Numerical investigation of transitional axisymmetric wakes at supersonic speeds

The spatial evolution of instability waves in the wake of an axisymmetric body with a blunt base is investigated using direct numerical simulations. The body is aligned with the supersonic free stream, In this paper transitional wake flows are considered. For the simulations a numerical method for solving the complete compressible Navier-Stokes equations in a cylindrical coordinate system was developed. In the numerical method a fourth order Runge-Kutta scheme is employed for the time integration. In axial and radial direction fourth-order accurate central-difference approximations are applied that are split into backward and forward differences at different intermediate time stops. The splitting introduces artificial viscosity, which damps mesh frequency oscillations. A pseudo-spectral method is employed in the circumferential direction. Disturbances are generated, either through a circular blowing and suction slot which is located close to the blunt base of the axisymmetric body or are introduced locally in the flow field. In this paper results of comparison calculations with incompress-ible wakes are discussed, and preliminary results for supcrsonic wrakes are presented. For the supersonic case with Mach number M_∞=2.46 the flow was stable with respect to axisymmetric disturbances for the frequencies that have been tested. Even for three-dimensional (helical) disturbances we found no disturbance amplification for disturbances that were introduced directly into the recirculation region.