Direct numerical simulation and stability analyses of three-dimensional swirling jets and wakes exhibiting vortex breakdown

Vortex breakdown of nominally axisymmetric, swirling incompressible jets and wakes issuing into a semi-infinite domain is studied by means of direct numerical simulations, as well as local and global linear stability analyses. From the point of view of specifying conditions at the open boundaries, this class of flows is particularly challenging due to its ability to support traveling waves. Several boundary conditions, ranging from free-slip and various homogeneous Neumann conditions to radiation conditions, are implemented in a staggered grid, finite difference algorithm that solves the unsteady Navier-Stokes equations in cylindrical coordinates by means of a fractional step method. Their advantages and shortcomings are evaluated in detail, and the question of the proper implementation of intermediate step boundary conditions is addressed. The data obtained from a large variety of test simulations points to the radiation condition as the most suitable lateral and outflow boundary condition for both high and low entrainment jets and wakes.; A two-parameterc low entrainment velocity profile for which the steady, axisymmetric breakdown is well studied is selected for further investigation. Hence, issues regarding the role of three-dimensionality and unsteadiness with respect to the existence, mode selection, and internal structure of vortex breakdown can be addressed 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, accurately predicts the parameter combination yielding breakdown, if applied locally to flows with supercritical inflow profiles.; Thus the basic form of breakdown is axisymmetric. 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. A global linear instability analysis proves the existence of two distinct eigenfunctions corresponding to an azimuthal wave number m = 1 and m = 2, yielding helical or double helical breakdown modes, respectively. Global growth rate, frequency and distinct structure of the eigenfunction in the wake of the axisymmetric breakdown bubble for the helical, and double helical breakdown mode has been validated by three-dimensional direct numerical simulations of the early stages of the mode selection.