AERO-ACOUSTIC PERFORMANCE PREDICTION OF WELLS TURBINES

Transcription

1 14 th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-14 February 7 th - March nd, 01, Honolulu, HI, USA AERO-ACOUSTIC PERFORMANCE PREDICTION OF WELLS TURBINES R. Starzmann* 1, Th. Carolus*, K. Tease #3, R. Arlitt 4 *Institut für Fluid und Thermodynamik, University of Siegen Siegen, Germany 1 ralf.starzmann@uni-siegen.de, thomas.carolus@uni-siegen.de # Voith Hydro Wavegen Limited Inverness IV1 1SY, United Kingdom 3 ken.tease@wavegen.com Voith Hydro Ocean Current Technologies 895 Heidenheim, Germany 4 raphael.arlitt@voith.com Abstract A Wells turbine is an axial air turbine, widely used as a power take off system for an oscillating water column wave energy plant. The main objective of this study is predicting the aero-acoustic sound power radiated from a model scale turbine. Semi-empirical correlations and scaling laws for airfoil self noise by Brook, Pope and Marcolini are applied to blade strips. The required aerodynamic input data originates from an aerodynamic performance prediction model based on blade element theory. Both prediction schemes describe the aerodynamic as well as the aero-acoustic performance of a Wells turbine reasonably well. Nomenclature C D drag coefficient C L lift coefficient D diameter [m] F L lift force [N] F D drag force [N] F ax axial force [N] F u tangential force [N] L chord length [m] L w sound power level [db] Ma Mach number P power [W] V & volume flow rate [m 3 /s] Y specific work [Nm/kg] c absolute flow velocity [m/s] f frequency [Hz] k cascade factor m& mass flow rate [kg/s] n rotational speed [rps] p pressure [Pa] u circumferential velocity [m/s] r radius [m] t angular blade spacing [m], time [s] w relative flow velocity [m/s] z number of blades p pressure drop [Pa] α angle of attack [ ] β flow angle [ ] ε drag/lift ratio φ flow rate coefficient ψ pressure coefficient λ power coefficient η efficiency ρ density [kg/m 3 ] ν hub-tip ratio σ solidity tip gap [m] Subscripts 0 reference, position in plenum chamber 1 position upstream rotor plane position downstream rotor plane 3 position far downstream rotor plane position in rotor plane b blade hub at hub iso isolated l loss low lower m axial p plant s sampling, static shaft shaft tip at tip ts total-static tt total-total 1

2 u circumferential up upper Abbreviations BE Blade Element BPM Brooks, Pope and Marcolini CAA Computational Aero Acoustics CFD Computational Fluid Dynamics CV Control Volume OWC Oscillating Water Column RSS Reference Sound Source Introduction A Wells turbine is a self-rectifying axial turbine, which is capable of extracting energy from an oscillating airflow [1]. Currently, this type of turbine is one of the most developed machines for application in an oscillating water column (OWC) power plant for wave energy conversion and has the highest peak efficiency []. Analytical investigations regarding the design and the aerodynamic performance prediction of a Wells turbine have been carried out in the last three decades [3-6]. Experimental work on the effect of different design parameters, mainly focused on improving steady-state aerodynamic performance, has also been reported [6-9]. Furthermore, flow field data and characteristics from numerical simulations have been presented in related literature [10-13]. The acoustics of Wells turbines has been addressed so far only by experimentalists [13-17]. As OWC technology faces commercial usage and hence needs to meet legal noise emission requirements, it is important to fully understand not only the aerodynamic performance of a turbine but the aero-acoustic as well. Acoustic prediction models, as used for e.g. axial fans [18] and wind turbines [19-0], have never been applied to a Wells turbine but have the potential of estimating the sound emission within the design phase. This might help to minimize environmental disturbance caused by onshore based renewable wave energy generation. Objectives of this study are: (i) Prediction of aerodynamic performance characteristics. (ii) Prediction of sound emitted. (iii) Experimental validation. Dimensionless Quantities The aerodynamic performance of a Wells turbine rotor is described by the flow rate coefficient π 3 φ = V& Dtipn, (1) 4 the pressure (or head) coefficient π ψ = p Dtipn ρ, () the power coefficient 4 π 5 3 λ = Pshaft Dtipn ρ, (3) 8 and the efficiency η = P V & p. (4) shaft Aerodynamic Performance Prediction System Analysis Figure 1 shows a schematic view of an OWC power plant cross section, consisting of a large plenum (0), a turbine section with reference planes (1) and (), and the free atmosphere (3) far away from the turbine. For simplicity we only consider flow direction from (0) to (3), but all results hold true for the reversed flow direction as well. Fig. 1: OWC power plant - schematically Application of the conservation of energy law results in the specific energy Y p provided by the plant and available to the turbine rotor without guide vanes and/or diffuser pt, pt,0 Yp = < 0, (5) ρ with the total pressure p t,0 in the plenum ρ pt,0 = ps,0 + c0, (6) and the total pressure p t, downstream of the rotor ρ ρ pt, = ps, + c = ps, + ( cm + cu ). (7) Assuming a large plenum (c 0 = 0 m/s) and setting p s, = 0 Pa as a reference pressure results in ps,0 1 Yp = + ( cm + cu ) < 0, (8) ρ with the static pressure p s,0 in the plenum chamber and the axial (c m ) and circumferential (c u ) velocity components downstream of the rotor (reference plane ()). With that we define the total-total 1 ψ Y u > 0 (9) ( ) tt p tip and total-static pressure coefficient ρ ψ p u > 0, (10) ( ) ts s,0 tip with the circumferential velocity at the blade tip u tip.

