# A Review of Advanced Air Lubrication Strategies for Resistance Reduction in the Naval Sector
## 3 Numerical Studies
### CFD Simulations on ALDR  
The air layer method has been studied through numerical simulations performed with the RANS, LES, and DNS methods. [PERSON] and [PERSON] [51], [PERSON] et al. [52], [PERSON] and [PERSON] [53], and [PERSON] et al. [54] implemented CFD simulations based on the RANS model. [PERSON] and [PERSON] [51] present a novel method combining linear stability analysis with Unsteady Reynolds-averaged Navier-Stokes (URANS) modelling for simulating air layer drag reduction and predicting flow instabilities. The study focuses on improving computational fluid dynamics (CFD) accuracy in turbulent flows with air layers and validates the method against experimental data, demonstrating effectiveness in modelling two-phase flows and predicting instabilities efficiently [55]. A mathematical model, which will be briefly discussed in Section 4.2, is also implemented to add an air injection fluctuation in the simulation. [PERSON] et al. [52] explore the use of a Winged Air Induction Pipe (WAIP) for drag reduction on ship hulls. The study employs OpenFOAM for simulations, focusing on parameters like the hydrofoil's submergence depth, angle of attack, and air inlet pressure. The study numerically investigates the drag reduction rate using the WAIP device, validating results against experimental data. [PERSON] and [PERSON] [53] combined the RANS and VOF models to investigate the dynamics of air layers in air cavities, examining the influence of cavity parameters on air layer morphology (Figure 16). Figure 15: Instantaneous velocity profile at a y–z plane. (**a**) Pure liquid and (**b**) liquid phase (Ref. [50] reproduced under a CC BY license). [PERSON] et al. [54] explore the complex interaction between different water depths and the efficiency of ALDR systems on ships using CFD. The study employs several sophisticated numerical models and methodologies to simulate and analyse these interactions. The core of the numerical analysis is based on the Reynolds-averaged Navier-Stokes (RANS) equations, which are well-suited for modelling the flow around ships. The turbulence in the fluid is captured using the RNG k-\(\varepsilon\) model, a refined version of the standard k-\(\varepsilon\) model that offers improved handling of strain rates and gradient flows which are prevalent in turbulent boundary layers and separated flows. The RNG k-\(\varepsilon\) turbulence model is specifically chosen for its enhanced capability to deal with complex flow patterns and its accuracy in predicting turbulence effects under various conditions. Additionally, the VOF model is utilized to accurately track the interface between air and water. This is crucial for evaluating the performance of air lubrication technologies, as the distribution and behaviour of the air layer significantly influence drag reduction. The simulations reveal that as water depth decreases, the morphology of the air layer experiences significant changes. In deeper waters, a stable and continuous air layer forms easily under the ship, effectively reducing the frictional drag. However, in shallow and ultra-shallow waters, the air layer becomes increasingly disturbed and fragmented, impacting its ability to reduce drag effectively. The results show that air layer drag reduction is most effective in deeper waters where the air layer remains stable and intact along the ship's bottom. In contrast, shallow waters lead to a decrease in the overall efficiency of drag reduction. This is attributed to the increased disturbance in the air layer caused by the proximity of the ship's hull to the water bed, which alters the flow dynamics around the ship. Numerically, the study quantifies the reduction in total drag and its components. In deeper water, the reduction in frictional drag due to the air layer can reach up to 30% under optimal conditions. As the water depth decreases, the contribution of the air layer to reducing frictional drag diminishes, and the reduction rates drop significantly in ultra-shallow waters.