STALL AIRFOILS SMALL WIND TURBINES

1

Stall and Pos-Stall of airfoils for small wind turbines: Numerical and Experimental Analysis Antonio G. Lopes1, Jorge A. V. Alé2, Almerindo D. Ferreira1, Gabriel da S. Simioni2, Vinicius K. Calgaro2 1 Department of Mechanical Engineering, University of Coimbra, Coimbra, Portugal 2 CE-EOLICA Wind Energy Center, Pontifícia Universidade Católica do Rio Grande do Sul, Porto Alegre, Brazil email: antonio.gameiro@dem.uc.pt, villar@pucrs.br , almerindo.ferreira@dem.uc.pt, simioni@pucrs.br.

ABSTRACT: Experimental and numerical results are presented for the aerodynamic coefficients of the NACA 0012 and NACA 0018 airfoils. Numerical tests include different turbulence models and advection schemes, using three software packages: EasyCFD_G, OpenFOAM and ANSYS Fluent. The obtained CFD simulations show that predictions of the aerodynamic coefficients agree very well with experimental data at low angles of attack. Limitations of the simulations are shown for airfoils operating at high angles of attack. An interesting bifurcation phenomenon was detected in the near post-stall region, with two numerical solutions for the flow: a steady and an unsteady solution. In the post-stall region, both drag and lift are overestimated for unsteady solutions.

KEY WORDS: Airfoils; Small Wind Turbines; CFD; Wind Tunnel Data.

1

INTRODUCTION

Wind turbines rotor blades are designed to optimize the energy captured from the wind. Most computer codes used to determine the aerodynamic performance of wind turbines are based on the blade element theory (BEM), which requires data of airfoils lift (CL) and drag (CD) coefficients. When blades operate at low angles of attack, numerical simulation is able to correctly reproduce experimental CL and CD values. However, when the angle of attack reaches, or exceeds, the stall angle, there is a wide divergence of computational results when compared with experimental results. Moreover, the vast majority of experimental data pertains conditions of interest for aviation industry, namely high Reynolds number and low angles of attack.

Efforts have been made by the wind industry to overcome these shortcomings, providing available data specific to wind rotors airfoils. Yet there are other limitations when working with wind turbine airfoils. The rotor blades of large turbines can operate in the Reynolds range of 2×106 to 6×106. However, small wind turbines operate in the Reynolds range of 5×104 to 5×105. In both cases, the available information is still limited to experimental results mostly in post stall region. These challenges have motivated the use of CFD models using the RANS equations to predict the aerodynamic coefficients of airfoils for wind turbines. Despite several efforts, there is a wide divergence of results mainly in the post stall. This paper aims to contribute to this research, presenting CFD results for the flow around the NACA 0012 and NACA 0018, obtained with EasyCFD_G [1] software, with OpenFOAM [2] and with ANSYS Fluent [3] software and comparing with experimental data.

2

THEORETICAL BACKGROUND

2.1

Basic transport equations

For present simulations, the Navier-Stokes equations are considered using a transient 2D form:

∂ ( ρu )

+

r  ∂  ∂ ∂ ∂  ∂u 2 ρu2 + ( ρ uw ) = Γ  2 − divV   + Γ ∂x ∂z ∂x  ∂x 3  ∂ z 

∂ ( ρ w)

+

∂ ∂ ∂  ( ρuw) + ρ w2 = Γ ∂x ∂z ∂z

∂t

∂t

(

)

(

)

r  ∂   ∂w 2  2 ∂ z − 3 divV   + ∂ x Γ   

 ∂ u ∂ w  ∂ p  ∂ z + ∂ x  − ∂ x  

 ∂ u ∂ w  ∂ p  ∂ z + ∂ x  − ∂ z  

(1)

(2)

where p is pressure and Γ is the total viscosity, which includes the contributions of the dynamic and turbulent components Γ , i.e. Γ = µ + µt . The three unknowns u, w, and p in these equations need the mass conservation equation to close the problem:

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

2

∂ρ ∂ ∂ + ( ρ u ) + ( ρ w) = 0 ∂t ∂ x ∂z

(3)

The turbulent viscosity µt is solved with the turbulence model. Both k-ε and the SST turbulence models were used in the present work. A brief description of both models is given next.

