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

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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Axisymmetric vortex breakdown Part 1. Confined swirling flow

Journal of Fluid Mechanics ◽

10.1017/s0022112090003664 ◽

1990 ◽

Vol 221 ◽

pp. 533-552 ◽

Cited By ~ 213

Author(s):

J. M. Lopez

Keyword(s):

Oscillatory Flow ◽

Stokes Equations ◽

Vortex Breakdown ◽

Swirling Flow ◽

Swirling Flows ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Axisymmetric Vortex ◽

Recirculation Zones ◽

Visualization Experiments

A comparison between the experimental visualization and numerical simulations of the occurrence of vortex breakdown in laminar swirling flows produced by a rotating endwall is presented. The experimental visualizations of Escudier (1984) were the first to detect the presence of multiple recirculation zones and the numerical model presented here, consisting of a numerical solution of the unsteady axisymmetric Navier-Stokes equations, faithfully reproduces these phenomena and all other observed characteristics of the flow. Further, the numerical calculations elucidate the onset of oscillatory flow, an aspect of the flow that was not clearly resolved by the flow visualization experiments. Part 2 of the paper examines the underlying physics of these vortex flows.

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

Journal of Fluid Mechanics ◽

10.1017/s0022112097005272 ◽

1997 ◽

Vol 340 ◽

pp. 177-223 ◽

Cited By ~ 142

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.

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Nonlinear Control of Axisymmetric Swirling Flows in a Long Finite-Length Pipe

Journal of Fluids Engineering ◽

10.1115/1.4031255 ◽

2015 ◽

Vol 138 (2) ◽

Cited By ~ 1

Author(s):

Lei Xu ◽

Zvi Rusak ◽

Shixiao Wang ◽

Steve Taylor

Keyword(s):

Reynolds Number ◽

Feedback Control ◽

High Reynolds Number ◽

Vortex Breakdown ◽

Basin Of Attraction ◽

Swirling Flows ◽

Active Feedback ◽

Active Feedback Control ◽

High Reynolds ◽

Control Methodology

Feedback stabilization of inviscid and high Reynolds number, axisymmetric, swirling flows in a long finite-length circular pipe using active variations of pipe geometry as a function of the evolving inlet radial velocity is studied. The complicated dynamics of the natural flow requires that any theoretical model that attempts to control vortex stability must include the essential nonlinear dynamics of the perturbation modes. In addition, the control methodology must establish a stable desired state with a wide basin of attraction. The present approach is built on a weakly nonlinear model problem for the analysis of perturbation dynamics on near-critical swirling flows in a slightly area-varying, long, circular pipe with unsteady changes of wall geometry. In the natural case with no control, flows with incoming swirl ratio above a critical level are unstable and rapidly evolve to either vortex breakdown states or accelerated flow states. Following an integration of the model equation, a perturbation kinetic-energy identity is derived, and an active feedback control methodology to suppress perturbations from a desired columnar state is proposed. The stabilization of both inviscid and high-Re flows is demonstrated for a wide range of swirl ratios above the critical swirl for vortex breakdown and for large-amplitude initial perturbations. The control gain for the fastest decay of perturbations is found to be a function of the swirl level. Large gain values are required at near-critical swirl ratios while lower gains provide a successful control at swirl levels away from critical. This feedback control technique cuts the feed-forward mechanism between the inlet radial velocity and the growth of perturbation's kinetic energy in the bulk and thereby enforces the decay of perturbations and eliminates the natural explosive evolution of the vortex breakdown process. The application of this proposed robust active feedback control method establishes a branch of columnar states with a wide basin of attraction for swirl ratios up to at least 50% above the critical swirl. This study provides guidelines for future flow control simulations and experiments. However, the present methodology is limited to the control of high-Reynolds number (nearly inviscid), axisymmetric, weakly nonparallel flows in long pipes.

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Anisotropic Characteristics of Turbulence Dissipation in Swirling Flow: A Direct Numerical Simulation Study

Advances in Mathematical Physics ◽

10.1155/2015/657620 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Xingtuan Yang ◽

Nan Gui ◽

Gongnan Xie ◽

Jie Yan ◽

Jiyuan Tu ◽

...

Keyword(s):

Numerical Simulation ◽

Energy Dissipation ◽

Direct Numerical Simulation ◽

Large Scale ◽

Isotropic Turbulence ◽

Vortex Breakdown ◽

Swirling Flow ◽

Turbulent Energy ◽

Swirling Flows ◽

Small Scale

This study investigates the anisotropic characteristics of turbulent energy dissipation rate in a rotating jet flow via direct numerical simulation. The turbulent energy dissipation tensor, including its eigenvalues in the swirling flows with different rotating velocities, is analyzed to investigate the anisotropic characteristics of turbulence and dissipation. In addition, the probability density function of the eigenvalues of turbulence dissipation tensor is presented. The isotropic subrange of PDF always exists in swirling flows relevant to small-scale vortex structure. Thus, with remarkable large-scale vortex breakdown, the isotropic subrange of PDF is reduced in strongly swirling flows, and anisotropic energy dissipation is proven to exist in the core region of the vortex breakdown. More specifically, strong anisotropic turbulence dissipation occurs concentratively in the vortex breakdown region, whereas nearly isotropic turbulence dissipation occurs dispersively in the peripheral region of the strong swirling flows.

