Power Plant Engineering

NON-CONVENTIONAL ENERGY RESOURCES AND UTILISATION 61

over time. Reversible hydrogen fuel cells may be an option in the future — they can produce hydrogen
to store energy, and then use the hydrogen to produce power at other times when the wind turbine
output is low.

The larger the wind turbine, the higher the tower that supports the blades must be. This isn’t just
to keep the blades a safe distance off the ground. The higher you go from ground level, the faster and
more uniform the wind so you get more power. So, as the power output of turbines increases, so does
their size. The only restriction on the size of a wind turbine is the strength of the materials from which
it is built. This is a serious engineering problem because whilst the turbine must be light enough to turn
in a light breeze, the structure must be strong enough to withstand storm force winds.

Forces on the Blades. There are two types of forces operating on the blades of a propeller-type
wind turbine. They are the circumferential forces in the direction of wheel rotation that provide the
torque and the axial forces in the direction of the wind stream that provide an axial thrust that must be
counteracted by proper mechanical design.

The circumferential force, or torque, T is obtained from

T =

P

ω

=

P

πDN

...(1)

where T = torque, N or lb,

ω = angular velocity of turbine wheel, m/s

D = diameter of turbine wheel = 4 A/π, m

N = wheel revolutions per unit time, s–1

For a turbine operating at power P, the torque is given by

T = η

1

(^8) gc
3
DV 1
N
ρ
...(2)
For a turbine operating at maximum efficiency ηmax = 16/27, the torque is given by Tmax,
Tmax =
2
27 gc
3
PDV 1
N
The axial force, or axial thrust, is
Fa =
1
2 gc
ρA(V 12 – V 22 ) =
8 gc
π
ρD^2 (V 12 – V 22 )
The axial force on a turbine wheel operating at maximum efficiency where Ve = 1/3;Vi is given
by
Fa, max =
4
9 gc
ρAV 12 =
9 gc
π
ρD^2 V 12
The axial forces are proportional to the square of the diameter of the turbine wheel which makes
them difficult to cope with in extremely large-diameter machines. There is thus an upper limit of diam-
eter that must be determined by design and economical considerations.