CHAPTER 7 ee eee ee Peareaneataed STEAM CYCLES eon ee paren RANKINE CYCLE soe eee Rankine cycle Is one of thermodynamic cycle that ‘converts neat nto work, Water Ts usualy te working Mad of {he cyce and heat supped external ina Coed system. Fore 71 showa ¢ simples version of typical Rnkine seam power plat eye Se ia | “There are four processes in a Rankine Cycle Process 1-2: High pressure liquid enters the boller and neat is added at's constant pressure until the working. "Mluld. becomes ‘superneated vapor Process 2-3: The superneated vapor then goes tothe turbine and expands Fentropically. Ths process decreases the pressure and temperature, and condensation Process 3-4: The wet vapor enters the condenser, where it Is condensed at a constant Pressure until it becomes Saturated tuida2 ‘The saturated lguid is pumped from tow to high pressure. At this stage, the pump requires low power Input since the working Mul is qu Energy Analysis for the Ideal Rankine Cycle For the turbine “The expansion of steam Inthe turbine ls isentropic, and the change in potential and kinetc energies can be considered ‘5 zer0 for an ideal cycle, hence the turbine work is ig Dae Sor bs =, For the condenser: In the condenser, the vapor condenses at constant Pressure and temperature, and the final state of steam i= Saturated liquid. There ls no work done, and the change in Potential and kinetic energies can be considered as rer, Nence the neat rejected in the condenser ie: ae Fated For the pump: “The saturated quid from the condenser enters the pump there the water is Isentropicaly compressed to boler pressure ‘The change In potential and Kinetic energies can be considered ‘2s zero, hence the work required to operate the pump :an n= Eo) “Oe eb nt nth hve aod nn te mol ting we 1 the water Is considered incompressible, ts specie. ‘volume wil be constant across the pump, ence, the pump work ‘an aso be! =f VOP = ome oP For the steam generator: In the steam generater, the heats added at a constant pressure, again, the change In potential and kinetic energies an be considered as zero, hence the heat added to water I Em = Cour]aaa 1 we perform eneray balance inthe whole system, we wll have, {ew = Eau] Hh = Oe, MW = 04 Hence; we can also write the thermal effcidncy as; en oth nie min he woke Sond seis wi, Tom he es er Woter is used as the working fluid in an Ideat Rankine Qyce, Saturated vapor enters the turbine at'@ pressive’ ont temperature of 20 MPa and 570°, respectively. The condense pressure I 8 kPa. Determine: ‘2. The network produced in kik. The neat transfer to the steam in the stearh generator in Kika The thermal emcteny. . The heat transfer to cooling water passing through the condenser in k/kg of steara, condensed.124 tte plas: hy = Py @0.008HPa = 173.88 0/9 hy =h@20NPe & 570°C =2452.3 81/ka from seam tables 15, + 8@200P98570"C » 6.4052 0/49-K 5, €0,006Pa- 0.5926 K/ko-K 540.0068 7.6361 /ka-K x =0.7632 oer ‘rom steam tables: ,@0,000MP= 173.00 1/49 ny @0.0064Pa = 2403.1 49/49 y= 2003.1197 3g yh = #4, rom steam tables: e = @0.0000Ma « 1.008410"! /49 ny = 154.0399 1/k9 We == Wy =n, hy = 0452.1-2009.1197) 40/9 W, = 1448,99021/45 Wy = -by-h,) = -b94.0399-173.09) 1/49 W, = 20.1599 ka kg “nthe mind ht math god of 1 te math eco ap42s Whe = (148.9803 - 20.1595) 1/9 Wan = 1428.8204 