高阶辐射换热有限元算法研究

随着航空航天技术的发展,飞行器热结构所需承受的温度越来越高,辐射换热变得非常重要;当前大部分商业软件对于辐射问题的有限元计算方法还是基于一致表面温度和辐射热流假设,使得计算精度和网格密度的矛盾越来越严重.进行了选用高阶单元、采用高斯积分精确计算单元表面变辐射热流方法的研究,从而摆脱了一致表面温度和辐射热流的假设,使得在相同网格密度的情况下计算精度大大提高;同时,从包含辐射换热问题的有限元计算方程出发,采用与有限元数值计算时相同的积分方案,只在独立的积分点处计算辐射热流,克服了积分方法计算效率低的缺点.经与ANSYS的计算结果对比,应用辐射热流积分方法于高阶单元能大大提高计算精度;并且在相同计算精度条件下,此方法的计算效率更高,具有一定的实用价值.

Research of the Higher-order Finite Element Arithmetic for Radiation Exchange

With the development of aeronautic and astronautic techniques, radiation becomes much more significant while the structure is exposed to the higher and higher temperature. Most of the current finite element software packages treat it using the net-radiation method or absorbed radiation method based on the assumption of isothermal surface with uniform radiation heat flux, which brings the conflict between the precision and the quantity of grids. Using integral method to compute the variable radiation heat flux in higher-order finite element, the precision can be improved greatly while using the same quantity of grids, because it is more consistent with the distribution of real temperature. In this paper, the integral is only processed on the same integral points as those used for solving the finite element equations, so it may be of high efficiency. In an academic testing model, the result is contrast to which get in ANSYS, proving the high precision of the method. Then an actual sandwich panel used in the thermal protection system is analyzed with the method, and the error is comparatively low to the analytical answer while the computation being of high efficiency.