10 Appendix A: The Brayton cycle
10.4 VARIATIONS ON THE BRAYTON CYCLE
By using the Brayton cycle as a basis, cycle variations can be evaluated by changing the configuration of the system. Note that all component parameters like efficiencies and pressure losses will stay constant, equal to the values stated previously. Completely different cycle characteristics are created with each of the variations and will be investigated for the best optimisation. The cycles that will be considered in this study are:
Recuperated cyk
Multi-stage compression with inter-coolb 10.4.1 The recuperated Brayton cycle
A characteristic of gas turbines is their high exhaust temperatures and by utilizing this heat, preheating the compressed air before combustion, it is possible to reduce fuel consumption and thus the energy needed by combustion. The cold inlet air never comes in direct contact with the hot exhaust gas, thus only exchanging heat in the recuperator. An illustration of the recuperated Brayton cycle can be seen in Figure 10.10, followed by the temperature - entropy [T-s] diagram in Figure 10.1 1. The temperature difference of the cold gas
T,
-T,
is equal to the temperature difference of the hot gas(T,
- T , ) and the recuperator efficiency is defined as actual heat exchanged over the maximum heat difference of the heat exchanger:The conceptual design for development 93
of a micro gas turbine generator.
Appendix A: Brayton cycle analysis
Figure 10.10: The recuperated Brayton cycle.
6 5
-
Recuperator2 3 4
0
Entropy
-
Figure 10.1 1: T-s diagram of the recuperated Brayton cycle.
Combustor 4
The specified work output differs only slightly from that experienced with the real Brayton cycle, and will not be evaluated in this part of the study.
The recuperator increases the temperature of the air entering the combustion chamber, which leads to a reduction in the fuel-to-air ratio and an increase in the thermal efficiency. The thermal efficiency is thus a function of the recuperator efficiency [qh = f (qrrl,)]. The effect of different recuperator efficiencies ranging from 80% to 95% are shown in Figure 10.12. A detailed discussion of the recuperator and its design will follow in Chapter 5.
Q
C o m ~ r e s s o Turbine
W
0 1 2 3 4 5 6 Ressure ratio
-.-.-
Real - RecuperatedFigure 10.12: Thermal efficiency as a function of pressure ratio of the recuperated Brayton cycle.
10.4.2 The multi-stage Brayton cycle
Multi-stage systems that are common today have evolved from the recuperated Brayton cycle by adding compressor or turbine stages. Various configurations of the multi-stage system are possible. Either the compressor or the turbine can be split into multiple stages. When the turbine is split into stages, each turbine can rotate independently. Multi-shaft turbine configurations are mainly used for high torque and large load applications.
In this study emphasis will fall on multi-stage compression systems as illustrated in Figure 10.13.
The following assumptions have been made:
1) Temperature at the inlet of the second stage compressor is equal to the temperature of the first compressor,
2) All the compressors have the same efficiencies and
3) The pressure ratios in both compressors are equal to
dm.
The conceptual design for development 95
of a micro gas turbine generator.
Appendix A: Brayton cycle analysis
Cooler
3Lw2 '
Figure 10.13: The multi-stage compression Brayton cycle.
Entropy
Figure 10.14: T-s diagram of a multi-stage compression Brayton cycle.
of the compressor(s) and the turbine(s) remain the same, all components operate at 100 % efficiency and no pressure losses occur due to friction or inertia.
The following ideal conceptual cycles will be investigated:
Ideal cycle without recuperation [IB]. (Standard Brayton cycle as discussed in the previous chapter.)
Ideal cycle with recuperation [IBR]. (Similar to the IB cycle, but with a recuperator added.) Ideal two-stage compression with inter-cooling and recuperation [ITCIR]. (IBR cycle with two compressors and inter-cooling.)
The boundary conditions in Table 10.1 will hold true during the first order analysis of this ideal cycle analysis.
Table 10.1: Boundary conditions for the first order analysis (Ideal Brayton cycles).
Component Condition
Mass flow rate 1 kg/s
Low pressure compressor inlet
temperature 26°C
Maximum Turbine Inlet Temperature TIT 700°C
Pressure ratio range 1.3 - 5.56
Ideal basic cycle without recuperation [IB]
Simple inspection of the IB cycle proved that efficiency is dependent on pressure ratio (Figure 10.15). The graph shows that in order to obtain high cycle efficiency, it is necessary to operate at high pressure ratios.
1 2 3 4 5 6
Overall pressure ratio
I - - - -
eta -work[kWs/kg]I
Figure 10.15: IB cycle efficiency and specific work as a function of overall pressure ratio.
10.5.1 Ideal basic cycle with recuperation [IBR]
An IBR cycle is created by adding a recuperator to the IB cycle. The benefit of having a recuperator in the cycle is discussed in Chapter 2 of this study. Having the ability to utilise the exhaust heat (waste heat) to heat the combustion inlet air minimizes the energy needed by the
The conceptual design for development of a micro gas turbine generator.
Appendix A: Brayton cycle analysis
combustor to reach the optimum TIT of 700°C. The cycle's thermal efficiency is hereby improved as illustrated in Figure 10.16.
The enhanced thermal efficiency of the IBR cycle ensures its specific work almost equals that of the IB cycle. Therefore the specific work of the IBR cycle is almost equal to that of the IB cycle, and has high values at increased pressure ratios. IBR cycle efficiency is significantly higher than that of the LB cycle, but reaches maximum work at a lower pressure ratio.
0 1 2 3 4 5 6
Overall pressure ratio
- - - -
eta-
work [kWs/kg]1
-
Figure 10.16: IBR cycle efficiency and specific work as a function of overall pressure ratio.
10.5.2 Ideal two-stage compression cycle with inter-cooling and recuperation [ITCIR]
An ITCIR cycle is created by adding a second compressor stage, with inter-cooling, to the TBR cycle. The addition of this inter-cooling will bring the temperature of the gas leaving the first stage compressor back to inlet temperatures. The following assumptions will hold true:
Compressor inter-stage temperature is equal to that of the inlet temperature and the compressor ratio of both compressors are equal to
,/m .
The cycle efficiency of the ITCIR cycle is equal to that of the IBR cycle, but the specific work output is boosted. The trends of the efficiency and specific work are the same as the IBR cycle and can be seen in Figure 10.17.
Figure 10.17: ITClR cycle efficiency and specific work as a function of overall pressure ratio.