3.3.3. Validation of RANS Results

The accuracy of RANS results is validated by comparing them with the experimental data. In Figure 14, the added resistance with inertial effects, heave and pitch RAOs in head waves are compared with the experimental data. It can be observed that the RANS results are in good agreement with the experimental data.

The RANS results in oblique waves are compared with experimental data in Figure 15. For different incidence wave angles, the computed steady wave surge forces, sway forces and yaw moments show acceptable agreements with experimental data. The error for the sway force at an incident angle of 60◦ is large. The reason is as-yet unknown. The yaw moments are of very small values in the oblique waves as the ship is zero speed.

**Figure 15.** Compare the CFD results with the experiment data for oblique wave cases. (**a**) Steady surge force; (**b**) Steady sway force; (**c**) Steady yaw moment.

The wave snapshots and pressure distribution on the hull surface for a head wave case in an encounter period are shown in Figure 16. It can be observed that the pressure near the bow region changes considerably as the waves propagate from front to back. Green water on the bow deck at *t* = 0.75 *Te* is observed.

**Figure 16.** Wave snapshots and hull surface pressure in an encounter period. (**a**) *t* = 0; (**b**) *t* = 0.25 *Te*; (**c**) *t* = 0.5 *Te*; (**d**) *t* = 0.75 *Te*.

The wave snapshots and pressure distribution on the hull surface on the starboard side for four oblique angles are presented in Figure 17.

**Figure 17.** Wave snapshots and hull surface pressure of four incidence angels. (**a**) *χ* = 30◦ ; (**b**) *χ* = 60◦ ; (**c**) *χ* = 120◦ ; (**d**) *χ* = 150◦ .

#### **4. Conclusions**

In this study, the wave-induced ship motions and steady wave force and moment for KVLCC2 are numerically predicted by using the RANS solver on OpenFOAM. New modules of wave boundary conditions are programed into OpenFOAM. The conclusions may be as follows:


Great efforts in future works will be devoted to the cases, considering a full appended ship (propeller and rudder), and will also concern the ship hydrodynamic performances in irregular waves.

**Author Contributions:** Conceptualization, J.Y.; Data curation, Q.G. and J.Y.; Formal analysis, J.Y.; Funding acquisition, L.S.; Investigation, Q.G. and J.Y.; Methodology, Q.G. and J.Y.; Project administration, J.Y. and L.S.; Resources, Q.G.; Software, Q.G. and J.Y.; Supervision, J.Y.; Validation, Q.G. and J.Y.; Visualization, Q.G. and J.Y.; Writing—original draft, Q.G.; Writing—review & editing, J.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant numbers 51809203, 51720105011, 51609188.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.

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