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Research Papers: Multiphase Flows

Energy Balance in Cavitation Erosion: From Bubble Collapse to Indentation of Material Surface

[+] Author and Article Information
R. Fortes-Patella

e-mail: regiane.fortes@legi.grenoble-inp.fr

G. Challier

LEGI,
Grenoble INP,
BP 53,
38041 Grenoble Cedex 9, France

J. L. Reboud

G2ELab,
CNRS, Institut Polytechnique Grenoble
and Joseph Fourier University,
BP 166,
38042 Grenoble Cedex 9, France
e-mail: jean-luc.reboud@ujf-grenoble.fr

A. Archer

EDF R&D,
78401 Chatou, France
e-mail: antoine.archer@edf.fr

Standard deviations are presented in parenthesis.

1Corresponding author.

2Present address: Snecma , Forêt de Vernon, BP 802, 27208 Vernon, France.

Manuscript received January 30, 2012; final manuscript received September 14, 2012; published online January 18, 2013. Assoc. Editor: Olivier Coutier-Delgosha.

J. Fluids Eng 135(1), 011303 (Jan 18, 2013) (11 pages) Paper No: FE-12-1046; doi: 10.1115/1.4023076 History: Received January 30, 2012; Revised September 14, 2012

An original approach based on energy balance between vapor bubble collapse, emitted pressure wave, and neighboring solid wall response was proposed, developed, and tested to estimate the aggressiveness of cavitating flows. In the first part of the work, to improve a prediction method for cavitation erosion (Fortes-Patella and Reboud, 1998, “A New Approach to Evaluate the Cavitation Erosion Power,” ASME J. Fluids Eng., 120(2), pp. 335–344; Fortes-Patella and Reboud, 1998, “Energetical Approach and Impact Efficiency in Cavitation Erosion,” Proceedings of Third International Symposium on Cavitation, Grenoble, France), we were interested in studying the pressure waves emitted during bubble collapse. The radial dynamics of a spherical vapor/gas bubble in a compressible and viscous liquid was studied by means of Keller's and Fujikawa and Akamatsu's physical models (Prosperetti, 1994, “Bubbles Dynamics: Some Things we did not Know 10 Years Ago,” Bubble Dynamics and Interface Phenomena, Blake, Boulton-Stone, Thomas, eds., Kluwer Academic Publishers, Dordrecht, the Netherlands, pp. 3–15; Fujikawa and Akamatsu, 1980, “Effects of Non-Equilibrium Condensation of Vapor on the Pressure Wave Produced by Collapse of a Bubble in Liquid,” J. Fluid Mech., 97(3), pp. 481–512). The pressure amplitude, the profile, and the energy of the pressure waves emitted during cavity collapses were evaluated by numerical simulations. The model was validated by comparisons with experiments carried out at Laboratoire Laser, Plasma et Procédés Photoniques (LP3-IRPHE) (Marseille, France) with laser-induced bubble (Isselin et al., 1998, “Investigations of Material Damages Induced by an Isolated Vapor Bubble Created by Pulsed Laser,” Proceedings of Third International Symposium on Cavitation, Grenoble, France; Isselin et al., 1998, “On Laser Induced Single Bubble Near a Solid Boundary: Contribution to the Understanding of Erosion Phenomena,” J. Appl. Phys., 84(10), pp. 5766–5771). The efficiency of the first collapse ηwave/bubble (defined as the ratio between pressure wave energy and initial bubble potential energy) was evaluated for different bubble collapses. For the cases considered of collapse in a constant-pressure field, the study pointed out the strong influence of the air contents on the bubble dynamics, on the emitted pressure wave characteristics, and on the collapse efficiency. In the second part of the study, the dynamic response and the surface deformation (i.e., pit profile and pit volume) of various materials exposed to pressure wave impacts was simulated making use of a 2D axisymmetric numerical code simulating the interaction between pressure wave and an elastoplastic solid. Making use of numerical results, a new parameter β (defined as the ratio between the pressure wave energy and the generated pit volume) was introduced and evaluated for three materials (aluminum, copper, and stainless steel). By associating numerical simulations and experimental results concerning pitted samples exposed to cavitating flows (volume damage rate), the pressure wave power density and the flow aggressiveness potential power were introduced. These physical properties of the flow characterize the cavitation intensity and can be related to the flow hydrodynamic conditions. Associated to β and ηwave/bubble parameters, these power densities appeared to be useful tools to predict the cavitation erosion power.

