变几何域传热的表面热流反演方法

Estimation of surface heat flux for variable geometry inverse heat conduction problem

变几何域的表面热流反演是一类特殊的热传导逆问题,在再入飞行器烧蚀型防热材料的表面热流反演中具有工程实用价值。本文首先对变几何域传热的正问题计算方法进行了校核验证,然后建立了求解变几何域表面热流反演问题的顺序函数法和共轭梯度法;给出了这两种反演方法的基本思想和算法推导,并针对典型算例进行了仿真。结果表明:两种反演方法都能计算出较好的反演结果,并且算法受测量噪声的影响较小,具有较好的鲁棒性;反演算法能适应不同的几何域变化函数,但几何域变化量的测量误差在表面热流的反演结果中会有较为直接的反映。

Estimation of surface heat flux for variable geometry heat conduction problem is a special kind of Inverse Heat Conduction Problem（IHCP） and of significant value in engineering practice of surface heat flux inversion for reentry vehicle＇s ablative thermal protection system. In this paper,the Finite Con- trol Volume（FCV） method used to solve the direct variable geometry heat conduction problem is valida- ted at first and two estimation methods,Sequential Function Specification Method（SFSM） and Conjugate Gradient Method（CGM）, are developed for the estimation of the surface heat flux from temperature 1 measurements. The basic idea and detailed algorithm of these two methods are presented and both meth- ods are applied to a typical exemplified case. Two conclusions can be drawn from the result. First, both SFSM and CGM are feasible estimation methods to solve this problem and are not very sensitive to the measurement noise. Second, both estimation methods are suitable for different geometry variation func- tion, but the measurement noise of geometry variation would be directly reflected in the estimation result of surface heat flux.