1 Introduction

The shipping industry plays a crucial role in the global economy as it primarily relies on ocean-going marine vessels for world trade [1]. However, 60% of fuel consumption in shipping is used to overcome the friction resistance between the ship’s hull and water, leading to the emission of harmful pollutants such as NOx and SOX from the burning of heavy fuel oil [2]. Efforts are being made to mitigate these environmental impacts through various initiatives and regulations [3, 4].

Air lubrication is a technique that has gained significant attention from maritime researchers in recent years due to its ability to effectively decrease friction resistance and ultimately reduce fuel consumption in ships [5, 6]. The frictional drag (\(D\)) can be calculated using

$$D = \frac{1}{2}C_{f} \rho \left( {U_{w} - U_{f} } \right)^{2} A,$$
(1)

where \({C}_{f}\) is the friction coefficient, \(\rho\) is the fluid density, and \(A\) is the area of the wetted hull. \({U}_{w}-{U}_{f}\) represents the relative speed between the ship and the water. The equation demonstrates that drag reduction is a result of the decrease in friction coefficient caused by the presence of bubbles in the boundary layer. The bubbles effectively reduce the wetted surface and lower the fluid density due to bubble inclusion in the boundary layer, contributing to friction reduction [7].

Previous studies [8, 9] demonstrated that drag reduction in turbulent flow regimes was achieved as a result of the inertia effect of air bubbles. This is due to the growth of the boundary layer thickness when the buoyancy force acts outward, resulting in drag reduction. Air lubrication can be performed via three primary methods: (i) the bubble method working based on dispersing bubbles into the boundary layer, (ii) the cavity method utilising a backward step upstream to create a sizeable gaseous space, and (iii) air film method implying long air films or froths to replace extreme shearwater with air [7, 10]. The air film method is found to be the most effective approach, though maintaining the airflow in this method is challenging, particularly at higher speeds. The persistence length of the air film is dependent on the supplied air. The cavity air lubrication method offers some solutions for bubble continuity, while its performance depends on operational conditions, such as ship motions (roll or pitch). In contrast, the bubble method addresses this issue without requiring significant structural changes to the ship hull [11] Ceccio [10] and Murai [7] reviewed the underlying physics and flow structure and important parameters associated with these three methods. Verschoof et al. [12] studied the impact of the void ratio and bubble size on drag reduction. They also showed the effect of bubble deformability on drag reduction in turbulent flows. Zotti and Miotto [13] reported that while the moving ship was subject to both viscous and wave resistance, the viscous effect was dominant at small Froude numbers, representing the ratio of the flow inertia to the external field. It was shown that drag reduction increases at larger airflow rates and lower water speeds [14].

Traditional air lubrication methods have been known to reduce drag by 10–15%. However, these techniques require the use of external compressors, air blowers, porous media, and water electrolysis to generate bubbles. Despite the energy savings achieved through drag reduction, 5–10% of the saved energy is consumed for bubble generation. This means a maximum net drag reduction of 5% for a vessel with a length of 162 m [15, 16]. To address this challenge, Kumagai et al. [17, 18] proposed an innovative device known as the “Winged Air Induction Pipe (WAIP)” (shown in Fig. 1a). This power-saving technology included a hydrofoil with the profile NACA 653–618 installed on the wetted surface of a hull and worked based on the Kelvin Helmholtz instability, which occurs at the interface of multiphase flows with different velocities [19]. The hydrofoil’s span, cord, and angle of attack were assumed to be 240 mm, 40 mm, and 12º, respectively. The low-pressure region between the hydrofoil and the hull derived the air through the pipe into the integrated chamber naturally or without significant air compression. As a result, bubbles and the air layer moved downstream of the device into the turbulent boundary layer, reducing shear stress and drag at shallow draughts [18, 19]. It is worth noting that the negative-pressure region above the hydrofoil was dependent on different parameters, including the vessel speed, the angle of attack and the foil profile. This device was installed on the ship hull, allowing for the use of available kinetic energy to generate bubbles without the need for additional power, particularly in shallow draughts. Duncan [20] studied how a hydrofoil deformed the free surface in a channel. As shown in Fig. 1b, Kumagai [17] found that installing WAIP close to a flat surface can effectively mix air and water to generate small bubbles without the need for additional bubble generators such as porous media. They verified this by observing instability at the air–water surface and the increase in microbubbles due to wave-breaking. This approach resulted in energy savings of 10–15%