3 Omitting mechanical losses, e.g. from bearings, but including all hydraulic losses Y l yields the specific blade work Yb = Yp Yl (11) and a definition of the hydraulic efficiency Yb η hyd =. (1) Y p Blade Element Model The aerodynamic performance prediction method employed is fundamentally based on a blade element (BE) model [5]. Because of its simplicity and low computational effort, the BE model is the most widely used theory for rotor design and analysis in turbo machinery applications. For that the bladed annulus of the turbine is segmented into small BEs with a small radial extension δr. The blade related flow velocities are assumed to be independent of radius at each BE. The mass flow rate through a BE can be calculated as m& = ρcm tδr, (13) where t is the angular spacing between two blades and c m is the axial flow velocity in the rotor plane. An essential element of the Wells turbine is a cascade of nonstaggered symmetrical airfoils, where the angle of attack α to the rotor blades equals the flow angle β, Fig.. The vector mean flow velocity in the rotor plane (Fig. ) is Yb w = tan β + 1 u u. (16) Alternatively, the circumferential force δf u can be expressed in terms of the lift (C L,iso ) and drag/lift ratio (ε), according to airfoil theory. The induced force on an isolated airfoil (Fig. 3) becomes ρ ε δ Fu = wlδrcl,iso sinβ 1 (17) tanβ with the chord length L. Equating the right hand sides of eqs. (15) and (17) and inserting eq. (14) yields u K Yb = (18) 4 K with the abbreviation ε K = CL,isoσ 1 tan β + 1, (19) tanβ where σ = L t (0) is the solidity of the cascade. Fig. 3: Turbine BE with isolated airfoil and induced angular force δf u Fig. : Turbine BE with control volume, velocity triangles and exerted angular force δf u Employing Euler s equation of turbo machinery for purely axial inflow, Yb = cu u (14) and the conservation of angular momentum on a control volume (CV) around one BE (Fig. ) finally yields ρcm tδryb δ Fu =. (15) u A typical Wells turbine cascade cannot realistically be viewed as a number of isolated airfoils. Their mutual interference effects must be taken into account [1]. For the ideal case, i.e. assuming no drag, the lift force on a cascade of unstaggered airfoils is a factor of 1 π k = tan σ (1) π σ times larger than in the isolated airfoil case []. Assuming that this also holds true when drag is present, we replace eq. (19) with ε K = kcl,isoσ 1 tan β + 1. () k tanβ 3

