一种新型热力学两温度模型数值计算方法  

A new numerical calculation method of thermodynamic two-temperature model

作　　者：李鹏 丁明松[1,2] 陈坚强 刘庆宗[2] 傅杨奥骁 江涛[2] 梅杰 许勇 LI Peng;DING Mingsong;CHEN Jianqiang;LIU Qingzong;FU Yang'aoxiao;JIANG Tao;MEI Jie;XU Yong(State Key Laboratory of Aerodynamics,Mianyang 621000,China;Computational Aerodynamics Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]空天飞行空气动力科学与技术全国重点实验室,绵阳621000 [2]中国空气动力研究与发展中心计算空气动力研究所,绵阳621000

出　　处：《航空学报》2024年第22期141-151,共11页Acta Aeronautica et Astronautica Sinica

基　　金：国家重点研发计划(2019YFA0405203);国家数值风洞工程。

摘　　要：高焓气体热力学参数的理论模式在两温度模型求解器中应用广泛,但在具体应用中存在程序运行效率低、数值稳定性差等问题。发展了一种更为简单高效的热力学两温度模型能量体系计算方法,借鉴单温度模型热力学平衡能量的拟合表征形式,通过重构再造内能模态表征形式,分别得到由平动温度表征的线性能量项、由振动温度表征的非线性能量项,进而引入Chemkin拟合式对非线性能量项进行表征计算,从而避免理论模式采用指数表征式存在的潜在数值问题。数值研究表明:该方法在预测热化学非平衡流动及其相关气动特性方面计算精度可靠,且相比于采用理论模式的求解器计算效率更高,其单步迭代平均耗时可减少约12%,计算收敛所用耗时可降低10%以上,对提升热化学非平衡流动模拟效率具有积极效果,具有良好的工程应用价值和前景。The theoretical model for calculating the thermodynamic parameters of high enthalpy gases,widely used in two-temperature model solvers,has the shortcomings such as low program operation efficiency and poor numerical stability in specific applications.A simpler and more effective method for calculating the thermodynamic energy system of the two-temperature model is developed.Drawing on the fitting expressions of the thermodynamic equilibrium energy in the one-temperature model,the representation forms of the internal energy modes are reconstructed to obtain separately a linear energy term characterized by translational temperature and a nonlinear energy term characterized by vibrational temperature.Meanwhile,Chemkin's fitting polynomials are introduced to characterize and calculate the nonlinear energy term,so as to avoid the potential numerical problems arising from the use of exponential expressions in the theoretical model.Numerical studies indicate that the new method has reliable computational accuracy in predicting thermochemical nonequilibrium flows and their associated aerodynamic characteristics,and has higher computational efficiency compared to the solvers that use the theoretical model.The average time of single step iteration can be reduced by about 12%,and the computational time for convergence can be reduced by more than 10%,which has a positive effect on improving the efficiency of simulation of thermochemical nonequilibrium flows,and has good pros-pects for engineering applications.

关 键 词：高超声速 热化学非平衡 两温度模型 高焓气体 Chemkin拟合方法 

分 类 号：V19[航空宇航科学与技术—人机与环境工程]