Abstract
Experimental simulations were carried out to investigate the onset of instability in negatively buoyant fountains by injecting glycerin–water mixtures into silicon oil. The transition from a stable to an unstable fountain structure is primarily governed by the Richardson number, and to a lesser extent, Reynolds number, viscosity ratio, Weber number and vent geometry. Transition nominally occurs at a Ri = 1.0. For a fountain issuing from a cylindrical pipe, the major effect of the Reynolds number is in determining whether or not the fountain is laminar or turbulent. The Reynolds number effect can be largely accounted for by basing a corrected Richardson number on the root mean square of the mean velocity. Viscosity ratio deviating from unity has the effect of stabilizing the flow structure and thereby reducing the transition Richardson number. Similarly, interfacial tension stabilizes the flow pattern resulting in a trend of increasing transition Richardson number with increasing Weber number. The results are valid in rectangular vents if the Richardson number and Reynolds number are based on the hydraulic diameter.
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Abbreviations
- φ:
-
Vent shape parameter (accounts for circularity and taper angle)
- d :
-
Characteristic size of the mingling void
- ρF, ρS:
-
Densities of the fountain and surrounding fluids
- μF, μS:
-
Viscosities of the fountain and surrounding fluids
- σ:
-
Interfacial tension between fountain and surrounding fluids
- \( \ifmmode\expandafter\bar\else\expandafter\=\fi{U} \) :
-
Average velocity of fountain at the vent exit based on volumetric flow rate \( {\left( {\ifmmode\expandafter\bar\else\expandafter\=\fi{U} = {\ifmmode\expandafter\dot\else\expandafter\.\fi{V}} \mathord{\left/ {\vphantom {{\ifmmode\expandafter\dot\else\expandafter\.\fi{V}} A}} \right. \kern-\nulldelimiterspace} A} \right)} \)
- f :
-
Characteristic instability frequency of the fountain
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This material is based on work supported by the National Science Foundation under Grant No. 0408946.
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Friedman, P.D., Vadakoot, V.D., Meyer, W.J. et al. Instability threshold of a negatively buoyant fountain. Exp Fluids 42, 751–759 (2007). https://doi.org/10.1007/s00348-007-0283-5
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DOI: https://doi.org/10.1007/s00348-007-0283-5