The problem of shock interaction with a vortex ring is investigated within the framework of axisymmetric Euler equations solved numerically by a shock-fitted sixth-order compact difference scheme. The vortex ring, which is based on Lamb’s formula, has an upstream circulation Γ=0.01 and its aspect ratio R lies in the range 8⩽R⩽100. The shock Mach number varies in the range 1.1⩽M1⩽1.8. The vortex ring/shock interaction results in the streamwise compression of the vortex core by a factor proportional to the ratio of the upstream and downstream mean velocity U1/U2, and the generation of a toroidal acoustic wave and entropy disturbances. The toroidal acoustic wave propagates and interacts with itself on the symmetry axis of the vortex ring. This self-interaction engenders high amplitude rarefaction/compression pressure peaks upstream/downstream of the transmitted vortex core. This results in a significant increase in centerline sound pressure levels, especially near the shock (due to the upstream movement of the rarefaction peak) and in the far downstream (due to the downstream movement of the compression peak). The magnitude of the compression peak increases nonlinearly with M1. For a given M1, vortex rings with smaller aspect ratios (R<20) generate pressure disturbances whose amplitudes scale inversely with R, while vortex rings with larger aspect ratios (R>40) generate pressure disturbances whose amplitudes are roughly independent of R.

1.
P. G.
Saffman
, “
Dynamics of vorticity
,”
J. Fluid Mech.
106
,
49
(
1981
).
2.
K. R. Meadows, “A study of fundamental shock noise mechanisms,” NASA Technical Paper 3605, April 1997.
3.
T.
Minota
,
T.
Kambe
, and
T.
Murakami
, “
Acoustic emission from interaction of a vortex ring with a sphere
,”
Fluid Dyn. Res.
3
,
357
(
1988
).
4.
T.
Minota
,
M.
Nishida
, and
M. G.
Lee
, “
Head-on collision of two compressible vortex rings
,”
Fluid Dyn. Res.
22
,
43
(
1998
).
5.
D.
Fabris
and
D.
Liepmann
, “
Vortex ring structure at late stages of formation
,”
Phys. Fluids
9
,
2801
(
1997
).
6.
A.
Glezer
and
D.
Coles
, “
An experimental study of a turbulent vortex ring
,”
J. Fluid Mech.
211
,
243
(
1990
).
7.
T.
Maxworty
, “
Some experimental studies of vortex rings
,”
J. Fluid Mech.
81
,
465
(
1977
).
8.
T.
Minota
,
M.
Nishida
, and
M. G.
Lee
, “
Shock formation by compressible vortex ring impinging on a wall
,”
Fluid Dyn. Res.
21
,
139
(
1997
).
9.
K.
Shariff
,
A.
Leonard
,
N. J.
Zabusky
, and
J. H.
Ferziger
, “
Acoustic and dynamics of coaxial interacting vortex rings
,”
Fluid Dyn. Res.
3
,
337
(
1988
).
10.
K.
Shariff
and
A.
Leonard
, “
Vortex rings
,”
Annu. Rev. Fluid Mech.
24
,
235
(
1992
).
11.
T.
Minota
, “
Interactions of a shock wave with a high-speed vortex ring
,”
Fluid Dyn. Res.
12
,
335
(
1993
).
12.
A. P.
Szumowski
and
G. B.
Sobieraj
, “
Sound generation by a ring vortex-shock wave interaction
,”
AIAA J.
34
,
1948
(
1995
).
13.
F.
Takayama
,
Y.
Ishii
,
A.
Sakurai
, and
T.
Kambe
, “
Self-intensification in shock wave and vortex interaction
,”
Fluid Dyn. Res.
12
,
343
(
1993
).
14.
N.
Tokugawa
,
Y.
Ishii
,
K.
Sugano
,
F.
Takayama
, and
T.
Kambe
, “
Observation and analysis of scattering interaction between a shock wave and a vortex ring
,”
Fluid Dyn. Res.
21
,
185
(
1997
).
15.
J. P.
Baird
, “
Supersonic vortex rings
,”
Proc. R. Soc. London, Ser. A
409
,
59
(
1987
).
16.
Y. Futagami and J. Iwamoto, “A study on the relation between pulsating flow and the noise,” SAE Paper 961822, 1996.
17.
M.
Endo
and
J.
Iwamoto
, “
Numerical analysis of pulsatile jet from exhaust pipe
,”
JSAE Rev.
20
,
243
(
1999
).
18.
K.
Takayama
, “
Shock wave development and propagation in automobile exhaust systems
,”
SAE Trans.
880082
,
4
.
66
(
1989
).
19.
J. M. Seiner and T. D. Norum, “Aerodynamic aspects of shock containing jet plumes,” Sixth Aeroacoustic Conference, AIAA, June, 1980, pp. 1–18.
20.
G.
Erlebacher
,
M. Y.
Hussaini
, and
T. L.
Jackson
, “
Nonlinear strong shock interactions: A shock-fitted approach
,”
Theor. Comput. Fluid Dyn.
11
,
1
(
1996
).
21.
M. Y.
Hussaini
and
G.
Erlebacher
, “
Interaction of an entropy spot with a shock
,”
AIAA J.
37
,
346
(
1999
).
22.
H. Lamb, Hydrodynamics (Dover, New York, 1932).
23.
H. S.
Ribner
, “
Cylindrical sound wave generated by shock-vortex interaction
,”
AIAA J.
23
,
1708
(
1985
).
24.
D. S.
Dosanjh
and
T. M.
Weeks
, “
Interaction of a starting vortex as well as a vortex street with a traveling shock wave
,”
AIAA J.
3
,
216
(
1965
).
25.
T. A.
Zang
,
M. Y.
Hussaini
, and
D. M.
Bushnell
, “
Numerical computations of turbulence amplification in shock-wave interactions
,”
AIAA J.
22
,
13
(
1984
).
26.
J. L.
Ellzey
,
M.
Henneke
,
J. M.
Picone
, and
E.
Oran
, “
The interaction of a shock with a vortex: Shock distortion and the production of acoustic waves
,”
Phys. Fluids
7
,
172
(
1995
).
27.
O.
Inoue
and
Y.
Hattori
, “
Sound generation by shock-vortex interaction
,”
J. Fluid Mech.
380
,
81
(
1999
).
28.
F.
Grasso
and
S.
Pirozzoli
, “
Shock-wave-vortex interactions: shock and vortex deformations, and sound production
,”
Theor. Comput. Fluid Dyn.
13
,
421
(
2000
).
29.
K. R.
Meadows
,
A.
Kumar
, and
M. Y.
Hussaini
, “
Computational study on the interaction between a vortex and a shock wave
,”
AIAA J.
29
,
174
(
1991
).
30.
D. G. Crighton, A. P. Dowling, J. E. Ffowcs Williams, M. Heckl, and F. G. Leppington, Modern Methods in Analytical Acoustics, Lecture Notes (Springer-Verlag, Berlin, 1992).
31.
M. H. Carpenter and C. A. Kennedy, “A fourth-order 2N-storage Runge–Kutta scheme,” NASA Report NASA-TM-109112.
32.
S. Ta’asan and D. Nark, “An absorbing buffer zone technique for acoustic wave propagation,” AIAA Paper No. 95-0164.
This content is only available via PDF.
You do not currently have access to this content.