Automatic Composition Initialization

Automatic Composition Initialization automatically obtains values for the mass fraction of chemical species that are present in the cylinder and the ports as a result of combustion.

The mass fractions are calculated as a function of the equivalence ratio at which the combustion takes place and of the exhaust gas recirculation (EGR) percentage.

Equivalence Ratio

The fuel-air equivalence ratio

Φ

is defined as the ratio of the fuel-air ratio to the stoichiometric fuel-air ratio as follows:

图 1. EQUATION_DISPLAY

Φ = \frac{\frac{\dot{F}}{\dot{A}}}{{\frac{\dot{F}}{\dot{A}} |}_{s}}

(591)

where:

$\dot{F}$ is the fuel mass flow rate (injected/premixed).
$\dot{A}$ is the air mass flow rate (EGR not included).
${\frac{\dot{F}}{\dot{A}} |}_{s}$ is the stoichiometric fuel-air ratio.

The air-fuel equivalence ratio $λ$ is related to the fuel-air equivalence ratio as:

图 2. EQUATION_DISPLAY

λ = \frac{1}{Φ}

(592)

Exhaust Gas Recirculation (EGR)

The following definitions of exhaust gas recirculation (EGR) are available:

图 3. EQUATION_DISPLAY

{E G R}_{1} = \frac{\dot{E}}{\dot{A}}

(593)

图 4. EQUATION_DISPLAY

{E G R}_{2} = \frac{\dot{E}}{\dot{A} + \dot{E}}

(594)

图 5. EQUATION_DISPLAY

{E G R}_{3} = \frac{\dot{E}}{\dot{A} + \dot{F}}

(595)

图 6. EQUATION_DISPLAY

{E G R}_{4} = \frac{\dot{E}}{\dot{A} + \dot{F} + \dot{E}}

(596)

where:

$\dot{E}$ is the recirculated exhaust gas mass flow rate.
$\dot{A}$ is the fresh air mass flow rate.
$\dot{F}$ is the injected/premixed fuel mass flow rate.

Exhaust Gas Composition

For initialization and boundary conditions, the composition of the exhaust gas is obtained from one-step combustion reactions depending on the specified global equivalence ratio of the fuel-air mixture (without EGR)

Φ_{g l o b a l}

For lean or stoichiometric mixtures (

Φ_{g l o b a l} \leq 1

), the reaction is given as:

图 7. EQUATION_DISPLAY

C_{n} H_{m} O_{p} + (n + \frac{m}{4} - \frac{p}{2}) O_{2} \to n C O_{2} + \frac{m}{2} H_{2} O

(597)

For rich mixtures ( $Φ_{g l o b a l} > 1$ ), the reaction is defined depending on the equivalence ratio as:

图 8. EQUATION_DISPLAY

C_{n} H_{m} O_{p} + (n_{1} + \frac{n_{2}}{2} + \frac{m}{4} - \frac{p}{2}) O_{2} \to n_{1} C O_{2} + n_{2} C O + \frac{m}{2} H_{2} O i f 1 < Φ_{g l o b a l} \leq Φ_{\lim 1}

(598)

图 9. EQUATION_DISPLAY

C_{n} H_{m} O_{p} + (\frac{n}{2} + \frac{m_{1}}{4} - \frac{p}{2}) O_{2} \to n C O + \frac{m_{1}}{2} H_{2} O + \frac{m_{2}}{2} H_{2} i f Φ_{\lim 1} < Φ_{g l o b a l} \leq Φ_{\lim 2}

(599)

图 10. EQUATION_DISPLAY

C_{n} H_{m} O_{p} + (\frac{n}{2} - \frac{p}{2}) O_{2} \to n C O + \frac{m}{2} H_{2} i f Φ_{\lim 2} < Φ_{g l o b a l}

(600)

where $n = n_{1} + n_{2}$ and $m = m_{1} + m_{2}$ .

The equivalence ratio limits $Φ_{\lim 1}$ and $Φ_{\lim 2}$ are defined as:

图 11. EQUATION_DISPLAY

Φ_{\lim 1} = \frac{n + \frac{m}{4} - \frac{p}{2}}{\frac{n}{2} + \frac{m}{4} - \frac{p}{2}}

(601)

图 12. EQUATION_DISPLAY

Φ_{\lim 2} = \frac{n + \frac{m}{4} - \frac{p}{2}}{\frac{n}{2} - \frac{p}{2}}

(602)

Assuming that the fuel is fully burnt and that the fresh charge is composed of air with a fixed N2/O2 ratio of 3.29, fuel, and EGR, the composition of the exhaust gas can be calculated from:

图 13. EQUATION_DISPLAY

Y_{O 2}^{e x h a u s t} + Y_{C O 2}^{e x h a u s t} + Y_{H 2 O}^{e x h a u s t} + Y_{C O}^{e x h a u s t} + Y_{H 2}^{e x h a u s t} + Y_{N 2}^{e x h a u s t} = 1

(603)

where the mass fractions of the exhaust species for lean or stoichiometric mixtures are given as:


