By Jim Davis    2021-08-30

# Wind Turbine Airfoil Design

At a high level, there are at least three aspects to consider: (1) aerodynamic forces, (2) structural/geometrical properties, and (3) noise. We will elaborate on each of these below.

## Aerodynamic Forces

Most of the aerodynamic criteria for airfoil design are based on the static lift and drag coefficients $$C_L$$ and $$C_D$$, as a function of the angle of attack $$\alpha$$. Other values that may be used include the variation of these values with Mach number $$M$$ and even dynamic properties of $$C_L$$ and $$C_D$$ when $$\alpha$$ or $$M$$ change fast enough that $$C_L$$ and $$C_D$$ differ significantly from their static values (these unsteady aerodynamics are particularly important for helicopters). Important criteria computed from $$C_L$$ and $$C_D$$ are listed below, followed by a description.

1. Minimize drag for frequently used angles of attack. This amounts to better efficiency/performance.
2. Keep the maximum $$C_L$$ below a threshold. This prevents extreme loads that could damage structures.
3. Keep the stall margin above a threshold. We will elaborate below.
4. "Soften" stall behavior. Again, we’ll elaborate below.
5. Minimize the gradient of the forces in typical operating scenarios (with time varying $$\alpha$$ and $$M$$). This lessens repetitive fatigue loads that can shorten the lifetime of components.
6. Limit the transition point location versus $$\alpha$$. This is sometimes used as a surrogate for acoustics and/or for roughness sensitivity—a wind turbine airfoil should perform well even after its shape is contaminated by insects, dirt, erosion, etc….

Typically, a desired lift force $$L$$ is known apriori, based on more preliminary rotor and system design. For wind turbines, a simple BEM analysis may be done beforehand to determine $$L$$. The value of $$\alpha$$ which will achieve $$L$$ is important and denoted by $$\alpha_O$$ here. Another important angle of attack is the one which gives the maximum $$C_L$$, denoted $$\alpha_M$$ here.

One of the criteria above was about the stall margin, which is $$\alpha_M-\alpha_O$$. If $$\alpha_M$$ is too close to $$\alpha_0$$, then small changes in the environment can cause airfoils to stall, resulting in poor performance and undesirable loads. For this reason, a sizable stall margin is attractive. On the flip side, too much stall margin is often associated with excess max $$C_L$$ and extreme loads.

Despite having a stall margin, the airfoil will likely end up in stall conditions (hopefully rarely). This is where criteria 2 and 4 come into play. If/when airfoils stall, we don’t want huge loads or even huge gradients in the loads. Soft stall criteria will limit the variation in $$C_L$$ and $$C_D$$ around $$\alpha_M$$. Unfortunately, this "stall behavior"—where $$\alpha$$ is around or above $$\alpha_M$$ is difficult to predict, and hence difficult to design for.

## Geometric Requirements

Geometric requirements exist for a variety of reasons, including manufacturing constraints, known shape/aerodynamic relationships, and efficient use of structural materials within the airfoil. A prominent example is the shape of an airfoil around its point of max thickness. Maximizing area and minimizing curvature around this point provides the most efficient use of structural material—less spar thickness is needed per unit stiffness.

Below are some geometric goals/constraints encountered in airfoil design.

1. Minimize the trailing edge thickness. This is typically for acoustic reasons.
2. Constrain the trailing edge thickness above a certain value, for manufacturing reasons.
3. Constraint the minimum area in various portions of the airfoil.
4. Ensure the airfoil's shape is compatible with surrounding airfoils. We’ll explain below.
5. Limit the absolute chord length to facilitate shipping. (Optimal performance on the inner portion of the blade, near the hub, often calls for a chord length that wouldn’t be shippable.)

The combination of points 1 and 2 may boil down to a simple specification that the absolute trailing edge thickness be fixed to the smallest manufacturable amount. The only tricky thing here is that, in practice, an airfoil will be applied with one or more specific chord lengths. To maintain the same absolute thickness, the aft region of the airfoil will need to be massaged somewhat.

Different airfoils will be used at different locations on a blade. For example, different airfoils may be designed at 25, 50, 70 and 85 percent radius. Between these locations, airfoil shapes are an interpolation/blend of the surrounding airfoils. Point #4 above is that some thought must be given to ensure this blending of airfoils results in feasible shapes. This is sometimes referred to as making airfoils compatible. Airfoils designed for 70 and 85 percent radius need to blend together to form acceptable airfoils at e.g. 75 and 80 percent radius.

## Acoustic Requirements

The noise generated by an airfoil is typically partitioned into several different noise types, e.g. flow separation noise and laminar boundary layer vortex shedding noise. One of these types often dominates the others. For example, boundary layer noise from the trailing edge (of the outermost 50% of the blade) of a wind turbine usually dominates other noise sources. Depending on the noise source, prediction can be difficult. Typical design criteria follow.

1. Minimize a weighted average of the dominant noise source over various operating conditions.
2. Constrain some noise sources to be below a threshold in certain operating conditions.
3. Constrain the maximum noise in the worst case operating condition to be below a threshold.
4. Outputs from a (non-acoustic) flow solver can be used as surrogates for some of these noise sources, e.g. constraints on the rate of movement of the suction side transition point as a function of $$\alpha$$

## Other Considerations

### Airfoil parameterization.

To perform an automated airfoil design, the shape of the airfoil will need to be parameterized. This is typically done with about 5 to 30 real numbers. One example are the CST parameters, which are based on Bernstein polynomials.

### Robust design.

A design process may account for the reality that manufacturing imperfections and/or post manufacturing events (contamination/dirt on a blade) will alter the airfoil shape. Also, numerous factors may perturb the expected operating conditions so that they are not as expected (e.g. imperfect blade control or excessive inflow turbulence). An example of this is keeping the stall margin above a threshold described above.

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