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Rus. J. Nonlin. Dyn., 2021, Volume 17, Number 1, Pages 119–138 (Mi nd745)  

Nonlinear engineering and robotics

Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

T. Raedera, V. A. Tenenevba, M. R. Korolevab, O. V. Mishchenkovaa

a Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia
b Udmurt Federal Research Center UB RAS, ul. T. Baramzinoi 34, Izhevsk, 426067 Russia

Abstract: The paper presents a modification of the digital method by S. K. Godunov for calculating real gas flows under conditions close to a critical state. The method is generalized to the case of the Van der Waals equation of state using the local approximation algorithm. Test calculations of flows in a shock tube have shown the validity of this approach for the mathematical description of gas-dynamic processes in real gases with shock waves and contact discontinuity both in areas with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with local approximation of the Van der Waals equation by a two-term equation of state was used for simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex shape, which is characteristic of the internal space of a safety valve. We have demonstrated that, under near-critical conditions, areas of nonclassical gas behavior may appear, which affects the nature of flows. We have studied nonlinear processes in a safety valve arising from the movement of the shut-off element, which are also determined by the device design features and the gas flow conditions.

Keywords: real gas, Van der Waals equation, critical state of substance, Godunov’s method

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation AAAA-A19-119092690104-4
The work was performed as part the research project of the Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences “Artificial Intelligence in the Development, Training, and Support of Expert Systems for Presentation and Use of Knowledge in Natural, Engineering, and Socio-Humanitarian Science” AAAA-A19-119092690104-4.


DOI: https://doi.org/10.20537/nd210109

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MSC: 35Q30, 76-10, 76N15
Received: 02.03.2021
Accepted:15.03.2021
Language:

Citation: T. Raeder, V. A. Tenenev, M. R. Koroleva, O. V. Mishchenkova, “Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State”, Rus. J. Nonlin. Dyn., 17:1 (2021), 119–138

Citation in format AMSBIB
\Bibitem{RaeTenKor21}
\by T. Raeder, V. A. Tenenev, M. R. Koroleva, O. V. Mishchenkova
\paper Nonlinear Processes in Safety Systems for Substances
with Parameters Close to a Critical State
\jour Rus. J. Nonlin. Dyn.
\yr 2021
\vol 17
\issue 1
\pages 119--138
\mathnet{http://mi.mathnet.ru/nd745}
\crossref{https://doi.org/10.20537/nd210109}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4240821}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85105142546}


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