**4. Conclusions**

In the study, RANS simulations for a navy vessel were performed to predict the aerodynamic drag of the vessel at different heading angles. Both model scale and full-scale simulations were performed using OpenFOAM, and drag coefficients were predicted, ignoring the free surface effect. Initially, a turbulence model dependency and a verification study were performed for model scale simulations to understand related dependencies. Next, 24 model scale simulations were performed for various heading angles. Finally, fullscale simulations were performed for five heading positions. Direct validation of the results

was not possible due to the absence of experimental or sea trial data. However, a relative comparison of results with similar hull forms confirmed the reliability of the results.

The study provides surge and sway force and roll and yaw moment coefficients for the aerodynamic loads on Tejo class vessels. The result curves show reasonable agreement with similar numerical studies available in the literature. The model scale and full-scale simulations show acceptable agreement in most cases. The comparison of the model and full-scale results show that the scale effect is insignificant for the surge and sway forces and more significant for the yaw moment. Reasons for such differences remain subject to further investigation.

In general, following the dependency studies and comparison with available data, it may be concluded that CFD is well capable of providing reliable data for the aerodynamic loads acting on the studied vessel, which can be used in further studies to improve the manoeuvring trajectories of the vessel under the action of wind. The paper contributes by providing reliable quantitative predictions of aerodynamic loads and moments for a highspeed vessel. It also demonstrates where scale effects are more prominent. However, the paper adopts a relatively low mesh resolution and skips detailed capturing of turbulence intensity and propagation, which are important for several operational aspects of a navy ship. Thus, to assess the difference, a more detailed approach following the air wake study group for simulators might be a future study target.

**Author Contributions:** Conceptualization, S.S. and C.G.S.; methodology, H.I., S.S. and C.G.S.; software, H.I.; validation, H.I., S.S. and C.G.S.; formal analysis, H.I. and S.S.; writing—original draft preparation, H.I.; writing—review and editing, S.S. and C.G.S.; visualization, H.I.; supervision, S.S. and C.G.S.; project administration, S.S. and C.G.S.; funding acquisition, S.S. and C.G.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work was performed within the NAVAD project "Simulation of manoeuvrability of ships in adverse weather conditions", which is co-funded by the European Regional Development Fund (Fundo Europeu de Desenvolvimento Regional—FEDER) and by the Portuguese Foundation for Science and Technology (Fundação para a Ciência e a Tecnologia—FCT) under contract 02/SAICT/032037/2017. This work contributes to the Strategic Research Plan of the Centre for Marine Technology and Ocean Engineering (CENTEC), which is financed by the Portuguese Foundation for Science and Technology (Fundação para a Ciência e Tecnologia—FCT) under contract UIDB/UIDP/00134/2020.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

