Generation and analysis of the chaos phenomenon in the molecular-distillation-Navier–Stokes (MDNS) nonlinear system - Qin, Wei; Li, Hui; Jiang, Zhiyu; Luo, Mingyue; Cong, Shuofeng (Frontiers in Physics, 2024)
Exploring the nature and physical practical applications for the Navier-Stokes equation is one of the most essential tasks for completeness of the complex nonlinear systems. As one of the routes to chaos, the Navier-Stokes equation with an external force has been investigated numerically in 1989. When the high symmetry was imposed on the velocity field, the complex nonlinear motions should have occurred even with the chaos phenomenon. However, most of the published papers are based on theoretical studies and rarely deal with practical engineering application. Resulting in a mismatch between them and loss of the integrity of the scientific system. This study analyzed the molecular distillation process in detail. Then, the mathematical model for the process of molecular distillation with one brushless DC motor (BLDCM) is built and named the Molecular-Distillation-Navier-Stokes (MDNS) equation. Also, its complex and potentially chaotic behaviors and chaotic processes are first discovered and demonstrated, such as chaotic attractors, chaotic co-attractors, phase portraits, timedomain waveforms, Lyapunov exponent spectrums, Poincare maps, the bifurcation diagrams, and so on. There is no doubt that the good agreement among theoretical analysis, simulation and experimental results verifies the practicability and flexibility of the configured model.