Computation of Inflow Turbulence Noise of a Tidal

Computation of Inflow Turbulence Noise of a Tidal Turbine Thomas P. Lloyd†‡ , Stephen R. Turnock† , Victor F. Humphrey‡ † Fluid

Structure Interactions Research Group; ‡ Institute of Sound and Vibration Research, Faculty of Engineering and the Environment, University of Southampton, Southampton, SO17 1BJ. UK. E-mail: {T.P.Lloyd; S.R.Turnock; V.F.Humphrey}@soton.ac.uk Abstract—Predictions of expected unsteady loads on tidal turbines are vital for ensuring longevity of installed devices. In addition, the acoustic signature of turbines has become a design consideration for environmental impact assessment. To address both these issues, we present numerical simulations of a model scale turbine. Inflow turbulence is used to replicate time-dependent flow conditions. Both the unsteady thrust and power spectra, and far field acoustic pressure are analysed. It is found that peaks in the thrust and power spectra are related to the interaction of multiple turbine blades with long axial turbulence structures. There is also evidence of these peaks in the acoustic spectra. Scaling of the predicted sound pressure level from model to full scale predicts a noise source level of 120.5dB re 1µP a2 m2 Hz −1 , which qualitatively agrees with the limited data available in the literature. The advantage of the method is the ability to generate inhomogeneous anisotropic turbulence fields (although not carried out here), motivating further simulation of more realistic tidal stream environments. Index Terms—Tidal energy; inflow turbulence; hydroacoustics; dynamic forces; computational fluid dynamics.

I. I NTRODUCTION Tidal turbines have the potential to harness a reliable and plentiful energy resource, but operate in a harsh environment. This includes large fluctuating velocities due to the oceanic turbulent boundary layer, which can contribute to fatigue loading [1]. It has also been shown that fluid-structure interaction can increase power generation [2]. Thus studying this behaviour in a dynamic environment would seem appropriate. The effect of turbulence on turbine wakes will also influence the layout of arrays so as to optimise total power capture [3], [4]. Another prudent design driver is the acoustic emission of a turbine, which is of concern as part of environmental impact assessment [5]. It is possible that tidal turbine noise will have some impact on marine life, but attempts to quantify this are limited. We direct the reader to work involving fullscale turbine noise measurement [6], [7], as well as noise estimation for smaller devices [8], [9]. Turbine noise sources are commonly defined in terms of a sound pressure level (SPL) measured at some far field distance. These are often corrected back to a source level (SL) at 1 m from the the rotor. A typical level defined in this way is of the order of 166 dB re 1µPa at 1 m [6]. Richards et al. [7] expect the dominant noise from horizontal axis tidal turbines to be due to rotating machinery in a frequency range ∼ 1 − 100 Hz.

Wang et al. [8] measured the noise of a 0.4 m diameter device, using a scaling procedure recommended by ITTC [10]. The reported maximum third-octave bandwidth SPLs (for a freestream velocity of 2.57 ms−1 ) were approximately 115 dB and 125 dB for model and scaled results respectively. A large dependency on the freestream velocity was also observed, with an increase of up to 30 dB predicted when moving from 2.57 ms−1 to 4.67 ms−1 . We have previously presented predictions of tidal turbine noise [11] as well as impact assessment [12], using empirical modelling. The approach was based on modelling the turbine unsteady thrust spectrum due to inflow turbulence, and predicting the noise assuming free field radiation [13]. The estimated source level was ∼ 145 dB re 1µP a2 m2 Hz −1 across a frequency range of ∼ 10-100 Hz. In this paper, we present a methodology for simulating the unsteady forces, and hence turbulence-induced acoustic sources on a model scale tidal turbine. First, we outline our computational methodology in §II. Results for the inflow turbulence are presented next (§III). Then the rotor forces and acoustics are presented (§IV). Finally, conclusions are drawn in §V. II. C OMPUTATIONAL M ETHODOLOGY A. Test case description The simulated turbine is a model scale device that has been previously tested by [14]. Key parameters are given in Table I. TABLE I T EST CASE PARTICULARS .

