## 留言板

 引用本文: 陈玮琪, 王宝寿, 颜开, 鲁海燕. 物体垂直出入水的非定常空泡数学模型[J]. 应用数学和力学, 2013, 34(11): 1130-1140.
CHEN Wei-qi, WANG Bao-shou, YAN Kai, LU Hai-yan. Model of the Unsteady Vertical Water-Entry and Water-Exit Cavities[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1130-1140. doi: 10.3879/j.issn.1000-0887.2013.11.002
 Citation: CHEN Wei-qi, WANG Bao-shou, YAN Kai, LU Hai-yan. Model of the Unsteady Vertical Water-Entry and Water-Exit Cavities[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1130-1140.

## 物体垂直出入水的非定常空泡数学模型

##### doi: 10.3879/j.issn.1000-0887.2013.11.002

###### 作者简介:陈玮琪(1971—),男,湖南人,高级工程师,博士(通讯作者. E-mail: tiger-cwq@aliyun.com).
• 中图分类号: O35;TV131.3+2

## Model of the Unsteady Vertical Water-Entry and Water-Exit Cavities

• 摘要: 研究了物体从水下向水面高速运动产生的非定常垂直空泡，建立了出水垂直空泡的数学模型，得到了匀速、空泡压力不变条件下的空泡外形、长度、体积随水深变化的解析解，给出了出水通气空泡发展为超空泡的条件．利用类似的方法建立了水平空泡和入水空泡的数学模型，并对3种空泡进行了比较研究．比较研究的结论是，随物体距水面的水深减小，出水空泡体积自身有增大趋势，空泡不容易发生泄气现象．且要保持出水空泡压力不变，空泡内的气体含量就应该增加（可通过人工通气方式）．入水空泡正好相反，随物体入水深度增加，空泡体积自身有收缩的趋势，并挤压空泡内的气体从环境压力较低的空泡尾部喷射而出，导致空泡内的气体含量减少，空泡压力降低．但是当空泡压力低于环境压力后，空泡尾部又将被环境高压所封闭，气体喷射不出来．随着入水深度继续增加，空泡尾部将重复上述过程，形成周期性的喷射封闭喷射封闭的脉动过程，这个脉动喷射过程将在空泡尾部的流体中形成一连串小气泡，并由于空泡内的压力波动而导致空泡形状发生波动现象．
•  [1] Michel J M. Introduction to cavitation and supercavitation[R]. RTO AVT Lecture. Brussels, 2001. [2] Semenenko V N. Artificial supercavitation. physices and calculation[R]. RTO AVT Lecture. Brussels, 2001. [3] Savchenko Y N, Semenenko V N, Putilin S L. Unsteady supercavitated motion of bodies[J].International Journal of Fluid Mechanics Research,2000, 37(1): 109-137. [4] Savchenko Y N, Semenenko V N. The gas absorption into supercavity from liquidgas bubble mixture[C]// Proc Third Internal Symposium on Cavitation.Vol 2. Grenoble, France, 1998: 49-53. [5] Logvinovical G V.Hydrodynamics of Flows With Free Boundaries [M]. Halsted Press, 1973. [6] Vasin A D. The principle of independence of the cavity sections expansion (Logvinovich’s principle) as the basis for investigation on cavitation flows[R]. RTO AVT Lecture. Brussels, 2001. [7] Savchenko Y N, Semenenko V N. Wave formation on the boundaries of cavities forming at water entry of a disk and cones[C]// Problems of HighSpeed Fluid Mechanics.Cheboksary: Chyvashi University Press, 1993: 231-239. [8] Semenenko V N. Dynamic processes of supercavitation and computer simulation[R]. RTO AVT Lecture. Brussels, 2001. [9] Bergmann R, Van der Meer D, Gekle S, Van der Bos A, Lohse D. Controlled impact of a disk on a water surface: cavity dynamics[J].J Fluid Mech,2009, 633: 381-409. [10] 鲁传敬, 李杰. 水下航行体出水空泡溃灭过程及其特性研究[C]//第十一届全国水动力学学术会议暨第二十四届全国水动力学研讨会并周培源教授诞辰110周年纪念大会文集. 北京: 海洋出版社, 2012: 54-67. (LU Chuan-jing, LI Jie. Research on the cavity collapse of the exitwater body[C]//Proceeding of the 11th National Congress on Hydrodynamics & 24th National Conference on Hydrodynamics and Commemoration of the 110th Anniversary of ZHOU Pei-yuan’s Birth.Beijing: Ocean Press, 2012: 54-67.(in Chinese)) [11] 王一伟, 黄晨光, 杜特专, 方新, 梁乃刚. 航行体垂直出水载荷与空泡溃灭机理分析[J]. 力学学报, 2012, 44(1): 39-48.( WANG Yi-wei, Huang Chen-guang, DU Te-zhuan, FANG Xin, LIANG Nai-gang. Mechanism analysis about cavitation collapse load of underwater vehicles in a vertical launching process[J].Chinese Journal of Theoretical and Applied Mechanics,2012, 44(1): 39-48.(in Chinese)) [12] 陈玮琪, 王宝寿, 颜开, 易淑群. 空化器出水非定常垂直空泡的研究[J]. 力学学报, 2013, 45(1): 76-82.(CHEN Wei-qi, WANG Bao-shou, YAN Kai, YI Shu-qun. Study on the unsteady vertical cavity of the exit-water cavitor[J].Chinese Journal of Theoretical and Applied Mechanics,2013, 45(1): 76-82.(in Chinese))
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##### 出版历程
• 收稿日期:  2013-05-20
• 修回日期:  2013-06-25
• 刊出日期:  2013-11-15

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