Page 118 - Fluid Mechanics and Thermodynamics of Turbomachinery

Axial-flow Turbines: Two-dimensional Theory 99
0
0
usually small. Thus, for a nozzle row, D N D ˛ C ˛ and for a rotor row,
2
1
0
0
D R D ˇ C ˇ can be used (the prime referring to the actual blade angles).
2 3
If the aspect ratio H/b is other than 3, a correction to the nominal loss coefficient
Ł
is made as follows:
for nozzles,
Ł
1 C 1 D .1 C /.0.993 C 0.021b/H/, (4.13a)
for rotors,
Ł
1 C 1 D .1 C /.0.975 C 0.075b/H/, (4.13b)
5
where 1 is the loss coefficient at a Reynolds number of 10 .
5
A further correction can be made if the Reynolds number is different from 10 .
As used in this section, Reynolds number is based upon exit velocity c 2 and the
hydraulic mean diameter D h at the throat section.
Re D 2 c 2 D h / , (4.14)
where

D h D 2sH cos ˛ 2 /.s cos ˛ 2 C H/.

(N.B. Hydraulic mean diameter D 4 ð flow area ł wetted perimeter.)
The Reynolds number correction is

5 1/4
10
2 D 1 . (4.15)
Re
Soderberg’s method of loss prediction gives turbine efficiencies with an error of
less than 3% over a wide range of Reynolds number and aspect ratio when additional
corrections are included to allow for tip leakage and disc friction. An approximate
correction for tip clearance may be incorporated by the simple expedient of multi-
plying the final calculated stage efficiency by the ratio of “blade” area to total area
(i.e. “blade” area C clearance area).

Types of axial turbine design
The process of choosing the best turbine design for a given application usually
involves juggling several parameters which may be of equal importance, for instance,
rotor angular velocity, weight, outside diameter, efficiency, so that the final design
lies within acceptable limits for each parameter. In consequence, a simple presen-
tation can hardly do justice to the real problem. However, a consideration of the
factors affecting turbine efficiency for a simplified case can provide a useful guide
to the designer.
Consider the problem of selecting an axial turbine design for which the mean
blade speed U, the specific work W, and the axial velocity c x , have already been
selected. The upper limit of blade speed is limited by stress; the limit on blade tip
speed is roughly 450 m/s although some experimental turbines have been operated