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.

**Hamidreza Abedi**Chalmers University of Technology, Sweden

Co-authors:

Hamidreza Abedi (1)

^{F}

^{P}Lars Davidson (1) Spyros Voutsinas (2)

(1) Chalmers University of Technology, GÃ¶teborg, Sweden (2) National Technical University of Athens, Athens, Greece

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## Presenter's biography

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

Hamidreza Abedi is a Ph.D. Student at the Division of Fluid Dynamics, Chalmers University of Technology in Sweden. He works in a project (financed through the Swedish Wind Power Technology Centre (SWPTC)), which aims to develop computational methods for predicting unsteady aerodynamic loads on wind turbine rotor blades. The focus of the project is to handle transient loads by Vortex Method. His project.

## Abstract

**Development of free vortex wake method for aerodynamic loads on rotor blades****Introduction**

There are different methods for modelling the aerodynamics of a wind turbine such as the BEM theory and Computational Fluid Dynamic.

The vortex theory, as a potential, inviscid and irrotational flow can be also used to predict the aerodynamic performance of wind turbines where compared with the BEM method, it is able to provide more physical solutions for attached flow conditions.

In this paper, the application of the vortex method for wind turbine aerodynamic performance is used. Different blade and wake models are studied, and the results of the different approaches are compared with the BEM method and GENUVP code.

**Approach**

The rotor inflow distribution is highly dependent on the wake geometry. Hence, predicting the geometry of trailing wake vortices and their strength makes it possible to analyze wind turbine aerodynamic performance. In other words, suitable modeling of the blade and trailing wake has a great influence on the prediction of inflow at the rotor blade. Here, three different applications for modeling the blade and wake by vortex filament method, i.e., lifting line prescribed wake, vortex

lattice prescribed wake and vortex lattice free wake are presented. In these methods, the blade is modeled by either lifting line or lifting surface, and the wake is modeled by either trailing horseshoe vortices or vortex ring elements.

In the prescribed wake model known as rigid wake, the upstream flow is uniform, both in time and space, and it is perpendicular to the rotor plane (parallel to the rotating axis), whereas, in the free wake model, it can be either uniform or non-uniform (varying both in time and space).

In the prescribed wake model, the wake that is shed from the blade trailing edge follows the helix equation which consists of a helical sheet of vorticity approximated by a series of points connected by a straight vortex filament with a constant diameter and pitch. Further, it moves downstream with a constant velocity including free stream and axial induced velocity, where the interaction between the vortex wake filaments is ignored.

In the free wake approach, a finite number of vortex wake elements move freely based on the local velocity field, allowing wake expansion as well. Each vortex wake element contains two points known as Lagrangian markers, where the induced velocity components are calculated using the Biot-Savart law, and their movements make the wake deformation. For both the prescribed and the free wake models, as it will be shown, since the effect of the induced velocity field by the far wake is small on the rotor blade, the wake extends only to three or four diameters downstream of the wind turbine rotor plane.

**Main body of abstract**

1- Lifting line prescribed wake

In the lifting line prescribed wake, the blade is divided into one or more sections that are replaced by a spanwise varying strength straight vortex filament called a bound vortex, which is located at 1/4 of the chord line along the span. The control points storing the bound vortex strength, the induced velocity, the free stream and the rotational velocities are located at the middle of the bound vortex of each spanwise section. The trailing vortices are generated by spanwise bound circulation difference where they originate from the blade bound vortices. They emanate from all points along the blade, making a helical vortex sheet for each blade with a constant diameter and pitch behind each rotor blade. This helical vortex sheet induces the velocity field around the rotor blade, reducing the angle of attack seen by each blade section. An iterative method is used to find the final wake configuration. Once the wake is prescribed, the velocity field, induced by all equally segmented vortex filaments of the wake is calculated for all control points located at the blade bound vortex by the Biot-Savart law. Computing the values of effective angle of attack for each blade section and using the aerodynamic table give the lift and drag forces per blade span, and the torque and power of the wind turbine are then computed by tangential and normal forces with respect to the rotor plane, respectively (see fig.).

2- Vortex lattice prescribed wake

The vortex lattice method (VLM) is based on the thin lifting surface theory of vortex ring elements, where the blade surface is replaced by vortex panels containing the vortex ring with strength (see fig.). The strength of the trailing vortex wake rings must be equal to the last vortex ring row in the chordwise direction. An iterative method is used in the prescribed vortex lattice model, where an initial helical wake geometry is constructed and the trailing vortices are divided into a number of small segments. By applying zero normal flow across the blade surface at each control point the strength of all vortex ring elements on the blade can be computed where the strength of the last vortex ring row of each blade section determines the wake vortex ring strength, which makes it possible to calculate the wake induced velocity on the blade control points. The Kutta-Jukowski theorem is applied at the mid point of the front edge of each blade vortex ring (see fig.) and gives the potential lift force.

