A Review of Advanced Air Lubrication Strategies for Resistance Reduction in the Naval Sector

Abstract

This review explores a variety of techniques that utilize air injections beneath a vessel’s hull to reduce drag and consequently improve energy efficiency. It focuses on the methodologies of microbubble drag reduction (MBDR), air layer drag reduction (ALDR), and air cavity drag reduction (ACDR), offering insights into their design, operational mechanisms, and potential applications. This review provides a detailed examination of the underlying principles of these technologies, incorporating a blend of experimental research, numerical simulations, and mathematical modelling to offer a comprehensive understanding. It references recent experimental data, highlighting how these findings corroborate with numerical simulations and are further explained through mathematical models. Conclusively, this review accentuates the transformative influence of air injection methods in drag reduction within the maritime industry, emphasizing their pivotal role in boosting operational efficiency, reducing environmental impact, and driving the evolution of naval design and transportation. Through a balanced and detailed analysis, this review provides a holistic view of the current state and future prospects of these innovative resistance reduction strategies.

1. Introduction

In the quest for greater efficiency and sustainability in maritime operations, the naval sector is increasingly focusing on resistance reduction strategies to enhance vessel performance and reduce environmental impact. The resistance to forward motion of a ship is fundamentally determined by three components: frictional drag, wave drag, and viscous drag. Notably, frictional drag, occurring due to viscous interactions between a ship’s hull and the water, is a significant component, especially in contexts where wetted surfaces are extensive, such as in surface ships. Frictional drag contributes to 60–70% of the total drag on cargo ships and roughly 80% on tankers [1,2,3].

In the context of reducing movement resistance in vessels, computational fluid dynamics (CFD) provides a crucial tool for detailed analysis and optimization [4] of ship design [5], especially within the realm of air lubrication techniques. CFD enables the simulation of complex interactions between water and naval structures, thereby facilitating the development of innovative solutions that enhance operational efficiency and meet sustainability challenges in the maritime sector [6]. CFD is used to model the flow behaviour around the hull and within air cavities, assessing the effectiveness of different configurations in reducing resistance [7]. Through CFD simulations, it is possible to predict how microbubbles, air films, or air cavities affect pressure distribution and velocity profiles along the hull, thus optimizing the design to maximize drag reduction. These simulations are crucial for understanding the delicate balance between the amount of air injected, the placement of injections, and the overall impact on the hydrodynamic resistance of the ship [8].

Within the strategies for drag reduction, air lubrication techniques represent an important technological frontier. The classification of these techniques is divided into three principal categories. Microbubble drag reduction (MBDR) involves the introduction of microbubbles into the ship’s boundary layer, leading to a reduction in frictional drag by lowering the mean density and altering the velocity profile. Air layer drag reduction (ALDR) employs a gas film which creates a physical separation between the ship and the water, resulting in friction attenuation. Air cavity drag reduction (ACDR), in contrast, establishes a gas-filled cavity that, by isolating a portion of the wetted surface, reduces drag in that area.

These techniques not only bring about improvements in terms of operational efficiency but also offer innovative responses to the pressing sustainability challenges in the maritime industry, reducing the fuel consumption of the vessels. It is essential to note that the transition from MBDR to ALDR mode and the subsequent implementation of ACDR are phenomena governed by the flow and pressure of air injected beneath the hull. The choice between these modes depends on the optimal balance between drag reduction efficacy and operational feasibility in relation to different types of ships and their specific operations.

The three mechanisms of air lubrication for drag reduction are depicted in Figure 1, showcasing MBDR (Figure 1a), ALDR (Figure 1b), and ACDR (Figure 1c).

The reported studies intend to deepen the understanding of air lubrication techniques, evaluating not just their efficiency in terms of drag reduction but also their overall impact on ship performance and the marine environment. In an era where sustainability has become a watchword for the industry, the potential of these technologies to contribute to a cleaner and greener future for the maritime sector is substantial.

Addressing the challenge of environmental sustainability is crucial across various design fields. The integration of air lubrication technologies should be considered within the broader context of ecological impact, energy consumption, and emissions reduction. In this context, Life Cycle Assessment (LCA) emerges as an essential tool, providing a comprehensive evaluation of the environmental impact of these technologies throughout their lifecycle. By incorporating LCA into design and operational strategies, a holistic approach to sustainability can be achieved.

LCA proves especially useful in fields like product design [9], guiding decisions on raw materials and production processes [10], and in experimental research [11], helping assess the environmental impact of new technologies or methods before their widespread implementation. For instance, in the maritime sector, LCA can assist in evaluating the environmental impact of different air lubrication technologies right from the experimental phase, ensuring that the choices made reduce environmental impact throughout the lifecycle of the vessel [12]. Environmental considerations were made by [13]. A simplified empirical model was developed to predict energy savings across different ship types and operational profiles. This model calculates the net percentage power savings by evaluating the reduction in frictional resistance through air lubrication.

2. Experimental Studies

2.1. Tests Performed on MBDR

To study friction reduction in the turbulent boundary layers of a liquid flow caused by the presence of bubbles, several experiments were conducted, the first of which was led by Tsai et al. [14]. In this study, a model was developed to predict the effectiveness of microbubble drag reduction techniques in a boundary layer on a flat plate. The experimental techniques included a system for injecting microbubbles through porous material and a resistance measuring system to assess the frictional drag of the flat plate both with and without injected microbubbles. These experiments were conducted in a wind tunnel and a towing tank, varying the flow velocity and air injection rate, to test the reliability of the proposed model’s predictions. The conclusions drawn by Tsai et al. highlighted that the drag reduction effect predicted by the boundary layer mixture model is almost directly proportional to the density ratio between the mixture and water, and that there exists an optimal air flow rate for each velocity in the towing tank.

In another study conducted by Sanders et al. [15], the reduction of bubble friction in a turbulent boundary layer on a high-Reynolds-number flat plate was investigated. The experiments were carried out in the US Navy’s Large Cavitation Channel, using a 12.9 m long flat plate to create a turbulent boundary layer with a near-zero pressure gradient. Air was injected through 40 µm sintered metal strips flush-mounted to the test model’s surface at high volumetric rates. The surface shear stress measurements without air injection, conducted by Sanders et al., revealed a systematic underestimation of frictional drag compared to the expected value based on Schultz-Grunow’s friction line [16].

Elbing et al. [17] conducted a series of experiments at the US Navy’s William B. Morgan Large Cavitation Channel (LCC) to explore skin friction drag reduction in a turbulent boundary layer (TBL) at high Reynolds numbers and large scales. These experiments involved injecting gas (air) from a line source through the wall of a TBL with nearly zero pressure gradient, formed on a flat-plate test model that was either hydraulically smooth or fully rough. The study focused on two specific phenomena of drag reduction: bubble drag reduction and air-layer drag reduction. The experiments measured the longitudinal distribution of skin friction drag reduction using six drag balances, with downstream-distance-based Reynolds numbers reaching up to 220 million and test speeds of up to 20.0 m/s. In the initial test, variables such as free-stream liquid velocity, gas injection rate, injection location, background surface tension, and injector type were altered to assess their impacts.

