02 Para Gleici - item5-04

02 Para Gleici - item5-04

(Parte 1 de 2)

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


João C. Gaigher Junior Julio Cesar C. Campos Álvaro M. Bigonha Tibiriça Henrique M. Pereira Rosa

Matheus M. Beraldo Universidade Federal de Viçosa – Departamento de Engenharia de produção e Mecânica. Rua PH Rolfs s/n joao.gaigher@ufv.br julio.campos@ufv.br alvaro.tibirica@ufv.br henrique.rosa@ufv.br matheus.beraldo@ufv.br

Antônio Carlos de Andrade Universidade Federal de Minas Gerais – Departamento de Engenharia Mecânica. Av. Antônio Carlos, 6627 andrade@demec.ufmg.br

Rogério Fernandes Brito Universidade Federal de Itajubá – Campus Avançado de Itabira. Rua Irmã Ivone Drumond, 200, Distrito Industrial I rogbrito@unifei.edu.br

Pedro Casanova Treto Universidad de Costa Rica – Instituto de Investigaciones en Ingeniería – INII. San Pedro de Montes de Oca pcasanova2000@gmail.com

Abstract. The objective of this work is to study the S809 airfoil profile used in the wind turbine blades of horizontal axis. Wind turbines developed rapidly in technological terms, showing reliability in generating energy from the wind. The methodology employed was the aerodynamics characterization from simulations on CFD to get the parameters such as lift, the drag coefficient, the relationship between lift and drag, speed, and the pressure contours for different angles of attack. Simulation results using ANSYS FLUENT® v16.1 presented important features. The focus was in the study of Reynolds numbers of about 75,400 and 134,500, using the turbulence model κ-omega (κ-ω) Standard and model (κ-ϵ) realizable. Stall has been noticed from 15°, where verify the detachment of the boundary layer, as well as, the effect of pressure through the speed contours and the simulated pressure for this angle of attack. The blade inclination of wind turbines are important when the design of such turbines is analyzed. Concludes that numerical study of the airfoil S809 served to characterize the aerodynamic profile of the blades of horizontal axis wind turbines.

Keywords: aerodynamic coefficients, numerical simulation, turbulence model, S809 airfoil


Wind turbines were first used to produce electricity in the twentieth century, in response to accelerated economic growth and increased power consumption. Nowadays wind energy is highly desirable for being a non-polluting and theoretically inexhaustible mode of power generation. Another relevant factor is the strong ecological appeal present in the wind energy generation, often listed as a requirement in current projects.

A class of lower-upper symmetric Gauss-Seidel implicit weighted essentially non oscillatory (WENO) schemes was developed by Huang, et al., 2009 for solving the preconditioned Navier-Stokes equations of primitive variables with Spalart-Allmaras one-equation turbulence model. The computations are performed for the two-dimensional lid driven cavity flow, low subsonic viscous flow over S809 airfoil, three-dimensional low speed viscous flow over 6:1 prolate spheroid, transonic flow over ONERA-M6 wing and hypersonic flow over HB-2 model. The viscous flow over S809 airfoil was considered at moderate angle of attack (AOA). The S809 airfoil was designed specially for horizontal-axiswind-turbine (HAWT) applications. The thickness ratio of the airfoil is 21%. A 600 m chord length model of the S809 airfoil has been tested in a 1.8 m x 1.25 m low turbulence wind tunnel (Ghia, et al., 1982). Four grid systems of C-type topology are generated for grid-independency testing. The grid points are 185 x 49, 273 x 73, 409 x 109 and 601 x 145 from coarse to fine grid system, and there are 137, 207, 321 and 481 points on airfoil surface, respectively, and the outer boundary for all four grid systems is about 20 chord lengths away from airfoil. The free stream Mach number is 0.001,

