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University of Oklahoma Design and Thermal Fluid Systems
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WMM
Power Cycles_ Diesel Cycle
WMM
Power Cycles
– The Carnot cycle (totally reversible, int. and ext.) is the ideal cycle for heat engines
– The Otto cycle is the ideal cycle for spark ignition automobile engines
– The Diesel cycle is the ideal cycle for compression ignition engines
– The Brayton cycle is the ideal cycle for gas turbine engines
– The Rankine cycle is the ideal cycle for vapor power plants
WMM
Diesel Cycle– The ideal cycle for compression-ignition engines– Diesel cycles are designed to operate at higher
compression ratios, typically between 12~24
• The 4 cycles of the Diesel engine are:
(1--------2) Isentropic compression
(2--------3) P=constant heat addition (combustion process)
(3--------4) Isentropic expansion
(4--------1) Constant volume heat rejection
WMM
Gasoline Vs. Diesel enginesSpark Plug
Gasoline Engine
Sparks
Diesel Engine
fuel
Fuel spray
In Diesel engines, the spark plug and carburetor is replaced by a fuel injector and only air is compressed during the compression process
Air-fuelmixture
v
Air
v
WMM
• The ideal Diesel cycle consists of four internally reversible processesDiesel Cycle
(1------2) Isentropic compression
(2------3) P=constant heat addition “combustion process”
(3------4) Isentropic expansion
(4------1) Constant volume heat rejection
P
v(1)
(4)
v4=v1
qout
s
T
(1)
(2)
s2=s1
(3)P2=P3 qin
(4)
s3=s4
v1=v4qout
T-s diagram
Team exercise: draw the P-v diagram for the Diesel cycle:
WMM
• The ideal Diesel cycle consists of four internally reversible processesDiesel Cycle
(1------2) Isentropic compression
(2------3) P=constant heat addition “combustion process”
(3------4) Isentropic expansion
(4------1) Constant volume heat rejection
P
v(1)
(4)
(3)(2)
v4=v1
qout
qin
s3=s4
s1=s2
p2=p3
s
T
(1)
(2)
s2=s1
(3)P2=P3 qin
(4)
s3=s4
v1=v4qout
P-v diagramT-s diagram
WMM
Diesel CycleP
v(1)
(4)
(3)(2)
v4=v1
qout
qin
s3=s4
s1=s2
p2=p3
s
TP-v diagram T-s diagram
(1)
(2)
s2=s1
(3)P2=P3 qin
(4)
s3=s4
1423 , uuqhhq outin −=−=
v1=v4qout
)( 2323 TTchhq pin−=−= )( 1414 TTcuuq vout
−=−=
WMM
Diesel Cycle• Cutoff ratio rc
» Is defined as the ratio of the cylinder volumes before and afterthe combustion process:
vv
VVrc
2
3
2
3 ==
(1------2) Isentropic compression
(2------3) P=constant heat addition
(3------4) Isentropic expansion
(4------1) Constant volume heat rejection
P2 = P3
vmax=v4=v1vmin
Cutoff ratio
Combustion process
Team exercise: write below the compression ratio for the Diesel cycle:
WMM
Diesel Cycle• Cutoff ratio rc
» Is defined as the ratio of the cylinder volumes before and afterthe combustion process:
vv
VVrc
2
3
2
3 ==
(1------2) Isentropic compression
(2------3) P=constant heat addition
(3------4) Isentropic expansion,
(4------1) Constant volume heat rejection vv
VV
VVr
2
1
2
1
min
max ===
P2 = P3
vmax=v4=v1vmin
Compression ratio
Cutoff ratio
Combustion process
WMM
Diesel Cycle h Vs. uNoting that the Diesel cycle is executed in a piston-cylinder (closed system) the amount of heat transferred to the working fluid at P=constant and and rejected from it at V=constant can be expressed as:
systemoutin EE ∆=−
uuwq outbin 23, −=−
Process (2-------3)
( )232
3
2
3
222,
vvp
dvpdvpw outb
−=
== ∫∫
uuvvpqin 232 )( 23 −=− −∴
)( 23223 vvpuuqin −+−=
( )222333 vpuvpuqin +−+== h3
= h2
hhqin 23−=∴
)( 2323 TTchhq pin−=−=∴
ThTh cc pp ∆=∆⇒
∂∂
= *Or in terms of temperatures inq ( )Tf using
p2= p3
D-1
P2 = P3
vmaxvmin
P2 = P3
vmaxvmin
WMM
Diesel Cycle h Vs. u
Employing process (4-------1)
uuqout 14−=
The heat X-fer out is given by:
uuqout 41−=−
)( 1414 TTcuuq vout−=−=
TuTu cc vv
∆=∆⇒∂∂
= *Or in terms of temperatures inq ( )Tf using
D-2∴
P2 = P3
vmaxvmin
P2 = P3
vmaxvmin
WMM
Diesel CycleThe thermal efficiency of the ideal Diesel cycle under the cold-air-standard assumptionsbecomes:
qqq
qw
in
out
in
outin
in
netDieselTh
−=−
== 1,η )( 2323 TTchhq pin
−=−= D-1
D-2)( 1414 TTcuuq vout−=−=
∴)
)1
23
14, (
(TTTT
cc
p
vDieselTh −
−−=η
cc
v
pk = (specific heat ratio)
)
)1
23
14, (
(TTkTT
DieselTh −
−−=η
⎟⎠
⎞⎜⎝
⎛−
⎟⎠
⎞⎜⎝
⎛−
−=
1
1
2
32
1
4
1
1
,
TTTk
TTT
DieselThη
