IOP Conference Series: Materials Science and Engineering [617466]

IOP Conference Series: Materials Science and Engineering
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Effect of yaw angle on the global performances of Horizontal Axis Wind
Turbine – QBlade simulation
To cite this article: D E Husaru et al 2019 IOP Conf. Ser.: Mater. Sci. Eng. 595 012047
 
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Published under licence by IOP Publishing LtdThe XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
1

Effect of yaw angle on the global performances of Horizontal
Axis Wind Turbine – QBlade simulation
D E Husaru1, P D Bârsănescu2 and D Zahariea3
1Mechanical Engineering,” Gheorghe Asachi” Technical University of Iași, Iași, Romania
2Mechanical Engineering, Mechatronics and Robotics Department, “Gheorghe Asachi”
Technical University of Iași, Iași, Romania
3Fluid Mechanics, Fluid Machinery and Fluid Power Systems Department, “Gheorghe Asachi”
Technical University of Iasi, Iasi, Romania
E-mail: [anonimizat]

Abstract. The yaw angle has a great importance in the wind turbine working. Even though most
of the large turbines have yaw mechanisms, they do not have an instant response. The
aerodynamic forces and torque on the blades flu ctuate, depending on the yaw angle. The design
and the numerical simulation of the wind turbine were performed with the Blade Element
Momentum method in open source QBlade software. The power coefficient , torque , thrust and
power output generated by wind turbine in no n-yawed flow were analysed . The simulations have
been performed for non-yawed flow , in rotational speed range between 2100 and 3300 rpm and
wind velocity of 15 m/s . Simulations f or yaw angle range have been performed between ± 60o,
with 5o step at rated rotation al speed of 2700 rpm. The result s are presented through charts for
global parameters in both non-yawed flow , and yawed flow. The effect of yaw angle on global
performances of the wind turbines is more important after the value of 25o when the power output
decrease with about 1 5% from power output in no n-yawed flow. The average value of the
exponent from conventional relation of power coefficient in yawed flow is 1.7 7 in good
concordance with experimental tests.
1. Introduction
Nowadays, the wind energy knows a continuous increase most of all because it is a renewable and non –
polluting energy. The kinetic energy of the wind is converted into mechanical energy by wind turbines.
The two main types of wind turbines are classified according rotational axis in HAWT (Horizontal Axis
Wind Turbine) and VAWT (Vertical Axis Wind Turbine) [1]. The HAWT are used in the most of windy
areas around the world due to higher efficiency, but in recent years in the most favourable areas already
are installed wind turbines, so new research directions have been identified in order to increase the
percentage of energy provided by wind turbines: installation of small wind turbines, expansion of
offshore areas and increase of rotor dimensions [2].
Several methods to design and predict aerodynamic performances of wind turbines such as vortex
methods, 3D viscous -inviscid interaction technique, computational fluid dynamics algorithms and Blade
Element Momentum (BEM) method are used. The most used method by the designers of wind turbines
is the BEM method . This method provides a good aerodynamic performance analysis with a relatively
simple procedure in different flow regime such as different wind speeds, yaw angles, setting angles of
blades [3,4]. The classical BEM method was first developed by Glauert [5] by combining momentum

The XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
2

theory and blade element theory. The BEM method involves discretization in N annular elements with
height dr of the stream tube introduced in the 1 -D momentum theory and no flow across the elements.
The annular elements are considered independent one to another (no radial dependency) and the force
on the blades are considered constant in each annular element due to hypothesis of a rotor with infinite
number of blades [6].
The classical BEM method is a two -dimensional method extrapolated into the third dimension
through applied semi -empirical corrections, tip and root losses induced by finite number of the blades
and 3D corrections, derived from experimental tests or CFD comput ations. The BEM method have a
main advantage in comparison to CFD computation due to less computational time, very low cost and
possibility to develop and test rapidly different rotor design, reaching at a rotor model that will be studied
with CFD techniqu e in details [7].
Most of the working time, HAWT operate in yawed flow because the direction of wind varies
continuously over time . Wind turbines working in yawed flow leads to difficult problems of
aerodynamics, control and aeroelasticity. Some of these for the moment are unresolved , [8]. Yaw angle ,
figure 1, represent the angle between wind turbine rotor plane and wind direction. Several researchers
have conducted numerical and to experimental test in order to predict the operation and to determinate
the global performances of the HA WT in yawed flow [9, 10].

