The simulation of fires using computational fluid dynamics (CFD) is a challenging endeavor.  It is difficult to couple the combustion chemistry that occurs at very small length scales with the resolvable hydrodynamic field.  It is possible to create a combustion model that tracks the significant species required to calculate the heat release rate; however, for most cases of interest in terms of building fire safety, it is too computationally expensive to construct a grid fine enough to resolve individual flame sheets. A method, therefore, was needed to model the combustion chemistry at the length scales of the resolvable flow field.

One relatively inexpensive method is to make use of the concept of mixture fraction [1].  The mixture fraction, defined as the fraction of the fluid mass that originated as fuel, is a single scalar quantity that obeys the same conservation equations as the fuel and air species typically tracked in a combustion model.  From it, mass fractions for all other species can be derived based on empirical state relationships.  Since this one parameter can account for the major species of interest in a combustion simulation, the mixture fraction greatly reduces the number of equations to be solved.

Typically, a mixture fraction-based combustion model assumes that the reaction is taking place on an infinitely thin flame sheet where both the fuel and oxygen concentrations go to zero. However, since we wish to avoid the expense of resolving the flow field at length scales fine enough to capture the actual flame sheet location, the traditional mixture fraction-based model is modified to allow for a reaction zone of finite thickness while not violating the combustion state equation. These modifications preserve the original chemical equation for the combustion process as well as provide a framework for the inclusion of minor combustion species such as carbon monoxide.

A mixture fraction combustion model has been added to the Fire Dynamics Simulator V1.0 (FDS) [2,3].  Validation of the new model is compared against experimental data from a large scale fire experiment in a decommissioned, German, nuclear power plant [4]. Results of the new combustion model are also compared against those from the previous model.

References

[1] Mell, W.E., McGrattan, K.B., and Baum, H.R.  Numerical Simulation of Combustion in Fire Plumes.  26th Symposium (International) on Combustion.  Combustion Institute.  1996.  pp 1523-1530.

[2] McGrattan, K.B., et al. Fire Dynamics Simulator ˆ Technical Reference Guide.  National Institute of Standards and Technology.  NISTIR 6467.  2000.

[3] McGrattan, K.B. and Forney, G.P. Fire Dynamics Simulator ˆ User‚s Manual.  National Institute of Standards and Technology.  NISTIR 6469.  2000.

[4] Floyd, J., Wolf, L. and Krawiec, J.  Evaluation of the HDR Fire Test Data and Accompanying Computational Activities With Conclusions From Present Code Capabilities, Volume 1: Test Series Description for T51 Gas Fire Test Series.  NIST GCR 97-727.  1997.