Decomposition of the lift force for each blade spanwise section into the normal and tangential directions with respect to the rotor plane (see fig.) gives the effective angle of attack for each section. Since the induced velocity field changes the lift force distribution over the blade in each iteration, the wake geometry can be updated. The generated power is set as the criterion for fulfilling the convergency criterion.

3- Vortex lattice free wake

This method is similar to the vortex lattice prescribed wake. Contrary to the prescribed wake, in the free wake method, the wake elements are trailed and shed based on the time-marching method (see fig.). The blade bound vortex strength is calculated by applying the zero normal flow boundary condition on all blade control points the at each time, and the vortex wake elements are trailed and shed at each time step, where their strengths remain constant (Kelvin theorem) and their corner points are moved based on the local velocity field, including the wind velocity and the induced velocity by all blade and wake vortex rings. Different numerical schemes may be used for the governing equation such as the explicit Euler method, the implicit method, the Adams-Bashforth method and the Predictor-Corrector method. In each time step, when the position of all the Lagrangian markers is calculated, we are able to compute the velocity field around the rotor blade as well as the lift force according to the Kutta-Jukowski theorem. Decomposition of the lift force of each spanwise section with respect to the rotor plane is used to find the effective angle of attack. Further, the generated power and thrust are determined.

**Conclusion**

The vortex method is a potential flow, it predicts more power than the BEM method. In the lifting line prescribed wake method, the 2D airfoil data are used. Hence the viscous drag effect is accounted for, which results in less power and more thrust compared with the pure potential methods, i.e. the vortex lattice prescribed wake (VLPW), the vortex lattice free wake (VLFW) and the GENUVP.

The circulation distribution along the blade is shown in fig. where the maximum circulation is located near the tip. There is also good agreement between the VLPW, VLFW and the GENUVP methods. However, the BEM method predicts higher circulation values, especially near the root. The effective angle of attack can be seen in fig.. The rotor blade in the lifting line prescribed wake method and the BEM method sees a smaller angle of attack compared with the other methods, which means that these methods predict a slightly larger induced velocity field over the blade. In the VLPW, VLFW and the GENUVP, the effective angle of attack is calculated based on the load distribution. Hence, the blade airfoil characteristics, based on the 2D airfoil data (CL and CD), are not detected by the solution and, contrary to the BEM and the LLPW methods, a smooth distribution of the angle of attack along the rotor blade can be observed. Figure shows the tangential force with respect to the rotor blade. Except for the BEM method , near the blade tip, the tangential force for all the methods is larger than near the blade root, which means that the tip region of the blade produces more power compared with the other parts of the blade, especially the root region. The normal force along the blade is shown in fig. where, in agreement with the conclusion, the pure potential methods, i.e. the VLPW, the VLFW and the GENUVP, predict lower thrust force with respect to the rotor plane.

**Learning objectives**

In order to calculate the aerodynamic loads on rotor blades, the blade and the wake can be modled in different ways. Different blade and wake parameters such as the blade discretization, both in spanwise and chordwise direction, the wake element discretization and the wake truncation length have been studied. The result shows how they affect the rotor blade aerodynamic loads. Also, the computational efficiency of different methods is represented.

**References**

[1] Martin O.L. Hansen. Aerodynamics Of Wind Turbines. 2nd edition, EarthScan, 2008.

[2] A. van Garrel. Development Of A Wind Turbine Aerodynamics Simulation Module. ECN report, ECN-Câ€“03-079, August 2003.

[3] L.J. Vermeer, J.N. SÃ¸rensen, and A. Crespo. Wind Turbine Wake Aerodynamics. Progress in Aerospace Sciences, 39:467â€“510, 2003.

[4] SG. Voutsinas. Vortex Methods In Aeronautics: How To Make ThingsWork. International Journal of Computational Fluid Dynamics, 20:3â€“18, 2006.

[5] J.G. Leishman and Mahendra J.B.A Bagai. Free Vortex FilamentMethods For The Analysis Of Helicopter Rotor Wakes. Journal of Aircraft, 39, 2002.

[6] Joseph Katz and Allen Plotkin. Low-Speed Aerodynamics. Cambridge University Press, 2nd edition, 2001.

[7] J. Jonkman, S. Butterfield, W. Musial, and G. Scott. Definition Of A 5-MW Reference Wind Turbine For Offshore System Development. National Renewable Energy Laboratory, Colorado, USA, 2009, NREL/TP-500-38060.

[8] Sandeep Gupta. Development Of A Time-Accurate Viscous Lagrangian Vortex Wake Model For Wind Turbine Applications, Publisher = University of Maryland, Department of Aerospace Engineering. 2006.

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