Page 149 - Advanced thermodynamics for engineers

6.5 MORE COMPLEX EXAMPLE OF THE USE OF FTT 135

isentropic expansion while 3-4 signifies a real, non-isentropic, expansion in a real turbine. The real
IFGT cycle 1-2-3-4-5-6-1 can now be analysed.
In order to perform the FTT analysis of the IFGT cycle under consideration, the following
assumptions are employed.
1. The flow is one-dimensional steady flow, and conservation of energy can be applied to each
component.
2. The working fluids (air and combustion gases) are ideal gases and possess constant specific heats.
The working fluids flow through the system in a one-dimensional quasi-static fashion.
3. The compression process (1-2) and expansion process (4-5) are adiabatic, but irreversible (i.e. not
isentropic). The deviations from isentropic processes are accounted for by the component
isentropic efficiencies. The isentropic efficiency, h T , of the turbine is the ratio of the power from
the actual expansion process to its isentropic counterpart. The isentropic efficiency of the
compressor, h C , is the ratio of the power required during the isentropic compression to that of the
actual compression. h T and h C have values between zero and unity – usually around 80–90%.

T 3 T 4
h ¼ (6.40)
T
T 3 T 4s
T 2s T 1
h ¼ (6.41)
C
T 2 T 1
4. The pressure ratio of the cycle is the ratio of the maximum pressure of the cycle, achieved at state
2, to the minimum pressure of the cycle at the turbine exit, assumed equal to that at compressor
inlet (state 1), i.e.

p 2
p C ¼ (6.42)
p 1
5. The pressure drop in the pipes connecting the components is defined using a coefficient of total
pressure recovery, i.e.

Dp
D ¼ 1 (6.43)
p
p 3 p 2
¼ D$ (6.44)
p 4 p 1
The working fluid is assumed to be an ideal gas with a constant thermal capacitance rate,
C wf ðC wf ¼ _ mc p Þ. The high-temperature (hot-side) heat reservoir is assumed to have a finite thermal
capacitance rate, C H . The inlet and outlet temperatures of the heating fluid are T Hin and T Hout ,
respectively. The low-temperature (cold-side) heat reservoir is also assumed to have a finite thermal
capacitance rate, C L , and the inlet and outlet temperatures of the cooling fluid are T Lin and T Lout ,
respectively. All heat exchangers, including the two heat reservoirs and the HTHE, are assumed to be
counterflow heat exchangers with constant heat conductances U H A H , U L A L and U HE A HE ,
respectively.