RBF-based morphing of B-Rep models for use in aerodynamic shape optimization

This paper presents a shape parameterization method based on morphing that acts directly onCAD-compatible Boundary-Representations (B-Rep), effectively integrated into aerodynamic shapeoptimization. The proposed technique requires the definition of a small number of ”handles”, which arestrategically placed around or on the B-Rep shapes to be optimized. Displacement vectors associatedwith these handles are used as design variables in the optimization method. Using Radial BasisFunctions (RBF) as an interpolation method, these displacements are transferred from the handles tothe Non-Uniform Rational Basis-Splines (NURBS) control points of the B-Rep model; this approachoffers the advantage that the updated surface remains in CAD format and is thus exportable to a STEPfile. The proposed method combines two successive deformation steps. Each deformation is controlledby an independent set of handles, increasing the flexibility of the morphing action. A strategy forupdating the CFD surface grid to the already changed B-Rep models enables the seamless inclusionof the proposed method into any optimization loop, avoiding any into-the-loop dependence on gridgeneration packages. The surface grid is updated by computing new nodal coordinates based on theupdated NURBS parametric coordinates; these are computed according to changes in the parametricdomain of trimmed surfaces by an RBF-based interpolation. The displacement of the surface nodes isthen used to displace the CFD volume grid. The tool is differentiated and integrated into gradient-basedoptimization loops using the adjoint method to compute the gradient of the objective and constraintfunctions with respect to the surface nodal positions. The performance of the proposed method isassessed in four aerodynamic shape optimization problems, concerning a 2D airfoil, a duct, an aircraftmodel and a compressor stationary blading. An assessment of the proposed method based on parametriceffectiveness, in the 2D case, is also presented