Multiplicity and stability of mixed convection in rotating curved ducts

Abstract

A numerical study is made on the fully-developed bifurcation structure and stability of the mixed convection in rotating curved ducts of square cross-section with the emphasis on the effect of buoyancy force. The rotation can be positive or negative. The fluid can be heated or cooled. The study reveals the rich solution and flow structures and complicated stability features. One symmetric and two symmetric/asymmetric solution branches are found with seventy-five limit points and fourteen bifurcation points. The flows on these branches can be symmetric, asymmetric, 2-cell and up to 14-cell structures. Dynamic responses of the multiple solutions to finite random disturbances are examined by the direct transient computation. It is found that possible physically realizable fully-developed flows evolve, as the variation of buoyancy force, from a stable steady multi-cell state at a large buoyancy force of cooling to the co-existence of three stable steady multi-cell states, a temporal periodic oscillation state, the co-existence of periodic oscillation and chaotic oscillation, a chaotic temporal oscillation, a subharmonic-bifurcation-driven asymmetric oscillating state, and a stable steady 2-cell state at large buoyancy force of heating.