資源目錄里展示的全都有，所見即所得。下載后全都有,請放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 Ocean Engineering 29 (2002) of Wells turbine design parameters bynumerical simulation of the OWC performanceA. Brito-Melo, L.M.C. Gato*, A.J.N.A. SarmentoMechanical Engineering Department, Instituto Superior Te cnico, Technical University of Lisbon, Av.Rovisco Pais, 1049-001 Lisbon, PortugalReceived 22 May 2001; accepted 30 August 2001AbstractThis paper investigates by numerical simulation the influence of the Wells turbine aerody-namic design on the overall plant performance, as affected by the turbine peak efficiency andthe range of flow rates within which the turbine can operate efficiently. The problem of match-ing the turbine to an oscillating water column (OWC) is illustrated by taking the wave climateand the OWC of the Azores power converter. The study was performed using a time-domainmathematical model based on linear water wave theory and on model experiments in a wavetank. Results are presented of numerical simulations considering several aerodynamic designsof the Wells turbine, with and without guide vanes, and with the use of a bypass pressure-relief valve. 2002 Elsevier Science Ltd. All rights reserved.Keywords: Wave energy; Oscillating water column; Equipment; Wells turbine1. IntroductionThe Wells turbine has been the most commonly adopted solution to the air-to-electricity energy conversion problem in oscillating water column (OWC) waveenergy converters. These essentially consist of a capture pneumatic chamber, openat the bottom front to the incident wave, a turbine and an electrical generator. Theincident wave motion excites the oscillation of the internal free surface of theentrained water mass in the pneumatic chamber, which produces a low-pressure reci-* Corresponding author. Tel.: +351-21-841-7411; fax: +351-21-841-7398.E-mail address: lgatohidro1.ist.utl.pt (L.M.C. Gato).0029-8018/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S0029-8018(01)00099-31464A. Brito-Melo et al. / Ocean Engineering 29 (2002) 14631477procating flow that drives the turbine. A few full-scale turbine prototypes have beenbuilt and installed in grid-connected power plants in European countries, e.g. the500 kW Wells monoplane turbine with guide vanes installed in the Island of Pico,Azores (Falca o, 2000), and 2250 kW biplane contrarotating turbine of the LIMPETplant, at Islay, Scotland (Heath et al., 2000).The greatest challenges to designers of equipment for wave energy converters arethe intrinsically oscillating nature and the random distribution of the wave energyresource. These features are absent or much less severe in other competing energytechnologies. The air turbine in an OWC converter is subject to flow conditions(randomly reciprocating flow), which, with respect to efficiency, are much moredemanding than in turbines in almost any other application. The Wells turbine, whilereaching only a moderately high peak efficiency as compared with conventional tur-bines, can operate in reciprocating flow without the need of a rectifying valve system.The turbine, on the one hand, is required to extract energy from air whose flow rate,in each of the two directions, oscillates between zero and a maximum value, whichin turn has an extremely large variation from wave to wave and with sea conditions.On the other hand, at fixed rotational speed, turbines in general, and Wells turbinesin particular, are capable of operating with good efficiency only within a limitedrange of flow conditions around the peak efficiency point. The power output of Wellsturbines is known to be low (or even negative) at small flow rates (the flow ratepasses through zero twice in a wave cycle) and it drops sharply for flow rates abovea critical value due to aerodynamic losses produced by rotor blade stalling. Therefore,the turbine is expected to perform poorly in very energetic sea-states or wheneverviolent wave peaks occur. Mounting a bypass pressure-relief valve on the top of theair chamber as proposed in the Azores plant may prevent this problem. The valveis controlled to limit the maximum pressure and suction in the chamber (dependingon the turbine rotational speed) to prevent the instantaneous air flow rate throughthe turbine from exceeding the values above which aerodynamic stalling at the rotorblades would produce a severe fall in power output. Numerical simulations (Brito-Melo et al., 1996; Falca o and Justino, 1999) indicate that a reduction in turbine sizeand a substantial increase in the annual production of electrical energy might beachieved by the use of a bypass pressure-relief valve. Moreover, recent studies(theoretical and model testing) indicate that blade sections especially designed forWells turbine rotors can significantly enlarge the range of flow rates within whichthe turbine operates efficiently and reduce aerodynamic losses under partially stalledflow conditions, in comparison with other blade designs which give a higher peakefficiency within a narrower