CFD studies on rotational augmentationat the … power from the NREL Combined Experiment (Phase II)...

JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 9, 023304 (2017)

CFD studies on rotational augmentation at the

inboard sections of a 10 MW wind turbine rotor

Galih Bangga, Thorsten Lutz, Eva Jost and Ewald KramerInstitute of Aerodynamics and Gas Dynamics (IAG)University of Stuttgart, Pfaffenwaldring 21 Stuttgart 70569, Germany

ABSTRACT: In the analysis of aerodynamic performance of wind turbines, the need to account for the

effects of rotation is important as engineering models often failed to predict these phenomena. Investigations

are carried out by employing unsteady computational fluid dynamics (CFD) approach on the generic 10

MW AVATAR blade. The focus of the studies is the evaluation of the 3D effect characteristics on thick

airfoils in the root area. For preliminary studies, 2D simulations of the airfoils constructing the blade and

3D simulations of the turbine near the rated condition are carried out. The 2D simulations are in a good

agreement with available measurements within linear lift region, but the accuracy deteriorates in the post

stall region. For the 3D wind turbine rotor results, the prediction is consistent with other CFD computa-

tions obtained from literature. Further calculations of the rotor are conducted at 5 different wind speeds

ranging from below to above rated conditions which correspond to 5 different angles of attack. The CFD

simulations demonstrate that the lift coefficient increases in the blade root region compared to the 2D con-

ditions caused by the centrifugal pumping and Coriolis force via reduction of the boundary layer thickness

and separation delay. The Coriolis force effect decreases with increasing wind speed and radial position. In

addition, the aerodynamic behaviour of the blade inboard region is influenced by the shedding direction of

the trailing vortices. The occurrence of downwash is observed causing local increase of the drag coefficient.

http://dx.doi.org/10.1063/1.4978681

Keywords: 3D effects, CFD, flow separation, rotational augmentation, wind turbine aerodynamics

1 INTRODUCTION

The fluid flow over horizontal axis wind turbine (HAWT) blades around the hub region is highly complex

and has become the subject of interest for many years because of the implication for accurate load prediction

of the wind turbines. The complexity stems from the fact that the inboard sections of the blade operate at

high angles of attack (α) and often in post-stall conditions, which in turn enhance the three-dimensionality

of the flow. The presence of rotational motion of the rotor plays an important role in this condition which can

be explained as follows: (i) secondary flow develops starting from the root section, (ii) the centrifugal force

transports the separated flow towards the middle section of the blade and develops a radial flow component,

and (iii) the Coriolis force accelerates the flow near the wall and then delays separation.

Post-print article generated by authors.

http://dx.doi.org/10.1063/1.4978681

http://dx.doi.org/10.1063/1.4978681

http://dx.doi.org/10.1063/1.4978681

http://dx.doi.org/10.1063/1.4978681

Bangga et al. J. Renewable Sustainable Energy 9, 023304 (2017)

The experimental studies conducted by Himmelskamp [1] were the first investigation which clearly ex-

plained the source of the above mentioned 3D effects commonly referred as rotational augmentation. The

lift coefficient (CL) of propeller sections was observed to deviate from the two-dimensional (2D) conditions

which was attributed to stall delay phenomenon generated by the radial flow within separated boundary

layers [2]. Extensive experimental, theoretical and numerical investigations were then directed towards the

study of radial flows [3]. However, due to limitations of the computer performance at that time, numerical

studies on rotating blades were limited to the analysis of laminar boundary layers [3–6]. Fogarty [4], Tan [7],

Rott and Smith [8] demonstrated that the rotational augmentation did not occurr for non-separated laminar

boundary layer. Banks and Gadd [5] and McCroskey and Yaggy [6] observed that the radial flow was more

pronounced on blade sections with a higher chordwise pressure gradient and was strongest in the beginning

of separation. Using the solution of the 3D boundary layer equations in integral form, Du and Selig [9, 10]

demonstrated that the effect of centrifugal pumping for separation delay was not as strong as it had been

thought before. In contrast, the Coriolis force was shown as the major reason for the delay of separation.

Furthermore, the effect was strongly influenced by the ratio of chord to radius (c/r) [9–17]. A detailed

evaluation of this particular parameter was given by Snel et al. [11, 12], inferring that the 3D effects scale

with increasing c/r. It was observed that the radial convective acceleration terms are of the order (c/r)2/3

compared to the main terms which are of order unity.

Measurements conducted in the NASA Ames 24.4 m x 36.6 m (80 ft x 120 ft) wind tunnel known as the

Unsteady Aerodynamic Experiment (UAE) have led better understanding of the 3D post stall aerodynamics

of wind turbines [18–21]. Measured power from the NREL Combined Experiment (Phase II) turbine exceeded

BEM (Blade Element Momentum) predictions by approximately 15-20% at high wind speeds [22], empha-

sizing the importance of 3D rotational effects in the aerodynamic calculations of wind turbines [13]. Schreck

and Robinson [23] evaluated surface pressure measurements from the NREL UAE wind turbine blade. The

rotational augmentation was independent of the Reynolds number influence and dependent strongly upon

the spanwise surface pressure gradients on the blade. Schreck [24] demonstrated a strong correlation of the

local inflow condition to the characteristics of the normal force coefficient standard deviation (σCn) which

determined the blade flow field structures under rotational augmentation. In his subsequent study, Schreck

et al. [25] compared the NREL UAE Phase VI blade to the MEXICO (Model Experiments in Controlled

Conditions) rotor and observed discrepancies of the 3D post stall characteristics between these two rotors.

The pressure coefficient (Cp) distribution for the UAE Phase VI blade implied a leading edge separation

followed by shear layer impingement and it was highly responsive to increasing wind speed for the inboard

blade sections [24,26], but the Cp distribution for the MEXICO rotor consistently showed the characteristics

of trailing edge separation. However, a strong correlation could be depicted from the variations of σCn with

respect to the angle of attack (α) [25].

With the development of high performance computers, computational fluid dynamics (CFD) approaches

have been employed to gain more insights into the physics of the flow past rotating wind turbine blades [27].

Different types of simulation codes have been validated against measurement since then [28]. Duque et al. [29]

performed computations of the NREL Phase II blade using a lifting line code and a CFD code that made

use of overset grids and an algebraic turbulence model known as Baldwin-Lomax. The results demonstrated

that the CFD code could predict the stalled rotor performance quite well while the lifting line method failed

to capture the rotor performance at high wind speeds, even with the inclusion of a 3D correction model. The

CFD predictions of a wind turbine rotor using two-equation turbulence models, namely Wilcox k − ω and

SST k−ω, were carried out by Le Pape and Lecanu [30]. The SST k−ω model was superior in predicting the

aerodynamic polar, but both models hardly showed a good prediction under post stall conditions. Sørensen

et al. [31] performed CFD calculations on the NREL Phase VI blade using SST k − ω with fully turbulent

2


boundary layer and a good agreement against experimental data was achieved. Johansen et al. [32] simulated

the same turbine in parked condition using Detached Eddy Simulations (DES) as well as the RANS SST

k − ω turbulence model. The DES results gave more information on the 3D flow structures than the one

predicted by the RANS, but the overall aerodynamic characteristics of the blade were not better predicted.