2.2

The k-ε turbulence model

The standard formulation of the k- ε model is described in [4]. The turbulent viscosity is given by:

µ t = Cµ

ρk2 ε

(4)

The turbulence kinetic energy, k, and its dissipation rate, ε, are computed with the following transport equations:

∂ ( ρk )

+

∂ ( ρε )

+

∂t

∂t

µ ∂ ∂ ∂  ( ρuk ) + ( ρ wk ) =  µ + t ∂x ∂z ∂ x  σk

 ∂ k  ∂  µt  µ +  + σk  ∂ x  ∂ z 

∂k   + Pk − ρε  ∂ z 

µ  ∂ε  ∂  µ  ∂ε  ε ∂ ∂ ∂  ( ρuε ) + ( ρwε ) =  µ + t   +  µ + t   + ( C1Pk − C2 ρε ) ∂x ∂z ∂ x  σε  ∂ x  ∂ z  σε  ∂ z  k

(5)

(6)

where Pk is the production rate of k as the result of the velocity gradients:

2 2   ∂u  2  ∂w   ∂u ∂w   + + Pk = µ t  2   + 2       ∂z   ∂z ∂x     ∂x 

(7)

The remaining model constants are:

σ k = 1.0

Cµ = 0.09 2.3

σ ε = 1.3

C1 = 1.44

C2 = 1.92

(8)

The k-ω SST turbulence model

The SST model [5] represents a combination of the k-ε and the k-ω models, taking benefit of the advantages of each of these models. The k-ω model is more accurate near the wall but presents a high sensitivity to the ω values in the free stream region, where the k-ε model shows a better behavior. The SST model blends the k-ε and the k-ω by using a weighting factor based on the nearest wall distance. The governing equations are: ∂ ( ρk ) ∂t

+

∂(ρ u k)

∂(ρω ) ∂t

∂x

+

+

∂ ( ρ wk )

∂ (ρ uω ) ∂x

+

∂z +

= Pk − β * ρ ω k +

∂ ( ρ wω ) ∂z

=

∂  ∂k ∂ ∂k ( µ + σ k µt )  +  ( µ + σ k µt )  ∂x  ∂x  ∂z  ∂z 

(9)

∂  ∂ω ∂ ∂ω ( µ + σ ω µt )  +  ( µ + σ ω µt )  +  ∂x  ∂x  ∂z  ∂z 

α Pk 1  ∂k ∂ω ∂k ∂ω  − β ρ ω 2 + 2 ( 1 − F1 ) ρ σ ω 2  + νt ω  ∂x ∂x ∂z ∂z 

(10)

where ω is the frequency of dissipation of turbulent kinetic energy [s-1]. The production of turbulent kinetic energy is limited to prevent the build-up of turbulence in stagnant regions: Pk = min ( Pk , 10 β * ρ k ω )

(11)

The weighting function F1 is given by:

   k 500ν  F1 = tanh min  max  ; 2  β * ω y y ω    

 4 ρ σ ω 2 k     ; 2  CDkω y  

  1 ∂k ∂ω CDkω = max  2 ρσ ω 2 , 10−10    ω ∂x j ∂x j  

4

    

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

(12)

(13)

3

where y represents the distance to the neighbour wall and ν is the laminar kinematic viscosity. F1 is zero away from the wall (k-ε model) and changes to unit inside the boundary layer (k-ω model). The turbulent viscosity is given by: νt =

a1 k max ( a1 ω ; S F2 )

where S represents the invariant measure of the strain rate:

S = Sij Sij

;

Sij =

(14)

1  ∂ui ∂u j +  2  ∂x j ∂xi

  2 k 500ν  F2 = tanh   max  ;  β *ω y y 2 ω   

    

2

   

(15)

   

(16)

The constants are computed as a blend of the k-ε and the k-ε models, through the following generic equation: α = F1 α 1 + (1 − F1 ) α 2

(17)

The constants are α1 = 5/9; β1 = 3/40; σk1 = 0.85; σω1 = 0.5; α2 = 0.44; β2 = 0.0828; σk2 = 1; σω2 = 0.856; β* = 0.09.

3

NACA 0012 AIRFOIL

Figure 1 shows the computational domain around the airfoil. Its dimensions were adjusted so as to ensure that effects from the upstream, downstream and lateral boundaries are negligible. For the inlet boundary, a 5% turbulence intensity was assigned.

