Page 45 - Advanced Gas Turbine Cycles

22 Advanced gas turbine cycles

For an ‘irreversible’ Carnot type cycle (ICAR) with all heat supplied at the top
temperature and all heat rejected at the lowest temperature (Tmm = T3, Tmin = To,
= 0, &;CAR = l), but with irreversible compression and expansion (qcm =
uB/crA < I), Eqs. (2.33) and (1.17) yield

(2.35)

However, use of Eqs. (2.34) and (2.35) together does not yield Eq. (2.33b) because the
values of IQ and IF” are not the same in the LTB, JB and ICAR cycles.

2.4. The maximum work output in a chemical reaction at To

The (maximum) reversible work in steady flow between reactants at an entry state
Ro(po, To) and products at a leaving state Po(po, To) is

(2.36)

It is supposed here that the various reactants entering are separated at (po.To); the
various products discharged are similarly separated at (po,To). The maximum work may
then be written as

where G is the Gibbs function, G = H - TS. This is the maximum work obtainable from
such a combustion process and is usually used in defining the rational efficiency of an open
circuit plant. However, it should be noted that if the reactants and/or products are not at
pressure po, then the work of delivery or extraction has to be allowed for in obtaining the
maximum possible work from the reactants and products drawn from and delivered to the
atmosphere. The expression for maximum work has to be modified.
Kotas [3] has drawn a distinction between the ‘environmental’ state, called the dead
state by Haywood [ 11, in which reactants and products (each at po, To) are in restricted
thermal and mechanical equilibrium with the environment; and the ‘truly or completely
dead state’, in which they are also in chemical equilibrium, with partial pressures (pk) the
same as those of the atmosphere. Kotas defines the chemical exergy as the sum of
the maximum work obtained from the reaction with components at po, To, [ - AGO], and
work extraction and delivery terms. The delivery work term is xkMkRkTo In(po/pk), where
pk is a partial pressure, and is positive. The extraction work is also xkMkRkTo In( po/pk) but
is negative.
In general, we shall not subsequently consider these extraction and delivery work terms
here, but use [-AGO] as an approximation to the maximum work output obtainable from a
chemical reaction, since the work extraction and delivery quantities are usually small.
Their relative importance is discussed in detail by Horlock et al. [4].