Maria Koroleva

    ul. T. Baramzinoi 34, Izhevsk, 426067 Russia
    Udmurt Federal Research Center UB RAS


    Korepanov M. A., Koroleva M. R., Mitrukova E. A., Nechay A. N.
    This paper considers krypton flow in a micronozzle with a cylindrical tube. A standardized conical nozzle elongated with cylindrical portion performs gas discharge into a vacuum chamber at a pressure of $10^{−2}$ Pa. Under such conditions, a low temperature area is formed in the central part of the jet with gas condensation. The particles are entrained by the gas flow. The portion with a constant section behind the nozzle should focus the supersonic flow part and the condensed particle flow and also decrease particle dispersion behind the nozzle throat.
    The paper expresses a mathematical model of homogeneous gas motion with respect to formation processes and the growth of condensation nuclei. Since the condensed particles are small, the research is carried out with a single velocity motion model. The results obtained have shown that the application of the cylindrical tube leads to nonlinear flow effects. The flow responds to: the geometrical exposure related to flow transition from the conical diverging nozzle into the cylindrical tube, heat exposure and mass outflow due to particle formation and growth, and considerable friction force exposure due to the small sizes of the channel. The sum total ofthese factors leads to an insignificant deceleration of the supersonic flow part and highly impacts condensation.
    Keywords: micronozzle, krypton, Navier – Stokes equations, condensed phase, numerical modeling
    Citation: Korepanov M. A., Koroleva M. R., Mitrukova E. A., Nechay A. N.,  Nonlinear Effects of Krypton Flow in a Micronozzle with a Cylindrical Tube, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 3, pp.  411-422
    Raeder T., Tenenev V. A., Koroleva M. R., Mishchenkova O. V.
    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
    Citation: Raeder T., Tenenev V. A., Koroleva M. R., Mishchenkova O. V.,  Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 1, pp.  119-138

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