Prediction of Cavitation Depth in an Al-Cu Alloy Melt with Bubble Characteristics Based on Synchrotron X-ray Radiography

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Abstract

The size of cavitation region is a key parameter to estimate the metallurgical effect of ultrasonic melt treatment (UST) on preferential structure refinement. We present a simple numerical model to predict the characteristic length of the cavitation region, termed cavitation depth, in a metal melt. The model is based on wave propagation with acoustic attenuation caused by cavitation bubbles which are dependent on bubble characteristics and ultrasonic intensity. In situ synchrotron X-ray imaging of cavitation bubbles has been made to quantitatively measure the size of cavitation region and volume fraction and size distribution of cavitation bubbles in an Al-Cu melt. The results show that cavitation bubbles maintain a log-normal size distribution, and the volume fraction of cavitation bubbles obeys a tanh function with the applied ultrasonic intensity. Using the experimental values of bubble characteristics as input, the predicted cavitation depth agrees well with observations except for a slight deviation at higher acoustic intensities. Further analysis shows that the increase of bubble volume and bubble size both leads to higher attenuation by cavitation bubbles, and hence, smaller cavitation depth. The current model offers a guideline to implement UST, especially for structural refinement.

Nomenclature

A

Vibration amplitude of the sonotrode

S

Area of cavitation region

C0, C1st, C2nd

Fitting constants

Re

Identifier of real number

Im

Identifier of imaginary number

Φ

Complex dimensionless parameter

ρ

Liquid density, 3340 kg/m3

kmix

Complex wave vector

α

attenuation coefficient

αth

Local attenuation corresponding to local intensity Ith

ω

Wave frequency (ω = 2πf)

ω0

Resonance frequency (Hz)

c

Sound speed in liquid at ambient pressure (m/s)

c0

Constant sound speed (m/s), 4600 m/s

cmix

Complex wave velocity

R

Equilibrium radius of bubbles (m)

f

Ultrasound frequency (Hz), 20 kHz

f(r, R)

Number distribution of cavitation bubbles with equilibrium radius R at distance r

fN(r)

Normalized form of f(r, R)

Nb

Total number of cavitation bubbles

β(r)

Volume fraction of cavitation bubbles at distance r

I

Acoustic intensity

I0

Applied acoustic intensity at the radiation face of ultrasonic horn

Ith

Intensity threshold of cavitation, 1.2 MW/m2

pun

Undisturbed pressure at bubble location (Pa), 105 Pa

pa

Pressure amplitude (Pa)

p0

Pressure input (Pa)

σs

Surface tension, 0.87 N/m

Φ

Complex dimensionless parameter

χ

Dimensionless parameter

γ

Specific heat ratio of gas inside bubbles, 1.4 for air bubble in water[39]

D

Thermal diffusivity of gas inside bubbles, 8.418 × 10−5 m2/s

b

Damping factor (1/s)

μ

Liquid viscosity (Pa s), 1 MPa s for aluminum melt at 700 °C[8]

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Notes

Acknowledgments

The authors would like to thank the financial support from the National Key R&D Program of China (No. 2016YFB0701405), the National Science Foundation of China (Nos. 51627802, 51704196, 51771118, and 51704195), the National Science Foundation of China and Steel Joint Project (No. U1760110), and Shanghai Science and Technology Committee (No. 16DZ2260602).

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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2018

Authors and Affiliations

  1. 1.Shanghai Key Lab of Advanced High-temperature Materials and Precision Forming, School of Materials Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Materials Genome Initiative CenterShanghai Jiao Tong UniversityShanghaiChina
  3. 3.Shanghai Synchrotron Radiation FacilityShanghai Institute of Applied Physics, CASShanghaiChina
  4. 4.Shanghai Innovation Institute for MaterialsShanghaiChina

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