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]
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).
References
- 1.F. Wang, D. Eskin, J. Mi, T. Connolley, J. Lindsay and M. Mounib: Acta Mater., 2016, vol. 116, pp. 354-363.CrossRefGoogle Scholar
- 2.G. I. Eskin: Ultrason. Sonochem., 2001, vol. 8(3), pp. 319-325.CrossRefGoogle Scholar
- 3.L. Zhang, D. G. Eskin and L. Katgerman: J. Mater. Sci., 2011, vol. 46(15), pp. 5252-5259.CrossRefGoogle Scholar
- 4.W. Zhai, Z. Y. Hong, X. L. Wen, D. L. Geng and B. Wei: Mater. Design, 2015, vol. 72, pp. 43-50.CrossRefGoogle Scholar
- 5.C. Ruirun, Z. Deshuang, M. Tengfei, D. Hongsheng, S. Yanqing, G. Jingjie and F. Hengzhi: Sci. Rep., 2017, vol. 7, pp. 1-15.CrossRefGoogle Scholar
- 6.X. Liu, Z. Zhang, W. Hu, Q. Le, L. Bao, J. Cui and J. Jiang: Ultrason. Sonochem., 2015, vol. 26, pp. 73-80.CrossRefGoogle Scholar
- 7.J. Yan, Z. Xu, L. Shi, X. Ma and S. Yang: Mater. Design, 2011, vol. 32(1), pp. 343-347.CrossRefGoogle Scholar
- 8.G. I. Eskin and D. G. Eskin: Ultrasonic Treatment of Light Alloy Melts. 2nd ed. CRC Press, London, 2014, pp. 17-74.Google Scholar
- 9.T. V. Atamanenko, D. G. Eskin, L. Zhang and L. Katgerman: Metall. Mater. Trans. A, 2010, vol. 41(8), pp. 2056-2066.CrossRefGoogle Scholar
- 10.F. Wang, D. Eskin, J. Mi, C. Wang, B. Koe, A. King, C. Reinhard and T. Connolley: Acta Mater., 2017, vol. 141, pp. 142-153.CrossRefGoogle Scholar
- 11.A. Ramirez, M. Qian, B. Davis, T. Wilks and D. H. StJohn: Scripta Mater., 2008, vol. 59(1), pp. 19-22.CrossRefGoogle Scholar
- 12.R. Chow, R. Blindt, R. Chivers and M. Povey: Ultrasonics, 2005, vol. 43(4), pp. 227-230.CrossRefGoogle Scholar
- 13.D. Shu, B. Sun, J. Mi and P. S. Grant: Metall. Mater. Trans. A, 2012, vol. 43(10), pp. 3755-3766.CrossRefGoogle Scholar
- 14.S. Labouret and J. Frohly: Eur. Phys. 2002, vol. 19(1), pp. 39-54.Google Scholar
- 15.A. Brotchie, F. Grieser and M. Ashokkumar: Phys. Rev. Lett., 2009, vol. 102(8), pp. 4302-4305.CrossRefGoogle Scholar
- 16.F. Burdin, N. A. Tsochatzidis, P. Guiraud, A. M. Wilhelm and H. Delmas: Ultrason. Sonochem., 1999, vol. 6(1-2), pp. 43-51.CrossRefGoogle Scholar
- 17.N. A. Tsochatzidis, P. Guiraud, A. M. Wilhelm and H. Delmas: Chem. Eng. Sci., 2001, vol. 56(5), pp. 1831-1840.CrossRefGoogle Scholar
- 18.T. Matsunaga, K. Ogata, T. Hatayama, K. Shinozaki and M. Yoshida: Compos. Part A, 2007, vol. 38(3), pp. 771-778.CrossRefGoogle Scholar
- 19.S. Komarov, K. Oda, Y. Ishiwata and N. Dezhkunov: Ultrason. Sonochem., 2013, vol. 20(2), pp. 754-761.CrossRefGoogle Scholar
