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-accurate time domain solvers 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.