This paper presents a combined experimental and numerical study that characterises the directivity of blade-tower interaction (BTI) noise. Numerical computations were performed using a hybrid approach combining unsteady Reynolds-averaged Navier-Stokes equations and Curle's acoustic analogy, allowing the noise from the blades and the tower to be computed separately. The noise directivity of the blade and the tower components have a dipole pattern and a monopole-like pattern, respectively; hence, the resulting BTI noise directivity resembles an oval. Partial cancellations between the blade and tower components are also shown to affect the BTI noise directivity.

Rotor-structure interactions play an important role in performance, structural integrity, and noise generation of the machinery involved.1 In the case of wind turbines, the interactions are between the turbine blades and their supporting tower.2 This aerodynamic noise due to the unsteady interaction between turbine blades and a tower is referred to as blade–tower interaction (BTI) noise. BTI noise is generated by the change in loading on the blades and tower. There are two mechanisms causing the change in loading: (1) the modification of the flow field that the blade is passing through due to the presence of the tower, which changes the loading on the blade itself and (2) blade-passage effects, where the pressure field around the passing blade interacts with the tower and alters the loading on both of them. Its acoustic signature is an acoustic pulse occurring each time a blade passes the tower; thus its frequency depends on the rotational speed and the number of blades, which is commonly referred to as the blade-passing frequency (BPF). As BTI generates noise at the BPF and its harmonics, it typically falls in the infrasound and low-frequency range. However, due to the impulsive nature of BTI noise, the acoustic spectra typically consist of a tonal peak at the BPF accompanied by additional peaks at its higher harmonics.3–5 The high levels of the harmonics suggests that although the BPF is in the infrasound range, the harmonic tones may be within the audible frequency range of human hearing.

The existence of BTI noise has been noted in previous experimental studies.3,4,6 A number of numerical studies on BTI noise have also been conducted, but they tend to focus only on the mechanism of the noise from blade due to the modified flow field.7–9 While blade passage effects on the aerodynamic performance have been widely researched,10–12 it is only recently that its effects on BTI noise production were investigated by Yauwenas et al.13 and Zajamšek et al.2 

These recent studies on BTI noise2,13 performed combined experimental and numerical studies on a simplified wind turbine model, where the distance between the blade and the tower, d, varies from d/D=2/7 to 1, where D is the rotor diameter. One major finding from these studies is that the flow field around the blade interacts strongly with the tower during blade passage. As a consequence, the tower contributes at least just as much as the blade, if not more, to BTI noise. This is important because previously the role of the tower had been ignored.7,8 However, the results presented in Refs. 2 and 13 were obtained from only one observer position, along the axis of the rotation. While directivity has been previously examined, typically there are discrepancies in the transverse direction (along the rotor plane) between measured and predicted noise.14,15 This unexpected directivity pattern has more recently been confirmed by Klein et al.,5 who found that the directivity of BTI noise and its tower component resemble an oval and a monopole, respectively. Such directivity patterns are particularly interesting as BTI noise has conventionally been assumed to have a dipole pattern.15 This indicated a knowledge gap in understanding the mechanism of BTI noise directivity, especially the noise component emanating from the tower.

In this study, noise signature emanating from a rotor rig used in Refs. 2 and 13 were obtained experimentally and predicted numerically at different observer directions. As BTI occurs in fan and turbine configurations, both of these are considered.

The aim of this paper is therefore to provide a better understanding of BTI noise directivity by presenting how the noise characteristic changes with direction around the tower, while taking into account the noise contribution of the blade and the tower separately.

A three-bladed rotor rig was used in the experiments and as a basis for the numerical computations. The airfoil profile of the blades is the symmetric NACA0012 airfoil, with a constant chord length, c, of 70 mm and a constant pitch angle of zero along its radius of R = 520 mm. To keep the boundary layer on the blade consistently turbulent, they were tripped at 10% of the chord length using 0.6 mm thick serrated tripping tape on both sides. This rig was used previously2,13 and for brevity's sake readers are directed to these papers for the full details. The general dimensions of the rotor rig and the axis orientation are shown in Fig. 1. Blade angular position is defined by its azimuthal angle, ϕ, which was defined to be positive in the direction of rotation and 180° when pointing downwards, parallel with the tower.

