The transient process accompanied by extreme acceleration in conical sections of hydraulic systems (e.g., draft tube, diffuser) can induce large cavitation bubbles both at the closed ends and in the bulk liquid. The collapses of the large cavitation bubbles can cause severe damage to the solid walls. We conduct experiments in the tubes with different conical-frustum shaped closed ends with the “tube-arrest” method and observe bubbles generated at these two locations. For the bubbles generated at the close end of the tube, we propose the onset criteria, consisting of two universal non-dimensional parameters Ca1 and Ca2, of large cavitation bubbles separating the water column. We investigate their dynamics including the collapse time and speed. The results indicate that the larger the conical angle, the faster the bubbles collapse. For the bubbles generated in the bulk liquid, we numerically study the collapse time, the jet characteristics, and the pressure pulse at the bubble collapse. We observe a much stronger jet and pressure pulse of bubbles in tubes, comparing with a bubble near an infinite plate. Our results can provide guidance in the design and safe operation of hydraulic machinery with complex geometries, considering the cavitation during the transient process.
References
1.
M.
Nishi
and S.
Liu
, “An outlook on the draft-tube-surge study
,” Int. J. Fluid Mach. Syst.
6
, 33
–48
(2013
).2.
C.
Mishra
and Y.
Peles
, “An experimental investigation of hydrodynamic cavitation in micro-Venturis
,” Phys. Fluids
18
, 103603
(2006
).3.
S.
Barre
, J.
Rolland
, G.
Boitel
, E.
Goncalves
, and R.
Fortes Patella
, “Experiments and modeling of cavitating flows in venturi: Attached sheet cavitation
,” Eur. J. Mech. B/Fluids
28
, 444
–464
(2009
).4.
H.
Zhang
, Z.
Zuo
, K. A.
Mørch
, and S.
Liu
, “Thermodynamic effects on venturi cavitation characteristics
,” Phys. Fluids
31
, 097107
(2019
).5.
C.
Bonin
, “Water-hammer damage to Oigawa power station
,” ASME J. Eng. Power
82
, 111
(1960
).6.
A.
Bergant
, A. R.
Simpson
, and A. S.
Tijsseling
, “Water hammer with column separation: A historical review
,” J. Fluids Struct.
22
, 135
–171
(2006
).7.
T.
Nonoshita
, H.
Matsumoto
, Y.
Ohashi
, and T.
Kubota
, “Water column separation in a straight draft tube
,” in Proceedings of the Third ASME-JSME Joint Fluids Engineering Conference
, San Francisco, 1999
.8.
S.
Pejovic
, B.
Karney
, and Q.
Zhang
, “Water column separation in long tailrace tunnel
,” in Hydroturbo 2004, International Conference on Hydro-Power Engineering
(2004
), pp. 18
–22
.9.
S.
Pejovic
, B.
Karney
, and A.
Gajic
, “Analysis of pump-turbine “S” instability and reverse waterhammer incidents in hydropower systems
,” in 4th International Meeting on Cavitation and Dynamic Problems in Hydraulic Machinery Systems
, Belgrade, Serbia, 2011
.10.
X.
Zhang
, Y.
Cheng
, L.
Xia
, and J.
Yang
, “CFD simulation of reverse water-hammer induced by collapse of draft-tube cavity in a model pump-turbine during runaway process
,” IOP Conf. Ser.
49
, 052017
(2016
).11.
X.
He
, J.
Yang
, J.
Yang
, J.
Hu
, and T.
Peng
, “Experimental study of cavitating vortex rope and water column separation in a pump turbine
,” Phys. Fluids
34
, 044101
(2022
).12.
B. B.
Sharp
, “Cavity formation in simple pipes due to rupture of the water column
,” Nature
185
, 302
–303
(1960
).13.
A. R.
Simpson
and E. B.
Wylie
, “Large water-hammer pressures for column separation in pipelines
,” ASCE J. Hydraul. Eng.
117
, 1310
–1316
(1991
).14.
B.
Brunone
, U.
Golia
, and M.
Greco
, “Modelling of fast transients by numerical methods
,” in Proceedings of the International Meeting on Hydraulic Transients with Column Separation
(Universidad Politecnica de Valencia
, Valencia, Spain
, 1991
), pp. 215
–222
.15.
A.
Bergant
and A. R.
Simpson
, “Pipeline column separation flow regimes
,” ASCE J. Hydraul. Eng.
125
, 835
–848
(1999
).16.
A.
