Wind Turbine Blade Efficiency (a theoretical approach)

Submitted by: Kripa Shankar Tiwari(NIT HAMIRPUR(H.P.))

Abstract• The performance of this turbine blade depends upon various

factors like tip speed ratio, its design, the material used to make it and other aerodynamics parameters.

• In order to increase the efficiency of wind turbine blade, we must have to analyze all these parameters and after doing all these, we need a reference through which we can compare our result. For that purpose, we have Betz law and its limit.

• Betz law says that, like Carnot engine, the wind turbine also cannot have 100% input to be converted into output. The maximum performance that can be attained is 59.3% only. In reality, no wind turbine is near to this value. The maximum efficiency that can be attained up to now is in the range of 40 to 45%. Therefore, to get better result, we need to understand all the theoretical parameters again and redesign our wind turbine to get optimum result.

Intoduction

• A wind turbine is a device that converts wind’s kinetic energy in to electrical work.• Wind turbine operates on a simple principle. The energy

in the wind turns two or three propeller like blades around the rotor. The rotor is connected to the main shaft which spins a generator to create electricity. • Simply, a wind turbine works opposite of a fan. Instead of

using electricity to make wind, like fan, wind turbines use wind to make electricity.

Losses in wind turbine

• In general, the losses in the wind turbine occur in the following components

1. Gearbox 2. Generator 3. Turbine blade• These three parameters define the difference in

efficiencies of actual wind turbine from Betz limit. 1% to 2% loss is due to slipping of gears in the gear box, 10 to 20% losses occur in generator and rest occurs on turbine blades.

Betz law and its limit

• The losses in efficiency for a practical wind turbine are caused by

1. The viscous drag on the blades, 2. The swirl imparted to the air flow by the rotor and, 3. The power losses in the transmission and electrical

system.

Assumptions taken

• The wind energy is assumed to be an ideal energy converter, meaning that:

1. It does not possess a hub.2. It possesses an infinite number of rotor blades

which do not result in any drag resistance to the wind flowing through them.

• In addition, uniformity is assumed over the whole area swept by the rotor, and the speed of the rotor beyond the rotor is considered to be axial. The ideal wind rotor is taken at rest and is placed in a moving fluid atmosphere.

Fig. A: pressure and speed variation in an ideal model of a wind turbine.

V1

S1

• The wind speed passing through the turbine rotor is considered uniform as V, with its value as V1 upwind, and as V 2 downwind at a distance from the rotor. Extraction of mechanical energy by the rotor occurs by reducing the kinetic energy of the air stream from upwind to downwind, or simply applying a braking action on the wind. This implies that:

V2<V1

• Consequently the air stream cross sectional area increases from upstream of the turbine to the downstream location, and:

S2>S1

• According to Betz limit, the maximum possible value of performance of wind turbine is,

Cp,opt =59.26 %• This is referred to as the Betz Criterion or the Betz Limit. It was

first formulated in 1919, and applies to all wind turbine designs. It is the theoretical power fraction that can be extracted from an ideal wind stream. Modern wind machines operate at a slightly lower practical non-ideal performance coefficient. It is generally reported to be in the range of:

Cp,prac=2/5= 40% (approx.)

Wind turbine blades design and requirements:

1. Maximum power from the wind at minimum cost2. The blades tend to be thicker than the aerodynamic

optimum close to the root, where stresses due to bending are greatest.

3. Compromise between aerodynamic and structural efficiency.

4. The choice of material and manufacturing processes.

Factors affecting the wind turbine blades:

1. Tip speed ratio2. No. of blades and its stability and smoothness3. Aerodynamics and structural requirements (lift, drag

and gravitational forces)4. Lift/drag ratio5. Minimum wind speed at which turbine blades can

rotate6. Wind capturing amount with the blades in order to

get the maximum wind energy conversion7. Level from the ground8. Material conditions

Tip speed ratio

• For slow rotation of rotor, wind will pass unperturbed through the gaps between the blades.

• For high rotation of rotor, blades will act as a solid wall for the winds and restrict the flow of wind through it.

• Therefore to get the maximum power from the wind, there should be an optimum speed ratio of the rotor speed and the wind speed. This ratio is the tip speed ratio (T.S.R.). Basically, it depends upon following parameters:

1. Structural design of the wind turbine blades. 2. The number of blades used.3. The aerodynamics of the blades’ profile used

Problems generated due to high tip speed ratio:

1. For high tip speed ratio of about 80m/sec, the rotor will be subjected to erosion of the leading edges from their impact with dust or sand particles in the air and will require the use of special erosion resistant coatings much like in the design of helicopter blades.

2. Noise generation in the audible and non-audible ranges.3. Vibrations particularly in the cases of two or single bladed

rotors.4. Starting difficulties if the shaft is stiff to start rotation.5. Reduced rotor efficiency due to drag and tip losses.6. Excessive rotor speeds would lead to a runaway turbine,

leading to its catastrophic failure and even disintegration.

The relationship between the wind speed and the rate of rotation of the rotor is characterized by a non-dimensional factor is known as the Tip Speed Ratio (T.S.R.) or Lambda (λ or Λ).Mathematically,

Optimal rotor tip speed ratio• The optimal tip speed ratio for the max power extraction is

influenced by relating the time taken for the distributed wind to re-establish itself ‘tw’ to the time taken for a rotor blade of rotational frequency to move into the position occupied by its predecessors ‘ts’.

