International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 12 | Dec 2022 www.irjet.net p-ISSN: 2395-0072
Comparison of Thermal Performance of Rankine Cycle, Reheat Cycle, Regenerative Cycle & One Stage Regenerative & reheat Rankine Cycle with Same Initial & Final Parameters
Nitin Badhe1, K.S. Gharge2 ,2
1
Abstract - Vapor power cycles are used in steam power plants. In a vapour power cycle heat energy (released by the burning of fuel) is converted into work (shaft work), in which a working fluid repeatedly performs a succession of processes. In a vapour power cycle, the working fluid is water, which undergoes a change of phase. Among the various types of vapor power cycles is the Carnot cycle, which is theoretically the most efficient cycle and sets the limit for the efficiency of any vapor cycle. This limit is known as the Carnot limit. The Rankine cycle and its modifications are used widely and are theoretically the cycles best suited to steam power plants. By studying these cycles, we know practically what all must be done to increase the efficiency and cost effectiveness.
Key Words: Vaporpowercycle,Carnotcycle,Rankinecycle, efficiency,Steampowerplant,water,heatenergy
1. INTRODUCTION
The steam power cycle is a useful method for constantly convertingheatenergyintomechanicalenergy.TheCarnot cyclehasthemaximumthermalefficiencyofallcyclesina certaintemperaturerange,inaccordwiththesecondlawof thermodynamics. WehaveseenthatCarnotcycleisnotthe theoretical/ideal cycle for steam turbine power plant becauseofthedifficultyofpumpingamixtureofwaterand steamanddeliveringitassaturated wateronly.However, this difficulty is eliminated in Rankin cycle by complete condensation of water vapor in the condenser, and then, pumpingthewaterisentropicallytoboilerpressure.Rankine cycle is a theoretical/ideal cycle for comparing the performanceofsteampowerplants.
Therefore, the Rankine cycle has become a basic cycle generally used in modern thermal power plants. Additionally, with the progress of science and technology, basedontheRankinecycle,therearereheatrankinecycle, regenerativerankinecycleandsoon.Atpresent,theactual cyclesofsteampowerplantsareverycomplex,buttheyare all improved based on the primary cycle. What are the economicdifferencesoftheseimprovedsteampowercycles? Letuscomparethemwithspecificexamples.
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2. Comparison
Example: In a power cycle, the initial parameters of fresh steamarep1=87bar,t1=510˚C,Thepressureofcondenseris pb=0.1bar.Whenthefreshsteamexpandstop2=20barin the steam turbine, a part of the steam is extracted for regenerativeheating,andtherestissenttothereheatertobe heatedto500˚C,andthenreturntothesteamturbinetodo work.Assumeturbineefficiency=65%and100TPH
2.1RankineCycle(ηt = 65%) T (510˚C) 87bar 0.1bar S
1 4 3 2
Fig. 1. T-sdiagramofrankinecycle
Fromh-sdiagram,thestateparametersofthecorresponding statepointareasfollows:
h1=3414.3kJ/kg=3414.3*0.23884=815.47kcal/kg h2’=2119.99kJ/kg=506.34kcal/kg(S1 =S2) but ηt=65%
ηt = = 0.65= h2=2573.01kJ/kg=614.54kcal/kg h3=191.8kJ/kg=45.809kcal/kg h4=200.57kJ/kg=47.90kcal/kg
Heatsupplied(qi )=h1 –h4 =3213.72kJ/kg=765.565kcal/kg
Turbinework(wt )=h1 –h2
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Student, Dept. of Mechanical Engineering, Government College of Engineering Karad, Maharashtra, India
Ass. Professor, Dept. of Mechanical Engineering, Government College of Engineering Karad, Maharashtra, India
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 12 | Dec 2022 www.irjet.net p-ISSN: 2395-0072
=841.27kJ/kg=200.93kcal/kg
PumpWork(wp)=h4 –h3 =8.77kJ/kg=2.096kcal/kg
Electricitygenerated=200.93*0.860*100/1000 =17.34MW=14909716.25kcal/hr
Firingduty= =109652857.1kcal/hr ηthermal= =25.9% ηcycle = =13.59%
Electricitygenerated=239.1*0.860*100/1000 =20.56MW=17678417.88kcal/hr
Firingduty= =121221428.6kcal/hr
ηthermal= =28.12%
ηcycle = =14.58%
2.3RegenerationCycle
2.2ReheatCycle T 87 bar 0.1 bar S
1 3 2 6 5 4
Fig. 2. T-sdiagramofreheatrankinecycle
Fromh-sdiagram,thestateparametersofthecorresponding statepointareasfollows:
h1=3414.3kj/kg=815.47kcal/kg h2 =3147.72kj/kg=751.80kcal/kg(ηHP=60%) h3 =3480kj/kg=831.16kcal/kg h4 =2745.5kj/kg=655.73kcal/kg(ηLP=65%) h5 =191.8kj/kg=45.80kcal/kg h6=193.80kj/kg=46.28kcal/kg
Heatsupplied(qi)=(h1 –h6)+(h3 –h2) =3552.79Kj/kg=848.55kcal/kg
Turbinework(wt)=(h1 –h2)+(h3 –h4) =1001.08Kj/kg=239.1kcal/kg
PumpWork(wp)=h6 –h5 =8.776Kj/kg=2.094kcal/kg
Fig.
