On the failure of the quasicylindrical approximation and the connection to vortex breakdown in turbulent swirling flow
Artikel i vetenskaplig tidskrift, 2007

This paper analyses the properties of viscous swirling flow in a pipe. The analysis is based on the time-averaged quasi-cylindrical Navier-Stokes equations and is applicable to steady, unsteady and turbulent swirling flow. A method is developed to determine the critical level of swirl (vortex breakdown) for an arbitrary vortex. The method can also be used for an estimation of the radial velocity profile if the other components are given or measured along a single radial line. The quasi-cylindrical equations are rearranged to yield a single ordinary differential equation for the radial distribution of the radial velocity component. The equation is singular for certain levels of swirl. It is shown that the lowest swirl level at which the equation is singular corresponds exactly to the sufficient condition for axisymmetric vortex breakdown as derived by Wang and Rusak [J. Fluid Mech. {340}, 177-223 (1997)] and Rusak et al. [AIAA J. {36}, 1848-1853 (1998)]. In narrow regions around the critical levels of swirl, the solution violates the quasi-cylindrical assumptions and the flow must undergo a drastic change of structure. The critical swirl level is determined by the sign change of the smallest eigenvalue of the discrete linear operator which relates the radial velocities to effects of viscosity and turbulence. It is shown that neither viscosity nor turbulence directly alters the critical level of swirl.

turbulence

swirling

vortex

breakdown

Författare

Walter Gyllenram

Chalmers, Tillämpad mekanik, Strömningslära

Håkan Nilsson

Chalmers, Tillämpad mekanik, Strömningslära

Lars Davidson

Chalmers, Tillämpad mekanik, Strömningslära

Physics of Fluids

1070-6631 (ISSN) 1089-7666 (eISSN)

Vol. 19

Ämneskategorier

Maskinteknik

Strömningsmekanik och akustik

DOI

10.1063/1.2717724