Figure 1. Yaw angle of HA WT.
Some researchers, based on the assumption that induction is constant with yaw angle, with x=3
(aerodynamics of the helicopter rotor in a forward flight) do not consider that aerodynamics of wind
turbines has additional difficulties and differences from the aerodynamics of the helicopter rotor.
It is proposed that the power coefficient, and implicitly, power output in yawed flow have a
cosinusoidal behaviour expressed in t he conventional form in equation (1) , [11].
 00 0ox
PPCψ C cos ψ
(1)
Experimental tests in wind tunnel and on field [12], shows that x varies from 1.88 and 5.15 while in
measurement on the rotor with diameter of 4.5 m in German Dutch Wind Tunnel [13], x is about 1.8 .
QBlade is an open source software dedicated to design and predict the aerodynamic performances of
Horizontal Axis Wind Turbines and Vertical Axis Wind Turbines blades using BEM method and the
integration in XFOIL enables to design custom airfoils and compute their polars and also allow to import
experimental polars .
In this paper , power coefficient and power curve generated for a HAWT with three blades , with
NACA 4415 airfoils and 0.58 m rotor diameter obtained with QBlade software in the range ± 60o for
yaw angle have been analysed.

The XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
3

The relatively small geometrical dimensions of the wind turbine rotor are due to the fact that this
research is part of a more complex analysis in which, in a further step, some experimental tests will be
carried out . For experimental tests the MF -TA4 wind tunnel from the Department of Fluid Mechanics,
Fluid Machinery and Fluid Power Systems will be used, for which the cross -section area of the test
section is 2.853 m2. In order to obtain a blockage ratio under 10% it was chosen that the swept area of
the rotor to be equal to 0.2642 m2, which correspond to the rotor diameter of 0.58 m.
2. Wind turbine rotor model
2.1. Airfoil characteristics
One of the important points in the design of wind turbine rotors is the selection of the blade airfoil. A
wind turbine blade can contain one or more airfoils. There are a multitude of bidimensional airfoils that
can be used in the design of HAWT blades. At low Reynolds numbers (<105), which is the case of this
research, there is d ifficult to find experimental polars. In [1 4], Eastman N. J. and Sherman A., have
conducted experimental tests for different airfoils at low Reynolds numbers , including NACA 4-digit
series of airfoils. These series of airfoil s have been used since the first half of the 20th century in different
applications, including wind turbines [ 15]. In this paper a NACA 4415 airfoil was used for the entire
blade length, being one of the airfoils that have been experimentally characterized for different Reynolds
numbers. In figure 2 are presented the dimensionless coordinates of the NACA 4415 airfoi l, having a
maximum camber of 4% located at 40% from the leading edge and having a maximum thickness of 15%
with respect to the airfoil chord length.

Figure 2. NACA 4415 airfoil dimensionless coordinates .
2.2. Polars of NACA 4415 airfoil
In this paper, the variation of the lift coefficient (
LC ) and drag coefficient (
DC ) in the range of the
incidence angle (
α) between -7° and 21. 2° corresponding to a Reynolds number equal with 83000 for
NACA 4415 airfoil were taken from charts resulting from experimental tests . Due to the small number
of points on the charts of incidence angle range , an interpolation of 100 point with 5th degree polynomial
was made. The polars of the airfoil was created in XFOIL and then was imported in QBlade software.
In figure 3, (a) lift coefficient and 3, (b) drag coefficient for incident angle in the range -7 and 21.2
degrees are presented . In figure 3, (c) are present ed the polar curves for NACA 4415 airfoil in QBlade.
The optimum incidence angle is 6.38 7 degrees conditioned by maximum ratio between lift coefficient
and drag coefficient equal with 40.05 5. At this value of the incidence angle, optimum lift coefficient
and drag coefficient are equals with 1.0386 and respectively 0.0259.

The XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
4

(a) (b)

(c)
Figure 3 . NACA 4415 Polars.
2.3. Blade design and Blade Element Momentum method
The design of the blade was accomplished by using BEM method considering the rated parameters of
the wind turbine rotor presented in table 1.
Table 1. Wind turbine rated parameters .
Wind velocity
V [m‧s-1] Rotational speed
n [rpm] Tip speed ratio
TSR [-] Rotor diameter
D [m] Reynolds Number
Re [-]
15 2700 5.46 0.58 83000
The total length of the blade is 0.2 7 m. The b lade was divided in 23 section s with 2 circular airfoils
with 0.016 m diameter, at radial positions 0.02 m and 0.03 m . Between section 2 (circular foil) and
section 3 (NACA 4415 airfoil) automatic linear interpolation was performed by QBlade.
The NACA 4415 airfoil chord varies from 0.044874 m in section 3 and 0.016946 m in the final
section . The chord along the blade is presented in figure 4, ( a). The total twist of the blade is 13.43
degree between 13.957 degrees at f irst section of the active zone of the blade and 0.5234 degrees at tip
of the blade . The variation of the twist angle along the blade is presented in figure 4, (b). Global solidity

The XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
5

of the blade is 6.1189 %. Geometry of the blade and airfoils used at each radial position are presented
in figure 4, (c).

