FINITE DIFFERENCE DYNAMICS MODEL OF A HOMOGENEOUS MIXTURE IN APPLICATION TO THE STUDY OF THE LARGE INTENSITY OF THE SHOCK WAVE IN A HYDROGEN-AIR ENVIRONMENT 

Tukmakov Dmitriy Alekseevich, candidate of physical and mathematical sciences, resecher Federal research center «Kazan scientific center Russian Academy of Sciences» (2/31 Lobachevsky street, Kazan, Russia), E-mail: tukmakovDA@imm.knc.ru 

533.27, 51-72 

10.21685/2227-8486-2020-1-7 

Subject and goals. In connection with the development of energy, an urgent area of research is the study of flows in complex media consisting of gases with different physical properties. Gas mixtures are also used in gas-discharge lasers, where it becomes necessary to simulate dynamic processes in mixtures. In hydrogen energy during the operation of aggregates, tanks and pipelines, shock-wave outflows of hydrogen into the air occur with the possible subsequent reflection of the shock wave from a solid surface. The difference between mathematical models of shock-wave flows is that it is necessary to take into account the compressibility of the medium. The aim of this work is to algorithmize for the software implementation of an explicit finite-different method as applied to solving the equations of a mathematical model of the dynamics of a homogeneous mixture, which allows describing nonlinear wave processes in a mixture of viscous, compressible, heatconducting gases in a two-dimensional formulation.
Methods. The mathematical model was developed in accordance with the methodology of the dynamics of heterogeneous media. The continuity equations for the density of the components of the mixture were written separately for each component. The conservation of the momentum of the mixture is described by a two-dimensional non-stationary system of Navier-Stokes equations for a compressible gas. The energy conservation equation was written for the whole mixture as a whole. As methods for implementing the mathematical model, an explicit finite-difference algorithm is used, supplemented by initial and boundary conditions.
Results and conclusions. Numerical calculations demonstrate that at the same intensity of the initial pressure rupture in the hydrogen-air mixture, there are large velocities of the moving and reflected shock waves, high velocities of satellite flows and high gas temperatures. An algorithm and a computer program are developed that implement a finite-difference solution of the equations of dynamics of a homogeneous mixture. A comparison of the shock-wave flows of the dynamics of a homogeneous and two-component media with the same initial intensity of the shock waves showed that the program allows us to identify differences associated with the heterogeneity of the simulated flows. 

homogeneous mixtures, shock waves, numerical simulation, explicit finite-difference scheme, Navier-Stokes equation, hydrogen-air mixtures