Development and Application of a Simulation Tool for

Proceedings of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition GT2013 June 3-7, 2013, San Antonio, Texas, USA

GT2013-94979

DEVELOPMENT AND APPLICATION OF A SIMULATION TOOL FOR VERTICAL AND HORIZONTAL AXIS WIND TURBINES David Marten ISTA, TU Berlin Berlin, Germany

Georgios Pechlivanoglou TU Berlin, SMART BLADE Berlin, Germany

Juliane Wendler ISTA, TU Berlin Berlin, Germany

Christian Navid Nayeri ISTA, TU Berlin Berlin, Germany

ABSTRACT A double-multiple-streamtube vertical axis wind turbine simulation and design module has been integrated within the open-source wind turbine simulator QBlade. QBlade also contains the XFOIL airfoil analysis functionalities, which makes the software a single tool that comprises all functionality needed for the design and simulation of vertical or horizontal axis wind turbines. The functionality includes two dimensional airfoil design and analysis, lift and drag polar extrapolation, rotor blade design and wind turbine performance simulation. The QBlade software also inherits a generator module, pitch and rotational speed controllers, geometry export functionality and the simulation of rotor characteristics maps. Besides that, QBlade serves as a tool to compare different blade designs and their performance and to thoroughly investigate the distribution of all relevant variables along the rotor in an included post processor. The benefits of this code will be illustrated with two different case studies. The first case deals with the effect of stall delaying vortex generators on a vertical axis wind turbine rotor. The second case outlines the impact of helical blades and blade number on the time varying loads of a vertical axis wind turbine.

NOMENCLATURE A Weibull distribution scale parameter AEP Annual energy production AoA Angle of Attack Inflow Angle α Blade twist angle α0 BEM Blade Element Momentum

CP Cl, Cd C N, C T CF_t_rot CF_x_rot CF_y_rot c

δ DMS HAWT k N r Re TSR θ

uup, udown VG Vup, Vdown V0 Veq VAWT W

Christian Oliver Paschereit ISTA, TU Berlin Berlin, Germany

Power coefficient Lift / Drag coefficient Normal / Thrust coefficient Tangential force coefficient of the rotor Streamwise force coefficient of the rotor Crosswise force coefficient of the rotor Chord length Angle between blade normal and turbine axis Double Multiple Streamtube Horizontal Axis Wind Turbine Weibull distribution shape parameter Blade number Local radius Reynolds Number Tip Speed Ratio Azimuthal angle Upwind / downwind interference factor Vortex generator Velocity at upwind / downwind rotor disc Freestream velocity Equilibrium velocity between the rotor discs Vertical Axis Wind Turbine Relative velocity at blade element

INTRODUCTION Recently, fuelled by offshore and urban wind turbine applications, interest in vertical axis wind turbine (VAWT) technology is increasing after their development almost ceased in the mid 90’s [1]. VAWTs offer some distinct advantages in the aforementioned applications over horizontal axis wind

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turbines (HAWT) such as their insensitivity to changes in wind direction or the possibility to store gearbox and generator below the rotor, reducing investment costs for offshore applications. However, compared to their horizontal axis counterparts only sparse knowledge on VAWT aerodynamics and no freely distributed simulation or design tools are available. The major goal of extending QBlade with a simulation module for VAWTs is to facilitate the research in this area with a new publicly available code for aerodynamic analysis. The software QBlade [2] was started in 2010 as a multiplatform software tool for the aerodynamic design and simulation of HAWTs without the need to import, convert or process data from other sources. Another focus was to embed the code in a convenient graphical user interface to improve accessibility over comparable simulation tools. In order to ease research on wind turbines worldwide, the software is distributed freely under the Gnu Public License (GPL). QBlade has been downloaded more that 20.000 times during the last two years and is being applied by universities, businesses and individuals around the world. A module for the design and simulation of VAWTs was recently integrated in a new release [3, 4]. The simulation algorithms are based on a Blade Element Momentum (BEM) theory algorithm for the simulation of HAWTs and on a Double Multiple Streamtube (DMS) algorithm for the simulation of VAWTs. Furthermore, modules for airfoil design and analysis or lift and drag polar extrapolation to 360° angle of attack (AoA) are provided inside the simulation tool. In the following, the basic functionality of QBlade, details of the newly integrated VAWT simulation module and its application in two case studies are described.

