Summary
The effects of non-equilibrium dissociation and that of the wave front curvature on the propagation of weak discontinuities headed by wave fronts of arbitrary shape and their consequent formation into shock waves are examined. It is found that all compressive waves, except in one special case of converging waves, grow without bound only if the magnitude of the initial discontinuity associated with the wave exceeds a critical value. It is shown that, in this special case, the stabilizing influence of curvature for converging waves is not strong enough to overcome the instabilities associated with the gasdynamic phenomenon involved.
Zusammenfassung
Es werden die Einflüsse der Nichtgleichgewichts-Dissoziation und die der Wellenfrontkrümmung auf die Ausbreitung schwacher, von allgemein geformten Wellenfronten vorangetriebener, Unstetigkeiten und ihre darauf folgende Aufsteilung zu Stoßwellen untersucht. Es wird gefunden, daß alle Verdichtungswellen mit Ausnahme eines Spezialfalles zusammenlaufender Wellen nur ohne Grenze anwachsen, wenn der Betrag der Anfangsunstetigkeit der Welle einen kritischen Wert überschreitet. Es wird gezeigt, daß in diesem speziellen Fall der stabilisierende Einfluß der Krümmung für zusammenlaufende Wellen nicht stark genug ist, um die dem gasdynamischen Phänomen zugeordneten Instabilitäten zu überwinden.
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Sharma, V.D. Weak discontinuities in a dissociating gas. Acta Mechanica 38, 249–256 (1981). https://doi.org/10.1007/BF01176468
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DOI: https://doi.org/10.1007/BF01176468