Symbol

Meaning

Value

R B U∞ Ω T SR θ

Rotor radius Number of blades Mean freestream velocity Rotational velocity Tip speed ratio Hub twist angle

0.4 m 3 1.4 ms−1 20.68 rads−1 5.96 15◦

The tip speed ratio is defined as T SR = ΩR/U∞ . For this case, the turbine thrust and power coefficients are 2 3 CT = 2T /ρAU∞ = 1 and CP = 2ΩQ/ρAU∞ = 0.36.

Here, T is thrust (kgms−2 ), Q torque (kgm2 s−2 ), ρ0 the fluid density (1000 kgm−3 ) and A (m2 ) the rotor projected area. The turbine was tested in low turbulence facilities, and hence the results reported here are not directly comparable. The experimental CT and CP are used primarily to assess the quality of the simulation grid. It should be noted that introducing inflow turbulence in the numerical simulation has little effect (< 1%) on the mean thrust and power coefficients [15]. A larger effect is observed for the root mean square of these quantities. B. Numerical models R Simulations were carried out using the OpenFOAM 2.1.0 libraries, augmented by custom solvers and boundary conditions. The key components of the setup are: • The dynamic mesh solver pimpleDyMFoam, which is based on the PISO algorithm [16], but allows larger time steps to be used. • A rotating domain containing the turbine. Rotation is specified using the solidBodyMotion dynamic mesh library, with data interpolation between the rotating and stationary domains handled using the arbitrary mesh interface (AMI). • Inflow turbulence generated using the forward stepwise method (FSM) of [17], based on the digital filtering approach of [18]. Inhomogeneous anisotropic turbulence may be generated. • Turbulence modelling based on large eddy simulation (LES), using the Smagorinsky [19] subgrid model. • Runtime processing using the turboPerformance libraries, available through the OpenFOAM Extend Project1 , giving transient data such as turbine thrust, power and efficiency.

C. Specifying the inflow turbulence Inflow turbulence is generated at a plane x/D = −2, where D is the turbine diameter. This is due to the fact that the fluctuating velocities are inserted into the flow solution on a ‘virtual grid’, which must be located some distance downstream of the domain inlet (see [17] for details). The chosen statistics are based on the recommendations of the IEC, and are the same as those used by [3]. The horizontal integral length scale is then Lx,z = 0.7D, with Ly = Lx,z /6. A turbulence intensity (T I) of 10% is used, which is specified as homogeneous and isotropic. Note the FSM has the ability to generate fully inhomogeneous, anisotropic mean velocity, length scale and turbulence intensity profiles more akin to realistic tidal flows. However, as a demonstration of our methodology, only anisotropic length scales are used here. D. Domain design Since the experimental data have been corrected for tunnel blockage effects, an unbounded domain is used for the simulations. Hence no correction is applied to the numerical results, whilst the corrected values provided in [14] are used. 1 http://www.extend-project.de

The domain has overall dimensions Lx × Ly × Lz = 10D × 6D × 6D, where x, y and z are the streamwise, vertical and horizontal directions (see Figure 1(b)). The inlet is located 3D upstream of the turbine rotor plane, which is centred at the domain origin. A cylindrical rotating region of dimensions Lx × R = 0.5 m × 0.5 m centred at the domain origin encompasses the turbine rotor. The computational grid is generated using the OpenFOAM utilites snappyHexMesh and mergeMeshes. Geometry files are used for the blades and rotating cylinder, with an idealised hub geometry constructed from simple cylinders and spheres. The stationary grid region is refined in the upstream and wake regions so as to improve the resolution of turbulence structures. The aim is to resolve a streamwise structure at least 6 times smaller than L, equivalent to approximately 0.045 m. This is in line with the resolution requirements for a LES [20]. The total number of cells for each of the rotating and stationary domains is approximately 1.6 × 106 . A uniform inlet velocity of 1.4 ms−1 is used, with a Neumann condition for pressure. A fixed pressure is specified at the outlet, with a convective condition for velocity. This allows vortical waves to leave the domain without reflection, which is important for LES. All other sides use a symmetry condition. The turbine hub is treated as a slip wall, in order to reduce the number of grid cells required in this region. A no-slip condition is used for velocity on the blades. Since the grid is not wall-resolved (y1+ ≈ 30), a wall function is used for the subgrid viscosity. y1+ is the non-dimensional first cell height based on the friction velocity and kinematic viscosity, and is a measure of how well the viscous sublayer is resolved. Although we were able to generate a wall-resolved (y1+ = 1) grid, the smaller time step required proved prohibitive in achieving a converged solution within a reasonable computational time. E. Solution settings Results were computed in parallel using 108 processors on the University of Southampton’s Iridis 3 High Performance Computing cluster. Both spatial and temporal discretisation utilise second-order schemes. In general, linear schemes are used, with some upwinding introduced for stability. The upper limit for the computational time step is set at 2×10−5 s (which is the same as the LES in [15]), corresponding to 0.024◦ of turbine rotation per time step. This time step is necessitated by the time accurate nature of the simulation, and is far below the 5◦ per time step recommended by [21]. In [15], it is recommended that the mesh rotation per time step should be equivalent to half the interface cell size; here we calculate ∼ 37 time steps per half cell of rotation. A turbulent field generated for a box of the same dimensions and approximate mesh distribution as the turbine grid was used as an initial condition. Thus the turbine blades immediately experience unsteady loading. The simulations were run for 4 turbine rotations before data were sampled; this corresponds to a time when the generated inflow turbulence has just passed the rotor. Sampling was carried out at 10 kHz for a further

