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