The realiable prediction of the added resistance in waves is a topic of high interest in the ship-design process. With the introduction of the EEDI (Energy Efficiency Design Index) and the consequential search for energy efficiency increasing measures the question of the minimum power requirement for the safe operation of the ship even in heavy seaways receives special attention. The decisive factor for the power requirement in operation is the wave induced added ship resistance, which is tradionally considered in the power estimation by a general margin. This Sea-Margin is typically specified by 10-20% of the calm water power requirement, regardless of the ship size. While the wave added resistance in realistic seaways can be very small compared to the calm water resistance for large ships, it can be on the same order as the calm water resistance for small ships. Hence, a general power margin can lead to an overestimation of the power requirement for large ships and an underestimation for small ships, respectively.
Figure 1: Snapshot of the simulation for the bulk-carrier at Froude Number 0.134 and head waves with 30% of ship length.
For a demand-oriented power estimation numerical calculations or model tests can be performed in order to determine the wave induced added resistance. These predictions are typically based on regular waves, whereby the head waves are tradionally believed to lead to highest wave resistance. In the scope of numerical methods both non-viscous, potential theory based methods in combination with analytical formulations for the wave resistance and viscous, RANS-equation based methods are applied. With respect to the computional effort potential theory based methods are prefered over RANS-codes. However, these methods can deliver inaccurate results, especially for full hull forms and waves shorter than the ship length, for which the added resistance is increasingly affected by viscous effects. Thus, the application of RANS-codes is particularly recommended for larger ships, considering typical wave lengths in realistic seaways.
FreSCo+ has been being successfully applied to the prediction of wave added resistance in the context of the BMWi funded project HyMOTT, which deals with the numerical prediction of the seakeeping and manoeuvring performance of offshore supply vessels under realistic operational conditions. For the validation of FreSCo+ the wave added resistances for three types of vessels were predicted and the results compared with model test data.
In 2009 model tests were conducted by HSVA for a panmax bulk-carrier with 217m length for a range of Froude numbers and head waves with two different wave lengths. Both wave lengths tested were significantly shorter than the ship length. Thus, it could be expected that the ship motions are small and, from that, most of the added wave resistance is caused by wave reflections (diffraction) from the ship`s bow. Simulations were performed for both calm water and head waves for two froude numbers.
Figure 2: Total resistance in fullscale for calm water and head waves for the bulk-carrier at various Froude Numbers.
The computed results (above) show a good agreement with the measurements for both simulated Froude numbers in both calm water and in waves. The maximum deviation from the measurement appears for the calm water condition at the lowest Froude Number and is less than 5%.
In the course of the Tokyo CFD-Workshop 2015 model test results for the KCS (Kriso Container Ship) were provided. The KCS is a panmax container vessel of 230m length, which is well documented and used for the validation of numerical methods in research. HSVA will participate in the workshop submitting the FreSCo+ results for comparison with model tests carried out by NMRI (National Maritime Research Institue, Japan) at a Froude Number of 0.26 and head waves of various wave lengths.
Figure 3: Snapshots of the simulations for the KCS in head waves with wave height H=2.35m and wave length 149.6m (top left/right) and wave height H=5.65m and wave length 315.3m (bottom left/right).
Figure 4: Total resistance in fullscale for calm water (solid lines) and head waves (lines with points) for the KCS.
Similar to the bulk carrier, the computed results for the container vessel match the measurements for both calm water and head waves very well. The maximum deviation from the model test is 4.7% and can be observed for the wave length of 1.37LPP. Further, it can be seen that, for the waves shorter than ship length, the added resistance is very small. This can be explained by the small ship motions and little wave radiation in combination with little wave defraction due to the slender bow. However, for wave lengths in the range of 1.2 to 1.4LPP the added resistance reaches its peak due to heavy ship motions and wave radiation caused by exciting the ship in its natural pitch frequency.
In the scope of the BMWi funded project PerSee HSVA carried out model tests for a cruise vessel of 220m length for a wide range of encounter angles and wave lengths. The results were presented in Newswave 2014/1 and are published within the proceedings of the ISOPE conference 2015. For the validation of FreSCo+ HSVA started with the computation of the head wave cases, followed by oblique, beam and following waves. The figure below shows the computed results for a Froude Number of 0.232 for calm water and head waves of three wave lengths. The maximum deviation from the model test is 3.9% and can be observed for the shortest wave length.
Figure 5: Total resistance in fullscale for calm water (solid lines) and head waves (lines with points) for the cruise vessel.
Figure 6: Snapshots of the model test (top) and simulation (bottom) for head waves with wave length of 18% LPP .Breaking waves can be observed at the bow and fore shoulder in both the model test and the simulation.
The computed results for the three vessels show how FreSCo+ can be applied to the prediction of the added resistance for various types of vessels accurately for both short and long waves.