Chiodi M. An innovative 3D-CFD-Approach towards Virtual Development of Internal Combustion Engines
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226 Appendix A
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Appendix B
B.1 Thermodynamic Properties of the Working Fluid
In this appendix the thermodynamic properties of the burned gas of a CNG-engine are reported
(see Chapters 8 and 11).
Fuel Specifications of Natural Gas
Natural Gas: C
1.02
H
4.02
N
0.01
with LHV = 49.14 MJ/kg.
Composition of Burned Gas after a Combustion of Natural Gas
Figure B.1: Burned gas composition as function of temperature -
O
=0.7 and
p
=1bar
(fuel: natural gas C
1.03
H
4.02
N
0.01
).
N
2
N
H
O
H
2
H
2
O
OH
NO
O
2
CO
CO
2
Species mass fraction w
i
, kg/kg
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
Temperature, K
1500 1750 2000 2250 2500 2750 3000
C
1.03
H
4.02
N
0.01
M. Chiodi, An Innovative 3D-CFD-Approach towards Virtual Development of
Internal Combustion Engines, DOI 10.1007/978-3-8348-8131-1,
© Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2011
228 Appendix B
Figure B.2: Burned gas composition as function of temperature - O=1.0 and
p
=1bar
(fuel: natural gas C
1.03
H
4.02
N
0.01
).
Figure B.3: Burned gas composition as function of temperature -
O
=1.3 and
p
=1bar
(fuel: natural gas C
1.03
H
4.02
N
0.01
).
N
2
N
H
OH
2
H
2
O
OH
NO
O
2
CO
CO
2
Species mass fraction w
i
, kg/kg
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
Temperature, K
1500 1750 2000 2250 2500 2750 3000
C
1.03
H
4.02
N
0.01
N
2
N
H
O
H
2
H
2
O
OH
NO
O
2
CO
CO
2
Species mass fraction w
i
, kg/kg
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
Temperature, K
1500 1750 2000 2250 2500 2750 3000
C
1.03
H
4.02
N
0.01
B.1 Thermodynamic Properties of the Working Fluid 229
Figure B.4: Burned gas composition as function of pressure - O=1.0 and
T
=2000K
(fuel: natural gas C
1.03
H
4.02
N
0.01
).
Figure B.5: Burned gas composition as function of pressure -
O
=1.0 and
T
=2800K
(fuel: natural gas C
1.03
H
4.02
N
0.01
).
N
2
H
O
H
2
H
2
O
OH
NO
O
2
CO
CO
2
Species mass fraction w
i
, kg/kg
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
Pressure, bar
0 10 20 30 40 50 60 70 80 90 100
C
1.03
H
4.02
N
0.01
N
2
H
O
H
2
H
2
O
OHNO
O
2
CO
CO
2
N
Species mass fraction w
i
, kg/kg
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
Pressure, bar
0 10 20 30 40 50 60 70 80 90 100
C
1.03
H
4.02
N
0.01
230 Appendix B
Figure B.6: Burned gas composition as function of lambda -
p
=1bar and
T
=2000K
(fuel: natural gas C
1.03
H
4.02
N
0.01
).
Figure B.7: Burned gas composition as function of lambda -
p
=1bar and
T
=2800K
(fuel: natural gas C
1.03
H
4.02
N
0.01
).
N
2
H
O
H
2
H
2
O
OH
NO
O
2
CO
CO
2
Species mass fraction w
i
, kg/kg
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
O
, -
0.5 1.0 1.5 2.0 2.5 3.0
C
1.03
H
4.02
N
0.01
N
2
H
O
H
2
H
2
O
OH
NO
O
2
COCO
2
Species mass fraction w
i
, kg/kg
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
O
, -
0.5 1.0 1.5 2.0 2.5 3.0
C
1.03
H
4.02
N
0.01
B.1 Thermodynamic Properties of the Working Fluid 231
Thermal Properties of Burned Gas after a Combustion of Natural Gas
Figure B.8: The real gas constant
R
as function of temperature and lambda.
