Three-dimensional velocity field modeling of bounded vortex flows based on a three-cell structure

Bounded vortices are common in engineering systems and typically exhibit complex three-dimensional turbulent flow structures. However, existing modeling approaches predominantly rely on simplified two-dimensional vortex models, which limit accurate prediction and theoretical understanding of such flows. Cyclone separators-a representative example of bounded vortex applications-lack robust analytical models capable of describing their three-dimensional velocity fields. In contrast, unbounded vortex models inspired by natural tornadoes have achieved theoretical maturity but fail to capture the boundary-induced forced downdrafts present in confined systems. Motivated by this gap, this study investigates the dynamic features of classical one-cell and two-cell tornado vortices and compares them with numerical flow fields in bounded configurations. A characteristic "three-cell vortex" pattern, composed of an outer downdraft, central updraft, and near-axis downdraft, is identified as a fundamental flow structure in bounded vortex systems. Using the Locus of Zero Vertical Velocity (LZVV) as a virtual boundary, overall flow field is divided into inner and outer regions. By applying physically reasonable assumptions in each region, the Navier-Stokes equations are simplified to obtain analytical expressions for tangential and axial velocities. A three-dimensional bounded vortex model-termed Guided External-Enhanced (GEE) model-is then formulated based on this framework. The GEE model is applied to reconstruct the flow fields under various geometric and operational conditions. Comparison with high-fidelity simulation results demonstrates strong consistency, particularly in capturing the key features of the three-cell vortex structure. These results confirm GEE model's effectiveness in providing rapid and reliable predictions for bounded vortex flows in industrial applications.