幂律流体在矩形通道中充分发展流动的数值模拟及阻力计算

针对假塑性幂律流体在矩形通道中充分发展流动问题,用帕坦卡方法作数值分析,文中讨论了不等距网格的划分方法和粘度系数的插值方法。数值解给出了流变指数n=0.1,0.2,…,1.0及矩形边长比s=0.1,0.2,…,1.0范围内的全部fRe,发现圆管阻力计算公式只在一定范围内适用。本文作者给出了上述广阔范围内以当量水力直径为定性尺寸的阻力系数计算公式,其最大误差为3.57％,平均误差为1.9％。

Numerical Simulation and fRe's Correlation for Fully Developed Flow of Power Law Fluid Through a Rectangular Duct

A theoretical investigation is presented for fully developed flow of power law fluid through a rectangular duct,this modelling is based upon the Patankar's control volumemethod -a famous numerical simulation method of fluid flow and heat transfer. Theneighbour grid length ratio to be used in non-equal length grid is discussed and the meth-od of calculating velocity gradient for viscosity is explained. The extensive results of fRefor the fluid with power exponent n=0.1, 0.2, 0.3, ...,1.0 and flowing in the rectangularduct with aspect ratio s = 0.1, 0.2, 0.3, ...,1.0 are given. It is found that circular pipe fReformula can only be used to calculate the fRe in rectangular duct in a very low accuracy,especially when aspect ratio becomes small. Finally, an expression to correlate fRe withpower exponent n and aspect ratio s of rectangular duct is presented, its largest error is3.57% and average error is 1.9%.