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