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 Tr. Mat. Inst. Steklova, 2018, Volume 300, Pages 205–215 (Mi tm3861)

Roll wave structure in long tubes with compliant walls

A. A. Chesnokovab, V. Yu. Liapidevskiiab

a Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, pr. Lavrent'eva 15, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: We consider a flow of a fluid in a long vertical tube with elastic walls and show that, for certain parameters of the flow, small perturbations of the flow at the inlet section of the tube give rise to roll waves. Depending on the properties of the closing relation, either regular or anomalous roll waves are formed. In the latter case, a roll wave is characterized by two strong discontinuities that connect regions of continuous flow. We present the results of numerical simulations of the development of a pulsatile flow mode for convex and nonconvex closing relations that demonstrate the formation of regular and anomalous roll waves. We also construct a two-parameter class of exact periodic solutions and obtain existence diagrams for roll waves.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00156 Ministry of Education and Science of the Russian Federation ÍØ-8146.2016.1 This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00156) and by a grant of the President of the Russian Federation (project no. NSh-8146.2016.1).

DOI: https://doi.org/10.1134/S037196851801017X

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 300, 196–205

Bibliographic databases:

UDC: 532.595+517.957

Citation: A. A. Chesnokov, V. Yu. Liapidevskii, “Roll wave structure in long tubes with compliant walls”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Tr. Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 205–215; Proc. Steklov Inst. Math., 300 (2018), 196–205

Citation in format AMSBIB
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