Why I am writing this article

With the rapid world-wide growth in wind energy installations, the number of people working in the field is increasing correspondingly. According to the International Renewable Energy Agency (2016), 1.1 million people were employed directly or indirectly in the wind energy industry world-wide in 2016. Whilst a number of wind energy degree programmes have been introduced in some countries (for example a Master’s degree at the University of Applied Sciences Bremerhaven, the University of Hannover and the University of Oldenburg in Germany, at the University of Strathclyde in the UK and at the Danish Technical University in Denmark as well as the European Wind Energy Master), the majority of people working in the wind energy industry have little or no formal education or training relating to wind energy technology. I do agree that on-the-job learning is very valuable, but there are nevertheless certain technical concepts, which, if understood properly, can strongly improve performance of staff in the business environment. Understanding wind energy technology not only allows you to negotiate more credibly, present yourself more competently and persuade stake-holders of products or investment ideas - it also helps you to form independent, informed decisions, to evaluate the threats and opportunities of a situation better and to assess state-of-the art technology.

In my opinion, there are five key technical concepts that are essential for people working in the wind energy industry to understand. These are:

  1. The physical limits of wind turbine performance
  2. Tip speed ratio and optimum performance
  3. The physical limits of wind turbine dimensions
  4. Loads and fatigue
  5. Performance indicators for wind energy

I am introducing each of these concepts in my next few blog articles. Last time I talked about the first concept – the physical limits of wind turbine performance. Today I’m going to talk about the second concept – tip speed ratio and optimum performance.

Tip speed ratio and optimum performance

In part 1, we considered the most ideal possible form of energy conversion and assumed that our wind turbine rotor was a flat, porous disk. Porous, flat disk-shaped objects do not, however, magically take energy out of the wind and convert it to electricity. An efficient way of generating electricity is to make a shaft turn and connect this to a generator, which transforms the rotational energy into electrical energy via a magnetic field. This is exactly what wind turbines do. The rotor blades are designed to create lift forces, which in turn exert a torque on the shaft, making the rotor and shaft turn.

Aerodynamic forces

The aerodynamic forces acting on an object subject to a fluid flow can be split into two perpendicular components – lift and drag.

Aerodynamic lift is created when a fluid flows over an object that it is shaped in a way that makes the flow deflect downwards. According to Newton’s third law, this creates an equal and opposite force on the object pointing upwards. Taking an example of an aeroplane wing in the Figure 1, the curved shape of the wing causes the flow to be deflected downwards as shown on the left-hand diagram, creating an upward force on the wing. Aerodynamic lift always points in a direction perpendicular to the flow direction. Increasing the angle between the wing and the air flow causes the lift to increase, because the flow is deflected downwards more, as can be seen on the middle diagram. This process has an upper limit, however, when the flow can no longer stick to the surface of the blade and follow its shape nicely. At some point, the flow “separates” from the surface and even starts to flow backwards, creating a region of reversed flow as shown on the right-hand diagram in the figure below. In this case, the lift can no longer be produced and the wing “stalls”.

 Figure 1. Lift and drag on an airfoil at different angles of attack.

Figure 1. Lift and drag on an airfoil at different angles of attack.

Aerodynamic drag is the force acting parallel to the flow direction. It has two main sources, which vary in magnitude depending on the shape and surface roughness of the object.

Friction drag is caused by friction between the object’s surface and the thin layer of fluid flow near to the surface, known as the boundary layer, as well as by the friction between the air particles within the boundary layer (known as viscosity). Friction drag dominates for flows over streamlined bodies, and its magnitude depends on the type of flow in the boundary layer – laminar or turbulent. The flow over an object generally starts off laminar, with the streamlines parallel to each other, but becomes turbulent at some point due to instabilities in the flow. In turbulent flow, the streamlines are no longer parallel to each other, but move in different directions and mix with each other, creating a higher friction drag.

Pressure drag is caused by flow separation behind an object and dominates for flows over less streamlined bodies, because the sharper the curvature of the rear of the object, the more easily the flow separates and the larger the area of the separated flow. Pressure drag is actually lower for turbulent boundary layers than for laminar boundary layers, because the mixing between the layers of the turbulent boundary layer increases the flow’s energy, causing flow separation to occur later and reducing the area of separated flow. This effect is utilised in golf ball design – the dimples cause the boundary layer to become turbulent, reducing the pressure drag and thus increasing the flight distance.

The magnitude of aerodynamic drag and lift is affected by a number of different parameters, including the exact shape of the airfoil. In fact, each airfoil design possesses a particular behaviour of lift and drag coefficient depending on the angle of the air flow (called the angle of attack), unique to that airfoil. An example is shown in Figure 2.

 Figure 2. Example polar diagrams of an airfoil.

Figure 2. Example polar diagrams of an airfoil.

 

Losses

There are some losses related to this torque creation process, which cause the actual rotor efficiency to always be lower than the Betz Limit. For example, rotational losses occur because the rotating blades actually transfer some of their own rotational energy to the incoming wind, making the rotor wake rotate in the opposite direction to the rotor. As the total energy within the system has to remain constant, this means that less energy is then available for the rotor in the energy conversion process. This rotational energy transferred to the flow over the blades decreases with increasing rotational speed, therefore rotational losses can be minimised by designing a rotor with a high rotational speed.

