Abstract
The method of matched asymptotic expansions is used to study the flow out of a long tube or pipeline caused by a sudden rupture. The flow in the tube generated by the expansion wave propagating into the tube from the break point is shown to be modified substantially by the presence of wall friction. This depends primarily on the fact that, when there is wall friction, the velocity derivative along the tube becomes singular at the broken end exit for all times, as long as the flow is critical at the exit.
Résumé
Le débit provenant d'un long tube ou d'un pipeline, suite à une rupture subite, a été étudié en employant la méthode des raccordements asymptotiques. On démontre que l'écoulement à l'intérieur du tube, généré par l'onde de détente qui se propage dans le tube à partir du point de rupture, subit une modification importante due au frottement pariétal. Ceci résulte principalement du fait qu'en cas de frottement pariétal, la dérive de vitesse le long du tube, à n'importe quel moment, devient singulière au point de rupture à condition que le débit soit critique à la sortie.
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Ryhming, I.L. On the expansion wave problem in a long pipe with wall friction. Z. angew. Math. Phys. 38, 378–390 (1987). https://doi.org/10.1007/BF00944957
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DOI: https://doi.org/10.1007/BF00944957