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Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct AcousticsPeriodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.
Document ID
19970001879
Acquisition Source
Langley Research Center
Document Type
Technical Memorandum (TM)
Authors
Watson, Willie R. (NASA Langley Research Center Hampton,VA United States)
Zorumski, William E. (NASA Langley Research Center Hampton,VA United States)
Date Acquired
September 6, 2013
Publication Date
June 1, 1996
Subject Category
Acoustics
Report/Patent Number
NASA-TM-110230
NAS 1.15:110230
Accession Number
97N11629
Funding Number(s)
PROJECT: RTOP 505-59-52
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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