Abstract
The effects of compressibility on vortex flows in pipes have been analyzed using both the axisymmetric Navier–Stokes (NS) equations and the quasi-cylindrical (QC) approximation. Numerical simulations of the full axisymmetric NS equations show that, for sufficiently large values of the Reynolds number, compressible flows present a multiplicity of steady-state solutions in a range of values of the swirl strength. The sensitivity of the vortex flow structure to the parameters of the problem: Mach number, Reynolds number, velocity profiles at the pipe entrance and pipe geometry has been also investigated. In particular, the critical swirl parameter necessary for the occurrence of vortex breakdown has been determined as a function of both the Mach number and the axial momentum of the flow at the pipe entrance. For large Reynolds number, the results of the QC approximation are found to be in good agreement with those of the full NS simulations. These results show that the upstream propagation of the sound waves seems to have a negligible influence on vortex breakdown and give support to the use of the QC approximation for the study of some aspects of the compressible swirling flows.
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