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.

The cross-slot geometry plays an important role in the study of nonlinear effects of viscoelastic fluids. The flow of viscoelastic fluid in a micro cross-slot with a high channel aspect ratio (AR, the ratio of channel depth to width) can be divided into three types, which are symmetric flow, steady-state asymmetric flow and time-dependent flow under the inlet condition with a constant velocity. However, the flow pattern of a viscoelastic fluid in the cross-slot when a stimulation is applied at inlets has been rarely reported. In this paper, the response of cross-slot flow under an external sinusoidal stimulation is studied by numerical simulations of a two-dimensional model representing the geometry with a maximum limit of AR. For the cases under constant inlet velocity conditions, three different flow patterns occur successively with the increase of Weissenberg number (Wi). For the cases under sinusoidal varying inlet velocity conditions, when the stimulation frequency is far away from the natural frequency of a viscoelastic fluid, the frequency spectrum of velocity fluctuation field shows the characteristics of a fundamental frequency and several harmonics. However, the harmonic frequency disappears when the stimulation frequency is close to the natural frequency of the viscoelastic fluid. Besides, the flow pattern shows spatial symmetry and changes with time. In conclusion, the external stimulation has an effect on the flow pattern of viscoelastic fluid in the 2D micro cross-slot channel, and a resonance occurs when the stimulation frequency is close to the natural frequency of the fluid.

Optimal sensor placement is a crucial issue in scientific and engineering research. This study proposes an autoencoder-based deep learning framework for automated optimal sensor layout and flow field reconstruction. A dataset is established based on transient Computational Fluid Dynamics (CFD) simulation results of a three-dimensional finite-span airfoil under various Reynolds numbers and angles of attack, enabling high-precision reconstruction of airfoil surface pressure distribution using sparse pressure coefficient data. The multilayer perceptron of both the encoder and decoder adopts an optimal five-layer structure with 200 nodes per layer, and the ReLU activation function delivers superior performance with a training loss reduction of over 45%. When using 50 sensors, the proposed architecture determined detailed placement and obtained a reconstruction error of 0.0604, which outperforms traditional manual sensor placement. The reconstruction accuracy of aerodynamic loads improves with increasing sensor count, but exhibits diminishing returns beyond the optimal threshold 50, necessitating a balanced selection that optimizes performance-to-cost ratio. The proposed method adaptively captures critical flow regions with high gradients, cutting sensor quantity by 60–80% versus grid-based placement. This method can flexibly use either CFD or experimental data in practical applications, offering an efficient solution for aerodynamic field reconstruction.