Fig. 1
figure 1

Microbubbles generated by the WAIP in Kumagai [17]

Full size image

In a series of real-world trials, the effectiveness of the WAIP technology was evaluated on four ships listed in Table 1. The results indicated that the drag reduction achieved using WAIP ranged from 4 to 16%, depending on factors such as ship size, the number of WAIP applications installed, and the use of external power sources such as compressors Kumagai et al. [17]. Overall, these trials demonstrated the potential for WAIP technology to significantly reduce fuel consumption and increase the efficiency of marine shipping.

Table 1 A summary of experiments on the WAIP in the real world [17]
Full size table

The utilisation of WAIP units is an effective method for reducing drag and improving propulsion efficiency. The WAIP device aimed to reduce the dependence on high-pressure air suppliers for air lubrication in shallow-draught ships. The technique involves injecting air into the water around the hydrofoil, creating a thin layer of air that reduces the friction between the hydrofoil and the water. In this technique, it is important to carefully control the amount of air being injected, as oversupply can lead to bubble accumulation downstream [17]. The critical factor in achieving optimal WAIP performance is maintaining the air–water interface above the hydrofoil [19]. For the ship draughts of less than 5 m, the air suction required for this process may be achieved naturally. However, a compressor is necessary for ships with deeper draughts to overcome the hydrostatic pressure and inject the required air.

Despite the potential benefits of WAIP systems, further research and development are required to fully optimise their performance and achieve significant drag reduction [18]. Previous research on WAIP technology has primarily been limited to two-dimensional configurations and lower ship speeds. Hence, this study aims to further analyse the effectiveness of the WAIP concept for larger ships. For this purpose, it focuses on detailed 3D computational simulations of a modified version of the WAIP technology with improved manufacturability, known as the gas-injected liquid lubrication system (GILLS). The GILLS technique aims to reduce friction resistance by introducing bubbles into the water to lubricate the wetted hull of a shallow-draught ship. The GILLS is designed to drive atmospheric air into the water when the pressure above the hydrofoil is lower than the hydrostatic pressure in the air chamber of the shallow-draught ship. This creates an instability known as the Kelvin Helmholtz instability, which generates and releases bubbles downstream of the hydrofoil. These bubbles act as a lubricant between the water and the wetted hull, resulting in a significant reduction of friction and drag, thus improving the ship’s overall efficiency. The numerical method is initially validated with existing experimental data. This is followed by a parametric study to understand the key factors directly impacting drag reduction. The study concludes with the proposal of the most effective GILLS system, which is characterised by higher fuel efficiency due to the decrease in the need for external power for bubble generation.

2 Problem statement

Figure 2 shows the computational domain and boundary conditions of a catamaran ship. The catamaran is a watercraft that features two demi-hulls of similar dimensions. The Sea Transport Solutions Designed Catamaran ROPAX ferry is 45.9 m long and 16.5 m wide. The sensitivity analysis to mitigate the effects of domain boundaries on the flow near the hull confirmed that a computational domain with dimensions of 180 m (y-direction), 30 m (x-direction) and 45 m (z-direction) is suitable. The upstream and downstream of the ship are assumed to be 1 and 2 times the length of the ship (LShip), respectively, which is consistent with the previous studies [21]. The water depth is determined by adding 30 m to the ship’s draught (30 m + hDraught). To reduce computational costs, only half of the ship is simulated, assuming symmetric flow fields around the YZ plane. The simulations are conducted at three speeds of 12, 16, and 20 knots, with ship draughts set at 1.2 and 1.5 m. All simulations are carried out in transient conditions in smooth sea conditions, as defined by the Douglas sea scale (Degree 2), with waves that have a height range of 0.1–0.5 m [22]. In this study, the height and length of regular waves are assumed to be 0.5 and 6 m, respectively, and modelled using the fifth-order Stokes wave method [23]. The pressure outlet is applied at the outlet, while the velocity inlet boundary condition is considered at the inlet.

