Development of cubic Bezier curve and curve-plane intersection method for parametric submarine hull form design to optimize hull resistance using CFD

Optimization analysis and computational fluid dynamics (CFDs) have been applied simultaneously, in which a parametric model plays an important role in finding the optimal solution. However, it is difficult to create a parametric model for a complex shape with irregular curves, such as a submarine hull form. In this study, the cubic Bezier curve and curve-plane intersection method are used to generate a solid model of a parametric submarine hull form taking three input parameters into account: nose radius, tail radius, and length-height hull ratio (L/H). Application program interface (API) scripting is also used to write code in the ANSYS design modeler. The results show that the submarine shape can be generated with some variation of the input parameters. An example is given that shows how the proposed method can be applied successfully to a hull resistance optimization case. The parametric design of the middle submarine type was chosen to be modified. First, the original submarine model was analyzed, in advance, using CFD. Then, using the response surface graph, some candidate optimal designs with a minimum hull resistance coefficient were obtained. Further, the optimization method in goal-driven optimization (GDO) was implemented to find the submarine hull form with the minimum hull resistance coefficient (Ct). The minimum Ct was obtained. The calculated difference in Ct values between the initial submarine and the optimum submarine is around 0.26%, with the Ct of the initial submarine and the optimum submarine being 0.001 508 26 and 0.001 504 29, respectively. The results show that the optimum submarine hull form shows a higher nose radius (rn) and higher L/H than those of the initial submarine shape, while the radius of the tail (rt) is smaller than that of the initial shape.

[1]  H. N. Das,et al.  Hydrodynamic Performance Evaluation of an Ellipsoidal Nose for a High Speed under Water Vehicle , 2010 .

[2]  B. Choi.  Surface Modeling for Cad/Cam , 1991 .

[3]  Md. Mashud Karim,et al.  NUMERICAL COMPUTATION OF VISCOUS DRAG FOR AXISYMMETRIC UNDERWATER VEHICLES , 2008 .

[4]  W. Lu,et al.  Modification of a NURBS curve with nose features , 1998 .

[5]  R. Goodson,et al.  THE OPTIMUM SHAPING OF AXISYMMETRIC BODIES FOR MINIMUM DRAG IN INCOMPRESSIBLE FLOW , 1972 .

[6]  Hyunyul Kim,et al.  A new surface modification approach for CFD-based hull form optimization , 2010 .

[7]  Bernard Mourrain,et al.  Bulbous Bow Shape Optimization , 2013 .

[8]  Ebru Sarıöz.  An optimization approach for fairing of ship hull forms , 2006 .

[9]  Leonardo Fernández Jambrina,et al.  Programmed design of ship forms , 2012 .

[10]  Juan Antonio Clemente,et al.  Geometric modelling of bulbous bows with the use of non-uniform rational B-spline surfaces , 2007 .

[11]  Anupam Saxena,et al.  Computer Aided Engineering Design , 2005 .

[12]  Gregory J. Grigoropoulos,et al.  Hull-form optimization in calm and rough water , 2010, Comput. Aided Des..

[13]  Ju Young Kang,et al.  Mesh-based morphing method for rapid hull form generation , 2010, Comput. Aided Des..

[14]  Cheng-Hung Huang,et al.  An inverse hull design approach in minimizing the ship wave , 2004 .

[15]  Leo Miguel González Gutierrez,et al.  RANSE with free surface computations around fixed DTMB 5415 model and other Baliño?s fishing vessels , 2007 .

[16]  F. Pérez,et al.  Constrained design of simple ship hulls with B-spline surfaces , 2011, Comput. Aided Des..

[17]  A. Rodríguez,et al.  Programmed design of ship forms , 2012, Comput. Aided Des..

[18]  E. Campana,et al.  Shape optimization in ship hydrodynamics using computational fluid dynamics , 2006 .

[19]  Ping Zhang,et al.  Parametric Approach to Design of Hull Forms , 2008 .

[20]  Antonio Mancuso,et al.  Parametric design of sailing hull shapes , 2006 .

[21]  Ju Hyun Lee,et al.  Flexible CFD meshing strategy for prediction of ship resistance and propulsion performance , 2010 .

[22]  Daniele Peri,et al.  Multidisciplinary Robust Optimization for Ship Design , 2010 .

[23]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[24]  Deddy Chrismianto,et al.  Parametric bulbous bow design using the cubic Bezier curve and curve-plane intersection method for the minimization of ship resistance in CFD , 2014 .