The Analysis Of The Effect Of Non-parallelism And Pressure Gradient On The Stability Of Boundary Layer

In this thesis, different types of stability equations, including Orr-Sommerfeld Equation (OSE) and Parabolized Stability Equation (PSE) based on the"slow change"hypothesis and the local method equation which is computed in local range, are derived from Navier-Stokes equation with"small disturbance"hypothesis. The linear and nonlinear stability of different disturbances in parallel and nonparallel boundary layer are researched. The development of growth rate of small disturbances and the effect of non-parallelism and pressure gradient on the stability of boundary layer are studied especially.The nonparallel linear stability of the two-dimensional and three-dimensional disturbance waves are studied by the parabolized stability equation which is developed in recent years and the local method based on the Landau expansion. Since the PSE is parabolized, the problem can be solved by the marching procedure which uses different method in the streamwise direction and spectral collocation method in the normalwise direction. With the predictor-corrector approach in the marching procedure, the normalization is satisfied and the stability of numerical calculation can be assured. The Muller iteration method is used in the computation of local method in the streamwise direction. The effect of non-parallelism of stability is studied by comparing the results of parallel and nonparallel flow. The effect of the pressure gradient on critical Reynolds number is also displayed and the influence rule of the different pressure fields on the flow stability is exploited.Furthermore, with the Fourier series technique, the disturbance is discomposed into predominant mode and high frequency harmonics, and the nonlinear stability of the nonparallel boundary layer is studied. The initial solutions of two-dimensional harmonic waves are given by Landau expansion and the mean-flow-distortion is calculated by the approximation equation. Furthermore, we employ iteration method and"Predictor-Corrector Approach"to solve the nonlinear equations in order to implement the marching procedure, and the result of nonlinear two-dimensional stability is obtained precisely. The effect of pressure gradient is also studied here.The research work of thesis is fully supported by the Doctoral Foundation of Ministry of Education of China (Grant No.20030287003).