Adjoint-based shape optimization of high-speed trains

Abstract

Following Othmer’s work (2008) on the continuous adjoint formulation for the computation of sensitivities of incompressible, steady-state, ducted flows, we use the continuous approach for the optimization of external flows around high-speed trains and the open source finite volume solver OpenFOAM (2011) to solve the governing primal and adjoint equations. For solving the primal Reynolds-Averaged Navier-Stokes (RANS)- equations a k-ω two-equation eddy-viscosity and a one-equation turbulence model were used. The solutions of the primal and the adjoint equations are used to calculate surface sensitivities. The results of the sensitivity analysis are transferred onto the surveyed geometry to create a new shape for further investigation. To obtain the new geometry, we use a CAD-free deformation procedure to morph the existing computational mesh instead of rerunning the entire process chain of CAD design and mesh generation. Following the approach of de Boer et al. (2007) and Bos (2009) we have developed a morphing tool using radial basis function interpolation and the OpenFOAM library to filter the sensitivities and to calculate the new positions of the surface and grid points. The focus of this study is to explore how far adjoint-based shape optimization, using the continuous approach, in conjunction with filtered gradients and CAD-free mesh morphing based on radial basis function interpolation, is capable of meeting the requirements of aerodynamic train design. The presented results considering shape optimization of high-speed trains with respect to the generated pressure wave and aerodynamic drag reveal the feasibility and capability of the developed process chain.