Transcript
Internal Combustion Engine
Modeling
Dr. Alan Kéromnès
University of Burgundy
ISAT (Superior Institute for Automotive and Transports)
2
Lecture layout• Very simple global model
• 0D thermodynamic model for internal combustion engine– Principle
– 0D Model
– Sub-models
– Model resolution
• Spark ignition engine model– Single zone semi-empiric model .
– Two zone semi-empiric model
– Physical approach
• Compression ignited engine– Semi-empiric model
– Physical approach
• Pollutants formation
To go further: J.B. Heywood, McGraw-Hill“Internal Combustion Engines Fundamentals”
Very simple model
Willans Lines
4
Very simple model : Willans lines
Global approach of the engine
– Willans line method
Willans line (source: Heywood Internal Combustion
Engines Fundamental, McGraw Hill)
(J/s) Value HeatingLower :
(%) efficiency indicated :
(W)power Friction :
(W)Power Effective :
(kg/s) fuel of rate flow Mass:
LHV
P
P
m
i
f
e
fuel
η
•
LHVi ⋅η
ffuelie PmLHVP −⋅⋅=•
η combthfuel
comb
comb
i
fuel
ii P
P
P
P
P
P ηηη ⋅=⋅==
5
Very simple model : Willans lines
%40≈thη
combη
rpm 2000 ; 300 ; 98.0 ;00
B A NB
Acombcombcomb ===
+−= ηηη
( )6060 ⋅
⋅⋅⋅+=⋅⋅⋅=
c
dp
c
df R
NVNff
R
NVFMEPP
FMEP : Friction Mean Effective Pressure (Pa)f = 105 Pa; fp = 20;
2 stroke engine : Rc = 14 stroke engine : Rc = 2
6
Very simple model : Willans lines
Finally:
Results for a 2L engine
( )
+−⋅
⋅⋅⋅++
=•
NB
AR
NVffP
m
combth
c
dpe
fuel
0
60
ηη
Engine (rpm)T
orq
ue (
Nm
)
BSFC (g/kW.h)
290295
300
310
320
340
360
380
400
450500
550600
1000 2000 3000 4000 5000 6000 700010
20
30
40
50
60
70
80
90
100
1000 2000 3000 4000 5000 6000 700010
20
30
40
50
60
70
80
90
100
Engine (rpm)
Fuel Mass flow rate (g/s)
Tor
que
(N
m)
1
2
3
4
5
6
Issues : - No influence of the external conditions (pressure and temperature)- No influence of engine speed and torque on the thermal efficiciency
0D thermodynamic model
for
internal combustion engines
8
0D thermodynamic model for engines
9
0D thermodynamic model for engines0D model equations
– First law of thermodynamic for an open system
– Perfect gas law (differential form)
– Mass conservation law
( )[ ]( )
( ) )1(wallcombi
out
iniiv
wallcombi
out
inii
i
out
iniipici
QQdVpdmhdmudTcm
QQWdmhdU
QWdmheedE
δδ
δδδ
δδ
++⋅−=⋅+⋅+⋅⋅
++=⋅+
+=+++
∑
∑
∑
( ) ( ) )2(dmTrdTrmdpVdVpTrmdVpd ⋅⋅+⋅⋅=⋅+⋅⇒⋅⋅=⋅
)3(∑=i
idmdm
10
0D thermodynamic model for engines
( )
=
⋅+++⋅−=⋅+⋅⋅
⋅−=⋅⋅−⋅⋅−⋅
∑
∑
ii
i
out
iniiwallcombv
dmdm
dmhQQdVpdmudTcm
dVpdmTrdTrmdpV
)3(
)1(
)2(
δδ
• 0D model equations
• Issues :
– u, cv and h varies with temperature => JANAF tables
– dV: need for a volume definition as a function of θ– δQcomb: Vibe burning law
– δQwall: empirical correlation for wall heat transfer
– dmi: mass transfer calculation model
11
0D thermodynamic model for engines
• Sub-models
1/ JANAF polynomial tables
+⋅=
⋅= ∑∑==
− 65
1
5
1
1 1)()( i
i
jjii
i
jjip aT
jaRThTaRTC
i
12
0D thermodynamic model for engines
