Abstract
Appropriately defined Gaussian error-functions are shown to represent closed-form solutions of self-preserving, axisymmetric, variable density, free turbulent jets. The turbulent diffusivities of momentum, mass or heat associated with such solutions are found to vary both in the streamwise and radial directions, and are different from each other. An entrainment function for the jet can also be derived from the present analysis. The entrainment coefficient is found to be uniquely related to the turbulent Reynolds number, Re t , of the jet, which is one of the two parameters in the closed-form solutions. Inverse centreline values of velocity, density, mass fraction and temperature are found to be linearly proportional to the streamwise coordinate as are the spread of velocity and scalar. If the two parameters are determined from jet spread data, the resulting closed-form solutions are in good agreement with measurements.
Zusammenfassung
Es wird gezeigt, daß geeignet definierte Gauss'sche Fehlerfunktionen für ähnliche achssymmetrische Freistrahlen Lösungen in geschlossener Form darstellen. Die mit solchen Lösungen verbundenen Impuls-, Stoff- und Energieaustauschgrößen verändern sich sowohl in Strömungs- als auch in Radialrichtung und sind voneinander verschieden. Auch eine „Entrainmentfunktion” des Freistrahls ist ableitbar von der vorliegenden Analyse. Es wird gezeigt, daß der „Entrainment-koeffizient“ des Freistrahls einzig von der turbulenten Reynolds-Zahl Re t , einem der zwei Parameter der Lösung, abhängig ist. Die Inversen der Geschwindigkeits-, Dichte-, Massenverhältnis- und Temperaturwerte auf der Strahlachse steigen in Strömungsrichtung linear an. Wenn die zwei Parameter aus den Versuchswerten der Strahlausbreitung ermittelt werden, ergibt die resultierende analytische Lösung eine gute Übereinstimmung mit den Messungen.
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So, R.M.C., Liu, T.M. On self-preserving, variable-density, turbulent free jets. Z. angew. Math. Phys. 37, 538–558 (1986). https://doi.org/10.1007/BF00945429
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DOI: https://doi.org/10.1007/BF00945429