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The asymptotic structure of weak shock waves in flows over symmetrical bodies at mach number unity

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Summary

The plane or axisymmetric flow of a viscous and heat conducting fluid far away from a body moving at sonic speed, is considered. The parameter characterizing the dissipative phenomena is assumed very small (highReynolds number), and in order to determine approximatively the flow the method of matched asymptotic expansions with respect to this parameter is applied. As a result, a description of the shock wave structure is obtained, being an extension of the previously known nondissipativeGuderley-Frankl solutions. Some restrictions concerning the region of validity of the obtained results are deduced from analysing the basic assumptions underlying the method of approximation.

Zusammenfassung

Es wird die ebene bzw. achsensymmetrische Strömung einer zähen, wärmeleitenden Flüssigkeit in großer Entfernung von einem sich mit Schallgeschwindigkeit bewegenden Körper untersucht. Der Dissipationsparameter wird als sehr klein vorausgesetzt (hoheReynolds-Zahl). Zur näherungsweisen Ermittlung der Strömung werden asymptotische Entwicklungen nach diesem Parameter unter Berücksichtigung stetiger Übergangsbedingungen ausgeführt. Die sich ergebende Stoßwellenstruktur stellt eine Erweiterung der bekanntenGuderlye-Frankl-Lösung dar. Einige Einschränkungen des Geltungsbereiches der erhaltenen Resultate werden aus der Betrachtung der Grundannahmen der verwendeten Näherungsmethode hergeleitet.

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  1. Institute for Fundamental Technical Research, Polish Academy of Sciences, ul. Swietokrzyska 21, Warsaw, Poland

    A. Szaniawski

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  1. A. Szaniawski
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Szaniawski, A. The asymptotic structure of weak shock waves in flows over symmetrical bodies at mach number unity. Acta Mechanica 5, 189–203 (1968). https://doi.org/10.1007/BF01178831

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  • DOI: https://doi.org/10.1007/BF01178831

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