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Figures

Grahic Jump Location
Fig. 1

Scheme of the proposed physical model—pressure wave emitted during the collapse of vapor structures is considered to be the phenomenon responsible for material damage. The collapse of vapor cavities is characterized by potential energy Epot (related to the pressure gradient and to the cavity volume) and by collapse efficiency ηwave/bubble; the emitted pressure wave is characterized by the acoustic energy Ewave; the material damage is described by the indentation volume Vpit = f(R10%,H).

Grahic Jump Location
Fig. 2

(a) History of bubble radius; (b) time distribution of the pressure signal at different radius. For this example: R0 = 0.1 mm; p=0.7025 atm; pg0 = 702.5 Pa.

Grahic Jump Location
Fig. 3

Time distribution of the pressure signal at r = 1 mm from bubble center: the wave passage time δt is given by the pressure signal width at p = pmax/2

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Fig. 4

Dimensionless pressure (p/pmax) versus dimensionless time (t/δt) in different cases with p = 1 bar; (a) R0 = 1 mm, pg0 = 1000 Pa, r = 1 mm; (b) R0 = 1 mm, pg0 = 200 Pa, r = 0.1 mm; (c) R0 = 0.1 mm, pg0 = 500 Pa, r = 1 mm

Grahic Jump Location
Fig. 5

Evolution of (cliq δt/R0) as a function of (pg0/p∞) in different cases: 2 mm < R0 < 0.01 mm, 50 Pa < pg0 < 1500 Pa, 0.7 bar < p < 3 bars, cliq ∼ 1500 m/s

Grahic Jump Location
Fig. 6

Time distribution of the pressure signal at a distance of r = 8.6 mm from bubble center (R0 = 1 mm, p = 1 atm). Comparison between experimental data and simulation.

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Fig. 7

Collapse efficiency as a function of pg0/p for different initial bubble radius (efficiency calculation is based on total energy value: Ewave = Etot). Results obtained by Refs. [14,19] are also plotted.

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Fig. 8

(a) Spatial pressure signal applied to the solid surface at seven different times. The pressure load corresponds to the impact of a pressure wave emitted at a distance L to the solid wall; (b) stress field (second invariant of the deviatoric part) in the material due to the pressure wave impact at one given time. Results are given in N/m2. The coordinates are cylindrical axisymmetric and only one meridian half-plane is presented.

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Fig. 9

Permanent surface deformation (nondimensional pit profile) calculated for pressure wave impact on material surface. Numerical results are compared with experimental ones measured by 3D laser profilometry and observed on sample surface exposed to different cavitation conditions [45]. Pit profile is characterized by the radius R10%, depth H, and volume Vpit obtained by trapeze integration. The damage is characterized by a plastic deformation of the surface material, without mass loss.

Grahic Jump Location
Fig. 10

Internal stress Eis and kinetic Ek energy distributions in the material during pressure wave impact on an aluminum solid sample. It can be seen the residual plastic energy Epl remaining in the material after impact.

Grahic Jump Location
Fig. 11

The figure illustrates the relation between the pressure wave energy and pit volume obtained by numerical simulations concerning three materials (316 L SS). Based on previous work [7], the ranges of the pressure wave characteristics adopted by simulations are: 0.8 GPa ≤ psolid ≤ 4 GPa; 10 ns ≤ δt ≤ 150 ns; 10 μm ≤ L ≤ 100 μm. The figure presents points evaluated from several calculations and the correspondent trend curves.

Grahic Jump Location
Fig. 12

Evaluation of β parameter as a function of the stress limit S0: calculated points and trend curves

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Fig. 13

MODULAB test rig. The cavitation appears in the wake zone of the jet. Generated vapor structures are convected downstream, and the samples are damaged during the collapses of these vapor structures.

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Fig. 14

Pressure wave power density (measured by three different materials) as a function of the flow velocity. For tested stainless steel samples, S0 ≈ 400 MPa and β ≈ 90 J/mm3.

Grahic Jump Location
Fig. 15

Flow aggressiveness potential power density (evaluated for three different materials) as a function of the flow velocity. For tested stainless steel samples, S0 ≈ 400 MPa and β ≈ 90 J/mm3.

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