Another method of study was conducted by Sayyaadi and Nematollahi [18], utilising an experimental model to conduct physical model experiments in a controlled environment. At the School of Mechanical Engineering’s Centre of Excellence in Hydrodynamics and Dynamics of Marine Vehicles, Sharif University of Technology, a series of experiments were conducted. These tests involved a catamaran model, 70 cm in length, crafted from plexiglass. The model was designed to facilitate air injection at three distinct locations: the bow, midship, and stern areas. A critical aspect of utilizing the microbubble method effectively lies in accurately estimating the rate of air injection. Although there is no direct conventional method to determine this rate, it can be inferred from the indices of the boundary water flow. The experimental results revealed a trend: as the speed increased, the peak drag reduction effect diminished, suggesting that the microbubble drag reduction technique is notably more effective for ships operating at lower speeds.

A different approach to improve the effectiveness of reducing frictional drag through bubble utilization, researched by Hyun Jin Park et al. [19], involves repetitive bubble injection (RBI) instead of the conventional continuous bubble injection approach. RBI maintains frictional drag reduction by generating bubble swarms, even with a low mean void fraction of injected bubbles into the turbulent boundary layer. The mechanism of enhanced drag reduction and the effectiveness of the RBI approach were thoroughly investigated by measuring the temporal variation of local wall shear stress, the velocity vector field of the liquid phase, and the gas–liquid interface in turbulent horizontal channel flows. The experimental setup included a horizontal rectangular channel made from transparent acrylic resin, using silicone oil as the working fluid. Two 4 MHz ultrasonic transducers were attached to measure the internal flow structures. The RBI approach was examined at Reynolds numbers greater than 1200.

To diminish the frictional drag during a ship’s progress, the introduction of small amounts of bubbles, as studied by Boris Jacob et al. [20], can be chosen. In the primary experiment, conducted in a 25 m long recirculating water channel, the focus was on understanding the reduction of viscous drag in a turbulent boundary layer over a flat plate, influenced by the presence of microbubbles. These microbubbles, having an average diameter similar to the local Kolmogorov length scale and a bulk void fraction of approximately 0.1%, were studied. The frictional drag of a 6 m long flat plate with microbubbles, generated through electrolysis, was initially measured in a towing tank. To assess the streamwise and wall-normal components of the liquid phase’s velocity, image analysis techniques and a Feature Tracking (FT) algorithm were employed. The void fraction of the bubbles was estimated by calculating the projected bubble volumes within the measurement volume. The distribution of bubbles in the near-wall region of the boundary layer was also analysed [21].

An alternative method to enhance the efficiency of frictional drag reduction using bubbles, studied by Yanuar et al., involves using a high-speed vessel model for experiments in a test basin. The basin had dimensions of 50 m in length and 40 m in width, with a constant water depth of 2 m.

The experiments encompassed a Froude number reaching as high as 0.65. Central to the setup was the ship model, which was affixed to a load cell transducer above the baseline. This arrangement permitted unobstructed vertical movement of the model. Throughout the range of Froude numbers tested, the total drag experienced by the model was recorded for each trial. A wire rope was used to tow the ship model, enabling the measurement of the total longitudinal force exerted on the model at different speeds. During these measurement trials, the ship model was allowed the freedom to both pitch and heave [22].

The authors Murai, Y. et al. [23] investigate skin friction reduction using large air bubbles in turbulent flow within a horizontal channel. They experimentally studied the relationship between local skin friction and the interfacial structure of the bubbles, employing relatively large air bubbles compared to the boundary layer thickness. They found a negative correlation between local skin friction and local void fraction, with significant skin friction reduction at the rear of large individual bubbles. This study provides new insights into the bubble-induced skin friction reduction process and suggests that bubbles of a certain size may be more effective in reducing friction. Another significant study on the effect of skin friction and its applicability to ships was conducted by Y. Kodama et al. [24]. This research explored the use of microbubbles in a water tunnel to analyse how they can reduce skin friction on ships [25]. The authors measured the friction reduction and investigated the relationship between local void fraction and friction reduction. The article also examines the impact of ship sizes on the effectiveness of microbubbles, laying the groundwork for future research on the applicability of this technology to real-sized ships.

In the endeavour to diminish the hydrodynamic drag experienced by a ship’s hull at cruising speeds of 15–20 knots, the research spearheaded by Kumagai et al. [26] has culminated in the inception of a novel energy-conserving apparatus (Figure 2). This apparatus harnesses small bubbles, generated via the Kelvin–Helmholtz instability phenomenon. The device is ingeniously designed, comprising strategically angled hydrofoils equipped with air introducers, which are adeptly positioned beneath the air release vents on the hull’s surface. The primary objective of this advanced technology is to substantially mitigate the turbulent momentum transfer, fundamentally targeting the reduction of skin friction along the hull’s surface. This is achieved through the strategic injection of diminutive bubbles, each measuring less than 0.5 mm in diameter, directly into the turbulent boundary layer.

Despite the precise scientific mechanism behind the drag reduction elicited by these minuscule bubbles remaining a topic of ongoing academic exploration, historical empirical observations have inferred that injecting such bubbles into the turbulent domain effectively attenuates the Reynolds shear stress [27]. This discovery suggests that the ideal condition for reducing drag is attained by maximizing bubble density at the point of peak Reynolds shear stress, usually located between the viscous sublayer and the buffer layer within the turbulent boundary layer [28]. Furthermore, it has been documented that small bubbles exhibit a natural propensity to accumulate within the turbulent shear layer, persisting for extended durations within the turbulent boundary layer and thereby countering the effects of turbulent diffusion [29]. More precisely, these small bubbles are prone to reside in regions of high entropy, characterized by negative values of the second invariant of the velocity gradient tensor [30]. In the context of a ship in motion, this region coincides with the layer most densely populated with active turbulent eddies, hence enabling the small bubbles to endure within the turbulent boundary layer for prolonged periods, effectively resisting turbulent diffusion.

A distinctive aspect of the system, referred to as the Winged Air Sensor Tube (WAIP) (Figure 3), is the incorporation of the aerofoil section NACA 653-618, which is positioned below the surface level and set at an angle of attack of 12 degrees. During the ship’s forward motion, the hydrofoil redirects the water flow, generating a low-pressure area above the foil, which in turn draws atmospheric air into the water.

This setup not only reduces the pressure above the hydrofoil but also accelerates the water flow above it while slowing it down beneath, thereby creating vortices downstream of the foil and assisting bubble formation both at the interface between gas and water, and behind the trailing edge.

The test model ship, developed specifically for evaluating the WAIP system, comprises four sections, identified as A, B, C, and D in Figure 4.

