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An experimental and numerical study of the vortex filaments in the wake of an operational, horizontal-axis, wind turbine
Journal of Wind Engineering and Industrial Aerodynamics 85 (2000) 177}189
An experimental and numerical study of the vortex "laments in the wake of an operational, horizontal-axis, wind turbine I. Grant *, M. Mo , X. Pan, P. Parkin , J. Powell , H. Reinecke , K. Shuang, F. Coton, D. Lee Department of Civil and owshore Engineering, Fluid Loading and Instrumentation Center, Heriot-Watt University, Edinburgh, Scotland, EH14 4AS, UK Beijing Petroleum University, Beijing, People's Republic of China University of Glasgow, Glasgow, Scotland, UK Received 13 August 1999; accepted 25 November 1999
Abstract The paper describes a wind-tunnel study of the wake dynamics of an operational, horizontal-axis wind turbine. The behaviour of the vorticity trailing from the turbine blade tips and the e!ect of was interference on wake development were considered. Laser sheet visualisation (LSV) techniques were used to measure the trajectories of the trailing vorticity under various conditions of turbine yaw and blade azimuth. Selected results obtained in the experimental study were compared with the predictions of a prescribed wake model and are being used in the further development of the method. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Wind tunnel; Horizontal-axis wind turbine (HAWT); Laser sheet visualisation (LSV); Prescribed wake; Vortex; Numerical simulation
1. Introduction The horizontal-axis wind turbine (HAWT) is the most frequently used type found in operation. Whilst being geometrically simple, its operating regime is aerodynamically complex [1] and, in some cases [2], particularly unsteady.
* Corresponding author. Tel.: #44-131-451-3156. E-mail address: [email protected] (I. Grant) 0167-6105/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 9 ) 0 0 1 3 9 - 7
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The present paper describes wind-tunnel tests of a full-size, `Marleca, turbine in two wind tunnels. In both cases, it was possible to ensure that the main thrust producing sections of the turbine rotor operated above the critical Reynolds number. Using laser sheet visualization (LSV), valuable information on the turbine wake structure and its sensitivity to operational conditions, such as wall e!ects and blockage, was obtained. This also gave the opportunity to measure wake expansion as a function of turbine yaw [3}5]. Historically, design assessments of the aerodynamics of the HAWT have been conducted by relatively simple blade-element momentum methods [6]. When timedependent details of the local #ow states are required, however. the more sophisticated free, or prescribed, wake methods have been used. The computationally e$cient, prescribed wake technique [7,8], used here, allows the wake boundaries to be de"ned on the basis of geometrically prescribed functions derived from momentum theory. The long-term is to alleviate the wind-tunnel wall e!ect by coupling the prescribed wake with a three-dimensional source panel method. The work on coupling the prescribed wake model to the panel method is at an advanced stage. In this paper, however, the emphasis is primarily on the LSV study. Nevertheless, comparisons of the measured data with the basic (i.e., unconstrained) prescribed wake method were made to illustrate the severity of the wall e!ect.
2. Description of experiments The experimental program was conducted in two phases, the "rst at Heriot-Watt University, Edinburgh, the second at the University of Glasgow. 2.1. Experimental arrangements phase 1 (Heriot-Watt) 2.1.1. Wind tunnel The "rst phase of the test programme was conducted in the Heriot-Watt University, closed return, low turbulence, wind tunnel where an open jet con"guration was used in order to minimise blockage and wake de#ection due to wall interference (Fig. 1). The tunnel was of closed circuit design with axial dimensions of 10 and 4.5 m. The working section was sited midway along one of the 10 m sides. In the tests the tunnel was operated in an open-jet con"guration giving a working section of 2.3 m in length. The jet issued from an octagonal aperature which measured 1.24 m between the #ats and the length of each side begin 0.51 m. 2.1.2. The turbine The wind turbine had an overall rotor diameter of 0.9 m and a hub diameter of 0.24 m. The turbine was run in either a two- or three-blade con"guration. The blades had an airfoil pro"le and were untwisted, tapered and set at a pitch angle of 12$0.53. At the tip the actual pro"le was approximately NACA4613 changing to NACA3712 a little further inboard with the largest portion of the blade being approximately NACA4611. The rotor was placed with the central axis of the hub co-incident with the
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Fig. 1. The Heriot-Watt University open-jet wind-tunnel experimental set up.
