Shape-optimization of 2D hydrofoils using one-way coupling of an isogeometric BEM solver with the boundary-layer model

K. Kostas, A. Ginnis, C. Politis, P. Kaklis

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This work combines an Isogeometric (IGA) Boundary-Analysis-Method (BEM) solver for potential flows with a boundary-layer correction model for developing and testing a framework for the shape optimization of hydrofoils placed in low-speed viscous flow.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. Adopting the approach presented in [1], the numerical solution of the resulting BIE is performed by an IGA-BEM method, combining: (i)a generic B-splines parametric modeler for generating hydrofoil shapes, using a set of eight 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 so that the null-pressure jump Kutta condition at the trailing edge.As for the boundary-layer correction model, we adopt the one-way coupled approach proposed in [2], where the effect of the boundary layer thickness is neglected and one single iteration is performed. More accurately, the external tangential velocity is inherited from the inviscid model with the condition of vanishing-normal velocity on the airfoil’s surface and then fed to the boundary-layer model. The drag coefficient can then be obtained using the Squire-Young formula [3], which in effect computes the momentum deficit as a function of the outcome of the boundary-layer calculations at the trailing edge.In fine, the optimization environment is developed based on the geometric parametric modeler for the hydrofoil, the IGA-BEM solver which feeds the above boundary-layer correction and an optimizer employing a controlled elitist genetic algorithm. Its performance is tested via shape optimization examples involving a variety of criteria such as, maximum lift coefficient, maximum lift-over-drag-ratio, minimum deviation of the hydrofoil area from a reference area, etc.
Original languageEnglish
Number of pages55
Publication statusPublished - 13 Jun 2017
EventVII International Conference on Coupled Problems in Science and Engineering - Rhodes, Rhodes, Greece
Duration: 12 Jun 201714 Jun 2017


ConferenceVII International Conference on Coupled Problems in Science and Engineering
Abbreviated titleCoupled Problems 2017
Internet address


  • shape-optimization
  • 2D hydrofoils
  • one-way coupling
  • IGA-BEM solver
  • boundary-layer model

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