CSRT与CST气动外形参数化方法对比

Comparison of the CSRT and the CST parameterization methods

类别形状修正函数变换(CSRT)方法是在类别形状函数变换(CST)方法的基础上添加修正函数以克服其不具备局部性的缺点发展而来的新型参数化方法。通过考察参数化过程中翼型的表示误差和线性系统条件数,对CSRT和CST参数化方法的表示精度和数值单值性进行了对比。使用基于以上两种参数化方法的远场组元(FCE)激波阻力优化算法对超声速翼身组合体进行了零升激波阻力优化,结果对比得到:基于CSRT方法的两级优化具有更好的优化效果,激波阻力系数降低了34.7%。研究表明:CSRT方法需要比CST方法更多的参数数量以达到相似的精度,随参数数量的增长,CSRT参数化过程的病态化程度远低于CST方法;CSRT参数化方法可以结合适当的优化算法进行气动外形二级优化,其效果优于使用相同参数数量的CST参数化方法所进行的单级整体优化。

Class Shape Refinement Transformation（CSRT）is a new shape parameterization method developed by adding the Refinement Function to the Class Shape Transformation（CST）to enbance the ability of local region shape definition.Based on the representation residuals and the condition numbers of linear systems in the parameterization process,a study is performed on the differences in the precision and the numerical uniqueness between the two parameterization methods mentioned above.Using the CSRT and CST methods respectively with the same parameter number,zero-lift wave drag optimizations and the corresponding result comparisons of the supersonic wing-body are carried out using the Far-field Composite Element（FCE）wave drag optimization method.The superior result is obtained by the two-level optimization based on CSRT,yielding a 34.7%reduction of wave drag.It is suggested that in comparison with the CST method,although the CSRT method requires more parameters to achieve the similar precision,its numerical uniqueness degrades much more slowly.Two-level shape optimizations based on the CSRT method,may have some more applicablity yielding superior results than that of single-level optimizations based on the CST method.