THICKNESSES 0111 0112 CALL THICK(C,U ,ALPSTAR,ITRIP,DELTAP,DSTRS,DSTRP,C0,VISC) 0113 0114 COMPUTE 0115 ............................ DIRECTIVITY FUNCTION 0116 0117 CALL DIRECTL(M,THETA,PHI,DBARL) 0118 CALL DIRECTH(M,THETA,PHI,DBARH) 0119 0120 0121 CALCULATE 0122 SUCTION 0123 ................................................... THE REYNOLDS NUMBERS DISPLACEMENT BASED ON PRESSURE THICKNESS 0124 0125 RDSTRS = DSTRS * U / VISC 0126 RDSTRP = DSTRP * U / VISC 0127 0128 DETERMINE 0129 'A' 0130 PEAK AND 'B' STROUHAL CURVE NUMBERS TO BE USED FOR CALCULATIONS .............................................. 0131 0132 ST1 = .02 * M ** (-.6) 0133 0134 IF (ALPSTAR 0135 IF ((ALPSTAR 0136 0137 1 ST2 IF .LE. = 1.333) .GT. ST2 = 1.333).AND. ST1 (ALPSTAR .LE. 12.5)) STI*I0.**(.0054*(ALPSTAR-I.333)**2. (ALPSTAR .GT. 12.5) ST2 = ) 4.72 * ST1 0138 0139 0140 STIPRIM = (STI+ST2)/2. 0141 0142 0143 CALL AOCOMP(RC,A0) 0144 CALL AOCOMP(3.*RC,A02) 0145 0146 EVALUATE 0147 .............................................. MINIMUM 0148 0149 CALL AMIN(A0,AMINA0) 0150 CALL AMAX(A0,AMAXA0) 122 AND MAXIMUM 'A' CURVES AT A0 AND 0151 0152 CALL AMIN(A02,AMINA02) 0153 CALL AMAX(A02,AMAXA02) 0154 0155 COMPUTE 'A' MAX/MIN ......................... 0156 RATIO 0157 0158 ARA0 = (20. + AMINA0) 0159 ARA02 = (20. + AMINA02)/ / (AMINA0 - AMAXA0) (AMINA02- AMAXA02) 0160 0161 COMPUTE 0162 ............................................... B0 TO BE USED IN 'B' CURVE CALCULATIONS 0163 0164 IF (RC 0165 IF ((RC 0166 1 0167 .LT. B0 IF 9.52E+04) .GE. = (RC B0 = .30 9.52E+04).AND.(RC .LT. 8.57E+05)) (-4.48E-13)*(RC-8.57E+05)**2. .GE. 8.57E+05) B0 + = .56 .56 0168 0169 EVALUATE 0170 .............................................. MINIMUM AND MAXIMUM 'B' CURVES AT B0 0171 0172 CALL BMIN(B0,BMINB0) 0173 CALL BMAX(B0,BMAXB0) 0174 0175 COMPUTE 0176 'B' MAX/MIN RATIO ......................... 0177 0178 BRB0 = (20. + BMINB0) / (BMINB0 - BMAXB0) 0179 0180 FOR EACH 0181 'A' PREDICTION 0182 CENTER FREQUENCY, FOR THE COMPUTE PRESSURE AN SIDE ..................................... 0183 0184 STPEAK = ST1 DO I=I,NFREQ 0185 0186 i00 0187 STP(I) = FRCEN(I) 0188 A = ALOGI0(STP(I) 0189 CALL AMIN(A,AMINA} 0190 CALL AMAX(A,AMAXA) 0191 AA = AMINA * DSTRP / / + ARA0 * U STPEAK (AMAXA ) - AMINA) 0192 0193 IF 0194 IF((RC (RC 0195 K1 0196 IF = .LT. 2.47E+05) .GE. 2.47E+O5).AND. -9.0 * .GT. 8.0E+05) (RC K1 = -4.31 (RC ALOGI0(RC) + K1 * ALOGI0(RC) .LT. + 156.3 8.0E+05)) 181.6 = 128.5 0197 0198 IF (RDSTRP 0199 .LE. 5000.) ALOGI0(RDSTRP) 0200 IF DELKI = -ALPSTAR*(5.29-1.43* DELKI = 0.0 ) (RDSTRP .GT. 5000.) 0201 0202 SPLP(I)=AA+KI-3.+I0.*ALOGI0(DSTRP*M**5.*DBARH*L/R**2. )+DELKI 0203 0204 O2O5 0206 0207 GAMMA = 27.094 * M + 0208 BETA = 72.650 * M + 0209 GAMMA0 = 23.430 * M + 0210 BETA0 =-34.190 * M - 3.31 10.74 4.651 13.820 0211 0212 IF (ALPSTAR 0213 IF ((ALPSTAR.GT.(GAMMA0-GAMMA)).AND.(ALPSTAR.LE.(GAMMA0+GAMMA))) 0214 0215 1 .LE. (GAMMA0-GAMMA)) K2 = -i000.0 K2=SQRT(BETA**2.-(BETA/GAMMA)**2.*(ALPSTAR-GAMMA0)**2.)