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Numerical Simulation of Confined Swirling Flows of Oldroyd Fluids

Volume 1: Symposia, Parts A, B and C ◽

10.1115/fedsm2009-78340 ◽

2009 ◽

Author(s):

Sahand Majidi ◽

Ashkan Javadzadegan

Keyword(s):

Numerical Simulation ◽

Vortex Breakdown ◽

Swirling Flow ◽

Maxwell Model ◽

Reynolds Numbers ◽

Weissenberg Number ◽

Swirling Flows ◽

Breakdown Phenomenon ◽

Volume Method ◽

Upper Convected Maxwell Model

The effect of a fluid’s elasticity has been investigated on the vortex breakdown phenomenon in confined swirling flow. Assuming that the fluid obeys upper-convected Maxwell model as its constitutive equation, the finite volume method together with a collocated mesh was used to calculate the velocity profiles and streamline pattern inside a typical lid-driven swirling flow at different Reynolds and Weissenberg numbers. The flow was to be steady and axisymmetric. Based on the results obtained in this work, it can be concluded that fluid’s elasticity has a strong effect on the secondary flow completely reversing its direction of rotation depending on the Weissenberg number. Even in swirling flows with low ratio of elasticity to inertia, vortex breakdown is postponed to higher Reynolds numbers. Also, the effect of retardation ratio on the flow structure of viscoelastic fluid with the Weissenberg number being constant was surveyed. Based on our results, by decreasing the retardation ratio the flow becomes Newtonian like.

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Application of Laser Velocimetry for Characterization of Confined Swirling Flow

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.3240225 ◽

1989 ◽

Vol 111 (1) ◽

pp. 36-45 ◽

Cited By ~ 29

Author(s):

A. S. Nejad ◽

S. P. Vanka ◽

S. C. Favaloro ◽

M. Samimy ◽

C. Langenfeld

Keyword(s):

Vortex Breakdown ◽

Swirling Flow ◽

Swirling Flows ◽

Interarrival Time ◽

Mean Flow ◽

Third Order ◽

Cold Flow ◽

Large Samples ◽

Turbulence Data

A two-component LDV was used in a cold flow dump combustor model to obtain detailed mean and turbulence data for both swirling and nonswirling inlet flows. Large samples were collected to resolve the second and third-order products of turbulent fluctuations with good accuracy. Particle interarrival time weighting was used to remove velocity bias from the data. The swirling flows, with and without vortex breakdown, exhibited significantly different mean flow and turbulent field behavior. A numerical scheme with the k–ε closure model was used to predict the flow fields. Comparison of the numerical and experimental results showed that the k–ε turbulence model is inadequate in representing the complex turbulent structure of confined swirling flows.

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Dual vortex breakdown in a two-fluid whirlpool

Scientific Reports ◽

10.1038/s41598-021-02514-6 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Sergey G. Skripkin ◽

Bulat R. Sharifullin ◽

Igor V. Naumov ◽

Vladimir N. Shtern

Keyword(s):

Vortex Breakdown ◽

Swirling Flow ◽

Immiscible Fluids ◽

Swirling Flows ◽

Disk Drives ◽

Circulation Cell ◽

Lower Fluid ◽

Culture Growth ◽

Rotation Strength ◽

Two Fluid

AbstractLooking for an optimal flow shape for culture growth in vortex bioreactors, an intriguing and impressive structure has been observed that mimics the strong swirling flows in the atmosphere (tornado) and ocean (waterspout). To better understand the flow nature and topology, this experimental study explores the development of vortex breakdown (VB) in a lab-scale swirling flow of two immiscible fluids filling a vertical cylindrical container. The rotating bottom disk drives the circulation of both fluids while the sidewall is stationary. The container can be either sealed with the still top disk (SC) or open (OC). As the rotation strength (Re) increases, a new circulation cell occurs in each fluid—the dual VB. In case SC, VB first emerges in the lower fluid at Re = 475 and then in the upper fluid at Re = 746. In case OC, VB first emerges in the upper fluid at Re = 524 and then in the lower fluid at Re = 538. The flow remains steady and axisymmetric with the interface and the free surface being just slightly deformed in the studied range of Re. Such two-VB swirling flows can provide efficient mixing in aerial or two-fluid bioreactors.

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Asymmetric Swirling Flows in Turbomachine Annuli

Journal of Engineering for Power ◽

10.1115/1.3446410 ◽

1978 ◽

Vol 100 (4) ◽

pp. 618-629 ◽

Cited By ~ 18

Author(s):

E. M. Greitzer ◽

T. Strand

Keyword(s):

Experimental Investigation ◽

Swirling Flow ◽

Three Dimensional ◽

Swirling Flows ◽

Experimental Measurements ◽

Strongly Coupled ◽

Flow Disturbances ◽

Different Types ◽

Theoretical Predictions ◽

Good Agreement

An analytical and experimental investigation of asymmetric annular swirling flows is presented. It is shown that, in contrast to the situation in nonswirling flow, the different types of flow disturbances (pressure and vorticity) are not separable in a swirling flow but are strongly coupled. The flows that occur due to this coupling are inherently three-dimensional and exhibit new features not seen in the nonswirling case. The theoretical predictions are in good agreement with experimental measurements carried out in an annular swirl rig.

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