Abstract: The paper presents recent research conducted within the NATO RTO Task Group AVT-204 “Assess the Ability to Optimize Hull Forms of Sea Vehicles for Best Performance in a Sea Environment.” The objective is the improvement of the hydrodynamic performances (resistance/powering requirements, seakeeping, etc.) of naval vessels, by integration of computational methods used to generate, evaluate, and optimize hull-form variants. Several optimization approaches are brought together and compared. A multi- objective optimization of the DTMB 5415 (specifically the MARIN variant 5415M) is used as a test case and results obtained so far using low-fidelity solvers show an average improvement for resistance and seakeeping performances of nearly 10 and 9%, respectively. Table 1. DTMB 5415 main particulars (full scale) Table 2. INSEAN/UI - Potential flow solver solution for the original hull Multi-objective Hydrodynamic Optimization of the DTMB 5415 for Resistance and Seakeeping Figure 2. INSEAN/UI - Panel-grid convergence analysis (WARP) are very small and grid G1 is deemed adequate for current studies. Figures 3a, 3b, and 3c show a comparison with EFD data from INSEAN (Olivieri et al, 2001), revealing a reasonable agreement especially for low speeds. Seakeeping results are presented in Figs. 3d and 3e in terms of heave and pitch response amplitude operators (RAOs) at Fr=0.41 and head wave. The trend is compared to UI data (Longo and Stern, 2005), showing a reasonable agreement at least for peak values and peak frequencies. Table 2 summarizes the main results for the original hull. Design Space Definition and Sensitivity Analysis. Four orthogonal basis functions and associated design variables are used for the hull, whereas two functions/variables are used for the sonar dome, as summarized in Table 3. Three design spaces are assessed: Figure 4. INSEAN/UI - Sensitivity analysis of the design variables Table 3. INSEAN/UI - Orthogonal functions parameters, for shape modification Table 4. INSEAN/UI - Multi-objective deterministic particle swarm optimization results A preliminary sensitivity analysis is performed, for calm water at Fr=0.25 (18 kn) and Fr=0.41 (30 kn), and for the seakeeping merit The design space C.1 has produced the most promising design, with an improvement of nearly 6.7% and 6.8% for F1 and F2, respectively. It may be noted that the design spaces C.2 and B.2 provide an average reduction of the objective functions F1 and F2 larger than C.1 (Table 4). Nevertheless, C.2 design also gives Table 6. INSEAN/UI - Summary results for selected designs (F2) Figure 5. INSEAN/UI - Pareto fronts for design space C.1 and C2 Figure 6. INSEAN/UI - Selected optimal shape for design space Cl Figure 7. INSEAN/UI - RAOs of heave (a) and pitch (b) at Fr=0.41 in head wave, and roll (c) at Fr=0.25 in 30 deg stern wav Figure 8. INSEAN/UI - Wave elevation pattern and pressure field of the selected optimal hull for design space C.1, compared with the original Figure 10. ITU - A graphical representation of static ANN during recall period Figure 9. ITU - Design variables (control points) on the hull Table 7. ITU - Computed viscous resistance components of the original hull form scaled model (LBP = 20 m) Table 8. ITU - First 10 hull variants in terms of the regression coefficients for each control point on the hull (from the database used in ANN training process) Figure 12. ITU - Predicted and measured (circles) heave RAOs in head seas (180 deg) Figure 11. ITU - Panel distribution over the hull and its free- surface vicinity Figure 13. ITU - Regression performance of the ANN training Figure 15. ITU - Comparison of the cross sections of the initial and the optimal hull forms BACT RTE UP EUMIECUEUUEE CTEM SCECRLEUEE UT EMER UPLEUMIEEGE UM FEM Ele LIAO on 250 variant hull forms and their performances in resistance and seakeeping and on a trained ANN over the sample space, a SQP Figure 14. ITU - Experimental area (sample space) and Pareto frontier determined by means of ANN and SQP where w = 0,0.1,...,0.9, 1.0 is employed as a weighting factor. The selected optimization algorithm is based on sequential quadratic programming (SQP) within Matlab optimization toolbox, since it is very suitable for constraint optimization problems whose design variables include upper and lower bounds. Schittkowski (1985) showed the success of this algorithm in many aspects such as accuracy, efficiency and Table 9. ITU - Comparative seakeeping performances Figure 17. ITU - Contour plot of the wave patterns of the initial and the optimal hull forms (30 kn) Figure 16. ITU - Wave deformations of the initial and the optimal Fig hull at 18 and 30 kn and process is carried out to optimize the prescribed aggregate objective function with weighting factors w. The optimal forms for each weighting factor (wW) are investigated by considering Fe mbinea in the ANN training process (see Table 8). The SQP application on the metamodel provided by ANN gives an optimal point, which is expected to be part of the overall Pareto front. An optimal point