Stability study of flow in a 90° bend based on the energy gradient theory

The energy gradient theory is used to analyze numerical simulation of the flow in a 90 degree bend with square cross-section. The Reynolds number based on the cross-sectional width and the averaged velocity is 158, 394 and 790, respectively. It is found that at Re = 790, the value of the energy gradient function K increases with the fluid entering the curved section, causing flow instability and forming a pair of secondary vortices; then the secondary vortices gradually stabilizes and the value of K decreases. At the exit of the bend, the total pressure distribution in the cross-section presents serious distortion, which leads to a transition of two vortices to four vortices. With the flow ahead, the maximum of K rises again, resulting in the transition of four vortices to eight vortices. At the low Reynolds number (Re = 158 and Re = 394), there is only one pair of vortices due to the low value of K, which are stable. This study shows that the occurrence of instability is closely related to the evolution of energy gradient function K.