The combined drag force experienced by sections B and C (notated as Dt) was assessed using a singular load cell. Concurrently, the drag impact on section B alone was independently gauged by a different load cell (marked as Do). Thus, the drag exerted on the 2.6 m long acrylic flat panel (referred to as Db) was calculated using an equation (Equation (1)) from these data points.

The process of bubble generation and its contribution to decreasing the frictional drag on the downstream horizontal flat wall were meticulously investigated through experiments in a circulating water channel, where the flow velocity was established at 5.6 m/s to replicate the typical cruising speed of ships. Here, B_h represents the horizontal width of the bubble-mixed layer and V denotes the flow velocity of the circulating water, with the water’s density indicated by $\rho$. For practical application to full-size ships, the total drag force F_total (Equation (2)) that is acting on a flat plate with length L is determined by the use of local friction factors with and without air bubbles, represented by C_f and C_f0, respectively.

$$D_b=D_t-D_0$$

(1)

$$F_{Total}=D_t-{\int }_0^L\frac{1}{2}\rho V^2{C}_{f_0}\left(1-\frac{C_f}{C_{f_0}}\right)B_{h}dx$$

(2)

This system, by avoiding the need for porous materials and overpressure, allows for the flow of air with the small bubbles created by the instability, demonstrating a significant advancement in drag reduction technology for maritime vessels.

In Figure 5, the optimal functioning of the WAIP system is graphically depicted, showing variation with the ship’s draught. In conditions where the draught is shallow (less than 5 m), the hydrofoil functions as a self-priming pump, effectively releasing small air bubbles near the hull through the hydrofoil device (Figure 5a). For ships with deeper draughts (over 5 m), where the hydrofoil’s pressure reduction capacity is insufficient, a slight increase in air pressure is necessary to sustain microbubble formation (Figure 5b). In this configuration, the flow required is supplied by an air compressor, which is channelled through pipes along the hull of the ship and released above the hydrofoil in the area of low pressure. In the situation illustrated in Figure 5c, employing blowers that deliver high rates of air flow may result in a state where the hydrofoil becomes entirely separated from the adjacent water flow, resulting in the formation of only large bubbles beyond the boundary layer. This situation is not only inefficient for bubble generation but also increases the resistance caused by the hydrofoil, making the system less effective and wasting energy in bubble production.

Tanaka et al. [31] investigate the effectiveness of repetitive bubble injection (RBI) for reducing frictional drag in turbulent boundary layers under a model ship. This study explores how periodic fluctuations in bubble injection can enhance drag reduction compared to continuous bubble injection (CBI). The experiments were conducted with a 36 m long flat-bottom model ship towed at a speed of 8.0 m/s, where the drag reduction ratio achieved up to 24%, a 5% improvement over CBI.

High-frequency cameras were used to monitor the flow and distribution of bubbles under the ship and the local wall shear stress was measured to evaluate the performance of the drag reduction techniques directly.

Analysis showed that the downstream persistence of drag reduction can be significantly enhanced by RBI, with the effect observable up to 15 times further downstream compared to CBI.

The findings suggest that the repetitive injection strategy alters the bubble dispersion in a way that extends the effective drag reduction zone along the ship’s hull, potentially offering a more efficient method for reducing hydrodynamic resistance in marine vessels. The technique for generating and injecting the air cushion beneath the base of the passenger vessel’s hull is shown in Figure 6.

As shown in Figure 7, potent blowers create air bubbles that move steadily beneath the hull’s bottom. The outlets for these bubbles are positioned symmetrically along the bottom on either side of the ship’s centre line.

Figure 7 displays a schematic of the MBDR system, featuring two blowers, a compressed air distribution line, and air distribution boxes on a large passenger vessel (cruise liner). According to [32], at present, several cruise ships have installed the MBDR system. This paper presents

Table 1. The list of cruise vessels with air lubrication systems delivered 2015–2019 [32].

Year	Vessel Name	Type	Length (m)
2015	Quantum of tir Sea	Cruise	348
2016	AIDA prima	Cruise	300
2017	AIDA perla	Cruise	300
2017	Norwegian Joy	Cruise	333
2018	Diamond Princess	Cruise	290

, which shows that since 2015, microbubble injection systems have been installed on the ships listed in the table.

As detailed in the same paper, the bubble generation systems consist of two centrifugal compressors. Each compressor has a flow rate of 5 kg/s and a power output of 700 kW, operating at a pressure of 1.4 bar.

2.2. Tests Performed on ALDR

The experimental method of air layering was studied by authors Jinbo Jang et al. [3]. Experiments were conducted using a flat plate measuring 7.5 m × 1.0 m × 8 cm, horizontally mounted in the test section of a water tunnel (Figure 8). Air was injected through a flush slit near the front end of the plate, and two floating-plate-type friction sensors measured changes in local frictional drag caused by air layers. Additionally, six independent air injection units were installed on the ship model, flush with the hull’s bottom surface to avoid unwanted drag increase. Compressed air was stored in receivers on the ship model’s deck, and the air flow to the injection units was regulated by PC-controlled mass flow meters (Figure 9).

The experiments demonstrated that a transitional air layer generated by air injection on the hull’s bottom can effectively reduce ships’ frictional drag. For a 66K DWT Supramax wide-beam bulk carrier, net power savings, accounting for air injection energy consumption, were estimated between 5% and 6%. This energy saving translates to an 8–10% reduction in effective power and a 7–9.5% reduction in delivered power due to less than 1% loss in quasi-propulsive efficiency. The results suggest significant potential for energy savings with air lubrication if there is no significant performance deterioration in real sea conditions.

In another study conducted by authors W. U. Hao et al. [33], experiments were performed to investigate friction reduction using an air layer beneath a flat plate in a towing tank. They observed the air layer formation and measured changes in drag. Drag and self-propulsion tests were also conducted on a ship model based on a 95,000 DWT container ship, using the method of friction reduction through a lower cavity air layer. Air layers were observed, and estimated energy savings were calculated. The results indicated that the provided power could be reduced by up to 15% in a full-scale ship, not accounting for the energy consumption for air injection.

In the study conducted by Wu H. et al. [34], the application of an air cavity on the bottom of a ship model for friction reduction was explored. The model (Figure 10), inspired by a large container ship, featured a flat bottom structure ideal for the implementation of ALDR technology. Two air injection devices were used to form an air layer within the cavity, and the cavity’s depth was varied to study its effects on the ship’s drag and propulsion. Air was injected through holes in the base plate of each device, and the depth of the cavity was adjusted to study its impact on the ship’s drag.

To further understand the impact of air flow rate and inflow velocity on air layer formation, the non-dimensional air flow rate coefficient (Equation (3)), C_q, is defined using the air flow rate (Q), inflow velocity (V), transverse width of the air injection entrance (B), and the thickness of the boundary layer at the air injection entrance without air injection (δ).

$$C_q=\frac{Q}{VB\delta }$$

(3)

The coefficient proposed allows to relate the flow rate of the air injected with the velocity condition of the boat. It is very important in order to take into account the effects of the speeds of the boat on the drag reduction of the system.

