【作者】 郑秋云；

【导师】 舒适； 李明军；

【作者基本信息】 湘潭大学 ， 计算数学， 2010， 博士

【摘要】 铁磁流体具有某些特殊的物理性质,它已广泛的应用到化学、机械、材料、磁路设计、医学等领域,对铁磁流体的建模及其数值求解已成为计算流体力学领域中研究的热点.虽然该方面的研究取得了很大的进展,但仍存在许多值得研究的问题.本文围绕铁磁流体化学机械抛光、铁磁流体热传导、铁磁流体R-T不稳定性三类模型问题的建模和数值求解进行研究,获得了若干理论与数值结果.针对铁磁流体化学机械抛光(CMP)模型问题.首先建立了以铁磁流体作为抛光液且具有离心力的CMP模型,数值求解表明外界磁场的作用可以有效的改变铁磁流体抛光液压力的分布和转角、倾角、膜厚对载荷与转矩的影响.其次,考虑流体的对流效应,通过对二维流体力学方程组进行简化,推导出对应的Reynolds润滑方程,建立了相应的CMP模型；数值分析了转角、倾角、膜厚对压力分布、载荷和转矩的影响,从而表明了所建模型的合理性.在考虑对流效应的基础上,研究了抛光液为铁磁流体的CMP过程,数值分析表明,在该模型中,外界磁场也能有效的改变抛光液流体压力的分布和大小.最后,通过数值实验比较,研究了不同铁磁流体CMP模型中,外界磁场对压力分布的作用,以及在外界磁场作用下,离心力、对流效应对铁磁流体CMP压力分布的作用.这些结果为改进CMP工艺提供了可供参考的依据.针对两种铁磁流体热传导问题,即二维封闭方腔铁磁流体自然对流和二维平板间铁磁流体热传导,建立它们所满足的模型方程.然后,在取外界磁场梯度一致的情况下,采用SIMPLE算法对这两种模型方程进行数值求解.对封闭方腔铁磁流体的自然对流,当磁场梯度与温度梯度方向相同时,外界磁场会增加封闭方腔内的自然对流和压力,且随着Rayleigh数的增大,磁Rayleigh数对封闭方腔内的自然对流和压力影响增大的趋势减弱.对开口系统的两平板间热传导问题,随着Rayleigh数的增大,磁Rayleigh数对平板间铁磁流体的热传导影响增大的趋势减弱.且当外界磁场梯度平行于开口方向时,随着外界磁场的增大,更易加强流体的热传导.最后,利用扩散抛物化理论,对铁磁流体热传导问题进行了抛物化简化,给出了铁磁流体热传导问题的层次结构理论,并对两平板间热传导问题的抛物化简化方程进行数值求解.通过与简化前的数值结果比较,验证了铁磁流体热传导抛物化简化的合理性.针对一种铁磁流体R-T不稳定性问题.推导了铁磁流体R-T不稳定问题满足的模型方程.在一致网格下,利用FD-WENO格式和TVD R-K格式对该模型方程建立了相应的离散系统.数值结果表明,当磁场梯度方向与流速方向一致时,外界磁场的作用会加速界面波头向前传播,反之则会减慢界面波头的传播.当磁场梯度方向与流速方向垂直时,则会增加界面的侧向不稳定性,使其对称性遭到破坏,而且在侧面会形成更多的泡沫状漩涡.这些结果对如何通过外界磁场的大小和方向来控制铁磁流体R-T不稳定性的发展具有参考价值.更多还原

【Abstract】 Some special physical characteristics of ferrofluid make it is widely ap-plied in the fields of chemistry, mechanism, materials science, magnetic circuit design, medicine, etc. So, modeling ferrofluid and its numerical computation have become a hot topic in field of computational mechanics. Although some great progresses on the topic have been achieved, some important problems remain unresolved. This thesis focuses on modeling and numerical compu-tation of three classes of problems, chemical mechanical polishing (CMP) of ferrofluid, heat conduction of ferrofluid and R-T instability of ferrofluid. Contribution of this thesis on them can be described as follows.As for CMP modeling of ferrofluid, a CMP model with centrifugal force and ferrofluid slurry is installed firstly. The simulation results show that external magnetic fields can effectively change pressure distribution and in-fluences of nominal clearance, rolling angle and pitch angle on the dimen-sionless resultant forces and moments. Considering convective effect of or-dinary fluid, a Reynolds lubrication equation is derived by simplifying the 2-D Navier-Stokes equations, which is used to build the corresponding CMP model. Rationality of the model is verified by analyzing influences of nomi-nal clearance, rolling angle, pitch angle on the dimensionless resultant forces and moments, in term of numerical computation. Based on the convective effects of fluid, CMP process model of ferrofluid is studied. Simulation anal-ysis shows that distribution and magnitude of the pressure will be changed by changing external magnetic field. At last, by comparing with numerical results, roles of external magnetic fields to the pressure distribution are stud-ied in different ferrofluid CMP models; and influences of centrifugal force or convective effect to the pressure distribution are also researches in different external magnetic fields. These results can work as reference for improving CMP technologies.As for two kinds of ferrofluid heat conduction problems, nature con-vection in 2-D closed square cavity and heat conduction between two plates, model equations about them are established. When gradient of external mag-netic field is uniform, the two kinds of equations are solved by the SIMPLE algorithm. When direction of gradient of external magnetic field is the same as that of gradient of temperature, the numerical results show that the ex-ternal magnetic field can increase the convection and the pressure in the 2-D closed square cavity, and the trends of increase of the influence on the con-vection and the pressure is decreased with increase of the magnetic Rayleigh number. For the heat conduction between two plates, a kind of open system, the numerical results show that if the magnetic Rayleigh is increased, trends of increase of the influence on the thermal conductivity is decreased too. And if direction of gradient of external magnetic field is parallel to that of the plates, external magnetic can accelerate the heat conduction. Based on these model equations and the diffusion parabolized theory, the heat conduc-tion equations of ferrofluid are simplified and the grade structure theory of the equations is also derived. As an example, the heat conduction model be-tween two plates is calculated numerically. The numerical results show that the simplified equations are more reasonable, compared with the previous ones.As for the R-T instability problem of ferrofluid, the simplified model equations are derived firstly. Under uniform mesh, the corresponding discrete systems are installed by using weighted essentially non-oscillatory (WENO) scheme and TVD R-K method. Simulation results show that, when direction of the external magnetic filed is the same as that of gravity, velocities of the interface arc increased by the external magnetic field, vice versa. When the direction of the external magnetic field is perpendicular to that of gravity, the case become that instability of the interface is increased, symmetry of the interface is destructed, and more foam like spiral vortexes emerge on the boundaries. These results are very helpful for controlling R-T instability of ferrofluid by adjusting magnitude and direction of external magnetic field.更多还原