Geometric Inversion of two-dimensional Stokes flows - Application to the flow between parallel planes

Mustapha Hellou (1)

1 LGCGM - Laboratoire de Génie Civil et Génie Mécanique

Geometric inversion is applied to two-dimensional Stokes flow in the objective to find new Stokes flow solutions. The principle of this method and the relations between the reference and inverse fluid velocity fields are presented. They are followed by applications to the flow between two parallel plates induced by a rotating or a translating cylinder. Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are straightforward deduced. Typically fluid flow patterns around two circular cylinders in contact placed in the centre of a rotating or a translating circular cylinder are illustrated.

Mots clés: microflow; viscous eddies; flow around a cylinder; geometric inversion; Stokes flow; inversion transformation

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Mustapha Hellou. Geometric Inversion of two-dimensional Stokes flows - Application to the flow between parallel planes. Engineering, 2010, 2 (10), pp.780-787. ⟨10.4236/eng.2010.210100⟩. ⟨hal-00982489⟩