Turbine Test and Design | Questions-Answers

Turbine Test and Design 1
Turbine Test and Design
By
Professor
University
Course
City
Date of submission

Turbine Test and Design 2
Turbine Test and Design
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. (10 Marks)
Conditions
Type – Horizontal axis wind turbine
Diameter- 35m
Radius- 35÷2 = 17.5
Wind speed = 7m/s
Density = 1.225kg/m3
Turbine efficiency = 0.42
Calculations
P=π × R2 × 1
2 × ρ× U3
= π × 17.52 × 1
2 ×1.225 ×73
= 202127.8624
= 202. 1278624kW
Finding annual energy production in (kWh)
= ŋ × P ×(365 ×24 hours )

Turbine Test and Design 3
= 0.42 × 202127.8624 × 8760
= 743668831.341
= 743668.831341 kwh
Solution
= 743668.831341 kWh
(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.
Conditions
Power- 300 kw
Speed- 8m/s
Density- 1.225kg/m3
CP – 16/27 = 59.3% = 0.593
Efficiency- 1
Calculations
P= 1
2 ρπ R2 C P ŋ U3
To find the diameter;
D=2
√ P
1
2 ρπ CP ŋU 3

Turbine Test and Design 4
= 2 ×
√ 300 kwh
1
2 × 1.225× π × 0.593× 1× 83
=22.964428001
= 22.96 m
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. (5 Marks)
First estimate Equation
U (z )
U ( zr )=
( z
zr )
α
α= 1/7 = 0.142
U ( 110 ) = ( 5 ) ( 110
10 )
0.142
= 0.06389326484
= 0.064 m/s
Second estimate equation
100mm = 0.1m
U ( z )
U ( zr )= ln z / z0
ln zr / z0
U (110) = (5) ln(110 /0.1)
ln(10 /0.1)