Ship-Hull Shape Optimization with a T-spline based BEM-Isogeometric Solver

In this work, we present a ship-hull optimization process combining a T-spline based parametric ship-hull model and an Isogeometric Analysis (IGA) hydrodynamic solver for the calculation of ship wave resistance. The surface representation of the ship-hull instances comprise one cubic T-spline with extraordinary points, ensuring C2C2 continuity everywhere except for the vicinity of extraordinary points where G1G1 continuity is achieved. The employed solver for ship wave resistance is based on the Neumann–Kelvin formulation of the problem, where the resulting Boundary Integral Equation is numerically solved using a higher order collocated Boundary Element Method which adopts the IGA concept and the T-spline representation for the ship-hull surface. The hydrodynamic solver along with the ship parametric model are subsequently integrated within an appropriate optimization environment for local and global ship-hull optimizations against the criterion of minimum resistance

VELOS: A VR Platform for Ship-Evacuation Analysis

“Virtual Environment for Life On Ships” (VELOS) is a multi-user Virtual Reality (VR) system that aims to support designers to assess (early in the design Process) passenger and crew activities on a ship for both normal and hectic Conditions of operations and to improve ship design accordingly. This paper focuses On presenting the novel features of VELOS related to both its VR and Evacuation-specific functionalities. These features include: i) capability of multiple Users’ immersion and active participation in the evacuation process, ii) Real-time interactivity and capability for making on-the-fly alterations of environment Events and crowd-behavior parameters, iii) capability of agents and Avatars to move continuously on decks, iv) integrated framework for both the Simplified and the advanced method of analysis according to the IMO/MSC 1033 Circular, v) enrichment of the ship geometrical model with a topological model Suitable for evacuation analysis, vi) efficient interfaces for the dynamic specification and handling of the required heterogeneous input data, and vii) post Processing of the calculated agent trajectories for extracting useful information For the evacuation process. VELOS evacuation functionality is illustrated using Three evacuation test cases for a ro-ro passenger ship

Shape-optimization of 2D hydrofoils using an Isogeometric BEM solver

In this paper, an optimization procedure, based on an Isogeometric BEM solver for the potential ow, is developed and used for the shape optimization of hydrofoils. The formulation of the exterior potential- ow problem reduces to a Boundary-Integral Equation (BIE) for the associated velocity potential exploiting the null-pressure jump Kutta condition at the trailing edge. The numerical solution of the BIE is performed by an Isogeometric Boundary-Element Method (BEM) combining a generic B-splines parametric modeler for generating hydrofoil shapes, using a set of eight parameters, the very same basis of the geometric representation for representing the velocity potential and collocation at the Greville abscissas of the knot vector of the hydrofoil's B-splines representation. Furthermore, the optimization environment is developed based on the geometric parametric modeler for the hydrofoil, the Isogeometric BEM solver and an optimizer employing a controlled elitist genetic algorithm. Multi-objective hydrofoil shape optimization examples are demonstrated with respect to the criteria i) maximum lift coefficient and ii) minimum deviation of the hydrofoil area from a reference area

VELOS : a VR platform for ship-evacuation analysis

Virtual Environment for Life On Ships (VELOS) is a multi-user Virtual Reality (VR) system that aims to support designers to assess (early in the design process) passenger and crew activities on a ship for both normal and hectic conditions of operations and to improve ship design accordingly. This article focuses on presenting the novel features of VELOS related to both its VR and evacuation-specific functionalities. These features include: (i) capability of multiple users’ immersion and active participation in the evacuation process, (ii) real-time interactivity and capability for making on-the-fly alterations of environment events and crowd-behavior parameters, (iii) capability of agents and avatars to move continuously on decks, (iv) integrated framework for both the simplified and advanced method of analysis according to the IMO/MSC 1033 Circular, (v) enrichment of the ship geometrical model with a topological model suitable for evacuation analysis, (vi) efficient interfaces for the dynamic specification and handling of the required heterogeneous input data, and (vii) post-processing of the calculated agent trajectories for extracting useful information for the evacuation process. VELOS evacuation functionality is illustrated using three evacuation test cases for a ro–ro passenger ship

A BEM-ISOGEOMETRIC method for the ship wave-resistance problem

In the present work IsoGeometric Analysis is applied to the solution of the Boundary Integral Equation associated with the Neumann-Kelvin problem and the calculation of the wave resistance of ships. As opposed to low-order panel methods, where the body is represented by a large number of quadrilateral panels and the velocity potential is assumed to be piecewise constant (or approximated by low degree polynomials) on each panel, the isogeometric concept is based on exploiting the same NURBS basis, used for representing exactly the body geometry, for approximating the singularity distribution (and, in general, the dependent physical quantities). In order to examine the accuracy of the present method, numerical results obtained in the case of submerged and surface piercing bodies are * Corresponding author. Tel: (+30) 2107721138, Fax: (+30) 2107721397, e-mail: [email protected] 2 compared against analytical solutions, experimental data and predictions provided by the low-order panel or other similar methods appeared in the pertinent literature, illustrating the superior efficiency of the isogeometric approach. The present approach by applying Isogeometric Analysis and Boundary Element Method to the linear NK problem has the novelty of combining modern CAD systems for ship-hull design with computational hydrodynamics tools

An Isogeometric Boundary Element Method for 3D lifting flows using T-splines

In this paper an Isogeometric Boundary Element Method for three-dimensional lifting flows based on Morino’s (Morino and Kuo, 1974) formulation is presented. Analysis-suitable T-splines are used for the representation of all boundary surfaces and the unknown perturbation potential is approximated by the same T-spline basis used for the geometry. A novel numerical application of the so-called Kutta condition is introduced that utilises the advantages of isogeometric analysis with regard to the smoothness of the trailing edge curve basis functions. The method shows good agreement with existing experimental results and superior behaviour when compared to a low order panel method. The effect of the tip singularity on Kutta condition is also investigated for different levels of refinement and positions of the trailing edge collocation points

