Final Exam (Dec.): Steam Cycle (with solution)

  • Due No Due Date
  • Points 12
  • Submitting on paper
  • Available after Dec 19, 2017 at 8:55am

A small-scale power plant uses a steam cycle with reheat, having a high-pressure turbine (HP) section and a low-pressure turbine (LP) section driving an electrical generator on a single shaft. There are two steam extractions from the turbine: one toward a feedwater tank (FWT) operating at 10 bar; and another one toward a closed feedwater preheater (CFWP) at 2 bar, whose condensate line is throttled into the condenser.

Calculate the electrical power output and the electrical efficiency of the cycle.

Disregard any pressure losses or thermal losses. Neglect the pump work.

 

The given input parameters are listed below:  

Total steam mass flow                                         100 kg/s

Steam superheat pressure & temperature           50 bar / 400 oC

Steam reheat pressure & temperature                 5 bar / 400 oC

Steam extraction pressure for the FWT               10 bar

Steam extraction pressure for the CFWP             2 bar

Feedwater temperature after CFWP                    110 oC  (towards FWT)

Condenser pressure                                             0.05 bar

Isentropic efficiency of HP turbine section            85 %

Isentropic efficiency of LP turbine section            90 %

Mechanical efficiency of turbine shaft                   93 %

Electrical Generator efficiency                              91 %

Boiler thermal efficiency                                       86 %

 

Hint:  The cycle layout chart is not provided here and is not necessary to draw it in the solution script either.

 

The list of partial answers below shows the necessary calculation steps:

 

Sub-task

  Units

  Points

1)

Enthalpy of HP superheated steam

   kJ/kg

   0.5

2)

Enthalpy after real expansion in HP turbine        

   kJ/kg

   0.75

3)

Enthalpy of LP reheated steam

   kJ/kg

   0.5

4)

Enthalpy after real expansion in LP turbine           

   kJ/kg

   0.75

5)

Enthalpy of steam extraction to FWT 

   kJ/kg

   0.5

6)

Enthalpy of steam extraction to CFWP 

  kJ/kg

   0.5

7)

Enthalpy of feedwater after condenser

  kJ/kg

   0.25

8)

Enthalpy of feedwater after CFWP

  kJ/kg

   0.25

9)

Enthalpy of feedwater after FWT           

  kJ/kg

   0.25

10)

Mass flow of steam extraction to FWT

  kg/s

   1.5

11)

Mass flow of steam extraction to CFWP

  kg/s

   1.5

12)

Gross power output from the HP turbine section (before losses)              

  MW

   1

13)

Gross power output from the LP turbine section (before losses)              

  MW

   1

14)

Total net electrical power output

  MW

   0.75

15)

Fuel thermal energy rate input to the boiler

  MW

   1

16)

Electrical efficiency of the cycle, in percent

  %

   1

 Final Exam solution (Dec.)- Steam Cycle_Page_1.jpg

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