wind-tunnel principal axis with the hub front face 0.6 m downstream from the open jet exit and on the centre axis of the wind tunnel. The spin rate of the turbine was monitored using an infrared emitter and sensor "xed to the turbine support, together with a re#ecting element "xed to one of the blades. The periodic signal produced by the sensor was used to trigger and synchronise the laser pulses with the blade azimuth angle. The turbine was run at 14.3$0.1 Hz with the wind speed being 6 m.s\. This gave a tip-speed ratio, q of 6.7$0.05 giving non-stalled blade #ow. Spin rate was controlled by varying the electrical load on the turbine as required. For convenience the turbine was yawed in the verticle plane since this greatly simpli"ed the laser illumination procedure. 2.1.3. Seeding system In both phases of the study the seeding system consisted of a compressed air fake which was used to introduce seeding particles downstream of the model and upstream of the tunnel fan. The particles were allowed to travel around the tunnel circuit several times, prior to image capture, in order to obtain a uniform distribution across the measurement plane. The particles had an average diameter, by number, of 6 lm. The use of seeding particles for quantitative #ow visualisation relies on the use of particles which are of a suitable size and density such that they e$ciently follow the #ow characteristics [9]. The seeding particles in the present were found to be forced outwards from the viscous core of the vortex in a manner dependent on the circulation resulting in voids. The centres of the resulting voids were identi"ed and measured using a particle density algorithm. 2.1.4. Illumination and image capture The beams from two frequency-doubled YAG : Nd lasers were aligned along the same optical path and were shaped to produce an expanding, illuminated sheet which was introduced through a small slot in the roof of the wind-tunnel control room. The
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sheet was aligned with the #ow and passed through the central axis of the turbine. Asymmetric wake de#ection was seen in the plane of the vertical laser sheet and thus readily detectable. The images were recorded on 35 mm technical pan "lm using a SLR camera aligned with its optical axis normal to the illuminating sheet. A Nikon 55 mm lens was used set to an aperture of f 2.8 and a shutter speed to encompass the illumination period, typically th s. This gave a magni"cation of approximately 0.25 at the "lm image capture stage. The image were digitised using a "lm scanner then analysed using in-house software. 2.1.5. Results from phase 1 The use of high image density visualisation provided the opportunity for improved conceptual appreciation of the variability of the dynamic wake. Two sets of images captured at random times are presented. Fig. 2 shows the variability of the wake expansion at a "xed yaw while Fig. 3 shows the variation of wake expansion with yaw angle. The latter is typical of the mode of operation of a wind turbine in the "eld where conditions of variable wind direction are commonly encountered. The wake expansion as a function of yaw angle at various downstream positions was measured from the images and the result shown in Fig. 4a and b. A detailed description of this work including quantitative velocity and vorticity measurements can be found elsewhere [3,5]. In addition, animations of the image sequences can be found in Ref. [4]. 2.2. Experimental arrangements phase 2 (University of Glasgow) 2.2.1. Wind tunnel The University of Glasgow, closed-return, low-speed wind tunnel, was used in Phase 2 of the study. This tunnel had a working section of 2.13 m;1.61 m and was capable of a top speed of 60 ms\ wind speeds ranging from 7.5 ms\ to a maximum of 9.3 ms\ were used in the tests. 2.2.2. Turbine model The turbine model, which was of a two-bladed upwind design, had a rotor diameter of 1 m. The NACA 4415 section blades used were manufactured from carbon "bre and had a chord length of 0.1 m. One blade was instrumented with 16 miniature pressure transducers positioned at the 75% of chord location to allow the temporal variation in blade loads experienced during yawed #ow operation to be measured in addition to the wake data. The entire turbine arrangement could be yawed about the support shaft and locked at any required yaw angle. The turbine was designed for rotational speeds of up to 50 Hz with its rotation being controlled by a similar electronic braking system to that used in the Phase 1 tests. 2.2.3. The illumination and image capture system The illumination system used was identical to that used in the Phase 1 tests except that the light sheet entered the working section of the tunnel horizontally. The light
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Fig. 2. Laser sheet visualisation showing the variability of the wake expansion at a "xed yaw angle. The laser sheet is co-planar with the mean #ow vector.
sheet illuminated an area extending approximately 1.5 m downstream of the turbine by 0.7 sm cross wind. The lasers were triggered by a pulse delivered from a synchronising unit, based on a shaft encoder, "xed to the turbine rotor shaft. The operation of the synchronising unit allowed images to be captured at various rotor azimuth angles. The lasers were operated with a typical time delay between them of 560 ls at approximately 15 Hz. Two Nikon F301 cameras each with a Nikkor 28 mm 1 : 2.8 lens were placed under the wind tunnel working section #oor, viewing the entire measurement plane between them through rectangular holes cut in the #oor (the cameras were placed such that
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Fig. 3. Laser sheet visualisation showing the variation of wake expansion with yaw angle. The laser sheet is co-planar with the mean #ow vector.
one was upstream and the other downstream.). The cameras were simultaneously triggered using a remote shutter release. Shutter times of an s ensured repeatable and successful image capture. Kodak T-Max 400 ISO "lm was used with the camera apertures set at f C 2.8. Images were captured for di!erent combinations of blade azimuth angle (453, 903 and 1353), tip speed ratio (4 and 5) and yaw angle (!403, to 403 in 103 increments). Image distortion was removed by appropriate calibration procedure. 2.2.4. Results from phase 2 Tests were conducted at tip speed ratios 4 and 5 and covered a range of yaw angles up to 403. In case of yawed operation, tests were conducted at both positive and negative yaw angles to capture PIV images corresponding to both extremes of the wake geometry. The data are presented in Section 4 below where a comparison is made with the predictions of the prescribed wake method.
