Solutions and compatibility conditions for a model describing the interaction of gases in a fuel tank

The fire safety is a relevant problem in aircraft fuel tanks design. One of the most suitable solutions is based on the introduction of nitrogen, through distributed nozzles, to decrease the tank flammability. This is given by the nitrogen that pulls the oxygen outboard. There exist several models and solutions to describe the interaction of gasses in a fuel tank, nonetheless it is still missing to provide the compatibility conditions required to ensure an inerted ullage. Following this idea, the intention is to provide new results about the required conditions to ensure that the vented convection, given by the fuel tank venting system, does not impact the propagation of the nitrogen to construct an inerted airspace. We introduce some new flat solutions that complement those already existing in the literature. The flat solutions can be used to assess the time required to get an inerted fuel tank configuration in a direct way, representing a simplification on the calculation of the time-to-inert compared to that existing in the current literature. The analytical approaches are validated with real data extracted from a flight test campaign in an Airbus A320. We highlight that the obtained results fit quite exactly with the flight test data.