In the study, the variation in the ship model’s relative drag reduction rate was observed in relation to wave length, considering different cavity depths and C_q values (0.112, 0.168, and 0.224) at a Froude number of 0.155. It was noted that the change in relative drag reduction rate with wave length followed the same trend across different C_q values. Generally, the relative drag reduction rate was higher in the 25 mm cavity and in long waves, reaching over 30% in long waves at a C_q of 0.224, which is lower than that in calm water.

The results showed an increase in drag due to the presence of the cavity, with a 13.9% increase at a cavity depth of 25 mm at the design speed. The investigation also highlighted the adaptability of ALDR technology to the mode of air injection, demonstrating no direct correlation between friction reduction and the mode of injection in this experiment. The study’s findings indicate that when the 25 mm cavity is constantly provided with air at an air flow coefficient C_q of 0.224 in calm water, there is an approximate 20% reduction in absolute drag at the ship’s design speed. Additionally, this effect of drag reduction persists even in the presence of long waves.

Elbing et al. [35] conducted an experimental study on air drag reduction using a 12.9 m long flat-plate model, altered by adding a 13 mm protrusion at the air injection site. The tests, performed at a speed of 6.3 m/s, evaluated the effect of vortex generators on the boundary layer, both with and without their use. A novel scaling for critical air flux was proposed, based on the analysis of a single bubble in shear flow. This scaling, suggesting that ALDR’s transition is influenced by the ratio of buoyancy to turbulent shear forces, successfully unified data across different surface conditions and air injection methodologies.

Yanuar et al. [36] studied the effectiveness of porous media in the injection of microbubbles and air layers for drag reduction on a self-propelled barge model. They used a 30 cm wide porous medium as a microbubble injector to generate bubbles and layers beneath the hull surface, with an average hole diameter of 100 μm, custom-built to meet experimental requirements. The study concluded that the microbubbles and air layers generated beneath the hull surface could significantly decrease water resistance, demonstrating the potential for efficiency improvements in maritime transport.

Elias A. et al. [37] conducted an experimental study on the reduction of skin friction drag using superhydrophobic-coated flat plates in high Reynolds number boundary layer flows. The research involved coating aluminium flat plates with hydrophobic nanoparticles to create two distinct types of superhydrophobic surfaces—one with a lower contact angle and higher contact angle hysteresis, and another with a higher contact angle and lower contact angle hysteresis. These coatings were tested in a high-speed towing tank system to measure the skin friction drag across various flow regimes, comparing the performance to that of an uncoated bare aluminium plate. Their findings demonstrated significant drag reduction in certain conditions, attributed to the air layer’s shear-reducing effects on the superhydrophobic surface

Additionally, the study delved into basic drag reduction (BDR) by employing a traversing probe system to assess void fraction and gas-phase velocity profiles. Despite the varying configurations of the vortex generators, these measurements indicated a consistent interfacial velocity profile, akin to that in single-phase flows. However, discrepancies in void fraction profiles were observed, likely attributable to measurement uncertainties near the wall. In summary, the study’s proposed scaling for ALDR represents a promising foundation for further investigation into this phenomenon, which is notably affected by upstream flow perturbations. This research has also contributed to bridging knowledge gaps in measuring void fraction and gas-phase velocity profiles in the context of BDR.

2.3. Tests Performed on ACDR

Research on the Air-Cavity Ship (ACS) is being studied as one of the most promising concepts for economical marine transport. The ACS employs an air injection system to isolate the ship’s lower wetted surface from the water, thus reducing frictional drag. Air cavities are created by injecting air at the keel level, extending along large portions of the hull bottom.

The experiment described in A. Slyozkin et al.’s [38] work used a simplified flat-plate model to study the effect of air cavities on reducing hydrodynamic drag. Conducted in the Emerson Cavitation Tunnel at Newcastle University, the primary objective was to understand the correlation between the length and volume of air cavities and the potential reduction in resistance. The study generated both fundamental and practical knowledge about the air cavity phenomenon. The results demonstrated that air cavities could significantly reduce hydrodynamic drag, effectively showing the relationship between cavity length, volume, and drag reduction. These findings contribute to a better understanding of air cavities and their potential practical applications.

The naval tank experiment described by Jamie Butterworth et al. [39] aimed to assess the effect of an air cavity on a ship’s hull to reduce hydrodynamic resistance. The study used a 2.2 m container ship model, modified to include an air cavity, and conducted a series of tests in a towing tank (Figure 11).

The outcomes of the study indicated a fluctuating decrease in resistance, influenced by both the air flow rate and the ship’s velocity. Alongside assessing the reduction in drag, the research also focused on the influence of the air cavity on the ship’s stability and seakeeping capabilities. To evaluate the effects of integrating an air cavity into the hull, three types of tests were carried out on a container ship model: static stability, resistance, and motion response. The results pointed towards a negligible effect of the air cavity on the ship’s static stability.

The introduction of the air cavity increased the hull’s drag by 10% compared to the standard model. Using various air flow levels resulted in nonlinear outcomes in drag reduction, achieving a 4% saving in drag by merely reducing the wetted surface area by 5%. Limited motion response tests in specific wave conditions suggest that the air cavity can induce nonlinear vertical motion behaviours, potentially affecting drag.

The study by Agostino De Marco et al. [40] involves experimental tests and numerical simulations on a stepped hull model to explore its hydrodynamics. Conducted in a towing tank test, these tests focused on drag, dynamic sinking, and the trim angle of the model. Numerical simulations employed various mesh techniques to model hull motion and water flow. The primary aim was to understand the complex hydrodynamic flow phenomena generated by the stepped hull, especially in the unwetted area behind the step. The naval tank tests revealed complex vortical flow phenomena in the unwetted aft body area of the stepped hull, particularly at towing speeds above 2.36 m/s. These vortices, originating from air spillage at the sides of the step, exhibited complex three-dimensional behaviour. The “down-thrust” method used for the tests enabled precise data collection, crucial for analysing drag, dynamic sinking, trim, and the dynamic wetted surface of the hull. These findings provide significant insight into the hydrodynamic behaviour of stepped hulls.

A significant contribution to the exploration of ACS systems is represented by the experimental study conducted by Cucinotta et al. [41]. This study focused on the towing tank test to evaluate different air cavity configurations in a planing hull (Figure 12). Four hull models (shown in Figure 12; the four models being A, B, C, and D) were meticulously designed and tested at various speeds and air flows, employing an evaluation method based on the Froude method.

The tests examined the towing drag under conditions with and without air flow, thus enabling a comparison of the effectiveness of various air cavity configurations in the hull. Specifically, Figure 13 features two unpublished images from the experimental study conducted at the naval tank of the University of Naples Federico II by the authors Cucinotta et al. [41].

