Parametric CFD-FEA Study on the Aerodynamic and Structural Performance of NaviScreen for Wind Resistance Reduction in Medium-Sized Commercial Ships

Abstract

Meeting the International Maritime Organization’s (IMO) 2050 targets for reducing greenhouse gas (GHG) emissions requires cost-effective solutions that minimize wind resistance without compromising safety, particularly for medium-sized multipurpose vessels (MPVs), which have been underrepresented in prior research. This study numerically evaluates 20 bow-mounted NaviScreen configurations using a coupled high-fidelity computational fluid dynamics (CFD) and finite element analysis (FEA) approach. Key design variables—including contact angle (35–50°), lower-edge height (1.2–2.0 m), and horn position (3.2–5.3 m)—were systematically varied. The sloped Type-15 shield reduced aerodynamic resistance by 17.1% in headwinds and 24.5% at a 30° yaw, lowering total hull resistance by up to 8.9%. Nonlinear FEA under combined dead weight, wind loads, and Korean Register (KR) green-water pressure revealed local buckling risks, which were mitigated by adding carling stiffeners and increasing plate thickness from 6 mm to 8 mm. The reinforced design satisfied KR yield limits, ABS buckling factors (>1.0), and NORSOK displacement criteria (L/100), confirming structural robustness. This dual-framework approach demonstrates the viability of NaviScreens as passive aerodynamic devices that enhance fuel efficiency and reduce GHG emissions, aligning with global efforts to address climate change by targeting not only CO2 but also other harmful emissions (e.g., NOx, SOx) regulated under MARPOL. The study delivers a validated CFD-FEA workflow to optimize performance and safety, offering shipbuilders a scalable solution for MPVs and related vessel classes to meet IMO’s GHG reduction goals.

1. Introduction

The maritime industry is at the forefront of addressing the dual challenges of sustainability and energy efficiency. Driven by global mandates such as the International Maritime Organization’s (IMO) 2050 decarbonization strategy, the transition toward eco-friendly practices has become increasingly urgent. This ambitious plan seeks to markedly lower greenhouse gas (GHG) emissions by adopting cutting-edge technologies and alternative energy sources. Among numerous solutions, wind energy conversion systems and aerodynamic optimizations emerge as critical strategies for reducing fuel consumption and promoting environmental stewardship within the shipping sector. As wind energy gains viability, efforts have focused on its seamless integration into modern vessel designs. These systems, drawing inspiration from traditional sailing methods yet enhanced with advanced materials and engineering, offer a renewable and cost-effective energy source. For example, NaviScreens and sails are being reengineered as dynamic components that both diminish aerodynamic drag and capture wind power to propel vessels more efficiently. Such innovations highlight the fusion of traditional maritime knowledge with modern technological advancements.

Despite the growing interest in aerodynamic optimization of ship structures, research on Wind Caps (or NaviScreens) has remained limited, with most studies focusing on large container ships or high-speed ferries. Recent advancements in computational fluid dynamics (CFD) have facilitated high-fidelity aerodynamic simulations of Wind Caps across various ship categories, including medium-sized commercial vessels. This study aims to advance the field by investigating the effect of Wind Caps on reducing aerodynamic resistance in an 82 m-class commercial vessel through CFD-based numerical analysis. Furthermore, we explore the structural challenges presented by green water pressure on NaviScreen structures. Green water is a phenomenon where large waves inundate the deck, and it imposes significant loads on the exposed structures, thereby testing their resilience and safety. Analyzing and reinforcing these structures is essential to ensure that energy-saving devices such as Wind Caps function reliably within harsh marine environments.

This research assesses the design and structural integrity of NaviScreens, a drag reduction device for large ships, via numerical analysis and proposes reinforcement strategies, including Carling reinforcement and thickness optimization. The study contributes to the broader discourse on sustainable and efficient shipping by providing practical insights into balancing environmental objectives with engineering feasibility, thereby advancing the progress of the maritime industry toward a greener future. A summary of relevant previous studies is provided below.

Andersen [1] examines wind loads on a 9000 TEU Post-Panamax container ship through wind tunnel experiments, analyzing the impact of container stacking configurations on wind forces and moments. Their results demonstrated that gaps between container stacks increase resistance by up to 100%, whereas aerodynamically optimized stacking reduces drag and yaw moments significantly.

Wnek & Soares [2] conducted a comparative study of wind loads on LNG carriers and floating LNG platforms using numerical analysis (CFD) and wind tunnel experiments. They calculated wind coefficients in the X and Y directions, as well as yaw moment coefficients, through numerical analysis, employing various mesh settings and analysis models to enhance result reliability. Generally, the numerical analysis aligned reasonably well with the wind tunnel experiment outcomes. However, the study observed minimal measured loads due to low wind speeds (10 m/s), and sensor sensitivity limitations affected result accuracy. Consequently, additional experimental investigations under high wind speed conditions are required.

Yunsik et al. [3] concentrate on aerodynamic modifications of container ship superstructures to minimize air resistance. The findings indicate that obstructing airflow between container gaps can decrease air resistance by up to 56%, making it the most effective approach. The findings provide insights into design optimization for fuel efficiency and emission reduction in large container ships.

Janssen et al. [4] quantitatively examined the impact of increased wind resistance on ship operations and port activities as container ships grow larger, utilizing numerical analyses and wind tunnel test data. The study evaluated how incorporating the spacing between containers and the intricacies of hull shape detail influenced wind load outcomes. Refining the shape of the ship reduced the disparity between numerical analysis and wind tunnel results, and integrating container spacing into the model decreased wind load by approximately 10%.

Fujiwara et al. [5] introduced a novel method for estimating wind forces and moments on ships using a component-based aerodynamic model. This technique segments a ship’s superstructure into several components, each individually analyzed in wind tunnel tests. Validated against full-scale measurement data, this approach enhances the predictive accuracy for ship design and maneuvering simulations.

Trivyza et al. [6] investigates aerodynamic effects on megayacht superstructures and their impact on passenger comfort and helicopter operations. Employing CFD simulations, the study assesses flow separation, turbulence, and vortex formation around the superstructure at various wind angles. Findings indicate that airwake turbulence becomes highly unstable at elevated wind speeds, making helicopter landings unsafe above 20 knots.

Majidian et al. [7] developed an advanced wind resistance prediction model for container ships operating under oblique wind conditions using CFD simulations and statistical data. Their research validates the model against actual voyage data from a 2748 TEU container ship. The proposed image method for modeling wind–sea interactions enhances prediction accuracy compared to conventional models.

Ricci et al. [8] presented results from a numerical CFD analysis of wind loads on a large passenger ship moored at the Rotterdam passenger terminal under various wind directions. A high-resolution mesh was utilized to accurately represent the ship’s structure and the distribution of wind load in relation to surrounding high-rise buildings. There are some deviations between the numerical analysis results derived from the study and the wind tunnel experiment, and it is necessary to always use the large eddy simulation (LES) model to improve the accuracy.

Portell [9] demonstrated the aerodynamic performance of a car carrier’s wind sail under extreme conditions using CFD simulations. The simulation results closely aligned with experimental data, though discrepancies appeared at certain angles. To more reliably validate the numerical analysis results, acquiring additional wind tunnel experimental data is necessary, and the impacts of vibration and fatigue induced by dynamic stall and vortex shedding on structural safety require more comprehensive analysis.

Yoo et al. [10] quantified the wind load generated when an FPSO and a shuttle tanker are positioned side by side during unloading operations through numerical simulations. The variations in wind load and shielding effects relative to the distance between the two vessels were analyzed and compared with wind tunnel experiments. The shuttle tanker exhibits a heightened shielding effect from the FPSO, evidenced by a reduced wind load coefficient. Owing to the limited precision of the experimental data and variations in the testing environment, discrepancies arose between experimental outcomes and numerical analyses at certain angles.