Lateral boundaries were assigned a free slip flow condition. After mesh independence tests, a total of approximately 130 000 control volumes were employed, as shown in Figure 1 for simulations with EasyCFD_G. Three mesh refinement regions were adopted around the airfoil, as a solution to provide a better resolution in the regions of interest without sacrificing too much computational resources. Near the airfoil surface, an inflation layer of nearly structured elements was used, with and height of 0.00015 m (for an airfoil cord length of 0.33 m). This allowed, typically, y+ values at the airfoil surface ranging from 0.1 to 6 with an average value of 1.7.

Figure 1. Domain chord dimensions and non-structured quadrilateral mesh detail of NACA 0012 airfoil.

Simulations were carried out for Reynolds numbers of 6×106 and 7×105. Although the first Reynolds number is too high for small wind turbines operating conditions, this case was taken as a test for drag and lift computations, for comparison with data available in the literature.

Figure 2 shows the dependence of the lift coefficient with the airfoil angle of attack α., for Re=6×106. Both the SST and the kε (Ke) turbulence models were used in these simulations; the influence of the the advection scheme was tested using the SST model. Experimental data is reported by Abbot and Doenhoff [6], and by Ladson [7] for the same Reynolds number. It is apparent that CFD results, produced by both turbulence models, are quite similar and agree very well with experimental data up

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

4 to separation, which presents its onset at α = 16 º . The two advection schemes give similar results up to separation, after which the lift drop in the stall region is more pronounced with the hybrid model. Separation is completely established at α = 18 º and for α ≥ 20 º the flow becomes unsteady, showing periodic oscillations on both aerodynamic coefficients. For the transient regime, presented data corresponds to average values over the oscillation period. It may be seen that data in the stall region is quite spread. It is recognized in the literature that it is difficult to obtain reliable experimental data in this region, due to the unsteady characteristics of the flow and tendency to present a 3D behavior.

2,0

NACA 0012 Re=6.000.000 1,8

Abbot and Doenhoff (Untripped) Ladson (Tripped)

Lift Coefficient - CL

1,5

EasyCFD_G (Quick SST) EasyCFD_G (Hybrid SST)

1,3

EasyCFD_G (Quick Ke)

1,0

0,8

0,5

0,3

0,0 0

2

4

6

8

10

12

14

16

18

20

Angle of attack (degrees)

Figure 2. Lift coefficient vs angle of attack. NACA 0012 airfoil. Re=6×106.

0,20

NACA 0012 Re=6.000.000 0,18

Abbot and Doenhoff (Untripped)

Drag Coefficient - CD

0,16

Ladson (Tripped) EasyCFD_G (Quick SST)

0,14

EasyCFD_G (Hybrid SST) EasyCFD_G (Quick Ke)

0,12 0,10 0,08 0,06 0,04 0,02 0,00 0,0

0,3

0,5

0,8

1,0

1,3

1,5

1,8

2,0

Lift Coefficient - CL

Figure 3. Drag coefficient vs lift coefficient. NACA 0012 airfoil. Re=6×106.

The relation between the drag and the lift coefficients is shown in Figure 3. It is interesting to note that deviations from experimental data are substantially larger for the k-ε model, certainly because the friction component plays an important role in drag and thus, correctly resolving the boundary layer is crucial for the drag computation. It is also interesting to notice that the advection scheme plays a very important role, with the higher order scheme QUICK showing much better agreement when compared with the experimental data.

Since, from previous results, it is evident that the SST turbulence model coupled with the high order QUICK scheme represents the best modelling solution, these numerical options were used when computing the aerodynamic coefficients for the same airfoil at a range of angles of attack between 0º and 90º, for a Reynolds number of 7×105. Experimental data are reported

by Timmer [8]. Results presented in Figure 4(a) show that, in what concerns lift, the agreement is very good up to the minimum lift on the stall region, even for the unsteady regime that is verified for angles larger than 18º. Lift coefficient is considerably

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

5 overestimated for large angles of attack, especially in the range 30º < α < 70º . One can, nevertheless, also conclude that drag is overestimated as well, since the ratio of lift to drag, presented in Figure 4(b), agrees very well with experimental data.

