Modern Engineering Thermodynamics

13.23 Second Law Analysis of Vapor and Gas Power Cycles 521
Since the motion of the bird could easily be connected to a shaft to
produce work, the drinking bird is clearly some form of an engine.
So how does this engine work?
By simple observation, we conclude that the evaporation of liquid
water from the head of the bird causes the physical changes in
the liquid inside the bird. Also, our observations tell us that the
relative humidity in the room must be below 100% for the bird
to operate. Therefore, it would seem that the bird is some form
of steam engine, where the steam is just the water vapor that evaporates
from the bird’s head, and the partial pressure of this
water vapor must be lower than the saturation pressure of water
vapor in the room air for the bird to operate. Since the bird’s
head is constantly moving, it is not unreasonable to assume that
its temperature is approximately equal to the wet bulb temperature
of the room. If we then complete the steam cycle by assuming
the evaporated water is condensed in the atmosphere at the
dew point temperature, we can construct the T–s vapor power
cycle shown Figure 13.61.
T WB
1
4s
p
T DP
2s
3, 4s
3
s
(a)
FIGURE 13.61
T–s and p–v diagrams for the drinking bird.
1
v
(b)
We can estimate its power-producing potential and operational
thermal efficiency as follows. The equivalent Carnot cycle thermal
efficiency is given by
ðη T Þ Carnot
= 1 − T L
= 1 − T DP
T H T WB
drinking bird
and the isentropic Rankine cycle thermal efficiency is
ðη T Þ Isentropic
= ðh 1 − h 2s Þ − ðh 4s − h 3 Þ
h 1 − h 4s
Rankine
drinking bird
where the states are identified using the relative humidity ϕ, the dry
bulb temperature T DB , the wet bulb temperature T WB ,andthedew
point temperature T DP as follows:
Station 1—Bird’s head
Station 2s—Beginning of
condensation
p 1 = ϕp sat ðT DB Þ T 2s = T DP
T 1 = T WB s 2s = s 1
h 1 = hp ð 1 , T 1 Þ h 2s = hT ð 2s , s 2s Þ
s 1 = sp ð 1 , T 1 Þ p 2s = pT ð 2s , s 2s Þ
Station 3—End of condensation
Station 4s—Liquid brought
back to pressure p 1
p 3 = p 2s p 4s = p 1
x 3 = 0:0 s 4s = s 3
h 3 = hp ð 3 , x 3 Þ h 4s = hp ð 4s , s 4s Þ
s 3 = sp ð 3 , x 3 Þ
2s
Figure 13.62 shows how these thermal efficiencies vary with room
relative humidity. Clearly, the driertheairintheroom,themore
efficient the drinking bird becomes.
Thermal efficiency (%)
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
25
Carnot cycle
Rankine cycle
34 43 52 61 70
Relative humidity of the surrounding air (%)
FIGURE 13.62
Thermal efficiency of a drinking bird.
The drinking bird thermal efficiency is roughly equivalent to the
low thermal efficiencies of the original Newcomen and Watt steam
engines. However, a scaled-up version could be effective as an
engine in dry climates.
Case study 13.3. Aircraft engine development
The world’s largest aircraft engine manufacturers developed a new
generation of gas turbine engines that provide 60,000 to 100,000 lbf
of thrust. Pratt & Whitney has its PW4000, Rolls Royce has its Trent,
and General Electric has its GE90. The PW4000 has an isentropic pressure
ratio of 31.5 and a bypass ratio of 5:1, producing 60,000 lbf of
thrust. The GE90 has an isentropic pressure ratio of 50.0, and a bypass
ratio of 10.0 to 1, producing a thrust in the 80,000 lbf range. This case
study focuses on the GE90 turbofan engine development.
Before we can discuss aircraft engine design, we need to do some
background work. The thrust produced by an aircraft engine is primarily
the difference between the rate of momentum imparted to
the gases exiting the engine and the momentum rate of the inlet
air. Neglecting the small momentum produced by the fuel flow
rate, the thrust can be written as
Thrust = T = _m a ðV exhaust − V aircraft Þ/g c
where, in this case, V aircraft = V inlet air and _m a = _m air = _m exhaust . Since
the exhaust velocity is always greater than the aircraft velocity, we
see from this equation that there are two ways to increase the
thrust of an aircraft engine:
1. Increase the engine’s exhaust gas velocity.
2. Increase the engine’s air mass flow rate.
A turbojet engine is a Brayton cycle gas turbine engine that produces
all of its thrust by generating a very high exhaust gas velocity. This
is done by forcing all the turbine’s hot exhaust gases through a
flow nozzle to maximize the exhaust velocity (see Figure 13.63a). A
turbofan engine is also a Brayton cycle gas turbine engine. But it
(Continued )