Pressure-driven Flow Instability with Convective Heat Transfer Through a Curved Rectangular Duct of Small Aspect Ratio

Abstract

The present study investigates unsteady fluid flow through a curved rectangular duct of aspect ratio 0.5 and curvature 0.5. Numerical calculations are carried out by using a spectral method, and covering a wide range of the pressure gradient parameter, the Dean number, 6000 ≤ Dn ≤ 12000 and the Grashof number, 100 ≤ Gr ≤ 2000 for two cases of the duct, Case-I: Stationary duct and Case-II: Rotating duct. The outer wall of the duct is heated while the inner wall cooled. The main concern of the present study is to discuss the unsteady flow behavior i.e whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn or Gr is increased. For a stationary duct, we investigate the unsteady flow characteristics for the Dean number 6000 ≤ Dn ≤ 12000 and the Grashof number 100 ≤ Gr ≤ 2000, and it is found that the unsteady flow undergoes in the scenario steady-state → periodic → multi-periodic → chaotic, if Gr is increased. For rotating duct, however, we investigate the unsteady flow characteristics for the Taylor number −100 Tr ≤ 1000, and it is found that the unsteady flow undergoes through various flow instabilities, if Dn or Gr is increased. Typical contours of secondary flow patterns and temperature profiles are also obtained, and it is found that the unsteady flow consists of a single-, two-, and multi-vortex solutions.