Recuperative cycle

Fig. 3.2. T.s diagram for reversible closed recuperative cycle, (CHTX]r.

Fig. 3.4. T. s diagram for reheating added lo reversible simple and recuperative cycles.

The analysis of Hawthorne and Davis [1] for irreversible a/s cycles is developed using the criteria of component irreversibility, firstly for the simple cycle and subsequently for the recuperative cycle. In the main analyses, the isentropic efficiencies are used for the turbomachinery components. Following certain significant relationships, alternative expressions, involving polytropic efficiency and. tc and jcj, are given, without a detailed derivation, in equations with p added to the number. 

For the closed recuperative cycle [CHTXJi, with states 1,2,X,3,4, Y as in the T,s diagram of Fig. 3.10, the net specific work is unchanged but the heat supplied has to be reassessed as heat qj is transferred from the turbine exhaust to the compressor delivery air. Using the heat exchanger effectiveness, e = (Tx — — Ti) the heat supplied... 

Fig. 3.10. T.s diagram for irreversible closed recuperative cycle ICHTJi. and the thermal efficiency is...

The Hawthorne and Davis approach thus aids considerably our understanding of a/s plant performance. The main point brought out by their graphical construction is that the maximum efficiency for the simple [CHT]i cycle occurs at high pressure ratio (above that for maximum specific work) whereas the maximum efficiency for the recuperative cycle [CHTX]i occurs at low pressure ratio (below that for maximum specific work). This is a fundamental point in gas turbine design. 

Before eonsidering the effects of water injection in an EGT type plant, it is worthwhile to refer to the earlier studies on the performanee of some dry recuperative cycles. Fig. 6.6 shows the T..s diagram of a [CBT i X r cyele, with a heat exchanger effectiveness of unity. It is implied that the surface area for heat transfer is very large, so that the outlet temperature on the cold side is the same as the inlet temperature on the hot side. However, due to the higher specific heat of the hot gas, its outlet temperature is higher than the inlet temperature of the cold air. 

Consider next a similar recuperative cycle, but one in which the compression process approximates to isothermal rather than isentropic, with the work input equal to the heat rejected (this may be achieved in a series of small compressions of polytropic efficiency Tjp, followed by a series of constant pressure heat rejections). It may then be shown that the thermal efficiency of this cycle is given by... 

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