INSTABILITIES IN FLOWS THROUGH CURVED DUCTS

Abstract It is well known that flows in curved ducts give rise to an instability that manifests itself as the formation of secondary flow patterns (cells in the transversal plane, perpendicular to the main flow direction). The mechanism for this behaviour was explained by Dean back in the 1930 th and it is basically due to an in-balance between centrifugal forces and the radial pressure gradient, tending to occur at moderate Reynolds number and therefore being a kind of inertia-generated instability. Later, in the 1970’s, a new pair of cells was observed by Cheng and Akiyama for Reynolds numbers beyond a certain critical value, thus highlighting the complexity of flows with curvature, even with Newtonian fluids. When the fluid is non-Newtonian and exhibits viscoelastic characteristics, the same kind of secondary flow patterns is generated at much lower Reynolds number and the instability becomes controlled by elastic effects instead of inertial ones. In this work we give preliminary results for the Newtonian flow instability at Reynolds number of order 600, in which case comparison against existing results by others gives an indication of the correctness of our simulations, and for the non-Newtonian viscoelastic flow instability that occurs at a certain level of elasticity, at different Reynolds number