Correcting inflow measurements from wind turbines using a lifting surface code

Correcting inflow measurements from wind turbines using a lifting surface code

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Unformatted text preview: J. Whale Post—doctoral Research Assocrate. Department of Aeronautical and Astronautical Engineering Universrty of Illinois at Urbana-Champaign. 306 Talbot Laboratory. 104 South Wright Street. Urbana. IL 61801-2935 C. J. Fisichella Graduate Student. Department of Mechanical and Industrial Engineering, Unrversrty of Illinois at Urbana—Champaign, 306 Talbot Laboratory. 104 South Wright Street. Urbana, IL 61801-2935 M. S. Selig Associate Professor. Department at Aeronautical and Astronautical Engineering. Universtty ot lllinois at Urbana-Champaign, 306 Talbot Laboratory, 104 South Wright Street. Urbana, IL 61801—2935 e—mail: [email protected] Introduction A key parameter in aerodynamic models of horizontal-axis wind turbines tHAWTs) is the angle of attack a defined as the angle between the chord of the blade airfoil profile and the effec- tive local velocitywthe resultant of the components of axial in- duced and rotational velocities. where the induced velocity is that produced by the shed wake from the rotor. Measurements of force coefficients made on rotating wind turbine blades. however. are typically correlated with measurements of a local inflow angle B obtained by flow angle sensors protruding from the leading edge of the blade (see Fig. 1). It is desirable to reduce the 3D field measurements in terms of the angle of attack a in order to provide accurate measured blade element data for comparison with 2D blade-element momentum (BEM) and dynamic stall models and other experimental results. The angle of attack is related to the inflow angle by: a=B—a., (1) where a“ is the angle due to the upwash induced at the local inflow point by the bound vorticity on the blade. Calculating a” is a relatively straightforward procedure in a wind tunnel where a 2D airfoil can be positioned at a particular angle a and a probe used to measure the local inflow angle ,8 at a point. There are significant differences. however. between 2D airfoil flow and 3D flow on a rotating blade. This is most noticeable at inboard sec— tions of the blade where the section is experiencing stall. The Coriolis component of the 3D flow suppresses separation: delay— ing stall and enhancing lift at the blade section. These effects are referred to as ‘stall-delay' or 'post-stall’ effects [1.2]. Various methods have been proposed for calculating the rela— tionship between a and B (and hence the 3D upwashl on a rotat— ing blade. Madsen [3] describes a method that uses BEM to cal- Contributed by the Solar Energy Division 01 The American Society 01 Mechani- cal Engineers for publication in the ASME JOL'RNAL 0F SOLAR ENERGY ENGI- N‘EERING. Manuscript received by the ASME Solar Energy Division. April 1999'. tinal rcvrsron. September 1000. Associate Technical Editor: D. Berg. 196 / Vol. 122, NOVEMBER 2000 Copyright © 2000 by ASME Correcting Inflow Measurements From Wind Turbines Using a Lilting-Suriace Code In order to provide accurate blade element data for wind turbine design codes, measured three-dimensional ( 3D) field data must be corrected in terms of the (sectional) angle of attack. A 3D LifiingSmj‘ace Inflow Correction Method ( LSIM l has been developed with the aid ofa vortex-panel code in order to calculate the relationship between measured local flow angle and angle of attack. The results show the advantages of using the 3D LSIM correction over 2D correction methods. particularly at the inboard sections of the blade where the local flow is affected by post—stall effects and the influence of the blade root. [SO 1 99-623 1 (00l00604—3] culate a HAWT power curve as a function of angle of attack at a particular spanwise position. The measured inflow angles are ad- justed until good agreement is provided between the calculated and measured power curves. The inverse BEM method [4.5] as- sumes the