Fig. 2
figure 2

Investigated catamaran ferry and computational domain

Full size image

Figure 3(a) shows a schematic view of the GILLS unit, including a blade with the profile of NACA653-618, a span of 240 mm, and a chord of 40 mm. The blade is parallelly aligned with the hull, where the hull is considered locally straight. An air pipe connects the air chamber behind the GILLS unit and atmospheric pressure.

Fig. 3
figure 3

GILLS configuration and arrangement on the catamaran ferry

Full size image

As recommended by the industry partner of this project (Harwood Marine Co.), 20 GILLS units are equally distributed across the two hulls. Figure 3(b) and (c) show the arrangement of GILLS units on the catamaran. On each side of the two wetted hulls, 5 GILLS units are installed in sets of 2 at the front and 3 at the midship. Separate AIPs connect the air chambers to the atmospheric pressure or external power to distribute the air evenly.

3 Methodology

3.1 Mathematical formulations

The Reynolds averaged Navier–Stokes (RANS) equations for a 3D viscous, incompressible, and multiphase flow in the transient state are expressed as:

$$\frac{{\partial U_{i} }}{{\partial x_{i} }} = 0,$$
(2)
$$\frac{{\partial \rho U_{i} }}{\partial t} + U_{j} \frac{{\partial \left( {\rho U_{i} } \right)}}{{\partial x_{j} }} = \frac{\partial P}{{\partial x_{i} }} + \mu \frac{{\partial^{2} U_{i} }}{{\partial x_{j} \partial x_{i} }} + \frac{{\partial \left( { - \overline{{\rho u_{i}{\prime} u_{j}{\prime} }} } \right)}}{{\partial x_{j} }} + \rho g_{i} + f_{\sigma } ,$$
(3)

where \({U}_{i}\) and \({u}_{i}{\prime}\) represent the average fluid velocity and velocity fluctuations, respectively. The Reynolds stress term (\(\overline{\rho {u }_{i}{\prime}{u}_{j}{\prime}}\)) is modelled by the k-ꞷ shear stress transport (SST) turbulence model combining the benefits of the k-ω turbulence model for the inner regions in the boundary layer and the k-ε turbulence model for the free shear flow to predict flow separation and adverse pressure gradients [24, 25]. P is the pressure, \(\rho\) is the density, g is the gravity, and \({f}_{\sigma }\) is the surface tension source [26].

The volume of fluid (VOF) model is adopted to capture the air–water interface and determine liquid volume fraction ζ which varies between 0 and 1 [27]. ζ = 0 refers to a computational cell full of air, whereas ζ = 1 refers to a computational cell full of liquid. While the VOF is an effective approach for such flows, it lacks accuracy in discretising the convection term for sharp surfaces. To address this issue, researchers have proposed the use of High-Resolution Interface Capturing (HRIC) schemes, which combine upwind and downwind interpolations to effectively capture and maintain the sharp interfaces between different phases [28, 29]. The VOF model captures the free surface by (i) determining the free surface location in cells, (ii) considering a sharp intersection between air and water, and (iii) applying boundary conditions on the intersection [30]. The volume fraction is then used to determine the distribution of phases in each cell, thus allowing for accurate fluid flow simulation.

The density (\(\rho\)) and dynamic viscosity (\(\mu\)) of the fluid across the interface are obtained as

$$\rho = \rho_{1} \zeta + \rho_{2} \left( {1 - \zeta } \right),$$
(4)
$$\mu = \mu_{1} \zeta + \mu_{2} \left( {1 - \zeta } \right),$$
(5)

where subscripts 1 and 2 refer to water and air phases.