Gu et al. [11] examined the dynamic response of a structure using a numerical analysis technique that accounts for the combined effects of nonlinear wave loads and structural deformation. The validity of the CFD–FEA method was established by comparison with both the existing latent flow-based model and the nonlinear numerical model. The CFD–FEA method successfully captured nonlinear wave interactions and simulated them more realistically than the latent flow-based model. To mitigate the high computational costs associated with the CFD–FEA method, efficient mesh configurations and enhanced calculation algorithms are necessary. Moreover, obtaining additional tank experimental data is essential to improve the reliability of the numerical analysis results.

Wang et al. [12] assesses various windshield shapes, identifying the optimal design that decreases aerodynamic drag by 20.67% under headwind conditions. The results demonstrate that windshield geometry significantly influences wind resistance and that advanced optimization techniques improve design efficiency.

Extensive research has been conducted to evaluate aerodynamic and hydrodynamic loads on marine structures using computational and experimental methods, yet significant limitations persist in both scope and methodology. Early foundational work by Wnek and Soares [2] employed comparative analyses between CFD simulations and wind tunnel experiments for LNG carriers and floating platforms, revealing critical discrepancies attributed to sensor sensitivity limitations and low wind-speed conditions; their findings underscored the necessity for high-wind-speed experimental validation to improve computational accuracy, though their focus remained narrowly confined to validation challenges without addressing structural implications. Janssen et al. [4] expanded the field by examining wind resistance in large container ships, demonstrating how vessel size amplifies aerodynamic drag and advocating for refined geometric modeling using RANS-based simulations; however, their work prioritized aerodynamic performance metrics while neglecting the structural integrity of drag-reduction devices under operational loads—an oversight similarly evident in Ricci et al. [8], who investigated wind loads on moored passenger ships near urban structures but limited their analysis to localized pressure variations without extending their methodology to structural reinforcement strategies. The most comprehensive aerodynamic optimizations were achieved by Nguyen and Watanabe [13,14,15,16,17] in their seminal series on 20,000 TEU container ships, where they systematically evaluated bow modifications, container arrangements, and wake-control devices, achieving up to 24% drag reduction through combined CFD and wind tunnel testing. Despite these advancements, their studies suffered from two critical shortcomings: first, their exclusive focus on ultra-large container ships left smaller vessel classes like MPVs unexplored; second, their optimization protocols ignored structural resilience under extreme environmental loads such as green water impacts, rendering their designs potentially vulnerable in real-world conditions. Similarly, while Portell [9] and Yoo et al. [10] made strides in analyzing wind sails and shielding effects, respectively, their work lacked integration with structural finite element analysis, and Gu et al. [11], though pioneering a CFD-FEA hybrid approach, focused on wave-structure interactions rather than aerodynamic devices, leaving unresolved the dual challenge of drag reduction and structural robustness.

This study transcends these limitations by introducing a holistic CFD-FEA framework that simultaneously optimizes aerodynamic performance and structural integrity for NaviScreens on medium-sized MPVs, a vessel class historically overlooked in prior research. Through systematic parametric analysis of 20 NaviScreen configurations, we identified the Type-15 design as optimal, achieving a 17.1% reduction in aerodynamic resistance under headwinds and 24.5% under oblique winds (30° yaw), while concurrently addressing the structural vulnerabilities inherent in prior designs. Crucially, our nonlinear FEA under combined deadweight, 50 m/s wind, and KR-classified green water pressure revealed localized buckling risks, which we mitigated through carling stiffeners and plate-thickness optimization (6 mm to 8 mm) interventions absent in earlier studies. The reinforced design not only satisfies KR yield limits but also exceeds ABS buckling factors (>1.0) and NORSOK displacement criteria (L/100), ensuring operational resilience in extreme environments.

2. Structure for Air Resistance Reduction

Main Components and Specifications

Figure 1 depicts a standard aerodynamic drag reduction structure mounted on the bow of a container vessel.

Similar to the roof fairing of a truck, this structure significantly diminishes air resistance in the extensive stagnant zone of the bow, which increases fuel efficiency and reduces GHG emissions [3].

The design streamlines the upper structure to minimize operational air resistance, enhance fuel efficiency, and decrease GHG emissions. The air resistance reduction structure, specifically the configurations denoted by solid lines in

Table 1. Summary of ships with windshield application performance.

Country	Company	Name	Ship Shape
Japan	Mitsui OSK Lines	MOL Marvel
Japan	Mitsui OSK Lines	ONE Trust ONE Tradition
France	CMA CGM	CMA CGM Marco Polo
France	CMA CGM	CMA CGM Paraty
Italy	MSC	MSC SYDNEY VI
Korea	Samsung	SAVER-WIND(C)

, exhibits key aerodynamic features aimed at minimizing drag forces on MPVs. These designs are chiefly defined by sloped, streamlined geometries that effectively reduce pressure buildup in stagnation zones, thereby optimizing airflow around the upper structure. The chosen configurations feature a sloped windshield design with optimized bow ratio angles between 35° and 50°. These angles are critical for channeling incoming airflow smoothly over the superstructure, thereby preventing excessive turbulence and flow separation. The lower edge height of the NaviScreen is maintained between 1200 mm and 2041 mm, ensuring optimal aerodynamic performance while meeting operational visibility requirements. Moreover, the presence and placement of a guiding horn markedly affect aerodynamic efficiency. Positioned at heights ranging from 3214 mm to 5338 mm, the horn serves as an auxiliary flow-directing element that promotes airflow attachment and minimizes the formation of recirculating wakes behind the structure. CFD simulations of these configurations indicate a maximum aerodynamic resistance reduction of approximately 17.1%, with certain designs achieving resistance decreases between 17.0% and 17.1% under standard operational conditions. Notably, configurations with bow angles of 35° (Type-15) and 50° (Type-19) exhibited superior performance, with Type-15 attaining the highest overall drag reduction efficiency. Additionally, the effectiveness of these designs was assessed under operational wind conditions. In scenarios representing a Beaufort scale 6 wind environment (12.35 m/s headwind), the selected configurations consistently maintained drag reduction performance, with Type-15 and Type-19 achieving roughly a 16.3% decrease in aerodynamic resistance, thereby enhancing vessel fuel efficiency. The performance of these structures under oblique wind conditions was also investigated.

The Type-15 configuration exhibited the highest aerodynamic resistance reduction at a wind angle of 30°, achieving a maximum attenuation effect of 24.5%, while maintaining operational feasibility. The findings indicate that the synergistic combination of sloped front geometry and an optimized guiding horn significantly enhances aerodynamic stability across diverse real-world wind conditions. By incorporating these aerodynamic improvements, MPVs can achieve a measurable reduction in fuel consumption, leading to decreased GHG emissions. The study demonstrated that total hull resistance decreased by up to 2.9% under typical operational scenarios, correlating directly with enhanced energy efficiency and adherence to International Maritime Organization (IMO) decarbonization targets.

This metric contextualizes the role of aerodynamic modifications within vessel design, underscoring the importance of drag-reduction devices in contemporary shipping. Figure 2 illustrates the MPV, a medium-sized, 91.4-m-long specialized ship primarily intended for transporting supplies, equipment, and personnel to offshore installations such as oil rigs, platforms, or other vessels. The figure supports the study by showing the location of the NaviScreen structure, thereby clarifying its placement and interaction with other ship components.

Figure 3 showcases the detailed 3D model of the MPV utilized for evaluating aerodynamic and hydrodynamic performance through CFD analysis. The model encompasses intricate superstructure elements, including the optimized NaviScreen configuration, ensuring precise simulation of airflow patterns and resistance characteristics. The model reflects the actual hull form and appendages as per the principal dimensions listed in

Table 2. Principal dimension of MPV (multipurpose vessel).

