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Pinch-off and formation number of negatively buoyant jets
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Image of FIG. 1.
FIG. 1.

The computational domain: (a) boundary conditions (not to scale); (b) a typical grid mesh (only every fourth mesh point shown in each direction; the center of the jet outlet is at x = 3D, y = 3D, Z = 0).

Image of FIG. 2.
FIG. 2.

Comparison of penetration height with experiment fitting line proposed by Kaye and Hunt (Ref. 18).

Image of FIG. 3.
FIG. 3.

Penetration height versus non-dimensional time. Markers: simulations; lines: model equations from Wang et al. (Ref. 29) adapted for negatively buoyant jets.

Image of FIG. 4.
FIG. 4.

Determined buoyant formation number versus Richardson number.

Image of FIG. 5.
FIG. 5.

Circulation within total domain and within head vortex rings for Rid  = −0.035 and −0.052.

Image of FIG. 6.
FIG. 6.

(Color) Vorticity distributions for Rid  = −0.04 (first row), −0.09 (second row), and −0.35 (third row).

Image of FIG. 7.
FIG. 7.

(Color) Physical map of vortex ring dynamics, where ΓVR  = 0.5fM U 0 D predicted by the slug model.

Image of FIG. 8.
FIG. 8.

(Color) Comparison of flow patterns around neutral point. Left panel: Rid  = −0.035; middle panel: Rid  = 0; right panel: Rid  = 0.035.

Image of FIG. 9.
FIG. 9.

Modified slug model applied to buoyant formation numbers.


Generic image for table
Table I.

Summary of maximum penetration distance at steady state in literature.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Pinch-off and formation number of negatively buoyant jets