FI Spark Ignition

The FI Spark Ignition model comprises two stages:

• A first stage that models the time delay between the spark and the appearance of the flame surface.
• A second stage that takes care of the actual deployment of the flame surface in the mean gases.

The first stage is simply modelled as a time delay, using an indicator function $I$ that starts from 0 and eventually reaches a value of 1. The function $I\left(t\right)$ is governed by the equation:where ${\rho }^{*}$ is the ratio between the current gas density and the air density at 1 bar and 300 K. ${A1}_{igni}$ and ${A2}_{igni}$ are tuning parameters.

${\tau }_f$ is given by:

When $I=1$ , a spherical flame surface is deployed with radius $R_k$ given by:where $F_{act\ker }$ and $R_{k\lim it}$ are tuning parameters.

The flame surface ${\mathrm{\Sigma }}_{init}$ is distributed throughout the computational domain with:

• a Gaussian distribution function with a mean at:

  $$X_{\mu }=R_k$$

  (3959)
• a standard deviation of:

  $$\sigma =k(1{\times 10}^{-3}+u^{\prime }(t-t_{spark}\left)\right)$$

  (3960)
  where $k$ is the flame initial distribution parameter, $t$ is time, and $t_{spark}$ is the start time of the spark.

and constrained by the requirement: where $V$ is the total volume, and $D_{facig}$ is the mesh-sector factor given by: where $\theta$ is the sector angle.