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The study of far-field pressure wavelet of air-gun bubble is the basic research of air-gun sources. In this paper, a boundary element bubble model is established to simulate the dynamics of bubble, and an energy equivalent method is put forward to solve the bottleneck of bubble jet. In our simplified model, the bubble model takes into consideration the thermodynamic factors such as heat transfer and gas release, and the numerical results agree with the data of Nucleus software well. Based on the established model, the influence of heat transfer coefficient, air-gun firing time, and specific heat at constant volume on the pressure wavelet are studied. Finally, the three-dimensional bubble merging numerical method is put forward, which is an expansion of the axisymmetric model. Thus, the preliminary study of coherent air-gun is conducted, especially the influence of the space between two bubbles on the wavelet. This paper provides a reference for the research of air-gun.
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Keywords:
- air-gun bubble /
- boundary element method /
- thermodynamics /
- coherent air-gun
[1] Chen H L, Quan H Y, Yu G P, Li W D 2008 Equip. Geophys. Prospect 18 211(in Chinese) [陈浩林, 全海燕, 於国平, 李维东, 刘原英 2008 物探装备 18 211]
[2] Chen H L, Quan H Y, Yu G P, Li W D 2008 Equip. Geophys. Prospect 18 300 (in Chinese) [陈浩林, 全海燕, 於国平, 李维东, 刘原英 2008 物探装备 18 300]
[3] Zhao M H, Qiu X L, Xia S H, Wang P, Xu H L, Ye C M, Kang Y 2008 Chinese J. Geophys 51 300 (in Chinese) [赵明辉, 丘学林, 夏少红, 王平, 徐辉龙, 叶春明, 康英 2008 地球 51 300]
[4] Rayleigh J W 1917 Phil. Mag 34 94
[5] Gilmore F R 1952 Hydro. Lab. Calif. inst. Technical. Report (California) 26 117
[6] Ziolkowski A 1970 GeophysJ. Roy. AstrS 21 137
[7] M L,r o, R Sollie 1992 Geophysics 57 1633
[8] Zhang A M 2006 Ph. D. Dissertation (Harbin: Harbin Engineering University) (in Chinese) [张阿漫 2006 博士论文(哈尔滨:哈尔滨工程大学)]
[9] S RungsiyaphornratE KlaseboerB C Khoo Yeo K S 2003 ComputFluids 32 1049
[10] Zhang A M, Zeng L Y, Wang S P, Yang S T, Yao X L, Wen X Y 2010 Appl. Math. Mech. 31 163 (in Chinese) [张阿漫, 曾令玉, 王诗平, 杨树涛, 姚雄亮, 闻雪友 2010 应用数学和力学 31 163]
[11] Wang S P, Zhang A M, Liu Y L, Wang C 2012 Acta MechSin 44 56 (in Chinese) [王诗平, 张阿漫, 刘云龙, 王超 2012 力学学报 44 56]
[12] Zhang H H, Gao B, Zhang C 2003 Acta Phys. Sin. 52 1714(in Chinese)[张寒虹, 高波, 张弛 2003 52 1714]
[13] Wang Q X, Yeo K S, B C Khoo, K Y Lam 1996 Comput. Fluids 25 607
[14] Wang Q X, Yeo K S, B C Khoo K Y Lam 2005 Theor. Comput. Fluid Dyn 00 1
[15] Wang Q X, Blake J R 2010 J. Fluid Mech 34 1
[16] Newman J N 1977 Marine Hydrodynamics (1st Ed.) (London: MIT Press) p131
[17] Shen W D, Tong J G 2007 Engineering Thermodynamics (4th Ed.)(Beijing: Higher Education Press) p43 (in Chinese) [沈维道, 童钧耕 2007 工程热力学第4版 (北京:高等教育出版社) 第43页]
[18] Wang L M 2010 Ph. D. Dissertation (Xi'an: Chang'an University) (in Chinese) [王立明 2010 博士论文 (西安:长安大学)]
[19] Zhang A M, Wang C, Wang C, Wang S P, Cheng X D 2012 Acta Phys. Sin. 61 084701 (in Chinese) [张阿漫, 王超, 王诗平, 程晓达 2012 61 084701]
[20] Y L Zhang, K S Yeo, B C Khoo, C Wang 2001 J. Comput. Phys. 166 336
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[1] Chen H L, Quan H Y, Yu G P, Li W D 2008 Equip. Geophys. Prospect 18 211(in Chinese) [陈浩林, 全海燕, 於国平, 李维东, 刘原英 2008 物探装备 18 211]
[2] Chen H L, Quan H Y, Yu G P, Li W D 2008 Equip. Geophys. Prospect 18 300 (in Chinese) [陈浩林, 全海燕, 於国平, 李维东, 刘原英 2008 物探装备 18 300]
[3] Zhao M H, Qiu X L, Xia S H, Wang P, Xu H L, Ye C M, Kang Y 2008 Chinese J. Geophys 51 300 (in Chinese) [赵明辉, 丘学林, 夏少红, 王平, 徐辉龙, 叶春明, 康英 2008 地球 51 300]
[4] Rayleigh J W 1917 Phil. Mag 34 94
[5] Gilmore F R 1952 Hydro. Lab. Calif. inst. Technical. Report (California) 26 117
[6] Ziolkowski A 1970 GeophysJ. Roy. AstrS 21 137
[7] M L,r o, R Sollie 1992 Geophysics 57 1633
[8] Zhang A M 2006 Ph. D. Dissertation (Harbin: Harbin Engineering University) (in Chinese) [张阿漫 2006 博士论文(哈尔滨:哈尔滨工程大学)]
[9] S RungsiyaphornratE KlaseboerB C Khoo Yeo K S 2003 ComputFluids 32 1049
[10] Zhang A M, Zeng L Y, Wang S P, Yang S T, Yao X L, Wen X Y 2010 Appl. Math. Mech. 31 163 (in Chinese) [张阿漫, 曾令玉, 王诗平, 杨树涛, 姚雄亮, 闻雪友 2010 应用数学和力学 31 163]
[11] Wang S P, Zhang A M, Liu Y L, Wang C 2012 Acta MechSin 44 56 (in Chinese) [王诗平, 张阿漫, 刘云龙, 王超 2012 力学学报 44 56]
[12] Zhang H H, Gao B, Zhang C 2003 Acta Phys. Sin. 52 1714(in Chinese)[张寒虹, 高波, 张弛 2003 52 1714]
[13] Wang Q X, Yeo K S, B C Khoo, K Y Lam 1996 Comput. Fluids 25 607
[14] Wang Q X, Yeo K S, B C Khoo K Y Lam 2005 Theor. Comput. Fluid Dyn 00 1
[15] Wang Q X, Blake J R 2010 J. Fluid Mech 34 1
[16] Newman J N 1977 Marine Hydrodynamics (1st Ed.) (London: MIT Press) p131
[17] Shen W D, Tong J G 2007 Engineering Thermodynamics (4th Ed.)(Beijing: Higher Education Press) p43 (in Chinese) [沈维道, 童钧耕 2007 工程热力学第4版 (北京:高等教育出版社) 第43页]
[18] Wang L M 2010 Ph. D. Dissertation (Xi'an: Chang'an University) (in Chinese) [王立明 2010 博士论文 (西安:长安大学)]
[19] Zhang A M, Wang C, Wang C, Wang S P, Cheng X D 2012 Acta Phys. Sin. 61 084701 (in Chinese) [张阿漫, 王超, 王诗平, 程晓达 2012 61 084701]
[20] Y L Zhang, K S Yeo, B C Khoo, C Wang 2001 J. Comput. Phys. 166 336
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