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. 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 University Research Presentation Day, 16 th January 2004 ___________________________________________________________________________________________________________________________________________________________________________

3. Introduction Background Roll damping is strongly affected by viscosity, it is feasible to try RANS equations for its prediction University Research Presentation Day, 16 th January 2004 ___________________________________________________________________________________________________________________________________________________________________________ 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, 16 th 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. Two-dimensional calculations Boundary conditions: Sliding Boundary Free surface No-slip wall Description of section r/B=0.00625 University Research Presentation Day, 16 th January 2004 ___________________________________________________________________________________________________________________________________________________________________________

6. Grid size independency studies 1l 1r 2l3l 3r 2r University Research Presentation Day, 16 th January 2004 ___________________________________________________________________________________________________________________________________________________________________________

7. Results and discussions Added moment of inertia (a) and damping moment (b) coefficients for the square body with rounded corners for the rolling amplitude 11.5 0. Respective curves for 5.75 0 amplitude are shown in (c) and (d) University Research Presentation Day, 16 th January 2004 ___________________________________________________________________________________________________________________________________________________________________________

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

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

10. Results and discussions Added moment of inertia (a) and damping moment (b) for the ro-ro hull rolling at the amplitude 5 0 ; respective plots for 10 0 amplitude are shown in (c) and (d) University Research Presentation Day, 16 th January 2004 ___________________________________________________________________________________________________________________________________________________________________________

11. Total 14 sections has been taken A CFD strip theory Result and discussions Comparison of added moment of inertia (a) and damping moment (b) coefficients for the ro-ro hull with rolling amplitude 5 0 University Research Presentation Day, 16 th January 2004 ___________________________________________________________________________________________________________________________________________________________________________

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

13. The running 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 University Research Presentation Day, 16 th January 2004 ___________________________________________________________________________________________________________________________________________________________________________

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

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

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

17. 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: University Research Presentation Day, 16 th January 2004 ___________________________________________________________________________________________________________________________________________________________________________

18. Thank you for your attention