mel713 : self study matterial
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Thermodynamic Analysis of Internal Combustion Engines
P M V SUBBARAOProfessor
Mechanical Engineering DepartmentIIT Delhi
Work on A Blue Print Before You Ride on an Actual Engine….It is a Sign of Civilized Engineering….
SI Engine Cycle
A I R
CombustionProducts
Ignition
IntakeStroke
FUEL
Fuel/AirMixture
CompressionStroke
PowerStroke
ExhaustStroke
ActualCycle
Actual SI Engine cycle
Ignition
Total Time Available: 10 msec
Early CI Engine Cycle
A I R
CombustionProducts
Fuel injectedat TC
IntakeStroke
Air
CompressionStroke
PowerStroke
ExhaustStroke
ActualCycle
Modern CI Engine Cycle
CombustionProducts
Fuel injectedat 15o bTC
IntakeStroke
A I R
Air
CompressionStroke
PowerStroke
ExhaustStroke
ActualCycle
Thermodynamic Cycles for CI engines
• In early CI engines the fuel was injected when the piston reached TC and thus combustion lasted well into the expansion stroke.
• In modern engines the fuel is injected before TC (about 15o)
• The combustion process in the early CI engines is best approximated by a constant pressure heat addition process Diesel Cycle
• The combustion process in the modern CI engines is best approximated by a combination of constant volume and constant pressure Dual Cycle
Fuel injection startsFuel injection starts
Early CI engine Modern CI engine
Thermodynamic Modeling
• The thermal operation of an IC engine is a transient cyclic process.• Even at constant load and speed, the value of thermodynamic
parameters at any location vary with time.• Each event may get repeated again and again.• So, an IC engine operation is a transient process which gets
completed in a known or required Cycle time.• Higher the speed of the engine, lower will be the Cycle time.• Modeling of IC engine process can be carried out in many ways.• Multidimensional, Transient Flow and heat transfer Model.• Thermodynamic Transient Model USUF.• Fuel-air Thermodynamic Mode.• Air standard Thermodynamic Model.
Ideal 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 fluid2) Combustion process not considered3) Intake and exhaust processes not considered4) Engine friction and heat losses not considered5) Specific heats independent of temperature
• The two types of reciprocating engine cycles analyzed are:1) Spark ignition – Otto cycle2) Compression ignition – Diesel cycle
AirTC
BC
Qin Qout
CompressionProcess
Const volume heat addition
Process
ExpansionProcess
Const volume heat rejection
Process
OttoCycle
Otto CycleA I R
CombustionProducts
Ignition
IntakeStroke
FUEL
Fuel/AirMixture
CompressionStroke
PowerStroke
ExhaustStroke
ActualCycle
Process 1 2 Isentropic compressionProcess 2 3 Constant volume heat additionProcess 3 4 Isentropic expansionProcess 4 1 Constant volume heat rejection
v2TC
TCv1BC BC
Qout
Qin
Air-Standard Otto cycle
3
4
2
1
vv
vvr
Compression ratio:
First Law Analysis of Otto Cycle
12 Isentropic Compression
)()( 12 mW
mQuu in
2
1
1
2
1
2
vv
TT
PP
AIR
)()( 1212 TTcuum
Wv
in
23 Constant Volume Heat Addition
mW
mQuu in )()( 23
)()( 2323 TTcuum
Qv
in
2
3
2
3
TT
PP
AIR Qin
TC
11
2
1
1
2
k
k
rvv
TT
3 4 Isentropic Expansion
AIR)()( 34 mW
mQuu out
)()( 4343 TTcuum
Wv
out
4
3
3
4
3
4
vv
TT
PP
4 1 Constant Volume Heat Removal
AIR QoutmW
mQuu out )()( 41
)()( 1414 TTcuum
Qv
out
1
1
4
4
TP
TP
BC
1
1
4
3
3
4 1
k
k
rvv
TT
23
1243
uuuuuu
QW
in
