Shape Optimization of Turbomachinery Rows using a Parametric Blade Modeller and the Continuous Adjoint Method Running on GPUS

Abstract

This paper presents a gradient-based shape optimization method for turbomachinery rows. The developed continuous adjoint method for incompressible flows, with a fully differentiated turbulence model, is coupled with an in-house 3D blade parameterization software, which is differentiated to support the gradient-based optimization process. The in-house flow and adjoint solvers are implemented on a cluster of NVDIA Graphics Processing Units (GPUs). The parameterization software creates the blade by superimposing thickness on both sides of the mean-camber surface. The design variables are NURBS coefficients which ensure smooth shape changes during the optimization, despite the great number of degrees of freedom. In addition, NURBS surfaces are used to describe the final shape. Geometric sensitivities, which stand for the ratio of boundary displacements over the corresponding variation in any of the CAD parameters, are computed by differentiating the parameterization software. Based on the chain rule these are combined with the gradient of the objective function with respect to (w.r.t.) the displacements of the blade or casing nodes, as computed by the adjoint method, and used to update the design variables. During the optimization, the grid is deformed according to the updated shape of the flow domain; regenerating the grid is avoided, by making use of the NURBS surface point inversion technique to retrieve the new surface grid and, then, Radial Basis Functions (RBFs) to propagate the displacement of the boundary nodes to the interior of the computational grid