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Nomenclature

We adopt the nomenclature introduced by Hawthorne and Davis, in which compressor, heater,

turbine and heat exchanger are denoted by C, H, T and X, respectively, and subscripts R and I

indicate internally reversible and irreversible processes. For the open cycle, the heater is replaced

by a burner; B. Subscripts U and C refer to uncooled and cooled turbines. Subscripts 1,2, Mindicate the number of cooling steps (one, two or multi-step cooling).

Comparison of simple and recuperative reversible cycle

The reversible simple (Joule-Brayton) cycle, [CHT]Rwith a maximum temperature T3 also called

turbine inlet temperature (TIT) and a compressor pressure ratio rC is shown in figure 3.1.

Hence the thermal efficiency is,

The thermal efficiency thus depends only on the pressure ratio and the nature of the gas. The

specific work output on which the size of a plant depends is given by

Simplifying, we get the non dimensional work (NDW) output as follows.

Where, t is called as temperature ratio (ratio of maximum temperature, TIT to the minimumtemperature, Tatm). A plot ofLth and NDW as a function of compressor pressure ratio is shown in

fig. 3.2.

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Figure shows that efficiency increases with pressure ratio and specific heat ratio. Also NDW

constant t curve- exhibits a maximum at certain pressure ratio, rc,opt. for any given value of t,

optimum pressure is given by evaluating,

The result is

This means that specific work output is maximum when pressure ratio is such that the

compressor and turbine outlet temperatures are equal. For all values of rC between 1 and ,T4 will be greater than T2 and a heat exchanger can be incorporated to reduce the heat transfer

from the external source and increase the efficiency. The reversible recuperative cycle [CHTX]R

with maximum possible heat transfer is shown in figure.

The cycle efficiency now becomes

The efficiency is dependent on not only pressure ratio but also on maximum cycle temperature

and clearly decreases with rc and reverse is true for t. The specific work output remains the same.

A plot of efficiency with rc for different values of t is shown in figure. The curves fall until a

value is reached where the efficiency falls below Lth of [CHT]R. for higher values of rc heat

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exchanger would cool the air leaving the compressor. The point at which both efficiencies

become equal corresponds to

Design point performance calculations

Problem statement

Schematic

Schematic and T-s diagrams are for [CHT]

Assumptions

Physical laws

Properties

Analysis

Discussion

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Cycle selected

The cycle selected is irreversible cooled recuperative cycle with single step turbine cooling i.e.

[CHTX]IC1.