• Sub-models
2/ Volume
L: connection rod length
B: cylinder bore
R: crankshaft radius
θ: crank angle
( )
−⋅⋅+=
−+−++=
θθθθπ
θ
θθπθ
222
22
2222
sin
cossinsin
4
sincos4
)(
RL
RR
B
d
dV
RLRRLB
VV CTD
13
0D thermodynamic model for engines
• Sub-models
3/ Vibe burning law• xb: burned mass fraction
• θi : ignition angle
• ∆θ: Combustion duration
• n: shape factor
( )
θθ
θθθ
θθθθθ
θθθ
d
dxLHVm
d
dQcomb
ena
d
dx
ex
bfuel
an
ib
a
b
ni
ni
⋅⋅=
∆−⋅
∆+⋅=
−=+
+
∆−−
∆−−
1
1
1
1
0 20 40 600
0.2
0.4
0.6
0.8
1
Crank Angle (°)
x b
n = 1n =3n =5
0 20 40 600
0.02
0.04
0.06
0.08
0.1
0.12
Crank Angle (°)dx
b/dθ
n = 1n = 3n = 5
14
0D thermodynamic model for engines
• Sub-models
4/ Wall heat transfer
Assumptions : Heat transfer mainly mainly occurs
through forced convection
Numerous correlation for h as a function of the engine type
(Gasoline, Diesel) : Woschni, Han, Eichelberg…
( ) .. valves, . cylinder,i: piston,TTShdt
dQ
iii ,∑ −⋅⋅=
15
0D thermodynamic model for engines
• Sub-models
5/ Mass flow
Assumptions:
•The flow is quasi-steady, adiabatic and compressible
•Flow from upstream (up) to downstream (ds)
•The flow is calculated for the conditions at the minimum area
( )
1
12
1
2 with ,max
1
2
−
+
+=
=
−
−⋅⋅=
γγ
γγ
γ
γ
γγ
ccup
ds
upupupdi
i
XXP
PX
XXTr
PCSdt
dmi
16
0D thermodynamic model for engines
• Model resolution
• System of ordinary differential equation (ODE)
– Type:
– Matlab ode solver (ex: ode45 : Runge-Kutta 4-5)
( )
⋅+++⋅−⋅−
=
⋅
⋅⋅−⋅−
∑
∑
ii
i
out
iniiwallcomb
dm
dmhQQdVp
dVp
dm
dT
dp
ucvm
TrrmV
δδ100
0
( ) ( )ytfytyM ,,' =⋅
17
0D thermodynamic model for engines• Results without combustion
0 90 180 270 360 450 540 630 720200
300
400
500
600
700
Crank Angle (°)
Tem
pera
ture
(K
)
0 90 180 270 360 450 540 630 7200
5
10
15
20
25
Crank Angle (°)
Pre
ssur
e (b
ar)
0 90 180 270 360 450 540 630 7200
100
200
300
400
500
600
700
Crank Angle (°)
Mas
s (m
g)
Engine specifications
Type Renault F4R (1998 cm3)
Bore (mm) 82.7
Stroke (mm) 93
Connecting Rod length (mm) 144
Compression ratio 11.5
Spark ignition engine modeling
19
Spark ignition engine modeling
• Semi-empiric approach : single-zone model
– A bit of physics
• Combustion:
flame front propagation
• Mixture:
homogeneous and stoichiometric
– Assumptions
• No change in the mixture
composition
• Combustion modeled by
Vibe burning law
20
Spark ignition engine modeling• Semi-empiric approach : single-zone model
2000 cm3 – 2000 rpm – full load
0 90 180 270 360 450 540 630 7200
100
200
300
400
500
600
700
Crank Angle (°)
Mas
s (m
g)
0 90 180 270 360 450 540 630 7200
500
1000
1500
2000
2500
3000
Crank Angle (°)
Tem
pera
ture
(K
)
0 90 180 270 360 450 540 630 7200
20
40
60
80P
ress
ure
(bar
)
40 100 200 300 400 600
1
10
100
Volume (cm3)
Pre
ssur
e (b
ar)
21
Spark ignition engine modeling• Semi-empiric approach : single-zone model
2000 cm3 – 2000 rpm – pint. : 0.4 bar
0 90 180 270 360 450 540 630 7200
500
1000
1500
2000
2500
