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本文从泡群中气泡动力学方程出发, 对泡壁运动方程进行线性约化, 得到球状泡群中气泡谐振频率的表达式, 并给出了泡群中气泡谐振频率与单泡Minnaert频率的修正系数. 讨论了泡群中气泡初始半径、气泡数量、气泡之间距离对谐振频率的影响. 研究结果表明: 考虑到气泡的相互作用后, 球状泡群中气泡的谐振频率明显小于单泡的Minnaert频率. 随着泡群中气泡数量的减少、气泡之间距离增大, 泡群中气泡之间的相互作用减弱, 气泡的谐振频率回归到Minnaert单泡谐振频率. 同时泡群中气泡的谐振频率随气泡之间距离、气泡数量的影响变化梯度也不相同. 泡群中气泡数量越多、气泡距离近越近, 气泡之间相互作用强, 谐振频率变化幅度快.The interaction between bubbles in bubble group mainly acts on the other bubble through radiation sound pressure between the bubbles. In this paper, based on the bubble dynamics equation in bubble clouds, the equation of bubble wall motion is linearly reduced, the expression of bubble resonance frequency in spherical bubble group is obtained and the correction coefficient of bubble resonance frequency and single bubble are given. Furthermore, the effects of the initial radius, the number of bubbles and the distance between bubbles on the resonance frequency are discussed. The results show that the phase of bubbles is taken into account. Considering the interaction between bubbles, the resonance frequency of bubbles in spherical bubble group is obviously less than that of single bubble. With the decrease of the number of bubbles in bubble group, the distance between bubbles increases, the interaction between bubbles in bubble group decreases, and the resonance frequency of bubbles returns to the resonance frequency of Minnaert single bubble. At the same time, the resonance frequency of bubbles in bubble group changes gradient with the increase of the distance between bubbles and the number of bubbles. However, when the number of bubbles increases a certain value, the resonant frequency of the bubble is almost constant. When the bubble group has a certain radius, the more the number of bubbles, the smaller the resonance frequency of the bubble is, but there exists a critical value. It is also found that a smaller correction coefficient is held by the bubble group with larger initial radius, which indicates the same number of bubble groups. Under the same bubble spacing, the interaction of small bubbles with smaller bubbles is more significant, and the resonance frequency of the bubble is obviously affected. Because the frequency and amplitude of driving sound pressure can only be given values in ultrasonic cavitation, the resonant frequency of cavitation bubbles will be reduced by properly injecting air bubbles into liquid, which makes most of cavitation bubbles undergo intense non-linear oscillating steady-state cavitation. Therefore, the occurrence of cavitation can be effectively suppressed.
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Keywords:
- bubble /
- resonant frequency /
- bubble number /
- distance
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图 1 球形空化云中气泡的运动 (a)气泡初始半径5 μm; (b)泡群中气泡数量为100; (c), (d)气泡初始半径5 μm, 泡群中气泡数量N = 100
Fig. 1. Movement of bubbles in spherical cavitation clouds: (a) Bubble initial radius 5 μm; (b) the number 100; (c), (d) bubble initial radius 5 μm, N = 100.
图 2 泡群中气泡的谐振频率 (a)气泡谐振频率与泡群中气泡之间距离关系; (b)气泡谐振频率与泡群中气泡数量之间关系, 气泡的初始半径均为20 μm
Fig. 2. Resonance frequency of bubbles in bubble group: (a) The relationship between bubble resonance frequency and distance in the bubble group; (b) the relationship between bubble resonance frequency and the number of bubbles in the bubble group, the initial radius of the bubbles is 20 μm.
图 3 修正系数M与泡群中气泡距离关系
Fig. 3. Relationship between correction coefficient and bubble distance.
图 4 气泡初始半径与泡群中气泡谐振频率的关系
Fig. 4. Relationship between the initial radius of bubbles and the resonant frequency of bubbles.
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[1] 陈伟中 2014 声空化物理 (北京, 科学出版社)第2—5页
Chen W Z 2014 Sound Cavitation Physics (Beijing: Science Press) pp2–5 (in Chinese)
[2] Rayleigh J W 1917 Philosophical Magazine 34 94
[3] Cole R H 1948 Underwater Eplosion (Princeton: Princeton U.P)pp60–65
[4] Npltingk B E 2002 Proc. Phys. Soc. 63 674
[5] Plesset M S, Chapmam R B 1977 J. Fluid Mech. 9 145
Google Scholar
[6] Mason T J, J P Lorimer 1988 Lorimer Application and Use of Ultrasound in Chemisty (USA: Ellis Horworrd Limited) pp130—135
[7] Madrazo A, Garcia N, Nieto-Vesperinas M 1998 Phys. Rev. Lett. 80 4590
Google Scholar
[8] Shim A 1971 J. Basic Engin. 93 426
Google Scholar
[9] An Y 2011 Phys. Rev. E 83 66313−1
Google Scholar
[10] 王成会, 林书玉 2010 力学学报 42 1050
Wang C H, Lin S Y 2010 Acta Mech. Sin. 42 1050
[11] 胡静, 林书玉, 王成会, 李锦 2013 物理学报 62 114334
Hu J, Lin S Y, Wang C H, Li J 2013 Acta Phys. Sin. 62 114334
[12] 王成会, 莫润阳, 胡静 2016 物理学报 65 144301
Google Scholar
Wang C H, Mo R Y, Hu J 2016 Acta Phys. Sin. 65 144301
Google Scholar
[13] 王成会, 程建春 2014 物理学报 63 134301
Google Scholar
Wang C H, Cheng J C 2014 Acta Phys. Sin. 63 134301
Google Scholar
[14] Yasui K, Iida Y, Tuziuti T, et al. 2008 Phys. Rev. E 77 66313−1
[15] Barber B P, Hiller R A, Ritva L, et al. 1997 Phys.Reports 281 65
Google Scholar
[16] Kwak H Y, Na J H 1996 Phys. Rev. Lett. 77 4454
Google Scholar
[17] Wang Q X 2004 Phys. Fluids 165 1610
[18] Hsiao C T, Choi J K, Singh S, Chahine G L, et al 2013 J. Fluid Mech. 716 137
Google Scholar
[19] Keith W, Seth J P 1996 Phys. Rev. E 54 R2205
Google Scholar
[20] Cui P, Wang Q X, Wang S P, Zhang A M 2016 Phys. Fluids 28 94
[21] 苗博雅, 安宇 2015 物理学报 64 204301−1
Google Scholar
Miao B Y, An Y 2015 Acta Phys. Sin. 64 204301−1
Google Scholar
[22] 蔡军, 淮秀兰等 2015 科学通报 56 947
Cai J, Huai X L, et al. 2015 Chinese Sci Bull. 56 947
[23] Wang C, Khoo B C, Yeo K S 2003 Comput. Fluids 32 1195
Google Scholar
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