Note on the Motion Inside a Region of Recirculation (Cavity Flow)

Abstract

It is shown that the flow in a region of recirculation may be divided into a core, in which the vorticity may be constant, and a boundary layer surrounding the core. An approximate solution is given for the flow inside a circular cylinder with partly fixed and partly moving walls. Flow patterns which include regions of recirculation occur frequently, for example, behind bluff bodies, in sharp bends, and in sudden expansions in ducts. Little is known about this type of flow, which will be referred to, for brevity, as ‘cavity’ flow. It used to be thought that the velocities in the ‘ cavity ’ were small compared with the stream velocity, but it is now known that the maximum velocity in the cavity may be about 30 per cent. of the stream velocity. This implies that the motion within the cavity cannot be neglected.