MODELING OF THE EXPLOSION PROCESS IN AN ANISOTROPIC MEDIUM WITH QUASICONFORMAL MAPPING METHODS
Journal Title: Вісник Кременчуцького національного університету імені Михайла Остроградського - Year 2017, Vol 1, Issue 105
Abstract
Purpose. At the present stage of development of mining of minerals, in particular, oil and natural gas, the practice of using explosives is quite common. It’s very important to develop and create the new mathematical models of the explosion processes. The article deals with a mathematical model of the explosion process. Methodology. This model based on the using of the quasiconformal mapping method and takes into account the influence of the quasi-potential gradient and permeability of the medium. Originality. A mathematical model and algorithm for solving such kind of nonlinear boundary value problems for isotropic porous media were modified for the case of anisotropic ones. Using the method of quasiconformal mappings based on solving the inverse problem instead of the direct one by gradually parametrizating the characteristics of the environment and process. This method automatically solves the problem of constructing a hydrodynamic mesh and speed field, and also allows to determine the position of the lines of the section of the hole, the slightly pressed and pressed soil areas that are formed as a result of the explosion. Practical value. The results of investigation can be used for the mining of minerals, specially nature gas and oil. Conclusion. A number of numerical experiments were conducted based on the developed algorithm. The obtained results are compared with the results for the case of an isotropic medium. The influence of the anisotropy of the porous medium on the explosion process and its consequences is analyzed. Their results showed that with a clearly pronounced anisotropy of the medi- um, the total flow rate is smaller and the vortex is slightly larger, moreover, it is slightly offset relative to the charge loop In the long run - simulation of explosive processes, in which the shape of the hole is predetermined, and it is nec- essary to find the power, shape and location of the "tabs" of the projectile, as well as the nature and degree of anisotropy of the medium. It is also promising to transfer the developed methodology to a three-dimensional case.
Authors and Affiliations
A. Bomba, К. Malash
Keywords
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