*5.2. The Impact of Hard Fouling on Open Water Characteristics*

The impact of hard fouling (R1) on the propeller performance in open water conditions is presented in Figure 10. The obtained changes in *KTO*, *KQO* and η*O*, due to the presence of hard fouling, are presented in Table 13. As can be seen from Figure 10 and Table 13, due to the presence of hard fouling *KTO* has decreased and *KQO* has increased resulting in significant reduction in η*O*. As fouling severity increases (i.e., from R6 to R1), fouling penalties related to decrease in *KTO* and increase in *KQO* increase as well. Additionally, at higher *J* the fouling penalty related to decrease in η*<sup>O</sup>* is higher. Therefore, it can be concluded that the ships operating at higher *J* values will experience a greater reduction in η*O*, i.e., propeller fouling penalty on the ship performance will be greater. Thus, due to the presence of hard fouling Δ*KTO* values for KP505 at *J* = 0.6 range from −6.22% (R6) to −12.05% (R1), for KP458 at *J* = 0.4 range from −7.44% (R6) to −14.45% (R1) and for WB at *J* = 0.48 range from −7.86% (R6) to −12.09% (R1). An increase in Δ*KQO* values for KP505 at *J* = 0.6 range from 4.66% (R6) to 11.37% (R1), for KP458 at *J* = 0.4 range from 2.59% (R6) to 7.46% (R1) and for WB at *J* = 0.48 range from 3.77% (R6) to 11.19% (R1). Fouling penalties on the propeller performance in open water conditions can be ascribed to fouling impact on the skin friction and the pressure field. Thus, due to the presence of hard fouling on propeller surfaces wall shear stress (τ*w*) increases, while the pressure difference between pressure and suction sides of propeller is reduced, which can be seen from Figures 11 and 12. In Figure 11, the obtained τ*<sup>w</sup>* distributions at KP505 surface at *J* = 0.7 for both smooth and R1 surface condition are shown. It is clear that due to the presence of hard fouling τ*<sup>w</sup>* values at KP505 surface are significantly increased resulting in increase in drag coefficient of the blade section and consequently in *KQO*. In Figure 12 the obtained pressure distribution shown as distribution of pressure coefficient (*CP*), which is defined as a ratio between pressure and <sup>1</sup> 2ρ*v*<sup>2</sup> *<sup>A</sup>*, at KP505 surface is presented. Since the magnitudes of *CP* at both pressure and suction sides of fouled KP505 are significantly reduced, the pressure difference between pressure and suction sides is reduced as well, resulting in a decrease in the lift coefficient of the blade section and, consequently, in *KTO*.

**Figure 10.** The impact of hard fouling (R1) on KP505 (**upper**), KP458 (**middle**) and WB (**lower**) performance in OWT.

**Table 13.** The obtained changes in *KTO*, *KQO* and η*<sup>O</sup>* due to the presence of hard fouling.


**Figure 11.** The obtained τ*w* distribution for smooth (**left**) and R1 (**right**) surface condition for KP505.

**Figure 12.** The obtained *CP* distribution on KP505 surface for suction (**upper**) and pressure (**lower**) side of propeller.

#### *5.3. The Impact of Hard Fouling on Propulsion Characteristics*

After CFD simulations of resistance and open water tests are carried out, CFD simulations of SPT for smooth and fouled ships are performed. As said before, the fouling penalty on the ship performance should be considered through the change in *PD* and *n*. The obtained increases in *PD* and *n* due to the presence of hard fouling are presented in Figure 13. From this figure, it is clear that for surface conditions R1, R2 and R3 KVLCC2 is most affected due to the presence of hard fouling, while for surface conditions R4, R5 and R6 the fouling penalties for KVLCC2 and BC are almost the same and higher than fouling penalties for KCS. The obtained increases in *PD* due to the presence of hard fouling for KVLCC2 range from 90.7% (R6) to 213.4% (R1), for BC range from 90.6% (R6) to 201.9% (R1) and for KCS range from 75.0% (R6) to 163.2% (R1), while the obtained increases in *n* for KVLCC2 range from 16.7% (R6) to 32.6% (R1), for BC range from 16.6% (R6) to 30.7% (R1) and for KCS range from 9.4% (R6) to 18.2% (R1). It is clear that the obtained increases in *PD* are significantly higher than the obtained increases in *PE* due to the presence of hard fouling, which can be related with the decrease in η*D*. This highlights the importance of the assessment of the impact of biofouling on *PD* rather than on *PE*. The increase in *PD* due to the presence of biofouling is dependent on many parameters. Thus, besides the portion of *RV* in *RT*, *k*/*L* and ship speed, which are important for the increase in *PE*, it is also important at which *J* propeller operates and the way the propeller loading defined with *KT*/*J* <sup>2</sup> is affected due to the presence of hard fouling. Namely, due to change in propeller loading, *J* value at which propeller operates changes as well. Thus, the change in *J* at which propeller operates as well as the absolute value of *J* is important, as, for ships which operate at higher *J* values, the fouling penalty on the propeller performance is higher.

