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

Abstract

This paper presents a shape parameterization method based on morphing that acts directly on CAD-compatible Boundary-Representations (B-Rep), effectively integrated into aerodynamic shape optimization. The proposed technique requires the definition of a small number of "handles", which are strategically placed around or on the B-Rep shapes to be optimized. Displacement vectors associated with these handles are used as design variables in the optimization method. Using Radial Basis Functions (RBF) as an interpolation method, these displacements are transferred from the handles to the Non-Uniform Rational Basis-Splines (NURBS) control points of the B-Rep model; this approach offers the advantage that the updated surface remains in CAD format and is thus exportable to a STEP file. The proposed method combines two successive deformation steps. Each deformation is controlled by an independent set of handles, increasing the flexibility of the morphing action. A strategy for updating the CFD surface grid to the already changed B-Rep models enables the seamless inclusion of the proposed method into any optimization loop, avoiding any into-the-loop dependence on grid generation packages. The surface grid is updated by computing new nodal coordinates based on the updated NURBS parametric coordinates; these are computed according to changes in the parametric domain of trimmed surfaces by an RBF-based interpolation. The displacement of the surface nodes is then used to displace the CFD volume grid. The tool is differentiated and integrated into gradient-based optimization loops using the adjoint method to compute the gradient of the objective and constraint functions with respect to the surface nodal positions. The performance of the proposed method is assessed in four aerodynamic shape optimization problems, concerning a 2D airfoil, a duct, an aircraft model and a compressor stationary blading. An assessment of the proposed method based on parametric effectiveness, in the 2D case, is also presented.

Simulations of flow over a bio-inspired undulated cylinder with dynamically morphing topography

“…The method described 80 4 in this paper falls under the basis vector approach, in which an analytical expression for the surface is developed and the changes from the initial to final state are prescribed by a sequence of vectors. The basis vector approach for dynamic meshing maintains the underlying structure of the mesh, which is beneficial for computational fluid dynamics (CFD) as it satisfies several requirements for fast simulation and convenient post-processing [20]. These benefits include the ability to consistently deform the target shape smoothly regardless of the complexity, utilize the minimum number of geometric variables to describe shape variations, maintain compatibility with existing geometries, and maintain stability of the solution.…”

Continuous adjoint‐based shape optimization of a turbomachinery stage using a 3D volumetric parameterization

“…However, the control grid vertices were restricted to move only in the peripheral direction and a mesh Morpher was employed for adapting the internal computational mesh. In Reference 21, RBF handles are introduced which act directly on the B‐Rep representation of the CAD model. This method is coupled with the necessary surface and volume mesh deformation kernels in order for this to be applied in turbomachinery applications, in which sliding on surfaces of revolution is necessary.…”