P Fig. 4. (a) The position of the intersection of the training vortex tube with the illuminating light sheet as a function of yaw angle. (b) The displacement of vortex centre from the zero yaw condition at 500 mm downstream. This corresponds to one revolution of the turbine.
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3. The prescribed wake method Precise details of the computational implementation of the prescribed wake model can be found in the papers by Robinson et al. [7,8] but the main features are summarised here. In order to provide a detailed assessment of the variations of aerodynamic coe$cients across the blade span, each blade was divided into a number of span-wise elements which were considered to be aerodynamically independent. The blade division was carried out in a manner which yielded a "ner distribution of elements at the blade tip, and so gave a more accurate representation of the rapidly changing aerodynamic conditions associated with this region. The distributed loading along the blade was approximated by assuming a uniform loading on each blade element which was evaluated at the quarter chord of the element mid-pan. The span-wise blade loading distribution was then represented by a series of straight-line vortex "laments which lay along the quarter chord line of each blade element, the strengths of which were evaluated by application of the Kuttah}Joukowski theorem on the basis of 2D airfoil data. By representing the turbine blades in this manner, a discontinuity in spanwise bound circulation was created at each element boundary. This was redressed by the introduction of trailed vortex "laments whose strengths corresponded to the di!erences in bound circulation between adjacent blade elements. The changes in blade incidence, associated with yawed #ow, required the introduction of shed vorticity into the wake to account for temporal changes in bound circulation. By discretising the rotation of the blades into a series of time steps, the wake was generated as a helical mesh of straight line, shed and trailed vortex-"laments which extended downstream from the blade tailing edge. On a multi-blade system, each blade generated its own wake structure which was superposed on those from the other blades. The details of the manner in which the wake shape was de"ned are discussed in Ref. [7]. In yawed in #ow, the blades can be subject to unsteady aerodynamic loads [8]. Unsteady e!ects are manifest if the reduced frequency for the e!ective pitching of the turbine blade is high enough. The loads produced under these circumstances can be much higher than the equivalent steady-state loads and may have important life-cycle implications for a wind turbine. This phenomenon has received much interest in the past few years and is clear that a comprehensive aerodynamic prediction scheme must be capable of modelling such e!ects. In the present scheme, the unsteady loading was modelled by coupling the unsteady aerodynamic model of Ref. [10] to be prescribed wake method. This unsteady aerodynamic model requires information such as the reduced pitching rates, the local relative velocity and the instantaneous angle of attack which the turbine blade experiences. In the unsteady prescribed wake method this information was determined by initial application of the prescribed wake scheme using static aerodynamic characteristics. This stage of the calculation procedure also produced the wake geometry for the subsequent dynamic calculation. On completion of this stage, the unsteady aerodynamic model was used iteratively with the wake model to obtain a more accurate estimate of the turbine performance.
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4. Comparison of the prescribed wake model predictions with LSV measurements 4.1. Introduction In scale model, wind-tunnel testing, it is relatively straightforward to match the tip-speed ratio of larger machines. This, however, often introduces di$culties since the resulting blade chord Reynolds number on the test turbine will be considerably lower than that on the corresponding full-scale turbine at the same tip-speed ratio. For modelling purposes, this is not a signi"cant problem since a prediction can be made on the basis of either case provided the blade section characteristics at the particular Reynolds number are known. For this reason, a series of low Reynolds number tests were conducted on the airfoil pro"le to be used for the turbine blade section. The results obtained from this test series provided the necessary blade sectional data input to the prescribed wake model to allow comparison with the model turbine tests. 4.2. Detail The results obtained from the LSV study were compared with predictions obtained from the basic prescribed wake model without the inclusion of wind-tunnel wall e!ects. The results highlight the manner in which the constraining e!ect of the tunnel walls is manifest in the wake structure. In the `normala #ow case, the most obvious e!ect of the wind-tunnel walls should be a constriction of the lateral expansion, of the wake structure. This behaviour can be observed in Fig. 5 where the calculated and measured lateral movement of the tip vortex was plotted against rotor cycle number for two tip-speed ratios in head-on #ow. The lateral position of the vortex is expressed as a fraction of the rotor radius. At a tip-speed ratio of 4, the measured tip vortex path shows very little expansion and appears to reach a maximum after about 1.5 rotations. In contrast, the predicted vortex path shows an expansion equivalent to approximately 10% of the rotor radius. It is, however, interesting to note that there is also very little predicted expansion after 1.5 rotations. Similar behaviour is also apparent at tip-speed ratio of 5, where once again, generally more expansion was predicted than was actually measured. Interestingly, however, the vortex locations measured close to the turbine correspond well with the predicted path of the vortex but then deviate sharply inboard after 1.5 rotations. The reason for this is unclear but it may be indicative of the wind tunnel #ow expanding after an initial contraction as it passes the turbine and its near wake. Given the above behaviour, it may be anticipated that a lateral constriction of the wake structure would be accompanied by an accelerated convection of the wake downstream. In fact, as illustrated in Fig. 6, which presents the measured and predicted downstream movement of the tip vortex for the same two tip-speed ratios, the opposite appears to be true.