The interface between air and water is tracked by solving the continuity equation for ζ, as follows.

$$\frac{\partial \zeta }{{\partial t}} + U_{i} \frac{\partial \zeta }{{\partial x_{i} }} = 0.$$
(6)

3.2 Numerical verification

Figure 4 shows a 3D trimmed hexahedral mesh generated using STAR CCM + to achieve a high-quality grid for the complex domain under consideration. To ensure optimal resolution in critical regions, local refinements are implemented through the use of volumetric controls and anisotropic refinements. Furthermore, finer mesh and prism layers are applied on the ship hull to capture the reduction of friction resistance. The height of the first prism layer is carefully selected to achieve desirable y+ values. The comprehensive wall treatment method integrates blended wall functions, ensuring accurate boundary conditions for flow and turbulence across various near-wall mesh densities. The All y+ Wall Treatment approach offers a more effective approach than traditional low-Re or high-Re treatments, particularly when the wall-cell centroid resides in the buffer region. Designed to closely mimic the behavior of both low-y+ treatment for y+ approaching zero and high-Re treatment for y+ greater than 30, it ensures accuracy across a wide range of flow conditions. This method enhances realism in modeling by employing damping functions for source terms in the transport equation and strategically adjusting the model’s source terms within the wall cell using blended wall laws. Recommended for most simulations, the blended wall laws adeptly capture the buffer layer by blending the characteristics of the viscous sub-layer and logarithmic regions. For momentum, Reichardt’s law is leveraged to refine the representation of momentum transfer near the wall [31]. Additionally, a uniform denser mesh is generated around the free surface to accurately capture sharp interfaces. A high mesh density is produced for the analysis of air suction inside the GILLS units and the determination of air lubrication persistence length. A finer mesh is also considered for the bow, stern, leading and trailing edges to ensure optimal resolution, while a coarser mesh is applied for further regions.

Fig. 4
figure 4

Mesh configuration of the computational domain

Full size image

Three different mesh configurations with 2.1, 5.2, and 7.4 M cells are considered for the mesh sensitivity study on the catamaran ferry without GILLS units while the ship speed and draught are assumed to be 12 knots and 1.5 m, respectively. The average friction resistance force on the wetted hull is monitored to check mesh sensitivity in Fig. 4. While increasing mesh size from 2.1 to 5.2 M considerably affects the prediction of the friction resistance force, further refinement to 7.4 M shows a marginal difference. Therefore, the mesh size of 5.2 M is chosen for similar simulations (Fig. 5).

Fig. 5
figure 5

Grid independence mesh study on the average friction resistance force over the wetted hull at speed = 12 knots and draught = 1.5 m

Full size image

While extensive computational studies have adopted the Richardson extrapolation method to estimate the discretisation error, it has limitations such as generalisation and complications [32]. The Grid Convergence Method (GCI) method, modified based on the Richardson extrapolation, provides a more reliable and acceptable estimation defined as follows [32]:

Grid size (h):

$$h = \left[ {\frac{1}{N}\mathop \sum \limits_{i = 1}^{N} \left( {\Delta V_{i} } \right)} \right]^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}}} ,$$
(7)

where ∆V is the cell volume, and N is the number of cells.

Grid refinement factor (r):

$$r = {\raise0.7ex\hbox{${h_{{{\text{coarse}}}} }$} \!\mathord{\left/ {\vphantom {{h_{{{\text{coarse}}}} } {h_{{{\text{fine}}}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${h_{{{\text{fine}}}} }$}}$$
(8)

This factor should be greater than 1.3. Assume h1 < h2 < h3, r21 = h2/h1, and r32 = h3/h2.