+BETA0 IF (ALPSTAR K2 = .GT. (GAMMA0+GAMMA)) K2 = -12.0 0216 0217 K2 + K1 0218 0219 0220 0221 STS(I) = FRCEN(I) * DSTRS / U 0222 0223 CHECK 0224 .......................................... FOR 'A' COMPUTATION FOR SUCTION SIDE 0225 123 0226 XCHECK = 0227 SWITCH = 0228 IF ( (ALPSTAR 0229 IF (.NOT. 0230 A 0231 CALL 0232 CALL 0233 AA GAMMA0 .FALSE. .GE. XCHECK).OR.(ALPSTAR SWITCH) = .GT. 12.5))SWITCH=.TRUE. THEN ALOG10(STS(I) / STIPRIM ) AMIN(A,AMINA) AMAX(A,AMAXA) = AMINA + ARA0 * (AMAXA - AMINA) 0234 0235 SPLS(I} = AA+K1-3.+10.*ALOG10(DSTRS*M**5.*DBARH* 0236 L/R**2.) 0237 0238 'B' CURVE COMPUTATION 0239 0240 0241 S 0242 CALL 0243 CALL 0244 BB 0245 SPLALPH(I)=BB+K2+I0.*ALOGI0(DSTRS*M**5.*DBARH*L/R**2.) = ABS(ALOGI0(STS(I) / ST2)) BMIN(B,BMINB) BMAX(B,BMAXB) = BMINB + BRB0 * (BMAXB-BMINB) 0246 0247 ELSE 0248 0249 THE 0250 .................................................. 'A' COMPUTATION IS DROPPED IF 'SWITCH' IS TRUE 0251 0252 0253 SPLS(I) 0254 = 0.0 1 0255 SPLP(I) 0256 + 10.*ALOGI0(DSTRS*M**5.*DBARL* L/R**2.) = 0.0 1 + 10.*ALOGI0(DSTRS*M**5.*DBARL* L/R**2.) 0257 B 0258 CALL 0259 CALL 0260 EB 0261 SPLALPH(I)=BB+K2+10.*ALOGI0(DSTRS*M**5.*DBARL* 0262 = ABS(ALOG10(STS(I) ST2)) AMAX(B,AMAXB) = AMINB + 1 0263 / AMIN(B,AMINB) ARA02 * (AMAXB-AMINB) L/R**2.) ENDIF 0264 0265 0266 SUM 0267 0268 PRESSURE BASIS 0269 ................................................... ALL CONTRIBUTIONS AND FROM SUCTION SIDE 'A' ON AND A 'B' ON MEAN-SQUARE PRESSURE 0270 0271 IF (SPLP(I} .LT. -I00.) SPLP(I) = -100. 0272 IF (SPLS(I) .LT. -i00.) SPLS(I) = -100. 0273 IF (SPLALPH(I) .LT. -i00.) SPLALPH(I) = -i00. 0274 0275 P1 = 10.**(SPLP(I) / 10.) 0276 P2 = 10.**(SPLS(I) / 10.) 0277 P4 = 10.**(SPLALPH(I) / 10.) 0278 0279 SPLTBL(I) 0280 0281 100 CONTINUE 0282 0283 RETURN 0284 END 124 = 10. * ALOG10(P1 + P2 + P4) BOTH 0001 SUBROUTINE AMIN(A,AMINA) 0002 0003 THIS 0004 TO THE Xl = 0009 IF (Xl .LE. .204) 0010 IF((Xl .GT. .204).AND. 0011 IF .GT. .244)AMINA=-I42.795*XI**3.+I03.656*X1**2.-57.757*XI+6.006 SUBROUTINE DEFINES A-CURVE FOR THE THE CURVE FIT MINIMUM CORRESPONDING ALLOWED REYNOLDS NUMBER. 0005 0006 0007 ASS(A) 0008 (Xl AMINA=SQRT(67.552-886.788*X1**2.)-8.219 (Xl .LE. .244))AMINA=-32.665*XI+3.981 0012 0013 RETURN 0014 END 0001 SUBROUTINE AMAX(A,AMAXA) 0002 0003 THIS 0004 TO THE Xl = 0008 IF (Xl .LE. .13)AMAXA=SQRT(67.552-886.788*XI**2. 0009 IF( (Xl .GT. .13).AND. 0010 IF (Xl .GT. .321)AMAXA=-4.669*XI**3.+3.491*XI**2.-16.699*XI+I.149 SUBROUTINE DEFINES A-CURVE FOR THE THE CURVE MAXIMUM FIT CORRESPONDING ALLOWED REYNOLDS NUMBER. 0005 0006 ABS(A) 0007 (Xl .LE. )-8.219 .321))AMAXA=-I5.901*XI+I.098 0011 0012 RETURN 0013 END 0001 SUBROUTINE BMIN(B,BMINB) 0002 0003 THIS 0004 TO THE Xl = 0008 IF (Xl 0009 IF((X1 0010 IF SUBROUTINE DEFINES B-CURVE FOR THE THE CURVE FIT MINIMUM CORRESPONDING ALLOWED REYNOLDS NUMBER. 0005 0006 ASS(B) 0007 .LE. .13)BMINB=SQRT(16.888-886.788*XI**2. .GT. .13).AND. (XI .LE. )-4.109 .145))BMINB=-83.607*XI+8.138 (X1.GT..145)BMINB=-817.81*XI**3.+355.21*XI**2.-135.024*XI+IO.619 0011 0012 RETURN 0013 END 0001 SUBROUTINE BMAX(B,BMAXB) 0002 0003 THIS 0004 TO THE X1 = 0008 IF (Xl 0009 IF((XI 0010 IF SUBROUTINE DEFINES B-CURVE FOR THE THE MAXIMUM CURVE FIT CORRESPONDING ALLOWED REYNOLDS NUMBER. 