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 as a virtual boundary, the 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 numerical simulation results demonstrates strong consistency, particularly in capturing the key features of the three-cell vortex structure. These results confirm the GEE model's effectiveness in providing rapid and reliable predictions for bounded vortex flows in industrial applications.