- 20.I. Tzanakis, G. S. B. Lebon, D. G. Eskin and K. A. Pericleous: J. Mater. Process. Technol., 2016, vol. 229, pp. 582-586.CrossRefGoogle Scholar
- 21.I. Tzanakis, G. S. Lebon, D. G. Eskin and K. A. Pericleous: Ultrason. Sonochem., 2017, vol. 34, pp. 651-662.CrossRefGoogle Scholar
- 22.T. L. Lee, J. C. Khong, K. Fezzaa and J. W. Mi: Mater. Sci. Forum, 2013, vol. 765, pp. 190-194.CrossRefGoogle Scholar
- 23.H. Huang, D. Shu, Y. Fu, J. Wang and B. Sun: Ultrason. Sonochem., 2014, vol. 21(4), pp. 1275-1278.CrossRefGoogle Scholar
- 24.W. W. Xu, I. Tzanakis, P. Srirangam, W. U. Mirihanage, D. G. Eskin, A. J. Bodey and P. D. Lee: Ultrason. Sonochem., 2016, vol. 31, pp. 355-361.CrossRefGoogle Scholar
- 25.L. V. Wijngaarden: J. Fluid Mech., 1968, vol. 33(33), pp. 465-474.CrossRefGoogle Scholar
- 26.R. E. Caflisch, M. J. Miksis, G. C. Papanicolaou and L. Ting: J. Fluid Mech., 1985, vol. 153, pp. 259-273.CrossRefGoogle Scholar
- 27.K. W. Commander and A. Prosperetti: J. Acoust. Soc. Am., 1989, vol. 85(2), pp. 732-746.CrossRefGoogle Scholar
- 28.H. J. Kim, M. H. Chi and I. K. Hong: Journal of Industrial & Engineering Chemistry, 2009, vol. 15(6), pp. 919-928.CrossRefGoogle Scholar
- 29.L. Nastac: Metall. Mater. Trans. B, 2011, vol. 42(6), pp. 1297-1305.CrossRefGoogle Scholar
- 30.G. Servant, J. L. Laborde, A. Hita, J. P. Caltagirone and A. Gérard: Ultrason. Sonochem., 2003, vol. 10(6), pp. 347-355.CrossRefGoogle Scholar
- 31.I. Tudela, V. Saez, M. D. Esclapez, M. I. Diez-Garcia, P. Bonete and J. Gonzalez-Garcia: Ultrason. Sonochem., 2014, vol. 21(3), pp. 909-919.CrossRefGoogle Scholar
- 32.G. S. B. Lebon, I. Tzanakis, K. Pericleous and D. Eskin: Ultrason. Sonochem., 2018, vol. 42, pp. 411-421.CrossRefGoogle Scholar
- 33.L. G. S. Bruno, I. Tzanakis, G. Djambazov, K. Pericleous and D. G. Eskin: Ultrason. Sonochem., 2017, vol. 37, pp. 660-668.CrossRefGoogle Scholar
- 34.H. Huang, D. Shu, J. Zeng, F. Bian, Y. Fu, J. Wang and B. Sun: Scripta Mater., 2015, vol. 106, pp. 21-25.CrossRefGoogle Scholar
- 35.M. Qian, A. Ramirez and A. Das: J. Cryst. Growth, 2009, vol. 311(14), pp. 3708-3715.CrossRefGoogle Scholar
- 36.R. Jamshidi, B. Pohl, U. A. Peuker and G. Brenner: Chem. Eng. J., 2012, vol. 189, pp. 364-75.CrossRefGoogle Scholar
- 37.Z. Xu, K. Yasuda and S. Koda: Ultrason. Sonochem., 2013, vol. 20(1), pp. 452-459.CrossRefGoogle Scholar
- 38.M. M. van Iersel, N. E. Benes and J. T. F. Keurentjes: Ultrason. Sonochem., 2008, vol. 15(4), pp. 294-300.CrossRefGoogle Scholar
- 39.C. D. Jr: J. Acoust. Soc. Am., 1959, vol. 31(12), pp. 1654-1667.CrossRefGoogle Scholar