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Numerical investigation of wavy and spiral Taylor-Görtler vortices in medium spherical gaps
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10.1063/1.4772196
/content/aip/journal/pof2/24/12/10.1063/1.4772196
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/12/10.1063/1.4772196

Figures

Image of FIG. 1.
FIG. 1.

(ϕ, θ)-plane distributions of the azimuthal vorticity component at four different times in the formation process of the spiral TG vortex flow IITS(T = 1, S P = 3) for β = 0.14, Re = 1110. The quantity is integrated along the radial direction over the gap. The contour levels range from −0.12 to 0.12 in (a) and (b), and from −0.14 to 0.14 in (c) and (d), in step of 0.02. Solid lines show positive values while dashed lines show negative values.

Image of FIG. 2.
FIG. 2.

(ϕ, θ)-plane distributions of the azimuthal vorticity component as in Figure 3, plus velocity vectors in one meridional plane (ϕ = 360°) for the wavy spiral TG vortex flow IIWTS(T = 1, S P = 3, m = 6) for Re = 1800, β = 0.14. The contour levels range from −0.28 to 0.28 in step of 0.04.

Image of FIG. 3.
FIG. 3.

Time history of the circumferential velocity component at a point (r, θ, ϕ) = (1 + 0.5β, 0.5π, 0). The fundamental period of the spiral TG vortex (Re = 1110) is simply counted between every solid peak, and its rotational period is simply T rot, s = 3T s due to S P = 3. The fundamental periods T w and T s of the wavy spiral TG vortex flow (Re = 1800) are indicated in the graph, and the rotational period T rot, w of the flow is counted between every six peak intervals due to m = 6. Clearance ratio β = 0.14.

Image of FIG. 4.
FIG. 4.

Variations of the wavy TG vortex flow IITW(T = 2, m = 5) with increasing Re number. For each frame, the left graph is instantaneous iso-values of the azimuthal angular velocity quantity (ω = v ϕ/rsin θ) in the unwrapped middle spherical surface r = (1 + β)/2, 0 ⩽ θ ⩽ π, 0 ⩽ ϕ ⩽ 2π, the middle graph is that in the meridional plane at ϕ = 2π, and the right graph is velocity vectors (v r , v θ) in the same meridional plane. The clearance ratio β = 0.14.

Image of FIG. 5.
FIG. 5.

The same as Figure 4 but for clearance ratio β = 0.18.

Image of FIG. 6.
FIG. 6.

Multiple 0-vortex flows with different numbers of shear waves at Re = 7200 for clearance ratio β = 0.18. For each frame, the left graph is instantaneous iso-values of the circumferential velocity component v θ in the unwrapped spherical surface r = 1 + 0.7β, 0 ⩽ θ ⩽ π, 0 ⩽ ϕ ⩽ 2π, the middle graph is that in the meridional plane at ϕ = 2π, and the right graph is velocity vectors (v r , v θ) in the same meridional plane. (a) 7 shear waves; (b) 8 shear waves; (c) 9 shear waves.

Image of FIG. 7.
FIG. 7.

The same as Figure 6 but for multiple 2-vortex flows with different numbers of shear waves. (a) 8 shear waves; (b) 9 shear waves; (c) 10 shear waves.

Image of FIG. 8.
FIG. 8.

The same as Figure 6 but for multiple 1-vortex flows with different numbers of shear waves at Re = 8000. (a) 5 shear waves; (b) 6 shear waves; (c) 6:5 shear waves.

Tables

Generic image for table
Table I.

Nondimensional rotational frequencies of TG vortex flows with shear waves for β = 0.18.

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/content/aip/journal/pof2/24/12/10.1063/1.4772196
2012-12-27
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Numerical investigation of wavy and spiral Taylor-Görtler vortices in medium spherical gaps
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/12/10.1063/1.4772196
10.1063/1.4772196
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