Equations. P v2

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1 P v2 Equations Thermodynamics - An Engineering Approach (5th Ed) - Cengel, Boles - Mcgraw-Hill (2006) - pg. 602 Problem (9-96) Effect of Number of Reheat Stages on Rankine Cycle Using EES (or other) software, investigate the effect of number of reheat stages on the performance of an ideal reheat Rankine cycle. The maximum and minimum pressures in the cycle are 15 MPa and 10 kpa, respectively, and steam enters all stages of the turbine at 500 C. The minimum For each case, maintain roughly the same pressure ratio across each turbine stage. Determine the thermal efficiency of the cycle and plot it against the number of reheat stages 1, 2, 4, and 8, and discuss the results. Let s modify this problem to include the effects of the turbine and pump efficiencies and also show the effects of reheat on the steam quality at the low pressure turbine exit. See Prob for a diagram window input version of this problem. $UnitSystem C kpa function x$(x) Functia intoarce un sir de caractere care indica starea vaporilor - this function returns a string t x$ = Vapori umezi ; (2) If(x > 1) then x$ = Abur supraincalzit ; (3) 1

2 If(x < 0) then x$ = Lichid subracit ; (4) end (5) procedure Reheat(NoRHStages : Q in,reheat, W t,lp, s5, h6) (6) $Common P_ratio,Eta_t,P[4],h[4],T[3],T[5] h4 1 = h 4 ; P 3 1 = P 4 ; T 3 1 = T 5 ; (7) Q in,reheat = 0; W t,lp = 0; P ratio,rh = (1/P ratio ) i max = NoRHStages 1; i = 0; repeat i = i + 1 [3] 1 NoRHStages+1 ; (8) (9) (10) (11) (12) (13) (14) h3 i = h (ST EAM, T = T 3 i, P = P 3 i ) ; s3 i = s (ST EAM, T = T 3 i, P = P 3 i ) ; (15) Q in,i = h3 i h4 i ; Q in,reheat = Q in,reheat + Q in,i ; [4s] (16) (17) (18) P 4 i+1 = P 3 i P ratio,rh ; s s4,i+1 = s3 i ; (19) h s4,i+1 = h (ST EAM, s = s s4,i+1, P = P 4 i+1 ) ; (20) T s4,i+1 = T (ST EAM, s = s s4,i+1, P = P 4 i+1 ) ; (21) [4] -iesire (22) h4 i+1 = h3 i η t (h3 i h s4,i+1 ) ; Randamentul turbinei - Definition of turbine efficiency(23) T 4 i+1 = T (ST EAM, P = P 4 i+1, h = h4 i+1 ) ; (24) s4 i+1 = s (ST EAM, P = P 4 i+1, h = h4 i+1 ) ; v4 i+1 = v (ST EAM, P = P 4 i+1, s = s4 i+1 ) ; (25) 2

3 x4 i+1 = x (ST EAM, P = P 4 i+1, h = h4 i+1 ) ; x4$ i+1 = x$(x4 i+1 ); x[4] tb > 1? (26) W t,i = h3 i h4 i+1 ; SSSF First Law for the turbine (27) W t,lp = W t,lp + W t,i ; SSSF First Law for the turbine (28) P 3 i+1 = P 4 i+1 ; Conditii initiale pentru treapta urmatoare (29) T 3 i+1 = T 5 ; until (i > i max ) s5 = s3 i ; h6 = h4 i+1 ; end (30) (31) (32) (33) Marimi de intrare NoRHStages = 2; (34) P 6 = 10 [kpa] ; P 3 = [kpa] ; (35) T 3 = 500 [C] ; T 5 = T 3 ; (36) η t = 1.0; Turbine isentropic efficiency (37) η p = 1.0; Pump isentropic efficiency (38) P extract = P 6 Presiunea de reincalzire minima - Select a lower limit on the reheat pressure (39) Calcul P ratio = P 3 P extract ; (40) Pompa - Pump analysis [1] (41) P 1 = P 6 ; x 1 = 0 Sat d liquid (42) h 1 = h (ST EAM, P = P 1, x = x 1 ) ; T 1 = T (ST EAM, P = P 1, x = x 1 ) ; (43) v 1 = v (ST EAM, P = P 1, x = x 1 ) ; s 1 = s (ST EAM, P = P 1, x = x 1 ) ; (44) [2] (45) 3

