Front propagation in the interaction of gases to model a fuel tank inerting process with a nonlinear parabolic operator

Abstract

Purpose The objective of this study is to model the propagating front in the interaction of gases in an aircraft fuel tank. To this end, we introduce a nonlinear parabolic operator, for which solutions are shown to be regular. Design/methodology/approach The authors provide an analytical expression for the propagating front, that shifts any combination of oxygen and nitrogen, in the tank airspace, into a safe condition to avoid potential explosions. The analytical exercise is validated with a real flight. Findings According to the flight test data, the safe condition, of maximum 7% of oxygen, is given for a time t = 45.2 min since the beginning of the flight, while according to our analysis, such a safe level is obtained for t = 41.42 min. For other safe levels of oxygen, the error between the analytical assessment and the flight data was observed to be below 10%. Originality/value The interaction of gases in a fuel tank has been little explored in the literature. Our value consists of introducing a set of nonlinear partial differential equations to increase the accuracy in modeling the interaction of gasses, which has been typically done via algebraic equations.