Flow field in a downward diverging channel and its application
-
Marek Večeř
und
Kamil Wichterle
Abstract
The flow in a downward divergent channel turns out to be an interesting experimental setup for the observation of upward floating bubbles that appear to be levitating in view of the observer. A more detailed analysis of this flow and its characteristic parameters is necessary for better understanding of this phenomenon. The boundary layer theory was used to derive the velocity field for the experimental setup. The actual flow of a liquid in the presence of a bubble was studied experimentally by measuring the position of the bubble; the data were then statistically processed by an image analysis. Observation of the bubble positions distribution showed that it is reasonable to assume a flat velocity profile of the liquid in the channel and that the bubbles do not tend to move into the boundary layer. In our experiments, volume of the air bubbles floating in water was 200 mm3 and of that of bubbles floating in aqueous glycerin was 300 mm3. Thus, the experiment used in this work is suitable for reliable determination of instantaneous and average bubble rising velocities as well as of those of horizontal and vertical oscillations.
Acknowledgements
The authors especially thank Jarda J. Ulbrecht for carefully reading and appropriate language corrections of the manuscript. This research was financially supported by grant no. 104/07/1110 from the Grant Agency of the Czech Republic and the project ICT-National Feasibility Study (No. LO1406).
Symbols
| az | acceleration of the bubble in the upward direction | m s−2 |
| cp | specific heat capacity | J kg−1 K−1 |
| D | local diameter of diverging tube | m |
| d | equivalent bubble diameter | m |
| Eo | Eötvös number | |
| Mo | Morton number | |
| N | number of counts | |
| Re | Reynolds number | |
| r | radius of divergent tube | m |
| t | time | s |
| U | liquid velocity outside the boundary m s−1 | layer |
| u(z, r) | liquid velocity as a function of vertical and radial position | m s−1 |
| uB | rise velocity of the bubble | m s−1 |
| V | volumetric flow rate | m3 s−1 |
| VB | bubble volume | mm3 |
| We | Weber number | |
| Z | distance from the leading edge of the tube | m |
| z | vertical position | m |
| α | angle of bubble inclination | rad |
| δ∗ | boundary layer displacement thickness | m |
| δ1% | boundary layer thickness | m |
| μ | liquid viscosity | Pa s |
| ρ | liquid density | kg m−3 |
| σ | surface tension | mN m−1 |
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- Original Paper
- Bioremediation of PCB-contaminated sediments and evaluation of their pre- and post-treatment ecotoxicity
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- UV light-assisted mineralisation and biodetoxification of Ponceau S with hydroxyl and sulfate radicals
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- Measuring free ellagic acid: influence of extraction conditions on recovery by studying solubility and UV-Visible spectra
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- TG-DTA-FTIR analysis and isoconversional reaction profiles for thermal and thermo-oxidative degradation processes in black chokeberry (Aroniamelanocarpa)
- Original Paper
- Flow field in a downward diverging channel and its application
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