Modern Engineering Thermodynamics

13.16 Brayton Cycle 495
Solution
Using the Lenoir cycle diagram shown in Figure 13.42, we can carry out the following analysis.
a. From the ideal gas equation of state, we can calculate p 1 = mRT 1 =V 1 . For this cycle, we have
Then,
V 1 = V 4 = mRT ð1:00 × 10 −3 lbmÞ 53:34 ft
. lbf
4
lbm . ð530 RÞ
R
=
p 4
14:7 lbf
= 0:0134 ft 3
in 2 144 in2
ft 2
p 1 = mRT ð1:00 × 10 −3 lbmÞ 53:34 ft
. lbf
1
lbm . ð800: RÞ
R
=
= 22:2 psia
V 1
ð0:0134 ft 3 Þ 144 in2
ft 2
b. For the Lenoir cycle, the isentropic compression ratio is CR = v 2s /v 3 = T 2s /T 3 . From Eq. (7.38), we have
Then, the isentropic compression ratio for this engine is
k−1 0:4
p 2s k
14:7 psia 1:4
T 2s = T 1 = ð800: RÞ = 711 R
p 1
22:2 psia
CR = v 2s
v 3
= T 2s
T 3
c. Equation (13.21) gives the Lenoir cold ASC thermal efficiency as
= 711 R
530: R = 1:34
ðη T Þ Lenoir
= 1 − kT 3ðCR − 1Þ 1:40ð530: RÞð1:34 − 1Þ
= 1 − = 0:0656 = 6:56%
T 1 − T 4
800: − 530: R
cold ASC
Exercises
31. If the maximum combustion temperature of the Lenoir model airplane jet engine in Example 13.11 is increased from
800. R to 1000. R, determine the corresponding combustion pressure, p 1 . Assume all the other variables remain
unchanged. Answer: p 1 = 27.7 psia
32. If the air intake temperature T 3 in Example 13.11 is lowered from 530. R to 500. R, determine the new isentropic
compression ratio for the engine. Assume all the other variables remain unchanged. Answer: CR= 1.40.
33. If the combustion temperature in Example 13.11 is increased from 800. R to 1500. R, determine the corresponding
Lenoir cold ASC thermal efficiency of the engine. Answer: (η T ) Lenoir cold ASC = 15.7%.
Its relatively simple construction and good reliability, and the fact that methane was readily available and
inexpensive in many urban areas (where it was already being used extensively for illumination), made the
Lenoir cycle engine quite successful from about 1860 to 1890. After the turn of the century, the Lenoir engine
lost popularity and became obsolete. However, the Lenoir cycle appeared briefly again in the German V-l rocket
engines (“buzz bombs”), used during World War II.
13.16 BRAYTON CYCLE
The main reason why the Lenoir cycle had such a poor thermal efficiency was that the fuel-air mixture was not
compressed before it was ignited. Many people recognized this fact, but it was not until 1873 that a more efficient
internal combustion engine, utilizing preignition compression, was developed. George B. Brayton (1830–
1892), an American engineer, adopted the dual reciprocating piston technique of Stirling and Ericsson but used
one piston only as a compressor and the second piston only to deliver power. A combustion chamber was
inserted between the two pistons to provide a constant pressure heat addition process. Thus, the Brayton ASC
consists (ideally) of two isentropic processes (compression and power) and two isobaric processes (combustion
and exhaust), as shown in Figure 13.44.