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8 Pages
Problem05
Course: NE 400, Spring 2010School: N.C. State
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Word Count: 732
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proposed A steam cycle for a liquid metal reactor is illustrated in Figure 1. The reactor is to operate at 3600 MW. Compute the cycle efficiency. Assume the high pressure turbine has an efficiency of 90 % and the low pressure turbine has an efficiency of 85 %. You may assume the pumps to be ideal and the pressure change across the sodium pump is 125 psi. 6 4 21 mp Steam Loop Sodium Loop Turbine Superheater...
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proposed A steam cycle for a liquid metal reactor is illustrated in Figure 1. The reactor is to operate at 3600 MW. Compute the cycle efficiency. Assume the high pressure turbine has an efficiency of 90 % and the low pressure turbine has an efficiency of 85 %. You may assume the pumps to be ideal and the pressure change across the sodium pump is 125 psi.
6 4 21 mp Steam Loop Sodium Loop Turbine Superheater Turbine 9 m1
22
3
5
m3 8
m2 2 7 Steam Drum Steam Generator m4
Open Heater 18 17 13
Condenser
10 Core 19 1 11 15 14
m5 20 Sodium Pump 16 12
Figure 1. Steam Cycle for a LMR
Advanced 18
Problem Data Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Pressure (psia) 1650 1600 1600 1600 560 160 140 20 1 Temperature (F) Quality
50 % 100% 900
224
476 1600
950 885
Advanced 18
SOLUTION
High Pressure Turbine P4 = 1600 psia T4 = 900 F h4 = 1425.2 Btu/lbm s4 = 1.5478 High Pressure Tap At P5 = 560 psia and an entropy of 1.5478, the steam is superheated. From the superheat tables h5s = 1293.9 + (1.5478 1.5431)
(1324.9 1293.9) = 1298.99 (1.5717 1.5431)
t =
h4 h5 h5 = h4 t (h4 h5 s ) h4 h5 s
h5 = 1425.2 - (0.90)(1425.2 1298.99) = 1322.61 Btu/lbm High Pressure Turbine Exhaust
x6s = s4 s f s fg @ P6 = 160 psia
sf = 0.5206 sfg = 1.0435
x6 s = 1.5478 0.5206 = 0.9844 1.0435
h6s = h f + x6s h fg @ P6 = 160 psia
hf = 336.1 Btu/lbm hfg = 859 Btu/lbm
h6 s = 336.1 + 0.9844 859 = 1181.7
t =
h4 h6 h6 = h4 t ( h4 h6s ) h4 h6s
h6 = 1425.2 (0.9)(1425.2 1181.7) = 1206.05
Low Pressure Turbine The entropy s6 at P6 = 160 psia and h6 = 1206.05 Btu/lbm is obtained by interpolating from the superheat tables
Advanced 18
s6 = 1.5641 + (1206.05 1195.1) = 1.5771
(1.5906 1.5641) (1217.4 1195.1)
High Pressure Tap At a pressure of 140 psia and an entropy of s6=1.5771 the steam is super heated and the ideal enthalpy at 7 is obtained by interpolating from the superheat tables
h7 s = 1193.0 + (1.5771 1.5752) = 1194.59 (1220.9 1193.0) (1.6085 1.5752)
t =
h6 h7 h7 = h6 t ( h6 h7 s ) h6 h7 s
h7 = 1206.05 (0.85)(1206.05 1194.59) = 1196.76
Low Pressure Turbine Tap
x8 s = s6 s f s fg @ P8 = 20 psia
sf = 0.3358 sfg = 1.3962
x8 s = 1.5771 0.3358 = 0.8891 1.3962
h8s = h f + x8s h fg @ P8 = 20 psia
hf = 196.27 Btu/lbm hfg = 960.1 Btu/lbm
h8 s = 196.27 + 0.8891 960.1 = 1049.85
t =
h6 h8 h8 = h6 t ( h6 h8 s ) h6 h8 s
h8 = 1206.05 (0.85)(1206.05 1049.85) = 1073.28
Low Pressure Turbine Exhaust
x9 s = s6 s f s fg @ P9 = 1 psia
sf = 0.1326 sfg = 1.8455
Advanced 18
x9 s =
1.5771 0.1326 = 0.7827 1.8455
