Modern Engineering Thermodynamics

502 CHAPTER 13: Vapor and Gas Power Cycles
EXAMPLE 13.13 (Continued )
and the engine’s actual thermal efficiency, based on temperature-dependent specific heats, is
ðη T Þ Brayton
= h 1 − h 2 − ðh 4 − h 3 Þ
h 1 − h 4
ðactual, variable
specific heatsÞ
where h 4 = 284:9 Btu/lbmðat 1175 RÞ and h 2 = 329:9 Btu/lbmðat 1350 RÞ. Then,
521 − 329:9 − ð284:9 − 124Þ
ðη T Þ Brayton
= = 0:128 = 12:8%
521 − 284:9
ðactual, variable
specific heatsÞ
3c. The maximum work Brayton cold ASC thermal efficiency is given by Eq. (13.27) as
rffiffiffiffiffi
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
T
ðη T Þ max work
= 1 − 3 520: R
= 1 − = 0:502 = 50:2%
T 1 2060 R
Brayton
cold ASC
This is much greater than the actual thermal efficiency for this engine, because an aircraft engine need produce only enough
work output to drive the engine’s auxiliary equipment (generator, fuel pump, etc.), and most of the engine’s energyoutput
is in the kinetic energy of its exhaust (which produces thrust).
Exercises
37. Determine the optimum compressor outlet temperature of the Pratt & Whitney jet engine analyzed in Example 13.13
that maximizes the net output work of the engine. Answer: (T 4s ) opt = 1035 R.
38. Determine the isentropic efficiency of the Brayton cycle compressor in Example 13.13 if the outlet pressure is increased
from 200. psia to 210. psia. Assume all the other variables remain unchanged. Answer: (η s ) compressor = 90.3%.
39. If the temperature at the entrance to the turbine in Example 13.13 is increased from 2060 R to 2460 R, determine the
new Brayton cycle cold ASC thermal efficiency of the engine. Assume all the other variables remain unchanged. Answer:
(η T ) Brayton cold ASC = 33.8%.
Note that, whereas the Brayton hot ASC cycle thermal efficiency of Example 13.13 is relatively high (about
30%), the actual thermal efficiency of an aircraft turbojet engine is normally quite low. This is not because of
poor engine design, but because most of the combustion energy is put into the kinetic energy of the exhaust
gas rather than into the mechanical shaft work output. In aircraft engine design, the thrust to weight ratio of the
engine is a key parameter, and the engine’s thermal efficiency is secondary.
13.18 OTTO CYCLE
The Stirling and Ericsson external combustion gas power cycles were originally developed to combat the
dangerous high-pressure boilers of the early steam engines. The Lenoir internal combustion engine was simpler,
smaller, and used a more convenient fuel than either of these engines, but it had a very poor thermal efficiency.
Brayton managed to increase the thermal efficiency of the internal combustion engine by providing a compression
process before combustion using the two-piston Stirling and Ericsson technique with a separate combustion
chamber. But the ultimate goal of commercial internal combustion engine development was to combine all
the basic processes of intake, compression, combustion, expansion (power), and exhaust within a single pistoncylinder
apparatus. This was finally achieved in 1876 by the German engineer Nikolaus August Otto
(1832–1891). The basic elements of the ASC model of the Otto cycle are shown in Figure 13.48. It is composed
of two isochoric processes and two isentropic processes.
After several years of experimentation, Otto finally built a successful internal combustion engine that allowed all
the basic processes to occur within a single piston-cylinder arrangement. The thermodynamic cycle of Otto’s
engine required four piston strokes and two crankshaft revolutions to complete, but it ran smoothly, was relatively
quiet, and was very reliable and efficient. Otto’s engine was an immediate success, and by 1886, more
than 30,000 had been sold. They became the first serious competitor to the steam engine in the small- and
medium-size engine market.
Initially, Otto’s engine used illuminating gas (methane) as its fuel, but by 1885, many Otto cycle engines were
already being converted into liquid hydrocarbon (gasoline) burning engines. The development of the ingenious
float-feed carburetor for vaporizing liquid fuel in 1892 by the German Wilhelm Maybach (1847–1929) heralded