Linear Analysis of Dispersive Waves in Bubbly Flows Based on Averaged Equations(Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid mechanics)
Linear Analysis of Dispersive Waves in Bubbly Flows Based on Averaged Equations(Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid mechanics)
复制标题
基于平均方程的气泡流中色散波的线性分析（电磁学、光学、声学、传热学、经典力学、流体力学）
DOI：
10.1143/jpsj.75.104401
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发表时间：
2006
影响因子：
1.7
通讯作者：
S. Fujikawa
中科院分区：
文献类型：
--
作者：
T. Yano;R. Egashira;S. Fujikawa
本文根据作者最近导出的一组平均方程组，对含有许多球形气泡的水流中的一维线性色散波进行了解析研究。方程组由气、液相守恒定律和气泡壁运动方程组成。除了在每个阶段的体积平均压力，在气泡壁的表面平均液体压力被纳入。水的可压缩性以及气泡中的气体的可压缩性被考虑在内，并且包括虚拟质量力的模型，尽管忽略了雷诺应力、粘度、热导率和跨气泡壁的相变。主要结果如下：（1）将波分解为快波、慢波和对流波（空隙波）。(ii)在均匀流中，对于所有的真实的波数，这三种模态都稳定存在。(iii)在空隙率无穷小的极限下，得到了基本解的显式表达式。(iv)在本平均方程适用的范围内，不稳定性不会出现。
One-dimensional linear dispersive waves in water flows containing a number of small spherical air bubbles are analytically studied on the basis of a set of averaged equations recently derived by the present authors. The set of equations consists of the conservation laws for gas and liquid phases and the equation of motion of bubble wall. In addition to the volume-averaged pressure in each phase, the surface-averaged liquid pressure at the bubble wall is incorporated. The compressibility of water is taken into account as well as that of gas in bubbles, and a model of virtual mass force is included, although the Reynolds stress, viscosity, heat conductivity, and the phase change across the bubble wall are disregarded. The results are summarized as follows: (i) the waves are decomposed into the fast mode, slow mode, and convection mode (void wave). (ii) In the uniform flows, the three modes stably exist for all real wave numbers. (iii) In the limit of infinitesimal void fraction, the explicit representation of the elementary solution is obtained. (iv) The instability does not appear in the range where the present averaged equations are applicable.