From the analysis of the results, it becomes clear that air cavities in planing hulls lead to a significant reduction in drag when comparing tests conducted without air to those with air. It has been observed that energy savings become more pronounced at speeds exceeding 5.04 m/s, with Model B proving to be the most efficient under all conditions of speed and air flow. For Model C, to discern the effect of air injection, an air flow exceeding 7500 L/min is required at a speed of 5.04 m/s. The air entrainment coefficient (C_Q) (3) used to represent drag data suggests that a value around 1 corresponds to a stationary air cavity. The article also highlights that a more complex hull geometry does not necessarily guarantee improvement, as planing hulls naturally develop low pressure at the bottom, aiding the maintenance of the air layer. Overall, the study provides a detailed analysis of the impact of different air cavity configurations on the drag and hydrodynamic behaviour of planing hulls.

One of the most recent studies on ACS hulls was carried out by Song Lin et al. [42] in a towing tank 135 m long, 7 m wide, and 3.6 m deep. The model (Figure 14a), made from wood–plastic panels, was carefully constructed and equipped with a transparent plexiglass window (Figure 14b).

The tests included various combinations of speeds and initial stern inclination angles, utilizing an air cavity pressure of 50 kPa to examine its impact on the ship’s drag. The model was subjected to drag tests with various air cavity pressures and initial stern inclination angles. Different speed and pressure condition combinations were explored. Drag was measured using a dynamometer, while pitch and inclination angles were detected with specific sensors. Data were collected in real-time via a data acquisition system.

The conclusions of the high-speed Air-Cavity Craft study indicate that selecting an appropriate initial stern inclination angle is key for effectively reducing drag, and this angle should vary with speed. Drag decreases as air pressure increases, stabilizing once optimal pressure is reached. At 50 kPa with a displacement of 125 tons, the minimum drag is observed at a 2.5° angle, showing an 18.3% reduction. Preliminary tests are crucial for validating feasibility and minimizing costs and time.

3. Numerical Studies

3.1. CFD Simulations on MBDR

Different studies have focused on the numerical simulation of the drag reduction via microbubbles. These studies differ in the turbulence model, which can vary between Reynolds-averaged Navier–Stokes (RANS), large eddy simulation (LES), and direct numerical simulation (DNS).

The RANS model has been used in Zhao et al. [43], Mohanarangam et al. [44], Gamal et al. [45], Xia et al. [46], and An et al. [47].

Zhao et al. [43] use an Eulerian–Eulerian two-fluid model in OpenFOAM for its simulations. The approach involves an Eulerian–Eulerian two-fluid model, used for both the continuous liquid phase and the dispersed bubble phase. It considers the interaction of microbubbles with the fluid flow around an axisymmetric body.

The standard k-ϵ model is applied to the continuous phase, while a separate turbulence model within OpenFOAM is used for the dispersed phase (gas).

The Interfacial Area Transport Equation is used to calculate bubble sizes based on the solution of the transport equation for interfacial area density. The model accounts for bubble coalescence and break-up dynamics.

Mohanarangam et al. [44] present a comprehensive study using an Eulerian–Eulerian two-fluid model with the Multiple-Size Group (MUSIG) approach.

An Eulerian–Eulerian framework is used to model both the liquid and bubble phases.

The MUSIG model resolves a wide range of bubble sizes, taking into account bubble coalescence and break-up dynamics.

Standard k-ε and Shear Stress Transport (SST) models are used for turbulence modelling in the liquid phase, while a zero-equation turbulence model is used for the microbubbles.

The results are validated against experimental data, emphasizing the capability of the MUSIG model to accurately represent bubble dynamics in microbubble-induced drag reduction scenarios.

Gamal et al. [45] focus on evaluating the drag reduction effects of microbubbles on container ships. The simulations are performed by solving RANS equations in the form of the realizable k-ε model, considering varying Froude numbers and air flow rates to assess the drag reduction effect.

Xia et al. [46] discuss the drag reduction characteristics of microbubbles on an underwater vehicle during its pitching movement. The study utilizes a Population Balance Model (PBM) to numerically simulate the aggregation and breakup of microbubbles under different ventilation parameters and motion characteristics.

A key aspect of the study is the numerical method established to address the turbulent flow, incorporating different turbulence models. Specifically, the turbulence is modelled using the Shear Stress Transport (SST) k-ω model, which is part of the Reynolds-averaged Navier–Stokes (RANS) methodology.

The results indicate that microbubbles significantly reduce drag, especially when the vehicle is surrounded by them during pitching. This reduction varies with the pitching frequency and angle, highlighting the complex interplay between vehicle dynamics and microbubble behaviour. To validate the numerical model used in the study, the authors conducted water tunnel experiments. These experiments used a self-designed apparatus along with a high-speed camera and a six-component force balance to measure the dynamic loads on the model underwater vehicle during its pitching movements.

By comparing the numerical results with these experimental observations, particularly focusing on the drag and lift coefficients under different conditions (e.g., varying microbubble diameters and ventilation volumes), the paper confirms that the numerical simulations align well with the experimental results. This correlation adds credibility to the effectiveness of the computational model, particularly in its use of the SST k-ω turbulence model.

An et al. [47] present a comprehensive numerical investigation into the microbubble drag reduction on an axisymmetric body submerged in water, particularly focusing on an underwater vehicle. They utilize the Eulerian multiphase model for simulating gas–liquid two-phase flows and employ the k-ω turbulence model to assess turbulence effects.

The paper highlights how microbubbles’ distribution and dynamics, influenced by the k-ω 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 Xiaosong 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 Newton’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.

Xu et al. [49] and Pang et al. [50] use the DNS model to resolve turbulence.

Xu 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.

Pang 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.

3.2. CFD Simulations on ALDR

The air layer method has been studied through numerical simulations performed with the RANS, LES, and DNS methods.

Montazeri and Alishahi [51], J. Zhang et al. [52], Hao and Yongpeng [53], and Ye et al. [54] implemented CFD simulations based on the RANS model.

Montazeri and Alishahi [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.

J. Zhang 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.

Hao and Yongpeng [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).

Ye 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-ε model, a refined version of the standard k-ε model that offers improved handling of strain rates and gradient flows which are prevalent in turbulent boundary layers and separated flows.

The RNG k-ε 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.

X. Zhang [56] study the efficiency of different cavity designs in reducing drag on a flat plate. It uses large eddy simulation (LES) to model turbulence and the Volume of Fluid (VOF) method for two-phase flow simulation, focusing on the air–water interface. The study evaluates the impact of injector direction and front wedge height on air layer formation and drag reduction. It finds that wedge height significantly affects air layer thickness and drag reduction, with simulations showing improved stability and uniformity of the gas layer when reducing the wedge height (Figure 17).

Xu et al. [57] detail a study on the application of the steady Coanda effect for controlling ship air flow, focusing on drag reduction and air wake manipulation using large eddy simulation (LES). The study employs the wall-adapting local eddy (WALE) viscosity model and enhances the flow control capabilities of a baseline Chalmers ship model (CSM) by introducing Coanda surfaces and injection slots at strategic locations on the ship.

