**UFRJ**

# 02 Para Gleici - item5-04

(Parte **2** de 2)

According to Logsdon (2006), the use of 2-D and 3-D models under the same simulation conditions showed very similar results. This makes valid the use of 2-D models, since they are more simplified and consumes less time and processing that 3-D models. Therefore, in this study we used the 2-D model to represent the physical phenomenon in airfoil S809.

The mesh has high importance in a FLUENT analysis. The quality of the elements will influence in the accuracy and stability of the simulation. Thus it is essential to check the quality of the mesh used.

In meshes generated by ICEM-CFD, assessing the quality of the elements can be done through the tool "Quality

Histogram". There, a scale from 0 to 1 is established, 0 is the worst quality and 1 the best one (FLUENT Database), and the number of elements per quality range is displayed. The minimum quality of a mesh should be greater than 0.3 to perform a simulation. In this study the quality of the elements, as shown in FIG. 2 was 0.9 (Skewness) and an aspect ratio less than 100, which features a mesh with good quality.

The influence of mesh refinement were used as output data Cl, Cd, Cp, residue and the historic convergence of these parameters. The residue scale for the mesh shown in Fig. 2 was of the order of 10-6.Then, they were compared with the data of Fig. 5. Although these results have been presented for Re = 75,400 and 134,500 it was realized a qualitative similarity to the data of Fig. 5. Figures 3, 4, and 5 show the drag ( ) and lift coefficients ( ) derived from Equations (4) and (5), respectively:

where is the drag force in Newtons, is the specific weight of the air in kg/m3, and is the platform area of the S809 airfoil in meters. This area is the product of the chord times the wingspan, as described by (Campos et al., 2014).

where is the lift force in Newtons. Standard κ-omega (κ-ω) and realizable (κ-ϵ) turbulence models.

23rd ABCM International Congress of Mechanical Engineering December 6-1, 2015, Rio de Janeiro, RJ, Brazil

Figure 3 (a,b) shows the drag (Cd) and lift (Cl) coefficients as a function of the angle of attack α in degrees, for a

Reynolds number (Re) of 75,400 using the realizable (κ-ϵ) and standard κ-omega (κ-ω) turbulence models, respectively.

Figure 3 (a) shows an increase in Cd when α is increased in both models. The maximum and minimum values for

Cd in the standard κ-omega (κ-ω) model were 0.14 and approximately 0.04, respectively. Likewise, the maximum and minimum values for Cd in the realizable (κ-ϵ) model were 0.1 and 0.02, respectively. Differences were generally observed between the analyzed turbulence models.

Figure 3 (b) illustrates a similar pattern, in which the slope of the lift coefficient (Cl) was close to 15o in the standard κ-omega (κ-ω) model. The slope in the realizable (κ-ϵ) model could not be clearly established. The slope observed in the standard κ-omega (κ-ω) model characterizes stall, or loss of lift from the S809 airfoil.

This slope can also be seen in Fig. 5 (b) for experimental results and in the numerical results described by (Gharali and Johansen, 2012, adapted).

The boundary layer separates at an angle of attack α = 15o; therefore, the realizable (κ-ϵ) model did not suffice to illustrate such slope.

(a) | (b) |

Figure 3. Drag (a) (Cd) and lift (b) (Cl) coefficients for a Reynolds (Re) number of 75,400

Figure 4 (a,b) shows the drag (Cd) and lift (Cl) coefficients as a function of the angle of attack (α) in degrees for a

Reynolds (Re) number of 134,500 using the realizable (κ-ϵ) and standard κ-omega (κ-ω) turbulence models, respectively. The Figure also reveals that closer results were obtained from the studied turbulence models as Re increased. The models also produced closer results for angles ranging between 0 and 8o, but Fig. 4 (b) shows that the realizable (κ-ϵ) model failed to elicit the slope at 15o.

(a) | (b) |

Figure 4. Drag (a) (Cd) and lift (b) (Cl) coefficients for a Reynolds (Re) number of 134,500

Figure 5 (a,b) shows the drag (Cd) and lift (Cl) coefficients as a function of the angle of attack (α) in degrees for a

Reynolds (Re) number of 106 using the realizable (κ-ϵ) and the SST-κ-omega (κ-ω) turbulence models, respectively. This Figure shows the experimental and numerical results published by Gharali and Johansen (2012).

