Evaluation of Power Saving Achieved by Rotor Sail Systems for Very Large Ore Carriers

1 Evaluation of Power Saving Achieved by Rotor Sail Systems for Very Large Ore Carriers Seungchul Shin1,*, Sang-Yeob Kim1, Min-Su Kim1, Joongyu Kim1, Cheolho Kim2 1 Korean Register, Busan, Republic of Korea 2 Siemens Industry Software Ltd., Republic of Korea Abstract. This study presents a comprehensive computational fluid dynamics (CFD) analysis to evaluate the aerodynamic performance and power-saving potential of a rotor sail system installed on a full-scale Very Large Ore Carrier (VLOC). The simulation framework incorporates realistic atmospheric boundary layer (ABL) wind profiles, apparent wind conditions, rotor operational constraints, and aerodynamic interactions between the rotor sails and the ship hull. Convergence testing and model validation were conducted to ensure the accuracy and reliability of the CFD results. The analysis showed that rotor-generated net thrust is maximized when the apparent wind angle approaches 90°, and scales proportionally with the square of the true wind speed. However, rotor RPM limitations at high wind speeds constrain further performance gains. The study also revealed that hull-induced flow distortions influence rotor effectiveness based on location and wind direction. Additionally, lateral forces were found to increase significantly with wind speed, raising potential concerns regarding vessel maneuverability. Route-based power-saving assessments, using wind data from the ERA5 hindcast model, yielded average net power savings of 283 kW and 309 kW for the Brazil–East Asia and Brazil–Europe routes, respectively—equivalent to 1.8–2.0% of calm water propulsion power. These similar results are attributed to comparable apparent wind conditions across both routes. As the estimates are based on hourly net power rather than annual saving, the findings offer route-specific, practical insights to support shipowners in making informed decisions regarding rotor sail implementation. Overall, the study provides both technical understanding and operational guidance for applying rotor sail systems on large commercial vessels Keywords: Rotor sail, Computational Fluid Dynamics, Power Saving. 1. Background The maritime industry faces increasing pressure to improve fuel efficiency and reduce greenhouse gas emissions as international regulations tighten. Wind-assisted propulsion technologies have re-emerged as promising solutions, with rotor sails (Flettner rotors) gaining particular attention as an effective means of harnessing wind power through the Magnus effect. A rotor sail is a powered spinning cylinder that generates lift perpendicular to the wind flow, augmenting a vessel’s thrust. Early trials of this concept date back to the 1920s, but modern advances and successful installations (e.g., by Norsepower) have demonstrated significant fuel savings potential— typically ranging from 5% to 20% under favorable conditions [1]—renewing interest in rotor sails as a viable emissions-reduction technology. This background underscores the growing motivation to quantitatively evaluate rotor sail performance on contemporary cargo ships. Several numerical studies have recently investigated the aerodynamic performance of rotor sails using Computational Fluid Dynamics (CFD), examining how design and operating parameters influence the generated forces. De Marco et al. (2016) [2] performed steady-state Reynolds-Averaged Navier–Stokes (RANS) CFD simulations to systematically vary key rotor design parameters—including spin ratio, aspect ratio, and the presence of end plates—and characterized the resulting lift and drag coefficients. Their study demonstrated that increasing spin ratios and aspect ratios enhances lift, and that end plates (Thom disks) improve aerodynamic efficiency by mitigating tip vortices. Kwon et al. (2022) [3] extended these analyses through additional parametric CFD investigations of standalone rotors, exploring a wide range of spin ratios and geometric configurations to assess their effects on aerodynamic forces and torque requirements. These studies provided valuable preliminary performance predictions for rotor sails under idealized conditions. * Correspondence to: [email protected] 16th International Symposium on Practical Design of Ships and Other Floating Structures PRADS 2025 Ann Arbor, MI, USA, October 19th – 23rd 2025 2 Despite these advances, most existing research has been limited to simplified geometries, small-scale models, or generalized wind conditions [2]. For instance, previous studies typically considered isolated rotors in uniform oncoming flow, often neglecting the presence of the ship’s hull and the variability of atmospheric wind profiles [3]. While some studies have attempted to apply higher-fidelity CFD approaches to refine rotor sail performance predictions, such efforts often remained confined to simplified single-rotor setups and steady-state assumptions [4]. Similarly, empirical and semi-empirical predictions frequently relied