Johansen and Sørensen [33] extracted the aerodynamic characteristics of the 3D CFD rotor computations

on three stall-regulated wind turbine rotors as test cases. With a sufficiently accurate CFD computation, it

was possible to reproduce the airfoil characteristics under rotational augmentation without using empirical

stall corrections models. The other examples of CFD studies on rotational augmentation were given Guntur

and Sørensen [34] and Herraez et al. [28] on the MEXICO rotor and by Bangga et al. [35] on the AVATAR

blade. Later, using the same turbine, Bangga et al. [36] showed that mild turbulence level on the inflow has

little influence on rotational augmentation, contrasting the observation by Sicot et al. [37]. The discrepancy

was explained due to the difference in the turbulence level studied.

As the need of wind power is remarkably increasing nowadays, the size of the rotor blade is also increasing

as a consequence to generate more power. It leads the turbine to operate at significantly higher Reynolds

number than smaller turbines. Contrasting Schreck and Robinson [23], Du and Selig [10] concluded that the

rotational augmentation is less important for large wind turbines because the Reynolds number is remarkably

larger. However, it should be kept in mind that the tip speed ratio of the larger turbines is comparable with

the smaller one, resulting in the congruous value of the Rossby number which influences the 3D effects

according to Dumitrescu and Cardos [13]. They identified that the local solidity, defined as r/c, and the

local relative to rotational velocity ratio, X = (1 + (U∞/(rΩ))2)0.5, as physically pertinent parameters in

their studies. Later, Herraez et al. [28] supported their argument by comparing the sectional Rossby number

of two different turbines, arguing that the 3D effects should be similar even though the size of the turbines

is different. On the other hand, no further quantification of the influence was given. In fact, the study

was solely performed for a small rotor. Troldborg et al. [38] conducted experimental and numerical studies

on a megawatt wind turbine blade, showing that the pressure distribution was affected by the rotation.

Bangga et al. [35] performed a CFD evaluation and grid studies of the generic 10 MW AVATAR rotor

operating near rated condition. The lift coefficient was observed to have a remarkably higher value than

in 2D conditions at the inboard blade region and the size of the separated zone was significantly reduced

due to 3D effects [39]. Furthermore, it was shown that extremely thick airfoils at the blade root promote

stronger separation than the thinner ones [40, 41] even at small angle of attack. Accordingly, this can lead

to the development of the radial flow component under rotational motion as observed in [35, 36]. Schreck

et al. [26] investigated the field test measurements of a 2.3 MW wind turbine equipped with thick flatback

airfoils in the inboard blade region. The use of thicker airfoils and enhanced trailing edge thicknesses was

observed not to hinder the rotational augmentation. A significant increase of aerodynamic forces by factors

as high as 2-3 relative to the results at stationary 2D conditions were observed. Zahle et al. [42] derived

3D airfoil characteristics by CFD calculations on the DTU 10 MW Reference Wind Turbine for aero-elastic

simulations. The aerodynamic polars were extracted and used in BEM calculations. The results show a

significant improvement on the sectional loads compared to the 3D correction model from Bak et al. [43],

but the mechanical power and thrust did not so much improved as the inboard region has small lever-arm.

Recently, Troldborg and Zahle [44] applied vortex generators in the inboard region of the same blade as [42]

to improve the aerodynamic performance. However, the rotational augmentation was shown to be alleviated

by the vortex generator in their later studies [45].

The present investigation aims to enhance knowledge concerning rotational effects on a large wind turbine.

Unsteady CFD calculations are performed on the AVATAR blade at several wind speeds. The angles of attack

are extracted from 3D simulations and then 2D calculations of the blade sections are performed and compared

3


with the 3D results. As main distinctions from preceding CFD studies [28,34–36], the present studies focus on

the characteristics of rotational augmentation on thick airfoils at the inboard blade region, bound circulation

analysis of the blade and quantification of the centrifugal and Coriolis forces. These are carried out to gain

deeper insights into the mechanism of the 3D effects.

The paper is organized as follows. The description of the blade, test cases, numerical methods and

extraction of the angle of attack are described in Section 2. Section 3 presents the results and discussion of

the 3D effects, and it will be concluded in Section 4.

2 METHODOLOGY

2.1 The AVATAR Blade and Test Cases

The generic 10 MW AVATAR blade [46,47] was chosen in the examination. The blade is twisted and tapered.

The list of airfoils used in the blade can be seen in Table 1. It is designed as a variation of the DTU 10

MW wind turbine [48] with the aim to model the aerodynamics of turbines larger than 10 MW with similar

accuracy as is done for commercially sized turbines today [49]. It shall be kept in mind that the rated wind

speed of the AVATAR rotor is smaller than the DTU 10MW rotor. As the rated power is kept constant, the

approach results in a larger blade radius [46]. The original DTU 10 MW blade is scaled by the factor of 1.15

in radial direction to a radius of R = 102.9 m. The axial induction (a) in the design condition is reduced to

below 1/3, resulting in 0.23 < a < 0.28 which is better from a cost of energy point of view [49]. This design

concept is denoted as low induction rotor or LIR concept.

In the present study, uniform wind speeds (U∞) ranging from 5 m/s to 25 m/s have been considered. The

chosen rated wind speed for this turbine is 10.75 m/s. The rotational speed and the pitch angle were kept

constant at 9.02 rpm (Ω ≈ 0.94 rad/s) and 0.0, respectively, in order to obtain different α seen by the blade

sections with the variation of the wind speeds. The present setup was selected not according to the original

designated blade operating condition [46, 47]. This was done to artifically generate massive separation and

to study the impact of Rossby number on the 3D effects. It is defined as Ro =(

U2∞

+ (Ωr)2)0.5

/Ωc, where r

and c represent the local blade radius and airfoil chord length, respectively. The calculations were performed

without tower to isolate the rotational augmentation from unsteady tower disturbances.

2.2 Numerical Setup and Computational Meshes

Numerical simulations presented in the present manuscript have been conducted using a CFD code, FLOWer,

from the German Aerospace Center (DLR) [50–52] employing the Unsteady Reynolds Averaged Navier -

Stokes (URANS) approaches. During the last years, the code was continuously developed at the IAG for wind

turbine applications [53–55]. The numerical procedure of the FLOWer code is based on structured meshes

employed with the overset (Chimera) technique. The spatial discretization scheme used in the present study is

Table 1: Airfoil sections used for the reference blade (Reproduced from AVATAR Deliverable D1.2: ReferenceBlade Design [46]. Public Domain Material).

Airfoil Thickness [t/c] Airfoil Type

60.0% Artificial based on thickest available DU40.1% DU 00-W2-40135.0% DU 00-W2-35030.0% DU 97-W30024.0% DU 91-W2-250 (modified for t/c = 24%)21.0% Based on DU 00-W212 added trailing edge thickness

4


Table 2: Grid convergence study for the AVATAR blade.

Parameter Power Thrust

Value fine 9.28 x 106 W 1.330 x 106 NValue medium 9.26 x 106 W 1.328 x 106 NValue coarse 9.20 x 106 W 1.326 x 106 NExtrapolated rel. error-fine 0.12% 0.27%-medium 0.36% 0.47%-coarse 1.02% 0.58%Grid convercence index 0.15% 0.34%

a central cell-centered Jameson-Schmidt-Turkel (JST) [56] finite volume formulation because it provides high

robustness and is well-suited for parallel applications [51]. The scheme is second order accurate in space on

smooth meshes. The method utilizes central space discretization with artificial viscosity and explicit hybrid

5-stage Runge-Kutta time-stepping schemes. Dual time-stepping according to Jameson [57] with second-

order accuracy in time, multi-grid level 2 and the implicit residual smoothing with variable coefficients

according to Radespiel et al. [58] were applied. Turbulent closure of the URANS equations is provided by

the eddy viscosity two-equation shear stress transport (SST) k − ω model according to Menter [59]. In the

present analysis, fully turbulent computations were carried out for the 3D rotor and 2D airfoils constructing

the AVATAR blade. However, in confirming the accuracy of the computations for simulating thick airfoils,

additional 2D simulations were performed and compared with available measurement data [60]. In these 2D

simulations, boundary layer tripping was introduced by applying a fixed transition location according to the

turbulator specified in the experiment.

