Equations describing premixed

In the early investigations of hydrodynamic instability [9], [190], it was presumed that the instability evolves to a chaotic state characteristic of turbulence. Thus self-turbulization of premixed flames was attributed to hydrodynamic instability (analogous, in a sense, to the development of turbulence in shear flows). This viewpoint must be revised if the instability evolves to stable nonplanar structures, as suggested above. From numerical experiments with equations describing the self-evolution of flame surfaces in the limit of small values of the density change across the flame, it has been inferred [152], [198]-[200] that the hydrodynamic instability evolves... 

The major mechanism of a vapor cloud explosion, the feedback in the interaction of combustion, flow, and turbulence, can be readily found in this mathematical model. The combustion rate, which is primarily determined by the turbulence properties, is a source term in the conservation equation for the fuel-mass fraction. The attendant energy release results in a distribution of internal energy which is described by the equation for conservation of energy. This internal energy distribution is translated into a pressure field which drives the flow field through momentum equations. The flow field acts as source term in the turbulence model, which results in a turbulent-flow structure. Finally, the turbulence properties, together with the composition, determine the rate of combustion. This completes the circle, the feedback in the process of turbulent, premixed combustion in gas explosions. The set of equations has been solved with various numerical methods e.g., SIMPLE (Patankar 1980) SOLA-ICE (Cloutman et al. 1976). 

Equations and Solutions. The governing equations that describe a one dimensional, premixed, laminar, unbounded flame for a multi-component ideal gas mixture are (2, 3 4) ... 

In our laboratory we have attempted to discern which structnre factor, hence which cntoff function, describes reality the best. In one study we fit structure factor measurements from soot aggregates in a premixed CH4/O2 flame to the exponential, Gaussian, and Monntain and MnlhoUand forms, i.e., Equation 14.43 with P = I, 2, and 2.5. If no polydispersity was inclnded in the fit, P = 1 worked the best. However, with any reasonable polydispersity, P = 1, the exponential, failed completely. Both P = 2 and 2.5 worked well, with p = 2, the Gaussian, yielding the best resnlt. 

Searby and Rochwerger [9] developed a model describing the effect of an acoustic field on the stability of a laminar, premixed flame, treated as a thin interface between two fluids of different densities and under the influence of a periodic gravitational field. Their model is an extension of the work by Markstein [8] and is consistent with the more recent flame theory of Clavin and Garcia-Ybarra [16]. Bychkov [17] later solved the problem analytically, presenting the following linear equation for the perturbation amplitude, /, of a flame under the influence of an acoustic field [17] ... 

The governing equations used for the gaseous and droplet phases are described briefly. In the Eulerian-Lagrangian formulation, the droplets are treated as point sources and influence the gas phase only through momentum-exchange terms [21]. The variable density, low-Mach number equations are solved for the gas phase and the reacting flow formulation is based on the flamelet, progressAariable approach developed by Pierce and Moin [5] for LES of non-premixed, turbulent combustion. 

We are now interested in the numerical simulation of a two-dimensional premixed flame propagating in gaseous mixture. Some simplifications of the underlying physical processes lead to the so-called thermo diffusive model described by the reaction-diffusion equations... 

The lifetime is here weighted to both the diffusion time in a manner similar to which is described for the manual reduction procedure by Equation (19), and the flame time, rp suitable for premixed flames. It can also be weighted to the scalar dissipation rate, a, in diffusion flames. 

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