Item	Value
Length Overall	95.2 m
Length Between Perpendiculars	93.1 m
Breadth (Mold)	18.5 m
Depth	7.0 m
Draft (Scantling)	4.8 m
Gross Tonnage	5100 t
Speed	18 knots
Classification	Multipurpose Vessel

, such as an overall length of 95.2 m and a beam of 18.5 m. Integrating the modified NaviScreen directly into the upper bow region allows this enhanced model to more accurately predict pressure distribution, stagnation zones, and separation effects under head and oblique wind conditions. This refinement improves the precision of drag reduction estimates and forms the foundation for subsequent optimization studies.

The MPV represents a groundbreaking platform for validating multi-fuel decarbonization technologies in maritime applications. As the world’s first ship integrating MW-scale batteries, hydrogen fuel cells, and carbon-neutral combustion engines, it enables comparative performance analysis of diverse propulsion systems under real operating conditions. Its 1100 V DC power distribution system optimizes energy efficiency in hybrid operations, while modular architecture allows dynamic selection of propulsion modes to minimize emissions. The vessel complies with IMO’s Carbon Intensity Indicator (CII) regulations and contributes to international safety standards through its publicly available full-ship fire simulation model (IMO MSC 109/MF.12). Energy-saving innovations include drag-reducing hull appendages, rotor sails, and low-noise propellers, supported by AI-driven hybrid system optimization. Designed initially with LNG dual-fuel capability, the MPV serves as a scalable testbed for carbon-reduction technologies, with active participation in ISO standardization efforts (e.g., ISO AWI 18962 for shipboard batteries) [18].

3. CFD Simulation

3.1. Numerical Analysis Method

The CFD simulations were performed using the commercial software STAR-CCM+ (version 10.03) to evaluate the aerodynamic performance of the proposed NaviScreen configurations for the MPV. The incompressible turbulent flow field was solved using the finite volume method (FVM) with the governing equations consisting of the continuity equation and the Reynolds-averaged Navier–Stokes (RANS) equations. Turbulence closure was achieved with the SST $k-\omega$ model, which offers improved predictive accuracy in separating flows under adverse pressure gradients [12].

The general form of the governing equations can be expressed as follows:

$${\displaystyle \frac{\mathsf{\partial }\rho }{\mathsf{\partial }\mathrm{t}}}+\mathsf{\nabla }·\left(\rho u\right)=0$$

(1)

$${\displaystyle \frac{\mathsf{\partial }\rho u}{\mathsf{\partial }\mathrm{t}}}+\mathsf{\nabla }·\left(\rho uu\right)=-\mathsf{\nabla }p+\mathsf{\nabla }·\tau -\mathsf{\nabla }·(\rho \overline{u^{\prime }{u}^{\prime }})+\rho g$$

(2)

where the Reynolds stress term −$\rho \overline{u^{\prime }{u}^{\prime }}$ is modeled according to the SST $k-\omega$ turbulence closure.

As previously mentioned, the numerical analysis of MPV was conducted using two distinct approaches to enhance computational efficiency. The numerical methods used in each simulation are summarized in

Table 3. Numerical methods for multiphase fluid analysis simulation.

Key Features	Model
Governing Equation	Reynolds-averaged Navier–Stokes
Time	Implicit Unsteady
Temporal Discretization	Second-Order Upwind
Time-step	0.001 s
Turbulence Model	SST (Menter) $k-\omega$
Wall Treatment	All Y+ Treatment
Y+	<50
Spatial Discretization	Cell centered FVM
	Second-Order Upwind
No. of grid	6.41 M
Velocity/Pressure coupling	SIMPLE Algorithm
Multiphase Model	VOF (Volume of Fluid)
Free surface problem	VOF waves (Flat Waves)

and

Table 4. Numerical methods for single-phase aerodynamic analysis simulation.

Key Features	Model
Governing Equation	Reynolds-averaged Navier–Stokes
Time	steady
Temporal Discretization	Second-Order Upwind
Turbulence Model	SST (Menter) $k-\omega$
Wall Treatment	All Y+ Treatment
Spatial Discretization	Cell centered FVM
	Second-Order Upwind
No. of grid	10.66 M
Velocity/Pressure coupling	SIMPLE Algorithm
Phase Model	Air

.

In this research, the computational domain and boundary conditions were refined based on established methodologies [19]. As illustrated in Figure 4, the computational domain was designed to adhere to the minimum length guidelines recommended by the ITTC [20], corresponding to the length overall (LOA) of the ship. To minimize computational time, a symmetry condition was imposed along the centerline of the ship, and a velocity inlet boundary condition was established at the domain inlet to replicate the ship’s forward speed (Vs).

Additionally, to maintain physical continuity, a velocity inlet condition was applied to the upper boundary of the numerical domain, whereas a pressure outlet condition was designated at the rear boundary. The lower boundary conditions varied between the two simulations: for the multiphase fluid analysis, a velocity inlet condition was utilized to preserve physical continuity; in contrast, for the single-phase aerodynamic simulation, a wall boundary condition was implemented to represent the free surface.

Figure 5 presents the updated mesh generation strategy for both aerodynamic and hydrodynamic simulations. Specifically, Figure 5a depicts the refinement of the free surface and the incorporation of prism layers adjacent to the hull and waterline, ensuring precise resolution of boundary layers and free surface interactions. Figure 5b highlights the localized mesh refinement applied to the superstructure and the NaviScreen region, where flow separation and recirculation are expected to occur. A high-resolution unstructured mesh, primarily composed of hexahedral and prismatic elements, was created, encompassing approximately 10.6 million cells for aerodynamic simulations. The mesh topology was refined to satisfy Y+ criteria for the SST k–ω turbulence model, ensuring accurate prediction of turbulent flow around the NaviScreen. This advanced meshing technique improves numerical precision in capturing drag-related phenomena and directly supports the aerodynamic efficiency analysis outlined in Section 3. The analysis of the grid convergence in this study was conducted through grid uncertainty analysis using Richardson’s extrapolation formula, and the convergence of the grid system was determined by estimating the virtual solution (ϕ_0) when the grid spacing becomes 0 [21].

3.2. Numerical Analysis Results of Design Models

The initial numerical analysis results for the MPV are summarized in

Table 5. First numerical analysis results of the MPV.

Case	Draft (m)	A.S.A (m2)	RT_A (N)	W.S.A (m2)	RT_W (N)	RT (N)
Case01	3.60	2457	2605	1573	105,315	107,920
Case02	4.00	2402	2533	1649	111,918	114,451

A.S.A denotes the air-contact surface area, RT_A denotes the wind resistance on the upper hull, W.S.A denotes the water-contact surface area, RT_W denotes the hydrodynamic resistance, and RT denotes the total resistance (aerodynamic plus hydrodynamic).

. These encompass a multiphase hydrodynamic simulation of the lower hull and a single-phase aerodynamic simulation of the upper structure prior to NaviScreen implementation. The total resistance of the hull was calculated as follows:

This study focused on the NaviScreen design to minimize aerodynamic resistance in the MPV. The initial NaviScreen shapes were based on actual ship designs and are displayed in Figure 6. These shapes underwent aerodynamic CFD simulations to assess their effectiveness in reducing resistance. The final NaviScreen designs were optimized through performance analyses and adherence to additional design requirements.

The initial NaviScreen shapes were refined by integrating design criteria to create a NaviScreen suitable for MPV applications.

Table 6. Design features of MPV NaviScreens.