0005 0006 ASS(B) 0007 .LE. .i) .GT..1).AND.(XI BMAXB=SQRT(16.888-886.788*XI**2.)-4.109 .LE..187))BMAXB=-31.313*Xl+I.854 (XI.GT..187)BMAXH=-80.541*XI**3.+44.174*XI**2.-39.381*XI+2.344 0011 0012 RETURN 0013 END 125 OO01 SUBROUTINE AOCOMP(RC,A0) 0002 0003 THIS 0004 TAKES SUBROUTINE ON DETERMINES A VALUE OF WHERE -20 THE A-CURVE dB. OO05 0006 IF (RC 0007 IF ( (RC 0008 1 .LT. A0 = 0009 IF 0010 RETURN 0011 END 0001 SUBROUTINE 9.52E+04) .GE. A0 = 9.52E+04).AND. .57 (RC .LT. 8.57E+05)) (-9.57E-13)*(RC-8.57E+05)**2. (RC .GE. 8.57E+05) + A0 = 1.13 1.13 DIRECTH(M,THETA,PHI,DBAR) 0002 0003 THIS 0004 DIRECTIVITY SUBROUTINE COMPUTES FUNCTION THE HIGH THE INPUT FOR FREQUENCY OBSERVER LOCATION 0005 0006 REAL M,MC 0007 0008 DEGRAD = .017453 0009 0010 MC = .8 0011 THETAR = THETA * 0012 PHIR = PHI M * * DEGRAD DEGRAD 0013 0014 0015 1 DBAR=2.*SIN(THETAR/2.)**2.*SIN(PHIR)**2./((I.+M*COS(THETAR))* (I.+(M-MC)*COS(THETAR))*'2.) 0016 RETURN 0017 END 0001 SUBROUTINE DIRECTL(M,THETA,PHI,DBAR) 0002 0003 THIS 0004 DIRECTIVITY SUBROUTINE COMPUTES FUNCTION FOR THE LOW THE INPUT FREQUENCY 0005 0006 REAL M,MC 0007 0008 DEGRAD = .017453 0009 0010 MC = 0011 THETAR = THETA .8 0012 PHIR = PHI * M * * DEGRAD DEGRAD 0013 0014 DBAR 0015 0016 RETURN 0017 END 126 = (SIN(THETAR)*SIN(PHIR))**2/(1.+M*COS(THETAR))**4 OBSERVER LOCATION 0001 SUBROUTINE 0002 BLUNT(ALPSTAR,C,U 1 ,FRCEN,ITRIP,SPLBLNT,THETA,PHI, L,R,H,PSI,NFREQ,VISC,C0) 0003 0004 OOO5 C 0006 C ***** 0007 C ................................ VARIABLE DEFINITIONS ***** 0008 0009 C 0010 C VARIABLE NAME DEFINITION UNITS 0011 0012 C ALPSTAR ANGLE 0013 C ATERM USED 0014 C C CHORD LENGTH 0015 C C0 SPEED OF 0016 C DBARH HIGH 0017 C DELTAP PRESSURE 0018 C 0019 C 0020 C 0021 OF ATTACK TO DEGREES COMPUTE PEAK STROUHAL NO. METERS SOUND METERS/SEC FREQUENCY DIRECTIVITY SIDE BOUNDARY LAYER THICKNESS METERS DSTARH AVERAGE C DSTRAVG AVERAGE 0022 C DSTRP PRESSURE 0023 C DSTRS SUCTION 0024 C ETA RATIO 0025 C FRCEN ARRAY 0026 C F4TEMP G5 0027 C G4 SCALED 0028 C G5 SPECTRUM 0029 C G50 G5 EVALUATED AT PSI=0.0 0030 C G514 G5 EVALUATED AT PSI=f4.0 0031 C H TRAILING 0032 C HDSTAR BLUNTNESS 0033 C 0034 C HDSTARL MINIMUM 0035 C HDSTARP MODIFIED 0036 C ITRIP TRIGGER 0037 C L SPAN 0038 C M MACH 0039 C NFREQ NUMBER 0040 C PHI DIRECTIVITY 0041 C PSI TRAILING 0042 C R SOURCE 0043 C RC REYNOLDS 0044 C SCALE SCALING 0045 C SPLBLNT SOUND 0046 C 0047 C STPEAK PEAK 0048 C STPPP STROUHAL 0049 C THETA DIRECTIVITY ANGLE 0050 C U FREESTREAM VELOCITY 0051 C VISC KINEMATIC DISPLACEMENT OVER THICKNESS TRAILING EDGE BLUNTNESS DISPLACEMENT SIDE THICKNESS METERS DISPLACEMENT SIDE THICKNESS DISPLACEMENT OF STROUHAL OF 1/3 THICKNESS METERS NUMBERS OCTAVE EVALUATED METERS AT CENTERED MINIMUM SPECTRUM SHAPE EDGE FREQ. HDSTARP HERTZ DB LEVEL DB FUNCTION DB DB DB BLUNTNESS OVER AVERAGE ALLOWED VALUE METERS DISPLACEMENT THICKNESS --- VALUE FOR OF OF HDSTAR HDSTAR BOUNDARY LAYER TRIPPING METERS NUMBER OF CENTERED FREQUENCIES ANGLE EDGE TO DEGREES ANGLE DEGREES OBSERVER DISTANCE NUMBER BASED METERS ON CHORD DUE TO --- FACTOR PRESSURE LEVELS BLUNTNESS DB STROUHAL NUMBER NUMBER METERS/SEC VISCOSITY M2/SEC 0052 0053 0054 PARAMETER (MAXFREQ = DIMENSION SPLBLNT(MAXFREQ) 27) 0055 0056 ,FRCEN(MAXFREQ) ,STPPP(MAXFREQ) 0057 0058 REAL M,L 0059 0060 C 0061 C COMPUTE NECESSARY ............................ QUANTITIES 0062 0063 M = U /CO 0064 RC = U * C / VISC 0065 0066 0067 C COMPUTE 0068 C .................................. BOUNDARY LAYER THICKNESSES 0069 0070 CALL THICK(C,U ,ALPSTAR,ITRIP,DELTAP,DSTRS,DSTRP,C0,VISC) 0071 0072 C 0073 C COMPUTE AVERAGE DISPLACEMENT THICKNESS 0074 0075 DSTRAVG = (DSTRS + DSTRP) / 2. 127 0076 HDSTAR = H / DSTRAVG 0077 0078 DSTARH = i. /HDSTAR 0079 0080 COMPUTE DIRECTIVITY ............................ 0081 FUNCTION 0082 0083 CALL DIRECTH(M,THETA,PHI,DBARH) 0084 0085 0086 COMPUTE 0087 ............................ PEAK STROUHAL NUMBER 0088 0089 ATERM = - .212 .0045 * PSI 0090 0091 IF 0092 0093 STPEAK IF 0094 .GE..2) (HDSTAR 1 (HDSTAR 1 = ATERM .LT. .2) STPEAK = / .1 * (1.+.235*DSTARH-.0132*DSTARH**2.) HDSTAR + .095 - .00_43 * PSI 0095 0096 COMPUTE 0097 ............................. SCALED SPECTRUM LEVEL 0098 0099 IF (HDSTAR .LE. 5.) G4=17.5*ALOG10(HDSTAR)+157.5-1.114*PSI 0100 IF (HDSTAR .GT. 5.) G4=169.7 - 1.114 * PSI 0101 0102 0103 FOR 0104 ............................................................. EACH FREQUENCY, COMPUTE SPECTRUM SHAPE 0105 0106 DO 1000 I=I,NFREQ 0107 0108 STPPP(I) = FRCEN(I) 0109 ETA = ALOGI0(STPPP(I)/STPEAK) * H / U 0110 0111 HDSTARL = HDSTAR 0112 0113 CALL G5COMP(HDSTARL,ETA,G514) 0114 0115 HDSTARP = 6.724 * HDSTAR **2.-4.019*HDSTAR+I.107 0116 0117 CALL G5COMP(HDSTARP,ETA,G50") 0118 0119 0120 G5 = 0121 IF (G5 0122 CALL 0123 IF G50 + .0714 .GT. 0.) * G5 PSI = * (G514-G50) = F4TEMP 0. G5COMP(.25,ETA,F4TEMP) (G5 .GT. F4TEMP) G5 0124 0125 0126 SCALE = i0. * ALOGI0(M**5.5*H*DBARH*L/R**2.) 0127 0128 SPLBLNT(I) 0129 0130 0131 1000 CONTINUE 0132 0133 RETURN 0134 END 128 = G4 + G5 + SCALE REFERENCED TO 0 DB 0001 SUBROUTINE G5COMP(HDSTAR,ETA,G5) 0002 0003 0004 REAL M,K,MU 0OO5 0006 0007 IF (BDSTAR 0008 IF ((HDSTAR 0009 1 0010 0011 .25) .GT. MU IF ((HDSTAR = + .GT. -.0308 = * .1211 .25).AND.(HDSTAR MU=-.2175*HDSTAR 1MU 0012 .LT. .62).AND.(HDSTAR HDSTAR + IF (HDSTAR .GE. 1.15)MU 0014 IF (HDSTAR .LE. .02) 0015 IF ((HDSTAR .GE. M=68.724*BDSTAR .LE. .62)) .LT. 1.15)) .LT. .5) .1755 .0596 = .0242 0013 0016 I 0017 0018 IF 1 0019 0020 = * ((HDSTAR = 224.811 .GT. * ((HDSTAR .GT. M IF 1 .GT. 308.475 IF 1 0021 0022 ((HDSTAR M M = 1583.28 = 0.0 .5).AND. (HDSTAR (HDSTAR HDSTAR - .LE. 1.15) * .AND. HDSTAR IF (HDSTAR .GT. 1.2} 0024 IF (M 0.0) M M = ) .62)) 121.23 .62).AND.(HDSTAR HDSTAR 69.354 0023 .LT. M .02).AND. 1.35 .LE. (HDSTAR - 1631.592 = 268.344 1.15)) .LT. 1.2)) 0.0 0025 0026 ETA0 = -SQRT((M*M*MU**4)/(6.25+M*M*MU*MU)) K = 2.5*SQRT(I.-(ETA0/MU)**2.)-2.5-M*ETA0 0027 0028 0029 0030 IF (ETA 0031 IF ((ETA 0032 IF((ETA.GT.0. 0033 IF (ETA .LE. .GT. ETA0) ).AND. .GT. G5 ETA0).AND. .03616) = M * (ETA ETA + K .LE. 0. ))G5=2.5*SQRT(1.-(ETA/MU)**2.)-2.5 (ETA.LE..03616))G5=SQRT(1.5625-1194.99*ETA**2.)