Numerical simulation of the propagation of probing pulses in a dense bed of a granular medium

Utkin P.S., Chuprov P.A.
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The need to model high-speed flows of compressible media with shock waves in the presence of dense curtains or layers of particles arises when studying various processes, such as the dispersion of particles from a layer behind a shock wave or propagation of combustion waves in heterogeneous explosives. These directions have been successfully developed over the past few decades, but the corresponding mathematical models and computational algorithms continue to be actively improved. The mechanisms of wave processes in two-phase media differ in different models, so it is important to continue researching and improving these models.

The paper is devoted to the numerical study of the propagation of disturbances inside a sand bed under the action of successive impacts of a normally incident air shock wave. The setting of the problem follows the experiments of A. T.Akhmetov with co-authors. The aim of this study is to investigate the possible reasons for signal amplification on the pressure sensor within the bed, as observed under some conditions in experiments. The mathematical model is based on a one-dimensional system of Baer –Nunziato equations for describing dense flows of two-phase media taking into account intergranular stresses in the particle phase. The computational algorithm is based on the Godunov method for the Baer – Nunziato equations.

The paper describes the dynamics of waves inside and outside a particle bed after applying first and second pressure pulses to it. The main components of the flow within the bed are filtration waves in the gas phase and compaction waves in the solid phase. The compaction wave, generated by the first pulse and reflected from the walls of the shock tube, interacts with the filtration wave caused by the second pulse. As a result, the signal measured by the pressure sensor inside the bed has a sharp peak, explaining the new effect observed in experiments.

Keywords: granular medium, particle bed, shock wave, compaction wave, intergranular stresses, Baer – Nunziato equations, Godunov method
Citation in English: Utkin P.S., Chuprov P.A. Numerical simulation of the propagation of probing pulses in a dense bed of a granular medium // Computer Research and Modeling, 2024, vol. 16, no. 6, pp. 1361-1384
Citation in English: Utkin P.S., Chuprov P.A. Numerical simulation of the propagation of probing pulses in a dense bed of a granular medium // Computer Research and Modeling, 2024, vol. 16, no. 6, pp. 1361-1384
DOI: 10.20537/2076-7633-2024-16-6-1361-1384
URL: http://crm-en.ics.org.ru/journal/article/3542/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

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