3. T-sdiagramofregenerativerankinecycle
Fromh-sdiagram,thestateparametersofthecorresponding statepointareasfollows:
h1=191.8kj/kg=45.80kcal/kg h2 =193.80kj/kg=46.28kcal/kg h3 =908.5kj/kg=216.98kcal/kg h4 =916.38kj/kg=218.86kcal/kg h5 =3414.3kj/kg=815.47kcal/kg h6=3121.41kj/kg=745.51kcal/kg(ηHP=65%) h7=2472.35kj/kg=590.49kcal/kg(ηHP=65%)
Energybalanceoffeedwaterheater mh6 +(1-m)h2 =h3 m=0.2441kg/kgofsteam
Heatsupplied(qi)=h5 –h4 =2497.92kj/kg=596.60kcal/kg
Turbinework(wt)=(h5 –h6)+(1-m)(h6 –h7) =783.50kj/kg=187.132kcal/kg
PumpWork(wp)=(h2 –h1)+(h4 -h3) =9.88kj/kg=2.35kcal/kg
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0.1 bar 20 bar 87 bar
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 09 Issue: 12 | Dec 2022 www.irjet.net p-ISSN: 2395-0072
Electricitygenerated=187.132*0.860*100/1000 =16.09MW=13834909.72kcal/hr
Firingduty= =85228571.43kcal/hr ηthermal= =30.97% ηcycle = =16.20%
2.4Onestageregenerationandonereheatcycle
Fromh-sdiagram,thestateparametersofthecorresponding statepointareasfollows:
h1=191.8kj/kg=45.80kcal/kg h2 =193.80kj/kg=46.28kcal/kg h3 =908.5kj/kg=216.986kcal/kg h4 =916.38kj/kg=218.86kcal/kg h5 =3414.3kj/kg=815.47kcal/kg h6=3143.94kj/kg=750.89kcal/kg(ηHP=60%) h7 =3467.3kj/kg=828.129kcal/kg h8 =2744.29kj/kg=655.44kcal/kg(ηLP=65%)
Byenergybalanceoffeedwaterheater
mh6+(1-m)h2 =h3 m=0.2422kg/kgofsteam
Heatsupplied(qi)=(h5 –h4)+(1-m)(h7 –h6) =2442.96Kj/kg=655.12kcal/kg
Turbinework(wt)=(h5 –h6)+(1-m)(h7 –h8) =818.256Kj/kg=195.43kcal/kg
PumpWork(wp)=(h2 –h1)+(h3–h4) =9.889Kj/kg=2.36kcal/kg
Electricitygenerated=195.43*0.860*100/1000 =16.80MW=144453399.83kcal/hr
Firingduty= =93588571.43kcal/hr
ηthermal= =29.47%
ηcycle = =15.43%
2.5CalculationResult
Underthesameinitialandfinalparameters,wecalculated thethermalefficiencyandcycleefficiency ofRankinecycle, reheat cycle, regenerative cycle, and cycle with one stage regenerative and one reheat, respectively. The results are showninTable1,2and3.
Table 1. Comparisonofcalculationresultsbetweenreheat cycleandRankinecycle.
reheatcycle result Comparisonwith Rankinecycle qi kJ/kg 3213.72 3552.79 ↑339.07 wt kJ/kg 841.29 1001.08 ↑159.79 wp kJ/kg 8.776 8.776 → ηthermal 25.90% 27.93% ↑2.03% ηcycle 13.59% 14.58% ↑0.99%
Rankine cycle
Table 2. Comparisonofcalculationresultsbetween regenerativecycleandRankinecycle.
Rankinecycle
regenerativecycle result Comparisonwith Rankinecycle
qi kJ/kg 3213.72 2497.92 ↓715.8 wt kJ/kg 841.29 783.507 ↓57.783 wp kJ/kg 8.776 9.88 ↑1.11
ηthermal 25.90% 30.97% ↑5.07% ηcycle 13.59% 16.20% ↑2.61%
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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Table 3. Comparisonofcalculationresultsbetweenone stageregenerationandonereheatcycleandRankine cycle.
Rankine cycle
onestageregenerationandone reheatcycle result
Comparisonwith Rankinecycle
qi kJ/kg 3213.72 2742.96 ↓470.76 wt kJ/kg 841.29 818.25 ↓23.04 wp kJ/kg 8.776 9.889 ↑1.11
ηthermal 25.90% 29.47% ↑3.57% ηcycle 13.59% 15.43% ↑1.84%
3. CONCLUSIONS
Fromtheaboveresultitcanbeseenthatthermalefficiency andcycleefficiencyishigherinregenerativerankinecycle thanreheataswellasonestageregenerationreheatrankine cyclecomparewiththesameparameters.
Heatenergysuppliedtotheboilerishigherinreheatrankine cycle and heat energy supplied to the boiler is lower in regenerativerankinecycle.
Work of turbine is higher in reheat rankine cycle i.e., electricity production is also high as compare to regenerationandasonestageregenerationreheatrankine cycle.
From the above result it can be seen that regeneration involves the utilization of heat within the system while reheatingorsuperheatingrequiresadditionalheataddition fromoutside.Thus,thesuitabledegreeofregenerationmay bebetteroverreheatingorsuperheatingoptions.
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