on fixed apparent wind angles or laboratory-scale Reynolds numbers [1]. Consequently, significant uncertainties persist when extrapolating these findings to full-scale ships operating in real environmental conditions [5]. Recent efforts have sought to bridge this gap. Tillig and Ringsberg (2020) [4] compared CFD predictions with sea trial data from ships equipped with rotor sails, revealing that while numerical models can capture general trends, real-world deviations often arise due to hull–rotor interactions and fluctuating atmospheric conditions. More recently, Sampaio et al. (2024) [5] advanced the field by conducting full-scale CFD simulations of a 325,000 DWT very large ore carrier (VLOC) fitted with five rotor sails, incorporating 40 years of ERA5 hindcast wind data to probabilistically assess system performance. Their study emphasized the influence of hull-induced flow distortion, rotor–rotor interference, and deckhouse turbulence on thrust variability, and highlighted the importance of optimizing spin ratio under realistic conditions. However, their approach primarily focused on long-term probabilistic trends rather than directly quantifying time-resolved net power savings for specific voyages. Building upon these insights and addressing the remaining gaps, the present study distinguishes itself by constructing detailed aerodynamic performance polar diagrams from full-scale CFD simulations and integrating them into a ship performance model. This methodology enables the direct estimation of hourly net power savings across different trade routes, providing practical and operationally relevant metrics for shipowners and retrofit designers. By coupling full-scale CFD-derived aerodynamic data with realistic environmental conditions, this work offers a more accurate and actionable evaluation of the power-saving potential of rotor sail systems under real service scenarios. Specifically, the present study conducts high-fidelity unsteady RANS simulations on a full-scale VLOC equipped with multiple rotor sails, developing thrust and drag polar diagrams across a wide range of apparent wind angles and speeds. These polar results are then incorporated into a ship performance framework to simulate power savings over representative trade routes using ERA5 wind data. First, the optimal rotor operating speed (RPM) is identified based on maximizing aerodynamic efficiency without incurring excessive drag or power consumption. Next, the derived aerodynamic forces are mapped to power-saving polar charts, illustrating the net power contribution achievable under varying environmental conditions. Finally, using these charts, projected power savings on different routes are compared, revealing how route-specific wind patterns influence rotor sail performance. Overall, the study demonstrates that by integrating full-scale CFD simulations with voyage-specific environmental profiles, it is possible to obtain more accurate and operationally meaningful predictions of windassisted propulsion benefits. The findings validate the rotor sail’s potential to reduce power consumption on large ore carriers and provide actionable insights for ship operators and designers, thereby bridging the gap between conceptual estimates and real-world operational performance. This work contributes to the advancement of windassisted propulsion technologies and supports the broader decarbonization objectives of the maritime industry. 2. Numerical methodology 1. Computational domain and boundary conditions The computational domain was constructed around a DWT 324,000-ton Very Large Ore Carrier (VLOC) equipped with five Flettner rotors installed along the ship's centerline. Each rotor has a diameter of 4 m and a height of 24 m. The endplate of each rotor has a diameter of 6 m and a thickness of 0.35 m. The overall ship geometry and the configuration of the computational domain are illustrated in Figure 1 and 2. Velocity inlets were defined at the front, left, right, and top boundaries of the domain, while a pressure outlet was applied at the rear boundary. The bottom boundary was set as a symmetry plane. A fully developed Atmospheric Boundary Layer (ABL) profile was applied at the velocity inlets. The ABL velocity distribution is defined as: 𝑈  = 𝑈  ( 𝑧 𝑧  )  (1) 3 where the exponent 𝛼 is 1/7 as recommended by the International Towing Tank Conference (2014) [6], the 𝑧 is the reference height set at 10 m and 𝑈 is the wind speed at the reference height. Figure 1. 