跨音速小扰动方程的多重解

MULTIPLE SOLUTIONS OF THE TRANSONIC PERTURBATION EQUATION

关键词:  跨音速流  小扰动流  数值法和计算方程  数值解  分析

Key words:  Transonic flow  Small-perturbation flow  Numerical method and procedure  Numerical solution  Analysis

摘要:

本文利用Engquist-Osher格式,离散跨音速小扰动方程(TSD)和边界条件,选择不同初场计算NACA0012翼型二维定常位势流场,得到了与试验值较符合的结果,同时用Murman-Cole非守恒和守恒两格式计算并进行了比较。着重用数值实验进一步探讨多重解问题,发现并总结出了几点很有参考价值的规律和现象。

Abstract:

In the present work, Engquist-Osher scheme was adopted to solve two-dimensional steady potential flow field over NACA0012 airfoil by discrete transonic perturbation equation (TSD). The solutions are in agreement with experimental results. In order to investigate the problem of multiple solusions, the nonconservative and conservative forms of Murman-Cole scheme were used and compared simultaneously. Some useful phenomena have been found as follows.The solutions with E-O scheme are not unique. Under the condition of narrow Mach number region (about 0.84-0.86) and zero angle of attack, there exist three converged solusions. One is a correct symmetric solution? and others positive and negative nonsymmetric solutions. In other cases, the solution is unique, when circulation strength (or symmetric specificity parameter) Γis greater than 10-3 in order of magnitude, the sym-metric solution can’t be obtained. Only if the zero potential field or almost completely symmetric field (Γ within 10-16-10-3) was taken as initial field,the symmetric solution can be solution.The converged solutions and characteristics of M-C conservative scheme are very similar to that of E-O scheme, but its pressure coefficient Cp value jumps sharply near parabolic points. Also one disagreement with conclusions reported before about M-C nonconservative scheme has been found in supercritical case.The nonuniqueness is supposed to be associated with transonic perturbation simulation model. To prevent solution from nonuniqueness, the relation of trailing edge boundary condition must be modified* so that the model can be in agreement with the practical physical flow.