First, 2D structured grids of the airfoil geometries constructing the AVATAR blade were generated in

order to study the grid dependency of the numerical results in 2D. The airfoils at three different radial

positions namely 0.25R, 0.35R and 0.6R were chosen. The grid of 280 x 128 cells with 32 cells across the

boundary layer was observed to sufficiently predict the averaged resulting forces of the 2D airfoils. The

distance of the first cell to the airfoil wall was set according to non-dimensional wall distance of y+ value

less than one. Then, the results of the 2D grid independency studies were applied to the 3D blade mesh.

The mesh of the blade is C-H type and was constructed using the commercial grid generator Gridgen with

the ”automesh” script [53] developed at the IAG. The 3D blade mesh quality was maintained as in the

2D grid with y+ < 1. Figure 1a shows the surface meshes and the sectional mesh of the blade used in the

present investigations. Cartesian coordinates (x, y, r) attached to the blade were adopted in this study. The

meshes for the other structures (background, refinement, spinner and nacelle) were constructed by hand using

Pointwise. The meshes were exploited 120-degrees symmetry of the wind turbine rotor by modeling only one

blade, assuming periodicity of the flow from one blade to the other blades. The background domain is 1/3 of

cylinder with periodic boundary condition on the symmetrical sides, while farfield boundary condition were

set on the other sides. The illustration of the grid setup is depicted in Figure 1b.

To show that the 3D CFD solutions are independent of the spatial resolution, 3D grid convergence index

(GCI) studies according to Celik et al. [61] have been performed to quantify the numerical uncertainty. For

this purpose, the studies were conducted at a constant wind speed and rotational speed of 10.5 m/s and

9.02 rpm, respectively, using three different resolutions of the blade mesh. The flow field resulted from these

operating conditions is massively separated in the inboard region that is crucial for the 3D effects. The

centrifugal force has a strong impact within this area by transporting the separated boundary layer to the

outer blade region, creating a strong radial flow component. A strong chordwise flow acceleration occurs as

a response of the flow to the Coriolis force. In addition, it was shown in [35,36] that the lift was significantly

5


higher than in the 2D conditions. The mesh was refined systematically with the refinement factor about 1.4

in radial direction. The blade coarse mesh consists of 136 cells (blade total cells number of 8.1 x 106), medium

mesh of 192 cells (10.9 x 106) and fine mesh of 272 cells (15.9 x 106). The background, refinement, spinner

and nacelle meshes consist of 1.9 x 106, 16.34 x 106 and 3.5 x 106 cells, respectively. They were maintained

constant without refinement. The simulations were run until the wake was fully developed (10 revolutions).

Then, the data were extracted and averaged over additional one revolution. It has been shown in [54,55] that

time-averaging over one revolution is sufficient to capture the general behaviour of the aerodynamic loads at

the inboard and outboard sections of blade for the wind speed of 10.5 m/s and 20 m/s. The results of the

GCI for power and thrust are shown in Table 2. The grid convergence index for the fine grid is very small

(less than 0.5%), stating that the solutions are spatially converged. It can be seen that the values of power

and thrust for the medium and the fine grids are very close. The extrapolated relative errors are less than

0.5% in both parameters, while a higher error is observed for the coarse grid due to inaccurate prediction of

the sectional forces in the blade inboard region as already shown in [35]. It shall be noted that the predicted

(a) Surface mesh and detailed cross-section mesh of the blade (viewed from inboard). Variablesx, y and r represent local coordinate of the blade section in the rotating frame of reference.

(b) Grid setup showing blade (pink); spinner and nacelle (red); refinement (yellow) and back-ground grids (green). Variables X, Y and Z represent coordinate system in the inertial frame ofreference.

Figure 1: Meshes used in the present CFD calculations.

6


r/R [-]

FT

hru

st [

kN

/m]

0 0.2 0.4 0.6 0.8 10.0

2.0

4.0

6.0

8.0

10.0

Coarse

Medium

Fine

(a) Sectional thrust force.

r/R [-]

FT

an

gen

tial [

kN

/m]

0 0.2 0.4 0.6 0.8 1-0.5

0.0

0.5

1.0

1.5

Coarse

Medium

Fine

(b) Sectional tangential force.

Figure 2: Time averaged sectional forces using three different blade meshes. The axial force acts in the samedirection as wind, and the direction of the tangential force is parallel with the rotor rotation creating thedriving moment. The error bars represent the standard deviation of the unsteady fluctuations.

sectional loads (FThrust and FTangential) in Figure 2 for all the grids show a strong fluctuation in the inboard

region. Nevertheless, the time averaged results for the medium and the fine meshes are similar. Furthermore,

it was observed that flow separation resulted from the medium and fine meshes is similar, inferring that 3D

assessment of the rotor using the medium grid is plausible. Detailed discussions of the 3D flow characteristics

will be given further in Section 3.2. Therefore, considering the computational cost and the solution accuracy,

the medium grid was chosen and used in all simulations presented in this paper. The computational effort

required for each 3D rotor computation was 8400 CPUh.

The timestep for the present study is 0.037 s which corresponds to 2 blade revolution per physical

timestep. The solution is marched into a quasi-steady result using 35 sub-iterations. The time integration

was carried out by an explicit hybrid multi-stage Runge-Kutta scheme. A temporal resolution study has

been conducted, and there was no significant change of power, thrust, and sectional loads using the smaller

timesteps [54]. Dual time-stepping according to Jameson [57] with second-order accuracy in time was applied.

Multigrid level 2 and the implicit residual smoothing with variable coefficients according to Radespiel et

al. [58] were used.

2.3 Extraction of the Angle of Attack

To compare 3D and 2D aerodynamic characteristics, the flow condition in both cases must be consistent.

Thereby, the effective angle of attack is a key parameter that needs be considered which is influenced by the

effects of bound circulation and wake, including the shed- and trailing-vortices, inductions. Thus, it cannot

be obtained directly from the blade surface pressure data.

The present study utilized the reduced axial velocity technique (also known as the averaging technique)

employed by Hansen et al. [62], Johansen and Sørensen [33] and Hansen and Johansen [63]. The velocity

was monitored during simulations at two axial positions one upstream and one downstream of the rotor

(see Figure 3a). The extraction plane covers the whole azimuth range of the 120 simulation model, starting

from the center of rotation up to the rotor tip, see Figure 3b. The actual inflow velocity was determined by

considering the decrease of the axial velocity due to the presence of rotor. It was calculated by averaging the

7


(a) Illustration of the thin annular planes for α ex-traction.

(b) Surface monitor covering the blade.

x

y

Vloc

(1-a)U

(1+a’)r

(c) Velocity triangle.

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

2D

3D

0.6R

(d) Comparison of Cp between rotating and non-rotating cases at 60% spanwise location.

Figure 3: Extraction of the angle of attack.

velocity through the azimuth range of -60 to 60 at a given radial position in each monitor plane. Then,

the linear interpolation was used to calculate the velocity in the rotor plane. This method has been coded

at the institute and was tested in [64]. The approach was used by other preceding authors to derive the 3D

characteristics of rotating wind turbine rotor with reasonable results [33,62,63]. Furthermore, Shen et al. [65]

confirmed this by comparing the method with the iterative bound circulation analysis using the Biot-Savart

law they proposed. Similarly, reasonable results were also obtained in [35,36].

