Presentation - Seakeping Numerical Method Taking Into Account the Influence of the Steady Wave Field
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1. The document presents a computational method for simulating ship seakeeping that considers fully nonlinear steady wave fields. Mathematical formulations are provided for steady and unsteady potential flow problems. 2. Numerical methods are described, including a desingularized Rankine panel method and a hybrid method combining the panel method and Green function method. The methods are validated against experimental data. 3. Effects of hull form variations are examined for steady wave distributions, hydrodynamic forces, and unsteady wave patterns. The importance of including nonlinear steady wave effects is demonstrated, especially in downstream regions.
Presentation - Seakeping Numerical Method Taking Into Account the Influence of the Steady Wave Field
- 1. A Seakeeping Computation Method Considering Fully Nonlinear Steady Wave Field by Mirel Nechita
- 2. Doctor of Engineering Course in Hiroshima University Faculty of Engineering - NAOE Department Ocean Space Engineering Laboratory Supervisor Professor Hidetsugu Iwashita Developed Codes: - Steady Flow Linear (UF, DBF) Nonlinear (FNL) -Unsteady Flow (UF, DBF, FNL) - H ybrid M ethod (DBF, FNL)
- 3. MATHEMATICAL FORMULATIONS Wave characteristics: Wave amplitude Circular frequency Encounter circular frequency Wave number Total potential Exact free surface boundary condition (1) (2)
- 4. STEADY FLOW Boundary conditions for iterative scheme: Steady wave elevation and steady pressure (4) (5) (3)
- 5. UNSTEADY FLOW Boundary conditions (6) (7) Where (8)
- 6. Hydrodynamic forces Unsteady waves (9) (10) (12) Ship motions (11)
- 7. Desingularized Rankine Panel Method ( Jensen, 1986 & Bertram, 1990) Constant source distributions on body surface and free surface Radiation condition Shifting technique NUMERICAL METHOD
- 8. Ship hull form of Series-60 (Cb=0.8) N H =1320
- 9. Computational grids of Series-60, Cb=0.8 (N H =1320, N F =1717)
- 10. Steady wave distribution for Series-60 (Cb=0.8) along several longitudinal axes at Fn=0.2
- 11. Contour plots of the steady wave for Series-60 (Cb=0.8)
- 12. Hull discretization for Series-60, Cb=0.8 - unsteady problem
- 13. Added mass and damping coefficients for heave and pitch for Series-60 (Cb=0.8) at Fn=0.2
- 14. Wave exciting forces and moment for Series-60 (Cb=0.8) at Fn=0.2, =180 degs.
- 15. Ship motions for Series-60 (Cb=0.8) at Fn=0.2, =180 degs.
- 16. Contour plots of heave radiation wave for Series-60 (Cb=0.8) at Fn=0.2, KL=24.0 and t=0
- 17. Contour plots of diffraction wave for Series-60 (Cb=0.8) at Fn=0.2, /L=0.5, =180 degs. and t=0
- 18. Ship hull form of Series-60 (Cb=0.6) N H =1320
- 19. Steady wave cuts for Series-60 at Fn=0.2 (Cb=0.6 left, Cb=0.8 right)
- 20. Steady wave contour plots for Series-60, slender model (Cb=0.6) at Fn=0.2
- 21. Wave exciting forces and moment for Series-60 at Fn=0.2, =180 degs.
- 22. The present Rankine panel method based on the desingularized method was confirmed to be effective to predict fully nonlinear steady wave field accurately. The solution obtained by this method is utilized to evaluate the influence terms of the steady wave field in the unsteady problem. The desingularized Rankine panel method is also effective for the unsteady problem but the shifting technique for satisfying the radiation condition numerically is applicable only for >0.5, from the practical point of view. The method was examined for different hull forms and it was confirmed that the consideration of the fully nonlinear steady wave field improves the estimation accuracy of the unsteady wave field. For the high frequency range, the desingularized Rankine panel method was validated by comprehensive comparisons of unsteady wave patterns with experimetal data. In this range the bluntness effect of the hull form on hydrodynamic forces appears remarkably in the pitch exciting moment. This suggests the significant effect of the hull form on the pressure distribution at the bow and the stern part. The heave radiation wave, computed by the present method, showed good agreement with experiments. A negligible discrepancy between computed results and measurements were observed for the diffraction wave, especially near the blunt bow. An insufficient grid resolution may be one of the cause of this discrepancy. It was also made clear the necessity of extending the method to the low frequency region . Conclusions RPM
- 23. HYBRID METHOD NEAR FIELD - Desingularized Rankine Panel Method FAR FIELD - Green Function Method
- 24. Unsteady potentials for the far field Free surface boundary condition for the far field Artificial surface boundary condition (13) (15) (14)
- 25. Side wall effect on the unsteady wave Fn=0.2 , KL=2.0 ( =0.283) Fn=0.2 , KL=1.3 ( =0.23)
- 26. Computational grids of Series-60 utilized in Hybrid Method
- 27. Coupled added mass and damping coefficients for heave and pitch for Series-60 (Cb=0.6) at Fn=0.2
- 28. Wave exciting forces and moment for Series-60 (Cb=0.6) at Fn=0.2, =180 degs.
- 29. Added mass and damping coefficients for heave and pitch for Series-60 (Cb=0.8) at Fn=0.2
- 30. Contour plot of heave radiation wave for Series-60 (Cb=0.8) at Fn=0.2, KL=1.32, =0.23
- 31. Perspective view of heave radiation wave for Series-60 (Cb=0.8) at Fn=0.2, KL=1.32, =0.23
- 32. In the low frequency range, the experimental data will be affected by the side wall effects of the towing tank. The obtained experimental data needs to be carefully validated, before we utilize them as an index of validation the computation codes. A simple time domain simulation was applied to make clear the side wall effect and it was confirmed that the unsteady wave, measured at =0.23, was not contaminated by the reflected wave from the side wall. Therefore, we can utilize this experimental data for the validation of the computation codes. It was developed a new hybrid method, which combines the advantages of the desingularized Rankine panel method for the high frequency range and and the Green function method for the low frequency range. The predicted hydrodynamic forces by this method, are in good agreement with experiments for a wide frequency range. The importance of the steady wave field on hydrodynamic forces is demonstrated through numerical results for the added mass, damping coefficients and the wave exciting forces. The hybrid method is able to estimate in good accuracy the unsteady waves for both, high and low frequency range. It was shown that fully nonlinear formulation, used in this study, was necessary in order to capture the influence of the steady wave field in high accuracy. The influence of the steady wave field is revealed especially in the downstream region of the ship. Conclusions Hybrid Method
- 33. Hull discretization for the fast ship N H =1007
- 34. Steady wave distributions along ship-side at Fn=0.6 Improved hull form Initial hull form
- 35. Steady wave contour plots, Fn=0.6
- 36. Initial hull form Improved hull form Steady pressure distributions on hull, Fn=0.6
- 37. Diffraction wave - 7 /A at Fn=0.6, /L=0.5, =180º and t=0
- 38. End of Presentation Thank you!