Design Features (○ = Present/Applied; × = Absent/Not Applied)
Model	Sloped	Width	Horn	Side Extension	Top Extension
Type-1	Smooth	Wide	×	×	×
Type-2	Angled	Wide	×	×	○
Type-3	Smooth	Narrow	○	○	○
Type-4	Smooth	Narrow	○	×	○
Type-5	Smooth	Narrow	×	○	×
Type-6	Smooth	Narrow	○	○	×
Type-7	Smooth	Narrow	○	○	○
Type-8	Smooth	Narrow	○	○	○

presents a comparative overview of the key design features across eight initial NaviScreen configurations (Type-1 to Type-8) evaluated for aerodynamic drag reduction on multipurpose vessels (MPVs). The table systematically categorizes each model based on four critical design parameters: (1) slope geometry (smooth or angled), (2) width (wide or narrow), (3) presence of a horn (a flow-directing protrusion), and (4) extensions (side or top). Notably, Type-1 and Type-2 represent baseline designs with wide profiles but differ in slope geometry (smooth vs. angled) and the inclusion of a top extension in Type-2. In contrast, Type-3 through Type-8 feature narrower widths, with variations in horn placement and extension configurations. For instance, Type-3 and Type-7 incorporate all three enhancements (horn, side, and top extensions), while Type-5 omits the horn but includes a side extension. This parametric variation underscores the study’s objective to isolate the aerodynamic effects of individual design elements. The absence of horns in Type-1, Type-2, and Type-5 highlights a deliberate exploration of streamlined vs. flow-controlled designs, whereas the consistent use of side/top extensions in later models (e.g., Type-6–Type-8) suggests their hypothesized role in mitigating turbulence. The table’s structured comparison lays the groundwork for subsequent CFD simulations, which quantitatively assess how these features influence drag reduction, a methodology pivotal to identifying optimal configurations like the sloped Type-15 (

Table 7. Third numerical analysis results of NaviScreens (slope).

Case	Bow Ratio (°)	Bottom Height (mm)	Position of Horn (mm)	RT_A (N)	Reduction Effect (%)
Base	-	-	-	2605.3	-
Type-8	32.5	2041	5338	2205.9	15.7
Type-14	32.5	2041	5338	2222.3	14.7
Type-15	35.0	2041	5338	2161.2	17.1
Type-16	37.5	2041	4888	2164.6	16.9
Type-17	40.0	2041	4497	2167.0	16.8
Type-18	45.0	2041	3794	2169.0	16.8
Type-19	50.0	2041	3214	2161.7	17.0
Type-20	35.0	1200	5338	2162.3	17.0
Type-21	41.0	1200	5720	2217.4	4.9
Type-22	35.0	1200	7331	2348.1	9.9
Type-23	35.0	2041	4288	2177.7	16.4
Type-24	35.0	2041	3214	2187.1	16.1

).

The design requirements included visibility constraints, contact angle, lower edge height, and horn position. Since the NaviScreen is installed on the foredeck, it has the potential to obstruct bridge visibility. Therefore, the visibility from the bridge was calculated, and the NaviScreen was designed to comply with the required visibility range. The contact angle refers to the inclination at which wind interacts with the NaviScreen. Lower edge height measures the vertical dimension of the base of the NaviScreen, which attaches to the vessel. Horn position describes the protruding feature at the upper center of the NaviScreen, while shape type denotes its overall geometric configuration. Table 7 summarizes these design requirements. To design an effective air resistance reduction structure for the bow area of MPVs, a CFD model was developed, meticulously incorporating multiple design parameters. These parameters were selected to address both operational constraints and aerodynamic optimization goals. The initial modeling phase explored various NaviScreen configurations, focusing on factors affecting flow separation, drag distribution, and bridge visibility. Five key design factors were examined, as detailed in

Table 8. Initial designs of MPV NaviScreens.

Component	Model Shape	Note
Visibility		Considering visibility on the ship’s bridge, the height of the NaviScreen is limited.
Contact angle		Changes the contact angle between the blowing wind and the NaviScreen.
Bottom height		Changes in the height of the lower part due to reasons such as securing workspace and adjusting the wind flow.
Position of horn		Changes the presence and position of horns to control the flow of wind.
Shape type		Use of various shapes such as inclined, cylindrical, spherical, etc.

:

(1)

Visibility Constraint (Height Limitation): Installed on the forecastle deck, the NaviScreen must not impede the line of sight from the navigation bridge. Consequently, its maximum height was constrained by a calculated visibility region, ensuring adherence to navigational safety standards and operational feasibility.

(2)

Contact Angle: This parameter defines the inclination between the NaviScreen surface and the oncoming airflow. Altering the contact angle modifies the aerodynamic interactions on the surface of the shield, affecting flow separation and overall aerodynamic resistance. Models with varying inclination angles were developed to identify nonlinear trends in drag reduction.

(3)

Bottom Height: The height of the lower edge of the NaviScreen above the deck influences both the available workspace and the wind deflection path. Adjusting this dimension changes the flow pattern around the bow’s lower section, thereby aiding drag management without reducing operational space.

(4)

Position of Horn (Protrusion Element): A horn-shaped protrusion was installed at the upper center of the NaviScreen. Its placement is a crucial design parameter that directs airflow over the top of the shield. Changes in this position affect turbulence and recirculation zones, which are closely linked to drag characteristics.

(5)

Shape Type: In addition to the standard sloped design, alternative geometries such as cylindrical and spherical configurations were incorporated to investigate different aerodynamic responses. These shapes differ in curvature and frontal area, significantly impacting pressure drag.

In total, 20 NaviScreen models were created based on combinations of these variables. Additionally, five side NaviScreen configurations were developed to examine crossflow conditions and their effect on total resistance. These models were evaluated using steady-state RANS-based CFD simulations, and their performances were assessed based on resistance reduction rates under constant inflow conditions. The comprehensive modeling approach enables a multivariable optimization study and serves as the foundation for evaluating the aerodynamic viability of NaviScreen installations on MPVs. This configuration facilitates the subsequent evaluation of resistance reduction effectiveness across diverse operating environments and design parameters. To identify the optimal NaviScreen setup for installation on the bow of an MPV, a comprehensive CFD-based aerodynamic analysis was conducted under varying design conditions.

3.3. CFD Results and Optimization

To determine the optimal NaviScreen configuration for application on the bow of an MPV, a comprehensive CFD-based aerodynamic analysis was performed under varying design conditions.

The simulation process was divided into three stages, methodically adjusting key geometric factors: contact angle, bottom height, and horn position. The findings revealed that aerodynamic performance, specifically air resistance reduction, was highly responsive to these variables. Among the 20 modeled configurations, Type-15 emerged as the most effective design, achieving a 17.1% decrease in aerodynamic resistance compared to the baseline model, as presented in Table 7. This optimal configuration featured a 35° bow angle, a bottom height of 2041 mm, and a horn position at 5338 mm. Additionally, two other configurations—Type-19 and Type-20—demonstrated strong performance, with drag reductions of 17.0%, confirming the efficacy of the sloped design type in mitigating aerodynamic forces. Specifically, Type-19 incorporated a steeper bow angle (50°) and a lower horn position, while Type-20 maintained the same contact angle and horn placement as Type-15 but with a reduced bottom height (1200 mm), as detailed in

Table 9. Main parameter of the NaviScreen.

Case	Shape Type	Bow Ratio (°)	Bottom Height (mm)	Position of Horn (mm)	Reduction Effect (%)
Type-15	Slope	35.0	2041	5338	17.1
Type-19		50.0	2041	3214	17.0
Type-20		35.0	1200	5338	17.0

.

