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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. Junsuke Murata Mie University, Japan
Co-authors:
Junsuke Murata (1) F P Takao Maeda (1) Yasunari Kamada (1) Shun Nishimura (1)
(1) Mie University, Tsu, Japan

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## Abstract

Numerical analysis of wake wind field of horizontal axis wind turbine by vortex panel method

Introduction

For the optimization of arrangement of wind turbines in wind farms, numerical analysis of wake wind field is needed for prediction of increased fatigue load and reduced power output due to wake. The purpose of this study is development of a calculation method of wake wind field for various inflow and operation conditions. For the purpose, expanding vortex core model is introduced to vortex panel method in order to consider the wake expansion and recovery of wind speed. The method is validated by comparison with results of wind tunnel experiment for different ambient turbulence intensities and yawed inflow.

Approach

In this study, vortex panel method  with free wake model is adopted for calculation of aerodynamic load and flow field. In contrast to blade element momentum theory (BEM) in which axisymmetric flow field is assumed in principle, this model is capable of calculation for unsteady and non-uniform inflow without empirical factors. Furthermore, the computational cost is much lower than that of computational fluid dynamics (CFD).
In the model, rotor blades and wake are represented as vortex panels. The vorticity for each panel is derived by applying Neumann type boundary condition at a collocation point. Wake vortex panels are shed from trailing edge of rotor blades and advected by local velocity.
Induced velocity from a vortex line is calculated by Rankine vortex model as the following, where r12, r1 and r2 are vectors from starting point to ending point of vortex line, from starting point to the point and from ending point to the point, respectively, as shown in Fig. 1. rp and e mean perpendicular distance and radius of vortex core. According to Core-Spreading method , the radius of vortex core is obtained by following differential equation, where c is a constant (=2.2418) and nt means eddy viscosity. Madsen et al.  formulated the eddy viscosity in wake as following, where b, R, Uc, UH, Iamb, k2 and kamb are wake half width, rotor radius, ambient wind speed, the minimum wake wind speed, ambient turbulence intensity, a calibration factor (=0.008) and an empirical constant, respectively. F1 and F2 are filter functions and calibrated by Madsen  and Larsen .
For validation of the model, the calculation results are compared to experimental results obtained in wind tunnel .
The wind tunnel has a 3600mm diameter nozzle and 6200mm length open test section. In order to change turbulence intensity in main flow, active turbulence grids are installed upstream of the wind tunnel outlet. Two-bladed upwind wind turbine was used for the experiment. The diameter is 500mm. The flow field behind the test wind turbine operating in the optimal condition was measured by an X-type hot wire anemometer. Main body of abstract

Power Coefficient
In order to verify the calculation of aerodynamic force, the power coefficient for steady uniform inflow is calculated by the model. Figure 2 shows the calculated results for power coefficient compared with the experimental results. The calculated results agree comparatively well with the experimental results. It confirms the validity of the aerodynamic load calculation. Wake Wind Field for Normal Inflow
The wind field behind the test wind turbine is calculated in the optimal tip speed condition for the experiment, that is, tip speed ratio is 3.36. The velocity distribution is obtained by averaging the temporal velocity field for 1 rotor revolution after 30 rotor revolutions simulation which is enough long to eliminate the influence of the starting vortex.

Figure 3 shows longitudinal velocity distribution in wake for normal inflow with 1.4% ambient turbulence intensity. The horizontal axis represents the non-dimensional longitudinal position x/D and the non-dimensional longitudinal velocity UN defined as the ratio of local longitudinal velocity to undisturbed wind velocity. One division of the scale corresponds to UN=1. The vertical axis represents the non-dimensional lateral position y/R. As shown in Fig. 3, the longitudinal velocity in wake decreases because of the extraction of wind energy by the rotor blade. The deficit area expands almost symmetrically with increase of longitudinal position. Near the wind turbine (x/D=0.5, 1), the calculated velocity distributions show a small peak around the center line (y/R=0) and agree with the experimental results qualitatively. It is because the wind energy isnâ€™t extracted inside of the blade root. At x/D=2, 3, 5 the experimental distribution changes from two valley shape to one valley shape. However, the calculated distribution still remains the two valley shape. The reason for the difference could be that the nacelle and the tower are not considered in the calculation. Far from the wind turbine (x/D=7, 10), the calculated results show good agreement with the experimental results.

