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Phenomenological description of the axisymmetric air-bubble plume. (English) Zbl 1135.76370
Summary: The axisymmetric air-bubble plume in water may be thought of as emanating from a virtual point source located at some distance below the real source. To give a phenomenological description of this system one has at one’s disposal the equation of continuity, the balance equation for momentum, and the balance equation for kinetic energy. The most common way of approach so far has been to make use of the first two of these equations, together with the assumption that the rate of entrainment be proportional to the vertical centerline velocity. This is the theory developed, in particular, by Ditmars & Cederwall (1974). The present paper presents an alternative theory, in which the rate-of-entrainment assumption is abandoned and use is made of the kinetic energy equation together with the assumption that the most dominant component of the Reynolds stress be self-preserved. Very good agreement is found in this way with the large scale experiments of Kobus (1968) and Milgram (1983). The agreement is somewhat better than that found for the plane plume; the analogous theory for this case was developed by one of the present authors (I.B.). The conclusion of our analysis is that the kinetic energy approach stands out as a quite viable alternative for engineering applications in the axisymmetric case.

MSC:
76Txx Multiphase and multicomponent flows
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