It may be written in terms of the absolute and relative velocities
H二 1 [ U3 -U42 寸 V32 -V42 寸 w42 -w32 ] (8-2)
2AC
For apositive poweroutput， the blade tip speed and whirl velocity combination at the inlet must be greater than at the exit. From Equation(8-2)， the flow must be radially inward so that centrifugal effects may be used. The velocity exiting from a turbine is considered to be unrecoverable;therefore， the utilization factor is defined as the ratio of the total head to the total head plus the absolute exit velocity.
E二 H寸 H 12 V42 (8-3)
The relative proportions of energy transfers obtained by a change of static and dynamic pressure are used to classify turbomachinery. The parameterused to describe this relationship is called the degree of reaction. Reaction， inthiscase， is energy transfer by means of a change in static pressure in a rotor to the total energy transfer in the rotor
2AU32 -U42寸 w42 -w32 R二 1 [ H ] (8-4)
The overall efficiency of a radial-inflow turbine is a function of efficiencies from various components such as the nozzle and rotor. A typical turbine expansion enthalpyjentropy diagram is shown in Figure 8-7. The totalenthalpy remains constant through thenozzle， since neither work nor heat is transferred to orfrom the fluid. Within therotor， the total enthalpy changes. Downstream of the rotor the total enthalpy remains constant.
Total pressure decrease in the nozzle and outlet diffuser are only from frictional losses. In an ideal nozzle or diffuser the total pressure drop is zero. Isentropic efficiency is defined as the ratio of the actual work to the isen-tropic enthalpy decrease， which is the expansion from the inlet total pressure to the outlet total pressure
ηis二 h 0ω -h 05 (8-5)
h-h
0ω 05is
The nozzle efficiency can be calculated as shown in the following relation-ship:
ηnoz二 h 0ω -h 2 (8-6)h 0-h 2is
ω
The rotor efficiency can be defined as shown in the following relationship:
ηrotor二 h 0ω -h 4 (8-7)h0ω -h 4is
Similar to the concept of small-stage efficiency in a compressor， the poly-tropic efficiency in a turbine is the small-stage efficiency in a turbine. The isentropic efficiency can be written in terms of the total pressure as follows:
7 -1
7
P 05
1 -
2ω
ηis二 P干-1(8-8) P 05 干
1 -
P
2ω
where P叫ρ7 equals constant and represents the polytropic process for any particular expansion process. The polytropic efficiency can be written
ηpoly二 Zh 0act 7-1 尝P o
Zh 0isen
二 1 - 1 -7P oω， ， (8-9)
-1P
1 -1 -干 尝oω ， ，
二 7-1 . 干干 P oω
-1
7干
The polytropic efficiency in a turbine can be related to the isentropic efficiency and obtained by combining the previous two equations
P05 ηpoly干-干 1
1 -ηis二 1 -PoPω 05 干-干 1(8-10)
Poω
or
干-1
干
17 1 -ηis寸 ηis P05 Poωηpoly二(8-11)
干 -1P05
干 17Poω
The relationship between the two efficiencies is plotted in Figure 8-8. The multistage turbine on an enthalpyjentropy diagram is shown in Figure 8-9.Examining the characteristic of the multistageunit， the isentropic enthalpy decrease of the incremental stages as compared to the isentropic enthalpydecrease of a single， whole stage encompassing the multistages is defined asthe reheat factor. Since the pressure lines diverge as entropy increases， the sum of the small-stage isentropic decreases are somewhat greater than theoverall isentropic decrease for the same pressure. Hence， the reheat factor isgreater thanunity， and the turbine's isentropic efficiency is greater than its polytropic efficiency of the turbine.
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本文链接地址：燃气涡轮工程手册 Gas Turbine Engineering Handbook 2(26)
