Handbook of Turbomachinery Second Edition Revised - Ventech!

The conservation of angular momentum requires that
$ r2
r1 rVzðrVyÞrdr¼ constant between blade rows ð3Þ
When there is also a change in entropy through any stream tube (e.g.,
from friction or from a transfer of heat into or out of a stream tube), the
total pressure changes according to the equation:
ðP2=P1Þ ðg 1Þ=g ¼ exp½ ðJ=RÞDSŠ ð4Þ
The corresponding static pressure and density are related by Eqs. (5) and
(6):
p2=p1 ¼ðt2=t1Þ g=ðg 1Þ p2=p1 ð5Þ
p2=p1 ¼ðp2=p1Þ=ðt2=t1Þ ð6Þ
Flow in Rotors
Rotors supply energy to the gas, and change the enthalpy in accordance
with Euler’s turbine equation:
JðH2 H1Þ ¼ðr2Vy;2 r1Vy;1Þ ð7Þ
Be aware, however, that any recirculation of gas between the inlet and outlet
of a rotor augments the enthalpy of the gas stream and causes H2 to be
greater than that given by Eq. (7). This phenomenon also increases the
entropy.
The relation corresponding to Eq. (1) is
I2 ¼ gJcpt2 þ 1
2 ðV2 z;2 þ V2 r;2 þ V2 y;2Þ ¼ gJcpt1 þ 1
2 ðV2 z;1 þ V2 r;1 þ V2 y;1Þ¼I2 ð8Þ
and Eq. (4) is changed to
ðP2=P1Þ ðg 1Þ=g ¼ðT2=T1Þ exp½ ðJ=RÞDSŠ ð9Þ
Equation (5) becomes
ðp2=p1Þ ¼ðt2=t1Þ g=ðy 1Þ g=ðy 1Þ
ðP2=P1Þ=ðT2=T1Þ
Equations (2) and (6) are applicable to rotors as well as stators.
Copyright © 2003 Marcel Dekker, Inc.
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