Numerical simulation for rotating internal weakly viscoelastic flows in rectangular ducts

Abstract

SUMMARYThe present work develops a numerical method for the solution of rotating internal weakly viscoelastic ows in rectangular ducts for dimensionless parameters such as the Reynolds, Rossby and Weissenberg numbers, taken respectively in the intervals between 171 and 12 000, 0.047 and 1=12 and up to 1=10 000. It is shown that the usual counter-rotating double-vortex conÿguration of secondary ow breaks down with the increase of the Reynolds number (over the threshold of 171). For higher Reynolds numbers such as 7500 and 12 000 the secondary ow di uses to the interior of the duct where it assumes a fully developed conÿguration and the transition to the turbulence structure is observed. The Sobolev norms increase almost proportionally to the increase of the Reynolds number, and play an essential role for more complex problems involving transition to turbulence modelling.