These results highlight the significance of synergistic parameter optimization in achieving optimal performance. Theoretical interpretation of the CFD results suggests that changes in contact angle induce alterations in flow separation behavior and stagnation pressure distribution on the shield surface. Nonetheless, the trend in drag reduction did not exhibit a strictly linear relationship with contact angle, indicating shape-dependent thresholds where flow attachment and detachment dictate the aerodynamic response. Similarly, bottom height had a minimal effect on aerodynamic performance unless set to extreme values, whereas horn position markedly influenced flow redirection and turbulence intensity near the shield’s upper edge. Parametric optimization revealed that the optimal aerodynamic benefit is achieved by combining a moderate contact angle with strategically positioned flow-directing elements, such as the horn. These results affirm that advanced CFD simulations are indispensable for the structural–aerodynamic integration of NaviScreen systems, ultimately leading to reduced resistance, fuel savings, and enhanced environmental efficiency in MPV operations.

3.4. Evaluation Under Operational Wind Conditions

To assess the aerodynamic performance of the proposed NaviScreen configurations under realistic marine environmental conditions, additional CFD simulations were conducted to incorporate variations in wind speed and direction. The analysis concentrated on the three most aerodynamically efficient models—Type-15, Type-19, and Type-20—previously identified through shape optimization studies. Wind speed scenarios were categorized based on the Beaufort scale, spanning from calm (BF.0) to strong breeze (BF.6), as presented in

Table 10. Setting the wind environment for the simulation.

Beaufort Scale	Wind Speed
	Range (m/s)	Average (m/s)
2	1.6~3.3	2.45
4	5.5~7.9	6.75
6	10.8~13.9	12.35

. The simulation results revealed that while the percentage reduction in air resistance remained relatively consistent across wind speeds, the absolute amount of reduced aerodynamic force increased substantially at higher wind speeds due to the nonlinear relationship between drag force and velocity.

Table 11. Fourth numerical analysis results of NaviScreens with wind speed environment (air resistance).

Case	Beaufort Scale	Wind Speed (m/s)	RT_A (N)	Reduction Effect (%)
Base	0	0	2605.3	-
	2	2.45	4915.6	-
	4	6.75	10,989.4	-
	6	12.35	22,210.0	-
Type-15	0	0	2161.2	17.1
	2	2.45	4139.8	15.8
	4	6.75	9115.9	17.0
	6	12.35	18,561.3	16.4
Type-19	0	0	2161.7	17.0
	2	2.45	4154.7	15.5
	4	6.75	9184.1	16.4
	6	12.35	18,594.3	16.3
Type-20	0	0	2162.3	17.0
	2	2.45	4146.2	15.7
	4	6.75	9144.4	16.8
	6	12.35	18,581.4	16.3

and Figure 7 show that the baseline vessel experiences an aerodynamic resistance of 22,210 N at Beaufort 6. The optimized Type-15 configuration decreases this resistance to 18,561 N, achieving a 16.4% reduction. Preliminary CFD results reveal that the optimal 35° bow angle and elevated horn position work together to streamline the incoming airflow, reducing stagnation pressure at the leading edge and suppressing flow separation. As noted in the manuscript, the sloped windshield geometry channels the incoming wind smoothly over the upper structure, preventing excessive turbulence and flow separation, while the guiding horn positioned 3.2~5.3 m above deck promotes flow attachment and minimizes the formation of recirculating wakes. This synergy decreases the size of the high-pressure stagnation zone and the low-pressure wake, thereby lowering pressure drag and improving stability in both head-on and oblique winds. To make these mechanisms explicit, we will include additional visualizations of the velocity vectors and pressure contours around the Type-15 configuration. These will show how the smooth 35° slope of the shield allows the flow to reattach along the top surface and how the horn prevents premature flow detachment. We will also discuss how varying each geometric variable—contact angle, lower-edge height, and horn position—modifies the flow. For example, reducing the contact angle to 35° maximizes drag reduction by directing the flow upward and over the structure; increasing the bottom height within 1.2~2.0 m ensures the shield intercepts the highest-velocity portion of the wind without obstructing visibility; and elevating the horn to around 5.3 m further suppresses vortex shedding in the wake.

Similarly, Types 19 and 20 realize reductions of 16.3%, confirming that all three shield geometries effectively mitigate drag as wind speed increases. The alignment between the numerical data in Table 11 and the trends in Figure 7 highlights the robustness of the optimized designs under varying dynamic-pressure conditions.

Regarding overall vessel performance,

Table 12. Fourth numerical analysis results of NaviScreens in a wind speed environment (total resistance).

		Total Resistance (N)
	BF. No.	0	2	4	6
Case
Base		107,920	110,231	116,304	127,525
Type-15		107,476	109,455	114,431	123,876
		0.4%	0.7%	1.6%	2.9%
Type-19		107,477	109,470	114,499	123,909
		0.4%	0.7%	1.6%	2.8%
Type-20		107,477	109,461	114,459	123,896
		0.4%	0.7%	1.6%	2.8%

details the total hydrodynamic and aerodynamic resistance for each scenario. Although the aerodynamic component accounts for a minor portion of the total resistance at low wind speeds (a 0.4% reduction at BF.0), its impact grows significantly under higher wind loads, resulting in a 2.9% reduction in total resistance at BF.6 with Type-15. This finding underscores the operational relevance of aerodynamic optimization for MPVs, especially in wind-dominant sea states.

Figure 8 depicts the angular conditions applied during the final stage of aerodynamic performance validation for the optimized NaviScreen model (Type-15). The simulation utilized a fixed wind speed (Beaufort scale 6, 12.35 m/s) and systematically varied the incident wind angle relative to the ship’s heading at 0°, 15°, 30°, and 45°.

According to Nguyen [16], ships encounter maximum aerodynamic drag within the 30° oblique wind range. This experimental setup was designed to capture the complete spectrum of aerodynamic responses under realistic environmental conditions, particularly focusing on head and quartering winds commonly experienced during navigation.

The results, presented in

Table 13. A comparison of numerical analysis results about RT_A of NaviScreen applied to wind direction.

Ship Speed (Knots)	BF. No.	Wind Speed (m/s)	Wind Deg. (°)	RT_A (N)
				Base	Type-15	Reduction Effect (%)
12.5	6	12.35	0	22.21	18.62	16.1
			15	49.27	44.44	9.8
			30	60.34	45.54	24.5
			45	62.72	55.75	11.1

and

Table 14. Comparison of numerical analysis results about RT of NaviScreen applied to wind direction.

Ship Speed (Knots)	BF. No.	Wind Speed (m/s)	Wind Deg. (°)	RT (N)
				Base	Type-15	Reduction Effect (%)
12.5	6	12.35	0	127,525	123,939	2.9
			15	154,587	149,754	3.1
			30	165,655	150,853	8.9
			45	168,031	161,061	4.1

, offer a comprehensive overview of the aerodynamic and total resistance behavior of the vessel with and without the implementation of the NaviScreen.

Table 13 specifically analyzes aerodynamic resistance (RT_A), isolating the air resistance component due to wind at various angles. The findings confirm that, in the absence of a NaviScreen, air resistance increases markedly with oblique wind angles, reaching a peak of 62.72 N at 45°. Conversely, the Type-15 NaviScreen exhibited a significant mitigation effect, especially at 30°, where aerodynamic resistance decreased from 60.34 N (Base) to 45.54 N—a 24.5% reduction. This suggests that the optimized geometry of the shield enhances airflow redirection and diffusion at critical flow incidence angles. Overall, the shield consistently diminished aerodynamic drag across all tested angles, substantiating its multidirectional effectiveness.

In contrast, Table 14 provides a comprehensive assessment of total ship resistance (RT), encompassing both hydrodynamic and aerodynamic elements. Although the percentage reduction in total resistance is lower than that of air resistance due to the dominant role of hydrodynamic drag, the trend aligns with that of Table 13. The highest total resistance reduction (8.9%) occurs at a 30° wind direction, matching the peak decrease in air resistance. This underscores the compounded benefit of minimizing air resistance on overall ship efficiency, especially under conditions where aerodynamic drag constitutes a larger proportion of total resistance. The primary distinction between Table 13 and Table 14 lies in the scope of resistance evaluated: Table 13 isolates aerodynamic effects, whereas Table 14 contextualizes them within the total operational resistance framework. The theoretical significance of these results resides in the interplay between the angle of attack and boundary layer behavior around the shield. At 30°, the shield facilitates favorable pressure recovery and delays flow separation, resulting in the lowest drag coefficients. These findings emphasize the importance of shape-tailored passive devices in mitigating wind loads, particularly when the ship encounters quartering winds, which are most aerodynamically disruptive.

