WIND TURBINE AMPLITUDE MODULATION NOISE DUE TO TIME- DEPENDENT INTERFERENCE

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1 WIND TURBINE AMPLITUDE MODULATION NOISE DUE TO TIME- DEPENDENT INTERFERENCE Abstract Stuart Braley Physics Department, University of Aucklan, Private Bag 9019, Aucklan, New Zealan Trailing ege noise from a turbine blae comprises sources which move in a circle so that the irect soun path an groun reflecte soun paths to a receiver perioically vary. At any one listener location, there is therefore a fluctuating intensity. A simple ray moel shows that this mechanism enhances the characteristics of win turbine amplitue moulation noise, an can lea to a sharper onset of the higher intensity soun at some frequencies. This time-epenent interference mechanism oes not epen on intermittent stall, although increase source intensity obviously leas to increase moulation noise. 1. Introuction Particularly over the past ecae noise from win turbines has become a major concern for the public, an therefore for the inustry. In aition to broa-ban noise, generally ientifie as trailing ege noise, there has been an increasing concern about the annoyance to people by amplitue moulation (AM) of win turbine noise [1]. A stuy by RenewableUK [] provies wie cover of ifferent aspects of AM an the more extreme version of moulation name other amplitue moulation (OAM). The main hypothesis for the cause of OAM in the RenewableUK stuy has been that it is ue to intermittent stall of a blae. Oerlemans [3] evelope a rotor simulation moel incluing a noise moel for a partially stalle airfoil an the moel results showe the general observe characteristics of OAM. The source irectivity characteristics of the stall noise are such that it is preferentially raiate upwin an ownwin of the win turbine an not in the cross win irection as characterizes AM. More recently, Masen et al. [4] have correlate AM with turbine blae inflow conitions. They foun a strong noise increase at low frequencies when a trailing ege stall initiates. For the turbine operating in a strong win shear a moulation of the surface spectra for frequencies below 00Hz is 14B. It was hypothesise that coupling with the turbine wake can cause abrupt changes in win spee over the rotor isc an for a variable spee turbine the rotor might not be able to accelerate fast enough to avoi transient stall for a few revolutions. This intermittent occurrence might explain many of the occurrences of OAM. The intermittent stall mechanism requires maintenance of stall conitions for a consierable time for the mechanism to be consistent with reporte an observe OAM. Furthermore, the hypothesise wake coupling has yet to be verifie with either a measurement program or via simulations. We have therefore in the current paper set out to explore an alternative, more continuously operating mechanism, time-epenent interference, to see if that might be plausible. This mechanism is base on the fact that, with three rotating blaes an groun reflections, there are six possible soun paths to a fixe microphone position. For example, the images in Fig. 1 each show part of a single frame capture from the Norsonic 848 Acoustic camera [5]. The frequency ban for these images is Hz, these 1

2 high frequencies being use because of the small size of the acoustic camera. Note that the acoustic camera shows soun arriving at the microphone array from ifferent irections, an oes not combine the soun from various paths as a single microphone or ear woul o. The left han image shows soun reaching the camera from two blaes. The central image shows soun being receive from a irect path an from an inirect path groun reflection. The image on the right is from a further angular rotation of the blae by about 0 (0.3 s after the central image) an shows no groun reflection. Soun from the two sources ientifiable in the left-han image, or the two sources ientifiable in the central image, reach the microphone array at the same time, but o not originate from the turbine at the same time because the path lengths to the array are ifferent B Figure 1. A single frame capture from a Norsonic 848 Acoustic camera showing soun originating from two blaes. The six pressure waves (a irect path an an inirect path from each of the three blaes) originate at the turbine at ifferent times an ifferent blae positions. The combination of the six pressure waves therefore inclues cancellations an reinforcements from the various amplitues an phases as well as multiple frequencies from the six ifferent Doppler shifte frequencies. The net result is to expect consierable moulation of the soun which woul be emitte from a single blae. It woul appear that this mechanism has not been previously investigate, possibly because most effort has concentrate on the soun generation mechanisms on the rotor blaes, an the soun propagation moelling has generally mae use of conventional soun propagation coes which o not allow for multiple moving sources.

3 In this paper we investigate the extent of the soun moulation at a point receiver position, but without incluing at this stage a full soun propagation treatment of groun impeance an refraction effects over the entire frequency ban likely to be relevant. However, these can reaily be ae since the methoology is well establishe an, for an elevate source, relatively straight-forwar, although the time elay treatments escribe in this current paper will nee to be inclue.. Soun Propagation Geometry an Timing Soun propagation moelling frequently involves shallow paths, but in the case of turbines the source is elevate. This means in practice that, in aition to a irect soun path, only one inirect ray reflecte from the groun surface will reach the listener [6]. The general propagation geometry is therefore as shown in Fig.. Here H is the hub height, h is the listener (or microphone) height, is the horizontal istance from turbine to listener, φ is the azimuth angle of the listener with respect to the turbine tower, R is the raial istance of the soun source, an V is the spee of the soun source. In this iagram the win, U, is in the +x irection an the turbine is revolving clockwise when viewe from the ve x axis (the turbine angular velocity Ω is in the +x irection). Also shown is the irect path from a time when the turbine blae ha an angle α with respect to the vertical, an the once-reflecte inirect path from an earlier time when the turbine blae ha an angle αi with respect to the vertical. Note that these paths are in general curve ue to refraction. z z V R ϕ α R αi β r H ri H p x φ y x φ y h h Figure. The general soun propagation geometry for a rotor isk of raius R at hub height H an a listener of height h at istance an azimuth φ. A irect ray is shown from a blae at rotation angle α an an inirect ray from a blae at angular position αi. 3

