Page 262 - The Mechatronics Handbook

0066_frame_C12 Page 27 Wednesday, January 9, 2002 4:22 PM

Decisions concerning cycle operating conditions normally recognize that the thermal efficiency tends to
increase as the average temperature of heat addition increases and/or the temperature of heat rejection
decreases. In the Rankine cycle, a high average temperature of heat addition can be achieved by superheating
the vapor prior to entering the turbine and/or by operating at an elevated steam-generator pressure. In the
Brayton cycle an increase in the compressor pressure ratio p 2 /p 1 tends to increase the average temperature of
heat addition. Owing to materials limitations at elevated temperatures and pressures, the state of the working
fluid at the turbine inlet must observe practical limits, however. The turbine inlet temperature of the Brayton
cycle, for example, is controlled by providing air far in excess of what is required for combustion. In a
Rankine cycle using water as the working fluid, a low temperature of heat rejection is typically achieved
by operating the condenser at a pressure below 1 atm. To reduce erosion and wear by liquid droplets on
the blades of the Rankine cycle steam turbine, at least 90% steam quality should be maintained at the
turbine exit: x 4 > 0.9.
The back work ratio, bwr, is the ratio of the work required by the pump or compressor to the work
developed by the turbine:

h 2 – h 1
bwr = ---------------- (12.28)
h 3 – h 4

As a relatively high specific volume vapor expands through the turbine of the Rankine cycle and a much
lower specific volume liquid is pumped, the back work ratio is characteristically quite low in vapor power
plants—in many cases on the order of 1–2%. In the Brayton cycle, however, both the turbine and compressor
handle a relatively high specific volume gas, and the back ratio is much larger, typically 40% or more.
The effect of friction and other irreversibilities for flow through turbines, compressors, and pumps is
commonly accounted for by an appropriate isentropic efficiency. Referring to Table 12.6 for the states, the
isentropic turbine efficiency is

h 3 –
η t = ----------------- (12.29a)
h 4
h 3 – h 4s
The isentropic compressor efficiency is

h 2s – h 1
η c = ----------------- (12.29b)
h 2 – h 1

, which takes the same form as Eq. (12.29b), the numerator is
In the isentropic pump efficiency, h p
frequently approximated via Eq. (12.24c) as h 2s − h 1 ≈ v 1 ∆p, where ∆p is the pressure rise across the pump.
Simple gas turbine power plants differ from the Brayton cycle model in significant respects. In actual
operation, excess air is continuously drawn into the compressor, where it is compressed to a higher
pressure; then fuel is introduced and combustion occurs; finally the mixture of combustion products
and air expands through the turbine and is subsequently discharged to the surroundings. Accordingly,
the low-temperature heat exchanger shown by a dashed line in the Brayton cycle schematic of Table 12.6
is not an actual component, but included only to account formally for the cooling in the surroundings
of the hot gas discharged from the turbine.
Another frequently employed idealization used with gas turbine power plants is that of an air-standard
analysis. An air-standard analysis involves two major assumptions: (1) As shown by the Brayton cycle
schematic of Table 12.6, the temperature rise that would be brought about by combustion is effected
instead by a heat transfer from an external source. (2) The working fluid throughout the cycle is air,
which behaves as an ideal gas. In a cold air-standard analysis the specific heat ratio k for air is taken as
constant. Equations (1) to (6) of Table 12.4 apply generally to air-standard analyses. Equations (1′) to (6′)

©2002 CRC Press LLC