【作者】 马国军；

【导师】 吴承伟；

【作者基本信息】 大连理工大学 ， 工程力学， 2007， 博士

【摘要】 经典流体力学和经典润滑力学均认为流体在固体表面上流动时表面流体分子与固体分子的速度绝对相等，即传统的无滑移边界假设。近年来，随着微纳米测试技术及其相关领域科学技术的飞速发展，人们发现微纳米尺度下的流体间隙流动与宏观尺度下流体的流动问题有着本质区别，尺度效应突现，“边界滑移”就是其中最有代表性的一类问题。所谓边界滑移，指的是固体表面上的流体与固体表面存在相对运动速度。研究表明，在微纳米尺度下的边界滑移对间隙流体的流动特性有着重要甚至是决定性的影响。目前有关边界滑移问题的研究主要集中于发现边界滑移现象和探索滑移的内在机理以及各因素对边界滑移的影响规律，包括试验研究和分子动力学模拟，而有关边界滑移对流体系统流体动力学行为影响的数值分析则相对较少。微纳米间隙流动边界滑移及其流体动力学研究中主要存在两方面的问题：一是目前最常用的线性滑移长度模型认为边界滑移总是存在的，并且边界滑移速度与剪切率成正比，但是许多实验发现在低剪切率下没有滑移，而在高剪切率下滑移呈很强的非线性行为，即线性滑移长度模型常常不能准确描述流体(液体)流动的边界滑移；二是采用极限剪应力滑移模型时，由于流体在边界上的滑移速度和方向都是未知的，导致数值求解上的困难，传统的基于有限差分方法的迭代求解技术计算量太大而且收敛性较差，尤其在二维流动问题中该方法基本不可行。针对上述问题，本文展开了以下几个方面的研究。基于流变学中的极限剪应力模型，结合参变量变分原理及其有限元参数二次规划方法，本文首次给出了求解球形挤压膜流动边界滑移问题的数值方法，为此类边界滑移问题的计算与分析提供了新方法。此外，通过对数值计算结果的分析，本文提出了当上下表面具有相同滑移性质时球形挤压膜流体动压承载力的拟合公式，为边界滑移的间接实验测量提供了有力的理论分析工具。通过数值计算结果与相关实验数据之间的定量比较和分析发现，极限剪应力滑移模型的理论预报值与实验测量值吻合很好，尤其在高剪切率时。一方面说明极限剪应力滑移模型可以用来准确描述间隙流动的边界滑移，另一方面也说明基于极限剪应力滑移模型的参变量变分原理及其有限元参数二次规划方法可以有效求解边界滑移问题，该方法计算效率高、收敛性好。此外，数值计算还表明边界滑移使挤压膜的流体动压力减小，而且固体表面的滑移性质对挤压膜的流体动压特性有着重要影响。当上下表面同时发生大面积的边界滑移时，挤压膜可能完全失去流体动压承载力，但若其中一个表面不发生边界滑移，则即使另一表面发生理想滑移(表面极限剪应力等于零)，挤压膜也仍能保持一定的承载力，且恰为无滑移时挤压膜承载力的四分之一。通过对Troian等的分子动力学模拟结果的考察，本文提出了一种包含线性滑移长度模型和极限剪应力滑移模型的非线性滑移模型，从而弥补了前者在高剪切率时的不足和后者在低剪切率时对微小边界滑移的忽略。在小剪切率时，该模型认为滑移长度为常数，与线性滑移模型一致。而在高剪切率时，该模型则和极限剪应力模型一致。基于该非线性模型，对平行板剪切流和挤压膜流动的边界滑移问题进行了数值分析并与他人实验数据进行了比较，发现理论预报与实验吻合很好。利用极限剪应力滑移模型和相应的参变量变分原理及其有限元参数二次规划技术，本文对各种一维间隙流动(与各种液体滑动轴承相对应，其典型间隙厚度在微米量级)的边界滑移及其流体动力学进行了数值分析。研究发现，当同一固体表面滑移性质处处相同时，边界滑移使流体系统的流体动压效应减小，而且与哪个表面发生运动有关。在运动的固体表面发生大面积边界滑移时，或运动和静止固体表面(两表面具有相同滑移性质)同时发生大面积滑移时，流体系统的流体动压效应剧减或完全消失。而间隙厚度减小、剪切率增加、流体粘性增加以及表面极限剪应力(其大小与表面的材料和液体的种类等有关)的减小均会使边界滑移容易发生或者使边界滑移加剧，这就从边界滑移的角度解释了为何在高速、窄隙(重载)以及轴承两表面为同种材料时轴承更容易失效，也解释了为何不同材料的轴承会有不同的极限转速(高于该转速轴承会失效)。计算分析还发现，边界滑移在大滑滚比时更容易使滑滚间隙流动系统(滚柱轴承、金属轧制润滑系统等属于此类间隙)的流体动压承载力减小，而且在纯滑动时系统可能完全丧失承载力，但纯滚动时则不会完全丧失承载力，这解释了实际当中轴承为何在纯滑动时比纯滚动时更容易发生破坏。当静止固体表面具有不同滑移性质(复合滑移表面)时，边界滑移对系统的流体动力学影响较为复杂，与表面滑移区域的位置、尺寸、极限剪应力大小以及间隙几何等参数有关，但滑移区域内边界滑移越严重，系统的流体动力学效应反而越好。以滑块轴承和轴颈轴承为例，通过简单的优化计算，不仅从理论上发现了“复合滑移轴承系统”(具有复合滑移表面的轴承系统)比传统无滑移轴承具有更高的流体动压承载能力和更低的表面摩擦系数，而且发现平行或发散间隙时系统仍能获得相当高的流体动压承载力，这打破了经典无滑移理论认为只有收敛间隙才能获得流体动压承载力的观点，为新型轴承系统的设计与制造提供了新思路。采用极限剪应力滑移模型求解二维间隙流动边界滑移问题时，由于边界滑移的大小和方向都事先未知，使求解变得更加困难。本文提出了分段线性化方法来逼近系统的非线性滑移控制函数，然后结合相应的参变量变分原理和有限元参数二次规划方法，提出了新的二维间隙流动边界滑移问题的数值计算方法。通过数值分析，讨论了在控制方程的线性化技术中所采用的正多边形的边数、多边形种类以及有限单元数目对求解精度的影响，数值算例表明，该方法计算效率高、精度好。使用该方法，对二维间隙流动边界滑移问题及其流体动力学进行了数值分析，发现当静止固体表面具有复合滑移性质时系统的流体动力学效应较好。进一步的分析还发现，二维复合滑移滑块轴承在静止固体表面滑移区为梯形且间隙大致平行时获得最大流体动压承载力，最大流体动压承载力是传统无滑移轴承最大承载力的约2.5倍，而表面摩擦系数则降低了50％以上。通过对复合滑移转子—轴承系统的动力学分析发现，与无滑移转子系统相比，复合边界滑移转子系统不仅可以使系统具有更高的承载力和更低的摩擦系数，而且能够提高转子系统的运转稳定性，并且从理论上发现系统会由于复合边界滑移的存在具有一种自我稳定运转的功能。这个发现或许有助于我们探索高性能、高运转稳定性的新型结构。但是对于静止表面滑移性质处处相同的转子—轴承系统而言，边界滑移则会使系统的动力学稳定性降低。最后在第九章介绍了作者在博士论文前期工作中开展的关于高温(900℃)强磁场处理技术改善镍铝合金力学性能的工作。尽管这部分工作相对独立，但由于工作比较新颖，挑战性和开拓性并存，我们还是简单介绍给读者，以期获得有益的讨论并在以后继续深入研究。本文发现利用强磁场处理技术使得镍铝合金的室温力学性能获得大幅度改善，与未经磁场处理的同种合金相比，抗弯强度提高～75％，拉伸和压缩强度都提高一倍以上，而且试件的断口形貌分析表明，强磁场处理改变了镍铝合金的室温断裂方式，使合金呈现韧性断裂特征。总之，本文首先提出和发展了极限剪应力滑移模型和非线性滑移模型用于描述边界滑移问题，并与目前较常用的线性滑移长度模型和相关实验数据进行了比较，发现前两者的适用范围远大于后者；其次本文成功解决了二维间隙流动问题的系统方程非线性求解困难；最后本文对间隙流动的边界滑移及其流体动力学分析揭示了许多以前未曾知晓的物理现象和规律，尤其是从理论上发现了复合边界滑移能使微纳米间隙流动系统的流体动力学等综合性能提高。这些对今后边界滑移相关问题的计算、分析及工程应用都具有重要的指导意义。更多还原

