The structure of concentrated vortex cores

Hall, Maurice C.

doi:10.1016/0376-0421(66)90006-6

Cited by 98 publications

(38 citation statements)

References 22 publications

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“…6 For swirl ratios below a critical value of order unity, the jet remains slender, and can be therefore described with relative errors of order R j Ϫ2 with the boundary-layer, or quasi-cylindrical ͑QC͒ approximation. 7 The resulting set of parabolic equations is integrated numerically by marching downstream from the orifice, providing a description for the jet development region independent of R j . A smooth transition towards the far-field solution is observed only for swirl ratios below a critical value, SϭS c , for which the emergence of appreciable axial gradients precludes the convergence of the numerical scheme at a given downstream location.…”

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The quasi-cylindrical description of submerged laminar swirling jets

Revuelta

Sánchez

Liñán³

2004

Physics of Fluids

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The quasi-cylindrical approximation is used to describe numerically the structure of a submerged swirling jet for subcritical values of the swirl ratio SрS c . The emerging flow structure is affected by the swirling motion, which enhances the entrainment rate of the jet and induces an adverse pressure gradient that reduces its momentum flux. The effect is more pronounced as the swirl ratio S is increased, yielding for sufficiently large values of S a jet with an annular structure. The integration describes the smooth transition towards the far-field self-similar solution for all values of S smaller than a critical value SϭS c , at which the numerical integration fails to converge at a given downstream location. The comparisons with previous experimental results confirm the correspondence between the onset of vortex breakdown and the failure of the quasi-cylindrical approximation. © 2004 American Institute of Physics. ͓DOI: 10.1063/1.1645850͔ This Brief Communication investigates the submerged swirling jet that forms when an incompressible fluid of density and kinematic viscosity v discharges with both forward and swirling motion through a circular orifice of radius a into a stagnant region of the same fluid, a flow configuration recently studied experimentally by Billant et al. 1 The initial fluxes of momentum J and angular momentum L of the jet can be used to define the swirl ratio SϭL/(Ja) and the jet Reynolds number R j ϭ͓J/( )͔ 1/2 /v as the main parameters characterizing the flow structure. The description below corresponds to moderately large values of R j , for which the laminar jet remains steady, and to values of S of order unity, a distinguished regime that allows us to explore the effect of the swirl on the flow structure and the onset of vortex breakdown. [2][3][4][5] Near the orifice, the jet is separated from the outer stagnant fluid by an annular mixing layer that thickens downstream, so that the effect of viscosity starts reducing significantly the velocity at the axis at distances of the order of R j times the jet radius. The swirling motion causes the pressure near the axis to be smaller than the ambient value, which in turn induces an adverse axial pressure gradient that is largest at the axis. 3 For SϳO(1), the pressure differences induced are of the order of the dynamic pressure, so that the swirling motion results in a significant flow deceleration in the jet development region, additional to that associated with viscous stresses. The magnitude of the azimuthal flow velocity is seen to decay more rapidly that the axial velocity, so that in the far-field self-similar solution that arises at distances from the orifice much larger than R j a the pressure gradient induced no longer affects the forward motion at leading order. 6 For swirl ratios below a critical value of order unity, the jet remains slender, and can be therefore described with relative errors of order R j Ϫ2 with the boundary-layer, or quasi-cylindrical ͑QC͒ approximation. 7 The resulting set of parabolic equations is integrate...

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The quasi-cylindrical description of submerged laminar swirling jets

Revuelta

Sánchez

Liñán³

2004

Physics of Fluids

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“…(i) vortex breakdown is similar to the separation of a two-dimensional boundary layer (Hall [2,3], Mager [4]);…”

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confidence: 99%

Vortex breakdown incipience: Theoretical considerations

Berger

Erlebacher

1995

Physics of Fluids

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The sensitivity of the onset and the location of vortex breakdowns in concentrated vortex cores, and the pronounced tendency of the breakdowns to move upstream have been characteristic observations of experimental investigations; they have also been features of numerical simulations and led to questions about the validity of these simulations. This movement upstream may be a migration in time for fixed values of the relevant parameters, or the movement of the breakdown location closer to the entrance to the flow or computational domain with small changes in these parameters. This behavior seems to be inconsistent with the strong time-like axial evolution of the flow, as expressed explicitly, for example, by the quasicylindrical approximate equations for this flow. An order-of-magnitude analysis of the equations of motion near breakdown leads to a modified set of governing equations, analysis of which demonstrates that the interplay between radial inertial, pressure, and viscous forces gives an elliptic character to these concentrated swirling flows. Analytical, asymptotic, and numerical solutions of a simplified nonlinear equation are presented; these qualitatively exhibit the features of vortex onset and location noted above.

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“…The vortex breakdown causes both a loss in lift and an increased nose-up moment. Many experiments have been done by Werlé, 1) Hall, 2) Casssidy et al, 3) Sarpkaya, 4) Leibovich.…”

Section: Introductionmentioning

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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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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The structure of concentrated vortex cores

Cited by 98 publications

References 22 publications

The quasi-cylindrical description of submerged laminar swirling jets

The quasi-cylindrical description of submerged laminar swirling jets

Vortex breakdown incipience: Theoretical considerations

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

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