On Hydrodynamic Stability of Dean Flow by Using Energy Gradient Methods

Abstract

ABSTRACTIn the present paper, we investigate the hydrodynamic instability of Dean flow under different Dean numbers ranging from 1 to 2500, curvature ratios from 0.0001 up to 1000 and temperatures ranging from 273.15 K to 373.15 K. To study of fluid flow instability, analytical velocity profiles under intended conditions and energy gradient function K in the energy gradient method are evaluated. The results of present study show that, as the curvature ratio increases the flow becomes more stable. Moreover, no regular and significant effects on the energy gradient function K were achieved by increasing of temperatures. We found that, the origin of instability in the entire flow field is located on the inner wall of the parallel curved walls, especially for larger curvature ratios. We also reported the critical value of the energy gradient function K for the onset of instability corresponding to the critical Dean number.