Temporal and Spatial Analysis on the Fractal Characteristics of the Helical Vortex Rope

Abstract

Vortex rope is a common phenomenon in the draft tube of hydraulic turbines. It may cause strong pressure pulsation, noise, and strong vibration of the unit especially when it is helical. Therefore, the study of vortex rope is of great significance. In order to study the helical vortex rope, the embedded large eddy simulation (ELES) method in the hybrid methods is used based on the vortex rope generator case. The Liutex method can show the three-dimensional shape of the vortex rope well. In order to quantitatively describe the helical vortex rope, the three-dimensional structure is divided into multiple two-dimensional sections, and then the shape of vortex rope on each section is processed to extract the perimeter and area of the vortex. Combined with the change trend of vortex number and section area, the helical vortex rope is divided into four zones. Then, the fractal dimension on each zone and section can be obtained, and it can be used to quantitatively analyze the change trend of the vortex rope in time and space. The fractal analysis method can be applied to the analysis of the vortex rope in the draft tube to help judge the flow pattern shape and the stability of the unit operating conditions.