A Numerical Study on Non-Isothermal Flow Through a Rotating Curved Duct with Square Cross Section

Abstract

Non-isothermal flow through a rotating curved duct with square cross section is studied numerically by using the spectral method, and covering a wide range of the Taylor number, Tr, 0 ≤ Tr ≤ 2000 and Dean number, Dn, 0 ≤ Dn ≤ 2000. A temperature difference is applied across the vertical sidewalls for Grashof number Gr=500, where the outer wall is heated and the inner one cooled. The rotation (Coriolis force) of the duct about the center of curvature is imposed. The Steady solutions are obtained by using Newton-Raphson iteration method and the Dean numbers are also discussed in detail. Then, in order to investigate the non-linear behavior of the steady and unsteady solutions, there is no stable steady solution, time evolution calculations as well as power spectrum of the periodic oscillations are obtained, and it is also found that for larger Dn, the unsteady flow undergoes in the scenario ＂steady→periodic→chaotic→steady＂, if Tr is increased. Finally spectral analysis and phase space are found to be very useful investigation of the Non-isothermal fluid flow behavior.