cycleth
23
14
23
1423 1uuuu
uuuuuu
Cycle thermal efficiency:
thin
thincycle
rr
umQ
krr
VPQ
Pimep
VVW
imep
1/
11
1 111121
Indicated mean effective pressure is:
Net cycle work:
1243 uumuumWWW inoutcycle
First Law Analysis Parameters
12
1
23
14 111)()(1
kv
v
rTT
TTcTTc
Effect of Compression Ratio on Thermal Efficiency
• Spark ignition engine compression ratio limited by T3 (autoignition) and P3 (material strength), both ~rk
• For r = 8 the efficiency is 56% which is twice the actual indicated value
Typical SI engines9 < r < 11
k = 1.4
111 k
const cth rV
Effect of Specific Heat Ratio on Thermal Efficiency
111 k
const cth rV
Specific heat ratio (k)
Cylinder temperatures vary between 20K and 2000K so 1.2 < k < 1.4k = 1.3 most representative
The net cycle work of an engine can be increased by either: i) Increasing the r (1’2)ii) Increase Qin (23”)
P
V2 V1
Qin Wcycle
1
2
3
(i)
4
(ii)
Factors Affecting Work per Cycle
1’
4’
4’’
3’’th
incycle
rr
VQ
VVW
imep
1121
Effect of Compression Ratio on Thermal Efficiency and MEP
k
in
rrr
VPQ
Pimep 11
1111
k = 1.3
Ideal Diesel Cycle
Air
BC
Qin Qout
CompressionProcess
Const pressure heat addition
Process
ExpansionProcess
Const volume heat rejection
Process
Process 1 2 Isentropic compressionProcess 2 3 Constant pressure heat additionProcess 3 4 Isentropic expansionProcess 4 1 Constant volume heat rejection
Air-Standard Diesel cycle
Qin
Qout
2
3vvrc
Cut-off ratio:
v2TC
v1BC
TC BC
23
1411hhuu
mQmQ
in
out
cycleDiesel
11111 1
c
kc
kconst cDiesel r
rkr
V
For cold air-standard the above reduces to:
Thermal Efficiency
111 kOtto r
recall,
Note 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 efficiencythan the Otto cycle
Note: CI needs higher r compared to SI to ignite fuel
Typical CI Engines15 < r < 20
When rc (= v3/v2)1 the Diesel cycle efficiency approaches the efficiency of the Otto cycle
Thermal Efficiency
Higher efficiency is obtained by adding less heat per cycle, Qin, run engine at higher speed to get the same power.
AirTC
BC
Qin Qout
CompressionProcess
Const pressure heat addition
Process
ExpansionProcess
Const volume heat rejection
Process
DualCycle
Qin
Const volume heat addition
Process
Thermodynamic Dual Cycle
Process 1 2 Isentropic compressionProcess 2 2.5 Constant volume heat additionProcess 2.5 3 Constant pressure heat additionProcess 3 4 Isentropic expansionProcess 4 1 Constant volume heat rejection
Dual Cycle
Qin
Qin
Qout
11
2
2
2.5
2.5
33
44
)()()()( 5.2325.25.2325.2 TTcTTchhuum
Qpv
in
Thermal Efficiency
)()(11
5.2325.2
14
hhuuuu
mQmQ
in
out
cycleDual
1)1(
111 1 c
kc
kcconst
Dual rkr
rv
111 kOtto r
11111 1
c
kc
kconst cDiesel r
rkr
V
Note, the Otto cycle (rc=1) and the Diesel cycle (=1) are special cases:
2
3
5.2
3 and where PP
vvrc
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), orii) maximum pressure P3.
Transformation of rc and into more natural variables yields
1
1111 111 krVP
Qk
kr kin
c
1
31PP
r k
For the same inlet conditions P1, V1 and the same compression ratio:
DieselDualOtto
For the same inlet conditions P1, V1 and the same peak pressure P3 (actual design limitation in engines):
ottoDualDiesel
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:
32
141
1
TdsTds
in
outth
Diesel
Dual
Otto
DieselDualOtto
“x” →“2.5”
Pmax
Tmax
Po
Po
Pres
sure
, P
Pres
sure
, P
Tem
pera
ture
, T
Tem
pera
ture
, T
Specific VolumeSpecific Volume
Entropy Entropy