With the increasingly stringent mandatory emission regulations for engines and the continuous growth of energy consumption, reducing energy consumption and emission pollution has become an inevitable choice for engine development. Against this backdrop, biodiesel and boot-shaped injection rates have attracted widespread attention. However, research results on the combination of boot-shaped injection and biodiesel applied to engines have not yet been reported. In order to provide direction for the optimal matching of the combustion system parameters of biodiesel engines under saddle-shaped injection conditions, this paper achieves boot-shaped injection using a dual solenoid valve control strategy for ultra-high-pressure fuel injection devices, establishes a simulation model of biodiesel engines under saddle-shaped injection conditions using software and validates the model based on experiments. Subsequently, the model is used to study the influence of nozzle numbers, swirl ratio and bore-to-stroke ratio on the performance of biodiesel engines under saddle-shaped injection conditions. The results show that under saddle-shaped injection conditions, appropriately increasing the nozzle hole can refine the fuel spray, which is beneficial for fuel–air mixing and combustion in the cylinder. However, too many nozzle holes can lead to interference between adjacent fuel sprays. When the swirl ratio is large, air flow accelerates, and the oxygen concentration in the cylinder increases, which can effectively control soot formation. When the bore-to-stroke ratio is large, the fuel spray is farther away from the combustion chamber side wall, facilitating sufficient contact between fuel and air, resulting in better fuel–air mixing and effectively reducing soot formation. However, the cylinder temperature also increases, leading to higher NOx formation.

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.

We propose a two-stage joint estimation method combining a multi-physics-constrained physics-informed neural network (PINN) with an adaptive extended Kalman filter (AEKF) for lithium-ion battery state-of-charge (SOC) estimation. Three constraints—an RC polarization dynamics ODE residual, discharge voltage–SOC monotonicity, and terminal-voltage physical bounds—are embedded into the PINN loss function; the converged network then serves as the nonlinear observation model within the AEKF. On LG 18650HG2 cells across six temperatures (−20 to 40 °C) under a strict cross-condition setup (training on LA92/UDDS; testing on US06 and two mixed profiles), the method maintains a temperature-averaged SOC mean absolute error (MAE) of 2.33% (1.54–4.48%, three random seeds), whereas the MAE for the equivalent circuit model with the AEKF (ECM-AEKF) degrades to 9.46% and 11.66% at −20 °C and −10 °C, and remains 1.5–4.6× worse with the per-temperature re-identified parameters; an end-to-end long short-term memory (LSTM) baseline averages 1.90% but degrades to a per-condition maxima of 22.6% at low temperatures. Multi-seed ablations locate the constraints’ value in providing low-temperature stability and physical consistency, with the RC-ODE constraint contributing most. The study further reveals that goodness of terminal-voltage fit does not imply SOC accuracy; the controlled comparisons trace this to the model structure rather than parameter settings, exposing the risk of voltage-fitting-based evaluation over wide temperature ranges.

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.