*3.2. Computational Domain and Boundary Conditions*

In this study, the impact of hard fouling on resistance, open water and propulsion characteristics is investigated using CFD simulations of resistance, open water and self-propulsion tests. It should be noted that the impact of hard fouling on resistance characteristics of KCS and KVLCC2 is already investigated in [16]. Therefore, within this paper, the impact of hard fouling on ship resistance characteristics is only briefly presented as it is important for further discussion. *RT* of a ship is determined using CFD simulations which include free surface effects, i.e., free surface simulations (FSS). Viscous resistance (*RV*) is obtained using double body simulations (DBS), which do not take free surface effects into account. In DBS, the flow around deeply immersed double body ship is simulated and thus the obtained *RT* is equal to *RV*. The frictional resistance (*RF*) is obtained by integrating the tangential stresses over the wetted surface, while viscous pressure resistance (*RVP*) is obtained by integrating the pressure over the wetted surface in DBS. Once *RV* and *RF* are determined, 1 + *k* is determined as a ratio between *RV* and *RF*. Wave resistance (*RW*) is obtained as difference between *RT* obtained in FSS and *RV* obtained in DBS. For more details regarding the performed CFD simulations of resistance tests, reference may be given to [16]. It should be noted that CFD simulations of resistance tests for BC are performed using the same computational domain and boundary conditions as in [16]. CFD simulations of OWT are performed using the cylindrical computational domain. The domain boundaries are placed sufficiently far from the investigated propeller and appropriate boundary conditions are applied in order to prevent their impact on the obtained solution, Figure 3. The computational domain for CFD simulations of SPT is the same as for CFD simulations of resistance test, however within CFD simulations of SPT symmetry condition is not applied, i.e., the whole computational domain is generated (Figure 4). In Figure 4, the applied boundary conditions are presented as well. It should be noted that the same boundary conditions are applied in CFD simulations of the resistance test, except for the symmetry boundary condition, which is applied at the symmetry plane within CFD simulations of resistance test. Possible occurrence of wave reflection is prevented by applying VOF wave damping at the inlet, outlet and side boundaries. More details regarding the applied damping function can be found in [33], and the VOF wave damping length is set to *Lpp*.

**Figure 3.** Computational domain for the open water test (OWT): KP505 (**upper**), KP458 (**middle**) and WB (**lower**).

**Figure 4.** Computational domain (**left**) and the applied boundary conditions (**right**) within computational fluid dynamics (CFD) simulations of the self-propulsion test (SPT).

### *3.3. Discretization of Computational Domain and Computational Setup*

Cut-cell grids with prism layer mesh on the walls were made utilizing the surface remesher, prism layer mesher and trimmer mesher within STAR-CCM+. The unstructured hexahedral mesh is refined locally in the critical regions. Thus, within DBS and FSS of resistance test, as well as in CFD simulations of SPT, mesh is refined near the hull surface, near the bow and stern and hull surface is discretized very fine, i.e., the cell size at the hull surface is set to 1/1000 *Lpp*. Within CFD simulations including free surface effects, mesh is refined in the region where free surface is expected, as well as in order to capture Kelvin wake around free surface. Additionally, mesh for CFD simulations of SPT is refined in the region where virtual disk is located. It should be noted that refinements are made in the same way within [8,25,34]. The mesh for CFD simulations of OWT is refined in the region around the propeller. Additionally, mesh is particularly refined along the leading and trailing edges of propeller in order to allow proper demarcation between the suction and pressure sides. The thickness of the first cell on the wall surfaces within all CFD simulations is chosen in a way that *y*<sup>+</sup> values are higher than 30 and *k*<sup>+</sup> values, as recommended by [15]. As a result of this, near wall mesh for smooth and fouled surfaces is not the same since investigated surface conditions represent very severe fouling conditions with high *k* values. The obtained mesh for CFD simulations of OWT is presented in Figure 5, while the obtained mesh for CFD simulations of SPT is shown in Figure 6. Within these two figures, the above mentioned refinements can be seen.

**Figure 5.** Propeller surface (**left**) and profile view (**right**) cross section of the volume mesh for KP505 (**upper**), KP458 (**middle**) and WB (**lower**).

**Figure 6.** The profile view cross-section of the domain for KCS (**upper left**), KVLCC2 (**middle left**) and BC (**lower left**) and mesh refinement in stern region of KCS (**upper right**), KVLCC2 (**middle right**) and BC (**lower right**).

CFD simulations of OWT are performed for full-scale KP505, KP458 and WB in a way that *n* = 1.5 rps is kept constant and advance velocity varies with *J*. CFD simulations for KP505 are performed for range of *J* from 0.1 to 0.8, with a step equal to 0.1, for KP458 for range of *J* from 0.1 to 0.7 with step equal to 0.1 and for WB for range of *J* from 0.08 to 0.88 with step equal to 0.08. CFD simulations of SPT are performed without discretization of propeller geometry, as the body force method is applied. Therefore, a virtual disk model is placed at the propeller location with the inner

radius of the virtual disk set to the propeller hub radius and the outer radius set to the propeller radius (*R*). Thickness of virtual disk model is set as propeller thickness, the inflow plane radius is set as 1.1*R* and the inflow plane offset is set as 2.2*R* towards the bow from the half of virtual disk thickness.

CFD simulations without free surface effects, i.e., DBS of resistance test and CFD simulations of OWT, are performed as steady simulations. The remaining CFD simulations include free surface effect, and they are performed with time step equal to *T*/200, where *T* is the ratio between *Lpp* and ship speed (*v*). FSS of resistance test and CFD simulations of SPT are stopped once *RT* and thrust (*T*) force became steady, i.e., once they oscillate around averaged value with oscillation amplitude lower than 0.5% of *RT* or *T* value.

#### **4. Verification and Validation Study**
