Question

A simple Rankine cycle uses water as the working fluid. The boiler operates at 6000 kPa and the condenser at 50 kPa. At ...


A simple Rankine cycle uses water as the working
fluid. The boiler operates at 6000 kPa and the condenser
at 50 kPa. At the entrance to the turbine, the temperature is
450C. The isentropic efficiency of the turbine is 94 percent,
pressure and pump losses are negligible, and the water leaving
the condenser is subcooled by 6.3C. The boiler is sized for a
mass flow rate of 20 kg/s. Determine the rate at which heat is
added in the boiler, the power required to operate the pumps,
the net power produced by the cycle, and the thermal efficiency.

Answer

Given data

Operating pressure of boiler PH = 60bar

Operating pressure of condenser low pressure PL = 0.5 bar 

Temperature at the entrance of the turbine T= 4500C

water is subcooled by 6.30C

Mass flow rate of steam ma = 20kg/sec

Isentropic efficiency of the turbine 94%

To determine 

Heat tansfer rater to the boiler.

Power required to operate pump.

Net power produced by the cycle.

Thermal efficiency of the cycle.   

 

 

 

As per the given conditions T-S diagram is shown below

Mechanical Engineering homework question answer, step 2, image 1

11-1 is subcooling of water

2-3 Heat addition in boiler 

4-1 Condensation of steam

1-2 Pump work

Point 1 is the inlet of pump

 Point 2 inlet of turbine 

Point 3 inlet of turbine 

Point 4 inlet of condenser 

Point 11 = Saturation point of water at 0.5 bar

 

Properties of water and steam are taken from the tables 

Properties at point 1

 boiling point of the water at 0.5 bar is 81.30C. As the water is subcooled by 6.30C at 0.5 bar properties of  water at point 1 are taken at 750C

Mechanical Engineering homework question answer, step 3, image 1

To get enthalpy at point 2 we have to calculate pump work

Mechanical Engineering homework question answer, step 3, image 2

Enthalpy at point 2 is

Mechanical Engineering homework question answer, step 3, image 3

Enthalpy at point 3 and 4is the isentropic efficiency is 100%

Mechanical Engineering homework question answer, step 3, image 4

From the given isentropic efficiency we get enthalpy at exit of turbine (i.e., point 4)

Mechanical Engineering homework question answer, step 3, image 5

 

 

 

 

Heat transfer rate in the boiler is

Mechanical Engineering homework question answer, step 4, image 1

Pump work is 

Mechanical Engineering homework question answer, step 4, image 2

Turbine work

Mechanical Engineering homework question answer, step 4, image 3

Net work in the cycle is 

Mechanical Engineering homework question answer, step 4, image 4

Thermal efficiency of the cycle is 

Mechanical Engineering homework question answer, step 4, image 5

Conclusions

  1. Heat tansfer rate to the boiler is 59597.4 KW
  2. Power required to operate the pump is 122.57 KW 
  3. Net power produced by the cycle 17925 KW
  4. Thermal efficiency of the cycle is 30%

 

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