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The mechanism of sound generation in the interaction between a shock wave and two counter-rotating vortices
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10.1063/1.3176473
/content/aip/journal/pof2/21/7/10.1063/1.3176473
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/7/10.1063/1.3176473

Figures

Image of FIG. 1.
FIG. 1.

Schematic diagram of the flow model. (a) shock interaction with two counter-rotating vortices; (b) shock interaction with a single vortex.

Image of FIG. 2.
FIG. 2.

The comparison of the sound pressure generated by the shock interaction with two counter-rotating vortices with the linear combination of the sound waves generated by the two interactions between the same shock and each vortex. , , , , and . Left: contours of the sound pressure. Solid line: vortex pair; dashed line: linear combination of two isolated vortices. Right: circumferential distribution of sound pressure. Lines: vortex pair; symbols: linear combination of two isolated vortices. (a) , (b) , (c) .

Image of FIG. 3.
FIG. 3.

The sound pressure along the radial direction from the middle of the two vortex centers to the point of the minimum value of the precursor in the negative region at , , , , and .

Image of FIG. 4.
FIG. 4.

The comparison of the sound pressure generated by the shock interaction with two counter-rotating vortices with the linear combination of the sound waves generated by the two interactions between the same shock and each vortex. , , , , and . Left: contours of the sound pressure. Solid line: vortex pair; dashed line: linear combination of two isolated vortices. Right: circumferential distribution of sound pressure. Lines: vortex pair; symbols: linear combination of two isolated vortices. (a) , (b) , (c) .

Image of FIG. 5.
FIG. 5.

The comparison of the circumferential distribution of the sound pressure generated by the shock interaction with two counter-rotating vortices with the linear combination of the sound waves generated by the two interactions between the same shock and each vortex. , , , , and . Lines: vortex pair; symbols: linear combination of two isolated vortices. (a) , (b) , (c) .

Image of FIG. 6.
FIG. 6.

The evolution of the vorticity field in the vortex coupling of . Solid lines represent the positive vorticity, and dashed lines represent the negative vorticity. (a) left: ; right: ; (b) left: ; right: ; (c) left: ; right: .

Image of FIG. 7.
FIG. 7.

The contours of the sound pressure in vortex coupling. Left: . Right: . Solid lines represent , while dashed lines represent . (a) , (b) , (c) .

Image of FIG. 8.
FIG. 8.

The circumferential (left) and radial (right) distributions of the sound pressure in vortex coupling at . (a) , (b) , (c) .

Image of FIG. 9.
FIG. 9.

The contours of the sound pressure by the interaction of a shock wave and a vortex dipole with . Solid lines represent , while dashed lines represent . (a) , (b) , (c) , (d) .

Image of FIG. 10.
FIG. 10.

The radial distribution of the sound pressure of shock vortex dipole interaction with .

Image of FIG. 11.
FIG. 11.

The sound pressure of the shock interaction with two counter-rotating vortices. , , , and .

Image of FIG. 12.
FIG. 12.

The evolution of the sound pressure of the shock interaction with two counter-rotating vortices. , , , and . (a) , (b) , (c) , (d) .

Image of FIG. 13.
FIG. 13.

The distribution of the sound pressure generated by the shock interaction with two counter-rotating vortices and a comparison with that of free vortex coupling along the line from the middle of two vortices to the point of the maximum value of the first sound wave in the positive plane. , , , and . Solid lines represent the sound pressure generated by the shock interaction with two counter-rotating vortices (SV). Dashed lines represent the sound wave generated by free vortex coupling (VC). (a) , (b) .

Image of FIG. 14.
FIG. 14.

The evolution of the sound pressure of the shock interaction with two counter-rotating vortices. , , , and . (a) , (b) , (c) , (d) .

Image of FIG. 15.
FIG. 15.

The distribution of the sound pressure along the line from the middle of two vortices to the point of the maximum value of the first sound wave in the positive plane for the shock interaction with a vortex pair and a comparison with that of free vortex coupling. , , , and . Solid lines represent the sound pressure generated by shock vortex interaction (SV). Dashed lines represent the sound wave generated by free vortex coupling (VC). (a) , (b) .

Image of FIG. 16.
FIG. 16.

The evolution of the sound pressure of the shock interaction with two counter-rotating vortices. , , , and . (a) , (b) , (c) , (d) .

Image of FIG. 17.
FIG. 17.

The distribution of the sound pressure along the line from the middle of two vortices to the point of the maximum value of the first sound wave in the positive plane for the shock vortex pair interaction. , , , , and .

Tables

Generic image for table
Table I.

Parameters used in the simulations of shock interaction with two counter-rotating vortices and different regimes each simulation falls into.

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/content/aip/journal/pof2/21/7/10.1063/1.3176473
2009-07-15
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The mechanism of sound generation in the interaction between a shock wave and two counter-rotating vortices
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/7/10.1063/1.3176473
10.1063/1.3176473
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