Airfoil Design and Analysis The basic requirement of any blade element based rotor performance simulation is tabulated data of lift and drag coefficients, over a range of AoA, for every airfoil geometry that is used in the rotor design. As a source of these airfoil coefficients XFOIL [5] can compute the two dimensional flow around subsonic isolated airfoils by combining a higher order panel method with a fully coupled viscous/inviscid interaction method. XFOIL was developed by Drela and Giles at Massachusetts Institute of Technology (MIT) and is considered as one of the standard low order analysis tools for airfoils. In 2003 Depperois [6] wrote a graphical user interface for XFOIL and expanded its functionality. The current version of this development, the open source code XFLR5, is integrated within the QBlade software to design or import airfoil geometries for rotor blade design, generate or import measured airfoil performance coefficients for rotor simulations and manage the airfoil database. It is well known [7] that blade element momentum balance coupled wind turbine simulation methods are highly sensitive to the quality of the lift and drag polar data that is used in a simulation. The benefits employing the XFOIL algorithm are the large number of experimental and numerical validations and the high quality of the simulated airfoil coefficients. Around the maximum lift coefficient and for immediate post-stall behavior however, XFOIL is known to give poor predictions. The RFOIL [8] code, developed at Delft University, improves the prediction of transition by incorporating three dimensional and rotational effects in the integral boundary layer equations of XFOIL. Other helpful features of airfoil design and simulation for wind turbines with XFOIL / XFLR5 are:

MODULES WITHIN QBLADE At its current state of development the QBlade software consists of four major modules, facilitating the design and simulation of a wind turbine rotor (Fig.1). These modules, embedded in a graphical user interface, are: • • • •

Airfoil design and analysis (XFOIL / XFLR5) Cl and Cd polar extrapolation to 360° AoA Rotor blade design and optimization Wind turbine setup and simulation

Fig.1 Modules in QBlade

• • • •

4 and 5 digit NACA airfoil generator Airfoil coordinate mixing for transition airfoils Inverse design of airfoils from pressure distribution Forced and free boundary layer transition ( e n method [5]) to simulate blade roughness effects

Extrapolation of Cl and Cd Coefficients The airfoil analysis with XFOIL is limited to the prediction of lift and drag coefficients at angles that lie before and just beyond the stall point. For higher AoA the separation region increases ad XFOILs assumption, that the viscous flow is confined to a small area around the airfoil, becomes increasingly invalid and convergence cannot be obtained anymore. However, in the root region of a HAWT blade and on VAWT blades in general AoA that lie beyond the stall point occur frequently. Therefore, to be used in the BEM or DMS algorithm and to ensure their smooth operation the Cl and Cd polars need to be extrapolated to the full range of 360° AoA. The general approach for this extrapolation is to apply curve fits to the completely stalled polar curve of a flat plate, under the assumption that an airfoil at high AoA behaves very much like a thin plate with a sharp leading edge. In QBlade, any polar that

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is contained in the database can be extrapolated via the Montgomerie (Fig.2) [9] or the Viterna-Corrigan [10] post stall model.

manufacture arc line approximation of the Troposkien. During the blade design three dimensional openGL visualization aids the design process. The geometry can later be exported as a cloud of points or into the .stl CAD format.

