fluid_mechanics

684 Chapter 12 ■ Turbomachines
For geometrically similar turbines and for negligible Reynolds number and surface roughness difference
effects, the relationships between the dimensionless parameters are given functionally by
that shown in Eqs. 12.29, 12.30, and 12.31. That is,
C H f 1 1C Q 2, C p f 2 1C Q 2, and h f 3 1C Q 2
where the functions f 1 , f 2 , and f 3 are dependent on the type of turbine involved. Also, for turbines
the efficiency, h, is related to the other coefficients according to h C pC H C Q .
As indicated above, the design engineer has a variety of turbine types available for any given
application. It is necessary to determine which type of turbine would best fit the job 1i.e., be most efficient2
before detailed design work is attempted. As with pumps, the use of a specific speed parameter
can help provide this information. For hydraulic turbines, the rotor diameter D is eliminated
between the flow coefficient and the power coefficient to obtain the power specific speed, N¿ s , where
N¿ s v2W# shaftr
1gh a 2 5 4
We use the more common, but not dimensionless, definition of specific speed
Specific speed may
be used to approximate
what kind of
turbine geometry
(axial to radial)
would operate most
efficiently.
N¿ sd v1rpm2 2W# shaft 1bhp2
(12.53)
3h a 1ft24 5 4
That is, N¿ is calculated with angular velocity, in rpm; shaft power, W # sd v,
shaft, in brake horsepower;
and actual head available, h a , in feet. Optimum turbine efficiency 1for large turbines2 as a function
of specific speed is indicated in Fig. 12.32. Also shown are representative rotor and casing cross
sections. Note that impulse turbines are best at low specific speeds; that is, when operating with
large heads and small flowrate. The other extreme is axial-flow turbines, which are the most efficient
type if the head is low and if the flowrate is large. For intermediate values of specific speeds,
radial- and mixed-flow turbines offer the best performance.
The data shown in Fig. 12.32 are meant only to provide a guide for turbine-type selection.
The actual turbine efficiency for a given turbine depends very strongly on the detailed design of
the turbine. Considerable analysis, testing, and experience are needed to produce an efficient turbine.
However, the data of Fig. 12.32 are representative. Much additional information can be found
in the literature.
Impulse turbines
Reaction turbines
Radial-flow Mixed-flow Axial-flow
100
90
10 20 40 60 80 100
N′
sd
Impulse
Francis
Kaplan
η %
80
70
N′
sd
and maximum efficiencies as a
function of specific speed.
F I G U R E 12.32
10 20 40 60 80 100
Typical turbine cross sections