Direct Numerical Simulations of a Plane Compressible Wake: Stability, Vorticity Dynamics, and Topology
Recent interest in supersonic combustion and problems of transatmospheric flight has prompted renewed research efforts in laminar-turbulent free shear flow transition. In the present work, linear stability theory and direct numerical simulations are used to study the effect of Mach number on the linear, nonlinear, and three-dimensional aspects of transition in a plane compressible wake. Direct numerical simulations are also used to study the sensitivity of a compressible wake to (1) phase effects and (2) two- and three-dimensional subharmonics. A linear stability analysis shows that the influence of increasing Mach number is stabilizing, resulting in reduced growth rates for both antisymmetric and symmetric modes of the wake. This reduction is due to baroclinic and dilatational effects as revealed from the linear eigenfunctions. For both low and high Mach numbers, the least stable wave is a two-dimensional antisymmetric mode aligned with the streamwise direction. Direct numerical simulations of a temporally-evolving wake were performed using a spectral collocation method. The results of two-dimensional simulations show that, for high Mach numbers, the same mechanisms responsible for the reduced growth rates from linear stability theory are also responsible for the delay in the roll-up of vortices. Two-dimensional simulations were also performed to study the effect of phase angle on the development of a subharmonic in a low Mach number wake. Three-dimensional simulations were performed to study the effect of phase angle between a fundamental and a pair of oblique waves on the development of the large -scale structures in a wake. Depending upon the phase angle, vortex loops may or may not form due to the interaction of the streamwise and spanwise vortices. Staggered "peak -valley-splitting" vortices, which have been observed in boundary-layers and incompressible wakes, develop if the simulations are forced with a pair of oblique subharmonic waves. Finally, the topology of the computed velocity, vorticity, and pressure gradient fields is determined using a generalized three-dimensional critical point theory.
- Pub Date:
- January 1990
- COMPRESSIBLE WAKE;