对流-辐射换热下功能三明治夹层结构热力耦合FVM研究  

Research of the thermoelastic performance of the functionally graded sandwich slabs with convective-radiative boundary conditions based on FVM

作　　者：刘琦 刘磊[1] 杜雁霞[1] 杨肖峰 肖光明[1] 桂业伟[1] LIU Qi;LIU Lei;DU YanXia;YANG XiaoFeng;XIAO GuangMing;GUI YeWei(State Key Laboratory of Aerodynamics,China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]中国空气动力研究与发展中心空气动力学国家重点实验室,绵阳621000

出　　处：《中国科学：物理学、力学、天文学》2022年第12期106-115,共10页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家重点研发计划(编号:2019YFA0405202);国家数值风洞(NNW)项目资助。

摘　　要：本文发展了一种适用于二维对流-辐射换热环境下功能型芯子夹层结构热力耦合问题的控制体有限元方法(CV-FVM).基于4点四边形单元,对控制方程及换热边界的离散过程进行了详细的推导.基于交错网格技术,将待解变量存储在单元节点,将材料参数存储在单元中心,为保证温度迭代求解收敛将辐射换热边界条件进行线性化处理.针对指数型芯子夹层结构的纯导热问题将本文计算结果与解析解进行对比,二者吻合良好.分别研究了几何参数和物理参数,如毕渥数、辐射-导热系数、环境温度比、面板厚度和功能型芯子梯度因子对结构内热弹性能的影响.结果表明:加热面毕渥数对结构内的热弹性影响很小,而冷却面毕渥数对热弹性影响较大;相比加热面,冷却面对环境温度的变化更加敏感;针对指数型芯子夹层结构,增加上面板厚度可降低上面板与芯子连接处的大梯度应力问题;相比指数型芯子,采用线性分布(p=1)功能型芯子结构应力分布更光滑,可更有效缓解结构内大幅度的应力变化.In this study, a two-dimensional control volume finite element method(CV-FVM) has been developed for the thermoelastic coupling problem of sandwich structures with functionally graded material core under a convectionradiation heat transfer environment. Based on a four-node quadrilateral element, the discrete process of the governing equation and the nonlinear heat transfer boundary are given in detail. Based on the staggered grid technology, the variables are stored at the node of the element, and the material parameters are defined at the center of the element. To ensure the convergence of the temperature solution, the radiation heat transfer boundary condition is handled by the linearization technique. The numerical method developed in this study is validated for the heat conduction problem of sandwich structures with an exponential core. The results showed that CV-FVM results are consistent with the analytical solution. The influences of the geometric and physical parameters, such as the Biot number, radiation conduction coefficient, environmental temperature ratio, panel thickness, and gradient index of the functionally graded core, on the thermoelastic performance of the structure are investigated. The results showed that the Biot number of the heating surface has only a slight effect on the thermoelastic response of the structure, whereas the Biot number of the cooling surface has a significant effect on the thermoelastic response. The cooling surface is more sensitive to the change in the environmental temperature than the heating surface. For sandwich structures with an exponential core, increasing the thickness of the upper panel can reduce the large gradient change of the stress at the junction between the upper panel and the core. The stress with a linear variation of the properties(p = 1) is smoother than that with a nonlinear variation of the properties(p = 0.1 and 10), and the large gradient change of the stress of the structure can be reduced significantly(p =1).

关 键 词：热弹性耦合 热防护系统 有限体积方法 对流-辐射换热 

分 类 号：TK124[动力工程及工程热物理—工程热物理] V214[动力工程及工程热物理—热能工程] V414[航空宇航科学与技术—航空宇航推进理论与工程]