Vortex ring research primarily focuses on the formation from circular openings. Consequently, the role of tunnel geometry is less understood, despite there being numerous research studies using noncircular shock tunnels. This experimental study investigated shockwaves and vortex rings from different geometry shock tunnels from formation at the tunnel opening to head on collision with another similarly formed vortex ring using schlieren imaging and statistical analysis. The velocity of the incident shockwave was found to be consistent across all four shock tunnel geometries, which include circle, hexagon, square, and triangle of the same cross-sectional area. The velocity was 1.2 ± 0.007 Mach and was independent of the tunnel geometry. However, the velocities of the resulting vortex rings differed between the shapes, with statistical analysis indicating significant differences between the triangle and hexagon vortex velocities compared to the circle. Vortex rings from the square and circle shock tunnels were found to have statistically similar velocities. All vortex rings slowed as they traveled due to corner inversion and air drag. All shock tunnels with corners produce a wobble in the vortex rings. Vortex rings interact with opposing incident shockwaves prior to colliding with each other. Vortex velocity before and after shock–vortex interaction was measured and evaluated, showing statistically similar results. Shock–vortex interaction slows the shockwave upon interaction, while the shock–shock interaction resulted in no change in shock velocity. Although the vortex rings travel at different velocities, all head-on vortex ring collisions produce a perpendicular shockwave that travels at 1.04 ± 0.005 Mach.

1.
D. V.
Reneer
,
R. D.
Hisel
,
J. M.
Hoffman
,
R. J.
Kryscio
,
B. T.
Lusk
, and
J. W.
Geddes
, “
A multi-mode shock tube for investigation of blast-induced traumatic brain injury
,”
J. Neurotrauma
28
(
1
),
95
104
(
2011
).
2.
B.
Rutter
et al, “
Shock wave physics as related to primary non-impact blast-induced traumatic brain injury
,”
Mil. Med.
186
(
Suppl 1
),
601
609
(
2021
).
3.
J. S.
Lee
,
S. J.
Park
,
J. H.
Lee
,
B. M.
Weon
,
K.
Fezzaa
, and
J. H.
Je
, “
Origin and dynamics of vortex rings in drop splashing
,”
Nat. Commun.
6
,
8187
(
2015
).
4.
P. S.
Krueger
,
A. A.
Moslemi
,
J. T.
Nichols
,
I. K.
Bartol
, and
W. J.
Stewart
, “
Vortex rings in bio-inspired and biological jet propulsion
Adv. Sci. Technol.
58
,
237
246
(
2008
).
5.
A.
Glezer
, “
The formation of vortex rings
,”
Phys. Fluids
31
(
12
),
3532
(
1988
).
6.
K.
Shariff
and
A.
Leonard
, “
Vortex rings
,”
Annu. Rev. Fluid Mech.
24
(
1
),
235
279
(
1992
).
7.
L.
Gao
and
S. C. M.
Yu
, “
Vortex ring formation in starting forced plumes with negative and positive buoyancy
,”
Phys. Fluids
28
(
11
),
113601
(
2016
).
8.
M.
Gharib
,
E.
Rambod
, and
K.
Shariff
, “
A universal time scale for vortex ring formation
,”
J. Fluid Mech.
360
,
121
140
(
1998
).
9.
H.
Feng
, “
On three-dimensional Navier-Stokes equations with axi-symmetric vortex rings as initial vorticity
,” Ph.D. dissertation, University of Minnesota Twin Cities,
2013
.
10.
S.
Stanaway
,
K.
Shariff
, and
F.
Hussain
, “
Head-on collision of viscous vortex rings
,” in Center for Turbulence Research Proceedings of the Summer Program, 1988; available at https://ui.adsabs.harvard.edu/abs/1988stun.proc..287S/abstract.
11.
K.
Ishii
,
K.
Kuwahara
, and
C. H.
Liu
, “
Navier—Stokes calculations for vortex rings in an unbounded domain
,”
Comput. Fluids
22
(
4
),
589
605
(
1993
).
12.
H.
Tryggeson
, “
Analytical vortex solutions to the Navier–Stokes equation
,”
Doctoral thesis
(
Växjö University Press
,
Växjö
,
2007
).
13.
J. P.
Baird
, “
Supersonic vortex rings
,”
Proc. R. Soc. A
409
(
1836
),
59
65
(
1987
).
14.
T. T.
Lim
and
T. B.
Nickels
, “
Instability and reconnection in the head-on collision of two vortex rings
,”
Nature
357
(
6375
),
225
(
1992
).
15.
A.
Mishra
,
A.
Pumir
, and
R.
Ostilla-Mónico
, “
Instability and disintegration of vortex rings during head-on collisions and wall interactions
,” arXiv:2107.12324 (
2021
).
16.
T. H.
New
,
S.
Shi
, and
B.
Zang
, “
Some observations on vortex-ring collisions upon inclined surfaces
,”
Exp. Fluids
57
(
6
),
109
(
2016
).
17.