symmetry plane inflow turbulence generation plane

3D 7D

3D inlet

x θ = 0◦

3 4 1 2 rotor

y

hub

outlet

AMI

upstream refinement region

θ = 90◦ z

wake refinement region

y x z

(a) Domain design. Simulation probe locations also shown as numbers Fig. 1.

(b) Coordinate system.

Schematic representations of simulated case.

12 rotations, or until one full domain flow-through had been achieved from initialisation. Ideally statistics would be collected over a further flow-through; however, time constraints prevented this. The linear solver exits each iteration loop when the total residual within the current time step has reduced to 10−5 (for pressure) or 10−9 (for all other variables). The total simulation time is of the order of 4.5 × 104 CPU hours. III. C HARACTERISTICS OF THE INFLOW TURBULENCE Visualisation of the inflow turbulence is provided in Figure 2(a). Fine scale turbulence structures are observed downstream of the inflow turbulence generation plane. Turbulence also appears to convect through the AMI without suffering significant numerical dissipation. This is confirmed in Figure 4, where streamwise lines of both the instantaneous and mean velocity through the AMI are plotted. At y/D = 0, a small change in the instantaneous velocity is seen across the AMI; however at y/D = 0.5 this change is seen to be no larger than the inherent unsteadiness in the flow. Hence we expect the AMI to have little effect on the flow into the rotor. In the wake, fine structures are less evident (Figure 2(b)). This is partially due to the coarser grid used in the wake region, but also caused by the interaction between the turbine blades and unsteady flow field at the rotor plane. The wake is instead dominated by two sets of counter-rotating vortices, generated at the blade tip and root. Notice that the turbulence structures downstream of the rotor appear more isotropic than those upstream, having been broken up by the rotor blades. Table II shows measures extracted from the velocity probe data. The integral length scale has been evaluated using the R and integrating with respect to autocorr function in matlab , time using Simpson’s rule. Statistics at probe location 2 most closely resemble those specified at the inlet. The turbulence intensity is however higher than expected at all probe locations upstream of the rotor. This is possibly due to the relatively short distance between the inflow generator plane and the

rotor. Since no tidal channel effects are modelled, there is no turbulence production, and the turbulence intensity required at the inflow plane must be estimated . Table II reveals that the TI has been over-predicted at the inflow plane. Note that the integral length scale is independent of this, and has been shown to quickly attain the specified value when using the FSM [22]. The increase in mean velocity and turbulence intensity away from the rotor centreline (probe 3) is attributed to the convection effect of the rotor. Downstream of the rotor (probe 4), the mean velocity is reduced, due to the power extracted from the flow by the turbine. The integral length scale is also noticeably smaller, as the rotor has broken up the long axial turbulence structures. The mean behaviour of the velocity field can be deduced from Figure 3. Upstream, the mean velocity profile is approximately homogeneous, as expected. Downstream, the power extraction at the rotor plane causes a large velocity deficit in the wake region. This reduces with downstream distance as the wake recovers to freestream velocity. These wake velocity profiles are characteristic of tidal turbines, with similar profiles predicted using steady methods [23]. Note that while the inflexion in the x/D = −0.5 velocity profile at y/R = 0.8 is expected, the decrease in velocity close to the hub is purely related to the vortices travelling along the extended hub. This effect is not present for a truncated hub geometry [23]. A final qualitative analysis of the velocity field is shown in Figure 5. The turbulent velocity field at x/D = −1.2 appears approximately homogeneous, with large positive and negative velocity fluctuations. At x/D = 0.6, the wake is dominated by the swirl of the tip vortices and fine scale structures are absent (as observed in Figure 2). The cylindrical wake shape here is well defined. Further downstream, where the tip vortices are no longer well resolved, the wake is less well defined and the velocity deficit has decreased. This illustrates the behaviour