The baseline ship model is adapted by adding Coanda surfaces and jet slots along its edges (roof and sides), aimed at manipulating the air flow around the ship.

The numerical model used is large eddy simulation (LES), specifically employing the wall-adapting local eddy (WALE) viscosity model. This approach is chosen for its ability to handle large-scale instabilities and turbulent structures, which are crucial for accurately simulating air flow control around a ship model. LES is particularly effective for fluid dynamics problems where capturing vortices and fluctuating phenomena is essential.

The numerical methods are validated with experimental data from tests conducted on the unmodified baseline model.

Four configurations were tested: a baseline no-jet case, and three jet configurations with varying locations of jet activation (roof, sides, and combined). The simulations reveal that the roof jet, in particular, significantly enhances the Coanda effect, more effectively directing air flow towards low-speed areas on the deck, reducing drag and modifying air wake characteristics.

The findings suggest that the manipulation of air flows using Coanda surfaces and jets can significantly impact ship aerodynamics by reducing drag and stabilizing air wake, which are critical for operations such as helicopter landings on ship decks. The study concludes that jets, especially from the roof, provide substantial benefits by directing high-momentum flows towards critical areas, thereby enhancing overall flow characteristics around the ship.

Kim et al. [58] investigate the air-layer drag reduction (ALDR) mechanism using direct numerical simulations (DNS). It explores different air injection rates and examines the stability and mechanism of ALDR, comparing the effects of high and low air injection rates. The study also includes a theoretical investigation of air layer stability using the Orr–Sommerfeld equations. The research aims to understand the role of the air injection rate on the stability of the air layer and its influence on drag reduction, concluding that the mean reattachment length of the flow is influenced by the presence of the air layer, indicating changes in the flow characteristics due to the air injection.

3.3. CFD Simulations on ACDR

Lotfi et al. [59], Cucinotta et al. [60], Cucinotta et al. [61], Cucinotta et al. [62], Tagliafierro et al. [63], Han et al. [64] and Cucinotta et al. [65] all performed CFD simulations based on the RANS model to evaluate the air cavity ventilation.

Lofti et al. [59] performed simulations with a ship free to heave and pitch. Key parameters like drag, lift, running draft, dynamic trim angle, and wetted area are analysed and compared with experimental data and a semi-empirical method. The CFD utilizes the k−ε turbulence model to consider the effects of turbulent flow. The paper also discusses the wake profile and reattachment location in relation to the stepped hull design.

Cucinotta et al. [60] aim to assess the effectiveness of the RANS CFD approach in studying such ships. The study is divided into two phases: the first phase without air injection, aimed at evaluating the ship’s drag curves, and the second with air injection to study air distribution under the hull. It employs a Shear Stress Transport k-ω turbulence model to simulate the interaction between air and water and assess the impact of injected air on the ship’s drag and air distribution under the hull. The results are compared with experimental data to validate the CFD approach.

Cucinotta et al. [61] employ the k–ε turbulence model for the study of turbulence, simulating different conditions by varying the diameters of air bubbles introduced into the system. These simulations aim to assess the impact of these bubbles on the frictional drag and overall hydrodynamic efficiency of the flat plates, which are a key component in the design and operation of ACS. The research provides insights into the optimization of the air cavity system for enhancing the performance of these specialized ships.

Cucinotta et al. [62] investigate the impact of longitudinal rails on the performance of a single-stepped planing hull with forced air ventilation on the bottom. The study includes a comparison between towing tank tests and CFD analyses. The study focuses on evaluating the effects of these rails on the drag and wetted surface (Figure 18), using the SST k-ω model equations with multiphase models for high-resolution interface capture between air and water. The simulations were performed across a range of velocities and air flow rates. This analysis aims to understand the influence of longitudinal rails on hull performance in terms of drag reduction and air–water interaction.

Han et al. [64] explore the effectiveness of air cavity technology in reducing drag and its impact on the heeling stability of planing hulls.

The study employs the three-dimensional Reynolds-averaged Navier–Stokes equations coupled with the Volume of Fluid method (RANS-VOF). This approach is well-suited for analysing the fluid dynamics involved in the formation and maintenance of air cavities under the hull. The turbulence model used in the study is the SST k-ω model.

The air cavity’s influence on drag reduction is predicted across a range of ventilation rates and heel angles. Various cavity forms, from meniscus growth cavity (MGC) to bottleneck stable cavity (BNSC), are evaluated to understand their effectiveness in drag reduction.

The study identifies critical ventilation rates that optimize drag reduction, noting that excessive ventilation can lead to inefficiencies by expanding the tail air leakage opening, which negatively affects the air cavity’s stability.

Drag reduction effectiveness diminishes at a heel angle of about 2 degrees, where the air cavity shape starts to degenerate, impacting the drag reduction benefits.

The air coverage provided by the cavity influences the ship’s heeling stability. As the heel angle increases, the restoring moment (which helps keep the ship upright) decreases significantly, thereby reducing heeling stability.

The study finds that while air cavities can reduce drag effectively, they also have a complex impact on heeling stability, making the management of heel angles critical for operational safety.

The document concludes that while air cavity technology can substantially reduce drag, thereby improving fuel efficiency and reducing operational costs, it requires careful management of ventilation rates and heel angles to maintain heeling stability. The trade-offs between drag reduction and stability are highlighted as areas for further research and development in marine vessel design.

Cucinotta et al. [65] focus on evaluating the bottom shape of a multi-stepped air cavity planing hull. The study includes both experimental and numerical investigations, varying velocity and air flow rate under the hull. Key areas of analysis include the influence of the Froude number on the air cushion shape and an observation of quantities like the frictional component of drag and air flow path lines, which are difficult to assess through traditional experimental tests. The turbulence model used in their CFD simulations is the SST k-ω.

Mukha et al. [66] evaluate the performance of a planing yacht with air cavity using the LES model.

The first part of the study assesses the drag curves of the hull without air injection using CFD; meanwhile, the second part investigates the injection of air under the hull.

The study includes a comparison between experimental and CFD results. It offers an analysis of the streamlines and air distribution, as well as an assessment of the wetted and ventilated areas of the hull. This evaluation helps in understanding the relationship between the flow rate, the velocity of the hull, and the distribution of air. The findings from this research are instrumental in modifying the hull geometry to better accommodate the air layer.

In additional, Matveev et al. [67] explored artificial cavitation by introducing air under a vessel to reduce drag. The study examined the complex interplay between cavitation and ship propulsion, offering a comprehensive model and parametric study to maximize efficiency. It concluded that while artificial cavitation significantly reduces drag, the actual benefits are influenced by complex interactions between the cavitation and the ship’s propulsion system. The study highlighted the necessity of a nuanced understanding of these interactions to fully leverage cavitation for drag reduction.