is selected on the Pareto front according to the changes in the Pareto curve, in order to give favorable results for both F1 and F2. Figure 14 shows F1 vs F2 values of the variant hull forms, the approximated Pareto front and the optimal design. The comparison of the cross sections of the initial and the optimal hull forms can be observed in Fig. 15. Wave deformations of the initial and the optimal hull forms, for 18 and 30 kn, are presented in Fig. 16, which points out the success of the selected optimal hull. The contour plot of the wave patterns of the initial and the optimal hull forms can be compared in Fig. 17. The summary of the seakeeping performance of the present multi-objective Figure 18. NTUA - Spline sheet on the computational grid SPP-86. The seakeeping qualities of the parent and the variant hull forms are calculated by the SPP-86 code, developed at LSMH of NTUA to implement the Salvensen, Tuck and Faltinsen (1970) strip theory. The code distributes Kelvin sources along the wetted part of each ship section following Frank (1967) method. The estimated dynamic responses encompasses vertical and lateral motions, velocities and accelerations and velocities at specific points for a variety of wave frequencies and heading angles. Figure 19. NTUA - Hull variants of the multi-objective optimization (a), and body plans of the (red) optimized hull compared to the (black) parent hull (b) SWAN2 2002. The Ship Wave ANalysis is a software package for the hydrodynamics analysis developed at MIT (Kring and Sclavounos, 1995). SWAN2 2002 distributes quadrilateral panels over the ship hull and the free surface to derive numerically the steady and unsteady free-surface potential flow around ships, using a three-dimensional Rankine Panel Method in the time domain. Only the calm water results are used in the present study. A batch file is used to integrate SWAN2 with the CAESES/FFW. Additional calculations in calm water have been carried out via a potential flow code developed in-house at Laboratory for Ship and Marine Hydrodynamics (LSMH) of NTUA (Tzabiras, 2008). The code solves the non-linear potential flow around the ship, by calculating iteratively the free surface, while both the dynamic and kinematic conditions are satisfied on it. The free surface and the solid boundary are covered by quadrilateral elements. The distribution of panels varies, being denser near geometrical discontinuities and areas of expected high pressures. The Laplace equation is solved according to the classical Hess and Smith (1968) method. An iterative Lagrangian procedure is adopted to cope with the non-linear problem, in conjunction with an Eulerian solution of the vertical momentum equation. Table 12 has been derived on the basis of this method. Within CAESES/FFW, the geometry of the hull form is represented by a set of basic curves, providing topological information (design waterline, centerline, deck-line) and a set of 19 section curves. All of them are either F-splines, or B-splines. The hull surface is generated by interpolating the parametric- modelled section curves. The parent hull is split into three regions: the main hull, the sonar dome and the skeg, assigning specific design variables for each of them. A total number of ten design variables is employed, five of which are used to define the sonar dome. Table 11 includes the upper and lower values of the design variables. Figure 21. NTUA - Wave deformations of the parent and optimized hull at 18 kn Figure 20. NTUA - Comparison of the wave elevation generated by the initial and the optimized geometry for the Fr=0.25 Figure 23. INSEAN/UI - Effects of the low-fidelity solver on the optimization outcomes: preliminary sensitivity analysis for total resistance improvement in calm water ECN/CNRS has verified the optimized geometry by INSEAN/UI (Fig. 6). At the current stage, the verification includes only calm water performance of the original and optimized C.1 geometries, in full scale, and at moderate and high Froude numbers (Fr=0.25 and 0.41). The hull performances are computed in a free to sink and trim condition by combining the free-surface and moving mesh capabilities with a rigid body motion solver for the flow/motion interaction. Table 14 summarizes the normalized computed forces and motions to reach the final equilibrium state. Concerning the EFD data for the original geometry in model scale (from IIHR; Longo and Stern, 2005), only the trim angle and the sink can be compared with the CFD values, under the hypothesis that the scale effect is weak on these quantities. EFD predicts a trim angle of 0.085 deg at Fr=0.25 and -0.421 deg at Fr=0.41 and the measured sink value is 0.189 at Fr=0.25 and 0.619 at Fr=0.41. Under the aforementioned hypothesis, this is in agreement with the CFD values from Table 14. It may be noted that the computed trim is close to the experiments for both RANSE and potential flow; for the computed sinkage, the agreement appears correct with RANSE, whereas it is under predicted at both speeds with the potential flow (see Table 3).
