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Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Aerodynamics and rotor design' taking place on Wednesday, 12 March 2014 at 09:00-10:30. The meet-the-authors will take place in the poster area.

Spyros Voutsinas National Technical University of Athens, Greece
Co-authors:
Vasilis Riziotis (1) P Lu Shi (2) F Spyros Voutsinas (1)
(1) National Technical University of Athens, Zografou / Athens, Greece (2) Huazhong University of Science and Technology, China-EU Institute for Clean and Renewable Energy, Wuhan, China

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Presenter's biography

Biographies are supplied directly by presenters at EWEA 2014 and are published here unedited

Faculty memeber at the National Technical University of Athens, Laboratory of Aerodynamics. Active in Wind Energy Research since 1990, participation in more than 40 RTD EU RTD projects on Wind Turbine, Helicopters and Aviation. Expertise in Aerodynamics, Aeroelasticity and Aeracoustics. Currently Board member of EAWE.

Abstract

Aerodynamic analysis of vertical axis wind turbines using a vortex type free wake model

Introduction

Recent advances, in the technology of floating wind turbines and in urban applications of wind energy have renewed the interest on Vertical Axis Wind Turbines (VAWT). Their simple design concept and light weight structure, the lack of yaw system, the close to the ground placement of the electrical converter system, the fact that they are suitable for low wind speed sites, are some of the advantages that rendered VAWT attractive for these type of applications. Aerodynamic design of VAWT calls for consistent aerodynamic models that can properly take into account the complex flow phenomena observed around this type of turbines.

Approach

Blade Element Momentum (BEM) models are widely used in the aerodynamic analysis of Horizontal Axis Wind Turbines (HAWT). Through the application of appropriate engineering corrections, dynamic inflow, unsteady aerodynamics and yaw misalignment effects have been taken into account and BEM models became a very powerful tool for the aeroelastic analysis of HAWT. Models based on momentum theory have also been developed for VAWT [1] however such models cannot properly account for phenomena like blade vortex interaction or streamline curvature observed in this type of turbines. As a result the accuracy of the predictions of BEM models is compromised when it comes to VAWT and at present no consistent engineering corrections have been tuned to improve their prediction capabilities. An efficient modelling alternative, also suitable for the purpose of aeroelastic analysis, lies in vortex type models.
In the present paper, a 2D vortex type free wake aerodynamic model is presented. A panel method is used for the modelling of the flow around the blades [2]. The model of the flow is essentially inviscid, therefore correction is required in order to take into account the effects of viscous drag and flow separation. It is noted that the flow around a VAWT rotor is separated over a big range of azimuth angles both on the advancing and the retreating side and for a big range of tip speed ratios. So, proper modelling of dynamic stall effects is crucial for the accurate prediction of aerodynamic loads.
Necessary viscous corrections are performed on the basis of the engineering ONERA model [3]. Circulation of the separated flow, provided by ONERA model is added to the potential circulation computed by the free wake model. Calculation of the circulation requires a consistent definition of the local to the section effective angle of attack which in the present model is determined kinematically and steady state lift and drag polars of the airfoil section.
The proposed model is validated against measurements from two different tests [4], [5]. Predictions of overall performance in terms of Cp and azimuth variations of aerodynamic loads are compared to measured data.


