**6. Conclusions**

In this paper, the impact of hard fouling on ship performance for three different ship types is investigated. This impact is investigated using the CFD simulations of resistance, open water and self-propulsion tests. The impact of hard fouling is represented through the modification of wall function, i.e., through the implementation of the Grigson Δ*U*<sup>+</sup> model in the wall function within CFD solver. The verification study for grid size and time step is carried out, and grid and temporal uncertainties are estimated using GCI method. The verification study is performed for several key variables, i.e., *KTO* and *KQO* for open water test and for *PD*, *n*, *T* and *J* for self-propulsion test. Relatively low simulation uncertainties are obtained for all key variables. Thereafter, the obtained results of the performed CFD simulations for smooth surface condition are validated with the extrapolated towing tank results using the ITTC 1978 Performance Prediction Method. Satisfactory agreement is achieved for all resistance, open water and propulsion characteristics. After the verification and validation study, the impact of hard fouling on the ship performance is studied in terms of the impact on resistance, open water and propulsion characteristics. The obtained results demonstrated the significant impact of hard fouling on the increase in frictional resistance and viscous resistance, as well for all three ships. It should be noted that the viscous resistance of KCS is mostly affected due to the presence of hard fouling, which is ascribed to the fact that KCS is investigated at the highest speed. As a result of this, friction velocity along the KCS hull is higher than along the KVLCC2 and BC hulls. Higher Δ*U*<sup>+</sup> values are obtained along the KCS hull in comparison with KVLCC2 and BC hulls, since the roughness Reynolds number and therefore Δ*U*<sup>+</sup> are dependent on the friction velocity. However, wave resistance has decreased for KCS and BC, due to the presence of hard fouling, while for KVLCC2, it is almost negligible, and has remained almost the same as for smooth surface condition. The impact of hard fouling on the wave resistance is in agreement with the impact of hard fouling on the wave elevations, i.e., wave elevations for KCS and BC due to the presence of hard fouling are decreased, while for KVLCC2, it remained the same as for the smooth surface condition. Therefore, the most affected ship due to the presence of hard fouling, related to the fouling penalty on the ship resistance, is KVLCC2. Obviously, beside the ship speed the portion of viscous resistance in total resistance is very important for the estimation of the fouling penalty on the ship resistance, as well as the ratio *k*/*L*. Significant detrimental effects due to the presence of hard fouling on the propeller performance in open water conditions are found. Thus, due to the presence of hard fouling on the propeller surfaces, *KTO* decreases and *KQO* increases, which results in a significant decrease in η*O*. Namely, due to the

presence of hard fouling drag coefficient of propeller blade section increases, causing the increase in *KQO*, and lift coefficient decreases, causing the decrease in *KTO*. The impact of hard fouling on the ship performance is best reflected through the impact on the delivered power and propeller rotation rate. From the obtained results, it is clear that increases in the delivered power are significantly larger than increases in the effective power, due to the presence of hard fouling for all three investigated ships. Therefore, the impact of hard fouling on propulsion efficiency must not be neglected, especially for fouled ship and propeller. The impact of hard fouling on the delivered power and propeller rotation rate is most pronounced for KVLCC2 for fouling conditions R1, R2 and R3, while for R4, R5 and R6, the obtained changes in the ship performance due to hard fouling are similar for BC and KVLCC2. This can be attributed to different impact of hard fouling on propulsion characteristics, as the fouling penalty on effective power for R4, R5 and R6 fouling conditions is higher for KVLCC2 than for BC. Namely, the additional important parameter that affects the impact of biofouling on the ship performance is the value of advance coefficient for self-propulsion point, since it is demonstrated that ships which operate at higher values of advance coefficient will be more affected in terms of propeller performance in open water conditions than ships which operate at lower values of advance coefficient. The impact of hard fouling on propulsion characteristics is presented for all three ships. From the obtained results it can be seen that propulsion characteristics of BC are mostly affected due to the presence of hard fouling, as the obtained changes in 1 − *t*, 1 − *w*, *J*, η*H*, η*<sup>O</sup>* and η*<sup>B</sup>* due to the presence of hard fouling are largest for BC. Additionally, the obtained changes in η*<sup>D</sup>* due to the presence of hard fouling for fouling conditions R4, R5 and R6 are the largest for BC as well, while, for R1, R2 and R3, they are the largest for KVLCC2. The largest change in *KT* and *KQ* values due to the presence of hard fouling are obtained for KCS, which is expected as KCS operate with the highest advance coefficient. Finally, the impact of hard fouling on the flow around fouled ship is studied through the analysis of the impact on wall shear stress distribution, boundary layer thickness, nominal wake distributions, wave elevations and pressure distributions.

The paper provided several valuable insights related to the impact of hard fouling on the ship performance amongst different ship forms. Future study will be focused on investigations related to the impact of biofouling for systematic series of certain ship at different speeds, which will allow more comprehensive insight into the impact of biofouling on the ship performance will be assessed. In this paper, the investigations related to the impact of hard fouling on the ship performance are performed for the presence of hard fouling on both propeller and hull surfaces. If analyzed per unit area, the impact of propeller fouling condition on the ship performance is significantly more important than the impact of hull fouling condition. Therefore, the future studies will be also focused on the investigations related to the impact of solely propeller cleaning on the ship performance. Thus, relatively cheap and effective practice for achieving significant energy saving will be demonstrated. The optimization of maintenance schedule is an important operational measure for reducing ship emissions and the successful application of this measure relies on the accurate assessment of the impact of cleaning, i.e., the impact of biofouling on the ship performance. Currently, these predictions are carried out using performance monitoring. However, performance monitoring has several important drawbacks [8], and the approach presented in this paper presents another way for this assessment. The important benefit of the proposed approach over the performance monitoring is that fouling effects on the ship performance can be analyzed independently of all other additional resistances, which may occur during sailing. However, since drag characterization studies are performed only for limited number of fouling conditions, CFD approach based on the modified wall function approach is limited to these fouling conditions. For more comprehensive assessment there is a need for further drag characterization studies. Additionally, the investigations performed in this paper are carried out for hull surface, which is treated as a uniformly rough surface with certain roughness length scale determined using Equation (6), as done in most of the conventional CFD studies dealing with biofouling. Since the fouling pattern along the immersed surface is not uniform, future studies will be focused on the investigations of the influence of fouling settlement on the ship performance. The locations of niche

areas along the hull surface will be found from the literature and in that areas, wall function model for certain fouling condition will be implemented within the wall function of CFD solver. In that way, more realistic fouling conditions will be analyzed, and the investigations regarding the partial cleaning of the ship hull will be performed as well. Based on that, the proposed method can be used for the assessment of fouling penalties on the ship performance, after the fouling condition of the hull and propeller are determined by divers in the port.

**Author Contributions:** Conceptualization, A.F. and N.D.; methodology, A.F., N.D., I.M. and R.D.; software, A.F.; validation, A.F.; formal analysis, A.F.; investigation, A.F., N.D. and I.M.; resources, A.F.; writing—Original draft preparation, A.F., N.D., I.M. and R.D.; writing—Review and editing, A.F., N.D., I.M. and R.D.; visualization, A.F.; supervision, N.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

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