Mass Fraction	$Φ_{g l o b a l} \leq 1$
$Y_{02}^{e x h a u s t}$	图 14. EQUATION_DISPLAY $\frac{1 - Φ_{g l o b a l}}{\frac{Φ_{g l o b a l}}{s} + 4.29}$ (604)
$Y_{C 02}^{e x h a u s t}$	图 15. EQUATION_DISPLAY $n \frac{M_{W}^{C O 2}}{M_{W}^{f u e l}} \frac{\frac{Φ_{g l o b a l}}{s}}{\frac{Φ_{g l o b a l}}{s} + 4.29}$ (605)
$Y_{H 2 O}^{e x h a u s t}$	图 16. EQUATION_DISPLAY $\frac{m}{2} \frac{M_{W}^{H 2 O}}{M_{W}^{f u e l}} \frac{\frac{Φ_{g l o b a l}}{s}}{\frac{Φ_{g l o b a l}}{s} + 4.29}$ (606)
$Y_{C O}^{e x h a u s t}$	0
$Y_{H 2}^{e x h a u s t}$	0
$Y_{N 2}^{e x h a u s t}$	图 17. EQUATION_DISPLAY $1 - Y_{O 2}^{e x h a u s t} - Y_{C O 2}^{e x h a u s t} - Y_{H 2 O}^{e x h a u s t}$ (607)

For rich mixtures, the mass fractions of the exhaust species are given as:


Mass Fraction	$1 < Φ_{g l o b a l} \leq Φ_{\lim 1}$
$Y_{02}^{e x h a u s t}$	0
$Y_{C 02}^{e x h a u s t}$	图 18. EQUATION_DISPLAY $[n (\frac{2}{Φ_{g l o b a l}} - 1) + (\frac{1}{Φ_{g l o b a l}} - 1) (\frac{m}{2} - p)] \frac{M_{W}^{C O 2}}{M_{W}^{f u e l}} \frac{\frac{Φ_{g l o b a l}}{s}}{\frac{Φ_{g l o b a l}}{s} + 4.29}$ (608)
$Y_{H 2 O}^{e x h a u s t}$	图 19. EQUATION_DISPLAY $\frac{m}{2} \frac{M_{W}^{H 2 O}}{M_{W}^{f u e l}} \frac{\frac{Φ_{g l o b a l}}{s}}{\frac{Φ_{g l o b a l}}{s} + 4.29}$ (609)
$Y_{C O}^{e x h a u s t}$	图 20. EQUATION_DISPLAY $(1 - \frac{1}{Φ_{g l o b a l}}) (2 n + \frac{m}{2} - p) \frac{M_{W}^{C O}}{M_{W}^{f u e l}} \frac{\frac{Φ_{g l o b a l}}{s}}{\frac{Φ_{g l o b a l}}{s} + 4.29}$ (610)
$Y_{H 2}^{e x h a u s t}$	0
$Y_{N 2}^{e x h a u s t}$	图 21. EQUATION_DISPLAY $1 - Y_{C O 2}^{e x h a u s t} - Y_{H 2 O}^{e x h a u s t} - Y_{C O}^{e x h a u s t}$ (611)


Mass Fraction	$Φ_{\lim 1} < Φ_{g l o b a l} \leq Φ_{\lim 2}$
$Y_{02}^{e x h a u s t}$	0
$Y_{C 02}^{e x h a u s t}$	0
$Y_{H 2 O}^{e x h a u s t}$	图 22. EQUATION_DISPLAY $[n (\frac{2}{Φ_{g l o b a l}} - 1) + \frac{m}{{2 Φ}_{g l o b a l}} + p (1 - \frac{1}{Φ_{g l o b a l}})] \frac{M_{W}^{H 2 O}}{M_{W}^{f u e l}} \frac{\frac{Φ_{g l o b a l}}{s}}{\frac{Φ_{g l o b a l}}{s} + 4.29}$ (612)
$Y_{C O}^{e x h a u s t}$	图 23. EQUATION_DISPLAY $n \frac{M_{W}^{C O}}{M_{W}^{f u e l}} \frac{\frac{Φ_{g l o b a l}}{s}}{\frac{Φ_{g l o b a l}}{s} + 4.29}$ (613)
$Y_{H 2}^{e x h a u s t}$	图 24. EQUATION_DISPLAY $[n (1 - \frac{2}{Φ_{g l o b a l}}) + (1 - \frac{1}{Φ_{g l o b a l}}) (\frac{m}{2} - p)] \frac{M_{W}^{H 2}}{M_{W}^{f u e l}} \frac{\frac{Φ_{g l o b a l}}{s}}{\frac{Φ_{g l o b a l}}{s} + 4.29}$ (614)
$Y_{N 2}^{e x h a u s t}$	图 25. EQUATION_DISPLAY $1 - Y_{H 2 O}^{e x h a u s t} - Y_{C O}^{e x h a u s t} - Y_{H 2}^{e x h a u s t}$ (615)


