Watanabe D., Takami H., Maekawa H., Suzuki H., Iida M.

Spatial direct numerical simulations are used to study the formation and development of three-dimensional structures and the resultant sound emission mechanism in a compressible boundary layer, for a high-speed train model, where the free stream Mach number is 0.5 and the Reynolds number at the inlet based on the displacement thickness 1000. In the present work, to overcome the difficulties of the spectral method or pade-type compact schemes for compressible free-shear flows at high Reynolds numbers, the spectral-like finite difference high-order upwind-biased compact schemes (Deng, Maekawa & Shen 1995) are employed. A 4th order Runge-Kutta scheme is used for time advancement. Boundary conditions based on characteristic analysis for the Navier-Stokes equations (Poinsot & Lele 1992) are used so that acoustic waves are not reflected back into the domain. A pair of stable oblique modes and a two-dimensional unstable T-S wave are superimposed on the laminar profile at the inlet plane of the boundary layer computational box. Rapid growth of oblique modes due to second instability of the laminar boundary layer with the amplified T-S waves produces peak-valley splitting structures downstream and later hairpin vortices (hairpin packet) on a low speed streak are observed. Simulation results show that the further complex development of the hairpin vortices lead to vortex interactions of the deformed hairpin vortices, which is responsible to sound generation in the transitional compressible boundary layer. The development of the peak-valley splitting structures is similar to the incompressible boundary layer measurements by Kachanov et al. (1977). Further comparisons of sound pressure levels between the numerical results and experimental data obtained by a moving model facility for high-speed 500km/h train will be made.