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Rankine Cycle Calculations k := 103 |
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v2a: |
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Boiler Inlet (actual) P2p := 963.17c-Pa |
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0.5144-k-J— kg-K |
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s2p : |
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v2p : |
Turbine Exit (actual — for using turbine inlet values)
kJ kJ
P4p t := 101.323c-Pa h4p t := 2679.7689— s4p t := 7.3655 v4p t :
4P_t 4P_t kg 4p-t kg-K 4p-t
Turbine Exit (ideal — for using turbine inlet values)
kJ k-J
P4 t := 101.325:-Pa h4 t := 2496.9084 s4 t := 6.8754
– 4_t kg 4-t kg-K
Turbine Exit (theoretical / actual — for using boiler exit values and dT)
P4p_b := 101.323c-Pa h4p_b := 3105.0094^ s4p_b := 8.263^^ v4p_b
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Turbine Exit (theoretical / ideal — for using boiler exit values and dT)
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wturbine_out_actual • h3t h4p_t |
k-J wturbine_out_actual _ 84 316kg |
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wturbine_out_ideal •“ h3t – h4_t |
wturbine_out_ideal _ 267 176]kg |
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wturbine_out_actual n turbine •“ w wturbine_out_ideal |
n turbine _ 31 558% |
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• h3t – h4p_t n turbine alt •“ , u h3t – h4_t |
n turbine_alt = 31 558% |
Theoretical Turbine Efficiency using Exit of Boiler for Turbine Inlet
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wturbine_out_theoretical • h3b h4p_b |
wturbine_out_theoretical 108325]kg |
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wturbine_out_ideal_theoretical •“ h3b – h4_b |
k – J wturbine out ideal theoretical _ 386.414 |
wturbine_out_theoretical
nturbine_theoretical •“ ~ nturbine_theoretical _ 28.033%
wturbine_out_ideal_theoretical
Boiler Efficiency (Using Turbine Inlet Temp as Point 3)
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qboiler_in_actual • h3t h2p |
3 k-J qboiler_in_actual _ 2 614 x 10 "kg |
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qboiler_in_ideal •“ h3t – h2 |
qboiler_in_ideal = 2663 x 103 "kg |
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qboiler in actual n boiler •“ n qboiler in ideal |
П boiler = 98 142% |
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qboiler in theoretical • h3b h2p |
qboiler_in_theoretical 3 063 x Ш |
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qboiler in ideal theoretical •_ h3b – h2 |
_ 3ii2 io>3 kJ qboiler in ideal theoretical _ 3112x 10 |
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qboiler in theoretical n boiler theoretical •_ n qboiler in ideal theoretical |
n boiler_theoretical _ 98 41% |
Condenser / Reservoir (for using turbine inlet values)
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qreservoir out actual • h4p t h1 |
_ 258 ^3 k-J qreservoir_out_actual _ 2 58 x 10 ^g |
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qreservoir out ideal •_ h4 t – h1 |
_ 2 397 iq3 k-J qreservoir out ideal _ 2-39/x 10 ^g |
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qreservoir out ideal n reservoir •_ q qreservoir out actual |
n ■ _ 92 912% reservoir |
Condenser / Reservoir (for using boiler exit values)
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qreservoir out actual b • h4p b h1 |
3 k – J qreservoir out actual b _ 3 005 x 10 "kg’ |
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qreservoir out ideal b •_ h4 b – h1 |
_ 2 727 k – J qreservoir_out_ideal_b _ 10 kg |
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qreservoir out ideal b n reservoir b •_ q qreservoir out actual b |
n reservoir_b _ 90 746% |
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wnet theoretical n cycle theoretical q qin theoretical |
n cycle theoretical 3511 % |
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(h3b – h4p_b) – (h2ap – hl) n cycle theoretical alt h3b – h2p |
n cycle_theoretical_alt _ 3’511%° |
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Ideal Rankine Cycle Efficiency wnet ideal wturbine out ideal – wpump in ideal |
wnet_ideal 266’315"kg |
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wnet_out_ideal •= (h3t – h4_t) – (h2a – h1) |
k – J wnet_out_ideal _ 266’315"kg |
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qin ideal •“ qboiler in ideal |
3 k-J qin_ideal = 2 663 x 10 "kg |
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wnet_ideal n cycle ideal •“ n qin ideal |
n cycle_ideal _ 10% |
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• (h3t – h4_t)-(h2a – h1) n cycle ideal alt h3t – h2 |
n cycle_ideal_alt _ 10% |
vnet_ideal_theoretical • wturbine_out_ideal_theoretical wpump_in_ideal
wnet_ideal_theoretical
wnet_out_ideal_theoretical 385553kg
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qin_ideal_theoretical 3112x 10 ^
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Comparison of Actual to Ideal
Comparison of Actual to Ideal (theoretical)
n cycle theoretical
n actual_to_ideal_theoretical •“ n actual_to_ideal_theoretical _
n cycle_ideal_theoretical
TC := 296.99K THt := 431.46K THb := 644.78K
TC
n camot t : 1 T n camot t = 31166%
TH t
TC
n camot b : 1 T ncamot b 53 939%
TH b
System Efficiency Compared to Carnot
n cycle
n rankine_to_camot_t := nrankine_to_camot_t = 10.252°%
n carnot t
n cycle
n rankine_to_carnot_b :=
n carnot b
nrankine to carnot b 5.924%
System Efficiency Compared to Carnot (theoretical)
n cycle_theoretical
n rankine_to_carnot_theoretical := n rankine_to_carnot_theoretical
n carnot b
APPENDIX M