13/9 =, = 6452.1-194,0399) 0/9 258.0601 1e/ko sexo0% = 1828:6204 1 /ka , 100% = 3756.0601 w/e (hs ha) = (2003.1397 173.88) 13/k9 829.2397 43 /kg IRREVERSIBILITIES AND LOSSES IN A RANKINE CYCLE cycle ireversbities are caused by friction and heat losses to the surroundings by cycle components and the pipes ‘that connect those components In the turbine, the ideal expansion is entropic, but because ofthe Mud Trion, the entropy ef the Muld increases asi flows through the turbine blades, These lstes are accounted by the turbine isentropic efficiency. In the pump, the frictional losses means the pump needs ‘more work to raise the water pressure causing an increase In entropy. These losses are accounted by the pump Isentropic ‘ficiency. Roh tro ots wth ur ough Wu top we me he126 Example 7-2: Consider the Rankine Cycle of Example 7-1, but ths time the cycle operates with turbine and pump efcencies of ‘80%. Determine! “The network produced In ko. 1 The heat transfer to the steam in the steam generator ine. The thermal efficiency. Solution: ae 482.1-m)iS : Bam a4 aooaao7)E w n, -2202,9158% 9 (094.0399--173.89) 2 6,173.80)We =e ~hy = (6452.1-2292.9158) 10/kg My = 1159.1842 10/9 Wi, = yh) = 199.0799 - 173,88) 9/eg W, 25.1999 e/g Wa = (1159.1842-25.1995)K1/ko Wg © 1133,9843 43 /k, (9452.1 - 199.0795) 1/9 253.0201 /ko = Was « s00% = 1223-9843 13/49 4 gid 3253.0201 17 /kg "0° te = 34.8696, ‘The effect of the pump and turbine efficiencies caused the thermal efciency ofthe cycle to decrease Wom 83.559 to 386%. “Une 0 that et, (et we etn the tat wel of a? IMPROVING RANKINE CYCLE THERMAL EFFICIENCY ‘Te Rankine thermal efficiency is given byt 100% ‘> Increase the thermal efficiency of @ Rankine cycle we can do the flowing? (@) Lower the exhaust condenser pressure ‘One effect of lowering the exhaust pressure in the condenser is an increase aust Pressure228 content ofthe steam leaving the turbine. This ts Very significant because 1e wll result i & ‘decrease laturoineefelency and may also cause trocion inthe turbine blaces. a oy ig ne ine taps tet ‘ee th ene of te ve yosore racer wt you wer ting fer" snps Compe () Trcrease the superheat temperature ‘in superheating the steam, we can notice an increase in the quality of steam leaving the turbine (©) Increase the boiler pressure during heat alton Terease inthe bller pressure reslted to almost {ame amount of net work, Dut the heat rected wos decreased, hence the Rankine cycle thermal tteleney increases.We fy ting fe 08 fe ‘mcg ning bet ht po fon et omer cha {IDEAL RANKINE WITH SINGLE STAGE REHEATER xamole 7:3: Modify the Ideal Rankine Cyce of Example 7-1. Now, the steam enters the high pressure turbine at 20 MPa, S70 and expands to 2 MPa and then is reheated to 570°C. The ‘Condenser pressure s 8 kPa. Determine: 2. The network produced in KY/kg. The heat transfer to the steam in the steam. ‘Senerator in Vk, The thermal eticiency. 