The other main source of losses are aerodynamic drag losses. These occur because some component of the drag forces inevitably acts against the rotation of the rotor, removing a proportion of the energy created by the lift forces.

These losses are dependent upon the rotational speed of the rotor. Actually, it is better to say that they are dependent upon the Tip Speed Ratio (TSR) of the rotor, which is given by the ratio of the blade tip linear speed and the wind speed as shown in Figure 3.

 Figure 3. Definition of Tip Speed Ratio.

Figure 3. Definition of Tip Speed Ratio.

 

Non-dimensional numbers like TSR (and power coefficient) are good for quantifying performance because they can be compared for different sizes of rotor.

The power coefficient of a wind turbine rotor (discussed in my last article) usually depends on the TSR in a manner similar to Figure 4, with an optimum value at a TSR of around 6-8 for a three-bladed rotor. Variable-speed wind turbines are designed to alter their rotational speed in order to hold a constant tip speed ratio when the wind speed changes, hence maximising the amount of time spent at the optimal power coefficient value.

 Figure 4. Typical power coefficient performance of a wind turbine rotor.

Figure 4. Typical power coefficient performance of a wind turbine rotor.

 

Optimising the aerodynamics

The exact shape of the power coefficient graph depends on details of the blade design, such as the chord distribution and twist distribution along the blade length as well as the airfoil shape.

Chord distribution

If we imagine the air flow over the blade at one radial location, it is clear that the magnitude of the lift and drag forces exerted on the blade are dependent on the chord length – the longer the chord, the more area the pressure is acting on and the higher the forces are. This in turn affects the wind speed reduction over the rotor. We looked at the Betz Limit in part 1 – this tells us that the optimal wind speed reduction over the rotor is 1/3. This means that the wind speed is reduced to 2/3 of its original value (e.g. from 6 m/s to 4 m/s).

It should be clear that the flow speed “seen” by the blade actually changes with radial location – the further towards the tip of the blade, the higher the linear speed due to the rotation (linear speed = radius multiplied by rotational speed). This makes sense if you imagine sitting on a roundabout at the playground – the further out toward the edge you sit, the stronger you feel the wind in your hair. At each radial location, we can therefore calculate the chord length that is required to achieve the optimal wind speed reduction of 1/3. The results are dependent on the TSR and on the number of blades, giving approximate optimal blade shapes as shown in Figure 5.

 Figure 5. Theoretical optimal shape of wind turbine blades.

Figure 5. Theoretical optimal shape of wind turbine blades.

 

Blade designers thus try to reach this optimum shape, whilst avoiding further manufacturing costs  and effort as well as avoiding large reductions in the blade’s stiffness.

Twist distribution

As can be seen in Figure 6, not only does the relative wind speed increase, but also the angle of the flow relative to the blade position (phi) reduces with increasing radius. If the blades are built straight, as shown on the left hand side, the angle of attack is equal to phi at each radial location. Looking at the lift coefficient vs. angle of attack diagram, this means that the lift coefficient varies with radial position and is rarely equal to its maximum value. Actually, we would quite like the lift coefficient to remain at its optimum value at every radial position in order to maximise the power production. We can realise this by twisting the blade about its own axis, as shown on the right hand side, allowing the angle of attack to remain constant with changing radial position.

 Figure 6. Straight blade (left) compared to twisted blade (right).

Figure 6. Straight blade (left) compared to twisted blade (right).

Modern blades are designed in order to optimise the twist distribution along the blade length as much as possible whilst keeping the manufacturing costs as low as possible.

Airfoil shape

By altering the airfoil shape, we can improve the polar diagrams and thus optimise the power production. The objective in the design of a wind turbine airfoil is to maximise the lift whilst minimising the drag at the most important operating points.

The main characteristics of an airfoil that affect the aerodynamic performance are:

  • Thickness
  • Position of maximum thickness
  • Camber

Generally, a thinner airfoil leads to better aerodynamic characteristics because it is presenting less blockage to the flow. However, a compromise must be reached in the airfoil design because thinner airfoils lead to lower structural stiffnesses, reducing the blade’s stability and therefore its lifetime.

Moving the position of maximum thickness further back reduces the airfoil’s friction drag because the flow remains laminar for longer. However, this technique only works is the blade remains free of surface dirt, because increased surface roughness can induce a turbulent boundary layer. This is particularly difficult for wind turbines, which are exposed to natural conditions causing dirt build-up such as insects and sand.

The camber of an airfoil refers to how much it is curved. Increasing the curvature increases the deflection of the air flow and therefore increases the aerodynamic lift. However, flow separation limits this increase in lift and the airfoil must be designed optimally for the desired application. Again, a compromise must be made between structural stability and aerodynamic performance.

Optimum performance

I hope it has become clear that there are a number of factors that affect the aerodynamic performance of a wind turbine rotor. The design process involves many different optimisation loops and processes, and each designer sets their priorities differently, leading to a large range of possible solutions.

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