Helical Breakdown Research Articles

Double helix vortex breakdown in a turbulent swirling annular jet flow

Double helical vortex breakdown is rarely observed in experiments and is mostly reported for laminar flows. A double helical breakdown structure in a turbulent annular jet is identified and its dynamics analyzed based on time-resolved tomographic particle image velocimetry measurements.

Obstacle-induced spiral vortex breakdown

An experimental investigation on vortex breakdown dynamics is performed. An adverse pressure gradient is created along the axis of a wing-tip vortex by introducing a sphere downstream of an elliptical hydrofoil. The instrumentation involves high-speed visualizations with air bubbles used as tracers and 2D Laser Doppler Velocimeter (LDV). Two key parameters are identified and varied to control the onset of vortex breakdown: the swirl number, defined as the maximum azimuthal velocity divided by the free-stream velocity, and the adverse pressure gradient. They were controlled through the incidence angle of the elliptical hydrofoil, the free-stream velocity and the sphere diameter. A single helical breakdown of the vortex was systematically observed over a wide range of experimental parameters. The helical breakdown coiled around the sphere in the direction opposite to the vortex but rotated along the vortex direction. We have observed that the location of vortex breakdown moved upstream as the swirl number or the sphere diameter was increased. LDV measurements were corrected using a reconstruction procedure taking into account the so-called vortex wandering and the size of the LDV measurement volume. This allows us to investigate the spatio-temporal linear stability properties of the flow and demonstrate that the flow transition from columnar to single helical shape is due to a transition from convective to absolute instability.

On the development of three-dimensional vortex breakdown in cylindrical regions

Three-dimensional and axisymmetric numerical simulations of the incompressible Navier-Stokes equations have been conducted to study the appearance and development of vortex breakdown in a family of columnar vortex flows in a straight pipe without wall friction. The numerical simulations show that the basic form of breakdown is axisymmetric, and a transition to helical breakdown modes is shown to be caused by a sufficiently large pocket of absolute instability inside the original axisymmetric “bubble” of recirculating flow. Depending on the values of the Reynolds and swirl parameters, two distinct unstable modes corresponding to azimuthal wave numbers n=+1 and n=+2 have been found to yield a helical or a double-helical breakdown mode, respectively. By means of a simple linear spatial stability analysis carried out in the sections of the pipe where the basic axisymmetric flow presents reverse flow, we have identified the frequencies and the dominant azimuthal wave numbers observed in the three-dimensional simulations.

Three-dimensional vortex breakdown in swirling jets and wakes: direct numerical simulation

Vortex breakdown of nominally axisymmetric, swirling incompressible flows with jet- and wake-like axial velocity distributions issuing into a semi-infinite domain is studied by means of direct numerical simulations. By selecting a two-parametric velocity profile for which the steady axisymmetric breakdown is well-studied (Grabowski & Berger 1976), issues are addressed regarding the role of three-dimensionality and unsteadiness with respect to the existence, mode selection, and internal structure of vortex breakdown, in terms of the two governing parameters and the Reynolds number. Low Reynolds numbers are found to yield flow fields lacking breakdown bubbles or helical breakdown modes even for high swirl. In contrast, highly swirling flows at large Reynolds numbers exhibit bubble, helical or double-helical breakdown modes, where the axisymmetric mode is promoted by a jet-like axial velocity profile, while a wake-like profile renders the flow helically unstable and ultimately yields non-axisymmetric breakdown modes. It is shown that a transition from super- to subcritical flow, as defined by Benjamin (1962), accurately predicts the parameter combination yielding breakdown, if applied locally to flows with supercritical inflow profiles. Thus the basic form of breakdown is axisymmetric, and a transition to helical breakdown modes is shown to be caused by a sufficiently large pocket of absolute instability in the wake of the bubble, giving rise to a self-excited global mode. Two distinct eigenfunctions corresponding to azimuthal wavenumbers have been found to yield a helical or double-helical breakdown mode, respectively. Here the minus sign represents the fact that the winding sense of the spiral is opposite to that of the flow.