Numerical investigation of a double-periodic compressible multi-vortex-field

Abstract

A three-dimensional time-dependent Chebyshev-Collocation-scheme was developed and tested. It was applied to a compressible double- or triple-periodic Vortex-field.

In the first triple-periodic case without boundary-layers the flowfield shows a kind of Taylor-Görtler-instability. The stable regime of the Reynolds-Mach-number-plane was determined. For higher Reynolds- or Mach-numbers secondary vortices along the edges are stochastically genererated. Further increasing of the two parameters results in destabilized Ekman-layers and a turbulent flow-field.

In the second problem with solid walls at top and bottom of the vortex-cells the boundary-layer above predominates the flowfield. An unsteady three-dimensional separation-bubble evolves in front of the stagnation lines. For higher Reynolds- or vice versa small Ekman-numbers the recirculation zone becomes turbulent and influences the complete vortex-cell.

The proposed two-dimensional array of vortices has no technical use for gas-gas-separation due to the prescribed instabilities. The stable Reynolds- and Mach-Numbers are orders of magnitude smaller than the corresponding values for real centrifuges.