Abstract

Steady laminar flow of an incompressible power-law fluid is a tube with an obstacle of given shape is numerically simulated. The mathematical description of the process is based on the vortex transport equation and the Poisson equation for the stream function, while the rheological properties of the medium are described by the Ostwald—de Waele power law. The steady solution of the problem is obtained using a time-dependent method based on the finite-difference approximation of the governing equations. The pressure distribution is determined by numerically solving the Poisson equation. A parametric investigation of the kinematic and dynamic flow parameters, as functions of the control parameters of the problem, is performed for non-Newtonian media. The effect of the Reynolds number, the nonlinearity exponent, and the obstacle geometry on the coefficient of the local fluid resistance is demonstrated.

中文翻译：

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流经变截面管的幂律流体的压力损失

摘要

不可压缩幂律流体的稳定层流是具有给定形状的障碍物的管的数值模拟。该过程的数学描述基于流函数的涡旋输运方程和Poisson方程，而介质的流变特性则由Ostwald-de Waele幂定律描述。使用时变方法基于控制方程的有限差分逼近来获得问题的稳定解。通过数值求解泊松方程来确定压力分布。对于非牛顿介质，根据问题的控制参数对运动和动态流动参数进行了参数研究。雷诺数，非线性指数的影响，