Modeling finite spark energy and ignition/no-ignition in FDS

[matejdebenc-spec]

As part of this research, I am investigating the ignition of premixed hydrogen/methane/air mixtures in a small Spark Test Apparatus (STA).

Experimentally, the ignition source is an electrical spark. The voltage and current are measured using an oscilloscope, so the instantaneous spark power (P(t)=U(t)I(t)) and the total spark energy, typically in the mJ range, are known.

I would like to ask whether FDS can model the spark as a finite energy deposition rather than as a prescribed ignition source.

More specifically, is it possible to:

prescribe a spark energy, e.g. 0.02–1 mJ, or preferably the measured time-dependent power (P(t));
deposit this energy within a small specified volume and time interval;
allow FDS to determine whether this energy is sufficient to initiate a self-sustaining flame in a specified H₂/CH₄/air mixture;
consequently obtain an ignition/no-ignition result without forcing the reaction to ignite?

The ultimate objective would be to numerically determine or reproduce the minimum ignition energy (MIE) of different H₂/CH₄/air mixtures and compare the calculations with experimental STA measurements.

If standard FDS cannot do this directly, is there an existing FDS feature, model modification, or recommended approach that could be used for this purpose?

I would also be interested to know whether the finite-rate chemistry implemented in FDS is suitable for resolving the initial flame-kernel formation and possible extinction following a very short, mJ-scale electrical spark.

[mcgratta]

One can specify a HRRPUV (Heat Release Rate Per Unit Volume` over a specified volume, and you can vary it in time. However, if you apply your spark energy to a single grid cell, that energy will be applied over the entire cell such that the temperature in the cell might not rise very high. It is a problem of resolution. Of course, if your grid is very fine, say 1 mm, you might "resolve" the spark, but for typical large scale grids, the spark will have no effect.

You can try using direct numerical simulation on a very small domain with a 1 mm grid, say. Finite chemistry too. It is not the typical FDS application, but it should work. If if does not, create a simple test case that we can debug.

[drjfloyd]

Beyond Kevin's note on needing a grid size small enough to resolve the spark, there is also the potential issue that FDS is a low-Mach number code. If you are dumping a mJ into volume on the order of 1 mm^3 in a ms or less time you might locally cause flow compressible flow conditions.

[matejdebenc-spec]

Thank you both for your helpful explanations and comments.

The points regarding both the required spatial resolution of the spark and the potential limitations of the low-Mach formulation are very useful. I will try a small test case with a sufficiently fine grid and finite-rate chemistry to see how FDS behaves for this type of energy deposition.

Thank you again for taking the time to clarify this.