1. The diesel cycle model assumes air is the working substance with constant specific heats. It is taken into the cylinder during the suction stroke at constant pressure and compressed adiabatically. 2. Heat is added at constant pressure, causing the substance to expand adiabatically in the cylinder. It then drops instantly to atmospheric pressure at constant volume. 3. The efficiency of the theoretical diesel cycle depends on the compression ratio, cut-off ratio, and specific heat ratio. Higher compression ratios increase efficiency up to the point of pre-ignition.

1. DIESEL CYCLEDIESEL CYCLE
Assumption:
1.1. The workingThe working
substance is air withsubstance is air with
constant specificconstant specific
heats.heats.
Theoretical indicatorTheoretical indicator
diagramdiagram
PP
RR
EE
SS
SS
UU
RR
EE
VOLUMEVOLUME
2.2. The workingThe working
substance is takensubstance is taken
in the enginein the engine
cylinder during thecylinder during the
suction stroke atsuction stroke at
constant pr.constant pr.
1100

2. PP
RR
EE
SS
SS
UU
RR
EE
VOLUMEVOLUMEγγ ==
CpCp
CvCv
22
AdiaAdiacc
1100
DIESEL CYCLEDIESEL CYCLE
Assumption:
Theoretical indicatorTheoretical indicator
diagramdiagram
3.3. The working sub isThe working sub is
compressed in thecompressed in the
engine cylinderengine cylinder
adiabatically,adiabatically,
according to the lawaccording to the law
pvpvγγ
= c. ( 1-2 )= c. ( 1-2 )
γ = ratio of sp. heats.γ = ratio of sp. heats.

3. PP
RR
EE
SS
SS
UU
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EE
VOLUMEVOLUME
4.4. Heat is added toHeat is added to
the workingthe working
substance atsubstance at
constant pressure.constant pressure.
(2-3)(2-3)
33QQAA22
AdiaAdiacc
1100
DIESEL CYCLEDIESEL CYCLE
Assumption:
Theoretical indicatorTheoretical indicator
diagramdiagram
5. The working sub.,5. The working sub.,
after cut off,after cut off,
expands, in theexpands, in the
engine cylinderengine cylinder
according to the lawaccording to the law
pvpvγγ
=c up to the end of the stroke. ( 3-4 )=c up to the end of the stroke. ( 3-4 )
44
AdiaAdiacc

4. 6. At the end of6. At the end of
expansion stroke,expansion stroke,
pressure of thepressure of the
working substanceworking substance
drops,drops,
instantaneously, atinstantaneously, at
constant volume, toconstant volume, to
the atmosphericthe atmospheric
pressure. ( 4-1 )pressure. ( 4-1 )
PP
RR
EE
SS
SS
UU
RR
EE
VOLUMEVOLUME
44
AdiaAdiacc
33QQAA22
AdiaAdiacc
1100
DIESEL CYCLEDIESEL CYCLE
Assumption:
Theoretical indicatorTheoretical indicator
diagramdiagram
QQRR

5. PP
RR
EE
SS
SS
UU
RR
EE
VOLUMEVOLUME
7. The working7. The working
substance issubstance is
exhausted, fromexhausted, from
the enginethe engine
cylinder, atcylinder, at
constant pressureconstant pressure
( 1-0 )( 1-0 )
QQRR
44
AdiaAdiacc
33QQAA22
AdiaAdiacc
1100
DIESEL CYCLEDIESEL CYCLE
Assumption:
Theoretical indicatorTheoretical indicator
diagramdiagram

6. ηηDieselDiesel inputinput==
heatheat
rejectedrejected––
heatheat
addedadded
heat addedheat added
==
== QQrr
QQaa
11 ––
outputoutput
Theoretical WDTheoretical WD
heat addedheat added==
VOLUMEVOLUME
pp
PP
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EE
SS
SS
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RR
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QQRR
AdiaAdiacc
QQAA
AdiaAdiacc
vv
3322
1100
44
ASE/ASE/
m x Cm x Cvv x (Tx (T44-T-T11))
== m x Cm x Cpp x (Tx (T33-T-T22))
11 –– 11 ––
TT44-T-T11
γγ
TT33-T-T22
––
11
== ……11
DIESEL CYCLEDIESEL CYCLE