Fig.2 Polar extrapolation to 360° after Montgomerie

Rotor Blade Design and Optimization The blade design module (Fig.3) in QBlade allows the efficient and intuitive design of HAWT or VAWT rotor geometries. A blade geometry is defined by a distribution of airfoil geometries at selected sections over the length of the blade. The discretization of a rotor blade during a simulation is independent of the number of sections that is specified in a blade design. If an element, during a simulation, is located between two different airfoil sections a linear interpolation between the polar data of these two airfoils is performed. Using XFOILs airfoil coordinate mixing, and computing the coefficients of the intermediate airfoil, the overall accuracy can be improved [2]. A HAWT blade is further defined by specifying: • • • • •

Chord length Twist Angle Edgewise offset Flapwise curvature Pitch axis

Also, for the distribution of twist angles and chord lengths shape optimization routines can be applied to the geometry. The twist can be optimized to yield the highest lift to drag ratio for a chosen tip speed ratio (TSR). The chord can be optimized after the theory of Betz (constant circulation) or Schmitz [11] (including wake rotation) for a chosen TSR and blade number. For the design of a VAWT blade the following parameters have to be specified: • • • •

Chord length Radial position Twist angle Azimuthal angle

The radial position of the VAWT blade sections can be automatically distributed to resemble a Troposkien [12] shape, a blade shape where the blade stress from centrifugal forces acts only normal to the blades cross section, or an easier to

Fig.3 VAWT blade design module

Wind Turbine Definition and Simulation A wind turbine in QBlade consists of a rotor design and additional parameters that further describe the turbine characteristics. The type of power regulation (stall, pitch, prescribed pitch), rotational speed control (single, two step, optimal, prescribed), cut in- and cut out velocity and generator efficiency have to be specified. A simulation can be performed in three different ways. One option is a rotor simulation over a range of TSRs. This simulation results only in dimensionless coefficients and is particularly useful to compare different rotor geometries independent of their size. The second option is a multiparameter simulation (Fig.4). The simulation is carried out over a range of wind speeds, rotational speeds and blade pitch angles simultaneously resulting in a three dimensional rotor performance matrix. These results can be used to develop custom wind turbine controller strategies or to investigate the turbine characteristics for several operational states. The third option is the turbine simulation that computes the specified turbines performance over a range of wind speeds and also yields the annual energy production (AEP) for a selected Weibull wind speed distribution. The simulation results can be analyzed in three different kinds of graphs. Rotor graphs plots the integral values, such as the power coefficient Cp and the thrust coefficient Ct over the TSR. The blade graph displays the distribution of blade variables such as thrust and normal force, lift and drag coefficients, AoA or relative velocities over the blade. In case of a VAWT simulation the additional azimuthal graph yields the

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distribution of variables depending on the azimuthal position of the blade during one rotation of the rotor.

Blade Element Momentum Method The HAWT rotor simulation follows the classical blade element momentum method, as described by Hansen [13], and in the following will not be discussed in greater detail. The BEM algorithm assumes a uniform, steady state inflow and radial independence of the two dimensional blade sections. Under these assumptions three dimensional effects, that play an important role in wind turbine aerodynamics, cannot be accounted for a priori. However, the impact of these effects on the rotor loads and its performance is included in a simulation by means of semi-empirical corrections. The corrections that are included in the BEM algorithm of QBlade are: • • • • •

Prandtl tip and hub loss correction [13] Shen tip and hub loss correction [14] Snel’s correction for blade crossflow [15] Buhl’s correction for the turbulent wake state [16] Reynolds number drag correction, from Hernandez and Crespo [17]

The BEM algorithm of QBlade has been validated numerous times against measured data [2, 18] and compared with different established and commercial BEM codes, such as Flex5 [18] by DTU and the GL certified WT_Perf [2, 19] from the National Renewable Energy Laboratory (NREL). Double Multiple Streamtube Algorithm

Fig.4 Multi parameter simulation module

HAWT AND VAWT SIMULATION ALGORITHMS The HAWT and VAWT simulation algorithms in QBlade are both based on blade element theory (to estimate the local blade forces) coupled with a multiple streamtube momentum balance (to account for the global flow field) over one (HAWT) or two (VAWT) rotor discs. The use of these lower order accuracy performance prediction methods allows for a rapid development of the aerodynamic rotor shape, based on the comparison of different rotor designs. These designs can be studied with more sophisticated CFD techniques in greater detail after the preliminary shape has been developed with a BEM based method. The well documented validation of these engineering methods with experimental and field data, their computational efficiency and robustness and the long term experience that exists are the reasons why they are widely used in industry and research.