**Figure 13.** The obtained increases in *PD* (**upper**) and *n* (**lower**) due to the presence of hard fouling.

In order to study the differences in the obtained fouling penalties more detailly, the impact of hard fouling on propulsion characteristics should be investigated. Within Tables 14–16, the obtained impact of hard fouling on propulsion characteristics is presented. From the obtained results, it is clear that most of the propulsion characteristics are affected by the presence of hard fouling on the hull and propeller surfaces. However, from Tables 14–16, it is clear that the impact of hard fouling on η*<sup>R</sup>* is minimal, i.e., it is lower than 0.45% for all analyzed fouling conditions and ships. What is more, the impact of hard fouling on 1 − *t* is present, however, it is relatively low. Thus, due to the presence of hard fouling, the 1 − *t* value for KCS and KVLCC2 decreases, while for BC, it increases. It should be noted that the 1 − *t* value depends on many different parameters, i.e., on the fouling penalty related to increase in *RT*, to propeller performance, as well as hull and propeller interaction. Obviously, the assessment of the effect of biofouling on 1 − *t* value is very complex. It should be noted that the obtained impact of hard fouling on 1 − *t* is within the obtained numerical uncertainty in the assessment of *RT* and *T*. Additionally, within the assessment of 1 − *t*, a modelling error is present as well, and it is related to turbulence modelling, modelling of the effect of ship propeller with body force method etc. Consequently, in order to assess this impact more accurately, numerical uncertainty as well as modelling error should be reduced through the application of more dense grids and lower time steps, as well as through the discretization of the propeller itself. Thus, a more accurate prediction of the impact of biofouling on 1 − *t* would be assessed. Therefore, based on the obtained results, it can be concluded that the impact of hard fouling on 1 − *t* is present, however, it is minimal. On the other hand, the impact of hard fouling on 1 − *w* is significant and detrimental, since it causes a decrease in the 1 − *w* value. Due to the presence of hard fouling, the obtained decreases in 1 − *w* values range from −6.99% (R6) to −11.7% (R1) for KCS, from −6.29% (R6) to −10.1% (R1) for KVLCC2 and from −8.46% (R6) to −12.0% (R1) for BC. The decrease in 1 − *w* can be attributed to slower flow around the propeller location for fouled ship, due to thicker boundary layer. The decrease in 1 − *w* has beneficial effect on η*<sup>H</sup>* (Equation (11)). Thus, due to the presence of hard fouling the obtained Δη*<sup>H</sup>* values range from 6.13% (R6) to 11.3% (R1) for KCS, from 6.11% (R6) to 10.2% (R1) for KVLCC2 and from −11.3% (R6) to 16.9% (R1) for BC. Regardless of the fact that the decrease in 1 − *w* has beneficial effect on η*H*, in general, the decrease in 1 − *w* has detrimental effect on η*<sup>D</sup>* and *PD*. Namely, the decrease in 1 − *w* points out

