Numerical study of unsteady fluid flow through a tightly coiled rectangular duct of large aspect ratio

Abstract

In this paper, a viscous incompressible fluid flow through a tightly coiled rectangular duct of large aspect ratio has been studied numerically by using a spectral method and covering a wide range of the pressure gradient parameter, the Dean number, Dn (0 < Dn ≤ 1000) for both isothermal and non-isothermal flow. For non-isothermal flow, a temperature difference is applied across the vertical sidewalls for the Grashof number Gr =1000, where the outer wall is heated and the inner wall cooled. The main concern of this paper is to investigate effects of aspect ratio on time-dependent solutions such as steady-state, periodic, multi-periodic or chaotic. To investigate non-linear behavior of the unsteady solutions, time evolution calculations are performed and flow transition between two types of solutions is determined by drawing the phase space of the time-dependent solutions. The study shows that if Dn is small, the flow is steady-state whether the flow is isothermal or non-isothermal. However, as Dn increases, the flow undergoes in the scenario ‘steady-state ⃗ periodic ⃗chaotic’. Secondary flow patterns, axial flow distribution and temperature profiles on the unsteady flow characteristics are also obtained and it is found that the time-dependent flow consists of asymmetric two- to eight-vortex solutions. Distribution of the time dependent solutions is shown in the Dean number vs. vortex-structure plane for both isothermal and non-isothermal flows. Finally, our numerical results are validated with the experimental investigations obtained so far.