# A Review of Advanced Air Lubrication Strategies for Resistance Reduction in the Naval Sector
## 3 Numerical Studies
### CFD Simulations on MBDR
They utilize the Eulerian multiphase model for simulating gas-liquid two-phase flows and employ the k-\(\omega\) turbulence model to assess turbulence effects. The paper highlights how microbubbles' distribution and dynamics, influenced by the k-\(\omega\) turbulence model, affect drag characteristics. Smaller bubbles tend to stick closer to the surface, enhancing frictional drag reduction but also increasing the likelihood of higher pressure drag due to enhanced flow separation. The research details the conditions under which flow separation occurs at the tail of the vehicle, especially at lower water velocities and higher air flow rates. This separation leads to increased pressure drag, offsetting some benefits of reduced frictional drag. To validate their numerical model, the authors correlate their findings with experimental data, confirming the accuracy of their simulations in predicting the actual performance of microbubble drag reduction systems in underwater vehicles. In [PERSON] et al. [48], the liquid phase is simulated using LES within the Euler framework. This approach filters the eddy in the flow field, directly solving the large-scale vortex structure while approximating small-scale ones using a sub-grid model. Bubbles are tracked using kinematic equations following [PERSON]'s second law. They are assumed to be non-deformable spheres, and their motion is influenced by forces like drag, lift, buoyancy, and fluid acceleration. The interactions between the Euler liquid phase and Lagrange bubble phase are managed by a two-way coupled solving algorithm. This includes computing hydrodynamic and collision forces on the bubbles, updating bubble locations, calculating local void fractions, and applying hydrodynamic forces acting on the bubbles to the liquid as source terms. To improve accuracy and stability, a Gaussian bubble volume distribution scheme is used for void fraction computation. This method averages the bubble volume into the grid it should be in, considering the shape of bubbles and their contribution to nearby cells. The method's accuracy is validated against experimental data and other simulations. This includes comparing rising velocities of bubbles in calm water and analysing bubble trajectories and deformations. [PERSON] et al. [49] and [PERSON] et al. [50] use the DNS model to resolve turbulence. [PERSON] et al. [49] investigate the impact of microbubbles on turbulent drag in channel flow. The study employs DNS to simulate the turbulent channel flow seeded with small rigid spherical bubbles. The Force-Coupling Method (FCM) represents each bubble as a finite force monopole, generating a body force distribution to transmit the bubbles' resultant force to the fluid. The simulations cover different bubble sizes and average void fractions, investigating the effects of bubble seeding levels and size. The study focuses on the drag force on the channel walls and the mean pressure gradient changes, providing evidence of drag reduction due to bubbles. [PERSON] et al. [50] also explore the effects of microbubbles on drag reduction in a horizontal channel. The liquid velocity field is solved using DNS and the bubble trajectory is tracked using Newtonian motion equations. The study specifically investigates conditions leading to low drag reduction rates, considering factors such as liquid-phase velocity changes (Figure 15), turbulence intensity, and Reynolds shear stress across the channel. Figure 15 shows the typical instantaneous velocity vectors at a cross section in the y-z plane of the channel. It clearly illustrates that, throughout the channel, the ejection and sweep motions of the liquid phase are suppressed compared to those of the pure liquid. The study pays attention to the distribution of microbubbles, their interaction with liquid turbulence, and the overall impact on drag reduction.