range of flow rates through the turbine. This raises thequestion of whether, in view of the total annual produced electrical energy and takinginto account the hydrodynamic performance of the OWC device, it is more appropri-ate to select a turbine aerodynamic design which allows an enlarged range of flowrates at which the turbine operates efficiently or whether it is better to adopt a turbinedesign which gives a higher peak efficiency value with a reduced range of flow ratesat which the turbine operates efficiently. Furthermore, it is of interest to know towhat extent this issue might be dependent on the use of a pressure-relief valve.The main objective of the present work is to investigate the influence of the Wells1465A. Brito-Melo et al. / Ocean Engineering 29 (2002) 14631477turbine aerodynamic design on the overall plant performance, as affected by theturbine peak efficiency and the range of flow rates within which the turbine canoperate efficiently. Realistic characteristics are assumed for the turbine and the useof a bypass pressure-relief valve is also considered. Since the resulting pressurechanges in the chamber are dependent on the turbine characteristics and the pressure-relief valve influences the turbine operation, the hydrodynamic process of energyextraction is also modified. The hydrodynamics of the conversion of wave energyinto pneumatic energy is predicted by using a time-domain mathematical modelbased on linear water wave theory and on model experiments in a wave tank asdescribed in Sarmento and Brito-Melo (1996). The conversion of pneumatic energyinto electrical energy is predicted by a suitable computational model of the powertake-off equipment based on the results extrapolated from aerodynamic tests on ascale-model and on empirical approximations for the generator losses (Brito-Meloet al., 1996). This paper presents the results of numerical simulations consideringseveral aerodynamic designs of the Wells turbine, with and without guide vanes,and the use of the pressure-relief valve. The problem of matching the turbine to anOWC is illustrated by taking the wave climate and the OWC of the Azores wavepower converter.2. Wave-to-wire model2.1. Plant operationThe wave-to-wire model concerns the operation of an OWC equipped with a Wellsturbine, a bypass valve of unlimited capacity and a variable speed turbo-generator,under a set of representative sea-state conditions.The Wells turbine is known to exhibit an approximately linear relationshipbetween the turbine pressure drop p(t) and the flow rate qt(t). Then we may writethe turbine characteristic as K ? p(t)/qt(t) ? ps(?)/qs(?), where ps(?), and qs(?)are maximum values of pressure and flow rate (prior to the onset of aerodynamicstall at the turbine rotor blades), which (for a given turbine) depend on the turbinerotational speed ?. The use of a properly controlled bypass pressure-relief valveprevents the occurrence of stall at the turbine rotor blades. The valve is controlledto ensure that |p(t)|?ps(?). Then |qs(t)|?qs(?). The excess flow rate qv(t) passesthrough the valve to (or from) the atmosphere.The inertia of the rotating parts is assumed large enough so that rotational speed? may be considered approximately constant over the time-intervals simulating agiven sea-state (about 15 minutes). This allows ? to be optimized for each represen-tative record of the sea-state, in order to maximize the electrical energy production.The turbine rotational speed is allowed to vary between the synchronous speed ofthe generator and twice its value. Summing the product of the time-averaged electri-cal power output with the occurrence frequency for all data records gives the overallannual average electrical power output.1466A. Brito-Melo et al. / Ocean Engineering 29 (2002) 146314772.2. Hydrodynamic modelThe hydrodynamic model is based on the pressure model presented in Sarmentoand Falca o (1985). According to the OWC performance description presented inSection 2.1, the mass balance across a control surface enclosing the pneumaticchamber is given byp(t)K? qv(t) ? q(t)?V0gPadp(t)dt(1)where q(t) is the volume flow rate displaced by the free-surface inside the chamber,V0denotes the volume of the air in the chamber under undisturbed conditions, Paisthe atmospheric pressure and g is the ratio of specific heats. As stated in Section2.1, qv(t) ? 0 if |p(t)| ? ps(?) (i.e. when the valve is not operating). According tothe linear water wave theory, the volume flow rate displaced by the free-surfaceinside the chamber may be decomposed as q(t) ? qd(t) ? qr(t), where qd(t) is thediffraction flow rate, due to incident wave action assuming the internal and the exter-nal free-surfaces at constant atmospheric pressure, and qr(t) is the radiation flow ratedue only to the pressure oscillation p(t) in otherwise calm waters. Under the assump-tions of the linearized wave theory, we may apply the convolution theorem to obtainthe solution of a linear problem in terms of an impulse response (Pipes and Harvill,1970), as follows:qr(t) ?thr(t?t)p?