Fig. 1.

Rotor-rig setup: (a) definition of blade-tower distance d and blade pitch angle, viewed from top; (b) locations of acoustic measurement (not all shown).

Fig. 1.

Rotor-rig setup: (a) definition of blade-tower distance d and blade pitch angle, viewed from top; (b) locations of acoustic measurement (not all shown).

Close modal

The rig was set up in two configurations, fan and turbine, although experimental data is only available for the fan case. In all cases, the rotational speed of the blades was 900 RPM. For the fan configuration, the blade pitch angle, θ, was a constant 5° in the positive direction indicated in Fig. 1(a) and the blades imparted energy to the fluid. For the turbine configuration, a freestream of U=8.45 m/s was present in the turbine case, which approached the rig in the positive x direction such that the blades are located upstream of the tower. Taking other parameters in this configuration into consideration, this corresponds to a tip-speed ratio of XTSR = 5.8. Here, tip-speed ratio was defined as XTSR=vtip/U, where vtip is the tip speed of the blades.

The pitch angle was also 5° across the radius of the blade in the turbine case, but due to the presence of the freestream the blades extracted energy from the flow instead. There was a blade-tower distance of d = 20 mm [see Fig. 1(a)], which is 2/7 of both the tower diameter and the chord length of the blade. The case with fan configuration was performed both experimentally and numerically, while the case with turbine configuration was only performed numerically.

The experimental measurements were conducted in the University of Adelaide's anechoic room using 37 microphones evenly distributed along a 180° arc parallel to the ground. The arc had a radius of 20c and a centre point at the intersection of the axis of rotation and the propeller plane, as shown in Fig. 1(b). The definition of observer direction, ξ, was as depicted in Fig. 1(b); note that not all microphone positions are shown here. The acoustic data were recorded using B&K tyype 4955 1/2 in. microphones for 60 s at a sampling rate of 216 Hz. To remove undesirable noise, the data were then filtered using a sixth order Butterworth filter with a cut-off frequency at 1 kHz.

The computational models and setup followed closely the previous study by Yauwenas et al.13 The noise computation used computational fluid dynamics (CFD) to obtain the flow field and surface pressure data, which were then fed into the compact formulation of Curle's acoustic analogy16 to model the sound wave propagation to the observer positions. Using this approach allowed the BTI noise contributions from the blades and the tower to be predicted separately.

For the CFD computations, ANSYS FLUENT 14 was utilised to solve unsteady Reynolds-averaged Navier-Stokes (URANS) equations, using kω as the turbulence model17 and SIMPLEC algorithm for the pressure-velocity coupling.18 The time step was chosen to be 0.185 ms, giving 1° rotation per time step and a Nyquist frequency of 2700 Hz. For consistency, the resulting acoustic data were filtered using the same parameters as their experimental counterparts (cut-off frequency at 1 kHz). Each case was run for a total of 5040 timesteps or 14 rotations of the turbine disk, which reached quasi-steady state after eight rotations. To simulate the rotation of the blades relative to the tower, the sliding mesh method was used. The validation for this computational model is available in Refs. 2 and 13 and is also presented as a part of the acoustic results in Sec. 3.2.

To help understand the change in BTI noise signature with direction, the forces acting on the blades and the tower are presented first. Figure 2 shows the force coefficient acting on the blade and the tower obtained from the numerical computation, for both configurations. The force coefficient on the tower is decomposed to its x and y components, which will be referred to as the thrust force and the sideways force, respectively. Force coefficient here is defined as

CF=F0.5ρvtip2A,
(1)

where F is the force on a single blade or the tower and A is the planform area of a single blade.

Fig. 2.

