Continuation or breakdown in tornado-like vortices

Burggraf, O. R.; Foster, M. R.

doi:10.1017/s0022112077002420

Cited by 80 publications

(50 citation statements)

References 13 publications

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“…Squire's form U,, K (P + a")-' (for constant a) which is an exact solution of the axisymmetric jet equations. Incidentally Foster & Smith (1988) note the relation between Long's vortex and the Squire profile (see also Burggraf & Foster 1977), while Batchelor & Gill (1962) suggest that the latter profile is neutrally stable for an azimuthal wavenumber of unity, a result verified in this work. As in Part 1 two streamwise scales operate: x-I,, = s3x1 and s6X with a corresponding fast time scale t = s6T.…”

Section: Introductionsupporting

confidence: 71%

On vortex/wave interactions. Part 2. Originating from axisymmetric flow with swirl

1996

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Following the study in Part 1 of cross-flow and other non-symmetric effects on vortex/wave interactions in boundary layers, the present Part 2 applies the ideas of Part 1 and related works to an incident axisymmetric flow supplemented by a small swirl or azimuthal velocity. This is with a view to possibly increasing understanding of vortex breakdown. The wave components involved are predominantly inviscid Rayleigh-like ones. The presence of the swirl leads to extra features and complications associated mainly with extra logarithmic contributions but for the dominant interactions essentially the same equations as in Part 1 are found. These dominant nonlinear interactions must be based on azimuthal wavenumbers of & 1 in the case of the Squire jet with swirl. In contrast to Part 1, which consisted mainly of an analysis of the quasi-bounded solutions, a representative set of numerical solutions of the full integro-differential amplitude equations is presented, for realistic axial and swirl velocity profiles. The work points also to the influence of further increases in the incident swirl.

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Section: Introductionsupporting

confidence: 71%

On vortex/wave interactions. Part 2. Originating from axisymmetric flow with swirl

1996

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“…For Long's problem Burggraf & Foster, [6] found such a term numerically, but here we will prove that this is a general feature of all conically self-similar free-vortex solutions to the Navier-Stokes equations. In [6] it was claimed on physical grounds that the second order contribution to the total axial momentum of their second order non-swirling correction term vanished. In the second half of this section we will prove that this claim is true for the extension of Long's problem suggested by Shtern & Hussain [18].…”

Section: On the Existence And Regularity Of A Second Order Non-swirlimentioning

confidence: 54%

“…The first of these conditions follows from (5), (6) and (2), but the second one requires in addition that…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…For this term it is also shown that the second order contribution to the total axial flow force vanishes in the cases of the entire space and a half-space, but that it need not vanish for general conical domains. In doing so an old claim by Burggraf & Foster (1977) is established mathematically, however not for Long's problem but for Shtern & Hussain's (1996) extension of this problem to the full Navier-Stokes equations and the entire space.…”

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confidence: 99%

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On the regularity and uniqueness of conically self-similar free-vortex solutions to the Navier-Stokes equations

Stein

2001

Z. angew. Math. Phys.

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In this paper the real analyticity of all conically self-similar free-vortex solutions to the Navier-Stokes equations is proven. Furthermore, it is mathematically established that such solutions are uniquely determined by the values of three derivatives on the symmetry axis, and hence a numerical method, invented and successfully used by Shtern & Hussain (1993,1996, is justified mathematically. In addition, it is proven that these results imply that for any conically self-similar free-vortex solution to the Navier-Stokes equations there exists a second order nonswirling correction term. For this term it is also shown that the second order contribution to the total axial flow force vanishes in the cases of the entire space and a half-space, but that it need not vanish for general conical domains. In doing so an old claim by Burggraf & Foster (1977) is established mathematically, however not for Long's problem but for Shtern & Hussain's (1996) extension of this problem to the full Navier-Stokes equations and the entire space. Mathematics Subject Classification (2000). 34A12, 34B15, 76D25, 76U05.

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“…on delta wing aircraft [1] and in vortex burners [2], and can also be observed in nature [3]. A field of ongoing research is swirling jet flows undergoing vortex breakdown [4].…”

Section: Introductionmentioning

confidence: 99%

Impact of rotating and fixed nozzles on vortex breakdown in compressible swirling jet flows

Luginsland

Gallaire

Kleiser

2016

European Journal of Mechanics - B/Fluids

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a b s t r a c tVortex breakdown of swirling, round jet flows is investigated in the compressible, subsonic regime by means of Direct Numerical Simulation (DNS). This is achieved by solving the compressible Navier-Stokes equations on a cylindrical grid using high-order spatial and temporal discretization schemes. TheReynolds number is Re = ρ The integral swirl number at the inflow is S int = 0.85. The parameters are chosen properly so as to make comparisons with existing experiments at lower Mach numbers possible while still enabling a study of compressible and baroclinic effects. Different from previous numerical investigations, a nozzle immersed in the fluid is included in the computational domain and is modelled as an isothermal no-slip wall, either rotating with the mean azimuthal flow direction or kept at rest. The present investigation aims to clarify the role played by the nozzle wall motion for the vortex breakdown of the swirling jet. We study the nozzle flow as well as the swirling jet flow simultaneously, a novelty for numerical investigations of vortex breakdown in swirling jets. Depending on the nozzle wall motion, the flow differs significantly upstream of the vortex breakdown: for the rotating nozzle, the flow inside the nozzle is purely laminar and the azimuthal boundary layer at the outer nozzle wall gives rise to the axisymmetric mode n = 0 and a single-helix type instability with azimuthal wave number n = 1. With the nozzle at rest, a transitional flow is observed within the nozzle where a helical instability with azimuthal wave number n = 12 dominates, growing in the boundary layer at the nozzle wall. For both nozzle setups, the helical instabilities observed for the nozzle flow interact with the developing vortex breakdown and the conical shear-layer downstream of the nozzle. For the nozzle at rest, this interaction results in a vortex breakdown configuration which is shifted in the upstream direction and which has a smaller radial and streamwise extent compared to the rotating nozzle case and the recirculation intensity is higher. The dominant frequency is highly influenced by the flow upstream of the vortex breakdown and is substantially higher for the nozzle at rest. Although the nozzle flow field differs for the two configurations and therefore alters the vortex breakdown downstream, a single-helix type instability n = 1 governing the vortex breakdown is found for both cases. This provides strong evidence for the robustness of the instability mechanisms leading to vortex breakdown.

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Continuation or breakdown in tornado-like vortices

Cited by 80 publications

References 13 publications

On vortex/wave interactions. Part 2. Originating from axisymmetric flow with swirl

On vortex/wave interactions. Part 2. Originating from axisymmetric flow with swirl

On the regularity and uniqueness of conically self-similar free-vortex solutions to the Navier-Stokes equations

Impact of rotating and fixed nozzles on vortex breakdown in compressible swirling jet flows

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