Stability of an axisymmetric swirled flow in a supersonic cocurrent stream for volume energy supply in the viscous vortex core
The results of numerical calculations of the stability of axisymmetric swirled flows in a viscous vortex embedded in a supersonic cocurrent stream with a constant circulation of the azimuthal velocity component are presented. The stability characteristics of the swirled three-dimensional viscous flow in the streamwise vortex are determined on the basis of the linearized system of Navier-Stokes equations for a viscous heat-conducting gas under the assumption that the basic undisturbed flow is locally plane-parallel. The disturbed flow stability is studied in the temporal formulation with respect to both symmetric and asymmetric three-dimensional waves traveling along the vortex axis and corresponding to both positive and negative values of the azimuthal wavenumber. It is shown that at external inviscid flow Mach numbers M∞ = 2 and 3 thermal energy supply in a small region near the vortex axis leads to considerable restructuring of the basic undisturbed flow in the vicinity of the vortex core, the growth of the adverse pressure gradient along the vortex axis, and a significant change in the small perturbation stability and behavior.
Keywordsswirled flows linear stability theory
Unable to display preview. Download preview PDF.
- 6.V. K. Akhmetov and V. Ya. Shkadov, “Development and stability of swirling flows,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 3 (1988).Google Scholar
- 7.V. K. Akhmetov and V. Ya. Shkadov, “New inviscid mode of free vortex instability,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 76 (1999).Google Scholar
- 8.C. Liu and S. Menne, “Simulation of a three-dimensional vortex breakdown,” AIAA Paper, No. 1806 (1989).Google Scholar
- 9.A. V. Kazakov, “Stability of the viscous subsonic vortex flow with volume energy supply,” in: Abstracts Intern. Cong. Theor. Appl. Mechanics. Kyoto, Japan, 1996 (1996), p. 194.Google Scholar
- 10.A. V. Kazakov, “Effect of volume energy supply on swirled flows in a subsonic cocurrent stream,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 47 (1998).Google Scholar
- 11.A. V. Kazakov, “Stability of a subsonic swirled flow of a viscous heat-conducting gas,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 50 (1998).Google Scholar
- 12.A. V. Kazakov and A. P. Kuryachii, “Stability of a compressible swirling flow in a circular pipe,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 1, 35 (1999).Google Scholar
- 13.A. V. Kazakov, “Effect of volume energy supply on the stability of a subsonic vortex flow,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 4, 56 (2003).Google Scholar