Numerical investigation of transitional and turbulent compressible axisymmetric wakes

Abstract

A numerical method has been developed for solving the complete compressible Navier-Stokes equations. The method is applicable for Direct Numerical Simulations (DNS) and Large-Eddy Simulations (LES) and was used here to study the evolution of three-dimensional disturbances in the laminar and turbulent near wake of axisymmetric bluff bodies with a blunt base in supersonic flows. The main objective of this research is to investigate the time dependent behavior of these disturbances and their influence on and interaction with the global flow field. The equations are solved in a cylindrical coordinate system using finite difference approximations of fourth-order accuracy in axial and radial directions and and a fourth-order accurate explicit Runge-Kutta scheme for the time integration. A pseudo-spectral method is employed in the azimuthal direction. Direct Numerical Simulations (DNS) were performed for a subsonic free stream Mach number of M ͚ = 0.2 and for supersonic free stream Mach numbers of M ͚ = 1.2 and M ͚ = 2.46. Large-Eddy Simulations (LES) were carried out for a subsonic free stream Mach number of M ͚ = 0.2 and a global Reynolds number of ReD = 2,000 and for a supersonic free stream Mach number of M ͚ = 2.46 and global Reynolds numbers of ReD = 30,000 and ReD = 100,000. Comparison of the instantaneous flow field for subsonic calculations with water channel experiments and incompressible simulations show good qualitative agreement. An absolute instability with regard to helical disturbances was found for the subsonic flow at ReD = 1,000 and for the supersonic flows for M ͚ = 1.2 and ReD ≥ 4,000 and for M ͚ = 2.46 and ReD ≥ 30,000. Small disturbances appear in the flow field near the corner of the base. As the disturbances are propagating downstream they grow and form intense vortical structures. These structures have a strong influence on the flow field, which results in a drastic change of the base pressure distribution and thus of the base drag.