Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019
Table 2. Coefficients of discretization error of Model 1. N1, N2, N3
1, 2, 3 r21, r32 p
q(p)
21
21
21
21
1.91E+06, 8.31E+05, 3.73E+05 4.37E-03, 4.35E-03, 4.26E-03 1.32, 1.31 4.999
4.66E-02 4.38E-03 0.025 0.17% 1.06%
Validation uncertainty (UV) by combining experimental and numerical uncertainty can be expressed as follows (Stern et al., 2002; De Luca et al., 2016).
2 = 2 + 2
(19)
In this calculation only grid-spacing converge error (UGCI) has been taken into consideration. UD is the uncertainty that occurs in the experiment. UD was calculated as ±1.16%. Detailed information about UD can be found in (Delen and Bal, 2015b). UV has been calculated as ± 1.57%. Finally, validation has been achieved because the absolute relative difference between the numerical result and the experiment (|% ΔCT| = 1.33%) has been found below the UV. Actually, other sources of uncertainty (e.g., iterative convergence error and time-step convergence error etc.) are also recommended to be included in the calculation. However, when these error components are included, UV value will increase and there will be no negative effect on validation of solution. Therefore, it has not been included in this study.
Figure 6. Wave profile along the y/LPP=0.1509. 7. RESULTS AND DISCUSSION
Numerical resistance coefficient (CT), sinkage () and trim () values have been compared with available experimental data in Table 3. The relative difference between the results of CFD and EFD has been calculated by ∆% = 100 × | − |/). There is a good agreement between the results (CT, and ) of CFD
Table 3. Comparison of EFD and CFD results at Fr=0.26. CT×103
λ
60.75 37.89
(Larsson et al., 2018) 31.6
(Larsson, et al., 2013) 1
EFD
4.430* 3.835
3.659** N/A
CFD % ΔCT 4.371 1.33%
Nominal wake coefficients of models and of full scale hull have been given in Table 4. Due to viscous effects, the wake of hull at full scale has been found quite different than that of hull at λ=31.6 scale ratio. Nominal wake distributions at x/LPP=0.9825 have been given in Figure 9 for GEOSIM models and full scale as recommended by ITTC (2014c).
σ×102 (m)
EFD CFD % Δσ N/A -0.722
- τ (degree)
EFD CFD % Δτ -0.161 -0.164 1.57%
3.938 2.68% -1.259 -1.180 6.28% -0.165 -0.167 1.73% 3.793 3.67% -1.394 -1.399 0.39% -0.169 -0.165 2.33%
2.294 - N/A -42.664
* Delen and Bal (2015b). **Measured resistance value has been modified to 15 ºC by ITTC (2014a).
- N/A -0.151 -
and EFD methods. In the study of Castro et al. (2011) resistance of the KCS hull at full scale without rudder effect has been computed. The resistance is found to be approximately 4.5% higher than that of the smooth wall surface. The reason for this difference between the two studies is the effect of rudder.
In order to validate the numerical method, the wave elevations at y/LPP=0.1509 have been shown for each model in Figure 6. The agreement between models is very satisfactory. The wave profiles on hull surface have also been plotted in Figure 7. Since the wave profiles on hull surface have not predominantly been affected by viscosity, the wave profiles of the models and of the full scale ship have been consistent with each other. Wave patterns on the free surface have also shown in Figure 8 for each model. Wave heights are compatible with each other.
©2019: The Royal Institution of Naval Architects
A-473
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