The axial distance of the extraction plane was set to 3 times of the local chord length, downstream and

upstream of the rotor (Figure 3a). In the present studies, the velocity distribution was recorded at each

physical timestep (∆t = 2). One blade revolution results in a dataset consisting of 180 different velocity

8


distributions. The angle of attack was calculated as

α = tan−1

(

(1− a)U∞

(1 + a′)rΩ

)

− β, (1)

where a, a′ and β are the axial induction, tangential induction and local twist angle, respectively. Illustration

of the velocity triangle is given in Figure 3c. From the calculated angle of attack, then the lift and drag forces

acting on the blade section can be obtained. This procedure was carried out for each velocity distribution

that, as a consequence, results in 180 different α data. Time averaging was then performed on the results.

To verify the obtained angle of attack, two dimensional simulation of a blade section at r/R = 0.6 was

carried out under the similar inflow conditions (α, Re and Ma). In Figure 3d, the result is compared with

the corresponding 3D sectional data. According to [6, 10, 37], the effect of rotation should be negligible at

this radial position (c/r = 0.07) and the flow is expected to have the 2D characteristics. It is clearly visible

that the pressure coefficient (Cp) distribution of the two cases almost coincides, implying that the angle of

attack extraction is correct.

3 RESULTS AND DISCUSSION

3.1 Comparison with 2D Measurements and other CFD Results

In Figure 4, results of the 2D unsteady CFD simulations are compared with the measurement data obtained

from Rooij [60]. The presented thick aerodynamic profiles are the airfoils constructing the AVATAR blade

as shown in Table 1. The Reynolds number used in the experiment and in the CFD computations is 3.0e6.

The measurements were conducted for tripped conditions and detailed information of the trip locations can

be seen in Figure 4. The transition was prescribed at turbulator position, i.e., turbulence production was

switched on at this location. For the DU 91-W2-250 airfoil, the boundary layer tripping was introduced only

on the suction side at x/c = 5%. The transition location on the pressure side was estimated using XFOIL [66]

for each angle of attack, resulting in 20 different transition location data. For the airfoil with 30% relative

thickness, DU 97-W300 airfoil, the location of trip in the CFD simulation is at the relative chordwise positions

of 5% and 20% on the suction and pressure sides, respectively. The relative thicknesses of the examined thicker

DU airfoils, DU 00-W2-350 and DU 00-W2-401 airfoils, are 35% and 40%, respectively. On these airfoils, the

boundary layer tripping at x/c = 2% and 10% on the suction and pressure sides, respectively, was applied. In

addition to that, CFD computations for fully turbulent boundary layer were also performed for comparison.

The transition location has an influence on the laminar or turbulent separation. As the size of separation

has a strong impact on the 3D effects, it is important to have a clearly defined condition. For instance, it

is shown in Figure 4 that the simulations with prescribed transition predict very similar results as for the

fully turbulent case for all studied airfoils within the linear lift region. This happens because the tripping

location on the suction side is close to the leading edge (≤ 5%). However, in the post stall region the tripping

affects the attained maximum lift and stall angle, especially in Figures 4a and 4b where the transition on

the suction side is located at x/c = 5%. Considering the 3D effects that most likely occur in the post stall

regime, flow transition is an important parameter that needs to be taken into account.

Figure 4a shows the CL polar for the DU 91-W2-250 airfoil with 25% relative thickness. This airfoil is

located at the outer section of the AVATAR blade. A very good agreement compared to the experiment is

achieved for the linear lift region, but the maximum lift coefficient is overpredicted. Figure 4b shows the

prediction for the DU 97-W300 airfoil. The predicted CL almost coincides with the measurements for the

linear region; but similar with the thinner airfoil, the CFD simulation hardly predicts the stall accurately.

9


[°]

CL [

-]

-20 -10 0 10 20-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Exp. 5%SS

CFD 5%SS

CFD Fully Turb.

DU 91-W2-250

(a)

[°]

CL [

-]

-20 -10 0 10 20-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Exp. 5%SS, 20%PS

Exp. 5%SS

CFD 5%SS, 20%PS

CFD Fully Turb.

DU 97-W300

(b)

[°]

CL [

-]

-20 -10 0 10 20-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Exp. 2%SS, 10%PS

CFD 2%SS, 10%PS

CFD Fully Turb.

DU 00-W2-350

(c)

[°]

CL [

-]

-20 -10 0 10 20-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Exp. 2%SS, 10%PS

CFD 2%SS, 10%PS

CFD Fully Turb.

DU 00-W2-401

(d)

Figure 4: Comparison of the 2D CFD simulations with measurement data obtained from [60]. The calculationsand measurements were conducted at Re = 3.0e6. SS and PS indicate the suction and pressure sides,respectively.

Inaccurate results are shown for the nonlinear CL in the post stall regime. However, the general behaviour

of the CL polar is reasonably captured. A greater challenge comes for the calculation of the thicker airfoils

in Figures 4c and 4d. The CL polars greatly show non-linearities and a very sharp change of CL gradient

is shown especially for the DU 00-W2-401 where the relative thickness is 40%. Nevertheless, the CFD

simulations can capture the general behaviour of the polar and the stall angle of the DU 00-W2-401 is

accurately predicted, even though the undershoot is not correctly captured. It shall be noted that for these

airfoils, flow separation occurs already at small angle of attack (even at α = 0) on the pressure side. This

makes the CFD computations hardly predicted the lift polar data as shown in Figure 4c.

The inaccuracy of the CFD predictions within the stall region is already expected as the simulations

employ the URANS method. It was documented in [40,41,67,68] that the simple two-equation eddy viscosity

turbulence models often gave inaccurate results of the airfoil in stalled conditions. Furthermore, simulations

are in two-dimensional configuration and no eddies are resolved, but modeled. Therefore, the choice of the

10


r/R [-]

FT

hru

st [

kN

/m]

0 0.2 0.4 0.6 0.8 10.0

2.0

4.0

6.0

8.0

10.0

Present (URANS)

DTU (RANS)

NTUA (RANS)

(a) Sectional thrust force.

r/R [-]

FT

an

gen

tial [

kN

/m]

0 0.2 0.4 0.6 0.8 1-0.5

0.0

0.5

1.0

1.5

Present (URANS)

DTU (RANS)

NTUA (RANS)

(b) Sectional tangential force.

Figure 5: Comparison of the present simulations with the other CFD results from [47] and a very goodagreement is obtained.

turbulence model can add to the variability of the predicted maximum lift [69].

There is no measurement data available for the AVATAR blade. Hence, a code-to-code comparison was

used in the AVATAR Report 2.3 [47] to verify consistency of the simulations. Figure 5 shows the comparison of

the present CFD simulations with the CFD results from Denmark Technical University (DTU) and National

Technical University of Athens (NTUA) for the wind speed of 10.5 m/s [47]. Description of the codes was

given in the AVATAR Report 2.3 [47]. The CFD results provided by the University of Stuttgart in the

report [47] were steady calculations with coarser mesh, 200 x 140 cells in chordwise and spanwise directions,

respectively. All simulations were carried out using the SST k − ω turbulence model [59] assuming a fully

turbulent boundary layer. The time averaged results of the present calculations agree well with the data

from DTU and NTUA for the sectional thrust (Figure 5a) and tangential forces (Figure 5b). In the figure,

the error bars indicate the standard deviation of the instantaneous fluctuations. For this particular case,

as already mentioned in Section 2.2, a strong radially separated flow was already observed in [35, 36]. The

inboard region is operating in the post-stall condition with α = 16 for r/R = 0.15 and with α = 11.5 for

r/R = 0.2, while the outer part of the blade is in the linear region of the lift curve. Thus, it is challenging

to obtain good agreements in the inboard region of the blade because the flow is massively separated with

a strong unsteady fluctuation.