4 Two further angles are shown in Fig. in connection with the irect path (similar angles can reaily be efine for the inirect path). They are β, the angle at which the microphone is forwar of the blae trailing ege (perpenicular to the rotor blae), an ϕ, the angle at which the microphone is lateral of the soun source (along the rotor blae). These angles are given in terms of other physical quantities by cos ϕ = ˆ Rˆ (1) r (where the caret inicates a unit vector an R is the raial vector from the hub along the blae to the noise source at the tip), an cosβ = pˆ Vˆ = ( r + ϕ ˆ ) ˆ r cos R V. () rˆ Vˆ = sin ϕ The combine intensity epenence on trailing ege noise irectivity an Doppler, or convective, amplification is [7] sin β sin ϕ 1 sin ϕ + rˆ Vˆ ( 1 M rˆ Vˆ ) 4 ( 1 M rˆ Vˆ ) 4 = (3) where M = V/c is the Mach number an the soun spee is c. Ignoring for the moment the change in soun spee ue to the win, the irect path length, r, an inirect path length, ri, are r r i = = ( cosφ) + ( sin φ + Rsin α ) + ( H + R cosα h) ( cosφ) + ( sin φ + Rsin α ) + ( H + R cosα + h) i i (4) Soun emitte when a blae rotation angle is α an αi reach the listener at time t where α α i = Ω t = Ω t r c ri c. (5) For each time t (4) an (5) nee to be solve for r(t) an ri(t). Then the two intensities can be foun from (3), an Doppler frequency shift values calculate. These parameters are all epenent on the geometry an the angular rotation rate of the turbine, but not on the soun source frequency spectrum. Once the path lengths are known as a function of time, the signals reaching the microphone can be combine with the correct phase for each emitte frequency f. 3. Selecte results For the following, the.3 MW turbine iscusse in Chapter 3 of Bowler an Leventhall [7] will be moelle. This has a rotor iameter D = R = 94 m, H = D, an a typical value Mach number of M = 0.. We consier a microphone at h = 1.5 m, an use c = 340 m s -1. 4

5 3.1 Locus of groun reflection point. The point on the groun at which reflection occurs traces out an approximately (but not exactly) elliptical route for soun from each blae. These loci are shown in Fig. 3 for the cases of f = 315 Hz, = D, an φ = 0 an 45. The closest approach of the reflection point to the microphone is when the soun originate from the top of the rotor sweep (note that acoustic camera images in Fig. 1 o not show the turbine blae an reflecte soun synchronise). One useful item of information from this plot is that the groun reflection from such an elevate source is in general very close to the microphone (a istance of -6 m away for this case of being rotor iameters, an 4-1 m for being 4 rotor iameters). This means that, for accurate soun propagation moelling, the groun impeance only nees to be known within a few meters of the microphone location. Figure 3. The approximately elliptical loci of groun reflection points for D = 94 m, = D, H = D, an h = 1.5 m, for φ = 0 (blue) an 45 (re). The straight lines are from the microphone location (shown here at the origin) towar the base of the turbine. 3. SPL from 1 blae, without consiering Doppler frequency shift. Fig. 4 shows the SPL ue to noise from a single blae base on (3), as well as the combination of irect an inirect soun paths for a single blae, using the same parameter choice as in the previous section. In this figure the convective amplification is inclue, but not the effect on phase ue to Doppler frequency shift. In this, an succeeing iagrams, the plots start at the time at which soun is receive at the microphone from the top of the blae sweep i.e. there is a normalise elay of Ω + ( H + R) πc. (6) 5

6 Figure 4. The SPL at the microphone for the irect path alone (blue) an for the combination of irect an inirect paths (re) from a single blae an a soun frequency of 315 Hz. It can be seen that, for this soun frequency, the moulation of the receive turbine noise is now aroun three times that of the rotation rate: if soun from the 3 blaes were to be receive inepenently there woul be 9 intensity peaks uring each rotation, or 3 intensity peaks per blae pass. 3.3 SPL from 1 blae an incluing Doppler frequency shift. Fig. 5 shows, for the same parameter selection, the effect of incluing Doppler frequency shift on the combination of the irect an inirect path reception from a single blae. Some of the moulation features of Fig. 4 are preserve, but there is a lot more structure an higher moulation frequencies present ue to the increase ifferences in frequency (an hence phase) of the soun in the irect an inirect paths. For this geometry an soun frequency, there is a moulation of aroun 10 times that of the blae pass rate. If the frequency is increase to f = 1 khz this moulation rate increases accoringly in proportion to f although, as in Fig. 5, the moulation is not uniformly sinusoial. Increasing the range from = D to = 4D makes the two paths shallower an the path ifferences smaller, with the result shown in Fig. 6. Shifting the microphone location from the ownwin position by 45 (Fig. 7) changes where the minimum Doppler shift occurs on the blae rotation cycle. The combination of irectivity an Doppler frequency ifferences with path causes a change in the moulation amplitue over the rotor cycle, but without changing the number of fluctuations per blae pass shown in Fig SPL from 3 blaes. Fig. 8 shows the amplitue an Fig. 9 the spectrum of the receive soun signal allowing for reception from the 6 paths an with Doppler frequency shifts. 6

