Stability Investigation Of Three-Dimensional Nonparallel Boundary Layers

In this thesis, the parabolic stability equations (PSE) in the different coordinate systems are driven from Navier-Stokes (N-S) equations. The stability problems of the boundary layers for three-dimensional body,and the spatial evolution process of the C-type instability are studied.The PSE in the curve coordinate systems are solved by the numerical techniques developed efficiently in this paper. A normal transform is introduced, and there are enough much grids in the region between the critical layer and the wall, where the variation of the disturbance is the quickest. The finite-difference of governing equations with fourth-order accuracy in the normal direction is utilized in full regions including points close the wall, and is very important for accurately discreting equations. The combination of global and local methods is implemented, and a new iterative formula is derived. Thus, the more precision eigenvalues can be obtained, and the convergence is made rapidly. In the examples we get some evolution curves, such as the growth rates and shape functions, which are used to analyze the stability problems for the boundary layers of the fuselage and the wing.With the Fourier series technique, the disturbance is discomposed into predominant mode and high frequency harmonics. The nonlinear stability of three-dimensional disturbances for the Blasius boundary layers is studied. We adopted here the high accuracy method of using the expansions in orthogonal functions along the normal direction and the effective algebraic mapping to deal with the problem in the infinite region. The initial solutions of two-dimensional harmonic waves are given by Landau expansion, and the mean-flow-distortion is calculated by the approximation equation. We can get the initial conditions of TS wave and sub-harmonic wave in the C-type instability by linear PSE method. Furthermore, we employ iteration and Predictor-Corrector-Approach to solve the nonlinear equations in order to implement the marching procedure. We investigate detailedly the process of the C-type instability for nonparallel boundary layers with three-dimensional disturbances.By investigating the nonparallel boundary layers of three-dimensional body, we...