Page 149 - Fluid Mechanics and Thermodynamics of Turbomachinery

130 Fluid Mechanics, Thermodynamics of Turbomachinery
and also blade thickness ratio, turbulence level at inlet to turbine, frequency of waves
and the relative Mach number. It was observed by Raghunathan et al. (1987) that
the Wells turbine has a characteristic feature which makes it significantly different
from most turbomachines: the absolute velocity of the flow is only a (small) fraction
of the relative velocity. It is theoretically possible for transonic flow conditions to
occur in the relative flow resulting in additional losses due to shock waves and an
interaction with the boundary layers leading to flow separation. The effects of the
variables listed above on the performance of the Wells turbine have been considered
by Raghunathan (1995) and a summary of some of the main findings is given below.

Effect of flow coefficient

The flow coefficient is a measure of the angle of incidence of the flow and the
aerodynamic forces developed are critically dependent upon this parameter. Typical
results based on predictions and experiments of the non-dimensional pressure drop
Ł
2
2
p D p/. ω D / and efficiency are shown in Figure 4.26. For a Wells turbine
t
a linear relationship exists between pressure drop and the flowrate (Figure 4.26a)
and this fact can be employed when making a match between a turbine and an
oscillating water column which also has a similar characteristic.
The aerodynamic efficiency (Figure 4.26b) is shown to increase up to a certain
value, after which it decreases, because of boundary layer separation.
Effect of blade solidity

The solidity is a measure of the blockage offered by the blades to the flow of air
and is an important design variable. The pressure drop across the turbine is, clearly,
proportional to the axial force acting on the blades. An increase of solidity increases
the axial force and likewise the pressure drop. Figure 4.27 shows how the variations
of peak efficiency and pressure drop are related to the amount of the solidity.
Raghunathan gives correlations between pressure drop and efficiency with
solidity:

2
Ł
2
Ł
1
p /p D 1 and / 0 D .1 /,
2
0
where the subscript 0 refers to values for a two-dimensional isolated aerofoil
( D 0). A correlation between pressure drop and solidity (for > 0) was also
expressed as
Ł
p D A 1.6
where A is a constant.
Effect of hub to tip ratio

The hub/tip ratio is an important parameter as it controls the volume flow rate
through the turbine but also influences the stall conditions, the tip leakage and, most
importantly, the ability of the turbine to run up to operating speed. Values of < 0.6
are recommended for design.