Internal Combustion Engines – MAK 493E
Ideal Standard Cycles
Prof.Dr. Cem Soruşbay
Istanbul Technical University
Internal Combustion Engines – MAK 493E
Ideal Air Standard Cycles
¾ Introduction
¾ Comparison between thermodynamic and mechanical cycles
¾ Performance parameters
imep, bmep, mechanical efficiency, indicated eff., volumetric eff.
¾ Ideal cycles and thermal efficiencies
Otto cycle, Diesel cycle, Dual cycle
¾ Comparison of cycles
¾ Deviations from actual engine cycles
1
Ideal Air Standard Cycles
Refferences :
Heywood, J.B., Internal Combustion Engine Fundamentals,
McGraw Hill Book Comp, New York, 1988.
Pages 161 – 183
Soruşbay, C., Ergeneman, M., Arslan, E., Safgönül, B.,
İçten Yanmalı Motorlar, Birsen Yayınevi, İstanbul, 2002 (3. Baskı)
Pages 3 – 23 and 38 - 41
Stone, R., Introduction to IC Engines, Macmillan, London, 1994.
Pages 33 - 34
Assumptions
Air standard cycles,
serve as introduction to the more detailed and accurate models of IC
engines
provide insight into some of the important parameters that effect
engine performance
Assumptions;
• Neglect heat transfer to and from cylinder walls,
• Replace combustion process by a heat addition process that occurs
at constant volume (in Otto cycle) or at constant pressure
(in Diesel cycle),
• Do not consider gas exchange process,
• Assume cylinder charge as a perfect gas (cp and cv are assumed
constant) which is pure air.
2
Otto Cycle
The Otto cycle is used as a basis of comparison for SI engines
The cycle consists of four processes,
1–2
isentropic compression from V1 to V2
2–3
addition of heat Q23 at constant volume
3–4
isentropic expansion to the original volume
4–1
rejection of heat Q41 at constant volume
Otto Cycle
3
Otto Cycle
Work done during the cycle, 1-2-3-4 is,
Wcycle = ∫ p dV = ∫ T ds
Constant volume heat input to the cycle per unit mass of working fluid
Q23 =
T3
∫c
v
dT = cv (T3 − T2 )
T2
Constant volume heat extraction from the cycle per unit mass
T1
Q41 = − ∫ cv dT = - cv (T1 − T4 ) = cv (T4 − T1 )
T4
Otto Cycle
1st law of thermodynamics
dE = dQ − dW
dE = 0
Thermal efficiency
η t -otto =
work done
W
=
Q23 heat input
η t -otto =
Q23 − Q41
Q
= 1 − 41
Q23
Q23
η t -otto = 1 −
T4 − T1
T3 − T2
4
Otto Cycle
Initial pressure p1 and temperature T1
p1V1k = p2V2k
using
for an adiabatic compression
pV = mRT
and
⎛V ⎞
p2 = p1 ⎜⎜ 1 ⎟⎟
⎝ V2 ⎠
from ideal gas law
k
⎛V ⎞
T2 = T1 ⎜⎜ 1 ⎟⎟
⎝ V2 ⎠
V1
V2
ε =
compression ratio
k −1
k=
cp
cv
(sıkıştırma oranı)
T2 = T1 ε k −1
Otto Cycle
from 2
→ 3 , constant volume heat addition
p3V3 = mRT3
p2V2 = mRT2
T3 = T2
defining
β =
p3
p2
V2 = V3
p3
p2
“pressure ratio”
(basınç artış oranı)
T3 = T1 β ε k −1
5
Otto Cycle
from 3
→
4 , adiabatic expansion,
p4V4k = p3V3k
p4V4 V4k −1 = p3V3 V3k −1
From ideal gas law
p4V4 = mRT4
p3V3 = mRT3
V4 V1
= =ε
V3 V2
T4V4k −1 = T3V3k −1
T4 =
T3
ε k −1
T4 = T1 β
Thermal Efficiency
Thermal efficiency of Otto cycle is given by,
η t -otto = 1 −
T4 − T1
T3 − T2
placing the temperatures T2, T3 and T4 in terms of T1
ηt −otto = 1 −
1
ε k −1
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Thermal Efficiency