The unsteady regimen is characterized by the alternate release of vortices, under a complex pattern that depends on both the Reynolds number and angle of attack. This leads to a time evolution of drag and lift, with local minimum and maxima that are not temporally coincident. Figure 5 shows the time evolution of lift and drag for 45º angle of attack and Figure 6 depicts the flow visualization for the situations of maximum and minimum drag for the same angle of attack.

1,6

2,5

NACA 0012

NACA 0012

Lift to Drag Relation CL/CD

Lift Coefficient CL

1,4 1,2 1,0 0,8 0,6 0,4

Timmer Re=730.000

0,2

EasyCFD_G ( SST)

Timmer Re=730.000

2,0

EasyCFD_G ( SST)

1,5

1,0

0,5

0,0 0

15

30

45

60

75

0,0

90

15

30

Angle of attack (degrees)

45

60

75

90

Angle of attack (degrees)

Figure 4. Aerodynamic coefficients for 90º angle of attack range. (a) drag coefficient; (b) lift /drag.

2

2,0

1,8

1,8

1,6

1,6

1,4

1,4

1,2

1,2

Lift Coefficient CL

1,0

Drag Coefficient (CD)

Lift Coefficient (CL)

NACA 0012 Re=700.000

1

Drag Coefficient CD 0,8

0,8 3,0

3,2

3,4

3,6

3,8

4,0

4,2

4,4

Time t [s]

Figure 5: Time evolution of lift and drag coefficients for 45º angle of attack.

(b)

(a) Figure 6: Flow visualization for 45º angle of attack: (a) maximum drag; (b) minimum drag.

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

6

4

NACA 0018 AIRFOIL

4.1 Experimental results without blockage corrections In the experimental component of this study, the pressure distribution on the airfoil surface was obtained through measurements in a wind tunnel with 1 m2 squared test section. A 900 mm wide NACA 0018 profile, with a cord length of 300 mm was tested. In order to minimize 3D effects, two acrylic plates were placed at both ends. In the airfoil surface, 29 pressure taps were uniformly distributed and connected to a multi column water manometer using silicon tubes. Tests were performed at an undisturbed speed of 20 m/s, 25 m/s and 29 m/s, corresponding to a Re=400.000, Re=500.000 and Re=580.000. Figure 7 shows a schematic view of the wind tunnel, along with the manometer and the airfoil model. The aerodynamic forces, corresponding to each angle of attack, were obtained by integrating the measured pressure distribution. The first tests were performed for an angle of attack ranging from 0 to 35°. The obtained results (without blockage corrections), shown in Figure 8, are compared against the experimental data of Jacobs and Sherman [9]. The lift coefficient presently obtained shows a similar lower slope in the linear region when compared with the reference data by Jacobs and Sherman [9]. A delayed stall (α = 20°) is observed in the present data as relative to the reference data (α = 15°). The obtained value for the maximum lift coefficient (CLmax= 1.03) is also lower than the reference value. The next section presents a methodology for correction of blockage effects in the wind tunnel as well as three-dimensional effects of the end plates used in the blade span.

Figure 7. Wind tunnel at the CE-EOLICA; cross test section is 1.0 m × 1.0 m.

1,5 NACA 0018

1,4 1,3 1,2

Lift Coefficient

1,1 1,0 0,9 0,8 0,7 0,6 0,5 CE-EOLICA Re=500.000

0,4

CE-EOLICA Re=400.000

0,3

CE-EOLICA Re=580.000

0,2

NACA-586 Re=650.000

0,1

NACA-586 Re=1.200.000

0,0 0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34 36 Angle of attack

Figure 8. CE-EOLICA results for the lift coefficient without blockage corrections.

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

7

4.2 Blockage Correction (Bidimensional Flow).

The confinement of a model within the wind tunnel test section modifies the flow by changing the pressure and the velocity field around the body. As a result, the aerodynamic forces are also changed and should be corrected to represent a twodimensional flow field. The presence of the body produces two effects on the flow field: one is due to the body physical interference, by reducing the flow area (solid blockage); the other is caused by the interference of the wind tunnel walls with the vortex wake behind the body (wake blockage). For airfoils, the latter effect is increased with the angle of attack. Both effects can be corrected with recourse to appropriate equations, such as described by Barlow et al [10]. This methodology is briefly described next. A blockage coefficient is defined as:

ε = εs +εw

(18)

where εs is the solid blockage, which depends on the body volume. For the case of airfoils, it is a function of the airfoil thickness (t), of the airfoil chord (c) and of the wind tunnel test section height (h). The solid blockage is computed as the product of the wind tunnel blockage factor (Λ) and model blockage factor (σ), as described in Barlow et al [10]. The term εw represents the wake blockage and depends on the geometric relationship between the airfoil chord and the wind tunnel test section height. The wake growth and its effect are quantified as function of the drag coefficient, which is determined in wind tunnel tests.

