Hydrodynamic stability study in a curved square duct by using the energy gradient method

Abstract

Curved non-circular ducts have remarkable applications in the macro and micro scales engineering. Stability of flow through the curved ducts is a challenging topic in the context of fluid mechanics. In the current paper, hydrodynamic stability of fully developed 3D steady flow of incompressible fluid through the 180° curved square duct is investigated via energy gradient method. To this accomplishment, different Dean numbers (De) ranging from 19.60 to 1181.25 at curvature ratio 6.45 are considered. To investigate of flow stability, we analyzed the distributions of velocity, total pressure and control parameter of energy gradient function K. Obtained results indicated an appropriate agreement via both experimental and CFD data. Results of our investigation show that the maximum of energy gradient function Kmax is decreased by a reduction in the Dean number. In addition, we found that the origin of Dean hydrodynamic instability (i.e., position of the Kmax) is placed in the radial position between the center of the duct and outer curvature wall at azimuthally angular position θ < 72°. Results of Kmax and its cylindrical coordinates corresponding to the onset of Dean flow instability under various Dean numbers are reported.