3D model of the vessel used in this study Figure 2. Computational domain and boundary conditions 4 2. Simulation setup To evaluate the power saving performance of Flettner rotors installed on the upper deck of the ship, the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equation is solved using commercial software STAR-CCM+ 18.06. The finite volume method is used to discretize the URANS. The Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm is adopted for velocity and pressure coupling [7]. A second order upwind scheme is used for the discretization of convection term and a first order forward Euler scheme for the temporal discretization is used throughout all simulation. For the full-scale simulation that corresponds to fully turbulent calculation, the 𝑘−𝜔 Shear-Stress Transport (SST) turbulence model is used to close the URANS equation [8]. The computational domain consists of a background region and an area of interest as shown in Figure 3. The background region was meshed using a hexahedral grid, which is advantageous for reducing computational time and generating lowskewness grids. In contrast, the region of interest including the rotor and the hull, where complex flow phenomena are expected, was meshed using a polyhedral grid due to its robustness in capturing intricate flow features and providing stable solutions in highly complex flow environments. (STAR-CCM+ user guide, 2023) [9]. The nondimensional wall distance (y+) value is set to less than 1 using the custom prism layer. It is important to recognize that the simulation time step is influenced by the RPM of the rotor. To ensure the stability of the numerical method, the time step must satisfy a constraint on the maximum cell-based Courant-Friedrichs-Lewy (CFL) number [10]. Consequently, as the angular velocity increases, the allowable time-step decreases. 3. Verification and validation 3.1 Convergence test To ensure the reliability of the numerical simulations, the grid convergence test was performed and evaluated using the Grid Convergence Index (GCI) method (Celik et al., 2008) [11], which is based on Richadson extrapolation (Richardson, 1910; Richardson and Gaunt, 1927) [12][13]. The Grid Convergence Index provides a numerical measure of the uncertainty in the grid system. The convergence test was conducted for a model-scale single Flettner Rotor at spin ratio of 1 and an aspect ratio of 5.1. Subscripts 1, 2, and 3 correspond to the fine, medium, and coarse grids, respectively. To obtain the Grid Convergence Index (GCI), the order of accuracy (𝑝) must first be calculated. Which is expressed as follows: 𝑝 = 1 ln ( 𝑟  ) | ln | 𝜖  𝜖  ⁄ | + 𝑞 | , 𝑞 = ln  𝑟   − 𝑠 𝑟   − 𝑠  , (1) Figure 3. Hybrid grid system 5 where 𝑟 is the grid refinement factor. 𝑆 = 𝑠𝑖𝑔𝑛  𝜖  𝜖   , (2) where 𝜖 =𝑆−𝑆, 𝜖 =𝑆−𝑆. The Grid Convergence Index can be calculated as follows: For the coarse-to-medium grid: 𝐺𝐶𝐼  = 𝐹   𝑒  𝑟   − 1  , (3) For the medium-to-fine grid: 𝐺𝐶𝐼  = 𝐹   𝑒  𝑟   − 1  , (4) where 𝑒 = 󰇻 󰇻, 𝑒 = 󰇻 󰇻, 𝐹 is a factor of safety of 1.25 which is applied by Roache (1998) [14]. Additionally, the convergence ratio (C𝑅) is a key parameter that indicates whether a solution is converging or diverging. It is defined as: 𝐶𝑅 = 𝜖  𝜖  , (5) The Richardson extrapolated value, which represents the solution on an infinitely fine mesh is calculated as follows: 𝑆  = 𝑆  + 𝑆  − 𝑆  𝑟   − 1 , (6) The results of convergence tests for three different grid systems are shown in Figure 4 and Table 1. The timestep for the grid convergence test was set to 0.001s to achieve a rotation of 4° per time-step. The convergence ratio was found to be between 0 and 1, indicating monotonic convergence. The lift coefficient in the medium grid was 1.375, while in the fine grid, it is 1.36. Both results were close to the extrapolated value of 1.34, with relative errors of 1.49% and 2.61%, respectively. The results are also supported by a low GCI value within 5%. Based on the results of the grid convergence tests, both the medium and the fine are considered acceptable. However, as shown in Figure 5, when the computational cost for the fine grid is approximately 1.5 times higher than that of the medium grid. Therefore, the medium grid was selected for further study. 6 Figure 4. Lift coefficient variation with respect to mesh refinement Table 1. Results of the grid convergence test While the grid convergence test estimates the dependency of the grid system, a time-step convergence test must be conducted to assess the dependency on time step. The time-step convergence tests were performed using the medium grid system with three different time steps, following the same GCI procedure described above. As shown in Figure 6 and Table 2, the temporal discretization error was found to be quite low, with a GCI value within 1%. Based on these results, a time-step corresponding to a rotation of 4° per time-step was considered the best compromise between computational cost and the temporal discretization error. Figure 5. Computational time for the different grid system Grid 𝐶  𝐷 / ∆ 𝑥 𝑟 𝐺𝐶𝐼 𝐶𝑅 𝑝 𝐶   Fine 1.360 100 1.40 1.93% 0.6 1.6 1.34 Medium 1.375 71 1.38 3.27% Coarse 1.400 50 - - 7 Figure 6. Lift coefficient variation with respect to time-step refinement Table 2. Result of the time-step convergence test 3.2 Validation To assess the accuracy of the present CFD model, the simulation results were compared to the experimental data for a cylinder without end plate which has an aspect ratio of 5.1 (Badalamenti, 2008) [15]. The experimental condition used for validation corresponds to 𝑅𝑒 =1.9 × 10. The lift and