【Abstract】 In the classical fluid mechanics and lubrication mechanics, it is assumed that no relative velocity exists between the fluid molecular and the solid molecular at the solid/liquid interface. This is the so-called no-slip boundary condition. During the recent years, with the rapid development of science and technology in micro- and nano-measuring technologies and the related area, it has been found that there are many significant differences between fluid flow at macro-scale and that at micro/nano-scale. Among of them, boundary slip (wall slip) is one of the most important problems. Boundary slip means that there is a finite relative velocity between the fluid and the solid molecular at the interface. It has been shown that boundary slip often plays an important or dominant role in the micro/nano-gap fluid flow. Researchers are now paying more attention to reveaI the boundary slip evidences and to search the physical principle of the boundary slip through experimental observation and molecular dynamics simulation (MDS). However, few studies are available on the numerical analysis of the effect of boundary slip on the hydrodynamics in a micro/nano-gap fluid flow. Furthermore, there are mainly two problems in the numerical analysis of the boundary slip. The first one is that the constant slip length model fails to predict many experimental results, especially at a large shear rate. The second one is that, due to the unknown amplitude and direction of the boundary slip, there are some numerical difficulties when the limiting shear stress slip model (LSSM) is used. The iterative solution technique based on the finite difference method meets problems in both the consuming time and the numerical convergence. In fact the iterative technique is impossible in the two-dimensional gap flow with boundary slip. The main work of the present dissertation is summarized as follows:In this dissertation, the limiting shear stress model proposed originally in rheological study is introduced to describe the boundary slip, and then, based on the parametric variational principle and the corresponding finite element parametric quadratic programming method (PVP and FEPQPM), the numerical solving process of a boundary slip problem is given. For a spherical squeeze film system often used in experimental studies of boundary slip phenomena, we propose a fitting formula of the hydrodynamic force. Further numerical analyses on a parallel plate system and a spherical squeeze film system show that our predictions are in good agreement with the existing experimental observations. This indicates that the LSSM is applicable to describe the boundary slip, and the PVP and FEPQPM can be used to effectively solve the boundary slip problem. Due to avoiding a time-consuming iteration process, the PVP and FEPQPM give rise to a high computational efficiency. The corresponding numerical results show that the boundary slip can make a decrease in hydrodynamic force of a spherical squeeze film system. Furthermore, it is found that the hydrodynamic response of the squeeze sphere system is controlled by the surface slippage properties. When a large slip occurs at both the upper and the down surface, the hydrodynamic load support may vanish entirely. However, as long as One of the surfaces has the limiting shear strength high enough to suppress any slip, even if the other surface has a null limiting shear stress, a finite hydrodynamic force can be obtained. Moreover, the value of this hydrodynamic force is just one