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Fig. 5. Predicted and measured wake expansion for tip-speed ratios 4 and 5 in head-on #ow.
Comparison of the predicted downstream convection of the tip vortex with the measured for the two cases, clearly indicates that the measured convection is slower than that predicted by which the wall constraint has on the in-#ow to the rotor disk. In an unconstrained #ow, the in#ow velocity to a wind tunnel, however, the velocity of the #ow measured upstream of the turbine disk may not be related in the same manner to the disk in#ow because of the constraint e!ect. If, for example, the #ow was signi"cantly retarded ahead of the turbine, it would e!ectively lower the wake convection speed of the turbine wake and reduce the wake expansion. Both of these e!ects are apparent in the measured data. Measured data obtained when the turbine was yawed to 203 are contrasted with the model predictions in Figs. 7 and 8. In Fig. 7 the predicted and measured lateral positions of the tip vortex produced at the extremes of the half of the rotor disk which is moved into the onset #ow are presented. Here the di!erence between the predicted and measured behaviour is stark. In particular, the measured data exhibit an initial expansion followed by a sudden and dramatic inboard movement of the vortex. This has also been observed during earlier tests in the open section wind tunnel [3], but the extent by which the vortex moved inboard was, in that case, much less than in the present case. In contrast, the predicted movement of the tip vortex indicates a gradual expansion of the wake outboard of the blade tip. Interestingly, for this case, Fig. 8 shows relatively good agreement between the predicted and measured downstream movement of the vortex.
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Fig. 6. Predicted and measured wake convection for tip-speed ratios 4 and 5 in head-on #ow.
Fig. 7. Predicted and measured wake convection for tip-speed ratio 5 and a rotor yaw angle of 203.
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Fig. 8. Predicted and measured wake convection for tip-speed ratio 5 and a rotor yaw angle of 203.
5. Concluding remarks In this paper quantitative laser sheet visualisation has been used to examine the wakes of two small wind turbines operating in two low-speed wind tunnels. The work has highlighted many of the key features of wind-turbine wakes and has provided valuable code validation information. The interaction between the turbine, its wake and the walls of the wind tunnel is particularly complex. The present results have served to highlight this e!ect and to indicate the severity of the problem. Future work will combine the prescribed wake model with a numerical representation of the wind-tunnel walls in a manner to aid understanding of many of the e!ects presented here.
Acknowledgements The work detailed in this paper was supported by a Grant (GR/K/14995) from the UK Engineering and Physical Sciences Research Council. The authors are indebted to Prof. R. Galbraith for his advice during the project and to Mr. T. Wang for his help with the prescribed wake model.
References [1] A.C. Hansen, C.P. Butter"eld, Aerodynamics of horizontal-axis wind turbines, Ann. Rev. Fluid Mech. 25 (1993) 115}149.
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[2] D.E. Shipley, M.S. Miller, M.C. Robinson, Dynamic stall occurrence on a horizontal axis wind turbine blade, Wind Energy ASME SED-16, 1995. [3] I. Grant, P. Parkin, X. Wang, Optical vortex tracking studies of a horizontal axis wind turbine in Yaw using laser-sheet, Flow visualisation, Exp. Fluids 23 (1997) 513}519. [4] I. Grant, M. Mo, X. Pan, P. Parkin, J. Powell, H. Reinecke, K. Shuang, F. Coton, D. Lee, Optical evaluation of the wake characteristics of a wind turbine and a prescribed wake model, in: G.M. Carlomagno, I. Grant (Eds.), Proceedings of the Eigth International symposium on Flow Visualization, Sorrento, September 1-4, 1998, paper 132, pp. 132.1}132.15, ISBN 0 9533991 0 9, http://www.ode-web.demon.co.uk/post-conf-web/#yer.html. [5] I. Grant, P. Parkin, A DPIV study of the trailing vortex elements from the blades of a horizontal wind turbine in Yaw, Exp. Fluids (2000) in press. [6] R.E. Wilson, B.S. Lissaman, Proceedings of the Symposium on Applied Aerodynamics of Wind Power Machines, Oregon State University, 1974. [7] D.J. Robison, F.N. Coton, R.A.McD. Galbraith, M. Vezza, Application of a prescribed wake aerodynamic prediction scheme to horizontal axis wind turbine in axial #ow, Wind Eng. 19(1) (1995). [8] D.J. Robison, F.N. Coton, R.A.McD. Galbraith, M. Vezza, The development of a prescribed wake model for performance prediction in steady yawed #ow, Proceedings of the 14th ASME/ETCE Wind Energy Symposium, Houston, Texas, 1996. [9] I. Grant, Particle image velocimetry; a review, Proceedings of the Institution of Mechanical Engineers Part C, J. Mech. Eng. Sci. C 211 (1997) 55}76. [10] J.G. Leishman, T.S. Beddoes, A semi-empirical model for dynamic stall, J. Am. Helicopter Soc. (1989).
