Computational Investigation of Confined Turbulent Swirling Flows Exhibiting Vortex Breakdown

2009 ◽  
pp. 247-268
Author(s):  
A.C. Benim ◽  
A. Nahavandi ◽  
K.J. Syed
Keyword(s):  
Vortex Breakdown ◽  
Swirling Flows ◽  
Computational Investigation

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

2015 ◽  
Vol 138 (2) ◽  
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.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
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.

Vortex breakdown of compressible subsonic swirling flows in a finite-length straight circular pipe

2015 ◽  
Vol 781 ◽  
pp. 3-27 ◽  
Author(s):  
Zvi Rusak ◽  
Jung J. Choi ◽  
Nicholas Bourquard ◽  
Shixiao Wang
Keyword(s):  
Differential Equation ◽  
Mach Number ◽  
Finite Length ◽  
Compressible Flows ◽  
Vortex Breakdown ◽  
Nonlinear Partial Differential Equation ◽  
Swirling Flows ◽  
Circular Pipe ◽  
Flow Profile ◽  
Inlet Flow

A global analysis of steady states of inviscid compressible subsonic swirling flows in a finite-length straight circular pipe is developed. A nonlinear partial differential equation for the solution of the flow stream function is derived in terms of the inlet flow specific total enthalpy, specific entropy and circulation functions. The equation reflects the complicated thermo–physical interactions in the flows. Several types of solutions of the resulting nonlinear ordinary differential equation for the columnar case together with a flow force condition describe the outlet state of the flow in the pipe. These solutions are used to form the bifurcation diagram of steady compressible flows with swirl as the inlet swirl level is increased at a fixed inlet Mach number. The approach is applied to two profiles of inlet flows, solid-body rotation and the Lamb–Oseen vortex, both with a uniform axial velocity and temperature. The computed results provide for each inlet flow profile theoretical predictions of the critical swirl levels for the appearance of vortex breakdown states as a function of the inlet Mach number, suggesting that the results are robust for a variety of inlet swirling flows. The analysis sheds light on the dynamics of compressible flows with swirl and vortex breakdown, and shows the delay in the appearance of breakdown with increase of the inlet axial flow Mach number in the subsonic range of operation. The present theory is limited to axisymmetric dynamics of swirling 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.

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.

Inviscid swirling flows and vortex breakdown

1995 ◽  
Vol 449 (1935) ◽  
pp. 139-153 ◽  
Keyword(s):  
Vortex Breakdown ◽  
Axial Flow ◽  
Relative Magnitude ◽  
Swirling Flows ◽  
Flow State ◽  
Euler Flow ◽  
Flow Geometry ◽  
Euler Model ◽  
Parameter Measuring ◽  
The Relationship

The steady axisymmetric Euler flow of an inviscid incompressible swirling fluid is described exactly by the Squire–Long equation. This equation is studied numerically for the case of diverging flow to investigate the dependence of solutions on upstream, or inlet, and downstream, or outlet, boundary conditions and flow geometry. The work is performed with a view to understanding how the phenomenon of vortex breakdown occurs. It is shown that solutions fail to exist or, alternatively, that the axial flow ceases to be unidirectional, so that breakdown can be inferred, when a parameter measuring the relative magnitude of rotation and axial flow (the Squire number) exceeds critical values depending upon the geometry and inlet profiles. A ‘quasi-cylindrical’ simplification of the Squire–Long equation is compared with the more complete Euler model and shown to be able to account for most of the latter’s behaviour. The relationship is examined between ‘failure’ of the quasi-cylindrical model and the occurrence of a ‘critical’ flow state in which disturbances can stand in the flow.

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.

scholarly journals Computational Investigation of Turbulent Swirling Flows in Gas Turbine Combustors

2008 ◽  
Vol 1 (1) ◽  
pp. 1-9 ◽  
Author(s):  
A.C. Benim ◽  
M.P. Escudier ◽  
P.J. Stopford ◽  
E. Buchanan ◽  
K.J. Syed
Keyword(s):  
Gas Turbine ◽  
Swirling Flows ◽  
Computational Investigation ◽  
Gas Turbine Combustors
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