【作者】 高鹏；

【导师】 陆夕云；

【作者基本信息】 中国科学技术大学 ， 流体力学， 2008， 博士

【摘要】 壁面吹吸和表面活性剂是影响流动稳定性的重要因素,相关问题广泛存在于工程实际问题中,已有的大量工作主要研究了这些因素对定常流动或者简单界面问题的作用。本文研究了带壁面吹吸的周期流动问题和带表面活性剂的多界面和振荡自由面问题,重点分析了流动的线性稳定性特征及其内在的物理机理,并发现了一些新现象。本文主要分析研究了四类典型流动问题,分别描述如下:(1)基于Floquet理论和线性稳定性分析,研究了周期性壁面吹吸对平面Poiseuille流动稳定性的影响。采用Chebyshev谱配置法计算分析了固定压力梯度和固定流量两种情况下的基本流场及其稳定性特征:在小吹吸振幅条件下(△《1),给出了基本流场和扰动增长率的渐近解。在所研究的参数范围内,流动的临界Reynolds数总是低于不带吹吸的情况,因此流动的稳定性减弱。渐近结果表明,壁面吹吸导致扰动增长率产生一个O(△~2)量级的增加,因而起着不稳定性的作用。此外,还发现壁面吹吸的不稳定性作用主要与基本速度的定常修正相关。(2)研究了均匀壁面吹吸对平板Stokes层稳定性的影响。首先发展了稳定性控制方程的半解析求解方法,推广应用到带壁面吹吸的流动问题,然后计算了典型参数下的扰动增长率、中性曲线、特征函数和临界Reynolds数R_c。结果表明,R_c随壁面吸气速度的增加单调上升,说明吸气起着增强流动稳定性的作用:吹气的作用则相反。在平行流假设下,计算得到了R_c的近似值,发现与精确结果非常接近,表明基本流场的法向速度分量对流动稳定性的贡献很小。分析给出了预测临界Reynolds数的经验公式,发现流动的临界Reynolds数近似地随吹吸速度成指数变化。(3)研究了双层薄膜流动的无惯性不稳定特性。这里包括两部分内容,一是采用较为直观的方法阐述了长波扰动的失稳机制,另一是分析了表面活性剂和界面活性剂对流动稳定性的影响。在长波条件下,证明了自由面和界面的变形满足两个相互耦合的对流扩散方程,根据其正则模解的形式可以直接判断出流动的稳定性。每个模态对应的自由面和界面波动之间并不是严格同相或者反相的,而是存在一个额外的相位差。研究发现,该相位差对应的扰动流场和重力法向分量驱动的扰动流场共同决定了扰动的指数增长。在有表面活性剂和界面活性剂的条件下,存在四个正则模,其中最多只有一个模态是不稳定的。根据参数的不同,表面活性剂和界面活性剂可以增强或者减弱流动的稳定性。特别当上层流体的粘性远大于下层流体时,表面活性剂会增强流动的无惯性不稳定性,这也是首次发现表面活性剂可以增强零剪切自由面的不稳定性。(4)研究了表面活性剂作用下的周期性振荡流体层的线性稳定性。在长波扰动条件下,采用摄动方法发现了两个与流动稳定性有关的Floquet模,它们的扰动增长率满足一个二次方程。表面活性剂会减小长波扰动出现不稳定的参数范围,因而可以增强长波扰动的稳定性。在任意波长条件下,采用Chebyshev谱配置法对控制方程进行了求解,计算分析了广泛参数条件下的临界Reynolds数。结果表明,当表面弹性较小时,表面活性剂会增强流动的稳定性;当表面弹性较大时,也可能促进流动的失稳。此外,还发现引入表面活性剂后有可能出现行波形式的不稳定性。更多还原

【Abstract】 Effects of wall suctioin/injection and surfactants play an important role in the stability of flows involved in a wide range of engineering applications.In a majority of previous studies on these topics,the basic flow configuration is usually treated as a steady system or has only one interface.This dissertation is devoted to the stability of periodic flows with the suction/injection,surfactant-laden multiple-layer films,and oscillatory fluid layer with surfactants.Four typical problems are investigated in detail and described briefly as follows:(1)The stability of plane Poiseuille flow modulated by oscillatory wall suction/injection is investigated based on linear stability analysis together with Floquet theory. The basic flow and the stability characteristics are analyzed using a Chebyshev collocation method.When the amplitudeΔof suction/injection is sufficiently small,asymptotic solutions of the basic velocity profile and the growth rate of disturbances are also obtained.For the parameters considered,the critical Reynolds number is always lower than one for the pure Poiseuille flow,and hence the flow becomes more unstable.The asymptotic results show that the correction terms for the growth rate are of O(Δ~2)and positive,indicating a destabilizing effect of the suction/injection.Moreover,it is found that the destabilizing effect is mainly connected to the steady corrections of the mean flow profile in the O(Δ~2)terms.(2)Effects of uniform wall suction/injection on the linear stability of flat Stokes layers are studied.A semi-analytical method is developed to examine the stability of time-periodic boundary flows in the presence of wall suction/injection.Typical growth rates,neutral curves and critical Reynolds numbers are obtained.Results show that the critical Reynolds number decreases monotonically as the velocity of suction/injection increases.Thus,the onset of instability of the flat Stokes layers can be suppressed by wall suction and enhanced by wall injection.The values of the critical Reynolds number predicted by the quasi-parallel approximation of the basic flow agree quite well with the exact results,indicating a negligible influence of the normal component of the basic velocity on the flow instability.It is also revealed that the critical Reynolds number is approximately dependent on the suction/injection velocity with an exponential relation. (3)The inertialess instability of a two-layer film flow is analyzed by interpreting the underlying mechanism of the long-wave instability in an intuitive way as well as examining the influence of insoluble surface and interfacial surfatants on the flow stability.In the limit of long waves,two coupled advection-diffusion equations for the surface and interracial displacements are derived.A normalmode analysis of the equations yields very tractable formulas for the growth rates and eigenfunctions,and the stability/instability can be readily identified.The surface and interfacial waves of the normal modes are not exactly in phase or out of phase byπ.Instead,there exists an additional phase shift.It is found that the coexistence of the disturbance flows related to this additional phase shift and the normal component of gravity leads to the inertialess instability.In the presence of surface and interfacial surfactants,four normal modes are detected,and at most one of the four modes may be unstable for a group of specified flow parameters. Both the surface and interfacial surfactants can act as stabilizing or destabilizing role.In particular,when the viscosity of the upper layer is much higher than that of the lower layer,the surface surfactant can enhance the intertialess instability of the flow.Note that the destabilizing effect of surfactants on a zero-shear free surface is revealed for the first time.(4)The linear stability of an oscillatory fluid layer covered by an insoluble surfactant is studied.In the limit of long-wavelength perturbations,two particular Floquet modes associated with the instability are identified and the corresponding growth rates are obtained by solving a quadratic equation.The surfactant tends to shrink the unstable regions for the stability parameters,and thus plays a stabilizing role in the long-wave disturbances.The stability of arbitrary-wavelength disturbances is numerically analyzed using a Chebyshev collocation method,and the critical Reynolds numbers are calculated for a wide range of amplitude and frequency of the modulation as well as surfactant elasticity.Results show that the flow is stabilized for small surfactant elasticity and can be destabilized for relatively large surfactant elasticity.The disturbance modes in the form of traveling waves may be induced by the surfactant and dominate the instability of the flow.更多还原