-1.25 G5=-155.543 * ETA + 4.375 0034 0035 RETURN 0036 END 129 OO01 SUBROUTINE TIPNOIS(ALPHTIP,ALPRAT,C,U 0002 ,FRCEN,SPLTIP,THETA,PHI, R,NFREQ,VISC,C0,ROUND) 0003 0004 ................................ 0005 ***** 0006 ................................ VARIABLE DEFINITIONS ***** 0007 0008 VARIABLE 0009 ....................... NAME DEFINITION UNITS 0010 0011 ALPHTIP TIP ANGLE OF 0012 ALPRAT TIP LIFT CURVE 0013 ALPTIPP CORRECTED 0014 C CHORD LENGTH 0015 C0 SPEED OF 0016 DBARH DIRECTIVITY 0017 FRCEN CENTERED 0018 L CHARACTERISTIC 0019 M MACH 0020 MM MAXIMUM 0021 NFREQ NUMBER 0022 PHI DIRECTIVITY 0023 R SOURCE 0024 ROUND LOGICAL 0025 SCALE SCALING 0026 SPLTIP SOUND 0027 ATTACK DEGREES SLOPE TIP ANGLE OF ATTACK DEGREES METERS SOUND METERS/SEC HERTZ FREQUENCIES LENGTH FOR TIP METERS NUMBER MACH OF NUMBER CENTERED FREQUENCIES ANGLE TO DEGREES OBSERVER SET DISTANCE TRUE IF TIP METERS IS ROUNDED TERM PRESSURE LEVEL DUE TO TIP MECHANISM DB 0028 STPP STROUHAL NUMBER 0029 TERM SCALING 0030 THETA DIRECTIVITY ANGLE DEGREES 0031 U FREESTREAM VELOCITY METERS/SEC 0032 UM MAXIMUM 0033 VISC KINEMATIC TERM VELOCITY METERS/SEC VISCOSITY M2/SEC 0034 0035 PARAMETER (MAXFREQ =27) 0037 DIMENSION SPLTIP(MAXFREQ},FRCEN(MAXFREQ) 0038 REAL LOGICAL L,M,MM ROUND 0042 ALPTIPP = ALPHTIP 0043 M = U 0036 0039 0040 0041 * / ALPRAT CO 0044 0045 CALL DIRECTH(M,THETA,PHI,DBARH) 0046 0047 IF 0048 (ROUND) L 0049 = THEN .008 * ALPTIPP * C ELSE 0050 IF (ABS(ALPTIPP) 0051 L 0052 ELSE 0053 (.023 = (.0378 L = 0054 .LE. + 2.) THEN .0169*ALPTIPP) + * .0095*ALPTIPP) C * C ENDIF 0055 ENDIF 0056 0057 0058 MM = (i. UM = MM + .036*ALPTIPP) * M 0059 0060 * CO 0061 0062 TERM 0063 IF 0064 = M*M*MM**3.*L**2.*DBARH/R**2. (TERM .NE. SCALE 0065 0.0) THEN = 10.*ALOGI0(TERM) = 0.0 ELSE 0066 SCALE 0067 ENDIF 0068 0069 DO 0070 0071 0072 100 I00 SPLTIP(I) CONTINUE 0073 RETURN 0074 END 130 I=I,NFREQ STPP = FRCEN(I) = 126.-30.5*(ALOGI0(STPP)+.3)**2. * L / UM + SCALE 0001 SUBROUTINE THICK(C,U ,ALPSTAR,ITRIP,DELTAP,DSTRS,DSTRP,C0,VISC) 0002 0003 0004 0005 0006 0007 UNITS 0008 OO09 0010 ALPSTAR ANGLE OF 0011 C CHORD LENGTH 0012 C0 SPEED OF 0013 DELTA0 BOUNDARY 0014 METERS SOUND METERS/SEC THICKNESS ANGLE DELTAP PRESSURE DSTR0 DISPLACEMENT DSTRP PRESSURE DSTRS SUCTION 0023 ITRIP TRIGGER 0024 M MACH 0025 RC REYNOLDS 0026 U FREESTREAM 0027 VISC KINEMATIC 0016 DEGREES LAYER ZERO 0015 ATTACK OF SIDE AT ATTACK METERS BOUNDARY LAYER THICKNESS 0017 0018 METERS THICKNESS ANGLE 0019 0020 OF AT ZERO ATTACK SIDE METERS DISPLACEMENT THICKNESS 0021 0022 METERS SIDE DISPLACEMENT THICKNESS METERS FOR BOUNDARY LAYER TRIPPING NUMBER NUMBER BASED ON CHORD VELOCITY METERS/SEC VISCOSITY M2/SEC 0028 0029 0030 COMPUTE 0031 THICKNESS ZERO ANGLE OF (METERS) ATTACK AND BOUNDARY REYNOLDS LAYER NUMBER 0032 0033 0034 M = U / CO RC = U * C/VISC DELTA0 = 10.**(I.6569-.9045*ALOGI0(RC)+ 0035 0036 0037 0038 0039 1 0040 .0596*ALOGI0(RC)**2.)*C IF (ITRIP .EQ. 2) DELTA0 = .6 * DELTA0 0041 0042 0043 COMPUTE 0044 .............................................. PRESSURE SIDE BOUNDARY LAYER THICKNESS 0045 0046 DELTAP = 10.