Figure B.9: The thermal enthalpy
h
as function of temperature.
p=1 bar
C
1.03
H
4.02
N
0.01
'O=0.3
0.7
1.9
Real gas constant R, J/kgK
290
300
310
320
330
340
350
Te
m
p
erature, K
1500 2000 2500 3000
p=100 bar
C
1.03
H
4.02
N
0.01
'O=0.3
0.7
1.9
Real gas constant R, J/kgK
290
300
310
320
330
340
350
Te
m
p
erature, K
1500 2000 2500 3000
1600 K
2800 K
3200 K
2400 K
2000 K
Real gas constant R, J/kgK
290
300
310
320
330
340
350
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=1 bar
C
1.03
H
4.02
N
0.01
1600 K
3200 K
'T=400 K
Real gas constant R, J/kgK
290
300
310
320
330
340
350
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=100 bar
C
1.03
H
4.02
N
0.01
'O=0.3
0.7
1.9
Thermal enthalpy h, MJ/kg
1.5
2.0
2.5
3.0
3.5
4.0
Te
m
p
erature, K
1500 2000 2500 3000
p=1 bar
C
1.03
H
4.02
N
0.01
'O=0.3
0.7
1.9
Thermal enthalpy h, MJ/kg
1.5
2.0
2.5
3.0
3.5
4.0
Te
m
p
erature, K
1500 2000 2500 3000
p=100 bar
C
1.03
H
4.02
N
0.01
232 Appendix B
Figure B.10: The thermal enthalpy h as function of lambda.
Figure B.11: The specific heat
p
c
as function of temperature and lambda.
'T=400 K
3200 K
1600 K
Thermal enthalpy h, MJ/kg
1.5
2.5
3.5
4.5
5.5
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=1 bar
C
1.03
H
4.02
N
0.01
'T=400 K
3200 K
1600 K
Thermal enthalpy h, MJ/kg
1.5
2.5
3.5
4.5
5.5
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=100 bar
C
1.03
H
4.02
N
0.01
p=1 bar
C
1.03
H
4.02
N
0.01
'O=0.3
0.7
1.9
Specific heat c
p
, J/kgK
1300
1350
1400
1450
1500
1550
1600
1650
Te
m
p
erature, K
1500 2000 2500 3000
p=100 bar
C
1.03
H
4.02
N
0.01
'O=0.3
0.7
1.9
Specific heat c
p
, J/kgK
1300
1350
1400
1450
1500
1550
1600
1650
Te
m
p
erature, K
1500 2000 2500 3000
Specific heat c
p
, J/kgK
1300
1400
1500
1600
1700
1800
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=1 bar
C
1.03
H
4.02
N
0.01
'T=400 K
3200 K
1600 K
Specific heat c
p
, J/kgK
1300
1400
1500
1600
1700
1800
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=100 bar
C
1.03
H
4.02
N
0.01
'T=400 K
3200 K
1600 K
B.1 Thermodynamic Properties of the Working Fluid 233
Enthalpy of Formation of Burned Gas after Combustion with Natural Gas
Figure B.12: The enthalpy of formation
f
h
as function of temperature, pressure and lambda.
O=1.0
O=0.7
O=1.3
O=1.6
O=1.9
Heat of formation h
f
, MJ/kg
-3.0
-2.5
-2.0
-1.5
-1.0
Te
m
p
erature, K
1500 2000 2500 3000
p=1 bar
C
1.03
H
4.02
N
0.01
O=1.0
O=0.7
O=1.3
O=1.6
O=1.9
Heat of formation h
f
, MJ/kg
-3.0
-2.5
-2.0
-1.5
-1.0
Te
m
p
erature, K
1500 2000 2500 3000
p=100 bar
C
1.03
H
4.02
N
0.01
C
1.03
H
4.02
N
0.01
O=0.7
O=1.0
O=1.3
O=1.6
O=1.9
Heat of formation h
f
, MJ/kg
-3.0
-2.0
-1.0
Pressure,
b
ar
0 25 50 75 100
T=2000 K
C
1.03
H
4.02
N
0.01
O=0.7
O=1.3
O=1.6
O=1.9
O=1.0
Heat of formation h
f
, MJ/kg
-3.0
-2.0
-1.0
Pressure,
b
ar
0 25 50 75 100
T=2800 K
p=1 bar
C
1.03
H
4.02
N
0.01
'T=400 K
3200 K
1600 K
Heat of formation h
f
, MJ/kg
-3.0
-2.0
-1.0
0.0
1.0
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=100 bar
C
1.03
H
4.02
N
0.01
'T=400 K
3200 K
1600 K
Heat of formation h
f
, MJ/kg
-3.0
-2.0
-1.0
0.0
1.0
O, -
0.5 1.0 1.5 2.0 2.5 3.0
234 Appendix B
Figure B.13: Gradient of heat of formation:
dTdh
f
as function of temperature, pressure and lambda.
