环形套管内非牛顿流体非定常旋转流动变分解析法研究

Research on Variation Analytical Approach for Time-dependent Rotation Flow of Non-newtonian Fluid in a Ring Sleeve

采用变分解析法即Kantorovich变分方法,研究了环形套管内上随体Maxwell非牛顿流体由一类定常流动状态向另一类定常流动状态的非定常旋转流动的速度场分布,把该问题的高阶偏微分方程的边、初值问题降阶化为低阶的各级近似的常微分方程问题,并给出解析答案,其结果与差分结果较为一致.

In this paper the time-dependent rotation flow of upper-convected Maxwll non-newtonian fluid is studied by variational method. In the time-dependent rotation flow problem,the initial and boundary values of high-order partial differential equations are reduced to the low-order approximation values of ordinary differential equation. The analytical solutions are given for the 1st,2nd order approximations. The results which are calculated by Kantorovich variational method are compared with that by finite difference method. The compared results are fundamentally the same.