3.2 3D Effects on Aerodynamic Coefficients

The 3D simulations of the AVATAR rotor have been carried out. The effective angle of attack was evaluated

using the reduced axial velocity method [62] described in Section 2.3. The extracted angle of attack is then

used to calculate the lift and the drag forces based on the calculated total force from the pressure and shear

stress distributions. It should be noted that the resulting forces are very sensitive towards the accuracy of

the effective angle of attack evaluation. The aerodynamic coefficients for the 3D rotating and the 2D non-

rotating cases at six radial positions from the inboard to the outboard sections are compared in Figures 6

and 7 in terms of CL and CD, respectively. The local flow velocity upstream of the rotor, including induction

effects, was used to non-dimensionalize the forces. The black lines represent the 3D case and the red lines

represent the 2D case. Each point of the 3D case in the figure corresponds to different wind speeds. A

11


higher angle of attack was obtained by increasing the wind speed and maintaining rotational speed and pitch

angle to be constant as explained in Section 2. The Reynolds number of the blade sections increases slightly

with increasing wind speed. On the other hand, the 2D simulations were performed at a constant Re. The

magnitude is correlated to the Re of the blade section for the case of U∞ = 10.5 m/s presented in the figure

caption. The difference between Re in the 3D case at maximum α to the 2D case is less than 10%. In the

figures, the horizontal and vertical error bars represent the standard deviation of the unsteady fluctuations

for the angle of attack and lift/drag coefficient, respectively. Large standard deviations in α and CL in the

inboard region at high α show that the case is highly unsteady.

Before discussing the 3D effects, the aerodynamic behaviour of the thick airfoils constructing the AVATAR

blade will be discussed to establish a more credible basis for the subsequent 3D aerodynamics. Especially for

the inboard airfoils where t/c = 0.75 (Figure 6a), 0.57 (Figure 6b) and 0.46 (Figure 6c), the two-dimensional

CL response is complex, and deviates significantly from routinely observed response for more conventional

thinner airfoils like those employed in the outer blade region, Figures 6d - 6f. It can be seen that CL decreases

with increasing angle of attack for a certain range. For the relative thickness of t/c = 0.75, this is observed

up to α = 12. A lesser extent of the phenomenon is shown with decreasing relative thickness. This occurs

within −2 < α < 10 for t/c = 0.57 and within 0 < α < 4 for t/c = 0.46. To study the root cause

of this observation in more detail, distributions of the pressure coefficient for the airfoil with t/c = 0.75

at α = 2 and 10 are presented in Figure 8; where Figures 8a and 8b are for the suction and pressure

sides, respectively. It can be seen that the minimum pressure becomes more positive with increasing α for

the Cp distribution on the suction side. On contrary, Cp becomes more negative on the pressure side for

increasing α. As a result, the lift coefficient reduces significantly for α = 10, even reaches negative value. It

can be seen that even for these small angles of attack, massive separation is observed for both airfoil sides.

This shows that decambering effect is likely to occur, reducing the effectiveness of the airfoil. Furthermore,

the turbulence states of the flow also play an important role. As can be seen in Figure 4, earlier transition

location results in the smaller maximum lift. Considering the simulations were carried out under a fully

turbulent boundary layer, this seems reasonable.

As massive flow separation is observed, a strong 3D effect is likely to occur for this airfoil, even for small

α. Figures 8c and 8d show the Cp distributions of the same airfoil extracted from the rotating blade. Two

angles of attack that are comparable with the 2D conditions are shown. It can be seen that the minimum

Cp becomes more negative with increasing α on the suction side, and more positive with increasing α on the

pressure side. As a result, the lift coefficient increases within this α range creating a big difference between

the 2D and 3D CL slopes. In Figure 9, the velocity fields around the airfoil for the 2D and 3D conditions

are shown. It can be seen that separation is delayed remarkably in the 3D condition. The size of separation

and negative streamwise velocity areas become smaller. The displacement effect borne out mainly by the

thickness of the boundary layer reduces for the rotating blade. In Figure 9, the vertical displacement of

the separation area relative to the trailing edge position is indicated by H (for 2D) and H2 (for 3D). It is

shown that H2 is significantly smaller than H, see Figures 9a and 9b. As a result, the decambering effect

that is strongly dependent upon the thickness of the boundary layer displacement is weaker than in the

2D case. The shallower separation area is caused by the effect of the centrifugal pumping that transports

the separated flow towards the blade outer area. This causes a boundary layer thinning that enhances the

stability of the flow towards separation [10]. The Coriolis force acts in chordwise direction and helps the flow

to overcome the adverse pressure gradient, delaying the occurrence of separation in both airfoil sides. The

latter was shown by Du and Selig [10] to have a stronger impact for the separation delay than the centrifugal

pumping. In addition, it exist a smaller secondary vortical structure in the 3D case close to the beginning of

separation point that is not observed for the 2D condition (Figure 9c). This small structure is created due

12


[°]

CL [

-]

-10 0 10 20 30 40-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.15R

(a) t/c = 0.75, 2D Re = 7.1e6.

[°]

CL [

-]

-10 0 10 20 30 40-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.20R

(b) t/c = 0.57, 2D Re = 9.2e6.

[°]

CL [

-]

-10 0 10 20 30 40-0.5

0.0

0.5

1.0

1.5

2.0

0.25R

(c) t/c = 0.46, 2D Re = 11.3e6.

[°]

CL [

-]

-10 0 10 20 30 40-0.5

0.0

0.5

1.0

1.5

0.35R

(d) t/c = 0.36, 2D Re = 14.2e6.

[°]

CL [

-]

-10 0 10 20 30 40-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.60R

(e) t/c = 0.25, 2D Re = 17.6e6.

[°]

CL [

-]

-10 0 10 20 30 40-0.5

0.0

0.5

1.0

1.5

2.0

2.5

2D

3D

0.95R

(f) t/c = 0.24, 2D Re = 14.2e6.

Figure 6: 3D and 2D CL polars. Variable t/c represents the relative thickness. 3D CL is remarkably higherthan in the 2D conditions, except near the tip region.

13


[°]

CD [

-]

-10 0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

0.15R

(a) t/c = 0.75, 2D Re = 7.1e6.

[°]

CD [

-]

-10 0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

0.20R

(b) t/c = 0.57, 2D Re = 9.2e6.

[°]

CD [

-]

-10 0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

0.25R

(c) t/c = 0.46, 2D Re = 11.3e6.

[°]

CD[-]

-10 0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

0.35R

-2 0 2 4 6 8 10

0.02

0.04

(d) t/c = 0.36, 2D Re = 14.2e6.

[°]

CD[-]

-10 0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

0.60R

0 2 4 60.01

0.012

0.014

(e) t/c = 0.25, 2D Re = 17.6e6.

[°]

CD[-]

-10 0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

2D

3D

0.95R

-4 -2 0 2 4 6 8 100.01

0.015

0.02

0.025

(f) t/c = 0.24, 2D Re = 14.2e6.

Figure 7: 3D and 2D Cd polars. Variable t/c represents the relative thickness. 3D Cd is smaller than in the2D conditions in general. It is higher than in 2D case near the tip and at high angle of attack in the inboardregion.

14


x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-3.0

-2.0

-1.0

0.0

1.0

2°

10°

2D

0.2R

SS

(a) 2D SS.

