Parametric Bulbous Bow Design for the Minimization of Ship Resistance by using CFD

Abstract

In the Computational Fluid Dynamic (CFD) analysis using the finite volume method, solid modeling is usually used in the early stage in order to prepare a mesh process before the computational process is executed. In recent developments, the optimization analysis and CFD have also been applied simultaneously, in which the parametric model plays an important role in finding the optimal solution. However, it is so difficult to create parametric modeling for a ship hull or bulbous bow that has a complex shape such as an irregular curve form. Therefore, the application program interface (API) must be applied to generate and modify a parametric bulbous bow modeling automatically. For the abovementioned purposes, in this study, the cubic Bezier curve and curve-plane intersection method are implemented to generate bulbous bow modification automatically. First, the bulbous bow curve is captured from the initial bulbous bow in solid modeling. Then, this curve is divided into sub-curves according to specific parameters that have been considered for optimal performance analysis using CFD. In this case, there are 4 sub-curves in the longitudinal plane and 2 sub-curves in the horizontal plane that have been created based on 4 parameters, that is, length coefficient of bulbous bow, height coefficient of bulbous bow, ratio of middle section length of bulbous bow to bulbous bow length, and ratio of middle section breadth of bulbous bow to bulbous bow breadth. While in the transverse plane, 2 sub-curves are created to connect 3 points in each cross-section. Furthermore, in relation to these initial sub-curves, the cubic Bezier curve method is applied to draw duplicate curves, respectively, in which the new curves must be identical to the initial curves. Next, the curve-plane intersection method is applied to find some point intersections between curves (both in longitudinal and horizontal plane) and a cross-section plane. Through 3 point intersections in each of the transverse planes, the new curve can be generated using the cubic Bezier curve method with tangent value (both direction and magnitude) which is the same as the initial curve. Finally, by using the lofting method, the curve in each of the transverse planes can be connected to generate a solid modeling of the bulbous bow. In addition, this bulbous bow is ready to be modified automatically using given parameters. Then, by using the original bulbous bow shape, the CFD analysis must be executed to obtain a resistance coefficient value that will be used as an output parameter in optimization calculation. After that, the goal driven optimization (GDO) method is implemented in optimization calculation to get the optimal bulbous bow shape with using 4 parameters bulbous bow as input parameters or design variables. Verification of the results have been done. The parametric bulbous bow has worked well, in which some example of application have been created in some different input parameters with using Kriso Container Ship (KCS type). The changing of the bulbous bow shape was shown to be smooth in continuous condition C1 in each of the changing parameters. For CFD analysis, some parameters have been taken into account, including the variation of domain dimensions, variation of mesh sizes, and variation of boundary conditions, in which the comparison between the numerical analysis and experimental datashowed good agreement in general. In the optimization results, three optimization methods in GDO such as screening, multi objectives genetic algorithm (MOGA) and Non Linear Programming by Quadratic Lagrangian (NLPQL) have been analyzed and compared. The optimal result of the bulbous bow shape can reduce the ship resistances about 0.651% for total resistance (Ct value). This matter shown that the optimal bulbous bow shape has an almost similar characteristic to the original bulbous shape, so it can be said that the original bulbous bow has a good performance in ship minimum resistance. In addition, to get the trend of the optimal bulbous bow in speed range, the smaller Fn value and the larger Fn value are also investigated. Here, there are four variations of Fn values, that is: Fn = 0.18, 0.22, 0.30, and 0.34 have already been calculated and compared each others. The results show that the optimal bulbous bows have the higher CZB value and the smaller ratio of the middle breadth than the original bulbous shape. Whereas, from the trend of Fn values show that the ship with larger Fn value has a larger CLPR and higher CZB value.

Keywords: Parametric bulbous bow design; Cubic Bezier curve; Curve-plane intersection method; Solid modeling.