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

Reynolds number is 2 x 106 and AOA is 9.22º. For all the cases computed, the solutions of the present algorithms are in very good agreement with the available experimental data. Investigation of the effects of near-wall grid spacing for the SST-κ-omega (κ-ω) model and study of the aerodynamic behavior of a horizontal axis wind turbine are the two goals of the Moshfeghi, et al. 2012s paper. The National Renewable Energy Laboratory (NREL) Phase VI is used as the aerodynamic model. Eight different cases are investigated for the near wall grid spacing study. Furthermore, one case is studied in both the SST-κ-omega (κ-ω) and the Langtry-Menter transitional models. For all cases the total number of nodes are fewer than 5,0,0. The results of this paper lead us to a general understanding about the wind turbine blade aerodynamics. Thrust forces, flow patterns and pressure coefficients are compared at different wind speeds. The thrust values of the SST-κ-omega (κ-ω) are not in a good agreement with the test results. The streamlines show that the inboard section of the blade has a severe complex 3D flow which separates at low velocities; the mid-span section stays attached for higher velocities and the outboard part has 2D-like behavior and separates as the last part. Besides, it is observed that Gamma-Theta transitional model behaves differently from the SST-κ-omega (κ-ω), especially at the inner part and the results are closer to the test results.

Airfoil aerodynamics research appears to be more concentrated on conventional aircraft design with Reynolds numbers above 5 x 105 and below stall conditions.

Countless aerodynamic profiles have been proposed as a result of the intense efforts made by the scientific community to improve the efficiency with which wind power is used. However, special attention is required when the S809 airfoil is considered, as it has been designed to operate in turbines at low speeds.

In this context the development of an experimental project on the S809 airfoil is justified. The main purpose is to assess airfoil aerodynamic performance at various angles of attack.

Therefore, justified the development of a project for the numerical study of the S809 airfoil, primarily used in horizontal wind turbine blades to meet the aerodynamic behavior for different angles of attack and Reynolds numbers of about 75,400 and 134,500, using the turbulence model κ-omega (κ-ω) Standard and model (κ-ϵ) realizable.


The first step of the numerical solution involves the description of the physical phenomenon, i.e., the physical variables acting on and affecting the physical system (Fortuna, 2000). Then a numerical model has to be designed with equations of conservation of mass, momentum, and energy that are valid within a given domain. The domain must be clearly defined in order for the numerical solution to accurately represent the analyzed flow conditions.

The analysis included variables pressure, velocity, and other parameters related to these variables as observed in an

S809 airfoil. Software package ANSYS FLUENT® v16.1 was used to produce a physical representation of the flow patterns over an S908 airfoil. Control volumes are cell-centered in this code, whereas on the CFX code control volumes are node-centered.

The computational method used in this code is the finite volume method. This discretization scheme uses conservation equations in integral form. Cebeci, et al., 2005 presented a generic conservation equation in integral form as follows:

where ∭ Ω represents the integral form of unknown control volume variable , ∬ ⃗. ⃗ is the integral form of flow vector ⃗ on the control surface, ∭ is the integral form of control volume variable , ∬ is the integral form of control surface variable , Ω is the control volume and the control surface. The variables of interest in Equation (1) are mass flow, momentum, and energy inside and outside the control volume. After discretization, it yields the conservation equation for each cell in the physical space, as shown in Eq. (2):

Equation (2) is then applied to elicit the equations for continuity, momentum, and energy for each cell in the physical space. Thus, the S809 airfoil domain was discretized for this set of control volumes.

Isothermal flow was analyzed in the simulations carried out on the S809 airfoil, which by its turn called for the analysis of turbulence. Many authors such as Neto (2002) and Freire (2002) have indicated that turbulence is present in most flow patterns. In this study turbulence was described as a highly diffuse, dissipative, rotational, and threedimensional phenomenon.

The simulation of complex flow patterns requires an understanding of the basic principles of the theory of turbulence and the means used to model it. With these principles in mind, the best turbulence model and near-wall treatment options for the problem at hand were chosen. Flow around the S809 airfoil was thus characterized as external and turbulent. The dimensionless parameter used in flow characterization was the Reynolds number, as defined in Eq. (3):

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

where is the Reynolds number for the S809 airfoil chord length c, is the S809 airfoil chord length in meters, is the air flow velocity in m/s over the S809 airfoil, and is the kinematic viscosity of the fluid over the S809 airfoil in

In this study the turbulence over the S809 airfoil was simulated using the RANS (Reynolds-averaged Navier-Stokes) equations. In this method the equations are obtained from a set of averaged Navier-Stokes and continuity equations. A key element in RANS modeling is the representation of the Reynolds stress, or turbulent stress, used to describe the effects of turbulent fluctuations in pressure and velocities.

