A brief survey of commonly used techniques for simulating turbulent combustion is presented, and it is noted that, except for direct numerical simulation (which is too computationally intensive even on foreseeable supercomputers), none of the current methods is able to predict details of chemical kinetics/turbulence interactions. A new approach, based on an extension of earlier work with one-dimensional mathematical models of turbulence by McDonough and co-workers (1984a, b, 1986, 1989), is applied to study a simple, single-step forward reaction H2-O2 combustion problem. The method requires no averaging, or modeling, at any level due to an additive multi-scale decomposition of governing equations. Thus, like direct numerical simulation, it is completely consistent with the original, unaveraged equations; but required arithmetic is significantly reduced via consistent linking of large-scale and small-scale phenomena, resulting in the ability to focus on local regions and consistently (with respect to the full equations) simulate phenomena within these regions to a high degree of accuracy. In addition, the method is naturally parallelizable at several algorithmic levels. This technique, termed additive turbulent decomposition, is treated theoretically, and then applied to the one-dimensional, viscous, compressible Navier-Stokes and species equations. Preliminary computational results showing detailed chemical kinetics/turbulence interactions at the tip of an H2-O2 diffusion flame are presented and discussed for a flow with Reynolds number 6000, and thermal and mass diffusion Peclet numbers of 1000 and 3000, respectively. Computed results show a relatively long period of increase in negative amplitude of H2 and O2 concentrations followed by onset of chaotic oscillations simultaneously in velocity and temperature. Corresponding fluctuations then begin to appear in the concentrations via feedback from advective and species production terms.
Carbon monoxide (CO) is considered to be the most important toxic gases that may be contained in fire effluents. Hence, it will be very beneficial for the evaluation of the hazard of smoke if the prediction of CO can be successfully introduced into fire models. Several experiments conducted to date suggest that the yield of CO is strongly affected by 'equivalence ratio'. So it seems worthwhile to develop an empirical model of CO yield as a function of equivalence ratio based on the existing experimental data, and to use this model as the source term in fire models for the prediction of CO concentrations in the buildings. In this paper, we introduce a combustion model of propane and determine each parameter used in the model as a function of equivalence ratio. The species assumed to be generated in the model are CO2, CO, O2, H2O, H2, C and unburned fuel. The model agrees reasonably well with the results of the existing experiments.
Radiation, convection and conduction are the three mechanisms which a zone fire model must consider when calculating the heat transfer between fires, wall surfaces and room gases. Radiation dominates the other two modes of heat transfer in rooms where there are fires or hot smoke layers. The computational requirements of a radiation model can also easily dominate the work required to calculate other physical sub-models in a zone fire model. This paper presents algorithms for efficiently computing the radiative heat exchange between four wall surfaces, several fires and two interior gases. A two-wall and a ten-wall radiation model are also discussed. The structure of this radiation model is exploited to show that only a few configuration factors need to be calculated directly (two rather than 16 for the four-wall model and eight rather than 100 for the ten-wall model) and matrices needed to solve for the net radiative flux striking each surface are shown, after the appropriate transformation is taken, to be diagonally dominant. Iterative methods may then be used to solve the linear equations more efficiently than direct methods such as Gaussian elimination.
In order to design robust and stable zone fire modeling algorithms, the numerical properties of the fire modeling differential equations must be understood. This paper examines some of these properties. Many sets of differential equations for zone fire modeling can be derived using the conservation of mass and energy. A comparison between various possible formulations is made in terms of numerical properties. One property that many formulations possess is the presence of multiple time scales. Pressures equilibrate much faster than other quantities such as density and temperature. Numerically, this property is known as stiffness. Stiffness, in the context of fire modeling, and numerical methods for handling it are discussed.
The nonadiabatic nature of low-speed combustion and fire, in which strongly exothermic reactions produce large temperature variations but only mild pressure variations, can cause difficulty when integrating zone models of enclosure fires. Examples of simple zone fire models are examined to illustrate the analytical nature of the problems encountered. These difficulties arise in the solution of the equations for the pressure in general enclosures because the pressure equilibrates much more rapidly than other dynamical variables. Singular perturbation methods and phase plane analyses, together with numerical integration of the nondimensionalized equations, are employed to study the stiff nature of the equations. We conclude that many of the difficulties associated with numerical integration of zone fire models may be circumvented by appropriate analysis of the zone fire model equations.