在低中高三种Re数下圆管入口流的有限元分析

圆管入口流问题的研究已有很长历史,但理论结果与实验结果不能很好地符合。本文用改进的Newton-Raphson方法线化由Navier-Stokes方程导出的有限元方程,用波阵法求解线化后的方程组。最后在0～800的Re数范围内得到了速度场及入口长度,并给出了描述入口长度随Re数变化关系的拟合公式。数值解与实验结果的比较是令人满意的。本文还对简化Navier-Stokes方程(SNSE)与完整Navier-Stokes方程(CNSE)在求解本问题过程中的一致性作了数值研究,得出了当Re≥80时CNSE和SNSE结果一致的结论。

Finite Element Analysis of the Entry Flow into a Circular Tube at Low Moderate and High Reynolds Numbers

The study of the entry flow into a circular tube is of long interest, but there have been some disagreements between the theoretical and experimental results in the literature. In the present paper, the finite element equations derived from the Navier-Stokes equations are first linearized by using the improved Newton Raphson's method. The linearized equations are then solved by the frontal method to yield the velocity fields and the entrance length in the Reynolds number range 0-800. Finally, fitting formulae are proposed to describe the relationship between the entrance length and the Reynlods number. It turns out that our numerical results are compared satisfactorily with the experimental ones. Moreover, the consistence of the Simplified Navier-Stokes Equations (SNSE ) and the Complete Navier-Stokes Equations (CNSF,) is numerically examined herein for the entry flow problem. It is concluded that the results of SNSE and CNSE are coincident when the Reynolds number is greater than or equal to 80.