N. K.
Jha
and
R. N.
Govardhan
, “
Interaction of a vortex ring with a single bubble: Bubble and vorticity dynamics
,”
J. Fluid Mech.
773
,
460
497
(
2015
).
18.
R. L.
Bauer
et al, “
Shock wave formation from head-on collision of two subsonic vortex rings
,”
Sci. Rep.
12
,
7492
(
2022
).
19.
S.
Poudel
,
L.
Chandrala
,
D.
Das
, and
A.
De
, “
Characteristics of shock tube generated compressible vortex rings at very high shock Mach numbers
,”
Phys. Fluids
33
(
9
),
096105
(
2021
).
20.
Z.-Y.
Li
,
Y.
Xu
,
L.-H.
Feng
, and
J.-J.
Wang
, “
Synthetic jet vortex rings impinging onto a porous wall: Reynolds number effect
,”
Int. J. Heat Mass Transfer
137
,
951
967
(
2019
).
21.
R.
Mariani
,
K.
Kontis
, and
N.
Gongora-Orozco
, “
Head on collisions of compressible vortex rings on a smooth solid surface: Effects of surface distance variation
,”
Shock Waves
23
(
4
),
381
398
(
2013
).
22.
T. H.
New
and
B.
Zang
, “
Head-on collisions of vortex rings upon round cylinders
,”
J. Fluid Mech.
833
,
648
676
(
2017
).
23.
T. H.
New
,
J.
Long
,
B.
Zang
, and
S.
Shi
, “
Collision of vortex rings upon V-walls
,”
J. Fluid Mech.
899
,
A2
(
2020
).
24.
T.
Minota
, “
The flow-field around a small square plate interacting with the vortex flow released from a shock tube
,” in
Shock Waves
, edited by
Z.
Jiang
(
Springer
,
Berlin, Heidelberg
,
2005
), pp.
677
682
.
25.
J. J.
Ai
,
S. C. M.
Yu
,
A. W.-K.
Law
, and
L. P.
Chua
, “
Vortex dynamics in starting square water jets
,”
Phys. Fluids
17
(
1
),
014106
(
2005
).
26.
A.
Ghasemi
,
V.
Roussinova
,
R. M.
Barron
, and
R.
Balachandar
, “
Large eddy simulation of the near-field vortex dynamics in starting square jet transitioning into steady state
,”
Phys. Fluids
28
(
8
),
085104
(
2016
).
27.
M.
Xu
,
A.
Pollard
,
J.
Mi
,
F.
Secretain
, and
H.
Sadeghi
, “
Effects of Reynolds number on some properties of a turbulent jet from a long square pipe
,”
Phys. Fluids
25
(
3
),
035102
(
2013
).
28.
A.
Ghasemi
,
B. A.
Tuna
, and
X.
Li
, “
Curvature-induced deformations of the vortex rings generated at the exit of a rectangular duct
,”
J. Fluid Mech.
864
,
141
180
(
2019
).
29.
A.
Bejan
,
S.
Ziaei
, and
S.
Lorente
, “
Evolution: Why all plumes and jets evolve to round cross sections
,”
Sci. Rep.
4
(
1
),
4730
(
2015
).
30.
A.
Ghasemi
,
B. A.
Tuna
, and
X.
Li
, “
Viscous diffusion effects on the self-induced distortions of rectangular vortex rings
,”
Phys. Fluids
30
(
12
),
124101
(
2018
).
31.
See https://www.grc.nasa.gov/www/BGH/reynolds.html for “
Reynolds Number
” (accessed November 29,
2021
).
32.
M.
Cheng
,
J.
Lou
, and
T. T.
Lim
, “
Collision and reconnection of viscous elliptic vortex rings
,”
Phys. Fluids
31
(
6
),
067107
(
2019
).
33.
P.
Chatelain
,
D.
Kivotides
, and
A.
Leonard
, “
Reconnection of colliding vortex rings
,”
Phys. Rev. Lett.
90
(
5
),
054501
(
2003
).
34.
D.
Barkley
, “
Theoretical perspective on the route to turbulence in a pipe
,”
J. Fluid Mech.
803
,
P1
(
2016
).
35.
B.
Rehm
,
D.
Consultant
,
A.
Haghshenas
,
A. S.
Paknejad
, and
J.
Schubert
, “
Chapter two—Situational problems in MPD
,” in
Managed Pressure Drilling
, edited by
B.
Rehm
,
J.
Schubert
,
A.
Haghshenas
,
A. S.
Paknejad
, and
J.
Hughes
(
Gulf Publishing Company
,
2008
), pp.
39
80
.
36.
See https://www.grc.nasa.gov/www/k-12/airplane/oblique.html for “
Oblique Shock Waves
” (accessed January 20, 2023).
37.
S.
Kitajima
,
J.
Iwamoto
, and
E.
Tamura
, “
A study on the behavior of shock wave and vortex ring discharged from a pipe
,” in FLUCOME 2009, 10th International Conference on Fluid Control, Measurements, and Visualization, Moscow, Russia, 17–21 August
2009
.
38.
R.
Mariani
,
Compressible Vortex Rings and Their Interaction with Stationary Surfaces
(
University of Manchester
,
2012
).
