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Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with FlowAn explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.
Document ID
Document Type
Technical Memorandum (TM)
Kreider, Kevin L. (NASA Lewis Research Center Cleveland, OH United States)
Baumeister, Kenneth J. (Akron Univ. Akron, OH United States)
Date Acquired
September 6, 2013
Publication Date
November 1, 1996
Subject Category
Report/Patent Number
NAS 1.15:107363
Funding Number(s)
Distribution Limits
Work of the US Gov. Public Use Permitted.

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NameType 19970010251.pdf STI