4 Neglecting volumetric as well as secondary losses, the hydraulic losses, eq. (11), become purely profile losses cdσw Yl =, (3) cm where c D is the airfoil drag coefficient. To provide reasonable accuracy within the BE model method, accurate -D airfoil wind-tunnel data is needed. Therefore XFOIL [3] is integrated to calculate complete sets of isolated airfoil polar data at each BE for the corresponding airfoil shape, Reynolds and Mach number. The BE model as described in this section is implemented in MATLAB and XFOIL is called automatically within the MATLAB code. Since the prediction of the airfoils aerodynamic coefficients using XFOIL is only valid up to stall, an extrapolation method proposed by Viterna et. al is used to provide information in the post-stall range [4]. Aiming at coaxial flow through the rotor the simple radial equilibrium equation dps, cu = ρ (4) dr r must be satisfied (see e.g. [5]). This results in a radial pressure distribution p,s (r) downstream of the rotor, for which rtip ps, π r dr = 0 (5) rhub must hold to meet the reference pressure level p s, = 0 at the outlet. For this reason, eq. (8) is modified as p s,(r) ps,0 1 Y p(r) = + ( c m(r) + c u(r) ). (6) ρ A strategy to achieve overall aerodynamic performance curves for a given rotor geometry, including the radial distribution of the blade-related flow velocities at each BE is as follows: Set a static pressure p s,0 in the plenum chamber. Fix main machine dimensions (diameter, rotational speed) of the turbine as well as the hub-tip ratio ν. Define detailed blade geometry of the rotor (airfoil shape, chord length l for each BE). Obtain a complete set of polar data from XFOIL for each BE. Solve the system of eqs. (11), (14), (18), (3), (6) by iteration. Acoustic Performance Prediction For the acoustic prediction of an isolated rotor it is assumed that the only acoustic source is the airfoil selfnoise at each BE. This seems to be justified, since measured turbulence intensity one diameter upstream of the rotor plane did not exceed % in the centre of the channel for all flow rates investigated. Therefore turbulenceinteraction noise is neglected in the following. Here, experimentally based correlations by Brooks, Pope and Marcolini (BPM), for a NACA001 airfoil section in an acoustic wind tunnel are employed [7]. In total, they identified five different self-noise sources: Turbulent boundary layer trailing edge noise Separation stall noise Laminar boundary layer vortex shedding noise Trailing edge bluntness vortex shedding noise Tip vortex formation noise As a result Brooks at al came up with third octave sound pressure spectra and scaling laws for each noise mechanism. The Wells turbine operating principle requires symmetrical airfoils and hence seems to be a rather unique and straight forward application of the BPM correlations. The flow around a single BE and hence the boundary layer parameters are believed to be identical to the one around a NACA001 airfoil section. A correction for airfoil camber as in fans or wind turbines is not necessary and is therefore neglected. Fully turbulent flow is assumed. Tip vortex formation noise is only considered at the tip BE. The aerodynamic input parameters angle of attack β and free stream velocity w in the rotating frame of reference are taken from the previously described BE model. The BE dimensions (radial extension δr, chord length l, trailing edge thickness) are needed to calculate sound pressure levels L p and spectra for each sound mechanism and for each BE. Finally, the overall sound power level L w of the turbine is achieved by summation over all mechanisms, all BEs and the number of blades. For that it is assumed that each BE act as an incoherent acoustic source which seems justified since Wells turbine noise is typically broadband. Eventually, varying plenum pressure, this leads to acoustic characteristics, i.e. sound power and third octave spectra for each point of turbine operation. Experimental Setup and Procedure Test Rig A unidirectional, steady state test rig is used for this study, Fig. 4. The turbine rotor is enclosed by a cylindrical annular duct of 400 mm diameter. The variable but steady volume flow rate is supplied by a centrifugal fan (c) with a variable speed drive. The plenum (e) contains screens and honeycombs (f) as flow straighteners upstream of the calibrated nozzle (g). Another honeycomb (j) is located directly upstream of the turbine section (k). The rotor torque is measured via an integral telemetric torque flange, which in turn is mounted on a water cooled 4

5 Fig. 4: Test facility: a) housing, b) splitter attenuator, c) centrifugal fan, d) splitter attenuator, e) plenum, f) honeycombs and turbulence control screens, g) nozzle, h) static pressure measurement, i) static pressure measurement, j) honeycombs, k) turbine section; synchronous motor-generator with variable speed drive. For the acoustic tests, the rig is equipped with highly efficient silencers (a), (b) and (d) around the air supply. Performance Tests The aerodynamic experiments within this study are carried out with a constant rotor speed of n = 4000 rpm. The pressure in the plenum chamber and the flow rate are increased from zero to a point beyond stall and then decreased back to zero. A control and data acquisition system is used to collect instantaneous data for each point of operation. The pneumatic power input to the rotor is calculated from measurement of flow rate φ and pressure in the plenum ψ ts, whilst the output power λ is obtained from torque and rotational speed. Based on the specified accuracy of the instruments, the uncertainty in total-static efficiency at optimum operating point lies within a band of ± 5 %. Note that the repeatability of the experiments was within a range of ± % of each data point. Flow Field Measurements Flow velocity measurements are performed along a radial line 40 mm downstream of the rotor plane (Fig. 5, position n) with a calibrated, spherical 5-hole Pitot tube. Time averaged axial and circumferential velocity components as well as the absolute flow angle are determined for each radial position. Acoustic Tests Acoustic and aerodynamic measurements are carried out simultaneously. The result is an acoustic characteristic curve in terms of the overall sound power level for each operating point. Due to the very efficient acoustic absorbers in the in- and outlet of the pressurized air supply, no correction for background noise is required. Sound power is determined via a calibrated reference sound source (RSS), a method according to DIN EN ISO 3741 [8]. Contrary to the standard, only one microphone was used to record time signals of the sound pressure. This is thought to be sufficient for comparison of different turbine designs. Figure 5 shows a schematic plan view of the turbine section with the microphone position. The time signals of the sound pressure were captured with a sampling rate of f s = 5,600 Hz and a length of t = 5s. Fig. 5: Acoustic measurement setup: j) honeycomb screen, l) nose cone, m) model rotor with torque flange, n) flow traverse position, o) generator, p) generator struts, q) RSS, r) microphone The signal analysis is based on the power spectral density which was obtained by the function pwelch in MATLAB Vers The parameters chosen for pwelch were window = hann(f s ), noverlap = 0.5xf s, and nfft = f s. The spectra from the windows have been averaged 9 times in order to obtain the final spectrum with a frequency resolution of f = 1 Hz. For all levels, the 5

