Accurate numerical simulations of vortex flows. I: Vortex breakdown

2011 ◽  
Vol 41 (1) ◽  
pp. 103-109 ◽  
Author(s):  
W. Kollmann
Keyword(s):  
Numerical Simulations ◽  
Vortex Breakdown ◽  
Vortex Flows

Numerical simulations of oblique shock/vortex interactions resulting in vortex breakdown

1997 ◽  
Author(s):  
Ashish Nedungadi ◽  
Mark Lewis ◽  
Ashish Nedungadi ◽  
Mark Lewis
Keyword(s):  
Numerical Simulations ◽  
Vortex Breakdown ◽  
Oblique Shock ◽  
Vortex Interactions

scholarly journals A weakly nonlinear mechanism for mode selection in swirling jets

2012 ◽  
Vol 699 ◽  
pp. 216-262 ◽  
Author(s):  
Philippe Meliga ◽  
François Gallaire ◽  
Jean-Marc Chomaz
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Vortex Breakdown ◽  
Double Helix ◽  
Mode Selection ◽  
Direct Numerical Simulations ◽  
Swirling Jets ◽  
Graphic Mode ◽  
Stable Solutions ◽  
Single Helix

AbstractGlobal linear and nonlinear bifurcation analysis is used to revisit the spiral vortex breakdown of nominally axisymmetric swirling jets. For the parameters considered herein, stability analyses single out two unstable linear modes of azimuthal wavenumber $m= \ensuremath{-} 1$ and $m= \ensuremath{-} 2$, bifurcating from the axisymmetric breakdown solution. These modes are interpreted in terms of spiral perturbations wrapped around and behind the axisymmetric bubble, rotating in time in the same direction as the swirling flow but winding in space in the opposite direction. Issues are addressed regarding the role of these modes with respect to the existence, mode selection and internal structure of vortex breakdown, as assessed from the three-dimensional direct numerical simulations of Ruith et al. (J. Fluid Mech., vol. 486, 2003, pp. 331–378). The normal form describing the leading-order nonlinear interaction between modes is computed and analysed. It admits two stable solutions corresponding to pure single and double helices. At large swirl, the axisymmetric solution bifurcates to the double helix which remains the only stable solution. At low and moderate swirl, it bifurcates first to the single helix, and subsequently to the double helix through a series of subcritical bifurcations yielding hysteresis over a finite range of Reynolds numbers, the estimated bifurcation threshold being in good agreement with that observed in the direct numerical simulations. Evidence is provided that this selection is not to be ascribed to classical mean flow corrections induced by the existence of the unstable modes, but to a non-trivial competition between harmonics. Because the frequencies of the leading modes approach a strong $2$:$1$ resonance, an alternative normal form allowing interactions between the $m= \ensuremath{-} 2$ mode and the first harmonics of the $m= \ensuremath{-} 1$ mode is computed and analysed. It admits two stable solutions, the double helix already identified in the non-resonant case, and a single helix differing from that observed in the non-resonant case only by the presence of a slaved, phase-locked harmonic deformation. On behalf of the finite departure from the $2$:$1$ resonance, the amplitude of the slaved harmonic is however low, and the effect of the resonance on the bifurcation structure is merely limited to a reduction of the hysteresis range.

Swirling flow states in finite-length diverging or contracting circular pipes

2017 ◽  
Vol 819 ◽  
pp. 678-712 ◽  
Author(s):  
Zvi Rusak ◽  
Yuxin Zhang ◽  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Finite Length ◽  
Vortex Breakdown ◽  
Steady States ◽  
Inviscid Limit ◽  
Circular Pipes ◽  
Outlet Flow ◽  
Separation Zones ◽  
Steady State Solutions

The dynamics of inviscid-limit, incompressible and axisymmetric swirling flows in finite-length, diverging or contracting, long circular pipes is studied through global analysis techniques and numerical simulations. The inlet flow is described by the profiles of the circumferential and axial velocity together with a fixed azimuthal vorticity while the outlet flow is characterized by a state with zero radial velocity. A mathematical model that is based on the Squire–Long equation (SLE) is formulated to identify steady-state solutions of the problem with special conditions to describe states with separation zones. The problem is then reduced to the columnar (axially-independent) SLE, with centreline and wall conditions for the solution of the outlet flow streamfunction. The solution of the columnar SLE problem gives rise to the existence of four types of solutions. The SLE problem is then solved numerically using a special procedure to capture states with vortex-breakdown or wall-separation zones. Numerical simulations based on the unsteady vorticity circulation equations are also conducted and show correlation between time-asymptotic states and steady states according to the SLE and the columnar SLE problems. The simulations also shed light on the stability of the various steady states. The uniqueness of steady-state solutions in a certain range of swirl is proven analytically and demonstrated numerically. The computed results provide the bifurcation diagrams of steady states in terms of the incoming swirl ratio and size of pipe divergence or contraction. Critical swirls for the first appearance of the various types of states are identified. The results show that pipe divergence promotes the appearance of vortex-breakdown states at lower levels of the incoming swirl while pipe contraction delays the appearance of vortex breakdown to higher levels of swirl and promotes the formation of wall-separation states.

