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1.
在竖直振动的圆柱形容器中,将Navier-Stokes方程线性化,利用两时间尺度奇异摄动展开法研究了弱粘性流体的单一自由面驻波运动.整个流场被分为外部势流区和内部边界层区两部分,对两部分区域分别求解,得到包含阻尼项和外驱动影响的线性振幅方程.利用稳定性分析,得到形成稳定表面波的条件,给出了临界曲线.此外,还获得了阻尼系数的解析表达式.最后,将线性阻尼加到理想流体条件下所得到的色散关系中对其进行修正,理论结果证明修正后的驱动频率更加接近实验的结果.通过计算发现,当驱动的频率较低时,流体的粘性对表面波模式选择有重要影响,而表面张力的影响不明显;但当驱动频率较高时,流体的表面张力起主要作用,而流体的粘性影响甚小.  相似文献   
2.
In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.  相似文献   
3.
菅永军  鄂学全 《中国物理》2004,13(8):1191-1200
Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.  相似文献   
4.
垂直激励圆柱形容器中的表面波特性研究   总被引:1,自引:0,他引:1  
利用奇异摄动理论的两时间变量展开法,研究了垂直强迫激励圆柱形容器中的单一水表面驻波模式。假设流体是无粘、不可压且运动是无旋的,在忽略了表面张力的影响下,得到一个具有立方项以及底部驱动项影响的非线性振幅方程。对上述方程进行了数值计算,并研究了特定(3,4)模式的表面驻波结构和特性,如驻波的节点分布及随某些参数的变化规律等,从计算的等高线的图象来看,和以往的实验结果相当吻合。  相似文献   
5.
菅永军  鄂学全  张杰  孟俊敏 《中国物理》2004,13(12):2013-2020
Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term,an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tensionwas introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important.However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.  相似文献   
6.
In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension. A nonlinear slowly varying amplitude equation, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from potential flow equation. The results show that, when forced frequency is lower, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is higher, the surface tension can not be neglected. This proved that the surface tension causes free surface returning to equilibrium location. In addition, due to considering the effect of surface tension, the theoretical result approaches to experimental results much more than that of no surface tension.  相似文献   
7.
具有正弦粗糙度的环形微管道中脉冲流动   总被引:1,自引:1,他引:0  
研究了具有正弦粗糙度的环形微管道中脉冲流动,其中壁面粗糙度用小振幅的正弦波表示,不可压缩粘性脉冲流动由周期振荡的压力梯度驱动,运用摄动展开法求解了柱坐标系下的动量方程,获得了环形微管道内脉冲流动的近似解析速度及其体积流率.在此基础上,研究了相关无量纲参数,如Reynolds(雷诺)数Re、压力梯度振幅A、正弦波状粗糙的小振幅ε、内外半径之比α、相位差β及其波数λ对速度u及平均体积流率Φ_m的影响.结果表明,剖面速度随A的增大而增大,随Re的增大而减小,相位滞后χ随振荡Reynolds数Re的增大而增大.  相似文献   
8.
刘勇波  菅永军 《物理学报》2016,65(8):84704-084704
柔性纳米通道是在刚性纳米通道壁面处添加一层带某种电荷的聚电解质层或固定电荷层的纳米通道. 本文在低Zeta势近似下, 通过解析求解电势满足的线性化Poisson-Boltzmann方程和速度满足的Cauchy动量方程, 给出了圆柱形柔性纳米通道中电解质溶液的流向势和电动能量转换效率的解析解. 在表面Zeta势取值相同, 且管径相同(聚电解质层厚度远小于管径前提下)的情形下, 将圆柱形柔性纳米通道和刚性纳米通道中电解质溶液的流向势和电动转换效率进行了比较. 结果表明, 柔性纳米通道中的流向势和转换效率明显高于刚性通道中的流向势和转换效率. 在本文选取的参数范围内, 柔性纳米通道中的电动转换效率比刚性纳米通道中的转换效率提高1.5-3倍.  相似文献   
9.
菅永军  鄂学全  张杰  孟俊敏 《中国物理》2004,13(10):1623-1630
The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge-Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.  相似文献   
10.
垂直参数激励表面波研究进展   总被引:4,自引:1,他引:3  
受外激励的充液刚性容器中流体的波动问题有实际的工程应用背景.竖直方向的受周期性外激励的充液容器的自由表面波问题--Faraday波问题是流体力学三大不稳定性难题之一(另外两个不稳定性问题是Rayleigh-B\'enard对流和Taylor-Couette流).本文综述了在理想流体中和弱粘性流体中Faraday波的研究成果;介绍了作者在底部垂直激励的圆柱形容器中流体表面波图谱的实验研究和理论分析的结果.最后提出有待进一步研究的问题.图13,参74  相似文献   
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