Lecture-7
Prepared under
QIP-CD Cell Project
Internal Combustion Engines
Ujjwal K Saha, Ph.D.
Department of Mechanical Engineering
Indian Institute of Technology Guwahati
1
Air Standard Cycles
1.
2.
3.
4.
Carnot
Otto
Diesel
Brayton
- maximum cycle efficiency
- spark-ignition (SI) engine
- compression-ignition (CI) engine
- gas turbine
2
Air Standard Cycles
• Air standard cycles are idealized cycles based on
the following approximations:
– the working fluid is air (ideal gas)
– all the processes are internally reversible
– the combustion process is replaced by heat
input from an external source
– heat rejection is used to restore fluid to initial
state
3
Thermodynamic Cycles
•
Air-standard analysis is used to perform elementary analyses
of IC engine cycles.
• Simplifications to the real cycle include:
1) Fixed amount of air (ideal gas) for working fluid
2) Combustion process not considered
3) Intake and exhaust processes not considered
4) Engine friction and heat losses not considered
5) Specific heats independent of temperature
4
SI Engine Cycle vs Thermodynamic Otto Cycle
FUEL
A
Ignition
I
R
Fuel/Air
Mixture
Combustion
Products
Actual
Cycle
Intake
Stroke
Compression
Stroke
Power
Stroke
Qin
Otto
Cycle
Air
Exhaust
Stroke
Qout
TC
BC
Compression
Process
Const volume
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process
5
Air-Standard Otto cycle
Process 1Æ 2
Process 2 Æ 3
Process 3 Æ 4
Process 4 Æ 1
Isentropic compression
Constant volume heat addition
Isentropic expansion
Constant volume heat rejection
Compression ratio:
r=
v1 v4
=
v2 v3
Qin
Qout
v2
TC
v1
BC
TC
BC
6
In
Otto
cycle,
the
combustion is so rapid
that the piston does not
move during the process,
and
therefore,
combustion is assumed to
take place at constant
volume.
Otto cycle efficiency
T4 − T1
T1(T4 / T1 − 1)
wnet
qout
η=
=1−
=1−
=1−
T2 (T3 / T2 − 1)
T3 − T2
qin
qin
7
Otto Cycle (Contd.)
For isentropic process:
pvk = constant with k=cp/cv
For process 1-2:
p1 v1k = p2 v2k
RT2
T2 v1
v1k p2
v2
=
=
=
T1 v 2
v k2 p1 RT1
v1
v1k v 2
T2
=
k
v 2 v1
T1
T2 v
=
T1 v
k −1
1
k −1
2
⎛v ⎞
= ⎜⎜ 1 ⎟⎟
⎝ v2 ⎠
k −1
8
Since m = constant:
k −1
T2 ⎛ v1 ⎞
=⎜ ⎟
T1 ⎝ v2 ⎠
k −1
⎛ V1 ⎞
=⎜ ⎟
⎝ V2 ⎠
k −1
⎛ VBDC ⎞
= ⎜⎜
⎟⎟
⎝ VTDC ⎠
= r k −1
For process 3-4, using the same analysis:
T3 ⎛ V4 ⎞
= ⎜⎜ ⎟⎟
T4 ⎝ V3 ⎠
Then
k −1
⎛V ⎞
= ⎜⎜ BDC ⎟⎟
⎝ VTDC ⎠
T2 T3
=
T1 T4
η =1−
k −1
or
= r k −1
T3 T4
=
T1
T2
1
r k −1
9
Increasing Compression Ratio
Increases the Efficiency
Typical
Compression
Ratios for
Gasoline Engines
10
Higher Compression Ratios?
• Higher compression ratio leads to
auto-ignition (without spark)
• Causes knock
• Engine damage
• Thus, there is an upper limit of high
compression ratio
11
CI Engine Cycle and the Thermodynamic Diesel Cycle
Fuel injected
at TC
A
I
R
Combustion
Products
Air
Actual
Cycle
Intake
Stroke
Compression
Stroke
Power
Stroke
Qin
Diesel
Cycle
Exhaust
Stroke
Qout
Air
BC
Compression
Process
Const pressure
heat addition
Process
Expansion
Process
Const volume
heat rejection
Process
12
Air-Standard Diesel cycle
Process 1Æ 2
Process 2 Æ 3
Process 3 Æ 4
Process 4 Æ 1
Isentropic compression
Constant pressure heat addition
Isentropic expansion
Constant volume heat rejection
Cut-off ratio:
Qin
rc =
v3
v2
Qout
v2
TC
v1
BC
TC
BC
13
Due to ignition delay and finite time required
for fuel injection, combustion process
continues till the beginning of power stroke.
This keeps the cylinder pressure at peak
levels for a longer period. Therefore, the
combustion process can be approximated
as
constant
pressure
heat
addition.
Remaining processes are similar to that of
Otto cycle.