• For an n bladed rotor, the time period for the blade to move to its predecessor’s position is given by,

• If the length of the strongly disturbed air stream upwind and downwind of the rotor is ‘s’, the time period of the wind to return to normal is given by,

• If ts >tw, some wind is unaffected. However, if ts < tw, some wind is not allowed to flow through the rotor. Therefore, for the maximum power extraction, these two time periods must be equal, i.e.

ts = tw

• Optimal frequency of rotation is,

• Consequently, for optimal power extraction, the rotor blade must rotate at a rotational frequency of that is related to the speed of the incoming wind. This rotor rotational frequency decreases as the radius of the rotor increases and can be characterized by calculating the optimal tip ratio as:

Effect of the number of rotor blades:

• The optimal T.S.R. depends on the number of rotor blades n of the wind turbine. The smaller the number of blades, the faster the wind turbine has to rotate to extract maximum power from the wind.

• For an n bladed machine, it has been empirically observed that,

• for n=2, a two bladed rotor, the maximum power extracted from the wind at Cp,max occurs at:

• For n=3, a three bladed rotor,

• For n=4, a four bladed rotor,

• We usually take 3 bladed rotors for wind turbines.• A typical three bladed rotor design would have a tip speed

ratio of,

• If poorly designed blades are used resulting in a tip speed ratio is too low, the wind turbine would have a tendency to slow and to stall.• If the tip speed ratio is too high, the turbine will rotate very

fast through turbulent air, and the power will not be only optimally extracted from the wind stream but the turbine will be highly stressed at the risk of catastrophic failure.

Inefficiencies and losses

1. Aero foil profile losses:2. Blade number losses3. Whirlpool losses4. End losses

Aerodynamics and structural requirements and other parameters:

• The blade design process starts with a best guess compromise between the aerodynamic and structural efficiency. The choice of materials and manufacturing process will also have an influence on how thin (hence aerodynamically ideal) the blade can be built. For instance, prepreg carbon fibre is stiffer and stronger than infused glass fibre. The chosen aerodynamic shape gives rise to loads, which are fed into the structural design.

• These aerodynamic and structural requirements depend on following parameters:

1. Wind2. Number of blades3. How blades capture wind power4. Twist 5. Blade section shape6. Blade planform shape7. Rotational speed

Ideal wind speed

The power available in wind varies as the cube of the wind speed. Therefore, the sites have to be selected carefully, below about 5 m/s (10 mph) wind speed there is not sufficient power in wind to be useful. Conversely, strong gust provide extremely high level of powers but it is not economically viable to build machines to be able to make most of the power peak as their capacity would be wasted most of the time. So the ideal is a site with steady winds and a machine that is able to make the most of the lighter winds whilst surviving the strongest gusts.

Rotational speed

• The speed at which the turbine rotates is a fundamental choice in the design, and is defined in terms of the speed of the blade tips relative to the “free” wind speed (i.e. before the wind is slowed down by the turbine). This is called the tip speed ratio.• High tip speed ratio means the aerodynamic force on the

blades (due to lift and drag) is almost parallel to the rotor axis, so relies on a good lift/drag ratio. The lift/drag ratio can be affected severely by dirt or roughness on the blades.• The other reduction in efficiency at low tip speed ratio

comes from tip losses, where high-pressure air from the upwind side of the blade escapes around the blade tip to the low-pressure side, thereby wasting energy.

Lift/ Drag dependency

• Though the details of the aerodynamics depend very much on the topology, some fundamental concepts apply to all turbines. Every topology has a maximum power for a given flow, and some topologies are better than others. The method used to extract power has a strong influence on this. In general, all turbines may be grouped as being either lift-based, or drag-based; the former being more efficient. The difference between these groups is the aerodynamic force that is used to extract the energy.

• The most common topology is the horizontal-axis wind turbine (HAWT). It is a lift-based wind turbine with very good performance. Accordingly, it is a popular choice for commercial applications and much research has been applied to this turbine. Despite being a popular lift-based alternative in the latter part of the 20th century, the Darrieus wind turbine is rarely used today. The Savonius wind turbine is the most common drag type turbine. Despite its low efficiency, it remains in use because of its robustness and simplicity to build and maintain.

Material condition

The characteristics that make composites, especially glass fibre- reinforced and wood/epoxy composites, suitable for wind turbine blades are low density, good mechanical properties, excellent corrosion resistance, tailorability of material properties, and versatility of fabrication methods. Although glass/vinylester and glass/polyvinyl composites based on hand lay-up have been the most widely used materials so far, many more types of fibers and resins have become available recently. The new carbon fibers are stronger and stiffer, while the new resins provide higher toughness and shorter process cycle time. A number of handbooks are now available to designers of composites (Lubin, 1982; Engineered Materials Handbook, 1987; Composites & Laminates, 1987).

Conclusion• After studying all these parameters, we have following conclusions:• Tip speed ratio should be maximum and its value for 2 bladed rotors is 6.28 and for 3 bladed

rotors is 4.19.• Effect of number of rotor blades says that the optimum value of tip speed ratio is considered

only when the rotor is stable and maximum power can be achieved by lower speed of turbine blades in order to avoid the resistance to the upstream wind. Therefore, 3 bladed rotors are superior to 2 bladed rotors.

• The rotor blades should be aerodynamically stable and can resist maximum wind force. For this purpose, the rotor blades are made thinner at edge and thicker at root and center.

• Wind turbine may be lift type or drag type. It also depends on the requirement of uses either it is commercial or personal.

• The minimum wind speed at which turbine blades can rotate depends upon the diameter of rotor blades and the height from the ground. However, in general, its value ranges from 5 m/s to 10 m/s.

• The turbine blades should be designed considering the maximum wind coverage for getting higher output.

• Generally, the wind turbine blades are installed at height range of 15 to 30m. This is the most suitable range of height because in this range, the wind speed lies in the range of 5 m/s to 10 m/s.

• Material of the wind turbine should have low density, good mechanical properties, excellent corrosion resistance, tailorability of material properties, and versatility of fabrication methods.

Thank you