Centrifugal-Coriolis instability through a rotating curved square duct with bottom wall heating and cooling from the ceiling

Investigation of unsteady flow characteristics through a curved duct is widely used in many engineering applications such as in fluid transportation, rotating machinery and metallic industry. Fluid behavior depends not only on the rotation of the duct but also on physical properties such as fluid pressure, curvature and aspect ratio of the duct. The present paper focuses on the time-dependent flow behavior through a rotating curved square duct. The bottom wall of the duct is heated while cooling from the ceiling, the inner and outer sidewalls being thermally insulated. Numerical calculations are carried out by using a spectral technique, where function expansion and collocation methods are applied for constant Dean number, Dn = 1000, the Grashof number, Gr = 100 and curvature, δ = 0.01 over a wide range of the Taylor number, −1500≤Tr≤1500. In this paper, we investigated flow characteristics for both positive and negative rotation of the duct. Due to combined action of the centrifugal, Coriolis and buoyancy forces various types of physically realizable transient solutions such as steady-state, periodic, multi-periodic and chaotic solutions have been obtained. Flow transitions are well determined by obtaining the power spectrum of the solutions. Typical contours of axial flow, secondary flow and temperature profiles have also been obtained and it is found that time-dependent solutions are comprised of two-to six-vortex solutions. The present study shows that convective heat transfer is significantly enhanced by the secondary flow and there is a strong interaction between the heating-induced buoyancy force and the centrifugal-Coriolis instability in the rotating curved duct that stimulates fluid mixing and consequently enhances heat transfer in the fluid. Finally, our numerical results have been compared with the experimental investigations and it is found that there is a good agreement between the numerical and experimental investigations.