**(-.04175*ALPSTAR+.00106*ALPSTAR**2. )*DELTA0 0047 0048 0049 COMPUTE ZERO ANGLE OF ATTACK DISPLACEMENT THICKNESS 0050 005_ 0052 IF ((ITRIP .EQ. I) .OR. 0053 IF (RC .LE. .3E+06) 0054 IF (RC .GT. .3E+06) 0055 i .EQ. = 2)) .0601 * THEN RC **(-.114)*C DSTR0=10.**(3.411--1.5397*ALOG10(RC)+.1059*ALOG10(RC)**2.)*C 0056 IF 0057 (ITRIP DSTR0 (ITRIP .EQ. 2) DSTR0 = DSTR0 * .6 ELSE 0058 DSTR0=10.**(3.0187-1.5397*ALOG10(RC)+.1059*ALOG10(RC)**2.)*C 0059 ENDIF 0060 0061 PRESSURE 0062 .................................... SIDE DISPLACEMENT THICKNESS 0063 0064 DSTRP 0065 IF = 10.**(-.0432*ALPSTAR+.00113*ALPSTAR**2. (ITRIP .EQ. 3) DSTRP = DSTRP * )*DSTR0 1.48 0066 0067 SUCTION 0068 SIDE DISPLACEMENT THICKNESS ................................... 0069 0070 IF (ITRIP .EQ. I) THEN 0071 IF (ALPSTAR .LE. 5.) 0072 IF( (ALPSTAR .GT. 5.) 0073 0074 0075 1 DSTRS IF = (ALPSTAR .381'i0.**( .GT. DSTRS=I0.**(.0679*ALPSTAR)*DSTR0 .AND. (ALPSTAR .LE. 12.5)) .1516*ALPSTAR)*DSTR0 12.5)DSTRS=I4.296*I0.**( .0258*ALPSTAR)*DSTR0 ELSE 131 0076 IF 0077 IF((ALPSTAR 0078 1 DSTRS 0079 0080 IF ENDIF 0081 0082 RETURN 0083 END 132 (ALPSTAR = (ALPSTAR .LE. 7.5)DSTRS .GT. 7.5).AND. =10.**(.0679*ALPSTAR)*DSTR0 (ALPSTAR .LE. 12.5) ) .0162*I0.**(.3066*ALPSTAR)*DSTR0 .GT. 12.5) DSTRS = 52.42"10.**( .0258*ALPSTAR)*DSTR0 References 1. Brooks, Thomas in Rotor 1983, F.; Broadband pp. 287 and Schlinker, Noise Research. Robert H.: Vertica, Vibration, vol. 3. Schlinker, Robert 78, no. 1, Sept. H.; and 5. Vortex Edge Prediction. Noise Ffowcs Williams, Sound Generation a Scattering Mar. 6. 1970, Brooks, Helicopter 1981. Turbulence Hall, to Flow of 20. Aerodynamic in the Mech., Vicinity vol. of 40, pt. 4, F.; and Self-Noise Marcolini, Using J., vol. 23, no. 2, Feb. S.-T.; and George, pp. 1821 Albert A.: Flow 1985, pp. 207-213. A. R.: Effect Trailing-Edge 1984, Michael Measured Noise. AIAA of Angle J., vol. R.; and Chou, 9. Axis Wind Shau-Tak: Broadband Turbines. AIAA Rotor pp. 217 11. Fink, 118, no. 2, Oct. 22, and CR-159311, W.; 13. Tam, Christopher foils. J. Acoust. Airframe Noise Amiet, Noise Reduction Investigation. Roy K.; Vortex Interaction Feb. 1974. K. W.: Soc. 26. 27. NASA Discrete America, Tones and Munch, Noise. AIAA of Isolated vol. 55, no. 6, June C. Air1974, 1177. 28. 1976, pp. 165 223. 15. Fink, M. R.: Fine on Y. N.: Lifting Michael J., Noise Rotors. A.: vol. Aero-Hydroacoustics Airfoil 24, for no. Ships, DTNSRDC-84/010, George, 2, U.S. VolNavy, A. R.: Effect of Blunt Noise. AIAA J., vol. 24, no. 8, Trailing 1382. F.; Marcolini, Airfoil Michael Trailing-Edge A.; Flow 1986, pp. and Pope, Measurements. 1245 1251. R. K.: Refraction of Sound by a Shear Layer. J. 64 Vibration, vol. 58, no. 4, June 1978, pp. 467-482. R. H.; and a Shear 79-0628, Mar. Robert Paper 77-1269, Fink, and Amiet, Pressure Roy Airfoil a NASA M. R.; Schlinker, Julius NASA S.; and Thomas J. American 1976. Method 1977. Edge R. H.; and (See CR-2611, Piersol, From MeasureAIAA Broadband Helicopter Soc., R. K.: Predic- Noise of Non- 1976. Allan G.: Procedures. F.; Marcolini, Rotor for Airframe Noise Amiet, Noise 29. Dowling, A. P.; and Ffowcs Williams, Sources of Sound. John Wiley & Sons, Main Ra- of an Airfoil Microphone. Vortex Analysis and Measurement Sons, Inc., c.1971. Stuart: Acoustic 1977. of Rotating-Blade Blades. AIAA CR-2733, Trailing Directional Oct. Bendat, of Sound 76-571.) R.: Noise Component Paper 77-1271, Oct. rotating K.: Characteristics Turbulence. R. H.: With Refraction Assessment. 