Time history data of the forces acting on the blades and the tower over one rotation cycle, shown for (a) the fan configuration and (b) the turbine configuration. The force coefficient on each blade is plotted individually. (c) Locus of CFt vector over one rotation cycle projected onto x1-x2 plane, shown for the fan and the turbine configurations. (d) Schematic diagrams of the pressure field formed around the passing blade positioned at ϕ=180°.

Fig. 2.

Time history data of the forces acting on the blades and the tower over one rotation cycle, shown for (a) the fan configuration and (b) the turbine configuration. The force coefficient on each blade is plotted individually. (c) Locus of CFt vector over one rotation cycle projected onto x1-x2 plane, shown for the fan and the turbine configurations. (d) Schematic diagrams of the pressure field formed around the passing blade positioned at ϕ=180°.

Close modal

The thrust force coefficient on each of the three blades, CFb, is shown separately and overlaid on one another. They are in the negative-x direction during the whole rotation cycle for the fan configuration [Fig. 2(a)] because the blades impart energy to the fluid, but are in the positive-x direction for the turbine configuration [Fig. 2(b)] because the blades extract energy from the fluid. In both cases, there is an impulsive change in CFb in the negative-x direction as each blade passes the tower.

The force fluctuations acting on the tower, CFt, is more complex than CFb, but the waveform patterns observed in both the fan and turbine cases are similar. For the thrust force, CFxt there is a strong impulsive peak towards the negative-x direction at ϕ180°, which is labelled CFxt,min in Fig. 2. This minimum peak is preceded and followed by weaker pulses towards the positive-x direction. The mechanism behind the thrust force fluctuations on the blade and the tower have been discussed by Zajamšek et al.2 

The sideways force waveform on the tower, CFyt, however, is dominated by two strong peaks. For the fan case, the first major peak is in the negative-y direction and is immediately followed by the second one in the positive-y direction, which are labelled CFyt,min and CFyt,max in Fig. 2(a), respectively. CFyt,min occurs when the blade is just about to pass the tower (ϕ175°) while CFyt,max occurs when the blade has just passed the tower (ϕ185°). For the turbine configuration, the waveform exhibits a similar pattern but with inverted phase. In this case, CFyt,max occurs when the blade is approaching the tower and CFyt,min immediately follows, as may be seen in Fig. 2(b).

To obtain a more complete picture of the force acting on the tower over one rotation cycle, Fig. 2(c) shows the locus of the vector of CFt projected onto x-y plane, with the points corresponding to ϕ=170°,180°, and 190° are marked. This provides another visual representation of CFt presented in Fig. 2, which demonstrates the dynamic nature of CFt during BTI and helps explain the noise directivity presented in Sec. 3.2.

The loci for both configurations follow a similar pattern, which is a cardioid-like shape almost symmetric along the x axis. This indicates that both resultant CFt vector loops about the axis of the tower during each blade passage, thus there are three such loops in one rotation cycle of the rotor. However, the sequence of the ϕ markers show that the CFt vector for the fan case loops in the opposite direction to the turbine case.

The patterns of force fluctuations on the tower shown in Figs. 2(a)–2(c) are due to its interaction with the high and low pressure fields around the passing blade.2,13 Schematic diagrams of these pressure fields when the passing blade is at ϕ=180° are shown in Fig. 2(d). High pressure regions are formed around the leading and trailing edges of the blades, with low pressure regions formed between the high pressure ones. In both configurations, CFxt,min in Figs. 2(a) and 2(b) is due to the low pressure region around the midchord of the passing blade being in the vicinity of the tower This results in a strong transient force on the tower towards the negative-x direction.

For the fan configuration, the interactions resulting in net sideways forces at ϕ175° and 185° are due to the high-pressure fields generated by the blade, as has been shown by Zajamšek et al.2 When the blade approaches the tower (ϕ175°), the high pressure region around the leading edge of the blade results in a net sideways force on the tower away from the blade (the negative-y direction) which peaks at CFyt,min in Fig. 2(a). Just after the blade has passed the tower (ϕ185°), the high-pressure field around the trailing edge now interacts with the tower. This results in a net sideways force away from the retreating blade (the positive-y direction), which peaks at CFyt,max in Fig. 2(a).

