壁面吹吸和表面活性劑作用下的流動穩(wěn)定性研究

1、附件2論文中英文摘要作者姓名：高鵬論文題目：壁面吹吸和表面活性劑作用下的流動穩(wěn)定性研究作者簡介：高鵬，男，1981年8月出生，2005年9月師從于中國科學(xué)技術(shù)大學(xué)陸夕云教授，于2008年7月獲博士學(xué)位。中 文 摘 要流動穩(wěn)定性分析是流體力學(xué)的一個重要研究領(lǐng)域。流動失穩(wěn)現(xiàn)象廣泛存在于工程問題和自然界中，導(dǎo)致流動不穩(wěn)定性的物理因素也是多種多樣的。壁面吹吸和表面活性劑是影響流動穩(wěn)定性的重要因素，同時也是進行流動控制的常用手段，在工業(yè)領(lǐng)域中具有廣泛的應(yīng)用背景。人們通過大量研究，對這些因素如何影響流動穩(wěn)定性特征建立了一些認識，例如：壁面吸氣可以增強邊界層的穩(wěn)定性，吹氣則相反；表面活性劑引起的 Maran

2、goni 效應(yīng)主要起著增強界面流動穩(wěn)定性的作用，而其不穩(wěn)定化作用只有在界面剪切率不為零時才有可能出現(xiàn)。然而，已有的工作主要集中于關(guān)于定常流動和簡單界面問題的研究，對于工業(yè)領(lǐng)域和自然界中廣泛存在的非定常和多界面流動問題，其穩(wěn)定性問題要復(fù)雜很多，而已有的結(jié)論能否直接推廣到這些復(fù)雜問題尚不清楚，亟待開展深入研究。本文以平面 Poiseuille 流動、平板振蕩 Stokes 層、薄膜流動等流體力學(xué)中的典型問題為研究對象，通過發(fā)展相關(guān)的解析、半解析和數(shù)值計算方法并將其相互結(jié)合，研究了壁面吹吸、表面活性劑、流動周期性變化和多界面等因素相互耦合作用下的復(fù)雜流動問題的穩(wěn)定性特征。研究發(fā)現(xiàn)，早期簡單流動條件下

3、得到的結(jié)論往往不適用于這些復(fù)雜流動問題，在一些情況下甚至可以得到完全相反的結(jié)論，取得的研究結(jié)果為人們利用吹吸和表面活性劑進行流動控制提供了全新的認識。本博士論文的相關(guān)研究成果均發(fā)表在本學(xué)科最為權(quán)威的學(xué)術(shù)期刊 Journal of Fluid Mechanics (5篇) 和 Physics of Fluids (1篇) 上。在這些工作中，主要創(chuàng)新及學(xué)術(shù)貢獻如下：1. 基于 Floquet 理論和線性穩(wěn)定性分析，研究了周期性壁面吹吸對平面 Poiseuille 流動穩(wěn)定性的影響。我們考慮了固定壓力梯度和固定流量兩種典型情況，并分別與不帶吹吸的流動以及定常吹吸作用下的流動問題進行了對比分析。采用

4、Chebyshev 譜配置法計算分析了基本流場和穩(wěn)定性特征，同時在小吹吸振幅條件下給出了基本流場和主要模態(tài)擾動增長率的漸近解，數(shù)值和解析兩種方法得到了相互印證的結(jié)果，進而探討了流動物理機理。結(jié)果表明：周期性吹吸帶來基本速度型的改變，在壁面附近引起類似于振蕩 Stokes 層的周期流場，并由于整流效應(yīng)產(chǎn)生了定常的速度修正；與不帶壁面吹吸的平面 Poiseuille 流動相比，在大部分吹吸參數(shù)下臨界模態(tài)的增長率都會變大，從而使得流動的臨界 Reynolds 數(shù)變小，說明周期吹吸會增強流動的不穩(wěn)定性，促進流動由層流向湍流的轉(zhuǎn)捩；由于定常吹吸作用下的 Poiseuille 流動具有更強的穩(wěn)定性，因此周