6 reference pressure is p 0 = x10 5 Pa, and the reference bandwidth f ref = 1 Hz. The overall sound power refers to a frequency interval between f low = 100 Hz to f up = 10 khz. Based on the employed method, the uncertainty regarding the overall sound power level was within ± db. Rotor Design and Blade Geometry Table 1 shows the two generic rotors investigated in this work. Both are designed by means of an analytical design method described elsewhere [6] with a hub-tip ratio ν = 0.43 but with different solidity at the hub σ hub. Tab. 1: Model rotors investigated Rotor A (σ hub = 0.65) B (σ hub = 0.80) φ Rotor A 0.1 experiment BE model ψ ts Fig. 6: Flow rate characteristic Rotor B ν = Rotor A Each BE is stacked with its center of gravity on a radial stacking line. The airfoils selected are a NACA001 at the hub and a NACA0015 at the tip with linear interpolation of the coordinates for intermediate blade elements. Table summarizes further design parameters. Tab. : Blade Design Parameters D tip = 0.4 m number of blades z = 5 n = 4000 rpm tip clearance: /D tip = % (Ma u,tip = 0.4) Results Aerodynamic characteristics are shown in Figs. 6 and 7 for both rotors A and B. A comparison of the results reveals a good agreement of predicted and measured aerodynamic performance curves over a large range of operating points. Note that the model is limited by the onset of stall at the blade hub element. The prediction curves are plotted beyond this point, which can be identified by the increased pressure-flow rate slope seen in Fig. 6, whereas the power curve (Fig. 7) is not affected. Since the stall mechanism of a Wells turbine is strongly affected by 3D effects [6], predicting the onset of stall is outside the validity of this analytical model. λ experiment BE model ψ ts Fig. 7: Power characteristic Rotor B According to Fig., the relevant blade related velocity distributions for the acoustic model can be calculated based on the downstream flow field measurements performed within this study. Figs. 8 and 9 show a comparison of the predicted and measured flow field for the investigated constant rotor speed. Besides well known secondary flow effects near the hub and tip region, the agreement is rather satisfactory for rotor A. Due to the high solidity of rotor B, the lower part of the bladed annulus is affected by strong secondary flow effects, which are outside the validity of the BE model. Figure 10 shows the aero-acoustic characteristic curves. Given the simplicity of the employed models, the overall tendencies are predicted well. It is worth to note that contrary to the flow field results, the agreement is better for rotor B. Exemplary for rotor A, narrow band sound power spectra are shown in Fig. 11. Obviously the spectrum is more or less broadband. Increasing levels are observed due to increasing flow rates, predominantly at lower frequencies. 6