Taking into account these corrections, the following equations (Table 1) are used, considering the sub index "u" as indicating variables measured in the wind tunnel without correction and the sub index "c" as representing the variables after applying the corrections. In Table 1, a summary of the used equations is presented. The term ∆α, in his table, is the correction coefficient for the angle of attack. Some approaches, such as the Maskell method (see Barlow et al [10]), include loss effects due to separation (stall) in the blockage coefficient of Eq.18, which is considered as a three-dimensional type correction. In the present work, three dimensional effects are included through the equations by Fuglsang et al [11] (see below).

Table 1. Equations for blockage correction.

Velocity

Reynolds number

Vc = Vu (1 + ε )

Re c = Re u (1 + ε )

Angle of attack

α c = α u + ∆α

Lift coefficient

Drag coefficient

CLc = CLu (1 − σ − 2ε )

CDc = CDu (1 − 3ε s − 2ε w )

4.3 Correction for Three Dimensional Effects A finite span airfoil (3D) generates tip vortices, leading to induced velocities. The airfoil theory shows that this effect increases the aerodynamic drag and reduces the curve slope for CL versus α. This effect is quantified as a function of the aspect ratio (AR=b2/A), blade span (b) and its projected area (A). To minimize three dimensional effects, end plates are applied to blades when used in wind tunnel tests. However, end blades cause aerodynamic losses, which should be quantified and included in corrections. The work by Fuglsang et al [11], taking as reference the method by Mangler [12], proposes equations for a correction of the angle of attack and drag coefficient, for a finite length blade with end plates. According to this method, the angle of attack and the drag coefficient are corrected with the following equations:

α = αt −

k C Lt 2 AR

C D = C Dt − where

k C Lt2 2 AR

(19)

(20)

α t is the measured angle of attack (in wind tunnel), C Lt is the measured lift coefficient, C Dt is the measured drag

coefficient and AR is the aspect ratio. The coefficient k, which depends on the end plates height and on the blade span, is obtained from Figure 11, in Mangler [12]. The blade element used in the tests features a chord c = 400 mm and a wingspan b = 900 mm. The end plates have diameter D = 400 mm. Corresponding to these dimensions, the rectangular blade element has an aspect ratio AR = 3, and k = 0.53. Accordingly, the experimental results presented hereafter are corrected using equations in Table 1, exception made to the angle of attack and drag coefficient, which are corrected by Eq. 19 and Eq. 20, respectively.

4.4 Results Using Blockage Correction and Three Dimensional Effects Figure 9 shows the uncorrected and the corrected (for blockage and for three dimensional effects) results of CL versus α, for the NACA 0018 profile under the test conditions (for Re = 580.000). This figure also presents experimental data by Jacobs and Scherman [9], for Re = 654.000.

It may be observed, in this figure, that the corrected lift coefficient shows a drastic drop in its magnitude. Furthermore, the lift curve slope increased, resulting in a better agreement with the benchmark curve slope. Figure 9 also shows that, when compared with the benchmark (reference) results of Jacobs and Scherman [9], the stall delay is practically eliminated. The main differences of the corrected curve, when compared to the reference, occur for α > 200. In this case, the CL results obtained by the

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

8

corrected curve are smaller than the reference values. When applying the correction equations, it was verified that the slope change in the pre-stall region is due to the correction for three-dimensional effects on the end plates, which is in accordance with the experimental data reported by Reddy et al [13]. On the other hand, the decrease in the magnitude of the aerodynamic lift in post-stall region is consequence of the correction for the wake blockage. Figure 10 shows the final result of this analysis, comparing the experimental reference results (Re = 654.000) and the corrected results obtained from three laboratory experiments carried out at the CE-EOLICA, with different Reynolds numbers.

