Adjoint-Based Shape Optimization of High-Speed Trains

Abstract

Given the operating speeds of modern high-speed trains, the improvement of aerodynamic performance has, by implication, become one of the most important issues in today's railway engineering. Many of the interesting aerodynamic features can be described by a set of objective functions which can be determined numerically using Computational Fluid Dynamics (CFD). Moreover, CFD can also be used to optimize the shape of a train with respect to one or several objective functions. Consequently, numerical shape optimization can significantly reduce the demand of time consuming and expensive wind tunnel experiments and speed up or even partly automate the design and optimization process. There are different ways to determine the required shape modifications leading to improved aerodynamic performance. In numerical aerodynamics, shape optimization with adjoint methods is based upon sensitivity analysis providing sensitivities on the surface of the investigated object. Sensitivities themselves are gradients, calculated from the flow field predicted by solving the Reynolds-averaged Navier-Stokes (RANS) equations and the corresponding adjoint equations. For each element of a discretized surface, the sensitivities indicate the influence of a surface-normal displacement of the cell center on the considered objective function. In cases aiming for the minimization (or maximization) of certain aerodynamic characteristics (e.g. drag or lift), the sensitivity distribution almost directly provides the necessary changes. Properly smoothed and scaled, in conjunction with the surface normal vectors of the surface cells, they can be used to identify the deformation vectors.