Axisymmetric vortex breakdown. Part 3 Onset of periodic flow and chaotic advection

Lopez, Juan M.; Perry, Anna-Kristina

doi:10.1017/s0022112092000867

Cited by 129 publications

(103 citation statements)

References 15 publications

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“…At the center of this plane is the stagnation point below the lower bubble, and its local topological property corresponds to the eigensystem of the stagnation point as shown in Eqs. (12) and (13). The repelling limit cycle extremely approaches to the center axis, and, finally, the limit cycle disappears as shown in Fig.…”

Section: The Cross Flows Normal To the Rotating Axismentioning

confidence: 85%

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Numerical Study on Detailed Structure of Vortex Breakdown Behaviour for Landing of Spaceplane

Yamada

Suzuki

2016

AEROSPACE TECHNOLOGY JAPAN

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To understand the fundamental features of the vortex breakdown phenomena, which may significantly affect the aerodynamic characteristics of a spaceplane having a delta wing flying at high-angles of attack in a low-speed regime, the numerical analyses have been conducted by solving the incompressible Navier-Stokes equations. For simplicity of analysis, the axisymmetric flow around the vortex axis was assumed. To clarify the complicated flowfield structure of the vortex breakdown, the mathematical theory of the dynamical system has been applied to the analysis of the three-dimensional vector field of the flow velocity. The presence of the fixed points and their topological types are successfully identified by analyzing the eigensystem of the local velocity gradient tensor numerically. The topological properties of the streamlines are also clarified by considering the variation of the two-dimensional crossflow pattern with respect to the location on the vortex axis. The appearance of the limit cycle on the crossflow plane has been mathematically explained in relation to the onset of the vortex breakdown.

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Section: The Cross Flows Normal To the Rotating Axismentioning

confidence: 85%

“…2, and gathering attention. Lopez and Perry 13) mapped the flow in the (r, z)-plane and elucidated the unsteady regime above dashed line in Fig. 1 from the viewpoint of Hamiltonian dynamical system.…”

Section: )mentioning

confidence: 99%

Numerical Study on Detailed Structure of Vortex Breakdown Behaviour for Landing of Spaceplane

Yamada

Suzuki

2016

AEROSPACE TECHNOLOGY JAPAN

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“…3͑b͒, however, is the recirculation bubble appearing around the cylinder axis, probably a reminiscence of the ͑much stronger͒ vortex breakdown effect known from the closed driven cavity. 1,3,25 See also Fig. 4, that shows the local velocity field in the bubble region.…”

Section: A Stationary Regimementioning

confidence: 99%

“…A common motivation among these experimental 1,2 and numerical simulations 3,4 is the suitability of the driven cavity as a model system to explore the routes to chaos and turbulence.…”

Section: Introductionmentioning

confidence: 99%

Early bifurcation in rotating fluid flow with free surface studied by axisymmetric numerical simulations

Santos

Sørensen

1996

Physics of Fluids

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Simulations of a fluid rotating inside a partially open cylindrical cavity, performed by numerical solution of the unsteady axisymmetric Navier-Stokes equations, are presented. The configuration consists of a cylindrical vessel holding the fluid, which is entrained into motion by a rotating lid. This one is a coaxial disk in contact with the fluid surface but without covering it entirely. The study focuses on the occurrence of time-dependent flow, more specifically, the first transition to unsteadiness, by considering cavity cases with different amounts of free surface, for a fixed aspect ratio. By following the time evolution of a few arbitrarily chosen dynamical variables as a function of the Reynolds number, the location of this first Hopf bifurcation is obtained for a collection of cavity cases. Results show a rather strong influence of the free surface both on the onset of the unsteadiness and on the dynamical features of the flow.

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“…Valentine and Jahnke [19] examined the flow field inside a cylindrical enclosure induced by the rotation of the top and bottom end walls with a fixed sidewall: a stable oscillatory solution was found for a Reynolds number Re = 3×10 3 and for aspect ratio γ = 1.5. A numerical study of the periodic flow for γ = 2.5 was conducted by Lopez and Perry [20]. They showed the existence of oscillatory modes.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Mixed Convection in Cylinrical Czochralski Configuration for Crystal Growth of Silicon

Atia¹,

Bouabdallah²,

Teggar³

et al. 2015

IJHT

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A numerical study of the mixed convection of liquid metal in Czochralski configuration for crystal growth was carried out. The finite volume method with SIMPLER Algorithm was used to solve the conservation equations of mass, momentum and energy. Due to computational constraints, the simulations were limited to axisymmetric geometries. The obtained results are compared to the experimental data of the literature. The effect of Richardson number on the flow structure and the thermal field has been presented and discussed for Ri = 0.1, 0.5, 1, 1.5 and 2. The effect of the aspect ratio of the cavity was also analysed. The results showed that increasing of Richardson number increases the velocity of the fluid in the cavity and reduces the rate of heat transfer. The aspect ratio had a significant effect on the velocity and thermal fields.

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Axisymmetric vortex breakdown. Part 3 Onset of periodic flow and chaotic advection

Cited by 129 publications

References 15 publications

Numerical Study on Detailed Structure of Vortex Breakdown Behaviour for Landing of Spaceplane

Numerical Study on Detailed Structure of Vortex Breakdown Behaviour for Landing of Spaceplane

Early bifurcation in rotating fluid flow with free surface studied by axisymmetric numerical simulations

Numerical Study of Mixed Convection in Cylinrical Czochralski Configuration for Crystal Growth of Silicon

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