Examples for Thermodynamic Cycles [Advanced Thermodynamics]

Examples for Thermodynamic Cycles [Advanced Thermodynamics]

1. 1 Examples for Thermodynamic Cycles

2. A regenerative gas turbine with intercooling and reheat operates at steady state. Air enters the compressor at 100 kPa, 300 K with a mass flow rate of 5.807 kg/s . The pressure ratio across the two-stage compressor is 10 . The pressure ratio across the two-stage turbine is also 10 . The intercooler and reheater each operate at 300 kPa . At the inlets to the turbine stages, the temperature is 1400 K . The temperature at the inlet to the second compressor stage is 300 K . The isentropic efficiency of each compressor and turbine stage is 80% . The regenerator effectiveness is 80% . Determine: 1. The thermal efficiency, 2. The back work ratio, 3. The net power developed, in kW. 1

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4. Line 1-2 represents :- Irreversible adiabatic compression Line 1-2s represents :- Ideal isentropic compression Line 2-3 represents :- Air is cooled in intercooler at constant pressure Line 3-4 represents :- Irreversible adiabatic compression Line 3-4s represents :- Ideal isentropic compression Line 4-5 represents :- High pressure air is heated at constant pressure by exhaust gases from LP turbine in the regenerator Line 5-6 represents :- High pressure air is further heated at constant pressure in combustor 1 to maximum temperature 4

5. Line 6-7 represents :- irreversible adiabatic expansion Line 6-7s represents :- ideal isentropic expansion Line 7-8 represents :- Exhaust air from HP turbine is heated at constant pressure in combustor 2 to maximum temperature Line 8-9 represents :- Irreversible adiabatic expansion Line 8-9s represents :- Ideal isentropic expansion Line 9-10 represents:- Air from LP turbine is passed to the regenerator where is energy is transferred to the air delivered from the HP compressor 5

6. Given :- T 1 = 300K P 1 = 100 KPa m = 5.807 Kg/s P 2 = P 3 = 300 KPa P 4 = P 5 =P 6 = 100 KPa T 6 = T 8 =1400 K P 7 = P 8 = 300 Kpa T 3 = 300K 6

7. Calculating for temperature values at compressor 410.62 K   7

8. Again, 423.17 K   8

9. Isentropic efficiency of compressor 1 :- = 80 % = 0.8 438.275 K   9

10. Isentropic efficiency of compressor 2 :- = 80 % = 0.8 453.96 K   10

11. Calculating for the temperature values at turbine 992.50 K   11

12. Again, 1022.83 K   12

13. Isentropic efficiency of turbine 1 :- = 80 % = 0.8 1074 K   13

14. Isentropic efficiency of turbine 2 :- = 80 % = 0.8 1098.264 K   14

15. Regenerator Effectiveness :- = 80 % = 0.8 969.40 K   15

16. Thermal Efficiency ( η th )   16

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19. Consider a regenerative cycle using steam as the working fluid. Steam leaves the boiler and enters the turbine at 4 MPa, 400 C . After expansion to 400 kPa , some of the steam is extracted from the turbine to heat the feedwater in an open feedwater heater. The pressure in the feedwater heater is 400 kPa , and the water leaving it is saturated liquid at 400 kPa . The steam not extracted expands to 10 kPa . Determine the cycle efficiency. 19

20. Fig :- Open Feed Water heater 20 Fig :- T-S Diagram

21. Finding the properties of steam which is at saturated liquid at state 1 from saturated properties of steam-pressure table for a corresponding saturation pressure of 10KPa Calculating the work required by low pressure pump 1 ) ) Calculating the enthalpy of steam at state 2   21

22. Finding the properties of steam at state 5 from superheated properties of steam for a corresponding pressure of 4MPa and temperature of 400℃ Calculating the entropy of steam at state 6 by considering isentropic expansion in turbine Calculating the entropy of steam at state 7 by considering isentropic expansion in turbine   22

23. Finding the properties of steam from saturated properties of steam-pressure table for a corresponding saturation pressure of 400KPa   23

24. Calculating the dryness of fraction of steam at state 6 Calculating the enthalpy of steam at state 6   24

25. Finding the properties of steam from saturated properties of steam-pressure table for a corresponding saturation pressure of 10KPa   25

26. Calculating the dryness of fraction of steam at state 7 Calculating the enthalpy of steam at state 7   26

27. Finding the properties of steam which is at saturated liquid at state 3 from saturated properties of steam-pressure table for a corresponding saturation pressure of 400KPa Calculating the fraction of steam blended from the turbine to the open feed water heated by use of energy equation for feed water heater.   27

28. Calculating the work output of the turbine Calculating the work required by high pressure pump 2 ) Calculating the enthalpy of steam at state 4   28

29. Calculating the net work output from the system Calculating the heat supplied to the system   29

30. Calculating the thermal efficiency of Rankine cycle   30

31. THANK YOU 31