PREDICTIONS OF UNSTEADY FLAME SPREAD AND BURNING PROCESSES BY THE VORTICITY-STREAM FUNCTION FORMULATION OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

A two-dimensional mathematical model of flame spread and solid burning is presented. For the gas phase, it consists of variable density, ful ly elliptic Navier-Stokes momentum, energy and chemical species mass e quations. Combustion processes are treated according to a one-step, fi nite-rate, reaction. The solid phase model describes a porous cellulos ic fuel for a range of thicknesses from the thermally thin to the ther mally thick limit. Conductive and convective heat transfer takes place as the solid degrades, by two first order Arrhenius reactions, to vol atiles and chars. Variations of solid phase densities account for fuel burn-out. Effects of gas phase and surface radiation are also include d. A steady formulation of gas phase equations with respect to the uns teady solid phase mathematical model is proposed, gas phase characteri stic times being much shorter than those of the solid phase. The non-c onstant density Navier-Stokes equations are formulated in terms of vor ticity and stream function, avoiding the pressure-velocity coupling an d, at the same time, the adoption of a sample-fixed coordinate system allows unsteady flame spread processes to be simulated. The solution i s computed numerically by means of an iterative, operator-splitting me thod based on implicit finite-difference approximations. Numerical sim ulations of the dynamics of flame spread over cellulosic solids are pr esented and extinction limits as a consequence of reduced rates of fue l generation are determined.