The order (p) of the method is calculated using:

$$p = \frac{1}{{{\text{ln}}\left( {r_{21} } \right)}}\left| {ln\left| {{\raise0.7ex\hbox{${\left( {\Phi_{3} - \Phi_{2} } \right)}$} \!\mathord{\left/ {\vphantom {{\left( {\Phi_{3} - \Phi_{2} } \right)} {\left( {\Phi_{2} - \Phi_{1} } \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\left( {\Phi_{2} - \Phi_{1} } \right)}$}}} \right| + ln\left( {\frac{{r_{21}^{p} - 1.sgn\left( {{\raise0.7ex\hbox{${\left( {\Phi_{3} - \Phi_{2} } \right)}$} \!\mathord{\left/ {\vphantom {{\left( {\Phi_{3} - \Phi_{2} } \right)} {\left( {\Phi_{2} - \Phi_{1} } \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\left( {\Phi_{2} - \Phi_{1} } \right)}$}}} \right)}}{{r_{32}^{p} - 1.sgn\left( {{\raise0.7ex\hbox{${\left( {\Phi_{3} - \Phi_{2} } \right)}$} \!\mathord{\left/ {\vphantom {{\left( {\Phi_{3} - \Phi_{2} } \right)} {\left( {\Phi_{2} - \Phi_{1} } \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\left( {\Phi_{2} - \Phi_{1} } \right)}$}}} \right)}}} \right)} \right|$$
(9)

Extrapolated values can be calculated as follows:

$$\Phi_{ext}^{21} = \left( {r_{21}^{p} \Phi_{1} - \Phi_{2} } \right)/\left( {r_{21}^{p} - 1} \right),$$
(10)

The approximate relative error (\({e}_{a}^{21}\)) and extrapolated relative error (\({e}_{ext}^{21}\)) are defined as:

$$e_{a}^{21} = \left| {\frac{{\left( {\Phi_{1} - \Phi_{2} } \right)}}{{\Phi_{1} }}} \right|,$$
(11)
$$e_{ext}^{21} = \left| {\frac{{\left( {\Phi_{ext}^{21} - \Phi_{1} } \right)}}{{\Phi_{ext}^{21} }}} \right|.$$
(12)

Finally, the convergence index (GCI) of the fine grid is calculated as:

$$GCI_{ext}^{21} = \left| {\frac{{1.25e_{a}^{21} }}{{r_{21}^{p} - 1}}} \right|.$$
(13)

Table 2 shows the numerical uncertainty of the fine grid (equal to 0.01) and other corresponding values.

Table 2 Sample calculations of discretization error
Full size table

Furthermore, the same methodology is applied to vessels equipped with 20 GILLS units. However, a finer mesh resolution is deemed necessary in the vicinity of the GILLS units to accurately capture the airflow, as illustrated in Fig. 4b and c. To achieve this, a mesh configuration comprising 6.9 million cells is adopted.

3.3 Numerical validation

The present numerical methodology is validated with Duncan’s experimental data [20]. This validation process has been widely conducted in numerous studies [19, 33]. These investigations predominantly employed the VOF model for capturing free-surface elevation. Furthermore, turbulence terms in RANS simulations are commonly modeled using the k-ω-SST model, followed by the k-ε model, reflecting widespread adoption and application in hydrodynamic studies. A recent study by Pernod et al. [34] further investigated Duncan’s experiments, revealing significant insights. They demonstrated that for submergence depths-to-chord ratios below 2, notable deformations of the free surface and shifts in hydrodynamic forces were observed compared to the deep immersion case.

Duncan [20] experimentally studied the influence of towing a hydrofoil on propagating waves, using a hydrofoil with the profile of NACA 0012 at an angle of attack of 5º with a chord (c) of 203 mm, towed at a speed of 0.8 m/s. In order to replicate the 2D effects reported by Duncan, a 2D numerical simulation is carried out to study the wave propagation caused by the hydrofoil in the experimental study [19, 20]. The computational domain and boundary conditions are assumed based on the study by Zhang et al. [19] for the validation case, which includes a turbulence intensity of 1% and a turbulence length of 1c.

