Exhaust piping in diesel engines is subject to severe thermal stress arising from high-temperature, high-pressure gas flows, and spray cooling with atomizing nozzles has become a widely adopted method to safeguard structural reliability. However, at present, the understanding of the spray fragmentation mechanism of two-phase flow under low inlet pressure is still not comprehensive. This study establishes a three-dimensional model of a gas–liquid impinging-jet nozzle and applies a coupled Volume-of-Fluid to Discrete-Phase-Model (VOF–DPM) approach to resolve the liquid breakup process in detail. High-speed imaging experiments were carried out to validate the numerical results. Orthogonal tests were conducted at five pressure levels for both gas and water—0.28, 0.24, 0.20, 0.16, and 0.12 MPa—producing 25 data pairs of spray cone angle and Sauter Mean Diameter (SMD). Within the 0–0.3 MPa air inlet pressure range explored here, raising the pressure consistently reduced the SMD and widened the cone angle, although both trends weakened as the pressure increased. Water inlet pressure exhibited a nonlinear influence, with local extrema appearing in the higher-pressure region. The overall SMD reached a minimum of 34.12 μm and a maximum of 149.04 μm. Using these 25 data points, a genetic algorithm was employed to optimize the pressure ratio under the constraint of total hydraulic power, yielding optimization strategies for different power budgets. An additional outcome of the simulation was the identification of a structural weakness: by reshaping the original flat impingement surface into a full conical surface, atomization quality improved by 29.36% under identical boundary conditions. These findings clarify the atomization mechanism of gas–liquid impinging jets under low inlet pressure and offer practical guidance for nozzle optimization.

This study proposes a multi-stage decomposition framework for auxiliary power prediction of underwater vehicles to support energy management. Isolation Forest first removes outliers from the load record; Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) then decomposes it, and the modes are aggregated by Sample Entropy (SE) into high-, medium-, and low-frequency sub-sequences; Variational Mode Decomposition (VMD) further refines the highest-entropy sub-sequence; and Long Short-Term Memory (LSTM) networks predict each sub-sequence and sum the results. Validation on measured data adopts a leak-free protocol in which normalization, outlier detection, and decomposition never access future observations and all models are evaluated on the original, unmodified test targets; as the test segment’s mean load level is lower, bias-corrected metrics are reported alongside raw ones. The proposed method attains the best bias-corrected R² (0.330) and NRMSE (0.109) among seven models, reducing NRMSE by 1.0% to 15.9% versus all benchmarks, while its MAPE (9.01%) stays within 0.71 percentage points of the best baseline; five-seed repetitions confirm that this advantage is not an artifact of a single training run, a capacity-matched comparison shows that it does not stem from the larger parameter count, and a 16-combination sweep indicates low sensitivity to the VMD hyperparameters. On the public Shifts vessel power dataset, the framework remains competitive (R² = 0.885 ± 0.077 over three seeds), although the EMD–LSTM and direct baselines are superior there owing to richer exogenous features, delimiting the applicability of the decomposition cascade.