Yang et al. [68] reported that the air cavity formed under a stepped planing hull significantly reduced the wetted area of the hull, thereby decreasing resistance and enhancing performance. The CFD simulations used in their study provided insights into the mechanisms through which air cavities influence hydrodynamics, suggesting directions for future hull design optimizations.

Amromin [69] found that the interaction between the ship bottom air cavities and boundary layers could lead to optimized drag reduction if properly managed. The study emphasized the importance of understanding these interactions to predict and control the air demand for ventilated cavities effectively, which is crucial for achieving the desired reductions in resistance and enhancing overall ship efficiency.

4. Mathematical Models

Mathematical models are valuable tools for assessing the performance and, consequently, the drag of ships. When experimental testing is not feasible, a viable solution may involve using previously calibrated mathematical models. These models can also be integrated with experimental tests or CFD simulations to provide more detailed insights into various drag reduction methodologies.

4.1. Models on MBDR

Yoshida et al. [70] present a mathematical model to study the effects of injecting micro air bubbles into the turbulent boundary layer of a liquid stream.

This model is used to analyse how these bubbles influence skin friction in the flow. It employs the Lagrangian method to track the motion of individual bubbles in three dimensions, allowing for the estimation of void fraction distributions across flow channel sections and the behaviour of bubbles locally. The model of the liquid phase is based on the mixing length (Equation (4)), and the interaction between the bubble-induced drag and the liquid phase is considered to assess the impact on turbulent shear stress.

$$l_m=\left(\kappa -\frac{{\lambda }_m}{d_b}{\alpha }^{2/3}\right)y$$

(4)

The mixing length $l_m$ depends on the law of wall constant in the absence of bubbles $\kappa$, the mean turbulence scale ${\lambda }_m$, the bubble diameter $d_b$, the local void fraction $\alpha$, and the y-coordinate.

Equation (4) was developed to represent the reduced skin friction in the presence of bubbles. This equation suggests a decrease in the mean mixing length compared to cases without bubbles, indicating a potential reduction in skin friction due to bubble injection.

To simplify the calculation, the local void fraction $\alpha$ is replaced by a mean void fraction ${\alpha }_m$.

The skin friction ratio could theoretically be influenced by the ratio of bubble diameter to the mean turbulence scale, highlighting an important parameter in understanding the impact of bubbles on skin friction reduction in turbulent flows.

A qualitative comparison with experimental results obtained in a cavitation tunnel has been carried out.

In [18], Sayyaadi and Nematollahi explore the optimal rate of air injection for maximum drag reduction in ships using microbubbles. This experimental study uses a catamaran model to analyse the impact of different air injection rates on drag reduction. The turbulent boundary theory is implemented to calculate the water flow rate inside the boundary layer $Q_w$ in order to estimate the injection coefficient $\alpha$.

The model, under some simplifications, leads to a $Q_w$ formulation in which the water flow rate depends on the ship length L, width W, and speed V (Equation (5)).

$$Q_w=0.293·L^{0.8}·{\vartheta }^{0.2}{V}^{0.8}·W$$

(5)

Different air injection rates have been tested and the results showed that the maximum rate of the drag reduction effect decreases as the speed increases. It was found that if there is an excessive injection of microbubbles, the efficiency of the drag reduction decreases.

In conclusion, the research finds that there is an optimum range of air injection rates that maximize drag reduction, and exceeding this range can decrease the effectiveness of the drag reduction.

4.2. Models on ALDR

In [51], the authors develop a computational model to understand and optimize ALDR on flat surfaces. This is particularly relevant for improving the aerodynamic efficiency of ships.

The study integrates CFD with linear stability analysis. CFD is used to simulate the air–water interface, focusing on how the air layer behaves under various conditions. The linear stability analysis is crucial for identifying the frequencies at which flow becomes unstable. This combination allows for a more accurate prediction of flow instabilities, which is essential for the effective application of ALDR in marine vehicles.

The key innovation in this study is the incorporation of a harmonic perturbation into the CFD model. By doing this, the authors can more accurately mimic the real-world conditions under which these air layers operate. This method showed significant improvements in modelling results when compared to experimental data.

The air layer thickness and velocity profile are extracted from the CFD results and a curve fit is performed.

The two-phase Orr–Sommerfeld equation is then solved to find the frequency of the most unstable mode (Figure 19).

This frequency is used to perform another CFD simulation, this time with an air injection fluctuation with the frequency obtained from Orr–Sommerfeld (Figure 20).

The results from this study provide valuable insights into the physics of ALDR, revealing new aspects not previously observed in experimental tests. This has practical implications for the design of more efficient air lubrication systems on marine vessels, potentially leading to significant reductions in fuel consumption and emissions. The study demonstrates a considerable improvement in the theoretical understanding of ALDR phenomena, bridging the gap between experimental observations and numerical modelling.

4.3. Models on ACDR

In [71,72], Matveev applies a method of hydrodynamic discrete sources for two-dimensional modelling of stepped planing surfaces. The focus is on modelling the deformations of the water surface, wetted hull lengths, and pressure distribution for hulls at various attitudes and Froude numbers, including configurations with pressurized air cavities.

The mathematical model utilizes the Bernoulli equation and hydrodynamic point sources distributed along a horizontal line. It assumes a steady, irrotational, incompressible, and inviscid flow (Figure 21).

The model calculates the water surface elevations, source intensities, and pressure distributions on the hull by solving Equations (6)–(8).

$$C_p=(p-p_0)/(\rho u_0^2/2)=-\sigma$$

(6)

$p_0$ is the upstream pressure, $p$ is the pressure on the water surface, and $u_0$ is the upstream velocity. $\sigma =(p_0-p)/(\rho u_0^2/2)$ is the ventilation number, defined to be zero on the free surface and nonzero on the surface of a pressurized cavity.

$$u^{\prime }(x_i^c)=\frac{1}{2\pi }{\sum }_j\frac{q_j}{x_i^c-x_j^s}$$

(7)

$x_i^c$ and $x_j^s$ are positions of the i-th collocation point and the j-th source with strength $q_j$.

$$\frac{1}{2}(\frac{q_i}{\mathsf{\Delta }{x}_i}+\frac{q_{i-1}}{\mathsf{\Delta }{x}_{i-1}})=-2u_0\frac{y_i^s-x_{i-1}^s}{x_i^s-x_{i-1}^s}$$

(8)

Δx is the cell size and y^s is the water surface elevation at a source location.

The model also considers the lift and drag coefficients, providing insights into the hydrodynamic performance of different hull configurations, including those with open and pressurized cavities.

The paper presents validation examples and parametric calculations for single-step and multi-step hulls, demonstrating the model’s effectiveness in capturing the complex interactions between hull geometry, air cavities, and water flow dynamics.

In [73], the objective is to estimate the loads experienced during the water entry of air-cavity hull sections. It includes drop tests with rigid two-dimensional hull sections simulating air-cavity hulls. These tests varied the platform’s vertical position to observe the impact force reduction.