measured normal and tangential forces are uniform over an annulus containing the blade section. The wake-induced velocities are calculated according to momentum theory. yielding the effective velocity vector and subsequently the angle of attack. Brand et al. [6] estimate the angle of attack using a stagnation point method. The intersection of the chord line and a line normal to the blade surface at the stagnation point yields a stagnation angle. which is used as an estimate for the angle of attack. In order to ascertain the B—a relationship for their Combined Experiment Rotor (CERl. researchers at the National Renewable Energy Laboratory (NREL) have conducted a series of 2D wind tunnel experiments [7]. A 2D scale model of the blade section was fitted with a flow sensor upstream of the section and placed in a wind tunnel. The 2D upwash obtained from these tests was used as an estimate for the 3D upwash. The current research aims to improve on these 2D methods by calculating the flow field around a HAWT rotor using a 3D vortex-panel method. A lifting—surface code is used to model the vorticity in the wake and along the rotor blades. The 3D upwash Fig. 1 section Angle of attack a and local flow angle B for a blade Transactions of the ASME induced by the flow field vorticity is calculated. yielding the ,B—a relationship at desired spanwise stations as a set of inflow correc— tion curves. This paper shows the initial results of using the code to correct 3D data from Phase III of the CER tests conducted at NREL. The Inflow Correction Method An inflow correction method has been developed at the Univer- sity of Illinois at Urbana-Champaign in order to provide accurate 3D corrections to HAWT aerodynamic data. The method makes use of a lifting-surface code and is referred to as the Lifting‘ Surface Inflow Correction Method (LSIM). The Lifting-Surface Code. The lifting-surface code used in the method is titled ‘Lifting-Surface Aerodynamics and Perfor- mance Analysis of Rotors in Axial Flight’ (LSAF). developed by Kocurek [8]. The code was written for the design and analysis of helicopter rotors and extended to wind turbines. The code simu- lates the rotor and the wake as a lattice of vortex panels. A pre- scribed wake model is used which allows for roll—up of tip and root vonices. and these features were used in the current model. The detailed blade aerodynamics are computed by combining the lifting—surface model with a blade-element analysis that requires as input a table of airfoil performance characteristics. Field veloc- ity routines in the code allow the computation of local flow angles at specified points in the flow. Development of the Method. LSIM evolved from the con- sideration of the differences in 2D and 3D upwash due to post— stall effects. For inboard stations at post-stall angles of attack. the circulation around a 3D blade section is expected to be greater than that around a 2D section. As Fig. 2 illustrates. the 3D post- stall upwash is thus expected to be greater than the 2D upwash. Thus, as Fig. 3 shows. for a particular angle of attack past stall the 3D inflow angle ,8 is higher than the 2D case (which is higher than the straight dotted line shown to represent the line of reflec- tion B=a). Consequently. for a particular inflow angle B past that of 2D stall. the 3D angle of attack a is lower than the angle predicted from the 2D correction curve. The application of the 3D correction to measured 3D lift data in Fig. 3 results in a curve that has higher lift at a given 01 than the curve that has been corrected with 2D data. This higher lift in turn would suggest (through a vortex lattice method and circulation considerations) greater val- ues of inflow angle ,8 for that particular a than specified in the 2D B-a correction curve of Fig. 3. It is this interplay between the ,B—a relationship and the corrected data curves that leads to the concept of an iterative inflow correction method. The strategy behind LSIM is to use an initial estimate of the 3D 3—01 relationship for each spanwise station of interest and apply the inflow corrections to convert the measured raw data into air- foil performance data according to the equations:1 c,=c,l cos a+c,sina (2) cdp=c,, sin a—c,cosa (3) [it must be noted that the convection used in Eqs. (2) and (3] is consrstent With a tangential force that rs defined as positive towards the leading edge of the blade. 