spark.h

Spark Model

Spark Model

This module defines a spark (hot spot) which is useful for the ingition of fuel-oxidizer mixtures in combustion simulations. The idea, based on the implementation of Cuoci et al. 2013, is to increase the temperature in a small spherical region of domain defined by the user. \displaystyle T = T_s - (T_s - 300.)e^{-30(t-t_s)} where T_s is the peak spark temperature, while t_s is the time of activation of the spark.

#define SPARK

User data

We define a struct that gathers all the data required by the spark model. The spark must be applied on a temperature field which must be provided as spark.T.

struct SparkModel {
  coord position;
  double time;
  double duration;
  double temperature;
  double diameter;
  scalar T;
};

struct SparkModel spark = {
  .position = {0.,0.,0.}, // Coordinate of the ignition point
  .time = 0.,             // Time at which the ignition starts
  .duration = 0.,         // Duration of the spark
  .temperature = 0.,      // Maximum temperature of the spark
  .diameter = 0.,         // Diameter of the spark
};

Implementation

Main spark event, where the cells included by the spark diameter are identified, and the temperature increase is applied on these cells.

event set_spark (i++) {
  if (t >= spark.time && t <= (spark.time + spark.duration)) {
    scalar spark_T = spark.T;
    foreach () {
      double dist = 0.;
      dist = sq (x - spark.position.x);
#if dimension > 1
      dist += sq (y - spark.position.y);
#endif
#if dimension > 2
      dist += sq (z - spark.position.z);
#endif
      dist = sqrt (dist);
      if (dist < 0.5*spark.diameter && spark_T[] < spark.temperature) {
        spark_T[] = spark.temperature -
          (spark.temperature - 300.)*exp (-30.*(t - spark.time));
      }
    }
  }
}

References

[cuoci2013numerical]

Alberto Cuoci, Alessio Frassoldati, Tiziano Faravelli, and Eliseo Ranzi. Numerical modeling of laminar flames with detailed kinetics based on the operator-splitting method. Energy & fuels, 27(12):7730–7753, 2013.