, Volume 52, Issue 6, pp 355–377 | Cite as

Fully developed turbulent flow in a pipe: an intermediate layer

  • N. Afzal


The fully developed mean turbulent pipe flow is analysed at large Reynolds number by the method of matched asymptotic expansions. From the study of various limiting processes, in the sense of Kaplun, a crucial intermediate limit is identified whose transverse dimension is of the order of geometric mean of the transverse dimensions of the classical inner and outer layers. The asymptotic expansions in the three layers (inner, intermediate and outer) are matched by the Millikan's argument leading to two overlap domains where velocity distribution is logarithmic but their slopes could be different. The measurements show that the sustantial log regions do in fact exist in the two overlap domains and the ratio of their slopes is 2.03. The present theory describes the velocity profile over a greater range when compared to the classical theory. The predictions of Reynolds stress and turbulent energy production are in remarkably good argreement with the data for almost entire turbulent flow region from the beginning of the buffer layer to the axis oj pipe.

Voll entwickelte turbulente Rohrströmung: eine Zwischenschicht


Die voll entwickelte turbulente Rohrströmung wird für größere Reynolds-Zahlen mit der Methode der asymptotischen Entwicklungen untersucht, wobei eine wichtige Zwischenschicht identifiziert wird. Die asymptotischen Entwicklungen für drei Schichten (innere, mittlere und äußere) werden mit Hilfe von Übergangsbedingungen nach Millikan angepaßt. Messungen zeigen, daß wesentliche logarithmische Gebiete in Wirklichkeit vorhanden sind, wobei das Verhältnis ihrer Neigungen 2.03 ist. Die vorliegende Theorie beschreibt das Geschwindigkeitsprofil über einen größeren Bereich als die klassische Theorie.


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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • N. Afzal
    • 1
  1. 1.Department of Mechanical EngineeringAligarh Muslim UniversityAligarhIndia

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