稳态三维不可压缩流体非等温有限元模拟

Finite Element Analysis of Steady Three Dimensional Non-isothermal Incompressible Fluid

针对幂律型流体,建立了稳态三维粘性不可压缩流体非等温流动的有限元模型。采用罚有限元法将连续性方程引入到动量方程,获得了速度场分布。能量方程采用SUPG(stre-amline upwind/Petrov-Galerkin formulation)方法构造非对称权函数,克服了对流项占优时数值解的失真现象,获得了稳定的温度场分布。以幂律型流体本构关系计算了剪切速率对粘度的影响,采用Arrhenius模型计算了温度对粘度的影响。以幂律型流体矩形截面稳态收敛流动为例,计算了区域内流体的速度和温度分布规律。计算结果表明,经过有限次迭代可获得合理速度场分布,在能量方程出现对流项占优的情况下,即便采用较粗的网格划分,仍能获得稳定的温度场分布。

The modeling for three dimensional incompressible viscous non-isothermal steady flow was presented by using penalty finite element method. The velocity field was established by introducing the continuity equation into momentum equation. By adopting SUPG（Streamline Upwind/ Petrov Galerkin formulation） for selection of the unsymmetrical weight function for energy equation, the distortion of the numerical results when the convective term is dominate was overcome, and the stable temperature distribution was obtained. The paper also coupled the viscosity with shear rate by power-law model, and coupled the viscosity with temperature by Arrhenius model. A power-law fluid flowing process though three-dimensional rectangular convergent channel was selected for the demonstration of the method. The velocity and temperature distributions are obtained. The results show that the reasonable velocity and temperature fields can be obtained within several iterations. When the convective term is dominant in energy equation, the reasonable temperature field can be also obtained even with the coarse mesh.