Hydrodynamic Stability Of Two Phase Flow In The Flat Plate Boundary Layer

Laminar turbulent transition in boundary layer provides a building block for many practical inhomogeneous flows. There still exist a great many unsolved problems which call for a broadening of the understanding of many aspects of laminar turbulent transition in boundary layer flow. Multiphase flows are commonly encountered in nature and in numerous practical applications, such as in the energy engineering, chemical engineering, metallurgy, environmental protection, building materials, etc. The particles suspended in fluid play a role in the turbulence modulation, which has been known for several years. The objective of the present work is to investigate the hydrodynamic stability of two phase flow in the flat plate boundary layer. The layout of the dissertation is as follows:The first chapter is the introduction of the motivation, flow description, and literature survey of the dissertation.The hydrodynamic stability theories in the boundary layer are numerous. Chapter two introduces the concept of boundary layer theory; linear stability theory; the conversion relation between temporal and the spatial linear stability (Gaster theory); weak nonlinear stability theories; and calculation method related to the hydrodynamic stability in the flat plate boundary layer in detail. On the one hand, the method adopt in the dissertation is feasible by comparison the present results with the data of previous author; on the other hand, the method on hydrodynamic stability for two phase flow in the boundary layer is decided by finding out the relationship among the various theories.Because of the complexity of two phase flow, the physical mode of hydrodynamic stability is decomposed into hydrodynamic stability for inhomogeneous density stratified flow and hydrodynamic stability for homogeneous two phase flow. In chapter three, the equations describing the motion of stratified flow are given and the hydrodynamic stability equations satisfied by small disturbances of a steady laminar flow are derived. The effect of stratification is described by two parameters, i.e. Richardson number and Schmidt number. It is shown that the stability characteristics for stratified flow are still determined by solutions of the Orr-Sommerfeld equation, but the basic stability equation replaced by a modified equation with an additional diffusion equation. It is intended to illustrate some features of the action of stratification with a sample for flat plate boundary layer in this paper. The results show that over-all Richardson number is the critical factor to determine the stability of stratified flows; the stratification stabilizes laminar flow for Ri＞0, and vice versa. The effect of Schmidt number is small and relies on the Richardson number and the ratio between diffusion and viscosity. In general, the effect of Schmidt number of stratification stabilizes laminar flow for Ri＞0.The linear stability of incompressible particle-laden Blasius boundary layer is studied in chapter four. The modified Orr-Sommerfeld equation is obtained, and then the equation is solved numerically. The stability characteristics are calculated for varying Stokes numbers and particle concentrations. The results, some of which agree with the calculations of earlier authors, show that the addition of fine particles tends to destabilize the flow while addition the coarse particles has a stabilizing action, there is critical value for the effect of Stokes number, and the value is about unit. The stabilizing effect of particles depends monotonously on the particle Concentration, the critical Reynolds number is direct proportion to the concentration in the range of stabilizing area, and vice versa for small Stokes number. The most damped mode occurs when Stokes number is of order 10 for different particle concentrations. The difference in the eigenfunctions and its derivative between the particle-laden flow and the clean gas flow is insignificant for fine particles, while the difference for coarse particles is obvious. For fine particles laden flow, the difference of perturbation velocity between particles and clean gas is negligible, the viscosity is reduced relatively because of the addition of particles, and the critical Reynolds number is smaller than that of clean gas; for coarse particles, the interaction between particles and clean gas is remarkable because of the difference of perturbation velocity, and then the viscous dissipation tends to stabilize the flow.The pressure gradient has observably effect on the hydrodynamic stability. A favorable pressure gradient stabilizes the flow and an adverse pressure gradient renders it less stable. But the effect of Stokes number is not changed by the pressure gradient.The parabolized stability equation (PSE) was derived to study the linear stability of particle-laden flow in growing Blasius boundary layer. The inclusion of the nonparallel terms produces a reduction in the values of the critical Reynolds number compared with the parallel flow. But the presence of the nonparallel terms does not affect the role of the particles in two phase flow. Qualitatively the effect of nonparallel mean flow is the same as for the case of parallel flows.Nonlinearity is an essential feature of transition. The final goal of nonlinear stability theory is the prediction of transition to turbulence, yet progress is scarce. The most convenient way to tackle with this problem consists of the application of expansions in terms of small amplitudes. The objective of chapter five is the study of the weakly nonlinear stability of two phase flow for Blasius boundary layer. The hydrodynamic stability equations are described and the nonlinear mathematical model and related computational results are presented. The first of the results calculated with numerical method shows that the averaged Reynolds stress is the fundamental consequence of the nonlinearity, and has an appreciable effect on the mean flow. The distortion of the mean flow modifies the rate of transfer of energy from the mean flow to disturbance. The existence of particle alleviates the distortedness. The second is that the minimum critical Reynolds number is close to but less than the value calculated from the linear stability equation. The result indicates that the weakly nonlinear stability equation is consistent to linear stability equation. The third is that nonlinear interaction between basic flow and perturbation velocity reduces the growth rates; while the nonlinear interaction between particle phase and gas phase increase the growth rates. The growth rates, the amplitude factor and the perturbation energy has the similar meaning and distribution, it is consistent for the three methods to evaluate the hydrodynamic stability.Chapter six is the summery of the dissertation and outlook on hydrodynamic stability for the future.