【摘要】 从Navier-Stocks(N-S)方程导出曲线坐标系下的抛物化稳定性方程(Parabolicstabilityequation,PSE),研究机翼非平行的可压缩边界层稳定性问题。发展了求解PSE的高效数值方法:引进法向变换,使得在临界层与壁面之间的扰动量变化最快的区域有更多法向网格点;采用包含边界邻域在内的完全四阶精度的法向差分格式,这对方程精确离散至关重要;以及全局法和局部法相结合的数值方法及其新的迭代公式,能大大加速收敛并得到更精确的特征值。算例分析研究了扰动增长因子和形状函数等演化曲线。更多还原

【Abstract】 The parabolic stability equations(PSEs) in curvilinear coordinates are derived from Navier-Stocks(N-S) equations,and the nonparallel stability of the compressible boundary layer on wings is analyzed.Numerical techniques are developed for solving PSEs.A normal transform is used to have much more grids in the region between the critical layer and the wall,where the disturbance variation is maximal.The finite-difference of governing equations with the fourth-order accuracy in the normal direction is utilized in the entire region including points close to the wall.It is very important for the discrete accuracy of equations.The combination of global and local methods and a new iterative formula can accelerate the convergence and obtain accurate eigenvalues.The evolution curves of disturbance growth rates and shape functions are used to analyze stability problems.Results are satisfactory.更多还原