Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

100 Fluid Mechanics, Thermodynamics of Turbomachinery
If the aspect ratio H/b is other than 3, a correction to the nominal loss coefficient z*
is made as follows:
for nozzles,
for rotors,
(4.13a)
(4.13b)
where z1 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 5 . As
used in this section, Reynolds number is based upon exit velocity c2 and the hydraulic
mean diameter Dh at the throat section.
where
Dh = 2sHcosa2 ( scos a2
+ H)
.
(N.B. Hydraulic mean diameter = 4 ¥ flow area ∏ wetted perimeter.)
The Reynolds number correction is
(4.14)
(4.15)
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 multiplying
the final calculated stage efficiency by the ratio of “blade” area to total area (i.e. “blade”
area + 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 presentation
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 DW, and the axial velocity cx, have already been selected.
The upper limit of blade speed is limited by stress; the limit on blade tip speed is roughly
450m/s although some experimental turbines have been operated at higher speeds. The
axial velocity is limited by flow area considerations. It is assumed that the blades are
sufficiently short to treat the flow as two-dimensional.
The specific work done is