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Ejecta mixing takes place at the interface between metal and gas under shock loading, i.e., the transport process of ejecta from metal surface happens in gas. Ejecta production and transport processes in gas are the focuses and key problems of shock wave physics at present. So far, extensive investigations have been devoted mainly to the ejecta formation from metal surface under shock-loaded conditions, and many experimental measurement techniques have been developed, such as the Asay foil, high-speed camera and holography technique. As a newly developed instrument, photon Doppler velocitymetry (PDV) which allows the simultaneous detection of velocities of multiple particles has been widely used in the dynamic impact areas, especially in micro-jetting and ejecta mixing experiments. Although PDV spectrogram includes abundant information about ejecta particles, it seems to be too hard to obtain the particle velocity history, which embarrasses the analysis and application of PDV spectrogram. In this paper, the equation of particle motion including the effects of aerodynamic damping force, pressure gradient force, and additional mass force is established, and the analytical solutions of the particle position and velocity are derived in the conditions of planar constant flow, constant flow, and constant acceleration flow. According to the analytical solutions, the characteristics of particle movement are analyzed. A simplified formulation of the relaxation time of the particle velocity, which reflects the particle decelerated speed, is given. And it is found that the relaxation time is proportional to the four-thirds power of particle diameter. Based on the characteristics of particle motion in the planar constant flow, a new method is proposed to analyze the spectrogram of PDV. The fastest velocity of particle in the mixing zone is obtained by extracting the upper part of PDV spectrogram. By integrating the fastest velocity, the time evolution of the head of mixing zone is deduced approximately. The thickness of the mixing zone can be obtained by subtracting the free surface position from the head of mixing zone. The relaxation time of particle velocity is inferred by the exponential fitting of the fastest velocity based on the motion equation of the particle in the planar constant flow. Furthermore, the equivalent diameter of the mixing zone head can also be obtained through the relaxation time. Based on the above methods, the spectrograms of various ejection mixing experiments under different shock-loaded conditions and gas environments are analyzed. The time evolutions of the mixing zone and equivalent diameter are presented, and the effects of shock loading strength and post-shock gas temperature on the mixing zone are analyzed. It is found that the deduced equivalent diameter in gas is smaller than that in vacuum, validating the pneumatic breakup of liquid metal particles in gas.
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Keywords:
- ejection mixing /
- photonic Doppler velocimetry /
- velocity spectrogram /
- equivalent diameter
[1] Ogorodnikov V A, Mikhailov A L, Burtsev V V, Lobastov S A, Erunov S V, Romanov A V, Rudnev A V, Kulakov E V, Bazarov Y B, Glushikhin V V, Kalashnik I A, Tsyganov V A, Tkachenko B I 2009 J. Exp. Theor. Phys. 109 530
[2] Or D M, Hammerberg J M, Buttler W T, Mariam F G, Morris C, Rousculp C, Stone J B 2012 AIP Conf. Proc. 1426 1351
[3] Fung J, Harrison A K, Chitanvis S, Margulies J 2013 Comput. Fluids 83177
[4] He A M, Wang P, Shao J L, Duan S Q 2014 Chin. Phys. B 23 047102
[5] Wang P, Sun H Q, Shao J L, Qin C S, Li X Z 2012 Acta Phys. Sin. 61 234703 (in Chinese) [王裴, 孙海权, 邵建立, 秦承森, 李欣竹 2012 物理学报 61 234703]
[6] Elias P, Chapron P, Mondot M 1989 Shock Compression of Condensed Matter Albuquerque, New Mexico, August 14-17, 1989 p783
