Page 37 - Advanced Gas Turbine Cycles

14 Advanced gas turbine cycles
is Hp4 = (1 + f)hp4. Hence

ha0 +fh, = w + (1 +f)hP4. (2.3)
where w = WIM, is the specific work (per unit air flow).
If the same quantities of fuel and air were supplied to a calorific value experiment at To
(Fig. 1.7) then the steady-flow energy equation for that process would yield
hao +fhm = (1 +f)hpo +f [Cvlo, (2.4)
where [CV], is the calorific value of the fuel. Combining these two equations yields

f [CVIO = w + (1 +f NhP4 - hw). (2.5)
This equation is often used as an ‘equivalent’ form to Eq. (2.1), the calorific value term
being regarded as the ‘heat supplied’ and the gas enthalpy difference term (I +f)X
(hp4 - hw) being regarded as the ‘heat rejected’ term.
In this chapter we will develop more rigorous approaches to the analysis of gas turbine
plants using both the first and second laws of thermodynamics.

2.2. Reversibility, availability and exergy

The concepts of reversibility and irreversibility are important in the analysis of gas
turbine plants. A survey of important points and concepts is given below, but the reader is
referred to standard texts [ 1-31 for detailed presentations.
A closed system moving slowly through a series of stable states is said to undergo a
reversible process if that process can be completely reversed in all thermodynamic
respects, i.e. if the original state of the system itself can be recovered (internal
reversibility) and its surroundings can be restored (external irreversibility). An irreversible
process is one that cannot be reversed in this way.
The objective of the gas turbine designer is to make all the processes in the plant as near
to reversible as possible, i.e. to reduce the irreversibilities, both internal and external, and
hence to obtain higher thermal efficiency (in a closed cycle gas turbine plant) or higher
overall efficiency (in an open gas turbine plant). The concepts of availability and exergy
may be used to determine the location and magnitudes of the irreversibilities.

2.2.1. Flow in the presence of an environment ut To (not involving chemical reuction)
Consider first the steady flow of fluid through a control volume CV between prescribed
stable states X and Y (Fig. 2. I) in the presence of an environment at ambient temperature
To (Le. with reversible heat transfer to that environment only). The maximum work which
is obtained in reversible flow between X and Y is given by

[(WCV)REVG = Bx - BY9 (2.6)
where B is the steady flow availability function
B = H - ToS, (2.7)