Investigation of a Parabolic Iterative Solver for Three-Dimensional Configurations

Aparabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCTLaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the ‘positive’ and ‘negative’ directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.