320 330 > L320 1 MO ‘1‘ f KC) \ I I (1 F2D a F30 > Pop 2D : 6120 3D : Ciao > 0120 Fig. 2 Difference between 2D and 3D flow physics at a blade section Journal of Solar Energy Engineering 3D corrected 2D corrected 2D stall Fig. 3 Expected trends for a 3D inflow correction where c, and c,l are taken from measured pressure data on the blade. and hence the drag coefficient is referred to as the pressure drag coefficient. The airfoil performance data are then input into the vortex panel code. and values of a and fl are extracted at each station of interest to form new B-a relationships. The new corrections are used to correct the raw data again and the resulting performance data is input into the code once more. This procedure is repeated until converged solutions for the 3—6: curves are reached and a final correction can be made to the raw data. Convergence is determined by the difference in 3 between the current and previ- ous iterations at each span station. When the maximum absolute value falls below a set tolerance. then the solution is assumed to have converged. A tolerance of 0.4 deg. 4—5 iterations for conver— Make initial estimate of the fi—oz relationship at each span station Convert raw cn—fl. ct—fi data to cl—a data and use together with suitable cd—a data as airfoil tables for input to LSAF Run LSAF to produce new 3D ,6—a relationship at each station Converged fi—a Apply [3-01 corrections to raw cn—B. Cg—fi data to produce final solutions for cl—a, cdp—a i Fig. 4 Flowchart of LSIM procedure NOVEMBER 2000, Vol. 122 / 197 Table 1 Operating parameters of the Phase III CER tests Machine Operation ‘ Number of blades 3 ‘ Rated power 19.8 kW Power regulation Stall Rotor location Downwind I, i Cut-in wind speed 6 m/s : Cutout Wind speed N/A (stall control) l Rotational speed 71.63 rpm ‘ l‘ Density 1.025 kg/m3 Coning angle 3.42 deg Blade Parameters : NREL in-house 1 Type Profile S809 l Chord 0.4572 in , Thickness 0.096 m Length 5.023 m Tip pitch Approx. 3 deg gence and less than l—min cpu time per iteration are typical. The overall procedure is outlined in Fig. 4. Additional details can be found in Whale and Selig [9.10]. Testing the Method. Testing of the correction method re- quires measured data that incorporates 3D flow characteristics at post-stall angles of attack. A large amount of 3D data has been gathered from the IEA Annex XIV Project: Field Rotor Aerody- namics [ll] which involved the coordination of five full-scale aerodynamic test programs aimed at capturing 3D data from ex- periments on rotating wind turbine blades. Of these tests. the most comprehensive body of data has been gathered at NREL due to the detailed instrumentation on the CER blade. In Phase III of the CER experiment [12], a highly twisted blade of constant chord was used. With the exception of the root. the blade has an NREL 5809 profile. an airfoil that has been tested in wind tunnels at Delft University of Technology (TUDelft), Ohio State University (OSU) and Colorado State University (CSU) [7]. Table 1 shows the blade geometry and operating parameters for the CER during Phase III. Measurements of the local inflow. at a distance in front of the leading edge of the blade equal to 79% of the chord. were made with lightweight flow sensor flags for span- wise stations of 30%, 47%, 63%. and 80% of the blade radius. For the purposes of testing LSIM. it was desirable to obtain a smooth set of performance data in which irregularities in the data (e.g.. due to unsteady conditions during measurement) were kept to a |-- 30% span ‘ 1—9- 47% span . —o— 63% span l ‘4- 80%span‘ ......... ................. . ................ 