7 Figure 5. The SPL at the microphone from a single blae, incluing both irect an inirect paths, an the effect of Doppler frequency shift on phase. Figure 6. The SPL, as for Fig. 5 but with the range = 4D instea of D. 7

8 Figure 7. The SPL, as for Fig. 5 but with the range φ = 45 instea of 0. Figure 8. The receive soun signal base on the parameters use in Fig. 4 an incluing the combination of Doppler-shifte signals from the 6 soun paths with appropriate time elays. This soun isplays strong amplitue moulation at all emitte frequencies. It is a continuous phenomenon. The spectrum, from this tonal emitte frequency, has finite banwith ue to the maximum 8

9 an minimum Doppler frequency shifts efine by the geometry. Amplitue moulation of tonal signals, in raio fro example, is achieve by aing structure in siebans aroun the central frequency. This is what appears in Fig. 9. For this example geometry, at f = 315 Hz, the banwith is limite to about ±100 Hz, but the main amplitue fluctuations apparent in Fig. 8 have a frequency of only.4 Hz. The explanation for this ifference lies in the time-varying nature of the Doppler shift which, in aition to AM, prouces frequency moulation (FM). This means that, to unerstan the receive soun, integration over the full emitte noise spectrum nees to be one since soun emitte in one 1/3-octave ban will be receive in another. Figure 9. The spectrum of the receive soun signal corresponing to Fig Refraction, Groun Impeance, an Full Spectrum While we have not inclue here refraction, groun impeance, an integration over the full spectrum of emitte noise, these influences on propagation are not ifficult to incorporate into our time-epenent interference moel. In particular, curve propagation paths still require a numerical solution of equations like (4) an (5), allowing for the various propagation times from the 6 paths. 5. Conclusions In response to concern whether intermittent stall coul account for sustaine AM or OAM, we have suggeste an alternative mechanism which is continuous in nature. This takes into account that soun reaching a receiver from multiple paths will have originate on the turbine blaes at ifferent blae positions. The result is that interference between soun travelling these ifferent paths is much more ominant, an not static but changes uring the turbine blae rotation cycle. This is a mechanism for moulation of the noise emitte from the turbine blae trailing ege. For turbines the noise source is elevate an it is possible to show that only one groun reflection will occur for soun from a single blae an for typical geometries. For 3 blaes this means that there are 6 paths for soun reaching a microphone. The interference between these 6 paths is strong an complex. Simulations at iscrete tonal emitte frequencies show classical amplitue moulation of the receive signal, which is typically at a high multiple of the blae pass frequency. However, examination 9

10 of the spectrum shows a wier banwith than woul account for the observe AM, because there is also FM arising from the more-or-less sinusoially changing Doppler shifte frequencies receive. Combining the full with of the emitte spectrum is likely to obscure this FM component while still retaining the strong AM nature. While investigation of this mechanism is ongoing, it is clear from the simulations shown here that many of the observe characteristics of AM an OAM are reprouce, incluing the reuction in moulation frequency if the microphone is move away from the ownwin or upwin irection. Interestingly, a goo way for istinguishing intermittent stall from time-epenent interference, woul be to use an acoustic camera. This is a strong motivation for the DTU esign of a Large Aperture Acoustic Camera (LAAC), which is iscusse in another paper at this conference. References [1] Bowler, D. Amplitue moulation of win turbine noise: a review of the evience. Institute of Acoustics Bulletin, 33, 31 41, 008. [] Bullmore, A., M. Can, S. Oerlemans, M. Smith, P. White, S. von Hünerbein, A. King, an B. Piper. Win Turbine Amplitue Moulation: Research to Improve Unerstaning as to its Cause an Effects. RUK, [3] Oerlemans, S. An explanation for enhance amplitue moulation of win turbine noise. In RenewableUK 013 report: Win Turbine Amplitue Moulation: Research to Improve Unerstaning as to its Cause & Effect, 013 [4] Masen, H. A., F. Bertagnolio, A. Fischer, an C. Bak Correlation of amplitue moulation to inflow characteristics. INTER-NOISE an NOISE-CON Congress an Conference Proceeings, Vol. 49 of, , 014 [5] 4Dnoise, 104: Norsonic vieo. (Accesse 014). [6] Salomons, E. M. Computational atmospheric acoustics. Springer Science \& Business Meia, 001 [7] Bowler, D., an G. Leventhall Win Turbine Noise. Bowler, Dick an Leventhall, Geoff, E. Multi-Science Publishing,