7 w / u rotor A (BE model) 0.5 rotor B (BE model) rotor A (exp) rotor B (exp) r/r tip Fig. 8: Measured and predicted radial distributions of relative velocity in the rotor plane (φ = 0.08) β [ ] rotor A (BE model) rotor B (BE model) rotor A (exp) rotor B (exp) r/r tip Fig. 9: Measured and predicted radial distributions of relative flow angle in rotor plane (φ = 0.08) L w [db] Rotor A Rotor B 90 experiment BPM model ψ ts Fig. 10: Aero-acoustic characteristic A comparison of measured and predicted third octave spectra for different operating points is shown in Figs. 1 and 13. Apart from deviations in the low frequency range, a satisfactory agreement, even for different operating conditions, is observed. As for the overall sound power level the prediction is better for rotor B, Fig. 13. L w [db] φ = 0.04 φ = 0.08 φ = f [Hz] Fig. 11: Rotor A: Measured narrow band spectra Conclusion Simple semi-analytical models are able to predict aerodynamic and aero-acoustic performance characteristics of a Wells turbine rotor reasonably well. More accurate aerodynamic performance prediction, including the stall margin, is expected from CFD, see e.g. [13]. Improved acoustic prediction requires very complex CAA-methods. Only an exemplary tip clearance was investigated here. Investigations on tip clearance effects, carried out for the Wells turbine, indicate a strong effect on aerodynamic performance, see e.g. [9, 30]. However, the acoustic influence of the detailed geometry of the tip and the tip gap itself has never been investigated before. This is a subject of future studies. In an OWC power plant, the Wells turbine is operated more or less along its complete characteristic curve from no load via optimum operation to overload. It is interesting to note that according to the experiments, greater noise levels of Wells turbines are observed close to stall and of course in stalled operation. Hence, avoiding these points of operation by a sophisticated control scheme can ensure low noise Wells turbine performance. 7

8 L w [db] φ = φ = 0.08 φ = f [Hz] Fig. 1: Rotor A: Measured ( ) and predicted (... ) third octave spectra L w [db] φ = φ = 0.08 φ = f [Hz] Fig. 13: Rotor B: Measured ( ) and predicted (... ) third octave spectra References [1] Wells, A.A., 1976, "Fluid driven rotary transducer", British Patent Spec No [] Falcão, A.F., 010, "Wave energy utilization: A review of the technologies", Renewable and Sustainable Energy Reviews, 14(3), pp [3] Tan, C.P., 1983, "Predictions and experimental investigations on the performance of Wells air turbine", Ph.D. thesis, The Queens University of Belfast. [4] Gato, L.M.C. and Falcão, A.F., 1984, "On the theory of the Wells turbine", ASME J. Eng Gas Turbines Power, 106, [5] Raghunathan, S., 1995, "The Wells air turbine for wave energy conversion". Prog. Aerospace Sci., 31, pp [6] Starzmann, R., Carolus, T.H., Tease, K., Arlitt, R., 011, "Wells turbine rotors: A comparison of the predicted and measured aerodynamic performance", In Proc. 9th European Turbomachinery Conference, Istanbul. [7] Setoguchi, T., Kaneko, Inoue, M., 1986, "Determination of optimum geometry of wells turbine rotor for wave power generator - part I", Current practices and new technology in ocean engineering, McGuinness, Ocean engineering division, ASME, New York, pp [8] Setoguchi, T., Kaneko, Inoue, M., 1986, "Determination of optimum geometry of wells turbine rotor for wave power generator - part II", Current practices and new technology in ocean engineering, McGuinness, Ocean engineering division, ASME, New York, pp [9] Curran, R., Gato, L.M.C., 1997, "The energy conversion performance of several types of Wells turbine designs", Proc. Inst. Mech. Engers., 11(A), pp [10] Watterson, J.K., Raghunathan, S., 1999, "Numerical Analysis of Wells Turbine Aerodynamics", J. of Propulsion and Power, 15, pp [11] Torresi, M., Camporeale, S.M., Pascazio, G., 009, "Detailed CFD Analysis of the Steady Flow in a Wells Turbine Under Incipient and Deep Stall Conditions", ASME J. Fluids Eng, 131, [1] Taha, Z., Sugiyono, Sawada, T., 010, "A comparison of computational and experimental results of Wells turbine performance for wave energy conversion", Applied Ocean Research, 3(1), [13] Starzmann, R., Carolus, T.H., Tease, K., Arlitt, R., 011, " Effect of design parameters on aero-acoustic and aerodynamic performance of Wells turbines", In OMAE Proceedings, ASME, Rotterdam. [14] de Moura, A.C., Carvalho, M., Patricio, S., Nunes, N., Soares, C., 010, "Airborne and underwater noise assessment at the Pico OWC Wave Power Plant", 3rd International Conference on Ocean Energy, Bilbao. [15] Tease, K., Lees, J., Hall, A., 007, "Advances in Oscillating Water Column Air Turbine Development", In Proc. 7th European Wave and Tidal Conference, Porto. [16] Takao, M., Setoguchi, T., Raghunathan, S., Inoue, M., 00, "Noise characteristics of turbines for wave power conversion", J Power and Energy, Proc. Instn. Mech. Engrs., 16, Part A, pp [17] Starzmann, R., Moisel, C., Carolus, T.H., Tease, K., Arlitt, R., 011, "Assessment Method for Sound Radiated by Cyclically Operating Wells Turbines", In 8

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