Experimental and numerical investigations of compressible, transient, and subcritical vessel outflows
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Date
2024
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Abstract
Das Ausströmen eines Gases aus einem unter Druck stehenden Behälter gehört zu den klassischen strömungsmechanischen Grundlagenproblemen. Gerade der kompressible und unterkritische Fall ist hierbei komplexer als sich zunächst vermuten lässt und es gibt keine allgemeine analytische Lösung. Dieser Fall soll hier näher untersucht werden. So wird zunächst eine allgemeine selbstähnliche Lösung hergeleitet sowie eine dimensionslose Kennzahl identifiziert, mit der die Ausströmung ohne aufwändige numerische Berechnungen charakterisiert werden kann. Dieses selbstähnliche Modell wird anhand von numerischen Simulationen und experimentellen Untersuchungen validiert.
Weiter bildet sich bei der Ausströmung aus dem Kessel in eine freie Umgebung ohne begrenzende Wände ein Freistrahl aus, welcher ebenfalls näher untersucht wird. Hierzu wird das transiente Geschwindigkeitsfeld von Luft-, Kohlenstoffdioxid- und Helium-Freistrahlen nach der schlagartigen Öffnung eines Kessels experimentell erstmalig mittels Laser Doppler Anemometrie und Phasen Doppler Anemometrie vermessen. Hierbei steht neben der Fragestellung nach der Selbstähnlichkeit des Geschwindigkeitsfeldes der Einfluss der Reynolds-Zahl und der Dichte des ausströmenden Gases im Fokus. Weiterführend werden die experimentellen Ergebnisse der transienten Freistrahlen mit numerischen Simulationen verglichen. Hierzu werden sowohl das etablierte 𝑘𝑘-𝜀𝜀 Turbulenzmodell als auch das relativ neue verallgemeinerte 𝑘𝑘-𝜔𝜔 (GEKO) Turbulenzmodell verwendet. Hierbei sollen potentielle Fehlerquellen wie Auftriebseffekte und schwankende Umgebungsbedingungen, wie sie in den experimentellen Untersuchungen auftauchen können, gezielt ausgeschaltet werden. Weiter wird untersucht, ob das GEKO Modell möglicherweise Vorteile gegenüber dem 𝑘𝑘-𝜀𝜀 Turbulenzmodell bei der Berechnung von Freistrahlen aufweist.
The outflow of a gas from a pressurised vessel is one of the classical fundamental problems in fluid mechanics. However, the compressible and subcritical case is more complex than one might think and there is no general analytical solution. This case will be examined in more detail in this dissertation. A general self-similar solution is first derived and a dimensionless number is identified with which the outflow can be characterised without time-consuming numerical simulations. This self-similar model is validated by means of numerical simulations and experimental investigations. Furthermore, a free jet is formed during the outflow from the vessel into a free environment without bounding walls, which is also investigated in more detail. For this purpose, the transient velocity field of air, carbon dioxide and helium free jets after the sudden opening of a vessel is measured experimentally for the first-time using laser Doppler anemometry and phase Doppler anemometry. In addition to the question of the self-similarity of the velocity field, the influence of the Reynolds number and of the density of the outflowing gas will be examined. The experimental results of the transient free jets are then compared with numerical simulations. For this purpose, both the established 𝑘𝑘-𝜀𝜀 turbulence model and the relatively-new generalised 𝑘𝑘-𝜔𝜔 (GEKO) turbulence model are used. Here, potential sources of error such as buoyancy effects and fluctuating ambient conditions, which can occur in the experimental investigations, are to be specifically eliminated. Finally, the question of whether or not the GEKO model possibly has advantages over the 𝑘𝑘-𝜀𝜀 turbulence model in the simulation of free jets is investigated.
The outflow of a gas from a pressurised vessel is one of the classical fundamental problems in fluid mechanics. However, the compressible and subcritical case is more complex than one might think and there is no general analytical solution. This case will be examined in more detail in this dissertation. A general self-similar solution is first derived and a dimensionless number is identified with which the outflow can be characterised without time-consuming numerical simulations. This self-similar model is validated by means of numerical simulations and experimental investigations. Furthermore, a free jet is formed during the outflow from the vessel into a free environment without bounding walls, which is also investigated in more detail. For this purpose, the transient velocity field of air, carbon dioxide and helium free jets after the sudden opening of a vessel is measured experimentally for the first-time using laser Doppler anemometry and phase Doppler anemometry. In addition to the question of the self-similarity of the velocity field, the influence of the Reynolds number and of the density of the outflowing gas will be examined. The experimental results of the transient free jets are then compared with numerical simulations. For this purpose, both the established 𝑘𝑘-𝜀𝜀 turbulence model and the relatively-new generalised 𝑘𝑘-𝜔𝜔 (GEKO) turbulence model are used. Here, potential sources of error such as buoyancy effects and fluctuating ambient conditions, which can occur in the experimental investigations, are to be specifically eliminated. Finally, the question of whether or not the GEKO model possibly has advantages over the 𝑘𝑘-𝜀𝜀 turbulence model in the simulation of free jets is investigated.
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Outflow, Free jet, Reynolds number, Phase Doppler anemometry, CFD