(t) dt(2)where p?(t) is the time-derivative of the pressure inside the chamber and t representsa time-lag. The upper limit of the integral in Eq. (2) represents the present instantt because the process is causal (Cummins, 1962). The impulse response functionhr(t) can be obtained from the hydrodynamic coefficients of the OWC computedwith a numerical model, such as the WAMIT (Lee et al., 1996) or the AQUADYN-OWC (Brito-Melo et al., 1999), or by tank testing. Here we use an estimate of theimpulse response function obtained in free-oscillation transient experiments from1:35 scale testing of the Azores OWC wave power plant (see Sarmento and Brito-Melo, 1996, for details).Time series for the diffraction flow, qd(t), have also been obtained in energy extrac-tion experiments with the scaled model subject to a set of 44 sea-states representativeof the Azores power plant site. In these experiments a device producing an equivalentair pressure drop simulated the turbine. The flow rate qt(t) could be obtained as afunction of p(t) from the device calibration curve. The diffraction flow time-seriesfor each of the 44 sea-states was estimated by solving Eq. (1) (with qv(t) ? 0) usingthe pressure records from the energy extraction experiments, and the experimentalestimate of hr(t) previously obtained in the transient experiments.1467A. Brito-Melo et al. / Ocean Engineering 29 (2002) 146314772.3. Power take-off equipmentThe power take-off sub-model is based on results extrapolated from small-scaleturbine tests (Gato et al., 1996; Webster and Gato, 1999a,b) and on empirical datafor the turbine and generator losses (Brito-Melo et al., 1996). The average power atthe turbine shaft for a period T is given byWs?T?0TL(?,qt(t)?Lm(?) dt(3)where L is the aerodynamically produced turbine-torque and Lmthe torque due tomechanical losses (especially bearing losses). For stall-free conditions, L is approxi-mated by a second-order polynomial. In order to provide the necessary performancedata to study the matching of the power take-off equipment and the pneumaticchamber, the data from small-scale turbine tests are modified using a simple mean-line turbine flow analysis method to take into account the rotor solidity S and thehub-to-tip ratio. Ignoring the postponement of stall when the Reynolds number isincreased, scale effects are taken into account by correcting the torque curve of theturbine model. This is done multiplying (dividing) the positive (negative) values ofL by f ? 0.8/0.706. This corrects the torque curve of the unswept NACA 0015bladed rotor with guide-vanes to match a peak efficiency of hmax? 0.80. For thepreliminary design of the turbine a maximum blade tip speed of 160 ms?1is assumed.The average electrical power output is obtained by subtracting the generator lossesfrom the average power at the turbine shaft. The model for the generator lossesincludes the Joule losses, the iron losses, the ventilation losses and the mechanicallosses (Brito-Melo et al., 1996).3. Results and discussionExperimental research on different types of rotor blades has been conductedrecently to improve the aerodynamic performance of the Wells turbine (Raghunathan,1995; Gato et al., 1996; Curran and Gato, 1997; Webster and Gato, 1999a,b). Amongthese types, we consider two turbine blade configurations, which may give a widerrange of flow rates within which the turbine can operate with fairly good efficiency,in comparison with that of the more standard NACA 0015 unswept bladed turbinerotor: they are the backward-swept NACA 0015 blades (Webster and Gato, 1999a),Fig. 1, and the optimized HSIM-15-262123-1576 unswept blades (Gato and Hen-riques, 1996), Fig. 2. For comparison we take results for the NACA 0015 unsweptblades (Gato et al., 1996).Figs. 3 and 4 show experimental results from unidirectional-flow small-scale test-ing at the IST rig (Webster and Gato, 1999a,b). Results presented in Figs. 3 and 4refer to high-solidity Wells turbine rotors (rotor outer radius R ? 0.295 m, constantchord c ? 125 mm, rotor solidity S ? 0.64, equipped with the blades referred to1468A. Brito-Melo et al. / Ocean Engineering 29 (2002) 14631477Fig. 1.Rotor blade sweep angle.Fig. 2.The NACA 0015 and HSIM 15-262123-1576 sections.above, with and without guide vanes. The figures show, in dimensionless form,experimentalresultsfortheefficiencyh ? L?