An experimental and numerical study of the vortex "laments in the wake of an operational, horizontal-axis, wind turbine I. Grant *, M. Mo , X. Pan, P. Parkin , J. Powell , H. Reinecke , K. Shuang, F. Coton, D. Lee Department of Civil and owshore Engineering, Fluid Loading and Instrumentation Center, Heriot-Watt University, Edinburgh, Scotland, EH14 4AS, UK Beijing Petroleum University, Beijing, People's Republic of China University of Glasgow, Glasgow, Scotland, UK Received 13 August 1999; accepted 25 November 1999
Abstract The paper describes a wind-tunnel study of the wake dynamics of an operational, horizontal-axis wind turbine. The behaviour of the vorticity trailing from the turbine blade tips and the e!ect of was interference on wake development were considered. Laser sheet visualisation (LSV) techniques were used to measure the trajectories of the trailing vorticity under various conditions of turbine yaw and blade azimuth. Selected results obtained in the experimental study were compared with the predictions of a prescribed wake model and are being used in the further development of the method. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Wind tunnel; Horizontal-axis wind turbine (HAWT); Laser sheet visualisation (LSV); Prescribed wake; Vortex; Numerical simulation
1. Introduction The horizontal-axis wind turbine (HAWT) is the most frequently used type found in operation. Whilst being geometrically simple, its operating regime is aerodynamically complex [1] and, in some cases [2], particularly unsteady.
* Corresponding author. Tel.: #44-131-451-3156. E-mail address: [email protected] (I. Grant) 0167-6105/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 9 ) 0 0 1 3 9 - 7
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I. Grant et al. / J. Wind Eng. Ind. Aerodyn. 85 (2000) 177}189
The present paper describes wind-tunnel tests of a full-size, `Marleca, turbine in two wind tunnels. In both cases, it was possible to ensure that the main thrust producing sections of the turbine rotor operated above the critical Reynolds number. Using laser sheet visualization (LSV), valuable information on the turbine wake structure and its sensitivity to operational conditions, such as wall e!ects and blockage, was obtained. This also gave the opportunity to measure wake expansion as a function of turbine yaw [3}5]. Historically, design assessments of the aerodynamics of the HAWT have been conducted by relatively simple blade-element momentum methods [6]. When timedependent details of the local #ow states are required, however. the more sophisticated free, or prescribed, wake methods have been used. The computationally e$cient, prescribed wake technique [7,8], used here, allows the wake boundaries to be de"ned on the basis of geometrically prescribed functions derived from momentum theory. The long-term is to alleviate the wind-tunnel wall e!ect by coupling the prescribed wake with a three-dimensional source panel method. The work on coupling the prescribed wake model to the panel method is at an advanced stage. In this paper, however, the emphasis is primarily on the LSV study. Nevertheless, comparisons of the measured data with the basic (i.e., unconstrained) prescribed wake method were made to illustrate the severity of the wall e!ect.
2. Description of experiments The experimental program was conducted in two phases, the "rst at Heriot-Watt University, Edinburgh, the second at the University of Glasgow. 2.1. Experimental arrangements phase 1 (Heriot-Watt) 2.1.1. Wind tunnel The "rst phase of the test programme was conducted in the Heriot-Watt University, closed return, low turbulence, wind tunnel where an open jet con"guration was used in order to minimise blockage and wake de#ection due to wall interference (Fig. 1). The tunnel was of closed circuit design with axial dimensions of 10 and 4.5 m. The working section was sited midway along one of the 10 m sides. In the tests the tunnel was operated in an open-jet con"guration giving a working section of 2.3 m in length. The jet issued from an octagonal aperature which measured 1.24 m between the #ats and the length of each side begin 0.51 m. 2.1.2. The turbine The wind turbine had an overall rotor diameter of 0.9 m and a hub diameter of 0.24 m. The turbine was run in either a two- or three-blade con"guration. The blades had an airfoil pro"le and were untwisted, tapered and set at a pitch angle of 12$0.53. At the tip the actual pro"le was approximately NACA4613 changing to NACA3712 a little further inboard with the largest portion of the blade being approximately NACA4611. The rotor was placed with the central axis of the hub co-incident with the
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Fig. 1. The Heriot-Watt University open-jet wind-tunnel experimental set up.