Figure 4 shows longitudinal velocity distribution in wake for higher ambient turbulence intensity (Iamb=13.5 [%]).
Compared with the result for lower ambient turbulence intensity as shown in Fig. 3, the velocity distributions are similar at just behind the wind turbine rotor (x/D=0.5), however, significant differences can be found at far from the wind turbine. The expansion of wake width and the recovery of wind speed are obviously promoted by higher ambient turbulence intensity. The calculation results show good agreement with the experimental results. It indicates that the model is capable of calculation for the influence of ambient turbulence intensity on wake wind field.  Wake Wind Field for Yawed Inflow
Figure 5 shows longitudinal velocity distribution in wake in 30 degrees yawed inflow condition with 1.4% ambient turbulence intensity. For yawed inflow, the deflection of deficit area to â€“y direction can be found. It is because of the existence of the lateral velocity component in wake due to the axial velocity component induced by the thrust force on the rotor plane. However the calculated velocity distribution shows slightly smaller deficit far from the wind turbine (x/D=5, 7, 10) compared with the experimental results, it shows good agreement.

Conclusion

For development of a calculation method of wake wind field for various inflow and operation conditions, the expanding vortex core model is introduced to vortex panel method. In the model, induced velocity from a vortex line is calculated by Rankine vortex model. The growth of vortex core is calculated by the differential equation used in Core-Spreading method. The eddy viscosity is calculated by the model formulated and calibrated by Madsen and Larsen, in order to consider the influence of ambient turbulence intensity on wake. The method is validated by comparison with results of wind tunnel experiment for various ambient turbulence intensities generated by active turbulence grids. In the experiment, the flow field behind the test wind turbine was measured by an X-type hot wire anemometer.
The main results obtained in this study are shown as follows:

The calculated power curve agrees comparatively well with the experimental results. It confirms the validity of the aerodynamic load calculation.

The expansion of wake diameter and recovery of wind speed are obviously promoted by higher ambient turbulence intensity. The calculation results show good agreement with the experimental results for different ambient turbulence intensities. It indicates that the model is capable of calculate the influence of ambient turbulence intensity on wake wind field.

For yawed inflow, the deflection of deficit area can be found in both the calculated and experimental results. However the calculated velocity distribution shows slightly smaller deficit far from the wind turbine (x/D=5, 7, 10) compared with the experimental results, it shows good agreement.

Learning objectives
This study aims to establish a calculation method for wake wind field with low computational cost. In addition, it provides knowledge of wake wind field for various ambient turbulence intensity and yawed inflow.

References
 Katz, J., Plotkin, A., â€śLow-Speed Aerodynamicsâ€ť, Cambridge University Press, 2001
 Leonard, A., â€śVortex methods for flow simulationâ€ť, J. Comp. Phys., Vol.37 pp.289-335, 1980
 Madsen, H. Aa., Larsen, G. C., Larsen, T. J., Troldborg, N., Mikkelsen, R., â€ťCalibration and Validation of the Dynamic Wake Meandering Model for Implementation in an Aeroelastic Codeâ€ť, Journal of Solar Energy Engineering, Vol. 132, 2010
 Larsen, T. J., Madsen, H. Aa., Larsen, G. C., Hansen, K. S., â€ť Validation of the dynamic wake meander model for
loads and power production in the Egmond aan Zee wind farmâ€ť, Wind Energy, 16:605-624, 2013
 Murata, J., Maeda, T., Kamada, Y., Kogaki, T., â€ťWind Field and Wind Turbine Load in Wake for Various Ambient Turbulence Intensitiesâ€ť, Proceedings of European Wind Energy Conference 2012 (Copenhagen), 2012