João C.G.J., Julio C.C.C., Álvaro M.B.T., Henrique M.P.R., Matheus M.B., Antônio C.A, Rogério F.B. and Pedro C.T S809 Airfoil: Reynolds Number Effect on the Aerodynamics of Wind Turbine Blades

(a) | (b) |

Figure 5. Drag (a) (Cd) and lift (b) (Cl) coefficients for a Reynolds (Re) number of 106, (Gharali and Johansen, 2012, adapted)

A comparison between Fig. 4 (a,b) and Fig. 5 (a,b) reveals that the results of the standard κ-omega (κ-ω) and SST-κomega (κ-ω) turbulence models drifted away from the results of the realizable (κ-ϵ) model, while the values for drag and lift coefficients remained quite close to each other. The numerical results seen in Figure 5 (a,b) were close to the observed experimental results.

Figure 6 shows the lift-to-drag ratio (Cl/Cd) as a function of the angle of attack (α) in degrees for Reynolds (Re) numbers of 75,400 and 134,500 using the realizable (κ-ϵ) model and the standard κ-omega (κ-ω) model. This figure illustrates a design point called the drag polar, a point at which the Cl/Cd ratio reaches its maximum value. It may be referred to as (Cl/Cd)max or maximum efficiency, Emax.

Figure 6. Lift-to-drag ratio (Cl/Cd)

Figure 6 shows that the lift-to-drag ratio reached its peak value when α = 8o for all studied Reynolds numbers and turbulence models. This is the angle at which horizontal axis wind turbines reach their maximum efficiency.

This point represents the angle of attack at which it is possible to maintain maximum lift with minimum drag, and significantly affects airfoil performance and the design of wind turbine blades.

The ratio increased as flow velocity increased, and reached its maximum for Re = 134,500 and Cl/Cd ≈ 32 and 2 in the realizable (κ-ϵ) and the standard (κ-ω) models, respectively.

Figures 7 to 10 show the velocity (m/s) and static pressure (Pa) contours for Re = 75,400 and 134,500 at α = 4o and 15o for the realizable κ-epsilon (κ- ϵ) model, respectively.

In profiles inclined at a positive angle in relation to the direction of airflow, air particles reach higher velocities in the upper surface of the profile when compared to the lower surface, thus generating a static pressure differential between the upper and lower surfaces and creating a lift force.

In the figures with α = 4o, the boundary layer was kept close to the S809 airfoil wall and tended not to separate from it, thus providing a favorable pressure gradient. For α = 15o, the boundary layer separated and vortices formed in the trailing edge, thus producing an adverse pressure gradient. The separation point moved toward the leading edge of the S809 airfoil and the separation bubble covered almost the entire surface of the airfoil. In such conditions stall sets in, lift is lost and aerodynamic drag increases.

23rd ABCM International Congress of Mechanical Engineering December 6-1, 2015, Rio de Janeiro, RJ, Brazil

(a) | (b) |

Figure 7. (a) Velocity (m/s) and (b) static pressure (Pa) contours for α = 4o; Reynolds number: 75,400; realizable (κϵ) model

(a) | (b) |

Figure 8. (a) Velocity (m/s) and (b) static pressure (Pa) contours for α = 15o, Reynolds number: 75,400; realizable (κ-ϵ) model

(a) | (b) |

Figure 9. (a) Velocity (m/s) and (b) static pressure (Pa) contours for α = 4o, Reynolds number: 134,500; realizable (κ-ϵ) model

João C.G.J., Julio C.C.C., Álvaro M.B.T., Henrique M.P.R., Matheus M.B., Antônio C.A, Rogério F.B. and Pedro C.T S809 Airfoil: Reynolds Number Effect on the Aerodynamics of Wind Turbine Blades

(a) | (b) |

Figure 10. (a) Velocity (m/s) and (b) static pressure (Pa) contours for α = 15o, Reynolds number: 134,500; realizable (κ-ϵ) model

4. CONCLUSIONS

The aerodynamic characterization of airfoil profiles should include smaller angles of attack, particularly of 20 degrees. Aerodynamic performance may be significantly affected, as important drag and lift forces act on the airfoil in this angle of attack range. This was described by Zhou, et al. 2011.