quarter of that without boundary slip.Based on the MDS of Troian et al., a nonlinear slip model (NSM) is presented here. It can be regarded as a combination of the SLM and the LSSM. When the shear rate is low, the NSM gives an approximate constant slip length, which is the same as what is predicted by the SLM. However, when the shear rate is high, the NSM is almost the same as the LSSM. Based on the NSM, this paper obtains the numerical solutions of the boundary slip problems for a parallel plate system and a sphere squeeze system. A good agreement occurs between the numerical result and experimental observation.Taking advantage of the LSSM, PVP and FEPQPM, this paper gives the detailed numerical analyses of the boundary slip and hydrodynamics of one-dimensional gap flow with different gap geometries. It is found that, when the surface has a homogenous slip property, i.e., the surface limiting shear stress has the same value on the entire surface, the boundary slip always decreases the hydrodynamics of the fluid system. Furthermore, this effect depends on what a surface is a moving. If a large slip occurs on the moving surface orboth the stationary and the moving surface, the hydrodynamic response of the fluid system decrease dramatically, even lose totally. It is also found that boundary slip can be induced or enhanced with the decrease in the fluid film thickness or the surface limiting shear stress, and the increase in shear rate or viscosity of fluid. From these results, we can know why a sliding bearing often fails to work for a thin gap film and a high sliding velocity. For a sliding-rolling gap fluid flow system, no load support is expected only in the case of large sliding/rolling ratio. This explains why the bearing failure occurs more easily in the case of pure sliding than in the case of pure rolling. It should be pointed out that the boundary slip always results in a low friction force.When the stationary surface has heterogeneous slip property (a complicated slip surface), the boundary slip has a complex influence on the hydrodynamics of the fluid system. This effect is controlled by such parameters as the location, the geometry shape, the geometry size and the limiting shear stress of the slip zone as well as the geometry of the fluid gap. In general, the larger the boundary slip at the slip zone, the more excellent hydrodynamic effect the fluid system has. Taking example for one-dimensional slider bearing and journal bearing, this paper shows theoretically that a "complicated slip bearing system" (CSBS) can give higher hydrodynamic load support capacity and lower friction coefficient than those of the corresponding traditional no-slip bearing system (TNBS). Moreover, it is found that a convergent geometry gap, the necessary condition for a TNBS to acquire hydrodynamic load capacity, will not be required for the CSBS. The CSBS can get a very high hydrodynamic load support with a parallel fluid gap or a slight divergence gap. Consequently, these effects induced by the complicate boundary slip can help us to design and manufacture some new types of bearing system.When the LSSM is used to solve the boundary slip problem in a two-dimensional flow, it is difficult to determine the slip velocity because both the amplitude and the direction of the slip velocity are not known a priori. A multi-linearity