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Unsteady pressure waves and shock waves in elastic tubes containing bubbly air-water mixtures

Zur Ausbreitung von Druck- und Stoßwellen in instationären Blasen-Flüssigkeitsströmungen durch elastische Leitungen

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Summary

The flow of a two-phase fluid through elastic tubes is more complex than that of a single phase fluid. The mathematical model is based on an one-dimensional approach to the flow of a liquid-gas mixture. The one-dimensional equations for transient two-phase flow through elastic tubes are a system of nonlinear hyperbolic partial differential equations if the bubbles and the liquid particles move with the same velocity. Included in the model are the effects of wall elasticity, compressibility of the gas and the liquid, the surface tension and the variable area change. The propagation of finite pressure waves and shock waves in a liquid containing gas bubbles has been investigated. The results show a differently strong influence of the parameters on the wave propagation speed and on the shock wave relations.

Zusammenfassung

Es ist bekannt, daß bei der mathematischen Beschreibung einer Zweiphasenströmung insofern Schwierigkeiten auftreten können, als unter bestimmten Voraussetzungen sowohl reelle als auch komplexe charakteristische Richtungen auftreten können. Für den Fall gleicher Geschwindigkeiten von Blasen und Flüssigkeit erhält man aus den instationären Gleichungen ein nichtlineares hyperbolisches Differentialgleichungssystem. Berücksichtigt werden die Elastizität der Wandungen, die Kompressibilität des Gases und der Flüssigkeit sowie die Oberflächenspannung. Wellenausbreitungsgeschwindigkeiten und Stoßrelationen werden angegeben. Die Resultate zeigen einen unterschiedlich starken Einfluß der verschiedenen Parameter auf die Wellenaus-breitungsgeschwindigkeit und die Stoßrelationen.

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  1. Institut für Mechanik, Universität Hannover, Appelstrasse 11, D-300, Hannover 1, Federal Republic of Germany

    H. J. Rath

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Rath, H.J. Unsteady pressure waves and shock waves in elastic tubes containing bubbly air-water mixtures. Acta Mechanica 38, 1–17 (1981). https://doi.org/10.1007/BF01351459

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