Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid

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Abstract

This paper numerical results are presented for the buoyancy-driven rise of a deformable bubble through an unbounded quiescent fluid. Complete solutions, including the bubble shape, are obtained for Reynolds numbers in the range 1 ≤ R ≤ 200 and for Weber numbers up to 20. For Reynolds numbers R ≤ 20 the shape of the bubble changes from nearly spherical to oblate-ellipsoidal to spherical-cap depending on Weber number; at higher Reynolds numbers ‘ disk-like ’ and‘saucer-like’ shapes appear at W = O(10). The present results show clearly that flow separation may occur at a smooth free surface at intermediate Reynolds numbers; this fact suggests a qualitative explanation of the often-observed irregular (zigzag or helical) paths of rising bubbles.

Original languageEnglish (US)
Pages (from-to)19-35
Number of pages17
JournalJournal of fluid Mechanics
Volume148
DOIs
StatePublished - Nov 1984

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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