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-3.0

-2.0

-1.0

0.0

1.0

2°

10°

2D

0.2R

PS

(b) 2D PS.

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-3.0

-2.0

-1.0

0.0

1.0

2.13°

11.25°

0.2R

3DSS

(c) 3D SS.

x/c [-]

Cp [

-]

0 0.2 0.4 0.6 0.8 1

-3.0

-2.0

-1.0

0.0

1.0

2.13°

11.25°

0.2R

3DPS

(d) 3D PS.

Figure 8: Time averaged Cp distributions of the 2D and 3D simulations at two different angles of attack. Inthe 2D case, Cp decreases on the pressure side and increases on the suction side at a higher angle of attack,marking the occurrence of the decambering effect. This is not observed in the 3D case.

to the 3D response of the chordwise flow acceleration by the Coriolis force. It can be seen that the direction

of the vortex is counter-clockwise, which implies that the near wall flow is not separated even though the

surrounding global flow feature is within the separated area.

In the inboard region of the blade, a strong augmentation of CL caused by the 3D effects is observed. The

lift stall is remarkably delayed in the 3D case compared to the 2D case. It is qualitatively in a good agreement

with the Himmelskamp effect [1], where the 3D lift increases due to the centrifugal pumping and the Coriolis

force [10, 31]. This observation confirmed the conclusion of the preceding studies [26, 35, 36, 38, 42, 44, 45]

that rotational augmentation was not hindered by the size of the blade. Figure 6a presents the CL polar

for the blade section at r = 0.15R. The relative thickness of the airfoil is 75%. At this position, the 3D CL

has a remarkably higher value than the 2D CL and this is observed also for the other radial positions up

to r = 0.35R (Figure 6d). In the middle section of the blade, the rotation shows smaller influence so that

the CL polars in both cases are close to each other, Figure 6e. When approaching the tip (r = 0.95R), the

opposite effect on the lift is observed. The lift reduces compared to 2D values and the reduction increases

with the angle of attack, which may indicate the rise of the tip loss with increasing wind speed (decreasing

TSR). However, it should be kept in mind that this behaviour may also originate from the inaccuracy of the

angle of attack extraction close to the tip because the wake expansion and distinct tip vortex are not well

represented using the averaged method [33]. On the other hand, the most outward region examined (r/R =

0.95) is still within the unaffected area of the strong wake expansion. Thus, the use of the averaging method

is still plausible. In addition, it was observed that α increased close to the tip [36] that indicates the tip loss

15


(a) 2D. (b) 3D. (c) Enlarged view of 9b.

Figure 9: Time averaged relative streamwise velocity field near the airfoil section. The velocity is non-dimensionalized by the local kinematic velocity. Separation area is significantly reduced,H2 < H and L2 < L.The area of the negative streamwise velocity (blue color) is remarkably smaller in the 3D case.

plays a major role, i.e., smaller extracted energy from the wind.

In Figure 7, the effect of rotation on Cd is shown. The drag is influenced by the 3D effects for all examined

radial positions. It is shown that 3D Cd is lower than the 2D case, except for r = 0.15R and r = 0.2R at

high α; and also for r = 0.95R for all studied α. Near the tip, the drag augmentation in Figure 7f may be

associated with the tip loss as also presents for the lift coefficient. The drag increase in the inboard region is

expected to stem from the downwash phenomenon. This will be described further in Section 3.3.

The drag reduction at the blade inboard section agrees well with the assumption made by Du and

Selig [9,10] regarding drag decrease in their 3D correction model [9]. The delay of separation which is mainly

caused by the Coriolis acceleration was identified as the main actor behind the phenomena. Contradicting the

present observation, the results from the NREL UAE Phase VI wind turbine showed that the rotational effect

was accompanied by a significant drag increase [31,33]. According to Lindenburg [70], the drag increase might

be associated to the energy needed for the radial pumping. On the other hand, the results of the MEXICO

measurements showed that the drag was not severely affected by the rotational effect. Guntur et al. [34]

tested several correction models for drag on the MEXICO rotor, showing that the 3D correction for drag

might be unnecessary. This study was confirmed by Herraez et al. [28] who studied the same turbine. They

claimed that the 3D effect for drag might be airfoil type dependent because the drag decrease was observed

for the MEXICO rotor at a radial station of 0.6R but did not occur at the inboard stations because different

airfoils were used; the DU91-W2-250 airfoil at r = 0.25R and r = 0.35R, and the RISØ-A1-21 airfoil at

r = 0.6R [28]. Because the uniqueness of the rotational augmentation for drag, a careful selection of the 3D

correction models should be taken into account. Therefore, it is clear that the drag correction models which

assume the drag increase, i.e., [43, 70, 71], should not be applied for the AVATAR blade, instead suggesting

the drag correction models proposed by Du and Selig [9] or Corrigan and Schillings [72].

Additionally, at r/R = 0.15 and 0.2, the 2D drag slightly decreases with increasing angle of attack around

0 < α < 10. It is caused by reduction of the separation zone within the rear-pressure side of the airfoil (see

Figure 9a for illustration) which contributes to drag. With increasing α, separation point on the pressure

side is shifted further downstream as can be depicted from the Cp distribution in Figure 8a. Furthermore,

smaller pressure side loading is observed for higher α which decreases the axial force, relative to the chord

line, of the airfoil that results in the further drag reduction.

16


r/R [-]

[m

2/s

]

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250

300

(a) Circulation.

r/R [-]

CD [

-]

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

U = 10.5 m/s

U = 15 m/s

U = 20 m/s

(b) Drag coefficient.

Figure 10: Time averaged circulation and drag coefficient distributions over the blade radius. A local increaseof the bound circulation is observed in the inboard region which is expected to cause the downwash.

3.3 Bound Circulation along the Blade Radius

It is worthwhile to mention again that the rotational speed and pitch angle were kept constant in this

study to artificially generate stronger separation at higher wind speed cases. This was done to study the 3D

aerodynamic characteristics at the inboard blade region which is strongly influenced by separation. In this

section, the bound circulation distribution of the blade is evaluated. This was calculated by Γ = 0.5cCLVloc,

where CL is obtained from the averaging technique explained in Section 2 and Vloc is the local flow velocity

including wake induction. The characteristics of the bound circulation over the blade radius is expected as

the cause of the local drag increase at radial stations of r = 0.15R and r = 0.2R at high α in Figures 7a and

7b.

Distributions of the averaged bound circulation for three wind speeds are plotted in Figure 10. The

circulation shows local increase or decrease near the root region. Any variation in the radial circulation

causes the trailing vortices, depicted in Figure 11a, which has an induction effect on the blade. The trailing

vortices plot is colored by the vorticity in Y -direction to roughly visualize the direction of the vortex. These

trailing vortices are the consequence of flow separation in the inboard region. Some distinct trailing vortices

are observed in the inboard blade region. Relating Figure 10 with Figure 11 leads to an expectation that a

strong downwash is likely to occur in between these vortices due to the variation of their direction, see the

direction of the arrow in Figure 11c. These vortices grow with increasing wind speed that can be inferred as

the downwash also. It is shown that the vortex system is weak and not dominant for U∞= 10.5 m/s, but it

becomes noticeably stronger for U∞= 25 m/s, see Figure 11. This is supported by the experimental studies

on a model rotor by Akay et al. [73, 74], which showed that the root vortices are more concentrated for the

blade operating at a smaller tip speed ratio (higher wind speed).

