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Sławomir Pietrowicz
 
The Rankine Cycle PDF Drukuj Email
20.11.2008.

II.                The Simple Rankine Cycle

 
  1. 1. A steam power plant operates on a simple ideal Rankine cycle between the pressure of 3 MPa and 50 kPa. The temperature of the steam at the turbine inlet is 400°C, and the mass flow rate of steam through the cycle is 60 kg/s. Show the cycle on a T-s and h-s diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle and (b) the net power output of the power plant.
  3. 2. Consider a 210 MW steam power plant that operates on a simple ideal Rankine cycle. Steam enters the turbine at 10 MPa and 500 °C and is cooled in the condenser at a pressure of 10 kPa. Show the cycle on a T-s and h-s diagrams with respect to saturation lines, and determine (a) the quality of the steam at the turbine exit, (b) the thermal efficiency of the cycle, and (c) the mass flow rate of the steam. Answers: (a) 0.793, (b) 40.2 percent, (c) 165 kg/s
  5. 3. Repeat Problem I.2 assuming an isentropic efficiency of 85 percent for both the turbine an the pump. Answers: (a) 0.874, (b) 34.1 percent, (c) 194 kg/s.
  7. 4. Consider a coal – fired steam power plant that produces 300 MW of electric power. The power plant operates on a simple ideal Rankine cycle with turbine inlet conditions of 5 MPa and 450°C and a condenser pressure of 25 kPa. The coal has a heating value (energy released when the fuel is burned) of 29 300 kJ/kg. Assuming that 75 percent of this energy is transferred to the steam in the boiler and that the electric generator has an efficiency of 96 percent, determine (a) the overall plant efficiency (the ratio of net electric power output to the energy input as fuel) and (b) the required rate of coal supply. Answers: (a) 24.6 percent, (b) 150 t/h
  9. 5. Consider a steam power plant that operates on a simple ideal Rankine cycle and has a net power output of 45 MW. Steam enters the turbine at 7 MPa and 500°C and is cooled in the condenser at a pressure of 10 kPa by running cooling water from a lake through the tubes of the condenser at a rate of 2000 kg/s. Show the cycle on a T-s and h-s diagrams with respect to saturation lines, and determine (a) the thermal efficiency of the cycle, (b) the mass flow rate of the steam, and (c) the temperature rise of the cooling water. Answers: (a) 38.9 percent, (b) 36 kg/s, (c) 8.45°C
  11. 6. Repeat Problem I.5 assuming an isentropic efficiency of 87 percent for both the turbine and the pump. Answers: (a) 33.8 percent, (b) 41,5 kg/s, (c) 10.5°C
 

III.             The Reheat Rankine Cycle

 
  1. 1. Consider a steam power plant that operates on a reheat Rankine cycle and has a net power output of 80MW. Steam enters the high-pressure turbine at 10 MPa and 500°C and the low-pressure turbine at 1 MPa and 500°C. Steam leaves the condenser as a saturated liquid at a pressure of 10 kPa. The isentropic efficiency of the turbine is 80 percent, and that of pump is 95 percent. Show the cycle on a T-s and h-s diagrams with respect to saturation lines, and determine (a) the quality (or temperature, if superheated) of the steam at the turbine exit, (b) the thermal efficiency of the cycle, and (c) the mass flow rate of the steam. Answer: (a) 87.5°C, (b) 34.1 percent, (c) 62.6 kg/s
  3. 2. A steam power plant operates on an ideal reheat Rankine cycle between the pressure limits of 9 MPa and 10 kPa. The mass flow rate of steam through the cycle is 25 kg/s. steam enters both stages of the turbine at 500°C. If the moisture content of the steam at the exit of the low- pressure turbine is not to exceed 10 percent, determine (a) the pressure at which reheating takes place, (b) the total rate of heat input in the boiler, and (c) the thermal efficiency of the cycle. Also, show the cycle on a T-s and h-s diagrams with respect to saturation lines.
   

III. Regenerative Rankine Cycle

 
  1. 1. A steam power plant operates on an ideal regenerative Rankine cycle. Steam eneters the turbine at 6 MPa and 450°C and is condensed in the condenser at 20 kPa. Steam is extracted from the turbine at 0.4 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a T-s and h-s diagrams, and determine (a) the net work output per kilogram of steam flowing through the boiler and (b) the thermal efficiency of the cycle. Answers:(a)1016 kJ-kg, )b= 37.8 percent.
  3. 2. A steam power plant operates on an ideal reheat - regenerative Rankine cycle and has a net power output of 80 MW. Steam enters the high – pressure turbine at 10 MPa and 550°C and leave at 0.8 MPa. Some steam is extracted at this pressure to heat the feedwater in an open feedwater heater. The rest of the steam is reheated to 500°C and is expanded in the low – pressure turbine to the condenser pressure of 10 kPa. Show the cycle on a T-s and h-s diagrams with respect to saturation lines, and determine (a) the mass flow rate of steam through the boiler and (b) the thermal efficiency of the cycle. Answers: (a)54.1 kg/s, (b) 44.8 percent
 

IV.             Cogeneration

1.      Steam enters the turbine of a cogeneration plant at 7 MPa and 500°C. One – fourth of the steam is extracted from the turbine at 600 kPa pressure for process heating. The remaining steam continues to expand to 10 kPa. The extracted steam is then condensed and mixed with feedwater at constant pressure and the mixture is pumped to the boiler pressure of 7 MPa. The mass flow rate of steam through the boiler is 30 kg/s. Disregarding any pressure drops and heat losses in the piping, and assuming the turbine and the pump to be isentropic, determine the net power produced and utlizition factor of the plant.

2.      Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at 6 MPa and 450 C and expands to a pressure of 0.4 MPa. At this pressure, 60 percent of the steam is extracted from the turbine, and the reminder expands to 10 kPa. Part of the extracted steam is used to heat the feedwater heater. The rest of the extract steam is used for process heating and leaves the process heater as a saturated liquid at 0.4 MPa. It is subsequently mixed with the feedwater leaving the feedwater heater, and the mixture is pumped to the boiler pressure. Assuming the turbines and the pumps to be isentropic, show the cycle on the T-s and h-s diagrams with respect to saturation lines, and determine the mass flow rate of steam through the boiler for a net power output of 15 MW. Answer: 17.7 kg/s
 
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