A mesh independence study is also conducted for the validation case where the lift coefficient is analysed using three different mesh resolutions with 172 k, 291 k, and 342 k cells. The results in Table 3 confirm that the impact of mesh is negligible, and as such, the grid with 172 k cells is chosen for further simulations, which is consistent with previous studies [19].

Table 3 Mesh independence study on the validation case
Full size table

Figure 6(a) compares the results of the present numerical method (free surface elevation) with the experimental data [20]. A good agreement is observed between the results up to the wavelength of 2c. The predicted wavelength is also compared to the experimental results at three different inlet Reynolds numbers in Fig. 6(b). The agreement between results proves that the present methodology is sufficiently accurate to study the GILLS configuration. The deviations between the predicted results and the experimental study are 7, 2.8, and 3% at the inlet Re numbers of 110,000, 150,000, and 190,000, respectively.

Fig. 6
figure 6

Validation of numerical results with experimental data [20]

Full size image

3.4 Numerical setup

The finite volume method (FVM) is adopted to discretize the computational domain in Star CCM + V 2022.1 that numerically solves the governing equations (Eqs. 2 and 3). A semi-implicit approach (SIMPLE) is adopted for the velocity–pressure coupling [29]. To balance numerical accuracy and stability, the 2nd-order upwind convection scheme and a 1st-order temporal discretisation are employed [35]. Furthermore, a small time-step of 0.001 s is considered to minimise variations in the solution between consecutive time steps [36].

4 Results and discussion

The results of the parametric study on the performance of 20 GILLS units are analysed and presented in this section to reduce friction resistance on the ship hull. The initial examination focuses on evaluating the effectiveness of natural air suction in GILLS units without using compressors or external power sources. Then, a range of inlet mass flow rates in AIPs are analysed to determine the optimal value resulting in significant drag reduction.

4.1 GILLS performance without external power

According to a study by Kumagai et al. [17], the use of hydrofoils in WAIP design can serve as a self-priming pump in shallow draughts (less than 5 m). This finding highlights the potential for utilising this device as a means of reducing resistance in shallow water conditions. While the hydrofoil may cause inherent resistance, its impact can be negligible compared to the drag reduction resulting from GILLS. In this section, an open boundary condition is assumed for the pipe end in the atmospheric pressure. As depicted in Fig. 7, the air volume fraction within the GILLS units and around the ferry is examined at the speed of 12 knots and a draught of 1.5 m. Based on the legend, blue represents the absence of air, while white indicates maximum air presence. The close-up view of the figure illustrates that while the upper GILLS units can utilise natural air suction, the lower units are filled with water with minimal airflow. This observation emphasizes the need for external power to overcome the hydrostatic pressure at the corresponding depth to effectively utilise the lower GILLS units in this particular operating condition.

Fig. 7
figure 7

Air volume fraction in the domain and air chambers at the speed of 12 knots and a draught of 1.5 m

Full size image

The GILLS units are designed to utilise the principle of natural suction to derive the atmospheric air into the water. To accomplish this, the units are engineered to provide a negative gauge pressure over the hydrofoil (blade) and in the gate entrance of the GILLS [17]. This design concept is illustrated in Fig. 8, presenting cross-sectional pressure contours on sections A–A and B–B shown in Fig. 7. The pressure contours, as indicated by the arrows in Fig. 8, demonstrate that the gauge pressure is negative in the entry gate of the upper units, resulting in natural suction. However, it is noted that the higher hydrostatic pressure present in the lower units, as discussed in Fig. 7, precludes the realization of this phenomenon.