5、期性吹吸與定常吹吸的作用效果完全相反，周期性吹吸更有利于增強流動混合；流動不穩(wěn)定性的增強主要是由周期性吹吸對基本速度型的整流效應(yīng)以及基本流場的周期性分量與擾動波之間的相互調(diào)制引起的；在固定壓力梯度和固定流量兩種情況下，壁面附近的基本流場具有類似的結(jié)構(gòu)，從而兩種流動的穩(wěn)定性特征也十分相似。該研究成果發(fā)表在 Physics of Fluids 上。2. 研究了定常均勻壁面吹吸對典型的周期性振蕩邊界層即平板 Stokes 層的穩(wěn)定性影響。首先推導(dǎo)給出了帶壁面吹吸時解析形式的基本流場，發(fā)現(xiàn)吸氣會減小 Stokes 層沿法向的貫穿深度，吹氣的作用則相反；吸氣和吹氣都會增大基本速度型沿法向的波長。由于流動

6、在空間上的半無限特征，穩(wěn)定性分析中的傳統(tǒng)數(shù)值計算具有很大的局限性。為此，我們將研究平板 Stokes 層穩(wěn)定性問題的半解析方法推廣到帶壁面吹吸的情況，分析了擾動模態(tài)的增長率和流場結(jié)構(gòu)。結(jié)果表明：擾動模態(tài)的結(jié)構(gòu)與不帶吹吸的 Stokes 層在定性上是相似的；流動的臨界 Reynolds 數(shù)隨著吹氣速度的增加單調(diào)下降，隨著吸氣速度的增加單調(diào)上升，表明壁面吸(吹)氣起著增強(減弱)流動穩(wěn)定性的作用；與定常邊界層不同，基本流場的非平行效應(yīng)對 Stokes 層穩(wěn)定性的影響幾乎可以忽略，因此壁面吹吸主要是通過改變基本速度場的流向分量來影響 Stokes 層的穩(wěn)定性；發(fā)現(xiàn)擾動增長對遠場速度型非常敏感，提供了

7、在經(jīng)典 Stokes 層穩(wěn)定性研究中實驗結(jié)果與理論結(jié)果不一致的一種合理解釋；基于流動物理分析，給出了預(yù)測臨界 Reynolds 數(shù)的近似公式，發(fā)現(xiàn)流動的臨界 Reynolds 數(shù)近似地隨吹吸速度成指數(shù)變化，這對實際應(yīng)用中利用壁面吹吸對周期性振蕩邊界層進行流動控制具有指導(dǎo)意義。該成果發(fā)表在 Journal of Fluid Mechanics 上。3. 研究了雙層薄膜流動的無慣性不穩(wěn)定特性以及活性劑的影響特性。該問題包含一個零剪切自由面和一個非零剪切界面。該項研究包括兩部分內(nèi)容，一是采用較為直觀的方法闡述了長波擾動的失穩(wěn)機制，另一是分析了表面活性劑和界面活性劑對流動穩(wěn)定性的影響特性。在長波條件下

8、，證明了自由面和界面的變形滿足兩個相互耦合的對流擴散方程，推導(dǎo)得到了其正則模解的基本形式，并由其直接判斷出流動是否會失穩(wěn)。首次揭示了自由面和界面擾動波之間的共振機制：每個模態(tài)對應(yīng)的自由面波和界面波之間并不是嚴格同相或者反相，而是存在一個相位差；該相位差對應(yīng)的擾動流場和重力法向分量驅(qū)動的擾動流場共同決定了擾動的指數(shù)增長，從而導(dǎo)致流動的失穩(wěn)。在有表面活性劑和界面活性劑的條件下，存在四個正則模，其中最多只有一個模態(tài)是不穩(wěn)定的。表面活性劑的作用取決于流體的粘性比：當上層流體的粘性大于但是仍接近下層流體的粘性時，表面活性劑會減弱流動的無慣性不穩(wěn)定；而當上層流體的粘性遠遠大于下層流體時，表面活性劑也有可能

