Page 147 - Fluid Mechanics and Thermodynamics of Turbomachinery

128 Fluid Mechanics, Thermodynamics of Turbomachinery
The power output from an elementary ring of area 2 r dr is given by

dW D ZU dy,

where Z is the number of blades and the tangential force on each blade element is
2
1
dY D C y . w l/dr.
2 1
The axial force acting on the blade elements at radius r is Z dX, where
2
1
dX D C X . w l/dr,
2 1
and where C x , C y are the axial and tangential force coefficients. Now the axial force
on all the blade elements at radius r can be equated to the pressure force acting on
the elementary ring:

2
1
p 2 /dr D ZC x . w l/dr,
2 r.p 1 1
2
∴ .p 1 p 2 / D ZC x l ,
1 c 2 2
2 x 2 r sin ˛ 1
where w 1 D c x / sin ˛ 1 .
An expression for the efficiency can now be derived from a consideration of all
the power losses and the power output. The power lost due to the drag forces is
dW f D w 1 dD, where

1
2
dD D ZC D . w l/dr
2 1
and the power lost due to exit kinetic energy is given by
1 2
dW k D . c /d Pm,
2 2
where d Pm D 2 r c x dr and c 2 is the absolute velocity at exit. Thus, the aerodynamic
efficiency, defined as power output/power input, can now be written as
t
R
h dW
D R .
t
h .dW C dW f C dW k /
Ł
The predictions for non-dimensional pressure drop p and aerodynamic efficiency
determined by Raghunathan et al. (1995) are shown in Figure 4.26a and b, respec-
tively, together with experimental results for comparison.
Design and performance variables

The primary input for the design of a Wells turbine is the air power based upon the
p 2 / and the volume flow rate Q at turbine inlet. The perfor-
pressure amplitude .p 1
mance indicators are the pressure drop, power and efficiency and their variation with
the flow rate. The aerodynamic design and consequent performance is a function of
several variables which have been listed by Raghunathan. In non-dimensional form