Some Kinds Of Ferrofluid Models And Their Numerical Computations

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.