that the flow around propeller is slower and consequently propeller operating point is changed when compared with the smooth hull surface. Additionally, due to the presence of hard fouling, the nominal wake field behind the fouled ship is more inhomogeneous than nominal wake field behind the smooth ship, and because of this, the operating point is changed as well. Therefore, *J* for self-propulsion point decreases since *vA* is lower. What is more, *J* for self-propulsion point decreases because of the increase in *n* as well. Due to the presence of hard fouling the obtained Δ*J* values for self-propulsion point range from −15.0% (R6) to −25.3% (R1) for KCS, from −19.7% (R6) to −32.2% (R1) for KVLCC2 and from −21.5% (R6) to −32.6% (R1) for BC. The decrease in the *J* value is unfavorable, as KP 505, KP 458 and WB operate at *J* lower than *J*, for which the η*<sup>O</sup>* function has a maximum value, which is common for all marine propellers. Consequently, due to the decrease in *J* value, η*<sup>O</sup>* value decreases as well. The decrease in η*<sup>O</sup>* value is related to the detrimental impact of hard fouling on the propeller performance in open water conditions. Thus, the obtained decreases in η*<sup>O</sup>* values are higher than the obtained increases in η*<sup>H</sup>* values. Due to the presence of hard fouling the obtained Δη*<sup>O</sup>* values range from −19.2% (R6) to −32.9% (R1) for KCS, from −21.1% (R6) to −37.3% (R1) for KVLCC2 and from −24.9% (R6) to −39.2% (R1) for BC. The obtained decreases in η*<sup>B</sup>* values are similar to the ones obtained for η*<sup>O</sup>* values, as the impact of hard fouling on η*<sup>R</sup>* value is negligible. The presence of hard fouling, therefore, has two detrimental effects on η*O*, because of detrimental effect on the open water characteristics and on the propeller operating point. These two effects can be equally meaningful. The importance of the impact of hard fouling on the propeller operating point can be seen from the obtained impact of biofouling on *KT* values. Even though the presence of hard fouling on the propeller surfaces causes the decrease in *KT*, due to the impact of hard fouling on the propeller operating point, *KT* increases as *J* for self-propulsion point of fouled ship is lower than *J* for self-propulsion point of smooth ship. The obtained Δ*KT* values due to the presence of hard fouling range from 26.8% (R6) to 42.6% (R1) for KCS, from 18.2% (R6) to 24.2% (R1) for KVLCC2 and from 15.1% (R6) to 22.1% (R1) for BC. The presence of hard fouling on hull and propeller surfaces causes an increase in *KQ* due to two reasons. Firstly, due to the presence of hard fouling on propeller surfaces *KQ* values in open water conditions are higher, and secondly due to the change in *J* for self-propulsion point *KQ* value increases. The obtained increases in *KQ* values due to the presence of hard fouling range from 33.6% (R6) to 59.6% (R1) for KCS, from 20.0% (R6) to 34.4% (R1) for KVLCC2 and from 20.2% (R6) to 35.3% (R1) for BC. Finally, from Tables 14–16, it is clear that the presence of hard fouling on the hull and propeller surfaces causes a significant decrease in η*D*, since decreases in η*<sup>B</sup>* are higher than increases in η*H*. The obtained decreases in η*<sup>D</sup>* values due to the presence of hard fouling range from −14.4% (R6) to −25.6% (R1) for KCS, from −16.1% (R6) to −31.0% (R1) for KVLCC2 and from −16.3% (R6) to −28.9% (R1) for BC. Since the impact of biofouling on η*<sup>D</sup>* value is not negligible, the increases in *PE* and *PD* are not the same, and it is therefore necessary to investigate the impact of biofouling on *PD* rather than on *PE*. It should be noted that the results presented in this subsection are obtained for the presence of biofouling on both propeller and hull surfaces. For clean propeller surfaces and fouled ship hull the obtained results, i.e., trends may not be the same. Thus, Song et al. [22], have obtained slight increases in η*<sup>D</sup>* values due to the presence of barnacles at hull surfaces, i.e., with a clean propeller. This can be attributed to the fact that the authors have obtained higher increases in η*<sup>H</sup>* due to the presence of barnacles than decreases in η*<sup>B</sup>* due to change in operating point. As a result of all this, the analysis of the impact of biofouling on propulsion characteristics is very important, i.e., the assessment of biofouling on the resistance characteristics and *PE* is not sufficient.


**Table 14.** The obtained impact of hard fouling on the propulsion characteristics for KCS.

**Table 15.** The obtained impact of hard fouling on the propulsion characteristics for KVLCC2.


From the results presented in Tables 14–16, it can be concluded that the impact of hard fouling on the propulsion characteristics is the most pronounced for BC. Namely, 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. What is more, 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. However, for fouling conditions R1, R2 and R3 the obtained decreases in η*<sup>D</sup>* are larger for KVLCC2 than for BC. For these fouling conditions, larger increase in η*<sup>H</sup>* which is obtained for BC has surpassed the larger decrease in η*B*, which has also been obtained for BC and because of this the obtained decreases in η*<sup>D</sup>* are larger for KVLCC2. The largest changes in Δ*KT* and Δ*KQ* are obtained for KCS and this can be attributed to the fact that KCS operates at a higher *J* value than KVLCC2 and BC. The largest decrease in the ratio between *KT* and *KQ* has been noticed, due to the presence of hard fouling for KCS as well. Nevertheless, amongst the investigated ships, the decrease in η*<sup>O</sup>* is the lowest, which can be attributed through the lowest obtained decrease in *J* for KCS. Namely, *J* for self-propulsion point decreases due to the increases in *n* and 1 − *w*. As can be seen from Figure 13, the obtained increases in *n* due to the presence of hard fouling are significantly lower for KCS than for KVLCC2 and BC, while increases in 1 − *w* due to the presence of hard fouling are relatively similar for all analyzed ships, Tables 14–16.


