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On the failure of the quasicylindrical approximation and the connection to vortex breakdown in turbulent swirling flow

Walter Gyllenram (Institutionen för tillämpad mekanik, Strömningslära) ; Håkan Nilsson (Institutionen för tillämpad mekanik, Strömningslära) ; Lars Davidson (Institutionen för tillämpad mekanik, Strömningslära)
Physics of Fluids (1070-6631). Vol. 19 (2007), 4,
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: swirling, turbulence, vortex, breakdown



Denna post skapades 2007-05-14. Senast ändrad 2014-09-29.
CPL Pubid: 41564

 

Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Strömningslära

Ämnesområden

Teknisk mekanik
Strömningsmekanik

Chalmers infrastruktur