Numerical investigation of transitional supersonic axisymmetric wakes

Abstract

Transitional 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. 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 axisymmetric 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. 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 co-exist 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 k=0 for ReD>100,000. It is concluded that azimuthal modes k=2 and k=4 are the dominant modes in the trailing wake, producing a four-lobe wake pattern. Two possible mechanisms responsible for the generation of longitudinal structures within the recirculation region are suggested.

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ORCID for Richard D. Sandberg: orcid.org/0000-0001-5199-3944

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