A more detailed explanation of this behaviour is elaborated through the radial circulation distribution

in Figure 10a. It can be seen that around the radial location of 17%, there is a local increase of the bound

circulation, indicated by a solid vertical line. The total induction at this location is influenced by the total

trailing vortices along the blade radius. The effect depends on the radial gradient of the circulation and its

distance to the reference position. In Figure 10b, the radial distribution of the drag coefficient is shown. It

can be seen that the two counter-rotating vortices in the inboard/outboard of the Γ peak induce a downwash

17


(a) (b)

(c)

Figure 11: Trailing vortices in the inboard region of the blade illustrated by Q-Criterion colored by Y -vorticity [1/s]. The inboard vortex system becomes stronger with increasing wind speed, showing distinctcounter-rotating trailing vortices which induces downwash.

at the peak location, locally increasing pressure drag higher than the 2D condition. Consistent with the

observation for the trailing vortex system in Figure 11 and circulation distribution in Figure 10a, the drag

augmentation is more pronounced at higher wind speed as the downwash is stronger.

In addition, the fact that these inboard regions use very thick airfoils with the maximum thickness

more than 40% leads to expectation that this phenomena might be associated with massive flow separation

and unsteady characteristics, compared to the usual downwash near the tip that is more steady. Further

investigation in this regard is necessary to quantify the interaction between the trailing vortices (due to

spatial gradient) and the shed vortices (due to temporal gradient).

3.4 Coriolis and Centrifugal Forces

In 3D rotor aerodynamics, there are complex radial flow characteristics that are influenced by many aspects,

among them are the radial pressure gradient due to the difference of the local flow velocity and airfoil shapes,

viscous effect, and also the Himmelskamp effect [1] governed mainly by the Coriolis and centrifugal forces. In

this section, quantification of the Coriolis and centrifugal forces is given. The ratio of these forces (η), that are

acting in orthogonal direction, indicates the angle of the resulting force (~F = ~FCoriolis+ ~Fcentrifugal) from the

blade axis. This resulting force will be called as the Himmelskamp force in this paper. In the extreme case: η

= 0 means that the resulting Himmelskamp force acts solely in positive radial direction; η → ∞ means that

the Himmelskamp force is solely in chordwise direction which results in a strong streamwise flow acceleration.

The relative magnitude of the forces can yield information about the impact of three-dimensionality of the

18


boundary layer. In this analysis, the ratio of these forces is weighted by the Rossby number defined as:

~FCoriolis

~Fcentrifugal

1

Ro=

−2(

~Ω× ~V)

~Ω×(

~Ω× ~r)

Ωc√

U2∞

+ (Ωr)2, (2)

where ~Ω is the rotational speed, ~r is the distance of the specific point to the center of rotation and ~V is the

fluid velocity in the rotating frame of reference. Ro is the Rossby number defining the ratio between the

inertial force to the Coriolis force. In this case, Ro is included, instead of only the Coriolis to centrifugal ratio

as used in [36], because variation of the wind speed produces variation in the inertial force as suggested by

Dumitrescu and Cardos [13]. In this parameter, the chord to radius ratio introduced by Snel et al. [11, 12]

is implicitly included as the local solidity (r/c). For a better insight about this, the reader is suggested to

refer to reference [13]. They also used the similar force ratio, in which the ratio of the centrifugal to Coriolis

forces was employed, implicitly included in the Rossby number. The results for three different wind speeds

are plotted in Figure 12 for the wind speeds of U∞ = 10.5 m/s (12a - 12c), U∞ = 15 m/s (12d - 12f) and

U∞ = 25 m/s (12g - 12i). Three different radial stations are evaluated, namely 0.15R, 0.2R and 0.35R.

In Figures 12a, the contour of η for the wind speeds of U∞ = 10.5 m/s at r/R = 0.15 is shown. It

can be seen that the magnitude of η reduces with increasing radial distance, as shown in Figures 12b and

12c. Similarly, this effect is also observed for the other studied wind speed cases of U∞ = 15 m/s and 25

m/s. This shows that the acting angle of the resulting acceleration, combination of the centrifugal and the

Coriolis forces, is larger approaching the root region. The affected region of the Coriolis force, defined by

parameter η enlarges with increasing size of separation. It seems that the angle is strongly controlled by

the parameter c/r. In the inboard region, where c/r is large, the flow within the separated area is radially

outward that leaves the centrifugal force influence in the separated region small, especially close to the line

of separation. Please note that the centrifugal force is felt only when the the flow has a curvature about

the rotational axis, i.e., when the cross product of the blade radius vector (~R) to the flow component is not

zero (~R× ~V 6= 0). As the flow close to the line of separation (in the inboard region) is radial, the centrifugal

force becomes reasonably smaller. On the other hand, the Coriolis force becomes stronger with increasing

c/r [11, 12]. As a result, this force determines the flow field close to the root in which the acceleration due

to the Himmelskamp effect acts mainly in chordwise direction. Thus, separation is delayed mainly by the

Coriolis force and slightly by the centrifugal effect. This physical behaviour might be the reason why Du and

Selig [10] observed that the Coriolis force is more dominant for separation delay.

With increasing wind speed, the angle of attack increases accordingly. It can be seen that the size of

separation is larger for the wind speeds of 15 m/s and 25 m/s compared to U∞ = 10.5 m/s. As the first

thought, one might think that stronger separation will lead to the stronger Coriolis effect. However, this is

not necessarily true for all cases. It is clearly shown that the η alleviates for the larger wind speeds. This

confirms the conclusion made by Du and Selig [10] regarding to the weakening of the separation delay at

higher wind speeds. In addition, the higher angle of attack (for the higher wind speed case) leads to a shif

of the region with a strong Coriolis acceleration (denoted by the red arrow) further upstream. It is logic

because separation point also moves further upstream. It supports the evaluation of banks and Gadd [5] and

McCroskey and Yaggy [6] that the radial flow is strongest in the beginning of separation.

Figure 13 shows the profile of η, w/Vkin and u/Vkin extracted from Figure 12. The location is at an

arbitrary position, x = 1 m, at different blade radii on the suction side of the airfoil. The magnitude of the

presented velocities are normalized by kinematic velocity and y is normalized by the boundary layer thickness

(δ) for a better comparison between different wind speed cases. The error bars indicate the standard deviation

19


(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 12: Time averaged ratio between the Coriolis to the centrifugal forces weighted by the Rossby numberat some selected inboad stations (0.15R, 0.2R and 0.35R) and for three different wind speeds: 10.5 m/s(12a-12c), 15 m/s (12d-12f) and 25 m/s (12g-12i). η decreases with radial distance and wind speed whileit is strongest incipient of the separation point. The red arrow indicates the area with a strong Coriolisacceleration.

of the instantaneous fluctuation. It can be seen clearly that the fluctuation becomes stronger for the higher

wind speed case.

In the outer boundary layer regime, it is shown that η → 0 which indicates that the Coriolis force is

negligible, supporting the discussion given above. In Figure 13a, it can be seen that the acceleration angle

increases closer to the wall. This implies that the viscous 3D effects act only within the boundary layer.

The maximum η magnitude near the wall decreases with increasing radial distance, e.g., from 0.65 for

r/R = 0.15 to 0.245 for r/R = 0.25. It can be also seen that η near wall reduces for the higher wind speed

cases. Interestingly, the strength of the reduction becomes more noticeable for the smaller radial position.

However, the opposite phenomenon is observed at larger y/δ, where η enhances with increasing wind speed.

These effects are explained in the following discussion.

