Final Exam (Dec.): Gas Turbine Cycle (with solution)

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

An externally-heated open-cycle gas turbine in a free power turbine arrangement is driven by a concentrating solar tower and operates with very low pressure ratio, relying on a large amount of regenerated (recuperated) heat. The layout sketch is shown below. The working fluid is pure air throughout the cycle. Assume dry technical air without any thermal losses. Calculate the net electrical efficiency of the cycle!

SPG exam Dec '17 GT calc.png

The following parameters are given:

Ambient air conditions (hot day)                                      1 bar, 40 °C (p₁=p₇=1bar)
Air mass flow through the cycle                                       10 kg/s
Pressure ratio of the compressor (p₂/p₁) 3
Isentropic efficiency of the compressor ( $\eta$ _SC) 87 %
Specific heat ratio for compression (k_C) 1.394
Isentropic efficiency of each expander ( $\eta$ _ST)   89 %
Specific heat ratio for each expander (k_T) 1.35
Pressure losses in the regenerator, both streams 10 %
Pressure losses in the solar air heater 5 %
Mechanical efficiency for each shaft ( $\eta$ mech)   95 %
El. Generator efficiency ( $\eta$ _gen) 95 %
Thermal energy rate exchanged in the regenerator 5000 kW
Air temperature after the solar heater (T₅ in °C) 850 °C

Hint: Work with air enthalpies as per the enthalpy table in the help file!

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

	Sub-task	Units	*Points*
1)	Enthalpy at entry to compressor (h1)	kJ/kg	0.25
2)	Temperature after the compressor (T2)	°C	1.5
3)	Enthalpy after the compressor (h2)	kJ/kg	0.5
4)	Main air pressure after regenerator (p3)	bar	0.5
5)	Main air enthalpy after regenerator (h3)	kJ/kg	1
6)	Main air temperat. after regenerator (t3)	°C	0.5
7)	Power need for compression process	kW	0.5
8)	Power that first turbine must deliver	kW	0.5
9)	Enthalpy after the first turbine (h4)	kJ/kg	0.5
10)	Temperature after the first turbine (t4)	°C	0.25
11)	Pressure after the first turbine (p4)	bar	1.5
12)	Pressure ratio across the second turbine (p5/p6)	-	0.75
13)	Energy rate delivered by the solar heater	kW	1
14)	Enthalpy after the solar heater (h5)	°C	0.25
15)	Temperature after second turbine (t6)	°C	1
16)	Net el. power delivered by the cycle	kW	0.5
17)	Net electrical efficiency of the cycle (in %)	%	1