Internal Combustion Engine Modeling

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


%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


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


( )

=

⋅+++⋅−=⋅+⋅⋅

⋅−=⋅⋅−⋅⋅−⋅

∑

∑

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


• Sub-models

1/ JANAF polynomial tables

+⋅=

⋅= ∑∑==

− 65

1

5

1

1 1)()( i

i

jjii

i

jjip aT

jaRThTaRTC

i

12


• 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


• 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


• 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


• 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


• 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


• 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


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


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


– 7 Unknown → 7 equations• Fresh gases:




• Burnt gases:




• Volume: dVu + dVb = dV

25


– 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


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


– 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


• Heat release rate :

31



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



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



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


• 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


• 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


• 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


• Multizone model: Hiroyasu (1983)

– Spray discretisation in 250 zones

– Temporal evolution of each zone

• Vaporisation

• Air entrainment

• Auto-ignition

• Combustion

38


• Multizone model: Hiroyasu (1983)

39

Pollutants formation

40


• 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


• 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


• 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 +↔+

Documents

Internal Combustion Engine Modeling