1.5 Normal Force, c O 10 20 Local Flow Angle, B (deg) 30 40 minimum. A ‘hypothetical‘ set of 3D data was produced for the CER by matching TUDelft 2D wind tunnel data and Phase III CER 3D data. Performance data from 2D wind tunnel tests on the S809 airfoil at TUDelft was input into the lifting-surface code and converted to uncorrected pre-stall data at 30%. 47%. 63%. and 80% span. Phase III CER 3D performance data was used as a guide in estimating the post-stall behavior of the hypothetical data. Plots of normal and tangential blade force coefficients versus local flow angle for the hypothetical 3D data are shown in Figs. 5(a) and 5(b), respectively. LSIM simulations were carried out using the hypothetical data using the line of reflection as an initial inflow correction (i.e.. a = B at iteration [tn 0). In constructing the performance tables to input to the vortex code. lift values were calculated using Eq. (2) and drag values were taken from 2D TUDelft data. Results The inflow correction curves output from LSIM were found to converge after 4-5 iterations of the method and the results are shown in Figs. 6(al—(d) for the 30%. 47%. 63%, and 80% span stations. respectively. In each case. the SD curves are compared with 2D inflow correction curves (i.e.. using 2D TUDelft lift and drag values as input to LSIM). At 30% span. there is a significant departure in the post—stall B—a relationship between the 2D and 3D correction methods. Figure 6(a) shows 330>Bzo for some post~stall a. as expected from the theory outlined in Fig. 2. In particular. at B=20 deg there is a difference of around 4 deg between applying a 2D LSIM or a 3D LSIM correction to the raw measurement data. At the 47% and 63% span stations. the deviation between the 2D and 3D curves is less significant with a difference of less than 0.5 deg between applying a 2D or a 3D correction across the range of raw ,8 values. Further outboard. at 80% span. the differences between the 2D and 3D curves are negligible. The converged 3D inflow correction curves were linearly ex- trapolated to higher angles of attack over the entire B range of the hypothetical input data and extended trendlines were used to ap- ply the 3D LSIM corrections to the data at each spanwise location. and produce values of lift and pressure drag in accordance with Eqs. (2) and (3). The errors introduced by extending the inflow correction curves are discussed before the conclusions of this pa- per. From the equations it can be seen that applying the inflow correction will affect both the general slope and intercept of the 3D performance curves. The 3D corrected lift and pressure drag curves produced by LSIM are shown in Fig. 7. together with corresponding 2D data from wind tunnel tests at TUDelft lRe=500.000). 30% span l 47% spani 63% span l 80% span l O 10 20 30 40 Local Flow Angle. (3 (deg) Fig. 5 Hypothetical performance data based on Phase lll CER values: (a) Normal force. (b) Tangential force 198 / Vol. 122. NOVEMBER 2000 Transactions of the ASME A a: V w o a m E «a. 20 2’ c» C < 3 9 u- / a 10 ,, ," .. , 8 ' l _. 1, - 2DLS|M l 3+ 3DLS|M I l -- Line of reflection! 0 10 20 30 Angle of Attack, (1 (deg) A O V (.0 O 20 . ,. .. .. .. (Iva/... .......... 10 ...... Local Flow Angle, (3 (deg) «>~ 20 LSIM [-9- 3D LSIM i - -- Line of reflection 0 10 20 30 Angle of Attack, (1 (deg) (b) 30 B CD 3 . ‘& 2O ‘ m‘ E) C < 3 2 u. ,’ U ,’ 3 0 2D LSlM i + 3D LSlM ‘—-- Line olreilection 0 , 0 10 20 30 Angle of Attack, or (deg) ((1)30 B CD ' , I E . n 20 .. . ... . ...... I). .. 