Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

280 Fluid Mechanics, Thermodynamics of Turbomachinery
(8.52)
The stagnation pressure ratio across the turbine stage is given by p03/p01 =
(T03ss/T01) g /(g-1) ; substituting this into eqn. (8.52) and rearranging, the exhaust energy
factor is
1
Now T = T 1+ ( g
-1)
M and
therefore,
03 3 2
3 2
[ ]
(8.53)
(8.54)
With further manipulation of eqn. (8.53) and using eqn. (8.54) the stagnation pressure
ratio is expressed explicitly as
(8.55)
Wood (1963) has calculated the pressure ratio (p01/p 03) using this expression, with h t =
0.9, g = 1.4 and for M3 = 0.7 and 1.0. The result is shown in Figure 8.14. In practice,
exhaust choking effectively occurs at nominal values of M3 0.7 (instead of at the
ideal value of M3 = 1.0) due to non-uniform exit flow.
The kinetic energy ratio (c3/c0) 2 has a first order effect on the pressure ratio limits of
single-stage turbines. The effect of any exhaust swirl present would be to lower the
limits of choking pressure ratio.
It has been observed by Wood that high pressure ratios tend to compel the use of
lower specific speeds. This assertion can be demonstrated by means of Figure 8.12
taken together with Figure 8.18. In Figure 8.12, for a given value of A3/A d, W s increases
with (c3/c 0) 2 increasing. From Figure 8.18, (p 01/p 03) decreases with increasing values of
(c3/c 0) 2 . Thus, for a given value of (c 3/c 0) 2 , the specific speed must decrease as the
design pressure ratio is increased.
Cooled 90deg IFR turbines
The incentive to use higher temperatures in the basic Brayton gas turbine cycle is
well known and arises from a desire to increase cycle efficiency and specific work
output. In all gas turbines designed for high efficiency a compromise is necessary
between the turbine inlet temperature desired and the temperature which can be
tolerated by the turbine materials used. This problem can be minimised by using an
auxiliary supply of cooling air to lower the temperature of the highly stressed parts