Journal Article10.1017/S0022112095000462
On the identification of a vortex
Jinhee Jeong,Fazle Hussain +1 more
TL;DR: In this article, the authors propose a definition of vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor, which captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers.
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Abstract: Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor ${\bm {\cal S}}^2 + {\bm \Omega}^2$ are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ${\bm \Delta}{\bm u}$. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier–Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of ${\bm \Delta}{\bm u}$ or the complex eigenvalues of ${\bm \Delta}{\bm u}$, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.
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Citations
Optimal Taylor–Couette flow: direct numerical simulations
TL;DR: In this article, the authors numerically simulate turbulent Taylor-Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh-Benard flow.
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2D Numerical Simulations of Blade-Vortex Interaction in a Darrieus Turbine
TL;DR: In this paper, the authors provide a detailed two-dimensional numerical analysis of the physical phenomena occurring during dynamic stall of a Darrieus wind turbine, which is particularly complex because as the turbine rotates, the incidence angle and the blade Reynolds number vary, causing unsteady effects in the flow field.
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2D Numerical Simulations of Blade-Vortex Interaction in a
Thierry Maître,Christian Pellone +1 more
- 01 Jan 2009
Abstract: The aim of this work is to provide a detailed two-dimensional numerical analysis of the physical phenomena occurring during dynamic stall of a Darrieus wind turbine. The flow is particularly complex because as the turbine rotates, the incidence angle and the blade Reynolds number vary, causing unsteady effects in the flow field. At low tip speed ratio, a deep dynamic stall occurs on blades, leading to large hysteresis lift and drag loops (primary effects). On the other hand, high tip speed ratio corresponds to attached boundary layers on blades (secondary effects). The optimal efficiency occurs in the middle range of the tip speed ratio where primary and secondary effects cohabit. To prove the capacity of the modeling to handle the physics in the whole range of operating condition, it is chosen to consider two tip speed ratios (λ=2 and λ=7), the first in the primary effect region and the second in the secondary effect region. The numerical analysis is performed with an explicit, compressible RANS k-ω code TURBFLOW , in a multiblock structured mesh configuration. The time step and grid refinement sensitivities are examined. Results are compared qualitatively with the visualization of the vortex shedding of Brochier (1986, "Water channel experiments of dynamic stall on Darrieus wind turbine blades," J. Propul. Power, 2(5), pp. 445-449). Hysteresis lift and drag curves are compared with the data of Laneville and Vitecoq (1986, "Dynamic stall: the case of the vertical axis wind turbine," Prog. Aerosp. Sci., 32, pp. 523-573).
118
Comparative study of turbulent mixing in jet in cross-flow configurations using LES
TL;DR: In this paper, the authors used the large eddy simulation (LES) methodology to investigate how turbulent mixing can be enhanced by varying the angle between the jet and the oncoming cross-flow.
118
Surface techniques for vortex visualization
Christoph Garth,Xavier Tricoche,Tobias Salzbrunn,Tom Bobach,Gerik Scheuermann +4 more
- 19 May 2004
TL;DR: An improved method for stream surface computation that delivers accurate results in regions of intricate flow is presented, along with a novel method to determine boundary surfaces of vortex cores.
118
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