RANKINE CYCLE CALCULATIONS

 Rankine Cycle Calculations k := 103

 v2a:

 Boiler Inlet (actual) P2p := 963.17c-Pa

 0.5144-k-J— kg-K

 s2p :

 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

Turbine Exit (theoretical / ideal — for using boiler exit values and dT)

 wturbine_out_actual • h3t h4p_t k-J wturbine_out_actual _ 84 316kg wturbine_out_ideal •“ h3t – h4_t wturbine_out_ideal _ 267 176]kg wturbine_out_actual n turbine •“ w wturbine_out_ideal n turbine _ 31 558% • 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

 wturbine_out_theoretical • h3b h4p_b wturbine_out_theoretical 108325]kg 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)

 qboiler_in_actual • h3t h2p 3 k-J qboiler_in_actual _ 2 614 x 10 "kg qboiler_in_ideal •“ h3t – h2 qboiler_in_ideal = 2663 x 103 "kg qboiler in actual n boiler •“ n qboiler in ideal П boiler = 98 142%

 qboiler in theoretical • h3b h2p qboiler_in_theoretical 3 063 x Ш qboiler in ideal theoretical •_ h3b – h2 _ 3ii2 io>3 kJ qboiler in ideal theoretical _ 3112x 10 qboiler in theoretical n boiler theoretical •_ n qboiler in ideal theoretical n boiler_theoretical _ 98 41%

Condenser / Reservoir (for using turbine inlet values)

 qreservoir out actual • h4p t h1 _ 258 ^3 k-J qreservoir_out_actual _ 2 58 x 10 ^g qreservoir out ideal •_ h4 t – h1 _ 2 397 iq3 k-J qreservoir out ideal _ 2-39/x 10 ^g qreservoir out ideal n reservoir •_ q qreservoir out actual n ■ _ 92 912% reservoir

Condenser / Reservoir (for using boiler exit values)

 qreservoir out actual b • h4p b h1 3 k – J qreservoir out actual b _ 3 005 x 10 "kg’ qreservoir out ideal b •_ h4 b – h1 _ 2 727 k – J qreservoir_out_ideal_b _ 10 kg qreservoir out ideal b n reservoir b •_ q qreservoir out actual b n reservoir_b _ 90 746%

 107.524-k-J kg

 Heat Input qin qboiler_in_actual Heat Input (theoretical) qin theoretical qboiler in theoretical

 Rankine Cycle Efficiency

 П cycle = 3195% n cycle_alt = 3195%

 h1)

 wnet theoretical n cycle theoretical q qin theoretical n cycle theoretical 3511 % (h3b – h4p_b) – (h2ap – hl) n cycle theoretical alt h3b – h2p n cycle_theoretical_alt _ 3’511%°

 Ideal Rankine Cycle Efficiency wnet ideal wturbine out ideal – wpump in ideal wnet_ideal 266’315"kg wnet_out_ideal •= (h3t – h4_t) – (h2a – h1) k – J wnet_out_ideal _ 266’315"kg qin ideal •“ qboiler in ideal 3 k-J qin_ideal = 2 663 x 10 "kg wnet_ideal n cycle ideal •“ n qin ideal n cycle_ideal _ 10% • (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

qin_ideal_theoretical 3112x 10 ^

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

Updated: August 22, 2015 — 2:25 am