wind-tunnel principal axis with the hub front face 0.6 m downstream from the open jet exit and on the centre axis of the wind tunnel. The spin rate of the turbine was monitored using an infrared emitter and sensor "xed to the turbine support, together with a re#ecting element "xed to one of the blades. The periodic signal produced by the sensor was used to trigger and synchronise the laser pulses with the blade azimuth angle. The turbine was run at 14.3$0.1 Hz with the wind speed being 6 m.s\. This gave a tip-speed ratio, q of 6.7$0.05 giving non-stalled blade #ow. Spin rate was controlled by varying the electrical load on the turbine as required. For convenience the turbine was yawed in the verticle plane since this greatly simpli"ed the laser illumination procedure. 2.1.3. Seeding system In both phases of the study the seeding system consisted of a compressed air fake which was used to introduce seeding particles downstream of the model and upstream of the tunnel fan. The particles were allowed to travel around the tunnel circuit several times, prior to image capture, in order to obtain a uniform distribution across the measurement plane. The particles had an average diameter, by number, of 6 lm. The use of seeding particles for quantitative #ow visualisation relies on the use of particles which are of a suitable size and density such that they e$ciently follow the #ow characteristics [9]. The seeding particles in the present were found to be forced outwards from the viscous core of the vortex in a manner dependent on the circulation resulting in voids. The centres of the resulting voids were identi"ed and measured using a particle density algorithm. 2.1.4. Illumination and image capture The beams from two frequency-doubled YAG : Nd lasers were aligned along the same optical path and were shaped to produce an expanding, illuminated sheet which was introduced through a small slot in the roof of the wind-tunnel control room. The
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sheet was aligned with the #ow and passed through the central axis of the turbine. Asymmetric wake de#ection was seen in the plane of the vertical laser sheet and thus readily detectable. The images were recorded on 35 mm technical pan "lm using a SLR camera aligned with its optical axis normal to the illuminating sheet. A Nikon 55 mm lens was used set to an aperture of f 2.8 and a shutter speed to encompass the illumination period, typically th s. This gave a magni"cation of approximately 0.25 at the "lm image capture stage. The image were digitised using a "lm scanner then analysed using in-house software. 2.1.5. Results from phase 1 The use of high image density visualisation provided the opportunity for improved conceptual appreciation of the variability of the dynamic wake. Two sets of images captured at random times are presented. Fig. 2 shows the variability of the wake expansion at a "xed yaw while Fig. 3 shows the variation of wake expansion with yaw angle. The latter is typical of the mode of operation of a wind turbine in the "eld where conditions of variable wind direction are commonly encountered. The wake expansion as a function of yaw angle at various downstream positions was measured from the images and the result shown in Fig. 4a and b. A detailed description of this work including quantitative velocity and vorticity measurements can be found elsewhere [3,5]. In addition, animations of the image sequences can be found in Ref. [4]. 2.2. Experimental arrangements phase 2 (University of Glasgow) 2.2.1. Wind tunnel The University of Glasgow, closed-return, low-speed wind tunnel, was used in Phase 2 of the study. This tunnel had a working section of 2.13 m;1.61 m and was capable of a top speed of 60 ms\ wind speeds ranging from 7.5 ms\ to a maximum of 9.3 ms\ were used in the tests. 2.2.2. Turbine model The turbine model, which was of a two-bladed upwind design, had a rotor diameter of 1 m. The NACA 4415 section blades used were manufactured from carbon "bre and had a chord length of 0.1 m. One blade was instrumented with 16 miniature pressure transducers positioned at the 75% of chord location to allow the temporal variation in blade loads experienced during yawed #ow operation to be measured in addition to the wake data. The entire turbine arrangement could be yawed about the support shaft and locked at any required yaw angle. The turbine was designed for rotational speeds of up to 50 Hz with its rotation being controlled by a similar electronic braking system to that used in the Phase 1 tests. 2.2.3. The illumination and image capture system The illumination system used was identical to that used in the Phase 1 tests except that the light sheet entered the working section of the tunnel horizontally. The light
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Fig. 2. Laser sheet visualisation showing the variability of the wake expansion at a "xed yaw angle. The laser sheet is co-planar with the mean #ow vector.
sheet illuminated an area extending approximately 1.5 m downstream of the turbine by 0.7 sm cross wind. The lasers were triggered by a pulse delivered from a synchronising unit, based on a shaft encoder, "xed to the turbine rotor shaft. The operation of the synchronising unit allowed images to be captured at various rotor azimuth angles. The lasers were operated with a typical time delay between them of 560 ls at approximately 15 Hz. Two Nikon F301 cameras each with a Nikkor 28 mm 1 : 2.8 lens were placed under the wind tunnel working section #oor, viewing the entire measurement plane between them through rectangular holes cut in the #oor (the cameras were placed such that
182
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Fig. 3. Laser sheet visualisation showing the variation of wake expansion with yaw angle. The laser sheet is co-planar with the mean #ow vector.
one was upstream and the other downstream.). The cameras were simultaneously triggered using a remote shutter release. Shutter times of an s ensured repeatable and successful image capture. Kodak T-Max 400 ISO "lm was used with the camera apertures set at f C 2.8. Images were captured for di!erent combinations of blade azimuth angle (453, 903 and 1353), tip speed ratio (4 and 5) and yaw angle (!403, to 403 in 103 increments). Image distortion was removed by appropriate calibration procedure. 2.2.4. Results from phase 2 Tests were conducted at tip speed ratios 4 and 5 and covered a range of yaw angles up to 403. In case of yawed operation, tests were conducted at both positive and negative yaw angles to capture PIV images corresponding to both extremes of the wake geometry. The data are presented in Section 4 below where a comparison is made with the predictions of the prescribed wake method.
