幂律流体连续运动平板边界层的数值研究

利用数值模拟方法研究了幂律流体在连续运动平板上的层流边界层问题。利用相似变换理论推导出无量纲剪切力的计算公式,数值求解了不同幂律指数n的流体在不同运动参数ξ的连续运动平板上的层流边界层流场,分析了各个参数对边界层速度分布和剪切力大小的影响。结果表明,边界层偏微分方程组的数值解与经过相似变换求得的非线性常微分方程的数值解吻合得很好,这既说明对幂律流体连续运动平板上的层流边界层问题的研究是有效且可靠的,同时也证明了连续运动平板问题存在相似解。

Numerical investigation of laminar boundary layer flow on continuous moving flat in power-law fluid

The laminar boundary layer flow on a continuous moving flat in power-law fluid was investigated numerically.The formula for calculating dimensionless shear stress was obtained by introducing a similarity transformation.And the laminar boundary layer flow field in different power-law exponent fluid and in different movement parameter was solved with the help of numerical simulation software.And furthermore,the effect of each parameter on boundary layer velocity distribution and shear stress size was analyzed.The results indicate that the numerical solution to the partial differential equation of the boundary layer is well coincident with the numerical solution to the non-linear constant differential equation by means of the similarity transformation.The reliability and the efficiency of simulation solutions are verified by the numerical results,and the existence of similarity solution to continuous moving flat problem is confirmed.