On the hydrodynamic interaction of two circular cylinders oscillating in a viscous fluid
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The present paper deals with the plane flow fields induced by two parallel circular cylinders with radiia andb oscillating in a direction which is i) parallel or ii) perpendicular to the plane containing their axes. The effect of the cylinders' hydrodynamic interaction on steady streaming has been studied analytically at high frequency by the method of matched asymptotic expansions.
It is found that ifa=b the steady streaming is directed symmetrically to the cylinders while whena≠b (in the case i)) the secondary steady flow is directed towards the larger cylinder and one of the outer steady vortices disappears.
It is shown in case i) that the drag force acting on each cylinder is smaller than the same force experienced on a single cylinder with the same radius which is placed in an unbounded oscillating flow. When the cylinder radii are equal, the drag is greater on the forward cylinder than on the rear one.
In contrast, in case ii), wherea=b, it is shown that the drag on each of the two cylinders is greater than the drag acting on a single cylinder with the same radius placed in an unbounded oscillating stream and also each of the cylinders experiences a repulsive force in a direction perpendicular to the oscillating flow.
KeywordsVortex Asymptotic Expansion Drag Force Circular Cylinder Steady Flow
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