/(qtp),pressuredropp?p/(r?2R2), and torque L? L/(r?2R5) as functions of the flow rate coefficient U*(r is the air density). Results in Fig. 3 for the turbines without guide vanes showthat the NACA 0015 unswept rotor has hmax? 0.583 at U? 0.114, and stalls atU? 0.21. The NACA 0015 30 backward-swept rotor has a lower hmax? 0.583,with a lower flow rate for the onset of stall, U? 0.17, but without exhibiting thesharp decrease in the torque that occurs in the unswept rotor. Furthermore, understall conditions, the torque of the swept rotor becomes negative at a much higherflow rate, U? 0.45, whereas for the unswept blades the efficiency becomes nega-tive for U? 0.3. The unswept HSIM bladed rotor shows a hmaxsimilar to that ofthe backward-swept rotor, but produces a soft progressive stall of the flow throughthe rotor blades, with notably higher efficiency for a wide range of flow rates afterthe onset of stall.Fig. 4 shows a corresponding plot for the same turbine rotors when equipped witha double row of guide vanes. The experimental results plotted in Fig. 4 show thatthe use of guide vanes increases hmaxfor any of the above geometries, i.e. from0.583 to 0.706, 0.551 to 0.613 and 0.553 to 0.669, for the NACA 0015 unswept and1469A. Brito-Melo et al. / Ocean Engineering 29 (2002) 14631477Fig. 3.Unswept and 30 backward-swept NACA 0015 and unswept HSIM bladed rotor turbines, withoutguide vanes: measured values of efficiency (a), pressure drop (b) and torque (c) against flow rate coef-ficient.1470A. Brito-Melo et al. / Ocean Engineering 29 (2002) 14631477Fig. 4.Unswept and 30 backward-swept NACA 0015 and unswept HSIM bladed rotor turbines, withguide vanes: measured values of efficiency (a), pressure drop (b) and torque (c) against flow rate coef-ficient.1471A. Brito-Melo et al. / Ocean Engineering 29 (2002) 14631477backward-swept rotors and the HSIM unswept rotor, respectively. Furthermore, wefind that the use of guide vanes narrows the range of flow rates within which theturbine works with positive torque.Table 1 summarizes the performance data for the six turbines, where UaandUbare the minimum and maximum flow rate coefficients respectively, at which theefficiency is nominally h ? 0.5hmax. Therefore, ? ? Ua/Uband ? ? Ua?Ubgivean indication of the operational range while (?p0/U)h ? hmaxis the pressureflowratio in the approximately rectilinear region. In the above performance comparison,constant overall solidity was assumed for the different turbine configurations. Resultsin Table 1 show that the rotor blade geometry has a remarkable influence on theturbine performance. In particular, some rotor geometries give a considerable widerrange of flow rates within which the turbine operates efficiently, in comparison withothers that have higher peak efficiency within a narrower range of flow rates.Figs. 57 plot the average electrical power output as given by the numerical simul-ation for the set of the 44 representative records of the wave climate for the AzoresPlant site, taking into account the frequency of occurrence of each sea-state. Theresults give the turbine characteristic K for several values of the rated powerW0? psqs. Table 2 indicates the values of the flow coefficient Usat which thedifferent types of turbine rotor were designed and the bypass pressure-relief valveis actuated.3.1. NACA 0015 unswept bladed rotor with and without guide vanesFig. 5 presents the results of the numerical simulation to study the effect of theuse of guide vanes with the NACA 0015 unswept bladed rotor. Fig. 5 shows thatthe use of guide vanes provides a significant increase in the average electrical poweroutput, both with and without the presence of the bypass pressure-relief valve. Thecurves plotted in Figs. 3 and 4 for the unswept NACA 0015 rotor, with and withoutguide vanes, respectively, show that the turbine with guide vanes has hmax?0.72Table 1Peak efficiency, useful flow rate range and damping ratio for several turbine models (overall solidityS=0.64)Turbine rotorWith guide vanesWithout guide vanesNACA 0015 NACA 0015 HSIMNACA 0015 NACA 0015 HSIMunsweptswept-backunsweptunsweptswept-backunswepthmax0.7060.6130.6690.5830.5510.553(U)h ? hmax0.1240.1370.1540.1140.1290.131Ua0.0500.0620.0570.0510.0580.059Ub0.1970.2090.2750.2510.2320.360?0.2540.2970.2070.2030.2500.164?0.1470.1470.2180.2000.1740.301(?p0/U)h ? hmax2.191.872.382.542.042.791472A. Brito-Melo et al. / Ocean Engineering 29 (2002) 14631477Fig. 5.Unswept NACA 0015 bladed rotor turbine with and without guide vanes working (a) with and(b) without the bypass valve: average electrical power conversion as a function of the turbine characteristicK, for several values of the turbine-rated power.whereas for the turbine without guide vanes hmax? 0.60. Nevertheless, the torquecurve for the turbine without guide vanes exhibits a wider range of flow rates overwhich the turbine performs with good efficiency. The results of the numerical simula-tions reveal the usefulness of the guide vanes. In addition, they show that, under theabove conditions, the aerodynamic design criterion for the turbine should be to max-imize the turbine peak efficiency even if that may result in a narrower curve ofefficiency versus flow rate. Furthermore, it may be found that the use of guide vanesleads to a small increase in the turbine size, which, however, should not constitutea significant penalty since the turbine cost is only a small fraction of the overallplant cost.Results in Fig. 5a also show that the trend for the electrical power output as afunction of the turbine-rated power is the same regardless of whether guide vanesare consider