Numerical investigation of transitional and turbulent supersonic axisymmetric wakes

Abstract

Transitional and turbulent supersonic axisymmetric wakes are investigated by conducting various numerical experiments. The main objective is to identify hydrodynamic instability mechanisms in the flow at M = 2.46 for several Reynolds numbers, and relating these to coherent structures that are found from various visualization techniques. The premise for this approach is the assumption that flow instabilities lead to the formation of coherent structures. The effect of these structures on the mean flow is of particular interest, as they strongly affect the base drag. Three high-order accurate compressible codes were developed in cylindrical coordinates for this research: A spatial Navier-Stokes (N-S) code to conduct Direct Numerical Simulations (DNS), a linearized N-S code for linear stability investigations using two-dimensional basic states, and a temporal N-S code for performing local stability analyses. The ability of numerical simulations to deliberately exclude physical effects is exploited. This includes intentionally eliminating certain azimuthal/helical modes by employing DNS for various circumferential domain-sizes. With this approach, the impact of structures associated with certain modes on the global wake-behavior can be scrutinized. It is concluded that azimuthal modes with low wavenumbers are responsible for a flat mean base-pressure distribution and that k = 2 and k = 4 are the dominant modes in the trailing wake, producing a four-lobe wake pattern. Complementary spatial and temporal calculations are carried out to investigate whether instabilities are of local or global nature. Circumstantial evidence is presented that absolutely unstable global modes within the recirculation region coexist with convectively unstable shear-layer modes. The flow is found to be absolutely unstable with respect to modes k > 0 for ReD > 5,000 and with respect to the axisymmetric mode for ReD > 100,000. Furthermore, it is investigated whether flow control measures designed to weaken the naturally most significant modes can decrease the base drag. Finally, the novel Flow Simulation Methodology (FSM), using state-of-the-art turbulence closures, is shown to reproduce DNS results at a fraction of the computational cost.