398
11 Power Gas Turbines
an additional resistance too. Heat transfer between gas and blades (11.17) may, with
an adapted definition of the heat transfer coefficient, be noted as
(11.19)
with T aw the mean adiabatic wall temperature. This is the temperature the wall
would adopt in absence of heat transfer. It approximately equals the gas temperature
at a low velocity, but non-negligible heating by friction occurs at high velocity. The
adiabatic film cooling effectiveness may be defined as
(11.20)
This effectiveness then expresses how much the adiabatic wall temperature decreases compared to the gas temperature, due to the protection by the film, as a
fraction of the temperature difference between the gas T g and the cooling air T e
leaving the ejection holes. It is a realistic approximation that the temperature of the
cooling air entering the film equals the blade temperature, due to the intense contact
between cooling air and blade within the ejection holes. We so may assume T T
e
b
=
and thus combine (11.19) and (11.20) into
From this reasoning emerges that film cooling decreases the heat transfer between
gas and blade. Film cooling efficiency may amount up to 30 %, so that film cooling
reduces the heat transfer to about 70 %. In combination with a thermal barrier coating, κ may be halved so that the resulting value is about 0.15 J/kJK.
The expansion of the cooled stage is represented by the h-s diagram in Fig. 11.13
(left). The 12ʹ part is the expansion with distributed cooling. The 2ʹ2ʺ part renders
the temperature drop by mixing and the 2ʺ2 part is the pressure drop by mixing.
In order to calculate the expansion through a turbine, the entire pressure drop
is divided into sufficiently small intervals. In Fig. 11.13 a pressure interval corresponds to the pressure difference p 1 − p 2 . This interval is considered as a stage. This
fictitious stage has a pressure drop that is much lower than a stage in reality. With a
first iteration, the pressure difference p 1 − p 2 ʹ may be set equal to p 1 − p 2 . On the 12ʹ
path, the energy equation is noted as
(11.21)
and
(11.22)
(
) ,
b
aw
b
Q A T
T
D
a
−
=
−
g
aw
f
g
e
T T .
T T
h
−
=
−
b
g
f
g
b
b
b
f
g
b
Q A (T
(T T ) T ) A ( 1
)(T T ).
D
a
h
a
h
−
=
−
−
−
=
−
−
(
) ,
g
b
dh
dW dq
dW 1 ( T T )
k
− = −
− = −
+
−
(
)
g
pg
g
g
b
RT dp
c dT
1 ( T T ) .
p
h
k
∞
−
=
−
+
−
11 Power Gas Turbines
an additional resistance too. Heat transfer between gas and blades (11.17) may, with
an adapted definition of the heat transfer coefficient, be noted as
(11.19)
with T aw the mean adiabatic wall temperature. This is the temperature the wall
would adopt in absence of heat transfer. It approximately equals the gas temperature
at a low velocity, but non-negligible heating by friction occurs at high velocity. The
adiabatic film cooling effectiveness may be defined as
(11.20)
This effectiveness then expresses how much the adiabatic wall temperature decreases compared to the gas temperature, due to the protection by the film, as a
fraction of the temperature difference between the gas T g and the cooling air T e
leaving the ejection holes. It is a realistic approximation that the temperature of the
cooling air entering the film equals the blade temperature, due to the intense contact
between cooling air and blade within the ejection holes. We so may assume T T
e
b
=
and thus combine (11.19) and (11.20) into
From this reasoning emerges that film cooling decreases the heat transfer between
gas and blade. Film cooling efficiency may amount up to 30 %, so that film cooling
reduces the heat transfer to about 70 %. In combination with a thermal barrier coating, κ may be halved so that the resulting value is about 0.15 J/kJK.
The expansion of the cooled stage is represented by the h-s diagram in Fig. 11.13
(left). The 12ʹ part is the expansion with distributed cooling. The 2ʹ2ʺ part renders
the temperature drop by mixing and the 2ʺ2 part is the pressure drop by mixing.
In order to calculate the expansion through a turbine, the entire pressure drop
is divided into sufficiently small intervals. In Fig. 11.13 a pressure interval corresponds to the pressure difference p 1 − p 2 . This interval is considered as a stage. This
fictitious stage has a pressure drop that is much lower than a stage in reality. With a
first iteration, the pressure difference p 1 − p 2 ʹ may be set equal to p 1 − p 2 . On the 12ʹ
path, the energy equation is noted as
(11.21)
and
(11.22)
(
) ,
b
aw
b
Q A T
T
D
a
−
=
−
g
aw
f
g
e
T T .
T T
h
−
=
−
b
g
f
g
b
b
b
f
g
b
Q A (T
(T T ) T ) A ( 1
)(T T ).
D
a
h
a
h
−
=
−
−
−
=
−
−
(
) ,
g
b
dh
dW dq
dW 1 ( T T )
k
− = −
− = −
+
−
(
)
g
pg
g
g
b
RT dp
c dT
1 ( T T ) .
p
h
k
∞
−
=
−
+
−