Page 65 - Advanced Gas Turbine Cycles

Chapter 3. Basic gas turbine cycles 41

process, assumed to be adiabatic,
[ha2 +&ol = Hg3 = (1 +f)hg3, (3.31)

where bo is the specific enthalpy of the fuel supplied at To.
But from the calorific value process, with heat [-AHo] =f[CV], abstracted to restore
the combustion products to the temperature To,
h& +fhfo = H@ + [-AH01 = (1 +f)hgO + [-A&]. (3.32)
From Eqs. (3.31) and (3.32)

f[CVIo = Wg3 - HgO) - (ha2 - ha01 = (1 +f)(hg3 - hgo) - (ha2 - h,)

where the ambient temperature is now taken as identical to the compressor entry
temperature (Le. To = TI). The non-dimensional heat supplied is, therefore

= {[(I +f>(P - Wn’l - (x - 1)MP - 11, (3.34)
where n‘ = (~~)12/(~~~)13.
The temperature rise in the combustion chamber may then be determined from
Eq. (3.33), in the approximate form (T3 - T2) = (uf + b). Strictly u and b are functions of
the temperature of the reactants and the fuel-air ratiof. but fixed values are assumed to
cover a reasonable range of conditions. Accordingly, the fuel-air ratio may be expressed as
f = { T3 - TI [ 1 + (x - 1)/7)c] - b}/u. (3.35)

Using this expression to determinef for given T3 and Tl, mean values of (yg)% and (cpg)34
for the turbine expansion may be determined from data such as those illustrated graphically
in Fig. 3.12. For the weak combustion used in most gas turbines, with excess air between
200 and 400%,f << 1. Strictly, for given T3 and Tl, the mean value of (cpg)34, and indeed
(y&, will vary with pressure ratio.
The (arbitrary) overall efficiency may be written as
70 = NDNWmHT
= ([cu(l +f>/nI[l - (1 + @/Y3 - (x - l)}/([(l +f)(P - l)/n’I - (x - l)}.
(3.36)
Calculation of the specific work and the arbitrary overall efficiency may now be made
parallel to the method used for the ah cycle. The maximum and minimum temperatures
are specified, together with compressor and turbine efficiencies. A compressor pressure
ratio (r) is selected, and with the pressure loss coefficients specified, the corresponding
turbine pressure ratio is obtained. With the compressor exit temperature T2 known and T3
specified, the temperature change in combustion is also known, and the fuel-air ratiof
may then be obtained. Approximate mean values of specific heats are then obtained from
Fig. 3.12. Either they may be employed directly, or n and n’ may be obtained and used.