In contrast to the fan configuration, the sideways force fluctuations on the tower for the turbine configuration are instead due to its interactions with the low-pressure field generated by the blade. The pressure field patterns are flipped along the chordline between the two configurations, because the circulation around the turbine blade is the opposite of its fan counterpart.2 As such, the suction side that produces a strong low-pressure field is facing towards the tower. This is why the sideways force fluctuations for the turbine case occurs with an inverted phase relative to fan case, despite having the same direction of rotation. Furthermore, the low-pressure region is typically at its strongest around the thickest part of the blade, which is closer to the leading edge at about 30% chord in this case. This results in the asymmetry of the force locus, where CFy is negative when the blade is aligned with the tower (ϕ=180°).

The different interactions between the two configurations also explains the larger force locus for the turbine case than that for the fan, as may be observed in Fig. 2(c). For CFy, the fluctuations are stronger for the turbine case because the interaction is dominated by the low-pressure region on the suction side of the passing blade. For lift-generating airfoil-shaped bodies, this low-pressure region is typically stronger than the high-pressure regions. The stronger CFx for the turbine case has a simpler explanation, which is due to the presence of the freestream that generates a stronger net force on the tower in the absence of BTI.2 

Figure 3 shows the time-history data of the measured and predicted acoustic pressure over one rotation cycle for both configurations, obtained from observer directions ξ=45°,135°, and 180°. These positions were chosen due to the noteworthy interactions between the acoustic waveforms emanating from the blades and the tower. For the predicted results, the noise components emanating from the blade and the tower are also presented individually. In the following discussion, p is acoustic pressure and its subscripts b, t, comp, and exp refers to the predicted blade noise component, the predicted tower noise component, the predicted combined total, and the experimental measurement, respectively. ptotal is used to refer to the total BTI noise in general, both computational and experimental.

Fig. 3.

Acoustic pressure waveform over one rotation cycle for the fan configuration, measured at ξ: (a) 45°, (b) 135°, (c) 180° and for the turbine configuration at ξ: (d) 45°, (e) 135°, and (f) 180°. The computed blade and tower noise components are also shown separately.

Fig. 3.

Acoustic pressure waveform over one rotation cycle for the fan configuration, measured at ξ: (a) 45°, (b) 135°, (c) 180° and for the turbine configuration at ξ: (d) 45°, (e) 135°, and (f) 180°. The computed blade and tower noise components are also shown separately.

Close modal

Similar to the forces results, there are three acoustic pulses in one rotation cycle, one for each blade passage. As Curle's formulation suggests, the acoustic pressure emanating from a surface is related to the rate-of-change of the force acting on it.16 Looking at the breakdown of the computed noise, the tower component dominates its blade counterpart at all observer positions investigated in this study in all directions. From Figs. 3(a)–3(c), the magnitude and the waveform of pcomp are shown to be in good agreement with pexp. The only major discrepancies are the three periods of additional oscillation over one rotation cycle of the blade for pexp [most clearly in Fig. 3(c)], which can be attributed to the thickness noise of the three rotating blades. This is confirmed by the absence of such oscillations at ξ=90° presented in Zajamšek et al.,2 because thickness noise is almost negligible at positions along the axis of rotation. The thickness noise mechanism is not taken into account by the compact formulation of Curle's analogy used in our acoustic model. This is to isolate the noise signature from the loading noise mechanism, which is the dominant noise source in BTI. Previous validations of the computed noise are available in Refs. 2 and 13.

For the fan configuration, the p waveforms at ξ=45° and 135° [Figs. 3(a) and 3(b)] exhibit a similar pattern, but with the relative phase inverted. The weakest local peak at ξ=45° occurs at the tail end of the waveform, whereas at ξ=135° the weakest local peak occurs at the beginning. Upon close examination, only the tower component has its phase inverted between these two positions, while the blade component remains in the same phase. However, the tower component is more dominant and thus dictates the shape of the total acoustic waveform. Additionally, the phase difference between the blade and tower components also affects the wave interference between the two components. Both components are in phase at ξ=45°, resulting in constructive interference, while at ξ=135° there are partial cancellations for some peaks (e.g., the two peaks around ϕ=180°). As a result, the amplitude of certain total peaks are lower than the sum of the blade and the tower components.