drag coefficient were compared in various spinning ratio. Figure 7 shows the lift and drag coefficients as the function of the rotor spin ratio (SR). Spin ratio is expressed as follows: 𝑆𝑅 = 𝑛𝜋𝐷 𝑈  , (5) where 𝑛 is the RPM of the rotor, 𝐷 is the diameter of the rotor and the 𝑈 is the freestream velocity. As shown in Figure 7, the present CFD simulation could predict well for lift coefficient in all spinning ratio. Conversely, while the trend of the drag coefficient with respect spin ratio is similar between the experiment and CFD results, a notable discrepancy has been observed. As discussed by Thouault (2012) [16], the fully turbulent calculations are not the appropriate approach at low Reynolds numbers. However, since this study focuses on high Reynolds numbers, turbulence modeling is essential. Nevertheless, due to the lack of experimental data at high Reynolds numbers, the turbulent model was applied to lower Reynolds number cases, which resulted in the observed discrepancies in drag force. Grid 𝐶  𝐷𝑒𝑔 / ∆ 𝑡 𝑟 𝐺𝐶𝐼 𝐶𝑅 𝑝 𝐶   Fine 1.379 2 1.93 0.27% 0.4 1.28 1.382 Medium 1.375 4 2.00 0.64% Coarse 1.365 8 - - 8 (a) Lift coefficient (b) Drag coefficient Figure 7. Validation of CFD results against experimental data 4. Result 4.1 RPM Optimization To properly evaluate the efficiency of the rotor sail, it is essential to determine the optimal RPM. For this purpose, lift and drag coefficients are obtained for spin ratios ranging from 0 to 8 under the conditions where the rotor sail is expected to perform most efficiently, specifically, at an apparent wind angle of 90°. Using the extracted coefficients, the thrust force in the direction of motion is calculated for various spin ratios under arbitrary apparent wind speeds and angles. This thrust force is then converted into power, and the net power is derived by subtracting the power required to rotate the rotor from the power generated in the thrust direction. The RPM that yields the highest net power under given conditions is selected as the optimal RPM. Figure 8 illustrates the process of the RPM optimalization. Figure 8. Flow chart for RPM optimization 9 4.2 Effect of hull (a) AWA=20° (b) AWA=41° (c) AWA=63° 16 (a) Route 1 : Brazil – East Asia (TWS) (b) Route 2 : Brazil – Europe (TWS) (c) Route 1 : Brazil – East Asia (AWS) (d) Route 2 : Brazil – Europe (AWS) Figure 16 Probability distribution of true and apparent wind speed The previously discussed true wind conditions (TWS and TWA) do not account for the vessel's motion; in reality, the ship encounters apparent wind speed (AWS) and apparent wind angle (AWA), which are influenced by the vector sum of wind and vessel velocity. Figure 16 (c), (d) and 17 (c), (d) illustrate these characteristics, assuming a constant vessel speed of 14.6 knots. Unlike the relatively Gaussian distribution of TWS and TWA, the AWS and AWA distributions are notably irregular and strongly dependent on routing and encounter geometry, often diverging from typical statistical models. In particular, Route 2 (Brazil–Europe) shows more frequent occurrences of both high AWS conditions exceeding 15 m/s and very low AWS conditions under 5 m/s, indicating a broader range of encounter scenarios. Regarding AWA—an important factor for rotor sail performance—both routes predominantly experience following winds between 135° and 225°, but with different characteristics: Route 1 (Brazil– East Asia) shows a relatively uniform spread across this range, allowing for more stable thrust generation, whereas Route 2 exhibits a concentrated peak near 180°, suggesting more frequent direct following wind, which may enhance instantaneous efficiency but could lead to greater variability in rotor-assisted propulsion due to its narrow directional distribution. 17 (a) Route 1 : Brazil – East Asia (TWA) (b) Route 2 : Brazil – Europe (TWA) (c) Route 1 : Brazil – East Asia (AWA) (d) Route 2 : Brazil – Europe (AWA) Figure 17 Probability distribution of true and apparent wind angle 18 2. Discussion on net power saving of rotor sail system A route-based assessment of wind-assisted propulsion performance was carried out to estimate the net power savings achievable using a rotor sail system installed on a Very Large Ore Carrier (VLOC). The analysis incorporates AIS-derived vessel positions and headings under the assumption of a fixed service speed of 14.6 knots, and accounts for instantaneous wind-ship interactions to calculate hourly power savings in kWh. While the reference vessel is a VLOC equipped with five rotor sails, the AIS data includes a broader population of ore carriers, and the study does not follow specific voyages between defined ports. As such, the results reflect general operational patterns along two major routes—Brazil–East Asia and Brazil–Europe—and provide insight into typical savings on an hourly basis, rather than total voyage consumption. The probability distributions of these hourly net power savings are depicted in Figure 18, showing average values of approximately 283 kWh for the Brazil–East Asia route and 