1979. W.; Paper ments R. K.: Experimental and Surface Schlinker, Anfiet, Layer to Incident tion R.; J. 302. Kim, AIAA J., vol. 24, no. 8, Aug. 30. Brooks, 14. Wright, S. E.: The Acoustic Spectrum of Axial Flow Machines. J. Sound 64 Vibration, vol. 45, no. 2, Mar. 22, UTRC78-10, Jan. 1978. S.: 25. Fink, Martin Noise. AIAA 1980. Lee: Isolated Airfoil-Tip Paper No. 74-194, Jan. 1173 D. A.: Clean-Airframe Robert Dennis Martin Airfoils. 252. pp. 1380 Thomas also AIAA 1987, and Marcolini, Broadband Brooks, Due 239. 12. Paterson, pp. vol. M. R.; and Bailey, Studies 1986, pp. 296 E.; Noise. No. and Aug. diation Noise and K.: S.-T.; on Rotor 24. Paterson, J. Propuls. pp. 246 William Chou, by F.; Formation Edge 1973, F. G.; Fink, of Isolated Vortex Formation June 1980. H. Rep. 1984. 23. Schlinker, 12, 64 Power, vol. 1, no. 4, July Aug. 1985, pp. 292 299. 10. Glegg, S. A. L.; Baxter, S. M.; and Glendinning, A. G.: The Prediction of Broadband Noise From Wind Turbines. 64 Vibration, 1986, Paper Noise Analyses. NASA CR-3797, 1984. Grosveld, Ferdinand W.: Prediction of Broadband Sound Feb. AIAA 1823. George, Horizontal Vortex 22. Amiet, Sound of Attack 22, no. 8. J. 21. Scaling Parameters. Najjar, Thomas Tip ume June Trailing 1985. L. H.: J. Fluid AIAA From (See Application CR-177938, Turbulent Chou, Dec. 18. Brooks, 117. CR-3470, On the Wall and Plane. Thomas on Rotor 69 K.: R.; Due to Tip AIAA-80-1010, pp. 657-670. of Airfoil 7. E.; by Half of NASA J. Edge Noise J. Sound 64 10, no. 5, May A. 19. Blake, S. J.: Model pp. Roy NASA Shamroth, a Hairpin 8, 1981, Amiet, Rotor Trailing Edge Noise. also AIAA Paper 81-2001.) N. S.; and vot. 17. George, Brooks, T. F.; and Hodgson, T. H.: Trailing Prediction From Measured Surface Pressures. Liu, Aircr., vol. 7, no. 4, 307. 2. 4. 16. Paterson, Robert W.; Vogt, Paul and Munch, C. Lee: Vortex Noise Progress Michael Noise vol. 34, Random John J. E.: c.1983. Sound A.; and Study no. Data: Wiley & and Pope, D. in the DNW. 2, Apr. 1989, pp. 3-12. Structure United of Airfoil Technologies Tone Research Frequency• Center, 31. Golub, of R. A.; Weir, the Helicopter Baseline Tone D. S.; and Rotonet Noise. Tracy, System AIAA-86-1904, to M. B.: the July Application Prediction of 1986. 133 cO ° O (D _w © _J [J _o < _ ._ _o_ooooo_ooo_o_o_o_o_o_o_ooo_o_o_o_oo_o_ _.____________ N- t_ _J W-S __O_O______O_OOO___ RR_R_C_RCR_ReRRRC_RR_RRRR_R_RRRRR_RCRC_CCR_R_R_R C_ O c_ oooooooooooooooooooooooooooooooooooooooooo__ooooooooo ,oo,,,,,.,oo.°°,°°o°°o°°,o°o°°,,°oooo****,°o,o.°o.°°o°°,° C_ # ,o,,,o,,o,oo,o,,,.,,o,..,o.,oo,o.o,,,o,o,o,,,,,o.,o,,oo,o _OO_O_OO_O_OOO_OOO_OOO_O_OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO .o O b_ _ _J O C_ .O 134 _mmm_m_mmmbmbmmmbmmmbmmm_m_mmm_mmm_m_mmm_m_mmmbm_mmm_mmmb _o 00000000000_00000000000000_00_000000000000000 #########################################_####### o 135 b- 00000000000000000000000000000000000000000000_00000__ © © _!