Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

TABLE 9.4. Calculated values of flow angles for
Example 9.4
Parameter Ratio r/rt
0.4 0.7 1.0
c q 2 m/s 9.955 5.687 3.982
tan a 2 0.835 0.4772 0.334
a 2 (deg) 39.86 25.51 18.47
U/c x2 1.019 1.7832 2.547
b 2 (deg) 10.43 52.56 65.69
b 3 (deg) 45.54 60.72 68.57
Hydraulic Turbines 313
where the blade tip speed is U 2 =WD 2/2 = (200 ¥ p/30) ¥ 2.9/2 = 30.37m/s
Values a 2, b 2 and b 3 shown in Table 9.4 have been derived from the following
relations:
Finally, Figure 9.18 illustrates the variation of the flow angles, from which the large
amount of blade twist mentioned earlier can be inferred.
Effect of size on turbomachine efficiency
Despite careful attention to detail at the design stage and during manufacture it is a
fact that small turbomachines always have lower efficiencies than larger geometrically
similar machines. The primary reason for this is that it is not possible to establish perfect
dynamical similarity between turbomachines of different size. In order to obtain this
condition, each of the the dimensionless terms in eqn. (1.2) would need to be the same
for all sizes of a machine.
To illustrate this consider a family of turbomachines where the loading term, y =
gH/N 2 D 2 is the same and the Reynolds number, Re = ND 2 /n is the same for every size
of machine, then