Utilizing the cutoff ratio rc and the isentropicIdeal gas relations for processes 1----2 and 3----4 the above expression simplifies to eq D-3
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
−−= − )1(
111 1, rr
r c
kc
kDieselTh kη cc
v
pk = Specific heat ratio vv
VVrc
2
3
2
3 == Cutoff ratio
vv
VV
VVr
2
1
2
1
min
max === Compression ratio
3
4
1
4
31
1
2
2
1
TT
vv
vv
TT
kk
=⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛=
−−
Solve for T4/T1 and T3/T2 and substituteinto equation D-3 to obtain the efficiency
D-3
WMM
Diesel Cycle
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
−−= − )1(
111 1, rr
r c
kc
kDieselTh kη
•Thermal efficiency of the ideal Diesel cycle as function of compression ratio and cutoff ratios of 1, 2, 3, and 4.• At rc = 1 implies that all the heat (combustion process) would take place at constant volume
K = 1.4
vv
VVrc
2
3
2
3 ==Cutoff ratio
vv
VV
VVr
2
1
2
1
min
max ===Compression ratio
Plotted
WMM
Diesel Cycle
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
−−= − )1(
111 1, rr
r c
kc
kDieselTh kηrkottoTh 1,
11 −−=η
• By comparing the efficiencies of the Diesel and Otto cycles the efficiency of the Diesel cycle differs from the efficiency of an Otto cycle by the quantity in the brackets
• The quantity present in the brackets for the Diesel cycle is always greater than 1. therefore,
If only if both cycles are operating on the same compression ratio
DieselthOttoth ,, ηη >
WMM
Diesel Cycle
• The Diesel cycle is the ideal cycle for CI (internal combustion) engines
• The CI engine, first proposed by Rudolph Diesel in the 1890s, is very similar to the SI (spark ignition engines) of the Otto cycle
• The only thing that differs between the Otto and Dieselcycle is the method to ignite the combustion
» In the Otto cycle (spark-ignition engines also known as gasoline engines) the air-fuel mixture is compressed to a temperature that is below the autoignition temperature of the fuel and the combustion process is initiated by firing a spark plug
» In the Diesel cycle (also known as the internal combustion engine) the air is compressed to a temperature that is above the autoignition temperature of the fuel, and combustion starts on contact as the fuel is injected into the hot air
WMM
Diesel Cycle
• Remember that Diesel engines operate at much higher compression ratios than the spark-ignition engines
• The Diesel engines also burn the fuel more completely since they usually operate lower resolutions per minute than spark-ignition engines
• Thermal efficiencies of large diesel engines range from about 35 to 40 percent
• The higher efficiency and lower fuel costs of diesel engines make them the clear choice in application requiring a relativelylarge amount of power such as in:
» Locomotive engines» Emergency power generation units» Large ships and » Heavy trucks » As an example of how large a diesel engine can be, a 12-cylinder diesel
engine built in 1964 by the Fiat Corp. of Italy had a normal power output of 25,200 hp (18.8 MW) at 122rpm, a cylinder of 90 cm, and a stroke of 91 cm.
WMM
• The ideal Diesel cycle consists of four internally reversible processesDiesel Cycle
T-s and P-v diagrams for the idealDiesel cycle
P-v diagram
T-s diagram
T-s and P-v diagrams for the idealOtto cycle
P-v diagram
T-s diagram
WMM
Diesel CycleConsider a Diesel cycle when the specific heats vary with
temperature (Air-Standard Assumptions)
Similar to the OTTO cycle the air tablesaccount explicitly for the variation of the specific heats with temperatures
1
2
1
2
vv
vv
r
r =122
1
1
2rrr v
rv
vv
v ==
Relative volumes
rationCompressiovv
r2
1=
Process 2-------3
3
33
2
22
TVP
TVP
= 32 PP =2
2
3
2
33 T
VV
PP
T = 222
33 TrT
VV
T c== ratiocutoffVV
rc2
3=
WMM
Diesel CycleProcess 3-------4
3
2
2
4
3
4
VV
VV
VV
=14 VV =
crr
VV
VV
VV
==3
2
2
1
3
4
23
1411hhuu
qqq
qw
in
out
in
outin
in
cycle
−−
−=−=−
==η
(Air-Standard Assumptions)
WMM
Diesel Cycle• Ideal Gas Isentropic Processes:
Cold-Air-Standard Analysis (constant specific heats at room temperature).
k
consts
k
consts
k
consts
k
consts
VV
PP
VV
PP
VV
TT
VV
TT
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
=
=
−
=
−
=
4
3
3
4
2
1
1
2
1
4
3
3
4
1
2
1
1
2
v
p
CC
k =
2
1
2
1
min
max
vv
VV
VV
r ===2
3
2
3
vv
VV
rc ==
Compression Ratio Cutoff Ratio
WMM
Diesel Cycleand assuming constant specific heats