P Fig. 4. (a) The position of the intersection of the training vortex tube with the illuminating light sheet as a function of yaw angle. (b) The displacement of vortex centre from the zero yaw condition at 500 mm downstream. This corresponds to one revolution of the turbine.
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3. The prescribed wake method Precise details of the computational implementation of the prescribed wake model can be found in the papers by Robinson et al. [7,8] but the main features are summarised here. In order to provide a detailed assessment of the variations of aerodynamic coe$cients across the blade span, each blade was divided into a number of span-wise elements which were considered to be aerodynamically independent. The blade division was carried out in a manner which yielded a "ner distribution of elements at the blade tip, and so gave a more accurate representation of the rapidly changing aerodynamic conditions associated with this region. The distributed loading along the blade was approximated by assuming a uniform loading on each blade element which was evaluated at the quarter chord of the element mid-pan. The span-wise blade loading distribution was then represented by a series of straight-line vortex "laments which lay along the quarter chord line of each blade element, the strengths of which were evaluated by application of the Kuttah}Joukowski theorem on the basis of 2D airfoil data. By representing the turbine blades in this manner, a discontinuity in spanwise bound circulation was created at each element boundary. This was redressed by the introduction of trailed vortex "laments whose strengths corresponded to the di!erences in bound circulation between adjacent blade elements. The changes in blade incidence, associated with yawed #ow, required the introduction of shed vorticity into the wake to account for temporal changes in bound circulation. By discretising the rotation of the blades into a series of time steps, the wake was generated as a helical mesh of straight line, shed and trailed vortex-"laments which extended downstream from the blade tailing edge. On a multi-blade system, each blade generated its own wake structure which was superposed on those from the other blades. The details of the manner in which the wake shape was de"ned are discussed in Ref. [7]. In yawed in #ow, the blades can be subject to unsteady aerodynamic loads [8]. Unsteady e!ects are manifest if the reduced frequency for the e!ective pitching of the turbine blade is high enough. The loads produced under these circumstances can be much higher than the equivalent steady-state loads and may have important life-cycle implications for a wind turbine. This phenomenon has received much interest in the past few years and is clear that a comprehensive aerodynamic prediction scheme must be capable of modelling such e!ects. In the present scheme, the unsteady loading was modelled by coupling the unsteady aerodynamic model of Ref. [10] to be prescribed wake method. This unsteady aerodynamic model requires information such as the reduced pitching rates, the local relative velocity and the instantaneous angle of attack which the turbine blade experiences. In the unsteady prescribed wake method this information was determined by initial application of the prescribed wake scheme using static aerodynamic characteristics. This stage of the calculation procedure also produced the wake geometry for the subsequent dynamic calculation. On completion of this stage, the unsteady aerodynamic model was used iteratively with the wake model to obtain a more accurate estimate of the turbine performance.
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4. Comparison of the prescribed wake model predictions with LSV measurements 4.1. Introduction In scale model, wind-tunnel testing, it is relatively straightforward to match the tip-speed ratio of larger machines. This, however, often introduces di$culties since the resulting blade chord Reynolds number on the test turbine will be considerably lower than that on the corresponding full-scale turbine at the same tip-speed ratio. For modelling purposes, this is not a signi"cant problem since a prediction can be made on the basis of either case provided the blade section characteristics at the particular Reynolds number are known. For this reason, a series of low Reynolds number tests were conducted on the airfoil pro"le to be used for the turbine blade section. The results obtained from this test series provided the necessary blade sectional data input to the prescribed wake model to allow comparison with the model turbine tests. 4.2. Detail The results obtained from the LSV study were compared with predictions obtained from the basic prescribed wake model without the inclusion of wind-tunnel wall e!ects. The results highlight the manner in which the constraining e!ect of the tunnel walls is manifest in the wake structure. In the `normala #ow case, the most obvious e!ect of the wind-tunnel walls should be a constriction of the lateral expansion, of the wake structure. This behaviour can be observed in Fig. 5 where the calculated and measured lateral movement of the tip vortex was plotted against rotor cycle number for two tip-speed ratios in head-on #ow. The lateral position of the vortex is expressed as a fraction of the rotor radius. At a tip-speed ratio of 4, the measured tip vortex path shows very little expansion and appears to reach a maximum after about 1.5 rotations. In contrast, the predicted vortex path shows an expansion equivalent to approximately 10% of the rotor radius. It is, however, interesting to note that there is also very little predicted expansion after 1.5 rotations. Similar behaviour is also apparent at tip-speed ratio of 5, where once again, generally more expansion was predicted than was actually measured. Interestingly, however, the vortex locations measured close to the turbine correspond well with the predicted path of the vortex but then deviate sharply inboard after 1.5 rotations. The reason for this is unclear but it may be indicative of the wind tunnel #ow expanding after an initial contraction as it passes the turbine and its near wake. Given the above behaviour, it may be anticipated that a lateral constriction of the wake structure would be accompanied by an accelerated convection of the wake downstream. In fact, as illustrated in Fig. 6, which presents the measured and predicted downstream movement of the tip vortex for the same two tip-speed ratios, the opposite appears to be true.