1,4

NACA 0018 CE-EÓLICA (Blockage and 3D corrections)

1,2

Lift Coefficient - CL

1,0

0,8

0,6

0,4 CE-EOLICA Re=580.000 (Corrections) NACA REPORT 586 Re=654.000

0,2

CE-EOLICA Re=580.000 0,0 0

5

10

15

20

25

30

Angle of attack

Figure 9. CE-EOLICA results for the lift coefficient without blockage and 3D corrections.

1,4 1,2

NACA 0018 CE-EÓLICA (Blockage and 3D corrections)

Lift Coefficient - CL

1,0 0,8 0,6 CE-EOLICA Re=580.000

0,4

CE-EOLICA Re=500.000 CE-EOLICA Re=480.000

0,2

NACA REPORT 586 Re=654.000

0,0 0

5

10

15

20

25

30

Angle of attack

Figure 10. CE-EOLICA results for the lift coefficient with blockage and 3D corrections.

4.5 Comparison between Experimental and Numerical Results The setup for the numerical simulation of the NACA 0018 airfoil reproduces the conditions at the wind tunnel of the CEEOLICA. For that purpose, a rectangular domain was setup, with top and bottom straight walls, 22 cords long. As for the NACA 0012 case, a sufficiently refined mesh was employed, with particular care on the refinement near the airfoil region. Simulations were done with the available 3 software packages: OpenFOAM, ANSYS Fluent and EasyCFD_G. Although the basic models were the same in all these software packages, namely the turbulence model (SST) and advection scheme (QUICK), differences exist in what concern discretization details and numerical solution procedures. For EasyCFD_G, the SIMPLEC algorithm is adopted, while for ANSYS-Fluent both SIMPLEC and Coupled algorithms were used. For OpenFOAM, the SIMPLE solver was adopted for low angles of attack, while PISO was selected for higher angles. Figure 11 shows the meshes used for each software

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

9

package. Mesh size and arrangement are not strictly similar for the three cases, but are equivalent in terms of mesh independency. OpenFoam uses a particularly interesting arrangement, with Cartesian-like elements away from the boundaries.

In this package, refinement is achieved with subdivisions of the original elements. As shown in Figure 11(b), in the neighborhood of boundaries, an inflation layer is adopted, in a similar way as to EasyCFD_G and ANSYS Fluent.

(a) Computational mesh airfoil NACA 1008 using EasyCFD_G

(b) Computational mesh airfoil NACA 0018 using OPENFOAM

(c) Computational mesh airfoil NACA 1008 using ANSYS FLUENT Figure 11. Domain chord dimensions reproducing the CE-EOLICA wind tunnel Figure 12 depicts the obtained computational results for the lift coefficient, compared with the experimental data. The flow is attached up to α = 10º. Separation occurs quite gradually, with stall starting to occur for α = 14º. Up to stall, numerical results slightly over predict lift, when compared to experimental data. After stall, OpenFOAM results agree well with experiments up to α = 22º, while the remaining models predict a much larger stall, with corresponding lift loss. Up to α = 18º, the flow occurs in steady state regime. For larger angles of attack, an interesting bifurcation phenomenon is verified in the simulations, leading to either an unsteady solution with larger lift values, or a steady solution with smaller lift values. This bifurcation was verified with both Fluent and EasyCFD_G. Concerning Fluent, the steady or the unsteady solution is obtained depending on whether the

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

10

pressure-velocity coupling algorithm is Coupled or SIMPLEC, respectively, while the EasyCFD_G solution (either steady or unsteady) depends on the time step historical. For all these cases, the solvers were run using a transient approach. Figure 13 shows a typical example of how the bifurcation problem occurs in EasyCFD_G. Using a small time step of 0.0001 s, the unsteady solution shows the oscillation of CL over time. Changing the time step to 0.0005 s, the solution changes into steadystate, with the corresponding lowering of CL. After attaining the steady-state solution, switching back to a smaller time step does not produce any further changes. A similar behavior is verified in Fluent: after running the Coupled solver to get the steady-state solution, switching back to SIMPLEC does not change the solution. The differences in the flow pattern for the steady-state and the transient solutions may be appreciated in Figure 14, for EasyCFD_G results at α = 20º. The steady-state solution shows a closed separation bubble with no flow oscillations downstream (Figure 14a), while, for the transient solution (Figure 14b), the recirculation bubble moves along the airfoil surface, producing an oscillation pattern in the downstream region.

