Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

For blades with a constant cross-sectional area, we get
(4.30a)
A rotor blade is usually tapered both in chord and in thickness from root to tip such
that the area ratio At/A h is between 1/3 and 1/4. For such a blade taper it is often assumed
that the blade stress is reduced to 2/3 of the value obtained for an untapered blade. A
blade stress taper factor can be defined as
K =
stress at root of tapered blade
stress at root of untapered blade .
Thus, for tapered blades
Axial-flow Turbines: Two-dimensional Theory 117
(4.30b)
Values of the taper factor K quoted by Emmert (1950), are shown in Figure 4.16 for
various taper geometries.
Typical data for the allowable stresses of commonly used alloys are shown in Figure
4.17 for the “1000hr rupture life” limit with maximum stress allowed plotted as a function
of blade temperature. It can be seen that in the temperature range 900–1100K,
nickel or cobalt alloys are likely to be suitable and for temperatures up to about
1300K molybdenum alloys would be needed.
By means of blade cooling techniques it is possible to operate with turbine entry
temperatures up to 1650–1700K, according to Le Grivès (1986). Further detailed information
on one of the many alloys used for gas turbines blades is shown in Figure 4.18.
This material is Inconel, a nickel-based alloy containing 13% chromium, 6% iron, with
a little manganese, silicon and copper. Figure 4.18 shows the influence of the “rupture
K
1.0
0.8
0.6
0.4
0.2
Linear taper
Conical taper
0 0.2 0.4 0.6 0.8 1.0
A t /A h
FIG. 4.16. Effect of tapering on centrifugal stress at blade root (adapted from
Emmert 1950).