Handbook of Turbomachinery Second Edition Revised - Ventech!

turbine with an effective diffuser, the rotor exit static pressure will be less
than the discharge value. We will examine both cases.
Turbine Without Diffuser
First we consider the turbine without a diffuser. Assuming perfect gas
behavior, the density is calculated from
r 2 ¼ p2
RgasT2
where the temperature and pressure are static values and Rgas is the gas
constant. The rotor exit total temperature is determined from
T 0 2 ¼ T 0 0
DhOA ZC
Cp
¼ 760 R
41:28 Btu=lbm
0:24 Btu=ðlbm RÞ 588:0R
The zero-clearance enthalpy drop is used because the local temperature
over the majority of the blade will reflect the higher work (a higher
discharge temperature will be measured downstream of the turbine after
mixing of the tip clearance flow has occurred). Next we calculate the rotor
exit critical Mach number to determine the static temperature. The critical
sonic velocity is calculated from
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2g
acr ¼ gRgasT
0
g þ 1
where g is a conversion factor. For air at low temperatures,
Rgas ¼ 53:34 ft-lbf=lbm R, resulting in
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
acr2 ¼
2ð1:4Þ
1 þ 1:4
ft lbf
32:174
lbm sec2 s
ft lbf
53:34 588 R
lbm R
¼ 1085 ft=sec
The static temperature is found from
T2 ¼ T 0 2 1
"
g 1
g þ 1
V2
#
2
acr2
with zero exit swirl, V2 ¼ Vx2 resulting in
"
T2 ¼ð588 RÞ 1
1:4 1
1 þ 1:4
535 ft=sec
1085 ft=sec
#
2
¼ 564:2R
Copyright © 2003 Marcel Dekker, Inc.