Basic design of the rotor
Each term in Eq. (8.4b) makes a contribution to the specific work done on the rotor. A significant contribution comes from the first term, namely, 1=2ðU2 2 U2Þ, and is the main reason why the inward-flow turbine has such an advantage over the outward-flow turbine where the contribution from this term would be negative. For the axial-flow turbine, where U2 5 U1, of course, no contribution to the specific work is obtained from this term. For the second term in Eq. (8.4b), a positive contribution to the specific work is obtained when w3 . w2. In fact, accelerating the relative velocity through the rotor is a most useful aim of the designer as this is conducive to achieving a low loss flow. The third term in Eq. (8.4b) indicates that the absolute velocity at rotor inlet should be larger than at rotor outlet so as to increase the work input to the rotor. With these considerations in mind the general shape of the velocity diagram shown in Figure 8.3 results.
Nominal design
The nominal design is defined by a relative flow of zero incidence at rotor inlet (i.e., w2 5 cr2) and an absolute flow at rotor exit, which is axial (i.e., c3 5 cx3).1 Thus, from Eq. (8.4a), with cθ3 5 0 and cθ2 5 U2, the specific work for the nominal design is simply
EXAMPLE 8.1
The rotor of an IFR turbine, which is designed to operate at the nominal condition, is 23.76 cm in diameter and rotates at 38,140 rev/min. At the design point, the absolute flow angle at rotor entry is 72o. The rotor mean exit diameter is one-half of the rotor diameter and the relative velocity at rotor exit is twice the relative velocity at rotor inlet.
Determine the relative contributions to the specific work of each of the three terms in Eq. (8.4b).
Solution
The blade tip speed is U2 5 πΩD2/60 5 π 3 38,140 3 0.2376/60 5 474.5 m/s.
Referring to Figure 8.3, w2 5 U2 cot α2 5 154.17 m/s and c2 5 U2/sin α2 5 498.9 m/s
Spouting velocity
The term spouting velocity c0 (originating from hydraulic turbine practice) is defined as that velocity that has an associated kinetic energy equal to the isentropic enthalpy drop from turbine inlet stagnation pressure p01 to the final exhaust pressure. The exhaust pressure here can have several interpretations depending upon whether total or static conditions are used in the related efficiency definition and upon whether or not a diffuser is included with the turbine. Thus, when no diffuser is used
At the best efficiency point of actual (frictional) 90o IFR turbines, it is found that this velocity ratio is, generally, in the range 0.68 ,U2/c0 , 0.71.