Fire Safety Science Digital Archive

The propagation of two-dimensional diffusive flame over combustible material is studied numerically by solving appropriate conservation equations for the reacting flow coupled with the energy equation in the solid fuel. Two kinds of mathematioal descriptions are considered. Firstly, boundary layer approaoh is taken into aooount but in some cases (specificly, when freestream velocity is not sufficient to damp the molecular heat and mass transfer in the upwind direction), the flame spread features can not be described correctly by this approximation. Hence, full two-dimensional elliptic equations are solved. Among other aspects of flame spread process, presented study has been focused mainly on the central issue of theoretical analysis of considered phenomena that consists in the prediction of steady flame spread rate. Because the solving of unsteady elliptic equations is fairly difficult from the view-point of computational efforts, mathematical model is formulated in the steady-state coordinate system fixed on the flame front. Here, set of steady equations is taken into account where steady flame spread rate appears as an eigenvalue. Generally accepted method of eigenvalue problem's solution relates to the using of integral mass balance in the solid fuel. As it was shown, two-dimensional eigenvalue problem has not unique solution if regression of burning surface is not neglected . It means that fuel's mass balance is kept for any assigned value of flame spread rate. A new algorithm for the prediction of steady flame spread rate is proposed by using the non-equilibrium thermodynamic approach. The flame spread over PMMA slabs and thin samples of paper is studied. The influence of some parameters such as free-stream velocity and ambient mass fraction of oxygen on the flame spread rate is investigated.