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This paper describes some experiments in swirling flows in a diverging cylindrical tube in which various types of vortex breakdowns were observed.In one set of experiments, the position of the breakdown, axial component of the velocity of the vortex core, swirl angle distribution ahead of the breakdown, and the pressure distribution along the tube were determined for various flow rates and for various values of circulation imparted to the fluid (water). Basically, three types of vortex breakdown were observed, viz. mild (double helix) breakdown, spiral breakdown (followed by turbulent mixing), and axisymmetric breakdown (followed by a thicker vortex core, then a spiral breakdown, and finally by turbulent mixing). The type and the location of the stationary breakdowns were found to be dependent, for the particular vortex tube used, upon the Reynolds and circulation numbers of the flow. In a spiral breakdown, the vortex core filament maintained the same sense of rotation as the upstream fluid elements. In an axisymmetric breakdown, the bubble included an inclined vortex-ring whose axis gyrated about the axis of the tube.In a second set of experiments, the response of the abrupt structural change along the axis of flow to gradual and abrupt changes in the upstream and downstream flow conditions was examined. The axisymmetric breakdown responded in a manner analogous to the hydraulic jump in open-channel flow before if reached a new stationary position along the axis of the tube.The observations reported and the evidence presented herein revealed that the axisymmetric breakdown is a finite transition between two sequent states of flow as proposed by Benjamin (1962, 1965, 1967) on theoretical grounds.

This paper presents the in-line force coefficients for circular cylinders in planar oscillatory flows of small amplitude. The results are compared with the theoretical predictions of Stokes (1851) and Wang (1968). For two-dimensional, attached- and laminar-flow conditions the data are, as expected, in good agreement with the Stokes–Wang analysis. The oscillatory viscous flow becomes unstable to axially periodic vortices above a critical Keulegan–Carpenter number K (K = Um T/D, Um = the maximum velocity in a cycle, T = the period of flow oscillation, and D = the diameter of the circular cylinder) for a given β (β = Re/K = D2/vT, Re = Um D/v, and v = the kinematic viscosity of fluid) as shown experimentally by Honji (1981) and theoretically by Hall (1984). The present investigation has shown that the Keulegan—Carpenter number at which the drag coefficient Cd deviates rather abruptly from the Stokes—Wang prediction nearly corresponds to the critical K at which the vortical instability occurs.

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