Modelling of opposed flame spread over thin electric wires: estimation of flame spread rates and limiting oxygen concentrations

Abstract

A model of opposed flame spread along thin electric wires is developed to estimate the variation of flame spread rate ( V f ) with oxygen concentrations and oxidiser flow velocity. The length of pyrolysis zone ( L py ) and V f are treated as eigenvalues of the problem, and one-dimensional energy balance equations for the wire core and insulation are formulated to derive their solutions. To obtain a set of steady solutions for L py and V f , the macroscopic energy balance equation for the entire system is calculated from the one-dimensional energy balance equations with appropriate boundary conditions. Since the equations are nonlinear function of L py and V f , multiple solutions appear. The physical meaning of each solution is evaluated based on the deviation of energy from the equilibrium. Comparison of the temperature distribution along the wire with experimental data confirms that the model reproduces well the actual flame spread process. The variation of V f with oxygen concentration shows a C-shaped curve. The upper branch is the stable solution, and the lower branch is the unstable solution and the merging point of two branches correspond to the limit condition for flame spread. Therefore, the model can be used to estimate the limiting oxygen concentration based on the existence of a solution for V f . Furthermore, the variation of V f with oxidiser flow velocity shows O-shaped curve, and it is confirmed that radiative extinction under low flow velocity and blow-off under high flow velocity can also be estimated with the model. Mapping of variations of radiative extinction and blow-off extinction with oxygen concentration reveals the U-shaped flammability diagram. The predicted flame spread limits are in good agreement with the limiting oxygen concentrations measured in both microgravity and normal gravity, demonstrating the validity of using this model to predict flammability characteristics of electric wires under various oxidiser flow velocity.