Investigation On Transition Of Laminar-turbulent In A Boundary Layer On A Flat Plate Based On The Spatial Model

In this paper, direct numerical simulation (DNS) was adopted for the laminar-turbulent transition of an incompressible boundary layer on a flat plate based on the spatial model with MPI technology. Studies on breakdown mechanism of laminar-turbulent transition was carried on sequentially. The priority was given to the effects of the modification of the mean flow profile on the process of breakdown in laminar-turbulent transition.The Reynolds number was taken as 732. The laminar Blasius similarity solution was taken as the basic flow. One two-dimensional T-S wave and two symmetrical three-dimensional T-S waves were taken as the disturbers at the entrance. Under Cartesian coordinate, the non-dimensional perturbation equations were taken as the governing equations. A third-order precision mixed explicit-implicit scheme was employed for time discretization and a combination method of high precision compact finite difference with the Fourier pseudo-spectral expansion was implemented for spatial discretization. The method of non-uniform meshes was applied in normal direction and the fringe method was applied in dealing with outlet boundary condition. By a simple case, the parallel programs were not only validated to be consistent with the linear theory, but also the results got by one computer.According to the magnitude of amplification, we simulated three cases of subharmonic transition. Then we anaylized the results from the following aspects: skin friction coefficient,mean fluctuation kinetic energy,disturbance velocity evolution in Fourier space,velocity vector at y-z plane,evolution of mean velocity profile,stability analysis,thicknesses of boundary and shape factor. From the analysis, we drew the following conclusions:1. Disturbance with different initial amplitude led to different transition positions at backward position. If the amplitudes of three-dimensional disturbers were smaller, obvious three-dimensional disturbances only began to exist at a length of one or two two-dimensional wavelengths in front of the breakdown, and the magnitudes of waves in z-direction approximate to the length of three-dimensional waves which were added at the entrance. Some higher frequency harmonic waves came into exist rapidly after the process of transition, the magnitudes of waves in z-direction became smaller, meanwhile, the modification of mean flow increased rapidly.2. In the prophase of breakdown, The skin friction coefficient non-dimensionized by local laminar boundary layer displacement thickness was equal at every point along x-direction. In the anaphase of breakdown, skin friction coefficient increased to the same value for the cases considered, the length of breakdown process was about 120 laminar boundary layer displacement thickness of the entrance.3. The evolution of mean fluctuation kinetic energy along x-direction was analogous with the one of skin friction coefficient, but it started to increase before the skin friction coefficient did. The total fluctuation kinetic energy could reach about 0.05, of which 0.03 was contributed by u, and the other 0.02 was contributed by v and w equally. In addition, the smaller the initial disturbers were, the longer distance from the entrance transition started and the bigger the mean fluctuation kinetic energy was along every direction, but the lengths of the regions that the mean fluctuation kinetic energy increased rapidly were almost the same.4. Different initial disturbers all caused transition, the amplitudes of two-dimensional waves were not the same until the breakdown, but the positions where mean flow was modified rapidly were the same, the processes that the modification of mean flow increased rapidly were almost the same. The position that modification of mean flow increased rapidly agreed with the one that two-dimensional wave began to be ruleless. At that position, the regular three-dimensional waves reached their maximum values of about 0.05, then the three-dimensional waves began to be ruleless. During this process, the three-dimensional waves increased rapidly, it may because the second stability of stability began to work. Before the transition, the amplitude evolution of two-dimensional disturber agreed with the linear stability theory, and the wavelength approximated to the one of the two-dimensional wave added at the entrance, to some extent, this might offer theory basis for EN method in transition forecasting.5. We analysised mean flow velocity stability for different positions along x direction,it indicated that the instability zone became smaller and smaller along x direction at first, when being very small, it began to increase to the maximum range, then smaller it became again, and to be very small. The position where instability zone began to increase corresponded to the one that skin friction coefficient began to increase rapidly, the position where instability zone reached it's maximum located at the 1/3 station of skin friction coefficient increased rapidly. The instability zone decreased again, the position that it was to be zero corresponded to the one where skin friction coefficient reached the maximum. When the disturber's amplitude increased in laminar flow, the nonlinear effect would modify the mean flow profile. When the mean flow profile was modified to certain extent, the instability zone would enlarge to be of great magnitude, more harmonic waves came into exist and they increased rapidly, then breakdown started. In the process of breakdown, because of the rapid increase of many harmonic waves, disturber's energy increased rapidly. In return, the rapidly increased energy accelerated the mean flow profile modification rapidly. All of these mutually rapid increases made the flow turn into turbulent rapidly. The results of this thesis were consistent with other investigations.6. In the process of transiton, the increase of displace thickness was slower than the one of the corresponding laminar displace thickness.