Abstract:Recently, the NURBS technique has been widely used in the 3D design software for ships. However, in most research, the NURBS technique is only applied to the mathematical representation of hull curves and surfaces, and the parametric deformation of hull surfaces based on geometric feature parameters is less understood. The aims of this paper are to establish the parametric design process of hull surfaces through the classification of geometric feature parameters and the design of feature curves, apply the NURB… Show more
“…Current research on underwater body shape for drag reduction mainly focuses on the parametric optimization using simplified models or constructing alternative models [6][7][8][9][10][11][12]. The vast majority of them are shape optimization of existing models, which are empirical, intuitive and not optimal results in a certain range of operating conditions.…”
This paper presents a variable density topology optimization method to numerically investigate the optimal drag-reduction shape of objects in the two-dimensional and three-dimensional flows with steady incompressible external flow conditions, taking into account material volume constraints. By introducing the porous media model, the artificial Darcy friction is added to the Navier-Stokes equation to characterize the influence of materials on the fluid. Material density is applied to implement material interpolation. By transforming the boundary integral form of viscous dissipative expression of drag into the volume integral of artificial Darcy friction and convection term, we solve the problem of drag expression on the implicit interface corresponding to the structure. The continuous adjoint method is used to analyze gradient information for iteratively solving topology optimization problems. We obtain the relevant topology optimization structures of the minimum drag shapes, investigate the effect of the low Reynolds number on the drag force corresponding to two objective functions and discuss the mechanism of drag reduction by a hydrodynamic body shape.
“…Current research on underwater body shape for drag reduction mainly focuses on the parametric optimization using simplified models or constructing alternative models [6][7][8][9][10][11][12]. The vast majority of them are shape optimization of existing models, which are empirical, intuitive and not optimal results in a certain range of operating conditions.…”
This paper presents a variable density topology optimization method to numerically investigate the optimal drag-reduction shape of objects in the two-dimensional and three-dimensional flows with steady incompressible external flow conditions, taking into account material volume constraints. By introducing the porous media model, the artificial Darcy friction is added to the Navier-Stokes equation to characterize the influence of materials on the fluid. Material density is applied to implement material interpolation. By transforming the boundary integral form of viscous dissipative expression of drag into the volume integral of artificial Darcy friction and convection term, we solve the problem of drag expression on the implicit interface corresponding to the structure. The continuous adjoint method is used to analyze gradient information for iteratively solving topology optimization problems. We obtain the relevant topology optimization structures of the minimum drag shapes, investigate the effect of the low Reynolds number on the drag force corresponding to two objective functions and discuss the mechanism of drag reduction by a hydrodynamic body shape.
“…As mentioned, PA is limited in the range of ship hull forms that can be reproduced; different hulls such as catamaran hulls may require specific methods, as can be found in [17]. Two recent references about the parametric design of ships are [18,19], showing that parametric ship design is an active subject for the Academy. Rhinoceros and Grasshopper have been used in parametric design in [20] for the parametric definition of SWATH hulls that can be defined with the use of equations.…”
CAD software is a daily tool in ship design offices and shipyards, and every software uses NURBS or B-splines curves and surfaces as common foundations. The CAD tools of today are not static software products and most of them now include parametric design modules, which enable users to change the shape of an object based on its key geometric feature parameters with the use of sliders or equivalent controls. Although B-spline techniques are commonly applied to the representation of the ship hull curves and surfaces, the parametric deformation of the hull surfaces based on geometric parameters is less used. This paper presents a methodology to define the parametric definition of a ship hull with the use of a standard and non-specialized CAD software that is of common use in the ship design offices and universities: Rhinoceros. The presented parametric design methodology will use specific ship hull parameters or feature parameters with a clear geometric meaning, such as displacement, waterplane area, LCB, and LCF, together with the properties of the B-spline curves and the power of Grasshopper, the parametric design tool inside Rhinoceros, to create parametric ship hulls.
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