Energy Transfer Characteristics of Surface Vortex Heat Flow Under Non-Isothermal Conditions Based on the Lattice Boltzmann Method

During liquid drainage from intermediate vessels in various industrial processes such as continuous steel casting, aircraft fuel supply, and chemical separation, free-surface vortices commonly occur. The formation and evolution of these vortices not only entrain surface slag and gas, but also lead to deterioration of downstream product quality and abnormal equipment operation. The vortex evolution process exhibits notable three-dimensional unsteadiness, multi-scale turbulence, and dynamic gas–liquid interfacial changes, accompanied by strong coupling effects between temperature gradients and flow field structures. Traditional macroscopic numerical models show clear limitations in accurately capturing these complex physical mechanisms. To address these challenges, this study developed a mesoscopic numerical model for gas-liquid two-phase vortex flow based on the lattice Boltzmann method. The model systematically reveals the dynamic behavior during vortex evolution and the multi-field coupling mechanism with the temperature field while providing an in-depth analysis of how initial perturbation velocity regulates vortex intensity and stability. The results indicate that vortex evolution begins near the bottom drain outlet, with the tangential velocity distribution conforming to the theoretical Rankine vortex model. The vortex core velocity during the critical penetration stage is significantly higher than that during the initial depression stage. An increase in the initial perturbation velocity not only enhances vortex intensity and induces low-frequency oscillations of the vortex core but also markedly promotes the global convective heat transfer process. With regard to the temperature field, an increase in fluid temperature reduces the viscosity coefficient, thereby weakening viscous dissipation effects, which accelerates vortex development and prolongs drainage time. Meanwhile, the vortex structure—through the induction of Taylor vortices and a spiral pumping effect—drives shear mixing and radial thermal diffusion between fluid regions at different temperatures, leading to dynamic reconstruction and homogenization of the temperature field. The outcomes of this study not only provide a solid theoretical foundation for understanding the generation, evolution, and heat transfer mechanisms of vortices under industrial thermal conditions, but also offer clear engineering guidance for practical production-enabling optimized operational parameters to suppress vortices and enhance drainage efficiency.