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Stability Studies Of Nonparallel Boundary Layers

Posted on:2003-04-21Degree:DoctorType:Dissertation
Country:ChinaCandidate:W Z WangFull Text:PDF
GTID:1100360092975962Subject:Fluid Mechanics
Abstract/Summary:PDF Full Text Request
The new theory of the parabolized stability equations (PSE) is used to study the stability of the boundary layer. The process of development and evolution of the disturbance wave and its harmonics in the boundary layer are investigated. The linear and nonlinear stability of different disturbances in nonparallel boundary layer are researched.Expansions in orthogonal functions is used to solve the Orr-Sommerfeld equation (OSE) in studies of the linear stability of parallel flow. For the plane Poiseuille flow the critical Reynold number is given accurately. Furthermore, the Blasius flow which is considered locally parallel has been studied, and the neutral stability curves, which are very important for the stability study, are given.The nonparallel linear stability of the two-dimensional and three-dimensional disturbance waves are studied by the parabolized stability equations. Since the equation used to study stability is parabolized, the problem can be solved by the marching procedure. Then the stability of nonparallel flow can be studied based on this characteristic of PSE. The numerical techniques developed here, including the high accuracy method of using expansions in orthogonal functions in normal direction and the effective algebraic mapping to deal with the problem of infinite region, can raise the calculation precision and the convergence velocity greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of numerical calculation can be assured.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 Floquet's three-dimensional linear stability theory is used and a set of stability equations is constructed. The secondary instability is studied, and the veryimportant initial conditions of sub-harmonic disturbances are obtained. With the initial solutions of two-dimensional harmonic waves given by Landau expansion and the mean-flow-distortion calculated by the approximation equation, the three-dimensional H-type evolution problem of the nonlinear boundary layer stability is studied.The effects of the different pressure gradients on the stability of nonparallel boundary layer are investigated. On the boundary layer with pressure gradient, the effect of the two-dimensional Tollmien-Schlichting wave with finite amplitude on growth and development of the subharmonic is studied. And the effects of different pressure gradients, including favorable and adverse pressure gradient of basic flow, on 'H-type' evolution are investigated in detail. All the results reveal the fact that favorable pressure gradient can delay the instability and retard the occurrence of transient. But the adverse pressure gradient accelerates the instability and promotes the transition of boundary layer.It is affirmed that the effect of non-parallelism on the stability of disturbances is obvious. The effect of non-parallelism on three-dimensional disturbance is stronger than that of two-dimensional disturbance. Sometimes, it even change the stable flow in parallel basic-flow into unstable. It is shown that using PSE to study nonparallel stability, especially to study nonlinear stability of nonparallel flow is much more effective. The result, which is comparable with Direct Navier-Stokes Simulations(DNS), can be obtained, and the time needed is lessened greatly. Obviously, the study on nonparallel boundary layer stability has an important sense in theory, on the other hand, the determination of precise gr...
Keywords/Search Tags:Nonparallel Flow, Boundary Layer Stability, Parabolized Stability Equations, Nonlinearity, Tollmien-Schlichting Wave, Secondary Instability, Pressure Gradient
PDF Full Text Request
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