4. The heat transfer to cooling water passing through the condenser in ki/ko of steam condensedse R =id >» ¢ pee ‘a. he wr es oe etna ee” ‘State points: pep “Aman of tag by hy 173.8810 /e9 cg mt ig ot h, = 194.0399 10/9 seinen hyo 52.10/49 ow cot tt 0 repttion fetesenm cremate gong From steam tables: ‘5 = @ 20MPAA 570°C ~ 6.4052 ki/kg-K 50 24P0= 2.4474 1/kg-K 5, 2MPa = 3.9935 1 /ko-K x = 1.0165aan beet ehy From steam tables: hy @2MPa = 908.79 19/9 hy @©2mPa «1890.7 kako y= 2830-6866 11/9 hy =me@anpaa.s70rc - 2622.95 W/kg 5628-828 From steam tables: 54 5@2HPARS7O"C~ 7.6239 1/kg-K §,@0.008MPa - 0.5926 13/ko-K 6361 10/k9-K 173.68 43/kg 2403.1 10/9 hy =2386.6544 10/9 Wan = WM = bemoan) W, = 6452.4-2830.6066) eg + (9622.95-2386.6544) /A9 1% =1857.709 10/49 he) = (194.0399 -173.88) 19/9 20.1599 41/k9 ™% Wa = (857.709 - 20.1598) 13/kg Wye = 1837.5491 10/9332 = bre bne-m) , « 6452.1 194.0399) 10 /ka + (8622.95 ~ 2830.6866) 1/9 , = 4050.3235 13/ko Ma s00 «18375491 10/49 To 800% «050.5235 07K9 19% a= 45.97% (n= she) = (23066544 -173.88) 10/9 = -2212.7744 43/k9 syne ty papery say “Tonto, tot wd tie “tae hort ‘THE MOLLIER DIAGRAM Mollier diagram was developed by Ricard Mater | (4863-1933) is 2 graphic Fepresentaton of the proper: tes of seam an erty | vs entropy coordinate. Ths ‘gram fz sometimes called | the hs diagram. Te contains 3 eres of constant pressure find temperature nes, series oF constant molstire. or ‘quay line, and series of | Sipereated tines133 Moller dlagrams are commonly used to simplify the calection of state points of steam” Figure 7.9 shows the ts Siagram of an ideal Rankine eycie with single reheater a= imustrated in| ‘aample 7-3. IDEAL RANKINE WITH DOUBLE STAGE REHEATER example 7-4: Mody the Idea! Rankine Cycle of Example 7-1, but nom, the modined yt has two stages of reheating, Steam expanding Inuaty from 20 MPa, 570°C. The two reheater pressures are 2 MPa and 0.8 MPa and the steam leaves each reheater at 570°. ‘The condenser pressure is 8 kPa. Determine: bs ‘ "The network produced in Wk. ‘The Meat transfer to the steam in the steam generator in Vk. ‘The thermal efficiency. ‘The heat transfer tO cooling water passing through the condenser ia Ki/kg of steam ‘condensedState points: hy =173.8810/4g hy = 194.0399 10/9 hy = 3052.1 0/49 hh, = 2830.6866 10/k9 thy sh@2MP28 570°C = 3622.954 bd/kg 55251 y From steam tables: 5, =$@24Paa 570°C - 7.6239 W/kg-K 5 @0.8Pa= 2.0462 10/kg-K 5, @0.8HPa = 4.6166 ki/kg-K xy = 1.2082 reohyohy From steam tables: Ny@0.enPa 721.1110 /eg 1 00.040 = 2048.0 10/9 \ th, = 23195.5026 1/49 | hy =h@O.8MPaa 570°C = 3633.21/k9 From steam tables: 5, 500.8448 570°C - 6.0560 0/k9-K | 5, @0.008HPa 0.5926 1/4g-K i 540.0064? = 7.6961 19 /kg-K 909774 “Ue mt of ey anid 0136 0h ‘From steam tables: 1 @0,008MPa = 173.68 1/9 hy @0.008tPa = 2403.1 10/kg hy = 2522.6700 11/9 Wee = We =f ta) yy) hy) Wy, = 452.1-2030,6066) Ag+ (2622.95-2195.5036) 10/9 +(633.2-2522.6700) kg Ww, = 2159.3038 10 /ko Wy = hy) = 198.0399 -173.88) 1/49 Wy = 20.599 107A Wa = @159.3938- 20.1599) 1/49 We =2839.2339 13/49 rab moat) eh) = (452.1-156.0399) kg + (0622.95 -2830.6866) 10/49 ++ (9633.2-3195.5036) 1/9 . = 4498.0239 13/k9 Wagan «2239-2339 1740 «tp Q “100% = 345.0239 0749 ne = 47.67% ni iu Ge =~ hy) = 42522.6700-173.8) 179 @, =-2348.79 13 /K9 i i148 yar 7a 2 74 Steam at 30 MPa and 620°C, enters @ Rankine turbine and expands toa pressure of 100 kPa. Determine (2) The turbine work, in kik. {(b) The heat added st the steam generator, In ki/ ‘a ©) The extt qualty of steam at the turbine outlet, in percent (2) The heat rejected atthe condenser, In kg (e) The eyde thermal efficiency. (As. x= 82.6%, = 39.0 %) Reconsider the Rankine cycle in Problem 