Fig.5 Sketch of the Double Multiple Streamtube model

The VAWT analysis in QBlade is an implementation of the DMS algorithm, as described by Paraschivoiu, and a detailed derivation of all equations that follow can be found in [20]. The turbine is modeled as two separate rotor discs (Fig.5), one for the upstream and one for the downstream half during one rotation. The rotor blade is discretized into an arbitrary, user specified, number of elements. The circular path of each element is divided into steps of 5°, as proposed in [20].

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The rotor extracts kinetic energy from the wind at both, the upstream and downstream, rotor discs. It is assumed that half of the decrease in velocity occurs as the flow passes each disc. Therefore:

Vup = u upV0

(1)

is the velocity at the upstream rotor disc and uup is the upstream interference factor

Veq = (2u up − 1)V0

(2)

is the velocity in the equilibrium plane between the two discs, and

Vdown = u down (2u up − 1)V0

(3)

is the velocity in the downstream rotor disc, with udown as the downstream interference factor. One limitation of the DMS model is that the theory fails if the upstream interference factor uup > 0.5. In this case the downstream disc experiences a change in flow direction and the algorithm fails to converge. In the current implementation of the DMS algorithm the interference factors are, for each height position, averaged over each half circle, resulting in one upstream and one downstream interference factor for each blade element. The formula for the upwind interference factor is derived from blade element theory and the momentum equation over each streamtube:

π 8π r  2 1 uup =  Nc  −∫π cosθ  2 2

 sin θ  W    C N cosθ − CT cos δ  V 2 dθ    up    2

For the first iteration an interference factor uup=1 is assumed to determine the upstream induced velocity Vup, from which a new uup is computed until convergence. The downwind interference factors are computed in a similar approach, with the velocity Vdown and the integration for the downwind interference factor is performed from π / 2 to 3π / 2 . Once the interference factors are known, the blade forces and performance can be obtained by averaging over one revolution. Analog to the BEM algorithm the DMS algorithm does not account for three dimensional or unsteady aerodynamic effects and thus has its limitations. However numerous empirical corrections for dynamic stall effects or the influence of struts and the tower exists. Also, more sophisticated model formulations, that take into account streamtube expansion or variable influence factors, are available in the literature [20, 21]. So far only the tip-loss correction as described by Paraschivoiu has been implemented in QBlade but more corrections, such as a correction for the tower shadow, and variable influence factors will be integrated in the near future.

−1

(4)

The normal and thrust coefficients are calculated from tabulated airfoil data:

C N = Cl cos α + Cd sin α

(5)

CT = Cl sin α − Cd cos α

Fig.6 Comparison of DMS results for the Sandia 17m turbine to measured and simulated data

The AoA depends on the azimuthal angle, blade geometry, the local TSR and the relative velocity:



V   rω  − sin θ  sin α 0  up  (6) V  W   up   

α = sin −1  cos θ cos δ cos α 0 −  

with the relative velocity: 2

W = Vup

 rω   − sin θ  + cos 2 θ cos 2 δ V   up 

To validate the implemented algorithms the predicted performance of the 2 bladed Sandia 17 m turbine [22] was compared to measured and simulated performance data from the CARDAA [20] code (Fig.6). The comparison shows good agreement between the two similar codes and the measured data, the differences between the two codes might be due to different polar data used during the simulation or small differences of the implementation, iteration or discretization. All other resulting simulation variables were compared to published [20] CARDAA results and show similar distributions.