method is developed to approach the non-linear control equation of the two-dimensional slip gap flow. Then, based on the PVP and FEPQPM, a new numerical method is proposed to solve the two-dimensional slip gap flow problem with boundary slip. Making use of this method, the present paper analyzes the boundary slip problem in a two-dimensional gap flow. It is found that the fluid system exhibits an excellent hydrodynamic response when the stationary surface has heterogeneous slip property. Through simple numerical optimizations, it is found that boundary slip on a trapezoid slip zone at the stationary surface makes the fluid system obtain an excellent hydrodynamic response. When the gap is parallel, comparing with the TNBS, the hydrodynamic load support of the complex slip slider bearing system is increased by about 150%, but the corresponding surface friction coefficient is decreased over 50%. Based on the numerical analyses of a rotor-bearing system with the heterogeneous slip surface, it is found that, comparing with the no-slip rotor-bearing system, the rotor-bearing system with the heterogeneous boundary slip gives rise to a high load support capacity, a very low surface friction coefficient as well as an excellent operation stability. Moreover, numerical results show that the rotor-bearing system with the heterogeneous slip surface is a self-stable operation system. Perhaps this finding will be useful for us to design a new bearing system with outstanding properties. However, when the stationary surface has a homogenous slip property, the boundary slip always decreases the operation stability of the rotor-bearing system.Finally, in chapter 9, the enhancement of the mechanical behavior of the NiAl alloy by strong magnetic treatment under high temperature of 900℃is introduced. Although this work has no straightforward relationship with the other parts of the present dissertation, a simple introduction is also given here due to its novelty and challenge. This work shows that the NiAl alloy treated with the strong magnetic field under high temperature gets a much better mechanical property than that without. The bending strength is increased by～75%, and the press strength and tensile strength are all increased more than 100%. Furthermore, the SEM observation of the fracture section shows that the magnetic field improves the alloy ductility, giving rise to a change in the fracture behavior.In conclusion, firstly, this dissertation proposes and develops the LSSM and the NSM to describe the boundary slip problem. Through the comparison between the LSSM, the NSM and the SLM, it is shown that the former two is more applicable than the latter at a wide range of the shear rate. Secondly, we successfully propose a new method to overcome the difficulty in solving the nonlinear equation of the two-dimensional slip system. Finally, this dissertation gives the detailed numerical analyses on the boundary slip and hydrodynamics for different gap flows. Some new physical phenomena and rules are revealed. Especially, it is theoretically found that a heterogeneous boundary slip improves the hydrodynamic effects and operation stability of the fluid flow system at micro/nano-scale. What is mentioned above will be very important for the computations, analyses and engineering applications of the boundary slip phenomena.更多还原