基于第一类Fredholm方程的充气飞艇结构表面风压分布求解

Research on the wind pressure distribution of inflable structure based on the first Fredholm integral equation

充气囊体除了受自重影响外,最重要的外荷载即为来流风压,研究充气囊体的表面风压分布具有重要的工程意义.目前的流体力学技术求解任意外形充气囊体表面风压是不可能的.本文针对轴对称体型充气囊体,根据源汇与平行流复合的方法将其压力分布归结为求解第一类Fredholm方程.改进了Tikhonov正则化方法,求解某充气囊体的表面风压分布,并与实验结果对比,表明该方法求解旋转体型囊体表面风压是有效的.本文还给出Tik-honov正则化方法小参数的选取建议,对工程应用有重要意义.

For airship, the most important external force is wind pressure, except gravity. The research about wind pressure distribution on the hull of airship has an important engineering significance. At present, using fluid mechanics to obtain the surface wind pressure of airship in random appearance is impossible. Because of the hull shape of airship usually being rotation body, it can be reduced to the first Fredholm equation while airship is in flight with horizontal altitude according to the source and sink method combined with the parallel flow. Using Tikhonov regular method, the pressure coefficient distribution of airship could be obtained and shows that the Tikhonov method is applicable for solving this problem compared with test results. And some suggestions are given about how to choose the parameter in Tikhonov regular method.