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This article is cited in 3 scientific papers (total in 3 papers)
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.
Keywords:
flow in elastic tube, hyperbolic equations, Whitham condition, roll waves.
Received: September 24, 2017
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, Trudy Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 205–215; Proc. Steklov Inst. Math., 300 (2018), 196–205
Linking options:
https://www.mathnet.ru/eng/tm3861https://doi.org/10.1134/S037196851801017X https://www.mathnet.ru/eng/tm/v300/p205
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