Finite Element Analysis of A Slip Casting Process of Slurry Based on Three Dimensional Filtration Theory

本文的主要研究成果如下：(1)将现代渗流理论推广到广义坐标系，建立了三维注浆浇注过程的基本方程组。它包括一个包含液体速度q和固体运移速率r的基本流量方程，以及将矢量q和r的发散度与孔隙度随时间变化联系起来的连续性方程，以及液体压力p_L和固体压缩压力p_S之间的关系，假设q和r方向重合-∇p_L=∇p_S，并借助于压缩渗透率(CP)特性，最终简化了两个偏微分方程组。这些方程在空间上用Galerkin有限元方法离散，在时间上用有限差分方法离散，在每个时间增量上用Gauss消去法求解得到的矩阵方程。考虑主曲率的影响，对滤饼表面和液体前沿进行了计算。圆柱形石膏型注浆铸件的数值计算结果表明，该方法不仅可以预测三维滤饼生长，而且可以预测各种内部条件的时间演化，如孔隙率、压力和流量，以及泥浆浓度的影响。(2)提出了一种简单的预测压缩渗透率(CP)特性的方法，该方法利用滤液体积V与过滤介质阻力Rm较大的单次恒压过滤初期的时间θ关系来确定压缩渗透率(CP)特性。用现代过滤理论和单纯形法寻找了10个参数来描述Cp特性和Rm特性，以使计算的(V与θ)关系与观测值的偏差最小。在高岭土泥浆体系中的应用表明，该方法能够快速、准确地测定高岭土泥浆的CP特性。

The main results of the present study are as follows :(1) Fundamental equation set governing three-dimensional slip casting process is proposed by extending modern filtration theory to generalized coordinate system. It consists of a basic flow rate euation, which contains the liquid velocity q and the solid migration rate r, and the continuity equations relating the divergence of vectors q and r to porosity variation with time, and a relationship between liquid pressure p_L and solid compressive pressure p_S Assuming that the direction of q and r coincide with -∇p_L=∇p_S and with the aids of compression permeability (CP)-characteristics, two partial differential equations are finally reduced. These equations were discretized with a Galerkin finite element method in space and with a finite difference method in time, and resultant matrix equations were solved using the Gauss elimination method at each time increment. Cake surface and liquid front were computed considering the effect of principal curvatures. The numerical results of slip castings in a cylindrical plaster mold showed that the proposed method enables the prediction of not only three dimensional cake growth but also time evolution of various internal conditions, such as porosity, pressure and flow rates, and further the effect of slurry concentration.(2) A simple predictive method to determine compression permeability (CP)-characteristics are proposed, using the filtrate volume V vs. the time θ relation in the initial stage of a single constant pressure filtration run with a relatively large filter medium resistance Rm. Ten parameters, for specifing the CP- and Rm-characteristics, are searched so as to minimize the deviation of computed (V vs.θ) relation from observed one using modern filtration theory and Simplex method. Application to a Kaolin slurry system showed that the proposed method enables the rapid determination of CP- characteristics with high accuracy.