Using the equation of state pV ¼ RT of ideal gas, after derivation of equation,
there is
T 2 =T 1 ¼ V 2 =V 1
ð
Þ
mÀ1
ð
Þ
T 2 =T 1 ¼ ðp 2 =p 1 Þ
mÀ1
ð
Þ=m
ð9:46Þ
where
m Variability index.
When two state parameters (e.g., p 1 , V 1 ) of nozzle inlet are known, the state
parameters of nozzle outlet can be calculated.
According to the equation of energy conservation, there is
C
2
1
2
þ h 1 ¼
C
02
1
2
þ h
0
2
where
h 1 Enthalpy of nozzle inlet;
C 1 Nozzle inlet velocity;
H
0
2
Actual enthalpy of nozzle outlet;
C
0
2 Actual velocity of nozzle outlet, C
0
2 ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 h 1 À h
0
2
À
Á þ
C 2
1
2
h
i
r
.
Generally, when the gas enters the nozzle from the gas generator, its velocity is
very small, which can be neglected compared with the outlet velocity, so the above
equation can be converted into
C
02
1 ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2 h 1 À h 0
2
À
Á
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2C p T 1 À T 2
ð
Þ
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2
k
k À 1
RT 1 1 À ðp 2 =p 1 Þ
mÀ1
m
h
i
r
ð9:47Þ
So the formula for calculating gas flow rate is
G ¼
f 2 C
02
1
V 0
2
¼
p 1 f 2
ffiffiffiffiffiffiffiffi
RT 1
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2k
k À 1
ðp 2 =p 1 Þ
2
m 1 À ðp 2 =p 1 Þ
mÀ1
m
h
i
r
ð9:48Þ
where
G Flow;
f 2 Nozzle outlet area;
V 2 Nozzle outlet specific volume;
T 1 Gas initial temperature (absolute standard temperature).
9.4 Design Principle of Small Gas Turbine for Missile
139
there is
T 2 =T 1 ¼ V 2 =V 1
ð
Þ
mÀ1
ð
Þ
T 2 =T 1 ¼ ðp 2 =p 1 Þ
mÀ1
ð
Þ=m
ð9:46Þ
where
m Variability index.
When two state parameters (e.g., p 1 , V 1 ) of nozzle inlet are known, the state
parameters of nozzle outlet can be calculated.
According to the equation of energy conservation, there is
C
2
1
2
þ h 1 ¼
C
02
1
2
þ h
0
2
where
h 1 Enthalpy of nozzle inlet;
C 1 Nozzle inlet velocity;
H
0
2
Actual enthalpy of nozzle outlet;
C
0
2 Actual velocity of nozzle outlet, C
0
2 ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 h 1 À h
0
2
À
Á þ
C 2
1
2
h
i
r
.
Generally, when the gas enters the nozzle from the gas generator, its velocity is
very small, which can be neglected compared with the outlet velocity, so the above
equation can be converted into
C
02
1 ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2 h 1 À h 0
2
À
Á
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2C p T 1 À T 2
ð
Þ
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2
k
k À 1
RT 1 1 À ðp 2 =p 1 Þ
mÀ1
m
h
i
r
ð9:47Þ
So the formula for calculating gas flow rate is
G ¼
f 2 C
02
1
V 0
2
¼
p 1 f 2
ffiffiffiffiffiffiffiffi
RT 1
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
2k
k À 1
ðp 2 =p 1 Þ
2
m 1 À ðp 2 =p 1 Þ
mÀ1
m
h
i
r
ð9:48Þ
where
G Flow;
f 2 Nozzle outlet area;
V 2 Nozzle outlet specific volume;
T 1 Gas initial temperature (absolute standard temperature).
9.4 Design Principle of Small Gas Turbine for Missile
139