diesel cycle and the brayton cycle chapter 9b. rudolph diesel german inventor who is famous for the...
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Diesel Cycle and the Brayton Cycle
Chapter 9b
Rudolph Diesel
German inventor who is famous for the development of the diesel engine
The diesel engine is based on a compression ignition system http://www.autonews.com/
files/euroauto/inductees/diesel.htm
Diesel Engines
No spark plugFuel is sprayed into hot compressed
air
State Diagrams for the Diesel Cycle
Diesel Cycle Otto Cycle
The only difference is in process 2-3
Consider Process 2-3
This is the step where heat is transferred into the system
We model it as constant pressure instead of constant volume
23,23, uuuwq outbin
2323, TTChvPuq pin
Consider Process 4-1
This is where heat is rejectedWe model this as a constant v process
That means there is no boundary work
uwq 4141
4141 TTCuqq vout 14 TTCq vout
As for any heat engine…
in
out
in
netth q
q
q
w 1 substitute
2314 and TTCqTTCq pinvout
23
14,
)(1
TTC
TTCn
p
vdieselth
23
141TTk
TT
Rearrange
1
11
232
141,
TTkT
TTTn dieselth
PV
T
PV
TP P
T
T
V
Vrc
3 3
3
2 2
23 2
3
2
3
2
where
rc is called the cutoff ratio – it’s the ratio of the cylinder volume before and after the combustion process
1
11
232
141,
TTkT
TTTn dieselth
rc
PV
T
PV
TV V
T
T
P
P
4 4
4
1 1
14 1
4
1
4
1
where
This doesn’t do us much good
4 4 3 3
1 1 2 2
andk k
k k
PV PV
PV PV
1
11
232
141,
TTkT
TTTn dieselth
rc
14 PP
Since Process 1-2 and Process 3-4
are both isentropic
k
k
k
k
V
V
P
P
V
V
P
P
2
3
2
3
1
4
1
4
1 1
kc
k
rV
V
2
3
1
,
2
11
1
kc
th diesel
c
T rn
kT r
Finally, Since process 1-2 is isentropic
1
1
2
2
1
k
V
V
T
TThe volume ratio from 1 to 2 is the compression ratio, r
1
2
1 1
k
rT
T
Which finally gives…
1
111
1,c
kc
kdieselth rk
r
r
k=1.4
The efficiency of the Otto cycle is always higher than the Diesel cycle
Why use the Diesel cycle?Because you can use higher
compression ratios
Typical range for gasoline engines
P-v Diagram for an ideal dual cycle
Brayton Cycle
Ideal Cycle for Gas Turbine EnginesUsually operate on an open cycle
Closed cycle model for a gas turbine engine
1-2 Isentropic Compression
2-3 Constant Pressure heat addition
3-4 Isentropic Expansion
4-1 Constant Pressure heat rejection
Closed cycle model for a gas turbine engine
1-2 Isentropic Compression
2-3 Constant Pressure heat addition
3-4 Isentropic Expansion
4-1 Constant Pressure heat rejection
23
14, 11
q
q
q
qn
in
outBraytonth
1414 TTChhq pout
2323 TTChhq pin
kkp
Braytonth r 1,
11
1
2
P
Prp
Remainder of the Chapter
I’m not skipping the other sections in this chapter because they are unimportant, or uninteresting
We just don’t have time!!