We propose a method of calculation of thermodynamic functions in the Thomas–Fermi model at finite temperature θ. Expressions for first and second derivatives of the free energy are analytically obtained in the framework of the model. A special treatment of thermodynamic functions at low temperatures is provided by asymptotic series expansion at θ → 0. A special algorithm is used to ensure required accuracy for all values in a wide range of volumes and temperatures. We compare the results of our computations with ideal Boltzmann and Fermi gas models.

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There exist evidence, that the gaseous detonation passing through a cloud of solid particles could be attenuated or even suppressed. Contrary to these known works, in the present article, we have found that just one single 160-micron particle can serve as a trigger for the detonation onset. By numerical simulation, we have obtained that there are the concentration ratio limits, in which single particle is enough to initiate gaseous detonation, although without particle the detonation is not ignited in the same conditions in a tube of restricted size. In other words, the presence of a solid particle in the combustible mixture could decrease significantly the ignition delay time. Using of temperature pattern visualization, we have demonstrated that the ignition arises in the subsonic region located between the particle and the bow shock front. The approximations of the used model are discussed. It is shown that used assumptions are valid within investigated time intervals. The work performed with use of the supercomputer resources Interdepartmental Supercomputer Center Russian Academy of Sciences (ISC RAS)