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Energy flows in a vortex tube

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Abstract

The energy separation within a vortex tube filled with turbulent compresible fluid is investigated with an order-of-magnitude analysis of the energy equation. The physical processes corresponding to the important terms are: a heat flux due to turbulent mixing of the compressible fluid through radial pressure and temperature gradients, a flux of total energy produced by Archimedean forces, and work fluxes associated with the two most important Reynolds' stresses. All these fluxes will commonly be outwards and will tend to cool the vortex core. Experimental results are used to estimate, the relative magnitudes of the contributions. The Archimedean effect seems to be the least important.

Zusammenfassung

Die Energieverteilung in einem mit turbulenter kompressibler Flüssigkeit gefüllten Wirbelrohr wird durch Berechnung der Gliedergrösse der Energiegleichung untersucht. Die physikalischen Vorgänge, die den wichtigen Gliedern entsprechen, sind folgende: ein Wärmefluss, veranlasst durch turbulente Mischung der kompressible Flüssigkeit infolge der radialen Druck- und Temperaturgradienten; ein Fluss des Gesamtwärmeinhaltes, verursacht durch die Schwimmkraft; und die Arbeitsflüsse, die von den beiden wichtigsten Reynoldsschen scheinbaren Spannungen abhängen. Alle diese Flüsse sind gewöhnlich nach aussen gerichtet und dienen zum Kühlen des Wirbelkerns. Die experimentellen Ergebnisse werden zu einer Abschätzung der Grösse dieser Beiträge gebraucht. Der Schwimmkrafteffekt scheint am wenigsten wichtig.

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Authors and Affiliations

  1. Cavendish Laboratory, Cambridge, UK

    Alan J. Reynolds

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  1. Alan J. Reynolds
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Reynolds, A.J. Energy flows in a vortex tube. Journal of Applied Mathematics and Physics (ZAMP) 12, 343–357 (1961). https://doi.org/10.1007/BF01591284

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  • DOI: https://doi.org/10.1007/BF01591284

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