7.1. Now, the manufacturer assured thatthe Isentrpic efficiency of the turbine and pump Is 93%. Calculate: “a The turbine work in kg. {(B) The heat added at the steam generator, in wahkg (0) Te heat rejected at the condenser, in kg (a) The cycle thermal efficiency. (Ans, 36.0%) Recalculate the Rankine cycle in Problem 7.1. Mow, i ‘modified to add one stage of reheat. The stew enters the turbine at 30°MPa and 620°C and i extracted and Feeated to 3.0 MPa and 500. The condenser pressure [5 100 kPa, Determine: a) The turbine work in/kg. (8) The heat added at the steam generator, i frkg (©) The ext qualty of steam at the condenser inlet, in percent. (2) The heat rejected a the condenser, in kg (Ce) The eyde thermal efficiency. (Ans, x= 98.0%, 39.5 9) Modity the reheat Rankine cycle in Problem 7.3. Now, 2 third stage of reheat Is added inthe system. The steam that enters the turbine t 30 MPa and 620° is extracted or owet af the poten You28 76 and reheated at the second stage to 9 pressure of 3 MPa and temperature of 500°C. The reheated steam is ‘again extracted and reheated inthe 3 stage rehester to’ pressure and temperature of 2.0 MPa and 450°C, Fespectively. Then the reheated steam reenters the turbine and exhaust a¢ 100 KPa 5 Determine: (o) The turbine work 1 Kika. () Te heat added at the steam generator, In arkg (©) Te Neat rejected a the condenser, in Kika (a) The cycle thermal efficiency. (Ans. ng = 41.0 %) ‘An open feedwater neater is added to the Rankine cycle described in Problem 7-1, operating at 2 MPa, The ‘condenser pressure i100 kPa. Determine (a) The turone work, in Kiko (©) Te heat added at the steam generator, in ‘orkg (©) The heat rejected a the condenser, in KYkg (4 The traction, y, of the total maze In the system that leaves the turbine and goes to the open feedwater heater, (e) The eyde thermal eftiiency, 1207, 92:4 %) tans. y, ody the Tdeat Rankine Cycle of Problem 7.1. Now a closed feedwater heater ts utiized in the system, The ‘operating pressure of the closed feedwater heater is ‘measured fo be 2 MPa. The condensate drains through 2 trap to the condenser. I the condenser pressure f= 100 KPa, determine: (a) The turbine work, in KK. (©) The heat added st the steam generator, in ‘oykg (2) The heat rejected a the condenser, in kY/kg (@) The traction, y, of the total mass in the system that ienves the turbine and goes to the closed feedwater heater (©) The eyes thermal eetency. (os. y= 0.265, 41.4 9)a ‘The Rankine cycle described in Problem 7.2 1 modified to utllze one open feedwater heater and one closed feedwater heater. Steam enters the turbine 330 MP2 ‘and 620°C and expands toa condenser pressure of 100, Ka. The frst extraction stage occurs ot 3 MPa Ina oced feedwater heater and the other extraction lsat 2 MPa in an open feedwater heater The condensate inthe dosed feedwater heater drains through a trap to the open feedwater heater. If the feed water Yeaves the cored heater at 30 MPa and a temperature equal to the Saturation temperature at 3 MPa and saturated gud leaves the open feed water heater at2 MPa, Determine (a) The turbine work, in Kika. (0) Te heat added st the steam genérator, in orkg (©) The heat rejected atthe condenser, in kiko (3) Me recone (@) The cycle thermal ec (Ans. y,= 0.0536, y,= 0.194, y,= 0.753 ng = 43.0%)