Publications

A partial non-dimensionalization of the Navier-Stokes equations is used to obtain order of magnitude estimates of the rate-controlling transport processes in the reacting portion of a fire plume as a function of length scale. Over continuum length scales, buoyant times scales vary as the square root of the length scale; advection time scales vary as the length scale, and diffusion time scales vary as the square of the length scale. Due to the variation with length scale, each process is dominant over a given range. The relationship of buoyancy and baroclinc vorticity generation is highlighted. For numerical simulation, first principles solution for fire problems is not possible with foreseeable computational hardware in the near future. Filtered transport equations with subgrid modeling will be required as two to three decades of length scale are captured by solution of discretized conservation equations. By whatever filtering process one employs, one must have humble expectations for the accuracy obtainable by numerical simulation for practical fire problems that contain important multi-physics/multi-length-scale coupling with up to 10 orders of magnitude in length scale.

A subgrid model is presented for use in CFD fire simulations to account for thermal suppressants and strain. The extinguishment criteria is based on the ratio of a local fluid-mechanics time-scale to a local chemical time-scale compared to an empirically-determined critical Damkohler number. Local extinction occurs if this time scale is exceeded, global fire extinguishment occurs when local extinction has occurred for all combusting cells. The fluid mechanics time scale is based on the Kolmogorov time scale and the chemical time scale is based on blowout of a perfectly stirred reactor. The input to the reactor is based on cell averaged temperatures, assumed stoichiometric fuel/air composition, and cell averaged suppressant concentrations including combustion products. A detailed chemical mechanism is employed. The chemical time-scale is precalculated and mixing rules are used to reduce the composition space that must be parameterized. Comparisons with experimental data for fire extinguishment in a flame-stabilizing, backward-facing step geometry indicates that the model is conservative for this condition.