Outside of the negative streamwise velocity area, the region above the shaded-green mark, the increasing

20


[-]

y /

[-]

-0.25 0 0.25 0.5 0.75

0.0

0.5

1.0

1.5

0.15R

(a)

[-]y

/ [

-]-0.25 0 0.25 0.5 0.75

0.0

0.5

1.0

1.5

0.20R

(b)

[-]

y /

[-]

-0.5 -0.25 0 0.25 0.5 0.75

0.0

0.5

1.0

1.5

0.25R

(c)

w/Vkin

[-]

y /

[-]

-0.5 0 0.5 1

0.0

0.5

1.0

1.5

0.15R

(d)

w/Vkin

[-]

y /

[-]

-0.5 0 0.5 1

0.0

0.5

1.0

1.5

0.20R

(e)

w/Vkin

[-]

y /

[-]

-0.5 0 0.5 1 1.5

0.0

0.5

1.0

1.5

0.25R

(f)

u/Vkin

[-]

y /

[-]

-0.5 0 0.5 1

0.0

0.5

1.0

1.5

0.15R

(g)

u/Vkin

[-]

y /

[-]

-0.5 0 0.5 1

0.0

0.5

1.0

1.5

0.20R

(h)

u/Vkin

[-]

y /

[-]

0 0.5 1

0.0

0.5

1.0

1.5

0.25R

(i)

Figure 13: Time averaged profiles at some selected inboard stations for η (13a-13c), w/Vkin (13d-13f) andu/Vkin (13g-13i). Solid line: U∞ = 10.5 m/s, dashed line: U∞ = 15 m/s and dashed-dot line: U∞ = 25 m/s.

21


wind speed reduces the streamwise flow but increases the radial velocity component. This is caused as the

response of the 3D boundary layer toward the change of the chordwise pressure gradient. As the angle of

attack increases (higher wind speed), the increasing pressure gradient alleviates the streamwise momentum

of the flow. This causes the boundary layer to be more sensitive toward changes of the flow condition. The

centrifugal force and the radial pressure gradient are believed to act within this area, creating a positive

radial velocity component. As a consequence, the lower magnitude of the streamwise velocity results in the

stronger radial flow.

In the near wall region, marked by the shaded-green area, the viscous effect due to friction and the

chordwise pressure gradient are strong. The latter makes the boundary layer in the detached flow situation.

This is supported by the the profiles of w/Vkin and u/Vkin in Figure 13. The radial velocity deficit increases

with increasing U∞. For example, in Figure 13d, the near wall radial flow is significantly lower for the wind

speed of 25 m/s than the other wind speed cases, similar with the η characteristics. This characteristic is

expected to arise due to the viscous losses. On the other hand, no much impact for the various studied

wind speeds on the near wall profile of the streamwise velocity, except for the radial position of 0.25R where

the larger wind speed shows stronger near wall velocity profile. The latter phenomenon is expected due to

the local effect of the secondary vortex as illustrated in Figure 9c. This behaviour is shown also for the

larger radial positions. It is worthwhile to mention again that the radial velocity is normalized by kinematic

velocity. The absolute velocity for the higher wind speed case was observed to be stronger.

Snel et. al. [11,12] mentioned that 3D correction models often overpredict the magnitude of CL at large

c/r because the models did not properly consider the viscous losses. In Figure 13, the viscous losses for the

radial flow are clearly shown and, thus, need to be taken into account in 3D correction models. The fact that

the losses become stronger for the smaller radial position leads to a thinking that this may be related to

increasing angle of attack and airfoil thickness. It shall be noted that the studies for 3D effects were usually

limited to moderate relative thickness that the viscous losses could be negligible.

4 CONCLUSION

Three-dimensional Computational Fluid dynamics simulations have been carried out to study the occurrence

of rotational augmentation for a 10 MW wind turbine rotor. The AVATAR turbine was selected and studied

for 5 different wind speeds from the attached to stalled flow conditions. Unsteady Reynolds-Averaged Navier-

Stokes computations were performed employing the eddy-viscosity two-equation Menter SST turbulence

model.

First, 2D simulations of the airfoils constructing the AVATAR blade are carried out. The results are

compared with available measurement data which indicates that the prediction of the lift polar is accurate

within the linear lift region, but overestimates the maximum lift coefficient. However, the general behaviour

of the lift polar is captured. There is no significant difference between the fully turbulent to the prescribed

transition calculations because the boundary layer tripping, specified in the experiment and CFD, is very

close to the leading edge especially in the linear lift regime. In the post stall region, earlier transition location

reduces the maximum attained lift coefficient. This shows that the consideration of the transition location

is important for the 3D effect studies because the rotational augmentation is strongly influenced by the size

of separation. After performing the 2D preliminary studies, the CFD calculations of the AVATAR blade are

performed at a selected wind speed for the grid and consistency examinations of the numerical simulations.

The results are compared with other CFD computations obtained from literature. An excellent agreement

is obtained in the predicted sectional loads.

With regard to 3D effects, the lift coefficient (CL) augmentation at the blade inboard region is observed

22


even though the studied blade sections consist of very thick airfoils with the maximum thickness more

than 40%. The 3D effects are observed to modifies the aerodynamic characteristics of the blade section

where remarkably higher lift slope is observed in 3D case. This is caused by the effects of the Coriolis and

centrifugal forces that delay the occurrence of separation and reduces the boundary layer thickness and the

size of separation area. Particularly with the thinner boundary layer, the rotation of the rotor seems to

alleviate the decambering effect, modifying the Cp distribution significantly.

The drag coefficient (CD) decreases compared to the 2D simulations due to 3D effects while it increases

at certain radial positions for high angle of attack. The local drag augmentation is associated with the

downwash occurring in the root region of the blade. It is observed that the root vortex system consist of

counter-rotating trailing vortices which becomes stronger for the higher wind speed case. At this location, a

local-distinct increase of the bound circulation is marked and accordingly the drag augmentation.

The quantification of the Coriolis to centrifugal forces (η) weighted by the Rossby number is presented.

The ratio of the forces describes the angle of the resulting 3D rotational forces, which can yield information

about the shear stress and boundary layer structure. Near the root region close to the line of separation,

the flow is radially outward which implies that the centrifugal force is small as the streamwise velocity

component approaching zero. On contrary, this area is strongly influenced by the Coriolis force, and moves

further upstream for the higher wind speed case. It is shown that η and the radial flow decrease with increasing

wind speed and radial position, especially near the wall. On the other hand, the reduction of η with increasing

wind speed occurs only adjacent to the wall but it is opposite for the rest of the boundary layer area. The

reduction of the radial flow near the wall is associated with the viscous losses due to frictional forces. On the

rest of boundary layer area, the 3D response of the flow is strongly characterized by the pressure gradient.

This implies that a stronger reduction of the chordwise flow momentum results in the stronger radial flow,

caused by the radial pressure gradient and the centrifugal force.

For future studies, the following aspects of the 3D effects can be considered. In developing 3D correction

models, the present observation of the viscous losses can be useful. The consideration of this particular issue

may improve predictions of the rotor performance in the extreme root region. Studies on interaction between

the viscous 3D rotational effects and the 3D inviscid flow on the boundary layer edge are suggested. This is

important since the 3D flow characteristics are already complex for the inviscid flow, and the viscous effect

is the response of the inviscid condition. By doing so, it may be possible to draw in more detail about the

mechanism of the 3D effects.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge these following institutions for the supports: Ministry of Research, Tech-

nology and Higher Education of Indonesia for the funding through Directorate General of Higher Education

(DGHE) scholarship, the AVATAR project for a good cooperation by providing the blade geometry and

test cases necessary for the study, the High Performance Computing Center Stuttgart (HLRS) for providing

computational time in the CFD simulations.

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