A comparison of integrated quantities for the whole rotor computed with the different models is shown in Table 10-1. For the case of no shear there is a very good correlation between the two codes based on the BEM modeling (FLEX5 and HAWC2) whereas the
results from the two more advanced codes are above and below, respectively. However, it should be noted that the airfoil data used in the BEM computations and in the ACL model have not been calibrated and the 3D corrections applied to the data on the inner part of the rotor seems to overestimate the performance of the airfoils.
The effect of wind shear is seen to cause different influence on the power. HAWC2 computes a reduction in power whereas FLEX5 computes a small increase. Likewise EllipSys3D also computes a small reduction in power whereas the ACL model computes a considerable increase. A clear tendency for the influence of the wind shear on rotor power coefficient can thus not bee extracted from the results. In Table 10-1 is also shown the maximum and minimum flapwise moment and also for these quantities a considerable deviation is seen.
Table 10-1 Comparison of electrical power and flapwise loads at 8 m/s. El. power [kW] no shear El. power [kW] shear max. Flap. Moment [kNm] min. Flap. moment [kNm] HAWC2 1906 1812 6306 3785 EllipSys3D 1867 1830 6295 1867 FLEX5 1900 1932 6677 3100 AC-Line 1995 2135 6860 3700
A comparison of the normal and tangential force distribution along the blade is shown in the next figures from Figure 10-13 to Figure 10-18 for the blade in upward and downward position, respectively. In particular there is a considerable difference in the tangential load and unfortunately the advanced models do not correlate very well and do not give a clear indication of what is the correct result.
In the last two figures the axial induced velocity is shown and again for the blade in upward and downward position, respectively. The BEM model implementation in the FLEX5 code gives the same induction for the blade in the two position whereas the BEM implementation in HAWC2 gives a higher induction for the blade pointing upwards than for the blade pointing downwards. Comparing with the result of the ACL model it is seen that this model predicts a higher induction for the blade pointing upwards than for the blade pointing downwards but not as much as predicted with HAWC2.
10.8 Conclusions
The investigation of the influence of wind shear in the inflow has shown that there is a considerable uncertainty in modeling this rather common inflow case for a rotor. The implementation of the BEM model to handle this flow case can be carried out in different ways and the results of two advanced models have not so far indicated what the correct results are.
In the new Aeroelastic Research Programme EFP2007 the investigations will be continued and the aspect of influence of individual pitch control on the blades will also be considered.
Comparing the results from the different codes show no distinct picture of the influence of wind shear
Figure 10-13 Comparison of the normal force distribution for the blade vertical upwards (0 deg. azimuth).
Figure 10-14 Comparison of the normal force distribution for the blade vertical downwards (180 deg. azimuth).
Figure 10-15 Comparison of the tangential force distribution for the blade vertical upwards (0 deg. azimuth).
Figure 10-16 Comparison of the tangential force distribution for the blade vertical downwards (180 deg. azimuth).
Figure 10-17 Comparison of the axial induced velocity distribution for the blade vertical upwards (0 deg. azimuth).
Figure 10-18 Comparison of the axial induced velocity distribution for the blade vertical downwards (180 deg. azimuth).
10.9 References
[1] Jonkman, J., IEA Annex XXIII document on NREL´s baseline wind turbine aeroelastic model. NREL/NWTC, August 11, 2005.
[2] Michelsen, J.A.. Basis3D - a Platform for Development of Multiblock PDE Solvers. Technical Report AFM 92-05, Technical University of Denmark, 1992.
[3] Michelsen J.A., ”Block structured Multigrid solution of 2D and 3D elliptic PDE's”, Technical Report AFM 94-06, Technical University of Denmark, 1994.
[4] Sørensen, N.N.. General Purpose Flow Solver Applied to Flow over Hills. Risø-R- 827-(EN), Risø National Laboratory, Roskilde, Denmark, June 1995.
[5] Rhie C.M. ”A numerical study of the flow past an isolated airfoil with separation” Ph.D. thesis, Univ. of Illinois, Urbane-Champaign, 1981.
[6] Issa R.I. Solution of the implicitly discretised fluid flow equations by operator- splitting’ J. Comp. Pys., 61, 1985
[7] Khosla P.K. and Rubin S.G., ”A diagonally dominant second-order accurate implicit scheme”, Computers Fluids, 2:207-209, 1974.
[8] Menter F.R., ”Zonal Two Equation k-ω Turbulence Models for Aerodyanmic Flows”. AIAA-paper-932906, 1993.
[9] Sørensen, N.N., Rotor computations using a 'Steady State' moving mesh. IEA Joint Action Committee on aerodynamics, Annex XI and 20. Aero experts meeting, Pamplona (ES), 25-26 May 2005.
[10] Sørensen, N.N.; Michelsen, J.A., and Schreck S.,Application of CFD to Wind Turbine Aerodynamics. In: CD-Rom proceedings. 4. GRACM congress on
computational mechanics, Patras (GR), 27-29 Jun 2002. Tsahalis, D.T. (ed.), (Greek Association of Computational Mechanics, [s.l.], 2002) 9 p.
[11] Demirdzic, I., Peric, M. (1988): Space conservation law in finite volume calculations of fluid flow. Int. J. Numer. Methods Fluids, 8, 1037-1050. [12] Madsen, H.A.; Sørensen, N.N.;Schreck, S.,YAW AERODYNAMICS
ANALYZED WITH THREE CODES IN COMPARISON WITH EXPERIMENT, 22rd ASME Wind Energy Symposium, RENO NV(US), 6-9 Jan 2003.
[13] Bertagnolio, F.; Gaunaa, M.; Hansen, M.; Sørensen, N.N.; Rasmussen, F., Computation of aerodynamic damping for wind turbine applications. In: CD-Rom proceedings. 4. GRACM congress on computational mechanics, Patras (GR), 27-29 Jun 2002. Tsahalis, D.T. (ed.), (Greek Association of Computational Mechanics, [s.l.], 2002) 8 p.
[14] Bertagnolio, F.; Gaunaa, M.; Sørensen, N.N.; Hansen, M.; Rasmussen, F., Computation of Modal Aerodynamic Damping Using CFD, 22rd ASME Wind Energy Symposium, RENO NV(US), 6-9 Jan 2003.
[15] Mikkelsen R. Actuator disc methods applied to wind turbines. Ph.D. dissertation, MEK-FM-PHD-2003-02, 2003,
http://www.fm.mek.dtu.dk/English/Publications/PHDtheses.aspx
[16] Shen WZ, Mikkelsen R, Sørensen JN, Bak, Chr. Tip loss corrections for wind turbine computations. Wind Energy, 2005;8:457-475
[17] Shen WZ, Sørensen JN, Mikkelsen R. Tip loss corrections for actuator/Navier- Stokes computations. J. Solar Energy Eng., May 2005;127:209-213