1,4

NACA 0018 (CFD results Re=500.000)

1,2

Lift Coefficient - CL

1,0

0,8

0,6 EasyCFD_G (Unsteady) EasyCFD_G (Steady)

0,4

OpenFOAM Fluent (Unsteady) Fluent (Steady)

0,2

Jacobs e Scherman Re=650.000 CE-EOLICA Re=580.000

0,0 0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

Angle of attack (degree)

Figure 12. Lift coefficient vs angle of attack. NACA 0018 airfoil.

0,00140

1,4

Time step Lift Coefficient (CL)

0,00100

Time step [s]

1,2 1

0,00080

0,8

0,00060

0,6

0,00040

0,4

EasyCFD_G NACA 0018 (Re=500.000 ) Angle of atack : 22 degree

0,00020

0,2

0,00000

0 0,4

0,6

0,8

1,0

1,2

1,4

Time [s]

Figure 13. Evolution of lift coefficient with changing time step.

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

1,6

Lift Coefficient

0,00120

11

(a) Steady-state solution

(b) transient solution

Figure 14. Flow visualization. NACA 0018 airfoil at α = 20º. Re=5×105.

5

CONCLUSIONS AND FUTURE RESULTS

CFD simulations for the NACA 0012 airfoil show that predictions of the aerodynamic coefficients agree very well with experimental data at low angles of attack. Limitations of simulations are shown for airfoils operating at high angles of attack. In such region, both drag and lift are considerably overestimated, although the ratio of lift to drag agrees well with reference experimental data.

For the NACA 0018 airfoil, surface pressure distribution was measured in wind tunnel and compared with reference results for angles attack ranging from 0° to 35°. Experimental data was obtained from the aerodynamic coefficients by applying corrections to take into account wind tunnel blockage effects and three-dimensional effects of the end plates. Applying these corrections, a significant improvement was observed for the comparison with reference results. Further tests with other airfoils are needed to validate this methodology.

Experimental results for the NACA 0018 were also used to compare the performance of different software packages. Some differences were found in the simulations using different packages, and none of them has shown to produce better results than the others. For large angles of attack, two types of solution were found, indicating the presence of a bifurcation problem. Further investigation will be undertaken in order to better understand differences between simulations and experimental data. The identified bifurcation problem will also be further investigated.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

A.M.G. Lopes, EasyCFD_G user’s manual. http://www.easycfd.net., 2015 http://www.openfoam.org. http://www.ansys.com.

BE Launder and DB Spalding (1972). Mathematical Models of Turbulence, Academic Press London and New York, JP Van Doormaal and GD Raithby (1984). Enhancements of the Simple Method for Predicting Incompressible Fluid Flows, Numerical Heat Transfer, 7, 147-163.

Abbott IH and Doenhoff AE von (1959). Theory of Wing Sections, Dover Publications, New York.

Ladson C.L. (1988). Effects of Independent Variation of Mach and Reynolds Numbers on the Low-Speed Aerodynamic Characteristics of the NACA 0012 Airfoil Section, NASA TM 4074, October 1988.

Timmer WA (2010). Aerodynamic characteristics of wind turbine blade airfoils at high angles-of-attack, TORQUE 2010: The Science of Making Torque from Wind, June 28-30, Crete, Greece Jacobs E.N., Sherman A. (1937) Airfoil Section Characteristics as Affected By Variations of the Reynolds Number, Report No. 586 Barlow J.B., Rae W.H. Pope A. Low-Speed Wind Tunnel Testing. John Wiley & Sons Inc. 1999. 3a Edition.

Fuglsang P., Antoniou I., Sørensen N. N, Madsen H. A. Validation of a Wind Tunnel Testing Facility for Blade Surface Pressure Measurements. Risø-R-981(EN). Risø National Laboratory, Roskilde. April 1998 Mangler, W, The Lift Distribution of Wings with End Plates, NACA. NACA Technical Memorandum No. 856, Washington, April 1938.

Reddy K. S. V., Sharma D. M., Poddar K. Effect of End Plates on the Surface Pressure Distribution of a Given Cambered Airfoil: Experimental Study. Pág. 286 on New Trends in Fluid Mechanics Research (Zhuang and Li). Proceedings of the Fifth International Conference on Fluid Mechanics (Shanghai), 2007.

14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015