309 kWh for the Brazil–Europe route. The modest difference between the two is consistent with the comparable AWS and AWA profiles identified earlier. However, the variation in each distribution also emphasizes the impact of route-specific wind conditions and ship-wind encounter angles on rotor sail effectiveness. A supplementary table summarizes key statistical metrics, including the ratio of net power savings to calm-water propulsion demand. Although this ratio depends heavily on vessel size, engine power, and hull resistance, it provides a relative benchmark for evaluating rotor sail contributions under realistic voyage conditions. (a) Route 1 : Brazil – East Asia (b) Route 2 : Brazil – Europe Figure 18 Probability distribution net power saving of rotor sail system Table 4 Statistical value of net power saving Route 1 Route 2 Region Brazil - East Asia Brazil - Europe Power saving (kWh) Mean 282.9 309.3 Median 47.2 76.7 Std. 638.6 662.7 Mean power saving ratio (% of calm sea propulsion) 1.8% 2.0% 19 5. Conclusion This study conducted a comprehensive computational fluid dynamics (CFD) analysis to evaluate the aerodynamic performance and power-saving potential of a rotor sail system installed on a full-scale Very Large Ore Carrier (VLOC). The simulation framework incorporated a realistic atmospheric boundary layer (ABL) profile, apparent wind conditions, rotor mechanical constraints, and aerodynamic interactions between the rotor sails and the ship hull. To ensure the reliability of the numerical results, both convergence testing and model validation against reference data were performed and confirmed prior to the main simulations. The results indicated that the net power contribution of the rotor sails was maximized between TWA=90° and TWA=120° and the performance scaled approximately with the square of the true wind speed. However, at higher wind speeds, mechanical limitations on rotor RPM imposed constraints on the effective power generation. Additionally, the presence of the ship hull was found to locally distort the inflow velocity field, affecting the thrust generated by each rotor depending on its position and wind direction. In the present vessel configuration, the presence of the ship hull was found to induce a local acceleration of the inflow, resulting in a positive impact on rotor thrust generation and, consequently, on net power savings. However, it should be noted that different hull geometries may produce varying effects on the inflow field, potentially leading to adverse outcomes. Therefore, careful consideration of hull-induced flow modifications is essential when determining the placement and installation of rotor sails to ensure optimal performance. Lateral forces acting on the vessel increased significantly with wind speed, raising potential concerns for maneuverability and rudder load. These findings underscore the importance of balancing power saving performance of RTS with navigational stability when designing rotor sail systems. Route-based energy saving assessments, conducted using wind data derived from the ERA5 hindcast model, revealed average net power savings of approximately 283 kWh and 309 kWh for the Brazil–East Asia and Brazil– Europe routes, respectively. These correspond to approximately 1.8–2.0% of the vessel’s calm water propulsion power of VLOC, suggesting that rotor sails offer modest but measurable gains in energy efficiency under realistic operating conditions. The small difference in net power savings between the two routes is primarily due to the similarity in the distributions of apparent wind angle (AWA) and apparent wind speed along both shipping routes. It should be noted, however, that the overall power saving performance of the rotor sail system can vary significantly depending on the size of the vessel, the scale of its engine power, and its operational speed profile. When same rotor sail system is applied to smaller vessels, the relative power saving percentage may appear larger due to the reduced calm water resistance. Therefore, caution must be exercised when interpreting power saving ratios expressed as percentages. As this study estimates power saving effects based on hourly net power contribution for specific routes—rather than long-term or annualized averages—it provides shipowners with more immediate and route-relevant performance insights to support practical decision-making on rotor sail installation. In summary, this research not only quantified the practical benefits and limitations of rotor sail systems under full-scale, route-specific scenarios, but also provided valuable insights into their aerodynamic behavior, design considerations, and operational implications for large commercial vessels. 20 References [1] J. Traut, P. Gilbert, R. Walsh, and A. Bows, “Propulsive power contribution of a kite and a Flettner rotor on selected shipping routes,” Applied Energy, vol. 113, pp. 362–372, 2014. [2] A. De Marco, S. Mancini, C. Pensa, G. Calise, and F. 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