An innovative decomposition of the velocity field with the corresponding generalized Bernoulli theorem for viscous flows

Abstract

This work addresses methods and consequent implementations of a unified formulation for unsteady aerodynamics and aeroacoustics. Specifically, the methodology is based upon the use of boundary integral representations for the primitive variables, including a decomposition of the velocity field, which provides an innovative tool for the integrated analysis of aerodynamics and aeroacoustics, from both the conceptual and the computational points of view. Within the context of aerodynamics, we describe the complete theoretical formulation for Navier-Stokes incompressible flows and its consequent numerical formulation. The results provided through the algorithm implemented are in good agreement with other numerical and experimental data. Ultimately, we achieve the primary object of the work, to provide a validation of the theoretical framework. With regards to the same formulation we provide a first step towards the complete formulation of Navier-Stokes compressible flow fields within the velocity decomposition introduced, this time in aeroacoustics. We present a novel reading of the source field contribution in terms of a source surface distribution, defining a corresponding so-called transpiration velocity for compressible flows. By means of this result we obtain the pressure in the field in terms of a transfer function applied to the pressure on the boundary surface and moreover we could relate the power-spectral-density in the ow eld to the same quantity evaluated on the body surface, providing a link between sets of data usually considered as independent. Again, the numerical results achieved are comforting. In addition, we present preliminary work towards the application of the velocity decomposition for the analysis of transonic flows. Thus, the formulations introduced, while of interest on their own merit even as stand-alone analysis, have been developed for a possible inclusion - as high level models - in the multidisciplinary design optimization analysis. Each task handled may be seen as a module, with increasing accuracy, while modelling aerodynamics and aeroacoustics. In order to illustrate this connection, ultimately, we describe the MDO algorithm used, along with some of the results obtained.