4 P 2 = P 3 ; (46) W p,s = v 1 (P 2 P 1 ) ; SSSF isentropic pump work assuming constant specific volume (47) W p = W p,s /η p ; (48) h 2 = h 1 + W p ; SSSF First Law for the pump (49) v 2 = v (ST EAM, P = P 2, h = h 2 ) ; s 2 = s (ST EAM, P = P 2, h = h 2 ) ; (50) T 2 = T (ST EAM, P = P 2, h = h 2 ) ; (51) Turbina de inalta presiune - High Pressure Turbine analysis [3] (52) h 3 = h (ST EAM, T = T 3, P = P 3 ) ; (53) s 3 = s (ST EAM, T = T 3, P = P 3 ) ; v 3 = v (ST EAM, T = T 3, P = P 3 ) ; (54) P extract,min = P (ST EAM, s = s 3, x = 1) ; (55) [4s] (56) s s,4 = s 3 ; (57) h s,4 = h (ST EAM, s = s s,4, P = P 4 ) ; T s,4 = T (ST EAM, s = s s,4, P = P 4 ) ; (58) [4] (59) P 4 = P 3 (1/P ratio ) 1 NoRHStages+1 ; (60) η t = h 3 h 4 h 3 h s,4 ; Randamentul turbinei - Definition of turbine efficiency (61) T 4 = T (ST EAM, P = P 4, h = h 4 ) ; s 4 = s (ST EAM, P = P 4, h = h 4 ) ; (62) v 4 = v (ST EAM, P = P 4, s = s 4 ) ; x 4 = x (ST EAM, P = P 4, h = h 4 ) ; x4$ = x$(x 4 ); x[4] tb > 1 h 3 = W t,hp + h 4 ; SSSF First Law for the high pressure turbine (64) Turbina de joasa presiune - Low Pressure Turbine analysis call Reheat(NoRHStages : Q in,reheat, W t,lp, s 5, h 6 ); (65) 4

5 Generatorul de abur - Boiler analysis Q in,boiler + h 2 = h 3 SSSF First Law for the Boiler (66) Q in = Q in,boiler + Q in,reheat ; (67) Condensatorul - Condenser analysis [6] (68) h 6 = Q out + h 1 SSSF First Law for the Condenser (69) T 6 = T ( steam, h = h 6, P = P 6 ) ; (70) s 6 = s ( steam, h = h 6, P = P 6 ) ; x 6 = x (ST EAM, h = h 6, P = P 6 ) ; (71) x6s$ = x$(x 6 ); (72) Ciclul - Cycle Statistics W t = W t,hp + W t,lp ; W net = W t W p ; η th = W net /Q in ; (73) (74) (75) Solution Variables in Main program η p = 1 η t = 1 η th = NoRHStages = 2 P extract = 10 [kpa] P extract,min = 1969 [kpa] P ratio = 1500 Q in = 4534 [kj/kg] Q in,boiler = 3102 [kj/kg] Q in,reheat = 1432 [kj/kg] Q out = 2627 [kj/kg] W net = 1907 [kj/kg] W p = [kj/kg] W p,s = [kj/kg] W t = 1922 [kj/kg] W t,hp = [kj/kg] W t,lp = 1332 [kj/kg] x4$ = Vapori umezi x6s$ = Abur supraincalzit Variables in Procedure Reheat NoRHStages = 2 Q in,reheat = 1432 [kj/kg] W t,lp = 1332 [kj/kg] s5 = [kj/kg-k] h6 = 2819 [kj/kg] P RAT IO = 1500 η T = 1 P [4] = 1310 [kpa] H[4] = 2719 [kj/kg] T [3] = 500 [C] T [5] = 500 [C] h4[1] = 2719 [kj/kg] P 3[1] = 1310 [kpa] T 3[1] = 500 [C] P ratio,rh = i max = 1 i = 2 P RAT IO = 1500 η T = 1 P [4] = 1310 [kpa] H[4] = 2719 [kj/kg] T [3] = 500 [C] T [5] = 500 [C] H3[1] = 3475 [kj/kg] S3[1] = [kj/kg-k] Q IN,1 = [kj/kg] P 4[2] = [kpa] S S4,2 = [kj/kg-k] H S4,2 = 2812 [kj/kg] T S4,2 = [C] H4[2] = 2812 [kj/kg] T 4[2] = [C] 5

6 S4[2] = [kj/kg-k] V 4[2] = [m 3 /kg] X4[2] = 100 X4$[2] = Abursupraincalzit W T,1 = [kj/kg] P 3[2] = [kpa] T 3[2] = 500 [C] H3[2] = 3488 [kj/kg] S3[2] = [kj/kg-k] Q IN,2 = 676 [kj/kg] P 4[3] = 10 [kpa] S S4,3 = [kj/kg-k] H S4,3 = 2819 [kj/kg] T S4,3 = 169 [C] H4[3] = 2819 [kj/kg] T 4[3] = 169 [C] S4[3] = [kj/kg-k] V 4[3] = [m 3 /kg] X4[3] = 100 X4$[3] = Abursupraincalzit W T,2 = 669 [kj/kg] P 3[3] = 10 [kpa] T 3[3] = 500 [C] Arrays Row P i T s,i T i s s,i s i h s,i h i v i x i [kpa] [C] [C] [kj/kg-c] [kj/kg-c] [kj/kg] [kj/kg] [m 3 /kg] NoRHStages Run NoRHStages Q in W net η th [kj/kg] [kj/kg]

7 T-s: Steam 7

8 Thermal Efficiency vs Number of Reheat Stages 8

9 Q in, W net vs Number of Reheat Stages 9

Equations P Se va nota cu y fractia din debitul masic care intra in turbina care e extrasa din turbina pentru preincalzitorul inchis

$Equations P Se va nota cu y fractia din debitul masic care intra in turbina care e extrasa din turbina pentru preincalzitorul inchis$ P10-110 Equations Thermodynamics - An Engineering Approach (5th Ed) - Cengel, Boles - Mcgraw-Hill (2006) - pg. 602 Ciclul Rankine cu regenerare cu preincalzitoare deschise multiple - Regeneration using