(a) Upstream of rotor plane (x from −0.7 m to 0 m).

(b) Downstream of rotor plane (x from 0 m to 2.1 m).

Fig. 2. Non-dimensional streamwise vorticity ωx∗ = ωx D/U∞ on a horizontal centreline plane. Approximate length of slices indicated in parentheses of each subfigure. The AMI is also visible as a black outline.

1.2 1

y/R

0.8 0.6 0.4 0.2 0 0.8

1.2 0.8 ux /U∞

Fig. 3. and 6.

1.2 0.4 ux /U∞

0.8

1.2 0.4

ux /U∞

0.8 ux /U∞

1.2 0.4

0.8 ux /U∞

1.2 0.4

0.8

1.2 0.4

ux /U∞

0.8

1.2

ux /U∞

Mean axial velocity along vertical lines, from turbine centreline to y/R = 1.2. Sampled locations are (left to right) x/D = −1, −0.5, 0.5, 1, 2, 4

analysed in Figure 3.

and CP (t) =

TABLE II S UMMARY OF VELOCITY PROBE DATA .

Probe

x/m

y/m

ux /U∞

T Ix /%

Lx /m

1 2 3 4

-0.3 -0.2 -0.2 0.2

0 0 0.28 0.28

1.21 0.97 1.09 0.8

16.4 15.0 20.7 19.3

1.00 0.55 0.48 0.27

IV. ROTOR RESPONSE A. Unsteady forces and power Turbine unsteady thrust and power are presented here in coefficient form as CT (t) =

2T (t) 2 ρAU∞

(1a)

2ΩQ(t) . 3 ρAU∞

(1b)

Figure 6 shows a time history of the unsteady thrust and power coefficients. Time has been non-dimensionalised as t∗ = tn, where n = Ω/2π. Low frequency oscillations in the data have not yet been explained. Fluctuations at higher frequency can be attributed to the effect of the turbulence impinging on the rotor blades. Mean thrust and power coefficients are presented in Table III. The agreement between experimental and numerical thrust coefficient is very good, and certainly within the numerical error for this type of simulation [24]. The numerical power coefficient shows reduced accuracy, being approximately 20% over-predicted. This is due to the use of wall functions to model part of the turbulent boundary layer, since viscous drag has more effect on power than thrust. Resolving the boundary layer would potentially improve this (as in [15]), but entail using many more cells. [24] showed that CP can be more accurately predicted, but used large grids

CT (t)

1.25

ux /U∞

1

ux ux

0.9 0.8 −0.3

−0.25

1

0.75

CP (t)

ux /U∞

1.2 1.1 1 0.9 0.8

0.5

−0.2

x/m

0.25 2n

3n t

Fig. 4. Non-dimensional streamwise velocity ux /U∞ on streamwise lines through the AMI: y/D = 0.5 (top) and y/D = 0 (bottom). AMI located at x = −0.25 m, denoted by the dotted line in the bottom figure.

Fig. 6.

4n

5n

∗

Time history of turbine thrust and power coefficients

P SD(CT )/Hz

10−3 10−4 10−5

P SD(CP )/Hz

10−6 10−3

Fig. 5. Non-dimensional streamwise velocity ux /U∞ on constant yz slices at x/D = −1.2, 0.6 and 2.5.

10−4 10−5 10−6 1 Bn 2

Bn

2Bn

5Bn

10Bn

f requency of up to 55 M cells. Since our primary interest is in inflow turbulence noise, where viscosity has very little importance, we cannot justify this improvement to the grid design.