3000
Crank Angle (°)
Tem
pera
ture
(K
)
0
5
10
15
20
25
30
Pre
ssur
e (b
ar)
0 90 180 270 360 450 540 630 7200
100
200
300
400
Crank Angle (°)
Mas
s (m
g)
40 100 200 300 400 600
1
10
100
Volume (cm3)
Pre
ssur
e (b
ar)
22
Spark ignition engine modeling• Semi-empiric approach : single-zone model
Engine speed (rpm)
Inta
ke p
ress
ure
(bar
)
230235
240
245
250
255
260
270
270
280
280
290
300
310
320350
400
400
450
450 500
1000 2000 3000 4000 5000 6000 70000.2
0.4
0.6
0.8
1
23
Spark ignition engine modeling• Semi-empiric approach : two-zone model
– Hypothesis:
• Combustion: flame front propagation
• Two zones: Burnt gases / Fresh gases
• Mixture: homogeneous in each zone
• Pressure: homogeneous inside the cylinder
– Unknown :
• Fresh gases: Tu, Vu, mu
• Burnt gases: Tb, Vb, mb
• Pressure: P
24
Spark ignition engine modeling• Semi-empiric approach : two-zone model
– 7 Unknown → 7 equations• Fresh gases:
– First law of thermodynamic for an open system
– Perfect gas law (differential form)
– Mass conservation law
• Burnt gases:
– First law of thermodynamic for an open system
– Perfect gas law (differential form)
– Mass conservation law
• Volume: dVu + dVb = dV
25
Spark ignition engine modeling• Semi-empiric approach : two-zone model
– 7 Unknown → 7 equations
=
⋅
−
−−
−−−
∑
∑
bwall
ibi
iui
uwall
ubbvb
bbbbb
uuuvu
uuuuu
Q
dm
dV
dm
Q
dVb
dmb
dTb
dVu
dmu
dTu
dP
Phucm
PTrrmV
Phucm
PTrrmV
,
,
,
,
,
,
0
0
0000
0100000
000
1001000
0000100
0000
000
δ
δ
26
Spark ignition engine modeling
0 90 180 270 360 450 540 630 7200
500
1000
1500
2000
2500
3000
Crank Angle (°)
Tem
pera
ture
(K
)
0 90 180 270 360 450 540 630 7200
100
200
300
400
500
600
700
Crank Angle (°)
Mas
s (m
g)
0 90 180 270 360 450 540 630 7200
20
40
60
80
100
Crank Angle (°)
Pre
ssur
e (b
ar)
0 200 400 600 8000
100
200
300
400
500
600
Crank Angle (°)
Vol
ume
(cm
3 )
27
Spark ignition engine modeling• Physical approach
• 3 zone model
– Flame front description
– Turbulence model
28
Compression ignition engine
modeling
29
Compression ignition engine modeling
• Semi-empiric approach : single-zone model
– A bit of physics
• Auto-ignition
• Combustion:
premixed flame + diffusion flame
• Mixture:
heterogeneous and lean (locally rich)
– Assumptions
• No change in the mixture
composition
• Combustion modeled by
two phases of Vibe
(Source: Bosch)
30
Compression ignition engine modeling
• Heat release rate :
31
Compression ignition engine modeling
• Semi-empiric approach : single-zone model
2000 cm3
2000 rpm
φ = 0.8
20 100 6001
10
100
Volume (cm3)P
ress
ure
(bar
)
0 90 180 270 360 450 540 630 7200
20
40
60
80
100
Crank Angle (°)
Pre
ssur
e (b
ar)
0 90 180 270 360 450 540 630 720
500
1000
1500
2000
Crank Angle (°)
Tem
pera
ture
(K
)
0 90 180 270 360 450 540 630 7200
100
200
300
400
500
600
Crank Angle (°)
Mas
s (m
g)
32
Compression ignition engine modeling
• Semi-empiric approach : single-zone model
2000 cm3
2000 rpm
