A LUMPED SPECIES APPROACH TO MODELING SIMPLE CHEMISTRY IN UNDER-VENTILATED FIRES
Craig Weinschenk, Randall McDermott, and Jason Floyd
Carbon monoxide inhalation remains one of the leading causes of fatalities in under-ventilated compartment fires, and modeling these scenarios is therefore of great interest to the fire community. In this work we present a new framework for tracking chemical species in the Fire Dynamics Simulator (FDS), which is a high-fidelity, physics-based fire model used routinely for fire safety analysis in high-occupancy buildings. The new “lumped species” approach is a simple yet flexible way to treat a spectrum of complexity in the chemical reaction network, from mixture-fraction-based state relations to detailed chemical kinetics.
The key assumption made in lumping the primitive species is that the new species groups transport together (implying equal diffusivities) and react together. For example, in the typical FDS problem we consider three lumped species: fuel, air, and products. Two of these species (fuel and products) are tracked explicitly (transport equations are solved). The third (air) is found from the requirement that the lumped species mass fractions sum to unity. Tracking all the primitive species (nitrogen, water vapor, etc.), depending on the reaction mechanism, could lead to solving 10-20 equations, each with an additional 5 % computational cost. An advantage of the new framework is that the user may easily specify which species or groups of species are tracked. If the user decides it is worth the cost, it is possible for the lumped species and primitive species to be equivalent (no lumping at all).
In the new FDS code, the mean chemical source term in the species transport equation is obtained from the solution of a system of coupled – potentially stiff – ordinary differential equations (ODEs) governing the reaction rates for the lumped species. The reaction rates are either mixing controlled (which accounts for turbulence-chemistry interaction) or finite rate (Arrhenius kinetics). To solve the ODEs we have implemented a third-order implicit (trapezoid) solver with error control and acceleration based on Richardson extrapolation. Verification exercises are presented to confirm the order of accuracy of the solver. Additionally, for a simple “bomb calorimeter” example, we compare the FDS results for equilibrium composition, temperature, and pressure against the NASA CEA code. Lastly, validation of the FDS code for predicting CO in under-ventilated fires is presented by comparison of simulation results against the NIST reduced scale enclosure experiments of Hamins (1994).