2” , at C < B 2 LI. 5 10 8 l _‘ -<>- 2D LSIM + an LSIM i - -- Line of reflection l O 1 0 20 30 Angle of Attack, on (deg) Fig. 6 LSIM inflow correction curves for CER hypothetical lift data: (a) 30% span, (b) 47% span, (c) 68% span, (d) 98% span At the 30% station (Fig. 7(a)), there is a marked enhancement of the 3D lift as compared with the 2D data. The increase in lift is as much as 75% at some angles of attack and the converged LSIM curve shows an ll-degrees delay in stall compared with the 2D data. Figures 7(b)—-(d) show that the differences between the 2D wind-tunnel lift data and the 3D predictions decrease significantly with spanwise location up to 80% span. In particular. there is good correlation with 2D data at 63% and 80% span. suggesting the upwash at these stations is too far outboard to be significantly influenced by post-stall effects and too far inboard to be affected by the tip vortex. Comparing the 2D wind-tunnel drag data with the 3D con- verged solutions in Fig. 7. there is a significant increase in 3D pressure drag over 2D values at 30% span and at some angles of attack. the increase is drag is as much as 120%. This seems con- trary to the theory of post-stall suppressed wake-enhanced lift (outlined in Fig. 2 and used by many researchers in modeling post-stall effects. e.g.. Montgomerie [l]. Du and Selig [13]). The phenomenon of greater 3D drag at inboard stations than ZD drag. however. has also been observed in experiments by Madsen [3] and Bjorck et al. [14] and warrants further investigation. Figures 7(b)-(d) show the discrepancies between 3D calculations of pres— sure drag and 2D data reduce with spanwise location up to 80% span. In particular. there is a very good agreement between 2D and 3D values at 80% span. highlighting the 2D nature of the fi0w at this span station. Comparison with 2D Methods. In order to compare the new 3D method with 2D methods. the converged 3D LSIM perfor- Journal of Solar Energy Engineering mance curves of Fig. 7 were compared with a 2D LSIM correction method. i.e.. using 2D TUDelft lift and drag values as input to the lifting-surface code. in addition. results are also shown from a 2D wind tunnel method (WTM) developed from 2D upwash trends established in OSU/CSU wind tunnel tests and currently used as a correction method at NREL. The equation for the 2D correction derived from the wind-tunnel tests is shown in Eq. (4): a: —5.427>< 10—5133+6.713x 10—3/33+0.6i7a—0.8293 (4) Figures 8(al—(d) show the comparison of corrected lift and pres- sure drag data at each spanwise station. At 30% span. the 3D LSIM predicts greater post-stall lift and pressure drag than the 2D LSIM. The graph shows differences of as much as 15% in c, and 35% in cl,” between applying a 2D or a 3D correction. For the 47% station (and stations further outboard). the difference be- tween applying a 2D or 3D correction is less than 0.1% and can be regarded as negligible. Comparisons of the 3D LSIM and 2D WTM curves show lower LSIM lift values for pre-stall angles of attack and higher LSIM lift values for post-stall angles of attack. This trend is most evident at 30% span (Fig. 8(a)) and may be explained by considering the associated behavior in upwash. At pre-stall angles of attack. the trend in lift suggests a lower LSlM upwash than the 2D upwash of the wind tunnel method and is likely to be due to the influence of the 3D geometry at the root of the blade. At post-stall angles of attack. 3D LSlM predicts greater upwash than the 2D WTM up- NOVEMBER 2000, Vol. 122 / 199 '1 . ‘--— ZDData ‘ 0 7 10 20 30 4o Angle of Attack. on (deg) 1 '—~- 20 Data 0.5 ,... ............... ... ............. .................. Lift and Drag Coells., Cr Cdp (—) o 10 20 30 4o Angle of Attack, on (deg) 7—.— )u- ZDData l ................ l_ SDLSIM l 0.5 . ................... ,,,,,, o '10 20 30 4o Angle of Attack. 0: (deg) --- 20 Data A -) a. \_/ N '— 30 LSIM _s 01 _s .0 U1 Lift and Drag Coeils., cl, cdp ( o '10 20 30 4o Angle of Attack. on (deg) Fig. 7 LSIM corrected performance curves for CER hypothetical lift data: (a) 30% span, (b) 47% span, (c) 68% span. (d) 98% span wash due to the 3D effects outlined in Fig. 2. In terms of pressure drag, the 3D model predicts high values at 30% span that appear to be associated with high post-stall lift (as discussed previously). Figures 8(a)—(d) show. as spanwise station increases. there is im— proved agreement between the LSIM and WTM curves due to the 2D nature of the flow at the outboard stations. Finally, it should be noted that these trends may differ in the case...
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