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For vibration and acoustics vehicle development, one of the main challenges is the identification and the analysis of the noise sources, which is required in order to increase the driving comfort and to meet the stringent legislative requirements for the vehicle noise emission. Transfer Path Analysis (TPA) is a fairly well established technique for estimating and ranking individual low-frequency noise or vibration contributions via the different transmission paths. This technique is commonly applied on test measurements, based on prototypes, at the end of the design process. In order to apply such methodology already within the design process, a contribution analysis method based on dynamic substructuring of a multibody system is proposed with the aim of improving the quality of the design process for vehicle NVH assessment and to shorten development time and cost.

The aim of this paper is to present the adjoint equations for shape optimization derived from steady incompressible Navier-Stokes (N-S) equations and an objective functional. These adjoint Navier-Stokes equations have a similar form as the N-S equations, while the source terms and the boundary conditions depend on the chosen objective. Additionally, the gradient of the targeted objective with respect to the design variables is calculated. Based on this, a modification of the geometry is computed to arrive at an improved objective value. In order to find out, whether a more sophisticated approach is needed, the adjoint equations are derived by using two different approaches. The first approach is based on the frozen turbulence assumption and the second approach, which is advanced in this paper, is derived from the near wall k − ζ − f turbulence model.