When a tube, sealed at one end and open to a quiescent environment at the other, is rotated about its axis, fluid flows from the open end along the axis towards the sealed end and returns in an annular boundary layer on the cylindrical wall. This paper describes the first known study to be made of this self-induced flow. Numerical solutions of the Navier–Stokes equations are shown to be in mainly good agreement with experimental results obtained using flow visualization and laser–Doppler anemometry in a rotating glass tube.
The self-induced flow in the tube can be described in terms of the length-to-radius ratio, G, and the Ekman number, E. However, for large values of G (G [ges ] 20), the flow outside the boundary layer on the endwall of the tube can be characterized by a single, modified, Ekman number, E*, where E* = GE. Although most of the fluid entering the open end of the tube is entrained into the annular (Stewartson-type) boundary layer, for small values of E* (E* < 0.2) some flow reaches the sealed end. For this so-called 'short-tube case’, the flow in the boundary layer on the endwall is shown to be similar to that associated with a disk rotating in a quiescent environment: the free disk. The self-induced flow for the short-tube case is believed to be responsible for the ’ hot-poker effect’ used, on some jet engines, to provide ice protection for the nose bullet.