非结构网格催化壁面的隐式处理方法

An Implicit Scheme with Unstructured Girdfor Catalytic Surface

关键词:  非结构网格  高超声速  化学非平衡  壁面催化  隐式处理方法

Key words:  Unstructured grid  Hypersonic  Chemical nonequilibrium  Surface catalysis  Implicit scheme

摘要:

为了解决格点型非结构有限体积法隐式处理完全催化壁面时边界上出现非物理解的情况，提出了壁面边界隐式矩阵“松弛”处理方法，使得格点型非结构有限体积法可以用于高超声速非平衡条件下气动热的预测。提出了考虑等温壁面和辐射平衡壁面下，处理完全催化壁面的“松弛”方法，并给出了边界控制体上隐式矩阵的具体形式。针对高超声速化学非平衡流动，使用非结构网格对典型的圆柱绕流以及球头绕流问题进行模拟，并与结构网格计算结果进行比较分析。验证了所提出的强制边界条件的“松弛”格式可以正确模拟完全催化壁面边界条件。在此基础上，针对不同质量分数配比的自由来流进行计算，分析壁面处组元的质量分数以及热流，计算结果显示即使在自由来流中两个组元质量分数各占50%的情况下，被“松弛”的组元质量方程的残差仍然能够到10-8量级，壁面上热流计算正确并且组元质量分数与自由来流保持一致。这表明本文方法在自由来流中质量分数最大组元不占优的情况下仍然有效。

Abstract:

In order to solve the nonphysical phenomenon when the unstructured finite volume solver based on cell-vertex scheme is employed for fully catalytic surface， the ‘relaxation’ method for implicit matrix on boundary is developed. Thus， the unstructured finite volume solver based on cell-vertex scheme can be used to predict aero-heating for hypersonic nonequilibrium. The strong implicit scheme with ‘relaxation’ considering fully catalytic surface under isothermal and radiative equilibrium wall is developed and the implicit matrix for the control volume on boundary is given. This scheme based on unstructured grid is implemented for the simulation of hypersonic chemical nonequilibrium flows around a cylinder and a sphere. Numerical results are obtained and compared with that of structured grid solver. It indicates that the ‘relaxation’ scheme for strong boundary condition can simulate fully catalytic surface accurately. Furthermore， the simulation for different mass fraction compositions of freestream is performed and the mass fraction and heat flux on the wall are analyzed. The results show that the residual order of mass conservation equation for the ‘relaxation’ species can reach 10-8 and the mass fraction on the wall is the same to that of freestream even if the mass fraction of two species both equal to 50%. It shows that the developed method is still effective when the maximum mass fraction species does not dominate.