[7] Buttler W T, Or D M, Preston D L, Mikaelian K O, Cherne F J, Hixson R S, Mariam F G, Morris C, Stone J B, Terrones G, Tupa D 2012 J. Fluid Mech. 703 60
[8] Prudhomme G, Mercier P, Berthe L, Bnier J, Frugier P A 2014 J. Phys. Conf. Ser. 500 142022
[9] Buttler W T, Or D M, Dimonte G, Morris C, Terrones G, Bainbridge J R, Hogan G E, Hollander B, Holtkamp D, Kwiatkowski K, Marr-Lyon M, Mariam F, Merrill F E, Nedrow P, Saunders A, Schwartz C L, Stone B, Tupa D, Vogan-Mcneil W S 2009 Report LA-UR-10-00739
[10] Zhao X W, Li X Z, Wang X J, Song P, Zhang H Z, Wu Q 2015 Acta Phys. Sin. 64 124701 (in Chinese) [赵信文, 李欣竹, 王学军, 宋萍, 张汉钊, 吴强 2015 物理学报 64 124701]
[11] Mercier P, Bnier J, Frugier P A, Contencin G, Veaux J, Lauriot-Basseuil S, Debruyne M 2009 Proc. SPIE 7126 7126O
[12] Prudhomme G, Mercier P, Berthe L 2014 J. Phys. Conf. Ser. 500 142027
[13] Fedorov A V, Mikhailov A L, Finyushin S A, Nazarov D V, Chudakov E A, Kalashnikov D A, Butusov E I 2013 Report Study of lead behavior features at shock loading and further unloading, Biennial Intl. Conference of the APS Topical Group on Shock Compression of Condensed Mater-2013
[14] Fang D Y 1988 Two Phase Flow Mechanics (Changsha: Science and Technology of National Defense Publisher) pp82-84 (in Chinese) [方丁酉 1988 两相流动力学(长沙: 国防科技大学出版社)第82-84页]
[15] Sorenson D S, Pazuchanics P, Johnson R P, Malone R M, Kaufman M I, Tibbitts A, Tunnell T, Marks D, Capelle G A, Grover M, Marshall B, Stevens G D, Turley W D, Lalone B 2014 Report LA-UR-14-24722
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[1] Ogorodnikov V A, Mikhailov A L, Burtsev V V, Lobastov S A, Erunov S V, Romanov A V, Rudnev A V, Kulakov E V, Bazarov Y B, Glushikhin V V, Kalashnik I A, Tsyganov V A, Tkachenko B I 2009 J. Exp. Theor. Phys. 109 530
[2] Or D M, Hammerberg J M, Buttler W T, Mariam F G, Morris C, Rousculp C, Stone J B 2012 AIP Conf. Proc. 1426 1351
[3] Fung J, Harrison A K, Chitanvis S, Margulies J 2013 Comput. Fluids 83177
[4] He A M, Wang P, Shao J L, Duan S Q 2014 Chin. Phys. B 23 047102
[5] Wang P, Sun H Q, Shao J L, Qin C S, Li X Z 2012 Acta Phys. Sin. 61 234703 (in Chinese) [王裴, 孙海权, 邵建立, 秦承森, 李欣竹 2012 物理学报 61 234703]
[6] Elias P, Chapron P, Mondot M 1989 Shock Compression of Condensed Matter Albuquerque, New Mexico, August 14-17, 1989 p783
[7] Buttler W T, Or D M, Preston D L, Mikaelian K O, Cherne F J, Hixson R S, Mariam F G, Morris C, Stone J B, Terrones G, Tupa D 2012 J. Fluid Mech. 703 60
[8] Prudhomme G, Mercier P, Berthe L, Bnier J, Frugier P A 2014 J. Phys. Conf. Ser. 500 142022
[9] Buttler W T, Or D M, Dimonte G, Morris C, Terrones G, Bainbridge J R, Hogan G E, Hollander B, Holtkamp D, Kwiatkowski K, Marr-Lyon M, Mariam F, Merrill F E, Nedrow P, Saunders A, Schwartz C L, Stone B, Tupa D, Vogan-Mcneil W S 2009 Report LA-UR-10-00739
[10] Zhao X W, Li X Z, Wang X J, Song P, Zhang H Z, Wu Q 2015 Acta Phys. Sin. 64 124701 (in Chinese) [赵信文, 李欣竹, 王学军, 宋萍, 张汉钊, 吴强 2015 物理学报 64 124701]
[11] Mercier P, Bnier J, Frugier P A, Contencin G, Veaux J, Lauriot-Basseuil S, Debruyne M 2009 Proc. SPIE 7126 7126O
[12] Prudhomme G, Mercier P, Berthe L 2014 J. Phys. Conf. Ser. 500 142027
[13] Fedorov A V, Mikhailov A L, Finyushin S A, Nazarov D V, Chudakov E A, Kalashnikov D A, Butusov E I 2013 Report Study of lead behavior features at shock loading and further unloading, Biennial Intl. Conference of the APS Topical Group on Shock Compression of Condensed Mater-2013
[14] Fang D Y 1988 Two Phase Flow Mechanics (Changsha: Science and Technology of National Defense Publisher) pp82-84 (in Chinese) [方丁酉 1988 两相流动力学(长沙: 国防科技大学出版社)第82-84页]
[15] Sorenson D S, Pazuchanics P, Johnson R P, Malone R M, Kaufman M I, Tibbitts A, Tunnell T, Marks D, Capelle G A, Grover M, Marshall B, Stevens G D, Turley W D, Lalone B 2014 Report LA-UR-14-24722
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