(7)

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APPLICATION TO WIND TURBINE SIMULATIONS In the following, the VAWT simulation module is applied in two different case studies to demonstrate its capabilities to analyze wind turbine performance and loads. During all simulations the tip loss correction was activated. All graphs and blade designs shown are screenshots taken from the QBlade software. Investigation of Vortex Generators on a VAWT rotor The effect of vortex generators (VG) on the performance of a generic 2 bladed Darrieus wind turbine was investigated. The rotor geometry matches the Sandia 17m turbine while NACA 63(3)-618 airfoils were used in this investigation. The rotational speed was at constant 35 rounds per minute (rpm). The airfoil polar data with and without installed VGs (Fig.7) originates from wind tunnel measurements [25] taken at the large wind tunnel of the Technical University of Berlin (TUB).

Fig.7 Lift and drag polar for NACA 63(3)-618 with and without VG, measured data at Re = 1.1x10^6, from [22]

VGs are passive flow control devices that delay stall by generating streamwise vortices that transfer momentum to the boundary layer. The disadvantage of VGs is that their application introduces an additional parasitic drag, which results in a decreasing aerodynamic efficiency for moderate AoA. However for AoA between the stall angle of the baseline airfoil and the stall angle of the VG outfitted airfoil the efficiency is increased.

Fig.8 The effect of VG’s on the rotor tangential force coefficient over the azimuthal angle theta at a TSR of 3

The outer blade section of a Darrieus rotor, close to where the blade is connected with the tower, generally experiences very low TSRs. At low TSRs the AoA is changing drastically during one rotation of a blade. In this case, at a TSR of 2 a blade section experiences a change in AoA of +-25°, which is far beyond the stall point of the baseline airfoil. For low TSR a VG can improve the performance of a VAWT (Fig.8), for high TSR the performance is decreased.

Fig.9 The effect of VG’s on the power output for three configurations

When a VAWT is operating at a constant angular frequency the performance will be increased for high- and decreased for low wind speeds (Fig.9). If the measure of performance is AEP it depends on the wind site if VGs can increase the overall performance. For a wind site described by the Weibull factors k=2 and A=6.21 the rotor described above was optimized for AEP by equipping different lengths of the rotor with VGs, starting from the blade tips. The optimum in AEP was found for

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the rotor where both outer 12 % of the blade had VGs installed. The AEP increased about 0.2 % due to the vortex generators. Another positive effect of VGs on VAWT rotors is that the increase in torque at low TSR aids the self starting ability of the rotor. Effect of Blade Shape on Time Varying Loads A VAWT has an inherent unsteady aerodynamic behavior because the AoA is constantly changing during the rotation of the blade [26]. This results in varying torque and streamwise or crosswise forces and introduces fatigue loads to the turbines structure. One way to reduce these loads is to increase the blade number, but this leads to additional manufacturing costs. Another option is to employ helical blades that introduce a phase shift angle between the upper and lower blade forces and in this way reduce the load variation. The effect of a blade inclination on the rotor tangential, streamwise and crosswise force coefficients is investigated for a two bladed rotor with shift angles of 0°, 60° and 120°. The simulation results are also compared to a rotor with higher blade number. The generic rotor design (Fig.10), employed in this investigation has straight blades, a solidity of 0.25 and NACA 0015 airfoils.

Fig.11 Comparison of the rotor tangential force coefficient over the azimuthal angle theta at a TSR of 1

At the design TSR an increased blade number from 2 to 3 very efficiently reduces the tangential (Fig.12) lengthwise and crosswise (Fig.13) force fluctuations and thus the fatigue loads. When the blade number is increased from 3 to 4, the effect on the fluctuations is far less pronounced. Introducing shift angles to the blade also is an effective means to alleviate the load fluctuations. Higher shift angles achieve a greater reduction. Ideally, under uniform inflow and without the tip loss effect, a shift angle of 180° would reduce the fluctuations to zero for all operational points of the turbine.

