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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.