For the turbine configuration, the waveform pattern at each observer direction shown in Fig. 3(d)–3(f) is similar to the fan configuration, except at ξ=180°, where the phase is inverted. This is due to the inverted phase of the sideways force for the turbine case relative to that of the fan, as discussed from comparing Figs. 2(a) and 2(b). Another notable difference is the blade-to-tower contribution ratio is higher than the turbine configuration. As in the case of the fan configuration, the wave interference between the blade and the tower components affects the noise directivity. At direction ξ=45°, the two components are in phase and reinforce one another, whereas partial cancellations between the blade and tower components are present at ξ=135° towards the end of blade passage [e.g., just after ϕ=180° as annotated in Fig. 3(c)].

From Figs. 3(c) and 3(f), the p waveforms at ξ=180° (on the propeller plane) for both the fan and turbine cases have a similar pattern, only with the amplitude inverted. The waveform pattern is dominated by one strong, impulsive acoustic pulse occurring between two weaker pulses during each blade passage. The strong pulse can be attributed to the sideways forces acting on the tower rapidly changing direction during blade passage [see Figs. 2(a) and 2(c)].

Figure 4 shows the noise directivity of both the fan and turbine configurations. The noise level is presented in its overall sound pressure level, which is defined as OASPL=20log10(prms/pref), where prms is the root mean square of the acoustic pressure and pref is the reference pressure, 2×105 Pa. There is a good agreement between the measured and computed noise directivity for the fan case, with the slight discrepancies around ξ=0° and 180° can be attributed to the neglected thickness noise in the computed noise. The directivity pattern is quantified as the root mean square of directivity index over ξ, DIrms, where directivity index itself is defined as the variation of OASPL from its averaged value, DI(ξ)=OASPL(ξ)OASPL(ξ)¯. As such, DIrms = 0 indicates a uniform directivity pattern and the value increases with non-uniformity. DIrms of pcomp,pb, and pt for the fan case are 0.59, 3.94, and 0.26 dB, respectively. While for the turbine case, DIrms of pcomp,pb, and pt are 1.18, 4.26, and 0.12 dB, respectively.

Fig. 4.

Directivity pattern of the BTI noise obtained in this study presented in OASPL, for (a) the fan configuration, (b) the turbine configuration. The computed blades and the tower noise components are also shown separately. The noise level is the OASPL, where the cut-off frequency is 1000 Hz.

Fig. 4.

Directivity pattern of the BTI noise obtained in this study presented in OASPL, for (a) the fan configuration, (b) the turbine configuration. The computed blades and the tower noise components are also shown separately. The noise level is the OASPL, where the cut-off frequency is 1000 Hz.

Close modal

From Fig. 4, it is interesting to note that the ptotal has a pattern resembling an oval, particularly for the turbine case. This is consistent with the findings made by Klein et al.5 At the propeller plane, ξ=0° and 180°,ptotal are in the same order as the level at the position along the axis of rotation, ξ=90°. This is inconsistent with the dipole noise directivity conventionally expected from BTI noise generated by the blades,15 but the reason behind the significant noise level at the rotation plane is clear when pb and pt are inspected separately. pb indeed shows a dipole directivity pattern, which is the strongest at the axis of rotation (ξ=90°) and is reduced at observer positions away from the axis and eventually becomes negligible at the observers on the propeller plane (ξ=0° and 180°). This implies that at observer positions along the propeller plane, BTI noise is produced almost exclusively by the tower. This observation reinforces previous findings that tower plays an important role in BTI.2,13 It may also explain the underprediction of computed BTI noise level on the propeller plane observed in previous studies,14,15 because only the blades were considered as the BTI noise source in the computations. The slight skew of the blade noise towards direction ξ=0° is due to the convective amplification effects, because the blade is moving towards that direction during BTI.