Adamkowski
and M.
Lewandowski
, “Investigation of hydraulic transients in a pipeline with column separation
,” ASCE J. Hydrual. Eng.
138
, 935
–944
(2012
).17.
A.
Adamkowski
and M.
Lewandowski
, “Cavitation characteristics of shutoff valves in numerical modeling of transients in pipelines with column separation
,” ASCE J. Hydraul. Eng.
141
, 04014077
(2015
).18.
J.
Daily
, J.
Pendlebury
, K.
Langley
, R.
Hurd
, S.
Thomson
, and T.
Truscott
, “Catastrophic cracking courtesy of quiescent cavitation
,” Phys. Fluids
26
, 091107
(2014
).19.
W. D.
Chesterman
, “The dynamics of small transient cavities
,” Proc. Phys. Soc., Sect. B
65
, 846
–858
(1952
).20.
Q.
Chen
and L.
Wang
, “Production of large size single transient cavitation bubbles with tube arrest method
,” Chin. Phys.
13
, 564
(2004
).21.
P.
Xu
, S.
Liu
, Z.
Zuo
, and Z.
Pan
, “On the criteria of large cavitation bubbles in a tube during a transient process
,” J. Fluid Mech.
913
, R6
(2021
).22.
T. B.
Benjamin
and A. T.
Ellis
, “The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries
,” Philos. Trans. R. Soc. London, Ser. A
260
, 221
–240
(1966
).23.
A.
Philipp
and W.
Lauterborn
, “Cavitation erosion by single laser-produced bubbles
,” J. Fluid Mech.
361
, 75
–116
(1998
).24.
Z.
Pan
, A.
Kiyama
, Y.
Tagawa
, D. J.
Daily
, and T. T.
Truscott
, “Cavitation onset caused by acceleration
,” Proc. Natl. Acad. Sci. U. S. A.
114
, 8470
–8474
(2017
).25.
H.
Onuki
, Y.
Oi
, and Y.
Tagawa
, “Microjet generator for highly viscous fluids
,” Phys. Rev. Appl.
9
, 014035
(2018
).26.
Q.
Zeng
, S. R.
Gonzalez-Avila
, R.
Dijkink
, P.
Koukouvinis
, M.
Gavaises
, and C.-D.
Ohl
, “Wall shear stress from jetting cavitation bubbles
,” J. Fluid Mech.
846
, 341
–355
(2018
).27.
S.
Wu
, B.
Li
, Z.
Zuo
, and S.
Liu
, “Dynamics of a single free-settling spherical particle driven by a laser-induced bubble near a rigid boundary
,” Phys. Rev. Fluids
6
, 093602
(2021
).28.
S. R.
Gonzalez-Avila
, F.
Denner
, and C.-D.
Ohl
, “The acoustic pressure generated by the cavitation bubble expansion and collapse near a rigid wall
,” Phys. Fluids
33
, 032118
(2021
).29.
M.
Rattray
, “Perturbation effects in cavitation bubble dynamics
,” Ph.D. thesis (California Institute of Technology
, 1951
).30.
M. S.
Plesset
and R. B.
Chapman
, “Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary
,” J. Fluids Mech.
47
, 283
–290
(1971
).31.
32.
D.
Obreschkow
, M.
Tinguely
, N.
Dorsaz
, P.
Kobel
, A.
de Bosset
, and M.
Farhat
, “Universal scaling law for jets of collapsing bubbles
,” Phys. Rev. Lett.
107
, 204501
(2011
).33.
E.
Ory
, H.
Yuan
, A.
Prosperetti
, S.
Popinet
, and S.
Zaleski
, “Growth and collapse of a vapor bubble in a narrow tube
,” Phys. Fluids
12
, 1268
–1277
(2000
).34.
O.
Supponen
, D.
Obreschkow
, M.
Tinguely
, P.
Kobel
, N.
Dorsaz
, and M.
Farhat
, “Scaling laws for jets of single cavitation bubbles
,” J. Fluids Mech.
802
, 263
–293
(2016
).35.
E. F.
Toro
, Riemann Solvers and Numerical Methods for Fluid Dynamics
(Springer
, Berlin, Heidelberg
, 1997
).36.
T.
Trummler
, S. H.
Bryngelson
, K.
Schmidmayer
, S. J.
Schmidt
, T.
Colonius
, and N. A.
Adams
, “Near-surface dynamics of a gas bubble collapsing above a crevice
,” J. Fluid Mech.
899
, A16
(2020
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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