Fuel-Air Modeling of IC Engine Cycles

P M V SubbaraoProfessor

Mechanical Engineering Department

Another Step towards Phenomenological Modeling.….

A Route to Know the Truth before trying

The Important part of Cycle is Executed in CM Mode

)()()()(

tWtQdt

med

dt

medCMCM

CM

fuelair

)()(

)()()( 1

tWtQdt

med

dt

med

dt

medCMCM

CM

j

n

jfuelair

More realistic representation of Compression???

Realization of Available Air : Running Cost Vs Capital Cost

Fuel-Air Models for Engine Cycles• Fuel-air analysis is more accurate analysis when compared to Air-

standard cycle analysis.

• An accurate representation of constituents of working fluid is considered.

• More accurate models are used for properties of each constituents.

Process SI Engine CI Engine

Intake Air+Fuel +Residual gas

Air+ Recycles gas + Residual gas

Compression Air+Fuel vapour +Residual gas

Air+ Recycles gas + Residual gas

Expansion Combustion products

Combustion Products

Exhaust Combustion products

Combustion Products

Fuel – Air Otto Cycle

Air+Fuel vapour +Residual gas

CompressionProcess

TC

Const volume combustion

Process

ExpansionProcess

Products of Combustin

BC

Const volume Blow down

Process

Products of Combustin

Fuel –Air Otto Cycle

• 1—2 Isentropic compression of a mixture of air, fuel vapour and residual gas without change in chemical composition.

• 2—3 Complete combustion at constant volume, without heat loss, with burned gases in chemical equilibrium.

• 3—4 Isentropic expansion of the burned gases which remain in chemical equilibrium.

• 4—5 Ideal adiabatic blow down.

Isentropic Compression Process

For a infinitesimal compression process: pdvduTds pdvdu 0

Mass averaged properties for an ideal gas mixture:

n

iii

n

iiviv

n

iipip RxRCxCCxC

11,

1, & &

pdvdTcv 0

dvv

RTdTcv 0

Use appropriate EoS:

Variation of Specific Heat of Ideal Gases

kgKkJT

CT

CT

CCcp /100010001000

3

3

2

210

Gas C0 C1 C2 C3

Air 1.05 -0.365 0.85 -0.39

Methane 1.2 3.25 0.75 -0.71

CO2 0.45 1.67 -1.27 0.39

Steam 1.79 0.107 0.586 -0.20

O2 0.88 -0.0001 0.54 -0.33

N2 1.11 -0.48 0.96 -0.42

Variable Properties of Air

0.5

0.7

0.9

1.1

1.3

1.5

0 200 400 600 800 1000 1200 1400

Temperature, K

cp

cv

Properties of Fuels

kgKkJT

CTC

TC

TCCc fp /

100010001000 24

3

3

2

210,

Fuel C0 C1 C2 C3 C4

Methane -0.29149 26.327 -10.610 1.5656 0.16573

Propane -1.4867 74.339 -39.065 8.0543 0.01219

Isooctane -0.55313 181.62 -97.787 20.402 -0.03095

Gasoline -24.078 256.63 -201.68 64.750 0.5808

Diesel -9.1063 246.97 -143.74 32.329 0.0518

True Phenomenological Model for Isentropic Compression

dvv

RTdTcv

v

dvR

T

dTcv

kgKkJTcTcTccc vvvvv /33,

22,1,0,

Let the mixture is modeled as:

1

231

32

3,21

22

2,121,

1

20, ln

32ln

v

vRTT

cTT

cTTc

T

Tc vv

vv

2

1

2

1

33,

22,1,0, v

dvR

T

dTTcTcTcc vvvv

r

RTTc

TTc

TTcT

Tc vv

vv

1ln

32ln 3

13

23,2

12

22,

121,1

20,

First Order Models for Variable Specific Heats

Tkac pp 1

Tkbc vv 1

ap = 0.9718 – 1.1 kJ/kg.K

bv = 0.685 – 0.823 kJ/kg.K

k1 = 1.32610-4 – 3.39510-4 kJ/kg.K2

Isentropic Compression model with variable properties

• For compression from 1 to 2:

1

2

1

2121 lnln

v

vR

T

TbTTk v

2

1

2

1

1 v

dvR

T

dTTkbv

r

RT

TbTTk v

1lnln

1

2121

2—3 Complete & Adiabatic combustion at constant volume

m

W

m

Quu in )()( 23

0 0

23 UU

l

i

T

T

iresvires

T

T

fuelvfuel

T

T

airvair

n

j

T

T

jvj dTCmdTCmdTCmdTCm1

,,,,,1

,

2

0

2

0

2

0

3

0

Quasi-static view of sudden process:

Second law limit on possible extent of reaction

• Reactants Products

• At any instant during the combustion process, a cylinder contains a combination of reactants and products.

• A reaction seizes when the entropy of an adiabatic reactor reaches its maximum value.

• The value of maximum entropy will vary with the pressure and temperature of the reaction.

• A reaction system and parameters of reaction should be designed such that the maximum entropy is obtained when the reaction is almost complete (>98%??).

BS-IV : Emission norms for passenger cars ( Petrol)

Norms CO( g/km) HC+ NOx)(g/km)1991Norms 14.3-27.1 2.0(Only HC)1996 Norms 8.68-12.40 3.00-4.361998Norms 4.34-6.20 1.50-2.18stage2000 norms

2.72 0.97

Bharat stage-II 2.2 0.5Bharat Stage-III 2.3 0.35(combined)Bharat Stage-IV 1.0 0.18(combined)

BS IV : Emission Norms for 2/3 Wheelers ( Petrol)

Norms CO ( g/km) HC+ NOx (g/km)1991 norms 12-30 8-12 (only HC)1996 norms 4.5 3.6stage 2000 norms

2.0 2.0

Bharat stage-II 1.6 1.5Bharat Stage-III 1.0 1.0

BS IV : Emission norms for Heavy diesel vehicles:

19

Norms CO (g/kwhr)

HC(g/kwhr)

Nox(g/kwhr)

PM(g/kwhr)

1991 Norms 14 3.5 18 -

1996 Norms 11.2 2.4 14.4 -

stage 2000 Norms 4.5 1.1 8.0 0.36

Bharat stage-II 4.0 1.1 7.0 0.15Bharat Stage-III 2.1 1.6 5.0 0.10Bharat Stage-IV 1.5 0.96 3.5 0.02

A move to Bharat Stage IV+ from 2016, before moving to Bharat Stage V in 2021