Instability of strongly nonlinear waves in vortex flows

1994 ◽  
Vol 269 ◽  
pp. 247-264 ◽  
Author(s):  
A. Kribus ◽  
S. Leibovich
Keyword(s):  
Linear Stability ◽  
Nonlinear Waves ◽  
Vortex Breakdown ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Vortex Flows ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Perturbation Problem ◽  
Bending Modes

Weakly nonlinear descriptions of axisymmetric cnoidal and solitary waves in vortices recently have been shown to have strongly nonlinear counterparts. The linear stability of these strongly nonlinear waves to three-dimensional perturbations is studied, motivated by the problem of vortex breakdown in open flows. The basic axisymmetric flow varies both radially and axially, and the linear stability problem is therefore nonseparable. To regularize the generalization of a critical layer, viscosity is introduced in the perturbation problem. In the absence of the waves, the vortex flows are linearly stable. As the amplitude of a wave constituting the basic flow increases owing to variation in the level of swirl, stability is first lost to non-axisymmetric ‘bending’ modes. This instability occurs when the wave amplitude exceeds a critical value, provided that the Reynolds number is larger enough. The critical wave amplitudes for instability typically are large, but not large enough to create regions of closed streamlines. Examination of the most-amplified eigenvectors shows that the perturbations tend to be concentrated downstream of the maximum streamline displacement in the wave, in a position consistent with the observed three-dimensional perturbations in the interior of a bubble type of vortex breakdown.

Wall-separation and vortex-breakdown zones in a solid-body rotation flow in a rotating finite-length straight circular pipe

2014 ◽  
Vol 759 ◽  
pp. 321-359 ◽  
Author(s):  
Zvi Rusak ◽  
Shixiao Wang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Solid Body ◽  
Finite Length ◽  
Vortex Breakdown ◽  
Swirling Flows ◽  
Flow Dynamics ◽  
Circular Pipe ◽  
Body Rotation ◽  
Solid Body Rotation

AbstractThe incompressible, inviscid and axisymmetric dynamics of perturbations on a solid-body rotation flow with a uniform axial velocity in a rotating, finite-length, straight, circular pipe are studied via global analysis techniques and numerical simulations. The investigation establishes the coexistence of both axisymmetric wall-separation and vortex-breakdown zones above a critical swirl level, ${\it\omega}_{1}$. We first describe the bifurcation diagram of steady-state solutions of the flow problem as a function of the swirl ratio ${\it\omega}$. We prove that the base columnar flow is a unique steady-state solution when ${\it\omega}$ is below ${\it\omega}_{1}$. This state is asymptotically stable and a global attractor of the flow dynamics. However, when ${\it\omega}>{\it\omega}_{1}$, we reveal, in addition to the base columnar flow, the coexistence of states that describe swirling flows around either centreline stagnant breakdown zones or wall quasi-stagnant zones, where both the axial and radial velocities vanish. We demonstrate that when ${\it\omega}>{\it\omega}_{1}$, the base columnar flow is a min–max point of an energy functional that governs the problem, while the swirling flows around the quasi-stagnant and stagnant zones are global and local minimizer states and become attractors of the flow dynamics. We also find additional min–max states that are transient attractors of the flow dynamics. Numerical simulations describe the evolution of perturbations on above-critical columnar states to either the breakdown or the wall-separation states. The growth of perturbations in both cases is composed of a linear stage of the evolution, with growth rates accurately predicted by the analysis of Wang & Rusak (Phys. Fluids, vol. 8, 1996a, pp. 1007–1016), followed by a stage of saturation to either one of the separation zone states. The wall-separation states have the same chance of appearing as that of vortex-breakdown states and there is no hysteresis loop between them. This is strikingly different from the dynamics of vortices with medium or narrow vortical core size in a pipe.

Significance of the Vortex Breakdown Phenomenon

1965 ◽  
Vol 87 (2) ◽  
pp. 518-522 ◽  
Author(s):  
T. B. Benjamin
Keyword(s):  
Vortex Breakdown ◽  
Swirling Flows ◽  
Longitudinal Vortex ◽  
Vortex Flows ◽  
Breakdown Phenomenon ◽  
Physical Principles

The essential points in the author’s published theory of this phenomenon are summarized, and their implications with regard to longitudinal vortex flows in general are reviewed. The primary aim is to emphasize the physical principles which underlie the theory, and most of the mathematical details are passed over here. It is proposed that these principles serve to rationalize a wide variety of possible behavior in swirling flows.

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