The point of maximum efficiency of the S809 airfoil used in the blades of horizontal axis wind turbines was reached when α = 8o.

The S809 airfoil stalled when the angle of attack was set in the region of 15o to 16o, which is the angle formed between the fluid stream and the chord. Stall reduces the efficiency of wind turbine blades. At this angle of attack turbulence forms and flow separates, leading to the formation of whirling masses of fluid called vortices behind the rotor of the wind turbine. This phenomenon was observed for Re = 75,400 and 135,400 and for α ≈ 15o-16o.

The turbulence models used in this study – the realizable (κ-ϵ) and the standard κ-omega (κ-ω) models – yielded results in agreement with the literature. However, the standard κ-omega (κ-ω) model presented more efficient results near the wall, while the realizable (κ-ϵ) model produced more efficient results far from the wall.

Stall should be avoided in the design of horizontal axis wind turbines. Stalling wind turbines lose torque. However, in high winds this characteristic may be needed to control the velocity and output of a wind turbine. In this context, blades with good stall characteristics should be picked.

5. ACKNOWLEDGEMENTS The authors would like to thank FAPEMIG for financial support provided.

6. REFERENCES

Campos, J. C. Costa, Gomes, A.O., Brito, R.F., Rosa, H.M.P., Tibiriça, A.M.B. and Treto, Pedro C., 2014.

“Experimental analysis of an S809 airfoil”. Thermal Engineering, Vol. 13, p. 28-32.

Cebeci, T., Shao, J.P., Kafyeke, F. and Laurendeau, E., 2005. Computational Fluid Dynamics for Engineers. Springer,

Long Beach, California.

Fadigas, E. and Amaral, A. F., 2011. Energia Eólica. Manole, São Paulo. FLUENT Database, 2011. ANSYS 14.0 Help User's guide. Fortuna, A. de O., 2000. Técnicas Computacionais para Dinâmica dos Fluidos - Conceitos Básicos e Aplicações.

Edusp, S.P.

Freire, A.P.S., 2002. Coleção Cadernos de Turbulência. Vol. 1. ABCM, Rio de Janeiro. Ghia, U., Ghia, K.N. and Shin, C.T., 1982, “High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method”. Journal of Computer Physical, Vol. 48, p. 387-411.

Gharali, K. and Johnson, D.A., 2012. “Numerical modeling of an S809 airfoil under dynamic stall, erosion and high reduced frequencies”. Applied Energy, Vol. 93, p. 45-52.

Huang J.-C, Lin H. and Yang, J.-Y, 2009, “Implicit preconditioned WENO scheme for steady viscous flow computation”. Journal of Computational Physics, Vol. 228, p. 420-438.

Logsdon, Nathan. 2006. A procedure for numerically analyzing airfoils and Wing sections. University of Missouri, Columbia.

23rd ABCM International Congress of Mechanical Engineering December 6-1, 2015, Rio de Janeiro, RJ, Brazil

Moshfeghi, M., Song, Y.J. and Xie, Y.H., 2012, "Effects of near-wall grid spacing on SST-K-ω model using NREL

Phase VI horizontal axis wind turbine". Journal of Wind Engineering and Industrial Aerodynamics, Vol. 107-108, p. 94-105.

Neto, A.S., 2002. Coleção Cadernos de Turbulência. Vol. 1. ABCM, Rio de Janeiro. Troldborg, Niels., 2013. Experimental and numerical investigation of 3D aerofoil characteristics on a MW wind turbine,

Roskilde, Denmark.

Zhou, Y., Md., Mahbub, Alam, Yang, H. X., Guo, H. and Wood, D. H., 2011, “Fluid forces on a very low Reynolds number airfoil and their prediction”. In Proceedings of Schulich School of Engineering, University of Calgary, Canada.

7. RESPONSIBILITY NOTICE The authors are the only responsible for the printed material included in this paper.

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