Page 75 - Advanced Gas Turbine Cycles

Chapter 4. Cycle eficiency with turbine cooling (cooling jlow rates specified) 51

component cycles. This interpretation will also be useful when we consider the internally
irreversible cycles later.
There is an apparent paradox here that as the cooled cycle contains an irreversible
process (constant pressure mixing), its efficiency might be expected to be lower than the
original uncooled cycle. The answer to this paradox follows from consideration of all
the irreversibilities in the cycle and we refer back to the analysis of Section 3.2.1.1, for the
rational efficiency of the [CHT]Ru cycle. The irreversibility associated with the heat
supply is unchanged, as given in Eq. (3.3), but the irreversibility associated with the heat
rejection QA between temperatures T6 and TI = TA becomes

(4.5)

The irreversibility in the adiabatic mixing is
IM = TA[(1 + $h - s3 - @21 = CpT~[[$ln(TdTd] - ln(TB/T5)19 (4.6)
since low Mach number and constant pressure mixing have been assumed.
The sum of the irreversibilities ZA and ZM is thus
IA + IM = QA - TAcp ln[(T6/TA)(TB/T5)1 + @pTA ln[(T5/T2)(TAIT6)1* (4.7)
But, since TB/T4 = T5/T6 = T2/TA = x, this equation becomes

IB + IM = QA - C~TA ln(T4/TA), (4.8)
which is the same as the irreversibility associated with heat rejection in the uncooled cycle
[cHT]RU given in Chapter 3, Eq. (3.4). Further the maximum work, W,,, is unchanged
from that given in the [cHT]Ru cycle, as is the rational efficiency. The sum of all the
irreversibilities are the same in the two cycles, [CHTIRu and [cHT]Rc, but they are broken
down and distributed differently. This point is amplified by Young and Wilcock [7].

4.2.1.2. Cycle [CHTIRc2 with two step cooling
A reversible cycle with turbine expansion split into two steps (high pressure, HP, and
low pressure, LP) is illustrated in the T, s diagram of Fig. 4.3. The mass flow through the
heater is still unity and the temperature rises from T2 to T3 = TB; hence the heat supplied
QB is unchanged, as is the overall isentropic temperature ratio (x). But cooling air of mass
flow &, is used at entry to the first HP turbine (of isentropic temperature ratio xH) and
additional cooling of mass flow & is introduced subsequently into the LP turbine (of
isentropic temperature ratio xL). The total cooling flow is then $ = + &.
As is shown in Fig. 4.3a, the lower pressure cooling is fed by air JIL at state 7, at a
corresponding pressure p7 and a temperature T7, and this mixes with air (1 + &) from the
HP exhaust at temperature TS to produce a temperature Ts as indicated in the diagram. The
full turbine gas flow (1 + I,+) then expands through a pressure ratio xL to a temperature TI,-,,
and subsequently rejects heat, finishing at TI = TA.
But this expansion through the LP turbine may be considered as two parallel
expansions. The first is of mass flow (1 + &,) from the temperature T9 to a temperature T6
(a continuation of the expansion of (1 + &,) from 5 to 9); and the second is of mass flow
& through a reversed compressor from state 7 to state 1 (which cancels out the