(a) (b)

(c)
Figure 4. Geometrical dimensions of the blade .

3. QBlade simulations and results
The functional performance analysis of wind turbine rotor was performed in BEM Simulation menu for
tip speed ratio range between 2 and 8 with 0.1 step. The air density and air viscosity are considered
1.225 kg/m3 and respectively 1.647e -05 Pa‧s. Prandl correction, 3D correction and Reynolds number
correction have been used. Figure 5, (a) shows the variation of Reynolds number along the blade and
figure 5, (b) shows the absolute error between the Reynold number of imported polar and Reynolds
number calculated by QBlade.
The largest absolute error is recorded at the hub area an d at the inactive part of the blade (16504 at
radius 0.03 m), while at active part of the blade the maximum absolute error for the Reynolds number
is -3275 (at radius 0.0902 m), which corresponds to a relative error of less than 4%.

The XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
6

(a) (b)
Figure 5. Reynolds number and absolute error .
The multi -parametric analysis of functional performances was performed in Multi -Parameter BEM
Simulation menu. The simulations were performed for rotational speed range between 2100 and 3300
rpm with 50 rpm step, and fo r wind velocity range between 5 and 25 m/s with 1 m/s step.
Global performances of the wind turbine rotor are sho wed in figure 6, (a) for power coefficient, (b)
for power output, (c) for torque and (d) for thrust according to rotational speed. For rated rotation al
speed of 2700 rpm and rated wind velocity of 15 m/s , the values of the calculated parameters are
presented in table 2 (red point from figure 6) .
Table 2 . Wind turbine global performances parameters .
Power coefficient
CP [-] Power
P [W] Torque
T [Nm] Thrust
S [N]
0.40408 220.69 0.7805 30.08

(a) (b)

(c) (d)
Figure 6. Global performances of wind turbine rotor .
The influence of yaw angle on global performances of wind turbine rotor was studied using LLT
(Lifting Line Theory) HAWT Simulation menu , [16] for the yaw angle range between ±60° with 5 ° step
size under an windfield defined by the mean wind velocity of 15 m/s , by the hub height of 0.88 m , and
by the turbulence intensity of 5 %. The LLT simulations were accomplish with 360 time steps , for 10

The XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
7

complete rotor revolution. In figure 7,(a) and 7, (b) are presented the positions of the wind turbine rotor
and the near wake for positive and respectively negative values of yaw angle.

(a) (b)
Figure 7. Position of the wind turbine rotor .
The results of the LLT simulations are in particular influenced by two free parameters used to adjust
the initial core size and its growth rate in time, vortex time offset (
CS ) and turbulent vortex viscosity (
vδ
). These parameters affect significant the performances of the wind turbine rotor analyzed. Too large
values for them reduces the induction in the near wake and leads to over predictions of rotor power
output, leading to significant discr epancies between the BEM results and LLT results , [16] . In this paper,
two cases with different values of these two parameters, presented in table 3, were analyzed .
Table 3. The significant parameters used in LLT simulations
Vortex time offset
CS
[-] Turbulent vortex viscosity
vδ
[-]
Case 1 2 1
Case 2 0.2 0.2
Power coefficient and power output according to yaw angle range are presented in figure 8, (a) and
respectively in figure 8, (b). The yaw angle increase causes a significant decrease of global parameters.
Maximum value s are obtaining at 0°, 0.504 for power coefficient and 275 W for power output in case 1
and 0.453 for power coefficient and 248 W for power output in case 2.
The effect of yaw angle on global performances of the wind turbines is more important after the
value of 25o when the power output decrease with about 1 5% with respect to the power output in no n-
yawed flow in both cases . At yaw angles greater than 45o the power output generated by wind turbine
decrease to half . Power coefficient and power output at equal positive and negative value of the yaw
angle have small differences, with greater values obtained at positive yaw angles more important after
50 degrees. For example, power output is 115.75 W at -50o and 117.29 W at 50o in case 1 and
respectively 98.7 W at -50o and 101.5 W at 50o in case 2.
At zero yaw angle, significant discrepancy between BEM results and LLT results has been noticed .
This discrepancy is mainly due to the chosen values of the two free parameters (vortex time offset and
turbulent vortex viscosity) , the simulations time steps number and some limitation of the LLT method .
The relative error between BEM results and the two cases of LLT simulat ions for power coefficient is
24.7 % in case 1 and 12.28 % in case 2.

The XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
8

(a) (b)
Figure 8. Influence of yaw angle on power coefficient and power output .
Further, using the results obtained in case 2, the x exponent of conventional expression for power
coefficient from equation (1) in yawed flow was determined. In figure 9, the x exponent values ( green
dots) according to yaw angle range from 5 ° to 5° are presented . The LLT computed data was
approximated with a 4th degree polynomial (brown line), described by equation (2) :
8 4 8 3 21.5581 10 2.4558 10 0.00024239 0.00074046 1.38 74 x ψ ψ ψ ψ          
(2)
The maximum and minimum values of the x exponent , in case 2, equal to 2.56, and 1. 18 have been
obtained at -60°, and respectively at 5°.
The mean of the exponent (red line) , equal with 1.77 has been computed with data presented in figure
9, being in a good concordance with the value obtained from experimental tests conducted in German
Dutch Wind Tunnel , which is 1.8, [13] , and also with the lo wer value , equal to 1.88 , of the x exponent
range presented in [12].

Figure 9. Exponent of conventional equation for power coefficient .
Relative deviation (
ε) of the x exponent with respect to its mean value is showed in figure 10, for
case 2 . Maximum deviation of 45% has been observed for yaw angle of -60o. The relative deviation
decrease in the range 0°÷ ±40°, reach es a minimum point at ±40°, and then increase t ill ±60°.

Figure 10. Relative deviation for power coefficient.

The XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
9

4. Conclusion
In this study , the global performances of HA WT in non-yawed and yawed flow were analyzed using
QBlade open source software . The design of the blade s was accomplished in QBlade using BEM
method . The most important design steps are the selection of optimum incidence and the calculation of
airfoil polars for a good approxim ation of the Reynolds number .
The yaw angle affects the global performances of the wind turbines no matter how small it is. In this
study has been observed that t he effect of yaw angle is more important after the value of 2 5, when the
power output decrease with about 15% from the power output in non -yawed flow . Moreover, at yaw
angles greater than 45o the power output generated by wind turbine decrease to half.
Researche rs opinions on the value of the x exponent from conventional equation for power
coefficient at different yaw angle s are divergent. In this paper, mean value of the x exponent of
conventional equation for power coefficient in the range ±60o is 1.7 7, being in good concordance with
the mean value obtain ed in several experimental tests.
The LLT results for those two cases analyzed in this paper have significant differences compared to
BEM results at zero yaw angle. In case 1, values of the global param eters for wind turbine model are
over predicted with 24.7 % compared to BEM results. In case 2, the relative error between LLT results
and BEM results decrease at 12.28 %. This discrepancy between the two methods results is influenced
by chosen values of t he two free parameters used in LLT simulations and the simulations time steps
number .
In order to obtain good prediction of the global parameters of wind turbines in LLT HAWT Simulation
menu it is necessary to adapt the values of the vortex time offset (
CS ) and turbulent vortex viscosity (
vδ
) to the dimension of computed wind turbine rotor. Large values for these parameters reduces
induction in the near wake and leads to over predictions of global parameters of wind turbine.
In the future, some experiment al tests (using MF -TA4 wind tunnel) and new numerical simulations
(using ANSYS Fluent) are necessary to improve the knowledge about the e ffect of the yaw angle on the
aerodynamic performances of HAWT and the v alue of the exponent from conventional expression for
yaw angle .

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The XXIInd National Conference on Thermodynamics with International Participation
IOP Conf. Series: Materials Science and Engineering 595 (2019) 012047 IOP Publishing
doi:10.1088/1757-899X/595/1/012047
10

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Acknowledgments
The authors would like to acknowledge the technical resources offered by the Laboratory of Computer –
Aided Fluid Engineering (equipped with technical resources with the financial suppo rt of the grant
ENERED, POSCCE -A2-O2.2.1 -2009 -4, ID 911), from the Department of Fluid Mechanics, Fluid
Machinery and Fluid Power Systems, “Gheorghe Asachi” Technical University of Iasi, Romania.