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In this study, a conservative phase-field lattice Boltzmann model is examined for simulating immiscible two-phase flows with large density and viscosity ratios. This model is built upon the Allen-Cahn equation, incorporating a filtered collision operator and high-order corrections in the equilibrium distribution functions. The numerical model is also integrated with the volumetric boundary scheme and the immersed boundary method to achieve various stationary and moving boundary conditions on arbitrary geometries for different application scenarios. A comprehensive evaluation of this phase-field solver is conducted through a range of academic and industrial cases. First, droplet splashing cases at different Reynolds numbers are studied. The phase-field LB model effectively captures the surface wave motion and splashing of the droplet, although some smearing of small structures is observed due to the diffused interface property of the numerical model. Second, a tuned liquid damper is simulated, accurately capturing sloshing forces on solid walls. In the simulation of a dam-breaking case, predicted gauge pressure and free-surface elevation time histories compare well with experimental data. Lastly, a gearbox case under dip lubrication is simulated, with both the gearbox churning loss and oil distribution being well predicted across a range of rotating speeds. The validation studies demonstrate the effectiveness of the present phase-field lattice Boltzmann model in simulating immiscible two-phase flows with large and realistic density and viscosity ratios. The strengths, limitations, and weaknesses of the conservative phase-field LB model are discussed, and suggestions for the development and application of this numerical model are provided. [ABSTRACT FROM AUTHOR]

• Key Findings: Sobol sensitivity analysis identifies non-dimensional maximum thickness as the most critical factor, contributing 44 % to the variance in total pressure loss and deviation angle. • Advanced Modeling: evaluated multiple neural network models, with the CNN-LSTM-SAM model demonstrating superior prediction accuracy and generalization capabilities. • Optimization Success: utilized particle swarm optimization (PSO) to minimize total pressure loss and deviation angle across a range of reynolds numbers and angles of attack. • Practical Implications: provides valuable insights and strategies for designing efficient compressor blades, especially for high-altitude UAV applications. This study addresses the challenges of designing high-efficiency compressors for long-endurance, high-altitude unmanned aerial vehicles (UAVs) under low Reynolds number (Re) and high load conditions, exploring the aerodynamic performance limits of compressor blades under extreme conditions. The research integrates advanced numerical simulations, experimental methods, and deep learning technologies to minimize profile losses and deviation angle on compressor blades. An orthogonal experimental design systematically explored the impact of key geometric factors on aerodynamic performance. A deep learning model incorporating neural networks with spatial attention mechanisms was developed to significantly enhance the accuracy of aerodynamic predictions. This model adeptly captured the complex nonlinear interactions between aerodynamic and geometric parameters. Sobol sensitivity analysis revealed that the dimensionless maximum thickness is the most critical factor, accounting for 44 % of the total variance in total pressure loss and deviation angle. The position of maximum thickness and the aspect ratio of the elliptical leading edge also significantly influenced performance. The optimized high-load compressor blade profile was validated through experimental data and detailed computational fluid dynamics analysis using large eddy simulation methods. This analysis revealed flow separation and reattachment mechanisms, shedding light on turbulence and vortex dynamics critical to performance. This research deepens the theoretical understanding of compressor cascade fluid dynamics and provides practical insights for designing more efficient compressors, especially for micro axial compressors in high-altitude UAVs. [ABSTRACT FROM AUTHOR]