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 1

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.

typedef enum {
  SPARK_CONSTANT,
  SPARK_LINEAR,
  SPARK_RAMP,
  SPARK_HEATFLUX,
} SparkPolicy;

struct SparkModel {
  coord position;
  double time;
  double duration;
  double temperature;
  double diameter;
  double baseline;
  scalar T;
  bool linear;
  bool constant;
  SparkPolicy policy;
};

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
  .baseline = 300.,           // Baseline/Minimum temperature value
  .linear = false,            // Linear temperature profile
  .constant = false,          // Constant temperature profile
  .policy = 3,                // Default spark policy is SPARK_HEATFLUX
};

Implementation

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

#if dimension == 1
# define sparkd(x, y, R) (sq(R) - sq(x - spark->position.x))
#elif dimension == 2
# define sparkd(x, y, R) (sq(R) - sq(x - spark->position.x) - sq(y - spark->position.y))
#elif dimension == 3
# define sparkd(x, y, z, R) (sq(R) - sq(x - spark->position.x) - sq(y - spark->position.y) - sq(z - spark->position.z))
#endif

Set Spark Function

We define a function that setups a spark given a spark struct.

void set_spark (struct SparkModel * spark) {
#if TREE
  if (t <= spark->time + spark->duration) {
    extern int maxlevel;
    refine (sparkd(x, y, 0.5*spark->diameter) > 0. && level < maxlevel);
  }
#endif

  scalar spark_T = spark->T;
  if (t >= spark->time && t <= (spark->time + spark->duration)) {
    foreach() {
      if (sparkd(x,y,0.5*spark->diameter) > 0.) {
        switch (spark->policy) {

          case 0:   // SPARK_CONSTANT
            spark_T[] = spark->temperature;
            break;

          case 1:   // SPARK_LINEAR
            spark_T[] = spark->baseline +
              (spark->temperature - spark->baseline)*(t - spark->time)/spark->duration;
            break;

          case 2:   // SPARK_RAMP
            spark_T[] = spark->temperature -
              (spark->temperature - spark->baseline)*exp (-30.*(t - spark->time));
            break;

          case 3:   // SPARK_HEATFLUX
            spark_T[] = spark->temperature;
            sgT[] += spark_T[]*rho2v[]*cp2v[]*cm[];
            break;

          default:
            fprintf (ferr, "WARNING: Spark policy not available\n.");
            break;
        }
      }
    }
  }
}

Apply Spark

We use the chemistry event to set the spark in order to include its effect in the calculation of the density material derivative. If multiple sparks must be used, they can be created in the simulation file and applied creating a similar chemistry event.

event chemistry (i++) {
  set_spark (&spark);
}

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.