• Cycle efficiency,
wnet
qout
η=
=1−
qin
qin
14
V3
Cutoff Ratio, rc =
V2
V1
Compression Ratio, r =
V2
V4
Expansion Ratio, re =
V3
Cutoff Ratio Χ Expansion Ratio = Compression Ratio
15
assuming constant specific heats:
η =1−
c v (T4 − T1 )
(T4 − T1 )
T (T4 / T1 − 1)
=1−
=1− 1
cp (T3 − T2 )
k(T3 − T2 )
T2 k(T3 / T2 − 1)
for isentropic process 1-2:
T1 ⎛ v 2 ⎞
=⎜ ⎟
T2 ⎝ v1 ⎠
k −1
for constant pressure process 2-3: p2 = p3
ideal gas law:
RT2 RT3
=
v2
v3
=>
T3 v3
=
= rc
T2 v2
16
for isentropic process 3-4:
T3 ⎛ v 4 ⎞
= ⎜⎜ ⎟⎟
T4 ⎝ v 3 ⎠
=>
k −1
⎛ v1 ⎞
= ⎜⎜ ⎟⎟
⎝ v3 ⎠
T ⎛v ⎞
T4
== 3 ⎜⎜ 3 ⎟⎟
T1
T2 ⎝ v 2 ⎠
then, η = 1 −
sin ce
k −1
k −1
1
r k −1
=
v1k −1
= k −1
v3
v3
v2
T2 k −1
v2
k −1
T2 ⎛ v 2 ⎞
T1
⎜⎜ ⎟⎟
=
=
k −1
v3
T1 ⎝ v 3 ⎠
⎛ v3 ⎞
⎜⎜ ⎟⎟
⎝ v2 ⎠
k −1
k
⎛v ⎞
= ⎜⎜ 3 ⎟⎟ = rck
⎝ v2 ⎠
rck − 1
k(rc − 1)
rck − 1
≥ 1, for given r
k(rc − 1)
ηdiesel ≤ ηOtto
but diesel cycle has higher r!
17
Thermal Efficiency
η Diesel
Recall,
k
⎡
r
1 1 ( c − 1) ⎤
⎥
= 1 − k −1 ⎢ ⋅
r ⎢ k ( rc − 1) ⎥
⎣
⎦
ηOtto = 1 −
1
r k −1
Note that the term in the square bracket is always larger
than one so for the same compression ratio (r), the
Diesel cycle has a lower thermal efficiency than the
Otto cycle.
Note: CI needs higher r compared to SI to ignite fuel
18
Remark
When rc (= v3/v2)Æ1 the Diesel cycle efficiency
approaches the efficiency of the Otto cycle
Compression ratio = 10-22 (Diesel)
Compression ratio = 6-10 (Otto)
Thus, efficiency of Diesel Cycle is greater than Otto Cycle.
Higher efficiency and low cost fuel makes diesel
engine suitable for larger power units such as
larger ships, heavy trucks, power generating
units, locomotives etc.
19
Diesel Cycle
Otto Cycle
The only
difference
is in
process
2-3
20
Remark
Both Otto cycle (Constant volume heat
addition) and Diesel cycle (Constant pressure
heat addition) are over-simplistic and
unrealistic. In actual case, combustion takes
place neither at constant volume (time
required for chemical reactions), nor at
constant
pressure
(rapid
uncontrolled
combustion).
Dual cycle is used to model the combustion
process. It is a compromise between Otto and
Diesel cycles, where heat addition takes place
partly at constant volume and partly at
constant pressure. This cycle is also known as
mixed cycle. In fact, Otto and Diesel cycles
are special cases of Dual cycle.
21
Modern CI Engine Cycle and the Thermodynamic Dual Cycle
Fuel injected
at 15o bTC
A
I
R
Air
Combustion
Products
Actual
Cycle
Intake
Stroke
Compression
Stroke
Power
Stroke
Qin
Dual
Cycle
Air
Exhaust
Stroke
Qin
Qout
TC
BC
Compression
Process
Const volume
heat addition
Process
Const pressure
heat addition
Process
Expansion
Process
Const volume
heat rejection
22
Process
Dual Cycle
Process 1 Æ 2 Isentropic compression
Process 2 Æ 2.5 Constant volume heat addition
Process 2.5 Æ 3 Constant pressure heat addition
Process 3 Æ 4 Isentropic expansion
Process 4 Æ 1 Constant volume heat rejection
2.5
Qin
3
3
2
Qin
4
2.5
4
2
1
1
Qout
23
Thermal Efficiency
η Dual = 1 −
cycle
Qout m
u4 − u1
= 1−
Qin m
(u2.5 − u2 ) + (h3 − h2.5 )
η Dual
const cv
⎤
αrck − 1
1 ⎡
= 1 − k −1 ⎢
r ⎣ (α − 1) + αk (rc − 1)⎥⎦
where rc =
v3
v2.5
and α =
P2.5
P2
Note, the Otto cycle (rc=1) and the Diesel cycle (α=1) are special cases:
ηOtto = 1 −
1
r k −1
η Diesel
const cV
(
(
)
)
1 ⎡ 1 rck − 1 ⎤
= 1 − k −1 ⎢ ⋅
⎥
r ⎣ k rc − 1 ⎦
24
The use of the Dual cycle requires information about either:
i) the fractions of constant volume and constant pressure heat
addition (common assumption is to equally split the heat
addition), or
ii) maximum pressure P3.
For the same inlet conditions P1, V1 and the same compression ratio:
ηOtto > η Dual > η Diesel
For the same inlet conditions P1, V1 and the same peak pressure P3
(actual design limitation in engines):
η Diesel > η Dual > ηotto
25
For the same inlet conditions P1, V1
and the same compression ratio P2/P1:
For the same inlet conditions P1, V1
and the same peak pressure P3:
Pressure, P
Pmax
Pressure, P
“x” →“2.5”
Po
Po
Specific Volume
Specific Volume
Entropy
Temperature, T
Temperature, T
tto
O al
Du
sel
Die
Tmax
el
Dies
al
Du
to
Ot
Entropy
26
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27
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