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A global stability approach to wake and path instabilities of nearly oblate spheroidal rising bubbles

Cano-Lozano, José Carlos and Tchoufag, Joël and Magnaudet, Jacques and Martínez-Bazán, Carlos A global stability approach to wake and path instabilities of nearly oblate spheroidal rising bubbles. (2016) Physics of Fluids, 28 (1). 014102. ISSN 1070-6631

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Official URL: http://dx.doi.org/10.1063/1.4939703

Abstract

A global Linear Stability Analysis (LSA) of the three-dimensional flow past a nearly oblate spheroidal gas bubble rising in still liquid is carried out, considering the actual bubble shape and terminal velocity obtained for various sets of Galilei (Ga) and Bond (Bo) numbers in axisymmetric numerical simulations. Hence, this study extends the stability analysis approach of Tchoufag et al. [“Linear stability and sensitivity of the flow past a fixed oblate spheroidal bubble,” Phys. Fluids 25, 054108 (2013) and “Linear instability of the path of a freely rising spheroidal bubble,” J. Fluid Mech. 751, R4 (2014)] (which considered perfectly spheroidal bubbles with an arbitrary aspect ratio) to the case of bubbles with a realistic fore-aft asymmetric shape (i.e., a flatter front and a more rounded rear). The critical curve separating stable and unstable regimes for the straight vertical path is obtained both in the (Ga,Bo) and the (Re,χ) planes, where Re is the bubble Reynolds number and χ its aspect ratio (i.e., the major-to-minor axes length ratio). This provides new insight into the effect of the shape asymmetry on the wake instability of bubbles held fixed in a uniform stream and on the path instability of freely rising bubbles, respectively. For the range of Ga and Bo explored here, we find that the flow past a bubble with a realistic shape is generally more stable than that past a perfectly spheroidal bubble with the same aspect ratio. This study also provides the first critical curve for the onset of path instability that can be compared with experimental observations. The tendencies revealed by this critical curve agree well with those displayed by available data. The quantitative agreement is excellent for O(1) Bond numbers. However, owing to two simplifying assumptions used in the LSA scheme, namely, the steadiness of the base state and the uncoupling between the bubble shape and the flow disturbances, quantitative discrepancies (up to 20%–30%) with experimental threshold values of the Galilei number remain for both small and large Bond numbers.

Item Type:Article
Additional Information:Thanks to AIP Publishing. The definitive version is available at http://scitation.aip.org The original PDF of the article can be found at Physics of Fluids website : http://scitation.aip.org/content/aip/journal/pof2/28/1/10.1063/1.4939703
HAL Id:hal-01330745
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Universidad de Jaén - UJA (SPAIN)
Laboratory name:
Funders:
Ministerio de Economía y Competitividad - MINECO (Spain) - European Funds
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Deposited On:13 Jun 2016 06:36

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