Review of recent studies on the axisymmetric vortex breakdown phenomenon

2000 ◽  
Author(s):  
Z. Rusak
Keyword(s):  
Vortex Breakdown ◽  
Axisymmetric Vortex ◽  
Breakdown Phenomenon

The dynamics of a swirling flow in a pipe and transition to axisymmetric vortex breakdown

1997 ◽  
Vol 340 ◽  
pp. 177-223 ◽  
Author(s):  
S. WANG ◽  
Z. RUSAK
Keyword(s):  
Steady State ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Theoretical Understanding ◽  
Axisymmetric Vortex ◽  
Constant Area ◽  
Breakdown Phenomenon ◽  
Length Constant ◽  
High Reynolds ◽  
The Stability

This paper provides a new study of the axisymmetric vortex breakdown phenomenon. Our approach is based on a thorough investigation of the axisymmetric unsteady Euler equations which describe the dynamics of a swirling flow in a finite-length constant-area pipe. We study the stability characteristics as well as the time-asymptotic behaviour of the flow as it relates to the steady-state solutions. The results are established through a rigorous mathematical analysis and provide a solid theoretical understanding of the dynamics of an axisymmetric swirling flow. The stability and steady-state analyses suggest a consistent explanation of the mechanism leading to the axisymmetric vortex breakdown phenomenon in high-Reynolds-number swirling flows in a pipe. It is an evolution from an initial columnar swirling flow to another relatively stable equilibrium state which represents a flow around a separation zone. This evolution is the result of the loss of stability of the base columnar state when the swirl ratio of the incoming flow is near or above the critical level.

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.

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