To investigate the flow-field characteristics of a submerged pre-mixed abrasive water jet impinging on a wall, a physical model of the conical–cylindrical nozzle and computation domain of a submerged pre-mixed abrasive-water-jet flow field were established. Based on the software of FLUENT 2022R2, numerical simulation of the solid–liquid two-phase flow characteristics of the submerged pre-mixed abrasive water jet impinging on a wall was conducted using the DPM particle trajectory model and the realizable $k–\epsilon$ turbulence model. The simulation results indicate that a “water cushion layer” forms when the submerged pre-mixed abrasive water jet impinges on a wall. Tilting the nozzle appropriately facilitates the rapid dispersion of water and abrasive particles, which is beneficial for cutting. The axial-jet velocity increases rapidly in the convergent section of the nozzle, continues to accelerate over a certain distance after entering the cylindrical section, reaches its maximum value inside the nozzle, and then decelerates to a steady value before exiting the nozzle. In addition, the standoff distance has minimal impact on the flow-field characteristic inside the nozzle. When impinging on a wall surface, rapid decay of axial-jet velocity generates significant stagnation pressure. The stagnation pressure decreases with increasing standoff distance for different standoff-distance models. Considering the effects of standoff distance on jet velocity and abrasive particle dynamics, a standoff distance of 5 mm is determined to be optimal for submerged pre-mixed abrasive-water-jet pipe-cutting operations. When the submergence depth is less than 100 m, its effect on the flow-field characteristics of a submerged pre-mixed abrasive water jet impinging on a wall surface remains minimal. For underwater oil pipelines operating at depths not exceeding 100 m, the influence of submergence depth can be disregarded during cutting operations.

In electric railways, the current collection quality of pantograph-catenary systems (PCS) is typically evaluated through numerical simulations using the finite element method, which is computationally expensive and time-consuming. To address this challenge, we propose a surrogate modelling approach that trains a conditional generative model to approximate the output of the reference numerical model. Specifically, we introduce Dual-Domain Conditional Generative Adversarial Networks (DD-CGAN) to generate contact force curves for various PCS parameter configurations. The generator network takes system parameters as input and produces the corresponding contact force curve, while the discriminator network distinguishes between real and predicted curves in both the time and frequency domains, ensuring greater consistency. Furthermore, the feature fusion module is proposed to extract and integrate time-domain and frequency-domain features by using a multi-scale channel attention mechanism. Extensive experimental results demonstrate the effectiveness and advantages of DD-CGAN for surrogate modelling of pantograph-catenary interactions. The contact force curves generated by our method exhibit high consistency with simulation results from high-fidelity numerical models with a mean absolute error of 0.9815, which is six times more accurate than state-of-the-art methods. Most importantly, our method achieves a speedup of nearly 1000x compared to traditional numerical simulations, highlighting its potential for practical use in designing and optimizing catenary structural parameters.

In electric railway systems, the interaction performance of pantograph-catenary systems (PCS) is essential for ensuring a stable electrical supply. Establishing high-fidelity numerical models using the finite element method is generally desirable, yet it involves considerable computational complexity and time demands. In this paper, we propose a novel dynamic modelling method that integrates physical information and data-driven approaches to solve the pantograph-catenary interaction, called Physics-Informed Enhanced Fourier Neural Operator (PI-EFNO). Firstly, the enhanced Fourier Neural Operator (EFNO) based on global perceptron is developed to capture the nonlinear mapping between parameter space and output solution space by approximating solutions to dynamic equations in the frequency domain. Then, we integrate multiple physics-informed loss terms into the EFNO architecture to handle implicit constraints within coupled equations, which leverages physical principles to guide learning while reducing the need for labelled training data. Additionally, a dynamic weighting mechanism adaptively balances the contributions of various terms in the physics-based loss function. Experimental results validate the effectiveness and advantages of PI-EFNO in modelling pantograph-catenary dynamics. It demonstrates exceptional accuracy, computational efficiency, and generalizability across diverse pantograph models and catenary conditions, exhibiting strong capability in learning physically coupled equation systems.

During the operation of high-speed railway, the transition-point disappearance phenomenon, which is caused by the deformation of pantograph head, poses a safety threat to the pantograph-catenary system. In this study, the analytical model for transition-point disappearance analysis is presented. The instantaneous profile, as well as the deformation process of the pantograph head under different contact force values and positions or different pantograph-head parameters can be solved using the model. Curve equation, force analysis, coordinate axis rotation, and few other methods are adopted to achieve simplified modeling. The proposed modeling method and analysis conclusion provide theoretical support for the permissible contact force range calculation and pantograph-head parameters optimization to prevent transition-point disappearance. The effectiveness of the proposed model is verified using both finite element simulation and experimental measurements. Finally, a case analysis for the prevention of transition-point disappearance is conducted, using pantographs with the models CX-GI and DSA250 as examples.