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Research Papers: Fundamental Issues and Canonical Flows

Spontaneous Break of Symmetry in Unconfined Laminar Annular Jets

[+] Author and Article Information
Christian Del Taglia1

 AFC Air Flow Consulting AG, 8006 Zurich, Switzerlandchristian.deltaglia@afc.ch

Alfred Moser

 Science Services Alfred Moser, 8400 Winterhur, Switzerland

Lars Blum

 Linde Kryotechnik AG, 8422 Pfungen, Switzerland

1

Corresponding author.

J. Fluids Eng 131(8), 081202 (Jul 24, 2009) (8 pages) doi:10.1115/1.3176960 History: Received June 30, 2008; Revised April 04, 2009; Published July 24, 2009

Numerical investigations show that the spontaneous break of symmetry in annular incompressible jets occurs in the laminar flow regime and is controlled by both the Reynolds number and the blockage ratio. In the blockage ratio range between 0.50 and 0.89 the transition critical Reynolds number decreases with increasing blockage ratio, according to a defined formula. Transition to asymmetry happens in the steady regime, before the transition to the unsteady flow. Asymmetry is characterized by a preferential flow direction from one side of the jet boundary layer to the diametrically opposite side. The plane of preferential direction passes through the geometry centerline and represents the single plane of flow symmetry. Experiments reported in literature have confirmed the existence of flow asymmetry in an annular jet flow.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 4

Bottom part of the computational domain. A uniform velocity profile of magnitude Uo was set at the annular slot. This annular inlet boundary condition is shown as vectors in the picture.

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Figure 1

Sketch of an annular jet. The three flow zones are described in Ref. 27.

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Figure 2

Summary of performed computations in the BR-Re plane

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Figure 3

The computational domain had a shape of a cylinder. The origin of the Cartesian system of reference was the bluff-body center. A pressure outlet boundary condition was set at the top surface of the cylindrical domain.

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Figure 5

Computational grid L086: Plane through the geometry centerline

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Figure 6

Computational grid L086: Lateral and top surfaces of the cylindrical computational domain.

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Figure 7

Computational grid L086: Detailed view of the central region of the top surface, where a pressure-specified boundary condition was set

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Figure 8

BR=0.89, Re=50: Axial velocity component on the geometry centerline, using different boundary conditions at the entrainment surface

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Figure 9

BR=0.89, Re=50: Radial velocity component on the geometry centerline, using different boundary conditions at the entrainment surface

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Figure 10

BR=0.89, Re=200: Time-averaged axial velocity component on the geometry centerline for different time steps and different grids (Table 4)

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Figure 11

BR=0.89, Re=200: Time-averaged radial velocity component on the geometry centerline for different time steps and different grids (Table 4).

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Figure 12

BR=0.89, Re=10: (u,v)-velocity components on the plane z=0.25D. The point in the center indicates the position of the geometry centerline.

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Figure 13

BR=0.89, Re=10: Velocity vectors on an arbitrary plane through the geometry centerline (vertical line). The point at the bottom indicates the position of the bluff-body center. The section shown in Fig. 1 is indicated by the horizontal line at z=0.25D.

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Figure 14

BR=0.89, Re=10: Isosurface of azimuthal vorticity ωθ at the value ωθD∕Uo=−0.516. (a) Perspective view. (b) Top view.

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Figure 15

BR=0.89, Re=50: (u,v)-velocity components on the plane z=0.25D. There is a net mass flow in the direction indicated by the line in the picture. The point in the center indicates the position of the geometry centerline.

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Figure 16

BR=0.89, Re=50: Velocity vectors on the plane of preferential direction. The geometry centerline is represented by the line in the picture. The point indicates the position of the bluff-body center. The section shown in Fig. 1 is indicated by the horizontal line at z=0.25D.

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Figure 17

BR=0.89, Re=50: Isosurface of azimuthal vorticity ωθ at the value ωθD∕Uo=−1.03. (a) Perspective view. (b) Top view. The line in (b) shows the plane of preferential direction.

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Figure 18

Transition to asymmetry for different blockage ratios

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Figure 19

Map of steady symmetric, steady asymmetric and unsteady states. All the computed points (circles) below the λ=λc-line reflect steady symmetric states. All the computed and converged points (white triangles, solid triangles, and the solid square) above the λ=λc-line reflect asymmetric states.

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Figure 20

Monotonic relationship between the asymmetry index α and the state parameter λ.

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