## 7.15. Spark Ignition Model

The purpose of the spark ignition is two-fold: First, it is required in order to provide the appropriate conditions to start the combustion at time and location of the spark. Second, the initial size of the spark volume may be too small to be resolved by the mesh. Therefore, a model is needed in order to describe the initial growth of the spark kernel

The current model assumes that the burnt region around the spark initially grows as a ball. During this phase the radius of the spark kernel, , is computed solving a zero-dimensional initial value problem (IVP). The radius at ignition, , is defined by the initial spark volume, :

| (7–102)

where

The spark kernel radius is mapped onto the three-dimensional flow field by averaging the reaction progress over the so-called phantom region. The phantom region is a ball of radius equal to the transition radius, , and center equal to the spark center, . While solving for the kernel radius, the reaction progress variable is algebraically set:

for

for

The initial value problem is solved until the kernel radius reaches the transition radius, , specified by the user. At this point, the IVP solver is stopped and transition to the principal combustion model is made (i.e., switch to the burning velocity model).

The growth rate for the kernel radius is the turbulent burning velocity with a modification accounting for high curvature while the kernel is small:

| (7–103)

where

The IVP solver uses quantities averaged over the phantom region for laminar and turbulent burning velocities, and , turbulence quantities, and , and densities of the burnt and the fresh mixture, and .

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