Effects of Curvature on Unsteady Solutions through a Curved Square Duct Flow

Abstract

The present study addresses numerical prediction of fully developed two-dimensional laminar flow of viscous incompressible fluid through a curved square duct with curvature ranging from 0.001 to 0.5. Numerical calculations are carried out over a wide range of the Dean number 0< Dn ≤6000 with a temperature difference between the vertical sidewalls for the Grashof number Gr = 1000, where the outer wall is heated and the inner wall cooled. Spectral method is used as a basic tool to solve the system of non-linear differential equations. First, we investigated steady solutions by using Newton-Raphson iterations method. As a result, a complex structure of steady solutions with two- and multi-vortex solutions is obtained. Then, in order to investigate the non-linear behavior of the unsteady solutions, time evaluations calculations are performed and the transition between two types of solutions is determined by drawing the phase spaces of the time evolution solutions. It is found that the unsteady flow undergoes in the scenario ‘ steady-state → periodic → multi - periodic → chaotic , if the Dean number is increased no matter what the curvature is. Secondary flow patterns, axial flow distribution and temperature profiles on the flow characteristics are also obtained.