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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 300, Pages 76–85
DOI: https://doi.org/10.1134/S0371968518010053 (Mi tm3865) 		 
Unsteady flows in deformable pipes: the energy conservation law

A. T. Il'icheva, S. I. Sumskoib, V. A. Shargatovb

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia
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DOI: https://doi.org/10.1134/S0371968518010053
Abstract: We derive a quasi-one-dimensional energy equation that corresponds to the flow of a compressible viscous fluid in a deformable pipeline. To describe the flow of such a fluid in a pipeline, we couple this equation with the previously derived continuity and momentum equations as well as with the equations of state for the internal energies of the fluid, the pipe deformations, pressure, and the cross-sectional area of the pipe. The derivation of the equations is based on averaging over the pipeline cross section. The equations obtained are designed for numerical simulations of long-distance transportation of a compressible fluid.
Funding agency Grant number
Russian Science Foundation 16-19-00188
This work is supported by the Russian Science Foundation under grant 16-19-00188.
Received: October 28, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 300, Pages 68–77
DOI: https://doi.org/10.1134/S0081543818010054
Bibliographic databases:
Document Type: Article
UDC: 532.5
Language: Russian
Citation: A. T. Il'ichev, S. I. Sumskoi, V. A. Shargatov, “Unsteady flows in deformable pipes: the energy conservation law”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Trudy Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 76–85; Proc. Steklov Inst. Math., 300 (2018), 68–77
Citation in format AMSBIB
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\paper Unsteady flows in deformable pipes: the energy conservation law
\inbook Modern problems and methods in mechanics
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov
\serial Trudy Mat. Inst. Steklova
\yr 2018
\vol 300
\pages 76--85
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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