φ = 0.8
340 360 380 4000
2000
4000
6000
8000
10000
Crank Angle (°)
Hea
t rel
ease
rat
e (J
/s)
33
Compression ignition engine modeling
• Semi-empiric approach : single-zone model
2000 cm3
2000 rpm
φ = 0.4
0 90 180 270 360 450 540 630 7200
100
200
300
400
500
600
Crank Angle (°)
Mas
s (m
g)
0 90 180 270 360 450 540 630 720
400
600
800
1000
1200
Crank Angle (°)
Tem
pera
ture
(K
)
0 90 180 270 360 450 540 630 7200
10
20
30
40
50
60
Crank Angle (°)
Pre
ssur
e (b
ar)
20 100 6001
10
100
Volume (cm3)P
ress
ure
(bar
)
34
Compression ignition engine modeling
• Auto-ignition modeling
– At high pressure and Temperature
• Slow and exothermic Oxydation
• Self-acceleration
• Explosion
– Chain reaction
• Increasing amout of active species (OH*,CH*,…)
• Enough concentration
=> Auto-ignition
35
Compression ignition engine modeling
• Auto-ignition modeling
– Chemical delay : Ignition Delay Time
– Example:
• Hydrogene : K = 3.7 10-6 s, Ea = 50 kJ/mol
• N-heptane : K = 5 10-9 s, Ea = 109 kJ/mol
• Conditions 1 : T, P atm
• Conditions 2 : 1000 K, 30 bar
0.5 exp( / )K P Ea RTτ −=
36
Compression ignition engine modeling
• Chmela single-model (1999)
– Instantaneous vaporisation of the fuel
– Spray kinetic energy is dominating
– Ignition delay calculation
• Detail
– Heat release:
• Assumptions:
– The heat release rate is proportionnal to the amount of fuel
available for the combustion
36
( ) ( )VkfQmfCd
dQf ,, 21mod=
θ
PCIQmQmf ff /),(1 −=
3),(2
V
kCrate
eVkf =Crate: Mixing rate parameterk: Turbulent kinetic energy densityV: Combustion chamber volume
37
Compression ignition engine modeling
• Multizone model: Hiroyasu (1983)
– Spray discretisation in 250 zones
– Temporal evolution of each zone
• Vaporisation
• Air entrainment
• Auto-ignition
• Combustion
38
Compression ignition engine modeling
• Multizone model: Hiroyasu (1983)
39
Pollutants formation
40
Pollutants formation
• NOx sources
– Thermal NOx: NOx formed at high temperature
Model : Zel’dovich mechanism
– Fuel NOx: Nitrogen already contained in the fuel
Conversion of fuel bound of nitrogen to NOx during combustion
– Prompt NOx: reaction of atmospheric nitrogen, N2, with radicals such as C*, CH*, and CH2
*
Model: Prompt NO mechanism
41
Pollutants formation
• Zel’dovich mechanism (1947)
NO + HN + OH
NO + O N + O
NO + N + O N
→←
→←
→←
3
22
12
133
)/3150(92
)/38000(131
101.4
104.6
106.7
×=
×=
×=−
−
k
ek
ekT
T
)/23650(143
)/19500(92
131
100.2
105.1
106.1
T
T
ek
ek
k
−−
−−
−
×=
×=
×=
[ ]
21
21
3221
222
21 ]OH[]O[(]NO[1
])N][O[(]NO[1]N][O[2
dt
NO
−−
−
=
++−=
kk
kkK
kkk
Kk
d
42
Pollutants formation
• Dissociation
Theoretically :
( ) 22222zyx N24
76.3OH2
CON763O24
OHC
−+++→+
−++ zyx
yx.
zyx
( ) 2N2O2HCO2OH2CO22zyx NnOnOHnCOnOHnCOnN763O24
OHC 22222
+++++→+
−++ .zy
xφ
For a lean mixture (Φ < 1): nCO = 0 and nH2 = 0
For a stoichiometric or rich mixture (Φ ≥ 1): Water-gas shift reaction et equilibrium
OHCOHCO 222 +↔+
top related