A mathematical model based on simplified added mass theory is developed. It considers forces on the hull sides (akin to semi-wedges), compression of trapped air in the cavity, and water–air interaction. The model accounts for actual gravitational forces, hull buoyancy, and the force due to adiabatic compression of air in the cavity. The aim was to predict water entry loads, especially assessing how cavity height variations impact force reduction.

The maximum acceleration can be calculated as in Equation (9).

$$a_{max}=\frac{m_{ad,p}}{m+m_{ad,p}}·\frac{4\left|v_0\right|c_w}{b}\sqrt{\theta }$$

(9)

$m_{ad,p}$ is the plate-added mass (which depends on the water density, hull section length, cavity width, wetted half-beam of the wedge, and deadrise angle), $v_0$ is the plate entry velocity, $c_w$ is the speed of sound in water, and $\theta$ is retrieved from empirical correlation.

The model is validated with experimental data, showing a reasonable correlation with the test results, particularly regarding the timing of peak acceleration occurrences.

5. Discussion

In this paper, techniques for reducing drag in maritime applications through air lubrication are explored and classified into three main categories: MBDR, ALDR, and ACDR. A brief description of mathematical models has been included in the paper in order to give the possibility to explore numerical solutions in case it is impossible to have experimental data or conduct tests in a naval tank. While the distinction between MBDR and ALDR depends on achieving a critical drag reduction rate, the primary difference between ALDR and ACDR lies in the presence of a sealed air chamber in ACDR that alters the water–gas interface. The existence of this chamber further reduces drag to motion but also introduces additional drags.

In MBDR, the main theories involve the use of jets to alter the fluid structure in the boundary layer, the effect of microbubbles on turbulent flow, and the formation of a thin film between the water and the wall that reduces shear force. Of great consideration is the implementation of the microbubble injection system on ships; it could be technically complex and usually it requires additional equipment.

Regarding ALDR and ACDR, it is considered that gas injection locally modifies the fluid’s viscosity and density, thus affecting the turbulent Reynolds number. Factors such as bubble size, incoming flow velocity, jet distribution, and gas type significantly impact the effectiveness of drag reduction. In MBDR, effectiveness increases with the reduction in bubble size and the increase in their concentration near the wall. The effectiveness of microbubble injection can vary with the size and type of the ship. It may not provide significant benefits for all types of vessels, and the system’s design must be tailored to the specific characteristics of each ship.

For ALDR, the increase in air injection flow improves the drag reduction rate up to a certain saturation point, after which its influence becomes negligible. The size of the air chamber greatly affects the amount of air needed for saturation and the stability of the chamber itself. Additionally, ALDR and ACDR are influenced by sea conditions, and the ship’s design can play a crucial role in the effectiveness of drag reduction. The appropriate design of the ship’s shape and the grooved structure at the bottom improve the attachment of the air layer or cavity, enhancing the efficiency of drag reduction.

In Figure 22, the papers considered in this research are categorized by year and by topic, using the SCOPUS database as a reference. Before 2016, the major interest was in MBDR, then the number of papers related to ALDR and ACDR increased rapidly going towards 2023.

This could possibly be due to the fact that MBDR is a more established technology and is now implemented mainly on cargo ships, so the research interest is shifting towards less industrially ready technologies like ACDR and ALDR.

All the drag reduction techniques have disadvantages, and they share various challenges in terms of feasibility. For the microbubble system, for example, the implementation of a microbubble injection system could be technically complex, and it requires additional equipment. This system is highly influenced by the marine ecosystem, particularly in its very harsh environment. The hull of the ship is attacked by microorganisms that produce fouling and the efficiency of the microbubble system can decrease in this situation. To maintain the efficiency of the microbubble, the ship needs to be taken to the dry dock and cleaned more regularly, leading to longer downtime during the vessel’s useful commercial life. Also, for systems such as ALDR and ACDR, implementing air layer drag reduction systems can be challenging due to the need for precise control and maintenance of the air layer. Designing systems that are effective across a range of ship speeds and conditions can be complex. In particular, concerning air cavity drag reduction, designers must include a cavity along the bottom of the hull during the design phase.

All these considerations impact on the construction dynamics in various ways, reducing internal spaces that could have been allocated for cargo or passenger areas. All of this needs to be taken into account when conducting a critical analysis of the costs and benefits.

A feedback control system has not yet been studied to correlate the value of air flow to inject with respect to the marine conditions and the speed of the ship. Another aspect to consider is the net energy of these systems. Generating microbubbles or injecting air under the hull require energy, and the energy consumed by the microbubble injection system or by the air injection system needs to be weighed against the potential fuel savings. In some cases, the net energy gain might be a critical consideration. In addition, the initial cost of installing these systems, as well as ongoing operational costs and potential maintenance expenses, needs to be considered. The return on investment must justify the implementation.

From this review analysis, it comes out that there are many studies that emphasize the positive aspects of these technologies and possible issues in terms of their direct impact on the resistance of the applied ship. However, it would be necessary to delve deeper and understand the potential risks in terms of feasibility, costs, and real environmental impact. Understanding how much it costs to have such complex systems on board and how this affects potential commercial space is crucial. Also, the actual energy needs of these systems, and thus the real net energy balance, need to be evaluated.

6. Conclusions

The conclusions of this study highlight the significant potential of air lubrication technologies as an effective method for energy saving and emission reduction in the maritime sector. The research suggests that for the effective application of these technologies on actual ships, both theoretical and practical aspects need to be considered. It is essential to define ship designs that adapt to the specific needs of different air lubrication technologies. Moreover, developing gas injection schemes that improve efficiency and reduce energy consumption, while accounting for environmental factors such as wind and waves, is crucial to maintain the uniformity and stability of gas injection. Additionally, integrating various air lubrication technologies to maximize drag reduction efficiency is a key aspect. It is very important to consider all the aspects of these technologies for understanding their feasibility in the different sectors of the ship industry. The same technology might be suitable for one sector of naval engineering but may not be suitable for another sector. An essential consideration lies in evaluating the net energy costs associated with each of these technologies. This assessment holds particular significance as it directly influences aspects such as net emissions, thereby impacting the overall environmental footprint of the entire system. Understanding the energy consumption of these technologies is crucial for a comprehensive analysis of their sustainability. It forms the basis for assessing their environmental efficiency, ensuring that advancements in naval engineering align not only with technological feasibility but also with environmentally responsible practices, contributing to a more sustainable and ecologically mindful industry. The final but equally crucial aspect pertains to costs. Conducting an in-depth cost analysis is essential, encompassing all stages of these technologies: installation, maintenance, the spatial impact of their presence, net effects on energy expenses, and ultimately, potential decommissioning costs. This comprehensive examination ensures a thorough understanding of the financial implications associated with the implementation and management of these technologies in the field of naval engineering.

The evaluation of all these aspects, focused on feasibility and the actual implementation of such technologies, if positive, will undoubtedly lead to progress and greater encouragement from industries to adopt them, thereby promoting a broader dissemination of these solutions.