机翼跨音速小扰动二级近似方法的数值分析

An Improved Method for Transonic Computationof Aircraft Wings

机翼跨音速小扰动二级近似方法的数值分析高超，罗时钧经典的跨音速小扰动方程在处理机翼绕流，尤其是具有较大后掠角机翼问题时，计算中常常出现收敛较慢，甚至发散的情况。数值解精度也不高。针对这一问题，为了扩大跨音速Ｊ＼扰动速势方程的应用范围，提高数值解的精度...

For transonic computation of aircraft wings, small perturbation method is still not satisfactory. For the conveneence of engineers me authors in a previous paperili proposed for thefirst take a 2nd order accuracy transonic small perturbation equation, given as Eq. (1) in theChinese text of this research summary. Now we present for the first time 2nd order accuracyboundary conditions to go with eq. (1): eqs. (2a) and (2b) for the wing surface and eq. (3)for the trailing vortex sheet. With eqs. (1) through (3), we can get results comparable inaccuracy with those obtained with frll potential method.Eq. (1) is discretized by means of Murmman-Cole non-coservative scheme (eq. 4) andsolved by implicit approximate fsctorization algorithm (eq. 5).Example 1 is NACA 0012 straight wing with aspect ratio AR=4. The results are givenin Figs. 1 and 2 for M∞=0. 82, α=0. From Fig. 1, it can be seen that the the pressure distributions on the wing basically coincide with those obtained with full potential method. Fig.2 indicates that, compared to classiCal small perturbation method, the iteration tAnes are reduced and the convergence speed is higher.Example 2 is ONERA M6 wing. Fig. 3 provides the results for M∞=0. 92, α=0. Theresults of present method are in good agreement with the full potential results of Ref. 2 andtest results of Ref. 3. In contrast, the numerical computation with classical small perturbation method does not converge:From the computation examples above, it can be deduced that, compared with classicalsmall perturbation methods, our method has the following advantages: better convergence,results closer to those obtainable with full potential method, convergence possible for widerrange of problems (including wings with bigger sweepback).