Quasi-three-dimensional nonreflecting boundary conditions for Euler equations calculations

Abstract

This article presents a theory for the construction of steady-state quasi-three-dimensional nonreflecting boundary conditions for the Euler equations. These allow calculations to he performed on truncated domains without the generation of spurious nonphysical reflections at the far-field boundaries. The theory is based upon Fourier analysis and eigenvectors applied to the linearized Euler equations. It is presented within the context of transonic axial flow turbomachinery computations. The effectiveness of the new boundary conditions is demonstrated by comparing results obtained using this new formulation and calculations performed with the standard onedimensional approach.

Implementation of a Quasi-Three-Dimensional Nonreflecting Blade Row Interface for Steady and Unsteady Analysis of Axial Turbomachines

“…This is however not a problem in the context of the Harmonic Balance method since the entire time period then is stored in the solution. It should also be noted that we employ the method proposed by Saxer and Giles [9] for extending the two dimensional theory developed by Giles to three dimensional flows.…”

“…In these cases different strategies have therefore been developed to ensure that the discontinuous flow field does not cause any spurious reflections. One approach is to treat all Fourier coefficients which do not have a counter part in the adjacent blade row using the nonreflecting boundary condition theory of Giles [6,7] for two dimensional flows and the extension of Giles' theory to three dimensional flows proposed by Saxer and Giles [9]. This approach has been applied to two dimensional flows by e.g.…”

Evaluation of an Euler Code with Non-Reflecting Boundary Conditions for the Analysis of 3D Flow in Compressors

“…methods reported in the literature, the one by Hirsch and Verhoff (1989), and the one by Giles (1990) and Saxer and Giles (1991). This paper presents the extension to full 3D non-reflecting boundary conditions of the 2D boundary conditions proposed by Giles (1990) and extended to quasi-3D by Saxer and Giles (1991). It studies the influence of these non-reflecting boundary conditions on the convergence and accuracy of the solution of the three-dimensional inviscid rotational flow inside axial and centrifugal compressor rotors.…”

Towards Fully Three-Dimensional Virtual Stirling Convertors For Multi-Physics Analysis and Optimization

“…Incorrect specifications of boundary conditions result in solution instability, non-convergence of solutions, and/or convergence to inaccurate results. It is well known that even for steady unidirectional harmonic flows, non-physical reflections can occur at inflow and outflow locations (Saxer and Giles, 1993). In essence, by artificially truncating the domain to model a single engine component, an artificial boundary condition is required.…”