zbMATH — the first resource for mathematics

Drag reduction by axisymmetric traveling wavy wall. (English) Zbl 1099.76506
Summary: This paper extends the previous two-dimensional analytical theory of the inviscid periodic separated flow over an infinitely long traveling wavy wall to axisymmetric flow, which serves as a theoretical guidance to the study on active drag-reduction flow control by flexible wall with traveling waves. Physically, at a special critical wave speed the flow may have a naturally periodical separated-reattached pattern, with each wave trough capturing a stable vortex ring. This row of vortex rings forms a “fluid roller bearing” over the wall, which separates the near-wall layer from the external main stream such that the former only has a weak periodic shearing. In this state the total drag of the columnar body due to both pressure and skin friction will tend to vanish. This paper establishes an inviscid theoretical model to mimic this flow physics by using two rows of staggered vortex rings. The theory confirms the unique existence of the critical wave speed and can be used to select the wave pattern of the flexible wall as well as the value of the critical wave speed. It is found that, as the radius of the columnar body approaches infinity, the asymptotic critical wave speed does not equal the two-dimensional value for the same amplitude.
76B75 Flow control and optimization for incompressible inviscid fluids
76B47 Vortex flows for incompressible inviscid fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)