Collectively, this analysis confirms that NaviScreens not only reduce aerodynamic resistance but also significantly contribute to total resistance reduction. The effectiveness of the shield increases under certain angular exposures, making it a valuable design enhancement for ships operating in high-wind maritime environments. The validated performance at 30° reveals potential for direction-specific optimization in forthcoming adaptive shield designs.

4. FE-Analysis and Results

4.1. Green Water Pressure

The accurate calculation of green water pressure on exposed decks is critical for assessing the structural integrity of marine vessels. The Korean Register [22] rules introduce a systematic approach to ascertain the minimum pressure exerted on exposed decks, factoring in vessel length and positional placement along the ship, as demonstrated in Equations (3) and (4). This section delineates the formula and its application, ensuring clarity and adherence to engineering principles. Pressure at specific locations, such as the superstructure deck and forecastle, is modified using a location factor (x).

$$P_D=x\times P_W$$

(3)

where $x$ is 0.75 and $P_W$ is 37.51 kN/m², the pressure on the superstructure deck becomes the following:

$$P_D=0.75\times 37.51=28.13 \mathrm{k}\mathrm{N}/{\mathrm{m}}^2 \mathrm{o}\mathrm{r} 0.0281 \mathrm{N}/{\mathrm{m}\mathrm{m}}^2$$

(4)

This formula provides a comprehensive and adaptable framework for evaluating green water pressure, essential for the structural design of exposed decks. The equations account for pressure variations, ensuring that different deck sections of the vessel are assessed in accordance with allowable criteria of KR, as depicted in

Table 15. Allowable stress (KR, 2024) [22].

Type	Criteria	Steel Grade	von Mises Stress (MPa)
			${\mathsf{\sigma }}_{\mathit{y}}$	${\mathsf{\sigma }}_{\mathit{a}}$
Fine mesh	$0.9\times \mathsf{\beta }\times {\sigma }_y/k^3$	MILD	235	264

. The allowable stress criteria outlined in the KR [22] rules offer a thorough methodology for assessing material safety under operational conditions. As listed in Table 15, allowable stress is calculated using the formula referred to as Criteria. This criterion ensures that the structural design remains within safe stress limits, accounting for mesh precision and material properties, thus providing a reliable framework for assessing structural integrity under various loading conditions. The computation highlights the importance of incorporating location-specific coefficients (e.g., x) to customize the outcomes for specific structural elements.

4.2. Wind Pressure

The wind pressure exerted on the NaviScreen structure is determined using established aerodynamic principles grounded in dynamic pressure theory. The wind-induced pressure $P$ is calculated via the general wind load Equation (5):

$$P=f\times V_k^2\times C_h\times C_s \left[\mathrm{N}/{\mathrm{m}}^2\right]$$

(5)

where $f$ denotes the wind coefficient, which is a constant derived from environmental assumptions and conversion factors, $V_k$ represents the wind speed at the reference height, typically in meters per second (m/s), $C_h$ indicates the height coefficient, accounting for the amplification of wind pressure with elevation above sea level, and $C_s$ denotes the shape coefficient, representing the geometric interaction between the wind and the exposed structure.

The wind speed of 50 m/s was utilized, representing a conservative design scenario based on operational conditions. This corresponds to a pressure of 0.00152 MPa, indicating the uniformly distributed external force on the shield’s windward surface. This methodology offers a logical and conservative foundation for assessing the structural adequacy of the NaviScreen under standard design wind conditions. The wind pressure value derived here serves as a primary load input for the finite element model discussed in the subsequent structural analysis.

Here, Criteria is a formula about allowable stress calculation, $\mathsf{\beta }$ denotes a coefficient of mesh density (100 mm, 1.25), $k$ is the material coefficient (MILD, 1.0), ${\sigma }_y$ represents the yield strength of material, and ${\sigma }_a$ indicates allowable stress.

4.3. Methodology

The process adheres to a systematic sequence of reinforcement, modeling, analysis, and iterative validations of structural performance, ensuring compliance with established standards, as depicted in Figure 9.

It commences with the reinforcement phase, where structural enhancements such as stiffeners and material thickness optimization are implemented to bolster strength and stability. Subsequently, a finite element model (FE model) is developed, integrating accurate boundary conditions, material properties, and loading scenarios pertinent to the operational environment. Upon completion of the model, a structural FE analysis is performed, assessing stress distribution, deformation, and structural stability under applied loads. The initial critical assessment within this analysis is yielding verification, which evaluates the resistance of the structure to plastic deformation against the criteria outlined in the Korean Register [22]. If the yielding assessment is satisfactory, the next evaluation step is buckling verification, ensuring the capacity of the structure to withstand compressive and shear loads without collapsing. This verification complies with the standards set by the American Bureau of Shipping (ABS) [23]. Should the structure fail this assessment, modifications and reinforcements are required, and the process cycles back to the reinforcement phase. The final stage of evaluation is displacement verification, which measures deflections under operational loads to confirm compliance with NORSOK [24] standards.

4.4. Model and Allowable Criteria

For this study, the commercial program NASTRAN [25], which performs engineering analyses based on the finite element method, was employed.

The model utilizes 4-node elements, each possessing six degrees of freedom per node. The MPV hull model comprises 205,445 shell elements, 29,720 beam elements, and 201,675 nodes. Meanwhile, the NaviScreen structure includes 30,421 shell elements and 29,598 nodes, with the element size capped at a maximum of 100 mm, as illustrated in Figure 10.

In general linear analysis, maximum stress varies significantly with element size. Therefore, an element size of 100 mm was chosen to accurately represent the geometric configuration of the stiffeners. If the element size is changed, the element size coefficient value will vary when calculating the allowable stress by KR criteria [22]. The material used in the analysis is carbon and low alloy steel (SS400) registered with the Korean Register of Shipping [22], and the fundamental material properties used in the analysis are listed in

Table 16. Material properties of the NaviScreen structure (KR, 2024) [22].

Item	Value
Elastic modulus (MPa)	210,000
Shear elastic modulus (MPa)	80,769
Yield strength (MPa)	235.0
Tensile strength (MPa)	480.0
Poisson’s ratio	0.3

. The material properties of the NaviScreen structure are listed in Table 16, including an elastic modulus of 210,000 MPa, a yield strength of 235 MPa, and a tensile strength of 480 MPa. These properties govern the behavior of the structural material under stress and are integral to FEA.

The hull is constrained with fixed supports in the x, y, and z directions at the buoyant section of the lower hull, and the NaviScreen is modeled as a continuously welded attachment to the bow, as shown in Figure 11. We also report the element formulation, mesh density, and model size used in these runs (four-node shell elements, maximum 100 mm element size for the shield, counts of elements and nodes), together with the SS400 material properties employed, so that the model can be replicated from first principles. This clarifies how loads are transferred from the shield into the forebody structure and makes the restraint set reproducible. The impact resistance reduction structure is welded to the bow of the ship and subjected to dead weight, wind load, and green water pressure. These boundary conditions comply with established classification society guidelines and international standards, as referenced by the Korean Register [22]. For further validation, references may include ISO 19902 (fixed steel offshore structures) [26] and DNV-RP-C208 (structural analysis of ship and offshore structures) [27], which provide methodologies for defining constraints and load applications in FEA. In this analysis, wind load is negligible; therefore, the evaluation was conducted using a combination of dead weight and green water pressure, as depicted in Figure 12a. Figure 12b illustrates the applied external load due to wind pressure, as derived from the theoretical dynamic wind pressure equation. A uniform pressure of 1527.5 N/m² was applied to the windward surface of the shield structure to simulate the aerodynamic load resulting from a wind speed of 50 m/s. This load case defines the design operating conditions and was utilized in subsequent finite element structural analyses to evaluate stress distribution, deformation, and safety margins in accordance with classification society criteria. If the maximum von Mises stress after load application was below the allowable stress recommended by the classification society, buckling safety was assessed in the subsequent step.