Isogeometric Boundary-Element Analysis for the Wave-Resistance Problem using T-splines

In this paper we couple collocated Boundary Element Methods (BEM) with unstructured analysis suitable T-spline surfaces for solving a linear Boundary Integral Equation (BIE) arising in the context of a ship-hydrodynamic problem, namely the so-called Neumann-Kelvin problem, following the formulation by Brard (1972) [1] and Baar & Price (1988) [2]. The local-refinement capabilities of the adopted T-spline bases, which are used for representing both the geometry of the hull and approximating the solution of the associated BIE, in accordance with the Isogeometric concept proposed by Hughes et al. (2005) [3], lead to a solver that achieves the same error level for many fewer degrees of freedom as compared with the corresponding NURBS-based Isogeometric-BEM solver recently developed in Belibassakis et al. (2013) [4]. In this connection, this paper makes a step towards integrating modern CAD representations for ship-hulls with hydrodynamic solvers of improved accuracy and efficiency, which is a prerequisite for building efficient ship-hull optimizers

Shape optimization of conductive-media interfaces using an IGA-BEM solver

In this paper, we present a method that combines the Boundary Element Method (BEM) with IsoGeometric Analysis (IGA) for numerically solving the system of Boundary Integral Equations (BIE) arising in the context of a 2-D steady-state heat conduction problem across a periodic interface separating two conducting and conforming media. Our approach leads to a fast solver with high convergence rate when compared with low-order BEM. Additionally, an optimization framework comprising a parametric model for the interface’s shape, our IGA-BEM solver, and evolutionary and gradient-based optimization algorithms is developed and tested. The optimization examples demonstrate the efficiency of the framework in generating optimum interfaces for maximizing heat transfer under various geometric constraints

Coupling an inviscid IGA – BEM solver with X-Foil's boundary-layer model for 2D flows

In this work we couple an IGA-BEM solver for 2D lifting flows with the viscous model in X-Foil [1], a vintage but still widely used software tool for the design and analysis of subsonic airfoils, towards deeper integration of the isogeometric concept in 2D flow models that incorporate boundary-layer corrections. The formulation of the exterior potential-flow problem reduces to a Boundary Integral Equation (BIE) for the associated velocity potential. Adopting the approach presented in [3], the resulting BIE is handled by an IGA-BEM method, combining: (i) A generic B-splines parametric modeler for generating hydrofoil shapes, using a set of 8 design-oriented parameters; (ii) The very same basis of the geometric representation for representing the velocity potential, and (iii) Collocation at the Greville abscissas of the knot vector of the hydrofoil’s B-splines representation, appropriately enhanced to accommodate the null-pressure jump Kutta condition at the trailing edge. For the viscous part of the solution, the two-equation model of X-Foil [2] is employed. X-Foil’s inviscid solver is “circumvented” and inviscid isogeometric parameters are sent to its viscous component, namely the integral momentum and kinetic energy shape parameter equations presented in [2]. The derived coupled system is tested for NACA4412 and NACA0012 airfoils and the output lift and drag coefficients for different angle of attacks are compared to experimental data, uncoupled X-Foil results and one-way coupling results obtained [4] via the software tool PABLO [5]. The so-resulting coupled system can be used in airfoil/hydrofoil shape optimisation algorithms with a variety of optimisation criteria such as maximum lift coefficient, maximum lift-over-drag-ratio, minimum deviation of the airfoil/hydrofoil area from a reference area, etc. REFERENCES [1] Drela, M. (1989) “XFOIL: An analysis and design system for low Reynolds number airfoils”, MIT, Massachusetts, USA. [2] Drela, M., Giles, M. (1987) “Viscous – inviscid analysis of transonic and low Reynolds number airfoils”, AIAA Journal, vol. 25(10), pp. 1347 – 1355. [3] Kostas, K.V., Ginnis, A.I., Politis, C.G., Kaklis, P.D. (2017) “Shape-optimization of 2D hydrofoils using an Isogeometric BEM solver”, Computer Aided Design, vol. 82, pp. 79-87. [4] Kostas, K.V., Ginnis, A.-A.I, Politis, C.G., Kaklis P.D. (2017) “Shape-optimization of 2D hydrofoils using one-way coupling of an IGA-BEM solver with a boundary-layer model”, Coupled Problems 2017, VII International Conference on Coupled Problems in Science and Engineering, June 12-14, 2017, Rhodes (GR)

Shape-optimization of 2D hydrofoils using an isogeometric BEM solver

In this paper, an optimization procedure, based on an Isogeometric BEM solver for the potential flow, is developed and used for the shape optimization of hydrofoils. The formulation of the exterior potential-flow problem reduces to a Boundary-Integral Equation (BIE) for the associated velocity potential exploiting the null-pressure jump Kutta condition at the trailing edge. The numerical solution of the BIE is performed by an Isogeometric Boundary-Element Method (BEM) combining a generic B-splines parametric modeler for generating hydrofoil shapes, using a set of eight parameters, the very same basis of the geometric representation for representing the velocity potential and collocation at the Greville abscissas of the knot vector of the hydrofoil's B-splines representation. Furthermore, the optimization environment is developed based on the geometric parametric modeler for the hydrofoil, the Isogeometric BEM solver and an optimizer employing a controlled elitist genetic algorithm. Multi-objective hydrofoil shape optimization examples are demonstrated with respect to the criteria (i) maximum lift coefficient and (ii) minimum deviation of the hydrofoil area from a reference area