Fig. 8
figure 8

Pressure contours for the front and back sets of GILLS units at the speed of 12 knots and a draught of 1.5 m (negative pressure regions highlighted by the red arrows)

Full size image

The significant difference in predicted pressure at the entry gates of upper and lower units can be attributed to the operational principle of GILLS units, which relies on the Kelvin–Helmholtz instability. This instability occurs at the interface of multiphase flows with different velocities, generating a negative pressure above the hydrofoil. This pressure is greatly influenced by various parameters, particularly the ship’s draught. When the ship’s draught is shallow, this phenomenon effectively operates, but in deeper draughts, it struggles to overcome the static pressure at that depth. Consequently, a negative pressure may not occur in the lower units under such conditions.

4.2 GILLS performance with external power

To address the previously discussed issue, external power is supplied to the AIPs by applying the air mass flow rate conditions to all GILLS units. The schematic diagram depicted in Fig. 9 illustrates the methodology employed for the distribution of compressed air to all 20 GILLS units. As shown in the figure, the utilisation of ball valves allows for precise airflow regulation to each unit, enabling the selective activation or deactivation of individual units as necessary.

Fig. 9
figure 9

Schematic diagram of air distribution from compressors to GILLS units

Full size image

Three air mass flow rates (ṁair) of 0.01, 0.05, and 0.1 kg/s are considered to apply on the API inlets after conducting a parametric study and reviewing correlations provided by Kumagai et al. [18]. Table 4 shows the reduction of the average friction resistance obtained from different air mass flow rates at two ship speeds. The reduction of the friction resistance (\(\Delta D\)) is calculated using Eq. 14 based on the results obtained in Sect. 4.1 for the ship without GILLS.

$$\Delta D = \frac{{D_{{\text{simple ship}}} - D_{{\text{ship with GILLS}}} }}{{D_{{\text{simple ship}}} }} \times 100,$$
(14)

where D is the friction resistance force and subscripts “simple ship” and “ship with GILLS” refer to the ship without and with GILLS, respectively.

Table 4 Effect of including 20 GILLS units on the average water friction resistance for various airflow rates and at a draught of 1.5 m
Full size table

As seen in Table 4, incorporating air suppliers into the GILLS units results in a notable enhancement in the reduction of friction resistance. The results indicate that as the air mass flow rate increases from 0.01 to 0.05 kg/s, there is a decrease in friction resistance for both ship speeds evaluated. Notably, the highest reduction in friction resistance is achieved at a ship speed of 20 knots. However, it should be noted that further increasing the air mass flow rate from 0.05 to 0.1 kg/s results in a minimal reduction in friction resistance despite the additional costs associated with larger air suppliers. This is consistent with the previous study by Kumagai et al. [18], which reported that further increases in the airflow rate may lead to the complete detachment of the hydrofoil from the water flow and obstruct the air injection process.

4.3 Performance of GILLS hybrid

The results in Sect. 4.2 confirmed that the air supply assisted the lower GILLS units in performing better. However, this comes at the cost of external power required to supply air. In this section, we introduce a cost-effective configuration for GILLS units, harnessing natural air suction for the upper units while employing compressors only for the lower units to deliver forced compressed air, as illustrated in Fig. 10. The mass flow rate of air emerges as a crucial parameter affecting the GILLS system’s performance. An optimal mass flow rate of 0.05 kg/s in Table 4 results in the optimum reduction of friction resistance. Hence, this boundary condition is considered for the forced compressed air of the lower GILLS units. The GILLS system’s performance is numerically evaluated, and the results indicate that this hybrid configuration has a significant potential to reduce friction resistance with ∆D = 10.41% at the speed of 20 knots and a draught of 1.5 m. The observed reduction closely aligns with the performance exhibited when forced compressed air is introduced at all inlets, with the air mass flow rate of 0.05 kg/s, reported in Table 4, while consuming less air flow rates and requiring less compressor power.

Fig. 10
figure 10

Schematic diagram of air distribution for the hybrid GILLS units

Full size image

The proposed hybrid GILLS configuration, integrating both natural air suction and forced compressed air, demonstrates a promising solution for significantly mitigating friction resistance within the system. By harnessing the synergistic effects of these two approaches, the hybrid configuration demonstrates remarkable efficiency in reducing resistance while ensuring optimal performance. Notably, this configuration demands considerably less external power when contrasted with alternative systems, underscoring its potential as a cost-effective and energy-efficient solution for enhancing fluid flow dynamics.