The guidelines of the classification society were employed to calculate the buckling stress of the effective plate between stiffeners, which was then compared against the allowable criteria. In this study, the buckling evaluation results of the classification society were further subjected to eigenvalue buckling analysis for additional verification. Moreover, a step-by-step evaluation method was proposed to determine the structural safety by applying the maximum allowable displacement criterion.

4.5. Ultimate Limit State (ULS)

In FEA, mesh size significantly influences the accuracy of stress predictions, particularly in regions with high stress gradients or geometric discontinuities. As illustrated in Figure 13, the maximum von Mises stress increased as the element size decreased from 300 mm to 50 mm, although the peak stress location remained unchanged. In the figure, the red line indicates the KR classification rule criterion (100 mm element size), while the blue line represents the von Mises stress values obtained from varying mesh sizes. This phenomenon is consistent with the fundamental philosophy of FEA: finer elements provide improved resolution of local stress fields, particularly near structural discontinuities such as notches, edges, or stiffener intersections. According to the KR classification rules [22], a 100 mm element size is recommended for assessing structural strength, striking a balance between computational efficiency and acceptable accuracy. Utilizing coarser elements, such as 200 mm or 300 mm, typically leads to underestimation of stress in peak concentration zones due to numerical averaging over larger elements. In contrast, finer meshes (e.g., 50 mm) produce more localized stress peaks but may artificially inflate stress values because of discretization artifacts and potential singularities.

As displayed in Figure 14, mesh refinement was focused on the area with maximum stress. Although stress magnitude varied with mesh density, the location of stress concentration remained consistent across all cases. This convergence in location, despite magnitude differences, indicates that mesh-independent structural behavior is determined by physical loading and geometry, whereas stress magnitude is influenced by element resolution. Theoretically, this behavior corresponds with the convergence property of FEA: as element size approaches zero, the numerical solution converges to the exact continuum solution. However, in practical applications governed by design codes such as KR, a standardized mesh size (e.g., 100 mm) is used to ensure comparability and conservatism in design as well as to prevent the overestimation of localized stress peaks that may not be physically meaningful (e.g., induced by stress singularities).

Therefore, the results displayed in Figure 13 and Figure 14 underscore the significance of mesh sensitivity analysis in validating the robustness of the structural assessment. Moreover, these findings support the application of mesh correction factors (e.g., β = 1.25 in KR Rules) to determine allowable stress values for a specific mesh resolution, thereby ensuring consistency and safety in structural design practices. The ultimate limit state (ULS) signifies the threshold beyond which a structure undergoes plastic deformation or total failure. In this study, ULS evaluation entails confirming that the maximum von Mises stress under applied loads, including wind pressure and green water impact, remains below the material’s allowable stress, which is calculated from yield strength incorporating safety factors derived from mesh sensitivity and material coefficients. This assessment is based on classical elasticity and plasticity theories, utilizing the von Mises yield criterion to predict the initiation of yielding in ductile materials. Per the KR [22] guidelines, ULS evaluations are crucial for averting structural failures that may result in loss of life, environmental harm, or substantial financial losses. Offshore and shipbuilding structures function in harsh environments, where high winds, waves, and other dynamic forces may arise unpredictably.

Figure 15 depicts the von Mises stress distribution across the NaviScreen subjected to green water pressure. By assessing ULS, designers ensure that structures perform reliably under extreme conditions, enabling uninterrupted operations in shipbuilding and offshore industries. For instance, oil and gas platforms and wind turbine foundations must maintain stability even under hurricane-force conditions. The findings reveal that the maximum stress remains below allowable levels, thereby confirming structural safety against expected loads.

4.6. Buckling Limit State (BLS)

The buckling limit state (BLS) relates to the stability of a structure under compressive stresses, especially in slender plate or shell components subjected to axial or lateral loading. Buckling occurs without prior material yielding and represents a critical failure mode in thin-walled structural elements, such as those in the NaviScreen panel regions, as shown in Figure 16. In this study, the NaviScreen is assessed for local and global buckling using finite element analysis under green water and wind loads. Verification follows ABS [23] standards, which utilize eigenvalue buckling analysis or nonlinear collapse analysis to ensure the critical buckling load factor exceeds one. Theoretically, this assessment is grounded in Euler’s buckling theory and plate stability formulations. Failure to meet BLS criteria may lead to sudden and catastrophic collapse, even if the material remains elastic. Thus, satisfying BLS ensures geometric stability and robustness under realistic marine loading conditions.

Ensuring buckling safety is crucial for maintaining the structural integrity of ships and offshore platforms. Thin plates in decks and NaviScreen structures are vulnerable to buckling under localized or distributed loads. Stability evaluation ensures safe operations and structural integrity. The results of the evaluation based on the buckling evaluation criteria presented by ABS classification for safety evaluation of the NaviScreen’s buckling limit state are displayed in Figure 16. According to ABS standards, the buckling coefficient must be below 1.0 to ensure stability, while values up to 1.99 require additional buckling reinforcement. The analysis identifies potential buckling hazards, necessitating design modifications. Notably, the buckling risk increased due to heightened green water pressure combined with vertical compressive forces from the self-weight on the lower part of the ship.

Figure 17 showcases an eigenvalue-based buckling analysis of the initial design, highlighting structural vulnerabilities that could lead to instability during operation. This analysis revealed high buckling risks within the same panel, aligning with the trends observed in the ABS classification results. The final buckling safety factor differed, likely influenced by the safety factor applied in the classification calculations.

Figure 18 illustrates the addition of a carling stiffener (flat-bar, web height 100 mm, thickness 10 mm) to the upper center of NaviScreen to enhance inadequate buckling stiffness. This reinforcement is a method of inducing a transition to a local buckling mode by adjusting the size of the buckling panel. The lower panel thickness was augmented from 6 to 8 mm, and six carling stiffeners were added at specific locations. The reinforcement thickness, along with the placement and number of stiffeners, was optimized to minimize weight. The reinforced design was evaluated using ABS buckling criteria, demonstrating significant stability enhancements as illustrated in Figure 19, thereby validating the effectiveness of the proposed reinforcements.

This demonstrates the effectiveness of the proposed reinforcements. The incorporation of carling stiffeners and increased plate thickness resulted in substantial improvements. The eigenvalue buckling factors for the reinforced model surpassed the safety threshold, complying with ABS standards. Figure 19 shows the maximum buckling factor after reinforcement according to ABS buckling criteria, while Figure 20 presents the results of eigenvalue buckling analysis, further highlighting the improvements post-reinforcement. Strengthening NaviScreens with carling stiffeners and increased thickness provides a practical approach to enhancing structural integrity under green water pressure. These modifications effectively redistribute stresses, reducing the risk of localized buckling. The study underscores the importance of targeted reinforcements in achieving cost-effective and safe designs. This analysis emphasizes the necessity of addressing buckling safety in marine NaviScreens exposed to extreme environmental loads. The reinforcement strategies employed in this study successfully enhanced buckling performance, ensuring compliance with safety standards.

