Transition of Combustion to Explosion and Decision Support Systems for Explosion Protection

Abstract

A simple mathematical model of the combustion-to-explosion transition is constructed. This model is based on solving mathematical problems of the hydrodynamic flame stability, which are reduced to solving eigenvalue problems for linearized differential equations of gas dynamics. The influence of viscosity and compressibility on the development of perturbations is analyzed. The turbulence scale (the average size of the flame cells) in the case of instability of the laminar combustion process is estimated. The possibilities of the transition of slow combustion to both a deflagration explosion and a detonation wave are considered. Theoretical estimates of the explosive induction distance and the time of the combustion-to-explosion transition are obtained. These estimates are expressed by algebraic formulas, the use of which saves computer resources and does not require significant computer time. The latter fact is extremely important for the online control of potentially explosive objects. The calculations of the explosive induction distance and the time of the combustion-to-explosion transition agree with experimental data and the numerical results of other authors. Estimation of the time of a possible combustion-to-explosion transition allows to make timely and correct decision on measures to prevent an explosion or minimize its consequences. The constructed model is universal: it is applicable to the combustion of both homogeneous gas mixtures and heterogeneous media. The application of fuzzy logic makes it possible to use the proposed mathematical model of the transition from slow combustion to explosion for the software of decision support systems on the explosion safety and explosion protection for real potentially explosive objects in industry and transport. The advantage of this decision support system is that it allows the decision makers to do without experts.KeywordsCombustionFlameDeflagrationExplosionDetonationShock wavePotentially explosive objectInstabilityTurbulenceMathematical modelExplosive induction distanceDecision support systemControl