9、增強流動的無慣性不穩(wěn)定，這也是首次發(fā)現(xiàn)表面活性劑可以增強零剪切自由面的不穩(wěn)定性。界面活性劑也有可能增強或減弱流動的穩(wěn)定性，主要取決于活性劑的濃度；特別地，當上層流體的粘性小于下層流體時，界面活性劑也會導(dǎo)致流動的失穩(wěn)。相關(guān)成果已在 Journal of Fluid Mechanics 上發(fā)表兩篇論文。4. 采用數(shù)值計算和漸近分析相結(jié)合的方法，研究了表面活性劑作用下的周期性振蕩流體層的線性穩(wěn)定性，探討了 Marangoni 效應(yīng)和周期性流動效應(yīng)共同作用下的新機制。在長波擾動條件下，采用漸近方法發(fā)現(xiàn)了兩個與流動穩(wěn)定性相關(guān)的 Floquet 模，它們的擾動增長率滿足一個二次方程。表面活性劑會減小長波擾

10、動出現(xiàn)不穩(wěn)定的參數(shù)范圍，因而可以增強長波擾動的穩(wěn)定性。在任意波長條件下，采用 Chebyshev 譜配置法對控制方程進行了求解，分析了廣泛參數(shù)條件下的臨界 Reynolds 數(shù)。結(jié)果表明：引入表面活性劑之后，流動可能出現(xiàn)行波擾動形式的失穩(wěn)，而沒有表面活性劑時流動只可能出現(xiàn)駐波形式的失穩(wěn)；當 Marangoni 數(shù)較小時，表面活性劑會增強流動的穩(wěn)定性；當 Marangoni 數(shù)較大時，活性劑也可能促進流動的失穩(wěn)。因而，表面活性劑不僅可以促進流動的失穩(wěn)，而且這種作用效應(yīng)在多層薄膜和非定常薄膜流動中普遍存在。同時，表明活性劑也可以促進零剪切自由面流動的不穩(wěn)定性，表明剪切率并不是活性劑不穩(wěn)定化作用的本

11、質(zhì)因素。相關(guān)成果已在 Journal of Fluid Mechanics 上發(fā)表兩篇論文。關(guān)鍵詞： 流動穩(wěn)定性，壁面吹吸，表面活性劑，F(xiàn)loquet理論， 周期流動，Stokes層，薄膜流動，自由面流動Studies on the Stability of Flows with Wall Suction/Injection and SurfactantGao PengABSTRACTHydrodynamic stability is an important area in fluid mechanics, since the instability or stability of flow

12、s exists widely in nature and engineering. The flow instability can be triggered by a variety of factors, among which wall suction/injection and surfactants play an important role on the instability. Meanwhile, the suction/injection and surfactants are two typical approaches for flow control and hav

13、e been widely employed in industrial applications. Based on extensive previous studies, effects of suction/injection and surfactants on the stability of flows seem to be well understood. For example, a wall suction/injection can enhance/weaken the stability of boundary layers, and the presence of su

14、rfactants stabilizes the interfacial flows through a Marangoni effect and has a destabilizing influence only when the interfacial shear is nonzero. However, most of previous studies are only devoted to steady flows with one interface. For widespread flow systems with unsteadiness and multiple interf

15、aces, the stability analysis becomes much more complicated, and it is still unclear whether the obtained conclusions can be straightforwardly extended to these complex flows. Therefore, it is desirable to further investigate the effects of suction/injection and surfactants on the stability of more e

16、xtensive flows. In this dissertation, we study the stability of planar Poiseuille flow, flat Stokes layer and film flow with combined effects of wall suction/injection, surfactants, time periodicity and multiple interfaces, using analytical and semi-analytical solutions as well as numerical calculat

17、ions. Our results show that the conclusions based on simple flows can not be extended to complex problems in general. In some cases, the effect of suction/injection and surfactants is completely opposite to the traditional one. Thus, the present work provides a better understanding for flow control

18、using wall suction/injection and surfactants. The relevant results have been published in the Journal of Fluid Mechanics (5 papers) and Physics of Fluids (1 paper), which are both the most prestigious journals in fluid mechanics. The main contributions are listed as follows: 1. The stability of plan

19、e Poiseuille flow modulated by oscillatory wall suction/injection is investigated based on linear stability analysis together with Floquet theory. Two typical flows with either the driven pressure gradient and or the flow rate constant are considered, and the stability characteristics are compared w

20、ith the Poiseuille flow subject to zero or steady suction/injection. The basic flow and the stability characteristics are analyzed using a Chebyshev collocation method. When the amplitude of suction/injection is sufficiently small, asymptotic solutions of the basic velocity profile and the growth ra

