Wind Turbine Technology and Application

In this part of assignment 2 there are SIX problems related to wind turbine which you need to answer all.

Question 1

(a) Estimate the annual energy production from a horizontal axis wind turbine with a 35 m diameter operating in a wind regime with an average wind speed of 7 m/s based on average speed data only. Assume that the wind turbine is operating under standard atmospheric conditions (air density ρ = 1.225 kg/m3) and the turbine efficiency is 0.42.

(b) Find the size of a wind turbine rotor (diameter in m) that will generate 300 kW of electrical power in a steady wind (hub height) of 8 m/s. Assume that power coefficient Cp = 16/27 and electro/mechanical efficiency η = 1.

Question 2

(a) Estimate the wind speed at a height of 110 m over surface terrain with a few trees, if the wind speed at a height of 10 m is 5 m/s.

(b) Wind turbine blades are made in many different ways and from many different materials. Discuss the most important factors in the selection of materials for blade construction and describe how wood composite and glass fibre reinforced plastic is used to make blades.

Question 3

(a) The capacity factor is a useful parameter when comparing the performance of energy sources. What is the definition of the capacity factor?

(b) A typical nuclear power plant has a capacity factor of around 90%, while the capacity factor for large scale wind turbines is around 40% (see Figure Q3). Discuss the reason for such wide gap between the capacity factors of these two types of energy production systems.

Figure Q3. Annual onshore, offshore and total wind power capacity factor

Question 4

A three-bladed wind turbine with radius of 50 m produce 1500 kW at a wind speed of 11 m/s. Air density is 1.225 kg/m3. Under these conditions

(i) What is the rotational speed of the rotor in rpm when it operates at tip speed ratio of TSR=6?

(ii) What is the tip speed of the rotor?

(iii) If the generator needs to turn at 1800 rpm, what gear ratio of generator to rotor is needed to match the rotor speed to the generator speed?

(iv) What is the overall efficiency of the complete wind turbine (blades, gearbox and generator) under these conditions?

Question 5

Design an optimum blade based on Betz and Schmitz for a three-bladed turbine. The lift-todrag ratio and the lift coefficient of the aerofoil against the angle of attack (AoA) are given in Figure Q5.1, and the exact values from these curves are tabulated in Table Q5.1. The curves giving the power coefficient against the tip speed ratio (TSR) for typical three-bladed machines can be found in Figure Q5.2.

(a) Give formulas for calculating the chord length and the pitch angle of the blade based on optimum Betz and Schmitz methods. Note that the pitch angle is defined as the angle between the chord line and the plane of blade rotation. Assume a pitch angle of zero. Explain all symbols and quantities that appear in the formulas and draw a figure explaining the angles.

(b) Apply the formulas to a three-bladed turbine for blades with radius R = 80m and a pitch angle of zero: explain how you select the values of the parameters appearing in the formulas, and fill in the Table below, with r being the distance from the hub along the blade in meter and the twist angle in degree. Plot variation of chord length c and twist angle beta versus r/R.

(c) Explain why the blades have to be twisted.

Question 6

Figure Q6(a) shows the lift and drag characteristics for a NACA 4415 aerofoil.

a) Using the graphs shown in Figure Q6(a), determine the best operating point (angle of attack) for the aerofoil at Reynold’s number (Re) of 3×106 . Find the values of lift coefficient (CL) and drag coefficient (CD) at this best point and at static stall?

Figure Q6(a). Lift and drag coefficient vs. AoA and CL-CD curve for NACA 4415 aerofoil.

(b) A yearly histogram of wind speed for a location and generated power is shown in Figure Q6(b). Find the maximum output and power capacity of this turbine.

Figure Q6(b). Histogram of wind speed and ideal power curve for the turbine.