Fig. 7. Power spectra density of turbine thrust and power coefficients. Spectral peaks at f = Bn and 2Bn marked; Bn ≈ 10Hz. Representative smooth broadband spectrum plotted as red dotted line.

TABLE III M EAN EXPERIMENTAL AND NUMERICAL INTEGRAL PERFORMANCE MEASURES

Coefficient

Experimental

Numerical

CT CP

1.0 0.36

0.98 0.43

Next frequency spectra of the signals in Figure 6 are considered, along with a spectrum of the individual blade axial force. The power spectral density (PSD) of the data in Figure

R 6 has been estimated using the pwelch algorithm in matlab . The signals are windowed 8 times using a Hamming window with 50% overlap. The resulting spectra are plotted in Figure 7, where frequency is represented as multiples of Bn, or the blade passing frequency (BPF), which is 9.87 Hz. Two main features are revealed in Figure 7. Firstly, the broadband nature of the spectra, which is due to the range of scales present in the impinging turbulence. The decay of the spectra confirm that the desired grid cutoff frequency of 50 Hz has been achieved, which corresponds to f = 5Bn.

10−5

10−6 1 Bn 2

Bn

2Bn

5Bn

10Bn

f requency Fig. 8. Power spectra density of the force coefficient for blade 1. Spectra for other two blades similar.

Secondly, clear spectral humps are seen. These are dominant at the first and second harmonics, with further harmonics present at higher frequencies. According to Blake [13, chap. 10], the spectrum shape will depend on the ratio of the axial integral length scale to the turbine pitch (P ). When: 1) Lx P/B, the spectrum will contain humps at multiples of Bn; 3) Lx > P , the spectrum will contain humps at multiples of Bn, of magnitude log(B). An estimate of the turbine hydrodynamic pitch can be made using the local resultant flow velocity seen by a blade section. Here we take a radius of 0.7R, and include axial and tangential inflow factors of 0.32 and 0.025 estimated using blade element momentum theory [25]. The pitch is then given by P/D = πtan(φ), where φ is the hydrodynamic pitch angle, or the angle between the local resultant flow velocity and the rotor plane (see [4] for a full description). This results in φ = 9.1◦ and P = 0.4 m. Therefore we expect spectral peaks of log(B). These are evident in Figure 7, where log(B) ≈ 4.8, which is equivalent to half a decade on the scale used in the Figure. Comparison can also be made to the spectrum of axial force on an individual blade, CX , which is plotted in Figure 8. This spectrum does not show the distinct humps, since considering only a single blade is equivalent to the criteria Lx 2D [28]. Note that the effects of the turbine hub on acoustic propagation are assumed to be negligible, since the wavelengths are large. In a true underwater scenario, the effects of propagation through the channel should be accounted for. Hence we choose r = 2D, since we expect this to be the range at which environmental impact may be important [12]. Figure 9 shows the sound pressure level for each of the three observers, where ! p2 (f ) SP L(f ) = 10log . (3) p2ref Here, p is that predicted using Equation 2, after which the frequency spectrum is estimated using pwelch. The reference pressure pref = 1µPa. Figure 9 depicts the acoustic spectra calculated using Equations 2 and 3 for the three observer angles. The spectral peak for the case θ = 0◦ is at f = 2Bn, which corresponds to the peak seen in Figure 7. This observer angle sees the highest SPL. Broadband loading noise exhibits a lobed shape, with the maximum SPL on the rotor axis [13]. Hence the noise diminishes significantly as the observer moves towards the

rotor plane. Whilst the SPL of the model scale turbine is not significant when compared to typical background noise levels in the ocean [7], the data can be used to make full scale noise predictions. We now utilise rudimentary scaling laws to estimate the peak SL for a typical full scale device. Note that the procedure outlined in [8] is not used, since this was designed for cavitation noise, which is not addressed here. The spectral peak of 80 dB is used to illustrate the method. The method requires: • the model scale far field SPL to be corrected to a distance r = 2D where D is the diameter of the full scale device; • the acoustic intensity at this location to be calculated using I = p2 /ρ0 c0 ; • scaling of the acoustic intensity, which assumes that I ∝ ρ0 u5 L2 /c20 r2 ; • using the resulting I to calculate p2 and the SPL. In addition, the source level is given as SL = SP L2D + 10log(r2 ). For the scaling of acoustic intensity, we assume all variables to be equivalent apart from L, which scales geometrically, and u. The chosen full scale values of D = 22m and u = U∞ = 2.5ms−1 are assumed typical for in-service devices (see [11], [12]). Scaling of the frequency is based on a Strouhal number St = f D/U∞ . Assuming the tip speed ratio remains constant during scaling, frequency can be scaled as nF DM U∞,F fF = = , fM nM DF U∞,M

