Use of Stokes’ Stream Function for Interactive Visualization System of Taylor Vortex Flow

The aspect ratio, which is the ratio of the cylinder length to the space between the cylinders, and the Reynolds number, which is inferred from the inner cylinder's velocity, are the two key variables in this study. Taylor's vortices make up torses regularly superimposed into the gap between the shaft and the bearing. The appearance of vortices is linked with the inertia forces generated by the shaft rotation. The behavior of the Taylor vortex flow—a mixture of laminar and turbulent flow patterns—between two concentrically rotating cylinders with a limited axial length has piqued a lot of curiosity. When mode bifurcation occurs, quantitative parameters such as the volume-averaged energy change rapidly. It is important to visualize the behaviors of vortices. In this work, a three-dimensional time visualization system is developed. This approach allows us to adjust the flow visualization's point of view, allowing us to see the path of a vortex from any location. The track of a vortex's center receives the volume-averaged energy projection. This technique allowed for precise measurement of changes in the values of physical quantities. The Reynolds number was altered during the computation to examine the behavior of the volume-averaged energy. The proposed system can help to investigate the relationship between the mode bifurcation process and the volume-averaged energy.