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Fig. 5. Predicted and measured wake expansion for tip-speed ratios 4 and 5 in head-on #ow.
Comparison of the predicted downstream convection of the tip vortex with the measured for the two cases, clearly indicates that the measured convection is slower than that predicted by which the wall constraint has on the in-#ow to the rotor disk. In an unconstrained #ow, the in#ow velocity to a wind tunnel, however, the velocity of the #ow measured upstream of the turbine disk may not be related in the same manner to the disk in#ow because of the constraint e!ect. If, for example, the #ow was signi"cantly retarded ahead of the turbine, it would e!ectively lower the wake convection speed of the turbine wake and reduce the wake expansion. Both of these e!ects are apparent in the measured data. Measured data obtained when the turbine was yawed to 203 are contrasted with the model predictions in Figs. 7 and 8. In Fig. 7 the predicted and measured lateral positions of the tip vortex produced at the extremes of the half of the rotor disk which is moved into the onset #ow are presented. Here the di!erence between the predicted and measured behaviour is stark. In particular, the measured data exhibit an initial expansion followed by a sudden and dramatic inboard movement of the vortex. This has also been observed during earlier tests in the open section wind tunnel [3], but the extent by which the vortex moved inboard was, in that case, much less than in the present case. In contrast, the predicted movement of the tip vortex indicates a gradual expansion of the wake outboard of the blade tip. Interestingly, for this case, Fig. 8 shows relatively good agreement between the predicted and measured downstream movement of the vortex.
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Fig. 6. Predicted and measured wake convection for tip-speed ratios 4 and 5 in head-on #ow.
Fig. 7. Predicted and measured wake convection for tip-speed ratio 5 and a rotor yaw angle of 203.
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Fig. 8. Predicted and measured wake convection for tip-speed ratio 5 and a rotor yaw angle of 203.
5. Concluding remarks In this paper quantitative laser sheet visualisation has been used to examine the wakes of two small wind turbines operating in two low-speed wind tunnels. The work has highlighted many of the key features of wind-turbine wakes and has provided valuable code validation information. The interaction between the turbine, its wake and the walls of the wind tunnel is particularly complex. The present results have served to highlight this e!ect and to indicate the severity of the problem. Future work will combine the prescribed wake model with a numerical representation of the wind-tunnel walls in a manner to aid understanding of many of the e!ects presented here.
Acknowledgements The work detailed in this paper was supported by a Grant (GR/K/14995) from the UK Engineering and Physical Sciences Research Council. The authors are indebted to Prof. R. Galbraith for his advice during the project and to Mr. T. Wang for his help with the prescribed wake model.
References [1] A.C. Hansen, C.P. Butter"eld, Aerodynamics of horizontal-axis wind turbines, Ann. Rev. Fluid Mech. 25 (1993) 115}149.
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[2] D.E. Shipley, M.S. Miller, M.C. Robinson, Dynamic stall occurrence on a horizontal axis wind turbine blade, Wind Energy ASME SED-16, 1995. [3] I. Grant, P. Parkin, X. Wang, Optical vortex tracking studies of a horizontal axis wind turbine in Yaw using laser-sheet, Flow visualisation, Exp. Fluids 23 (1997) 513}519. [4] I. Grant, M. Mo, X. Pan, P. Parkin, J. Powell, H. Reinecke, K. Shuang, F. Coton, D. Lee, Optical evaluation of the wake characteristics of a wind turbine and a prescribed wake model, in: G.M. Carlomagno, I. Grant (Eds.), Proceedings of the Eigth International symposium on Flow Visualization, Sorrento, September 1-4, 1998, paper 132, pp. 132.1}132.15, ISBN 0 9533991 0 9, http://www.ode-web.demon.co.uk/post-conf-web/#yer.html. [5] I. Grant, P. Parkin, A DPIV study of the trailing vortex elements from the blades of a horizontal wind turbine in Yaw, Exp. Fluids (2000) in press. [6] R.E. Wilson, B.S. Lissaman, Proceedings of the Symposium on Applied Aerodynamics of Wind Power Machines, Oregon State University, 1974. [7] D.J. Robison, F.N. Coton, R.A.McD. Galbraith, M. Vezza, Application of a prescribed wake aerodynamic prediction scheme to horizontal axis wind turbine in axial #ow, Wind Eng. 19(1) (1995). [8] D.J. Robison, F.N. Coton, R.A.McD. Galbraith, M. Vezza, The development of a prescribed wake model for performance prediction in steady yawed #ow, Proceedings of the 14th ASME/ETCE Wind Energy Symposium, Houston, Texas, 1996. [9] I. Grant, Particle image velocimetry; a review, Proceedings of the Institution of Mechanical Engineers Part C, J. Mech. Eng. Sci. C 211 (1997) 55}76. [10] J.G. Leishman, T.S. Beddoes, A semi-empirical model for dynamic stall, J. Am. Helicopter Soc. (1989).