**Table 16.** The obtained impact of hard fouling on the propulsion characteristics for BC.

### *5.4. The Impact of Hard Fouling on the Flow Around Fouled Ship*

The impact of hard fouling on the ship performance is investigated for three ships at their design speeds presented in Table 2. This resulted in different τ*<sup>w</sup>* distributions for smooth surface condition, Figure 14. From this figure it is clear that the highest τ*<sup>w</sup>* values are obtained for KCS, followed by BC and KVLCC2, which was expected as KCS is investigated at the highest design speed. As a result of this, the highest *k*<sup>+</sup> values are also obtained along the KCS hull, which can be seen from Figure 15. The obtained *k*<sup>+</sup> distributions for R1 fouling condition along the KCS, KVLCC2 and BC hull are shown. Since the highest *k*<sup>+</sup> values are obtained along the KCS hull, the highest Δ*U*<sup>+</sup> values are present as well, which resulted in more significant increase in τ*<sup>w</sup>* and *CF* for KCS than for BC and KVLCC2. The obtained τ*<sup>w</sup>* distributions for R1 fouling condition along the KCS, KVLCC2 and BC hull are presented in Figure 16.

**Figure 14.** The obtained τ*w* distributions for smooth surface condition along the KCS (**upper**), KVLCC2 (**middle**) and BC (**lower**) hull.

**Figure 15.** The obtained *k*<sup>+</sup> distributions for R1 fouling condition along the KCS (**upper**), KVLCC2 (**middle**) and BC (**lower**) hull.

**Figure 16.** The obtained τ*w* distributions for R1 fouling condition along the KCS (**upper**), KVLCC2 (**middle**) and BC (**lower**) hull.

The increase in τ*<sup>w</sup>* along the hull causes a decrease in the velocity in the turbulent boundary layer, i.e., turbulent boundary layer thickness increases due to the presence of roughness, which can be seen from Figure 17. In this figure, boundary layers, which are defined as the distance between the hull surface and the point where the axial velocity magnitude of the flow reaches the proportion of 0.99 of the ship speed, are shown for smooth and R1 surface condition. The boundary layers for KCS are given at locations *x* = 30 m and *x* = 50 m, for KVLCC2 at locations *x* = 50 m and *x* = 70 m and for BC at *x* = 17.5 m and *x* = 35 m. The obtained increases in the boundary layer thickness, due to the presence of biofouling or roughness, is in line with previously published experimental results in the literature [43,44].

**Figure 17.** The obtained boundary layers for smooth ships (**upper**) and fouled ships with fouling condition R1 (**lower**).

As the boundary layer thickness increases it is obvious that the presence of hard fouling will cause the change in the nominal wake distribution. In Figure 18, the obtained contours of 1 − *wN* for smooth and fouled ships (R1) in the propeller disc plane are shown. It should be noted that 1 − *wN* is calculated as the ratio between axial velocity and ship speed [45]. From this figure, it is clear that the presence of hard fouling causes the significant reduction of the flow in the propeller disc plane for all three investigated ships. This reduction causes the change of *J* for self-propulsion point and in that way, it affects propeller efficiency, as already explained.

**Figure 18.** The obtained contours of 1 − *wN* for smooth and fouled KCS (**left**), KVLCC2 (**middle**) and BC (**right**) with fouling condition R1 in the propeller disc plane.

In addition to the impact of hard fouling on τ*<sup>w</sup>* values, the presence of hard fouling causes the change in pressure distribution along the hull. However, this change mainly occurs in the area near the stern of fouled ship [16]. In Figure 19, the obtained *CP* distributions are presented for the area near the stern of investigated ships for smooth and R1 fouling conditions within CFD simulations of SPT. It should be noted that *CP* is obtained as a ratio between pressure and <sup>1</sup> <sup>2</sup>ρ*v*2. From this figure, it is clear that due to the presence of hard fouling pressure recovery at the stern is reduced and because of this *RVP* increases. Additionally, the impact of hull and propeller fouling on *CP* distribution at the rudder can be noticed, i.e., *CP* values at the rudder surface are slightly reduced.

**Figure 19.** The impact of hard fouling on *CP* distribution for the area near the stern.

In Figure 20, the obtained wave patterns around the hulls of the investigated ships for smooth surface condition and R1 fouling condition from CFD simulations of resistance tests are presented. From the comparison between wave pattern for smooth KCS and BC and wave pattern for KCS and BC fouled with R1, it can be noticed that due the presence of hard fouling wave elevations are reduced. On the other hand, wave elevations for KVLCC2 are almost the same for smooth and R1 fouling condition. The similar finding is noticed within [16,20]. Reductions of wave elevations and consequently *RW*, due to the presence of hard fouling can be related to the increase in viscosity [15]. It can be concluded that the impact of hard fouling on the wave elevations is in agreement with the obtained decreases in *RW*, i.e., for KCS and BC this impact is relevant, while for KVLCC2 this impact is negligible.

**Figure 20.** The obtained wave patterns around KCS (**left**), KVLCC2 (**middle**) and BC (**right**).