4.7. Serviceability Limit State (SLS)

The serviceability limit state (SLS) evaluates the structural performance under normal operating conditions, focusing on criteria such as displacement, deformation, and vibration, which can affect functionality and safety without causing structural failure. Excessive displacement of the NaviScreen under operational loads may compromise aerodynamics or visibility from the bridge of the ship. This study adopts the NORSOK (2013) [24] criteria for displacement limits, which specify maximum allowable deflections for non-load-bearing structures to ensure service performance, prevent fatigue accumulation, and avoid interference with adjacent systems. Serviceability limit state (SLS) evaluation is theoretically based on linear elasticity theory and employs FEA to predict deformation under service loads, such as wave-induced motions and moderate wind. The focus is on functional adequacy rather than material strength, encompassing the maintenance of structural alignment, clearance, and user comfort.

SLS criteria ensure that a structure remains functional and fit for purpose under normal operating conditions, unlike ULS, which aim to prevent catastrophic failure. SLS assessments evaluate the ability of a structure to sustain usability, comfort, and serviceability throughout its operational life. In shipbuilding and offshore structures, SLS is essential for addressing deformation, vibration, and durability issues. NORSOK N-004 [24] specifies the maximum allowable displacement of the free end structure as L/100. The cantilever beam deflection of the NaviScreen with reinforced buckling stiffness reaches a maximum of 1.55 mm, well within the allowable standard of 3.42 mm, as displayed in Figure 21. The reported maximum displacement of 1.55 mm at the free edge of the NaviScreen corresponds to the relative deflection under combined green water pressure and operational loads, as derived from the finite element analysis (FEA). This value represents the absolute displacement of the structure’s critical node (Node 683,314, Figure 21) in the Z-direction (vertical axis), measured against its fixed support boundary conditions. This confirms that the yield strength, buckling strength, and deflection criteria are all satisfied.

The NaviScreen is installed on the foredeck, and its design parameters—contact angle, lower-edge height, and horn position—were selected to balance aerodynamic efficiency with bridge visibility and structural constraints. Because the device is optimized for bow placement on MPVs, we note that different mounting locations would require geometry changes to maintain flow attachment and prevent visibility issues. The current design and performance of vessels outside this envelope—such as shallow-water operations, high-speed ferries, or radically different hull forms—must be approached with caution. Although our sloped windshield and guiding horn geometry provide significant drag reduction (up to 24.5% at a 30° wind angle) for MPVs, these results were obtained under wind speeds and wave conditions typical of medium-speed offshore supply operations.

5. Conclusions and Future Work

This study presents a thorough aerodynamic and structural evaluation of a NaviScreen device designed for MPVs, targeting the reduction of aerodynamic drag and ensuring structural integrity under extreme environmental loads, especially green water pressure. Utilizing high-fidelity CFD and FEA, the research optimizes the geometry of the device, assesses its operational performance, and verifies its structural safety.

Through CFD-based parametric optimization—varying contact angle, bottom height, and horn position—the NaviScreen configuration designated Type-15 emerged as the optimal design, achieving a maximum aerodynamic resistance reduction of 17.1% under standard headwind conditions. Under Beaufort scale 6 winds, this configuration consistently yielded drag reductions exceeding 16.3%, with total ship resistance decreasing by up to 2.9%, validating the aerodynamic advantages in realistic sea states. Furthermore, under oblique wind conditions (30° incidence), the NaviScreen achieved a 24.5% reduction in air resistance and an 8.9% decrease in total resistance, highlighting its superior performance in quartering wind scenarios. Simultaneously, the structural performance of the NaviScreen was assessed under green water pressure using nonlinear FEA. The initial design was prone to local buckling under vertical compressive loads. To mitigate this, targeted reinforcements were added, including carling stiffeners and increased plate thickness.

Post-reinforcement analysis confirmed that the structure satisfied critical safety criteria defined by ABS (buckling factor > 1.0), KR (yield strength limits), and NORSOK (displacement within L/100), ensuring operational resilience and serviceability. In summary, the following key conclusions are drawn:

• Aerodynamic Performance: The sloped NaviScreen design featuring a 35° bow angle and optimized horn placement (Type-15) achieved the most significant reduction in aerodynamic drag under both head-on and oblique wind conditions.
• Operational Effectiveness: The NaviScreen consistently performed across diverse wind speeds and directions, offering practical advantages in real-world marine settings by decreasing overall hull resistance and thus enhancing fuel efficiency.
• Structural Reinforcement: The addition of carling stiffeners and increased plate thickness improved structural integrity, reduced localized buckling, and ensured adherence to classification society safety standards under green water loading.
• Design Validation: The combination of CFD and FEA methodologies establishes a validated workflow for the safe and efficient implementation of NaviScreens on MPVs, with scalability potential for other vessel types.
• Building on the current study, future research should integrate advanced computational and experimental techniques to further optimize NaviScreen designs and enhance their applicability across diverse maritime conditions.
• AI-Driven Design Optimization: Leverage machine learning (ML) and deep learning algorithms, such as generative adversarial networks (GANs) or reinforcement learning, to automate the exploration of optimal NaviScreen geometries. These methods can rapidly evaluate thousands of design variants, identifying configurations that maximize aerodynamic efficiency while minimizing structural weight. Implement surrogate modeling techniques (e.g., Gaussian processes or neural networks) to reduce computational costs associated with high-fidelity CFD-FEA simulations, enabling real-time design adjustments.
• Digital Twin Technology: Develop a digital twin of the NaviScreen-equipped vessel to monitor performance in real-world conditions. IoT sensors and edge computing can provide live data on wind loads, structural stresses, and fuel efficiency, enabling adaptive control systems to dynamically adjust the NaviScreen’s orientation or retractability based on environmental feedback.
• Advanced Materials and Additive Manufacturing: Investigate lightweight composite materials (e.g., carbon fiber-reinforced polymers or graphene-enhanced alloys) to improve strength-to-weight ratios and corrosion resistance. Utilize 3D printing for prototyping and production, allowing complex, topology-optimized designs that are impractical with traditional manufacturing.
• Hybrid Renewable Integration: Explore synergies between NaviScreens and onboard renewable energy systems, such as integrating photovoltaic coatings or vertical-axis wind turbines into the shield structure to further reduce GHG emissions.
• Autonomous and Adaptive Systems: Incorporate shape-memory alloys or morphing structures to enable adaptive NaviScreens that dynamically alter their geometry in response to wind direction and speed, optimizing performance across varying operational scenarios.
• Extended Environmental and Operational Validation: Conduct scaled experiments in wind–wave basins equipped with particle image velocimetry (PIV) and pressure-sensitive paint (PSP) to validate CFD predictions under combined aerodynamic and hydrodynamic loads. Expand fatigue and vibration analyses using nonlinear FEA coupled with machine learning to predict long-term degradation under cyclic loading.
• Regulatory and Scalability Frameworks: Collaborate with classification societies to establish standardized testing protocols for aerodynamic devices, ensuring compliance with evolving IMO regulations. Extend the methodology to other vessel classes (e.g., bulk carriers or LNG tankers) by developing modular, scalable NaviScreen designs tailored to distinct superstructure profiles.

By integrating these cutting-edge technologies, future work can transform NaviScreens into intelligent, multifunctional systems that not only reduce drag but also contribute to the broader decarbonization and digitalization goals of the maritime industry. This work distinguishes itself from existing container-ship studies by demonstrating a holistic design framework for MPVs that balances aerodynamic drag reduction and structural safety. While previous research achieved moderate drag reductions on large container ships through CFD analysis alone, we have shown that integrating high-fidelity CFD with nonlinear FEA enables the NaviScreen to reduce aerodynamic resistance by up to 24.5% under quartering winds while remaining resilient to green-water pressures thanks to carling stiffeners and optimized plate thicknesses. These innovations make the NaviScreen a scalable solution aligned with IMO-2050 decarbonization goals.