Thermal effects on axisymmetric vortex breakdown in a spherical gap

1993 ◽  
Vol 5 (5) ◽  
pp. 1211-1223 ◽  
Author(s):  
A. Arkadyev ◽  
P. Bar‐Yoseph ◽  
A. Solan ◽  
K. G. Roesner
Keyword(s):  
Thermal Effects ◽  
Vortex Breakdown ◽  
Axisymmetric Vortex

Axisymmetric Vortex Breakdown in Rotating Fluid Within a Container

1982 ◽  
Vol 49 (4) ◽  
pp. 921-923 ◽  
Author(s):  
H. J. Lugt ◽  
H. J. Haussling
Keyword(s):  
Vortex Breakdown ◽  
Rotating Fluid ◽  
Axisymmetric Vortex

An active feedback flow control theory of the axisymmetric vortex breakdown process

2015 ◽  
Vol 774 ◽  
pp. 488-528 ◽  
Author(s):  
Zvi Rusak ◽  
Joshua Granata ◽  
Shixiao Wang
Keyword(s):  
Feedback Control ◽  
Control Theory ◽  
Radial Velocity ◽  
Flow Injection ◽  
Vortex Breakdown ◽  
Flow Dynamics ◽  
Control Law ◽  
Breakdown Process ◽  
Axisymmetric Vortex ◽  
Active Feedback

An active feedback flow control theory of the axisymmetric vortex breakdown process in incompressible swirling flows in a finite-length straight circular pipe is developed. Flow injection distributed along the pipe wall is used as the controller. The flow is subjected to non-periodic inlet and outlet conditions where the inlet profiles of the axial velocity, circumferential velocity and azimuthal vorticity are prescribed, along with no radial velocity at the outlet. A long-wave asymptotic analysis at near-critical swirl ratios, which involves a rescaling of the axial distance and time, results in a model problem for the dynamics and the nonlinear control of both inviscid and high-Reynolds-number ($\mathit{Re}$) flows. The approach provides the bifurcation diagram of steady states and the stability characteristics of these states. In addition, an energy analysis of the controlled flow dynamics suggests a feedback control law that relates the flow injection to the evolving maximum radial velocity at the inlet. Computed examples of the flow dynamics based on the full Euler and Navier–Stokes formulations at various swirl levels demonstrate the evolution to near-steady breakdown states when swirl is above a critical level that depends on $\mathit{Re}$. Moreover, applying the proposed feedback control law during flow evolution shows for the first time the successful and robust elimination of the breakdown states and flow stabilization on an almost columnar state for a wide range of swirl (up to at least 30 %) above critical. The feedback control cuts the natural feed-forward mechanism of the breakdown process. Specifically, in the case of high-$\mathit{Re}$ flows, the control approach establishes a branch of columnar states for all swirl levels studied, where in the natural flow dynamics no such states exist. The present theory is limited to the control of axisymmetric flows in pipes where the wall boundary layer is thin and attached and does not interact with the flow in the bulk.

The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown

1998 ◽  
Vol 366 ◽  
pp. 211-237 ◽  
Author(s):  
Z. RUSAK ◽  
S. WANG ◽  
C. H. WHITING
Keyword(s):  
Vortex Breakdown ◽  
Swirling Flow ◽  
Nonlinear Ordinary Differential Equation ◽  
Swirling Flows ◽  
Axisymmetric Vortex ◽  
Burgers Vortex ◽  
Theoretical Predictions ◽  
Necessary And Sufficient Criteria ◽  
High Reynolds ◽  
Necessary And Sufficient

The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown is studied through numerical computations. These unique simulations are guided by a recent rigorous theory on this subject presented by Wang & Rusak (1997a). Using the unsteady and axisymmetric Euler equations, the nonlinear dynamics of both small- and large-amplitude disturbances in a swirling flow are described and the transition to axisymmetric breakdown is demonstrated. The simulations clarify the relation between our linear stability analyses of swirling flows (Wang & Rusak 1996a, b) and the time-asymptotic behaviour of the flow as described by steady-state solutions of the problem presented in Wang & Rusak (1997a). The numerical calculations support the theoretical predictions and shed light on the mechanism leading to the breakdown process in swirling flows. It has also been demonstrated that the fundamental characteristics which lead to vortex instability and breakdown in high-Reynolds-number flows may be calculated from considerations of a single, reduced-order, nonlinear ordinary differential equation, representing a columnar flow problem. Necessary and sufficient criteria for the onset of vortex breakdown in a Burgers vortex are presented.

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