Mass Fraction	$Φ_{\lim 2} < Φ_{g l o b a l}$
$Y_{02}^{e x h a u s t}$	0
$Y_{C 02}^{e x h a u s t}$	0
$Y_{H 2 O}^{e x h a u s t}$	0
$Y_{C O}^{e x h a u s t}$	图 26. EQUATION_DISPLAY $n \frac{M_{W}^{C O}}{M_{W}^{f u e l}} \frac{\frac{Φ_{\lim 2}}{s}}{\frac{Φ_{\lim 2}}{s} + 4.29}$ (616)
$Y_{H 2}^{e x h a u s t}$	图 27. EQUATION_DISPLAY $[n (1 - \frac{2}{Φ_{\lim 2}}) + (1 - \frac{1}{Φ_{\lim 2}}) (\frac{m}{2} - p)] \frac{M_{W}^{H 2}}{M_{W}^{f u e l}} \frac{\frac{Φ_{\lim 2}}{s}}{\frac{Φ_{\lim 2}}{s} + 4.29}$ (617)
$Y_{N 2}^{e x h a u s t}$	图 28. EQUATION_DISPLAY $1 - Y_{C O}^{e x h a u s t} - Y_{H 2}^{e x h a u s t}$ (618)

$s$ is the stoichiometric factor defined as:

图 29. EQUATION_DISPLAY

s = (n + \frac{m}{4} - \frac{p}{2}) \frac{M_{W}^{O 2}}{M_{W}^{f u e l}}

(619)

where $M_{W}^{O 2}$ and $M_{W}^{f u e l}$ are the molecular weight of oxygen and the specified fuel, respectively.

Gas Initialization and Boundary Conditions

For initialization, the species mass fractions in the different zones of the engine—cylinder, intake port, exhaust port, and plenums—, are calculated from:

图 30. EQUATION_DISPLAY

Y_{O 2}^{z o n e} + Y_{N 2}^{z o n e} + Y_{C O 2}^{z o n e} + Y_{H 2 O}^{z o n e} + Y_{C O}^{z o n e} + Y_{H 2}^{z o n e} + Y_{f u e l}^{z o n e} = 1

(620)

with:

图 31. EQUATION_DISPLAY

Y_{O 2}^{z o n e} = Z_{02}^{a i r_z o n e} + Y_{e x h a u s t}^{t_z o n e} Y_{O 2}^{e x h a u s t}

(621)

图 32. EQUATION_DISPLAY

Y_{N 2}^{z o n e} = 3.29 Z_{02}^{a i r_z o n e} + Y_{e x h a u s t}^{t_z o n e} Y_{N 2}^{e x h a u s t}

(622)

图 33. EQUATION_DISPLAY

Y_{C O 2}^{z o n e} = Y_{e x h a u s t}^{t_z o n e} Y_{C O 2}^{e x h a u s t}

(623)

图 34. EQUATION_DISPLAY

Y_{H 2 O}^{z o n e} = Y_{e x h a u s t}^{t_z o n e} Y_{H 2 O}^{e x h a u s t}

(624)

图 35. EQUATION_DISPLAY

Y_{C O}^{z o n e} = Y_{e x h a u s t}^{t_z o n e} Y_{C O}^{e x h a u s t}

(625)

图 36. EQUATION_DISPLAY

Y_{H 2}^{z o n e} = Y_{e x h a u s t}^{t_z o n e} Y_{H 2}^{e x h a u s t}

(626)

图 37. EQUATION_DISPLAY

Y_{f u e l}^{z o n e} = Z_{02}^{a i r_z o n e} \frac{Φ_{l o c a l}^{z o n e}}{s}

(627)

where:

图 38. EQUATION_DISPLAY

Z_{02}^{a i r_z o n e} = \frac{1 - Y_{e x h a u s t}^{t_z o n e}}{4.29 + \frac{Φ_{l o c a l}^{z o n e}}{s}}

(628)

$Y_{e x h a u s t}^{t_z o n e}$ is calculated depending on the specified EGR level as:


Mass Fraction	${E G R}_{1}$	${E G R}_{2}$	${E G R}_{3}$	${E G R}_{4}$
$Y_{e x h a u s t}^{t_z o n e}$	$\frac{{E G R}_{1}^{z o n e}}{1 + {E G R}_{1}^{z o n e} + \frac{Φ_{l o c a l}^{z o n e}}{4.29 s}}$	$\frac{{E G R}_{2}^{z o n e}}{1 + \frac{Φ_{l o c a l}^{z o n e}}{4.29 s} (1 - {E G R}_{2}^{z o n e})}$	$\frac{{E G R}_{3}^{z o n e}}{1 + {E G R}_{3}^{z o n e}}$	${E G R}_{4}^{z o n e}$

$Φ_{l o c a l}^{z o n e}$ is the specified equivalence ratio of the premixed unburnt fuel-air mixture.

At the inlets and outlets, Simcenter STAR-CCM+ In-cylinder applies the mass fractions as calculated for the respective intake ports and exhaust ports.