h9s = h f + x9s h fg @ P9 = 1 psia
hf = 69.73 Btu/lbm hfg = 1036.1 Btu/lbm
h9 s = 69.73 + 0.7827 1036.1 = 880.7
t =
h6 h9 h9 = h6 t ( h6 h9s ) h6 h9s
h9 = 1206.05 (0.85)(1206.05 880.7) = 929.5
Condensate Pump
wcp = ( P P ) = (0.0161)(140 1)(144 / 778) = 0.414 11 10
h10 = h f @ P = 1 psia = 69.73 Btu / lbm 10 h11 = h10 wcp h11 = 69.73 + 0.414 = 70.14
h12 = h f @ P = 20 psia = 196.27 Btu / lbm 12
h13 h f @ T13 = 224 F = 192.27 Btu / lbm h14 = h f @ P = 140 psia = 325 Btu / lbm 14
Low Pressure Feed Pump
wlpfp = ( P P ) = (0.018)(1600 140)(144 / 778) = 4.86 15 14
h15 = h14 wlpfp h15 = 325 + 4.86 = 329.86
h16 = h f @ P = psia 560 = 460.9 + (560 550) 16
h17 h f @ T17 = 476 F = 459.9 Btu / lbm
(471.7 460.9) = 463.06 (600 550)
h18 = h f @ P = 1600 psia = 624.2 18
Boiler Feed Pump
Advanced 18
w fp = ( P P ) = (0.02387)(1650 1600)(144 / 778) = 0.221 1 18 h1 = h18 w fp h1 = 624.2 + 0.221 = 624.42
h2 = h f + x2 h fg @ P2 = 1600 psia
hf = 624.2 Btu/lbm hfg = 540.3 Btu/lbm
h2 = 642.2 + (0.5)540.3 = 894.35
h3 = hg @ P3 = 1600 psia = 1164.5 Steam Drum
& & & & m1h17 + m5h2 = m5h18 + m1h3 & m5 h3 h17 1164.5 459.9 = = = 2.608 & m1 h2 h18 894.35 624.2
High Pressure Heater
& & & & m1h17 + m2 h16 = m1h15 + m2 h5 & m2 h17 h15 459.9 329.86 = = = 0.1513 & m1 h5 h16 1322.61 463.06
Open Feed Heater
& & & & & & m2 h16 + m3 h7 + (m1 m2 m3 )h13 = m1h14
&& && & m3 h14 (m2 /m1 )h16 (1 m2 /m1 )h13 = & m1 h7 h13 & m3 325 (0.1513) 463.06 (1 0.1513) 192.27 = = 0.0913 & m1 1196.76 192.27
Low Pressure Feed Heater
& & & & m4 (h8 h12 ) = (m1 m2 m3 )(h13 h11 )
& && && m4 (1 m2 /m1 m3 /m1 )(h13 h11 ) = & m1 h8 h12 & m4 (1 0.1513 0.0913)(192.27 70.14) = = 0.1055 & m1 1073.28 196.27
Advanced 18
Superheater
& & m p C p (T21 T22 ) = m1 (h4 h3 )
& mp h4 h3 = & m1 C p (T21 T22 )
& mp 1425.2 1164.5 = = 13.28 & m1 0.302 (950 885) Steam Generator
& & m p C p (T22 T19 ) = m5 (h2 h1 )
T19 = T22 = 885 = 710
&& m5 m1 (h2 h1 ) && m1 m p C p 2.608 (894.35 624.42) 13.28 .303
Sodium Pump
125 wsp = (P) = (144 / 778) = 0.431 53.7
C p (T20 T19 ) = wsp T20 = T19 wsp Cp 0.431 = 711.4 0.307
T20 = 710 +
Cycle Efficiency
=
& & & & & & & & Wnet (Wthp + Wtlp + Wcp + Wlpfp + W fp + Wsp ) / m1 = & & /m Q Q &1
& & & & & Wthp = m1h4 m2 h5 (m1 m2 )h6 & Wthp && && = h4 (m2 / m1 )h5 (1 m2 / m1 )h6 & m1 & Wthp = 1425.2 (0.1513) 1322.61 (1 0.1513) 1206.05 & m1 = 201.51
Advanced 18
& & & & & & & & & Wtlp = (m1 m2 )h6 m3 h7 m4 h8 (m1 m2 m3 m4 )h9 & Wtlp && && && && && && = (1 m2 / m1 )h6 (m3 / m1 )h7 (m4 / m1 )h8 (1 m2 / m1 m3 / m1 m4 / m1 )h9 & m1
= (1 0.1513) 1206.05 (0.0913) 1196.76 (0.1055) 1073.28 (1 0.1513 0.0913 0.1055) 929.5 = 195.14
& & & & Wcp = (m1 m2 m3 ) wcp & Wcp && && = (1 m2 / m1 m3 / m1 ) wcp & m1
= (1 0.1513 0.0913)(0.414) = 0.314
& & Wlpfp = m1wlpfp & Wlpfp = wlpfp & m1 = 4.86 & & W fp = m5 w fp & W fp m5 & w fp = & & m1 m1 = 2.608 (0.221) = 0.576 & & Wsp = m p wsp & & Wsp m p w = & & sp m1 m1 = 13.28 (.431) = 5.72
&& Q = m p C p (T21 T20 ) & & Q mp = C p (T21 T20 ) & & m1 m1 = 13.28 0.303 (950 711.4) = 960.1
=
=
& & & & & & & & Wnet (Wthp + Wtlp + Wcp + Wlpfp + W fp + Wsp ) / m1 = & & /m Q Q &1
(201.51 + 195.14 0.314 4.86 0.576 5.72) 960.1 = 40.1%
Advanced 18
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