Auto-Ignition

Auto-ignition is a spontaneous ignition of the combustible mixture, without an external source of ignition. Pre-ignition kinetics are not directly resolved by the ECFM model—an ignition delay is computed and used to establish the time when ignition occurs.

Simcenter STAR-CCM+ provides two auto-ignition models:

ECFM Standard Auto-Ignition
ECFM TKI Auto-Ignition

ECFM Standard Auto-Ignition

The ECFM standard auto-ignition model provides source terms for the species, such as fuel, according to:

Figure 1. EQUATION_DISPLAY

{\dot{ω}}_{f} = A {[F]}^{b_{f}} {[O_{2}]}^{b_{o}} e^{- \frac{T_{c, a c t}}{T_{b}}}

(4019)

where

b_{f}

and

b_{o}

are the fuel exponent and oxygen exponent, respectively, for the ignition reaction.

A

is the ignition reaction pre-exponential factor,

T_{c, a c t}

is the fuel consumption reaction activation temperature, and

T_{b}

is the temperature of the burnt gasses.

The auto-ignition delay $τ_{d}$ is calculated based on semi-empirical correlations.

Compression Ignition: $τ_{d}$ is calculated as:
Figure 2. EQUATION_DISPLAY

$τ_{d} [c o m p r e s s i o n] = A_{d} {[F]}^{a_{f}} {[O_{2}]}^{a_{o}} ρ^{a_{ρ}} (\frac{F_{c n}}{C N}) e^{T_{d, a c t} / T_{u}}$

(4020)
where $a_{f}$ , $a_{o}$ , and $a_{ρ}$ are the delay fuel, delay oxidizer, and delay density exponents, respectively. $[F]$ and $[O_{2}]$ are the molar concentrations of the fuel and oxygen respectively. $F_{c n}$ is the delay cetane number factor and $C N$ is the cetane number (maximum value = 60).
Knock: $τ_{d}$ is calculated as:
Figure 3. EQUATION_DISPLAY

$τ_{d} [k n o c k] = {A_{d} (\frac{R O N}{F_{o n}})}^{a_{o n}} {[\frac{p}{1 + X_{r e s}}]}^{a_{p}} e^{T_{d, a c t} / T_{u}}$

(4021); where $a_{o n}$ and $a_{p}$ are the delay octane number exponent and delay pressure exponent respectively. $R O N$ is the octane number, $F_{o n}$ is the delay octane number factor, $X_{r e s}$ is the mole fraction of the residual gases, and $ρ$ is the density.

$A_{d}$ is the delay pre-exponent factor, $T_{d, a c t}$ is the reaction-delay activation temperature, and $T_{u}$ is the unburnt temperature.

An ignition progress variable function

Y_{i g i}

is defined to track the development of the reactions prior to autoignition:

Figure 4. EQUATION_DISPLAY

\frac{d Y_{i g i}}{d t} = Y_{u, f} F (τ_{d})

The condition for auto-ignition is:

Figure 4. EQUATION_DISPLAY

c_{i g i} = {\begin{matrix} 1 & {\begin{matrix} Y \end{matrix}}_{i g i} > Y_{u, f} a n d Y_{u, f} > 1 e - 10 \\ 0 & o t h e r w i s e \end{matrix}

(4023)

(4022)

ECFM TKI Auto-Ignition

The alternative is to use Tabulated Kinetic Ignition (TKI) tables. With this approach, the ignition delay is derived by taking values from pre-computed tables based on complex chemistry. If required, these values can be adjusted by multiplying with a delay factor. The auto-ignition saturation coupling option takes into account the local equivalence ratio profile near fuel droplets and uses this as input for the TKI libraries. Ignition delay and auto-ignition reaction rates (DELAY and DCDT in the TKI tables output respectively) are derived from the pre-computed TKI tables based on complex chemistry. The TKI libraries are fuel dependant.

When using the ECFM TKI auto-ignition model, the TKI tables provide source terms for the species.

When adjusting the auto-ignition reaction rates with a burning rate factor, the auto-ignition reaction rate that is used in the CFD simulation (

{\frac{d c}{d t}}_{C F D}

) is calculated by:

Figure 6. EQUATION_DISPLAY

{\frac{d c}{d t}}_{C F D} = \frac{d c}{d t} F_{b r}

(4024)

where

\frac{d c}{d t}

is the DCDT value in the TKI table output and

F_{b r}

is the burning rate factor.

An ignition progress variable function

Y_{i g i}

is defined to track the development of the reactions prior to auto-ignition:

Figure 7. EQUATION_DISPLAY

\frac{d Y_{i g i}}{d t} = Y_{u, f} F_{(τ_{d})}

(4025)

where

F_{(τ_{d})}

is a function of auto-ignition delay

τ_{d}

(DELAY in the TKI table output).

When adjusting the auto-ignition delay with a delay factor, the ignition delay that is used in the CFD simulation (

τ_{d, C F D}

) is calculated by:

Figure 8. EQUATION_DISPLAY

τ_{d, C F D} = τ_{d} F_{τ_{d}}

(4026)

where

F_{τ_{d}}

is the auto-ignition delay factor.

Once a delay criterion is reached, for example:

Figure 9. EQUATION_DISPLAY

Y_{i g i} > Y_{u, f}

(4027)

an extra flame surface area

Σ_{i n i t}

is added to the existing flame surface within the unburnt gases:

Figure 10. EQUATION_DISPLAY

Σ_{i n i t} = \max [Σ, \min (c_{i g i} | \nabla c |, V^{- 1 / 3})]

(4028)

where

V

is the ignition cell volume and:

Figure 11. EQUATION_DISPLAY

c_{i g i} = {\begin{matrix} 1 & {\begin{matrix} Y \end{matrix}}_{i g i} > 0.99 \cdot Y_{u, f} a n d Y_{u, f} > 1 e - 4 \\ 0 & o t h e r w i s e \end{matrix}

(4029)

where $Y_{u, f}$ is the subgrid mixed-level unburnt fuel conditional mass fraction.