拟塑性流体三维流动的高精度有限体积算法

以拟塑性流体为研究对象,针对剪切应力与剪切速率的非线性关系给数值计算带来的困难,提出了一种适用于拟塑性流体三维流动的高精度有限体积算法。采用幂律模型作为拟塑性流体的本构方程,通过给定非均匀的初始速度场和限定表观黏度数值变化的范围,消除了应力计算时可能出现的"零障碍"和"无穷大障碍"奇点问题。计算了长直方管和大曲率弯管中拟塑性流体的层流流动,验证该计算方法在幂律流体三维流动数值模拟中的可靠性。长直方管计算结果中给出了不同流动指数的摩擦因子系数和广义雷诺数之间的关系,与前人的实验数据和数值研究结果均吻合良好。

A High-Order Finite Volume Method for Simulating Three-Dimensional Flow of Pseudoplastic Fluids

A high-order finite volume method (FVM) is proposed for simulating three-dimensional flow of pseudoplastic fluids in this paper. The relationship of shear stress and shear rate of pseudoplastic fluids is nonlinear, which will impose a special difficulty to the calculating process. The power-law model is used to quantitatively describe the rheological behavior of pseudoplastic fluids. In order to avoid the singularities of viscosity at zero and infinite shear rates, the non-uniform initial velocity field is adopted and a strategy of limiting the range of apparent viscosity is proposed. The high-order finite volume method for three-dimensional laminar flow of pseudoplastic fluids is verified in both a straight tunnel and a strongly curved duct. The finite-volume solutions are the numerical values of the friction factor-Reynolds number relation in a straight tunnel for different power-law indices. The results agree well with previous experimental and numerical studies.