8-90 Steam enters a turbine at 9 MPa, 600 degrees C, and 60 m/s and leaves at 20

Question

8-90 Steam enters a turbine at 9 MPa, 600 degrees C, and 60 m/s and leaves at 20 kPa and 90 m/s with a moisture content of 5 percent. The turbine is not adequately insulated and it estimated that heat is lost from the turbine at a rate of 220 kW. The power output of the turbine is 4.5 MW. Assuming the surroundings to be at 25 degrees C, determine (a) the reversible power output of the turbine, (b) the exergy destroyed within the turbine, and (c) the second-law efficiency of the turbine. (d) Also, estimate the possible increase in the power output of the turbine if the turbine were perfectly insulated.

Explanation / Answer

Ti = 220 deg. C
pi = 12 Mpa
Vi = 60 m/s
Po = 20 kPa
Vo = 130 m/s
moisture content, 1 - xo = 5% --> xo = 95% = 0.95
Q = - 150 kW
W = 2.5 MW
To = 25 deg, C

(a) Reversible power output, si = so
Energy balance for actual condition,
0 = Q - W + m_dot*[(hi-ho) + (Vi^2-Vo^2)/2]
m_dot = W - Q / [(hi-ho) + (Vi^2-Vo^2)/2]
hi = h(Ti,pi)
ho = h(xo,po)

Energy balance for reversible turbine at steady state,
dEcv/dt = 0 = Q - Wr + m_dot*[(hi-ho) + (Vi^2-Vo^2)/2]
Wr = Q + m_dot*[(hi-ho) + (Vi^2-Vo^2)/2]
hi = h(Ti,pi)
ho = h(po,si)

(b) The exergy destroyed, Ed
Exergy balance for turbine at steady state,
dExcv/dt = 0 = (1 - To/Tb)Q - W + m_dot(efi - efo) - Ed
Ed = (1 - To/Tb)Q - W + m_dot(efi - efo)
with exergy accompany by flow,
efi - efo = (hi-ho) - To(si-so) + Vi^2-Ve^2/2
This can be solved if we may assume average outer surface temperature, Tb.

c. Exergetic efiiciency
= W / [ (efi - efo) - (1-To/Tb)Q ], exergy accompany by heat transfer must be positive.

d. Possible increase,
Energy balance,
W' = m_dot*[(hi-ho) + (Vi^2-Vo^2)/2]
W' = W - Q
with,
ho = h(po,xo)

Exergy destruction
Ed' = -W_max + m_dot(efi - efo), Q = 0
Ed' = m_dot(efi - efo) - W

Exergetic efficiency,
' = W_max / (efi - efo)

Ed' and ', should carefully counted as final state will be differ from actual condition.
--
I still in doubt whether reversible process should count for heat transfer, as heat transfer is irreversible process. I assume turbine undergo internal reversible process and added Q to energy balance. My answer is only suggestion, if you have any other reasoning, then you should appy your own steps.

Related Questions

Navigate

• Browse (All)
• Browse 8
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.