7. VOLUMEVOLUME
pp
PP
RR
EE
SS
SS
UU
RR
EE
vv
QQRR
AdiaAdiacc
QQAA
AdiaAdiacc
3322
1100
44
This efficiency can also beThis efficiency can also be
written in terms of the ratiowritten in terms of the ratio
of compression (r) & the cutof compression (r) & the cut
off ratio ( ).off ratio ( ).
δδ
DIESEL CYCLEDIESEL CYCLE
T2
T1
r
γ-1
= ……22
T2
T1
= )
γ-1
(
v1
v2
Ratio of compressionRatio of compression ==
v1
v2
for adiabatic compfor adiabatic compnn
(1-2)(1-2)
== rr

8. VolVolmm
at cutoffat cutoff
VolVolmm
at injection startsat injection starts
VOLUMEVOLUME
pp
PP
RR
EE
SS
SS
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vv
QQRR
AdiaAdiacc
QQAA
AdiaAdiacc
3322
1100
44
For constant pressure process 2-3For constant pressure process 2-3
T3
v3
T2
v2
=
p2 p3=......
DIESEL CYCLEDIESEL CYCLE
δδ
==
v3
v2
Let be the cut off ratio.Let be the cut off ratio.
δδ
==
v2
x
v3
T3 = T2
......
xT3 = T2
...... δδ
r
γ-1
xT3 = T1
...... δδ
……44
……33

9. v4 v2
VOLUMEVOLUME
pp
PP
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SS
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vv
QQRR
AdiaAdiacc
QQAA
AdiaAdiacc
3322
1100
44T4......
T4
p3v3
T3
=
p4 v4
T3
=
p4 v4
p3v3
......
p4v4
γ
p3v3
γ
=
p4
p3
=
γ
( )
v3
v4
= ( )
v4
v3
)
γ
(
v3
v4
= )
γ-1
(
v3
v4
T4......
T3
DIESEL CYCLEDIESEL CYCLE
AdiaAdiacc
expansion (3-4)expansion (3-4)
γ-1
)(
v2
v3
= v4v1 =......

10. r
T4
T3
γ-1
T4
VOLUMEVOLUME
pp
PP
RR
EE
SS
SS
UU
RR
EE
vv
QQRR
AdiaAdiacc
QQAA
AdiaAdiacc
3322
1100
44
r =
v1
v2
δδ v3
v2
=
δδ
=
DIESEL CYCLEDIESEL CYCLE
......
From (4) substitutingFrom (4) substituting
the value of Tthe value of T33
=...... δδ
r
γ-1
T1
x
)(
δδ
)(
γ-1
x
……55=
δδ
T1
x
γT4
......
v2
)
γ-1
(
v3
v2
v1
=
T3
r
=T4
...... T3x
δδ
r
γ-1
)(
T4......

11. TT33-T-T22
VOLUMEVOLUME
pp
PP
RR
EE
SS
SS
UU
RR
EE
vv
QQRR
AdiaAdiacc
QQAA
AdiaAdiacc
3322
1100
44
ηηDieselDiesel 11 ––
TT44-T-T11
γγ
––
11
==
Efficiency of theoreticalEfficiency of theoretical
Diesel cycle isDiesel cycle is
Substitute the value of TSubstitute the value of T44 & T& T33 from (5) & (3)from (5) & (3)
ηηDieselDiesel 11 ––
γγ
11
==
δδ
T1
γγ
––
–– T1
δδ
T2 –– T2
DIESEL CYCLEDIESEL CYCLE

12. VOLUMEVOLUME
pp
PP
RR
EE
SS
SS
UU
RR
EE
vv
QQRR
AdiaAdiacc
QQAA
AdiaAdiacc
3322
1100
44
ηηDieselDiesel 11––
γγ
11
== ––
δδ
γγ –– 11
δδ
–– 11
r
γ-1
11
ηηDieselDiesel 11 ––
γγ
11
== ––
δδ
–– 11
δδ
–– 11 T2
T1
x
γγ
DIESEL CYCLEDIESEL CYCLE
Substitute the value of TSubstitute the value of T11 / T/ T22 fromfrom (2)(2)

13. P
V
Thus from the efficiency
expression we may conclude that in
order to increase the efficiency the
engine we may have higher
compression ratios of compression is
limited by ignition temperature of the
mixture. If the ration compression may
higher before the end of compression
than the ignition temperature of the
mixture and the pre ignition occur.