Diesel Cycle
7
Diesel Cycle
Work done during the cycle, 1-2-3-4 is,
Wcycle = ∫ p dV = ∫ T ds
Constant pressure heat input to the cycle per unit mass of working fluid
Q23 =
T3
∫c
p
dT = c p (T3 − T2 )
T2
Constant volume heat extraction from the cycle per unit mass
T1
Q41 = − ∫ cv dT = - cv (T1 − T4 ) = cv (T4 − T1 )
T4
Diesel Cycle
1st law of thermodynamics
dE = dQ − dW
dE = 0
Thermal efficiency
ηt-diesel =
W
work done
=
Q23 heat input
ηt-diesel =
Q23 − Q41
Q
= 1 − 41
Q23
Q23
ηt-diesel = 1 −
T4 − T1
k (T3 − T2 )
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Diesel Cycle
T2 = T1 ε k −1
T3 = T2
T4 =
V3
= T1 α ε k −1
V2
T3α k −1
ε
k −1
= T1 α k
Diesel Cycle
Defining “cut-off ratio” or “load ratio” (hacim artış oranı)
α =
V3
V2
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Thermal Efficiency
Thermal efficiency of Diesel cycle is given by,
ηt -diesel = 1 −
T4 − T1
T3 − T2
placing the temperatures T2, T3 and T4 in terms of T1
ηt −diesel = 1 −
1
ε k −1
α k −1
k (α − 1)
Thermal Efficiency
As the value of α increases ( heat addition is extended towards expansion)
the efficiency is reduced due to additional heat required to compansate the
expansion
10
Dual Cycle
Dual Cycle
Work done during the cycle, 1-2-3’-3-4 is,
Wcycle = ∫ p dV = ∫ T ds
Constant volume heat input followed by constant pressure heat input to the
cycle per unit mass of working fluid
Q23 = cv (T3' − T2 ) + c p (T3 − T3' )
Constant volume heat extraction from the cycle per unit mass
T1
Q41 = − ∫ cv dT = - cv (T1 − T4 ) = cv (T4 − T1 )
T4
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Dual Cycle
Thermal efficiency
ηt-dual = 1 −
cv (T4 − T )1
cv (T3' − T2 ) + c p (T3 − T3' )
Dual Cycle
T2 = T1 ε k −1
T3' = T1 β ε k −1
T3 = T1 β α ε k −1
T4 = T1 α k β
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Thermal Efficiency
Thermal efficiency of Dual cycle is given by,
ηt −dual = 1 −
Putting
βα k − 1
β − 1 + k β (α − 1)
1
ε k −1
α=1
Otto cycle thermal efficiency
β=1
Diesel cycle thermal efficiency
is obtained
Thermal Efficiency
Otto cycle
ηth −Otto = 1 −
1
ε k −1
Diesel cycle
ηth − Diesel = 1 −
1
ε k −1
α k −1
k (α − 1)
Dual cycle
ηth − Dual = 1 −
1
ε k −1
β α k −1
β − 1 + kβ (α − 1)
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Comparison of Ideal Cycles
For α > 1 and k > 1
αk −1
k (α − 1)
term is greater than 1
therefore
ηt-otto > ηt-diesel
Also
ηt-otto > ηt-dual > ηt-diesel
for a constant value of compression ratio
efficiency of Dual cycle lies between Otto and Diesel cycles
according to the value of β
Comparison of Ideal Cycles
In real engines,
SI engines have a compression ratio between 10:1 to 12:1
this value is limited due to engine knock
CI engines have compression ratio higher than 14:1 to provide
temperature and pressure required for self ignition of the fuel
compression ratio of 16:1 to 18:1 is sufficient for efficiency, but
used for improving ignition quality
high compression ratio increases thermal and mechanical stresses
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