dh
f
/dT, J/kg
K
-1000
0
1000
2000
3000
4000
Te
m
p
erature, K
1500 2000 2500 3000
p=1 bar
O=1.3
O=1.0
O=0.7
C
1.03
H
4.02
N
0.01
O=1.6
O=1.9
dh
f
/dT, J/kg
K
-1000
0
1000
2000
3000
4000
Te
m
p
erature, K
1500 2000 2500 3000
p=100 bar
O=1.3
O=1.0
O=0.7
C
1.03
H
4.02
N
0.01
O=1.6
O=1.9
C
1.03
H
4.02
N
0.01
dh
f
/dT, J/kgK
0
50
100
150
200
250
300
Pressure,
b
ar
0 25 50 75 100
T=2000 K
O=1.3
O=1.0
O=0.7
O=1.6
O=1.9
C
1.03
H
4.02
N
0.01
dh
f
/dT, J/kgK
0
500
1000
1500
2000
2500
3000
Pressure,
b
ar
0 25 50 75 100
T=2800 K
O=1.3
O=0.7
O=1.6
O=1.0
O=1.9
'T=400 K
3200 K
1600 K
dh
f
/dT, J/kg
K
-1000
0
1000
2000
3000
4000
5000
6000
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=1 bar
C
1.03
H
4.02
N
0.01
'T=400 K
3200 K
1600 K
dh
f
/dT, J/kg
K
-1000
0
1000
2000
3000
4000
5000
6000
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=100 bar
C
1.03
H
4.02
N
0.01
B.1 Thermodynamic Properties of the Working Fluid 235
Figure B.14: Gradient of heat of formation:
dpdh
f
as function of temperature, pressure and lambda.
O=1.3
O=1.0
O=0.7
O=1.6
O=1.9
dh
f
/dp, J/kg/Pa
-5.0
-4.0
-3.0
-2.0
-1.0
0
Te
m
p
erature
,
K
1500 2000 2500 3000
p=1 bar
C
1.03
H
4.02
N
0.01
O=1.3
O=1.0
O=0.7
O=1.6
O=1.9
dh
f
/dp, J/kg/Pa
-0.014
-0.012
-0.010
-0.008
-0.006
-0.004
-0.002
0
Te
m
p
erature
,
K
1500 2000 2500 3000
p=100 bar
C
1.03
H
4.02
N
0.01
C
1.03
H
4.02
N
0.01
dh
f
/dp, J/kg/Pa
-0.16
-0.12
-0.08
-0.04
0
Pressure
,
b
ar
0 25 50 75 100
T=2000 K
O=1.0
O=0.7
C
1.03
H
4.02
N
0.01
dh
f
/dp, J/kg/Pa
-0.16
-0.12
-0.08
-0.04
0
Pressure
,
b
ar
0 25 50 75 100
T=2800 K
O=1.0
O=0.7
O=1.3
O=1.9
O=1.6
'T=400 K
3200 K
1600 K
dh
f
/dp, J/kg/Pa
-9.0
-6.0
-3.0
0
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=1 bar
C
1.03
H
4.02
N
0.01
'T=400 K
3200 K
1600 K
dh
f
/dp, J/kg/Pa
-0.03
-0.02
-0.01
0
0.01
O, -
0.5 1.0 1.5 2.0 2.5 3.0
p=100 bar
C
1.03
H
4.02
N
0.01