A RANS Based Prediction Method of Ship Roll Damping Moment

1. A RANS Based Prediction Method of Ship Roll Damping Moment Kumar Bappaditya Salui Supervisors of study: Professor Dracos Vassalos and Dr. Vladimir Shigunov The Ship Stability Research Centre Department of Naval Architecture and Marine Engineering Universities of Glasgow and Strathclyde

2. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Overview of Presentation Introduction Model Two dimensional calculations Three dimensional calculations without forward speed A cfd-strip Theory Three dimensional calculations with forward speed Conclusions

3. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Background Roll damping is strongly affected by viscosity, it is feasible to try RANS equations for its prediction Introduction Unstructured mesh SIMPLE algorithm for pressure correction equation HRIC algorithm for free surface simulation Dynamic fluid pressure on the ship hull Calculation of added moment of inertia and damping moment using Fourier analysis

4. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Description of the model and test procedure • harmonic rolling oscillations: • the roll axis is fixed with respect to the hull • Post-processing: • Moment due to hydrodynamic pressure is considered, hydrostatic part of pressure (with respect to the initial undisturbed free surface) is subtracted • As the moment due to shear stresses is negligible compared to the pressure part, • it was neglected • linear component of the damping moment (~to the angular velocity) • estimated by Fourier analysis of the time history of the hydrodynamic moment • the coefficient of this moment: Non-dimensional

5. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Two-dimensional calculations Description of section No-slip wall Sliding Boundary Free surface Boundary conditions: r/B=0.00625 No-slip wall

6. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Grid size independency studies 1l 2l 3l 1r 2r 3r

7. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Results and discussions Added moment of inertia (a) and damping moment (b) coefficients for the square body with rounded corners for the rolling amplitude 11.50. Respective curves for 5.750 amplitude are shown in (c) and (d)

8. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ 3-d Calculations without forward speed Boundary conditions Sliding condition Domain boundary: No-slip condition Ship hull- No-slip boundary

9. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ 3-d Calculations without forward speed Grid generation

10. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Results and discussions Added moment of inertia (a) and damping moment (b) for the ro-ro hull rolling at the amplitude 50; respective plots for 100 amplitude are shown in (c) and (d)

11. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ A CFD strip theory Result and discussions Total 14 sections has been taken Comparison of added moment of inertia (a) and damping moment (b) coefficients for the ro-ro hull with rolling amplitude 50

12. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Description of the model and test procedure 3-d calculations with forward speed Body plan of a high-speed vessel

13. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ • Therunning trim and sinkage defined in towing tests without rolling: • In forced rolling tests trim and sinkage were fixed to respective values • The same fixed values were used in the calculations

14. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Boundary conditions Inlet Hydrostatic pressure Sliding Condition No-slip b. c. on the hull surface

15. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Example grid

16. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ Damping dependency on frequency, forward velocity and amplitude

17. University Research Presentation Day, 16th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ • The method in general predicting the roll damping moment quite accurately in the low and medium frequency range • At high frequency, in case of simulations without forward speed computed results have large errors • At the high Froude numbers and high frequency, the deviation of the computed results from the experiments may be larger • Maximum deviation is about 14% for roll with forward speed • Further improvement of grid quality will decrease this discrepancy Conclusions:

18. Thank you for your attention