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Advance Computational Fluid Dynamics EML 6726, Dr. Ghenai

CFD Analysis of a Horizontal Axis Wind Turbine (HAWT) Blade

Matt M. Hejazi

Department of Mechanical Engineering Florida Atlantic University

777 Glades Rd. Boca Raton, FL, 33431

ABSTRACT

The primary focus of this project was on CFD analysis of a wind turbine blade, using k ω− SST model for turbulent viscosity, for a horizontal axis wind turbine (HAWT) airfoil, in which, effect of dimensionless lift coefficient (CL), drag coefficient (CD) and pitching moment coefficient (Cm) at different angle of attack, was tested. Sample results are presented for an airfoil from the 6th series of NACA laminar wing section family, tested in low turbulence pressure tunnel at NASA [1]. Comparisons with experimental data are provided to establish the efficiency and accuracy of the present model.

This project presents an exposure on the set up and solution of an external aerodynamics problem using the k ω− approach turbulence model.

INTRODUCTION

Wind turbines interact with the wind, capturing part of its kinetic energy and converting it into usable energy. This energy conversion is the result of several phenomena. The wind is characterized by its speed and direction, which are affected by several factors, e.g. geographic location, climate characteristics, height above ground, and surface topography. Atmospheric turbulence causes important fluctuating aerodynamic forces on wind turbines [2]. Turbulence is an important source of aerodynamic forces on wind turbine rotors. Some commonly used turbulence terms that refer to the physical descriptions of the wind are defined below. Turbulence is an irregular motion of fluid that appears when fluids flow past soil surfaces or when streams of fluid flow past or over each other [2]. Many of the rotors found on current available HAWT systems are designed using a combination of 2-D airfoil tools, 3-D blade element and momentum (BEM) theory, in which, the unsteady flow effects are either ignored, or modeled using a synthesis of 2-D data; hence, these methods are not capable of accurately modeling three-dimensional dynamic stall processes, tower shadow effects, tip relief effects, and sweep effects. These three-dimensional effects can alter the air loads, influence the fatigue life, and significantly influence the maintenance cost of HAWT systems.

The first step is to determine which model is appropriate in solving the problem. In this analysis the shear-stress transport (SST) k ω− model was utilized which incorporates a damped cross-diffusion derivative term in the ω equation. The SST k ω− model is similar to standard k ω− model but the definition of the turbulent viscosity is modified to account for the transport of the turbulent shear stress.

The flow on wind turbine blade being often separated due to the angle of attack encountered which depends on turbulence level, tower shadow or yaw misalignment. The present report is focused on the influence of turbulence on the wind turbine blade airfoil. After presenting the experimental data, the turbulence effects on the blade is studied.

The boundary layer flow passing through a wind turbine is inherently inhomogeneous, unsteady and turbulent, consisting of rapid velocity and pressure fluctuations. Turbulence occurs since inertial effects increasingly overwhelm viscous stresses inherent in the flow stream as the flow speed increases (even at very small wind speeds for air), resulting in intrinsically unstable flow that can become turbulent with even the slightest flow perturbation [3].

GOVERNING EQUATION

For the 2-D, steady and incompressible flow the continuity equation is :

Momentum equation for viscous flow in x direction is:

yxxx zxx

Du fDt x x y z

ττ τρρ ρ∂∂ ∂∂

= − + + + +∂ ∂ ∂ ∂

Where due to characteristics of the 2-D flow in continuity equation the term ( )w

zρ∂∂

and in momentum equation, zx

zτ∂∂

drop out. In all the simulations a standard k ω− SST model has been used for turbulence viscosity. For flow, continuity and momentum equations please refer to Fluent user guide hand book.

Copyright © 2008 by M. Hejazi 2

NUMERICAL METHOD

The numerical method utilized for the simulation had a density based solver with implicit formulation, 2-D domain geometry, absolute velocity formulation, and superficial velocity for porous formulation. For this test, a coupled implicit solver and an external compressible flow model for the turbulence was utilized. The green-gauss cell based was used for the gradient option. There are different equations used for flow, turbulence, species, and energy. A simple method was used for the pressure-velocity coupling. For the discretization, a standard pressure was used, and density, momentum and turbulent kinetic energy were set to second order upwind.

GOMETRY AND BOUNDARY CONDITIONS An airfoil from the 6th series of NACA laminar wing section family is utilized. The airfoil maximum relative thickness is 15%, which is located at 35% of the chord length. Reynolds number for the experiments and simulations is Re=3x106, and turbulence intensity is 0.07%. A fully turbulent flow solution was used in Fluent, where k-w SST model was used for turbulent viscosity [4]. Since a coupled solver was utilized and Mach number for the flow is greater than 0.1 (~.132), the operating pressure was set to zero. Calculations were done for the “linear” region, i.e. for angles of attack ranging from -2 to 6 degrees, due to greater reliability of both experimental and computed values in this region. The airfoil profile and boundary conditions were all created in Gambit. The airfoil consists of 50 vertices and two edges (upper and lower edge) as shown in figure 1-a:

Figure 1-a NACA 632(2)15 Airfoil Profile

Once the Airfoil edges were created, a face was created from the two edges and in order to create boundary layers for the airfoil, another face was created from 3 vertices to include the airfoil from which, the airfoil face was subtracted. The geometry and boundary conditions are presented in figure 2-a shown below:

Figure 2-a Full view Boundary Conditions

Next the created geometry was meshed. The resolution of the mesh is greater in regions where greater computational accuracy was needed, such as the region of the leading edge and the trailing edge wake. The mesh consists of 15851 quadrilateral/triangular cells, of which 146 is on the airfoil (figure 3-a).