This particular method was chosen for the modeling quality it provides and the computational cost it offers to produce turbulence models. Many authors have described the low computational cost and high grade modeling the RANS method offers vis-à-vis other turbulence models. More specifically, the Standard κ-omega (κ-ω) turbulence model – a method known in the literature for its applications in the description of aerodynamic flow – was used in this study, along with the Realizable κ-ϵ model.

2.1 Geometry and Mesh

The domain was discretized, i.e., divided into points for which a solution was obtained. The set of discretized points is referred to as the mesh.

The geometry of the S809 airfoil was designed on software program Solidworks®. The resulting geometry was then exported to the ANSYS® ICEM-CFD® mesh generator. Figure 1 shows the geometry of the S809 airfoil designed on Solidworks®. The mesh defines the cells in the computational domain for which flow variables such as velocity and pressure are calculated.

Figure 1 shows the asymmetric profile of the S809 airfoil, with a convex upper surface, a rounded edge called leading edge, and a sharp edge referred to as the trailing edge. The asymmetry stems from the shape of the lower surface of the S809 airfoil.

Asymmetric S809 airfoils are optimized to generate higher levels of lift when the lower surface of the airfoil is positioned closer to the direction of airflow (Fadigas, 2011).

Figure 1. The profile of an S809 airfoil

The ANSYS® ICEM CFD meshing software was used to generate a C-H mesh for the S809 airfoil. This is one of the most critical steps of the simulation effort, once it yields a representation of a continuous domain of interconnected points from which the equations governing the physical phenomenon are solved.

Figure 2 (a, b) shows the respective representations of the 2D mesh and the C-H mesh over the S809 airfoil surface. The mesh contained 1,528,900 elements. In order to enhance the modeling of drag forces and turbulence, the mesh was extended to cover points near the wall, with the first point on the grid located in the viscous sublayer, y+ < 10. The grid extended in the radial direction for a length equivalent to 20·c from the center of gravity of the S809 airfoil.

The length of 20·c was needed to ensure the computational domain was large enough not to allow reverse flows. The structured mesh had flat quadrilateral cells around the S809 airfoil as shown in Fig. 2 (b).

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


Figure 2. Structured mesh: (a) C-H mesh generated on ICEM-CFD®; (b) mesh over the profile of the S809 airfoil

2.2 Boundary Conditions

Proper boundary conditions have to be set if one wishes to obtain CFD solutions that represent the physical phenomenon more closely. The simpler of the boundary conditions applies to the wall. Once in this case the fluid cannot pass across the wall, the normal velocity component is equal to zero, thus characterizing a prescribed wall boundary condition. Therefore, the walls were considered adiabatic and a no-slip boundary condition was applied to them.

Similarly, boundary conditions were defined at the inlet and exit of the S809 airfoil. In this scenario, the fluid – air – entered and left the computational domain.

In this study, inlet velocity was set to range from 1 to 5 m/s and ambient pressure away from the S809 airfoil was defined as the specified pressure condition. Pressure and velocity close to the S809 airfoil, i.e., in its upper and lower surfaces, were calculated for Reynolds numbers of 75,400 and 135,400, respectively.


The use of computational fluid dynamics (CFD) allows to analyze a model when exposed to different flow conditions. This technique is commonly used in the analysis of aerodynamic behavior at different types of airfoil. This analysis can be made in two-dimensional models (2-D) and in three-dimensional (3-D).

In some studies, there is no interest in the influences generated by edge effects, being only the results for the mid span sections of the airfoil important. In such cases the 3-D models have similar features to the 2-D (Troldborg, 2013).

(Parte 1 de 2)