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Power spectral distributions of pseudo-turbulent bubbly flows
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10.1063/1.4800782
/content/aip/journal/pof2/25/4/10.1063/1.4800782
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4800782

Figures

Image of FIG. 1.
FIG. 1.

Terminal velocity of single bubbles as a function of equivalent diameter. The symbols denote experiments conducted in different liquids: (○), water; (⋄) water-glycerin 30%; (□) water-glycerin 50%. The filled and empty symbols refer to small and large bubbles, respectively. The lines show the predictions of Ref. for the three liquids used here: (–), Mo = 2.6 × 10; (- - -), Mo = 3.9 × 10; (-·- ·), Mo = 3.1 × 10.

Image of FIG. 2.
FIG. 2.

Optical fiber setup.

Image of FIG. 3.
FIG. 3.

Bubble collision sequence with both hot-film probe and optical fiber tip. For clarity, in these images the optical probes are shown in the side of the hot-film sensor.

Image of FIG. 4.
FIG. 4.

Effect of the signal length on the shape of the PSD. The signal length, , is defined by the number of data points of the total sample, acquired at 15 000 samples per second. Each line represents the average power spectral distribution obtained for different values of .

Image of FIG. 5.
FIG. 5.

(a) Power spectral density: Spectral distribution obtained with and without length validation criteria, thick and thin lines, respectively. (b) Power decay: Rate of decay of the PSD, , as a function of frequency with and without length validation criteria, thick and thin lines respectively. The horizontal lines show the classical −3 (dashed line) and −5/3 (dashed-dotted line) values of . For the case shown here = 4.7, α = 5%, = 342, and = 3.2.

Image of FIG. 6.
FIG. 6.

Typical mono-dispersed bubbly flows. Images obtained for different liquids for a gas volume fraction of α = 0.02. The top and bottom rows show images obtained for the small and large capillary array, respectively. Water, (a) and (d); water-glycerin (70-30), (b) and (e); water-glycerin (50-50), (c) and (f). The size of each image is approximately 5 × 5 cm.

Image of FIG. 7.
FIG. 7.

Normalized bubble velocity as a function of gas volume fraction, for monodisperse flows. The symbols denote experiments conducted in different liquids: (○), water; (⋄) water-glycerin 30%; (□) water-glycerin 50%. The filled and empty symbols refer to small and large bubbles, respectively. The dashed and dashed-dotted lines represents the fits from Eqs. (6) and (7) , respectively; the thick and thin lines show the fits for the highest ( = 0.49 and = 0.1) and smallest Reynolds number experiments ( = 0.25 and = 0.15), respectively. For clarity, only one set of data shows typical error bars.

Image of FIG. 8.
FIG. 8.

Normalized liquid velocity variance as a function of gas volume fraction, α. All symbols are the same as in Fig. 7 . The (+) and (×) symbols show experiments from Martinez-Mercado , for which (Re,We) are (500,1.7) and (200,2.0), respectively. The lines show trends of the form ∼ α: continuous line, = 0.4; and dashed line, = 1.0. For clarity, only the ( )-data show error bars.

Image of FIG. 9.
FIG. 9.

Variation of PSD with gas volume fraction. (a) Power spectral density: spectral distribution; (b) power decay: rate of decay of the PSD, as a function of frequency. The horizontal lines show the classical −3 (dashed line) and −5/3 (dashed-dotted line) values of . The liquid used in this case was the 70-30 water-glycerin solution; the bubble size is ≈ 3.4 mm.

Image of FIG. 10.
FIG. 10.

Variation of PSD with liquid viscosity and bubble diameter. (a) Power spectral density: spectral distribution; (b) power decay: rate of decay of the PSD, . The horizontal lines show the classical −3 (dashed line) and −5/3 (dashed-dotted line) values of . A gas volume fraction of α = 0.02 was used for all the cases.

Image of FIG. 11.
FIG. 11.

PDF of liquid velocity for all cases tested here. The black, blue and red lines show the results for water, W-G 70-30 and W-G 50-50 mixtures, respectively. The continuous and dashed lines show the results for small and large bubbles, respectively. (a) PSD and (b) power decay. The green thick line show a typical result from Ref. .

Image of FIG. 12.
FIG. 12.

Normalized PDF of liquid velocity for all cases tested here. The black, blue, and red lines show the results for water, W-G 70-30 and W-G 50-50 mixtures, respectively. The continuous and dashed lines show the results for small and large bubbles, respectively. (a) and (b) show normalization proposed by Ref. (Eqs. (12) and (13)) and that proposed here (Eqs. (14) and (15) ).

Tables

Generic image for table
Table I.

Physical properties of the test liquids: water and water-glycerin (W-G) mixtures. Morton number: Mo = μ/ρσ.

Generic image for table
Table II.

Experimental results for isolated bubbles. For each liquid, two bubbles sizes were produced (two capillary sizes). The letters “O” and “S” correspond to the type of trajectory observed for each bubble, oscillating or straight, respectively. The Reynolds and Weber numbers are defined as Re = ρ /μ, We = , respectively. The superscript “0” refers to isolated bubble conditions.

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/content/aip/journal/pof2/25/4/10.1063/1.4800782
2013-04-16
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Power spectral distributions of pseudo-turbulent bubbly flows
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4800782
10.1063/1.4800782
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