_ _0_0_00 0000°.0 _ , 0_0_ .,,000000 000000_ **+000. 0_0_00 .0000°00 < 0 _ +_oo+oo oo++_ooo_° ++_oooo ooooo+oo _0_0 __ _ 0000000 0 _0_0_0_ ................. 000000000 _0_ _0__ 0000000 00000000 k,+ 0 r..) 0 000000000000_______0000000000000 _lr', 136 0"13 ,_.£1 ¢lX:l U'O _J:::l t_JEI 0"113 _lrl O'O ¢lr_ O'O _r_ _r_ _lJ:::l O'O t_.EI _lJ:::l O'EI mJE:l ¢I.Q ¢lr_ _tn O'O r_r_ 0"13 _t-, O'EI tO v _000000000o_00000000000_00000000 O) _J _= 0 o_ .e 137 Report ':; pac [2. 1. ReportNAsANO.RP_1218 4. Title Documentation Page _- Adm,nisrraTlon and Government Accession No. 3. Recipient's Subtitle Airfoil 5. Report Self-Noise and Prediction Catalog No. Date July 1989 6. Performing Organization Code 8. Performing Organization Report 7. Author(s) Thomas 9. F. Brooks, Performing D. Stuart Organization Name and NASA Langley Research Hampton, VA 23665-5225 12. Sponsoring Agency Name and Pope, A. Marcolini No. L-16528 10. Work Unit No. 505-63-51-06 Center 11. Contract 13. Type Address or Grant of Report Reference Administration 14. Sponsoring No. and Period Covered Publication Agency Code Notes Thomas F. Brooks and Michael D. Stuart Pope: PRC Kentron, 16. Michael Address National Aeronautics and Space Washington, DC 20546-0001 15. Supplementary and A. Marcolini: Inc., Aerospace Langley Research Center, Hampton, Technologies Division, Hampton, Virginia. Virginia. Abstract A prediction method is developed for the self-generated smooth flow. The prediction methods for the individual and are based on previous theoretical studies and data noise of an airfoil self-noise mechanisms obtained from tests blade encountering are semiempirical of two- and three- dimensional airfoil blade sections. The self-noise mechanisms are due to specific boundary-layer phenomena, that is, the boundary-layer turbulence passing the trailing edge, separated-boundarylayer and stalled flow over an airfoil, vortex shedding due to laminar-boundary-layer instabilities, vortex shedding from blunt trailing edges, and the turbulent vortex flow existing near the tip of lifting blades. The predictions are compared successfully with published data from three self-noise studies of different airfoil shapes. An application of the prediction method is reported for a largescale-model helicopter rotor, and the predictions compared well with experimental broadband noise measurements. A computer code of the method is given. 17. Key Words Airframe (Suggested 18. Distribution by Authors(s)) noise Statement Unclassified--Unlimited Helicopter rotor Rotor broadband acoustics noise Propeller noise Wind turbine noise Trailing-edge Vortex-shedding 19. Security Classif. noise noise (of this Subject report) 20. Unclassified NASA FORM Security Classif. (of this 71 page) Unclassified 1626 Category 21. No. 142 of Pages 22. Price A07 OCT sG NASA For sale View publication stats by the National Technical Information Service, Springfield, Virginia 22161-2171 Laugh. 1989