柱坐标系强守恒型动量方程离散方法研究  

Study on Discretization Method for Strong Conservation Momentum Equation in Cylindrical Coordinate System

作　　者：石国赟 陈宇杰 朱剑琴[4] 李海旺[3] 宇波[1] SHI Guoyun;CHEN Yujie;ZHU Jianqin;LI Haiwang;YU Bo(School of Mechanical Engineering,Beijing Institute of Petrochemical Technology,Beijing 102617,China;Beijing Academy of Safety Engineering and Technology,Beijing 102617,China;School of Power and Energy,Beihang University,Beijing 102617,China;Research Institute of Aero-Engine,Beihang University,Beijing 102617,China)

机构地区：[1]北京石油化工学院机械工程学院,北京102617 [2]北京市安全生产工程技术研究院,北京102617 [3]北京航空航天大学航空发动机研究院,北京102617 [4]北京航空航天大学能源与动力工程学院,北京102617

出　　处：《工程热物理学报》2024年第4期1049-1054,共6页Journal of Engineering Thermophysics

基　　金：国家自然科学基金重点基金资助项目(No.51904031)。

摘　　要：柱坐标系中,为了便于统一形式和编程实施方便,学者们对动量方程形式进行了多种变换,导致其守恒性质不明或有待进一步定量验证。针对这一问题,本文根据柱坐标系基向量关系推导了张量形式强守恒型方程的分量形式,并基于AUSM格式给出了对应的离散过程和离散结果。通过激波和均匀流动问题求解验证表明,本文所推导的动量方程在任意网格下均可严格满足守恒性,而将部分项放入源项处理则导致守恒性无法满足,需要大量网格才能保证计算结果的可靠性。本文研究内容可为强守恒型动量方程的应用提供参考。For the sake of a unified form and easy programming implementation,researchers have transformed the momentum equation form in the cylindrical coordinate system in a variety of ways,which results in the unknown conservation properties or further quantitative verification.This study uses the basis vector relations of the cylindrical coordinate system to obtain the component forms of the strong conservation equations in tensor form and then presents the corresponding discrete processes and discrete outcomes using the AUSM methodology.It has been established that the momentum equations developed in this paper can strictly satisfy the conservation under arbitrary grid,whereas the conservation cannot be satisfied by putting some terms into the source term,and a large number of grids are necessary to ensure the accuracy of the computational results.The findings presented in this paper can be used as a guide when applying strong conservation momentum equations.

关 键 词：N-S方程 守恒性 柱坐标 数值模拟 

分 类 号：TK123[动力工程及工程热物理—工程热物理]