STEADY AND UNSTEADY SOLUTIONS OF THE THERMAL FLOWS THROUGH A CURVED DUCT
DOI:
https://doi.org/10.53808/KUS.2007.8.1.0703-PSKeywords:
Curved duct, thermal flows, steady solutions, dean number, Grashof numberAbstract
Steady and unsteady solutions of the thermal flows through a curved duct with various aspect ratios are numerically studied by using the spectral method over a wide range of the Dean number, Dn. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr = 100, 500 and 1000, where the outer wall is heated and the inner wall is cooled. Firstly, steady solutions are obtained by the Newton-Raphson iteration method. As a result, we obtain multiple branches of steady solutions with multi-vortex solutions on various branches. Then, we perform time evolution calculations with a view to study the non-linear behavior of the unsteady solutions. It is found that time periodic solutions appear when Dn or Gr is increased. If they are increased further, the chaotic solution is obtained. For large aspect ratios, however, chaotic solutions occur for small Dn or for small Gr.
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