Direct numerical simulation of by-pass transition of the supersonic flat plate turbulent boundary layer

Using the characteristic boundary conditions and high-order finite difference schemes, direct numerical simulation(DNS) was performed to investigate the effect of phase and frequency of the periodic blow and suction disturbance which was used to trigger the by-pass transition of the flat plate boundary layer with free stream Ma_∞=2.25, Re_∞=2.5×10⁷/m (635 000/inch). The numerical results show that the randomness of the disturbance phase is not the necessary condition to trigger the transition, and with the deterministic disturbance phase, the average location of transition moves backward when the disturbance frequency increases. However, if the frequency is bigger than a critical value, the transition in the boundary layer will not happen. A DNS database was established under the condition of deterministic disturbance phase. The Van Direst velocity agrees well with the wall and logarithm law of incompressible flat plate boundary layer, and the turbulence intensities coincide with the incompressible flat plate experimental datum.The averaged thermodynamic variables are very close to that of reference results. These verify the present DNS results. Then, the statistics of thermodynamic variables fluctuation and Reynolds stress are extracted from the DNS database. Compared with the relative references' DNS results, the disturbance, boundary conditions and numerical methods have observably effect on the second order statistics and the averaged transition position.