39.
K. R.
Williams
, “
Investigating the focusing effect of charge geometry with computer simulations, witness plates, and high-speed videography
,” Ph.D. thesis (
Missouri University of Science and Technology
,
Missouri
,
2021
).
40.
Y.
Shi
,
N.
Wang
,
J.
Cui
,
C.
Li
, and
X.
Zhang
, “
Experimental and numerical investigation of charge shape effect on blast load induced by near-field explosions
,”
Process Saf. Environ. Prot.
165
,
266
277
(
2022
).
41.
K.
Williams
and
C. E.
Johnson
, “
Investigating anisotropic blast wave parameters near the explosive-air boundary using computer simulation and experimental techniques with varying charge geometry
,”
J. Appl. Phys.
130
(
20
),
205902
(
2021
).
42.
K.
Williams
and
C. E.
Johnson
, “
Evaluating blast wave overpressure from non-spherical charges using time of arrival from high-speed video
,”
Propellants, Explos., Pyrotech.
8
(
7
),
e202200346
(
2023
).
43.
W.
Xiao
,
M.
Andrae
, and
N.
Gebbeken
, “
Effect of charge shape and initiation configuration of explosive cylinders detonating in free air on blast-resistant design
,”
J. Struct. Eng.
146
(
8
),
04020146
(
2020
).
44.
M.
Kainuma
,
M.
Havermann
,
M.
Sun
, and
K.
Takayama
, “
Effects of the shock tube open-end shape on vortex loops released from it
,” in
Shock Waves
, edited by
Z.
Jiang
(
Springer
,
Berlin, Heidelberg
,
2005
), pp.
505
510
.
46.
See https://www.phantomhighspeed.com/products/cameras/ultrahighspeed/%20v2012 for “
Phantom v2012
” (accessed September 4,
2022
).
47.
See https://www.phantomhighspeed.com/resourcesandsupport/phantomresources/pccsoftware for “
PCC Software
” (accessed April 13,
2022
).
48.
T.
Mizukaki
, “
Visualization of compressible vortex rings using the background-oriented schlieren method
,”
Shock Waves
20
(
6
),
531
537
(
2010
).
49.
See https://www.engineeringtoolbox.com/air-absolute-kinematic-viscosity-d_601.html for “
Air—Dynamic and Kinematic Viscosity
” (accessed November 29,
2021
).
50.
L.
Hirschberg
,
S. J.
Hulshoff
,
J.
Collinet
,
C.
Schram
, and
T.
Schuller
, “
Vortex nozzle interaction in solid rocket motors: A scaling law for upstream acoustic response
,”
J. Acoust. Soc. Am.
144
(
1
),
EL46
EL51
(
2018
).
51.
L.
Qin
,
Y.
Xiang
,
S.
Qin
, and
H.
Liu
, “
On the structures of compressible vortex rings generated by the compressible starting jet from converging and diverging nozzles
,”
Aerosp. Sci. Technol.
106
,
106188
(
2020
).
52.
J.
Zhu
and
S.
Elbel
, “
CFD simulation of vortex flashing flows in convergent-divergent nozzles
,”
2018
.
53.
F. F.
Grinstein
, “
Vortex dynamics and entrainment in rectangular free jets
,”
J. Fluid Mech.
437
,
69
101
(
2001
).
54.
J. C.
Stapel
and
W. P.
Medendorp
, “
Panoramic uncertainty in vertical perception
,”
Front. Integr. Neurosci.
(published online 2021).
55.
L.
Vega
, “
The dynamics of vortex filaments with corners
,”
Commun. Pure Appl. Anal.
14
(
4
),
1581
1601
(
2015
).
56.
“Vortex Rings from notched nozzles.” arXiv:1708.05639 (
2015
).
57.
L.
Wang
,
L.-H.
Feng
,
J.-J.
Wang
, and
T.
Li
, “
Evolution of low-aspect-ratio rectangular synthetic jets in a quiescent environment
,”
Exp. Fluids
59
(
6
),
91
(
2018
).
58.
R.
Belanger
,
D. W.
Zingg
, and
P.
Lavoie
, “
Vortex structure of a synthetic jet issuing into a turbulent boundary layer from a finite-span rectangular orifice
,” AIAA Paper No. AIAA 2020-1815,
2020
.
59.
Y.
Xiang
,
L.
Qin
,
S.
Qin
, and
H.
Liu
, “
Circulation production model and unified formation number of compressible vortex rings generated by a shock tube
,”
Phys. Fluids
35
(
3
),
036121
(
2023
).
60.
J. C.
Straccia
and
J. A. N.
Farnsworth
, “
Axis switching in low to moderate aspect ratio rectangular orifice synthetic jets
,”
Phys. Rev. Fluids
6
(
5
),
054702
(
2021
).
61.
R. S.
Miller
,
C. K.
Madnia
, and
P.
Givi
, “
Numerical simulation of non-circular jets
,”
Comput. Fluids
24
(
1
),
1
25
(
1994
).
You do not currently have access to this content.