Final Exam (Jan): Steam Cycle (with solution)

  • Due No Due Date
  • Points 12
  • Submitting on paper
  • Available after Jan 11, 2018 at 8:55am

Q3.  Steam Cycle  (12 points)

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 only two steam extractions from the turbine: one toward a feedwater tank (FWT) operating at 3 bar; and another one toward a closed feedwater preheater (CFWP) at 10 bar, whose condensate line is throttled into the FWT.

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                                            50 kg/s 
Steam superheat pressure & temperature             50 bar / 350 oC 
Steam reheat pressure & temperature                   5 bar / 350 oC 
Feedwater temperature after CFWP                      170 oC  (towards boiler) 
Steam extraction pressure for the CFWP              10 bar 
Steam extraction pressure for the FWT                 3 bar 
Condenser pressure                                              0.2 bar 
Isentropic efficiency of HP turbine section             85 % 
Isentropic efficiency of LP turbine section              90 % 
Mechanical efficiency of turbine shaft                    97 % 
Electrical Generator efficiency                               93 % 
Boiler thermal efficiency                                         90 %

 

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 CFWP 

  kJ/kg

  0.5

6)

Enthalpy of steam extraction to FWT

  kJ/kg

  0.5

7)

Enthalpy of feedwater after condenser

  kJ/kg

  0.25

8)

Enthalpy of feedwater after FWT

  kJ/kg

  0.25

9)

Enthalpy of feedwater after CFWP          

  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 (Jan.)- Steam_Cycle_page1.pngFinal Exam solution (Jan.)- Steam_Cycle_page2.pngFinal Exam solution (Jan.)- Steam_Cycle_page3.png

0