Chebyshev谱方法研究非稳态Maxwell流体在轴向余弦振荡圆柱上的斜驻点流动

A Chebyshev Spectral Method for the Unsteady Maxwell Oblique Stationary Point Flow on an Axially Cosine Oscillating Cylinder

研究了非稳态Maxwell流体斜撞击轴向余弦振荡圆柱的斜驻点流动.首先,基于斜驻点流动特性,在柱面坐标系下求得关于压力的二阶常微分方程,对压强进行修正,建立了非稳态Maxwell流体在振荡圆柱上斜驻点流动的边界层模型.接着,合理的相似变换将模型转化,使用Chebyshev谱方法求得模型的数值解.结果表明,在贴近圆柱表面的流体随着圆柱体做周期性运动;圆柱的曲率越大越会使在同一时刻同一位置处的流体质点的速度越大;相反,非稳态参数及流体的记忆特性也会在更靠近圆柱壁面处阻碍流体流动.

The oblique stationary point flow of the Maxwell fluid impacting an axially cosine oscillating cylinder was studied.Firstly,based on the oblique stationary point flow characteristics,the pressure was corrected with the 2nd-order ordinary differential equation of pressure obtained in the cylindrical coordinate system.Later,the boundary layer model for the unsteady Maxwell fluid on an oscillating cylinder was established.The model was converted through the reasonable similarity transform,and the numerical solutions were obtained with the Chebyshev spectral method.The results show that,the fluid near the surface of the cylinder moves periodically with the cylinder.The larger the curvature of the cylinder is,the higher the velocity of the fluid particle will be in the same position at the same time.In contrast,the unsteady state parameter and the memory properties of the fluid hinder the flow closer to the cylinder wall.