Fig.10 The different rotor configurations: 2 blades: 0° shift, 60° shift, 120° shift; 3 blades: 0° shift; 4 blades: 0° shift

When the blade number is increased the chord length is reduced to maintain a constant solidity. The Reynolds number was assumed as constant (Re = 1.000.000) during the simulations. The CP over TSR curve is identical for all 2 bladed rotor designs, only the rotors with additional blades have slightly higher CP values. This is because of smaller tip losses, due to a higher aspect ratio of the blades. All simulation results were computed dimensionless over a range of tip speed ratios. At low tip speed ratios (Fig.11) (TSR < 2 for this design) the blade inclination is more efficient in reducing the varying rotor torque compared to an increased blade number. This plays an important role for the self starting capacity of a VAWT. For all straight blade configurations there are rotor positions where no or even negative torque occurs. This disqualifies the rotors for a self start. Inclined blades however introduce a phase shift between the upper and lower blade sections so that torque minima only affect local blade sections, but not the whole blade.

Fig.12 Comparison of the rotor tangential force coefficient over the azimuthal angle theta at the design TSR of 3

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Fig.13 Rotor crosswise force coefficient over streamwise force coefficient for one full rotation at a TSR of 3

CONCLUSION AND FUTURE WORK The current paper presents in brief the functionality and theory of the wind turbine simulator QBlade. By means of two case studies the tools potential for wind turbine research and design was demonstrated. The software in its current state is a very comprehensive and flexible tool and to the authors knowledge it is the only code that combines HAWT and VAWT simulation, blade design and airfoil analysis in one interface. The free distribution (Fig.14) of the software leads to a broad application and thorough validation of the software. QBlade was downloaded more than 20.000 times and has been applied numerous times for research and teaching [18, 19, 23, 24, 25]. The software also serves as a modular platform for further implementations and extensions of its functionality such as genetic algorithms that exploit the combination of parametric airfoil design and wind turbine simulation. In the near future it is planned to extend the functionality to unsteady simulations, include a wind field generator and integrate the open source aeroelastics code FAST [7, 27] from the National Renewable Energy Laboratory (NREL).

Fig.14 QBlades webpage can be found at: qblade.fd.tu-berlin.de

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[17] Hernandez, J., Crespo, A., 1987, “Aerodynamics Calculation of the Performance of Horizontal Axis Wind Turbines and Comparison with Experimental Results”, Wind Eng., 11(4), pp. 177-187 [18] Soland, T.H., 2012, “Investigations of different airfoils on outer sections of large rotor blades”, Bachelor Thesis, Mälardalen University, Sweden [19] Widjarnako, M.D., 2010, “Steady blade element momentum code for wind turbine design validation tool”, Internship Report, Universiteit Twente, The Netherlands [20] Paraschivoiu, I., 2002, “Wind Turbine Design – With Emphasis on Darrieus Concept”, Presses Internationales Polytechnique [21] Paraschivoiu, I., Delclaux, F., 1982, “Double Multiple Streamtube Model with recent Improvements”, Technical Report, Journal of Energy, Vol. 7, No.3, IREQ [22] Worstell, M.H., 1978, “Aerodynamic Performance of the 17 Meter Diameter Darrieus Wind Turbine”, Technical Report SAND78-1737, Sandia Laboratories [23] Pechlivanoglou, G., Nayeri, C.N., Paschereit, C.O., 2010, “Fixed Leading Edge Auxiliary Wing as Performance

Increasing Device for HAWT Blades”, Proceedings of the DEWEK 2010, Germany [24] Weinzierl, G., 2011, “A BEM based simulation-tool for wind turbine blades with active flow control elements“, Diploma Thesis, TU Berlin, Germany [25] Mueller-Vahl, H., Pechlivanoglou, G., Nayeri, C.N., Paschereit, C.O., 2012, “Vortex Generators for Wind Turbine Blades: A Combined Wind Tunnel and Wind Turbine Parametric Study”, Proceedings of the ASME Turbo Expo 2012, Denmark [26] Ferreira, S., Bijl, H., van Bussel, G., van Kuik, G., 2007, ”Simulating Dynamic Stall in a VAWT: Modeling Strategy, Verification and Validation with Particle Image Velomecitry Data”, Journal of Physics: Conference Series Volume 75 [27] Jonkman, J.M., Buhl, M.L., 2005, “FAST User’s Guide”, Technical Report NREL/EL-500-38230, National Renewable Energy Laboratory

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