Michael J . Mora. Fundamentals of Engineering Thermodynamics(7th Edition). John Wiley & Sons, Inc. 2011
Chapter 8 : Vapour Power Systems Example
Consider a regenerative vapor power cycle with one open feedwater heater.
Steam enters the turbine at 8.0 MPa, 480°C and expands to 0.7 MPa,
Some of the steam is extracted and diverted to the open feedwater heater operating at 0.7 MPa.
The remaining steam expands through the second-stage turbine to the condenser pressure of 0.008 MPa
Saturated liquid exits the open feedwater heater at 0.7 MPa.
The isentropic efficiency of each turbine stage is 85% and each pump operates isentropically.
If the net power output of the cycle is 100 MW, determine
(a) the thermal efficiency %
(b) the mass flow rate of steam entering the first turbine stage, in kg/h.
SOLUTION
Known: A regenerative vapor power cycle operates with steam as the working fluid. Operating pressures and temperatures are specified; the isentropic efficiency of each turbine stage and the net power output are also given.
Find: Determine the thermal efficiency and the mass flow rate into the turbine, in kg/h.
Engineering Model:
Analysis:
Let us determine the specific enthalpies at the principal states of the cycle.
In [1]:
# determine the specific enthalpies at the principal states of the cycle.
import seuif97 as if97
# State 1 : steam entering the turbine at 8MPa, 480C.
p1 = 8.0
t1 = 480.0
h1=if97.pt2h(p1,t1)
s1=if97.pt2s(p1,t1)
print(h1,s1)
# State 2 : p2 =0.7MPa
p2=0.7
h2s=if97.ps2h(p2,s1)
etat1=0.85
h2=h1-etat1 * (h1-h2s)
s2=if97.ph2s(p2,h2)
t2=if97.ph2t(p2,h2)
print(t2,h2,s2)
# State 3 :p3 =0.008MPa s3s =s2
p3=0.008
s3s=s2
h3s=if97.ps2h(p3,s3s)
etat2=etat1
h3=h2-etat2*(h2-h3s)
t3=if97.ph2t(p3,h3)
s3=if97.ph2s(p3,h3)
print(t3,h3,s3)
# State 4 :p4 =0.008MPa Saturated water
p4=0.008
t4=if97.px2t(p4,0)
h4=if97.px2h(p4,0)
s4=if97.px2s(p4,0)
print(t4,h4,s4)
# State 5 :s5=s4
p5=0.7
s5=s4
t5=if97.ps2t(p5,s5)
h5=if97.ps2h(p5,s5)
print(t5,h5)
# State 6 :p6=0.7 Saturated water
p6=0.7
t6=if97.px2t(p6,0)
h6=if97.px2h(p6,0)
s6=if97.px2s(p6,0)
print(t6,h6,s6)
# State 7 :s7=s6,p7=8.0Mpa
p7=8.0
s7=s6
t7=if97.ps2t(p7,s7)
h7=if97.ps2h(p7,s7)
print(t7,h7)
Applying mass and energy rate balances to a control volume enclosing the open heater, we find the fraction $y$ of the flow extracted at state 2 from
$y=\frac{h_6-h_5}{h_2-h_5}$
In [2]:
# Applying mass and energy rate balances to a control volume enclosing the open heater,
# we find the fraction y of the flow extracted at state 2 from
y = (h6-h5)/(h2-h5)
print(y)
SOLUTION
(a) On the basis of a unit of mass passing through the first-stage turbine, the total turbine work output is
$\frac{\dot{W}_{t}}{\dot{m}_1}=(h_1-h_2)+(1-y)(h_2-h_3)$
The total pump work per unit of mass passing through the first-stage turbine is
$\frac{\dot{W}_{p}}{\dot{m}_1}=(h_7-h_6)+-(1-y)(h_5-h_4)$
The heat added in the steam generator per unit of mass passing through the first-stage turbine is
$\frac{\dot{Q}_{in}}{\dot{m}_1}=h_1-h_7$
efficiency is then
$\eta =\frac{\dot{W}_t/\dot{m}_1-\dot{W}_{p}/\dot{m}_1}{\dot{Q}_{in}/\dot{m}_1}$
In [3]:
# Part(a)
wtdot = (h1-h2) + (1-y)*(h2-h3) # the total turbine work output, units in KJ/Kg
wpdot = (h7-h6) + (1-y)*(h5-h4) # The total pump work per unit of mass passing through the first-stage turbine,in KJ/kg
qindot = h1 - h7 # in kj/kg
eta = (wtdot-wpdot)/qindot
# Results
print(' The thermal efficiency is {:>.2f}%'.format(100*eta))
(b) The mass flow rate of the steam entering the turbine, $m_1$, can be determined using the given value for the net power output, 100 MW. Since
$W_{cycle}=W_{t}-W_{p}$
$m_1=\frac{W_{cycle}}{W_{1}/m_1-W_{p}/m_1}$
In [4]:
# Part(b)
Wcycledot=100.0
m1dot = (Wcycledot*3600*10**3)/(wtdot-wpdot)
# Results
print(' The mass flow rate of steam entering the first turbine stage, is {:>.2f}kg/h.'.format(m1dot))
If the mass flow rate of steam entering the first-stage turbine were 150 kg/s
(a) what would be the net power, in MW
(b) the fraction of steam extracted, y?
In [5]:
m1dot=150*3600
Wcycledot=m1dot*(wtdot-wpdot)/(3600*10**3)
print('The net power is {:>.2f}MW'.format(Wcycledot))
In [ ]: