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# Chapter 8

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• 1. Vapor Cycles
• 2. Course Outcomes • Ability to acquire and explain the basic concepts in thermodynamics. • Ability to apply and correlate the concept with the appropriate equations and principles to analyze and solve engineering problems.
• 3. Course Learning Outcomes The student should be able to: • Describe the principles of carnot vapor cycles and its impracticalities • Explain the principles of an ideal rankine power cycle • Explain how pressure and temperature affect thermal efficiency of an ideal rankine power cycle • Explain the principle of the reheat Rankine power cycles. • Sketch the T-s diagram for carnot,ideal rankine and ideal reheat rankine cycles. • Solve problems related to ideal rankine and reheat rankine cycles.
• 4. 8.1 Carnot Vapor Cycle 8.2 Rankine Vapor Cycle 8.3 Reheat Rankine Cycle
• 5. 8.1 Carnot Vapor Cycle It is most efficient cycle operating between two specified temperature limits BUT it IS NOT a suitable model for power cycles, BECAUSE: Process 1-2 Limiting the heat transfer processes to two-phase systems severely limits the maximum temperature that can be used in the cycle (374°C for water) Process 2-3 The turbine cannot handle steam with a high moisture content because of the impingement of liquid droplets on the turbine blades causing erosion and wear. Process 4-1 It is not easy to control the condensation process so precisely to achieve quality at point 1. And it is not practical to design a compressor that handles two phases. 1-2 isothermal heat addition in a boiler 2-3 isentropic expansion in a turbine 3-4 isothermal heat rejection in a condenser 4-1 isentropic compression in a compressor T-s diagram of two Carnot vapor cycles.
• 6. Those problems can be eliminated by executing Carnot cycle in figure (b), HOWEVER this cycle presents other problem. isentropic compression to extremely high pressures isothermal heat transfer at variable pressures. Conclusion Carnot cycle cannot be approximated in actual devices It is not realistic model for vapor power cycles IDEAL CYCLE for vapor power cycle is RANKINE CYCLE
• 7. 8.2 Rankine Vapor Cycle Impracticalities associated with the Carnot cycle can be eliminated by superheating the steam in the boiler and condensing it completely in the condenser. The ideal Rankine cycle does not involve any internal irreversibilities. The simple ideal Rankine cycle.
• 8. Energy Analysis of the Ideal Rankine Cycle Steady-flow energy equation ( q in -q o u t ) - ( w o u t -w in ) = h e - hi (k J /k g ) The thermal efficiency can be interpreted as the ratio of the area enclosed by the cycle on a T-s diagram to the area under the heat-addition process.
• 9. Example 10.1 Consider a steam power plant operating on the simple ideal Rankine cycle. Steam enters the turbine at 3 MPa and 350° and is condensed in the C condenser at a pressure of 75 kPa. Determine the thermal efficiency of this cycle.
• 10. Problem 10.22 Consider a steam power plant that operates on a simple ideal A simple Rankine cycle and has a net power output of 45 MW. Steam enters the turbine at 7 MPa and 500° and is cooled in the C condenser at pressure of 10 kPa by running cooling water from the lake through the tubes of condenser at rate of 2000 kg/s. i. ii. iii. iv. Show the T-s diagram with respect to saturation line Determine the thermal efficiency of the cycle Determine the mass flowrate of the steam Determine the temperature rise of the cooling water.
• 11. HOW CAN WE INCREASE THE EFFICIENCY OF THE RANKINE CYCLE? To increase the thermal efficiency… Increase the average temperature at which heat is transferred to the working fluid in the boiler, or decrease the average temperature at which heat is rejected from the working fluid in the condenser. Lowering the Condenser Pressure (Lowers Tlow,avg) Superheating the Steam to High Temperatures (Increases Thigh,avg) Increasing the Boiler Pressure (Increases Thigh,avg)
• 12. Lowering the Condenser Pressure (Lowers Tlow,avg) To take advantage of the increased efficiencies at low pressures, the condensers of steam power plants usually operate well below the atmospheric pressure. There is a lower limit to this pressure depending on the temperature of the cooling medium cannot be lower than Psat corresponding to the temperature of the cooling medium. Side effect: Lowering the condenser pressure increases the moisture content of the steam at the final stages of the turbine.
• 13. Superheating the Steam to High Temperatures (Increases Thigh,avg) Both the net work and heat input increase as a result of superheating the steam to a higher temperature. The overall effect is an increase in thermal efficiency since the average temperature at which heat is added increases. Side effect: Superheating to higher temperatures decreases the moisture content of the steam at the turbine exit, which is desirable. The effect of superheating the steam to higher temperatures on the ideal Rankine cycle. The temperature is limited by metallurgical considerations. Presently the highest steam temperature allowed at the turbine inlet is about 620°C.
• 14. Increasing the Boiler Pressure (Increases Thigh,avg) For a fixed turbine inlet temperature, the cycle shifts to the left and the moisture content of steam at the turbine exit increases. This side effect can be corrected by reheating the steam. The effect of increasing the boiler pressure on the ideal Rankine cycle. Today many modern steam power plants operate at supercritical pressures (P > 22.06 MPa) and have thermal efficiencies of about 40% for fossil-fuel plants and 34% for nuclear plants. A supercritical Rankine cycle.
• 15. Example 10.3 Consider a steam power plant operating on the ideal Rankine cycle. Steam enters the turbine at 3 MPa and 350° and is condensed in the condenser at a C pressure of 10 kPa. Determine: (a) The thermal efficiency of this power plant (b) The thermal efficiency if steam is superheated of 600° instead of 350°C C (c) The thermal efficiency if the boiler pressure is raised to 15 MPa while the turbine inlet temperature is maintained at 600° C.
• 16. 8.3 Reheat Rankine Cycle How can we take advantage of the increased efficiencies at higher boiler pressures without facing the problem of excessive moisture at the final stages of the turbine? Answer: 1. Superheat the steam to very high temperatures. It is limited metallurgically. 2. Expand the steam in the turbine in two stages, and reheat it in between (reheat)
• 17. The ideal reheat Rankine cycle.
• 18. Additional info.: • The single reheat in a modern power plant improves the cycle efficiency by 4 to 5% by increasing the average temperature at which heat is transferred to the steam. • The average temperature during the reheat process can be increased by increasing the number of expansion and reheat stages approach an isothermal process at the maximum temperature. The use of more than two reheat stages is not practical. The theoretical improvement in efficiency from the second reheat is about half of that which results from a single reheat. • The reheat temperatures are very close or equal to the turbine inlet temperature. • The optimum reheat pressure is about onefourth of the maximum cycle pressure. The average temperature at which heat is transferred during reheating increases as the number of reheat stages is increased. What is the purpose of reheat cycle?
• 19. Example 10.4 Consider a steam power plant operates on the ideal reheat Rankine cycle. Steam enters the high-pressure turbine at 15 MPa and 600° and is C condensed in the condenser at a pressure of 10 kPa. If the moisture content of the steam at the exit of the low-pressure is not to exceed 10.4 percent, determine: (a) The pressure at which the steam should be reheated (b) The thermal efficiency of the cycle Assume the steam is reheated to the inlet temperature of the high-pressure turbine.