21、te of disturbances are also obtained to explore the underlying mechanism. The numerical and analytical results agree well with each other. Results show that the modulation leads to a periodic flow field adjacent to the wall, which is similar to the oscillatory Stokes layer, and to a steady velocity

22、correction because of streaming effect. Compared with the pure Poiseuille flow, the growth rates of the dominant mode is increased and the critical Reynolds number becomes lower, indicating that wall suction/injection has a destabilizing effect and promotes the transition from laminar flow to turbul

23、ence. Since steady suction/injection is stabilizing, oscillatory suction/injection is preferred for flow mixing. The destabilizing effect is caused by the steady correction of the velocity profile and the modulation between the periodic component of the basic flow and the disturbance wave. The stabi

24、lity characteristics of flows with fixed pressure gradient and fixed flow rate are similar with each other because the basic velocity profiles near the wall have the same asymptotic form. This work has been published in the Physics of Fluids. 2. Effects of uniform and steady wall suction/injection o

25、n the linear stability of a typical periodic boundary layer, i.e. flat Stokes layer, are studied. An analytical solution of the basic velocity profile is derived and indicates that suction/injection decreases/increases the penetration length of the Stokes layer, and both suction and injection can in

26、crease the normal wavelength. The traditional numerical methods for stability analysis cannot be used because of the spatial semi-infinite behavior of the problem. Alternatively, a semi-analytical method for the linear stability of pure Stokes layer is extended to the case with wall suction/injectio

27、n and is employed to calculate the growth rate and flow structure of disturbances. It is shown that the structures of perturbation modes are qualitatively similar to the zero suction/injection case. The critical Reynolds number for the onset of instability decreases monotonically with increasing inj

28、ection velocity and increases with the suction velocity, indicating a stabilizing/destabilizing effect of suction/injection. Different from steady boundary layers, the change of the stability behavior of Stokes layers is primarily contributed from the modification of the streamwise velocity, while t

29、he nonparallel effect is nearly negligible. We found that the disturbance growth is sensitive to the far-field velocity, which provides a reasonable explanation of the discrepancy between the experimental and theoretical results on the stability of pure Stokes layers. Furthermore, an empirical formu

30、la is presented to predict the critical Reynolds number, which can be approximated using an exponential relation with the suction/injection velocity. This work has been published in the Journal of Fluid Mechanics. 3. The inertialess instability of a two-layer film flow is investigated together with

31、the effects of surfactants. This problem consists of a free surface with a zero shear rate and an interface with a nonzero shear rate. We presented an intuitive interpretation of the underlying mechanism of the long-wave instability on the one hand, and examined the effects of surface and interfacia

32、l surfactants on the other hand. In the limit of long waves, two coupled advection-diffusion equations for the surface and interfacial displacements are derived. The normal-mode solution of these equations has a very simple formulation and the stability/instability can be readily identified. We expl

33、ained the resonance mechanism between the surface and interfacial waves for the first time: the waves are not exactly in phase or out of phase by, but with an additional phase difference; the combined effects of the disturbance flow associated with this phase difference and the flow driven by gravit

34、y lead to an exponential growth of the disturbances and hence the instability. In the presence of surface and interfacial surfactants, four normal modes are detected, and at most one of them may be unstable. The effect of surface surfactants depends on the viscosity ratio: it is stabilizing when the

35、 viscosity of the upper fluid is larger but close to the lower fluid and can enhance the inertialess instability when the viscosity of the upper fluid is much larger than the lower one. This is the first time to discover the destabilizing effect of surfactants on a zero-shear surface. The interfacia

36、l surfactants can also be stabilizing or destabilizing depending on the concentration of the surfactants. Specifically, it destabilizes the flow when the viscosity of the upper fluid is larger. Based on these results, two papers have been published in the Journal of Fluid Mechanics. 4. Using numeric

37、al calculations and asymptotic analysis, the linear stability of an oscillatory fluid layer covered by an insoluble surfactant is studied for the purpose of investigating the new mechanism of Marangoni effect on periodic flow. In the limit of long-wave perturbations, two particular Floquet modes associated with the instability are identified and the corresponding growth rates are