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Dynamics of a Crankshaft Mechanism under the Pressure of a Viscous Gas

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Abstract

We study an initial–boundary value problem with free boundary for one-dimensional equations of viscous gas dynamics. The problem models the motion of a crankshaft mechanism under gas pressure. It is assumed that the gas fills a cylinder, which is modeled by the interval \([0,1]\). A variable point \(a(t)\in[0,1]\) models a piston moving inside the cylinder. The piston is assumed to be connected to a planar three-link crankshaft mechanism. We also assume that a velocity distribution on the boundary of the cylinder and a density distribution on gas inflow segments are given. The gas motion is described by the one-dimensional Navier–Stokes equations of viscous compressible fluid dynamics. It is required to determine the joint motion of the gas and crankshaft mechanism. We prove that this problem has a weak renormalized solution.

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, pr. Lavrent’eva 15, Novosibirsk, 630090, Russia

    P. I. Plotnikov

  2. Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447, Warszawa, Poland

    J. Sokołowski

  3. Department of Scientific Computing, Informatics Center, Federal University of Paraíba, 471 Rua dos Escoteiros s/n, Mangabeira, João Pessoa, Paraíba, 58058-600, Brazil

    J. Sokołowski

  4. Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine, Nancy 1, B.P. 70239, 54506, Vandoeuvre-lès-Nancy Cedex, France

    J. Sokołowski

Authors
  1. P. I. Plotnikov
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  2. J. Sokołowski
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Correspondence to P. I. Plotnikov.

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Plotnikov, P.I., Sokołowski, J. Dynamics of a Crankshaft Mechanism under the Pressure of a Viscous Gas. Proc. Steklov Inst. Math. 310, 220–249 (2020). https://doi.org/10.1134/S0081543820050181

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  • DOI: https://doi.org/10.1134/S0081543820050181

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