The low Reynolds number deformation of a gas bubble in shear flow: a general approach via integral equations

1992 ◽  
Vol 9 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Henry Power
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Integral Equations ◽  
Low Reynolds Number ◽  
Gas Bubble ◽  
Low Reynolds

scholarly journals Low-Reynolds-number flow past cylindrical bodies of arbitrary cross-sectional shape

1986 ◽  
Vol 164 ◽  
pp. 401-427 ◽  
Author(s):  
S. H. Lee ◽  
L. G. Leal
Keyword(s):  
Reynolds Number ◽  
Integral Equations ◽  
Low Reynolds Number ◽  
Uniform Flow ◽  
Two Dimensions ◽  
Cross Sectional ◽  
General Solutions ◽  
Flow Past ◽  
Low Reynolds ◽  
Sectional Shape

A numerical implementation of the method of matched asymptotic expansions is proposed to analyse two-dimensional uniform streaming flow at low Reynolds number past a straight cylinder (or cylinders) of arbitrary cross-sectional shape. General solutions for both the Stokes and Oseen equations in two dimensions are expressed in terms of a boundary distribution of fundamental single- and double-layer singularities. These general solutions are then converted to integral equations for the unknown distributions of singularity strengths by application of boundary conditions at the cylinder surface, and matching conditions between the Stokes and Oseen solutions. By solving these integral equations, using collocation methods familiar from three-dimensional application of ‘boundary integral’ methods for solutions of Stokes equation, we generate a uniformly valid approximation to the solution for the whole domain.We demonstrate the method by considering, as numerical examples, uniform flow past an elliptic cylinder, uniform flow past a cylinder of rectangular cross-section, and uniform flow past two parallel cylinders which may be either equal in radius, or of different sizes.

Linear shear flow over a square cylinder at low Reynolds number

2005 ◽  
Vol 17 (7) ◽  
pp. 078103 ◽  
Author(s):  
M. Cheng ◽  
S. H. N. Tan ◽  
K. C. Hung
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Low Reynolds Number ◽  
Square Cylinder ◽  
Linear Shear ◽  
Low Reynolds
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