Numerical research on sloshing dynamic characteristics in cylindrical tank with internal components with dynamic mode decomposition method

Understanding sloshing modes in cylindrical tanks with internal components is essential for risk mitigation. Moreover, the complex geometries make theoretical analysis difficult. While dynamic mode decomposition (DMD) has been widely adopted in fluid dynamics, it is meaningful to study its application in sloshing. Unlike conventional flow modes, DMD may face unique challenges due to the discontinuous free surface dynamics. To address this issue, this study selected a container with cylindrical components as the research object. The DMD method was employed to extract sloshing modes from numerical simulations using the Volume of Fluid method. The DMD accuracy is validated through comparison with simulation results. The Froude number (Fr) is used to assess DMD's robustness across different sloshing regimes. Results show that DMD method can effectively capture the sloshing modes. In linear sloshing, the overall modes are governed by the liquid-wall impact. When excited at the first order natural frequency, a nonlinear wave collision pattern is found and generates acceptable errors. Under the second order natural frequency excitation, the errors are sharply increased. Additionally, the relationship between DMD and Fr is independent of the tank filling rate. When Fr < 0.198, the DMD calculation result is reliable. For 0.198 ≤ Fr ≤ 0.368, DMD maintains high reconstruction accuracy, but the prediction error increases by 134.6%. When Fr > 0.368, both prediction and reconstruction errors surge by 128.3% and 127.5%. This work proposes a novel and effective framework in tank's sloshing analysis using DMD. The results provide valuable guidance for tank design, especially with complex geometries and internal components.