In figure, S is entropy, P1 and P2 are isobaric curves. It can be seen from the
figure that the enthalpy of point 2
0 is higher than that of the end point 2 of adiabatic
process, and the entropy is also increased. The process is no longer an isentropic
process. In thermodynamics, it is called a variable process. Next, the flow process
equation of the variable process is derived.
If the inner surface of the nozzle is uniformly machined and the roughness is the
same, it can be assumed that the micro heat generated by friction is proportional to
the decrease of enthalpy. There is
dq ¼ Àndh
ð9:41Þ
where
n Nozzle loss coefficient.
From the second analytic expression of the first law of thermodynamics, it can be
obtained
dq ¼ dq m ¼ dh À Vdp
That is
Àndh ¼ dh À Vdp
1 þ n
ð
Þdh À Vdp ¼ 0
ð9:42Þ
Because of
dh ¼ C p dT ¼ kd pV
ð Þ= k À 1
ð
Þ
ð9:43Þ
Substituting (9.43) into (9.42), it can be obtained
1 þ n
ð
ÞÁk pdV þ Vdp
ð
Þ = k À 1
ð
ÞÀVdp ¼ 0
After sorting, there is
mdV=V þ dp=p ¼ 0
ð9:44Þ
m ¼ k 1 þ n
ð
Þ= kn þ 1
ð
Þ
Integral Eq. (9.44), it can be obtained
pV
m
¼ constant value
ð9:45Þ
138
9 High-Temperature and High-Speed Gas Turbine Pump …