This leads to the next noteworthy observation, that the BTI noise emanating from the towers appears to have a monopole directivity pattern. However, it is not a true monopole source but rather a result of the resultant force vector on the tower rotating about its axis during BTI, as has previously discussed from Fig. 2(c). It appears to be a monopole because the acoustic pressure was time-averaged to obtain the polar plot, as discussed from Fig. 3(b).

Furthermore, the total directivity patterns in both cases are not simple summations of their respective blade and tower components. It may be observed at observer positions 100°ξ170° for the fan case [Fig. 4(a)], where the noise level of ptotal is actually less than that of the tower contribution itself. This is due to the partial cancellations between the blade and tower components that occurs at particular observer directions, as discussed from Fig. 3(b). The effect is not as apparent in the directivity plot as the noise level is presented in log scale. In contrast, at ξ=45° the two acoustic components are in-phase and reinforce each other instead [see Fig. 3(a)].

Similar phenomenon is present in the directivity of the turbine configuration in Fig. 4(b), where the noise components reinforces each other more strongly in the streamwise directions (ξ90° and 270°) than in the propeller plane directions (ξ0° and 180°). The acoustic waveform for the turbine configuration at ξ=90° has been shown by Zajamsek et al.2 to have blade and tower components that are in-phase, thus resulting in strong constructive interference. This is not the case at ξ=0° and 90° and thus the resulting BTI noise is not much higher than the dominant contribution from the tower. The role of partial cancellations in determining the level of BTI noise presents an avenue for noise control. For example, by introducing skew to the blades and varying the tower diameter with height to adjust the phase of each component for maximum cancellation effect.

A combined experimental and numerical study characterising the directivity of BTI noise in fan and turbine configurations has been presented. BTI noise emanating from a rotor rig with three blades was measured from different observer directions about the tower. The geometry of the rotor rig was recreated for a numerical model combining URANS and Curle's acoustic analogy to predict the noise, including the contributions from the blade and the tower separately. Although the directivity of BTI noise has been briefly touched on in previous studies, there were some discrepancies between measured and calculated directivity patterns.14,15 This indicated a need for a better understanding of BTI noise mechanism in different directions about the tower, which has been presented in this paper.

The aerodynamic results showed that the sideways force fluctuations on the tower during BTI has a comparable amplitude to, and the waveform is about as complex as, the thrust/streamwise force fluctuations. Plotting the locus of the resultant force on the tower shows that its vector on the tower rotates about the axis of the tower during BTI. Furthermore, as recent studies also have suggested, the amplitude of the force fluctuations on the tower was found larger than that of the blade in both configurations.

The acoustic results in this study found that both measured and predicted BTI noise is almost uniform in all direction, which is contrary to the conventional assumption that the directivity pattern is dipole. This is due to the erroneous previous assumption, especially in wind turbine applications, that only the blades play a role in BTI noise production. The blade component of BTI noise was indeed found to have a dipole directivity pattern, but interestingly the tower component of BTI noise appeared to have a monopole pattern. However, recalling the force vector loci suggests that this was a result of the force vector on the tower rotating about the axis of the tower during blade passage and thus the monopole-like pattern was a result of a time-averaged rotating dipole.

Due to a combination of the findings above, the resulting total directivity pattern resembles an oval, depending on the individual strength of the contributions from the blade and the tower. Such a pattern is predominantly due to the interaction between the pressure field around the passing blade and the tower. Barring extreme changes in geometry, altering the flow conditions beyond this study will affect the intensity but not the pattern of the pressure field. Thus, the exact directivity pattern may be altered (such as the eccentricity of the oval) but the underlying mechanism holds. The directivity pattern is also consistent with that observed by Klein et al.5 and the aerodynamic findings in this study explain its mechanisms. Another factor that influences the directivity of BTI noise is the partial cancellations between from the blade and the tower components, which presents a potential way to control noise by maximising these partial cancellations.

We gratefully acknowledge the financial support from the Australian Government through the Australian Research Council, Project No. DP130103136.

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