To shed more light on the reduction of friction resistance by the hybrid model, Fig. 11 offers a comparative overview of the wall shear stress distribution over the hulls of two distinct scenarios: one without GILLS and another incorporating the hybrid GILLS system. Both scenarios operate under identical conditions, with a vessel speed of 20 knots and a draught of 1.5 m.

Fig. 11
figure 11

Wall shear stress on the ship hull (bottom view) at speed = 20 knots and draught = 1.5 m

Full size image

The findings reveal a noteworthy pattern: while both vessels exhibit high shear stress levels at their leading edges and bows, the ship fitted with the hybrid GILLS system shows a remarkable decrease in shear stress along its hull. This substantial reduction in shear stress signifies the efficacy of the hybrid GILLS system in mitigating friction resistance across the catamaran ship’s hull. These observations carry significant implications for the design and optimisation of ship hulls. By demonstrating the tangible benefits of integrating the hybrid GILLS system, this study underscores the potential for enhancing vessel performance and efficiency in real-world maritime operations.

Table 5 presents a comparison of the ratio of friction resistance to surface area at three different submerging depths for a ship equipped with a hybrid GILLS system. This ratio could be an important indicator of the friction resistance independent of the wetted surface. The results demonstrate that as the submerging depth increases, this ratio also increases due to the combined effects of buoyant force and the increased pressure on the catamaran ship’s hull at deeper depths. Based on these findings, it is recommended to use more GILLS units in deeper submerging conditions. This is supported by the observations of this study that 60% of all GILLS units are placed within a distance of 0–1 m from the ship keel.

Table 5 Friction resistance of the hybrid model at different zones at a speed of 20 knots and a draught of 1.5 m
Full size table

It can be concluded that the use of the hybrid configuration can effectively reduce the drag on ships and thereby improve their efficiency. The results of this study provide valuable insight into the design and optimisation of the GILLS system, and they could be used as a reference for further research in this field. Further research is required to validate these findings with actual data and to explore the potential benefits of implementing these recommendations in different real-world scenarios.

5 Conclusions

The study aimed to evaluate the efficiency of a novel technique, the GILLS, in reducing friction between water and the surface of marine vessels. Unlike traditional air lubrication methods, GILLS requires minimal external power to introduce air bubbles between the water and the wetted surface of marine vessels. The computational fluid dynamics model, based on the VOF approach, enabled the simulation of the interaction between water and air in real-world conditions. Through simulations conducted under smooth sea conditions, the effectiveness of GILLS in decreasing friction resistance was demonstrated. Key findings indicate that GILLS offers a promising solution for reducing friction resistance and enhancing fuel efficiency in marine transportation, potentially contributing to meeting environmental regulations without requiring extensive engine modifications. The main findings can be summarized as follows:

  • The ship’s speed and draught could directly affect the friction resistance across the wetted hull. An increase in the ship’s speed from 12 to 20 knots and draught from 1.2 m to 1.5 m resulted in a remarkable increase in friction resistance.

  • While the GILLS is designed to work naturally at shallow ships, the GILLS units at deep depths require external power to expel airflow into the water.

  • Applying uniform air mass flow rates of 0.01, 0.05, and 0.1 kg/s to each GILLS unit reduced the friction resistance by 8.74, 9.11, and 9.15% for the speed of 12 knots and 10.36, 10.43, and 10.45% for the speed of 20 knots at the draught of 1.5 m.

  • A hybrid model consisting of 60% GILLS with natural air suction and 40% GILLS connected to the compressors with a mass flow rate of 0.05 kg/s resulted in 10.41% friction resistance reduction at the speed of 20 knots and the draught of 1.5 m.