Figure 3-a Mesh around NACA 63(2)215 airfoil

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RESULTS

Below are the simulation outcomes of static pressure and Mach number distribution at 4.0o angle of attack ,α, which are shown in figures 2-a and 2-b respectively.

Figure 2-a Contours of Static Pressure (pascal)

As shown above, figure2-a demonstrates the pressure distribution over the airfoil. The pressure on the lower surface of the airfoil is greater than that of the incoming flow stream and as a result of that it effectively “pushes” the airfoil upward, normal to the incoming flow stream. On the other hand, the components of the pressure distribution parallel to the incoming flow stream tend to slow the velocity of the incoming flow relative to the airfoil, as do the viscous stresses.

Figure2-b Contour Plot of Much Number

It could be observed that the upper surface on the airfoil experiences a higher velocity compared to the lower surface. By increasing the velocity at higher Mach numbers there would be a shock wave on the upper surface that could cause discontinuity. On the upper surface in some regions the Mach number on the upper surface close to the shock wave reaches to its maximum value (.174), which is colored by red color, and behind the trailing edge it drops.

Below is the XY plot of the pressure distribution on top and bottom surfaces of the airfoil. Since the Mach number is not that high in this case, the shock wave created is not that strong; however, the impact of this week shock wave is still reflected on the pressure distribution of the upper airfoil surface as shown in figure 2-c presented below:

Figure 2-c XY Plot of Pressure

Figure 2-d demonstrates the x component of the shock wave on the upper surface of the airfoil. By observing velocity or Mach number distribution over the airfoil surface, the variation of the x component of the shock wave along the upper and lower surface of the airfoil could be justified.

Figure 2-d XY Plot of x Wall Shear Stress

The velocity vectors are also shown in figure 2-e, in which colored by the magnitude and the direction of the velocity magnitude. The position shown is near the upper wall, behind the shock.

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Figure 2-e Velocity Vectors Near Upper Wall

VALIDATION OF THE MODEL

After solving the simulations for the case above with angle of attack of at 4.0o

now a parametric study of angle of attack is done in order to be able to compare the results with the experimental data; to do so, the model should be solved with a range of different angles of attack from -20 to 60. On an airfoil, the resultants of these forces are usually resolved into two forces and one moment. The component of the net force acting normal to the incoming flow stream is known as the lift force and the component of the net force acting parallel to the incoming flow stream is known as the drag force.

Figure 3-a Lift and Pitching Moment coefficient Curves

It could be observed that at low angles of attack, the dimensionless lift coefficient (CL), increases linearly with angle of attack. The pitching moment is usually defined about an axis normal to the airfoil cross-section, located a quarter of the distance from the leading edge to the trailing edge of the airfoil and as shown in figure 3-a, Cm increases linearly with angle of attack.

In fact, the pressure distribution on both sides of the airfoil contributes to the lift. The part of the drag force related to the pressure distribution around the airfoil is known as the pressure drag. The part of the drag force related to the viscous stresses is known as the skin-friction drag. Their sum, the total drag force, is commonly referred to as form drag. The viscous stresses generally make a negligible contribution to the lift force, as well.

Figure 3-b Drag Coefficient Curve

Flow is attached to the airfoil throughout this regime. At an angle of attack of roughly 6° or 7°, the flow on the upper surface of the airfoil begins to separate and a condition known as stall begins to develop. The lift coefficient peaks and the drag coefficient increases as stall increases. It could be seen that the drag is reasonably small (figure 3-b). CONCLUSION AND DISSCUSION

The primary focus of this project was on CFD analysis of a wind turbine blade, using k ω− SST model for turbulent viscosity, in which, effect of dimensionless lift coefficient (CL), drag coefficient (CD) and pitching moment coefficient (Cm) at different angle of attack, was tested. For this test, a coupled solver and a turbulent viscosity model was utilized. The Sutherland law for viscosity was utilized in the model, since it is well suited for high-speed compressible flows. While Density and Viscosity were made temperature-dependent, Cp and Thermal Conductivity were left constant. Since for high-speed compressible flows, thermal dependency of the physical properties is generally recommended.

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REFERENCES

1. I.H. Abbott, A.E. von Doenhoff, L. Stivers, NACA Report No. 824 – Summary of Airfoil Data, National Advisory Committee for Aeronautics.

2. J. R. Connell and R. L. George. Accurate correlation of wind turbine response with wind speed using a new characterization of turbulent wind. Solar Energy Engineering. Pg. 109, 281, 321-329 (1987).

3. J.M. Jonkman. Modeling of the UAE Wind Turbine for Refinement of FAST_AD. Pg. 11. (2003)

4. FLUENT 6.1 User’s Guide, Fluent Inc., Feb. 2003