Nonreflecting Boundary Conditions for Aeroelastic Analysis in Time and Frequency Domain 3D RANS Solvers

Abstract

This paper describes the implementation of a set of nonreflecting boundary conditions of increasing approximation quality for time-accurate and time-linearized 3D RANS solvers in the time and frequency domain. The implementations are based on the computation of eigenfunctions, either analytically or numerically, of the linearized Euler or Navier-Stokes equations for increasingly complex background flows. This results in a hierarchy of nonreflecting boundary conditions based on 1D characteristics, 2D circumferential mode decomposition, and 3D circumferential and radial mode decomposition, including viscous effects in the latter, for the frequency domain solver. By applying a Fourier transform in time at the boundaries the frequency domain implementations can be employed in the time domain solver as well. The limitations of each approximation are discussed and it is shown that increasing the precision of the boundary treatment the nonreflecting property of the boundary conditions is preserved for more complex flows without incurring an excessive increase in computing time. Results of a flutter analysis of a low pressure turbine blade obtained by time and frequency domain simulations are validated against each other and against reference results obtained with a 3D Euler frequency domain solver. The comparison of the results for different boundary conditions reveals the importance of using high quality boundary conditions.

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

“…Our final implementation is to some extent similar to the work reported by Robens et al [17] in which phase shifting of the waves from the interior cells is employed to obtain a definition of the exterior solution. The eigenvectors, which scale the perturbations of the primitive flow variables induced by the corresponding wave, have in this work been chosen to be the same as those reported by Kersken et al [14].…”

“…This factor never becomes zero and thus ensures that we always obtain two unique acoustic eigenvalues whenω is used in Eq. (14). To prove this, assume that Λ(ω) = 0 + 0i under some circumstance.…”

“…If in contrast radial flow variations would be included in Eq. (5) the whole boundary must be considered simultaneously in the analysis [14]. This has the benefit of potentially improving the results, but also increases the complexity and computational cost of the implementation.…”

“…It is believed that this is the case, but it might happen that the introduction of ε requires some additional constraints that have not been considered in this work. It should also be pointed out that the structure of the eigenvectors adopted in this work is the same as used in [14].…”

A Hybrid Mesh Harmonic Balance Solver for the Aeroelastic Analysis of Turbomachinery

“…Particularly in the context of aeroelasticity or aeroacoustics boundary conditions are of the utmost importance. The implementation in TRACE of these boundary conditions is described in [12].…”