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

Rusak, Zvi; Granata, Joshua; Wang, Shixiao

doi:10.1017/jfm.2015.276

Cited by 10 publications

(4 citation statements)

References 42 publications

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“…The modes of the temporal-azimuthal Fourier series decomposition, extracted using frequency selection, are displayed as axial velocity isocontours to provide an overview of their structures in Figs. [13][14][15][16]. The juxtaposition of these structures with the cascade of the amplitude Fourier spectra (Fig.…”

Section: Temporal-azimuthal Fourier Series Modesmentioning

confidence: 99%

“…This interpretation was further validated by the global stability analysis of a nonparallel flow by solving the eigenvalue problem of the 3D linearized Navier-Stokes [9] equations around a base flow (see [10,11]). The vortex breakdown stemming from a Grabowski-Berger vortex in an open geometry has become a benchmark model for disturbance analysis (see [12,13]).…”

Section: Introductionmentioning

confidence: 99%

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Onset of chaos in helical vortex breakdown at low Reynolds number

2018

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The nonlinear dynamics of a swirling wake flow stemming from a Graboswksi-Berger vortex [Grabowski and Berger, J. Fluid Mech. 75, 525 (1976)] in a semi-infinite domain is addressed at low Reynolds numbers for a fixed swirl number S = 1.095, defined as the ratio between the characteristic tangential velocity and the centerline axial velocity. In this system, only pure hydrodynamic instabilities develop and interact through the quadratic nonlinearities of the Navier-Stokes equations. Such interactions lead to the onset of chaos at a Reynolds value of Re = 220. This chaotic state is reached by following a Ruelle-Takens-Newhouse scenario, which is initiated by a Hopf bifurcation (the spiral vortex breakdown) as the Reynolds number increases. At larger Reynolds value, a frequency synchronization regime appears followed by a chaotic state again. This scenario is corroborated by nonlinear time series analyses. Stability analysis around the time-average flow and temporal-azimuthal Fourier decomposition of the nonlinear flow distributions both identify successfully the developing vortices and provide deeper insight into the development of the flow patterns leading to this route to chaos. Three single-helical vortices are involved: the primary spiral associated with the spiral vortex breakdown, a downstream spiral, and a near-wake spiral. As the Reynolds number increases, the frequencies of these vortices become closer, increasing their interactions by nonlinearity to eventually generate a strong chaotic axisymmetric oscillation.

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Section: Temporal-azimuthal Fourier Series Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Onset of chaos in helical vortex breakdown at low Reynolds number

2018

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“…We also conducted numerical simulations of the flow dynamics based on (2.3), (2.4a) and (2.4b) and the assumed boundary conditions. These simulations are based on a modified code of Rusak et al (2012) and Rusak, Granata & Wang (2015), which includes the viscous terms and axial periodic boundary conditions. For the case of a base flow with β = 1 and 0 < α < 1, we used various initial conditions given by…”

Section: Solid-body Rotation Flow Between Two Coaxial Rotating Cylindersmentioning

confidence: 99%

Extension to nonlinear stability theory of the circular Couette flow

2016

Self Cite

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A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric finite-amplitude perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol'd energyCasimir function A rd of Wang (Phys. Fluids, vol. 2, 2009, 084104). A weighted kinetic energy of the perturbation, which has a form of A rd , the difference between the reduced Arnol'd function and its base flow value, is used as a Lyapunov function. We show that all the inviscid flow effects as well as all the viscous-dependent terms that are related to the flow boundaries vanish. The evolution of A rd depends only on the viscous effects of the perturbation's dynamics inside the flow domain. The requirement for the temporal decay of A rd leads to two novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric perturbations. The linearized version of these conditions for infinitesimally small perturbations recovers the recent linear stability results by Kloosterziel (J. Fluid Mech., vol. 652, 2010, pp. 171-193). By examining the nonlinear stability conditions, we establish a definite operational region of the viscous circular Couette flow that is independent of the fluid viscosity. In this region of operation, the flow is nonlinearly stable in response to perturbations of any size, provided that the initial total circulation function is above a minimum level determined by the operational conditions of the base flow. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (Ing.). When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the set-up of the rotating cylinders. Finally, we derive upper-bound estimates on the decay rate of finite-amplitude perturbations for the solid-body rotation flow between two coaxial rotating cylinders and for the circular Couette flow. We demonstrate via numerical simulations that the theoretical upper bound is relevant to the dynamics of various axisymmetric perturbations tested, where it is strictly obeyed. This present study provides new physical insights into a classical flow problem that was studied for many decades.

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“…Tănasă et al (2013) used a flow-feedback method with the water taken from downstream in the draft tube to keep the nominal discharge constant. Rusak, Granata, and Wang (2015) studied a flow injection distributed along a finite-length straight circular pipe wall to control the vortex breakdown process in incompressible axisymmetric swirling flows. They demonstrated that applying the proposed control method during flow evolution is successful in eliminating the breakdown states.…”

Section: Introductionmentioning

confidence: 99%

Active flow control of the vortex rope and pressure pulsations in a swirl generator

Javadi

Nilsson

2016

Engineering Applications of Computational Fluid Mechanics

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The vortex rope and pressure pulsations caused by a radial pressure gradient in the conical diffuser of a swirl generator is controlled using continuous slot jets with different momentum fluxes and angles injected from the runner crown. The swirl apparatus is designed to generate flows similar to those in the different operating conditions of a Francis turbine. The study is done with numerical modelling using the hybrid URANS-LES (Unsteady Reynolds-Averaged Navier-Stokes-Large Eddy Simulation) method with the rotor-stator interaction. The comprehensive studies of Javadi and Nilsson [Time-accurate numerical simulations of swirling flow with rotor-stator interaction. Flow, Turbulence and Combustion, Vol. 95,, and Javadi, Bosioc, Nilsson, Muntean and Susan-Resiga [Experimental and numerical investigation of the precessing helical vortex in a conical diffuser, with rotor-stator interaction. ASME Journal of Fluids Engineering, doi:10.1115/1.4033416] are considered as the bench mark, and the capabilities of the technique is studied in the present work with the validated numerical results presented in those studies. The pressure pulsations caused by the pressure gradient generated by the swirl, present at off-design conditions, are cumbersome for hydropower structures. The investigation shows that the pressure pulsation, velocity fluctuations and the size of the vortex rope decrease when the jet is injected from the runner crown. The flow rate of the jet is less than 3% of the flow rate of the swirl generator. The momentum flux, angle of injection of the jet and the position of the slot are important factors for the effectiveness of the flow control technique. ARTICLE HISTORY

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

Cited by 10 publications

References 42 publications

Onset of chaos in helical vortex breakdown at low Reynolds number

Onset of chaos in helical vortex breakdown at low Reynolds number

Extension to nonlinear stability theory of the circular Couette flow

Active flow control of the vortex rope and pressure pulsations in a swirl generator

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