Main body of abstract

In the sequel predictions of the free wake model are compared against measured data from two different tests.
The first test is an open field test that concerns a three bladed 12 kW H-type VAWT which has been designed, constructed and tested at Uppsala University [4]. The two ends of the blades of the turbine (upper and lower) are tapered. The tapering begins at 1 m from the tips and gives a chord at the tip which is 60% of the chord at the mid section of the blade. Since the present model is two dimensional, the tapering of the blades has not been taken into account in the analysis. Simulations are performed for the mid section of the rotor. The main characteristics of the wind turbine are shown in Figure 1.
Measurements consist of about 350 hours of valid data of normal operation after certain amount of data has been rejected. An estimation of the mean power performance and the maximum possible error has been provided in [4] and it is shown in Figure 2 (min and max in the plot indicate minimum and maximum errors) along with the predictions of the free wake model. The large error according to the experimentalists is caused by uncertainties in the wind speed measurement. Two sets of predictions are presented. In the first, aerodynamic loads are calculated using predicted local flow angle of attack and steady state CL, CD polars of the NACA0021. In the second set the potential loads obtained by the free wake model have been corrected for flow separation using the ONERA dynamic stall model. Both sets seem to over-predict the measured data by 10-15% for the tip speed ratio range of 2-3.5. This is due to 3D effects on lift which are not taken into account in the 2D model and they are expected to result to lower Cp. At higher λ values deviations are higher. This is because of the 3D induced drag effect which is also suppressed. Drag is expected to dominate power performance at lower wind speeds. Overall consistent predictions are obtained taking into account the uncertainties involved in an open field test.
The second test is a wind tunnel test conducted at the low speed wind tunnel of NTUA [5]. The test campaign concerns an H-type 2 bladed model VAWT. The characteristics of the wind turbine are shown in Figure 3. In this test, the mid section of the blades was instrumented with pressure taps. So, azimuth variations of the instantaneous forces on the blades are obtained. Comparisons of the normal force CN and tangential force CT coefficients vs. the azimuth angle are presented in Figures 5-8 for two different values of λ. The first corresponds to a low wind speed (λ=4) where only light separation takes place on the advancing side while the second corresponds to a high wind speed (λ=2) where the blades enter deep stall conditions both on the advancing and the retreating side of the revolution. Figure 4 shows a wake pattern where the interaction of the blades with their own wake but also the wake of the other blade is clearly depicted. Two sets of predictions are presented, the first is the potential load obtained by the free wake code while the second is the viscous corrected load based on ONERA stalled circulation. A good agreement between predictions and measurements is noted (Figure 5 and 6) both in the normal and the tangential force coefficient for the case of high λ. The difference between the potential and the viscous corrected CN is small indicating that there is only light separation that appears on the advancing side when the blade is in the azimuth range 0o-180o. The difference between the potential and viscous corrected results is higher in CT because in the viscous corrected results the effect of the drag has been taken into account. In Figure 7 a good agreement between the viscous corrected results and measurements is noted in the prediction of CN while larger differences are obtained in the CT (Figure 8). In this case, the difference between the potential and the viscous corrected CN is much bigger and extends over the whole range of azimuth angles.
















Conclusion

A vortex type free wake aerodynamic model for the analysis of VAWT is presented in the paper. The flow around the blades is represented by singularity distributions (source and vorticity) while the wake is simulated by vortex particles moving freely with the velocity of the free flow. The free wake representation of the wake is well suited approach for consistently accounting for blade vortex interaction effects. Corrections are applied to the inviscid flow model in order to take into account dynamic stall effect as well as viscous drag based on the engineering ONERA dynamic stall model. Validation of the model against field and wind tunnel measurements indicates that it can consistently predict power performance and loads of a VAWT. A 10-15% over-prediction of the power coefficient is noted in comparison to full scale field tests on an 12 kW three-bladed turbine. The above reported difference is attributed to three dimensional effects on lift. Good agreement against wind tunnel measurements, on a model two bladed turbine is obtained, in the azimuthal variation of normal and tangential force coefficients at high tip speed ratio values while acceptable agreement is obtained at very low tip speed ratios. The model is expected to predict loads of A VAWT with better accuracy than momentum based methods and it is aimed to be used in the aeroelastic analysis of VAWT as an alternative to this type of models. The method is directly extendable to the three dimensions and it can be coupled to boundary layer methods for more accurate prediction of dynamic stall effects.


Learning objectives
- Physical modelling of the Aerodynamic performance of Vertical Axis Wind Turbines (VAWT)
- Implementation of viscous corrections in vortex type models to account for dynamic stall effects which appear over a big range of the operational envelope of VAWT
- Validation of vortex type aerodynamic models against measurements
- Understanding of complex phenomena like blade vortex interaction and streamlines curvature



References
[1] Larsen, T.J., Madsen, H.A., “On the way to reliable aeroelastic load simulation on VAWT’s,” Proceedings of EWEA 2013. EWEA - The European Wind Energy Association, 2013
[2] Riziotis, V.A., Voutsinas, S.G. “Dynamic stall modeling on airfoils based on strong viscous-inviscid interaction coupling,” J. Numerical Methods in Fluids, 2008, 56, pp 185-208.
[3] Petot, D., “Differential Equation Modelling of Dynamic Stall,” Recherché Aerospatiale, 1989, 5, 59–72.
[4] J. Kjellin, F. Bolow, S. Eriksson, P. Deglaire, M. Leijon and H Bernhoff “Power Coefficient Measurements on a 12 kW Straight Bladed Vertical Axis Wind Turbine,” Renewable Energy 36, 2011 3050-3053.
[5] E. Morfiathakis, “Theoretical and Experimental study of unsteady phenomena inTurbines,” PhD thesis,1991.