(4)

where M and F denote the model and full scale values. In this case, the spectral peak in Figure 9 will shift from ∼ 20Hz to ∼ 1.3Hz. TABLE IV F ULL SCALE TURBINE ACOUSTIC SCALING RESULTS .

Acoustic quantity

Symbol

Value

Intensity ratio Sound pressure level Source level

IF /IM ∼ 1 × 104 SP LF,2D 87.8 dB re 1µP a2 Hz −1 SLF 120.5 dB re 1µP a2 m2 Hz −1

thrust and power are also available, allowing further performance analysis. The agreement between the numerical and experimental thrust coefficient is observed to be very good; the power coefficient is less well predicted however. This has been attributed to the use of wall functions to model the turbine blade boundary layer. In another LES study of the same turbine [15], CP was also less well predicted than CT , despite the blades being ‘wall-resolved’. This study also included the turbine nacelle tower, which helps to break up the tip vortices and improve the wake recovery. Including this might also improve the prediction of CP here. The effect of the total simulation duration on the derived statistics needs to be investigated further, both in terms of the mean performance measures and the acoustic spectra. A key advantage of the method is the ability to control the characteristics of the inflow turbulence, in order to replicate realistic flows. In this case, we generated a homogeneous velocity field, but included highly anisotropic length scales. The effect of long integral length scales on unsteady thrust spectra is well known [13]; hence including this in the simulation allows a more realistic rotor response to be predicted than when using simpler methods. The humps in the unsteady thrust spectra, which occur at multiples of the BPF, are attributed to blades cutting through the same eddy. This feature is also related to the noise spectra, since sound is generated by unsteady forces on the blades. The proposed acoustic scaling procedure allows simplified predictions of full scale turbine noise levels. These can be used for environmental impact assessment. The maximum SPL estimated in this case would not be expected to cause significant impact to fish [12]. However, the SL predicted here is lower than that from the analytical model utilised in [11]. A more detailed comparison of the two approaches is required. A key advantage of the method is the ability to examine the effect of different turbine designs and inflow turbulence characteristics on turbine noise levels. This will be the focus of future work. ACKNOWLEDGMENTS

Table IV presents a full scale turbine source level (SL) similar to that derived by Wang et al. [8] from experimental measurements. This qualitative comparison provides some indication of the success of our method. However no direct comparison is possible, due to differences between the experimental and numerical cases which are not easily corrected for. Further detailed analyses scaling the entire spectrum are required, as well as an investigation of the sensitivity of the scaling to the assumed parameters. V. C ONCLUSION A promising numerical method for predicting tidal turbine performance in an unsteady environment has been discussed. The motivation is primarily to investigate acoustic emission due to inflow turbulence. Unsteady blades forces and turbine

Thanks to Yusik Kim for providing the FSM inflow generator. The authors acknowledge the use of the IRIDIS 3 High Performance Computing Facility, and associated support services at the University of Southampton. Mr Lloyd wishes to acknowledge the financial support of a University of Southampton Postgraduate Scholarship, dstl and QinetiQ. R EFERENCES [1] G. N. Mccann, “Tidal current turbine fatigue loading sensitivity to waves and turbulence a parametric study,” in Proceedings of the 7th European Wave and Tidal Energy Conference, 11th-13th September, Porto, 2007. [2] R. Nicholls-Lee, S. Turnock, and S. Boyd, “Application of bend-twist coupled blades for horizontal axis tidal turbines,” Renewable Energy, vol. 50, pp. 541–550, Feb. 2013. [3] S. Gant and T. Stallard, “Modelling a tidal turbine in unsteady flow,” in Proceedings of the 18th ISOPE, Vancouver, 2008, pp. 473–479.

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